Finite Group Databasebeta

← C2×#23777830 #35195881

Subgroups — C2×#23777830 #35195881

Order 20224.

7086 conjugacy classes of subgroups.

The subgroup lattice has 872 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#23777830C2132yesmaximal, direct product factor
2C2×#19099315C214yesmaximal, complemented
3C2×#19099292C211yesmaximal, characteristic, complemented
4C2×#19099271C212yesmaximal, complemented
5C2×#19099257C212yesmaximal, complemented
6C2×Q8×D316C212yesmaximal, complemented
7C2×#19099228C211yesmaximal, characteristic, complemented
8C2×#19099221C212yesmaximal, complemented
9C2×#19099217C211yesmaximal, characteristic, complemented
10C2×#19099191C212yesmaximal, complemented
11C2×#19099186C212yesmaximal, complemented
12C2×#19099171C212yesmaximal, complemented
13C2×#19099154C214yesmaximal, complemented
14C2×#19099133C212yesmaximal, complemented
15C2×C4⋊Q8×D79C211yesmaximal, characteristic, complemented
16C2×#19099100C211yesmaximal, characteristic, complemented
17C2×#19099095C211yesmaximal, characteristic, complemented
18C2×#556×C79C211yesmaximal, characteristic, complemented
19C22×#11929623C2212yes—
20C22×Q8×D79C2212yes—
21C22×Q8×D79C2212yes—
22#19099315C22164yescomplemented
23#19099292C22116yescomplemented
24#19099271C22132yescomplemented
25#19099257C22132yescomplemented
26Q8×D316C22132yescomplemented
27#19099228C22116yescomplemented
28#19099221C22132yescomplemented
29#19099217C22116yescomplemented
30#19099191C22132yescomplemented
31#19099186C22132yescomplemented
32#19099171C22132yescomplemented
33#19099154C22164yescomplemented
34#19099133C22132yescomplemented
35C2×#14579161C2214yes—
36C2×#14579161C2211yescharacteristic
37C2×#14579161C2212yes—
38C2×#14579160C2212yes—
39C2×#14579160C2212yes—
40C2×#14579160C2212yes—
41C2×#14579159C2212yes—
42C4⋊Q8×D79C22116yescomplemented
43#19099100C22116yescomplemented
44#19099095C22116yescomplemented
45C2×#14579156C2214yes—
46C2×#14579156C2212yes—
47C2×#14579155C2214yes—
48C2×#14579154C2212yes—
49C2×#14579153C2214yes—
50C2×#14579152C2211yescharacteristic
51C2×#14579152C2212yes—
52C2×#14579152C2211yescharacteristic
53C2×#14579152C2214yes—
54C2×#14579151C2214yes—
55C2×#14579150C2211yescharacteristic
56C2×#14579148C2211yescharacteristic
57C2×#14579147C2214yes—
58C2×#14579146C2212yes—
59C2×#14579145C2214yes—
60C2×#14579143C2214yes—
61C2×#14579143C2214yes—
62C2×#14579143C2212yes—
63C2×#14579141C2214yes—
64C2×#14579141C2212yes—
65C2×#14579141C2211yescharacteristic
66C2×#14579141C2214yes—
67C2×#14579139C2214yes—
68C2×#14579138C2214yes—
69C2×#14579138C2214yes—
70C2×#14579138C2214yes—
71C2×#14579137C2212yes—
72C2×#14579137C2211yescharacteristic
73C2×#14579136C2211yescharacteristic
74C2×#14579135C2212yes—
75C2×#14579134C2214yes—
76C2×#14579132C2211yescharacteristic
77C2×Q8×Dic79C2212yes—
78C2×C4×Dic158C2212yes—
79C2×C4×Dic158C2211yescharacteristic
80C2×C4×D316C2211yescharacteristic
81C2×C4×D316C2212yes—
82C2×C4×D316C2214yes—
83C2×#14579123C2212yes—
84C2×C4×C22⋊D79C2212yes—
85C2×(C22⋊D79)⋊C4C2214yes—
86C2×#14579120C2212yes—
87C2×#14579118C2212yes—
88C22×C4⋊Dic79C2212yes—
89C2×C4⋊C4×D79C2212yes—
90C2×C4⋊C4×D79C2212yes—
91C2×C42×D79C2211yescharacteristic
92#556×C79C22116yescomplemented
93C2×C4⋊Q8×C79C2211yescharacteristic
94C2×#126×C79C2214yes—
95C2×#124×C79C2212yes—
96C2×C22⋊Q8×C79C2212yes—
97C2×C4×Q8×C79C2212yes—
98C2×C4×Q8×C79C2211yescharacteristic
99C2×C4×D4×C79C2211yescharacteristic
100C2×#117×C79C2212yes—
101C2×#11929623—48no—
102C2×#11929623C23116yes—
103C22×Dic158C2311yescharacteristic
104C22×Dic158C2312yes—
105C22×Dic158C2314yes—
106C22×Dic158C2314yes—
107C2×Q8×D79—48no—
108C2×Q8×D79—48no—
109C2×Q8×D79C23116yes—
110C2×Q8×D79C23116yes—
111C22×D316C2311yescharacteristic
112C22×D316C2312yes—
113C22×C22⋊D79C2312yes—
114C22×C22⋊D79C2314yes—
115C23×Dic79C2314yes—
116C22×C4×D79C2311yescharacteristic
117C22×C4×D79C2311yescharacteristic
118C22×C4×D79C2311yescharacteristic
119C22×C4×D79C2312yes—
120C22×C4×D79C2314yes—
121C22×C4×D79C2314yes—
122#14579161C23132yes—
123#14579161C2318yes—
124#14579161C23116yes—
125#14579160C23116yes—
126#14579160C23116yes—
127#14579160C23116yes—
128#14579159C23116yes—
129#14579156C23132yes—
130#14579156C23116yes—
131#14579155C23132yes—
132#14579154C23116yes—
133#14579153C23132yes—
134#14579152C23132yes—
135#14579152C2318yes—
136#14579152C2318yes—
137#14579152C23116yes—
138#14579151C23132yes—
139#14579150C2318yes—
140#14579148C2318yes—
141#14579147C23132yes—
142#14579146C23116yes—
143#14579145C23132yes—
144#14579143C23116yes—
145#14579143C23132yes—
146#14579143C23132yes—
147#14579141C23132yes—
148#14579141C23116yes—
149#14579141C23132yes—
150#14579141C2318yes—
151#14579139C23132yes—
152#14579138C23132yes—
153#14579138C23132yes—
154#14579138C23132yes—
155#14579137C23116yes—
156#14579137C2318yes—
157#14579136C2318yes—
158#14579135C23116yes—
159#14579134C23132yes—
160#14579132C2318yes—
161Q8×Dic79C23116yes—
162C4×Dic158C23116yes—
163C4×Dic158C2318yes—
164C4×D316C23132yes—
165C4×D316C2318yes—
166C4×D316C23116yes—
167#14579123C23116yes—
168C4×C22⋊D79C23116yes—
169(C22⋊D79)⋊C4C23132yes—
170#14579120C23116yes—
171#14579118C23116yes—
172C2×C4⋊Dic79C23116yes—
173C2×C4⋊Dic79C2312yes—
174C2×C4⋊Dic79C2312yes—
175C2×C4⋊Dic79C2311yescharacteristic
176C2×C4⋊Dic79C2314yes—
177C2×C4⋊Dic79C2312yes—
178C2×C4⋊Dic79C2312yes—
179C2×C4⋊Dic79C2312yes—
180C2×C4⋊Dic79C2314yes—
181C2×C4⋊Dic79C2311yescharacteristic
182C2×C4⋊Dic79C2314yes—
183C2×Dic79⋊C4C2314yes—
184C2×Dic79⋊C4C2314yes—
185C2×Dic79⋊C4C2312yes—
186C2×Dic79⋊C4C2312yes—
187C2×Dic79⋊C4C2314yes—
188C2×Dic79⋊C4C2312yes—
189C2×Dic79⋊C4C2314yes—
190C2×Dic79⋊C4C2312yes—
191C4⋊C4×D79C23116yes—
192C4⋊C4×D79C23116yes—
193C2×C22⋊Dic79C2312yes—
194C2×C22⋊Dic79C2312yes—
195C2×C22⋊Dic79C2312yes—
196C2×(C2×D79)⋊C4C2312yes—
197C2×(C2×D79)⋊C4C2312yes—
198C2×(C2×D79)⋊C4C2312yes—
199C2×(C2×D79)⋊C4C2312yes—
200C2×(C2×D79)⋊C4C2314yes—
201C2×(C2×D79)⋊C4C2314yes—
202C2×(C2×D79)⋊C4C2312yes—
203C2×(C2×D79)⋊C4C2312yes—
204C2×C4×Dic79C2311yescharacteristic
205C2×C4×Dic79C2311yescharacteristic
206C2×C4×Dic79C2311yescharacteristic
207C2×C4×Dic79C2312yes—
208C2×C4×Dic79C2314yes—
209C42×D79C2318yes—
210C22×Q8×C79C2311yescharacteristic
211C22×Q8×C79C2312yes—
212C22×D4×C79C2311yescharacteristic
213C23×C4×C79C2312yes—
214C4⋊Q8×C79C2318yes—
215#126×C79C23132yes—
216#124×C79C23116yes—
217C22⋊Q8×C79C23116yes—
218C4×Q8×C79C23116yes—
219C4×Q8×C79C2318yes—
220C4×D4×C79C2318yes—
221#117×C79C23116yes—
222C2×C4⋊C4×C79C2311yescharacteristic
223C2×C4⋊C4×C79C2312yes—
224C2×C4⋊C4×C79C2311yescharacteristic
225C2×C4⋊C4×C79C2314yes—
226C2×C4⋊C4×C79C2312yes—
227C2×C4⋊C4×C79C2312yes—
228C2×C22⋊C4×C79C2314yes—
229C2×C22⋊C4×C79C2312yes—
230C2×C22⋊C4×C79C2314yes—
231C2×C42×C79C2314yes—
232C2×C42×C79C2311yescharacteristic
233C2×C42×C79C2312yes—
234C23×D79C2412yes—
235C23×D79C2411yescharacteristic
236#11929623—432no—
237C2×Dic158—24no—
238C2×Dic158—28no—
239C2×Dic158—48no—
240C2×Dic158—48no—
241C2×Dic158C2414yes—
242C2×Dic158C2418yes—
243C2×Dic158C24116yes—
244C2×Dic158C24116yes—
245Q8×D79—432no—
246Q8×D79—432no—
247C2×D316—28no—
248C2×D316—24no—
249C2×D316C2414yes—
250C2×D316C2418yes—
251C2×C22⋊D79—28no—
252C2×C22⋊D79—48no—
253C2×C22⋊D79C2418yes—
254C2×C22⋊D79C24116yes—
255C22×Dic79—48no—
256C22×Dic79C2411yescharacteristic
257C22×Dic79C2412yes—
258C22×Dic79C2414yes—
259C22×Dic79C2412yes—
260C22×Dic79C2412yes—
261C22×Dic79C2411yescharacteristic
262C22×Dic79C2411yescharacteristic
263C22×Dic79C24116yes—
264C2×C4×D79—24no—
265C2×C4×D79—24no—
266C2×C4×D79—28no—
267C2×C4×D79—24no—
268C2×C4×D79—48no—
269C2×C4×D79—48no—
270C2×C4×D79C2414yes—
271C2×C4×D79C2418yes—
272C2×C4×D79C2414yes—
273C2×C4×D79C2414yes—
274C2×C4×D79C24116yes—
275C2×C4×D79C24116yes—
276C4⋊Dic79C2418yes—
277C4⋊Dic79C2418yes—
278C4⋊Dic79C2414yes—
279C4⋊Dic79C24116yes—
280C4⋊Dic79C2418yes—
281C4⋊Dic79C2418yes—
282C4⋊Dic79C2418yes—
283C4⋊Dic79C24116yes—
284C4⋊Dic79C2414yes—
285C4⋊Dic79C24116yes—
286Dic79⋊C4C24116yes—
287Dic79⋊C4C24116yes—
288Dic79⋊C4C2418yes—
289Dic79⋊C4C2418yes—
290Dic79⋊C4C24116yes—
291Dic79⋊C4C2418yes—
292Dic79⋊C4C24116yes—
293Dic79⋊C4C2418yes—
294C22⋊Dic79C2418yes—
295C22⋊Dic79C2418yes—
296C22⋊Dic79C2418yes—
297(C2×D79)⋊C4C2418yes—
298(C2×D79)⋊C4C2418yes—
299(C2×D79)⋊C4C2418yes—
300(C2×D79)⋊C4C2418yes—
301(C2×D79)⋊C4C24116yes—
302(C2×D79)⋊C4C24116yes—
303(C2×D79)⋊C4C2418yes—
304(C2×D79)⋊C4C2418yes—
305C4×Dic79C2414yes—
306C4×Dic79C2414yes—
307C4×Dic79C2414yes—
308C4×Dic79C2418yes—
309C4×Dic79C24116yes—
310C24×C79C2412yes—
311C2×Q8×C79—28no—
312C2×Q8×C79—24no—
313C2×Q8×C79C2418yes—
314C2×Q8×C79C2414yes—
315C2×D4×C79—24no—
316C2×D4×C79C2414yes—
317C22×C4×C79—28no—
318C22×C4×C79C2414yes—
319C22×C4×C79C2412yes—
320C22×C4×C79C2412yes—
321C22×C4×C79C2411yescharacteristic
322C22×C4×C79C2412yes—
323C22×C4×C79C2418yes—
324C22×C4×C79C2411yescharacteristic
325C22×C4×C79C2411yescharacteristic
326C4⋊C4×C79C2414yes—
327C4⋊C4×C79C2418yes—
328C4⋊C4×C79C2414yes—
329C4⋊C4×C79C24116yes—
330C4⋊C4×C79C2418yes—
331C4⋊C4×C79C2418yes—
332C22⋊C4×C79C24116yes—
333C22⋊C4×C79C2418yes—
334C22⋊C4×C79C24116yes—
335C42×C79C24116yes—
336C42×C79C2414yes—
337C42×C79C2418yes—
338C23×C79—24no—
339C23×C79—24no—
340C23×C79—24no—
341C23×C79C2514yes—
342C23×C79C2511yescharacteristic
343C22×D79—22no—
344C22×D79—22no—
345C22×D79—24no—
346C22×D79—24no—
347C22×D79—24no—
348C22×D792−1+414yes—
349C22×D79C2514yes—
350C22×D79C2512yes—
351Q8×C79—216no—
352Q8×C79—28no—
353D4×C79—28no—
354C2×C4×C79—28no—
355C2×C4×C79—22no—
356C2×C4×C79—24no—
357C2×C4×C79—24no—
358C2×C4×C79—24no—
359C2×C4×C79—216no—
360C2×C4×C79H(5,𝔽2)14yes—
361C2×C4×C792−1+414yes—
362C2×C4×C79C2514yes—
363C2×C4×C79C2512yes—
364C2×C4×C79C2514yes—
365C2×C4×C79C2514yes—
366C2×C4×C79C2518yes—
367C2×C4×C79C2512yes—
368C2×C4×C79C2512yes—
369C22⋊D79—216no—
370C22⋊D79—416no—
371C2×Dic79—24no—
372C2×Dic79—22no—
373C2×Dic79—24no—
374C2×Dic79—28no—
375C2×Dic79—22no—
376C2×Dic79—22no—
377C2×Dic79—24no—
378C2×Dic79—416no—
379C2×Dic79C2514yes—
380C2×Dic79C2512yes—
381C2×Dic79C2512yes—
382C2×Dic79C2512yes—
383C2×Dic79C2514yes—
384C2×Dic79C2518yes—
385C2×Dic79C2514yes—
386D316—216no—
387D316—28no—
388C4×D79—28no—
389C4×D79—28no—
390C4×D79—216no—
391C4×D79—28no—
392C4×D79—416no—
393C4×D79—416no—
394Dic158—28no—
395Dic158—216no—
396Dic158—416no—
397Dic158—416no—
398C22×C79—24no—
399C22×C79—24no—
400C22×C79—24no—
401C22×C79—48no—
402C22×C79C2×H(5,𝔽2)12yes—
403C22×C79C2×2−1+412yes—
404C22×C79C2×2−1+412yes—
405C22×C79C2611yescharacteristic
406C2×D79—22no—
407C2×D79—22no—
408C2×D79—28no—
409C2×D79—24no—
410C2×D79—24no—
411C2×D79—24no—
412C2×D79—48no—
413C2×D79C2×2−1+414yes—
414C4×C79—28no—
415C4×C79—24no—
416C4×C79—24no—
417C4×C79—22no—
418C4×C79—24no—
419C4×C79C2×H(5,𝔽2)14yes—
420C4×C79C2×2−1+414yes—
421Dic79—28no—
422Dic79—24no—
423Dic79—22no—
424Dic79—24no—
425Dic79—24no—
426Dic79—22no—
427Dic79—22no—
428C2×#3552—791nomaximal, Sylow
429C2×C79—44no—
430C2×C79#355214yescomplemented
431C2×C79C22×H(5,𝔽2)11yescharacteristic
432C2×C79C22×2−1+411yescharacteristic
433C2×C79C22×2−1+411yescharacteristic
434D79—24no—
435D79—44no—
436#3552—7932no—
437C2×#563—794no—
438C2×#557—791no—
439C2×#556D7911yescharacteristic, complemented
440C2×#554—792no—
441C2×#553—792no—
442C2×D4×Q8—791no—
443C2×D4×Q8—792no—
444C2×#548—792no—
445C2×#547—791no—
446C2×#544—792no—
447C2×#542—792no—
448C2×#541—792no—
449C2×#539—794no—
450C2×#536—792no—
451C22×C4⋊Q8—791no—
452C2×#529—791no—
453C2×#529—791no—
454C79C2×#355211yescharacteristic, complemented, Sylow
455C22×#41—792no—
456C23×Q8—792no—
457C23×Q8—792no—
458#563—7964no—
459#557—7916no—
460#556C2×D79116yescomplemented
461#554—7932no—
462#553—7932no—
463D4×Q8—7916no—
464D4×Q8—7932no—
465#548—7932no—
466#547—7916no—
467#544—7932no—
468#542—7932no—
469#541—7932no—
470#539—7964no—
471#536—7932no—
472C2×C4⋊Q8—792no—
473C2×C4⋊Q8—7916no—
474C2×C4⋊Q8—792no—
475C2×C4⋊Q8—792no—
476C2×C4⋊Q8—792no—
477C2×C4⋊Q8—791no—
478C2×C4⋊Q8—792no—
479C2×C4⋊Q8—794no—
480C2×C4⋊Q8C2×D7911yescharacteristic
481#529—7916no—
482#529—7916no—
483C2×#126—792no—
484C2×#126—794no—
485C2×#126—792no—
486C2×#126—794no—
487C2×#126C2×D7914yes—
488C2×#125—791no—
489C2×#125—791no—
490C2×#125—794no—
491C2×#125—794no—
492C2×#125—792no—
493C2×#125—794no—
494C2×#124—791no—
495C2×#124—791no—
496C2×#124—794no—
497C2×#124C2×D7912yes—
498C2×#123—792no—
499C2×#123—792no—
500C2×#123—794no—
501C2×#123—794no—
502C2×#123—794no—
503C2×C22⋊Q8—791no—
504C2×C22⋊Q8—792no—
505C2×C22⋊Q8—791no—
506C2×C22⋊Q8—794no—
507C2×C22⋊Q8—794no—
508C2×C22⋊Q8—792no—
509C2×C22⋊Q8—794no—
510C2×C22⋊Q8—794no—
511C2×C22⋊Q8—794no—
512C2×C22⋊Q8—794no—
513C2×C22⋊Q8C2×D7912yes—
514C2×#121—791no—
515C2×#121—792no—
516C2×#121—791no—
517C2×#121—794no—
518C2×C4×Q8—792no—
519C2×C4×Q8—791no—
520C2×C4×Q8—792no—
521C2×C4×Q8C2×D7911yescharacteristic
522C2×C4×Q8C2×D7912yes—
523C2×C4×D4—792no—
524C2×C4×D4—792no—
525C2×C4×D4—794no—
526C2×C4×D4—791no—
527C2×C4×D4—792no—
528C2×C4×D4—794no—
529C2×C4×D4C2×D7911yescharacteristic
530C2×#117—792no—
531C2×#117—792no—
532C2×#117C2×D7912yes—
533C22×C4⋊C4—792no—
534C22×C4⋊C4—792no—
535C22×C4⋊C4—792no—
536C22×C42—791no—
537C2×#41—3168no—
538C2×#41—7916no—
539C22×Q8—3168no—
540C22×Q8—3168no—
541C22×Q8—7916no—
542C22×Q8—7916no—
543C22×Q8—794no—
544C22×Q8—794no—
545C22×Q8—791no—
546C22×Q8—792no—
547C22×Q8C22×D7911yescharacteristic
548C22×Q8C22×D7912yes—
549C22×D4—794no—
550C22×D4—792no—
551C22×D4—792no—
552C22×D4—791no—
553C22×D4C22×D7911yescharacteristic
554C23×C4—794no—
555C23×C4—794no—
556C23×C4—794no—
557C23×C4—791no—
558C23×C4—791no—
559C23×C4—792no—
560C23×C4—791no—
561C23×C4C22×D7912yes—
562C4⋊Q8—7916no—
563C4⋊Q8—7916no—
564C4⋊Q8—7916no—
565C4⋊Q8—7916no—
566C4⋊Q8—798no—
567C4⋊Q8—7916no—
568C4⋊Q8—7932no—
569C4⋊Q8C22×D7918yes—
570#126—7916no—
571#126—7932no—
572#126—7916no—
573#126—7932no—
574#126C22×D79132yes—
575#125—798no—
576#125—798no—
577#125—7932no—
578#125—7932no—
579#125—7916no—
580#125—7932no—
581#124—798no—
582#124—798no—
583#124—7932no—
584#124C22×D79116yes—
585#123—7916no—
586#123—7916no—
587#123—7932no—
588#123—7932no—
589#123—7932no—
590C22⋊Q8—798no—
591C22⋊Q8—7916no—
592C22⋊Q8—798no—
593C22⋊Q8—7932no—
594C22⋊Q8—7932no—
595C22⋊Q8—7916no—
596C22⋊Q8—7932no—
597C22⋊Q8—7932no—
598C22⋊Q8—7932no—
599C22⋊Q8—7932no—
600C22⋊Q8C22×D79116yes—
601#121—798no—
602#121—7916no—
603#121—798no—
604#121—7932no—
605C4×Q8—7916no—
606C4×Q8—798no—
607C4×Q8—7916no—
608C4×Q8C22×D7918yes—
609C4×Q8C22×D79116yes—
610C4×D4—7916no—
611C4×D4—7916no—
612C4×D4—7932no—
613C4×D4—798no—
614C4×D4—7916no—
615C4×D4—7932no—
616C4×D4C22×D7918yes—
617#117—7916no—
618#117—7916no—
619#117C22×D79116yes—
620C2×C4⋊C4—791no—
621C2×C4⋊C4—792no—
622C2×C4⋊C4—794no—
623C2×C4⋊C4—794no—
624C2×C4⋊C4—794no—
625C2×C4⋊C4—792no—
626C2×C4⋊C4—7916no—
627C2×C4⋊C4—792no—
628C2×C4⋊C4—792no—
629C2×C4⋊C4—792no—
630C2×C4⋊C4—792no—
631C2×C4⋊C4—794no—
632C2×C4⋊C4—792no—
633C2×C4⋊C4—794no—
634C2×C4⋊C4—792no—
635C2×C4⋊C4—791no—
636C2×C4⋊C4—794no—
637C2×C4⋊C4—794no—
638C2×C4⋊C4—792no—
639C2×C4⋊C4—7916no—
640C2×C4⋊C4—7916no—
641C2×C4⋊C4C22×D7912yes—
642C2×C4⋊C4C22×D7912yes—
643C2×C4⋊C4C22×D7911yescharacteristic
644C2×C4⋊C4C22×D7911yescharacteristic
645C2×C4⋊C4C22×D7914yes—
646C2×C4⋊C4C22×D7912yes—
647C2×C22⋊C4—792no—
648C2×C22⋊C4—792no—
649C2×C22⋊C4—792no—
650C2×C22⋊C4—792no—
651C2×C22⋊C4—792no—
652C2×C22⋊C4—792no—
653C2×C22⋊C4—792no—
654C2×C22⋊C4—794no—
655C2×C22⋊C4—794no—
656C2×C22⋊C4—792no—
657C2×C22⋊C4—792no—
658C2×C22⋊C4C22×D7914yes—
659C2×C22⋊C4C22×D7914yes—
660C2×C22⋊C4C22×D7912yes—
661C2×C42—791no—
662C2×C42—791no—
663C2×C42—792no—
664C2×C42—794no—
665C2×C42—791no—
666C2×C42—798no—
667C2×C42C22×D7912yes—
668C2×C42C22×D7914yes—
669C2×C42C22×D7911yescharacteristic
670C24—791no—
671C24—792no—
672C24C23×D7912yes—
673#41—31632no—
674C2×Q8—28no—
675C2×Q8—24no—
676C2×Q8—3168no—
677C2×Q8—3168no—
678C2×Q8—31632no—
679C2×Q8—31632no—
680C2×Q8—7916no—
681C2×Q8—7916no—
682C2×Q8—794no—
683C2×Q8—798no—
684C2×Q8—1584no—
685C2×Q8—1588no—
686C2×Q8C23×D7914yes—
687C2×Q8C23×D7918yes—
688C2×D4—24no—
689C2×D4—3168no—
690C2×D4—7916no—
691C2×D4—798no—
692C2×D4—798no—
693C2×D4—794no—
694C2×D4—1588no—
695C2×D4—1588no—
696C2×D4—1584no—
697C2×D4C23×D7914yes—
698C22×C4—28no—
699C22×C4—3168no—
700C22×C4—3168no—
701C22×C4—3168no—
702C22×C4—7916no—
703C22×C4—7916no—
704C22×C4—7916no—
705C22×C4—792no—
706C22×C4—791no—
707C22×C4—791no—
708C22×C4—791no—
709C22×C4—792no—
710C22×C4—794no—
711C22×C4—792no—
712C22×C4—794no—
713C22×C4—794no—
714C22×C4—794no—
715C22×C4—798no—
716C22×C4—1584no—
717C22×C4—1584no—
718C22×C4—1588no—
719C22×C4—1584no—
720C22×C4C23×D7918yes—
721C22×C4C23×D7912yes—
722C22×C4C23×D7911yescharacteristic
723C22×C4C23×D7912yes—
724C22×C4C23×D7912yes—
725C22×C4C23×D7914yes—
726C22×C4C23×D7911yescharacteristic
727C22×C4C23×D7911yescharacteristic
728C4⋊C4—7916no—
729C4⋊C4—7916no—
730C4⋊C4—798no—
731C4⋊C4—798no—
732C4⋊C4—7916no—
733C4⋊C4—798no—
734C4⋊C4—7916no—
735C4⋊C4—798no—
736C4⋊C4—794no—
737C4⋊C4—798no—
738C4⋊C4—7916no—
739C4⋊C4—798no—
740C4⋊C4—798no—
741C4⋊C4—798no—
742C4⋊C4—798no—
743C4⋊C4—7916no—
744C4⋊C4—794no—
745C4⋊C4—7916no—
746C4⋊C4C23×D7918yes—
747C4⋊C4C23×D7918yes—
748C4⋊C4C23×D7914yes—
749C4⋊C4C23×D7914yes—
750C4⋊C4C23×D79116yes—
751C4⋊C4C23×D7918yes—
752C22⋊C4—798no—
753C22⋊C4—798no—
754C22⋊C4—798no—
755C22⋊C4—798no—
756C22⋊C4—798no—
757C22⋊C4—798no—
758C22⋊C4—798no—
759C22⋊C4—7916no—
760C22⋊C4—7916no—
761C22⋊C4—798no—
762C22⋊C4—798no—
763C22⋊C4C23×D79116yes—
764C22⋊C4C23×D79116yes—
765C22⋊C4C23×D7918yes—
766C42—794no—
767C42—794no—
768C42—794no—
769C42—798no—
770C42—7916no—
771C42C23×D7914yes—
772C42C23×D7918yes—
773C42C23×D79116yes—
774C23—24no—
775C23—24no—
776C23—24no—
777C23—794no—
778C23—792no—
779C23—794no—
780C23—1584no—
781C23—1584no—
782C23—1584no—
783C23—1582no—
784C23—1582no—
785C23C24×D7914yes—
786C23C24×D7911yescharacteristic
787Q8—216no—
788Q8—28no—
789Q8—31616no—
790Q8—31616no—
791Q8—1588no—
792Q8—15816no—
793D4—28no—
794D4—31616no—
795D4—15816no—
796D4—15816no—
797D4—1588no—
798C2×C4—28no—
799C2×C4—22no—
800C2×C4—24no—
801C2×C4—24no—
802C2×C4—24no—
803C2×C4—216no—
804C2×C4—31616no—
805C2×C4—31616no—
806C2×C4—31616no—
807C2×C4—794no—
808C2×C4—792no—
809C2×C4—792no—
810C2×C4—792no—
811C2×C4—794no—
812C2×C4—798no—
813C2×C4—794no—
814C2×C4—1588no—
815C2×C4—1584no—
816C2×C4—1588no—
817C2×C4—1584no—
818C2×C4—1582no—
819C2×C4—1582no—
820C2×C4—1584no—
821C2×C4—1582no—
822C2×C4—1588no—
823C2×C4—15816no—
824C2×C4—1588no—
825C2×C4#1457920714yes—
826C2×C4#1457920814yes—
827C2×C4C24×D7914yes—
828C2×C4C24×D7912yes—
829C2×C4C24×D7914yes—
830C2×C4C24×D7914yes—
831C2×C4C24×D7918yes—
832C2×C4C24×D7912yes—
833C2×C4C24×D7912yes—
834C22—24no—
835C22—24no—
836C22—24no—
837C22—48no—
838C22—3168no—
839C22—794no—
840C22—1584no—
841C22—1584no—
842C22—1584no—
843C22—1588no—
844C22—1582no—
845C22—1582no—
846C22C2×#1457920712yes—
847C222−1+4×D7912yes—
848C22C2×#1457920812yes—
849C22C25×D7911yescharacteristic
850C4—28no—
851C4—22no—
852C4—24no—
853C4—24no—
854C4—24no—
855C4—1584no—
856C4—1588no—
857C4—1584no—
858C4—1582no—
859C4—1582no—
860C4—1584no—
861C4—1582no—
862C4C2×#1457920714yes—
863C4C2×#1457920814yes—
864C2—44no—
865C2—3164no—
866C2—1584no—
867C2#2377783014yesdirect product factor
868C2C22×#1457920711yescharacteristic
869C2C2×2−1+4×D7911yescharacteristic
870C2C22×#1457920811yescharacteristic
subgroupG/H
centerC23C24×D79
commutator, cosocleC22×C79C26
FrattiniC22C25×D79
FittingC2×#556×C79C2
socleC23×C79C25
hypercenterC2×#556D79
hypocenterC79C2×#3552
LCSG ▷ C22×C79 ▷ C79
UCSC1 ◁ C23 ◁ C2×#556

Complements

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

NH ≅ G/Ntype
1. #23777830C2direct (N × H)
2. C2×#19099315C2semidirect
3. C2×#19099292C2semidirect
4. C2×#19099271C2semidirect
5. C2×#19099257C2semidirect
6. C2×Q8×D316C2semidirect
7. C2×#19099228C2semidirect
8. C2×#19099221C2semidirect
9. C2×#19099217C2semidirect
10. C2×#19099191C2semidirect
11. C2×#19099186C2semidirect
12. C2×#19099171C2semidirect
13. C2×#19099154C2semidirect
14. C2×#19099133C2semidirect
15. C2×C4⋊Q8×D79C2semidirect
16. C2×#19099100C2semidirect
17. C2×#19099095C2semidirect
18. C2×#556×C79C2semidirect
22. #19099315C22semidirect
23. #19099292C22semidirect
24. #19099271C22semidirect
25. #19099257C22semidirect
26. Q8×D316C22semidirect
27. #19099228C22semidirect
28. #19099221C22semidirect
29. #19099217C22semidirect
30. #19099191C22semidirect
31. #19099186C22semidirect
32. #19099171C22semidirect
33. #19099154C22semidirect
34. #19099133C22semidirect
42. C4⋊Q8×D79C22semidirect
43. #19099100C22semidirect
44. #19099095C22semidirect
92. #556×C79C22semidirect
430. C2×C79#3552semidirect
439. C2×#556D79semidirect
454. C79C2×#3552semidirect
460. #556C2×D79semidirect
867. C2#23777830direct (N × H)

Maximal subgroups

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

subgroupindex
#237778302
C2×#190993152
C2×#190992922
C2×#190992712
C2×#190992572
C2×Q8×D3162
C2×#190992282
C2×#190992212
C2×#190992172
C2×#190991912
C2×#190991862
C2×#190991712
C2×#190991542
C2×#190991332
C2×C4⋊Q8×D792
C2×#190991002
C2×#190990952
C2×#556×C792
C2×#355279