Finite Group Databasebeta

← C2×#23777153 #35196701

Subgroups — C2×#23777153 #35196701

Order 20224.

7206 conjugacy classes of subgroups.

The subgroup lattice has 904 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#23777153C2132yesmaximal, direct product factor
2C2×#19099281C212yesmaximal, complemented
3C2×#19099268C212yesmaximal, complemented
4C2×#19099253C214yesmaximal, complemented
5C2×#19099252C212yesmaximal, complemented
6C2×#19099248C212yesmaximal, complemented
7C2×#19099242C214yesmaximal, complemented
8C2×#19099194C211yesmaximal, characteristic, complemented
9C2×#19099178C212yesmaximal, complemented
10C2×#19099171C212yesmaximal, complemented
11C2×#19099134C211yesmaximal, characteristic, complemented
12C2×#19099117C212yesmaximal, complemented
13C2×#19099095C212yesmaximal, complemented
14C2×#19099070C211yesmaximal, characteristic
15C22×#14579141C211yesmaximal, characteristic, complemented
16C2×#19099040C211yesmaximal, characteristic, complemented
17C2×#117×D79C211yesmaximal, characteristic, complemented
18C2×#520×C79C211yesmaximal, characteristic, complemented
19C23×Dic158C2211yescharacteristic
20C23×C4×D79C2211yescharacteristic
21#19099281C22132yescomplemented
22#19099268C22132yescomplemented
23#19099253C22164yescomplemented
24#19099252C22132yescomplemented
25#19099248C22132yescomplemented
26#19099242C22164yescomplemented
27#19099194C22116yescomplemented
28#19099178C22132yescomplemented
29#19099171C22132yescomplemented
30#19099134C22116yescomplemented
31#19099117C22132yescomplemented
32C2×#14579160C2212yescomplemented
33C2×#14579160C2212yescomplemented
34C2×#14579159C2212yescomplemented
35#19099095C22132yescomplemented
36C2×#14579156C2214yes—
37C2×#14579155C2214yes—
38C2×#14579154C2214yescomplemented
39C2×#14579154C2214yescomplemented
40C2×#14579153C2214yescomplemented
41C2×#14579152C2212yescomplemented
42C2×#14579152C2212yescomplemented
43C2×#14579151C2214yescomplemented
44C2×#14579151C2214yescomplemented
45C2×#14579148C2212yescomplemented
46C2×#14579147C2214yes—
47#19099070C22116yes—
48C2×#14579144C2214yes—
49C2×#14579143C2214yes—
50C2×#14579142C2212yes—
51C2×#14579142C2214yes—
52C2×#14579141C2212yes—
53C2×#14579141C2212yes—
54C2×#14579141C2212yes—
55C2×#14579141C2212yes—
56C2×#14579141C22116yescomplemented
57C2×#14579140C2214yes—
58C2×#14579140C2214yescomplemented
59C2×#14579140C2212yescomplemented
60C2×#14579140C2212yescomplemented
61C2×#14579139C2214yes—
62C2×#14579137C2211yescharacteristic
63C2×#14579137C2211yescharacteristic
64C2×#14579132C2211yescharacteristic
65C2×#14579132C2211yescharacteristic
66C2×#14579129C2212yes—
67#19099040C22116yescomplemented
68C2×C4×Dic158C2212yescomplemented
69C2×C4×Dic158C2212yescomplemented
70C2×C4×Dic158C2214yescomplemented
71C2×#14579126C2212yescomplemented
72C2×#14579126C2212yescomplemented
73C2×C4×C22⋊D79C2212yes—
74C2×C4×C22⋊D79C2212yes—
75C2×C4×C22⋊D79C2214yes—
76C2×#14579120C2211yescharacteristic
77C2×#14579120C2211yescharacteristic
78C2×#14579120C2214yescomplemented
79C2×#14579119C2211yescharacteristic
80C2×#14579119C2211yescharacteristic
81C2×#14579118C2212yes—
82C2×#14579118C2214yes—
83C2×#14579117C2212yes—
84C2×#14579117C2214yes—
85#117×D79C22116yescomplemented
86C22×C4⋊Dic79C2212yes—
87C2×C4⋊C4×D79C2211yescharacteristic
88C2×C4⋊C4×D79C2211yescharacteristic
89C22×(C2×D79)⋊C4C2212yes—
90C2×C22⋊C4×D79C2212yes—
91C2×C42×D79C2212yes—
92C22×#41×C79C2211yescharacteristic
93#520×C79C22116yescomplemented
94C2×C4×Q8×C79C2212yescomplemented
95C2×C4×D4×C79C2214yes—
96C2×C4×D4×C79C2212yescomplemented
97C2×#117×C79C2211yescharacteristic
98C2×#117×C79C2212yescomplemented
99C22×C4⋊C4×C79C2211yescharacteristic
100C22×C4⋊C4×C79C2212yescomplemented
101C24×D79C2311yescharacteristic
102C22×Dic158—28no—
103C22×Dic158C2312yes—
104C22×Dic158C2312yes—
105C22×Dic158C2318yes—
106C22×Dic158C2314yes—
107C22×C22⋊D79C2312yes—
108C22×C22⋊D79C2312yes—
109C23×Dic79C2312yes—
110C23×Dic79C2311yescharacteristic
111C22×C4×D79—28no—
112C22×C4×D79C2311yescharacteristic
113C22×C4×D79C2312yes—
114C22×C4×D79C2311yescharacteristic
115C22×C4×D79C2318yes—
116C22×C4×D79C2311yescharacteristic
117C22×C4×D79C2311yescharacteristic
118C22×C4×D79C2312yes—
119#14579160C23116yescomplemented
120#14579160C23116yescomplemented
121#14579159C23116yescomplemented
122#14579156C23132yes—
123#14579155C23132yes—
124#14579154C23132yescomplemented
125#14579154C23132yescomplemented
126#14579153C23132yescomplemented
127#14579152C23116yescomplemented
128#14579152C23116yescomplemented
129#14579151C23132yescomplemented
130#14579151C23132yescomplemented
131#14579148C23116yescomplemented
132#14579147C23132yes—
133#14579144C23132yes—
134#14579143C23132yes—
135#14579142C23132yes—
136#14579142C23116yes—
137#14579141C23116yes—
138#14579141C23116yes—
139#14579141C23116yes—
140#14579141C23116yes—
141#14579140C23132yes—
142#14579140C23132yescomplemented
143#14579140C23116yescomplemented
144#14579140C23116yescomplemented
145#14579139C23132yes—
146#14579137C2318yes—
147#14579137C2318yes—
148#14579132C2318yes—
149#14579132C2318yes—
150#14579129C23116yes—
151C4×Dic158C23116yescomplemented
152C4×Dic158C23116yescomplemented
153C4×Dic158C23132yescomplemented
154#14579126C23116yescomplemented
155#14579126C23116yescomplemented
156C4×C22⋊D79C23132yes—
157C4×C22⋊D79C23116yes—
158C4×C22⋊D79C23116yes—
159#14579120C2318yes—
160#14579120C2318yes—
161#14579120C23132yescomplemented
162#14579119C2318yes—
163#14579119C2318yes—
164#14579118C23116yes—
165#14579118C23132yes—
166#14579117C23132yes—
167#14579117C23116yes—
168C2×C4⋊Dic79C23116yes—
169C2×C4⋊Dic79C2311yescharacteristic
170C2×C4⋊Dic79C2311yescharacteristic
171C2×C4⋊Dic79C2314yes—
172C2×C4⋊Dic79C2314yes—
173C2×C4⋊Dic79C2311yescharacteristic
174C2×C4⋊Dic79C2311yescharacteristic
175C2×C4⋊Dic79C2314yes—
176C2×Dic79⋊C4C2312yes—
177C2×Dic79⋊C4C2312yes—
178C2×Dic79⋊C4C2314yes—
179C2×Dic79⋊C4C2314yes—
180C2×Dic79⋊C4C2314yes—
181C2×Dic79⋊C4C2314yes—
182C2×Dic79⋊C4C2312yes—
183C2×Dic79⋊C4C2312yes—
184C2×Dic79⋊C4C2314yes—
185C2×Dic79⋊C4C2314yes—
186C4⋊C4×D79C2318yes—
187C4⋊C4×D79C2318yes—
188C2×C22⋊Dic79C2312yes—
189C2×C22⋊Dic79C2312yes—
190C2×C22⋊Dic79C2312yes—
191C2×C22⋊Dic79C2314yes—
192C2×C22⋊Dic79C2312yes—
193C2×C22⋊Dic79C2314yes—
194C2×(C2×D79)⋊C4C23116yes—
195C2×(C2×D79)⋊C4C2312yes—
196C2×(C2×D79)⋊C4C2312yes—
197C2×(C2×D79)⋊C4C2314yes—
198C2×(C2×D79)⋊C4C2314yes—
199C2×(C2×D79)⋊C4C2312yes—
200C2×(C2×D79)⋊C4C2312yes—
201C22⋊C4×D79C23116yes—
202C2×C4×Dic79C2312yes—
203C2×C4×Dic79C2312yes—
204C2×C4×Dic79C2312yes—
205C2×C4×Dic79C2314yes—
206C2×C4×Dic79C2314yes—
207C2×C4×Dic79C2312yes—
208C42×D79C23116yes—
209C2×#41×C79—28no—
210C2×#41×C79C2318yes—
211C22×Q8×C79C2311yescharacteristic
212C22×D4×C79C2312yes—
213C22×D4×C79C2311yescharacteristic
214C23×C4×C79C2312yes—
215C23×C4×C79C2312yes—
216C23×C4×C79C2314yes—
217C23×C4×C79C2311yescharacteristic
218C4×Q8×C79C23116yescomplemented
219C4×D4×C79C23132yes—
220C4×D4×C79C23116yescomplemented
221#117×C79C2318yes—
222#117×C79C23116yescomplemented
223C2×C4⋊C4×C79C2318yes—
224C2×C4⋊C4×C79C2312yes—
225C2×C4⋊C4×C79C2312yes—
226C2×C4⋊C4×C79C2311yescharacteristic
227C2×C4⋊C4×C79C2314yes—
228C2×C4⋊C4×C79C2311yescharacteristic
229C2×C4⋊C4×C79C23116yescomplemented
230C2×C22⋊C4×C79C2312yes—
231C2×C22⋊C4×C79C2314yes—
232C2×C42×C79C2312yes—
233C2×C42×C79C2314yes—
234C23×D79—24no—
235C23×D79—24no—
236C23×D79—42no—
237C23×D79C2411yescharacteristic
238C23×D79C2414yes—
239C23×D79C2411yescharacteristic
240C2×Dic158—28no—
241C2×Dic158—28no—
242C2×Dic158—232no—
243C2×Dic158—48no—
244C2×Dic158C2418yes—
245C2×Dic158C2418yes—
246C2×Dic158C24116yes—
247C2×C22⋊D79—28no—
248C2×C22⋊D79—44no—
249C2×C22⋊D79C2418yes—
250C2×C22⋊D79C2418yes—
251C22×Dic79—28no—
252C22×Dic79—24no—
253C22×Dic79C2412yes—
254C22×Dic79C2414yes—
255C22×Dic79C2412yes—
256C22×Dic79C2418yes—
257C22×Dic79C2411yescharacteristic
258C22×Dic79C2412yes—
259C22×Dic79C2412yes—
260C22×Dic79C2411yescharacteristic
261C22×Dic79C2414yes—
262C2×C4×D79—28no—
263C2×C4×D79—24no—
264C2×C4×D79—24no—
265C2×C4×D79—24no—
266C2×C4×D79—24no—
267C2×C4×D79—232no—
268C2×C4×D79—44no—
269C2×C4×D79C2414yes—
270C2×C4×D79C2418yes—
271C2×C4×D79C2414yes—
272C2×C4×D79C2414yes—
273C2×C4×D79C2414yes—
274C2×C4×D79C2418yes—
275C4⋊Dic79C2414yes—
276C4⋊Dic79C2414yes—
277C4⋊Dic79C24116yes—
278C4⋊Dic79C24116yes—
279C4⋊Dic79C2414yes—
280C4⋊Dic79C2414yes—
281C4⋊Dic79C24116yes—
282Dic79⋊C4C2418yes—
283Dic79⋊C4C2418yes—
284Dic79⋊C4C24116yes—
285Dic79⋊C4C24116yes—
286Dic79⋊C4C24116yes—
287Dic79⋊C4C24116yes—
288Dic79⋊C4C2418yes—
289Dic79⋊C4C2418yes—
290Dic79⋊C4C24116yes—
291Dic79⋊C4C24116yes—
292C22⋊Dic79C2418yes—
293C22⋊Dic79C2418yes—
294C22⋊Dic79C2418yes—
295C22⋊Dic79C24116yes—
296C22⋊Dic79C2418yes—
297C22⋊Dic79C24116yes—
298(C2×D79)⋊C4C2418yes—
299(C2×D79)⋊C4C2418yes—
300(C2×D79)⋊C4C24116yes—
301(C2×D79)⋊C4C24116yes—
302(C2×D79)⋊C4C2418yes—
303(C2×D79)⋊C4C2418yes—
304C4×Dic79C2418yes—
305C4×Dic79C2418yes—
306C4×Dic79C2418yes—
307C4×Dic79C24116yes—
308C4×Dic79C24116yes—
309C4×Dic79C2418yes—
310C24×C79C2412yes—
311C24×C79C2411yescharacteristic
312#41×C79—232no—
313C2×Q8×C79—24no—
314C2×Q8×C79C2414yes—
315C2×D4×C79—28no—
316C2×D4×C79—24no—
317C2×D4×C79C2418yes—
318C2×D4×C79C2414yes—
319C22×C4×C79—28no—
320C22×C4×C79—48no—
321C22×C4×C79—44no—
322C22×C4×C79#4118yes—
323C22×C4×C79C2414yes—
324C22×C4×C79C2412yes—
325C22×C4×C79C2412yes—
326C22×C4×C79C2412yes—
327C22×C4×C79C2418yes—
328C22×C4×C79C2418yes—
329C22×C4×C79C24116yes—
330C22×C4×C79C2411yescharacteristic
331C22×C4×C79C2411yescharacteristic
332C22×C4×C79C2414yes—
333C4⋊C4×C79C2418yes—
334C4⋊C4×C79C2418yes—
335C4⋊C4×C79C2414yes—
336C4⋊C4×C79C24116yes—
337C4⋊C4×C79C2414yes—
338C22⋊C4×C79C2418yes—
339C22⋊C4×C79C24116yes—
340C42×C79C2418yes—
341C42×C79C24116yes—
342C23×C79—22no—
343C23×C79—22no—
344C23×C79—24no—
345C23×C79—24no—
346C23×C79—24no—
347C23×C79C2×#4114yes—
348C23×C79C2514yes—
349C23×C79C2512yes—
350C23×C79C2511yescharacteristic
351C22×D79—22no—
352C22×D79—22no—
353C22×D79—28no—
354C22×D79—22no—
355C22×D79—22no—
356C22×D79—22no—
357C22×D79—28no—
358C22×D79—44no—
359C22×D79—416no—
360C22×D792−1+414yes—
361C22×D79C2512yes—
362C22×D79C2512yes—
363Q8×C79—28no—
364D4×C79—216no—
365D4×C79—28no—
366C2×C4×C79—24no—
367C2×C4×C79—24no—
368C2×C4×C79—24no—
369C2×C4×C79—28no—
370C2×C4×C79—216no—
371C2×C4×C79—48no—
372C2×C4×C79—416no—
373C2×C4×C79C2×#4114yes—
374C2×C4×C79C2×#4114yes—
375C2×C4×C79C2×#41116yes—
376C2×C4×C79C2514yes—
377C2×C4×C79C2514yes—
378C2×C4×C79C2514yes—
379C2×C4×C79C2518yes—
380C2×C4×C79C2512yes—
381C2×C4×C79C2512yes—
382C22⋊D79—216no—
383C22⋊D79—48no—
384C2×Dic79—28no—
385C2×Dic79—22no—
386C2×Dic79—22no—
387C2×Dic79—216no—
388C2×Dic79—28no—
389C2×Dic79—24no—
390C2×Dic79—24no—
391C2×Dic79—24no—
392C2×Dic79—24no—
393C2×Dic79C2512yes—
394C2×Dic79C2514yes—
395C2×Dic79C2514yes—
396C2×Dic79C2518yes—
397C2×Dic79C2514yes—
398C2×Dic79C2514yes—
399C2×Dic79C2512yes—
400C4×D79—216no—
401C4×D79—28no—
402C4×D79—28no—
403C4×D79—28no—
404C4×D79—28no—
405C4×D79—48no—
406Dic158—216no—
407Dic158—216no—
408Dic158—416no—
409C22×C79—22no—
410C22×C79—22no—
411C22×C79—28no—
412C22×C79—24no—
413C22×C79—24no—
414C22×C79—24no—
415C22×C79—48no—
416C22×C79C22×#4114yes—
417C22×C79C22×#4112yes—
418C22×C79C2×2−1+412yes—
419C22×C79#58512yes—
420C22×C79C2611yescharacteristic
421C2×D79—22no—
422C2×D79—22no—
423C2×D79—28no—
424C2×D79—22no—
425C2×D79—22no—
426C2×D79—22no—
427C2×D79—416no—
428C2×D79—44no—
429C2×D79C2×2−1+414yes—
430C4×C79—24no—
431C4×C79—24no—
432C4×C79—28no—
433C4×C79—24no—
434C4×C79C22×#4114yes—
435C4×C79C22×#4114yes—
436Dic79—28no—
437Dic79—22no—
438Dic79—22no—
439Dic79—24no—
440Dic79—24no—
441Dic79—24no—
442Dic79—24no—
443C2×#3495—791nomaximal, Sylow
444C2×C79—24no—
445C2×C79—44no—
446C2×C79#349514yescomplemented
447C2×C79C23×#4111yescharacteristic
448C2×C79C22×2−1+411yescharacteristic
449C2×C79C2×#58511yescharacteristic
450D79—24no—
451D79—42no—
452#3495—7932no—
453C2×#556—792no—
454C2×#554—792no—
455C2×#552—794no—
456C2×#552—792no—
457C2×#552—792no—
458C2×#551—794no—
459C2×#544—791no—
460C2×#542—792no—
461C2×#541—792no—
462C2×#536—791no—
463C2×#533—792no—
464C2×#529—792no—
465C2×#525—791no—
466C22×C22⋊Q8—791no—
467C2×#520D7911yescharacteristic, complemented
468C2×#519—791no—
469C22×#117—791no—
470C79C2×#349511yescharacteristic, complemented, Sylow
471C22×#41C2×D7911yescharacteristic
472C23×Q8—791no—
473C24×C4—791no—
474#556—7932no—
475#554—7932no—
476#552—7964no—
477#552—7932no—
478#552—7932no—
479#551—7964no—
480#544—7916no—
481#542—7932no—
482#541—7932no—
483#536—7916no—
484#533—7932no—
485C2×C4⋊Q8—792no—
486C2×C4⋊Q8—792no—
487C2×C4⋊Q8—792no—
488#529—7932no—
489C2×#126—794no—
490C2×#126—794no—
491C2×#126—794no—
492C2×#126—794no—
493C2×#125—792no—
494C2×#125—794no—
495C2×#125—794no—
496C2×#125—792no—
497C2×#125—794no—
498C2×#124—792no—
499C2×#124—794no—
500#525—7916no—
501C2×#123—792no—
502C2×#123—794no—
503C2×#123—794no—
504C2×#123—794no—
505C2×C22⋊Q8—791no—
506C2×C22⋊Q8—791no—
507C2×C22⋊Q8—792no—
508C2×C22⋊Q8—792no—
509C2×C22⋊Q8—794no—
510C2×C22⋊Q8—794no—
511C2×C22⋊Q8—792no—
512C2×C22⋊Q8—792no—
513C2×C22⋊Q8—792no—
514C2×C22⋊Q8—792no—
515C2×C22⋊Q8—7916no—
516C2×C22⋊Q8—794no—
517C2×#121—791no—
518C2×#121—791no—
519C2×#120—792no—
520#520C2×D79116yescomplemented
521#519—7916no—
522C2×C4×Q8—792no—
523C2×C4×Q8—792no—
524C2×C4×Q8—792no—
525C2×C4×Q8—792no—
526C2×C4×Q8—794no—
527C2×C4×Q8C2×D7912yescomplemented
528C2×C4×D4—792no—
529C2×C4×D4—792no—
530C2×C4×D4—794no—
531C2×C4×D4C2×D7914yes—
532C2×C4×D4C2×D7912yescomplemented
533C2×#117—791no—
534C2×#117—791no—
535C2×#117—794no—
536C2×#117—7916no—
537C2×#117—791no—
538C2×#117—791no—
539C2×#117—792no—
540C2×#117—794no—
541C2×#117—792no—
542C2×#117—794no—
543C2×#117C2×D7911yescharacteristic
544C2×#117C2×D7912yescomplemented
545C22×C4⋊C4—792no—
546C22×C4⋊C4—791no—
547C22×C4⋊C4—791no—
548C22×C4⋊C4C2×D7911yescharacteristic
549C22×C4⋊C4C2×D7912yescomplemented
550C22×C22⋊C4—792no—
551C22×C22⋊C4—792no—
552C22×C42—792no—
553C25—791no—
554C2×#41—28no—
555C2×#41C22×D7918yes—
556C22×Q8—794no—
557C22×Q8—792no—
558C22×Q8—792no—
559C22×Q8—798no—
560C22×Q8—1588no—
561C22×Q8C22×D7911yescharacteristic
562C22×D4—792no—
563C22×D4—792no—
564C22×D4C22×D7912yes—
565C22×D4C22×D7911yescharacteristic
566C23×C4—792no—
567C23×C4—792no—
568C23×C4—791no—
569C23×C4—792no—
570C23×C4—791no—
571C23×C4—791no—
572C23×C4—791no—
573C23×C4—798no—
574C23×C4—791no—
575C23×C4—1588no—
576C23×C4C22×D7912yes—
577C23×C4C22×D7912yes—
578C23×C4C22×D7914yes—
579C23×C4C22×D7911yescharacteristic
580C4⋊Q8—7916no—
581C4⋊Q8—7916no—
582C4⋊Q8—7916no—
583#126—7932no—
584#126—7932no—
585#126—7932no—
586#126—7932no—
587#125—7916no—
588#125—7932no—
589#125—7932no—
590#125—7916no—
591#125—7932no—
592#124—7916no—
593#124—7932no—
594#123—7916no—
595#123—7932no—
596#123—7932no—
597#123—7932no—
598C22⋊Q8—798no—
599C22⋊Q8—798no—
600C22⋊Q8—7916no—
601C22⋊Q8—7916no—
602C22⋊Q8—7932no—
603C22⋊Q8—7932no—
604C22⋊Q8—7916no—
605C22⋊Q8—7916no—
606C22⋊Q8—7916no—
607C22⋊Q8—7916no—
608C22⋊Q8—7932no—
609#121—798no—
610#121—798no—
611#120—7916no—
612C4×Q8—7916no—
613C4×Q8—7916no—
614C4×Q8—7916no—
615C4×Q8—7916no—
616C4×Q8—7932no—
617C4×Q8C22×D79116yescomplemented
618C4×D4—7916no—
619C4×D4—7916no—
620C4×D4—7932no—
621C4×D4C22×D79132yes—
622C4×D4C22×D79116yescomplemented
623#117—798no—
624#117—798no—
625#117—7932no—
626#117—798no—
627#117—798no—
628#117—7916no—
629#117—7932no—
630#117—7916no—
631#117—7932no—
632#117C22×D7918yes—
633#117C22×D79116yescomplemented
634C2×C4⋊C4—792no—
635C2×C4⋊C4—791no—
636C2×C4⋊C4—791no—
637C2×C4⋊C4—792no—
638C2×C4⋊C4—794no—
639C2×C4⋊C4—794no—
640C2×C4⋊C4—7916no—
641C2×C4⋊C4—791no—
642C2×C4⋊C4—791no—
643C2×C4⋊C4—794no—
644C2×C4⋊C4—794no—
645C2×C4⋊C4—794no—
646C2×C4⋊C4—794no—
647C2×C4⋊C4—794no—
648C2×C4⋊C4—792no—
649C2×C4⋊C4—792no—
650C2×C4⋊C4—794no—
651C2×C4⋊C4—794no—
652C2×C4⋊C4—798no—
653C2×C4⋊C4—798no—
654C2×C4⋊C4C22×D7911yescharacteristic
655C2×C4⋊C4C22×D7911yescharacteristic
656C2×C4⋊C4C22×D7912yes—
657C2×C4⋊C4C22×D7912yes—
658C2×C4⋊C4C22×D7918yes—
659C2×C4⋊C4C22×D7914yes—
660C2×C4⋊C4C22×D79116yescomplemented
661C2×C22⋊C4—792no—
662C2×C22⋊C4—792no—
663C2×C22⋊C4—792no—
664C2×C22⋊C4—794no—
665C2×C22⋊C4—792no—
666C2×C22⋊C4—794no—
667C2×C22⋊C4—792no—
668C2×C22⋊C4—792no—
669C2×C22⋊C4—794no—
670C2×C22⋊C4—794no—
671C2×C22⋊C4—7916no—
672C2×C22⋊C4—792no—
673C2×C22⋊C4—792no—
674C2×C22⋊C4—7916no—
675C2×C22⋊C4C22×D7912yes—
676C2×C22⋊C4C22×D7914yes—
677C2×C42—792no—
678C2×C42—794no—
679C2×C42—794no—
680C2×C42—792no—
681C2×C42—792no—
682C2×C42—792no—
683C2×C42—7916no—
684C2×C42C22×D7912yes—
685C2×C42C22×D7914yes—
686C24—3162no—
687C24—794no—
688C24—791no—
689C24—791no—
690C24—1584no—
691C24—1584no—
692C24C23×D7912yes—
693C24C23×D7911yescharacteristic
694#41—232no—
695C2×Q8—24no—
696C2×Q8—3168no—
697C2×Q8—7916no—
698C2×Q8—798no—
699C2×Q8—798no—
700C2×Q8—1588no—
701C2×Q8—1588no—
702C2×Q8—15832no—
703C2×Q8C23×D7914yes—
704C2×D4—28no—
705C2×D4—24no—
706C2×D4—3164no—
707C2×D4—798no—
708C2×D4—798no—
709C2×D4—1588no—
710C2×D4C23×D7918yes—
711C2×D4C23×D7914yes—
712C22×C4—28no—
713C22×C4—48no—
714C22×C4—44no—
715C22×C4—3164no—
716C22×C4—798no—
717C22×C4—798no—
718C22×C4—794no—
719C22×C4—791no—
720C22×C4—792no—
721C22×C4—792no—
722C22×C4—792no—
723C22×C4—792no—
724C22×C4—794no—
725C22×C4—791no—
726C22×C4—794no—
727C22×C4—798no—
728C22×C4—794no—
729C22×C4—794no—
730C22×C4—794no—
731C22×C4—1588no—
732C22×C4—1584no—
733C22×C4—1588no—
734C22×C4—1584no—
735C22×C4—1584no—
736C22×C4—1584no—
737C22×C4—1584no—
738C22×C4—15832no—
739C22×C4#1192962418yes—
740C22×C4C23×D7918yes—
741C22×C4C23×D7912yes—
742C22×C4C23×D7912yes—
743C22×C4C23×D7912yes—
744C22×C4C23×D7914yes—
745C22×C4C23×D7918yes—
746C22×C4C23×D79116yes—
747C22×C4C23×D7914yes—
748C22×C4C23×D7911yescharacteristic
749C22×C4C23×D7911yescharacteristic
750C4⋊C4—798no—
751C4⋊C4—798no—
752C4⋊C4—7916no—
753C4⋊C4—7916no—
754C4⋊C4—7916no—
755C4⋊C4—7916no—
756C4⋊C4—798no—
757C4⋊C4—798no—
758C4⋊C4—7916no—
759C4⋊C4—7916no—
760C4⋊C4—794no—
761C4⋊C4—794no—
762C4⋊C4—7916no—
763C4⋊C4—7916no—
764C4⋊C4—794no—
765C4⋊C4—794no—
766C4⋊C4—7916no—
767C4⋊C4C23×D7914yes—
768C4⋊C4C23×D7914yes—
769C4⋊C4C23×D7918yes—
770C4⋊C4C23×D7918yes—
771C4⋊C4C23×D79116yes—
772C22⋊C4—798no—
773C22⋊C4—798no—
774C22⋊C4—798no—
775C22⋊C4—7916no—
776C22⋊C4—798no—
777C22⋊C4—7916no—
778C22⋊C4—798no—
779C22⋊C4—798no—
780C22⋊C4—7916no—
781C22⋊C4—7916no—
782C22⋊C4—798no—
783C22⋊C4—798no—
784C22⋊C4C23×D7918yes—
785C22⋊C4C23×D79116yes—
786C42—798no—
787C42—798no—
788C42—798no—
789C42—7916no—
790C42—7916no—
791C42—798no—
792C42C23×D7918yes—
793C42C23×D79116yes—
794C23—22no—
795C23—22no—
796C23—24no—
797C23—24no—
798C23—24no—
799C23—31616no—
800C23—3164no—
801C23—794no—
802C23—792no—
803C23—792no—
804C23—1588no—
805C23—1582no—
806C23—1582no—
807C23—1588no—
808C23—1582no—
809C23—1582no—
810C23—1582no—
811C23C2×#1192962414yes—
812C23C24×D7914yes—
813C23C24×D7912yes—
814C23C24×D7911yescharacteristic
815Q8—28no—
816Q8—31616no—
817Q8—15816no—
818Q8—15816no—
819D4—216no—
820D4—28no—
821D4—3168no—
822D4—15816no—
823C2×C4—24no—
824C2×C4—24no—
825C2×C4—28no—
826C2×C4—24no—
827C2×C4—216no—
828C2×C4—416no—
829C2×C4—48no—
830C2×C4—3168no—
831C2×C4—792no—
832C2×C4—794no—
833C2×C4—794no—
834C2×C4—794no—
835C2×C4—798no—
836C2×C4—794no—
837C2×C4—792no—
838C2×C4—15816no—
839C2×C4—1584no—
840C2×C4—1584no—
841C2×C4—1584no—
842C2×C4—1584no—
843C2×C4—1588no—
844C2×C4—1582no—
845C2×C4—1582no—
846C2×C4—15816no—
847C2×C4—1588no—
848C2×C4—1588no—
849C2×C4—1588no—
850C2×C4—1588no—
851C2×C4—1588no—
852C2×C4C2×#1192962414yes—
853C2×C4C2×#1192962414yes—
854C2×C4C2×#11929624116yes—
855C2×C4C24×D7914yes—
856C2×C4C24×D7914yes—
857C2×C4C24×D7914yes—
858C2×C4C24×D7918yes—
859C2×C4C24×D7912yes—
860C2×C4C24×D7912yes—
861C22—28no—
862C22—22no—
863C22—22no—
864C22—24no—
865C22—24no—
866C22—24no—
867C22—48no—
868C22—31616no—
869C22—3164no—
870C22—794no—
871C22—1582no—
872C22—1582no—
873C22—1582no—
874C22—1588no—
875C22—1582no—
876C22—1582no—
877C22C22×#1192962414yes—
878C22C22×#1192962412yes—
879C222−1+4×D7912yes—
880C22#1909939812yes—
881C22C25×D7911yescharacteristic
882C4—24no—
883C4—24no—
884C4—24no—
885C4—28no—
886C4—1582no—
887C4—1582no—
888C4—1588no—
889C4—1584no—
890C4—1584no—
891C4—1584no—
892C4—1584no—
893C4C22×#1192962414yes—
894C4C22×#1192962414yes—
895C2—24no—
896C2—44no—
897C2—3162no—
898C2—1584no—
899C2#2377715314yesdirect product factor
900C2C23×#1192962411yescharacteristic
901C2C2×2−1+4×D7911yescharacteristic
902C2C2×#1909939811yescharacteristic
subgroupG/H
centerC23C24×D79
commutator, cosocleC22×C79C26
FrattiniC22C25×D79
FittingC2×#520×C79C2
socleC23×C79C25
prime radicalC2×#19099070C2
hypercenterC2×#520D79
hypocenterC79C2×#3495
LCSG ▷ C22×C79 ▷ C79
UCSC1 ◁ C23 ◁ C2×#520

Complements

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

NH ≅ G/Ntype
1. #23777153C2direct (N × H)
2. C2×#19099281C2semidirect
3. C2×#19099268C2semidirect
4. C2×#19099253C2semidirect
5. C2×#19099252C2semidirect
6. C2×#19099248C2semidirect
7. C2×#19099242C2semidirect
8. C2×#19099194C2semidirect
9. C2×#19099178C2semidirect
10. C2×#19099171C2semidirect
11. C2×#19099134C2semidirect
12. C2×#19099117C2semidirect
13. C2×#19099095C2semidirect
15. C22×#14579141C2semidirect
16. C2×#19099040C2semidirect
17. C2×#117×D79C2semidirect
18. C2×#520×C79C2semidirect
21. #19099281C22semidirect
22. #19099268C22semidirect
23. #19099253C22semidirect
24. #19099252C22semidirect
25. #19099248C22semidirect
26. #19099242C22semidirect
27. #19099194C22semidirect
28. #19099178C22semidirect
29. #19099171C22semidirect
30. #19099134C22semidirect
31. #19099117C22semidirect
32. C2×#14579160C22semidirect
33. C2×#14579160C22semidirect
34. C2×#14579159C22semidirect
35. #19099095C22semidirect
38. C2×#14579154C22semidirect
39. C2×#14579154C22semidirect
40. C2×#14579153C22semidirect
41. C2×#14579152C22semidirect
42. C2×#14579152C22semidirect
43. C2×#14579151C22semidirect
44. C2×#14579151C22semidirect
45. C2×#14579148C22semidirect
56. C2×#14579141C22semidirect
58. C2×#14579140C22semidirect
59. C2×#14579140C22semidirect
60. C2×#14579140C22semidirect
67. #19099040C22semidirect
68. C2×C4×Dic158C22semidirect
69. C2×C4×Dic158C22semidirect
70. C2×C4×Dic158C22semidirect
71. C2×#14579126C22semidirect
72. C2×#14579126C22semidirect
78. C2×#14579120C22semidirect
85. #117×D79C22semidirect
93. #520×C79C22semidirect
94. C2×C4×Q8×C79C22semidirect
96. C2×C4×D4×C79C22semidirect
98. C2×#117×C79C22semidirect
100. C22×C4⋊C4×C79C22semidirect
119. #14579160C23semidirect
120. #14579160C23semidirect
121. #14579159C23semidirect
124. #14579154C23semidirect
125. #14579154C23semidirect
126. #14579153C23semidirect
127. #14579152C23semidirect
128. #14579152C23semidirect
129. #14579151C23semidirect
130. #14579151C23semidirect
131. #14579148C23semidirect
142. #14579140C23semidirect
143. #14579140C23semidirect
144. #14579140C23semidirect
151. C4×Dic158C23semidirect
152. C4×Dic158C23semidirect
153. C4×Dic158C23semidirect
154. #14579126C23semidirect
155. #14579126C23semidirect
161. #14579120C23semidirect
218. C4×Q8×C79C23semidirect
220. C4×D4×C79C23semidirect
222. #117×C79C23semidirect
229. C2×C4⋊C4×C79C23semidirect
446. C2×C79#3495semidirect
467. C2×#520D79semidirect
470. C79C2×#3495semidirect
520. #520C2×D79semidirect
527. C2×C4×Q8C2×D79semidirect
532. C2×C4×D4C2×D79semidirect
544. C2×#117C2×D79semidirect
549. C22×C4⋊C4C2×D79semidirect
617. C4×Q8C22×D79semidirect
622. C4×D4C22×D79semidirect
633. #117C22×D79semidirect
660. C2×C4⋊C4C22×D79semidirect
899. C2#23777153direct (N × H)

Maximal subgroups

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

subgroupindex
#237771532
C2×#190992812
C2×#190992682
C2×#190992532
C2×#190992522
C2×#190992482
C2×#190992422
C2×#190991942
C2×#190991782
C2×#190991712
C2×#190991342
C2×#190991172
C2×#190990952
C2×#190990702
C22×#145791412
C2×#190990402
C2×#117×D792
C2×#520×C792
C2×#349579