Finite Group Databasebeta

← C2×#23777914 #35195597

Subgroups — C2×#23777914 #35195597

Order 20224.

8122 conjugacy classes of subgroups.

The subgroup lattice has 1416 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#23777914C2132yesmaximal, direct product factor
2C2×#19099308C212yesmaximal, complemented
3C2×#19099306C212yesmaximal, complemented
4C2×#19099299C211yesmaximal, characteristic, complemented
5C2×#19099296C211yesmaximal, characteristic, complemented
6C2×#19099222C211yesmaximal, characteristic, complemented
7C2×#19099219C211yesmaximal, characteristic, complemented
8C2×#19099210C211yesmaximal, characteristic, complemented
9C2×#19099207C211yesmaximal, characteristic, complemented
10C2×#19099207C212yesmaximal, complemented
11C2×#19099200C212yesmaximal, complemented
12C2×D4×C22⋊D79C211yesmaximal, characteristic, complemented
13C2×#19099180C211yesmaximal, characteristic, complemented
14C2×#19099178C211yesmaximal, characteristic, complemented
15C2×#19099148C212yesmaximal, complemented
16C2×#19099148C212yesmaximal, complemented
17C2×#19099145C212yesmaximal, complemented
18C2×#19099130C211yesmaximal, characteristic, complemented
19C2×#19099126C211yesmaximal, characteristic, complemented
20C2×#19099122C212yesmaximal, complemented
21C2×#19099108C211yesmaximal, characteristic, complemented
22C2×#19099093C211yesmaximal, characteristic, complemented
23C22×#14579148C211yesmaximal, characteristic, complemented
24C2×D42×C79C211yesmaximal, characteristic, complemented
25C22×#11929624C2211yescharacteristic, complemented
26C22×#11929623C2212yescomplemented
27C22×#11929623C2211yescharacteristic, complemented
28C23×Dic158C2211yescharacteristic, complemented
29C23×C22⋊D79C2212yescomplemented
30C22×D4×D79C2211yescharacteristic, complemented
31#19099308C22132yescomplemented
32#19099306C22132yescomplemented
33#19099299C22116yescomplemented
34#19099296C22116yescomplemented
35#19099222C22116yescomplemented
36#19099219C22116yescomplemented
37#19099210C22116yescomplemented
38#19099207C22116yescomplemented
39#19099207C22132yescomplemented
40#19099200C22132yescomplemented
41D4×C22⋊D79C22116yescomplemented
42#19099180C22116yescomplemented
43#19099178C22116yescomplemented
44#19099148C22132yescomplemented
45#19099148C22132yescomplemented
46#19099145C22132yescomplemented
47#19099130C22116yescomplemented
48#19099126C22116yescomplemented
49#19099122C22132yescomplemented
50#19099108C22116yescomplemented
51C2×#14579160C2211yescharacteristic, complemented
52C2×#14579157C2211yescharacteristic
53C2×#14579157C2211yescharacteristic, complemented
54#19099093C22116yescomplemented
55C2×#14579156C2211yescharacteristic, complemented
56C2×#14579154C2212yescomplemented
57C2×#14579154C2212yescomplemented
58C2×#14579154C2211yescharacteristic, complemented
59C2×#14579151C2211yescharacteristic, complemented
60C2×#14579149C2211yescharacteristic, complemented
61C2×#14579148C2211yescharacteristic, complemented
62C2×#14579148C2212yescomplemented
63C2×#14579148C2211yescharacteristic, complemented
64C2×#14579148C2211yescharacteristic, complemented
65C2×#14579148C2211yescharacteristic, complemented
66C2×#14579148C2211yescharacteristic, complemented
67C2×#14579148C2212yescomplemented
68C2×#14579148C2212yescomplemented
69C2×#14579148C2212yescomplemented
70C2×#14579148C22116yescomplemented
71C2×#14579147C2212yescomplemented
72C2×#14579147C2212yescomplemented
73C2×#14579147C2212yescomplemented
74C2×#14579147C2211yescharacteristic, complemented
75C2×#14579147C2212yescomplemented
76C2×#14579147C2212yescomplemented
77C2×#14579145C2211yescharacteristic, complemented
78C2×#14579144C2212yescomplemented
79C2×#14579144C2212yescomplemented
80C2×#14579143C2212yescomplemented
81C2×#14579143C2212yescomplemented
82C2×#14579142C2212yescomplemented
83C2×#14579142C2211yescharacteristic, complemented
84C2×#14579142C2212yescomplemented
85C2×#14579142C2212yescomplemented
86C2×#14579142C2212yescomplemented
87C2×#14579141C2211yescharacteristic, complemented
88C2×#14579140C2212yescomplemented
89C2×#14579140C2211yescharacteristic, complemented
90C2×#14579139C2212yescomplemented
91C2×#14579138C2212yescomplemented
92C2×#14579138C2212yescomplemented
93C2×#14579138C2211yescharacteristic, complemented
94C2×#14579135C2211yescharacteristic, complemented
95C2×#14579133C2211yescharacteristic
96C2×#14579133C2212yescomplemented
97C2×#14579133C2212yescomplemented
98C2×#14579133C2212yescomplemented
99C2×#14579133C2212yescomplemented
100C2×#14579133C2212yescomplemented
101C2×#14579133C2212yescomplemented
102C2×#14579133C2212yescomplemented
103C2×#14579132C2211yescharacteristic
104C2×#14579132C2212yescomplemented
105C2×#14579132C2212yescomplemented
106C2×#14579132C2212yescomplemented
107C2×#14579130C2212yescomplemented
108C2×#14579130C2212yescomplemented
109C2×#14579130C2212yescomplemented
110C2×#14579130C2212yescomplemented
111C2×#14579129C2212yescomplemented
112C2×#14579129C2212yescomplemented
113C2×#14579129C2212yescomplemented
114C2×#14579129C2212yescomplemented
115C2×C4×Dic158C2211yescharacteristic, complemented
116C2×C4×Dic158C2211yescharacteristic, complemented
117C2×#14579126C2211yescharacteristic, complemented
118C2×D4×Dic79C2211yescharacteristic, complemented
119C2×D4×Dic79C2212yescomplemented
120C2×D4×Dic79C2212yescomplemented
121C2×D4×Dic79C2211yescharacteristic, complemented
122C2×#14579123C2211yescharacteristic, complemented
123C2×C4×C22⋊D79C2211yescharacteristic, complemented
124C2×C4×C22⋊D79C2211yescharacteristic, complemented
125C2×C4×C22⋊D79C2212yescomplemented
126C2×(C22⋊D79)⋊C4C2212yescomplemented
127C2×(C22⋊D79)⋊C4C2212yescomplemented
128C2×#14579120C2211yescharacteristic, complemented
129C2×#14579118C2211yescharacteristic, complemented
130C22×C22⋊Dic79C2212yescomplemented
131C22×C22⋊Dic79C2212yescomplemented
132C22×C22⋊Dic79C2212yescomplemented
133C2×C22⋊C4×D79C2212yescomplemented
134C22×C4×Dic79C2211yescharacteristic, complemented
135C23×D4×C79C2211yescharacteristic
136C23×D4×C79C2212yescomplemented
137C23×D4×C79C2211yescharacteristic, complemented
138D42×C79C22116yescomplemented
139C2×#127×C79C2211yescharacteristic
140C2×#121×C79C2211yescharacteristic
141C2×#121×C79C2211yescharacteristic, complemented
142C2×#121×C79C2212yescomplemented
143C2×#120×C79C2212yescomplemented
144C2×#120×C79C2212yescomplemented
145C2×C4×D4×C79C2211yescharacteristic, complemented
146C2×C4×D4×C79C2211yescharacteristic, complemented
147C24×D79C2312yes—
148C2×#11929624—44no—
149C2×#11929624C2318yescomplemented
150C2×#11929623—44no—
151C2×#11929623—48no—
152C2×#11929623C23116yescomplemented
153C2×#11929623C2318yescomplemented
154C22×Dic158—44no—
155C22×Dic158C2311yescharacteristic
156C22×Dic158C2311yescharacteristic
157C22×Dic158C2311yescharacteristic
158C22×Dic158C2312yes—
159C22×Dic158C2312yes—
160C22×Dic158C2318yescomplemented
161C22×D316C2311yescharacteristic
162C22×C22⋊D79—48no—
163C22×C22⋊D79C2312yes—
164C22×C22⋊D79C2311yescharacteristic
165C22×C22⋊D79C2312yes—
166C22×C22⋊D79C2311yescharacteristic
167C22×C22⋊D79C2312yes—
168C22×C22⋊D79C2312yes—
169C22×C22⋊D79C2312yes—
170C22×C22⋊D79C2312yes—
171C22×C22⋊D79C2312yes—
172C22×C22⋊D79C2312yes—
173C22×C22⋊D79C2312yes—
174C22×C22⋊D79C23116yescomplemented
175C2×D4×D79—44no—
176C2×D4×D79C2318yescomplemented
177C23×Dic79C2311yescharacteristic
178C23×Dic79C2311yescharacteristic
179C23×Dic79C2312yes—
180C23×Dic79C2312yes—
181C23×Dic79C2312yes—
182C23×Dic79C2312yes—
183C22×C4×D79C2311yescharacteristic
184C22×C4×D79C2312yes—
185C22×C4×D79C2312yes—
186#14579160C2318yescomplemented
187#14579157C2318yes—
188#14579157C2318yescomplemented
189#14579156C2318yescomplemented
190#14579154C23116yescomplemented
191#14579154C23116yescomplemented
192#14579154C2318yescomplemented
193#14579151C2318yescomplemented
194#14579149C2318yescomplemented
195#14579148C23116yescomplemented
196#14579148C23116yescomplemented
197#14579148C2318yescomplemented
198#14579148C23116yescomplemented
199#14579148C2318yescomplemented
200#14579148C2318yescomplemented
201#14579148C2318yescomplemented
202#14579148C2318yescomplemented
203#14579148C23116yescomplemented
204#14579147C23116yescomplemented
205#14579147C23116yescomplemented
206#14579147C23116yescomplemented
207#14579147C23116yescomplemented
208#14579147C2318yescomplemented
209#14579147C23116yescomplemented
210#14579145C2318yescomplemented
211#14579144C23116yescomplemented
212#14579144C23116yescomplemented
213#14579143C23116yescomplemented
214#14579143C23116yescomplemented
215#14579142C23116yescomplemented
216#14579142C23116yescomplemented
217#14579142C23116yescomplemented
218#14579142C2318yescomplemented
219#14579142C23116yescomplemented
220#14579141C2318yescomplemented
221#14579140C23116yescomplemented
222#14579140C2318yescomplemented
223#14579139C23116yescomplemented
224#14579138C2318yescomplemented
225#14579138C23116yescomplemented
226#14579138C23116yescomplemented
227#14579135C2318yescomplemented
228#14579133C2318yes—
229#14579133C23116yescomplemented
230#14579133C23116yescomplemented
231#14579133C23116yescomplemented
232#14579133C23116yescomplemented
233#14579133C23116yescomplemented
234#14579133C23116yescomplemented
235#14579133C23116yescomplemented
236#14579132C2318yes—
237#14579132C23116yescomplemented
238#14579132C23116yescomplemented
239#14579132C23116yescomplemented
240#14579130C23116yescomplemented
241#14579130C23116yescomplemented
242#14579130C23116yescomplemented
243#14579130C23116yescomplemented
244#14579129C23116yescomplemented
245#14579129C23116yescomplemented
246#14579129C23116yescomplemented
247#14579129C23116yescomplemented
248C4×Dic158C2318yescomplemented
249C4×Dic158C2318yescomplemented
250#14579126C2318yescomplemented
251D4×Dic79C23116yescomplemented
252D4×Dic79C23116yescomplemented
253D4×Dic79C2318yescomplemented
254D4×Dic79C2318yescomplemented
255#14579123C2318yescomplemented
256C4×C22⋊D79C23116yescomplemented
257C4×C22⋊D79C2318yescomplemented
258C4×C22⋊D79C2318yescomplemented
259(C22⋊D79)⋊C4C23116yescomplemented
260(C22⋊D79)⋊C4C23116yescomplemented
261#14579120C2318yescomplemented
262#14579118C2318yescomplemented
263C2×C4⋊Dic79C2311yescharacteristic
264C2×C4⋊Dic79C2311yescharacteristic
265C2×C4⋊Dic79C2311yescharacteristic
266C2×C4⋊Dic79C2311yescharacteristic
267C2×C4⋊Dic79C2312yes—
268C2×Dic79⋊C4C2311yescharacteristic
269C2×Dic79⋊C4C2311yescharacteristic
270C2×Dic79⋊C4C2312yes—
271C2×Dic79⋊C4C2312yes—
272C2×Dic79⋊C4C2311yescharacteristic
273C2×Dic79⋊C4C2311yescharacteristic
274C2×Dic79⋊C4C2311yescharacteristic
275C2×Dic79⋊C4C2312yes—
276C2×Dic79⋊C4C2311yescharacteristic
277C2×Dic79⋊C4C2312yes—
278C2×C22⋊Dic79C2312yes—
279C2×C22⋊Dic79C2311yescharacteristic
280C2×C22⋊Dic79C2312yes—
281C2×C22⋊Dic79C2312yes—
282C2×C22⋊Dic79C2312yes—
283C2×C22⋊Dic79C2312yes—
284C2×C22⋊Dic79C2312yes—
285C2×C22⋊Dic79C2312yes—
286C2×C22⋊Dic79C2312yes—
287C2×C22⋊Dic79C2312yes—
288C2×C22⋊Dic79C2312yes—
289C2×C22⋊Dic79C2311yescharacteristic
290C2×C22⋊Dic79C2311yescharacteristic
291C2×C22⋊Dic79C2311yescharacteristic
292C2×C22⋊Dic79C2312yes—
293C2×C22⋊Dic79C2312yes—
294C2×C22⋊Dic79C2312yes—
295C2×C22⋊Dic79C2312yes—
296C2×C22⋊Dic79C23116yescomplemented
297C2×C22⋊Dic79C23116yescomplemented
298C2×C22⋊Dic79C23116yescomplemented
299C2×(C2×D79)⋊C4C2311yescharacteristic
300C2×(C2×D79)⋊C4C2312yes—
301C2×(C2×D79)⋊C4C2311yescharacteristic
302C2×(C2×D79)⋊C4C2311yescharacteristic
303C2×(C2×D79)⋊C4C2312yes—
304C2×(C2×D79)⋊C4C2312yes—
305C2×(C2×D79)⋊C4C2311yescharacteristic
306C2×(C2×D79)⋊C4C2312yes—
307C2×(C2×D79)⋊C4C2312yes—
308C22⋊C4×D79C23116yescomplemented
309C2×C4×Dic79C2311yescharacteristic
310C2×C4×Dic79C2311yescharacteristic
311C2×C4×Dic79C2311yescharacteristic
312C2×C4×Dic79C2311yescharacteristic
313C2×C4×Dic79C2311yescharacteristic
314C2×C4×Dic79C2312yes—
315C2×C4×Dic79C2312yes—
316C2×C4×Dic79C2318yescomplemented
317C25×C79C2312yes—
318C25×C79C2312yes—
319C22×D4×C79—44no—
320C22×D4×C79—44no—
321C22×D4×C79—48no—
322C22×D4×C79C2311yescharacteristic
323C22×D4×C79C2311yescharacteristic
324C22×D4×C79C2312yes—
325C22×D4×C79C2311yescharacteristic
326C22×D4×C79C2311yescharacteristic
327C22×D4×C79C2318yes—
328C22×D4×C79C2312yes—
329C22×D4×C79C2312yes—
330C22×D4×C79C2312yes—
331C22×D4×C79C2312yes—
332C22×D4×C79C2312yes—
333C22×D4×C79C23116yescomplemented
334C22×D4×C79C2318yescomplemented
335C23×C4×C79C2311yescharacteristic
336C23×C4×C79C2311yescharacteristic
337C23×C4×C79C2312yes—
338#127×C79C2318yes—
339#121×C79C2318yes—
340#121×C79C23116yescomplemented
341#121×C79C2318yescomplemented
342#120×C79C23116yescomplemented
343#120×C79C23116yescomplemented
344C4×D4×C79C2318yescomplemented
345C4×D4×C79C2318yescomplemented
346C2×C4⋊C4×C79C2311yescharacteristic
347C2×C4⋊C4×C79C2311yescharacteristic
348C2×C22⋊C4×C79C2311yescharacteristic
349C2×C22⋊C4×C79C2312yes—
350C2×C22⋊C4×C79C2311yescharacteristic
351C2×C22⋊C4×C79C2312yes—
352C2×C22⋊C4×C79C2312yes—
353C2×C42×C79C2311yescharacteristic
354C23×D79—44no—
355C23×D79—44no—
356C23×D79—44no—
357C23×D79C2411yescharacteristic
358C23×D79C2412yes—
359C23×D79C2418yes—
360#11929624—416no—
361#11929623—432no—
362#11929623—416no—
363C2×Dic158—24no—
364C2×Dic158—24no—
365C2×Dic158—416no—
366C2×Dic158—44no—
367C2×Dic158—42no—
368C2×Dic158—44no—
369C2×Dic158C2414yes—
370C2×Dic158C2414yes—
371C2×Dic158C2418yes—
372C2×Dic158C2418yes—
373C2×Dic158C2414yes—
374C2×D316—24no—
375C2×D316C2414yes—
376C2×C22⋊D79—28no—
377C2×C22⋊D79—24no—
378C2×C22⋊D79—432no—
379C2×C22⋊D79—44no—
380C2×C22⋊D79—44no—
381C2×C22⋊D79—44no—
382C2×C22⋊D79—44no—
383C2×C22⋊D79—44no—
384C2×C22⋊D79—44no—
385C2×C22⋊D79—44no—
386C2×C22⋊D79—44no—
387C2×C22⋊D79—42no—
388C2×C22⋊D79C2418yes—
389C2×C22⋊D79C2414yes—
390C2×C22⋊D79C2418yes—
391C2×C22⋊D79C2418yes—
392C2×C22⋊D79C2418yes—
393C2×C22⋊D79C2418yes—
394C2×C22⋊D79C2414yes—
395C2×C22⋊D79C2418yes—
396C2×C22⋊D79C2418yes—
397C2×C22⋊D79C2418yes—
398C2×C22⋊D79C2418yes—
399D4×D79—416no—
400C22×Dic79—24no—
401C22×Dic79—44no—
402C22×Dic79—44no—
403C22×Dic79—44no—
404C22×Dic79—42no—
405C22×Dic79—44no—
406C22×Dic79C2411yescharacteristic
407C22×Dic79C2412yes—
408C22×Dic79C2412yes—
409C22×Dic79C2411yescharacteristic
410C22×Dic79C2411yescharacteristic
411C22×Dic79C2412yes—
412C22×Dic79C2414yes—
413C22×Dic79C2411yescharacteristic
414C22×Dic79C2411yescharacteristic
415C22×Dic79C2411yescharacteristic
416C22×Dic79C2411yescharacteristic
417C22×Dic79C2418yes—
418C22×Dic79C2418yes—
419C22×Dic79C2418yes—
420C22×Dic79C2414yes—
421C22×Dic79C2418yes—
422C2×C4×D79—24no—
423C2×C4×D79—44no—
424C2×C4×D79—44no—
425C2×C4×D79C2414yes—
426C2×C4×D79C2418yes—
427C2×C4×D79C2418yes—
428C4⋊Dic79C2414yes—
429C4⋊Dic79C2414yes—
430C4⋊Dic79C2414yes—
431C4⋊Dic79C2414yes—
432C4⋊Dic79C2418yes—
433Dic79⋊C4C2414yes—
434Dic79⋊C4C2414yes—
435Dic79⋊C4C2418yes—
436Dic79⋊C4C2418yes—
437Dic79⋊C4C2414yes—
438Dic79⋊C4C2414yes—
439Dic79⋊C4C2414yes—
440Dic79⋊C4C2418yes—
441Dic79⋊C4C2414yes—
442Dic79⋊C4C2418yes—
443C22⋊Dic79C2418yes—
444C22⋊Dic79C2414yes—
445C22⋊Dic79C2418yes—
446C22⋊Dic79C2418yes—
447C22⋊Dic79C2418yes—
448C22⋊Dic79C2418yes—
449C22⋊Dic79C2418yes—
450C22⋊Dic79C2418yes—
451C22⋊Dic79C2418yes—
452C22⋊Dic79C2418yes—
453C22⋊Dic79C2418yes—
454C22⋊Dic79C2414yes—
455C22⋊Dic79C2414yes—
456C22⋊Dic79C2414yes—
457C22⋊Dic79C2418yes—
458C22⋊Dic79C2418yes—
459C22⋊Dic79C2418yes—
460C22⋊Dic79C2418yes—
461(C2×D79)⋊C4C2414yes—
462(C2×D79)⋊C4C2418yes—
463(C2×D79)⋊C4C2414yes—
464(C2×D79)⋊C4C2414yes—
465(C2×D79)⋊C4C2418yes—
466(C2×D79)⋊C4C2418yes—
467(C2×D79)⋊C4C2414yes—
468(C2×D79)⋊C4C2418yes—
469(C2×D79)⋊C4C2418yes—
470C4×Dic79C2414yes—
471C4×Dic79C2414yes—
472C4×Dic79C2414yes—
473C4×Dic79C2414yes—
474C4×Dic79C2414yes—
475C4×Dic79C2418yes—
476C4×Dic79C2418yes—
477C24×C79—28no—
478C24×C79—44no—
479C24×C79—44no—
480C24×C79—44no—
481C24×C79—44no—
482C24×C79—44no—
483C24×C79C2412yes—
484C24×C79C2411yescharacteristic
485C24×C79C2412yes—
486C24×C79C2412yes—
487C24×C79C2411yescharacteristic
488C24×C79C2418yes—
489C24×C79C2418yes—
490C2×D4×C79—28no—
491C2×D4×C79—24no—
492C2×D4×C79—24no—
493C2×D4×C79—24no—
494C2×D4×C79—24no—
495C2×D4×C79—416no—
496C2×D4×C79—416no—
497C2×D4×C79—44no—
498C2×D4×C79—44no—
499C2×D4×C79—44no—
500C2×D4×C79—44no—
501C2×D4×C79—44no—
502C2×D4×C79—432no—
503C2×D4×C79C2418yes—
504C2×D4×C79C2414yes—
505C2×D4×C79C2414yes—
506C2×D4×C79C2414yes—
507C2×D4×C79C2414yes—
508C2×D4×C79C2418yes—
509C2×D4×C79C2418yes—
510C2×D4×C79C2418yes—
511C2×D4×C79C2418yes—
512C2×D4×C79C2418yes—
513C22×C4×C79—24no—
514C22×C4×C79—24no—
515C22×C4×C79—44no—
516C22×C4×C79C2411yescharacteristic
517C22×C4×C79C2411yescharacteristic
518C22×C4×C79C2412yes—
519C22×C4×C79C2414yes—
520C22×C4×C79C2414yes—
521C22×C4×C79C2411yescharacteristic
522C22×C4×C79C2411yescharacteristic
523C22×C4×C79C2418yes—
524C22×C4×C79C2411yescharacteristic
525C4⋊C4×C79C2414yes—
526C4⋊C4×C79C2414yes—
527C22⋊C4×C79C2414yes—
528C22⋊C4×C79C2418yes—
529C22⋊C4×C79C2414yes—
530C22⋊C4×C79C2418yes—
531C22⋊C4×C79C2418yes—
532C42×C79C2414yes—
533C23×C79—22no—
534C23×C79—22no—
535C23×C79—24no—
536C23×C79—24no—
537C23×C79—24no—
538C23×C79—22no—
539C23×C79—24no—
540C23×C79—24no—
541C23×C79—22no—
542C23×C79—24no—
543C23×C79—24no—
544C23×C79—22no—
545C23×C79—24no—
546C23×C79—24no—
547C23×C79—216no—
548C23×C79—48no—
549C23×C79—48no—
550C23×C79—48no—
551C23×C79—48no—
552C23×C79—48no—
553C23×C79—816no—
554C23×C79—816no—
555C23×C79H(5,𝔽2)14yes—
556C23×C79C2514yes—
557C23×C79C2512yes—
558C23×C79C2514yes—
559C23×C79C2514yes—
560C23×C79C2512yes—
561C23×C79C2511yescharacteristic
562C22×D79—22no—
563C22×D79—24no—
564C22×D79—24no—
565C22×D79—22no—
566C22×D79—24no—
567C22×D79—22no—
568C22×D79—48no—
569C22×D79—48no—
570C22×D79—48no—
571C22×D79—816no—
572C22×D79C2512yes—
573C22×D79C2514yes—
574D4×C79—216no—
575D4×C79—28no—
576D4×C79—28no—
577D4×C79—28no—
578D4×C79—28no—
579D4×C79—48no—
580D4×C79—48no—
581D4×C79—48no—
582D4×C79—48no—
583D4×C79—48no—
584C2×C4×C79—22no—
585C2×C4×C79—24no—
586C2×C4×C79—22no—
587C2×C4×C79—22no—
588C2×C4×C79—22no—
589C2×C4×C79—28no—
590C2×C4×C79—28no—
591C2×C4×C79—48no—
592C2×C4×C79H(5,𝔽2)14yes—
593C2×C4×C79C2512yes—
594C2×C4×C79C2512yes—
595C2×C4×C79C2514yes—
596C2×C4×C79C2512yes—
597C2×C4×C79C2512yes—
598C2×C4×C79C2512yes—
599C22⋊D79—28no—
600C22⋊D79—216no—
601C22⋊D79—48no—
602C22⋊D79—48no—
603C22⋊D79—48no—
604C22⋊D79—48no—
605C22⋊D79—48no—
606C22⋊D79—44no—
607C22⋊D79—48no—
608C22⋊D79—48no—
609C22⋊D79—48no—
610C2×Dic79—22no—
611C2×Dic79—22no—
612C2×Dic79—24no—
613C2×Dic79—22no—
614C2×Dic79—28no—
615C2×Dic79—22no—
616C2×Dic79—24no—
617C2×Dic79—24no—
618C2×Dic79—22no—
619C2×Dic79—22no—
620C2×Dic79—22no—
621C2×Dic79—44no—
622C2×Dic79—48no—
623C2×Dic79—48no—
624C2×Dic79—48no—
625C2×Dic79—48no—
626C2×Dic79C2512yes—
627C2×Dic79C2512yes—
628C2×Dic79C2512yes—
629C2×Dic79C2512yes—
630C2×Dic79C2512yes—
631C2×Dic79C2514yes—
632C2×Dic79C2514yes—
633C2×Dic79C2514yes—
634C2×Dic79C2512yes—
635C2×Dic79C2512yes—
636D316—28no—
637C4×D79—28no—
638C4×D79—48no—
639C4×D79—48no—
640Dic158—28no—
641Dic158—28no—
642Dic158—48no—
643Dic158—44no—
644Dic158—48no—
645C22×C79—22no—
646C22×C79—22no—
647C22×C79—28no—
648C22×C79—22no—
649C22×C79—24no—
650C22×C79—24no—
651C22×C79—24no—
652C22×C79—24no—
653C22×C79—22no—
654C22×C79—24no—
655C22×C79—24no—
656C22×C79—24no—
657C22×C79—22no—
658C22×C79—24no—
659C22×C79—24no—
660C22×C79—48no—
661C22×C79—48no—
662C22×C79—44no—
663C22×C79—48no—
664C22×C79—816no—
665C22×C79—816no—
666C22×C79C2×H(5,𝔽2)14yes—
667C22×C79C2×H(5,𝔽2)12yes—
668C22×C79C2×H(5,𝔽2)12yes—
669C22×C79#58512yes—
670C22×C79C2611yescharacteristic
671C2×D79—22no—
672C2×D79—24no—
673C2×D79—22no—
674C2×D79—24no—
675C2×D79—24no—
676C2×D79—22no—
677C2×D79—48no—
678C2×D79—44no—
679C2×D79—816no—
680C4×C79—22no—
681C4×C79—22no—
682C4×C79—22no—
683C4×C79—24no—
684C4×C79—22no—
685C4×C79C2×H(5,𝔽2)14yes—
686Dic79—22no—
687Dic79—24no—
688Dic79—22no—
689Dic79—22no—
690Dic79—24no—
691Dic79—24no—
692Dic79—22no—
693Dic79—22no—
694Dic79—22no—
695Dic79—22no—
696C2×#3558—791nomaximal, Sylow
697C2×C79—24no—
698C2×C79—44no—
699C2×C79—44no—
700C2×C79—42no—
701C2×C79—44no—
702C2×C79#355814yescomplemented
703C2×C79C22×H(5,𝔽2)11yescharacteristic
704C2×C79C22×H(5,𝔽2)11yescharacteristic
705C2×C79C2×#58511yescharacteristic
706D79—44no—
707D79—42no—
708#3558—7932no—
709C2×#562—792no—
710C2×H(3,𝔽4)—792no—
711C2×#559—791no—
712C2×#559—791no—
713C2×#548—791no—
714C2×#548—791no—
715C2×#546—792no—
716C2×#546—791no—
717C2×#546—791no—
718C2×#546—792no—
719C2×D42—791no—
720C2×D42D7911yescharacteristic, complemented
721C2×#542—791no—
722C2×#542—791no—
723C2×#538—792no—
724C2×#538—792no—
725C2×#538—792no—
726C2×#535—791no—
727C2×#535—791no—
728C2×#534—792no—
729C2×#532—791no—
730C2×#529—791no—
731C22×#124—791no—
732C79C2×#355811yescharacteristic, complemented, Sylow
733C22×#41—792no—
734C22×#41—791no—
735C22×#41—791no—
736C23×Q8—791no—
737C23×D4—792no—
738C23×D4—791no—
739C23×D4C2×D7911yescharacteristic
740C23×D4C2×D7912yescomplemented
741C23×D4C2×D7911yescharacteristic, complemented
742#562—7932no—
743H(3,𝔽4)—7932no—
744#559—7916no—
745#559—7916no—
746#548—7916no—
747#548—7916no—
748#546—7932no—
749#546—7916no—
750#546—7916no—
751#546—7932no—
752D42—7916no—
753D42C2×D79116yescomplemented
754#542—7916no—
755#542—7916no—
756#538—7932no—
757#538—7932no—
758#538—7932no—
759#535—7916no—
760#535—7916no—
761#534—7932no—
762#532—7916no—
763C2×C4⋊Q8—791no—
764C2×#127—791no—
765C2×#127—791no—
766C2×#127C2×D7911yescharacteristic
767#529—7916no—
768C2×#126—791no—
769C2×#126—791no—
770C2×#126—792no—
771C2×#126—792no—
772C2×#125—791no—
773C2×#124—791no—
774C2×#124—791no—
775C2×#124—792no—
776C2×#124—791no—
777C2×#124—791no—
778C2×#124—792no—
779C2×#124—7916no—
780C2×#124—791no—
781C2×#124—792no—
782C2×#124—792no—
783C2×#124—791no—
784C2×#124—792no—
785C2×#124—792no—
786C2×#124—792no—
787C2×#124—792no—
788C2×#124—792no—
789C2×#124—791no—
790C2×#123—791no—
791C2×#123—792no—
792C2×#123—792no—
793C2×#123—792no—
794C2×#123—792no—
795C2×#123—792no—
796C2×#123—792no—
797C2×#123—791no—
798C2×#123—792no—
799C2×#123—792no—
800C2×C22⋊Q8—791no—
801C2×C22⋊Q8—792no—
802C2×C22⋊Q8—792no—
803C2×C22⋊Q8—791no—
804C2×C22⋊Q8—791no—
805C2×C22⋊Q8—792no—
806C2×C22⋊Q8—792no—
807C2×#121—791no—
808C2×#121—792no—
809C2×#121—792no—
810C2×#121—792no—
811C2×#121—792no—
812C2×#121—792no—
813C2×#121—792no—
814C2×#121—792no—
815C2×#121—792no—
816C2×#121—792no—
817C2×#121—792no—
818C2×#121—791no—
819C2×#121—791no—
820C2×#121C2×D7911yescharacteristic
821C2×#121C2×D7911yescharacteristic, complemented
822C2×#121C2×D7912yescomplemented
823C2×#120—792no—
824C2×#120—792no—
825C2×#120—792no—
826C2×#120—792no—
827C2×#120—792no—
828C2×#120—792no—
829C2×#120—792no—
830C2×#120—792no—
831C2×#120C2×D7912yescomplemented
832C2×#120C2×D7912yescomplemented
833C2×C4×Q8—791no—
834C2×C4×Q8—791no—
835C2×C4×Q8—791no—
836C2×C4×D4—791no—
837C2×C4×D4—792no—
838C2×C4×D4—792no—
839C2×C4×D4—791no—
840C2×C4×D4—791no—
841C2×C4×D4—791no—
842C2×C4×D4—792no—
843C2×C4×D4—791no—
844C2×C4×D4—792no—
845C2×C4×D4—792no—
846C2×C4×D4C2×D7911yescharacteristic, complemented
847C2×C4×D4C2×D7911yescharacteristic, complemented
848C2×#117—791no—
849C2×#117—791no—
850C22×C22⋊C4—792no—
851C22×C22⋊C4—792no—
852C22×C22⋊C4—792no—
853C22×C22⋊C4—792no—
854C22×C42—791no—
855C25—792no—
856C25C22×D7912yes—
857C25C22×D7912yes—
858C2×#41—3164no—
859C2×#41—3164no—
860C2×#41—3168no—
861C2×#41—7916no—
862C2×#41—798no—
863C2×#41—798no—
864C22×Q8—3164no—
865C22×Q8—791no—
866C22×Q8—792no—
867C22×Q8—792no—
868C22×Q8—798no—
869C22×Q8—791no—
870C22×Q8—791no—
871C22×D4—44no—
872C22×D4—44no—
873C22×D4—48no—
874C22×D4—3168no—
875C22×D4—3164no—
876C22×D4—791no—
877C22×D4—792no—
878C22×D4—792no—
879C22×D4—792no—
880C22×D4—792no—
881C22×D4—792no—
882C22×D4—792no—
883C22×D4—792no—
884C22×D4—792no—
885C22×D4—7916no—
886C22×D4—798no—
887C22×D4—792no—
888C22×D4—791no—
889C22×D4—791no—
890C22×D4C22×D7912yes—
891C22×D4C22×D7911yescharacteristic
892C22×D4C22×D7911yescharacteristic
893C22×D4C22×D7911yescharacteristic
894C22×D4C22×D7911yescharacteristic
895C22×D4C22×D7912yes—
896C22×D4C22×D7912yes—
897C22×D4C22×D7912yes—
898C22×D4C22×D7912yes—
899C22×D4C22×D7912yes—
900C22×D4C22×D7918yes—
901C22×D4C22×D79116yescomplemented
902C22×D4C22×D7918yescomplemented
903C23×C4—792no—
904C23×C4—791no—
905C23×C4—792no—
906C23×C4—792no—
907C23×C4—792no—
908C23×C4—792no—
909C23×C4—792no—
910C23×C4—791no—
911C23×C4—791no—
912C23×C4C22×D7911yescharacteristic
913C23×C4C22×D7911yescharacteristic
914C23×C4C22×D7912yes—
915C4⋊Q8—798no—
916#127—798no—
917#127—798no—
918#127C22×D7918yes—
919#126—798no—
920#126—798no—
921#126—7916no—
922#126—7916no—
923#125—798no—
924#124—798no—
925#124—798no—
926#124—7916no—
927#124—798no—
928#124—798no—
929#124—7916no—
930#124—798no—
931#124—7916no—
932#124—7916no—
933#124—798no—
934#124—7916no—
935#124—7916no—
936#124—7916no—
937#124—7916no—
938#124—7916no—
939#124—798no—
940#123—798no—
941#123—7916no—
942#123—7916no—
943#123—7916no—
944#123—7916no—
945#123—7916no—
946#123—7916no—
947#123—798no—
948#123—7916no—
949#123—7916no—
950C22⋊Q8—798no—
951C22⋊Q8—7916no—
952C22⋊Q8—7916no—
953C22⋊Q8—798no—
954C22⋊Q8—798no—
955C22⋊Q8—7916no—
956C22⋊Q8—7916no—
957#121—798no—
958#121—7916no—
959#121—7916no—
960#121—7916no—
961#121—7916no—
962#121—7916no—
963#121—7916no—
964#121—7916no—
965#121—7916no—
966#121—7916no—
967#121—7916no—
968#121—798no—
969#121—798no—
970#121C22×D7918yes—
971#121C22×D7918yescomplemented
972#121C22×D79116yescomplemented
973#120—7916no—
974#120—7916no—
975#120—7916no—
976#120—7916no—
977#120—7916no—
978#120—7916no—
979#120—7916no—
980#120—7916no—
981#120C22×D79116yescomplemented
982#120C22×D79116yescomplemented
983C4×Q8—798no—
984C4×Q8—798no—
985C4×Q8—798no—
986C4×D4—798no—
987C4×D4—7916no—
988C4×D4—7916no—
989C4×D4—798no—
990C4×D4—798no—
991C4×D4—798no—
992C4×D4—7916no—
993C4×D4—798no—
994C4×D4—7916no—
995C4×D4—7916no—
996C4×D4C22×D7918yescomplemented
997C4×D4C22×D7918yescomplemented
998#117—798no—
999#117—798no—
1000C2×C4⋊C4—791no—
1001C2×C4⋊C4—791no—
1002C2×C4⋊C4—791no—
1003C2×C4⋊C4—791no—
1004C2×C4⋊C4—791no—
1005C2×C4⋊C4—791no—
1006C2×C4⋊C4—791no—
1007C2×C4⋊C4—791no—
1008C2×C4⋊C4—792no—
1009C2×C4⋊C4—792no—
1010C2×C4⋊C4—792no—
1011C2×C4⋊C4—791no—
1012C2×C4⋊C4—792no—
1013C2×C4⋊C4—792no—
1014C2×C4⋊C4—791no—
1015C2×C4⋊C4C22×D7911yescharacteristic
1016C2×C4⋊C4C22×D7911yescharacteristic
1017C2×C22⋊C4—791no—
1018C2×C22⋊C4—792no—
1019C2×C22⋊C4—792no—
1020C2×C22⋊C4—792no—
1021C2×C22⋊C4—792no—
1022C2×C22⋊C4—792no—
1023C2×C22⋊C4—792no—
1024C2×C22⋊C4—792no—
1025C2×C22⋊C4—792no—
1026C2×C22⋊C4—792no—
1027C2×C22⋊C4—792no—
1028C2×C22⋊C4—7916no—
1029C2×C22⋊C4—7916no—
1030C2×C22⋊C4—7916no—
1031C2×C22⋊C4—791no—
1032C2×C22⋊C4—791no—
1033C2×C22⋊C4—791no—
1034C2×C22⋊C4—792no—
1035C2×C22⋊C4—792no—
1036C2×C22⋊C4—792no—
1037C2×C22⋊C4—792no—
1038C2×C22⋊C4—791no—
1039C2×C22⋊C4—792no—
1040C2×C22⋊C4—791no—
1041C2×C22⋊C4—791no—
1042C2×C22⋊C4—791no—
1043C2×C22⋊C4—792no—
1044C2×C22⋊C4—792no—
1045C2×C22⋊C4—792no—
1046C2×C22⋊C4—792no—
1047C2×C22⋊C4—7916no—
1048C2×C22⋊C4C22×D7912yes—
1049C2×C22⋊C4C22×D7911yescharacteristic
1050C2×C22⋊C4C22×D7912yes—
1051C2×C22⋊C4C22×D7912yes—
1052C2×C22⋊C4C22×D7911yescharacteristic
1053C2×C42—791no—
1054C2×C42—791no—
1055C2×C42—791no—
1056C2×C42—792no—
1057C2×C42—792no—
1058C2×C42—791no—
1059C2×C42—791no—
1060C2×C42—798no—
1061C2×C42C22×D7911yescharacteristic
1062C24—28no—
1063C24—44no—
1064C24—44no—
1065C24—44no—
1066C24—44no—
1067C24—44no—
1068C24—3164no—
1069C24—3164no—
1070C24—3164no—
1071C24—798no—
1072C24—791no—
1073C24—792no—
1074C24C23×D7912yes—
1075C24C23×D7911yescharacteristic
1076C24C23×D7912yes—
1077C24C23×D7912yes—
1078C24C23×D7911yescharacteristic
1079C24C23×D7918yes—
1080C24C23×D7918yes—
1081#41—31616no—
1082#41—31616no—
1083#41—31632no—
1084C2×Q8—31616no—
1085C2×Q8—3164no—
1086C2×Q8—3162no—
1087C2×Q8—3164no—
1088C2×Q8—794no—
1089C2×Q8—798no—
1090C2×Q8—798no—
1091C2×Q8—794no—
1092C2×Q8—794no—
1093C2×Q8—1584no—
1094C2×Q8—1584no—
1095C2×D4—24no—
1096C2×D4—28no—
1097C2×D4—24no—
1098C2×D4—24no—
1099C2×D4—24no—
1100C2×D4—416no—
1101C2×D4—416no—
1102C2×D4—44no—
1103C2×D4—44no—
1104C2×D4—44no—
1105C2×D4—44no—
1106C2×D4—44no—
1107C2×D4—432no—
1108C2×D4—31632no—
1109C2×D4—31616no—
1110C2×D4—3164no—
1111C2×D4—3164no—
1112C2×D4—3164no—
1113C2×D4—3164no—
1114C2×D4—3162no—
1115C2×D4—3164no—
1116C2×D4—3164no—
1117C2×D4—3164no—
1118C2×D4—3164no—
1119C2×D4—794no—
1120C2×D4—798no—
1121C2×D4—798no—
1122C2×D4—798no—
1123C2×D4—798no—
1124C2×D4—798no—
1125C2×D4—798no—
1126C2×D4—798no—
1127C2×D4—798no—
1128C2×D4—798no—
1129C2×D4—794no—
1130C2×D4—794no—
1131C2×D4—1584no—
1132C2×D4—1588no—
1133C2×D4—1584no—
1134C2×D4C23×D7918yes—
1135C2×D4C23×D7914yes—
1136C2×D4C23×D7914yes—
1137C2×D4C23×D7914yes—
1138C2×D4C23×D7914yes—
1139C2×D4C23×D7918yes—
1140C2×D4C23×D7918yes—
1141C2×D4C23×D7918yes—
1142C2×D4C23×D7918yes—
1143C2×D4C23×D7918yes—
1144C22×C4—24no—
1145C22×C4—24no—
1146C22×C4—44no—
1147C22×C4—3164no—
1148C22×C4—3164no—
1149C22×C4—3162no—
1150C22×C4—3164no—
1151C22×C4—3164no—
1152C22×C4—3164no—
1153C22×C4—3164no—
1154C22×C4—794no—
1155C22×C4—798no—
1156C22×C4—798no—
1157C22×C4—798no—
1158C22×C4—798no—
1159C22×C4—798no—
1160C22×C4—798no—
1161C22×C4—794no—
1162C22×C4—791no—
1163C22×C4—791no—
1164C22×C4—791no—
1165C22×C4—791no—
1166C22×C4—791no—
1167C22×C4—792no—
1168C22×C4—792no—
1169C22×C4—792no—
1170C22×C4—791no—
1171C22×C4—791no—
1172C22×C4—794no—
1173C22×C4—1584no—
1174C22×C4—1584no—
1175C22×C4C23×D7914yes—
1176C22×C4C23×D7914yes—
1177C22×C4C23×D7911yescharacteristic
1178C22×C4C23×D7911yescharacteristic
1179C22×C4C23×D7912yes—
1180C22×C4C23×D7911yescharacteristic
1181C22×C4C23×D7911yescharacteristic
1182C22×C4C23×D7918yes—
1183C22×C4C23×D7911yescharacteristic
1184C4⋊C4—794no—
1185C4⋊C4—794no—
1186C4⋊C4—794no—
1187C4⋊C4—794no—
1188C4⋊C4—798no—
1189C4⋊C4—798no—
1190C4⋊C4—794no—
1191C4⋊C4—798no—
1192C4⋊C4—798no—
1193C4⋊C4—794no—
1194C4⋊C4—794no—
1195C4⋊C4—794no—
1196C4⋊C4—794no—
1197C4⋊C4—794no—
1198C4⋊C4—798no—
1199C4⋊C4C23×D7914yes—
1200C4⋊C4C23×D7914yes—
1201C22⋊C4—794no—
1202C22⋊C4—798no—
1203C22⋊C4—798no—
1204C22⋊C4—798no—
1205C22⋊C4—798no—
1206C22⋊C4—798no—
1207C22⋊C4—798no—
1208C22⋊C4—798no—
1209C22⋊C4—798no—
1210C22⋊C4—798no—
1211C22⋊C4—798no—
1212C22⋊C4—794no—
1213C22⋊C4—794no—
1214C22⋊C4—794no—
1215C22⋊C4—798no—
1216C22⋊C4—798no—
1217C22⋊C4—798no—
1218C22⋊C4—798no—
1219C22⋊C4—794no—
1220C22⋊C4—798no—
1221C22⋊C4—794no—
1222C22⋊C4—794no—
1223C22⋊C4—794no—
1224C22⋊C4—798no—
1225C22⋊C4—798no—
1226C22⋊C4—798no—
1227C22⋊C4—798no—
1228C22⋊C4C23×D7918yes—
1229C22⋊C4C23×D7914yes—
1230C22⋊C4C23×D7918yes—
1231C22⋊C4C23×D7918yes—
1232C22⋊C4C23×D7914yes—
1233C42—794no—
1234C42—794no—
1235C42—794no—
1236C42—794no—
1237C42—794no—
1238C42—798no—
1239C42—798no—
1240C42C23×D7914yes—
1241C23—22no—
1242C23—22no—
1243C23—22no—
1244C23—24no—
1245C23—24no—
1246C23—24no—
1247C23—24no—
1248C23—22no—
1249C23—24no—
1250C23—24no—
1251C23—24no—
1252C23—24no—
1253C23—22no—
1254C23—24no—
1255C23—216no—
1256C23—48no—
1257C23—48no—
1258C23—48no—
1259C23—48no—
1260C23—48no—
1261C23—816no—
1262C23—816no—
1263C23—3168no—
1264C23—3168no—
1265C23—3168no—
1266C23—792no—
1267C23—794no—
1268C23—63216no—
1269C23—1584no—
1270C23—1584no—
1271C23—1582no—
1272C23—1582no—
1273C23—1584no—
1274C23—1582no—
1275C23#1457920614yes—
1276C23C24×D7914yes—
1277C23C24×D7912yes—
1278C23C24×D7914yes—
1279C23C24×D7914yes—
1280C23C24×D7912yes—
1281C23C24×D7911yescharacteristic
1282Q8—3168no—
1283Q8—3168no—
1284Q8—3164no—
1285Q8—1588no—
1286Q8—1588no—
1287D4—28no—
1288D4—216no—
1289D4—28no—
1290D4—28no—
1291D4—28no—
1292D4—48no—
1293D4—48no—
1294D4—48no—
1295D4—48no—
1296D4—48no—
1297D4—3168no—
1298D4—3168no—
1299D4—3168no—
1300D4—3168no—
1301D4—3164no—
1302D4—3168no—
1303D4—3168no—
1304D4—3168no—
1305D4—3168no—
1306D4—1588no—
1307D4—15816no—
1308D4—1588no—
1309C2×C4—22no—
1310C2×C4—22no—
1311C2×C4—22no—
1312C2×C4—24no—
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—3164no—
1324C2×C4—792no—
1325C2×C4—792no—
1326C2×C4—792no—
1327C2×C4—792no—
1328C2×C4—792no—
1329C2×C4—794no—
1330C2×C4—794no—
1331C2×C4—794no—
1332C2×C4—792no—
1333C2×C4—792no—
1334C2×C4—1582no—
1335C2×C4—1582no—
1336C2×C4—1582no—
1337C2×C4—1584no—
1338C2×C4—1584no—
1339C2×C4—1584no—
1340C2×C4—1582no—
1341C2×C4—1588no—
1342C2×C4—1582no—
1343C2×C4—1582no—
1344C2×C4—1582no—
1345C2×C4—1588no—
1346C2×C4#1457920614yes—
1347C2×C4C24×D7912yes—
1348C2×C4C24×D7912yes—
1349C2×C4C24×D7914yes—
1350C2×C4C24×D7912yes—
1351C2×C4C24×D7912yes—
1352C2×C4C24×D7912yes—
1353C22—28no—
1354C22—22no—
1355C22—22no—
1356C22—22no—
1357C22—24no—
1358C22—24no—
1359C22—24no—
1360C22—24no—
1361C22—22no—
1362C22—24no—
1363C22—24no—
1364C22—24no—
1365C22—24no—
1366C22—22no—
1367C22—24no—
1368C22—44no—
1369C22—48no—
1370C22—48no—
1371C22—48no—
1372C22—816no—
1373C22—816no—
1374C22—3164no—
1375C22—3168no—
1376C22—63216no—
1377C22—1584no—
1378C22—1584no—
1379C22—1582no—
1380C22—1582no—
1381C22—1584no—
1382C22—1582no—
1383C22C2×#1457920614yes—
1384C22C2×#1457920612yes—
1385C22C2×#1457920612yes—
1386C22#1909939812yes—
1387C22C25×D7911yescharacteristic
1388C4—22no—
1389C4—22no—
1390C4—22no—
1391C4—24no—
1392C4—22no—
1393C4—1582no—
1394C4—1582no—
1395C4—1582no—
1396C4—1584no—
1397C4—1584no—
1398C4—1584no—
1399C4—1582no—
1400C4—1582no—
1401C4—1582no—
1402C4—1582no—
1403C4C2×#1457920614yes—
1404C2—24no—
1405C2—42no—
1406C2—44no—
1407C2—44no—
1408C2—44no—
1409C2—3162no—
1410C2—3164no—
1411C2#2377791414yesdirect product factor
1412C2C22×#1457920611yescharacteristic
1413C2C22×#1457920611yescharacteristic
1414C2C2×#1909939811yescharacteristic
subgroupG/H
centerC23C24×D79
commutator, cosocleC22×C79C26
FrattiniC22C25×D79
FittingC2×D42×C79C2
socleC23×C79C25
hypercenterC2×D42D79
hypocenterC79C2×#3558
LCSG ▷ C22×C79 ▷ C79
UCSC1 ◁ C23 ◁ C2×D42

Complements

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

NH ≅ G/Ntype
1. #23777914C2direct (N × H)
2. C2×#19099308C2semidirect
3. C2×#19099306C2semidirect
4. C2×#19099299C2semidirect
5. C2×#19099296C2semidirect
6. C2×#19099222C2semidirect
7. C2×#19099219C2semidirect
8. C2×#19099210C2semidirect
9. C2×#19099207C2semidirect
10. C2×#19099207C2semidirect
11. C2×#19099200C2semidirect
12. C2×D4×C22⋊D79C2semidirect
13. C2×#19099180C2semidirect
14. C2×#19099178C2semidirect
15. C2×#19099148C2semidirect
16. C2×#19099148C2semidirect
17. C2×#19099145C2semidirect
18. C2×#19099130C2semidirect
19. C2×#19099126C2semidirect
20. C2×#19099122C2semidirect
21. C2×#19099108C2semidirect
22. C2×#19099093C2semidirect
23. C22×#14579148C2semidirect
24. C2×D42×C79C2semidirect
25. C22×#11929624C22semidirect
26. C22×#11929623C22semidirect
27. C22×#11929623C22semidirect
28. C23×Dic158C22semidirect
29. C23×C22⋊D79C22semidirect
30. C22×D4×D79C22semidirect
31. #19099308C22semidirect
32. #19099306C22semidirect
33. #19099299C22semidirect
34. #19099296C22semidirect
35. #19099222C22semidirect
36. #19099219C22semidirect
37. #19099210C22semidirect
38. #19099207C22semidirect
39. #19099207C22semidirect
40. #19099200C22semidirect
41. D4×C22⋊D79C22semidirect
42. #19099180C22semidirect
43. #19099178C22semidirect
44. #19099148C22semidirect
45. #19099148C22semidirect
46. #19099145C22semidirect
47. #19099130C22semidirect
48. #19099126C22semidirect
49. #19099122C22semidirect
50. #19099108C22semidirect
51. C2×#14579160C22semidirect
53. C2×#14579157C22semidirect
54. #19099093C22semidirect
55. C2×#14579156C22semidirect
56. C2×#14579154C22semidirect
57. C2×#14579154C22semidirect
58. C2×#14579154C22semidirect
59. C2×#14579151C22semidirect
60. C2×#14579149C22semidirect
61. C2×#14579148C22semidirect
62. C2×#14579148C22semidirect
63. C2×#14579148C22semidirect
64. C2×#14579148C22semidirect
65. C2×#14579148C22semidirect
66. C2×#14579148C22semidirect
67. C2×#14579148C22semidirect
68. C2×#14579148C22semidirect
69. C2×#14579148C22semidirect
70. C2×#14579148C22semidirect
71. C2×#14579147C22semidirect
72. C2×#14579147C22semidirect
73. C2×#14579147C22semidirect
74. C2×#14579147C22semidirect
75. C2×#14579147C22semidirect
76. C2×#14579147C22semidirect
77. C2×#14579145C22semidirect
78. C2×#14579144C22semidirect
79. C2×#14579144C22semidirect
80. C2×#14579143C22semidirect
81. C2×#14579143C22semidirect
82. C2×#14579142C22semidirect
83. C2×#14579142C22semidirect
84. C2×#14579142C22semidirect
85. C2×#14579142C22semidirect
86. C2×#14579142C22semidirect
87. C2×#14579141C22semidirect
88. C2×#14579140C22semidirect
89. C2×#14579140C22semidirect
90. C2×#14579139C22semidirect
91. C2×#14579138C22semidirect
92. C2×#14579138C22semidirect
93. C2×#14579138C22semidirect
94. C2×#14579135C22semidirect
96. C2×#14579133C22semidirect
97. C2×#14579133C22semidirect
98. C2×#14579133C22semidirect
99. C2×#14579133C22semidirect
100. C2×#14579133C22semidirect
101. C2×#14579133C22semidirect
102. C2×#14579133C22semidirect
104. C2×#14579132C22semidirect
105. C2×#14579132C22semidirect
106. C2×#14579132C22semidirect
107. C2×#14579130C22semidirect
108. C2×#14579130C22semidirect
109. C2×#14579130C22semidirect
110. C2×#14579130C22semidirect
111. C2×#14579129C22semidirect
112. C2×#14579129C22semidirect
113. C2×#14579129C22semidirect
114. C2×#14579129C22semidirect
115. C2×C4×Dic158C22semidirect
116. C2×C4×Dic158C22semidirect
117. C2×#14579126C22semidirect
118. C2×D4×Dic79C22semidirect
119. C2×D4×Dic79C22semidirect
120. C2×D4×Dic79C22semidirect
121. C2×D4×Dic79C22semidirect
122. C2×#14579123C22semidirect
123. C2×C4×C22⋊D79C22semidirect
124. C2×C4×C22⋊D79C22semidirect
125. C2×C4×C22⋊D79C22semidirect
126. C2×(C22⋊D79)⋊C4C22semidirect
127. C2×(C22⋊D79)⋊C4C22semidirect
128. C2×#14579120C22semidirect
129. C2×#14579118C22semidirect
130. C22×C22⋊Dic79C22semidirect
131. C22×C22⋊Dic79C22semidirect
132. C22×C22⋊Dic79C22semidirect
133. C2×C22⋊C4×D79C22semidirect
134. C22×C4×Dic79C22semidirect
136. C23×D4×C79C22semidirect
137. C23×D4×C79C22semidirect
138. D42×C79C22semidirect
141. C2×#121×C79C22semidirect
142. C2×#121×C79C22semidirect
143. C2×#120×C79C22semidirect
144. C2×#120×C79C22semidirect
145. C2×C4×D4×C79C22semidirect
146. C2×C4×D4×C79C22semidirect
149. C2×#11929624C23semidirect
152. C2×#11929623C23semidirect
153. C2×#11929623C23semidirect
160. C22×Dic158C23semidirect
174. C22×C22⋊D79C23semidirect
176. C2×D4×D79C23semidirect
186. #14579160C23semidirect
188. #14579157C23semidirect
189. #14579156C23semidirect
190. #14579154C23semidirect
191. #14579154C23semidirect
192. #14579154C23semidirect
193. #14579151C23semidirect
194. #14579149C23semidirect
195. #14579148C23semidirect
196. #14579148C23semidirect
197. #14579148C23semidirect
198. #14579148C23semidirect
199. #14579148C23semidirect
200. #14579148C23semidirect
201. #14579148C23semidirect
202. #14579148C23semidirect
203. #14579148C23semidirect
204. #14579147C23semidirect
205. #14579147C23semidirect
206. #14579147C23semidirect
207. #14579147C23semidirect
208. #14579147C23semidirect
209. #14579147C23semidirect
210. #14579145C23semidirect
211. #14579144C23semidirect
212. #14579144C23semidirect
213. #14579143C23semidirect
214. #14579143C23semidirect
215. #14579142C23semidirect
216. #14579142C23semidirect
217. #14579142C23semidirect
218. #14579142C23semidirect
219. #14579142C23semidirect
220. #14579141C23semidirect
221. #14579140C23semidirect
222. #14579140C23semidirect
223. #14579139C23semidirect
224. #14579138C23semidirect
225. #14579138C23semidirect
226. #14579138C23semidirect
227. #14579135C23semidirect
229. #14579133C23semidirect
230. #14579133C23semidirect
231. #14579133C23semidirect
232. #14579133C23semidirect
233. #14579133C23semidirect
234. #14579133C23semidirect
235. #14579133C23semidirect
237. #14579132C23semidirect
238. #14579132C23semidirect
239. #14579132C23semidirect
240. #14579130C23semidirect
241. #14579130C23semidirect
242. #14579130C23semidirect
243. #14579130C23semidirect
244. #14579129C23semidirect
245. #14579129C23semidirect
246. #14579129C23semidirect
247. #14579129C23semidirect
248. C4×Dic158C23semidirect
249. C4×Dic158C23semidirect
250. #14579126C23semidirect
251. D4×Dic79C23semidirect
252. D4×Dic79C23semidirect
253. D4×Dic79C23semidirect
254. D4×Dic79C23semidirect
255. #14579123C23semidirect
256. C4×C22⋊D79C23semidirect
257. C4×C22⋊D79C23semidirect
258. C4×C22⋊D79C23semidirect
259. (C22⋊D79)⋊C4C23semidirect
260. (C22⋊D79)⋊C4C23semidirect
261. #14579120C23semidirect
262. #14579118C23semidirect
296. C2×C22⋊Dic79C23semidirect
297. C2×C22⋊Dic79C23semidirect
298. C2×C22⋊Dic79C23semidirect
308. C22⋊C4×D79C23semidirect
316. C2×C4×Dic79C23semidirect
333. C22×D4×C79C23semidirect
334. C22×D4×C79C23semidirect
340. #121×C79C23semidirect
341. #121×C79C23semidirect
342. #120×C79C23semidirect
343. #120×C79C23semidirect
344. C4×D4×C79C23semidirect
345. C4×D4×C79C23semidirect
702. C2×C79#3558semidirect
720. C2×D42D79semidirect
732. C79C2×#3558semidirect
740. C23×D4C2×D79semidirect
741. C23×D4C2×D79semidirect
753. D42C2×D79semidirect
821. C2×#121C2×D79semidirect
822. C2×#121C2×D79semidirect
831. C2×#120C2×D79semidirect
832. C2×#120C2×D79semidirect
846. C2×C4×D4C2×D79semidirect
847. C2×C4×D4C2×D79semidirect
901. C22×D4C22×D79semidirect
902. C22×D4C22×D79semidirect
971. #121C22×D79semidirect
972. #121C22×D79semidirect
981. #120C22×D79semidirect
982. #120C22×D79semidirect
996. C4×D4C22×D79semidirect
997. C4×D4C22×D79semidirect
1411. C2#23777914direct (N × H)

Maximal subgroups

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

subgroupindex
#237779142
C2×#190993082
C2×#190993062
C2×#190992992
C2×#190992962
C2×#190992222
C2×#190992192
C2×#190992102
C2×#190992072
C2×#190992002
C2×D4×C22⋊D792
C2×#190991802
C2×#190991782
C2×#190991482
C2×#190991452
C2×#190991302
C2×#190991262
C2×#190991222
C2×#190991082
C2×#190990932
C22×#145791482
C2×D42×C792
C2×#355879