Finite Group Databasebeta

← C2×#23777888 #35195989

Subgroups — C2×#23777888 #35195989

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#23777888C2132yesmaximal, direct product factor
2C2×#19099314C214yesmaximal, complemented
3C2×Q8×Dic158C211yesmaximal, characteristic, complemented
4C2×#19099292C211yesmaximal, characteristic, complemented
5C2×#19099291C212yesmaximal, complemented
6C2×#19099286C212yesmaximal, complemented
7C2×#19099286C211yesmaximal, characteristic, complemented
8C2×#19099284C212yesmaximal, complemented
9C2×#19099273C211yesmaximal, characteristic, complemented
10C2×#19099247C212yesmaximal, complemented
11C2×#19099190C212yesmaximal, complemented
12C2×#19099184C212yesmaximal
13C2×#19099175C212yesmaximal, complemented
14C2×#19099174C212yesmaximal, complemented
15C2×#19099172C214yesmaximal, complemented
16C2×#19099120C211yesmaximal, characteristic, complemented
17C2×#19099097C211yesmaximal, characteristic
18C2×#533×C79C211yesmaximal, characteristic, complemented
19#19099314C22164yescomplemented
20Q8×Dic158C22116yescomplemented
21#19099292C22116yescomplemented
22#19099291C22132yescomplemented
23#19099286C22132yescomplemented
24#19099286C22116yescomplemented
25#19099284C22132yescomplemented
26#19099273C22116yescomplemented
27#19099247C22132yescomplemented
28#19099190C22132yescomplemented
29#19099184C22132yes—
30#19099175C22132yescomplemented
31#19099174C22132yescomplemented
32#19099172C22164yescomplemented
33#19099120C22116yescomplemented
34C2×#14579161C2212yes—
35C2×#14579161C2212yes—
36C2×#14579161C2211yescharacteristic
37C2×#14579161C2211yescharacteristic
38C2×#14579160C2212yes—
39C2×#14579160C2214yes—
40C2×#14579159C2214yes—
41#19099097C22116yes—
42C2×#14579156C2214yes—
43C2×#14579156C2214yes—
44C2×#14579156C2214yes—
45C2×#14579156C2214yes—
46C2×#14579155C2212yes—
47C2×#14579154C2214yes—
48C2×#14579154C2214yes—
49C2×#14579153C2212yes—
50C2×#14579153C2212yes—
51C2×#14579153C2211yescharacteristic
52C2×#14579152C2212yes—
53C2×#14579152C2214yes—
54C2×#14579151C2214yes—
55C2×#14579151C2214yes—
56C2×#14579151C2214yes—
57C2×#14579151C2214yes—
58C2×#14579149C2212yes—
59C2×#14579149C2211yescharacteristic
60C2×#14579147C2214yes—
61C2×#14579144C2212yes—
62C2×#14579143C2214yes—
63C2×#14579140C2211yescharacteristic
64C2×#14579140C2212yes—
65C2×#14579140C2212yes—
66C2×#14579139C2214yes—
67C2×#14579139C2214yes—
68C2×#14579137C2214yes—
69C2×#14579137C2212yes—
70C2×#14579137C2212yes—
71C2×#14579135C2211yescharacteristic
72C2×Q8×Dic79C2212yes—
73C2×Q8×Dic79C2212yes—
74C2×C4×Dic158C2212yes—
75C2×C4×Dic158C2212yes—
76C2×C4×Dic158C2212yes—
77C2×C4×Dic158C2211yescharacteristic
78C2×C4×Dic158C2212yes—
79C2×C4×Dic158C2212yes—
80C2×#14579126C2214yes—
81C2×C4×D316C2212yes—
82C2×C4×D316C2211yescharacteristic
83C2×C4×C22⋊D79C2212yes—
84C2×#14579120C2212yes—
85C2×#14579119C2212yes—
86C2×#14579119C2214yes—
87C2×#14579118C2212yes—
88C2×C4⋊C4×D79C2212yes—
89#533×C79C22116yescomplemented
90C2×C4⋊Q8×C79C2211yescharacteristic
91C2×C4⋊Q8×C79C2211yescharacteristic
92C2×#125×C79C2212yes—
93C2×C22⋊Q8×C79C2211yescharacteristic
94C2×C22⋊Q8×C79C2211yescharacteristic
95C2×C22⋊Q8×C79C2212yes—
96C2×C4×Q8×C79C2211yescharacteristic
97C2×C4×Q8×C79C2212yes—
98C2×C4×Q8×C79C2211yescharacteristic
99C2×#117×C79C2212yes—
100C22×C42×C79C2211yescharacteristic
101C22×Dic158C2312yes—
102C22×Dic158C2311yescharacteristic
103C22×Dic158C2314yes—
104C22×Dic158C2312yes—
105C22×D316C2311yescharacteristic
106C22×C22⋊D79C2312yes—
107C22×C4×D79C2312yes—
108C22×C4×D79C2314yes—
109#14579161C23116yes—
110#14579161C23116yes—
111#14579161C2318yes—
112#14579161C2318yes—
113#14579160C23132yes—
114#14579160C23116yes—
115#14579159C23132yes—
116#14579156C23132yes—
117#14579156C23132yes—
118#14579156C23132yes—
119#14579156C23132yes—
120#14579155C23116yes—
121#14579154C23132yes—
122#14579154C23132yes—
123#14579153C23116yes—
124#14579153C23116yes—
125#14579153C2318yes—
126#14579152C23132yes—
127#14579152C23116yes—
128#14579151C23132yes—
129#14579151C23132yes—
130#14579151C23132yes—
131#14579151C23132yes—
132#14579149C23116yes—
133#14579149C2318yes—
134#14579147C23132yes—
135#14579144C23116yes—
136#14579143C23132yes—
137#14579140C2318yes—
138#14579140C23116yes—
139#14579140C23116yes—
140#14579139C23132yes—
141#14579139C23132yes—
142#14579137C23116yes—
143#14579137C23116yes—
144#14579137C23132yes—
145#14579135C2318yes—
146Q8×Dic79C23116yes—
147Q8×Dic79C23116yes—
148C4×Dic158C23116yes—
149C4×Dic158C23116yes—
150C4×Dic158C23116yes—
151C4×Dic158C23116yes—
152C4×Dic158C23116yes—
153C4×Dic158C2318yes—
154#14579126C23132yes—
155C4×D316C23116yes—
156C4×D316C2318yes—
157C4×C22⋊D79C23116yes—
158#14579120C23116yes—
159#14579119C23132yes—
160#14579119C23116yes—
161#14579118C23116yes—
162C2×C4⋊Dic79C2312yes—
163C2×C4⋊Dic79C2312yes—
164C2×C4⋊Dic79C2314yes—
165C2×C4⋊Dic79C2311yescharacteristic
166C2×C4⋊Dic79C2312yes—
167C2×C4⋊Dic79C2311yescharacteristic
168C2×C4⋊Dic79C2312yes—
169C2×C4⋊Dic79C2314yes—
170C2×C4⋊Dic79C2314yes—
171C2×Dic79⋊C4C2314yes—
172C2×Dic79⋊C4C2312yes—
173C2×Dic79⋊C4C2312yes—
174C2×Dic79⋊C4C2312yes—
175C2×Dic79⋊C4C2314yes—
176C2×Dic79⋊C4C2314yes—
177C2×Dic79⋊C4C2314yes—
178C2×Dic79⋊C4C2314yes—
179C2×Dic79⋊C4C2314yes—
180C2×Dic79⋊C4C2314yes—
181C2×Dic79⋊C4C2312yes—
182C4⋊C4×D79C23116yes—
183C2×C22⋊Dic79C2314yes—
184C2×C22⋊Dic79C2312yes—
185C2×(C2×D79)⋊C4C2312yes—
186C2×(C2×D79)⋊C4C2312yes—
187C2×(C2×D79)⋊C4C2312yes—
188C2×(C2×D79)⋊C4C2314yes—
189C2×(C2×D79)⋊C4C2314yes—
190C2×(C2×D79)⋊C4C2314yes—
191C2×(C2×D79)⋊C4C2312yes—
192C2×C4×Dic79C2312yes—
193C2×C4×Dic79C2314yes—
194C2×C4×Dic79C2314yes—
195C2×C4×Dic79C2314yes—
196C2×C4×Dic79C2314yes—
197C22×Q8×C79C2311yescharacteristic
198C22×Q8×C79C2311yescharacteristic
199C22×Q8×C79C2312yes—
200C23×C4×C79C2311yescharacteristic
201C23×C4×C79C2311yescharacteristic
202C23×C4×C79C2311yescharacteristic
203C4⋊Q8×C79C2318yes—
204C4⋊Q8×C79C2318yes—
205#125×C79C23116yes—
206C22⋊Q8×C79C2318yes—
207C22⋊Q8×C79C2318yes—
208C22⋊Q8×C79C23116yes—
209C4×Q8×C79C2318yes—
210C4×Q8×C79C23116yes—
211C4×Q8×C79C2318yes—
212#117×C79C23116yes—
213C2×C4⋊C4×C79C2312yes—
214C2×C4⋊C4×C79C2312yes—
215C2×C4⋊C4×C79C2312yes—
216C2×C4⋊C4×C79C2312yes—
217C2×C4⋊C4×C79C2312yes—
218C2×C4⋊C4×C79C2312yes—
219C2×C4⋊C4×C79C2311yescharacteristic
220C2×C4⋊C4×C79C2311yescharacteristic
221C2×C4⋊C4×C79C2312yes—
222C2×C22⋊C4×C79C2312yes—
223C2×C22⋊C4×C79C2312yes—
224C2×C42×C79C2311yescharacteristic
225C2×C42×C79C2311yescharacteristic
226C2×C42×C79C2311yescharacteristic
227C2×C42×C79C2311yescharacteristic
228C2×C42×C79C2318yes—
229C2×C42×C79C2312yes—
230C2×C42×C79C2312yes—
231C23×D79C2412yes—
232C2×Dic158—28no—
233C2×Dic158—24no—
234C2×Dic158—44no—
235C2×Dic158—48no—
236C2×Dic158C2418yes—
237C2×Dic158C2414yes—
238C2×Dic158C24116yes—
239C2×Dic158C2418yes—
240C2×D316—24no—
241C2×D316C2414yes—
242C2×C22⋊D79—44no—
243C2×C22⋊D79C2418yes—
244C22×Dic79C2412yes—
245C22×Dic79C2414yes—
246C22×Dic79C2412yes—
247C22×Dic79C2414yes—
248C22×Dic79C2412yes—
249C2×C4×D79—28no—
250C2×C4×D79—48no—
251C2×C4×D79C2418yes—
252C2×C4×D79C24116yes—
253C4⋊Dic79C2418yes—
254C4⋊Dic79C2418yes—
255C4⋊Dic79C24116yes—
256C4⋊Dic79C2414yes—
257C4⋊Dic79C2418yes—
258C4⋊Dic79C2414yes—
259C4⋊Dic79C2418yes—
260C4⋊Dic79C24116yes—
261C4⋊Dic79C24116yes—
262Dic79⋊C4C24116yes—
263Dic79⋊C4C2418yes—
264Dic79⋊C4C2418yes—
265Dic79⋊C4C2418yes—
266Dic79⋊C4C24116yes—
267Dic79⋊C4C24116yes—
268Dic79⋊C4C24116yes—
269Dic79⋊C4C24116yes—
270Dic79⋊C4C24116yes—
271Dic79⋊C4C24116yes—
272Dic79⋊C4C2418yes—
273C22⋊Dic79C24116yes—
274C22⋊Dic79C2418yes—
275(C2×D79)⋊C4C2418yes—
276(C2×D79)⋊C4C2418yes—
277(C2×D79)⋊C4C2418yes—
278(C2×D79)⋊C4C24116yes—
279(C2×D79)⋊C4C24116yes—
280(C2×D79)⋊C4C24116yes—
281(C2×D79)⋊C4C2418yes—
282C4×Dic79C2418yes—
283C4×Dic79C24116yes—
284C4×Dic79C24116yes—
285C4×Dic79C24116yes—
286C4×Dic79C24116yes—
287C24×C79C2411yescharacteristic
288C2×Q8×C79—24no—
289C2×Q8×C79—24no—
290C2×Q8×C79—44no—
291C2×Q8×C79C2414yes—
292C2×Q8×C79C2414yes—
293C2×Q8×C79C2418yes—
294C22×C4×C79—24no—
295C22×C4×C79—24no—
296C22×C4×C79—42no—
297C22×C4×C79C2411yescharacteristic
298C22×C4×C79C2412yes—
299C22×C4×C79C2411yescharacteristic
300C22×C4×C79C2411yescharacteristic
301C22×C4×C79C2411yescharacteristic
302C22×C4×C79C2414yes—
303C22×C4×C79C2414yes—
304C22×C4×C79C2412yes—
305C22×C4×C79C2412yes—
306C22×C4×C79C2412yes—
307C22×C4×C79C2414yes—
308C22×C4×C79C2411yescharacteristic
309C22×C4×C79C2411yescharacteristic
310C4⋊C4×C79C2418yes—
311C4⋊C4×C79C2418yes—
312C4⋊C4×C79C2418yes—
313C4⋊C4×C79C2418yes—
314C4⋊C4×C79C2418yes—
315C4⋊C4×C79C2418yes—
316C4⋊C4×C79C2414yes—
317C4⋊C4×C79C2414yes—
318C4⋊C4×C79C2418yes—
319C22⋊C4×C79C2418yes—
320C22⋊C4×C79C2418yes—
321C42×C79C2414yes—
322C42×C79C2414yes—
323C42×C79C2414yes—
324C42×C79C2414yes—
325C42×C79C2418yes—
326C42×C79C2418yes—
327C23×C79—22no—
328C23×C79—22no—
329C23×C79—22no—
330C23×C79C2512yes—
331C23×C79C2511yescharacteristic
332C22×D79—24no—
333C22×D79—24no—
334C22×D79—24no—
335C22×D79C2514yes—
336Q8×C79—28no—
337Q8×C79—28no—
338Q8×C79—48no—
339C2×C4×C79—22no—
340C2×C4×C79—22no—
341C2×C4×C79—24no—
342C2×C4×C79—24no—
343C2×C4×C79—24no—
344C2×C4×C79—22no—
345C2×C4×C79—24no—
346C2×C4×C79—22no—
347C2×C4×C79—28no—
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×C79C2514yes—
360C2×C4×C79C2512yes—
361C2×C4×C79C2512yes—
362C22⋊D79—48no—
363C2×Dic79—24no—
364C2×Dic79—24no—
365C2×Dic79—28no—
366C2×Dic79—28no—
367C2×Dic79—24no—
368C2×Dic79C2514yes—
369C2×Dic79C2518yes—
370C2×Dic79C2514yes—
371C2×Dic79C2514yes—
372C2×Dic79C2518yes—
373D316—28no—
374C4×D79—216no—
375C4×D79—416no—
376Dic158—216no—
377Dic158—28no—
378Dic158—416no—
379Dic158—48no—
380C22×C79—22no—
381C22×C79—22no—
382C22×C79—22no—
383C22×C79—44no—
384C22×C79C2×2−1+412yes—
385C22×C79C2×2−1+412yes—
386C22×C79#58512yes—
387C22×C79C2611yescharacteristic
388C2×D79—24no—
389C2×D79—24no—
390C2×D79—24no—
391C2×D79—48no—
392C4×C79—22no—
393C4×C79—22no—
394C4×C79—24no—
395C4×C79—24no—
396C4×C79—22no—
397C4×C79—22no—
398C4×C79—24no—
399C4×C79—24no—
400C4×C79C2×2−1+414yes—
401C4×C79C2×2−1+414yes—
402Dic79—24no—
403Dic79—28no—
404Dic79—24no—
405Dic79—24no—
406Dic79—28no—
407C2×#3555—791nomaximal, Sylow
408C2×C79—42no—
409C2×C79#355514yescomplemented
410C2×C79C22×2−1+411yescharacteristic
411C2×C79C22×2−1+411yescharacteristic
412C2×C79C2×#58511yescharacteristic
413D79—44no—
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—792no—
427C2×#541—794no—
428C2×#541—792no—
429C2×#533—791no—
430C2×#533D7911yescharacteristic, complemented
431C2×#529—791no—
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—7932no—
445#541—7964no—
446#541—7932no—
447#533—7916no—
448#533C2×D79116yescomplemented
449C2×C4⋊Q8—794no—
450C2×C4⋊Q8—794no—
451C2×C4⋊Q8—792no—
452C2×C4⋊Q8—791no—
453C2×C4⋊Q8—791no—
454C2×C4⋊Q8—792no—
455C2×C4⋊Q8—792no—
456C2×C4⋊Q8C2×D7911yescharacteristic
457C2×C4⋊Q8C2×D7911yescharacteristic
458#529—7916no—
459C2×#126—794no—
460C2×#126—794no—
461C2×#126—794no—
462C2×#126—794no—
463C2×#126—794no—
464C2×#126—794no—
465C2×#126—792no—
466C2×#125—794no—
467C2×#125—794no—
468C2×#125—794no—
469C2×#125—794no—
470C2×#125—794no—
471C2×#125—792no—
472C2×#125—791no—
473C2×#125—792no—
474C2×#125—792no—
475C2×#125C2×D7912yes—
476C2×#124—794no—
477C2×#124—791no—
478C2×#124—792no—
479C2×#123—792no—
480C2×#123—794no—
481C2×C22⋊Q8—792no—
482C2×C22⋊Q8—792no—
483C2×C22⋊Q8—794no—
484C2×C22⋊Q8—791no—
485C2×C22⋊Q8—792no—
486C2×C22⋊Q8—792no—
487C2×C22⋊Q8—794no—
488C2×C22⋊Q8—794no—
489C2×C22⋊Q8C2×D7911yescharacteristic
490C2×C22⋊Q8C2×D7911yescharacteristic
491C2×C22⋊Q8C2×D7912yes—
492C2×#121—791no—
493C2×C4×Q8—792no—
494C2×C4×Q8—792no—
495C2×C4×Q8—794no—
496C2×C4×Q8—791no—
497C2×C4×Q8—792no—
498C2×C4×Q8—792no—
499C2×C4×Q8—792no—
500C2×C4×Q8—792no—
501C2×C4×Q8—792no—
502C2×C4×Q8C2×D7911yescharacteristic
503C2×C4×Q8C2×D7912yes—
504C2×C4×Q8C2×D7911yescharacteristic
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×#117C2×D7912yes—
513C22×C4⋊C4—792no—
514C22×C42C2×D7911yescharacteristic
515C22×Q8—792no—
516C22×Q8—794no—
517C22×Q8—791no—
518C22×Q8—792no—
519C22×Q8C22×D7911yescharacteristic
520C22×Q8C22×D7911yescharacteristic
521C22×Q8C22×D7912yes—
522C22×D4—792no—
523C22×D4—791no—
524C23×C4—794no—
525C23×C4—792no—
526C23×C4C22×D7911yescharacteristic
527C23×C4C22×D7911yescharacteristic
528C23×C4C22×D7911yescharacteristic
529C4⋊Q8—7932no—
530C4⋊Q8—7932no—
531C4⋊Q8—7916no—
532C4⋊Q8—798no—
533C4⋊Q8—798no—
534C4⋊Q8—7916no—
535C4⋊Q8—7916no—
536C4⋊Q8C22×D7918yes—
537C4⋊Q8C22×D7918yes—
538#126—7932no—
539#126—7932no—
540#126—7932no—
541#126—7932no—
542#126—7932no—
543#126—7932no—
544#126—7916no—
545#125—7932no—
546#125—7932no—
547#125—7932no—
548#125—7932no—
549#125—7932no—
550#125—7916no—
551#125—798no—
552#125—7916no—
553#125—7916no—
554#125C22×D79116yes—
555#124—7932no—
556#124—798no—
557#124—7916no—
558#123—7916no—
559#123—7932no—
560C22⋊Q8—7916no—
561C22⋊Q8—7916no—
562C22⋊Q8—7932no—
563C22⋊Q8—798no—
564C22⋊Q8—7916no—
565C22⋊Q8—7916no—
566C22⋊Q8—7932no—
567C22⋊Q8—7932no—
568C22⋊Q8C22×D7918yes—
569C22⋊Q8C22×D7918yes—
570C22⋊Q8C22×D79116yes—
571#121—798no—
572C4×Q8—7916no—
573C4×Q8—7916no—
574C4×Q8—7932no—
575C4×Q8—798no—
576C4×Q8—7916no—
577C4×Q8—7916no—
578C4×Q8—7916no—
579C4×Q8—7916no—
580C4×Q8—7916no—
581C4×Q8C22×D7918yes—
582C4×Q8C22×D79116yes—
583C4×Q8C22×D7918yes—
584C4×D4—7916no—
585C4×D4—798no—
586C4×D4—7916no—
587#117—7916no—
588#117—7932no—
589#117—7916no—
590#117—7916no—
591#117C22×D79116yes—
592C2×C4⋊C4—792no—
593C2×C4⋊C4—794no—
594C2×C4⋊C4—792no—
595C2×C4⋊C4—792no—
596C2×C4⋊C4—794no—
597C2×C4⋊C4—792no—
598C2×C4⋊C4—791no—
599C2×C4⋊C4—792no—
600C2×C4⋊C4—792no—
601C2×C4⋊C4—791no—
602C2×C4⋊C4—794no—
603C2×C4⋊C4—794no—
604C2×C4⋊C4—794no—
605C2×C4⋊C4—794no—
606C2×C4⋊C4—794no—
607C2×C4⋊C4—792no—
608C2×C4⋊C4—794no—
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×D7911yescharacteristic
616C2×C4⋊C4C22×D7912yes—
617C2×C4⋊C4C22×D7912yes—
618C2×C4⋊C4C22×D7912yes—
619C2×C4⋊C4C22×D7912yes—
620C2×C4⋊C4C22×D7912yes—
621C2×C4⋊C4C22×D7912yes—
622C2×C22⋊C4—794no—
623C2×C22⋊C4—792no—
624C2×C22⋊C4—792no—
625C2×C22⋊C4—792no—
626C2×C22⋊C4—792no—
627C2×C22⋊C4—794no—
628C2×C22⋊C4—794no—
629C2×C22⋊C4—792no—
630C2×C22⋊C4—794no—
631C2×C22⋊C4C22×D7912yes—
632C2×C22⋊C4C22×D7912yes—
633C2×C42—794no—
634C2×C42—792no—
635C2×C42—794no—
636C2×C42—794no—
637C2×C42—794no—
638C2×C42C22×D7911yescharacteristic
639C2×C42C22×D7912yes—
640C2×C42C22×D7912yes—
641C2×C42C22×D7911yescharacteristic
642C2×C42C22×D7911yescharacteristic
643C2×C42C22×D7911yescharacteristic
644C2×C42C22×D7918yes—
645C24—792no—
646C24C23×D7911yescharacteristic
647C2×Q8—24no—
648C2×Q8—24no—
649C2×Q8—44no—
650C2×Q8—3164no—
651C2×Q8—3168no—
652C2×Q8—798no—
653C2×Q8—7916no—
654C2×Q8—794no—
655C2×Q8—798no—
656C2×Q8—1584no—
657C2×Q8—1588no—
658C2×Q8C23×D7914yes—
659C2×Q8C23×D7914yes—
660C2×Q8C23×D7918yes—
661C2×D4—3164no—
662C2×D4—798no—
663C2×D4—794no—
664C2×D4—1584no—
665C22×C4—24no—
666C22×C4—24no—
667C22×C4—42no—
668C22×C4—3168no—
669C22×C4—7916no—
670C22×C4—794no—
671C22×C4—792no—
672C22×C4—792no—
673C22×C4—792no—
674C22×C4—794no—
675C22×C4—798no—
676C22×C4—1588no—
677C22×C4C23×D7914yes—
678C22×C4C23×D7914yes—
679C22×C4C23×D7911yescharacteristic
680C22×C4C23×D7912yes—
681C22×C4C23×D7912yes—
682C22×C4C23×D7912yes—
683C22×C4C23×D7911yescharacteristic
684C22×C4C23×D7911yescharacteristic
685C22×C4C23×D7911yescharacteristic
686C22×C4C23×D7912yes—
687C22×C4C23×D7914yes—
688C22×C4C23×D7911yescharacteristic
689C22×C4C23×D7911yescharacteristic
690C4⋊C4—7916no—
691C4⋊C4—798no—
692C4⋊C4—798no—
693C4⋊C4—798no—
694C4⋊C4—7916no—
695C4⋊C4—7916no—
696C4⋊C4—7916no—
697C4⋊C4—7916no—
698C4⋊C4—7916no—
699C4⋊C4—7916no—
700C4⋊C4—798no—
701C4⋊C4—798no—
702C4⋊C4—798no—
703C4⋊C4—7916no—
704C4⋊C4—794no—
705C4⋊C4—798no—
706C4⋊C4—794no—
707C4⋊C4—798no—
708C4⋊C4—7916no—
709C4⋊C4—7916no—
710C4⋊C4C23×D7914yes—
711C4⋊C4C23×D7918yes—
712C4⋊C4C23×D7914yes—
713C4⋊C4C23×D7918yes—
714C4⋊C4C23×D7918yes—
715C4⋊C4C23×D7918yes—
716C4⋊C4C23×D7918yes—
717C4⋊C4C23×D7918yes—
718C4⋊C4C23×D7918yes—
719C22⋊C4—7916no—
720C22⋊C4—798no—
721C22⋊C4—798no—
722C22⋊C4—798no—
723C22⋊C4—798no—
724C22⋊C4—7916no—
725C22⋊C4—7916no—
726C22⋊C4—798no—
727C22⋊C4—7916no—
728C22⋊C4C23×D7918yes—
729C22⋊C4C23×D7918yes—
730C42—7916no—
731C42—798no—
732C42—7916no—
733C42—7916no—
734C42—7916no—
735C42C23×D7914yes—
736C42C23×D7914yes—
737C42C23×D7914yes—
738C42C23×D7914yes—
739C42C23×D7918yes—
740C42C23×D7918yes—
741C23—22no—
742C23—22no—
743C23—22no—
744C23—794no—
745C23—1584no—
746C23—1584no—
747C23—1584no—
748C23C24×D7912yes—
749C23C24×D7911yescharacteristic
750Q8—28no—
751Q8—28no—
752Q8—48no—
753Q8—3168no—
754Q8—31616no—
755Q8—1588no—
756Q8—15816no—
757D4—3168no—
758D4—1588no—
759C2×C4—22no—
760C2×C4—24no—
761C2×C4—24no—
762C2×C4—22no—
763C2×C4—22no—
764C2×C4—22no—
765C2×C4—24no—
766C2×C4—24no—
767C2×C4—28no—
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—1584no—
777C2×C4—1588no—
778C2×C4—1584no—
779C2×C4—1588no—
780C2×C4—1584no—
781C2×C4—15816no—
782C2×C4#1457920814yes—
783C2×C4#1457920914yes—
784C2×C4C24×D7912yes—
785C2×C4C24×D7914yes—
786C2×C4C24×D7914yes—
787C2×C4C24×D7914yes—
788C2×C4C24×D7912yes—
789C2×C4C24×D7912yes—
790C2×C4C24×D7912yes—
791C2×C4C24×D7914yes—
792C2×C4C24×D7912yes—
793C2×C4C24×D7912yes—
794C22—22no—
795C22—22no—
796C22—22no—
797C22—44no—
798C22—3168no—
799C22—1584no—
800C22—1584no—
801C22—1584no—
802C22C2×#1457920812yes—
803C22C2×#1457920912yes—
804C22#1909939912yes—
805C22C25×D7911yescharacteristic
806C4—22no—
807C4—24no—
808C4—24no—
809C4—22no—
810C4—22no—
811C4—22no—
812C4—24no—
813C4—24no—
814C4—1584no—
815C4—1588no—
816C4—1584no—
817C4—1588no—
818C4—1584no—
819C4C2×#1457920814yes—
820C4C2×#1457920914yes—
821C2—42no—
822C2—3164no—
823C2#2377788814yesdirect product factor
824C2C22×#1457920811yescharacteristic
825C2C22×#1457920911yescharacteristic
826C2C2×#1909939911yescharacteristic
subgroupG/H
centerC23C24×D79
commutator, cosocleC22×C79C26
FrattiniC22C25×D79
FittingC2×#533×C79C2
socleC23×C79C25
prime radicalC2×#14579135C22
hypercenterC2×#533D79
hypocenterC79C2×#3555
LCSG ▷ C22×C79 ▷ C79
UCSC1 ◁ C23 ◁ C2×#533

Complements

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

NH ≅ G/Ntype
1. #23777888C2direct (N × H)
2. C2×#19099314C2semidirect
3. C2×Q8×Dic158C2semidirect
4. C2×#19099292C2semidirect
5. C2×#19099291C2semidirect
6. C2×#19099286C2semidirect
7. C2×#19099286C2semidirect
8. C2×#19099284C2semidirect
9. C2×#19099273C2semidirect
10. C2×#19099247C2semidirect
11. C2×#19099190C2semidirect
13. C2×#19099175C2semidirect
14. C2×#19099174C2semidirect
15. C2×#19099172C2semidirect
16. C2×#19099120C2semidirect
18. C2×#533×C79C2semidirect
19. #19099314C22semidirect
20. Q8×Dic158C22semidirect
21. #19099292C22semidirect
22. #19099291C22semidirect
23. #19099286C22semidirect
24. #19099286C22semidirect
25. #19099284C22semidirect
26. #19099273C22semidirect
27. #19099247C22semidirect
28. #19099190C22semidirect
30. #19099175C22semidirect
31. #19099174C22semidirect
32. #19099172C22semidirect
33. #19099120C22semidirect
89. #533×C79C22semidirect
409. C2×C79#3555semidirect
430. C2×#533D79semidirect
432. C79C2×#3555semidirect
448. #533C2×D79semidirect
823. C2#23777888direct (N × H)

Maximal subgroups

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

subgroupindex
#237778882
C2×#190993142
C2×Q8×Dic1582
C2×#190992922
C2×#190992912
C2×#190992862
C2×#190992842
C2×#190992732
C2×#190992472
C2×#190991902
C2×#190991842
C2×#190991752
C2×#190991742
C2×#190991722
C2×#190991202
C2×#190990972
C2×#533×C792
C2×#355579