Finite Group Databasebeta

← C2×#23777355 #35196355

Subgroups — C2×#23777355 #35196355

Order 20224.

8006 conjugacy classes of subgroups.

The subgroup lattice has 1376 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#23777355C2132yesmaximal, direct product factor
2C2×#19099295C211yesmaximal, characteristic, complemented
3C2×#19099282C211yesmaximal, characteristic, complemented
4C2×#19099275C212yesmaximal, complemented
5C2×#19099243C212yesmaximal, complemented
6C2×#19099239C212yesmaximal, complemented
7C2×Q8×C22⋊D79C211yesmaximal, characteristic, complemented
8C2×#19099224C211yesmaximal, characteristic, complemented
9C2×#19099221C211yesmaximal, characteristic, complemented
10C2×#19099207C211yesmaximal, characteristic, complemented
11C2×#19099206C211yesmaximal, characteristic, complemented
12C2×#19099203C212yesmaximal, complemented
13C2×D4×C22⋊D79C211yesmaximal, characteristic, complemented
14C2×#19099177C212yesmaximal, complemented
15C2×#19099151C212yesmaximal, complemented
16C2×#19099147C212yesmaximal, complemented
17C2×#19099112C211yesmaximal, characteristic, complemented
18C2×#19099097C211yesmaximal, characteristic, complemented
19C2×#19099092C211yesmaximal, characteristic, complemented
20C2×#19099092C211yesmaximal, characteristic, complemented
21C2×#124×D79C211yesmaximal, characteristic, complemented
22C2×#19099036C212yesmaximal, complemented
23C2×C4×#11929624C211yesmaximal, characteristic, complemented
24C22×#124×C79C211yesmaximal, characteristic, complemented
25C22×#11929625C2211yescharacteristic, complemented
26C22×#11929624C2211yescharacteristic
27C22×#11929623C2211yescharacteristic, complemented
28C22×Q8×D79C2211yescharacteristic, complemented
29C23×C22⋊D79C2212yes—
30C22×D4×D79C2211yescharacteristic
31#19099295C22116yescomplemented
32#19099282C22116yescomplemented
33#19099275C22132yescomplemented
34#19099243C22132yescomplemented
35#19099239C22132yescomplemented
36Q8×C22⋊D79C22116yescomplemented
37#19099224C22116yescomplemented
38#19099221C22116yescomplemented
39#19099207C22116yescomplemented
40#19099206C22116yescomplemented
41#19099203C22132yescomplemented
42D4×C22⋊D79C22116yescomplemented
43#19099177C22132yescomplemented
44#19099151C22132yescomplemented
45#19099147C22132yescomplemented
46#19099112C22116yescomplemented
47C2×#14579159C2212yescomplemented
48C2×#14579159C2211yescharacteristic, complemented
49C2×#14579157C2211yescharacteristic
50#19099097C22116yescomplemented
51#19099092C22116yescomplemented
52#19099092C22116yescomplemented
53C2×#14579155C2212yescomplemented
54C2×#14579154C2212yescomplemented
55C2×#14579154C2212yescomplemented
56C2×#14579154C2212yescomplemented
57C2×#14579154C2212yescomplemented
58C2×#14579153C2211yescharacteristic, complemented
59C2×#14579150C2211yescharacteristic, complemented
60C2×#14579150C2212yescomplemented
61C2×#14579149C2211yescharacteristic, complemented
62C2×#14579148C2211yescharacteristic
63C2×#14579147C2212yescomplemented
64C2×#14579147C2212yescomplemented
65C2×#14579147C2212yescomplemented
66C2×#14579147C2212yescomplemented
67#124×D79C22116yescomplemented
68C2×#14579145C2212yescomplemented
69C2×#14579144C2212yescomplemented
70C2×#14579143C2212yescomplemented
71C2×#14579143C2212yescomplemented
72C2×#14579143C2212yescomplemented
73C2×#14579143C2212yescomplemented
74C2×#14579142C2212yescomplemented
75C2×#14579140C2211yescharacteristic, complemented
76C2×#14579140C2212yescomplemented
77C2×#14579138C2212yescomplemented
78C2×#14579138C2212yescomplemented
79C2×#14579137C2212yescomplemented
80C2×#14579137C2211yescharacteristic, complemented
81C2×#14579137C2211yescharacteristic, complemented
82C2×#14579137C2212yescomplemented
83C2×#14579135C2211yescharacteristic
84C2×#14579135C2212yescomplemented
85C2×#14579134C2212yescomplemented
86C2×#14579134C2212yescomplemented
87C2×#14579134C2212yescomplemented
88C2×#14579134C2212yescomplemented
89C2×#14579133C2212yes—
90C2×#14579133C2212yescomplemented
91C2×#14579132C2211yescharacteristic
92C2×#14579132C2211yescharacteristic
93C2×#14579131C2212yescomplemented
94C2×#14579130C2212yes—
95C2×#14579130C2212yescomplemented
96C2×#14579129C2212yes—
97#19099036C22132yescomplemented
98C4×#11929624C22116yescomplemented
99C2×Q8×Dic79C2211yescharacteristic, complemented
100C2×Q8×Dic79C2211yescharacteristic, complemented
101C2×C4×Dic158C2211yescharacteristic, complemented
102C2×C4×Dic158C2211yescharacteristic, complemented
103C2×C4×Dic158C2211yescharacteristic, complemented
104C2×C4×D316C2211yescharacteristic, complemented
105C2×C4×D316C2211yescharacteristic, complemented
106C2×C4×D316C2211yescharacteristic, complemented
107C2×D4×Dic79C2211yescharacteristic
108C2×D4×Dic79C2211yescharacteristic, complemented
109C2×C4×C22⋊D79C2211yescharacteristic
110C2×C4×C22⋊D79C2211yescharacteristic
111C2×C4×C22⋊D79C2212yes—
112C2×C4×C22⋊D79C2211yescharacteristic, complemented
113C2×C4×C22⋊D79C2211yescharacteristic, complemented
114C2×C4×C22⋊D79C2212yescomplemented
115C2×C4×C22⋊D79C2212yescomplemented
116C2×(C22⋊D79)⋊C4C2212yescomplemented
117C2×(C22⋊D79)⋊C4C2212yescomplemented
118C2×(C22⋊D79)⋊C4C2212yescomplemented
119C2×(C22⋊D79)⋊C4C2212yescomplemented
120C2×(C22⋊D79)⋊C4C2212yescomplemented
121C2×(C22⋊D79)⋊C4C2212yescomplemented
122C2×#14579120C2211yescharacteristic, complemented
123C2×#14579118C2211yescharacteristic, complemented
124C2×#14579118C2211yescharacteristic, complemented
125C2×#14579118C2212yescomplemented
126C2×#14579117C2212yescomplemented
127C2×#14579117C2212yescomplemented
128C2×#14579117C2212yescomplemented
129C22×C22⋊Dic79C2212yescomplemented
130C2×C22⋊C4×D79C2212yescomplemented
131C2×C22⋊C4×D79C2212yescomplemented
132C2×C22⋊C4×D79C2212yescomplemented
133C2×C42×D79C2211yescharacteristic, complemented
134C2×C42×D79C2211yescharacteristic, complemented
135C23×Q8×C79C2211yescharacteristic, complemented
136C23×D4×C79C2211yescharacteristic
137C2×#124×C79C2211yescharacteristic
138C2×#124×C79C2211yescharacteristic
139C2×#124×C79C2212yescomplemented
140C2×#124×C79C2211yescharacteristic, complemented
141C2×#124×C79C2212yescomplemented
142C2×#124×C79C2211yescharacteristic, complemented
143C2×#124×C79C22116yescomplemented
144C22×C22⋊C4×C79C2212yescomplemented
145C22×C22⋊C4×C79C2212yescomplemented
146C22×C42×C79C2211yescharacteristic, complemented
147C24×D79C2312yes—
148C2×#11929625—44no—
149C2×#11929625C2318yescomplemented
150C2×#11929624—28no—
151C2×#11929624C2318yes—
152C2×#11929623—44no—
153C2×#11929623C2318yescomplemented
154C22×Dic158C2311yescharacteristic
155C22×Dic158C2311yescharacteristic
156C22×Dic158C2312yes—
157C2×Q8×D79—44no—
158C2×Q8×D79C2318yescomplemented
159C22×D316C2311yescharacteristic
160C22×D316C2311yescharacteristic
161C22×D316C2312yes—
162C22×C22⋊D79—216no—
163C22×C22⋊D79C23116yes—
164C22×C22⋊D79C2312yes—
165C22×C22⋊D79C2312yes—
166C22×C22⋊D79C2312yes—
167C22×C22⋊D79C2311yescharacteristic
168C22×C22⋊D79C2312yes—
169C22×C22⋊D79C2312yes—
170C22×C22⋊D79C2312yes—
171C22×C22⋊D79C2312yes—
172C22×C22⋊D79C2311yescharacteristic
173C2×D4×D79—44no—
174C2×D4×D79C2318yes—
175C23×Dic79C2312yes—
176C23×Dic79C2312yes—
177C23×Dic79C2312yes—
178C22×C4×D79C2311yescharacteristic
179C22×C4×D79C2311yescharacteristic
180C22×C4×D79C2311yescharacteristic
181C22×C4×D79C2311yescharacteristic
182C22×C4×D79C2311yescharacteristic
183C22×C4×D79C2311yescharacteristic
184C22×C4×D79C2312yes—
185C22×C4×D79C2312yes—
186C22×C4×D79C2312yes—
187#14579159C23116yescomplemented
188#14579159C2318yescomplemented
189#14579157C2318yes—
190#14579155C23116yescomplemented
191#14579154C23116yescomplemented
192#14579154C23116yescomplemented
193#14579154C23116yescomplemented
194#14579154C23116yescomplemented
195#14579153C2318yescomplemented
196#14579150C23116yescomplemented
197#14579150C2318yescomplemented
198#14579149C2318yescomplemented
199#14579148C2318yes—
200#14579147C23116yescomplemented
201#14579147C23116yescomplemented
202#14579147C23116yescomplemented
203#14579147C23116yescomplemented
204#14579145C23116yescomplemented
205#14579144C23116yescomplemented
206#14579143C23116yescomplemented
207#14579143C23116yescomplemented
208#14579143C23116yescomplemented
209#14579143C23116yescomplemented
210#14579142C23116yescomplemented
211#14579140C23116yescomplemented
212#14579140C2318yescomplemented
213#14579138C23116yescomplemented
214#14579138C23116yescomplemented
215#14579137C23116yescomplemented
216#14579137C23116yescomplemented
217#14579137C2318yescomplemented
218#14579137C2318yescomplemented
219#14579135C2318yes—
220#14579135C23116yescomplemented
221#14579134C23116yescomplemented
222#14579134C23116yescomplemented
223#14579134C23116yescomplemented
224#14579134C23116yescomplemented
225#14579133C23116yes—
226#14579133C23116yescomplemented
227#14579132C2318yes—
228#14579132C2318yes—
229#14579131C23116yescomplemented
230#14579130C23116yes—
231#14579130C23116yescomplemented
232#14579129C23116yes—
233Q8×Dic79C2318yescomplemented
234Q8×Dic79C2318yescomplemented
235C4×Dic158C2318yescomplemented
236C4×Dic158C2318yescomplemented
237C4×Dic158C2318yescomplemented
238C4×D316C2318yescomplemented
239C4×D316C2318yescomplemented
240C4×D316C2318yescomplemented
241D4×Dic79C2318yes—
242D4×Dic79C2318yescomplemented
243C4×C22⋊D79C2318yes—
244C4×C22⋊D79C23116yes—
245C4×C22⋊D79C2318yes—
246C4×C22⋊D79C2318yescomplemented
247C4×C22⋊D79C23116yescomplemented
248C4×C22⋊D79C2318yescomplemented
249C4×C22⋊D79C23116yescomplemented
250(C22⋊D79)⋊C4C23116yescomplemented
251(C22⋊D79)⋊C4C23116yescomplemented
252(C22⋊D79)⋊C4C23116yescomplemented
253(C22⋊D79)⋊C4C23116yescomplemented
254(C22⋊D79)⋊C4C23116yescomplemented
255(C22⋊D79)⋊C4C23116yescomplemented
256#14579120C2318yescomplemented
257#14579118C2318yescomplemented
258#14579118C23116yescomplemented
259#14579118C2318yescomplemented
260#14579117C23116yescomplemented
261#14579117C23116yescomplemented
262#14579117C23116yescomplemented
263C2×C4⋊Dic79C2311yescharacteristic
264C2×C4⋊Dic79C2311yescharacteristic
265C2×C4⋊Dic79C2311yescharacteristic
266C2×C4⋊Dic79C2311yescharacteristic
267C2×C4⋊Dic79C2312yes—
268C2×C4⋊Dic79C2312yes—
269C2×Dic79⋊C4C2311yescharacteristic
270C2×Dic79⋊C4C2312yes—
271C2×Dic79⋊C4C2312yes—
272C2×Dic79⋊C4C2312yes—
273C2×Dic79⋊C4C2312yes—
274C2×Dic79⋊C4C2312yes—
275C2×Dic79⋊C4C2311yescharacteristic
276C2×Dic79⋊C4C2311yescharacteristic
277C2×Dic79⋊C4C2311yescharacteristic
278C2×Dic79⋊C4C2312yes—
279C2×Dic79⋊C4C2312yes—
280C2×Dic79⋊C4C2312yes—
281C2×C22⋊Dic79C2312yes—
282C2×C22⋊Dic79C2312yes—
283C2×C22⋊Dic79C2312yes—
284C2×C22⋊Dic79C2311yescharacteristic
285C2×C22⋊Dic79C2312yes—
286C2×C22⋊Dic79C2312yes—
287C2×C22⋊Dic79C2311yescharacteristic
288C2×C22⋊Dic79C2312yes—
289C2×C22⋊Dic79C2312yes—
290C2×C22⋊Dic79C23116yescomplemented
291C2×(C2×D79)⋊C4C2311yescharacteristic
292C2×(C2×D79)⋊C4C2312yes—
293C2×(C2×D79)⋊C4C2312yes—
294C2×(C2×D79)⋊C4C2312yes—
295C2×(C2×D79)⋊C4C2312yes—
296C2×(C2×D79)⋊C4C2312yes—
297C2×(C2×D79)⋊C4C2311yescharacteristic
298C2×(C2×D79)⋊C4C2311yescharacteristic
299C2×(C2×D79)⋊C4C2311yescharacteristic
300C2×(C2×D79)⋊C4C2312yes—
301C2×(C2×D79)⋊C4C2312yes—
302C2×(C2×D79)⋊C4C2312yes—
303C22⋊C4×D79C23116yescomplemented
304C22⋊C4×D79C23116yescomplemented
305C22⋊C4×D79C23116yescomplemented
306C2×C4×Dic79C2311yescharacteristic
307C2×C4×Dic79C2311yescharacteristic
308C2×C4×Dic79C2311yescharacteristic
309C2×C4×Dic79C2311yescharacteristic
310C2×C4×Dic79C2311yescharacteristic
311C2×C4×Dic79C2311yescharacteristic
312C2×C4×Dic79C2312yes—
313C2×C4×Dic79C2312yes—
314C2×C4×Dic79C2312yes—
315C42×D79C2318yescomplemented
316C42×D79C2318yescomplemented
317C25×C79C2312yes—
318C22×Q8×C79—44no—
319C22×Q8×C79C2311yescharacteristic
320C22×Q8×C79C2311yescharacteristic
321C22×Q8×C79C2312yes—
322C22×Q8×C79C2318yescomplemented
323C22×D4×C79—44no—
324C22×D4×C79C2311yescharacteristic
325C22×D4×C79C2311yescharacteristic
326C22×D4×C79C2318yes—
327C22×D4×C79C2312yes—
328C23×C4×C79C2311yescharacteristic
329C23×C4×C79C2311yescharacteristic
330C23×C4×C79C2311yescharacteristic
331C23×C4×C79C2312yes—
332#124×C79C2318yes—
333#124×C79C2318yes—
334#124×C79C23116yescomplemented
335#124×C79C2318yescomplemented
336#124×C79C23116yescomplemented
337#124×C79C2318yescomplemented
338C2×C22⋊C4×C79C2312yes—
339C2×C22⋊C4×C79C2312yes—
340C2×C22⋊C4×C79C2312yes—
341C2×C22⋊C4×C79C2312yes—
342C2×C22⋊C4×C79C2312yes—
343C2×C22⋊C4×C79C2312yes—
344C2×C22⋊C4×C79C2312yes—
345C2×C22⋊C4×C79C2312yes—
346C2×C22⋊C4×C79C23116yescomplemented
347C2×C22⋊C4×C79C23116yescomplemented
348C2×C42×C79C2311yescharacteristic
349C2×C42×C79C2311yescharacteristic
350C2×C42×C79C2311yescharacteristic
351C2×C42×C79C2311yescharacteristic
352C2×C42×C79C2318yescomplemented
353C23×D79—28no—
354C23×D79—44no—
355C23×D79—44no—
356C23×D79C2412yes—
357C23×D79C2411yescharacteristic
358C23×D79C2411yescharacteristic
359C23×D79C2418yes—
360#11929625—416no—
361#11929624—232no—
362#11929623—416no—
363C2×Dic158—24no—
364C2×Dic158—24no—
365C2×Dic158—44no—
366C2×Dic158C2414yes—
367C2×Dic158C2414yes—
368C2×Dic158C2418yes—
369Q8×D79—416no—
370C2×D316—24no—
371C2×D316—24no—
372C2×D316—44no—
373C2×D316C2414yes—
374C2×D316C2414yes—
375C2×D316C2418yes—
376C2×C22⋊D79—28no—
377C2×C22⋊D79—24no—
378C2×C22⋊D79—28no—
379C2×C22⋊D79—28no—
380C2×C22⋊D79—264no—
381C2×C22⋊D79—44no—
382C2×C22⋊D79—44no—
383C2×C22⋊D79—44no—
384C2×C22⋊D79—44no—
385C2×C22⋊D79#4118yescomplemented
386C2×C22⋊D79C2414yes—
387C2×C22⋊D79C2418yes—
388C2×C22⋊D79C2418yes—
389C2×C22⋊D79C2418yes—
390C2×C22⋊D79C2418yes—
391C2×C22⋊D79C2418yes—
392C2×C22⋊D79C2418yes—
393C2×C22⋊D79C2418yes—
394C2×C22⋊D79C2414yes—
395D4×D79—416no—
396C22×Dic79—28no—
397C22×Dic79—44no—
398C22×Dic79—44no—
399C22×Dic79C2411yescharacteristic
400C22×Dic79C2412yes—
401C22×Dic79C2411yescharacteristic
402C22×Dic79C2411yescharacteristic
403C22×Dic79C2412yes—
404C22×Dic79C2411yescharacteristic
405C22×Dic79C2411yescharacteristic
406C22×Dic79C2412yes—
407C22×Dic79C2418yes—
408C22×Dic79C2418yes—
409C22×Dic79C2418yes—
410C22×Dic79C2411yescharacteristic
411C2×C4×D79—24no—
412C2×C4×D79—24no—
413C2×C4×D79—24no—
414C2×C4×D79—24no—
415C2×C4×D79—44no—
416C2×C4×D79—44no—
417C2×C4×D79—42no—
418C2×C4×D79—42no—
419C2×C4×D79—44no—
420C2×C4×D79C2414yes—
421C2×C4×D79C2414yes—
422C2×C4×D79C2414yes—
423C2×C4×D79C2414yes—
424C2×C4×D79C2418yes—
425C2×C4×D79C2418yes—
426C2×C4×D79C2414yes—
427C2×C4×D79C2414yes—
428C2×C4×D79C2418yes—
429C4⋊Dic79C2414yes—
430C4⋊Dic79C2414yes—
431C4⋊Dic79C2414yes—
432C4⋊Dic79C2414yes—
433C4⋊Dic79C2418yes—
434C4⋊Dic79C2418yes—
435Dic79⋊C4C2414yes—
436Dic79⋊C4C2418yes—
437Dic79⋊C4C2418yes—
438Dic79⋊C4C2418yes—
439Dic79⋊C4C2418yes—
440Dic79⋊C4C2418yes—
441Dic79⋊C4C2414yes—
442Dic79⋊C4C2414yes—
443Dic79⋊C4C2414yes—
444Dic79⋊C4C2418yes—
445Dic79⋊C4C2418yes—
446Dic79⋊C4C2418yes—
447C22⋊Dic79C2418yes—
448C22⋊Dic79C2418yes—
449C22⋊Dic79C2418yes—
450C22⋊Dic79C2414yes—
451C22⋊Dic79C2418yes—
452C22⋊Dic79C2418yes—
453C22⋊Dic79C2414yes—
454C22⋊Dic79C2418yes—
455C22⋊Dic79C2418yes—
456(C2×D79)⋊C4C2414yes—
457(C2×D79)⋊C4C2418yes—
458(C2×D79)⋊C4C2418yes—
459(C2×D79)⋊C4C2418yes—
460(C2×D79)⋊C4C2418yes—
461(C2×D79)⋊C4C2418yes—
462(C2×D79)⋊C4C2414yes—
463(C2×D79)⋊C4C2414yes—
464(C2×D79)⋊C4C2414yes—
465(C2×D79)⋊C4C2418yes—
466(C2×D79)⋊C4C2418yes—
467(C2×D79)⋊C4C2418yes—
468C4×Dic79C2414yes—
469C4×Dic79C2414yes—
470C4×Dic79C2414yes—
471C4×Dic79C2414yes—
472C4×Dic79C2414yes—
473C4×Dic79C2414yes—
474C4×Dic79C2418yes—
475C4×Dic79C2418yes—
476C4×Dic79C2418yes—
477C24×C79—28no—
478C24×C79—44no—
479C24×C79—44no—
480C24×C79C2412yes—
481C24×C79C2412yes—
482C24×C79C2411yescharacteristic
483C24×C79C2418yes—
484C2×Q8×C79—24no—
485C2×Q8×C79—24no—
486C2×Q8×C79—44no—
487C2×Q8×C79—416no—
488C2×Q8×C79C2414yes—
489C2×Q8×C79C2414yes—
490C2×Q8×C79C2418yes—
491C2×D4×C79—24no—
492C2×D4×C79—24no—
493C2×D4×C79—416no—
494C2×D4×C79—44no—
495C2×D4×C79C2414yes—
496C2×D4×C79C2414yes—
497C2×D4×C79C2418yes—
498C22×C4×C79—24no—
499C22×C4×C79—24no—
500C22×C4×C79—42no—
501C22×C4×C79—44no—
502C22×C4×C79C2411yescharacteristic
503C22×C4×C79C2412yes—
504C22×C4×C79C2414yes—
505C22×C4×C79C2411yescharacteristic
506C22×C4×C79C2411yescharacteristic
507C22×C4×C79C2411yescharacteristic
508C22×C4×C79C2411yescharacteristic
509C22×C4×C79C2414yes—
510C22×C4×C79C2412yes—
511C22×C4×C79C2414yes—
512C22×C4×C79C2418yes—
513C22×C4×C79C2411yescharacteristic
514C22⋊C4×C79C2418yes—
515C22⋊C4×C79C2418yes—
516C22⋊C4×C79C2418yes—
517C22⋊C4×C79C2418yes—
518C22⋊C4×C79C2418yes—
519C22⋊C4×C79C2418yes—
520C22⋊C4×C79C2418yes—
521C22⋊C4×C79C2418yes—
522C42×C79C2414yes—
523C42×C79C2414yes—
524C42×C79C2414yes—
525C42×C79C2414yes—
526C23×C79—22no—
527C23×C79—22no—
528C23×C79—24no—
529C23×C79—24no—
530C23×C79—24no—
531C23×C79—24no—
532C23×C79—24no—
533C23×C79—24no—
534C23×C79—216no—
535C23×C79—48no—
536C23×C79—48no—
537C23×C79—816no—
538C23×C79C2×#4114yes—
539C23×C79C2514yes—
540C23×C79C2514yes—
541C23×C79C2512yes—
542C23×C79C2511yescharacteristic
543C22×D79—22no—
544C22×D79—22no—
545C22×D79—22no—
546C22×D79—24no—
547C22×D79—22no—
548C22×D79—24no—
549C22×D79—22no—
550C22×D79—24no—
551C22×D79—216no—
552C22×D79—48no—
553C22×D79—48no—
554C22×D79—816no—
555C22×D79C2×#4114yes—
556C22×D79C2514yes—
557C22×D79C2512yes—
558C22×D79C2512yes—
559Q8×C79—28no—
560Q8×C79—28no—
561Q8×C79—48no—
562D4×C79—28no—
563D4×C79—28no—
564D4×C79—48no—
565C2×C4×C79—22no—
566C2×C4×C79—22no—
567C2×C4×C79—28no—
568C2×C4×C79—24no—
569C2×C4×C79—24no—
570C2×C4×C79—22no—
571C2×C4×C79—22no—
572C2×C4×C79—22no—
573C2×C4×C79—28no—
574C2×C4×C79—44no—
575C2×C4×C79—48no—
576C2×C4×C79H(5,𝔽2)14yes—
577C2×C4×C79C2512yes—
578C2×C4×C79C2512yes—
579C2×C4×C79C2512yes—
580C2×C4×C79C2514yes—
581C2×C4×C79C2514yes—
582C2×C4×C79C2512yes—
583C2×C4×C79C2512yes—
584C2×C4×C79C2512yes—
585C22⋊D79—216no—
586C22⋊D79—28no—
587C22⋊D79—216no—
588C22⋊D79—216no—
589C22⋊D79—48no—
590C22⋊D79—48no—
591C22⋊D79—48no—
592C22⋊D79—48no—
593C22⋊D79C2×#41116yescomplemented
594C2×Dic79—22no—
595C2×Dic79—24no—
596C2×Dic79—22no—
597C2×Dic79—22no—
598C2×Dic79—24no—
599C2×Dic79—22no—
600C2×Dic79—24no—
601C2×Dic79—22no—
602C2×Dic79—216no—
603C2×Dic79—48no—
604C2×Dic79—48no—
605C2×Dic79C2×#4114yes—
606C2×Dic79C2512yes—
607C2×Dic79C2512yes—
608C2×Dic79C2514yes—
609C2×Dic79C2512yes—
610C2×Dic79C2512yes—
611C2×Dic79C2512yes—
612C2×Dic79C2514yes—
613C2×Dic79C2514yes—
614C2×Dic79C2512yes—
615D316—28no—
616D316—28no—
617D316—48no—
618C4×D79—28no—
619C4×D79—28no—
620C4×D79—28no—
621C4×D79—28no—
622C4×D79—44no—
623C4×D79—48no—
624C4×D79—44no—
625C4×D79—48no—
626C4×D79—48no—
627Dic158—28no—
628Dic158—28no—
629Dic158—48no—
630C22×C79—22no—
631C22×C79—22no—
632C22×C79—28no—
633C22×C79—24no—
634C22×C79—24no—
635C22×C79—24no—
636C22×C79—24no—
637C22×C79—24no—
638C22×C79—24no—
639C22×C79—48no—
640C22×C79—48no—
641C22×C79—816no—
642C22×C79C22×#4114yes—
643C22×C79C22×#4112yes—
644C22×C79C2×H(5,𝔽2)12yes—
645C22×C79#58512yes—
646C22×C79C2611yescharacteristic
647C2×D79—22no—
648C2×D79—22no—
649C2×D79—28no—
650C2×D79—24no—
651C2×D79—22no—
652C2×D79—22no—
653C2×D79—24no—
654C2×D79—22no—
655C2×D79—24no—
656C2×D79—44no—
657C2×D79—48no—
658C2×D79—816no—
659C2×D79C22×#4114yes—
660C4×C79—22no—
661C4×C79—22no—
662C4×C79—22no—
663C4×C79—24no—
664C4×C79—24no—
665C4×C79—22no—
666C4×C79—22no—
667C4×C79C2×H(5,𝔽2)14yes—
668Dic79—24no—
669Dic79—22no—
670Dic79—22no—
671Dic79—24no—
672Dic79—22no—
673Dic79—22no—
674Dic79—24no—
675Dic79—22no—
676Dic79C22×#4114yes—
677C2×#3514—791nomaximal, Sylow
678C2×C79—24no—
679C2×C79—44no—
680C2×C79—44no—
681C2×C79#351414yescomplemented
682C2×C79C23×#4111yescharacteristic
683C2×C79C22×H(5,𝔽2)11yescharacteristic
684C2×C79C2×#58511yescharacteristic
685D79—24no—
686D79—42no—
687D79—44no—
688#3514—7932no—
689C2×#559—791no—
690C2×#556—791no—
691C2×#555—792no—
692C2×#551—792no—
693C2×#551—792no—
694C2×D4×Q8—791no—
695C2×#548—791no—
696C2×#548—791no—
697C2×#546—791no—
698C2×#546—791no—
699C2×#546—792no—
700C2×D42—791no—
701C2×#542—792no—
702C2×#538—792no—
703C2×#538—792no—
704C2×#532—791no—
705C2×#529—791no—
706C2×#529—791no—
707C2×#529—791no—
708C22×#124—791no—
709C22×#124D7911yescharacteristic, complemented
710C2×#518—792no—
711C2×C4×#41—791no—
712C79C2×#351411yescharacteristic, complemented, Sylow
713C22×#41—791no—
714C22×#41—791no—
715C22×#41—791no—
716C23×Q8—791no—
717C23×Q8C2×D7911yescharacteristic, complemented
718C23×D4—791no—
719C23×D4—792no—
720C23×D4C2×D7911yescharacteristic
721#559—7916no—
722#556—7916no—
723#555—7932no—
724#551—7932no—
725#551—7932no—
726D4×Q8—7916no—
727#548—7916no—
728#548—7916no—
729#546—7916no—
730#546—7916no—
731#546—7932no—
732D42—7916no—
733#542—7932no—
734#538—7932no—
735#538—7932no—
736#532—7916no—
737C2×C4⋊Q8—791no—
738C2×C4⋊Q8—792no—
739C2×#127—791no—
740#529—7916no—
741#529—7916no—
742#529—7916no—
743C2×#126—792no—
744C2×#126—792no—
745C2×#126—792no—
746C2×#126—792no—
747C2×#126—792no—
748C2×#125—791no—
749C2×#124—791no—
750C2×#124—792no—
751C2×#124—791no—
752C2×#124—7916no—
753C2×#124—792no—
754C2×#124—792no—
755C2×#124—792no—
756C2×#124—792no—
757C2×#124—791no—
758C2×#124C2×D7911yescharacteristic
759C2×#124C2×D7911yescharacteristic
760C2×#124C2×D7911yescharacteristic, complemented
761C2×#124C2×D7912yescomplemented
762C2×#124C2×D7911yescharacteristic, complemented
763C2×#124C2×D7912yescomplemented
764C2×#124C2×D79116yescomplemented
765C2×#123—792no—
766C2×#123—792no—
767C2×#123—792no—
768C2×#123—792no—
769C2×#123—792no—
770C2×#123—792no—
771C2×#123—792no—
772C2×C22⋊Q8—791no—
773C2×C22⋊Q8—791no—
774C2×C22⋊Q8—792no—
775C2×C22⋊Q8—792no—
776C2×C22⋊Q8—791no—
777C2×C22⋊Q8—792no—
778C2×C22⋊Q8—792no—
779C2×C22⋊Q8—792no—
780C2×#121—791no—
781C2×#121—791no—
782C2×#121—792no—
783C2×#121—792no—
784C2×#121—791no—
785C2×#121—792no—
786C2×#121—792no—
787C2×#121—792no—
788C2×#121—792no—
789C2×#121—792no—
790C2×#120—792no—
791C2×#120—792no—
792C2×#120—792no—
793C2×#120—792no—
794#518—7932no—
795C4×#41—7916no—
796C2×C4×Q8—791no—
797C2×C4×Q8—791no—
798C2×C4×Q8—791no—
799C2×C4×Q8—791no—
800C2×C4×Q8—791no—
801C2×C4×D4—791no—
802C2×C4×D4—791no—
803C2×C4×D4—791no—
804C2×C4×D4—791no—
805C2×C4×D4—791no—
806C2×C4×D4—791no—
807C2×C4×D4—792no—
808C2×C4×D4—792no—
809C2×C4×D4—792no—
810C2×C4×D4—792no—
811C2×C4×D4—792no—
812C2×C4×D4—792no—
813C2×C4×D4—792no—
814C2×C4×D4—792no—
815C2×C4×D4—792no—
816C2×C4×D4—791no—
817C2×C4×D4—791no—
818C2×C4×D4—791no—
819C2×#117—791no—
820C2×#117—792no—
821C2×#117—792no—
822C2×#117—792no—
823C2×#117—791no—
824C2×#117—791no—
825C2×#117—792no—
826C22×C22⋊C4—792no—
827C22×C22⋊C4—792no—
828C22×C22⋊C4—792no—
829C22×C22⋊C4—792no—
830C22×C22⋊C4C2×D7912yescomplemented
831C22×C22⋊C4C2×D7912yescomplemented
832C22×C42—791no—
833C22×C42—791no—
834C22×C42C2×D7911yescharacteristic, complemented
835C25—792no—
836C25C22×D7912yes—
837C2×#41—3164no—
838C2×#41—3164no—
839C2×#41—798no—
840C2×#41—798no—
841C2×#41—798no—
842C2×#41—1588no—
843C22×Q8—44no—
844C22×Q8—3164no—
845C22×Q8—798no—
846C22×Q8—792no—
847C22×Q8—791no—
848C22×Q8—791no—
849C22×Q8C22×D7911yescharacteristic
850C22×Q8C22×D7911yescharacteristic
851C22×Q8C22×D7912yes—
852C22×Q8C22×D7918yescomplemented
853C22×D4—44no—
854C22×D4—3164no—
855C22×D4—792no—
856C22×D4—792no—
857C22×D4—792no—
858C22×D4—792no—
859C22×D4—798no—
860C22×D4—791no—
861C22×D4—791no—
862C22×D4—792no—
863C22×D4—792no—
864C22×D4—792no—
865C22×D4—7916no—
866C22×D4—792no—
867C22×D4—791no—
868C22×D4—791no—
869C22×D4—15816no—
870C22×D4C22×D7911yescharacteristic
871C22×D4C22×D7911yescharacteristic
872C22×D4C22×D7912yes—
873C22×D4C22×D7918yes—
874C23×C4—792no—
875C23×C4—792no—
876C23×C4—791no—
877C23×C4—792no—
878C23×C4—792no—
879C23×C4—792no—
880C23×C4—791no—
881C23×C4—792no—
882C23×C4—791no—
883C23×C4—791no—
884C23×C4—791no—
885C23×C4—791no—
886C23×C4C22×D7911yescharacteristic
887C23×C4C22×D7911yescharacteristic
888C23×C4C22×D7911yescharacteristic
889C23×C4C22×D7912yes—
890C4⋊Q8—798no—
891C4⋊Q8—7916no—
892#127—798no—
893#126—7916no—
894#126—7916no—
895#126—7916no—
896#126—7916no—
897#126—7916no—
898#125—798no—
899#124—798no—
900#124—7916no—
901#124—798no—
902#124—7916no—
903#124—7916no—
904#124—7916no—
905#124—7916no—
906#124—798no—
907#124C22×D7918yes—
908#124C22×D7918yes—
909#124C22×D7918yescomplemented
910#124C22×D79116yescomplemented
911#124C22×D7918yescomplemented
912#124C22×D79116yescomplemented
913#123—7916no—
914#123—7916no—
915#123—7916no—
916#123—7916no—
917#123—7916no—
918#123—7916no—
919#123—7916no—
920C22⋊Q8—798no—
921C22⋊Q8—798no—
922C22⋊Q8—7916no—
923C22⋊Q8—7916no—
924C22⋊Q8—798no—
925C22⋊Q8—7916no—
926C22⋊Q8—7916no—
927C22⋊Q8—7916no—
928#121—798no—
929#121—798no—
930#121—7916no—
931#121—7916no—
932#121—798no—
933#121—7916no—
934#121—7916no—
935#121—7916no—
936#121—7916no—
937#121—7916no—
938#120—7916no—
939#120—7916no—
940#120—7916no—
941#120—7916no—
942C4×Q8—798no—
943C4×Q8—798no—
944C4×Q8—798no—
945C4×Q8—798no—
946C4×Q8—798no—
947C4×D4—798no—
948C4×D4—798no—
949C4×D4—798no—
950C4×D4—798no—
951C4×D4—798no—
952C4×D4—798no—
953C4×D4—7916no—
954C4×D4—7916no—
955C4×D4—7916no—
956C4×D4—7916no—
957C4×D4—7916no—
958C4×D4—7916no—
959C4×D4—7916no—
960C4×D4—7916no—
961C4×D4—7916no—
962C4×D4—798no—
963C4×D4—798no—
964C4×D4—798no—
965#117—798no—
966#117—7916no—
967#117—7916no—
968#117—7916no—
969#117—798no—
970#117—798no—
971#117—7916no—
972C2×C4⋊C4—791no—
973C2×C4⋊C4—792no—
974C2×C4⋊C4—792no—
975C2×C4⋊C4—792no—
976C2×C4⋊C4—792no—
977C2×C4⋊C4—791no—
978C2×C4⋊C4—791no—
979C2×C4⋊C4—791no—
980C2×C4⋊C4—791no—
981C2×C4⋊C4—791no—
982C2×C4⋊C4—792no—
983C2×C4⋊C4—792no—
984C2×C4⋊C4—791no—
985C2×C4⋊C4—791no—
986C2×C4⋊C4—792no—
987C2×C4⋊C4—792no—
988C2×C4⋊C4—792no—
989C2×C4⋊C4—792no—
990C2×C22⋊C4—791no—
991C2×C22⋊C4—792no—
992C2×C22⋊C4—792no—
993C2×C22⋊C4—792no—
994C2×C22⋊C4—7916no—
995C2×C22⋊C4—792no—
996C2×C22⋊C4—791no—
997C2×C22⋊C4—792no—
998C2×C22⋊C4—792no—
999C2×C22⋊C4—792no—
1000C2×C22⋊C4—791no—
1001C2×C22⋊C4—792no—
1002C2×C22⋊C4—792no—
1003C2×C22⋊C4—792no—
1004C2×C22⋊C4—792no—
1005C2×C22⋊C4—792no—
1006C2×C22⋊C4—791no—
1007C2×C22⋊C4—791no—
1008C2×C22⋊C4—791no—
1009C2×C22⋊C4—792no—
1010C2×C22⋊C4—792no—
1011C2×C22⋊C4—792no—
1012C2×C22⋊C4—7916no—
1013C2×C22⋊C4—7916no—
1014C2×C22⋊C4—7916no—
1015C2×C22⋊C4C22×D7912yes—
1016C2×C22⋊C4C22×D7912yes—
1017C2×C22⋊C4C22×D7912yes—
1018C2×C22⋊C4C22×D7912yes—
1019C2×C22⋊C4C22×D7912yes—
1020C2×C22⋊C4C22×D7912yes—
1021C2×C22⋊C4C22×D7912yes—
1022C2×C22⋊C4C22×D7912yes—
1023C2×C22⋊C4C22×D79116yescomplemented
1024C2×C22⋊C4C22×D79116yescomplemented
1025C2×C42—791no—
1026C2×C42—791no—
1027C2×C42—792no—
1028C2×C42—792no—
1029C2×C42—791no—
1030C2×C42—792no—
1031C2×C42—791no—
1032C2×C42—791no—
1033C2×C42—791no—
1034C2×C42—798no—
1035C2×C42—798no—
1036C2×C42C22×D7911yescharacteristic
1037C2×C42C22×D7911yescharacteristic
1038C2×C42C22×D7911yescharacteristic
1039C2×C42C22×D7911yescharacteristic
1040C2×C42C22×D7918yescomplemented
1041C24—28no—
1042C24—44no—
1043C24—44no—
1044C24—3164no—
1045C24—3164no—
1046C24—798no—
1047C24—791no—
1048C24—792no—
1049C24—791no—
1050C24—1588no—
1051C24C23×D7912yes—
1052C24C23×D7912yes—
1053C24C23×D7911yescharacteristic
1054C24C23×D7918yes—
1055#41—31616no—
1056#41—31616no—
1057#41—15832no—
1058C2×Q8—24no—
1059C2×Q8—24no—
1060C2×Q8—44no—
1061C2×Q8—416no—
1062C2×Q8—3164no—
1063C2×Q8—31616no—
1064C2×Q8—798no—
1065C2×Q8—794no—
1066C2×Q8—794no—
1067C2×Q8—1584no—
1068C2×Q8—1584no—
1069C2×Q8C23×D7914yes—
1070C2×Q8C23×D7914yes—
1071C2×Q8C23×D7918yes—
1072C2×D4—24no—
1073C2×D4—24no—
1074C2×D4—416no—
1075C2×D4—44no—
1076C2×D4—3164no—
1077C2×D4—31616no—
1078C2×D4—3164no—
1079C2×D4—3164no—
1080C2×D4—3164no—
1081C2×D4—3164no—
1082C2×D4—798no—
1083C2×D4—798no—
1084C2×D4—798no—
1085C2×D4—798no—
1086C2×D4—798no—
1087C2×D4—794no—
1088C2×D4—794no—
1089C2×D4—798no—
1090C2×D4—798no—
1091C2×D4—798no—
1092C2×D4—798no—
1093C2×D4—794no—
1094C2×D4—794no—
1095C2×D4—1584no—
1096C2×D4—1588no—
1097C2×D4—15864no—
1098C2×D4—1588no—
1099C2×D4—1588no—
1100C2×D4—1584no—
1101C2×D4—1584no—
1102C2×D4C23×D7914yes—
1103C2×D4C23×D7914yes—
1104C2×D4C23×D7918yes—
1105C22×C4—24no—
1106C22×C4—24no—
1107C22×C4—44no—
1108C22×C4—42no—
1109C22×C4—3162no—
1110C22×C4—3164no—
1111C22×C4—3162no—
1112C22×C4—3164no—
1113C22×C4—3164no—
1114C22×C4—3164no—
1115C22×C4—3164no—
1116C22×C4—798no—
1117C22×C4—798no—
1118C22×C4—794no—
1119C22×C4—794no—
1120C22×C4—798no—
1121C22×C4—798no—
1122C22×C4—798no—
1123C22×C4—791no—
1124C22×C4—798no—
1125C22×C4—791no—
1126C22×C4—791no—
1127C22×C4—791no—
1128C22×C4—792no—
1129C22×C4—791no—
1130C22×C4—791no—
1131C22×C4—792no—
1132C22×C4—792no—
1133C22×C4—794no—
1134C22×C4—794no—
1135C22×C4—794no—
1136C22×C4—794no—
1137C22×C4—1584no—
1138C22×C4—1584no—
1139C22×C4—1588no—
1140C22×C4—1584no—
1141C22×C4—1584no—
1142C22×C4C23×D7914yes—
1143C22×C4C23×D7914yes—
1144C22×C4C23×D7911yescharacteristic
1145C22×C4C23×D7911yescharacteristic
1146C22×C4C23×D7911yescharacteristic
1147C22×C4C23×D7912yes—
1148C22×C4C23×D7912yes—
1149C22×C4C23×D7911yescharacteristic
1150C22×C4C23×D7911yescharacteristic
1151C22×C4C23×D7914yes—
1152C22×C4C23×D7918yes—
1153C22×C4C23×D7911yescharacteristic
1154C4⋊C4—794no—
1155C4⋊C4—798no—
1156C4⋊C4—798no—
1157C4⋊C4—798no—
1158C4⋊C4—798no—
1159C4⋊C4—794no—
1160C4⋊C4—794no—
1161C4⋊C4—794no—
1162C4⋊C4—798no—
1163C4⋊C4—798no—
1164C4⋊C4—798no—
1165C4⋊C4—798no—
1166C4⋊C4—794no—
1167C4⋊C4—794no—
1168C4⋊C4—794no—
1169C4⋊C4—794no—
1170C4⋊C4—798no—
1171C4⋊C4—798no—
1172C22⋊C4—794no—
1173C22⋊C4—798no—
1174C22⋊C4—798no—
1175C22⋊C4—798no—
1176C22⋊C4—798no—
1177C22⋊C4—794no—
1178C22⋊C4—798no—
1179C22⋊C4—798no—
1180C22⋊C4—798no—
1181C22⋊C4—794no—
1182C22⋊C4—798no—
1183C22⋊C4—798no—
1184C22⋊C4—798no—
1185C22⋊C4—798no—
1186C22⋊C4—798no—
1187C22⋊C4—794no—
1188C22⋊C4—794no—
1189C22⋊C4—794no—
1190C22⋊C4—798no—
1191C22⋊C4—798no—
1192C22⋊C4—798no—
1193C22⋊C4C23×D7918yes—
1194C22⋊C4C23×D7918yes—
1195C22⋊C4C23×D7918yes—
1196C22⋊C4C23×D7918yes—
1197C22⋊C4C23×D7918yes—
1198C22⋊C4C23×D7918yes—
1199C22⋊C4C23×D7918yes—
1200C22⋊C4C23×D7918yes—
1201C42—794no—
1202C42—794no—
1203C42—794no—
1204C42—794no—
1205C42—794no—
1206C42—794no—
1207C42—798no—
1208C42—798no—
1209C42—798no—
1210C42C23×D7914yes—
1211C42C23×D7914yes—
1212C42C23×D7914yes—
1213C42C23×D7914yes—
1214C23—22no—
1215C23—22no—
1216C23—24no—
1217C23—24no—
1218C23—24no—
1219C23—24no—
1220C23—24no—
1221C23—24no—
1222C23—216no—
1223C23—48no—
1224C23—48no—
1225C23—816no—
1226C23—3168no—
1227C23—3168no—
1228C23—792no—
1229C23—794no—
1230C23—794no—
1231C23—792no—
1232C23—63216no—
1233C23—15816no—
1234C23—1584no—
1235C23—1582no—
1236C23—1582no—
1237C23—1584no—
1238C23—1582no—
1239C23—1584no—
1240C23—1582no—
1241C23—1582no—
1242C23#41×D7914yes—
1243C23C24×D7914yes—
1244C23C24×D7914yes—
1245C23C24×D7912yes—
1246C23C24×D7911yescharacteristic
1247Q8—28no—
1248Q8—28no—
1249Q8—48no—
1250Q8—3168no—
1251Q8—1588no—
1252Q8—1588no—
1253D4—28no—
1254D4—28no—
1255D4—48no—
1256D4—3168no—
1257D4—3168no—
1258D4—3168no—
1259D4—3168no—
1260D4—3168no—
1261D4—7916no—
1262D4—1588no—
1263D4—15816no—
1264D4—15816no—
1265D4—15816no—
1266D4—1588no—
1267D4—1588no—
1268C2×C4—22no—
1269C2×C4—24no—
1270C2×C4—24no—
1271C2×C4—22no—
1272C2×C4—22no—
1273C2×C4—22no—
1274C2×C4—22no—
1275C2×C4—28no—
1276C2×C4—28no—
1277C2×C4—44no—
1278C2×C4—48no—
1279C2×C4—3168no—
1280C2×C4—3168no—
1281C2×C4—3164no—
1282C2×C4—3168no—
1283C2×C4—3164no—
1284C2×C4—3168no—
1285C2×C4—3168no—
1286C2×C4—792no—
1287C2×C4—794no—
1288C2×C4—792no—
1289C2×C4—792no—
1290C2×C4—794no—
1291C2×C4—792no—
1292C2×C4—792no—
1293C2×C4—792no—
1294C2×C4—794no—
1295C2×C4—794no—
1296C2×C4—1588no—
1297C2×C4—1588no—
1298C2×C4—15816no—
1299C2×C4—1582no—
1300C2×C4—1584no—
1301C2×C4—1582no—
1302C2×C4—1582no—
1303C2×C4—1584no—
1304C2×C4—1582no—
1305C2×C4—1584no—
1306C2×C4—1582no—
1307C2×C4—1588no—
1308C2×C4—1588no—
1309C2×C4#1457920614yes—
1310C2×C4C24×D7912yes—
1311C2×C4C24×D7912yes—
1312C2×C4C24×D7912yes—
1313C2×C4C24×D7914yes—
1314C2×C4C24×D7914yes—
1315C2×C4C24×D7912yes—
1316C2×C4C24×D7912yes—
1317C2×C4C24×D7912yes—
1318C22—28no—
1319C22—22no—
1320C22—22no—
1321C22—24no—
1322C22—24no—
1323C22—24no—
1324C22—24no—
1325C22—24no—
1326C22—24no—
1327C22—48no—
1328C22—48no—
1329C22—816no—
1330C22—3168no—
1331C22—3164no—
1332C22—794no—
1333C22—63216no—
1334C22—1582no—
1335C22—1584no—
1336C22—1584no—
1337C22—1582no—
1338C22—1582no—
1339C22—1584no—
1340C22—1588no—
1341C22—1582no—
1342C22—1582no—
1343C22C2×#41×D7914yes—
1344C22C2×#41×D7912yes—
1345C22C2×#1457920612yes—
1346C22#1909939912yes—
1347C22C25×D7911yescharacteristic
1348C4—22no—
1349C4—22no—
1350C4—22no—
1351C4—24no—
1352C4—24no—
1353C4—22no—
1354C4—22no—
1355C4—794no—
1356C4—1584no—
1357C4—1582no—
1358C4—1582no—
1359C4—1584no—
1360C4—1582no—
1361C4—1582no—
1362C4—1584no—
1363C4—1582no—
1364C4C2×#1457920614yes—
1365C2—24no—
1366C2—44no—
1367C2—44no—
1368C2—3164no—
1369C2—3162no—
1370C2—1584no—
1371C2#2377735514yesdirect product factor
1372C2C22×#41×D7911yescharacteristic
1373C2C22×#1457920611yescharacteristic
1374C2C2×#1909939911yescharacteristic
subgroupG/H
centerC23C24×D79
commutator, cosocleC22×C79C26
FrattiniC22C25×D79
FittingC22×#124×C79C2
socleC23×C79C25
hypercenterC22×#124D79
hypocenterC79C2×#3514
LCSG ▷ C22×C79 ▷ C79
UCSC1 ◁ C23 ◁ C22×#124

Complements

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

NH ≅ G/Ntype
1. #23777355C2direct (N × H)
2. C2×#19099295C2semidirect
3. C2×#19099282C2semidirect
4. C2×#19099275C2semidirect
5. C2×#19099243C2semidirect
6. C2×#19099239C2semidirect
7. C2×Q8×C22⋊D79C2semidirect
8. C2×#19099224C2semidirect
9. C2×#19099221C2semidirect
10. C2×#19099207C2semidirect
11. C2×#19099206C2semidirect
12. C2×#19099203C2semidirect
13. C2×D4×C22⋊D79C2semidirect
14. C2×#19099177C2semidirect
15. C2×#19099151C2semidirect
16. C2×#19099147C2semidirect
17. C2×#19099112C2semidirect
18. C2×#19099097C2semidirect
19. C2×#19099092C2semidirect
20. C2×#19099092C2semidirect
21. C2×#124×D79C2semidirect
22. C2×#19099036C2semidirect
23. C2×C4×#11929624C2semidirect
24. C22×#124×C79C2semidirect
25. C22×#11929625C22semidirect
27. C22×#11929623C22semidirect
28. C22×Q8×D79C22semidirect
31. #19099295C22semidirect
32. #19099282C22semidirect
33. #19099275C22semidirect
34. #19099243C22semidirect
35. #19099239C22semidirect
36. Q8×C22⋊D79C22semidirect
37. #19099224C22semidirect
38. #19099221C22semidirect
39. #19099207C22semidirect
40. #19099206C22semidirect
41. #19099203C22semidirect
42. D4×C22⋊D79C22semidirect
43. #19099177C22semidirect
44. #19099151C22semidirect
45. #19099147C22semidirect
46. #19099112C22semidirect
47. C2×#14579159C22semidirect
48. C2×#14579159C22semidirect
50. #19099097C22semidirect
51. #19099092C22semidirect
52. #19099092C22semidirect
53. C2×#14579155C22semidirect
54. C2×#14579154C22semidirect
55. C2×#14579154C22semidirect
56. C2×#14579154C22semidirect
57. C2×#14579154C22semidirect
58. C2×#14579153C22semidirect
59. C2×#14579150C22semidirect
60. C2×#14579150C22semidirect
61. C2×#14579149C22semidirect
63. C2×#14579147C22semidirect
64. C2×#14579147C22semidirect
65. C2×#14579147C22semidirect
66. C2×#14579147C22semidirect
67. #124×D79C22semidirect
68. C2×#14579145C22semidirect
69. C2×#14579144C22semidirect
70. C2×#14579143C22semidirect
71. C2×#14579143C22semidirect
72. C2×#14579143C22semidirect
73. C2×#14579143C22semidirect
74. C2×#14579142C22semidirect
75. C2×#14579140C22semidirect
76. C2×#14579140C22semidirect
77. C2×#14579138C22semidirect
78. C2×#14579138C22semidirect
79. C2×#14579137C22semidirect
80. C2×#14579137C22semidirect
81. C2×#14579137C22semidirect
82. C2×#14579137C22semidirect
84. C2×#14579135C22semidirect
85. C2×#14579134C22semidirect
86. C2×#14579134C22semidirect
87. C2×#14579134C22semidirect
88. C2×#14579134C22semidirect
90. C2×#14579133C22semidirect
93. C2×#14579131C22semidirect
95. C2×#14579130C22semidirect
97. #19099036C22semidirect
98. C4×#11929624C22semidirect
99. C2×Q8×Dic79C22semidirect
100. C2×Q8×Dic79C22semidirect
101. C2×C4×Dic158C22semidirect
102. C2×C4×Dic158C22semidirect
103. C2×C4×Dic158C22semidirect
104. C2×C4×D316C22semidirect
105. C2×C4×D316C22semidirect
106. C2×C4×D316C22semidirect
108. C2×D4×Dic79C22semidirect
112. C2×C4×C22⋊D79C22semidirect
113. C2×C4×C22⋊D79C22semidirect
114. C2×C4×C22⋊D79C22semidirect
115. C2×C4×C22⋊D79C22semidirect
116. C2×(C22⋊D79)⋊C4C22semidirect
117. C2×(C22⋊D79)⋊C4C22semidirect
118. C2×(C22⋊D79)⋊C4C22semidirect
119. C2×(C22⋊D79)⋊C4C22semidirect
120. C2×(C22⋊D79)⋊C4C22semidirect
121. C2×(C22⋊D79)⋊C4C22semidirect
122. C2×#14579120C22semidirect
123. C2×#14579118C22semidirect
124. C2×#14579118C22semidirect
125. C2×#14579118C22semidirect
126. C2×#14579117C22semidirect
127. C2×#14579117C22semidirect
128. C2×#14579117C22semidirect
129. C22×C22⋊Dic79C22semidirect
130. C2×C22⋊C4×D79C22semidirect
131. C2×C22⋊C4×D79C22semidirect
132. C2×C22⋊C4×D79C22semidirect
133. C2×C42×D79C22semidirect
134. C2×C42×D79C22semidirect
135. C23×Q8×C79C22semidirect
139. C2×#124×C79C22semidirect
140. C2×#124×C79C22semidirect
141. C2×#124×C79C22semidirect
142. C2×#124×C79C22semidirect
143. C2×#124×C79C22semidirect
144. C22×C22⋊C4×C79C22semidirect
145. C22×C22⋊C4×C79C22semidirect
146. C22×C42×C79C22semidirect
149. C2×#11929625C23semidirect
153. C2×#11929623C23semidirect
158. C2×Q8×D79C23semidirect
187. #14579159C23semidirect
188. #14579159C23semidirect
190. #14579155C23semidirect
191. #14579154C23semidirect
192. #14579154C23semidirect
193. #14579154C23semidirect
194. #14579154C23semidirect
195. #14579153C23semidirect
196. #14579150C23semidirect
197. #14579150C23semidirect
198. #14579149C23semidirect
200. #14579147C23semidirect
201. #14579147C23semidirect
202. #14579147C23semidirect
203. #14579147C23semidirect
204. #14579145C23semidirect
205. #14579144C23semidirect
206. #14579143C23semidirect
207. #14579143C23semidirect
208. #14579143C23semidirect
209. #14579143C23semidirect
210. #14579142C23semidirect
211. #14579140C23semidirect
212. #14579140C23semidirect
213. #14579138C23semidirect
214. #14579138C23semidirect
215. #14579137C23semidirect
216. #14579137C23semidirect
217. #14579137C23semidirect
218. #14579137C23semidirect
220. #14579135C23semidirect
221. #14579134C23semidirect
222. #14579134C23semidirect
223. #14579134C23semidirect
224. #14579134C23semidirect
226. #14579133C23semidirect
229. #14579131C23semidirect
231. #14579130C23semidirect
233. Q8×Dic79C23semidirect
234. Q8×Dic79C23semidirect
235. C4×Dic158C23semidirect
236. C4×Dic158C23semidirect
237. C4×Dic158C23semidirect
238. C4×D316C23semidirect
239. C4×D316C23semidirect
240. C4×D316C23semidirect
242. D4×Dic79C23semidirect
246. C4×C22⋊D79C23semidirect
247. C4×C22⋊D79C23semidirect
248. C4×C22⋊D79C23semidirect
249. C4×C22⋊D79C23semidirect
250. (C22⋊D79)⋊C4C23semidirect
251. (C22⋊D79)⋊C4C23semidirect
252. (C22⋊D79)⋊C4C23semidirect
253. (C22⋊D79)⋊C4C23semidirect
254. (C22⋊D79)⋊C4C23semidirect
255. (C22⋊D79)⋊C4C23semidirect
256. #14579120C23semidirect
257. #14579118C23semidirect
258. #14579118C23semidirect
259. #14579118C23semidirect
260. #14579117C23semidirect
261. #14579117C23semidirect
262. #14579117C23semidirect
290. C2×C22⋊Dic79C23semidirect
303. C22⋊C4×D79C23semidirect
304. C22⋊C4×D79C23semidirect
305. C22⋊C4×D79C23semidirect
315. C42×D79C23semidirect
316. C42×D79C23semidirect
322. C22×Q8×C79C23semidirect
334. #124×C79C23semidirect
335. #124×C79C23semidirect
336. #124×C79C23semidirect
337. #124×C79C23semidirect
346. C2×C22⋊C4×C79C23semidirect
347. C2×C22⋊C4×C79C23semidirect
352. C2×C42×C79C23semidirect
385. C2×C22⋊D79#41semidirect
593. C22⋊D79C2×#41semidirect
681. C2×C79#3514semidirect
709. C22×#124D79semidirect
712. C79C2×#3514semidirect
717. C23×Q8C2×D79semidirect
760. C2×#124C2×D79semidirect
761. C2×#124C2×D79semidirect
762. C2×#124C2×D79semidirect
763. C2×#124C2×D79semidirect
764. C2×#124C2×D79semidirect
830. C22×C22⋊C4C2×D79semidirect
831. C22×C22⋊C4C2×D79semidirect
834. C22×C42C2×D79semidirect
852. C22×Q8C22×D79semidirect
909. #124C22×D79semidirect
910. #124C22×D79semidirect
911. #124C22×D79semidirect
912. #124C22×D79semidirect
1023. C2×C22⋊C4C22×D79semidirect
1024. C2×C22⋊C4C22×D79semidirect
1040. C2×C42C22×D79semidirect
1371. C2#23777355direct (N × H)

Maximal subgroups

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

subgroupindex
#237773552
C2×#190992952
C2×#190992822
C2×#190992752
C2×#190992432
C2×#190992392
C2×Q8×C22⋊D792
C2×#190992242
C2×#190992212
C2×#190992072
C2×#190992062
C2×#190992032
C2×D4×C22⋊D792
C2×#190991772
C2×#190991512
C2×#190991472
C2×#190991122
C2×#190990972
C2×#190990922
C2×#124×D792
C2×#190990362
C2×C4×#119296242
C22×#124×C792
C2×#351479