Finite Group Databasebeta

← #29712795

Subgroups — #29712795

Order 15616.

1340 conjugacy classes of subgroups.

The subgroup lattice has 870 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840100C211yesmaximal, characteristic, complemented
2C2×#16840083C211yesmaximal, characteristic, complemented
3#21448411C211yesmaximal, characteristic, complemented
4#21447019C211yesmaximal, characteristic, complemented
5#21447012C211yesmaximal, characteristic, complemented
6#21447005C211yesmaximal, characteristic, complemented
7#21446998C211yesmaximal, characteristic, complemented
8#21446137C211yesmaximal, characteristic, complemented
9#21446127C211yesmaximal, characteristic, complemented
10#21446012C211yesmaximal, characteristic, complemented
11#21446007C211yesmaximal, characteristic, complemented
12#21445759C211yesmaximal, characteristic, complemented
13#21445759C211yesmaximal, characteristic, complemented
14#21445731C211yesmaximal, characteristic, complemented
15C2×C61×#537C211yesmaximal, characteristic
16C2×#14519736C2211yescharacteristic
17C22×C4⋊Dic61C2211yescharacteristic
18#16840100—24no—
19#16840083—24no—
20C2×#14519710C2211yescharacteristic
21C2×#14519710C2211yescharacteristic
22C2×#14519708C2211yescharacteristic
23C2×#14519708C2211yescharacteristic
24C2×#14519701C2211yescharacteristic
25C2×#14519701C2211yescharacteristic
26C2×#14519701C2211yescharacteristic
27C2×#14519701C2211yescharacteristic
28C2×#14519698C2211yescharacteristic
29C2×#14519698C2211yescharacteristic
30C2×#14519698C2211yescharacteristic
31C2×#14519698C2211yescharacteristic
32C2×C22⋊#92418C2211yescharacteristic
33C2×C22⋊#92418C2211yescharacteristic
34C2×C22⋊#92418C2211yescharacteristic
35C2×C22⋊#92418C2211yescharacteristic
36C2×C22⋊#92418C2211yescharacteristic
37C2×C22⋊#92418C2211yescharacteristic
38#16839669—21no—
39#16839665—21no—
40#16839642—21no—
41#16839642—21no—
42#16839622C2211yescharacteristic
43#16839622C2211yescharacteristic
44#16839622C2211yescharacteristic
45#16839622C2211yescharacteristic
46#16839524C2211yescharacteristic
47#16839524C2211yescharacteristic
48#16839524C2211yescharacteristic
49#16839524C2211yescharacteristic
50C22×#41×C61C2211yescharacteristic
51C22×#41×C61C2211yescharacteristic
52C61×#537—24no—
53C61×#537—24no—
54C2×C22⋊Q8×C61—21no—
55C2×C22⋊Q8×C61C2211yescharacteristic
56C2×C22⋊Q8×C61C2211yescharacteristic
57C2×#121×C61—21no—
58C2×#121×C61—21no—
59C2×#121×C61—21no—
60C2×#121×C61C2211yescharacteristic
61C2×#121×C61C2211yescharacteristic
62C22×C4⋊C4×C61C2211yescharacteristic
63C23×Dic61—21no—
64C22×#92418C2311yescharacteristic
65C22×#92418C2311yescharacteristic
66C22×#92418C2311yescharacteristic
67C22×#92418C2311yescharacteristic
68#14519736—22no—
69#14519736—22no—
70C2×C4⋊Dic61—21no—
71C2×C4⋊Dic61—41no—
72C2×C4⋊Dic61—41no—
73C2×C4⋊Dic61C2311yescharacteristic
74C2×C4⋊Dic61C2311yescharacteristic
75C2×C4⋊Dic61C2311yescharacteristic
76C2×C4⋊Dic61C2311yescharacteristic
77C2×C22⋊Dic61—21no—
78C2×C22⋊Dic61—21no—
79C2×C22⋊Dic61—21no—
80C2×C22⋊Dic61—21no—
81C2×C22⋊Dic61—21no—
82C2×C4×Dic61—21no—
83#14519710—22no—
84#14519710—22no—
85#14519708—22no—
86#14519708—22no—
87#14519701—22no—
88#14519701—22no—
89#14519701—41no—
90#14519701—41no—
91#14519698—22no—
92#14519698—22no—
93#14519698—41no—
94#14519698—41no—
95C22⋊#92418—22no—
96C22⋊#92418—22no—
97C22⋊#92418—22no—
98C22⋊#92418—22no—
99C22⋊#92418—41no—
100C22⋊#92418—41no—
101#14519684—21no—
102#14519684—21no—
103#14519684—21no—
104#14519684—21no—
105C2×#41×C61—22no—
106C2×#41×C61—22no—
107C2×#41×C61—22no—
108C2×#41×C61—22no—
109C2×#41×C61—22no—
110C2×#41×C61—22no—
111C2×#41×C61—22no—
112C2×#41×C61—22no—
113C2×#41×C61—41no—
114C2×#41×C61—41no—
115C2×#41×C61—41no—
116C2×#41×C61—41no—
117C22×Q8×C61D411yescharacteristic
118C22×Q8×C61C2311yescharacteristic
119C22×D4×C61—21no—
120C22×D4×C61—21no—
121C22×D4×C61—21no—
122C22×D4×C61D411yescharacteristic
123C22×D4×C61D411yescharacteristic
124C22×D4×C61D411yescharacteristic
125C22×D4×C61C2311yescharacteristic
126C23×C4×C61—21no—
127C23×C4×C61—21no—
128C23×C4×C61C2311yescharacteristic
129C23×C4×C61C2311yescharacteristic
130C23×C4×C61C2311yescharacteristic
131C22⋊Q8×C61—28no—
132C22⋊Q8×C61—22no—
133C22⋊Q8×C61—22no—
134C22⋊Q8×C61—22no—
135C22⋊Q8×C61D414yes—
136#121×C61—28no—
137#121×C61—28no—
138#121×C61—28no—
139#121×C61—22no—
140#121×C61—22no—
141#121×C61—22no—
142#121×C61D414yes—
143C2×C4⋊C4×C61—21no—
144C2×C4⋊C4×C61—21no—
145C2×C4⋊C4×C61—21no—
146C2×C4⋊C4×C61—22no—
147C2×C4⋊C4×C61—22no—
148C2×C4⋊C4×C61C2311yescharacteristic
149C2×C4⋊C4×C61C2311yescharacteristic
150C2×C22⋊C4×C61—21no—
151C2×C22⋊C4×C61—21no—
152C2×C22⋊C4×C61—21no—
153C2×C22⋊C4×C61—21no—
154C24×C61—21no—
155C24×C61C2×D411yescharacteristic
156C24×C61C2×D411yescharacteristic
157C24×C61C2×D411yescharacteristic
158#41×C61—44no—
159#41×C61—44no—
160#41×C61—44no—
161#41×C61—44no—
162#41×C61—44no—
163#41×C61—44no—
164#41×C61—44no—
165#41×C61—44no—
166C2×Q8×C61—22no—
167C2×Q8×C61—22no—
168C2×Q8×C61—21no—
169C2×Q8×C61—21no—
170C2×Q8×C61—21no—
171C2×Q8×C61—21no—
172C2×Q8×C61—21no—
173C2×Q8×C61—41no—
174C2×Q8×C61C2×D412yes—
175C2×D4×C61—24no—
176C2×D4×C61—22no—
177C2×D4×C61—22no—
178C2×D4×C61—22no—
179C2×D4×C61—22no—
180C2×D4×C61—24no—
181C2×D4×C61—24no—
182C2×D4×C61—22no—
183C2×D4×C61—22no—
184C2×D4×C61—21no—
185C2×D4×C61—21no—
186C2×D4×C61—21no—
187C2×D4×C61—21no—
188C2×D4×C61—21no—
189C2×D4×C61—41no—
190C2×D4×C61—41no—
191C2×D4×C61—41no—
192C2×D4×C61—42no—
193C2×D4×C61—42no—
194C2×D4×C61—81no—
195C2×D4×C61—81no—
196C2×D4×C61—81no—
197C2×D4×C61—81no—
198C2×D4×C61C2×D412yes—
199C22×C4×C61—21no—
200C22×C4×C61—21no—
201C22×C4×C61—21no—
202C22×C4×C61—21no—
203C22×C4×C61—21no—
204C22×C4×C61—21no—
205C22×C4×C61—21no—
206C22×C4×C61—21no—
207C22×C4×C61—24no—
208C22×C4×C61—21no—
209C22×C4×C61—21no—
210C22×C4×C61—21no—
211C22×C4×C61—24no—
212C22×C4×C61—21no—
213C22×C4×C61—21no—
214C22×C4×C61—21no—
215C22×C4×C61—21no—
216C22×C4×C61—21no—
217C22×C4×C61—21no—
218C22×C4×C61—42no—
219C22×C4×C61—42no—
220C22×C4×C61—81no—
221C22×C4×C61—81no—
222C22×C4×C61C2×D411yescharacteristic
223C22×C4×C61C2×D411yescharacteristic
224C22×C4×C61C2×D412yes—
225C22×C4×C61C2×D412yes—
226C22×C4×C61C2×D411yescharacteristic
227C22×C4×C61#4112yes—
228C22×C4×C61#4112yes—
229C22×C4×C61C2411yescharacteristic
230C22×Dic61—21no—
231C22×Dic61—21no—
232C22×Dic61—21no—
233C22×Dic61—21no—
234C22×Dic61—42no—
235C22×Dic61—81no—
236C22×Dic61—81no—
237C4⋊C4×C61—24no—
238C4⋊C4×C61—24no—
239C4⋊C4×C61—24no—
240C4⋊C4×C61—21no—
241C4⋊C4×C61—21no—
242C4⋊C4×C61C2×D412yes—
243C4⋊C4×C61C2×D412yes—
244C22⋊C4×C61—24no—
245C22⋊C4×C61—24no—
246C22⋊C4×C61—24no—
247C22⋊C4×C61—24no—
248C22⋊Dic61—42no—
249C22⋊Dic61—81no—
250C22⋊Dic61—81no—
251C22⋊Dic61—81no—
252C22⋊Dic61—81no—
253C4⋊Dic61—21no—
254C4⋊Dic61—21no—
255C4⋊Dic61—21no—
256C4⋊Dic61—21no—
257C4⋊Dic61—21no—
258C4⋊Dic61—21no—
259C4⋊Dic61—21no—
260C4⋊Dic61—21no—
261C4⋊Dic61—42no—
262C4×Dic61—42no—
263C2×#92418—21no—
264C2×#92418—21no—
265C2×#92418—21no—
266C2×#92418—21no—
267C2×#92418—21no—
268C2×#92418—21no—
269C2×#92418—21no—
270C2×#92418—21no—
271C2×#92418—21no—
272C2×#92418—21no—
273C2×#92418—21no—
274C2×#92418—21no—
275C23×C61—21no—
276C23×C61—21no—
277C23×C61—21no—
278C23×C61—21no—
279C23×C61—21no—
280C23×C61—21no—
281C23×C61—21no—
282C23×C61—21no—
283C23×C61—21no—
284C23×C61—21no—
285C23×C61—21no—
286C23×C61—21no—
287C23×C61—21no—
288C23×C61—22no—
289C23×C61—21no—
290C23×C61—21no—
291C23×C61—21no—
292C23×C61—21no—
293C23×C61—21no—
294C23×C61—21no—
295C23×C61—41no—
296C23×C61—41no—
297C23×C61—41no—
298C23×C61—41no—
299C23×C61—41no—
300C23×C61—41no—
301C23×C61#12012yes—
302C23×C61#12312yes—
303C23×C61C22×D411yescharacteristic
304Q8×C61—22no—
305Q8×C61—22no—
306Q8×C61—44no—
307Q8×C61—41no—
308Q8×C61—41no—
309D4×C61—22no—
310D4×C61—22no—
311D4×C61—44no—
312D4×C61—44no—
313D4×C61—44no—
314D4×C61—48no—
315D4×C61—41no—
316D4×C61—41no—
317D4×C61—84no—
318D4×C61—84no—
319C2×C4×C61—21no—
320C2×C4×C61—21no—
321C2×C4×C61—21no—
322C2×C4×C61—21no—
323C2×C4×C61—22no—
324C2×C4×C61—22no—
325C2×C4×C61—22no—
326C2×C4×C61—22no—
327C2×C4×C61—22no—
328C2×C4×C61—22no—
329C2×C4×C61—22no—
330C2×C4×C61—22no—
331C2×C4×C61—22no—
332C2×C4×C61—22no—
333C2×C4×C61—22no—
334C2×C4×C61—21no—
335C2×C4×C61—21no—
336C2×C4×C61—21no—
337C2×C4×C61—48no—
338C2×C4×C61—41no—
339C2×C4×C61—41no—
340C2×C4×C61—41no—
341C2×C4×C61—41no—
342C2×C4×C61—41no—
343C2×C4×C61—41no—
344C2×C4×C61—41no—
345C2×C4×C61—41no—
346C2×C4×C61—41no—
347C2×C4×C61—41no—
348C2×C4×C61—84no—
349C2×C4×C61#12012yes—
350C2×C4×C61#12312yes—
351C2×C4×C61C22×D411yescharacteristic
352C2×C4×C61C22×D411yescharacteristic
353C2×C4×C61C2×#4111yescharacteristic
354C2×C4×C61C2×#4111yescharacteristic
355C2×C4×C61H(5,𝔽2)11yescharacteristic
356C2×C4×C61H(5,𝔽2)11yescharacteristic
357C2×Dic61—41no—
358C2×Dic61—41no—
359C2×Dic61—41no—
360C2×Dic61—41no—
361C2×Dic61—41no—
362C2×Dic61—41no—
363C2×Dic61—41no—
364C2×Dic61—41no—
365C2×Dic61—41no—
366C2×Dic61—41no—
367C2×Dic61—41no—
368C2×Dic61—41no—
369C2×Dic61—84no—
370#92418—41no—
371#92418—41no—
372#92418—41no—
373#92418—41no—
374#24017—611nomaximal, Sylow
375C22×C61—22no—
376C22×C61—22no—
377C22×C61—22no—
378C22×C61—22no—
379C22×C61—22no—
380C22×C61—22no—
381C22×C61—41no—
382C22×C61—41no—
383C22×C61—41no—
384C22×C61—41no—
385C22×C61—41no—
386C22×C61—41no—
387C22×C61—41no—
388C22×C61—41no—
389C22×C61—41no—
390C22×C61—41no—
391C22×C61—42no—
392C22×C61—41no—
393C22×C61—41no—
394C22×C61—41no—
395C22×C61—41no—
396C22×C61—42no—
397C22×C61—41no—
398C22×C61—42no—
399C22×C61—81no—
400C22×C61—81no—
401C22×C61—81no—
402C22×C61—81no—
403C22×C61C2×#12011yescharacteristic
404C22×C61C2×#12311yescharacteristic
405C22×C61#53411yescharacteristic
406C22×C61#57611yescharacteristic
407C22×C61#57711yescharacteristic
408C22×C61#57711yescharacteristic
409C22×C61#57811yescharacteristic
410C4×C61—22no—
411C4×C61—22no—
412C4×C61—41no—
413C4×C61—42no—
414C4×C61—42no—
415C4×C61—42no—
416C4×C61#54611yescharacteristic
417C4×C61#54611yescharacteristic
418C4×C61#54611yescharacteristic
419C4×C61#54611yescharacteristic
420Dic61—81no—
421Dic61—81no—
422Dic61—81no—
423Dic61—81no—
424C2×#537D6111yescharacteristic
425C2×#485—611no—
426C2×#482—611no—
427#2311—611no—
428#2036—611no—
429#2035—611no—
430#2034—611no—
431#2033—611no—
432#1874—611no—
433#1872—611no—
434#1853—611no—
435#1852—611no—
436#1788—611no—
437#1788—611no—
438#1780—611no—
439C2×C61—42no—
440C2×C61—42no—
441C2×C61—81no—
442C2×C61—82no—
443C2×C61#240511yescharacteristic
444C2×C61#301211yescharacteristic
445C2×C61#301311yescharacteristic
446C2×C61#309811yescharacteristic
447C2×C61#309911yescharacteristic
448C2×C61#319811yescharacteristic
449C2×C61#320111yescharacteristic
450C22×#41C2×D6111yescharacteristic
451C22×#41C2×D6111yescharacteristic
452#537—24no—
453#537—24no—
454C2×C22⋊Q8—21no—
455C2×C22⋊Q8C2×D6111yescharacteristic
456C2×C22⋊Q8C2×D6111yescharacteristic
457C2×#121—21no—
458C2×#121—21no—
459C2×#121—21no—
460C2×#121C2×D6111yescharacteristic
461C2×#121C2×D6111yescharacteristic
462C2×#117—611no—
463C22×C4⋊C4—611no—
464C22×C4⋊C4C2×D6111yescharacteristic
465#485—1224no—
466#482—1224no—
467C2×#107—611no—
468C2×#107—611no—
469C2×#106—611no—
470C2×#106—611no—
471C2×#103—611no—
472C2×#103—611no—
473C2×#103—611no—
474C2×#103—611no—
475C2×#102—611no—
476C2×#102—611no—
477C2×#102—611no—
478C2×#102—611no—
479C2×C22⋊C8—611no—
480C2×C22⋊C8—611no—
481C2×C22⋊C8—611no—
482C2×C22⋊C8—611no—
483C2×C22⋊C8—611no—
484C2×C22⋊C8—611no—
485#391—1221no—
486#390—1221no—
487#386—1221no—
488#386—1221no—
489#380—611no—
490#380—611no—
491#380—611no—
492#380—611no—
493#340—611no—
494#340—611no—
495#340—611no—
496#340—611no—
497C61#2401711yescharacteristic, complemented, Sylow
498C2×#41—22no—
499C2×#41—22no—
500C2×#41—22no—
501C2×#41—22no—
502C2×#41—22no—
503C2×#41—22no—
504C2×#41—22no—
505C2×#41—22no—
506C2×#41—41no—
507C2×#41—41no—
508C2×#41—41no—
509C2×#41—41no—
510C22×Q8C22⋊D6111yescharacteristic
511C22×Q8C22×D6111yescharacteristic
512C22×D4—21no—
513C22×D4—21no—
514C22×D4—21no—
515C22×D4C22⋊D6111yescharacteristic
516C22×D4C22⋊D6111yescharacteristic
517C22×D4C22⋊D6111yescharacteristic
518C22×D4C22×D6111yescharacteristic
519C23×C4—21no—
520C23×C4—21no—
521C23×C4—1221no—
522C23×C4C22×D6111yescharacteristic
523C23×C4C22×D6111yescharacteristic
524C23×C4C22×D6111yescharacteristic
525C22×C8—611no—
526C22×C8—611no—
527C22×C8—611no—
528C22×C8—611no—
529C22⋊Q8—28no—
530C22⋊Q8—22no—
531C22⋊Q8—22no—
532C22⋊Q8—22no—
533C22⋊Q8C22⋊D6114yes—
534#121—28no—
535#121—28no—
536#121—28no—
537#121—22no—
538#121—22no—
539#121—22no—
540#121C22⋊D6114yes—
541#117—1222no—
542#117—1222no—
543C2×C4⋊C4—21no—
544C2×C4⋊C4—21no—
545C2×C4⋊C4—21no—
546C2×C4⋊C4—22no—
547C2×C4⋊C4—22no—
548C2×C4⋊C4—611no—
549C2×C4⋊C4—611no—
550C2×C4⋊C4—611no—
551C2×C4⋊C4—611no—
552C2×C4⋊C4—1221no—
553C2×C4⋊C4—2441no—
554C2×C4⋊C4—2441no—
555C2×C4⋊C4C22×D6111yescharacteristic
556C2×C4⋊C4C22×D6111yescharacteristic
557C2×C22⋊C4—21no—
558C2×C22⋊C4—21no—
559C2×C22⋊C4—21no—
560C2×C22⋊C4—21no—
561C2×C22⋊C4—1221no—
562C2×C22⋊C4—1221no—
563C2×C22⋊C4—1221no—
564C2×C22⋊C4—1221no—
565C2×C22⋊C4—1221no—
566C2×C42—1221no—
567#107—1222no—
568#107—1222no—
569#106—1222no—
570#106—1222no—
571#103—1222no—
572#103—1222no—
573#103—2441no—
574#103—2441no—
575#102—1222no—
576#102—1222no—
577#102—2441no—
578#102—2441no—
579C22⋊C8—1222no—
580C22⋊C8—1222no—
581C22⋊C8—1222no—
582C22⋊C8—1222no—
583C22⋊C8—2441no—
584C22⋊C8—2441no—
585#95—1221no—
586#95—1221no—
587#95—1221no—
588#95—1221no—
589C24—21no—
590C24C2×C22⋊D6111yescharacteristic
591C24C2×C22⋊D6111yescharacteristic
592C24C2×C22⋊D6111yescharacteristic
593#41—44no—
594#41—44no—
595#41—44no—
596#41—44no—
597#41—44no—
598#41—44no—
599#41—44no—
600#41—44no—
601C2×Q8—21no—
602C2×Q8—22no—
603C2×Q8—22no—
604C2×Q8—21no—
605C2×Q8—21no—
606C2×Q8—21no—
607C2×Q8—21no—
608C2×Q8—41no—
609C2×Q8C2×C22⋊D6112yes—
610C2×D4—24no—
611C2×D4—22no—
612C2×D4—22no—
613C2×D4—22no—
614C2×D4—22no—
615C2×D4—24no—
616C2×D4—24no—
617C2×D4—21no—
618C2×D4—21no—
619C2×D4—21no—
620C2×D4—21no—
621C2×D4—21no—
622C2×D4—22no—
623C2×D4—22no—
624C2×D4—41no—
625C2×D4—41no—
626C2×D4—41no—
627C2×D4—42no—
628C2×D4—42no—
629C2×D4—81no—
630C2×D4—81no—
631C2×D4—81no—
632C2×D4—81no—
633C2×D4C2×C22⋊D6112yes—
634C22×C4—21no—
635C22×C4—21no—
636C22×C4—21no—
637C22×C4—21no—
638C22×C4—21no—
639C22×C4—21no—
640C22×C4—21no—
641C22×C4—21no—
642C22×C4—24no—
643C22×C4—21no—
644C22×C4—21no—
645C22×C4—21no—
646C22×C4—24no—
647C22×C4—21no—
648C22×C4—21no—
649C22×C4—21no—
650C22×C4—21no—
651C22×C4—21no—
652C22×C4—21no—
653C22×C4—42no—
654C22×C4—42no—
655C22×C4—81no—
656C22×C4—81no—
657C22×C4—1221no—
658C22×C4—1221no—
659C22×C4—1221no—
660C22×C4—1221no—
661C22×C4—4881no—
662C22×C4—4881no—
663C22×C4—2442no—
664C22×C4#1175822412yes—
665C22×C4#1175822412yes—
666C22×C4C2×C22⋊D6111yescharacteristic
667C22×C4C2×C22⋊D6112yes—
668C22×C4C2×C22⋊D6112yes—
669C22×C4C2×C22⋊D6111yescharacteristic
670C22×C4C2×C22⋊D6111yescharacteristic
671C22×C4C23×D6111yescharacteristic
672C2×C8—1221no—
673C2×C8—1221no—
674C2×C8—1221no—
675C2×C8—1221no—
676C2×C8—1221no—
677C2×C8—1221no—
678C2×C8—1221no—
679C2×C8—1221no—
680C2×C8—1221no—
681C2×C8—1221no—
682C2×C8—1221no—
683C2×C8—1221no—
684C4⋊C4—24no—
685C4⋊C4—24no—
686C4⋊C4—21no—
687C4⋊C4—21no—
688C4⋊C4—24no—
689C4⋊C4—1221no—
690C4⋊C4—1221no—
691C4⋊C4—1221no—
692C4⋊C4—1221no—
693C4⋊C4—1221no—
694C4⋊C4—1221no—
695C4⋊C4—1221no—
696C4⋊C4—1221no—
697C4⋊C4—2442no—
698C4⋊C4C2×C22⋊D6112yes—
699C4⋊C4C2×C22⋊D6112yes—
700C22⋊C4—24no—
701C22⋊C4—24no—
702C22⋊C4—24no—
703C22⋊C4—24no—
704C22⋊C4—4881no—
705C22⋊C4—4881no—
706C22⋊C4—4881no—
707C22⋊C4—4881no—
708C22⋊C4—2442no—
709C42—2442no—
710C23—21no—
711C23—21no—
712C23—21no—
713C23—21no—
714C23—21no—
715C23—21no—
716C23—21no—
717C23—21no—
718C23—21no—
719C23—21no—
720C23—21no—
721C23—21no—
722C23—21no—
723C23—22no—
724C23—21no—
725C23—21no—
726C23—21no—
727C23—21no—
728C23—21no—
729C23—21no—
730C23—41no—
731C23—41no—
732C23—41no—
733C23—41no—
734C23—41no—
735C23—41no—
736C23#1451974612yes—
737C23#1451975812yes—
738C23C22×C22⋊D6111yescharacteristic
739Q8—22no—
740Q8—22no—
741Q8—44no—
742Q8—41no—
743Q8—41no—
744D4—22no—
745D4—22no—
746D4—44no—
747D4—44no—
748D4—44no—
749D4—48no—
750D4—41no—
751D4—41no—
752D4—84no—
753D4—84no—
754C2×C4—21no—
755C2×C4—21no—
756C2×C4—21no—
757C2×C4—21no—
758C2×C4—22no—
759C2×C4—22no—
760C2×C4—22no—
761C2×C4—22no—
762C2×C4—22no—
763C2×C4—22no—
764C2×C4—22no—
765C2×C4—22no—
766C2×C4—22no—
767C2×C4—22no—
768C2×C4—22no—
769C2×C4—21no—
770C2×C4—21no—
771C2×C4—21no—
772C2×C4—48no—
773C2×C4—41no—
774C2×C4—41no—
775C2×C4—41no—
776C2×C4—41no—
777C2×C4—41no—
778C2×C4—41no—
779C2×C4—41no—
780C2×C4—41no—
781C2×C4—41no—
782C2×C4—41no—
783C2×C4—84no—
784C2×C4—4884no—
785C2×C4—2441no—
786C2×C4—2441no—
787C2×C4—2441no—
788C2×C4—2441no—
789C2×C4—2441no—
790C2×C4—2441no—
791C2×C4—2441no—
792C2×C4—2441no—
793C2×C4—2441no—
794C2×C4—2441no—
795C2×C4—2441no—
796C2×C4—2441no—
797C2×C4#1451974612yes—
798C2×C4#1451975812yes—
799C2×C4C22×C22⋊D6111yescharacteristic
800C2×C4C22×C22⋊D6111yescharacteristic
801C2×C4C2×#1175822411yescharacteristic
802C2×C4C2×#1175822411yescharacteristic
803C2×C4#1451982211yescharacteristic
804C2×C4#1451982211yescharacteristic
805C8—2441no—
806C8—2441no—
807C8—2441no—
808C8—2441no—
809C22—22no—
810C22—22no—
811C22—22no—
812C22—22no—
813C22—22no—
814C22—22no—
815C22—41no—
816C22—41no—
817C22—41no—
818C22—41no—
819C22—41no—
820C22—41no—
821C22—41no—
822C22—41no—
823C22—41no—
824C22—42no—
825C22—41no—
826C22—41no—
827C22—42no—
828C22—41no—
829C22—41no—
830C22—42no—
831C22—41no—
832C22—41no—
833C22—81no—
834C22—81no—
835C22—81no—
836C22—81no—
837C22C2×#1451974611yescharacteristic
838C22C2×#1451975811yescharacteristic
839C22#1684032111yescharacteristic
840C22#1684056511yescharacteristic
841C22#1684057011yescharacteristic
842C22#1684057311yescharacteristic
843C22#1684057711yescharacteristic
844C4—22no—
845C4—22no—
846C4—42no—
847C4—42no—
848C4—41no—
849C4—42no—
850C4—4881no—
851C4—4881no—
852C4—4881no—
853C4—4881no—
854C4#1684040611yescharacteristic
855C4#1684040611yescharacteristic
856C4#1684040611yescharacteristic
857C4#1684040611yescharacteristic
858C2—42no—
859C2—42no—
860C2—81no—
861C2—82no—
862C2#2144914211yescharacteristic
863C2#2145512311yescharacteristic
864C2#2145513411yescharacteristic
865C2#2145579311yescharacteristic
866C2#2145580411yescharacteristic
867C2#2145666511yescharacteristic
868C2#2145669511yescharacteristic
subgroupG/H
centerC23C22×C22⋊D61
commutator, cosocleC22×C4×C61C24
FrattiniC22×C4C23×D61
Fitting, prime radicalC2×C61×#537C2
socleC23×C61C22×D4
hypercenterC2×#537D61
hypocenterC61#24017
LCSG ▷ C22×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C22×#41 ◁ C2×#537

Complements

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

NH ≅ G/Ntype
1. C2×#16840100C2semidirect
2. C2×#16840083C2semidirect
3. #21448411C2semidirect
4. #21447019C2semidirect
5. #21447012C2semidirect
6. #21447005C2semidirect
7. #21446998C2semidirect
8. #21446137C2semidirect
9. #21446127C2semidirect
10. #21446012C2semidirect
11. #21446007C2semidirect
12. #21445759C2semidirect
13. #21445759C2semidirect
14. #21445731C2semidirect
497. C61#24017semidirect

Maximal subgroups

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

subgroupindex
C2×#168401002
C2×#168400832
#214484112
#214470192
#214470122
#214470052
#214469982
#214461372
#214461272
#214460122
#214460072
#214457592
#214457312
C2×C61×#5372
#2401761