Finite Group Databasebeta

← C2×#23777264 #35196347

Subgroups — C2×#23777264 #35196347

Order 20224.

7130 conjugacy classes of subgroups.

The subgroup lattice has 880 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#23777264C2132yesmaximal, direct product factor
2C2×#19099295C212yesmaximal, complemented
3C2×#19099288C212yesmaximal, complemented
4C2×#19099287C212yesmaximal, complemented
5C2×#19099284C212yesmaximal, complemented
6C2×#19099282C212yesmaximal, complemented
7C2×#19099271C212yesmaximal, complemented
8C2×#19099255C212yesmaximal, complemented
9C2×#19099247C212yesmaximal, complemented
10C2×#19099157C214yesmaximal, complemented
11C2×#19099137C211yesmaximal, characteristic, complemented
12C2×#19099116C211yesmaximal, characteristic, complemented
13C2×#19099109C211yesmaximal, characteristic
14C2×#19099090C214yesmaximal, complemented
15C2×#19099046C211yesmaximal, characteristic, complemented
16C2×#19099043C211yesmaximal, characteristic, complemented
17C22×Q8×Dic79C211yesmaximal, characteristic, complemented
18C2×#536×C79C211yesmaximal, characteristic, complemented
19C22×#11929624C2211yescharacteristic
20#19099295C22132yescomplemented
21#19099288C22132yescomplemented
22#19099287C22132yescomplemented
23#19099284C22132yescomplemented
24#19099282C22132yescomplemented
25#19099271C22132yescomplemented
26#19099255C22132yescomplemented
27#19099247C22132yescomplemented
28#19099157C22164yescomplemented
29#19099137C22116yescomplemented
30#19099116C22116yescomplemented
31#19099109C22116yes—
32C2×#14579160C2211yescharacteristic
33C2×#14579160C2211yescharacteristic
34C2×#14579159C2211yescharacteristic
35C2×#14579159C2212yes—
36C2×#14579157C2211yescharacteristic
37#19099090C22164yescomplemented
38C2×#14579156C2214yes—
39C2×#14579156C2214yes—
40C2×#14579154C2214yes—
41C2×#14579154C2214yes—
42C2×#14579152C2211yescharacteristic
43C2×#14579152C2211yescharacteristic
44C2×#14579152C2214yes—
45C2×#14579151C2214yes—
46C2×#14579151C2214yes—
47C2×#14579150C2211yescharacteristic
48C2×#14579150C2212yes—
49C2×#14579148C2211yescharacteristic
50C2×#14579147C2214yes—
51C2×#14579145C2214yes—
52C2×#14579144C2214yes—
53C2×#14579143C2214yes—
54C2×#14579141C2214yes—
55C2×#14579138C2212yes—
56C2×#14579138C2214yes—
57C2×#14579138C2212yes—
58C2×#14579137C2212yes—
59C2×#14579137C2212yes—
60C2×#14579133C2212yes—
61C2×#14579133C2212yes—
62#19099046C22116yescomplemented
63#19099043C22116yescomplemented
64C2×Q8×Dic79C2212yes—
65C2×Q8×Dic79C2212yes—
66C2×Q8×Dic79C2212yes—
67C2×Q8×Dic79C2212yes—
68C2×Q8×Dic79C2212yes—
69C2×Q8×Dic79C22116yescomplemented
70C2×C4×Dic158C2212yes—
71C2×C4×Dic158C2212yes—
72C2×C4×Dic158C2212yes—
73C2×#14579126C2214yes—
74C2×C4×D316C2212yes—
75C2×D4×Dic79C2214yes—
76C2×D4×Dic79C2212yes—
77C2×C4×C22⋊D79C2212yes—
78C2×C4×C22⋊D79C2212yes—
79C2×(C22⋊D79)⋊C4C2214yes—
80C2×(C22⋊D79)⋊C4C2214yes—
81C2×#14579120C2212yes—
82C2×#14579120C2211yescharacteristic
83C2×#14579119C2212yes—
84C2×#14579119C2214yes—
85C2×#14579117C2214yes—
86C22×C4⋊Dic79C2211yescharacteristic
87C22×C4⋊Dic79C2212yes—
88C22×C4⋊Dic79C2212yes—
89C2×C4⋊C4×D79C2212yes—
90C22×C4×Dic79C2212yes—
91C22×C4×Dic79C2211yescharacteristic
92C22×#41×C79C2211yescharacteristic
93C23×Q8×C79C2211yescharacteristic
94#536×C79C22116yescomplemented
95C2×C4⋊Q8×C79C2212yes—
96C2×#124×C79C2212yes—
97C2×#123×C79C2214yes—
98C2×C22⋊Q8×C79C2212yes—
99C2×C22⋊Q8×C79C2212yes—
100C2×#117×C79C2211yescharacteristic
101C2×#11929624—28no—
102C2×#11929624C2318yes—
103C22×Dic158C2312yes—
104C22×Dic158C2311yescharacteristic
105C22×Dic158C2312yes—
106C22×D316C2311yescharacteristic
107C22×C22⋊D79C2312yes—
108C22×C22⋊D79C2312yes—
109C22×C22⋊D79C2312yes—
110C23×Dic79C2311yescharacteristic
111C23×Dic79C2312yes—
112C23×Dic79C2311yescharacteristic
113C23×Dic79C2314yes—
114C22×C4×D79C2312yes—
115C22×C4×D79C2314yes—
116#14579160C2318yes—
117#14579160C2318yes—
118#14579159C23116yes—
119#14579159C2318yes—
120#14579157C2318yes—
121#14579156C23132yes—
122#14579156C23132yes—
123#14579154C23132yes—
124#14579154C23132yes—
125#14579152C23132yes—
126#14579152C2318yes—
127#14579152C2318yes—
128#14579151C23132yes—
129#14579151C23132yes—
130#14579150C23116yes—
131#14579150C2318yes—
132#14579148C2318yes—
133#14579147C23132yes—
134#14579145C23132yes—
135#14579144C23132yes—
136#14579143C23132yes—
137#14579141C23132yes—
138#14579138C23116yes—
139#14579138C23132yes—
140#14579138C23116yes—
141#14579137C23116yes—
142#14579137C23116yes—
143#14579133C23116yes—
144#14579133C23116yes—
145Q8×Dic79C23116yes—
146Q8×Dic79C23116yes—
147Q8×Dic79C23116yes—
148Q8×Dic79C23116yes—
149Q8×Dic79C23116yes—
150C4×Dic158C23116yes—
151C4×Dic158C23116yes—
152C4×Dic158C23116yes—
153#14579126C23132yes—
154C4×D316C23116yes—
155D4×Dic79C23132yes—
156D4×Dic79C23116yes—
157C4×C22⋊D79C23116yes—
158C4×C22⋊D79C23116yes—
159(C22⋊D79)⋊C4C23132yes—
160(C22⋊D79)⋊C4C23132yes—
161#14579120C2318yes—
162#14579120C23116yes—
163#14579119C23132yes—
164#14579119C23116yes—
165#14579117C23132yes—
166C2×C4⋊Dic79C23116yes—
167C2×C4⋊Dic79C23116yes—
168C2×C4⋊Dic79C2312yes—
169C2×C4⋊Dic79C2311yescharacteristic
170C2×C4⋊Dic79C2312yes—
171C2×C4⋊Dic79C2314yes—
172C2×C4⋊Dic79C2314yes—
173C2×C4⋊Dic79C2314yes—
174C2×C4⋊Dic79C2318yes—
175C2×C4⋊Dic79C2312yes—
176C2×C4⋊Dic79C2311yescharacteristic
177C2×C4⋊Dic79C2312yes—
178C2×Dic79⋊C4C2314yes—
179C2×Dic79⋊C4C2312yes—
180C2×Dic79⋊C4C2314yes—
181C2×Dic79⋊C4C2312yes—
182C2×Dic79⋊C4C2312yes—
183C2×Dic79⋊C4C2312yes—
184C2×Dic79⋊C4C2314yes—
185C2×Dic79⋊C4C2312yes—
186C2×Dic79⋊C4C2312yes—
187C4⋊C4×D79C23116yes—
188C2×C22⋊Dic79C2312yes—
189C2×C22⋊Dic79C2312yes—
190C2×C22⋊Dic79C2314yes—
191C2×C22⋊Dic79C2312yes—
192C2×(C2×D79)⋊C4C2312yes—
193C2×(C2×D79)⋊C4C2314yes—
194C2×(C2×D79)⋊C4C2314yes—
195C2×(C2×D79)⋊C4C2314yes—
196C2×(C2×D79)⋊C4C2312yes—
197C2×C4×Dic79C2314yes—
198C2×C4×Dic79C2314yes—
199C2×C4×Dic79C2311yescharacteristic
200C2×C4×Dic79C2311yescharacteristic
201C2×C4×Dic79C2311yescharacteristic
202C2×C4×Dic79C2311yescharacteristic
203C2×C4×Dic79C23116yes—
204C2×C4×Dic79C2318yes—
205C2×C4×Dic79C2314yes—
206C2×C4×Dic79C2314yes—
207C2×C4×Dic79C2312yes—
208C2×#41×C79—28no—
209C2×#41×C79C2318yes—
210C22×Q8×C79—28no—
211C22×Q8×C79C2318yes—
212C22×Q8×C79C2312yes—
213C22×Q8×C79C2312yes—
214C22×Q8×C79C2311yescharacteristic
215C22×D4×C79C2312yes—
216C22×D4×C79C2311yescharacteristic
217C23×C4×C79C2312yes—
218C23×C4×C79C2312yes—
219C23×C4×C79C2311yescharacteristic
220C4⋊Q8×C79C23116yes—
221#124×C79C23116yes—
222#123×C79C23132yes—
223C22⋊Q8×C79C23116yes—
224C22⋊Q8×C79C23116yes—
225#117×C79C2318yes—
226C2×C4⋊C4×C79C2311yescharacteristic
227C2×C4⋊C4×C79C2311yescharacteristic
228C2×C4⋊C4×C79C2314yes—
229C2×C4⋊C4×C79C2314yes—
230C2×C22⋊C4×C79C2312yes—
231C2×C22⋊C4×C79C2314yes—
232C2×C22⋊C4×C79C2314yes—
233C2×C42×C79C2312yes—
234C23×D79C2412yes—
235#11929624—232no—
236C2×Dic158—28no—
237C2×Dic158—24no—
238C2×Dic158—44no—
239C2×Dic158C2414yes—
240C2×Dic158C2418yes—
241C2×Dic158C2418yes—
242C2×D316—24no—
243C2×D316C2414yes—
244C2×C22⋊D79—28no—
245C2×C22⋊D79—28no—
246C2×C22⋊D79—44no—
247C2×C22⋊D79C2418yes—
248C2×C22⋊D79C2418yes—
249C2×C22⋊D79C2418yes—
250C22×Dic79—24no—
251C22×Dic79—44no—
252C22×Dic79—42no—
253C22×Dic79—48no—
254C22×Dic79C2411yescharacteristic
255C22×Dic79C2412yes—
256C22×Dic79C2412yes—
257C22×Dic79C2412yes—
258C22×Dic79C2411yescharacteristic
259C22×Dic79C2414yes—
260C22×Dic79C2414yes—
261C22×Dic79C2411yescharacteristic
262C22×Dic79C2418yes—
263C22×Dic79C2414yes—
264C22×Dic79C24116yes—
265C22×Dic79C2411yescharacteristic
266C2×C4×D79—28no—
267C2×C4×D79—48no—
268C2×C4×D79C2418yes—
269C2×C4×D79C24116yes—
270C4⋊Dic79C2418yes—
271C4⋊Dic79C2414yes—
272C4⋊Dic79C2418yes—
273C4⋊Dic79C24116yes—
274C4⋊Dic79C24116yes—
275C4⋊Dic79C24116yes—
276C4⋊Dic79C2418yes—
277C4⋊Dic79C2414yes—
278C4⋊Dic79C2418yes—
279Dic79⋊C4C24116yes—
280Dic79⋊C4C2418yes—
281Dic79⋊C4C24116yes—
282Dic79⋊C4C2418yes—
283Dic79⋊C4C2418yes—
284Dic79⋊C4C2418yes—
285Dic79⋊C4C24116yes—
286Dic79⋊C4C2418yes—
287Dic79⋊C4C2418yes—
288C22⋊Dic79C2418yes—
289C22⋊Dic79C2418yes—
290C22⋊Dic79C24116yes—
291C22⋊Dic79C2418yes—
292(C2×D79)⋊C4C2418yes—
293(C2×D79)⋊C4C24116yes—
294(C2×D79)⋊C4C24116yes—
295(C2×D79)⋊C4C24116yes—
296(C2×D79)⋊C4C2418yes—
297C4×Dic79C24116yes—
298C4×Dic79C24116yes—
299C4×Dic79C2414yes—
300C4×Dic79C2414yes—
301C4×Dic79C2414yes—
302C4×Dic79C2414yes—
303C4×Dic79C24116yes—
304C4×Dic79C24116yes—
305C4×Dic79C2418yes—
306C24×C79C2412yes—
307C24×C79C2411yescharacteristic
308#41×C79—232no—
309C2×Q8×C79—28no—
310C2×Q8×C79—28no—
311C2×Q8×C79—232no—
312C2×Q8×C79—24no—
313C2×Q8×C79C2418yes—
314C2×Q8×C79C2418yes—
315C2×Q8×C79C2414yes—
316C2×D4×C79—28no—
317C2×D4×C79—24no—
318C2×D4×C79C2418yes—
319C2×D4×C79C2414yes—
320C22×C4×C79—28no—
321C22×C4×C79—28no—
322C22×C4×C79#4118yes—
323C22×C4×C79C2412yes—
324C22×C4×C79C2412yes—
325C22×C4×C79C2414yes—
326C22×C4×C79C2412yes—
327C22×C4×C79C2418yes—
328C22×C4×C79C2418yes—
329C22×C4×C79C2411yescharacteristic
330C22×C4×C79C2414yes—
331C22×C4×C79C2411yescharacteristic
332C4⋊C4×C79C2414yes—
333C4⋊C4×C79C2414yes—
334C4⋊C4×C79C24116yes—
335C4⋊C4×C79C24116yes—
336C22⋊C4×C79C2418yes—
337C22⋊C4×C79C24116yes—
338C22⋊C4×C79C24116yes—
339C42×C79C2418yes—
340C23×C79—22no—
341C23×C79—22no—
342C23×C79—24no—
343C23×C79—24no—
344C23×C79—24no—
345C23×C79C2×#4114yes—
346C23×C79C2514yes—
347C23×C79C2512yes—
348C23×C79C2511yescharacteristic
349C22×D79—24no—
350C22×D79—24no—
351C22×D79—24no—
352C22×D79C2514yes—
353Q8×C79—216no—
354Q8×C79—216no—
355Q8×C79—28no—
356D4×C79—216no—
357D4×C79—28no—
358C2×C4×C79—24no—
359C2×C4×C79—216no—
360C2×C4×C79—28no—
361C2×C4×C79—24no—
362C2×C4×C79—24no—
363C2×C4×C79—216no—
364C2×C4×C79C2×#4114yes—
365C2×C4×C79C2×#4114yes—
366C2×C4×C79C2×#41116yes—
367C2×C4×C79C2518yes—
368C2×C4×C79C2514yes—
369C2×C4×C79C2514yes—
370C2×C4×C79C2514yes—
371C2×C4×C79C2512yes—
372C2×C4×C79C2512yes—
373C22⋊D79—216no—
374C22⋊D79—216no—
375C22⋊D79—48no—
376C2×Dic79—24no—
377C2×Dic79—22no—
378C2×Dic79—24no—
379C2×Dic79—28no—
380C2×Dic79—24no—
381C2×Dic79—22no—
382C2×Dic79—22no—
383C2×Dic79—28no—
384C2×Dic79—44no—
385C2×Dic79—416no—
386C2×Dic79—48no—
387C2×Dic792−1+414yes—
388C2×Dic79C2512yes—
389C2×Dic79C2518yes—
390C2×Dic79C2514yes—
391C2×Dic79C2512yes—
392C2×Dic79C2514yes—
393C2×Dic79C2512yes—
394C2×Dic79C2514yes—
395C2×Dic79C2512yes—
396D316—28no—
397C4×D79—216no—
398C4×D79—416no—
399Dic158—28no—
400Dic158—216no—
401Dic158—48no—
402C22×C79—22no—
403C22×C79—22no—
404C22×C79—28no—
405C22×C79—24no—
406C22×C79—24no—
407C22×C79—24no—
408C22×C79—48no—
409C22×C79C22×#4114yes—
410C22×C79C22×#4112yes—
411C22×C79C2×2−1+412yes—
412C22×C79#58512yes—
413C22×C79C2611yescharacteristic
414C2×D79—24no—
415C2×D79—24no—
416C2×D79—24no—
417C2×D79—48no—
418C4×C79—24no—
419C4×C79—28no—
420C4×C79—24no—
421C4×C79—24no—
422C4×C79C22×#4114yes—
423C4×C79C22×#4114yes—
424Dic79—24no—
425Dic79—24no—
426Dic79—22no—
427Dic79—22no—
428Dic79—22no—
429Dic79—24no—
430Dic79—28no—
431Dic79C2×2−1+414yes—
432C2×#3507—791nomaximal, Sylow
433C2×C79—24no—
434C2×C79—44no—
435C2×C79#350714yescomplemented
436C2×C79C23×#4111yescharacteristic
437C2×C79C22×2−1+411yescharacteristic
438C2×C79C2×#58511yescharacteristic
439D79—44no—
440#3507—7932no—
441C2×#559—792no—
442C2×#557—792no—
443C2×#556—792no—
444C2×#556—792no—
445C2×#556—792no—
446C2×#554—792no—
447C2×#552—792no—
448C2×#552—792no—
449C2×#539—794no—
450C2×#536—791no—
451C2×#536D7911yescharacteristic, complemented
452C2×#533—791no—
453C2×#532—791no—
454C2×#529—794no—
455C2×#520—791no—
456C2×#520—791no—
457C22×C4×Q8—791no—
458C79C2×#350711yescharacteristic, complemented, Sylow
459C22×#41—791no—
460C22×#41C2×D7911yescharacteristic
461C23×Q8C2×D7911yescharacteristic
462#559—7932no—
463#557—7932no—
464#556—7932no—
465#556—7932no—
466#556—7932no—
467#554—7932no—
468#552—7932no—
469#552—7932no—
470#539—7964no—
471#536—7916no—
472#536C2×D79116yescomplemented
473#533—7916no—
474#532—7916no—
475C2×C4⋊Q8—791no—
476C2×C4⋊Q8—792no—
477C2×C4⋊Q8—791no—
478C2×C4⋊Q8—791no—
479C2×C4⋊Q8C2×D7912yes—
480C2×#127—791no—
481#529—7964no—
482C2×#126—794no—
483C2×#126—794no—
484C2×#126—794no—
485C2×#126—794no—
486C2×#125—794no—
487C2×#125—791no—
488C2×#125—791no—
489C2×#125—794no—
490C2×#125—794no—
491C2×#124—791no—
492C2×#124—792no—
493C2×#124—791no—
494C2×#124—794no—
495C2×#124C2×D7912yes—
496C2×#123—794no—
497C2×#123—794no—
498C2×#123—794no—
499C2×#123C2×D7914yes—
500C2×C22⋊Q8—792no—
501C2×C22⋊Q8—792no—
502C2×C22⋊Q8—794no—
503C2×C22⋊Q8—792no—
504C2×C22⋊Q8—792no—
505C2×C22⋊Q8—794no—
506C2×C22⋊Q8C2×D7912yes—
507C2×C22⋊Q8C2×D7912yes—
508C2×#121—792no—
509C2×#121—792no—
510#520—7916no—
511#520—7916no—
512C2×C4×Q8—792no—
513C2×C4×Q8—792no—
514C2×C4×Q8—792no—
515C2×C4×Q8—792no—
516C2×C4×Q8—7916no—
517C2×C4×Q8—792no—
518C2×C4×Q8—794no—
519C2×C4×Q8—792no—
520C2×C4×Q8—792no—
521C2×C4×Q8—792no—
522C2×C4×D4—794no—
523C2×C4×D4—792no—
524C2×C4×D4—792no—
525C2×C4×D4—792no—
526C2×C4×D4—794no—
527C2×C4×D4—794no—
528C2×C4×D4—792no—
529C2×#117—791no—
530C2×#117—792no—
531C2×#117—792no—
532C2×#117—794no—
533C2×#117—794no—
534C2×#117C2×D7911yescharacteristic
535C22×C4⋊C4—791no—
536C22×C4⋊C4—792no—
537C22×C4⋊C4—792no—
538C22×C4⋊C4—792no—
539C22×C42—792no—
540C22×C42—791no—
541C2×#41—28no—
542C2×#41—798no—
543C2×#41—1588no—
544C2×#41C22×D7918yes—
545C22×Q8—28no—
546C22×Q8—792no—
547C22×Q8—792no—
548C22×Q8—791no—
549C22×Q8C22×D7912yes—
550C22×Q8C22×D7912yes—
551C22×Q8C22×D7911yescharacteristic
552C22×Q8C22×D7918yes—
553C22×D4—792no—
554C22×D4—792no—
555C22×D4—792no—
556C22×D4—791no—
557C22×D4C22×D7912yes—
558C22×D4C22×D7911yescharacteristic
559C23×C4—792no—
560C23×C4—791no—
561C23×C4—794no—
562C23×C4—794no—
563C23×C4—791no—
564C23×C4—792no—
565C23×C4C22×D7912yes—
566C23×C4C22×D7912yes—
567C23×C4C22×D7911yescharacteristic
568C4⋊Q8—798no—
569C4⋊Q8—7916no—
570C4⋊Q8—798no—
571C4⋊Q8—798no—
572C4⋊Q8C22×D79116yes—
573#127—798no—
574#126—7932no—
575#126—7932no—
576#126—7932no—
577#126—7932no—
578#125—7932no—
579#125—798no—
580#125—798no—
581#125—7932no—
582#125—7932no—
583#124—798no—
584#124—7916no—
585#124—798no—
586#124—7932no—
587#124C22×D79116yes—
588#123—7932no—
589#123—7932no—
590#123—7932no—
591#123C22×D79132yes—
592C22⋊Q8—7916no—
593C22⋊Q8—7916no—
594C22⋊Q8—7932no—
595C22⋊Q8—7916no—
596C22⋊Q8—7916no—
597C22⋊Q8—7932no—
598C22⋊Q8C22×D79116yes—
599C22⋊Q8C22×D79116yes—
600#121—7916no—
601#121—7916no—
602C4×Q8—7916no—
603C4×Q8—7916no—
604C4×Q8—7916no—
605C4×Q8—7916no—
606C4×Q8—7916no—
607C4×Q8—7932no—
608C4×Q8—7916no—
609C4×Q8—7916no—
610C4×Q8—7916no—
611C4×D4—7932no—
612C4×D4—7916no—
613C4×D4—7916no—
614C4×D4—7916no—
615C4×D4—7932no—
616C4×D4—7932no—
617C4×D4—7916no—
618#117—798no—
619#117—7916no—
620#117—7916no—
621#117—7932no—
622#117—7932no—
623#117C22×D7918yes—
624C2×C4⋊C4—792no—
625C2×C4⋊C4—791no—
626C2×C4⋊C4—792no—
627C2×C4⋊C4—794no—
628C2×C4⋊C4—794no—
629C2×C4⋊C4—798no—
630C2×C4⋊C4—794no—
631C2×C4⋊C4—794no—
632C2×C4⋊C4—7916no—
633C2×C4⋊C4—7916no—
634C2×C4⋊C4—791no—
635C2×C4⋊C4—792no—
636C2×C4⋊C4—792no—
637C2×C4⋊C4—794no—
638C2×C4⋊C4—792no—
639C2×C4⋊C4—792no—
640C2×C4⋊C4—792no—
641C2×C4⋊C4—792no—
642C2×C4⋊C4—792no—
643C2×C4⋊C4—794no—
644C2×C4⋊C4—792no—
645C2×C4⋊C4—7916no—
646C2×C4⋊C4C22×D7911yescharacteristic
647C2×C4⋊C4C22×D7911yescharacteristic
648C2×C4⋊C4C22×D7914yes—
649C2×C4⋊C4C22×D7914yes—
650C2×C22⋊C4—792no—
651C2×C22⋊C4—792no—
652C2×C22⋊C4—794no—
653C2×C22⋊C4—792no—
654C2×C22⋊C4—792no—
655C2×C22⋊C4—794no—
656C2×C22⋊C4—794no—
657C2×C22⋊C4—792no—
658C2×C22⋊C4—794no—
659C2×C22⋊C4C22×D7914yes—
660C2×C22⋊C4C22×D7912yes—
661C2×C22⋊C4C22×D7914yes—
662C2×C42—794no—
663C2×C42—794no—
664C2×C42—794no—
665C2×C42—792no—
666C2×C42—791no—
667C2×C42—791no—
668C2×C42—794no—
669C2×C42—791no—
670C2×C42—791no—
671C2×C42—7916no—
672C2×C42—798no—
673C2×C42C22×D7912yes—
674C24—792no—
675C24C23×D7912yes—
676C24C23×D7911yescharacteristic
677#41—232no—
678#41—15832no—
679C2×Q8—28no—
680C2×Q8—28no—
681C2×Q8—232no—
682C2×Q8—24no—
683C2×Q8—3164no—
684C2×Q8—798no—
685C2×Q8—798no—
686C2×Q8—794no—
687C2×Q8—1588no—
688C2×Q8—1584no—
689C2×Q8C23×D7918yes—
690C2×Q8C23×D7918yes—
691C2×Q8C23×D7914yes—
692C2×D4—28no—
693C2×D4—24no—
694C2×D4—3164no—
695C2×D4—798no—
696C2×D4—798no—
697C2×D4—798no—
698C2×D4—794no—
699C2×D4—1588no—
700C2×D4—1588no—
701C2×D4—1584no—
702C2×D4C23×D7918yes—
703C2×D4C23×D7914yes—
704C22×C4—28no—
705C22×C4—28no—
706C22×C4—3168no—
707C22×C4—3164no—
708C22×C4—3168no—
709C22×C4—3162no—
710C22×C4—798no—
711C22×C4—794no—
712C22×C4—7916no—
713C22×C4—7916no—
714C22×C4—791no—
715C22×C4—794no—
716C22×C4—791no—
717C22×C4—794no—
718C22×C4—792no—
719C22×C4—791no—
720C22×C4—792no—
721C22×C4—791no—
722C22×C4—792no—
723C22×C4—798no—
724C22×C4—1584no—
725C22×C4—1588no—
726C22×C4#1192962318yes—
727C22×C4C23×D7918yes—
728C22×C4C23×D7918yes—
729C22×C4C23×D7912yes—
730C22×C4C23×D7914yes—
731C22×C4C23×D7912yes—
732C22×C4C23×D7912yes—
733C22×C4C23×D7914yes—
734C22×C4C23×D7911yescharacteristic
735C22×C4C23×D7911yescharacteristic
736C4⋊C4—7916no—
737C4⋊C4—798no—
738C4⋊C4—7916no—
739C4⋊C4—798no—
740C4⋊C4—798no—
741C4⋊C4—798no—
742C4⋊C4—798no—
743C4⋊C4—7916no—
744C4⋊C4—798no—
745C4⋊C4—798no—
746C4⋊C4—794no—
747C4⋊C4—798no—
748C4⋊C4—7916no—
749C4⋊C4—7916no—
750C4⋊C4—7916no—
751C4⋊C4—794no—
752C4⋊C4—798no—
753C4⋊C4—798no—
754C4⋊C4C23×D7914yes—
755C4⋊C4C23×D7914yes—
756C4⋊C4C23×D79116yes—
757C4⋊C4C23×D79116yes—
758C22⋊C4—798no—
759C22⋊C4—798no—
760C22⋊C4—7916no—
761C22⋊C4—798no—
762C22⋊C4—798no—
763C22⋊C4—7916no—
764C22⋊C4—7916no—
765C22⋊C4—798no—
766C22⋊C4—7916no—
767C22⋊C4C23×D79116yes—
768C22⋊C4C23×D7918yes—
769C22⋊C4C23×D79116yes—
770C42—7916no—
771C42—794no—
772C42—794no—
773C42—7916no—
774C42—794no—
775C42—794no—
776C42—7916no—
777C42—7916no—
778C42—798no—
779C42C23×D7918yes—
780C23—22no—
781C23—22no—
782C23—24no—
783C23—24no—
784C23—24no—
785C23—794no—
786C23—1584no—
787C23—1584no—
788C23—1584no—
789C23C2×#1192962314yes—
790C23C24×D7914yes—
791C23C24×D7912yes—
792C23C24×D7911yescharacteristic
793Q8—216no—
794Q8—216no—
795Q8—28no—
796Q8—3168no—
797Q8—15816no—
798Q8—1588no—
799D4—216no—
800D4—28no—
801D4—3168no—
802D4—15816no—
803D4—15816no—
804D4—1588no—
805C2×C4—24no—
806C2×C4—24no—
807C2×C4—24no—
808C2×C4—216no—
809C2×C4—28no—
810C2×C4—216no—
811C2×C4—31616no—
812C2×C4—3168no—
813C2×C4—31616no—
814C2×C4—3164no—
815C2×C4—794no—
816C2×C4—792no—
817C2×C4—792no—
818C2×C4—798no—
819C2×C4—794no—
820C2×C4—792no—
821C2×C4—794no—
822C2×C4—792no—
823C2×C4—794no—
824C2×C4—1588no—
825C2×C4—1582no—
826C2×C4—1584no—
827C2×C4—1588no—
828C2×C4—1584no—
829C2×C4—1582no—
830C2×C4—1582no—
831C2×C4—1584no—
832C2×C4—15816no—
833C2×C4C2×#1192962314yes—
834C2×C4C2×#1192962314yes—
835C2×C4C2×#11929623116yes—
836C2×C4C24×D7914yes—
837C2×C4C24×D7918yes—
838C2×C4C24×D7914yes—
839C2×C4C24×D7914yes—
840C2×C4C24×D7912yes—
841C2×C4C24×D7912yes—
842C22—22no—
843C22—22no—
844C22—28no—
845C22—24no—
846C22—24no—
847C22—24no—
848C22—48no—
849C22—3168no—
850C22—1584no—
851C22—1584no—
852C22—1584no—
853C22C22×#1192962314yes—
854C22C22×#1192962312yes—
855C222−1+4×D7912yes—
856C22#1909940012yes—
857C22C25×D7911yescharacteristic
858C4—24no—
859C4—28no—
860C4—24no—
861C4—24no—
862C4—794no—
863C4—1584no—
864C4—1582no—
865C4—1584no—
866C4—1588no—
867C4—1584no—
868C4—1582no—
869C4—1582no—
870C4C22×#1192962314yes—
871C4C22×#1192962314yes—
872C2—24no—
873C2—44no—
874C2—3164no—
875C2#2377726414yesdirect product factor
876C2C23×#1192962311yescharacteristic
877C2C2×2−1+4×D7911yescharacteristic
878C2C2×#1909940011yescharacteristic
subgroupG/H
centerC23C24×D79
commutator, cosocleC22×C79C26
FrattiniC22C25×D79
FittingC2×#536×C79C2
socleC23×C79C25
prime radicalC2×#19099109C2
hypercenterC2×#536D79
hypocenterC79C2×#3507
LCSG ▷ C22×C79 ▷ C79
UCSC1 ◁ C23 ◁ C2×#536

Complements

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

NH ≅ G/Ntype
1. #23777264C2direct (N × H)
2. C2×#19099295C2semidirect
3. C2×#19099288C2semidirect
4. C2×#19099287C2semidirect
5. C2×#19099284C2semidirect
6. C2×#19099282C2semidirect
7. C2×#19099271C2semidirect
8. C2×#19099255C2semidirect
9. C2×#19099247C2semidirect
10. C2×#19099157C2semidirect
11. C2×#19099137C2semidirect
12. C2×#19099116C2semidirect
14. C2×#19099090C2semidirect
15. C2×#19099046C2semidirect
16. C2×#19099043C2semidirect
17. C22×Q8×Dic79C2semidirect
18. C2×#536×C79C2semidirect
20. #19099295C22semidirect
21. #19099288C22semidirect
22. #19099287C22semidirect
23. #19099284C22semidirect
24. #19099282C22semidirect
25. #19099271C22semidirect
26. #19099255C22semidirect
27. #19099247C22semidirect
28. #19099157C22semidirect
29. #19099137C22semidirect
30. #19099116C22semidirect
37. #19099090C22semidirect
62. #19099046C22semidirect
63. #19099043C22semidirect
69. C2×Q8×Dic79C22semidirect
94. #536×C79C22semidirect
435. C2×C79#3507semidirect
451. C2×#536D79semidirect
458. C79C2×#3507semidirect
472. #536C2×D79semidirect
875. C2#23777264direct (N × H)

Maximal subgroups

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

subgroupindex
#237772642
C2×#190992952
C2×#190992882
C2×#190992872
C2×#190992842
C2×#190992822
C2×#190992712
C2×#190992552
C2×#190992472
C2×#190991572
C2×#190991372
C2×#190991162
C2×#190991092
C2×#190990902
C2×#190990462
C2×#190990432
C22×Q8×Dic792
C2×#536×C792
C2×#350779