Finite Group Databasebeta

← C2×#23777214 #35196598

Subgroups — C2×#23777214 #35196598

Order 20224.

7478 conjugacy classes of subgroups.

The subgroup lattice has 864 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#23777214C2132yesmaximal, direct product factor
2C2×Q8×Dic158C211yesmaximal, characteristic, complemented
3C2×#19099293C211yesmaximal, characteristic, complemented
4C2×#19099290C212yesmaximal, complemented
5C2×#19099271C212yesmaximal, complemented
6C2×#19099270C211yesmaximal, characteristic, complemented
7C2×#19099268C212yesmaximal, complemented
8C2×D4×Dic158C212yesmaximal, complemented
9C2×#19099226C214yesmaximal, complemented
10C2×#19099193C212yesmaximal, complemented
11C2×#19099192C214yesmaximal, complemented
12C2×#19099117C211yesmaximal, characteristic, complemented
13C2×#19099115C212yesmaximal, complemented
14C22×#14579160C212yesmaximal, complemented
15C2×C4⋊Q8×D79C211yesmaximal, characteristic, complemented
16C2×#19099042C212yesmaximal
17C2×C4×#11929623C211yesmaximal, characteristic
18C2×#554×C79C211yesmaximal, characteristic, complemented
19C22×#11929623C2211yescharacteristic
20C23×Dic158C2214yes—
21C22×Q8×D79C2212yes—
22Q8×Dic158C22116yescomplemented
23#19099293C22116yescomplemented
24#19099290C22132yescomplemented
25#19099271C22132yescomplemented
26#19099270C22116yescomplemented
27#19099268C22132yescomplemented
28D4×Dic158C22132yescomplemented
29#19099226C22164yescomplemented
30#19099193C22132yescomplemented
31#19099192C22164yescomplemented
32#19099117C22116yescomplemented
33#19099115C22132yescomplemented
34C2×#14579161C2212yes—
35C2×#14579161C2211yescharacteristic
36C2×#14579160C2214yes—
37C2×#14579160C2214yes—
38C2×#14579160C2212yes—
39C2×#14579160C2214yes—
40C2×#14579160C2212yes—
41C2×#14579160C2212yes—
42C2×#14579160C2212yes—
43C2×#14579160C2211yescharacteristic
44C2×#14579160C2212yes—
45C2×#14579160C22132yescomplemented
46C2×#14579159C2212yes—
47C2×#14579159C2214yes—
48C2×#14579159C2211yescharacteristic
49C4⋊Q8×D79C22116yescomplemented
50C2×#14579152C2212yes—
51C2×#14579151C2212yes—
52C2×#14579151C2214yes—
53C2×#14579151C2214yes—
54C2×#14579151C2214yes—
55C2×#14579141C2214yes—
56C2×#14579141C2211yescharacteristic
57C2×#14579140C2214yes—
58C2×#14579140C2212yes—
59C2×#14579139C2214yes—
60C2×#14579139C2212yes—
61C2×#14579138C2214yes—
62C2×#14579138C2214yes—
63C2×#14579138C2214yes—
64C2×#14579137C2211yescharacteristic
65#19099042C22132yes—
66C4×#11929623C22116yes—
67C2×Q8×Dic79C2212yes—
68C2×C4×Dic158C2211yescharacteristic
69C2×C4×Dic158C2212yes—
70C2×C4×Dic158C2212yes—
71C2×C4×Dic158C2211yescharacteristic
72C2×#14579126C2211yescharacteristic
73C2×#14579126C2212yes—
74C2×#14579126C2214yes—
75C2×#14579126C2212yes—
76C2×D4×Dic79C2211yescharacteristic
77C2×D4×Dic79C2212yes—
78C2×C4×C22⋊D79C2212yes—
79C2×C4×C22⋊D79C2214yes—
80C2×(C22⋊D79)⋊C4C2212yes—
81C2×(C22⋊D79)⋊C4C2214yes—
82C2×#14579119C2211yescharacteristic
83C2×#14579118C2212yes—
84C2×#14579117C2212yes—
85C2×#14579117C2214yes—
86C22×C4⋊Dic79C2212yes—
87C22×Dic79⋊C4C2214yes—
88C2×C4⋊C4×D79C2212yes—
89C2×C4⋊C4×D79C2212yes—
90C22×C4×Dic79C2212yes—
91C2×C42×D79C2211yescharacteristic
92#554×C79C22116yescomplemented
93C2×C4⋊Q8×C79C2211yescharacteristic
94C2×#125×C79C2212yes—
95C2×C22⋊Q8×C79C2214yes—
96C2×C22⋊Q8×C79C2212yes—
97C2×C4×Q8×C79C2211yescharacteristic
98C2×C4×D4×C79C2211yescharacteristic
99C2×C4×D4×C79C2212yes—
100C22×C4⋊C4×C79C2212yes—
101C2×#11929623Q8116yescomplemented
102C2×#11929623C2318yes—
103C22×Dic158—416no—
104C22×Dic158C2311yescharacteristic
105C22×Dic158C2314yes—
106C22×Dic158C2312yes—
107C22×Dic158C23132yes—
108C22×Dic158C2312yes—
109C22×Dic158C2314yes—
110C22×Dic158C2314yes—
111C22×Dic158C2311yescharacteristic
112C2×Q8×D79—48no—
113C2×Q8×D79C23116yes—
114C22×C22⋊D79C2312yes—
115C23×Dic79C2312yes—
116C23×Dic79C2314yes—
117C23×Dic79C2312yes—
118C22×C4×D79C2311yescharacteristic
119C22×C4×D79C2311yescharacteristic
120C22×C4×D79C2314yes—
121C22×C4×D79C2311yescharacteristic
122#14579161C23116yes—
123#14579161C2318yes—
124#14579160C23132yes—
125#14579160C23132yes—
126#14579160C23116yes—
127#14579160C23132yes—
128#14579160C23116yes—
129#14579160C23116yes—
130#14579160C23116yes—
131#14579160C23116yes—
132#14579160C2318yes—
133#14579159C23116yes—
134#14579159C23132yes—
135#14579159C2318yes—
136#14579152C23116yes—
137#14579151C23116yes—
138#14579151C23132yes—
139#14579151C23132yes—
140#14579151C23132yes—
141#14579141C23132yes—
142#14579141C2318yes—
143#14579140C23132yes—
144#14579140C23116yes—
145#14579139C23132yes—
146#14579139C23116yes—
147#14579138C23132yes—
148#14579138C23132yes—
149#14579138C23132yes—
150#14579137C2318yes—
151Q8×Dic79C23116yes—
152C4×Dic158C23116yes—
153C4×Dic158C2318yes—
154C4×Dic158C2318yes—
155C4×Dic158C23116yes—
156#14579126C23132yes—
157#14579126C23116yes—
158#14579126C2318yes—
159#14579126C23116yes—
160D4×Dic79C2318yes—
161D4×Dic79C23116yes—
162C4×C22⋊D79C23132yes—
163C4×C22⋊D79C23116yes—
164(C22⋊D79)⋊C4C23116yes—
165(C22⋊D79)⋊C4C23132yes—
166#14579119C2318yes—
167#14579118C23116yes—
168#14579117C23116yes—
169#14579117C23132yes—
170C2×C4⋊Dic79C2312yes—
171C2×C4⋊Dic79C2312yes—
172C2×C4⋊Dic79C2311yescharacteristic
173C2×C4⋊Dic79C23116yes—
174C2×C4⋊Dic79C2314yes—
175C2×C4⋊Dic79C2311yescharacteristic
176C2×C4⋊Dic79C2312yes—
177C2×C4⋊Dic79C2314yes—
178C2×Dic79⋊C4C23132yes—
179C2×Dic79⋊C4C2314yes—
180C2×Dic79⋊C4C2314yes—
181C2×Dic79⋊C4C2312yes—
182C2×Dic79⋊C4C2314yes—
183C2×Dic79⋊C4C2314yes—
184C2×Dic79⋊C4C2312yes—
185C2×Dic79⋊C4C2312yes—
186C2×Dic79⋊C4C2312yes—
187C2×Dic79⋊C4C2312yes—
188C2×Dic79⋊C4C2314yes—
189C2×Dic79⋊C4C2314yes—
190C2×Dic79⋊C4C2312yes—
191C2×Dic79⋊C4C2312yes—
192C4⋊C4×D79C23116yes—
193C4⋊C4×D79C23116yes—
194C2×C22⋊Dic79C2312yes—
195C2×C22⋊Dic79C2314yes—
196C2×(C2×D79)⋊C4C2312yes—
197C2×(C2×D79)⋊C4C2312yes—
198C2×(C2×D79)⋊C4C2312yes—
199C2×C4×Dic79C2311yescharacteristic
200C2×C4×Dic79C2311yescharacteristic
201C2×C4×Dic79C2311yescharacteristic
202C2×C4×Dic79C2312yes—
203C2×C4×Dic79C2312yes—
204C2×C4×Dic79C2312yes—
205C2×C4×Dic79C23116yes—
206C2×C4×Dic79C2314yes—
207C2×C4×Dic79C2314yes—
208C2×C4×Dic79C2312yes—
209C42×D79C2318yes—
210C22×Q8×C79C2311yescharacteristic
211C22×Q8×C79C2312yes—
212C22×D4×C79C2311yescharacteristic
213C23×C4×C79C2312yes—
214C23×C4×C79C2314yes—
215C4⋊Q8×C79C2318yes—
216#125×C79C23116yes—
217C22⋊Q8×C79C23132yes—
218C22⋊Q8×C79C23116yes—
219C4×Q8×C79C2318yes—
220C4×D4×C79C23116yes—
221C4×D4×C79C2318yes—
222C2×C4⋊C4×C79C2311yescharacteristic
223C2×C4⋊C4×C79C2314yes—
224C2×C4⋊C4×C79C2312yes—
225C2×C4⋊C4×C79C23116yes—
226C2×C4⋊C4×C79C2311yescharacteristic
227C2×C4⋊C4×C79C2312yes—
228C2×C4⋊C4×C79C2312yes—
229C2×C4⋊C4×C79C2314yes—
230C2×C22⋊C4×C79C2312yes—
231C2×C22⋊C4×C79C2314yes—
232C2×C42×C79C2312yes—
233C2×C42×C79C2311yescharacteristic
234C23×D79C2411yescharacteristic
235#11929623C2×Q8164yescomplemented
236C2×Dic158—216no—
237C2×Dic158—28no—
238C2×Dic158—24no—
239C2×Dic158—44no—
240C2×Dic158—48no—
241C2×Dic158—48no—
242C2×Dic158—464no—
243C2×Dic158C2×Q818yescomplemented
244C2×Dic158C24116yes—
245C2×Dic158C2418yes—
246C2×Dic158C2414yes—
247C2×Dic158C2418yes—
248C2×Dic158C24116yes—
249C2×Dic158C24116yes—
250C2×Dic158C2414yes—
251Q8×D79—432no—
252C2×C22⋊D79C2×Q8116yescomplemented
253C2×C22⋊D79C2418yes—
254C22×Dic79—28no—
255C22×Dic79—48no—
256C22×Dic79C2×Q8116yescomplemented
257C22×Dic79C2412yes—
258C22×Dic79C2418yes—
259C22×Dic79C2412yes—
260C22×Dic79C2414yes—
261C22×Dic79C2412yes—
262C22×Dic79C2411yescharacteristic
263C22×Dic79C24116yes—
264C22×Dic79C2412yes—
265C22×Dic79C2411yescharacteristic
266C22×Dic79C2418yes—
267C22×Dic79C2411yescharacteristic
268C2×C4×D79—24no—
269C2×C4×D79—24no—
270C2×C4×D79—48no—
271C2×C4×D79C2×Q818yescomplemented
272C2×C4×D79C2414yes—
273C2×C4×D79C2414yes—
274C2×C4×D79C24116yes—
275C2×C4×D79C2414yes—
276C4⋊Dic79C2418yes—
277C4⋊Dic79C2418yes—
278C4⋊Dic79C2414yes—
279C4⋊Dic79C24116yes—
280C4⋊Dic79C2414yes—
281C4⋊Dic79C2418yes—
282C4⋊Dic79C24116yes—
283Dic79⋊C4C24116yes—
284Dic79⋊C4C24116yes—
285Dic79⋊C4C2418yes—
286Dic79⋊C4C24116yes—
287Dic79⋊C4C24116yes—
288Dic79⋊C4C2418yes—
289Dic79⋊C4C2418yes—
290Dic79⋊C4C2418yes—
291Dic79⋊C4C2418yes—
292Dic79⋊C4C24116yes—
293Dic79⋊C4C24116yes—
294Dic79⋊C4C2418yes—
295Dic79⋊C4C2418yes—
296C22⋊Dic79C24116yes—
297C22⋊Dic79C2418yes—
298(C2×D79)⋊C4C2418yes—
299(C2×D79)⋊C4C2418yes—
300(C2×D79)⋊C4C2418yes—
301C4×Dic79C2414yes—
302C4×Dic79C2414yes—
303C4×Dic79C2414yes—
304C4×Dic79C2418yes—
305C4×Dic79C2418yes—
306C4×Dic79C2418yes—
307C4×Dic79C24116yes—
308C4×Dic79C24116yes—
309C4×Dic79C2418yes—
310C24×C79C2412yes—
311C2×Q8×C79—24no—
312C2×Q8×C79—44no—
313C2×Q8×C79C2414yes—
314C2×Q8×C79C2418yes—
315C2×D4×C79C2×Q818yescomplemented
316C2×D4×C79C2414yes—
317C22×C4×C79—28no—
318C22×C4×C79—48no—
319C22×C4×C79C2412yes—
320C22×C4×C79C2411yescharacteristic
321C22×C4×C79C2414yes—
322C22×C4×C79C2412yes—
323C22×C4×C79C2412yes—
324C22×C4×C79C2418yes—
325C22×C4×C79C24116yes—
326C22×C4×C79C2411yescharacteristic
327C22×C4×C79C2411yescharacteristic
328C4⋊C4×C79C2414yes—
329C4⋊C4×C79C24116yes—
330C4⋊C4×C79C2418yes—
331C4⋊C4×C79C2414yes—
332C4⋊C4×C79C2418yes—
333C4⋊C4×C79C2418yes—
334C4⋊C4×C79C24116yes—
335C22⋊C4×C79C24116yes—
336C22⋊C4×C79C2418yes—
337C42×C79C2418yes—
338C42×C79C2414yes—
339C23×C79—24no—
340C23×C79—24no—
341C23×C79C22×Q818yes—
342C23×C79C2514yes—
343C23×C79C2511yescharacteristic
344C22×D79—22no—
345C22×D79—22no—
346C22×D79C22×Q814yes—
347C22×D79C2512yes—
348Q8×C79—28no—
349Q8×C79—48no—
350D4×C79C22×Q8116yescomplemented
351C2×C4×C79—22no—
352C2×C4×C79—28no—
353C2×C4×C79—24no—
354C2×C4×C79—24no—
355C2×C4×C79—24no—
356C2×C4×C79—216no—
357C2×C4×C79—416no—
358C2×C4×C79C22×Q814yes—
359C2×C4×C792−1+414yes—
360C2×C4×C79C2514yes—
361C2×C4×C79C2514yes—
362C2×C4×C79C2512yes—
363C2×C4×C79C2518yes—
364C2×C4×C79C2514yes—
365C2×C4×C79C2512yes—
366C2×C4×C79C2512yes—
367C22⋊D79C22×Q8132yescomplemented
368C2×Dic79—28no—
369C2×Dic79—24no—
370C2×Dic79—24no—
371C2×Dic79—22no—
372C2×Dic79—24no—
373C2×Dic79—216no—
374C2×Dic79—416no—
375C2×Dic79C22×Q814yes—
376C2×Dic79C22×Q818yes—
377C2×Dic79C22×Q8132yescomplemented
378C2×Dic79H(5,𝔽2)14yes—
379C2×Dic79C2514yes—
380C2×Dic79C2514yes—
381C2×Dic79C2512yes—
382C2×Dic79C2514yes—
383C2×Dic79C2518yes—
384C2×Dic79C2514yes—
385C2×Dic79C2512yes—
386C2×Dic79C2512yes—
387C4×D79—28no—
388C4×D79—28no—
389C4×D79—416no—
390C4×D79C22×Q8116yescomplemented
391Dic158—28no—
392Dic158—232no—
393Dic158—216no—
394Dic158—48no—
395Dic158—416no—
396Dic158—416no—
397Dic158C22×Q8116yescomplemented
398C22×C79—24no—
399C22×C79—24no—
400C22×C79—216no—
401C22×C79C23×Q818yes—
402C22×C79C23×Q812yes—
403C22×C79C2×H(5,𝔽2)12yes—
404C22×C79C2×2−1+412yes—
405C22×C79C2611yescharacteristic
406C2×D79—22no—
407C2×D79—22no—
408C2×D79—28no—
409C2×D79C23×Q814yes—
410C4×C79—24no—
411C4×C79—28no—
412C4×C79—22no—
413C4×C79—24no—
414C4×C79—24no—
415C4×C79C23×Q814yes—
416C4×C79C2×2−1+414yes—
417Dic79—28no—
418Dic79—24no—
419Dic79—24no—
420Dic79—24no—
421Dic79—22no—
422Dic79C23×Q818yes—
423Dic79C23×Q814yes—
424Dic79C2×H(5,𝔽2)14yes—
425C2×#3503—791nomaximal, Sylow
426C2×C79—28no—
427C2×C79#350314yescomplemented
428C2×C79C24×Q811yescharacteristic
429C2×C79C22×H(5,𝔽2)11yescharacteristic
430C2×C79C22×2−1+411yescharacteristic
431D79—24no—
432#3503—7932no—
433C2×Q82—791no—
434C2×Q82—791no—
435C2×#557—792no—
436C2×#554—792no—
437C2×#554—791no—
438C2×#554—792no—
439C2×#554D7911yescharacteristic, complemented
440C2×D4×Q8—794no—
441C2×D4×Q8—792no—
442C2×#544—792no—
443C2×#544—794no—
444C2×#533—792no—
445C2×#533—791no—
446C22×C4⋊Q8—791no—
447C22×C4⋊Q8—792no—
448C2×#520—792no—
449C2×C4×#41—791no—
450C79C2×#350311yescharacteristic, complemented, Sylow
451C22×#41—791no—
452C23×Q8—792no—
453C23×Q8—794no—
454Q82—7916no—
455Q82—7916no—
456#557—7932no—
457#554—7932no—
458#554—7916no—
459#554—7932no—
460#554C2×D79116yescomplemented
461D4×Q8—7964no—
462D4×Q8—7932no—
463#544—7932no—
464#544—7964no—
465#533—7932no—
466#533—7916no—
467C2×C4⋊Q8—792no—
468C2×C4⋊Q8—791no—
469C2×C4⋊Q8—794no—
470C2×C4⋊Q8—7916no—
471C2×C4⋊Q8—792no—
472C2×C4⋊Q8—791no—
473C2×C4⋊Q8—794no—
474C2×C4⋊Q8—794no—
475C2×C4⋊Q8—792no—
476C2×C4⋊Q8—792no—
477C2×C4⋊Q8—792no—
478C2×C4⋊Q8—7932no—
479C2×C4⋊Q8—794no—
480C2×C4⋊Q8—792no—
481C2×C4⋊Q8—791no—
482C2×C4⋊Q8—792no—
483C2×C4⋊Q8C2×D7911yescharacteristic
484C2×#125—792no—
485C2×#125—794no—
486C2×#125—794no—
487C2×#125—794no—
488C2×#125—792no—
489C2×#125C2×D7912yes—
490C2×C22⋊Q8—791no—
491C2×C22⋊Q8—792no—
492C2×C22⋊Q8—794no—
493C2×C22⋊Q8—792no—
494C2×C22⋊Q8—791no—
495C2×C22⋊Q8—794no—
496C2×C22⋊Q8—794no—
497C2×C22⋊Q8—794no—
498C2×C22⋊Q8—794no—
499C2×C22⋊Q8—794no—
500C2×C22⋊Q8C2×D7912yes—
501C2×C22⋊Q8C2×D7914yes—
502#520—7932no—
503C4×#41—7916no—
504C2×C4×Q8—792no—
505C2×C4×Q8—791no—
506C2×C4×Q8—792no—
507C2×C4×Q8—794no—
508C2×C4×Q8—792no—
509C2×C4×Q8—791no—
510C2×C4×Q8—792no—
511C2×C4×Q8—792no—
512C2×C4×Q8—791no—
513C2×C4×Q8C2×D7911yescharacteristic
514C2×C4×D4—791no—
515C2×C4×D4—792no—
516C2×C4×D4—792no—
517C2×C4×D4—794no—
518C2×C4×D4—792no—
519C2×C4×D4—794no—
520C2×C4×D4C2×D7911yescharacteristic
521C2×C4×D4C2×D7912yes—
522C2×#117—791no—
523C2×#117—792no—
524C2×#117—794no—
525C2×#117—792no—
526C22×C4⋊C4—794no—
527C22×C4⋊C4—792no—
528C22×C4⋊C4—792no—
529C22×C4⋊C4—792no—
530C22×C4⋊C4C2×D7912yes—
531C22×C42—792no—
532C22×C42—791no—
533C2×#41—7916no—
534C2×#41—798no—
535C22×Q8—31616no—
536C22×Q8—3168no—
537C22×Q8—7916no—
538C22×Q8—794no—
539C22×Q8—794no—
540C22×Q8—792no—
541C22×Q8—7932no—
542C22×Q8—791no—
543C22×Q8—791no—
544C22×Q8—794no—
545C22×Q8—792no—
546C22×Q8C22×D7911yescharacteristic
547C22×Q8C22×D7912yes—
548C22×D4—792no—
549C22×D4C22×D7911yescharacteristic
550C23×C4—794no—
551C23×C4—794no—
552C23×C4—792no—
553C23×C4—791no—
554C23×C4—792no—
555C23×C4—791no—
556C23×C4—791no—
557C23×C4C22×D7912yes—
558C23×C4C22×D7914yes—
559C4⋊Q8—7916no—
560C4⋊Q8—798no—
561C4⋊Q8—7932no—
562C4⋊Q8—7916no—
563C4⋊Q8—798no—
564C4⋊Q8—7932no—
565C4⋊Q8—7932no—
566C4⋊Q8—7916no—
567C4⋊Q8—7916no—
568C4⋊Q8—7916no—
569C4⋊Q8—7932no—
570C4⋊Q8—7916no—
571C4⋊Q8—798no—
572C4⋊Q8—7916no—
573C4⋊Q8C22×D7918yes—
574#125—7916no—
575#125—7932no—
576#125—7932no—
577#125—7932no—
578#125—7916no—
579#125C22×D79116yes—
580C22⋊Q8—798no—
581C22⋊Q8—7916no—
582C22⋊Q8—7932no—
583C22⋊Q8—7916no—
584C22⋊Q8—798no—
585C22⋊Q8—7932no—
586C22⋊Q8—7932no—
587C22⋊Q8—7932no—
588C22⋊Q8—7932no—
589C22⋊Q8—7932no—
590C22⋊Q8C22×D79116yes—
591C22⋊Q8C22×D79132yes—
592C4×Q8—7916no—
593C4×Q8—798no—
594C4×Q8—7916no—
595C4×Q8—7932no—
596C4×Q8—7916no—
597C4×Q8—798no—
598C4×Q8—7916no—
599C4×Q8—7916no—
600C4×Q8—798no—
601C4×Q8C22×D7918yes—
602C4×D4—798no—
603C4×D4—7916no—
604C4×D4—7916no—
605C4×D4—7932no—
606C4×D4—7916no—
607C4×D4—7932no—
608C4×D4C22×D7918yes—
609C4×D4C22×D79116yes—
610#117—798no—
611#117—7916no—
612#117—7932no—
613#117—7916no—
614C2×C4⋊C4—794no—
615C2×C4⋊C4—792no—
616C2×C4⋊C4—791no—
617C2×C4⋊C4—792no—
618C2×C4⋊C4—794no—
619C2×C4⋊C4—794no—
620C2×C4⋊C4—792no—
621C2×C4⋊C4—7932no—
622C2×C4⋊C4—794no—
623C2×C4⋊C4—794no—
624C2×C4⋊C4—7916no—
625C2×C4⋊C4—792no—
626C2×C4⋊C4—792no—
627C2×C4⋊C4—792no—
628C2×C4⋊C4—791no—
629C2×C4⋊C4—792no—
630C2×C4⋊C4—794no—
631C2×C4⋊C4—792no—
632C2×C4⋊C4—792no—
633C2×C4⋊C4—794no—
634C2×C4⋊C4—792no—
635C2×C4⋊C4—794no—
636C2×C4⋊C4—7916no—
637C2×C4⋊C4—7916no—
638C2×C4⋊C4C22×D7912yes—
639C2×C4⋊C4C22×D7912yes—
640C2×C4⋊C4C22×D7911yescharacteristic
641C2×C4⋊C4C22×D7914yes—
642C2×C4⋊C4C22×D79116yes—
643C2×C4⋊C4C22×D7911yescharacteristic
644C2×C4⋊C4C22×D7914yes—
645C2×C4⋊C4C22×D7912yes—
646C2×C22⋊C4—794no—
647C2×C22⋊C4—792no—
648C2×C22⋊C4—792no—
649C2×C22⋊C4—792no—
650C2×C22⋊C4—792no—
651C2×C22⋊C4C22×D7914yes—
652C2×C22⋊C4C22×D7912yes—
653C2×C42—791no—
654C2×C42—792no—
655C2×C42—794no—
656C2×C42—794no—
657C2×C42—792no—
658C2×C42—792no—
659C2×C42—792no—
660C2×C42—791no—
661C2×C42—7916no—
662C2×C42—791no—
663C2×C42—798no—
664C2×C42C22×D7912yes—
665C2×C42C22×D7911yescharacteristic
666C24—791no—
667C24C23×D7912yes—
668#41—7964no—
669C2×Q8—24no—
670C2×Q8—44no—
671C2×Q8—3168no—
672C2×Q8—3168no—
673C2×Q8—3164no—
674C2×Q8—31664no—
675C2×Q8—31632no—
676C2×Q8—798no—
677C2×Q8—7916no—
678C2×Q8—7916no—
679C2×Q8—798no—
680C2×Q8—794no—
681C2×Q8—794no—
682C2×Q8—7916no—
683C2×Q8—798no—
684C2×Q8—1588no—
685C2×Q8—15816no—
686C2×Q8—1584no—
687C2×Q8C23×D7914yes—
688C2×Q8C23×D7918yes—
689C2×D4—7916no—
690C2×D4—798no—
691C2×D4Q8×D7918yescomplemented
692C2×D4C23×D7914yes—
693C22×C4—28no—
694C22×C4—48no—
695C22×C4—3168no—
696C22×C4—3168no—
697C22×C4—7916no—
698C22×C4—7916no—
699C22×C4—7916no—
700C22×C4—798no—
701C22×C4—792no—
702C22×C4—791no—
703C22×C4—791no—
704C22×C4—798no—
705C22×C4—794no—
706C22×C4—798no—
707C22×C4—792no—
708C22×C4—791no—
709C22×C4—792no—
710C22×C4—792no—
711C22×C4—794no—
712C22×C4—794no—
713C22×C4—794no—
714C22×C4—1584no—
715C22×C4—1588no—
716C22×C4—1584no—
717C22×C4C23×D7918yes—
718C22×C4C23×D7912yes—
719C22×C4C23×D7912yes—
720C22×C4C23×D7911yescharacteristic
721C22×C4C23×D7914yes—
722C22×C4C23×D7912yes—
723C22×C4C23×D79116yes—
724C22×C4C23×D7911yescharacteristic
725C22×C4C23×D7911yescharacteristic
726C4⋊C4—7916no—
727C4⋊C4—798no—
728C4⋊C4—7916no—
729C4⋊C4—7916no—
730C4⋊C4—7916no—
731C4⋊C4—798no—
732C4⋊C4—798no—
733C4⋊C4—798no—
734C4⋊C4—798no—
735C4⋊C4—7916no—
736C4⋊C4—798no—
737C4⋊C4—7916no—
738C4⋊C4—798no—
739C4⋊C4—798no—
740C4⋊C4—794no—
741C4⋊C4—798no—
742C4⋊C4—7916no—
743C4⋊C4—794no—
744C4⋊C4—798no—
745C4⋊C4—7916no—
746C4⋊C4C23×D7918yes—
747C4⋊C4C23×D7918yes—
748C4⋊C4C23×D7914yes—
749C4⋊C4C23×D79116yes—
750C4⋊C4C23×D7914yes—
751C4⋊C4C23×D79116yes—
752C4⋊C4C23×D7918yes—
753C22⋊C4—7916no—
754C22⋊C4—798no—
755C22⋊C4—798no—
756C22⋊C4—798no—
757C22⋊C4—798no—
758C22⋊C4C23×D79116yes—
759C22⋊C4C23×D7918yes—
760C42—794no—
761C42—794no—
762C42—798no—
763C42—798no—
764C42—798no—
765C42—794no—
766C42—7916no—
767C42—7916no—
768C42—798no—
769C42C23×D7914yes—
770C42C23×D7918yes—
771C23—24no—
772C23—24no—
773C23—792no—
774C23—794no—
775C23—1582no—
776C23—1582no—
777C23C2×Q8×D7918yes—
778C23C24×D7914yes—
779C23C24×D7911yescharacteristic
780Q8—28no—
781Q8—48no—
782Q8—31616no—
783Q8—31616no—
784Q8—3168no—
785Q8—7916no—
786Q8—15816no—
787Q8—15832no—
788Q8—1588no—
789D4—7932no—
790D4C2×Q8×D79116yescomplemented
791C2×C4—24no—
792C2×C4—28no—
793C2×C4—22no—
794C2×C4—24no—
795C2×C4—24no—
796C2×C4—216no—
797C2×C4—416no—
798C2×C4—31616no—
799C2×C4—31616no—
800C2×C4—794no—
801C2×C4—794no—
802C2×C4—792no—
803C2×C4—792no—
804C2×C4—794no—
805C2×C4—798no—
806C2×C4—7932no—
807C2×C4—7916no—
808C2×C4—794no—
809C2×C4—792no—
810C2×C4—794no—
811C2×C4—798no—
812C2×C4—794no—
813C2×C4—1588no—
814C2×C4—15816no—
815C2×C4—1588no—
816C2×C4—1584no—
817C2×C4—1584no—
818C2×C4—1582no—
819C2×C4—1584no—
820C2×C4—1588no—
821C2×C4C2×Q8×D7914yes—
822C2×C4#1457920814yes—
823C2×C4C24×D7914yes—
824C2×C4C24×D7914yes—
825C2×C4C24×D7912yes—
826C2×C4C24×D7918yes—
827C2×C4C24×D7914yes—
828C2×C4C24×D7912yes—
829C2×C4C24×D7912yes—
830C22—24no—
831C22—24no—
832C22—216no—
833C22—794no—
834C22—1582no—
835C22—1582no—
836C22—1588no—
837C22C22×Q8×D7918yes—
838C22C22×Q8×D7912yes—
839C22H(5,𝔽2)×D7912yes—
840C22C2×#1457920812yes—
841C22C25×D7911yescharacteristic
842C4—24no—
843C4—28no—
844C4—22no—
845C4—24no—
846C4—24no—
847C4—794no—
848C4—798no—
849C4—794no—
850C4—1588no—
851C4—1584no—
852C4—1584no—
853C4—1582no—
854C4—1584no—
855C4C22×Q8×D7914yes—
856C4C2×#1457920814yes—
857C2—28no—
858C2—1584no—
859C2#2377721414yesdirect product factor
860C2C23×Q8×D7911yescharacteristic
861C2C2×H(5,𝔽2)×D7911yescharacteristic
862C2C22×#1457920811yescharacteristic
subgroupG/H
centerC23C24×D79
commutator, cosocleC22×C79C26
FrattiniC22C25×D79
FittingC2×#554×C79C2
socleC23×C79C25
prime radicalC22×#11929623C22
hypercenterC2×#554D79
hypocenterC79C2×#3503
LCSG ▷ C22×C79 ▷ C79
UCSC1 ◁ C23 ◁ C2×#554

Complements

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

NH ≅ G/Ntype
1. #23777214C2direct (N × H)
2. C2×Q8×Dic158C2semidirect
3. C2×#19099293C2semidirect
4. C2×#19099290C2semidirect
5. C2×#19099271C2semidirect
6. C2×#19099270C2semidirect
7. C2×#19099268C2semidirect
8. C2×D4×Dic158C2semidirect
9. C2×#19099226C2semidirect
10. C2×#19099193C2semidirect
11. C2×#19099192C2semidirect
12. C2×#19099117C2semidirect
13. C2×#19099115C2semidirect
14. C22×#14579160C2semidirect
15. C2×C4⋊Q8×D79C2semidirect
18. C2×#554×C79C2semidirect
22. Q8×Dic158C22semidirect
23. #19099293C22semidirect
24. #19099290C22semidirect
25. #19099271C22semidirect
26. #19099270C22semidirect
27. #19099268C22semidirect
28. D4×Dic158C22semidirect
29. #19099226C22semidirect
30. #19099193C22semidirect
31. #19099192C22semidirect
32. #19099117C22semidirect
33. #19099115C22semidirect
45. C2×#14579160C22semidirect
49. C4⋊Q8×D79C22semidirect
92. #554×C79C22semidirect
101. C2×#11929623Q8semidirect
235. #11929623C2×Q8semidirect
243. C2×Dic158C2×Q8semidirect
252. C2×C22⋊D79C2×Q8semidirect
256. C22×Dic79C2×Q8semidirect
271. C2×C4×D79C2×Q8semidirect
315. C2×D4×C79C2×Q8semidirect
350. D4×C79C22×Q8semidirect
367. C22⋊D79C22×Q8semidirect
377. C2×Dic79C22×Q8semidirect
390. C4×D79C22×Q8semidirect
397. Dic158C22×Q8semidirect
427. C2×C79#3503semidirect
439. C2×#554D79semidirect
450. C79C2×#3503semidirect
460. #554C2×D79semidirect
691. C2×D4Q8×D79semidirect
790. D4C2×Q8×D79semidirect
859. C2#23777214direct (N × H)

Maximal subgroups

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

subgroupindex
#237772142
C2×Q8×Dic1582
C2×#190992932
C2×#190992902
C2×#190992712
C2×#190992702
C2×#190992682
C2×D4×Dic1582
C2×#190992262
C2×#190991932
C2×#190991922
C2×#190991172
C2×#190991152
C22×#145791602
C2×C4⋊Q8×D792
C2×#190990422
C2×C4×#119296232
C2×#554×C792
C2×#350379