Finite Group Databasebeta

← C2×#23777884 #35195990

Subgroups — C2×#23777884 #35195990

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#23777884C2132yesmaximal, direct product factor
2C2×#19099317C214yesmaximal, complemented
3C2×Q8×Dic158C211yesmaximal, characteristic, complemented
4C2×#19099289C212yesmaximal, complemented
5C2×#19099287C211yesmaximal, characteristic, complemented
6C2×#19099287C212yesmaximal, complemented
7C2×#19099286C212yesmaximal, complemented
8C2×#19099273C211yesmaximal, characteristic, complemented
9C2×#19099251C212yesmaximal, complemented
10C2×#19099193C212yesmaximal, complemented
11C2×#19099185C212yesmaximal
12C2×#19099174C212yesmaximal, complemented
13C2×#19099172C214yesmaximal, complemented
14C2×#19099171C212yesmaximal, complemented
15C2×#19099118C211yesmaximal, characteristic, complemented
16C2×#19099117C211yesmaximal, characteristic, complemented
17C2×#19099100C211yesmaximal, characteristic
18C2×#557×C79C211yesmaximal, characteristic, complemented
19#19099317C22164yescomplemented
20Q8×Dic158C22116yescomplemented
21#19099289C22132yescomplemented
22#19099287C22132yescomplemented
23#19099287C22116yescomplemented
24#19099286C22132yescomplemented
25#19099273C22116yescomplemented
26#19099251C22132yescomplemented
27#19099193C22132yescomplemented
28#19099185C22132yes—
29#19099174C22132yescomplemented
30#19099172C22164yescomplemented
31#19099171C22132yescomplemented
32#19099118C22116yescomplemented
33#19099117C22116yescomplemented
34C2×#14579161C2212yes—
35C2×#14579161C2211yescharacteristic
36C2×#14579160C2212yes—
37C2×#14579160C2211yescharacteristic
38C2×#14579160C2214yes—
39C2×#14579160C2214yes—
40C2×#14579159C2211yescharacteristic
41#19099100C22116yes—
42C2×#14579156C2214yes—
43C2×#14579156C2212yes—
44C2×#14579156C2214yes—
45C2×#14579156C2214yes—
46C2×#14579156C2214yes—
47C2×#14579156C2214yes—
48C2×#14579155C2214yes—
49C2×#14579153C2212yes—
50C2×#14579153C2214yes—
51C2×#14579152C2212yes—
52C2×#14579152C2214yes—
53C2×#14579152C2211yescharacteristic
54C2×#14579151C2214yes—
55C2×#14579151C2212yes—
56C2×#14579151C2214yes—
57C2×#14579150C2212yes—
58C2×#14579150C2211yescharacteristic
59C2×#14579149C2214yes—
60C2×#14579146C2214yes—
61C2×#14579146C2212yes—
62C2×#14579141C2214yes—
63C2×#14579141C2211yescharacteristic
64C2×#14579141C2212yes—
65C2×#14579141C2212yes—
66C2×#14579139C2214yes—
67C2×#14579139C2214yes—
68C2×#14579139C2212yes—
69C2×#14579137C2212yes—
70C2×#14579137C2211yescharacteristic
71C2×#14579137C2212yes—
72C2×#14579137C2211yescharacteristic
73C2×#14579136C2211yescharacteristic
74C2×Q8×Dic79C2212yes—
75C2×Q8×Dic79C2212yes—
76C2×Q8×Dic79C2212yes—
77C2×C4×Dic158C2212yes—
78C2×C4×Dic158C2212yes—
79C2×C4×Dic158C2211yescharacteristic
80C2×C4×Dic158C2214yes—
81C2×#14579126C2212yes—
82C2×C4×D316C2212yes—
83C2×C4×D316C2212yes—
84C2×C4×D316C2211yescharacteristic
85C2×#14579119C2212yes—
86C2×#14579119C2212yes—
87C2×#14579119C2214yes—
88C2×#14579118C2212yes—
89C2×#14579118C2212yes—
90C2×C4⋊C4×D79C2212yes—
91C2×C42×D79C2211yescharacteristic
92#557×C79C22116yescomplemented
93C2×C4⋊Q8×C79C2211yescharacteristic
94C2×C4⋊Q8×C79C2212yes—
95C2×#125×C79C2212yes—
96C2×#125×C79C2214yes—
97C2×C4×Q8×C79C2212yes—
98C2×C4×Q8×C79C2211yescharacteristic
99C2×C4×Q8×C79C2211yescharacteristic
100C2×C4×Q8×C79C2212yes—
101C22×Dic158C2311yescharacteristic
102C22×Dic158C2312yes—
103C22×Dic158C2312yes—
104C22×Dic158C2314yes—
105C22×D316C2311yescharacteristic
106C22×D316C2312yes—
107C22×C4×D79C2311yescharacteristic
108C22×C4×D79C2311yescharacteristic
109C22×C4×D79C2312yes—
110C22×C4×D79C2311yescharacteristic
111C22×C4×D79C2314yes—
112#14579161C23116yes—
113#14579161C2318yes—
114#14579160C23132yes—
115#14579160C23116yes—
116#14579160C2318yes—
117#14579160C23132yes—
118#14579159C2318yes—
119#14579156C23132yes—
120#14579156C23116yes—
121#14579156C23132yes—
122#14579156C23132yes—
123#14579156C23132yes—
124#14579156C23132yes—
125#14579155C23132yes—
126#14579153C23132yes—
127#14579153C23116yes—
128#14579152C23116yes—
129#14579152C23132yes—
130#14579152C2318yes—
131#14579151C23132yes—
132#14579151C23116yes—
133#14579151C23132yes—
134#14579150C23116yes—
135#14579150C2318yes—
136#14579149C23132yes—
137#14579146C23132yes—
138#14579146C23116yes—
139#14579141C23116yes—
140#14579141C23132yes—
141#14579141C2318yes—
142#14579141C23116yes—
143#14579139C23132yes—
144#14579139C23132yes—
145#14579139C23116yes—
146#14579137C23116yes—
147#14579137C2318yes—
148#14579137C23116yes—
149#14579137C2318yes—
150#14579136C2318yes—
151Q8×Dic79C23116yes—
152Q8×Dic79C23116yes—
153Q8×Dic79C23116yes—
154C4×Dic158C23116yes—
155C4×Dic158C23132yes—
156C4×Dic158C23116yes—
157C4×Dic158C2318yes—
158#14579126C23116yes—
159C4×D316C23116yes—
160C4×D316C23116yes—
161C4×D316C2318yes—
162#14579119C23132yes—
163#14579119C23116yes—
164#14579119C23116yes—
165#14579118C23116yes—
166#14579118C23116yes—
167C2×C4⋊Dic79C2312yes—
168C2×C4⋊Dic79C2311yescharacteristic
169C2×C4⋊Dic79C2312yes—
170C2×C4⋊Dic79C2312yes—
171C2×C4⋊Dic79C2311yescharacteristic
172C2×C4⋊Dic79C2312yes—
173C2×C4⋊Dic79C2314yes—
174C2×C4⋊Dic79C2314yes—
175C2×C4⋊Dic79C2314yes—
176C2×Dic79⋊C4C2314yes—
177C2×Dic79⋊C4C2312yes—
178C2×Dic79⋊C4C2312yes—
179C2×Dic79⋊C4C2312yes—
180C2×Dic79⋊C4C2312yes—
181C2×Dic79⋊C4C2314yes—
182C2×Dic79⋊C4C2312yes—
183C2×Dic79⋊C4C2314yes—
184C2×Dic79⋊C4C2312yes—
185C2×Dic79⋊C4C2312yes—
186C2×Dic79⋊C4C2314yes—
187C4⋊C4×D79C23116yes—
188C2×(C2×D79)⋊C4C2312yes—
189C2×(C2×D79)⋊C4C2312yes—
190C2×(C2×D79)⋊C4C2312yes—
191C2×(C2×D79)⋊C4C2312yes—
192C2×(C2×D79)⋊C4C2312yes—
193C2×(C2×D79)⋊C4C2314yes—
194C2×(C2×D79)⋊C4C2314yes—
195C2×(C2×D79)⋊C4C2314yes—
196C2×(C2×D79)⋊C4C2314yes—
197C2×(C2×D79)⋊C4C2312yes—
198C2×(C2×D79)⋊C4C2312yes—
199C2×C4×Dic79C2311yescharacteristic
200C2×C4×Dic79C2311yescharacteristic
201C2×C4×Dic79C2311yescharacteristic
202C2×C4×Dic79C2312yes—
203C2×C4×Dic79C2314yes—
204C2×C4×Dic79C2314yes—
205C2×C4×Dic79C2314yes—
206C42×D79C2318yes—
207C22×Q8×C79C2311yescharacteristic
208C22×Q8×C79C2312yes—
209C22×Q8×C79C2311yescharacteristic
210C4⋊Q8×C79C23116yes—
211C4⋊Q8×C79C2318yes—
212#125×C79C23132yes—
213#125×C79C23116yes—
214C4×Q8×C79C23116yes—
215C4×Q8×C79C23116yes—
216C4×Q8×C79C2318yes—
217C4×Q8×C79C2318yes—
218C2×C4⋊C4×C79C2311yescharacteristic
219C2×C4⋊C4×C79C2311yescharacteristic
220C2×C4⋊C4×C79C2312yes—
221C2×C4⋊C4×C79C2314yes—
222C2×C4⋊C4×C79C2312yes—
223C2×C4⋊C4×C79C2312yes—
224C2×C4⋊C4×C79C2314yes—
225C2×C4⋊C4×C79C2314yes—
226C2×C4⋊C4×C79C2312yes—
227C2×C42×C79C2312yes—
228C2×C42×C79C2314yes—
229C2×C42×C79C2311yescharacteristic
230C2×C42×C79C2312yes—
231C23×D79C2411yescharacteristic
232C23×D79C2412yes—
233C2×Dic158—24no—
234C2×Dic158—44no—
235C2×Dic158—44no—
236C2×Dic158—48no—
237C2×Dic158C2414yes—
238C2×Dic158C2418yes—
239C2×Dic158C2418yes—
240C2×Dic158C24116yes—
241C2×D316—24no—
242C2×D316—44no—
243C2×D316C2414yes—
244C2×D316C2418yes—
245C22×Dic79C2412yes—
246C22×Dic79C2414yes—
247C22×Dic79C2411yescharacteristic
248C22×Dic79C2412yes—
249C22×Dic79C2411yescharacteristic
250C22×Dic79C2411yescharacteristic
251C22×Dic79C2412yes—
252C2×C4×D79—24no—
253C2×C4×D79—24no—
254C2×C4×D79—28no—
255C2×C4×D79—48no—
256C2×C4×D79—42no—
257C2×C4×D79C2414yes—
258C2×C4×D79C2414yes—
259C2×C4×D79C2418yes—
260C2×C4×D79C2414yes—
261C2×C4×D79C24116yes—
262C4⋊Dic79C2418yes—
263C4⋊Dic79C2414yes—
264C4⋊Dic79C2418yes—
265C4⋊Dic79C2418yes—
266C4⋊Dic79C2414yes—
267C4⋊Dic79C2418yes—
268C4⋊Dic79C24116yes—
269C4⋊Dic79C24116yes—
270C4⋊Dic79C24116yes—
271Dic79⋊C4C24116yes—
272Dic79⋊C4C2418yes—
273Dic79⋊C4C2418yes—
274Dic79⋊C4C2418yes—
275Dic79⋊C4C2418yes—
276Dic79⋊C4C24116yes—
277Dic79⋊C4C2418yes—
278Dic79⋊C4C24116yes—
279Dic79⋊C4C2418yes—
280Dic79⋊C4C2418yes—
281Dic79⋊C4C24116yes—
282(C2×D79)⋊C4C2418yes—
283(C2×D79)⋊C4C2418yes—
284(C2×D79)⋊C4C2418yes—
285(C2×D79)⋊C4C2418yes—
286(C2×D79)⋊C4C2418yes—
287(C2×D79)⋊C4C24116yes—
288(C2×D79)⋊C4C24116yes—
289(C2×D79)⋊C4C24116yes—
290(C2×D79)⋊C4C24116yes—
291(C2×D79)⋊C4C2418yes—
292(C2×D79)⋊C4C2418yes—
293C4×Dic79C2414yes—
294C4×Dic79C2414yes—
295C4×Dic79C2414yes—
296C4×Dic79C2418yes—
297C4×Dic79C24116yes—
298C4×Dic79C24116yes—
299C4×Dic79C24116yes—
300C2×Q8×C79—28no—
301C2×Q8×C79—24no—
302C2×Q8×C79—24no—
303C2×Q8×C79C2414yes—
304C2×Q8×C79C2418yes—
305C2×Q8×C79C2414yes—
306C22×C4×C79C2412yes—
307C22×C4×C79C2411yescharacteristic
308C22×C4×C79C2412yes—
309C22×C4×C79C2412yes—
310C22×C4×C79C2412yes—
311C22×C4×C79C2414yes—
312C22×C4×C79C2411yescharacteristic
313C22×C4×C79C2411yescharacteristic
314C4⋊C4×C79C2414yes—
315C4⋊C4×C79C2414yes—
316C4⋊C4×C79C2418yes—
317C4⋊C4×C79C24116yes—
318C4⋊C4×C79C2418yes—
319C4⋊C4×C79C2418yes—
320C4⋊C4×C79C24116yes—
321C4⋊C4×C79C24116yes—
322C4⋊C4×C79C2418yes—
323C42×C79C2418yes—
324C42×C79C24116yes—
325C42×C79C2414yes—
326C42×C79C2418yes—
327C23×C79C2511yescharacteristic
328C22×D79—22no—
329C22×D79—22no—
330C22×D79—24no—
331C22×D79—24no—
332C22×D79—24no—
333C22×D79—22no—
334C22×D79C2512yes—
335C22×D79C2514yes—
336Q8×C79—216no—
337Q8×C79—28no—
338Q8×C79—28no—
339C2×C4×C79—24no—
340C2×C4×C79—28no—
341C2×C4×C79—24no—
342C2×C4×C79—24no—
343C2×C4×C79—22no—
344C2×C4×C79—24no—
345C2×C4×C792−1+414yes—
346C2×C4×C792−1+414yes—
347C2×C4×C79C2518yes—
348C2×C4×C79C2514yes—
349C2×C4×C79C2512yes—
350C2×C4×C79C2514yes—
351C2×C4×C79C2514yes—
352C2×C4×C79C2514yes—
353C2×C4×C79C2512yes—
354C2×C4×C79C2512yes—
355C2×Dic79—22no—
356C2×Dic79—22no—
357C2×Dic79—24no—
358C2×Dic79—24no—
359C2×Dic79—28no—
360C2×Dic79—22no—
361C2×Dic79—24no—
362C2×Dic79C2512yes—
363C2×Dic79C2514yes—
364C2×Dic79C2514yes—
365C2×Dic79C2512yes—
366C2×Dic79C2514yes—
367C2×Dic79C2512yes—
368C2×Dic79C2518yes—
369D316—28no—
370D316—48no—
371C4×D79—28no—
372C4×D79—28no—
373C4×D79—216no—
374C4×D79—44no—
375C4×D79—416no—
376Dic158—28no—
377Dic158—416no—
378Dic158—48no—
379Dic158—48no—
380C22×C79C2×2−1+412yes—
381C22×C79C2×2−1+412yes—
382C22×C79#58512yes—
383C22×C79C2611yescharacteristic
384C2×D79—22no—
385C2×D79—22no—
386C2×D79—24no—
387C2×D79—24no—
388C2×D79—24no—
389C2×D79—22no—
390C2×D79—44no—
391C2×D79—48no—
392C4×C79—28no—
393C4×C79—24no—
394C4×C79—24no—
395C4×C79—22no—
396C4×C79—24no—
397C4×C79—24no—
398C4×C79C2×2−1+414yes—
399C4×C79C2×2−1+414yes—
400Dic79—24no—
401Dic79—22no—
402Dic79—22no—
403Dic79—24no—
404Dic79—24no—
405Dic79—28no—
406Dic79—22no—
407C2×#3555—791nomaximal, Sylow
408C2×C79#355514yescomplemented
409C2×C79C22×2−1+411yescharacteristic
410C2×C79C22×2−1+411yescharacteristic
411C2×C79C2×#58511yescharacteristic
412D79—42no—
413D79—44no—
414#3555—7932no—
415C2×#563—794no—
416C2×Q82—791no—
417C2×#557—792no—
418C2×#557D7911yescharacteristic, complemented
419C2×#556—792no—
420C2×#556—791no—
421C2×#556—792no—
422C2×#554—791no—
423C2×#552—792no—
424C2×#544—792no—
425C2×#542—792no—
426C2×#541—792no—
427C2×#541—794no—
428C2×#541—792no—
429C2×#533—791no—
430C2×#533—791no—
431C2×#529—791no—
432C79C2×#355511yescharacteristic, complemented, Sylow
433#563—7964no—
434Q82—7916no—
435#557—7932no—
436#557C2×D79116yescomplemented
437#556—7932no—
438#556—7916no—
439#556—7932no—
440#554—7916no—
441#552—7932no—
442#544—7932no—
443#542—7932no—
444#541—7932no—
445#541—7964no—
446#541—7932no—
447#533—7916no—
448#533—7916no—
449C2×C4⋊Q8—791no—
450C2×C4⋊Q8—791no—
451C2×C4⋊Q8—794no—
452C2×C4⋊Q8—792no—
453C2×C4⋊Q8—794no—
454C2×C4⋊Q8—791no—
455C2×C4⋊Q8—792no—
456C2×C4⋊Q8C2×D7911yescharacteristic
457C2×C4⋊Q8C2×D7912yes—
458#529—7916no—
459C2×#126—792no—
460C2×#126—794no—
461C2×#126—794no—
462C2×#126—794no—
463C2×#126—794no—
464C2×#126—794no—
465C2×#126—794no—
466C2×#125—791no—
467C2×#125—792no—
468C2×#125—792no—
469C2×#125—794no—
470C2×#125—794no—
471C2×#125—794no—
472C2×#125—792no—
473C2×#125—794no—
474C2×#125C2×D7914yes—
475C2×#125C2×D7912yes—
476C2×#124—791no—
477C2×#124—792no—
478C2×#124—794no—
479C2×#123—792no—
480C2×#123—794no—
481C2×C22⋊Q8—791no—
482C2×C22⋊Q8—792no—
483C2×C22⋊Q8—791no—
484C2×C22⋊Q8—792no—
485C2×C22⋊Q8—791no—
486C2×C22⋊Q8—792no—
487C2×C22⋊Q8—792no—
488C2×C22⋊Q8—794no—
489C2×C22⋊Q8—792no—
490C2×C22⋊Q8—794no—
491C2×C22⋊Q8—794no—
492C2×#121—791no—
493C2×C4×Q8—792no—
494C2×C4×Q8—792no—
495C2×C4×Q8—792no—
496C2×C4×Q8—792no—
497C2×C4×Q8—792no—
498C2×C4×Q8—791no—
499C2×C4×Q8—792no—
500C2×C4×Q8—794no—
501C2×C4×Q8C2×D7911yescharacteristic
502C2×C4×Q8C2×D7911yescharacteristic
503C2×C4×Q8C2×D7912yes—
504C2×C4×Q8C2×D7912yes—
505C2×C4×D4—792no—
506C2×C4×D4—791no—
507C2×C4×D4—792no—
508C2×#117—792no—
509C2×#117—794no—
510C2×#117—792no—
511C2×#117—792no—
512C2×#117—792no—
513C22×C4⋊C4—792no—
514C22×C42—791no—
515C22×Q8—792no—
516C22×Q8—792no—
517C22×Q8—794no—
518C22×Q8—791no—
519C22×Q8C22×D7912yes—
520C22×Q8C22×D7911yescharacteristic
521C22×Q8C22×D7911yescharacteristic
522C22×D4—792no—
523C22×D4—791no—
524C23×C4—794no—
525C23×C4—791no—
526C23×C4—792no—
527C23×C4—791no—
528C23×C4—791no—
529C4⋊Q8—798no—
530C4⋊Q8—798no—
531C4⋊Q8—7932no—
532C4⋊Q8—7916no—
533C4⋊Q8—7932no—
534C4⋊Q8—798no—
535C4⋊Q8—7916no—
536C4⋊Q8C22×D7918yes—
537C4⋊Q8C22×D79116yes—
538#126—7916no—
539#126—7932no—
540#126—7932no—
541#126—7932no—
542#126—7932no—
543#126—7932no—
544#126—7932no—
545#125—798no—
546#125—7916no—
547#125—7916no—
548#125—7932no—
549#125—7932no—
550#125—7932no—
551#125—7916no—
552#125—7932no—
553#125C22×D79132yes—
554#125C22×D79116yes—
555#124—798no—
556#124—7916no—
557#124—7932no—
558#123—7916no—
559#123—7932no—
560C22⋊Q8—798no—
561C22⋊Q8—7916no—
562C22⋊Q8—798no—
563C22⋊Q8—7916no—
564C22⋊Q8—798no—
565C22⋊Q8—7916no—
566C22⋊Q8—7916no—
567C22⋊Q8—7932no—
568C22⋊Q8—7916no—
569C22⋊Q8—7932no—
570C22⋊Q8—7932no—
571#121—798no—
572C4×Q8—7916no—
573C4×Q8—7916no—
574C4×Q8—7916no—
575C4×Q8—7916no—
576C4×Q8—7916no—
577C4×Q8—798no—
578C4×Q8—7916no—
579C4×Q8—7932no—
580C4×Q8C22×D7918yes—
581C4×Q8C22×D7918yes—
582C4×Q8C22×D79116yes—
583C4×Q8C22×D79116yes—
584C4×D4—7916no—
585C4×D4—798no—
586C4×D4—7916no—
587#117—7916no—
588#117—7932no—
589#117—7916no—
590#117—7916no—
591#117—7916no—
592C2×C4⋊C4—792no—
593C2×C4⋊C4—794no—
594C2×C4⋊C4—792no—
595C2×C4⋊C4—791no—
596C2×C4⋊C4—792no—
597C2×C4⋊C4—792no—
598C2×C4⋊C4—792no—
599C2×C4⋊C4—792no—
600C2×C4⋊C4—791no—
601C2×C4⋊C4—792no—
602C2×C4⋊C4—792no—
603C2×C4⋊C4—792no—
604C2×C4⋊C4—794no—
605C2×C4⋊C4—794no—
606C2×C4⋊C4—794no—
607C2×C4⋊C4—794no—
608C2×C4⋊C4—792no—
609C2×C4⋊C4—792no—
610C2×C4⋊C4—794no—
611C2×C4⋊C4—794no—
612C2×C4⋊C4—7916no—
613C2×C4⋊C4C22×D7911yescharacteristic
614C2×C4⋊C4C22×D7912yes—
615C2×C4⋊C4C22×D7914yes—
616C2×C4⋊C4C22×D7912yes—
617C2×C4⋊C4C22×D7911yescharacteristic
618C2×C4⋊C4C22×D7912yes—
619C2×C4⋊C4C22×D7914yes—
620C2×C4⋊C4C22×D7912yes—
621C2×C4⋊C4C22×D7914yes—
622C2×C22⋊C4—792no—
623C2×C22⋊C4—792no—
624C2×C22⋊C4—792no—
625C2×C22⋊C4—794no—
626C2×C22⋊C4—792no—
627C2×C22⋊C4—794no—
628C2×C22⋊C4—792no—
629C2×C22⋊C4—794no—
630C2×C22⋊C4—792no—
631C2×C22⋊C4—794no—
632C2×C22⋊C4—792no—
633C2×C42—794no—
634C2×C42—791no—
635C2×C42—792no—
636C2×C42—794no—
637C2×C42—794no—
638C2×C42—791no—
639C2×C42—791no—
640C2×C42—798no—
641C2×C42C22×D7912yes—
642C2×C42C22×D7912yes—
643C2×C42C22×D7911yescharacteristic
644C2×C42C22×D7914yes—
645C24—791no—
646C24—792no—
647C2×Q8—28no—
648C2×Q8—24no—
649C2×Q8—24no—
650C2×Q8—3164no—
651C2×Q8—3164no—
652C2×Q8—3168no—
653C2×Q8—798no—
654C2×Q8—798no—
655C2×Q8—7916no—
656C2×Q8—794no—
657C2×Q8—1584no—
658C2×Q8C23×D7918yes—
659C2×Q8C23×D7914yes—
660C2×Q8C23×D7914yes—
661C2×D4—3164no—
662C2×D4—798no—
663C2×D4—794no—
664C2×D4—1584no—
665C22×C4—3168no—
666C22×C4—3162no—
667C22×C4—794no—
668C22×C4—7916no—
669C22×C4—791no—
670C22×C4—792no—
671C22×C4—792no—
672C22×C4—791no—
673C22×C4—792no—
674C22×C4—794no—
675C22×C4—791no—
676C22×C4—794no—
677C22×C4—794no—
678C22×C4—798no—
679C22×C4—1584no—
680C22×C4—1588no—
681C22×C4—1584no—
682C22×C4C23×D7914yes—
683C22×C4C23×D7912yes—
684C22×C4C23×D7911yescharacteristic
685C22×C4C23×D7912yes—
686C22×C4C23×D7912yes—
687C22×C4C23×D7912yes—
688C22×C4C23×D7911yescharacteristic
689C22×C4C23×D7911yescharacteristic
690C4⋊C4—7916no—
691C4⋊C4—798no—
692C4⋊C4—798no—
693C4⋊C4—798no—
694C4⋊C4—798no—
695C4⋊C4—798no—
696C4⋊C4—7916no—
697C4⋊C4—7916no—
698C4⋊C4—798no—
699C4⋊C4—798no—
700C4⋊C4—7916no—
701C4⋊C4—798no—
702C4⋊C4—798no—
703C4⋊C4—794no—
704C4⋊C4—794no—
705C4⋊C4—798no—
706C4⋊C4—798no—
707C4⋊C4—7916no—
708C4⋊C4—7916no—
709C4⋊C4—7916no—
710C4⋊C4C23×D7914yes—
711C4⋊C4C23×D7918yes—
712C4⋊C4C23×D79116yes—
713C4⋊C4C23×D7918yes—
714C4⋊C4C23×D7914yes—
715C4⋊C4C23×D7918yes—
716C4⋊C4C23×D79116yes—
717C4⋊C4C23×D7918yes—
718C4⋊C4C23×D79116yes—
719C22⋊C4—798no—
720C22⋊C4—798no—
721C22⋊C4—798no—
722C22⋊C4—798no—
723C22⋊C4—7916no—
724C22⋊C4—7916no—
725C22⋊C4—798no—
726C22⋊C4—7916no—
727C22⋊C4—798no—
728C22⋊C4—7916no—
729C22⋊C4—798no—
730C42—794no—
731C42—794no—
732C42—794no—
733C42—7916no—
734C42—798no—
735C42—7916no—
736C42—7916no—
737C42C23×D7914yes—
738C42C23×D7918yes—
739C42C23×D7918yes—
740C42C23×D79116yes—
741C23—792no—
742C23—794no—
743C23—1582no—
744C23—1584no—
745C23—1582no—
746C23—1584no—
747C23—1584no—
748C23—1582no—
749C23C24×D7911yescharacteristic
750Q8—216no—
751Q8—28no—
752Q8—28no—
753Q8—3168no—
754Q8—3168no—
755Q8—31616no—
756Q8—1588no—
757D4—3168no—
758D4—1588no—
759C2×C4—28no—
760C2×C4—24no—
761C2×C4—24no—
762C2×C4—24no—
763C2×C4—22no—
764C2×C4—24no—
765C2×C4—31616no—
766C2×C4—3164no—
767C2×C4—792no—
768C2×C4—794no—
769C2×C4—794no—
770C2×C4—792no—
771C2×C4—794no—
772C2×C4—792no—
773C2×C4—798no—
774C2×C4—1582no—
775C2×C4—1582no—
776C2×C4—1584no—
777C2×C4—1584no—
778C2×C4—1588no—
779C2×C4—1582no—
780C2×C4—1584no—
781C2×C4—1588no—
782C2×C4—1588no—
783C2×C4—15816no—
784C2×C4#1457920814yes—
785C2×C4#1457920914yes—
786C2×C4C24×D7918yes—
787C2×C4C24×D7914yes—
788C2×C4C24×D7912yes—
789C2×C4C24×D7914yes—
790C2×C4C24×D7914yes—
791C2×C4C24×D7914yes—
792C2×C4C24×D7912yes—
793C2×C4C24×D7912yes—
794C22—3164no—
795C22—3168no—
796C22—1582no—
797C22—1584no—
798C22—1582no—
799C22—1584no—
800C22—1584no—
801C22—1582no—
802C22C2×#1457920812yes—
803C22C2×#1457920912yes—
804C22#1909940012yes—
805C22C25×D7911yescharacteristic
806C4—28no—
807C4—24no—
808C4—24no—
809C4—24no—
810C4—22no—
811C4—24no—
812C4—1582no—
813C4—1582no—
814C4—1584no—
815C4—1584no—
816C4—1588no—
817C4—1582no—
818C4—1584no—
819C4C2×#1457920814yes—
820C4C2×#1457920914yes—
821C2—3162no—
822C2—3164no—
823C2#2377788414yesdirect product factor
824C2C22×#1457920811yescharacteristic
825C2C22×#1457920911yescharacteristic
826C2C2×#1909940011yescharacteristic
subgroupG/H
centerC23C24×D79
commutator, cosocleC22×C79C26
FrattiniC22C25×D79
FittingC2×#557×C79C2
socleC23×C79C25
prime radicalC2×#14579136C22
hypercenterC2×#557D79
hypocenterC79C2×#3555
LCSG ▷ C22×C79 ▷ C79
UCSC1 ◁ C23 ◁ C2×#557

Complements

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

NH ≅ G/Ntype
1. #23777884C2direct (N × H)
2. C2×#19099317C2semidirect
3. C2×Q8×Dic158C2semidirect
4. C2×#19099289C2semidirect
5. C2×#19099287C2semidirect
6. C2×#19099287C2semidirect
7. C2×#19099286C2semidirect
8. C2×#19099273C2semidirect
9. C2×#19099251C2semidirect
10. C2×#19099193C2semidirect
12. C2×#19099174C2semidirect
13. C2×#19099172C2semidirect
14. C2×#19099171C2semidirect
15. C2×#19099118C2semidirect
16. C2×#19099117C2semidirect
18. C2×#557×C79C2semidirect
19. #19099317C22semidirect
20. Q8×Dic158C22semidirect
21. #19099289C22semidirect
22. #19099287C22semidirect
23. #19099287C22semidirect
24. #19099286C22semidirect
25. #19099273C22semidirect
26. #19099251C22semidirect
27. #19099193C22semidirect
29. #19099174C22semidirect
30. #19099172C22semidirect
31. #19099171C22semidirect
32. #19099118C22semidirect
33. #19099117C22semidirect
92. #557×C79C22semidirect
408. C2×C79#3555semidirect
418. C2×#557D79semidirect
432. C79C2×#3555semidirect
436. #557C2×D79semidirect
823. C2#23777884direct (N × H)

Maximal subgroups

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

subgroupindex
#237778842
C2×#190993172
C2×Q8×Dic1582
C2×#190992892
C2×#190992872
C2×#190992862
C2×#190992732
C2×#190992512
C2×#190991932
C2×#190991852
C2×#190991742
C2×#190991722
C2×#190991712
C2×#190991182
C2×#190991172
C2×#190991002
C2×#557×C792
C2×#355579