Finite Group Databasebeta

← C2×#23777419 #35196259

Subgroups — C2×#23777419 #35196259

Order 20224.

8774 conjugacy classes of subgroups.

The subgroup lattice has 1420 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#23777419C2132yesmaximal, direct product factor
2C2×#19099277C211yesmaximal, characteristic, complemented
3C2×#19099272C211yesmaximal, characteristic, complemented
4C2×#19099265C211yesmaximal, characteristic, complemented
5C2×#19099259C211yesmaximal, characteristic, complemented
6C2×#19099256C212yesmaximal, complemented
7C2×#19099233C211yesmaximal, characteristic, complemented
8C2×#19099207C212yesmaximal, complemented
9C2×#19099200C212yesmaximal, complemented
10C2×#19099200C212yesmaximal, complemented
11C2×D4×C22⋊D79C211yesmaximal, characteristic, complemented
12C2×D4×C22⋊D79C211yesmaximal, characteristic, complemented
13C2×#19099167C211yesmaximal, characteristic, complemented
14C2×#19099166C211yesmaximal, characteristic, complemented
15C2×#19099150C212yesmaximal, complemented
16C2×#19099148C212yesmaximal, complemented
17C2×#19099108C211yesmaximal, characteristic, complemented
18C2×#19099093C211yesmaximal, characteristic, complemented
19C2×#19099069C212yesmaximal, complemented
20C22×#14579133C212yesmaximal, complemented
21C2×#19099038C211yesmaximal, characteristic, complemented
22C2×#19099035C211yesmaximal, characteristic, complemented
23C22×D4×Dic79C211yesmaximal, characteristic, complemented
24C2×D42×C79C211yesmaximal, characteristic, complemented
25C22×#11929623C2212yescomplemented
26C22×#11929623C2212yescomplemented
27C23×C22⋊D79C2212yescomplemented
28C23×C22⋊D79C2212yescomplemented
29C22×D4×D79C2211yescharacteristic
30C24×Dic79C2212yescomplemented
31#19099277C22116yescomplemented
32#19099272C22116yescomplemented
33#19099265C22116yescomplemented
34#19099259C22116yescomplemented
35#19099256C22132yescomplemented
36#19099233C22116yescomplemented
37#19099207C22132yescomplemented
38#19099200C22132yescomplemented
39#19099200C22132yescomplemented
40D4×C22⋊D79C22116yescomplemented
41D4×C22⋊D79C22116yescomplemented
42#19099167C22116yescomplemented
43#19099166C22116yescomplemented
44#19099150C22132yescomplemented
45#19099148C22132yescomplemented
46#19099108C22116yescomplemented
47C2×#14579160C2211yescharacteristic, complemented
48C2×#14579157C2211yescharacteristic, complemented
49C2×#14579157C2211yescharacteristic, complemented
50#19099093C22116yescomplemented
51C2×#14579156C2212yescomplemented
52C2×#14579156C2211yescharacteristic, complemented
53C2×#14579154C2212yescomplemented
54C2×#14579154C2211yescharacteristic, complemented
55C2×#14579153C2211yescharacteristic, complemented
56C2×#14579152C2211yescharacteristic, complemented
57C2×#14579151C2211yescharacteristic, complemented
58C2×#14579148C2212yescomplemented
59C2×#14579147C2211yescharacteristic, complemented
60C2×#14579147C2212yescomplemented
61C2×#14579147C2212yescomplemented
62#19099069C22132yescomplemented
63C2×#14579145C2211yescharacteristic, complemented
64C2×#14579145C2212yescomplemented
65C2×#14579145C2212yescomplemented
66C2×#14579143C2212yescomplemented
67C2×#14579143C2212yescomplemented
68C2×#14579142C2211yescharacteristic, complemented
69C2×#14579142C2212yescomplemented
70C2×#14579142C2212yescomplemented
71C2×#14579140C2212yescomplemented
72C2×#14579138C2212yescomplemented
73C2×#14579138C2212yescomplemented
74C2×#14579138C2211yescharacteristic, complemented
75C2×#14579135C2211yescharacteristic, complemented
76C2×#14579135C2211yescharacteristic, complemented
77C2×#14579133C2211yescharacteristic
78C2×#14579133C2212yescomplemented
79C2×#14579133C2212yescomplemented
80C2×#14579133C2212yescomplemented
81C2×#14579133C2212yescomplemented
82C2×#14579133C2212yescomplemented
83C2×#14579133C2212yescomplemented
84C2×#14579133C2212yescomplemented
85C2×#14579133C2212yescomplemented
86C2×#14579133C2212yescomplemented
87C2×#14579133C2212yescomplemented
88C2×#14579133C2212yescomplemented
89C2×#14579133C22132yescomplemented
90C2×#14579132C2211yescharacteristic, complemented
91C2×#14579132C2211yescharacteristic, complemented
92C2×#14579132C2212yescomplemented
93C2×#14579132C2212yescomplemented
94C2×#14579130C2212yescomplemented
95C2×#14579130C2212yescomplemented
96C2×#14579129C2212yescomplemented
97C2×#14579129C2212yescomplemented
98#19099038C22116yescomplemented
99#19099035C22116yescomplemented
100C2×C4×Dic158C2211yescharacteristic, complemented
101C2×C4×D316C2211yescharacteristic, complemented
102C2×D4×Dic79C2211yescharacteristic
103C2×D4×Dic79C2211yescharacteristic
104C2×D4×Dic79C2211yescharacteristic
105C2×D4×Dic79C2212yescomplemented
106C2×D4×Dic79C2211yescharacteristic, complemented
107C2×D4×Dic79C2212yescomplemented
108C2×D4×Dic79C2211yescharacteristic, complemented
109C2×D4×Dic79C2212yescomplemented
110C2×D4×Dic79C2211yescharacteristic, complemented
111C2×D4×Dic79C2212yescomplemented
112C2×D4×Dic79C2211yescharacteristic, complemented
113C2×D4×Dic79C2212yescomplemented
114C2×D4×Dic79C22116yescomplemented
115C2×#14579123C2211yescharacteristic, complemented
116C2×C4×C22⋊D79C2211yescharacteristic, complemented
117C2×C4×C22⋊D79C2211yescharacteristic, complemented
118C2×C4×C22⋊D79C2212yescomplemented
119C2×(C22⋊D79)⋊C4C2212yescomplemented
120C2×(C22⋊D79)⋊C4C2212yescomplemented
121C2×(C22⋊D79)⋊C4C2212yescomplemented
122C2×#14579120C2211yescharacteristic, complemented
123C2×#14579120C2211yescharacteristic, complemented
124C2×#14579119C2211yescharacteristic, complemented
125C2×#14579118C2211yescharacteristic, complemented
126C2×#14579117C2212yescomplemented
127C22×C4⋊Dic79C2211yescharacteristic, complemented
128C22×Dic79⋊C4C2212yescomplemented
129C22×C22⋊Dic79C2212yescomplemented
130C22×C22⋊Dic79C2212yescomplemented
131C22×C22⋊Dic79C2212yescomplemented
132C22×(C2×D79)⋊C4C2212yescomplemented
133C2×C22⋊C4×D79C2212yescomplemented
134C22×C4×Dic79C2211yescharacteristic, complemented
135C23×D4×C79C2211yescharacteristic
136C23×D4×C79C2211yescharacteristic
137C23×D4×C79C2212yescomplemented
138D42×C79C22116yescomplemented
139C2×#127×C79C2211yescharacteristic, complemented
140C2×#121×C79C2212yescomplemented
141C2×#121×C79C2211yescharacteristic, complemented
142C2×#121×C79C2211yescharacteristic, complemented
143C2×#120×C79C2212yescomplemented
144C2×#120×C79C2212yescomplemented
145C2×C4×D4×C79C2211yescharacteristic
146C2×C4×D4×C79C2211yescharacteristic, complemented
147C24×D79C2312yes—
148C2×#11929623—48no—
149C2×#11929623—48no—
150C2×#11929623C23116yescomplemented
151C2×#11929623C23116yescomplemented
152C22×Dic158C2311yescharacteristic
153C22×Dic158C2312yes—
154C22×D316C2311yescharacteristic
155C22×C22⋊D79—48no—
156C22×C22⋊D79—48no—
157C22×C22⋊D79C2312yes—
158C22×C22⋊D79C2312yes—
159C22×C22⋊D79C2312yes—
160C22×C22⋊D79C2311yescharacteristic
161C22×C22⋊D79C2311yescharacteristic
162C22×C22⋊D79C2312yes—
163C22×C22⋊D79C2312yes—
164C22×C22⋊D79C2312yes—
165C22×C22⋊D79C2312yes—
166C22×C22⋊D79C2312yes—
167C22×C22⋊D79C2312yes—
168C22×C22⋊D79C23116yescomplemented
169C22×C22⋊D79C23116yescomplemented
170C2×D4×D79—28no—
171C2×D4×D79C2318yes—
172C23×Dic79—48no—
173C23×Dic79C2311yescharacteristic
174C23×Dic79C2311yescharacteristic
175C23×Dic79C2312yes—
176C23×Dic79C2312yes—
177C23×Dic79C2312yes—
178C23×Dic79C2312yes—
179C23×Dic79C2312yes—
180C23×Dic79C2312yes—
181C23×Dic79C2312yes—
182C23×Dic79C2312yes—
183C23×Dic79C23116yescomplemented
184C22×C4×D79C2311yescharacteristic
185C22×C4×D79C2312yes—
186C22×C4×D79C2312yes—
187#14579160C2318yescomplemented
188#14579157C2318yescomplemented
189#14579157C2318yescomplemented
190#14579156C2318yescomplemented
191#14579156C23116yescomplemented
192#14579154C2318yescomplemented
193#14579154C23116yescomplemented
194#14579153C2318yescomplemented
195#14579152C2318yescomplemented
196#14579151C2318yescomplemented
197#14579148C23116yescomplemented
198#14579147C23116yescomplemented
199#14579147C23116yescomplemented
200#14579147C2318yescomplemented
201#14579145C23116yescomplemented
202#14579145C23116yescomplemented
203#14579145C2318yescomplemented
204#14579143C23116yescomplemented
205#14579143C23116yescomplemented
206#14579142C23116yescomplemented
207#14579142C23116yescomplemented
208#14579142C2318yescomplemented
209#14579140C23116yescomplemented
210#14579138C23116yescomplemented
211#14579138C23116yescomplemented
212#14579138C2318yescomplemented
213#14579135C2318yescomplemented
214#14579135C2318yescomplemented
215#14579133C2318yes—
216#14579133C23116yescomplemented
217#14579133C23116yescomplemented
218#14579133C23116yescomplemented
219#14579133C23116yescomplemented
220#14579133C23116yescomplemented
221#14579133C23116yescomplemented
222#14579133C23116yescomplemented
223#14579133C23116yescomplemented
224#14579133C23116yescomplemented
225#14579133C23116yescomplemented
226#14579133C23116yescomplemented
227#14579132C23116yescomplemented
228#14579132C23116yescomplemented
229#14579132C2318yescomplemented
230#14579132C2318yescomplemented
231#14579130C23116yescomplemented
232#14579130C23116yescomplemented
233#14579129C23116yescomplemented
234#14579129C23116yescomplemented
235C4×Dic158C2318yescomplemented
236C4×D316C2318yescomplemented
237D4×Dic79C2318yes—
238D4×Dic79C2318yes—
239D4×Dic79C2318yes—
240D4×Dic79C23116yescomplemented
241D4×Dic79C23116yescomplemented
242D4×Dic79C2318yescomplemented
243D4×Dic79C2318yescomplemented
244D4×Dic79C23116yescomplemented
245D4×Dic79C23116yescomplemented
246D4×Dic79C23116yescomplemented
247D4×Dic79C2318yescomplemented
248D4×Dic79C2318yescomplemented
249#14579123C2318yescomplemented
250C4×C22⋊D79C2318yescomplemented
251C4×C22⋊D79C2318yescomplemented
252C4×C22⋊D79C23116yescomplemented
253(C22⋊D79)⋊C4C23116yescomplemented
254(C22⋊D79)⋊C4C23116yescomplemented
255(C22⋊D79)⋊C4C23116yescomplemented
256#14579120C2318yescomplemented
257#14579120C2318yescomplemented
258#14579119C2318yescomplemented
259#14579118C2318yescomplemented
260#14579117C23116yescomplemented
261C2×C4⋊Dic79C2311yescharacteristic
262C2×C4⋊Dic79C2311yescharacteristic
263C2×C4⋊Dic79C2312yes—
264C2×C4⋊Dic79C2311yescharacteristic
265C2×C4⋊Dic79C2311yescharacteristic
266C2×C4⋊Dic79C2311yescharacteristic
267C2×C4⋊Dic79C2312yes—
268C2×C4⋊Dic79C2311yescharacteristic
269C2×C4⋊Dic79C2318yescomplemented
270C2×Dic79⋊C4C2311yescharacteristic
271C2×Dic79⋊C4C2312yes—
272C2×Dic79⋊C4C2312yes—
273C2×Dic79⋊C4C2312yes—
274C2×Dic79⋊C4C2311yescharacteristic
275C2×Dic79⋊C4C2311yescharacteristic
276C2×Dic79⋊C4C2311yescharacteristic
277C2×Dic79⋊C4C2312yes—
278C2×Dic79⋊C4C2311yescharacteristic
279C2×Dic79⋊C4C2311yescharacteristic
280C2×Dic79⋊C4C23116yescomplemented
281C2×C22⋊Dic79C2312yes—
282C2×C22⋊Dic79C2311yescharacteristic
283C2×C22⋊Dic79C2311yescharacteristic
284C2×C22⋊Dic79C2312yes—
285C2×C22⋊Dic79C2312yes—
286C2×C22⋊Dic79C2312yes—
287C2×C22⋊Dic79C2312yes—
288C2×C22⋊Dic79C2312yes—
289C2×C22⋊Dic79C2312yes—
290C2×C22⋊Dic79C2312yes—
291C2×C22⋊Dic79C2312yes—
292C2×C22⋊Dic79C2311yescharacteristic
293C2×C22⋊Dic79C2311yescharacteristic
294C2×C22⋊Dic79C2312yes—
295C2×C22⋊Dic79C23116yescomplemented
296C2×C22⋊Dic79C23116yescomplemented
297C2×C22⋊Dic79C23116yescomplemented
298C2×(C2×D79)⋊C4C2311yescharacteristic
299C2×(C2×D79)⋊C4C2312yes—
300C2×(C2×D79)⋊C4C2311yescharacteristic
301C2×(C2×D79)⋊C4C2312yes—
302C2×(C2×D79)⋊C4C2312yes—
303C2×(C2×D79)⋊C4C2312yes—
304C2×(C2×D79)⋊C4C2312yes—
305C2×(C2×D79)⋊C4C2311yescharacteristic
306C2×(C2×D79)⋊C4C2311yescharacteristic
307C2×(C2×D79)⋊C4C23116yescomplemented
308C22⋊C4×D79C23116yescomplemented
309C2×C4×Dic79C2311yescharacteristic
310C2×C4×Dic79C2311yescharacteristic
311C2×C4×Dic79C2311yescharacteristic
312C2×C4×Dic79C2311yescharacteristic
313C2×C4×Dic79C2312yes—
314C2×C4×Dic79C2312yes—
315C2×C4×Dic79C2311yescharacteristic
316C2×C4×Dic79C2318yescomplemented
317C25×C79C2312yes—
318C25×C79C2312yes—
319C22×D4×C79—28no—
320C22×D4×C79—28no—
321C22×D4×C79—48no—
322C22×D4×C79C2318yes—
323C22×D4×C79C2318yes—
324C22×D4×C79C2311yescharacteristic
325C22×D4×C79C2312yes—
326C22×D4×C79C2312yes—
327C22×D4×C79C2312yes—
328C22×D4×C79C2311yescharacteristic
329C22×D4×C79C2311yescharacteristic
330C22×D4×C79C2312yes—
331C22×D4×C79C2312yes—
332C22×D4×C79C2312yes—
333C22×D4×C79C2311yescharacteristic
334C22×D4×C79C23116yescomplemented
335C23×C4×C79C2311yescharacteristic
336C23×C4×C79C2311yescharacteristic
337C23×C4×C79C2312yes—
338#127×C79C2318yescomplemented
339#121×C79C23116yescomplemented
340#121×C79C2318yescomplemented
341#121×C79C2318yescomplemented
342#120×C79C23116yescomplemented
343#120×C79C23116yescomplemented
344C4×D4×C79C2318yes—
345C4×D4×C79C2318yescomplemented
346C2×C4⋊C4×C79C2311yescharacteristic
347C2×C4⋊C4×C79C2311yescharacteristic
348C2×C22⋊C4×C79C2312yes—
349C2×C22⋊C4×C79C2311yescharacteristic
350C2×C22⋊C4×C79C2311yescharacteristic
351C2×C22⋊C4×C79C2312yes—
352C2×C22⋊C4×C79C2312yes—
353C2×C42×C79C2311yescharacteristic
354C23×D79—28no—
355C23×D79—44no—
356C23×D79—44no—
357C23×D79C2411yescharacteristic
358C23×D79C2412yes—
359C23×D79C2418yes—
360#11929623—432no—
361#11929623—432no—
362C2×Dic158—24no—
363C2×Dic158—44no—
364C2×Dic158C2414yes—
365C2×Dic158C2418yes—
366C2×D316—24no—
367C2×D316C2414yes—
368C2×C22⋊D79—28no—
369C2×C22⋊D79—24no—
370C2×C22⋊D79—28no—
371C2×C22⋊D79—28no—
372C2×C22⋊D79—24no—
373C2×C22⋊D79—432no—
374C2×C22⋊D79—432no—
375C2×C22⋊D79—44no—
376C2×C22⋊D79—44no—
377C2×C22⋊D79—44no—
378C2×C22⋊D79—44no—
379C2×C22⋊D79—44no—
380C2×C22⋊D79—44no—
381C2×C22⋊D79C2418yes—
382C2×C22⋊D79C2418yes—
383C2×C22⋊D79C2418yes—
384C2×C22⋊D79C2414yes—
385C2×C22⋊D79C2414yes—
386C2×C22⋊D79C2418yes—
387C2×C22⋊D79C2418yes—
388C2×C22⋊D79C2418yes—
389C2×C22⋊D79C2418yes—
390C2×C22⋊D79C2418yes—
391C2×C22⋊D79C2418yes—
392D4×D79—232no—
393C22×Dic79—28no—
394C22×Dic79—24no—
395C22×Dic79—28no—
396C22×Dic79—24no—
397C22×Dic79—44no—
398C22×Dic79—44no—
399C22×Dic79—44no—
400C22×Dic79—44no—
401C22×Dic79—44no—
402C22×Dic79—44no—
403C22×Dic79—432no—
404C22×Dic79C2411yescharacteristic
405C22×Dic79C2412yes—
406C22×Dic79C2411yescharacteristic
407C22×Dic79C2414yes—
408C22×Dic79C2418yes—
409C22×Dic79C2411yescharacteristic
410C22×Dic79C2412yes—
411C22×Dic79C2411yescharacteristic
412C22×Dic79C2411yescharacteristic
413C22×Dic79C2411yescharacteristic
414C22×Dic79C2414yes—
415C22×Dic79C2412yes—
416C22×Dic79C2418yes—
417C22×Dic79C2418yes—
418C22×Dic79C2418yes—
419C22×Dic79C2418yes—
420C22×Dic79C2418yes—
421C22×Dic79C2418yes—
422C22×Dic79C2418yes—
423C22×Dic79C2411yescharacteristic
424C2×C4×D79—24no—
425C2×C4×D79—44no—
426C2×C4×D79—44no—
427C2×C4×D79C2414yes—
428C2×C4×D79C2418yes—
429C2×C4×D79C2418yes—
430C4⋊Dic79C2414yes—
431C4⋊Dic79C2414yes—
432C4⋊Dic79C2418yes—
433C4⋊Dic79C2414yes—
434C4⋊Dic79C2414yes—
435C4⋊Dic79C2414yes—
436C4⋊Dic79C2418yes—
437C4⋊Dic79C2414yes—
438Dic79⋊C4C2414yes—
439Dic79⋊C4C2418yes—
440Dic79⋊C4C2418yes—
441Dic79⋊C4C2418yes—
442Dic79⋊C4C2414yes—
443Dic79⋊C4C2414yes—
444Dic79⋊C4C2414yes—
445Dic79⋊C4C2418yes—
446Dic79⋊C4C2414yes—
447Dic79⋊C4C2414yes—
448C22⋊Dic79C2418yes—
449C22⋊Dic79C2414yes—
450C22⋊Dic79C2414yes—
451C22⋊Dic79C2418yes—
452C22⋊Dic79C2418yes—
453C22⋊Dic79C2418yes—
454C22⋊Dic79C2418yes—
455C22⋊Dic79C2418yes—
456C22⋊Dic79C2418yes—
457C22⋊Dic79C2418yes—
458C22⋊Dic79C2418yes—
459C22⋊Dic79C2414yes—
460C22⋊Dic79C2414yes—
461C22⋊Dic79C2418yes—
462(C2×D79)⋊C4C2414yes—
463(C2×D79)⋊C4C2418yes—
464(C2×D79)⋊C4C2414yes—
465(C2×D79)⋊C4C2418yes—
466(C2×D79)⋊C4C2418yes—
467(C2×D79)⋊C4C2418yes—
468(C2×D79)⋊C4C2418yes—
469(C2×D79)⋊C4C2414yes—
470(C2×D79)⋊C4C2414yes—
471C4×Dic79C2414yes—
472C4×Dic79C2414yes—
473C4×Dic79C2414yes—
474C4×Dic79C2414yes—
475C4×Dic79C2418yes—
476C4×Dic79C2418yes—
477C4×Dic79C2414yes—
478C24×C79—28no—
479C24×C79—28no—
480C24×C79—28no—
481C24×C79—44no—
482C24×C79—44no—
483C24×C79—44no—
484C24×C79C2411yescharacteristic
485C24×C79C2412yes—
486C24×C79C2412yes—
487C24×C79C2418yes—
488C24×C79C2412yes—
489C24×C79C2411yescharacteristic
490C24×C79C2418yes—
491C2×D4×C79—28no—
492C2×D4×C79—28no—
493C2×D4×C79—28no—
494C2×D4×C79—24no—
495C2×D4×C79—232no—
496C2×D4×C79—232no—
497C2×D4×C79—24no—
498C2×D4×C79—24no—
499C2×D4×C79—44no—
500C2×D4×C79—44no—
501C2×D4×C79—44no—
502C2×D4×C79—432no—
503C2×D4×C79#4118yescomplemented
504C2×D4×C79C2418yes—
505C2×D4×C79C2414yes—
506C2×D4×C79C2418yes—
507C2×D4×C79C2418yes—
508C2×D4×C79C2414yes—
509C2×D4×C79C2414yes—
510C2×D4×C79C2418yes—
511C2×D4×C79C2418yes—
512C2×D4×C79C2418yes—
513C2×D4×C79C2414yes—
514C22×C4×C79—24no—
515C22×C4×C79—24no—
516C22×C4×C79—44no—
517C22×C4×C79C2411yescharacteristic
518C22×C4×C79C2412yes—
519C22×C4×C79C2411yescharacteristic
520C22×C4×C79C2411yescharacteristic
521C22×C4×C79C2411yescharacteristic
522C22×C4×C79C2414yes—
523C22×C4×C79C2414yes—
524C22×C4×C79C2418yes—
525C22×C4×C79C2411yescharacteristic
526C4⋊C4×C79C2414yes—
527C4⋊C4×C79C2414yes—
528C22⋊C4×C79C2418yes—
529C22⋊C4×C79C2414yes—
530C22⋊C4×C79C2414yes—
531C22⋊C4×C79C2418yes—
532C22⋊C4×C79C2418yes—
533C42×C79C2414yes—
534C23×C79—22no—
535C23×C79—22no—
536C23×C79—24no—
537C23×C79—24no—
538C23×C79—22no—
539C23×C79—216no—
540C23×C79—24no—
541C23×C79—24no—
542C23×C79—24no—
543C23×C79—24no—
544C23×C79—24no—
545C23×C79—22no—
546C23×C79—216no—
547C23×C79—24no—
548C23×C79—22no—
549C23×C79—216no—
550C23×C79—48no—
551C23×C79—48no—
552C23×C79—48no—
553C23×C79—432no—
554C23×C79—816no—
555C23×C79C2×#4118yes—
556C23×C79H(5,𝔽2)14yes—
557C23×C79C2512yes—
558C23×C79C2514yes—
559C23×C79C2514yes—
560C23×C79C2514yes—
561C23×C79C2512yes—
562C23×C79C2511yescharacteristic
563C22×D79—22no—
564C22×D79—24no—
565C22×D79—24no—
566C22×D79—24no—
567C22×D79—22no—
568C22×D79—22no—
569C22×D79—216no—
570C22×D79—48no—
571C22×D79—48no—
572C22×D79—816no—
573C22×D79C2512yes—
574C22×D79C2514yes—
575D4×C79—216no—
576D4×C79—216no—
577D4×C79—216no—
578D4×C79—28no—
579D4×C79—28no—
580D4×C79—28no—
581D4×C79—48no—
582D4×C79—48no—
583D4×C79—48no—
584D4×C79C2×#41116yescomplemented
585C2×C4×C79—22no—
586C2×C4×C79—22no—
587C2×C4×C79—22no—
588C2×C4×C79—24no—
589C2×C4×C79—22no—
590C2×C4×C79—28no—
591C2×C4×C79—28no—
592C2×C4×C79—48no—
593C2×C4×C79C2×#4114yes—
594C2×C4×C79C2512yes—
595C2×C4×C79C2512yes—
596C2×C4×C79C2514yes—
597C2×C4×C79C2512yes—
598C2×C4×C79C2512yes—
599C2×C4×C79C2512yes—
600C22⋊D79—216no—
601C22⋊D79—28no—
602C22⋊D79—216no—
603C22⋊D79—28no—
604C22⋊D79—216no—
605C22⋊D79—48no—
606C22⋊D79—48no—
607C22⋊D79—48no—
608C22⋊D79—48no—
609C22⋊D79—48no—
610C22⋊D79—48no—
611C2×Dic79—22no—
612C2×Dic79—22no—
613C2×Dic79—24no—
614C2×Dic79—22no—
615C2×Dic79—24no—
616C2×Dic79—22no—
617C2×Dic79—28no—
618C2×Dic79—22no—
619C2×Dic79—24no—
620C2×Dic79—22no—
621C2×Dic79—28no—
622C2×Dic79—216no—
623C2×Dic79—216no—
624C2×Dic79—48no—
625C2×Dic79—48no—
626C2×Dic79—48no—
627C2×Dic79—48no—
628C2×Dic79—48no—
629C2×Dic79—48no—
630C2×Dic79H(5,𝔽2)14yes—
631C2×Dic79C2512yes—
632C2×Dic79C2514yes—
633C2×Dic79C2512yes—
634C2×Dic79C2512yes—
635C2×Dic79C2512yes—
636C2×Dic79C2514yes—
637C2×Dic79C2512yes—
638C2×Dic79C2512yes—
639C2×Dic79C2514yes—
640C2×Dic79C2512yes—
641D316—28no—
642C4×D79—28no—
643C4×D79—48no—
644C4×D79—48no—
645Dic158—28no—
646Dic158—48no—
647C22×C79—22no—
648C22×C79—24no—
649C22×C79—24no—
650C22×C79—22no—
651C22×C79—216no—
652C22×C79—28no—
653C22×C79—22no—
654C22×C79—24no—
655C22×C79—24no—
656C22×C79—22no—
657C22×C79—24no—
658C22×C79—24no—
659C22×C79—24no—
660C22×C79—24no—
661C22×C79—22no—
662C22×C79—432no—
663C22×C79—48no—
664C22×C79—48no—
665C22×C79—44no—
666C22×C79—816no—
667C22×C79C22×#4118yes—
668C22×C79C22×#4112yes—
669C22×C79C2×H(5,𝔽2)12yes—
670C22×C79C2×H(5,𝔽2)14yes—
671C22×C79C2×H(5,𝔽2)12yes—
672C22×C79C2611yescharacteristic
673C2×D79—24no—
674C2×D79—22no—
675C2×D79—22no—
676C2×D79—22no—
677C2×D79—24no—
678C2×D79—24no—
679C2×D79—48no—
680C2×D79—44no—
681C2×D79—816no—
682C4×C79—22no—
683C4×C79—22no—
684C4×C79—22no—
685C4×C79—24no—
686C4×C79—22no—
687C4×C79C22×#4114yes—
688Dic79—22no—
689Dic79—22no—
690Dic79—24no—
691Dic79—22no—
692Dic79—22no—
693Dic79—24no—
694Dic79—22no—
695Dic79—24no—
696Dic79—22no—
697Dic79C2×H(5,𝔽2)14yes—
698C2×#3519—791nomaximal, Sylow
699C2×C79—28no—
700C2×C79—24no—
701C2×C79—44no—
702C2×C79—44no—
703C2×C79—42no—
704C2×C79#351914yescomplemented
705C2×C79C23×#4111yescharacteristic
706C2×C79C22×H(5,𝔽2)11yescharacteristic
707C2×C79C22×H(5,𝔽2)11yescharacteristic
708D79—44no—
709D79—42no—
710#3519—7932no—
711C2×#555—791no—
712C2×#554—791no—
713C2×#553—792no—
714C2×#553—791no—
715C2×#553—791no—
716C2×#550—791no—
717C2×#546—792no—
718C2×#546—792no—
719C2×#546—792no—
720C2×D42—791no—
721C2×D42—791no—
722C2×D42D7911yescharacteristic, complemented
723C2×#540—791no—
724C2×#540—791no—
725C2×#538—792no—
726C2×#538—792no—
727C2×#532—791no—
728C2×#529—791no—
729C2×#525—792no—
730C22×#121—792no—
731C2×#518—791no—
732C2×#518—791no—
733C22×C4×D4—791no—
734C79C2×#351911yescharacteristic, complemented, Sylow
735C22×#41—792no—
736C22×#41—792no—
737C23×D4—792no—
738C23×D4—792no—
739C23×D4—791no—
740C23×D4C2×D7911yescharacteristic
741C23×D4C2×D7911yescharacteristic
742C23×D4C2×D7912yescomplemented
743C24×C4—792no—
744#555—7916no—
745#554—7916no—
746#553—7932no—
747#553—7916no—
748#553—7916no—
749#550—7916no—
750#546—7932no—
751#546—7932no—
752#546—7932no—
753D42—7916no—
754D42—7916no—
755D42C2×D79116yescomplemented
756#540—7916no—
757#540—7916no—
758#538—7932no—
759#538—7932no—
760#532—7916no—
761C2×C4⋊Q8—791no—
762C2×#127—791no—
763C2×#127—791no—
764C2×#127C2×D7911yescharacteristic, complemented
765#529—7916no—
766C2×#126—791no—
767C2×#126—792no—
768C2×#126—791no—
769C2×#126—792no—
770C2×#125—791no—
771C2×#125—791no—
772C2×#125—791no—
773C2×#124—792no—
774C2×#124—791no—
775C2×#124—792no—
776C2×#124—792no—
777#525—7932no—
778C2×#123—792no—
779C2×#123—791no—
780C2×#123—792no—
781C2×#123—792no—
782C2×#123—791no—
783C2×#123—792no—
784C2×#123—792no—
785C2×#123—792no—
786C2×C22⋊Q8—792no—
787C2×C22⋊Q8—791no—
788C2×C22⋊Q8—792no—
789C2×C22⋊Q8—792no—
790C2×#121—791no—
791C2×#121—792no—
792C2×#121—792no—
793C2×#121—792no—
794C2×#121—792no—
795C2×#121—792no—
796C2×#121—792no—
797C2×#121—792no—
798C2×#121—792no—
799C2×#121—792no—
800C2×#121—792no—
801C2×#121—792no—
802C2×#121—791no—
803C2×#121—791no—
804C2×#121—792no—
805C2×#121—792no—
806C2×#121—7932no—
807C2×#121—791no—
808C2×#121—791no—
809C2×#121C2×D7911yescharacteristic, complemented
810C2×#121C2×D7912yescomplemented
811C2×#121C2×D7911yescharacteristic, complemented
812C2×#120—792no—
813C2×#120—792no—
814C2×#120—792no—
815C2×#120—792no—
816C2×#120C2×D7912yescomplemented
817C2×#120C2×D7912yescomplemented
818#518—7916no—
819#518—7916no—
820C2×C4×Q8—791no—
821C2×C4×D4—791no—
822C2×C4×D4—792no—
823C2×C4×D4—791no—
824C2×C4×D4—791no—
825C2×C4×D4—792no—
826C2×C4×D4—791no—
827C2×C4×D4—7916no—
828C2×C4×D4—792no—
829C2×C4×D4—791no—
830C2×C4×D4—791no—
831C2×C4×D4—792no—
832C2×C4×D4—791no—
833C2×C4×D4—792no—
834C2×C4×D4—792no—
835C2×C4×D4—791no—
836C2×C4×D4—791no—
837C2×C4×D4—791no—
838C2×C4×D4—792no—
839C2×C4×D4—792no—
840C2×C4×D4—792no—
841C2×C4×D4—791no—
842C2×C4×D4C2×D7911yescharacteristic
843C2×C4×D4C2×D7911yescharacteristic, complemented
844C2×#117—791no—
845C2×#117—791no—
846C2×#117—791no—
847C2×#117—792no—
848C2×#117—791no—
849C22×C4⋊C4—791no—
850C22×C4⋊C4—792no—
851C22×C22⋊C4—792no—
852C22×C22⋊C4—792no—
853C22×C22⋊C4—792no—
854C22×C22⋊C4—792no—
855C22×C22⋊C4—792no—
856C22×C42—791no—
857C25—792no—
858C25C22×D7912yes—
859C25C22×D7912yes—
860C2×#41—3168no—
861C2×#41—3168no—
862C2×#41—7916no—
863C2×#41—7916no—
864C22×Q8—792no—
865C22×Q8—791no—
866C22×D4—28no—
867C22×D4—28no—
868C22×D4—48no—
869C22×D4—3168no—
870C22×D4—3168no—
871C22×D4—792no—
872C22×D4—792no—
873C22×D4—792no—
874C22×D4—792no—
875C22×D4—792no—
876C22×D4—792no—
877C22×D4—7916no—
878C22×D4—7916no—
879C22×D4—792no—
880C22×D4—792no—
881C22×D4—791no—
882C22×D4—791no—
883C22×D4—792no—
884C22×D4—798no—
885C22×D4—791no—
886C22×D4—1588no—
887C22×D4C22×D7912yes—
888C22×D4C22×D7912yes—
889C22×D4C22×D7911yescharacteristic
890C22×D4C22×D7911yescharacteristic
891C22×D4C22×D7918yes—
892C22×D4C22×D7912yes—
893C22×D4C22×D7911yescharacteristic
894C22×D4C22×D7918yes—
895C22×D4C22×D7912yes—
896C22×D4C22×D7912yes—
897C22×D4C22×D7912yes—
898C22×D4C22×D7911yescharacteristic
899C22×D4C22×D79116yescomplemented
900C23×C4—3168no—
901C23×C4—792no—
902C23×C4—792no—
903C23×C4—792no—
904C23×C4—792no—
905C23×C4—792no—
906C23×C4—792no—
907C23×C4—7916no—
908C23×C4—792no—
909C23×C4—792no—
910C23×C4—791no—
911C23×C4—792no—
912C23×C4—792no—
913C23×C4—791no—
914C23×C4—791no—
915C23×C4C22×D7911yescharacteristic
916C23×C4C22×D7911yescharacteristic
917C23×C4C22×D7912yes—
918C4⋊Q8—798no—
919#127—798no—
920#127—798no—
921#127C22×D7918yescomplemented
922#126—798no—
923#126—7916no—
924#126—798no—
925#126—7916no—
926#125—798no—
927#125—798no—
928#125—798no—
929#124—7916no—
930#124—798no—
931#124—7916no—
932#124—7916no—
933#123—7916no—
934#123—798no—
935#123—7916no—
936#123—7916no—
937#123—798no—
938#123—7916no—
939#123—7916no—
940#123—7916no—
941C22⋊Q8—7916no—
942C22⋊Q8—798no—
943C22⋊Q8—7916no—
944C22⋊Q8—7916no—
945#121—798no—
946#121—7916no—
947#121—7916no—
948#121—7916no—
949#121—7916no—
950#121—7916no—
951#121—7916no—
952#121—7916no—
953#121—7916no—
954#121—7916no—
955#121—7916no—
956#121—7916no—
957#121—798no—
958#121—798no—
959#121—7916no—
960#121—7916no—
961#121—798no—
962#121—798no—
963#121C22×D7918yescomplemented
964#121C22×D79116yescomplemented
965#121C22×D7918yescomplemented
966#120—7916no—
967#120—7916no—
968#120—7916no—
969#120—7916no—
970#120C22×D79116yescomplemented
971#120C22×D79116yescomplemented
972C4×Q8—798no—
973C4×D4—798no—
974C4×D4—7916no—
975C4×D4—798no—
976C4×D4—798no—
977C4×D4—7916no—
978C4×D4—798no—
979C4×D4—7916no—
980C4×D4—798no—
981C4×D4—798no—
982C4×D4—7916no—
983C4×D4—798no—
984C4×D4—7916no—
985C4×D4—7916no—
986C4×D4—798no—
987C4×D4—798no—
988C4×D4—798no—
989C4×D4—7916no—
990C4×D4—7916no—
991C4×D4—7916no—
992C4×D4—798no—
993C4×D4C22×D7918yes—
994C4×D4C22×D7918yescomplemented
995#117—798no—
996#117—798no—
997#117—798no—
998#117—7916no—
999#117—798no—
1000C2×C4⋊C4—791no—
1001C2×C4⋊C4—791no—
1002C2×C4⋊C4—792no—
1003C2×C4⋊C4—791no—
1004C2×C4⋊C4—792no—
1005C2×C4⋊C4—798no—
1006C2×C4⋊C4—792no—
1007C2×C4⋊C4—792no—
1008C2×C4⋊C4—7916no—
1009C2×C4⋊C4—791no—
1010C2×C4⋊C4—791no—
1011C2×C4⋊C4—791no—
1012C2×C4⋊C4—791no—
1013C2×C4⋊C4—791no—
1014C2×C4⋊C4—791no—
1015C2×C4⋊C4—791no—
1016C2×C4⋊C4—792no—
1017C2×C4⋊C4—792no—
1018C2×C4⋊C4—791no—
1019C2×C4⋊C4—791no—
1020C2×C4⋊C4C22×D7911yescharacteristic
1021C2×C4⋊C4C22×D7911yescharacteristic
1022C2×C22⋊C4—792no—
1023C2×C22⋊C4—791no—
1024C2×C22⋊C4—792no—
1025C2×C22⋊C4—791no—
1026C2×C22⋊C4—792no—
1027C2×C22⋊C4—792no—
1028C2×C22⋊C4—792no—
1029C2×C22⋊C4—792no—
1030C2×C22⋊C4—792no—
1031C2×C22⋊C4—792no—
1032C2×C22⋊C4—7916no—
1033C2×C22⋊C4—7916no—
1034C2×C22⋊C4—7916no—
1035C2×C22⋊C4—792no—
1036C2×C22⋊C4—791no—
1037C2×C22⋊C4—791no—
1038C2×C22⋊C4—792no—
1039C2×C22⋊C4—791no—
1040C2×C22⋊C4—792no—
1041C2×C22⋊C4—791no—
1042C2×C22⋊C4—792no—
1043C2×C22⋊C4—792no—
1044C2×C22⋊C4—7916no—
1045C2×C22⋊C4—791no—
1046C2×C22⋊C4—791no—
1047C2×C22⋊C4—792no—
1048C2×C22⋊C4—792no—
1049C2×C22⋊C4—7916no—
1050C2×C22⋊C4C22×D7912yes—
1051C2×C22⋊C4C22×D7912yes—
1052C2×C22⋊C4C22×D7911yescharacteristic
1053C2×C22⋊C4C22×D7912yes—
1054C2×C22⋊C4C22×D7911yescharacteristic
1055C2×C42—791no—
1056C2×C42—792no—
1057C2×C42—792no—
1058C2×C42—791no—
1059C2×C42—791no—
1060C2×C42—791no—
1061C2×C42—791no—
1062C2×C42—798no—
1063C2×C42C22×D7911yescharacteristic
1064C24—28no—
1065C24—28no—
1066C24—28no—
1067C24—44no—
1068C24—44no—
1069C24—44no—
1070C24—3164no—
1071C24—3164no—
1072C24—798no—
1073C24—791no—
1074C24—792no—
1075C24—1588no—
1076C24C23×D7911yescharacteristic
1077C24C23×D7912yes—
1078C24C23×D7912yes—
1079C24C23×D7918yes—
1080C24C23×D7912yes—
1081C24C23×D7911yescharacteristic
1082C24C23×D7918yes—
1083#41—31632no—
1084#41—31632no—
1085C2×Q8—3164no—
1086C2×Q8—798no—
1087C2×Q8—794no—
1088C2×Q8—1584no—
1089C2×D4—28no—
1090C2×D4—28no—
1091C2×D4—24no—
1092C2×D4—28no—
1093C2×D4—232no—
1094C2×D4—232no—
1095C2×D4—24no—
1096C2×D4—24no—
1097C2×D4—44no—
1098C2×D4—44no—
1099C2×D4—44no—
1100C2×D4—432no—
1101C2×D4—31632no—
1102C2×D4—3164no—
1103C2×D4—3164no—
1104C2×D4—3164no—
1105C2×D4—3164no—
1106C2×D4—3164no—
1107C2×D4—3164no—
1108C2×D4—31632no—
1109C2×D4—798no—
1110C2×D4—798no—
1111C2×D4—798no—
1112C2×D4—798no—
1113C2×D4—798no—
1114C2×D4—798no—
1115C2×D4—798no—
1116C2×D4—798no—
1117C2×D4—794no—
1118C2×D4—794no—
1119C2×D4—798no—
1120C2×D4—794no—
1121C2×D4—1584no—
1122C2×D4—1588no—
1123C2×D4—1588no—
1124C2×D4—1584no—
1125C2×D4—1588no—
1126C2×D4—15832no—
1127C2×D4—1584no—
1128C2×D4#1192962318yescomplemented
1129C2×D4C23×D7918yes—
1130C2×D4C23×D7918yes—
1131C2×D4C23×D7914yes—
1132C2×D4C23×D7914yes—
1133C2×D4C23×D7918yes—
1134C2×D4C23×D7914yes—
1135C2×D4C23×D7918yes—
1136C2×D4C23×D7918yes—
1137C2×D4C23×D7918yes—
1138C2×D4C23×D7914yes—
1139C22×C4—24no—
1140C22×C4—24no—
1141C22×C4—44no—
1142C22×C4—3164no—
1143C22×C4—3164no—
1144C22×C4—3164no—
1145C22×C4—3164no—
1146C22×C4—3164no—
1147C22×C4—3164no—
1148C22×C4—3164no—
1149C22×C4—3164no—
1150C22×C4—31632no—
1151C22×C4—798no—
1152C22×C4—798no—
1153C22×C4—798no—
1154C22×C4—798no—
1155C22×C4—798no—
1156C22×C4—798no—
1157C22×C4—798no—
1158C22×C4—798no—
1159C22×C4—791no—
1160C22×C4—794no—
1161C22×C4—794no—
1162C22×C4—798no—
1163C22×C4—798no—
1164C22×C4—791no—
1165C22×C4—791no—
1166C22×C4—792no—
1167C22×C4—791no—
1168C22×C4—791no—
1169C22×C4—791no—
1170C22×C4—792no—
1171C22×C4—791no—
1172C22×C4—792no—
1173C22×C4—794no—
1174C22×C4—1584no—
1175C22×C4—1588no—
1176C22×C4—1588no—
1177C22×C4—1584no—
1178C22×C4—1584no—
1179C22×C4C23×D7914yes—
1180C22×C4C23×D7914yes—
1181C22×C4C23×D7911yescharacteristic
1182C22×C4C23×D7911yescharacteristic
1183C22×C4C23×D7912yes—
1184C22×C4C23×D7911yescharacteristic
1185C22×C4C23×D7911yescharacteristic
1186C22×C4C23×D7918yes—
1187C22×C4C23×D7911yescharacteristic
1188C4⋊C4—794no—
1189C4⋊C4—798no—
1190C4⋊C4—798no—
1191C4⋊C4—798no—
1192C4⋊C4—794no—
1193C4⋊C4—794no—
1194C4⋊C4—794no—
1195C4⋊C4—794no—
1196C4⋊C4—798no—
1197C4⋊C4—794no—
1198C4⋊C4—794no—
1199C4⋊C4—794no—
1200C4⋊C4—798no—
1201C4⋊C4—794no—
1202C4⋊C4—794no—
1203C4⋊C4—794no—
1204C4⋊C4—798no—
1205C4⋊C4—794no—
1206C4⋊C4C23×D7914yes—
1207C4⋊C4C23×D7914yes—
1208C22⋊C4—798no—
1209C22⋊C4—794no—
1210C22⋊C4—794no—
1211C22⋊C4—798no—
1212C22⋊C4—798no—
1213C22⋊C4—798no—
1214C22⋊C4—798no—
1215C22⋊C4—798no—
1216C22⋊C4—798no—
1217C22⋊C4—798no—
1218C22⋊C4—798no—
1219C22⋊C4—794no—
1220C22⋊C4—794no—
1221C22⋊C4—798no—
1222C22⋊C4—794no—
1223C22⋊C4—798no—
1224C22⋊C4—794no—
1225C22⋊C4—798no—
1226C22⋊C4—798no—
1227C22⋊C4—794no—
1228C22⋊C4—794no—
1229C22⋊C4—798no—
1230C22⋊C4—798no—
1231C22⋊C4C23×D7918yes—
1232C22⋊C4C23×D7918yes—
1233C22⋊C4C23×D7914yes—
1234C22⋊C4C23×D7918yes—
1235C22⋊C4C23×D7914yes—
1236C42—794no—
1237C42—794no—
1238C42—794no—
1239C42—794no—
1240C42—798no—
1241C42—798no—
1242C42—794no—
1243C42C23×D7914yes—
1244C23—22no—
1245C23—24no—
1246C23—24no—
1247C23—22no—
1248C23—24no—
1249C23—24no—
1250C23—22no—
1251C23—24no—
1252C23—22no—
1253C23—216no—
1254C23—24no—
1255C23—22no—
1256C23—216no—
1257C23—24no—
1258C23—24no—
1259C23—216no—
1260C23—48no—
1261C23—48no—
1262C23—48no—
1263C23—432no—
1264C23—816no—
1265C23—3168no—
1266C23—3168no—
1267C23—792no—
1268C23—794no—
1269C23—63216no—
1270C23—1584no—
1271C23—1582no—
1272C23—1584no—
1273C23—1582no—
1274C23—1582no—
1275C23—1584no—
1276C23—15816no—
1277C23C2×#1192962318yes—
1278C23#1457920614yes—
1279C23C24×D7912yes—
1280C23C24×D7914yes—
1281C23C24×D7914yes—
1282C23C24×D7912yes—
1283C23C24×D7914yes—
1284C23C24×D7911yescharacteristic
1285Q8—3168no—
1286Q8—1588no—
1287D4—28no—
1288D4—216no—
1289D4—216no—
1290D4—216no—
1291D4—28no—
1292D4—28no—
1293D4—48no—
1294D4—48no—
1295D4—48no—
1296D4—3168no—
1297D4—3168no—
1298D4—3168no—
1299D4—3168no—
1300D4—3168no—
1301D4—3168no—
1302D4—1588no—
1303D4—15816no—
1304D4—1588no—
1305D4—15816no—
1306D4—15816no—
1307D4—1588no—
1308D4C2×#11929623116yescomplemented
1309C2×C4—22no—
1310C2×C4—22no—
1311C2×C4—24no—
1312C2×C4—22no—
1313C2×C4—22no—
1314C2×C4—28no—
1315C2×C4—28no—
1316C2×C4—48no—
1317C2×C4—3168no—
1318C2×C4—3168no—
1319C2×C4—3168no—
1320C2×C4—3168no—
1321C2×C4—3168no—
1322C2×C4—3168no—
1323C2×C4—3168no—
1324C2×C4—3168no—
1325C2×C4—794no—
1326C2×C4—792no—
1327C2×C4—792no—
1328C2×C4—792no—
1329C2×C4—794no—
1330C2×C4—792no—
1331C2×C4—792no—
1332C2×C4—792no—
1333C2×C4—794no—
1334C2×C4—792no—
1335C2×C4—794no—
1336C2×C4—1588no—
1337C2×C4—15816no—
1338C2×C4—15816no—
1339C2×C4—1584no—
1340C2×C4—1582no—
1341C2×C4—1584no—
1342C2×C4—1582no—
1343C2×C4—1582no—
1344C2×C4—1582no—
1345C2×C4—1584no—
1346C2×C4—1582no—
1347C2×C4—1588no—
1348C2×C4—1582no—
1349C2×C4—1588no—
1350C2×C4C2×#1192962314yes—
1351C2×C4C24×D7912yes—
1352C2×C4C24×D7912yes—
1353C2×C4C24×D7914yes—
1354C2×C4C24×D7912yes—
1355C2×C4C24×D7912yes—
1356C2×C4C24×D7912yes—
1357C22—28no—
1358C22—216no—
1359C22—22no—
1360C22—22no—
1361C22—24no—
1362C22—24no—
1363C22—22no—
1364C22—24no—
1365C22—24no—
1366C22—24no—
1367C22—24no—
1368C22—22no—
1369C22—24no—
1370C22—22no—
1371C22—24no—
1372C22—432no—
1373C22—48no—
1374C22—44no—
1375C22—48no—
1376C22—816no—
1377C22—3164no—
1378C22—3168no—
1379C22—63216no—
1380C22—1582no—
1381C22—1584no—
1382C22—1584no—
1383C22—1582no—
1384C22—1584no—
1385C22—1582no—
1386C22C22×#1192962318yes—
1387C22C22×#1192962312yes—
1388C22H(5,𝔽2)×D7912yes—
1389C22C2×#1457920614yes—
1390C22C2×#1457920612yes—
1391C22C25×D7911yescharacteristic
1392C4—22no—
1393C4—22no—
1394C4—22no—
1395C4—22no—
1396C4—24no—
1397C4—794no—
1398C4—1582no—
1399C4—1584no—
1400C4—1582no—
1401C4—1584no—
1402C4—1582no—
1403C4—1582no—
1404C4—1582no—
1405C4—1584no—
1406C4—1582no—
1407C4C22×#1192962314yes—
1408C2—24no—
1409C2—28no—
1410C2—44no—
1411C2—42no—
1412C2—44no—
1413C2—3162no—
1414C2—3164no—
1415C2#2377741914yesdirect product factor
1416C2C23×#1192962311yescharacteristic
1417C2C2×H(5,𝔽2)×D7911yescharacteristic
1418C2C22×#1457920611yescharacteristic
subgroupG/H
centerC23C24×D79
commutator, cosocleC22×C79C26
FrattiniC22C25×D79
FittingC2×D42×C79C2
socleC23×C79C25
hypercenterC2×D42D79
hypocenterC79C2×#3519
LCSG ▷ C22×C79 ▷ C79
UCSC1 ◁ C23 ◁ C2×D42

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. #23777419C2direct (N × H)
2. C2×#19099277C2semidirect
3. C2×#19099272C2semidirect
4. C2×#19099265C2semidirect
5. C2×#19099259C2semidirect
6. C2×#19099256C2semidirect
7. C2×#19099233C2semidirect
8. C2×#19099207C2semidirect
9. C2×#19099200C2semidirect
10. C2×#19099200C2semidirect
11. C2×D4×C22⋊D79C2semidirect
12. C2×D4×C22⋊D79C2semidirect
13. C2×#19099167C2semidirect
14. C2×#19099166C2semidirect
15. C2×#19099150C2semidirect
16. C2×#19099148C2semidirect
17. C2×#19099108C2semidirect
18. C2×#19099093C2semidirect
19. C2×#19099069C2semidirect
20. C22×#14579133C2semidirect
21. C2×#19099038C2semidirect
22. C2×#19099035C2semidirect
23. C22×D4×Dic79C2semidirect
24. C2×D42×C79C2semidirect
25. C22×#11929623C22semidirect
26. C22×#11929623C22semidirect
27. C23×C22⋊D79C22semidirect
28. C23×C22⋊D79C22semidirect
30. C24×Dic79C22semidirect
31. #19099277C22semidirect
32. #19099272C22semidirect
33. #19099265C22semidirect
34. #19099259C22semidirect
35. #19099256C22semidirect
36. #19099233C22semidirect
37. #19099207C22semidirect
38. #19099200C22semidirect
39. #19099200C22semidirect
40. D4×C22⋊D79C22semidirect
41. D4×C22⋊D79C22semidirect
42. #19099167C22semidirect
43. #19099166C22semidirect
44. #19099150C22semidirect
45. #19099148C22semidirect
46. #19099108C22semidirect
47. C2×#14579160C22semidirect
48. C2×#14579157C22semidirect
49. C2×#14579157C22semidirect
50. #19099093C22semidirect
51. C2×#14579156C22semidirect
52. C2×#14579156C22semidirect
53. C2×#14579154C22semidirect
54. C2×#14579154C22semidirect
55. C2×#14579153C22semidirect
56. C2×#14579152C22semidirect
57. C2×#14579151C22semidirect
58. C2×#14579148C22semidirect
59. C2×#14579147C22semidirect
60. C2×#14579147C22semidirect
61. C2×#14579147C22semidirect
62. #19099069C22semidirect
63. C2×#14579145C22semidirect
64. C2×#14579145C22semidirect
65. C2×#14579145C22semidirect
66. C2×#14579143C22semidirect
67. C2×#14579143C22semidirect
68. C2×#14579142C22semidirect
69. C2×#14579142C22semidirect
70. C2×#14579142C22semidirect
71. C2×#14579140C22semidirect
72. C2×#14579138C22semidirect
73. C2×#14579138C22semidirect
74. C2×#14579138C22semidirect
75. C2×#14579135C22semidirect
76. C2×#14579135C22semidirect
78. C2×#14579133C22semidirect
79. C2×#14579133C22semidirect
80. C2×#14579133C22semidirect
81. C2×#14579133C22semidirect
82. C2×#14579133C22semidirect
83. C2×#14579133C22semidirect
84. C2×#14579133C22semidirect
85. C2×#14579133C22semidirect
86. C2×#14579133C22semidirect
87. C2×#14579133C22semidirect
88. C2×#14579133C22semidirect
89. C2×#14579133C22semidirect
90. C2×#14579132C22semidirect
91. C2×#14579132C22semidirect
92. C2×#14579132C22semidirect
93. C2×#14579132C22semidirect
94. C2×#14579130C22semidirect
95. C2×#14579130C22semidirect
96. C2×#14579129C22semidirect
97. C2×#14579129C22semidirect
98. #19099038C22semidirect
99. #19099035C22semidirect
100. C2×C4×Dic158C22semidirect
101. C2×C4×D316C22semidirect
105. C2×D4×Dic79C22semidirect
106. C2×D4×Dic79C22semidirect
107. C2×D4×Dic79C22semidirect
108. C2×D4×Dic79C22semidirect
109. C2×D4×Dic79C22semidirect
110. C2×D4×Dic79C22semidirect
111. C2×D4×Dic79C22semidirect
112. C2×D4×Dic79C22semidirect
113. C2×D4×Dic79C22semidirect
114. C2×D4×Dic79C22semidirect
115. C2×#14579123C22semidirect
116. C2×C4×C22⋊D79C22semidirect
117. C2×C4×C22⋊D79C22semidirect
118. C2×C4×C22⋊D79C22semidirect
119. C2×(C22⋊D79)⋊C4C22semidirect
120. C2×(C22⋊D79)⋊C4C22semidirect
121. C2×(C22⋊D79)⋊C4C22semidirect
122. C2×#14579120C22semidirect
123. C2×#14579120C22semidirect
124. C2×#14579119C22semidirect
125. C2×#14579118C22semidirect
126. C2×#14579117C22semidirect
127. C22×C4⋊Dic79C22semidirect
128. C22×Dic79⋊C4C22semidirect
129. C22×C22⋊Dic79C22semidirect
130. C22×C22⋊Dic79C22semidirect
131. C22×C22⋊Dic79C22semidirect
132. C22×(C2×D79)⋊C4C22semidirect
133. C2×C22⋊C4×D79C22semidirect
134. C22×C4×Dic79C22semidirect
137. C23×D4×C79C22semidirect
138. D42×C79C22semidirect
139. C2×#127×C79C22semidirect
140. C2×#121×C79C22semidirect
141. C2×#121×C79C22semidirect
142. C2×#121×C79C22semidirect
143. C2×#120×C79C22semidirect
144. C2×#120×C79C22semidirect
146. C2×C4×D4×C79C22semidirect
150. C2×#11929623C23semidirect
151. C2×#11929623C23semidirect
168. C22×C22⋊D79C23semidirect
169. C22×C22⋊D79C23semidirect
183. C23×Dic79C23semidirect
187. #14579160C23semidirect
188. #14579157C23semidirect
189. #14579157C23semidirect
190. #14579156C23semidirect
191. #14579156C23semidirect
192. #14579154C23semidirect
193. #14579154C23semidirect
194. #14579153C23semidirect
195. #14579152C23semidirect
196. #14579151C23semidirect
197. #14579148C23semidirect
198. #14579147C23semidirect
199. #14579147C23semidirect
200. #14579147C23semidirect
201. #14579145C23semidirect
202. #14579145C23semidirect
203. #14579145C23semidirect
204. #14579143C23semidirect
205. #14579143C23semidirect
206. #14579142C23semidirect
207. #14579142C23semidirect
208. #14579142C23semidirect
209. #14579140C23semidirect
210. #14579138C23semidirect
211. #14579138C23semidirect
212. #14579138C23semidirect
213. #14579135C23semidirect
214. #14579135C23semidirect
216. #14579133C23semidirect
217. #14579133C23semidirect
218. #14579133C23semidirect
219. #14579133C23semidirect
220. #14579133C23semidirect
221. #14579133C23semidirect
222. #14579133C23semidirect
223. #14579133C23semidirect
224. #14579133C23semidirect
225. #14579133C23semidirect
226. #14579133C23semidirect
227. #14579132C23semidirect
228. #14579132C23semidirect
229. #14579132C23semidirect
230. #14579132C23semidirect
231. #14579130C23semidirect
232. #14579130C23semidirect
233. #14579129C23semidirect
234. #14579129C23semidirect
235. C4×Dic158C23semidirect
236. C4×D316C23semidirect
240. D4×Dic79C23semidirect
241. D4×Dic79C23semidirect
242. D4×Dic79C23semidirect
243. D4×Dic79C23semidirect
244. D4×Dic79C23semidirect
245. D4×Dic79C23semidirect
246. D4×Dic79C23semidirect
247. D4×Dic79C23semidirect
248. D4×Dic79C23semidirect
249. #14579123C23semidirect
250. C4×C22⋊D79C23semidirect
251. C4×C22⋊D79C23semidirect
252. C4×C22⋊D79C23semidirect
253. (C22⋊D79)⋊C4C23semidirect
254. (C22⋊D79)⋊C4C23semidirect
255. (C22⋊D79)⋊C4C23semidirect
256. #14579120C23semidirect
257. #14579120C23semidirect
258. #14579119C23semidirect
259. #14579118C23semidirect
260. #14579117C23semidirect
269. C2×C4⋊Dic79C23semidirect
280. C2×Dic79⋊C4C23semidirect
295. C2×C22⋊Dic79C23semidirect
296. C2×C22⋊Dic79C23semidirect
297. C2×C22⋊Dic79C23semidirect
307. C2×(C2×D79)⋊C4C23semidirect
308. C22⋊C4×D79C23semidirect
316. C2×C4×Dic79C23semidirect
334. C22×D4×C79C23semidirect
338. #127×C79C23semidirect
339. #121×C79C23semidirect
340. #121×C79C23semidirect
341. #121×C79C23semidirect
342. #120×C79C23semidirect
343. #120×C79C23semidirect
345. C4×D4×C79C23semidirect
503. C2×D4×C79#41semidirect
584. D4×C79C2×#41semidirect
704. C2×C79#3519semidirect
722. C2×D42D79semidirect
734. C79C2×#3519semidirect
742. C23×D4C2×D79semidirect
755. D42C2×D79semidirect
764. C2×#127C2×D79semidirect
809. C2×#121C2×D79semidirect
810. C2×#121C2×D79semidirect
811. C2×#121C2×D79semidirect
816. C2×#120C2×D79semidirect
817. C2×#120C2×D79semidirect
843. C2×C4×D4C2×D79semidirect
899. C22×D4C22×D79semidirect
921. #127C22×D79semidirect
963. #121C22×D79semidirect
964. #121C22×D79semidirect
965. #121C22×D79semidirect
970. #120C22×D79semidirect
971. #120C22×D79semidirect
994. C4×D4C22×D79semidirect
1128. C2×D4#11929623semidirect
1308. D4C2×#11929623semidirect
1415. C2#23777419direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
#237774192
C2×#190992772
C2×#190992722
C2×#190992652
C2×#190992592
C2×#190992562
C2×#190992332
C2×#190992072
C2×#190992002
C2×D4×C22⋊D792
C2×#190991672
C2×#190991662
C2×#190991502
C2×#190991482
C2×#190991082
C2×#190990932
C2×#190990692
C22×#145791332
C2×#190990382
C2×#190990352
C22×D4×Dic792
C2×D42×C792
C2×#351979