Finite Group Databasebeta

← C2×#23777890 #35195981

Subgroups — C2×#23777890 #35195981

Order 20224.

6446 conjugacy classes of subgroups.

The subgroup lattice has 828 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#23777890C2132yesmaximal, direct product factor
2C2×#19099316C214yesmaximal, complemented
3C2×Q8×Dic158C211yesmaximal, characteristic, complemented
4C2×#19099291C211yesmaximal, characteristic, complemented
5C2×#19099290C212yesmaximal, complemented
6C2×#19099283C212yesmaximal, complemented
7C2×#19099283C211yesmaximal, characteristic, complemented
8C2×#19099282C212yesmaximal, complemented
9C2×#19099270C211yesmaximal, characteristic, complemented
10C2×#19099253C212yesmaximal, complemented
11C2×#19099191C212yesmaximal, complemented
12C2×#19099180C212yesmaximal
13C2×#19099175C212yesmaximal, complemented
14C2×#19099173C212yesmaximal, complemented
15C2×#19099170C214yesmaximal, complemented
16C2×#19099120C211yesmaximal, characteristic, complemented
17C2×#19099120C211yesmaximal, characteristic, complemented
18C2×#529×C79C211yesmaximal, characteristic
19#19099316C22164yescomplemented
20Q8×Dic158C22116yescomplemented
21#19099291C22116yescomplemented
22#19099290C22132yescomplemented
23#19099283C22132yescomplemented
24#19099283C22116yescomplemented
25#19099282C22132yescomplemented
26#19099270C22116yescomplemented
27#19099253C22132yescomplemented
28#19099191C22132yescomplemented
29#19099180C22132yes—
30#19099175C22132yescomplemented
31#19099173C22132yescomplemented
32#19099170C22164yescomplemented
33#19099120C22116yescomplemented
34#19099120C22116yescomplemented
35C2×#14579161C2211yescharacteristic
36C2×#14579161C2211yescharacteristic
37C2×#14579161C2212yes—
38C2×#14579161C2211yescharacteristic
39C2×#14579161C2211yescharacteristic
40C2×#14579160C2212yes—
41C2×#14579160C2214yes—
42C2×#14579160C2214yes—
43C2×#14579159C2212yes—
44C2×#14579154C2214yes—
45C2×#14579154C2214yes—
46C2×#14579154C2214yes—
47C2×#14579154C2214yes—
48C2×#14579154C2214yes—
49C2×#14579154C2214yes—
50C2×#14579153C2212yes—
51C2×#14579153C2212yes—
52C2×#14579153C2212yes—
53C2×#14579152C2214yes—
54C2×#14579152C2212yes—
55C2×#14579151C2214yes—
56C2×#14579151C2214yes—
57C2×#14579151C2214yes—
58C2×#14579151C2214yes—
59C2×#14579148C2212yes—
60C2×#14579148C2214yes—
61C2×#14579142C2214yes—
62C2×#14579140C2212yes—
63C2×#14579140C2212yes—
64C2×#14579140C2212yes—
65C2×#14579140C2211yescharacteristic
66C2×#14579140C2211yescharacteristic
67C2×#14579140C2212yes—
68C2×#14579140C2212yes—
69C2×#14579138C2214yes—
70C2×#14579138C2214yes—
71C2×#14579138C2214yes—
72C2×Q8×Dic79C2212yes—
73C2×C4×Dic158C2212yes—
74C2×C4×Dic158C2212yes—
75C2×C4×Dic158C2211yescharacteristic
76C2×C4×Dic158C2212yes—
77C2×C4×Dic158C2212yes—
78C2×C4×Dic158C2211yescharacteristic
79C2×C4×Dic158C2212yes—
80C2×#14579126C2212yes—
81C2×#14579126C2214yes—
82C2×#14579126C2212yes—
83C2×D4×Dic79C2212yes—
84C2×#14579120C2212yes—
85C2×#14579120C2212yes—
86C2×#14579120C2212yes—
87C2×#14579117C2214yes—
88C22×C4⋊Dic79C2212yes—
89#529×C79C22116yes—
90C2×#126×C79C2212yes—
91C2×#125×C79C2211yescharacteristic
92C2×#124×C79C2211yescharacteristic
93C2×#123×C79C2212yes—
94C2×C22⋊Q8×C79C2211yescharacteristic
95C2×#121×C79C2211yescharacteristic
96C2×C4×Q8×C79C2211yescharacteristic
97C2×C4×D4×C79C2212yes—
98C2×C4×D4×C79C2211yescharacteristic
99C2×#117×C79C2212yes—
100C22×C42×C79C2211yescharacteristic
101C22×Dic158C2312yes—
102C22×Dic158C2311yescharacteristic
103C22×Dic158C2311yescharacteristic
104C22×Dic158C2314yes—
105C22×Dic158C2312yes—
106C22×Dic158C2312yes—
107C23×Dic79C2314yes—
108#14579161C2318yes—
109#14579161C2318yes—
110#14579161C23116yes—
111#14579161C2318yes—
112#14579161C2318yes—
113#14579160C23132yes—
114#14579160C23116yes—
115#14579160C23132yes—
116#14579159C23116yes—
117#14579154C23132yes—
118#14579154C23132yes—
119#14579154C23132yes—
120#14579154C23132yes—
121#14579154C23132yes—
122#14579154C23132yes—
123#14579153C23116yes—
124#14579153C23116yes—
125#14579153C23116yes—
126#14579152C23132yes—
127#14579152C23116yes—
128#14579151C23132yes—
129#14579151C23132yes—
130#14579151C23132yes—
131#14579151C23132yes—
132#14579148C23116yes—
133#14579148C23132yes—
134#14579142C23132yes—
135#14579140C23116yes—
136#14579140C23116yes—
137#14579140C23116yes—
138#14579140C2318yes—
139#14579140C2318yes—
140#14579140C23116yes—
141#14579140C23116yes—
142#14579138C23132yes—
143#14579138C23132yes—
144#14579138C23132yes—
145Q8×Dic79C23116yes—
146C4×Dic158C23116yes—
147C4×Dic158C23116yes—
148C4×Dic158C23116yes—
149C4×Dic158C2318yes—
150C4×Dic158C23116yes—
151C4×Dic158C23116yes—
152C4×Dic158C2318yes—
153#14579126C23132yes—
154#14579126C23116yes—
155#14579126C23116yes—
156D4×Dic79C23116yes—
157#14579120C23116yes—
158#14579120C23116yes—
159#14579120C23116yes—
160#14579117C23132yes—
161C2×C4⋊Dic79C23116yes—
162C2×C4⋊Dic79C2311yescharacteristic
163C2×C4⋊Dic79C2312yes—
164C2×C4⋊Dic79C2314yes—
165C2×C4⋊Dic79C2312yes—
166C2×C4⋊Dic79C2311yescharacteristic
167C2×C4⋊Dic79C2312yes—
168C2×C4⋊Dic79C2312yes—
169C2×C4⋊Dic79C2312yes—
170C2×C4⋊Dic79C2312yes—
171C2×C4⋊Dic79C2312yes—
172C2×C4⋊Dic79C2314yes—
173C2×Dic79⋊C4C2312yes—
174C2×Dic79⋊C4C2314yes—
175C2×Dic79⋊C4C2312yes—
176C2×Dic79⋊C4C2314yes—
177C2×Dic79⋊C4C2314yes—
178C2×Dic79⋊C4C2314yes—
179C2×Dic79⋊C4C2312yes—
180C2×Dic79⋊C4C2314yes—
181C2×Dic79⋊C4C2314yes—
182C2×Dic79⋊C4C2312yes—
183C2×Dic79⋊C4C2314yes—
184C2×Dic79⋊C4C2314yes—
185C2×C22⋊Dic79C2314yes—
186C2×C22⋊Dic79C2314yes—
187C2×C22⋊Dic79C2312yes—
188C2×C22⋊Dic79C2314yes—
189C2×C22⋊Dic79C2312yes—
190C2×C22⋊Dic79C2314yes—
191C2×C4×Dic79C2314yes—
192C2×C4×Dic79C2314yes—
193C2×C4×Dic79C2312yes—
194C2×C4×Dic79C2314yes—
195C2×C4×Dic79C2312yes—
196C2×C4×Dic79C2314yes—
197C22×Q8×C79C2311yescharacteristic
198C22×D4×C79C2311yescharacteristic
199C22×D4×C79C2312yes—
200C23×C4×C79C2311yescharacteristic
201C23×C4×C79C2311yescharacteristic
202C23×C4×C79C2312yes—
203C23×C4×C79C2311yescharacteristic
204#126×C79C23116yes—
205#125×C79C2318yes—
206#124×C79C2318yes—
207#123×C79C23116yes—
208C22⋊Q8×C79C2318yes—
209#121×C79C2318yes—
210C4×Q8×C79C2318yes—
211C4×D4×C79C23116yes—
212C4×D4×C79C2318yes—
213#117×C79C23116yes—
214C2×C4⋊C4×C79C2312yes—
215C2×C4⋊C4×C79C2312yes—
216C2×C4⋊C4×C79C2311yescharacteristic
217C2×C4⋊C4×C79C2312yes—
218C2×C4⋊C4×C79C2311yescharacteristic
219C2×C4⋊C4×C79C2312yes—
220C2×C22⋊C4×C79C2312yes—
221C2×C22⋊C4×C79C2312yes—
222C2×C22⋊C4×C79C2312yes—
223C2×C22⋊C4×C79C2312yes—
224C2×C22⋊C4×C79C2312yes—
225C2×C42×C79C2311yescharacteristic
226C2×C42×C79C2311yescharacteristic
227C2×C42×C79C2311yescharacteristic
228C2×C42×C79C2311yescharacteristic
229C2×C42×C79C2318yes—
230C2×C42×C79C2312yes—
231C2×Dic158—24no—
232C2×Dic158—24no—
233C2×Dic158—28no—
234C2×Dic158—44no—
235C2×Dic158—44no—
236C2×Dic158—48no—
237C2×Dic158C2418yes—
238C2×Dic158C2414yes—
239C2×Dic158C2414yes—
240C2×Dic158C24116yes—
241C2×Dic158C2418yes—
242C2×Dic158C2418yes—
243C22×Dic79—48no—
244C22×Dic79C2412yes—
245C22×Dic79C2414yes—
246C22×Dic79C2414yes—
247C22×Dic79C2412yes—
248C22×Dic79C2412yes—
249C22×Dic79C2412yes—
250C22×Dic79C24116yes—
251C4⋊Dic79C2414yes—
252C4⋊Dic79C2418yes—
253C4⋊Dic79C24116yes—
254C4⋊Dic79C2418yes—
255C4⋊Dic79C2414yes—
256C4⋊Dic79C2418yes—
257C4⋊Dic79C2418yes—
258C4⋊Dic79C2418yes—
259C4⋊Dic79C2418yes—
260C4⋊Dic79C2418yes—
261C4⋊Dic79C24116yes—
262Dic79⋊C4C2418yes—
263Dic79⋊C4C24116yes—
264Dic79⋊C4C2418yes—
265Dic79⋊C4C24116yes—
266Dic79⋊C4C24116yes—
267Dic79⋊C4C24116yes—
268Dic79⋊C4C2418yes—
269Dic79⋊C4C24116yes—
270Dic79⋊C4C24116yes—
271Dic79⋊C4C2418yes—
272Dic79⋊C4C24116yes—
273Dic79⋊C4C24116yes—
274C22⋊Dic79C24116yes—
275C22⋊Dic79C24116yes—
276C22⋊Dic79C2418yes—
277C22⋊Dic79C24116yes—
278C22⋊Dic79C2418yes—
279C22⋊Dic79C24116yes—
280C4×Dic79C24116yes—
281C4×Dic79C24116yes—
282C4×Dic79C2418yes—
283C4×Dic79C24116yes—
284C4×Dic79C2418yes—
285C4×Dic79C24116yes—
286C24×C79C2412yes—
287C24×C79C2411yescharacteristic
288C2×Q8×C79—24no—
289C2×Q8×C79C2414yes—
290C2×D4×C79—24no—
291C2×D4×C79—44no—
292C2×D4×C79C2414yes—
293C2×D4×C79C2418yes—
294C22×C4×C79—24no—
295C22×C4×C79—28no—
296C22×C4×C79—24no—
297C22×C4×C79—42no—
298C22×C4×C79C2411yescharacteristic
299C22×C4×C79C2411yescharacteristic
300C22×C4×C79C2412yes—
301C22×C4×C79C2411yescharacteristic
302C22×C4×C79C2411yescharacteristic
303C22×C4×C79C2414yes—
304C22×C4×C79C2414yes—
305C22×C4×C79C2412yes—
306C22×C4×C79C2412yes—
307C22×C4×C79C2418yes—
308C22×C4×C79C2414yes—
309C22×C4×C79C2411yescharacteristic
310C22×C4×C79C2411yescharacteristic
311C4⋊C4×C79C2418yes—
312C4⋊C4×C79C2418yes—
313C4⋊C4×C79C2414yes—
314C4⋊C4×C79C2418yes—
315C4⋊C4×C79C2414yes—
316C4⋊C4×C79C2418yes—
317C22⋊C4×C79C2418yes—
318C22⋊C4×C79C2418yes—
319C22⋊C4×C79C2418yes—
320C22⋊C4×C79C2418yes—
321C22⋊C4×C79C2418yes—
322C42×C79C2414yes—
323C42×C79C2414yes—
324C42×C79C2414yes—
325C42×C79C2414yes—
326C42×C79C2418yes—
327C23×C79—24no—
328C23×C79—22no—
329C23×C79—22no—
330C23×C79—24no—
331C23×C79—24no—
332C23×C79—22no—
333C23×C79C2512yes—
334C23×C79C2514yes—
335C23×C79C2511yescharacteristic
336Q8×C79—28no—
337D4×C79—28no—
338D4×C79—48no—
339C2×C4×C79—22no—
340C2×C4×C79—22no—
341C2×C4×C79—24no—
342C2×C4×C79—24no—
343C2×C4×C79—22no—
344C2×C4×C79—22no—
345C2×C4×C79—24no—
346C2×C4×C79—28no—
347C2×C4×C79—216no—
348C2×C4×C79—28no—
349C2×C4×C79—44no—
350C2×C4×C792−1+414yes—
351C2×C4×C792−1+414yes—
352C2×C4×C79C2512yes—
353C2×C4×C79C2514yes—
354C2×C4×C79C2514yes—
355C2×C4×C79C2514yes—
356C2×C4×C79C2512yes—
357C2×C4×C79C2512yes—
358C2×C4×C79C2512yes—
359C2×C4×C79C2512yes—
360C2×C4×C79C2512yes—
361C2×Dic79—24no—
362C2×Dic79—24no—
363C2×Dic79—28no—
364C2×Dic79—24no—
365C2×Dic79—28no—
366C2×Dic79—24no—
367C2×Dic79—416no—
368C2×Dic79C2518yes—
369C2×Dic79C2514yes—
370C2×Dic79C2514yes—
371C2×Dic79C2514yes—
372C2×Dic79C2518yes—
373C2×Dic79C2514yes—
374Dic158—28no—
375Dic158—28no—
376Dic158—216no—
377Dic158—416no—
378Dic158—48no—
379Dic158—48no—
380C22×C79—22no—
381C22×C79—22no—
382C22×C79—24no—
383C22×C79—24no—
384C22×C79—22no—
385C22×C79—24no—
386C22×C79—44no—
387C22×C79—48no—
388C22×C79C2×2−1+412yes—
389C22×C79C2×2−1+412yes—
390C22×C79#58512yes—
391C22×C79C2611yescharacteristic
392C4×C79—22no—
393C4×C79—24no—
394C4×C79—22no—
395C4×C79—24no—
396C4×C79—22no—
397C4×C79—22no—
398C4×C79—24no—
399C4×C79C2×2−1+414yes—
400C4×C79C2×2−1+414yes—
401Dic79—24no—
402Dic79—24no—
403Dic79—28no—
404Dic79—24no—
405Dic79—28no—
406Dic79—24no—
407C2×#3555—791nomaximal, Sylow
408C2×C79—42no—
409C2×C79—44no—
410C2×C79#355514yescomplemented
411C2×C79C22×2−1+411yescharacteristic
412C2×C79C22×2−1+411yescharacteristic
413C2×C79C2×#58511yescharacteristic
414#3555—7932no—
415C2×#563—794no—
416C2×Q82—791no—
417C2×#557—792no—
418C2×#557—791no—
419C2×#556—792no—
420C2×#556—792no—
421C2×#556—791no—
422C2×#554—791no—
423C2×#552—792no—
424C2×#544—792no—
425C2×#542—792no—
426C2×#541—794no—
427C2×#541—792no—
428C2×#541—792no—
429C2×#533—791no—
430C2×#533—791no—
431C2×#529D7911yescharacteristic
432C79C2×#355511yescharacteristic, complemented, Sylow
433#563—7964no—
434Q82—7916no—
435#557—7932no—
436#557—7916no—
437#556—7932no—
438#556—7932no—
439#556—7916no—
440#554—7916no—
441#552—7932no—
442#544—7932no—
443#542—7932no—
444#541—7964no—
445#541—7932no—
446#541—7932no—
447#533—7916no—
448#533—7916no—
449C2×C4⋊Q8—792no—
450C2×C4⋊Q8—794no—
451C2×C4⋊Q8—792no—
452C2×C4⋊Q8—794no—
453C2×C4⋊Q8—791no—
454C2×C4⋊Q8—791no—
455C2×C4⋊Q8—791no—
456C2×C4⋊Q8—791no—
457C2×C4⋊Q8—792no—
458#529C2×D79116yes—
459C2×#126—794no—
460C2×#126—794no—
461C2×#126—794no—
462C2×#126—794no—
463C2×#126—794no—
464C2×#126—794no—
465C2×#126C2×D7912yes—
466C2×#125—794no—
467C2×#125—794no—
468C2×#125—794no—
469C2×#125—792no—
470C2×#125—794no—
471C2×#125—794no—
472C2×#125—792no—
473C2×#125—792no—
474C2×#125—792no—
475C2×#125C2×D7911yescharacteristic
476C2×#124—792no—
477C2×#124—794no—
478C2×#124C2×D7911yescharacteristic
479C2×#123—794no—
480C2×#123C2×D7912yes—
481C2×C22⋊Q8—792no—
482C2×C22⋊Q8—791no—
483C2×C22⋊Q8—791no—
484C2×C22⋊Q8—792no—
485C2×C22⋊Q8—792no—
486C2×C22⋊Q8—792no—
487C2×C22⋊Q8—792no—
488C2×C22⋊Q8—794no—
489C2×C22⋊Q8—794no—
490C2×C22⋊Q8—794no—
491C2×C22⋊Q8C2×D7911yescharacteristic
492C2×#121C2×D7911yescharacteristic
493C2×C4×Q8—792no—
494C2×C4×Q8—794no—
495C2×C4×Q8—792no—
496C2×C4×Q8—792no—
497C2×C4×Q8—792no—
498C2×C4×Q8—791no—
499C2×C4×Q8—792no—
500C2×C4×Q8—792no—
501C2×C4×Q8—791no—
502C2×C4×Q8—792no—
503C2×C4×Q8—792no—
504C2×C4×Q8C2×D7911yescharacteristic
505C2×C4×D4—792no—
506C2×C4×D4C2×D7912yes—
507C2×C4×D4C2×D7911yescharacteristic
508C2×#117—792no—
509C2×#117—792no—
510C2×#117—792no—
511C2×#117—794no—
512C2×#117C2×D7912yes—
513C22×C4⋊C4—792no—
514C22×C42C2×D7911yescharacteristic
515C22×Q8—792no—
516C22×Q8—792no—
517C22×Q8—794no—
518C22×Q8—791no—
519C22×Q8—791no—
520C22×Q8—792no—
521C22×Q8C22×D7911yescharacteristic
522C22×D4C22×D7911yescharacteristic
523C22×D4C22×D7912yes—
524C23×C4—794no—
525C23×C4C22×D7912yes—
526C23×C4C22×D7911yescharacteristic
527C23×C4C22×D7911yescharacteristic
528C23×C4C22×D7911yescharacteristic
529C4⋊Q8—7916no—
530C4⋊Q8—7932no—
531C4⋊Q8—7916no—
532C4⋊Q8—7932no—
533C4⋊Q8—798no—
534C4⋊Q8—798no—
535C4⋊Q8—798no—
536C4⋊Q8—798no—
537C4⋊Q8—7916no—
538#126—7932no—
539#126—7932no—
540#126—7932no—
541#126—7932no—
542#126—7932no—
543#126—7932no—
544#126C22×D79116yes—
545#125—7932no—
546#125—7932no—
547#125—7932no—
548#125—7916no—
549#125—7932no—
550#125—7932no—
551#125—7916no—
552#125—7916no—
553#125—7916no—
554#125C22×D7918yes—
555#124—7916no—
556#124—7932no—
557#124C22×D7918yes—
558#123—7932no—
559#123C22×D79116yes—
560C22⋊Q8—7916no—
561C22⋊Q8—798no—
562C22⋊Q8—798no—
563C22⋊Q8—7916no—
564C22⋊Q8—7916no—
565C22⋊Q8—7916no—
566C22⋊Q8—7916no—
567C22⋊Q8—7932no—
568C22⋊Q8—7932no—
569C22⋊Q8—7932no—
570C22⋊Q8C22×D7918yes—
571#121C22×D7918yes—
572C4×Q8—7916no—
573C4×Q8—7932no—
574C4×Q8—7916no—
575C4×Q8—7916no—
576C4×Q8—7916no—
577C4×Q8—798no—
578C4×Q8—7916no—
579C4×Q8—7916no—
580C4×Q8—798no—
581C4×Q8—7916no—
582C4×Q8—7916no—
583C4×Q8C22×D7918yes—
584C4×D4—7916no—
585C4×D4C22×D79116yes—
586C4×D4C22×D7918yes—
587#117—7916no—
588#117—7916no—
589#117—7916no—
590#117—7932no—
591#117C22×D79116yes—
592C2×C4⋊C4—791no—
593C2×C4⋊C4—792no—
594C2×C4⋊C4—794no—
595C2×C4⋊C4—7916no—
596C2×C4⋊C4—792no—
597C2×C4⋊C4—792no—
598C2×C4⋊C4—791no—
599C2×C4⋊C4—792no—
600C2×C4⋊C4—794no—
601C2×C4⋊C4—792no—
602C2×C4⋊C4—792no—
603C2×C4⋊C4—792no—
604C2×C4⋊C4—792no—
605C2×C4⋊C4—794no—
606C2×C4⋊C4—794no—
607C2×C4⋊C4—794no—
608C2×C4⋊C4—794no—
609C2×C4⋊C4—794no—
610C2×C4⋊C4—792no—
611C2×C4⋊C4—792no—
612C2×C4⋊C4—792no—
613C2×C4⋊C4—794no—
614C2×C4⋊C4—794no—
615C2×C4⋊C4—794no—
616C2×C4⋊C4C22×D7912yes—
617C2×C4⋊C4C22×D7912yes—
618C2×C4⋊C4C22×D7911yescharacteristic
619C2×C4⋊C4C22×D7912yes—
620C2×C4⋊C4C22×D7911yescharacteristic
621C2×C4⋊C4C22×D7912yes—
622C2×C22⋊C4—792no—
623C2×C22⋊C4—794no—
624C2×C22⋊C4—792no—
625C2×C22⋊C4—794no—
626C2×C22⋊C4—794no—
627C2×C22⋊C4—794no—
628C2×C22⋊C4C22×D7912yes—
629C2×C22⋊C4C22×D7912yes—
630C2×C22⋊C4C22×D7912yes—
631C2×C22⋊C4C22×D7912yes—
632C2×C22⋊C4C22×D7912yes—
633C2×C42—794no—
634C2×C42—792no—
635C2×C42—792no—
636C2×C42—794no—
637C2×C42—794no—
638C2×C42—794no—
639C2×C42C22×D7911yescharacteristic
640C2×C42C22×D7912yes—
641C2×C42C22×D7911yescharacteristic
642C2×C42C22×D7911yescharacteristic
643C2×C42C22×D7911yescharacteristic
644C2×C42C22×D7918yes—
645C24C23×D7911yescharacteristic
646C24C23×D7912yes—
647C2×Q8—24no—
648C2×Q8—3164no—
649C2×Q8—3164no—
650C2×Q8—3168no—
651C2×Q8—798no—
652C2×Q8—798no—
653C2×Q8—7916no—
654C2×Q8—794no—
655C2×Q8—794no—
656C2×Q8—798no—
657C2×Q8—1584no—
658C2×Q8—1584no—
659C2×Q8—1588no—
660C2×Q8C23×D7914yes—
661C2×D4—24no—
662C2×D4—44no—
663C2×D4C23×D7914yes—
664C2×D4C23×D7918yes—
665C22×C4—28no—
666C22×C4—24no—
667C22×C4—24no—
668C22×C4—42no—
669C22×C4—3168no—
670C22×C4—7916no—
671C22×C4—794no—
672C22×C4—792no—
673C22×C4—792no—
674C22×C4—792no—
675C22×C4—794no—
676C22×C4—792no—
677C22×C4C23×D7914yes—
678C22×C4C23×D7914yes—
679C22×C4C23×D7918yes—
680C22×C4C23×D7911yescharacteristic
681C22×C4C23×D7912yes—
682C22×C4C23×D7912yes—
683C22×C4C23×D7912yes—
684C22×C4C23×D7911yescharacteristic
685C22×C4C23×D7911yescharacteristic
686C22×C4C23×D7911yescharacteristic
687C22×C4C23×D7914yes—
688C22×C4C23×D7911yescharacteristic
689C22×C4C23×D7911yescharacteristic
690C4⋊C4—798no—
691C4⋊C4—7916no—
692C4⋊C4—798no—
693C4⋊C4—798no—
694C4⋊C4—7916no—
695C4⋊C4—7916no—
696C4⋊C4—7916no—
697C4⋊C4—7916no—
698C4⋊C4—7916no—
699C4⋊C4—798no—
700C4⋊C4—7916no—
701C4⋊C4—7916no—
702C4⋊C4—794no—
703C4⋊C4—798no—
704C4⋊C4—7916no—
705C4⋊C4—798no—
706C4⋊C4—794no—
707C4⋊C4—798no—
708C4⋊C4—798no—
709C4⋊C4—798no—
710C4⋊C4—798no—
711C4⋊C4—798no—
712C4⋊C4—7916no—
713C4⋊C4C23×D7918yes—
714C4⋊C4C23×D7918yes—
715C4⋊C4C23×D7914yes—
716C4⋊C4C23×D7918yes—
717C4⋊C4C23×D7914yes—
718C4⋊C4C23×D7918yes—
719C22⋊C4—798no—
720C22⋊C4—7916no—
721C22⋊C4—798no—
722C22⋊C4—7916no—
723C22⋊C4—7916no—
724C22⋊C4—7916no—
725C22⋊C4C23×D7918yes—
726C22⋊C4C23×D7918yes—
727C22⋊C4C23×D7918yes—
728C22⋊C4C23×D7918yes—
729C22⋊C4C23×D7918yes—
730C42—7916no—
731C42—798no—
732C42—798no—
733C42—7916no—
734C42—7916no—
735C42—7916no—
736C42C23×D7914yes—
737C42C23×D7914yes—
738C42C23×D7914yes—
739C42C23×D7914yes—
740C42C23×D7918yes—
741C23—22no—
742C23—22no—
743C23—24no—
744C23—24no—
745C23—22no—
746C23—24no—
747C23C24×D7912yes—
748C23C24×D7914yes—
749C23C24×D7911yescharacteristic
750Q8—28no—
751Q8—3168no—
752Q8—3168no—
753Q8—31616no—
754Q8—1588no—
755Q8—1588no—
756Q8—15816no—
757D4—28no—
758D4—48no—
759C2×C4—22no—
760C2×C4—24no—
761C2×C4—22no—
762C2×C4—24no—
763C2×C4—22no—
764C2×C4—22no—
765C2×C4—24no—
766C2×C4—28no—
767C2×C4—216no—
768C2×C4—28no—
769C2×C4—44no—
770C2×C4—31616no—
771C2×C4—798no—
772C2×C4—794no—
773C2×C4—794no—
774C2×C4—794no—
775C2×C4—798no—
776C2×C4—794no—
777C2×C4—1584no—
778C2×C4—1584no—
779C2×C4—1588no—
780C2×C4—1584no—
781C2×C4—1588no—
782C2×C4—1584no—
783C2×C4#1457920814yes—
784C2×C4#1457920814yes—
785C2×C4C24×D7912yes—
786C2×C4C24×D7914yes—
787C2×C4C24×D7914yes—
788C2×C4C24×D7914yes—
789C2×C4C24×D7912yes—
790C2×C4C24×D7912yes—
791C2×C4C24×D7912yes—
792C2×C4C24×D7912yes—
793C2×C4C24×D7912yes—
794C22—22no—
795C22—22no—
796C22—24no—
797C22—24no—
798C22—22no—
799C22—24no—
800C22—44no—
801C22—48no—
802C22C2×#1457920812yes—
803C22C2×#1457920812yes—
804C22#1909939912yes—
805C22C25×D7911yescharacteristic
806C4—22no—
807C4—24no—
808C4—22no—
809C4—24no—
810C4—22no—
811C4—22no—
812C4—24no—
813C4—1584no—
814C4—1584no—
815C4—1588no—
816C4—1584no—
817C4—1588no—
818C4—1584no—
819C4C2×#1457920814yes—
820C4C2×#1457920814yes—
821C2—42no—
822C2—44no—
823C2#2377789014yesdirect product factor
824C2C22×#1457920811yescharacteristic
825C2C22×#1457920811yescharacteristic
826C2C2×#1909939911yescharacteristic
subgroupG/H
centerC23C24×D79
commutator, cosocleC22×C79C26
FrattiniC22C25×D79
FittingC2×#529×C79C2
socleC23×C79C25
prime radicalC2×#121×C79C22
hypercenterC2×#529D79
hypocenterC79C2×#3555
LCSG ▷ C22×C79 ▷ C79
UCSC1 ◁ C23 ◁ C2×#529

Complements

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

NH ≅ G/Ntype
1. #23777890C2direct (N × H)
2. C2×#19099316C2semidirect
3. C2×Q8×Dic158C2semidirect
4. C2×#19099291C2semidirect
5. C2×#19099290C2semidirect
6. C2×#19099283C2semidirect
7. C2×#19099283C2semidirect
8. C2×#19099282C2semidirect
9. C2×#19099270C2semidirect
10. C2×#19099253C2semidirect
11. C2×#19099191C2semidirect
13. C2×#19099175C2semidirect
14. C2×#19099173C2semidirect
15. C2×#19099170C2semidirect
16. C2×#19099120C2semidirect
17. C2×#19099120C2semidirect
19. #19099316C22semidirect
20. Q8×Dic158C22semidirect
21. #19099291C22semidirect
22. #19099290C22semidirect
23. #19099283C22semidirect
24. #19099283C22semidirect
25. #19099282C22semidirect
26. #19099270C22semidirect
27. #19099253C22semidirect
28. #19099191C22semidirect
30. #19099175C22semidirect
31. #19099173C22semidirect
32. #19099170C22semidirect
33. #19099120C22semidirect
34. #19099120C22semidirect
410. C2×C79#3555semidirect
432. C79C2×#3555semidirect
823. C2#23777890direct (N × H)

Maximal subgroups

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

subgroupindex
#237778902
C2×#190993162
C2×Q8×Dic1582
C2×#190992912
C2×#190992902
C2×#190992832
C2×#190992822
C2×#190992702
C2×#190992532
C2×#190991912
C2×#190991802
C2×#190991752
C2×#190991732
C2×#190991702
C2×#190991202
C2×#529×C792
C2×#355579