Finite Group Databasebeta

← C2×#23777785 #35195972

Subgroups — C2×#23777785 #35195972

Order 20224.

7182 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#23777785C2132yesmaximal, direct product factor
2C2×#19099309C214yesmaximal, complemented
3C2×#19099279C212yesmaximal, complemented
4C2×#19099278C211yesmaximal, characteristic, complemented
5C2×#19099273C211yesmaximal, characteristic, complemented
6C2×#19099263C212yesmaximal, complemented
7C2×#19099247C212yesmaximal, complemented
8C2×#19099224C212yesmaximal, complemented
9C2×#19099216C211yesmaximal, characteristic, complemented
10C2×#19099190C212yesmaximal, complemented
11C2×#19099183C214yesmaximal, complemented
12C2×#19099164C212yesmaximal, complemented
13C2×#19099143C212yesmaximal, complemented
14C2×#19099137C212yesmaximal, complemented
15C2×#19099118C211yesmaximal, characteristic, complemented
16C2×#19099110C211yesmaximal, characteristic, complemented
17C2×#19099100C211yesmaximal, characteristic, complemented
18C2×D4×Q8×C79C211yesmaximal, characteristic, complemented
19C22×#11929625C2212yes—
20C22×#11929624C2212yes—
21#19099309C22164yescomplemented
22#19099279C22132yescomplemented
23#19099278C22116yescomplemented
24#19099273C22116yescomplemented
25#19099263C22132yescomplemented
26#19099247C22132yescomplemented
27#19099224C22132yescomplemented
28#19099216C22116yescomplemented
29#19099190C22132yescomplemented
30#19099183C22164yescomplemented
31#19099164C22132yescomplemented
32#19099143C22132yescomplemented
33#19099137C22132yescomplemented
34#19099118C22116yescomplemented
35#19099110C22116yescomplemented
36C2×#14579161C2211yescharacteristic
37C2×#14579160C2211yescharacteristic
38C2×#14579159C2214yes—
39C2×#14579157C2211yescharacteristic
40#19099100C22116yescomplemented
41C2×#14579156C2212yes—
42C2×#14579154C2214yes—
43C2×#14579153C2212yes—
44C2×#14579152C2212yes—
45C2×#14579152C2211yescharacteristic
46C2×#14579151C2214yes—
47C2×#14579150C2214yes—
48C2×#14579150C2211yescharacteristic
49C2×#14579150C2214yes—
50C2×#14579147C2212yes—
51C2×#14579147C2214yes—
52C2×#14579146C2214yes—
53C2×#14579146C2212yes—
54C2×#14579144C2214yes—
55C2×#14579144C2214yes—
56C2×#14579143C2214yes—
57C2×#14579141C2212yes—
58C2×#14579139C2214yes—
59C2×#14579139C2214yes—
60C2×#14579137C2214yes—
61C2×#14579137C2212yes—
62C2×#14579137C2212yes—
63C2×#14579137C2211yescharacteristic
64C2×#14579137C2212yes—
65C2×#14579136C2212yes—
66C2×#14579136C2211yescharacteristic
67C2×#14579136C2211yescharacteristic
68C2×#14579136C2214yes—
69C2×#14579135C2212yes—
70C2×#14579135C2214yes—
71C2×#14579134C2214yes—
72C2×#14579134C2214yes—
73C2×#14579134C2212yes—
74C2×#14579132C2211yescharacteristic
75C2×#14579132C2212yes—
76C2×Q8×Dic79C2212yes—
77C2×#14579126C2212yes—
78C2×C4×D316C2211yescharacteristic
79C2×C4×D316C2211yescharacteristic
80C2×C4×D316C2212yes—
81C2×C4×D316C2212yes—
82C2×C4×C22⋊D79C2214yes—
83C2×C4×C22⋊D79C2212yes—
84C2×#14579120C2212yes—
85C2×#14579119C2214yes—
86C2×#14579119C2212yes—
87C2×#14579119C2212yes—
88C2×#14579118C2212yes—
89C2×C4⋊C4×D79C2212yes—
90C2×C4⋊C4×D79C2212yes—
91C2×C42×D79C2211yescharacteristic
92C23×Q8×C79C2212yes—
93D4×Q8×C79C22116yescomplemented
94C2×C4⋊Q8×C79C2212yes—
95C2×C4⋊Q8×C79C2211yescharacteristic
96C2×C22⋊Q8×C79C2214yes—
97C2×C22⋊Q8×C79C2212yes—
98C2×C4×Q8×C79C2211yescharacteristic
99C2×C4×D4×C79C2212yes—
100C2×C4×D4×C79C2211yescharacteristic
101C2×#11929625—48no—
102C2×#11929625C23116yes—
103C2×#11929624—48no—
104C2×#11929624C23116yes—
105C22×Dic158C2312yes—
106C22×Dic158C2312yes—
107C22×D316C2311yescharacteristic
108C22×D316C2311yescharacteristic
109C22×D316C2312yes—
110C22×D316C2314yes—
111C22×D316C2312yes—
112C22×C22⋊D79C2314yes—
113C22×C22⋊D79C2312yes—
114C22×C22⋊D79C2312yes—
115C22×C22⋊D79C2312yes—
116C22×C4×D79C2311yescharacteristic
117C22×C4×D79C2311yescharacteristic
118C22×C4×D79C2312yes—
119C22×C4×D79C2312yes—
120C22×C4×D79C2311yescharacteristic
121C22×C4×D79C2314yes—
122C22×C4×D79C2314yes—
123#14579161C2318yes—
124#14579160C2318yes—
125#14579159C23132yes—
126#14579157C2318yes—
127#14579156C23116yes—
128#14579154C23132yes—
129#14579153C23116yes—
130#14579152C23116yes—
131#14579152C2318yes—
132#14579151C23132yes—
133#14579150C23132yes—
134#14579150C23132yes—
135#14579150C2318yes—
136#14579147C23116yes—
137#14579147C23132yes—
138#14579146C23132yes—
139#14579146C23116yes—
140#14579144C23132yes—
141#14579144C23132yes—
142#14579143C23132yes—
143#14579141C23116yes—
144#14579139C23132yes—
145#14579139C23132yes—
146#14579137C2318yes—
147#14579137C23116yes—
148#14579137C23116yes—
149#14579137C23116yes—
150#14579137C23132yes—
151#14579136C2318yes—
152#14579136C23132yes—
153#14579136C23116yes—
154#14579136C2318yes—
155#14579135C23116yes—
156#14579135C23132yes—
157#14579134C23132yes—
158#14579134C23132yes—
159#14579134C23116yes—
160#14579132C23116yes—
161#14579132C2318yes—
162Q8×Dic79C23116yes—
163#14579126C23116yes—
164C4×D316C23116yes—
165C4×D316C2318yes—
166C4×D316C2318yes—
167C4×D316C23116yes—
168C4×C22⋊D79C23132yes—
169C4×C22⋊D79C23116yes—
170#14579120C23116yes—
171#14579119C23132yes—
172#14579119C23116yes—
173#14579119C23116yes—
174#14579118C23116yes—
175C2×C4⋊Dic79C2311yescharacteristic
176C2×C4⋊Dic79C2312yes—
177C2×C4⋊Dic79C2312yes—
178C2×C4⋊Dic79C2312yes—
179C2×C4⋊Dic79C2311yescharacteristic
180C2×C4⋊Dic79C2314yes—
181C2×Dic79⋊C4C2314yes—
182C2×Dic79⋊C4C2314yes—
183C2×Dic79⋊C4C2312yes—
184C2×Dic79⋊C4C2312yes—
185C2×Dic79⋊C4C2312yes—
186C2×Dic79⋊C4C2314yes—
187C2×Dic79⋊C4C2314yes—
188C4⋊C4×D79C23116yes—
189C4⋊C4×D79C23116yes—
190C2×C22⋊Dic79C2314yes—
191C2×C22⋊Dic79C2312yes—
192C2×(C2×D79)⋊C4C2312yes—
193C2×(C2×D79)⋊C4C2312yes—
194C2×(C2×D79)⋊C4C2312yes—
195C2×(C2×D79)⋊C4C2314yes—
196C2×(C2×D79)⋊C4C2314yes—
197C2×(C2×D79)⋊C4C2314yes—
198C2×(C2×D79)⋊C4C2312yes—
199C2×(C2×D79)⋊C4C2312yes—
200C2×(C2×D79)⋊C4C2314yes—
201C2×(C2×D79)⋊C4C2312yes—
202C2×(C2×D79)⋊C4C2312yes—
203C2×C4×Dic79C2311yescharacteristic
204C2×C4×Dic79C2311yescharacteristic
205C2×C4×Dic79C2311yescharacteristic
206C2×C4×Dic79C2314yes—
207C2×C4×Dic79C2314yes—
208C42×D79C2318yes—
209C22×Q8×C79—48no—
210C22×Q8×C79C2311yescharacteristic
211C22×Q8×C79C2312yes—
212C22×Q8×C79C23116yes—
213C22×Q8×C79C2314yes—
214C22×D4×C79C2311yescharacteristic
215C23×C4×C79C2312yes—
216C23×C4×C79C2314yes—
217C4⋊Q8×C79C23116yes—
218C4⋊Q8×C79C2318yes—
219C22⋊Q8×C79C23116yes—
220C22⋊Q8×C79C23132yes—
221C4×Q8×C79C2318yes—
222C4×D4×C79C23116yes—
223C4×D4×C79C2318yes—
224C2×C4⋊C4×C79C2312yes—
225C2×C4⋊C4×C79C2311yescharacteristic
226C2×C4⋊C4×C79C2311yescharacteristic
227C2×C4⋊C4×C79C2312yes—
228C2×C4⋊C4×C79C2314yes—
229C2×C4⋊C4×C79C2312yes—
230C2×C22⋊C4×C79C2314yes—
231C2×C22⋊C4×C79C2312yes—
232C2×C42×C79C2311yescharacteristic
233C2×C42×C79C2312yes—
234C23×D79C2411yescharacteristic
235C23×D79C2412yes—
236C23×D79C2412yes—
237#11929625—432no—
238#11929624—432no—
239C2×Dic158—44no—
240C2×Dic158—44no—
241C2×Dic158C2418yes—
242C2×Dic158C2418yes—
243C2×D316—24no—
244C2×D316—24no—
245C2×D316—44no—
246C2×D316—48no—
247C2×D316—44no—
248C2×D316C2414yes—
249C2×D316C2414yes—
250C2×D316C2418yes—
251C2×D316C24116yes—
252C2×D316C2418yes—
253C2×C22⋊D79—44no—
254C2×C22⋊D79—44no—
255C2×C22⋊D79—44no—
256C2×C22⋊D79—48no—
257C2×C22⋊D79C2418yes—
258C2×C22⋊D79C2418yes—
259C2×C22⋊D79C24116yes—
260C2×C22⋊D79C2418yes—
261C22×Dic79C2411yescharacteristic
262C22×Dic79C2414yes—
263C22×Dic79C2412yes—
264C22×Dic79C2411yescharacteristic
265C22×Dic79C2412yes—
266C22×Dic79C2411yescharacteristic
267C2×C4×D79—24no—
268C2×C4×D79—28no—
269C2×C4×D79—24no—
270C2×C4×D79—28no—
271C2×C4×D79—48no—
272C2×C4×D79—48no—
273C2×C4×D79—42no—
274C2×C4×D79C2414yes—
275C2×C4×D79C2418yes—
276C2×C4×D79C2414yes—
277C2×C4×D79C2418yes—
278C2×C4×D79C24116yes—
279C2×C4×D79C2414yes—
280C2×C4×D79C24116yes—
281C4⋊Dic79C2414yes—
282C4⋊Dic79C2418yes—
283C4⋊Dic79C2418yes—
284C4⋊Dic79C2418yes—
285C4⋊Dic79C2414yes—
286C4⋊Dic79C24116yes—
287Dic79⋊C4C24116yes—
288Dic79⋊C4C24116yes—
289Dic79⋊C4C2418yes—
290Dic79⋊C4C2418yes—
291Dic79⋊C4C2418yes—
292Dic79⋊C4C24116yes—
293Dic79⋊C4C24116yes—
294C22⋊Dic79C24116yes—
295C22⋊Dic79C2418yes—
296(C2×D79)⋊C4C2418yes—
297(C2×D79)⋊C4C2418yes—
298(C2×D79)⋊C4C2418yes—
299(C2×D79)⋊C4C24116yes—
300(C2×D79)⋊C4C24116yes—
301(C2×D79)⋊C4C24116yes—
302(C2×D79)⋊C4C2418yes—
303(C2×D79)⋊C4C2418yes—
304(C2×D79)⋊C4C24116yes—
305(C2×D79)⋊C4C2418yes—
306(C2×D79)⋊C4C2418yes—
307C4×Dic79C2414yes—
308C4×Dic79C2414yes—
309C4×Dic79C2414yes—
310C4×Dic79C24116yes—
311C4×Dic79C24116yes—
312C24×C79C2412yes—
313C2×Q8×C79—28no—
314C2×Q8×C79—24no—
315C2×Q8×C79—48no—
316C2×Q8×C79—432no—
317C2×Q8×C79C2418yes—
318C2×Q8×C79C2414yes—
319C2×Q8×C79C24116yes—
320C2×D4×C79—24no—
321C2×D4×C79C2414yes—
322C22×C4×C79—28no—
323C22×C4×C79—48no—
324C22×C4×C79C2411yescharacteristic
325C22×C4×C79C2412yes—
326C22×C4×C79C2418yes—
327C22×C4×C79C2412yes—
328C22×C4×C79C2412yes—
329C22×C4×C79C2414yes—
330C22×C4×C79C24116yes—
331C22×C4×C79C2411yescharacteristic
332C22×C4×C79C2411yescharacteristic
333C4⋊C4×C79C2418yes—
334C4⋊C4×C79C2414yes—
335C4⋊C4×C79C2414yes—
336C4⋊C4×C79C2418yes—
337C4⋊C4×C79C24116yes—
338C4⋊C4×C79C2418yes—
339C22⋊C4×C79C24116yes—
340C22⋊C4×C79C2418yes—
341C42×C79C2414yes—
342C42×C79C2418yes—
343C23×C79—24no—
344C23×C79—24no—
345C23×C79—24no—
346C23×C79C2514yes—
347C23×C79C2511yescharacteristic
348C22×D79—22no—
349C22×D79—24no—
350C22×D79—24no—
351C22×D79—22no—
352C22×D79—24no—
353C22×D79—24no—
354C22×D79—24no—
355C22×D79—22no—
356C22×D79—24no—
357C22×D79C2512yes—
358C22×D79C2514yes—
359C22×D79C2514yes—
360Q8×C79—216no—
361Q8×C79—28no—
362Q8×C79—416no—
363D4×C79—28no—
364C2×C4×C79—28no—
365C2×C4×C79—24no—
366C2×C4×C79—24no—
367C2×C4×C79—24no—
368C2×C4×C79—22no—
369C2×C4×C79—216no—
370C2×C4×C79—416no—
371C2×C4×C79H(5,𝔽2)14yes—
372C2×C4×C792−1+414yes—
373C2×C4×C79C2514yes—
374C2×C4×C79C2512yes—
375C2×C4×C79C2518yes—
376C2×C4×C79C2514yes—
377C2×C4×C79C2514yes—
378C2×C4×C79C2512yes—
379C2×C4×C79C2512yes—
380C22⋊D79—48no—
381C22⋊D79—416no—
382C22⋊D79—48no—
383C22⋊D79—48no—
384C2×Dic79—24no—
385C2×Dic79—22no—
386C2×Dic79—22no—
387C2×Dic79—24no—
388C2×Dic79—22no—
389C2×Dic79—28no—
390C2×Dic79C2512yes—
391C2×Dic79C2514yes—
392C2×Dic79C2518yes—
393C2×Dic79C2512yes—
394C2×Dic79C2512yes—
395C2×Dic79C2514yes—
396D316—28no—
397D316—28no—
398D316—48no—
399D316—48no—
400D316—416no—
401C4×D79—28no—
402C4×D79—216no—
403C4×D79—28no—
404C4×D79—216no—
405C4×D79—44no—
406C4×D79—416no—
407C4×D79—416no—
408Dic158—48no—
409Dic158—48no—
410C22×C79—24no—
411C22×C79—24no—
412C22×C79—24no—
413C22×C79—48no—
414C22×C79C2×H(5,𝔽2)12yes—
415C22×C79C2×2−1+412yes—
416C22×C79#58512yes—
417C22×C79C2611yescharacteristic
418C2×D79—22no—
419C2×D79—24no—
420C2×D79—24no—
421C2×D79—22no—
422C2×D79—24no—
423C2×D79—24no—
424C2×D79—24no—
425C2×D79—24no—
426C2×D79—22no—
427C2×D79—44no—
428C2×D79—48no—
429C2×D79—48no—
430C4×C79—24no—
431C4×C79—24no—
432C4×C79—28no—
433C4×C79—22no—
434C4×C79—24no—
435C4×C79C2×H(5,𝔽2)14yes—
436C4×C79C2×2−1+414yes—
437Dic79—22no—
438Dic79—24no—
439Dic79—22no—
440Dic79—24no—
441Dic79—22no—
442Dic79—28no—
443C2×#3547—791nomaximal, Sylow
444C2×C79—44no—
445C2×C79#354714yescomplemented
446C2×C79C22×H(5,𝔽2)11yescharacteristic
447C2×C79C22×2−1+411yescharacteristic
448C2×C79C2×#58511yescharacteristic
449D79—42no—
450D79—44no—
451D79—44no—
452#3547—7932no—
453C2×#562—794no—
454C2×#555—792no—
455C2×#555—791no—
456C2×#554—791no—
457C2×#553—792no—
458C2×#552—792no—
459C2×D4×Q8D7911yescharacteristic, complemented
460C2×#548—792no—
461C2×#547—791no—
462C2×#544—792no—
463C2×#542—794no—
464C2×#540—792no—
465C2×#537—792no—
466C2×#536—792no—
467C2×#533—791no—
468C2×#532—791no—
469C2×#529—791no—
470C79C2×#354711yescharacteristic, complemented, Sylow
471C22×#41—792no—
472C22×#41—792no—
473C23×Q8C2×D7912yes—
474#562—7964no—
475#555—7932no—
476#555—7916no—
477#554—7916no—
478#553—7932no—
479#552—7932no—
480D4×Q8C2×D79116yescomplemented
481#548—7932no—
482#547—7916no—
483#544—7932no—
484#542—7964no—
485#540—7932no—
486#537—7932no—
487#536—7932no—
488#533—7916no—
489#532—7916no—
490C2×C4⋊Q8—794no—
491C2×C4⋊Q8—791no—
492C2×C4⋊Q8—791no—
493C2×C4⋊Q8C2×D7911yescharacteristic
494C2×C4⋊Q8C2×D7912yes—
495C2×#127—791no—
496#529—7916no—
497C2×#126—792no—
498C2×#126—794no—
499C2×#125—791no—
500C2×#125—792no—
501C2×#125—794no—
502C2×#125—792no—
503C2×#124—791no—
504C2×#124—794no—
505C2×#124—794no—
506C2×#124—792no—
507C2×#124—794no—
508C2×#123—794no—
509C2×#123—794no—
510C2×#123—792no—
511C2×#123—794no—
512C2×#123—794no—
513C2×C22⋊Q8—791no—
514C2×C22⋊Q8—792no—
515C2×C22⋊Q8—792no—
516C2×C22⋊Q8—792no—
517C2×C22⋊Q8—794no—
518C2×C22⋊Q8—792no—
519C2×C22⋊Q8—794no—
520C2×C22⋊Q8—794no—
521C2×C22⋊Q8C2×D7912yes—
522C2×C22⋊Q8C2×D7914yes—
523C2×#121—791no—
524C2×#121—792no—
525C2×#121—792no—
526C2×#121—794no—
527C2×#121—791no—
528C2×#121—791no—
529C2×#121—794no—
530C2×#121—792no—
531C2×#121—792no—
532C2×#121—794no—
533C2×#121—794no—
534C2×C4×Q8—792no—
535C2×C4×Q8—792no—
536C2×C4×Q8C2×D7911yescharacteristic
537C2×C4×D4—792no—
538C2×C4×D4—794no—
539C2×C4×D4—791no—
540C2×C4×D4—792no—
541C2×C4×D4—791no—
542C2×C4×D4—792no—
543C2×C4×D4C2×D7911yescharacteristic
544C2×C4×D4C2×D7912yes—
545C2×#117—792no—
546C2×#117—792no—
547C2×#117—794no—
548C2×#117—792no—
549C2×#117—792no—
550C22×C4⋊C4—792no—
551C22×C4⋊C4—792no—
552C22×C42—791no—
553C2×#41—3168no—
554C2×#41—3168no—
555C2×#41—7916no—
556C2×#41—7916no—
557C22×Q8—48no—
558C22×Q8—792no—
559C22×Q8—792no—
560C22×Q8C22×D7912yes—
561C22×Q8C22×D7911yescharacteristic
562C22×Q8C22×D7914yes—
563C22×Q8C22×D79116yes—
564C22×D4—794no—
565C22×D4—792no—
566C22×D4—792no—
567C22×D4—792no—
568C22×D4—792no—
569C22×D4—794no—
570C22×D4—792no—
571C22×D4—791no—
572C22×D4—791no—
573C22×D4C22×D7911yescharacteristic
574C23×C4—794no—
575C23×C4—794no—
576C23×C4—791no—
577C23×C4—792no—
578C23×C4—792no—
579C23×C4—791no—
580C23×C4—791no—
581C23×C4C22×D7912yes—
582C23×C4C22×D7914yes—
583C4⋊Q8—7932no—
584C4⋊Q8—798no—
585C4⋊Q8—798no—
586C4⋊Q8C22×D7918yes—
587C4⋊Q8C22×D79116yes—
588#127—798no—
589#126—7916no—
590#126—7932no—
591#125—798no—
592#125—7916no—
593#125—7932no—
594#125—7916no—
595#124—798no—
596#124—7932no—
597#124—7932no—
598#124—7916no—
599#124—7932no—
600#123—7932no—
601#123—7932no—
602#123—7916no—
603#123—7932no—
604#123—7932no—
605C22⋊Q8—798no—
606C22⋊Q8—7916no—
607C22⋊Q8—7916no—
608C22⋊Q8—7916no—
609C22⋊Q8—7932no—
610C22⋊Q8—7916no—
611C22⋊Q8—7932no—
612C22⋊Q8—7932no—
613C22⋊Q8C22×D79116yes—
614C22⋊Q8C22×D79132yes—
615#121—798no—
616#121—7916no—
617#121—7916no—
618#121—7932no—
619#121—798no—
620#121—798no—
621#121—7932no—
622#121—7916no—
623#121—7916no—
624#121—7932no—
625#121—7932no—
626C4×Q8—7916no—
627C4×Q8—7916no—
628C4×Q8C22×D7918yes—
629C4×D4—7916no—
630C4×D4—7932no—
631C4×D4—798no—
632C4×D4—7916no—
633C4×D4—798no—
634C4×D4—7916no—
635C4×D4C22×D7918yes—
636C4×D4C22×D79116yes—
637#117—7916no—
638#117—7916no—
639#117—7932no—
640#117—7916no—
641#117—7916no—
642C2×C4⋊C4—791no—
643C2×C4⋊C4—792no—
644C2×C4⋊C4—794no—
645C2×C4⋊C4—794no—
646C2×C4⋊C4—792no—
647C2×C4⋊C4—791no—
648C2×C4⋊C4—792no—
649C2×C4⋊C4—792no—
650C2×C4⋊C4—792no—
651C2×C4⋊C4—792no—
652C2×C4⋊C4—794no—
653C2×C4⋊C4—794no—
654C2×C4⋊C4—794no—
655C2×C4⋊C4—7916no—
656C2×C4⋊C4—7916no—
657C2×C4⋊C4C22×D7911yescharacteristic
658C2×C4⋊C4C22×D7912yes—
659C2×C4⋊C4C22×D7911yescharacteristic
660C2×C4⋊C4C22×D7914yes—
661C2×C4⋊C4C22×D7912yes—
662C2×C4⋊C4C22×D7912yes—
663C2×C22⋊C4—794no—
664C2×C22⋊C4—792no—
665C2×C22⋊C4—792no—
666C2×C22⋊C4—792no—
667C2×C22⋊C4—794no—
668C2×C22⋊C4—792no—
669C2×C22⋊C4—794no—
670C2×C22⋊C4—794no—
671C2×C22⋊C4—792no—
672C2×C22⋊C4—792no—
673C2×C22⋊C4—794no—
674C2×C22⋊C4—792no—
675C2×C22⋊C4—792no—
676C2×C22⋊C4C22×D7914yes—
677C2×C22⋊C4C22×D7912yes—
678C2×C42—794no—
679C2×C42—794no—
680C2×C42—791no—
681C2×C42—791no—
682C2×C42—791no—
683C2×C42—798no—
684C2×C42C22×D7912yes—
685C2×C42C22×D7911yescharacteristic
686C24—792no—
687C24—791no—
688C24—792no—
689C24C23×D7912yes—
690#41—31632no—
691#41—31632no—
692C2×Q8—24no—
693C2×Q8—28no—
694C2×Q8—48no—
695C2×Q8—432no—
696C2×Q8—3164no—
697C2×Q8—3164no—
698C2×Q8—798no—
699C2×Q8—798no—
700C2×Q8C23×D7918yes—
701C2×Q8C23×D7914yes—
702C2×Q8C23×D79116yes—
703C2×D4—24no—
704C2×D4—3164no—
705C2×D4—3164no—
706C2×D4—3168no—
707C2×D4—3164no—
708C2×D4—3168no—
709C2×D4—3164no—
710C2×D4—3164no—
711C2×D4—7916no—
712C2×D4—798no—
713C2×D4—798no—
714C2×D4—798no—
715C2×D4—798no—
716C2×D4—7916no—
717C2×D4—798no—
718C2×D4—794no—
719C2×D4—794no—
720C2×D4—1584no—
721C2×D4—1584no—
722C2×D4C23×D7914yes—
723C22×C4—28no—
724C22×C4—48no—
725C22×C4—3168no—
726C22×C4—3162no—
727C22×C4—3168no—
728C22×C4—794no—
729C22×C4—7916no—
730C22×C4—7916no—
731C22×C4—791no—
732C22×C4—792no—
733C22×C4—794no—
734C22×C4—791no—
735C22×C4—791no—
736C22×C4—792no—
737C22×C4—794no—
738C22×C4—794no—
739C22×C4—798no—
740C22×C4—798no—
741C22×C4—1588no—
742C22×C4—1584no—
743C22×C4—1588no—
744C22×C4—1584no—
745C22×C4C23×D7918yes—
746C22×C4C23×D7912yes—
747C22×C4C23×D7911yescharacteristic
748C22×C4C23×D7914yes—
749C22×C4C23×D7912yes—
750C22×C4C23×D7912yes—
751C22×C4C23×D79116yes—
752C22×C4C23×D7911yescharacteristic
753C22×C4C23×D7911yescharacteristic
754C4⋊C4—7916no—
755C4⋊C4—7916no—
756C4⋊C4—798no—
757C4⋊C4—798no—
758C4⋊C4—798no—
759C4⋊C4—7916no—
760C4⋊C4—7916no—
761C4⋊C4—794no—
762C4⋊C4—798no—
763C4⋊C4—798no—
764C4⋊C4—794no—
765C4⋊C4—798no—
766C4⋊C4—7916no—
767C4⋊C4C23×D7914yes—
768C4⋊C4C23×D7918yes—
769C4⋊C4C23×D7914yes—
770C4⋊C4C23×D79116yes—
771C4⋊C4C23×D7918yes—
772C4⋊C4C23×D7918yes—
773C22⋊C4—7916no—
774C22⋊C4—798no—
775C22⋊C4—798no—
776C22⋊C4—798no—
777C22⋊C4—7916no—
778C22⋊C4—798no—
779C22⋊C4—7916no—
780C22⋊C4—7916no—
781C22⋊C4—798no—
782C22⋊C4—798no—
783C22⋊C4—7916no—
784C22⋊C4—798no—
785C22⋊C4—798no—
786C22⋊C4C23×D79116yes—
787C22⋊C4C23×D7918yes—
788C42—794no—
789C42—794no—
790C42—794no—
791C42—7916no—
792C42—7916no—
793C42C23×D7914yes—
794C42C23×D7918yes—
795C23—24no—
796C23—24no—
797C23—24no—
798C23—794no—
799C23—792no—
800C23—794no—
801C23—1584no—
802C23—1582no—
803C23—1584no—
804C23—1584no—
805C23—1582no—
806C23—1584no—
807C23—1584no—
808C23—1582no—
809C23—1584no—
810C23C24×D7914yes—
811C23C24×D7911yescharacteristic
812Q8—28no—
813Q8—216no—
814Q8—416no—
815Q8—3168no—
816Q8—3168no—
817D4—28no—
818D4—3168no—
819D4—31616no—
820D4—3168no—
821D4—3168no—
822D4—31616no—
823D4—3168no—
824D4—3168no—
825D4—1588no—
826D4—1588no—
827C2×C4—24no—
828C2×C4—24no—
829C2×C4—28no—
830C2×C4—24no—
831C2×C4—22no—
832C2×C4—216no—
833C2×C4—416no—
834C2×C4—31616no—
835C2×C4—31616no—
836C2×C4—3164no—
837C2×C4—792no—
838C2×C4—794no—
839C2×C4—798no—
840C2×C4—792no—
841C2×C4—792no—
842C2×C4—794no—
843C2×C4—1584no—
844C2×C4—1582no—
845C2×C4—1582no—
846C2×C4—1584no—
847C2×C4—1582no—
848C2×C4—1588no—
849C2×C4—15816no—
850C2×C4—1588no—
851C2×C4—1588no—
852C2×C4—15816no—
853C2×C4#1457920614yes—
854C2×C4#1457920914yes—
855C2×C4C24×D7914yes—
856C2×C4C24×D7912yes—
857C2×C4C24×D7918yes—
858C2×C4C24×D7914yes—
859C2×C4C24×D7914yes—
860C2×C4C24×D7912yes—
861C2×C4C24×D7912yes—
862C22—24no—
863C22—24no—
864C22—24no—
865C22—48no—
866C22—3168no—
867C22—3164no—
868C22—3168no—
869C22—1584no—
870C22—1584no—
871C22—1582no—
872C22—1584no—
873C22—1582no—
874C22—1584no—
875C22—1584no—
876C22—1582no—
877C22—1584no—
878C22C2×#1457920612yes—
879C22C2×#1457920912yes—
880C22#1909940012yes—
881C22C25×D7911yescharacteristic
882C4—24no—
883C4—24no—
884C4—28no—
885C4—24no—
886C4—22no—
887C4—1584no—
888C4—1582no—
889C4—1582no—
890C4—1584no—
891C4—1582no—
892C4—1588no—
893C4C2×#1457920614yes—
894C4C2×#1457920914yes—
895C2—44no—
896C2—3164no—
897C2—3162no—
898C2—3164no—
899C2#2377778514yesdirect product factor
900C2C22×#1457920611yescharacteristic
901C2C22×#1457920911yescharacteristic
902C2C2×#1909940011yescharacteristic
subgroupG/H
centerC23C24×D79
commutator, cosocleC22×C79C26
FrattiniC22C25×D79
FittingC2×D4×Q8×C79C2
socleC23×C79C25
hypercenterC2×D4×Q8D79
hypocenterC79C2×#3547
LCSG ▷ C22×C79 ▷ C79
UCSC1 ◁ C23 ◁ C2×D4×Q8

Complements

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

NH ≅ G/Ntype
1. #23777785C2direct (N × H)
2. C2×#19099309C2semidirect
3. C2×#19099279C2semidirect
4. C2×#19099278C2semidirect
5. C2×#19099273C2semidirect
6. C2×#19099263C2semidirect
7. C2×#19099247C2semidirect
8. C2×#19099224C2semidirect
9. C2×#19099216C2semidirect
10. C2×#19099190C2semidirect
11. C2×#19099183C2semidirect
12. C2×#19099164C2semidirect
13. C2×#19099143C2semidirect
14. C2×#19099137C2semidirect
15. C2×#19099118C2semidirect
16. C2×#19099110C2semidirect
17. C2×#19099100C2semidirect
18. C2×D4×Q8×C79C2semidirect
21. #19099309C22semidirect
22. #19099279C22semidirect
23. #19099278C22semidirect
24. #19099273C22semidirect
25. #19099263C22semidirect
26. #19099247C22semidirect
27. #19099224C22semidirect
28. #19099216C22semidirect
29. #19099190C22semidirect
30. #19099183C22semidirect
31. #19099164C22semidirect
32. #19099143C22semidirect
33. #19099137C22semidirect
34. #19099118C22semidirect
35. #19099110C22semidirect
40. #19099100C22semidirect
93. D4×Q8×C79C22semidirect
445. C2×C79#3547semidirect
459. C2×D4×Q8D79semidirect
470. C79C2×#3547semidirect
480. D4×Q8C2×D79semidirect
899. C2#23777785direct (N × H)

Maximal subgroups

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

subgroupindex
#237777852
C2×#190993092
C2×#190992792
C2×#190992782
C2×#190992732
C2×#190992632
C2×#190992472
C2×#190992242
C2×#190992162
C2×#190991902
C2×#190991832
C2×#190991642
C2×#190991432
C2×#190991372
C2×#190991182
C2×#190991102
C2×#190991002
C2×D4×Q8×C792
C2×#354779