Finite Group Databasebeta

← #29604284

Subgroups — #29604284

Order 15616.

2046 conjugacy classes of subgroups.

The subgroup lattice has 1174 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16839664C211yesmaximal, characteristic
2C2×#16839654C211yesmaximal, characteristic, complemented
3C2×#16839653C211yesmaximal, characteristic, complemented
4C2×#16839647C211yesmaximal, characteristic, complemented
5C2×#16839640C211yesmaximal, characteristic
6C2×#16839636C211yesmaximal, characteristic, complemented
7C2×C4×#11758198C211yesmaximal, characteristic, complemented
8#21444086C211yesmaximal, characteristic, complemented
9#21444065C211yesmaximal, characteristic, complemented
10#21444065C211yesmaximal, characteristic, complemented
11#21444059C211yesmaximal, characteristic
12#21444057C211yesmaximal, characteristic, complemented
13#21444057C211yesmaximal, characteristic, complemented
14#21444049C211yesmaximal, characteristic, complemented
15C4×#95×C61C211yesmaximal, characteristic, complemented
16C23×D244C2211yescharacteristic
17C23×C4×D61C2211yescharacteristic
18C22×C4⋊Dic61C2211yescharacteristic
19C22×C4⋊Dic61C2211yescharacteristic
20C22×C4⋊Dic61C2211yescharacteristic
21C22×#11758196C2211yescharacteristic
22C22×#11758198C2211yescharacteristic
23C22×#11758198C2211yescharacteristic
24C22×#11758198C2211yescharacteristic
25C22×#11758198C2211yescharacteristic
26C22×#11758198C2211yescharacteristic
27C22×#11758198C2211yescharacteristic
28C22×#11758198C2211yescharacteristic
29C22×#11758198C2211yescharacteristic
30C22×#11758198C2211yescharacteristic
31C22×#11758198C2211yescharacteristic
32C22×#11758198C2211yescharacteristic
33C22×C4×Dic61C2211yescharacteristic
34#16839664C418yescomplemented
35#16839654—24no—
36#16839653—24no—
37#16839647—24no—
38#16839640—24no—
39#16839636—24no—
40C4×#11758198—24no—
41C2×#14519684C2211yescharacteristic
42C2×#14519684C2211yescharacteristic
43C2×#14519684C2211yescharacteristic
44C2×#14519684C2211yescharacteristic
45C2×#14519684C2211yescharacteristic
46C2×#14519684C2211yescharacteristic
47C2×#14519684C2211yescharacteristic
48C2×#14519684C2211yescharacteristic
49C2×#14519684C2211yescharacteristic
50C2×#14519684C2211yescharacteristic
51C22×C42×C61C2211yescharacteristic
52C22×C42×C61C2211yescharacteristic
53C22×C42×C61C2211yescharacteristic
54C2×#95×C61C2211yescharacteristic
55C2×#95×C61C2211yescharacteristic
56C2×#95×C61C2211yescharacteristic
57C2×#95×C61C2211yescharacteristic
58C24×D61C2311yescharacteristic
59C24×D61C2311yescharacteristic
60C22×D244—22no—
61C22×D244—22no—
62C22×D244—22no—
63C22×D244—22no—
64C22×D244—41no—
65C22×D244—41no—
66C22×D244C2×C414yes—
67C23×Dic61C2311yescharacteristic
68C23×Dic61C2311yescharacteristic
69C23×Dic61C2311yescharacteristic
70C23×Dic61C2311yescharacteristic
71C23×Dic61C2311yescharacteristic
72C23×Dic61C2311yescharacteristic
73C22×C4×D61—22no—
74C22×C4×D61—22no—
75C22×C4×D61—22no—
76C22×C4×D61—22no—
77C22×C4×D61—22no—
78C22×C4×D61—41no—
79C22×C4×D61—41no—
80C2×C4⋊Dic61—22no—
81C2×C4⋊Dic61—22no—
82C2×C4⋊Dic61—22no—
83C2×C4⋊Dic61—22no—
84C2×C4⋊Dic61—22no—
85C2×C4⋊Dic61—22no—
86C2×C4⋊Dic61—41no—
87C2×C4⋊Dic61—41no—
88C2×C4⋊Dic61C2×C414yescomplemented
89C2×#11758196—22no—
90C2×#11758196—22no—
91C2×#11758196—22no—
92C2×#11758198—22no—
93C2×#11758198—22no—
94C2×#11758198—22no—
95C2×#11758198—22no—
96C2×#11758198—22no—
97C2×#11758198—22no—
98C2×#11758198—22no—
99C2×#11758198—22no—
100C2×#11758198—22no—
101C2×#11758198—22no—
102C2×#11758198—22no—
103C2×#11758198—22no—
104C2×#11758198—22no—
105C2×#11758198—22no—
106C2×#11758198—22no—
107C2×#11758198—22no—
108C2×#11758198—22no—
109C2×#11758198—22no—
110C2×#11758198—22no—
111C2×#11758198—22no—
112C2×#11758198—22no—
113C2×#11758198—22no—
114C2×#11758198—22no—
115C2×#11758198—41no—
116C2×#11758198—41no—
117C2×#11758198—41no—
118C2×#11758198—41no—
119C2×#11758198—41no—
120C2×#11758198—41no—
121C2×#11758198C2×C414yes—
122C2×#11758198C2×C414yes—
123C2×#11758198C2×C414yescomplemented
124C2×#11758198C2×C414yescomplemented
125C2×C4×Dic61—22no—
126C2×C4×Dic61—22no—
127C2×C4×Dic61—22no—
128#14519684—22no—
129#14519684—22no—
130#14519684—22no—
131#14519684—22no—
132#14519684—22no—
133#14519684—22no—
134#14519684—22no—
135#14519684—22no—
136#14519684—22no—
137#14519684—22no—
138C23×C4×C61C2311yescharacteristic
139C23×C4×C61C2311yescharacteristic
140C23×C4×C61C2311yescharacteristic
141C23×C4×C61C2311yescharacteristic
142C23×C4×C61C2311yescharacteristic
143C23×C4×C61C2311yescharacteristic
144C23×C4×C61C2311yescharacteristic
145C2×C42×C61—22no—
146C2×C42×C61—41no—
147C2×C42×C61—41no—
148C2×C42×C61—41no—
149C2×C42×C61—41no—
150C2×C42×C61—41no—
151C2×C42×C61—41no—
152C2×C42×C61C2×C414yescomplemented
153C2×C42×C61D414yescomplemented
154#95×C61—22no—
155#95×C61—22no—
156#95×C61D414yes—
157#95×C61D414yescomplemented
158C24×C61C2411yescharacteristic
159C23×D61—21no—
160C23×D61—21no—
161C23×D61—21no—
162C23×D61—21no—
163C23×D61—21no—
164C23×D61—21no—
165C23×D61—21no—
166C23×D61—21no—
167C23×D61—21no—
168C23×D61—21no—
169C23×D61—21no—
170C23×D61—21no—
171C23×D61—21no—
172C23×D61—21no—
173C23×D61—21no—
174C23×D61—21no—
175C23×D61—21no—
176C23×D61—21no—
177C23×D61—21no—
178C23×D61—21no—
179C23×D61—21no—
180C23×D61—21no—
181C23×D61—21no—
182C23×D61—21no—
183C23×D61—21no—
184C23×D61—21no—
185C23×D61C22×C412yes—
186C23×D61C22×C412yes—
187C23×D61#4112yes—
188C23×D61#4112yes—
189C22×C4×C61—21no—
190C22×C4×C61—21no—
191C22×C4×C61—21no—
192C22×C4×C61—21no—
193C22×C4×C61—21no—
194C22×C4×C61—21no—
195C22×C4×C61—21no—
196C22×C4×C61—21no—
197C22×C4×C61—21no—
198C22×C4×C61—21no—
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—21no—
208C22×C4×C61—21no—
209C22×C4×C61—21no—
210C22×C4×C61—21no—
211C22×C4×C61—21no—
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—21no—
219C22×C4×C61—21no—
220C22×C4×C61—21no—
221C22×C4×C61—21no—
222C22×C4×C61—21no—
223C22×C4×C61C22×C412yes—
224C22×C4×C61C22×C412yes—
225C22×C4×C61C22×C412yes—
226C22×C4×C61C2×D412yes—
227C22×C4×C61C2×D412yes—
228C22×C4×C61C2×D412yes—
229C22×C4×C61C2×D412yes—
230C22×C4×C61C2×D412yes—
231C22×C4×C61C2×D412yes—
232C22×C4×C61C2×D412yes—
233C22×C4×C61C2×D412yes—
234C22×C4×C61C2×D412yes—
235C22×C4×C61#4112yes—
236C22×C4×C61#4112yes—
237C22×C4×C61#4112yes—
238C22×Dic61—21no—
239C22×Dic61—21no—
240C22×Dic61—21no—
241C22×Dic61—21no—
242C22×Dic61—21no—
243C22×Dic61—21no—
244C22×Dic61—21no—
245C22×Dic61—21no—
246C22×Dic61—21no—
247C22×Dic61—21no—
248C22×Dic61—21no—
249C22×Dic61—21no—
250C22×Dic61—21no—
251C22×Dic61—21no—
252C22×Dic61—21no—
253C22×Dic61—21no—
254C22×Dic61—21no—
255C22×Dic61—21no—
256C22×Dic61—21no—
257C22×Dic61—21no—
258C22×Dic61—21no—
259C22×Dic61—21no—
260C22×Dic61—21no—
261C22×Dic61—21no—
262C22×Dic61—21no—
263C22×Dic61—21no—
264C22×Dic61—21no—
265C22×Dic61—21no—
266C22×Dic61—21no—
267C22×Dic61—21no—
268C22×Dic61—21no—
269C22×Dic61—21no—
270C22×Dic61—21no—
271C22×Dic61—21no—
272C22×Dic61—21no—
273C22×Dic61—21no—
274C22×Dic61—21no—
275C22×Dic61—21no—
276C22×Dic61C22×C412yes—
277C22×Dic61C22×C412yes—
278C22×Dic61#4112yes—
279C22×Dic61#4112yes—
280C2×D244—28no—
281C2×D244—28no—
282C2×D244—44no—
283C2×D244—44no—
284C2×D244—44no—
285C2×D244—44no—
286C2×D244—44no—
287C2×C4×D61—28no—
288C2×C4×D61—44no—
289C2×C4×D61—44no—
290C2×C4×D61—44no—
291C2×C4×D61—44no—
292C2×C4×D61—44no—
293C2×C4×D61—44no—
294C42×C61—44no—
295C42×C61—44no—
296C42×C61—44no—
297#11758198—28no—
298#11758198—28no—
299#11758198—28no—
300#11758198—28no—
301#11758198—28no—
302#11758198—44no—
303#11758198—44no—
304#11758198—44no—
305#11758198—44no—
306#11758198—44no—
307#11758198—44no—
308C4⋊Dic61—28no—
309C4⋊Dic61—44no—
310C4⋊Dic61—44no—
311#11758196—44no—
312C4×Dic61—44no—
313C23×C61C23×C411yescharacteristic
314C23×C61C22×D411yescharacteristic
315C23×C61C22×D411yescharacteristic
316C23×C61C22×D411yescharacteristic
317C23×C61C2×#4111yescharacteristic
318C23×C61C2×#4111yescharacteristic
319C23×C61C2×#4111yescharacteristic
320C23×C61C2×#4111yescharacteristic
321C23×C61C2×#4111yescharacteristic
322C23×C61C2×#4111yescharacteristic
323C23×C61C2×#4111yescharacteristic
324C23×C61H(5,𝔽2)11yescharacteristic
325C23×C61H(5,𝔽2)11yescharacteristic
326C23×C61H(5,𝔽2)11yescharacteristic
327C23×C612−1+411yescharacteristic
328C22×D61—22no—
329C22×D61—22no—
330C22×D61—22no—
331C22×D61—22no—
332C22×D61—22no—
333C22×D61—22no—
334C22×D61—22no—
335C22×D61—22no—
336C22×D61—22no—
337C22×D61—22no—
338C22×D61—22no—
339C22×D61—22no—
340C22×D61—22no—
341C22×D61—22no—
342C22×D61—22no—
343C22×D61—22no—
344C22×D61—22no—
345C22×D61—22no—
346C22×D61—22no—
347C22×D61—22no—
348C22×D61—22no—
349C22×D61—22no—
350C22×D61—22no—
351C22×D61—22no—
352C22×D61—22no—
353C22×D61—41no—
354C22×D61—41no—
355C22×D61—41no—
356C22×D61—41no—
357C22×D61—41no—
358C22×D61—41no—
359C22×D61—41no—
360C22×D61—41no—
361C22×D61—41no—
362C22×D61—41no—
363C22×D61—41no—
364C22×D61—41no—
365C22×D61—41no—
366C22×D61—41no—
367C22×D61—41no—
368C22×D61—41no—
369C22×D61—41no—
370C22×D61—41no—
371C22×D61—41no—
372C22×D61—41no—
373C22×D61—41no—
374C22×D61—41no—
375C22×D61—41no—
376C22×D61—41no—
377C22×D61—41no—
378C22×D61—41no—
379C22×D61—41no—
380C22×D61—41no—
381C22×D61—41no—
382C22×D61—41no—
383C22×D61—41no—
384C22×D61—41no—
385C22×D61—41no—
386C22×D61—41no—
387C22×D61—41no—
388C22×D61—41no—
389C22×D61—41no—
390C22×D61—41no—
391C22×D61—41no—
392C22×D61—41no—
393C22×D61—41no—
394C22×D61—41no—
395C22×D61—41no—
396C22×D61—41no—
397C22×D61#11714yes—
398C2×C4×C61—22no—
399C2×C4×C61—22no—
400C2×C4×C61—22no—
401C2×C4×C61—22no—
402C2×C4×C61—22no—
403C2×C4×C61—22no—
404C2×C4×C61—22no—
405C2×C4×C61—22no—
406C2×C4×C61—22no—
407C2×C4×C61—22no—
408C2×C4×C61—22no—
409C2×C4×C61—22no—
410C2×C4×C61—22no—
411C2×C4×C61—22no—
412C2×C4×C61—22no—
413C2×C4×C61—22no—
414C2×C4×C61—22no—
415C2×C4×C61—22no—
416C2×C4×C61—22no—
417C2×C4×C61—22no—
418C2×C4×C61—22no—
419C2×C4×C61—22no—
420C2×C4×C61—22no—
421C2×C4×C61—22no—
422C2×C4×C61—22no—
423C2×C4×C61—22no—
424C2×C4×C61—22no—
425C2×C4×C61—22no—
426C2×C4×C61—22no—
427C2×C4×C61—22no—
428C2×C4×C61—22no—
429C2×C4×C61—22no—
430C2×C4×C61—22no—
431C2×C4×C61—41no—
432C2×C4×C61—41no—
433C2×C4×C61—41no—
434C2×C4×C61—41no—
435C2×C4×C61—41no—
436C2×C4×C61—41no—
437C2×C4×C61—41no—
438C2×C4×C61—41no—
439C2×C4×C61—41no—
440C2×C4×C61—41no—
441C2×C4×C61—41no—
442C2×C4×C61—41no—
443C2×C4×C61C4×D414yes—
444C2×C4×C61C4×D414yes—
445C2×C4×C61C4×D414yes—
446C2×C4×C61#12714yes—
447C2×Dic61—22no—
448C2×Dic61—22no—
449C2×Dic61—22no—
450C2×Dic61—22no—
451C2×Dic61—22no—
452C2×Dic61—22no—
453C2×Dic61—22no—
454C2×Dic61—22no—
455C2×Dic61—22no—
456C2×Dic61—22no—
457C2×Dic61—22no—
458C2×Dic61—22no—
459C2×Dic61—41no—
460C2×Dic61—41no—
461C2×Dic61—41no—
462C2×Dic61—41no—
463C2×Dic61—41no—
464C2×Dic61—41no—
465C2×Dic61—41no—
466C2×Dic61—41no—
467C2×Dic61—41no—
468C2×Dic61—41no—
469C2×Dic61—41no—
470C2×Dic61—41no—
471C2×Dic61—41no—
472C2×Dic61—41no—
473C2×Dic61—41no—
474C2×Dic61—41no—
475C2×Dic61—41no—
476C2×Dic61—41no—
477C2×Dic61—41no—
478C2×Dic61—41no—
479C2×Dic61—41no—
480C2×Dic61—41no—
481C2×Dic61—41no—
482C2×Dic61—41no—
483C2×Dic61—41no—
484C2×Dic61—41no—
485C2×Dic61—41no—
486C2×Dic61—41no—
487C2×Dic61—41no—
488C2×Dic61—41no—
489D244—416no—
490C4×D61—416no—
491#14084—611nomaximal, Sylow
492C22×C61C2×#11711yescharacteristic
493C22×C61C2×C4×D411yescharacteristic
494C22×C61C2×C4×D411yescharacteristic
495C22×C61C2×C4×D411yescharacteristic
496C22×C61C4×#4111yescharacteristic
497C22×C61#51811yescharacteristic
498C22×C61#52011yescharacteristic
499C22×C61#52511yescharacteristic
500C22×C61#52511yescharacteristic
501C22×C61#52911yescharacteristic
502C22×C61#52911yescharacteristic
503C22×C61C2×#12711yescharacteristic
504C22×C61#53211yescharacteristic
505C22×C61#53211yescharacteristic
506C22×C61#53211yescharacteristic
507C22×C61#53411yescharacteristic
508C22×C61#53711yescharacteristic
509C22×C61#53811yescharacteristic
510C22×C61#53911yescharacteristic
511C22×C61#54611yescharacteristic
512C22×C61#54611yescharacteristic
513C22×C61#54611yescharacteristic
514C22×C61#54611yescharacteristic
515C22×C61#54611yescharacteristic
516C22×C61#54611yescharacteristic
517C22×C61#54811yescharacteristic
518C22×C61#54811yescharacteristic
519C22×C61#55111yescharacteristic
520C22×C61#55111yescharacteristic
521C22×C61#55211yescharacteristic
522C22×C61#55311yescharacteristic
523C22×C61#55311yescharacteristic
524C22×C61#55311yescharacteristic
525C22×C61#55611yescharacteristic
526C22×C61#55911yescharacteristic
527C2×D61—24no—
528C2×D61—24no—
529C2×D61—24no—
530C2×D61—42no—
531C2×D61—42no—
532C2×D61—42no—
533C2×D61—42no—
534C2×D61—42no—
535C2×D61—42no—
536C2×D61—42no—
537C2×D61—42no—
538C2×D61—42no—
539C2×D61—42no—
540C2×D61—42no—
541C2×D61—42no—
542C2×D61—42no—
543C2×D61—42no—
544C2×D61—42no—
545C2×D61—42no—
546C2×D61—42no—
547C2×D61—42no—
548C2×D61—42no—
549C2×D61—81no—
550C2×D61—81no—
551C2×D61—81no—
552C2×D61—81no—
553C2×D61—81no—
554C2×D61—81no—
555C2×D61—81no—
556C2×D61—81no—
557C4×C61—24no—
558C4×C61—24no—
559C4×C61—24no—
560C4×C61—24no—
561C4×C61—42no—
562C4×C61—42no—
563C4×C61—42no—
564Dic61—42no—
565Dic61—42no—
566Dic61—42no—
567Dic61—42no—
568Dic61—81no—
569Dic61—81no—
570C2×#390—611no—
571C2×#388—611no—
572C2×#388—611no—
573C2×#387—611no—
574C2×#386—611no—
575C2×#385—611no—
576C2×C4×C22⋊C4—611no—
577#1445—611no—
578#1439—611no—
579#1439—611no—
580#1438—611no—
581#1437—611no—
582#1437—611no—
583C4⋊#95—611no—
584C4×#95D6111yescharacteristic, complemented
585C2×C61#229011yescharacteristic
586C2×C61C4×#12711yescharacteristic
587C2×C61#232511yescharacteristic
588C2×C61#234211yescharacteristic
589C2×C61#235211yescharacteristic
590C2×C61#236411yescharacteristic
591C2×C61#236711yescharacteristic
592C2×C61#253911yescharacteristic
593C2×C61#254011yescharacteristic
594C2×C61#255711yescharacteristic
595C2×C61#255811yescharacteristic
596C2×C61#255911yescharacteristic
597C2×C61#256011yescharacteristic
598C2×C61#260111yescharacteristic
599C2×C61#260211yescharacteristic
600D61—44no—
601D61—82no—
602C23×D4—611no—
603C24×C4—611no—
604C22×C4⋊C4—611no—
605C22×C4⋊C4—611no—
606C22×C4⋊C4—611no—
607C22×C4⋊C4—611no—
608C22×C22⋊C4—611no—
609C22×C22⋊C4—611no—
610C22×C22⋊C4—611no—
611C22×C22⋊C4—611no—
612C22×C22⋊C4—611no—
613C22×C22⋊C4—611no—
614C22×C22⋊C4—611no—
615C22×C22⋊C4—611no—
616C22×C22⋊C4—611no—
617C22×C22⋊C4—611no—
618C22×C22⋊C4—611no—
619C22×C42—611no—
620C22×C42C2×D6111yescharacteristic
621C22×C42C2×D6111yescharacteristic
622C22×C42C2×D6111yescharacteristic
623#390—618no—
624#388—1224no—
625#388—1224no—
626#387—1224no—
627#386—1224no—
628#385—1224no—
629C4×C22⋊C4—1224no—
630C2×#95—611no—
631C2×#95—611no—
632C2×#95—611no—
633C2×#95—611no—
634C2×#95—611no—
635C2×#95—611no—
636C2×#95—611no—
637C2×#95—611no—
638C2×#95—611no—
639C2×#95—611no—
640C2×#95C2×D6111yescharacteristic
641C2×#95C2×D6111yescharacteristic
642C2×#95C2×D6111yescharacteristic
643C2×#95C2×D6111yescharacteristic
644C61#1408411yescharacteristic, complemented, Sylow
645C25—611no—
646C25—611no—
647C22×D4—614no—
648C22×D4—1222no—
649C22×D4—1222no—
650C22×D4—1222no—
651C22×D4—1222no—
652C22×D4—2441no—
653C22×D4—2441no—
654C23×C4—611no—
655C23×C4—611no—
656C23×C4—611no—
657C23×C4—611no—
658C23×C4—611no—
659C23×C4—611no—
660C23×C4—1222no—
661C23×C4—1222no—
662C23×C4—1222no—
663C23×C4—1222no—
664C23×C4—1222no—
665C23×C4—2441no—
666C23×C4—2441no—
667C23×C4C22×D6111yescharacteristic
668C23×C4C22×D6111yescharacteristic
669C23×C4C22×D6111yescharacteristic
670C23×C4C22×D6111yescharacteristic
671C23×C4C22×D6111yescharacteristic
672C23×C4C22×D6111yescharacteristic
673C23×C4C22×D6111yescharacteristic
674C2×C4⋊C4—614no—
675C2×C4⋊C4—1222no—
676C2×C4⋊C4—1222no—
677C2×C4⋊C4—1222no—
678C2×C4⋊C4—1222no—
679C2×C4⋊C4—1222no—
680C2×C4⋊C4—1222no—
681C2×C4⋊C4—1222no—
682C2×C4⋊C4—1222no—
683C2×C4⋊C4—1222no—
684C2×C4⋊C4—2441no—
685C2×C4⋊C4—2441no—
686C2×C22⋊C4—614no—
687C2×C22⋊C4—614no—
688C2×C22⋊C4—614no—
689C2×C22⋊C4—614no—
690C2×C22⋊C4—1222no—
691C2×C22⋊C4—1222no—
692C2×C22⋊C4—1222no—
693C2×C22⋊C4—1222no—
694C2×C22⋊C4—1222no—
695C2×C22⋊C4—1222no—
696C2×C22⋊C4—1222no—
697C2×C22⋊C4—1222no—
698C2×C22⋊C4—1222no—
699C2×C22⋊C4—1222no—
700C2×C22⋊C4—1222no—
701C2×C22⋊C4—1222no—
702C2×C22⋊C4—1222no—
703C2×C22⋊C4—1222no—
704C2×C22⋊C4—1222no—
705C2×C22⋊C4—1222no—
706C2×C22⋊C4—1222no—
707C2×C22⋊C4—1222no—
708C2×C22⋊C4—1222no—
709C2×C22⋊C4—1222no—
710C2×C22⋊C4—1222no—
711C2×C22⋊C4—1222no—
712C2×C22⋊C4—1222no—
713C2×C22⋊C4—2441no—
714C2×C22⋊C4—2441no—
715C2×C22⋊C4—2441no—
716C2×C22⋊C4—2441no—
717C2×C22⋊C4—2441no—
718C2×C22⋊C4—2441no—
719C2×C42—22no—
720C2×C42—41no—
721C2×C42—41no—
722C2×C42—41no—
723C2×C42—41no—
724C2×C42—41no—
725C2×C42—41no—
726C2×C42—1222no—
727C2×C42—1222no—
728C2×C42—1222no—
729C2×C42C4×D6114yescomplemented
730C2×C42D24414yescomplemented
731#95—22no—
732#95—22no—
733#95—1222no—
734#95—1222no—
735#95—1222no—
736#95—1222no—
737#95—1222no—
738#95—1222no—
739#95—1222no—
740#95—1222no—
741#95—1222no—
742#95—1222no—
743#95D24414yes—
744#95D24414yescomplemented
745C24—612no—
746C24—612no—
747C24—612no—
748C24—612no—
749C24—1221no—
750C24—1221no—
751C24—1221no—
752C24—1221no—
753C24—1221no—
754C24—1221no—
755C24—1221no—
756C24—1221no—
757C24—1221no—
758C24—1221no—
759C24—1221no—
760C24—1221no—
761C24—1221no—
762C24—1221no—
763C24—1221no—
764C24—1221no—
765C24—1221no—
766C24—1221no—
767C24—1221no—
768C24—1221no—
769C24—1221no—
770C24—1221no—
771C24—1221no—
772C24—1221no—
773C24—1221no—
774C24—1221no—
775C24C23×D6111yescharacteristic
776C2×D4—1228no—
777C2×D4—1228no—
778C2×D4—2444no—
779C2×D4—2444no—
780C2×D4—2444no—
781C2×D4—2444no—
782C2×D4—2444no—
783C22×C4—21no—
784C22×C4—21no—
785C22×C4—21no—
786C22×C4—21no—
787C22×C4—21no—
788C22×C4—21no—
789C22×C4—21no—
790C22×C4—21no—
791C22×C4—21no—
792C22×C4—21no—
793C22×C4—21no—
794C22×C4—21no—
795C22×C4—21no—
796C22×C4—21no—
797C22×C4—21no—
798C22×C4—21no—
799C22×C4—21no—
800C22×C4—21no—
801C22×C4—21no—
802C22×C4—21no—
803C22×C4—21no—
804C22×C4—21no—
805C22×C4—21no—
806C22×C4—21no—
807C22×C4—21no—
808C22×C4—21no—
809C22×C4—21no—
810C22×C4—21no—
811C22×C4—21no—
812C22×C4—21no—
813C22×C4—21no—
814C22×C4—21no—
815C22×C4—21no—
816C22×C4—21no—
817C22×C4—612no—
818C22×C4—612no—
819C22×C4—612no—
820C22×C4—612no—
821C22×C4—1228no—
822C22×C4—1221no—
823C22×C4—1221no—
824C22×C4—1221no—
825C22×C4—1221no—
826C22×C4—1221no—
827C22×C4—1221no—
828C22×C4—1221no—
829C22×C4—1221no—
830C22×C4—1221no—
831C22×C4—1221no—
832C22×C4—1221no—
833C22×C4—1221no—
834C22×C4—1221no—
835C22×C4—1221no—
836C22×C4—1221no—
837C22×C4—1221no—
838C22×C4—1221no—
839C22×C4—1221no—
840C22×C4—1221no—
841C22×C4—1221no—
842C22×C4—1221no—
843C22×C4—1221no—
844C22×C4—1221no—
845C22×C4—1221no—
846C22×C4—1221no—
847C22×C4—1221no—
848C22×C4—1221no—
849C22×C4—1221no—
850C22×C4—1221no—
851C22×C4—1221no—
852C22×C4—1221no—
853C22×C4—1221no—
854C22×C4—1221no—
855C22×C4—1221no—
856C22×C4—1221no—
857C22×C4—1221no—
858C22×C4—1221no—
859C22×C4—1221no—
860C22×C4—2444no—
861C22×C4—2444no—
862C22×C4—2444no—
863C22×C4—2444no—
864C22×C4—2444no—
865C22×C4—2444no—
866C22×C4C2×C4×D6112yes—
867C22×C4C2×C4×D6112yes—
868C22×C4C2×C4×D6112yes—
869C22×C4C2×D24412yes—
870C22×C4C2×D24412yes—
871C22×C4C2×D24412yes—
872C22×C4C2×D24412yes—
873C22×C4C2×D24412yes—
874C22×C4C2×D24412yes—
875C22×C4C2×D24412yes—
876C22×C4C2×D24412yes—
877C22×C4C2×D24412yes—
878C22×C4#1175822212yes—
879C22×C4#1175822212yes—
880C22×C4#1175822212yes—
881C4⋊C4—1228no—
882C4⋊C4—2444no—
883C4⋊C4—2444no—
884C4⋊C4—2444no—
885C22⋊C4—1228no—
886C22⋊C4—1228no—
887C22⋊C4—1228no—
888C22⋊C4—1228no—
889C22⋊C4—1228no—
890C22⋊C4—2444no—
891C22⋊C4—2444no—
892C22⋊C4—2444no—
893C22⋊C4—2444no—
894C22⋊C4—2444no—
895C22⋊C4—2444no—
896C42—44no—
897C42—44no—
898C42—44no—
899C42—2444no—
900C23—614no—
901C23—1222no—
902C23—1222no—
903C23—1222no—
904C23—1222no—
905C23—1222no—
906C23—1222no—
907C23—1222no—
908C23—1222no—
909C23—1222no—
910C23—1222no—
911C23—1222no—
912C23—1222no—
913C23—1222no—
914C23—1222no—
915C23—1222no—
916C23—1222no—
917C23—1222no—
918C23—1222no—
919C23—1222no—
920C23—1222no—
921C23—1222no—
922C23—1222no—
923C23—1222no—
924C23—1222no—
925C23—1222no—
926C23—2441no—
927C23—2441no—
928C23—2441no—
929C23—2441no—
930C23—2441no—
931C23—2441no—
932C23—2441no—
933C23—2441no—
934C23—2441no—
935C23—2441no—
936C23—2441no—
937C23—2441no—
938C23—2441no—
939C23—2441no—
940C23—2441no—
941C23—2441no—
942C23—2441no—
943C23—2441no—
944C23—2441no—
945C23—2441no—
946C23—2441no—
947C23—2441no—
948C23—2441no—
949C23—2441no—
950C23—2441no—
951C23—2441no—
952C23—2441no—
953C23—2441no—
954C23—2441no—
955C23—2441no—
956C23—2441no—
957C23—2441no—
958C23—2441no—
959C23—2441no—
960C23—2441no—
961C23—2441no—
962C23—2441no—
963C23—2441no—
964C23—2441no—
965C23—2441no—
966C23—2441no—
967C23—2441no—
968C23—2441no—
969C23—2441no—
970C23C22×C4×D6111yescharacteristic
971C23C22×D24411yescharacteristic
972C23C22×D24411yescharacteristic
973C23C22×D24411yescharacteristic
974C23#41×D6111yescharacteristic
975C23#41×D6111yescharacteristic
976C23#41×D6111yescharacteristic
977C23#41×D6111yescharacteristic
978C23C2×#1175822211yescharacteristic
979C23C2×#1175822211yescharacteristic
980C23C2×#1175822211yescharacteristic
981C23#1451982211yescharacteristic
982C23#1451982211yescharacteristic
983C23#1451982211yescharacteristic
984C23#1451982511yescharacteristic
985D4—24416no—
986C2×C4—22no—
987C2×C4—22no—
988C2×C4—22no—
989C2×C4—22no—
990C2×C4—22no—
991C2×C4—22no—
992C2×C4—22no—
993C2×C4—22no—
994C2×C4—22no—
995C2×C4—22no—
996C2×C4—22no—
997C2×C4—22no—
998C2×C4—22no—
999C2×C4—22no—
1000C2×C4—22no—
1001C2×C4—22no—
1002C2×C4—22no—
1003C2×C4—22no—
1004C2×C4—22no—
1005C2×C4—22no—
1006C2×C4—22no—
1007C2×C4—22no—
1008C2×C4—22no—
1009C2×C4—22no—
1010C2×C4—22no—
1011C2×C4—22no—
1012C2×C4—22no—
1013C2×C4—22no—
1014C2×C4—22no—
1015C2×C4—22no—
1016C2×C4—22no—
1017C2×C4—22no—
1018C2×C4—22no—
1019C2×C4—41no—
1020C2×C4—41no—
1021C2×C4—41no—
1022C2×C4—41no—
1023C2×C4—41no—
1024C2×C4—41no—
1025C2×C4—41no—
1026C2×C4—41no—
1027C2×C4—41no—
1028C2×C4—41no—
1029C2×C4—41no—
1030C2×C4—41no—
1031C2×C4—1222no—
1032C2×C4—1222no—
1033C2×C4—1222no—
1034C2×C4—1222no—
1035C2×C4—1222no—
1036C2×C4—1222no—
1037C2×C4—1222no—
1038C2×C4—1222no—
1039C2×C4—1222no—
1040C2×C4—1222no—
1041C2×C4—1222no—
1042C2×C4—1222no—
1043C2×C4—24416no—
1044C2×C4—2441no—
1045C2×C4—2441no—
1046C2×C4—2441no—
1047C2×C4—2441no—
1048C2×C4—2441no—
1049C2×C4—2441no—
1050C2×C4—2441no—
1051C2×C4—2441no—
1052C2×C4—2441no—
1053C2×C4—2441no—
1054C2×C4—2441no—
1055C2×C4—2441no—
1056C2×C4—2441no—
1057C2×C4—2441no—
1058C2×C4—2441no—
1059C2×C4—2441no—
1060C2×C4—2441no—
1061C2×C4—2441no—
1062C2×C4—2441no—
1063C2×C4—2441no—
1064C2×C4—2441no—
1065C2×C4—2441no—
1066C2×C4—2441no—
1067C2×C4—2441no—
1068C2×C4—2441no—
1069C2×C4—2441no—
1070C2×C4—2441no—
1071C2×C4—2441no—
1072C2×C4—2441no—
1073C2×C4—2441no—
1074C2×C4C4×D24414yes—
1075C2×C4C4×D24414yes—
1076C2×C4C4×D24414yes—
1077C2×C4#1451977414yes—
1078C22—1224no—
1079C22—1224no—
1080C22—1224no—
1081C22—4881no—
1082C22—4881no—
1083C22—4881no—
1084C22—4881no—
1085C22—4881no—
1086C22—4881no—
1087C22—4881no—
1088C22—4881no—
1089C22—2442no—
1090C22—2442no—
1091C22—2442no—
1092C22—2442no—
1093C22—2442no—
1094C22—2442no—
1095C22—2442no—
1096C22—2442no—
1097C22—2442no—
1098C22—2442no—
1099C22—2442no—
1100C22—2442no—
1101C22—2442no—
1102C22—2442no—
1103C22—2442no—
1104C22—2442no—
1105C22—2442no—
1106C22—2442no—
1107C22—2442no—
1108C22#117×D6111yescharacteristic
1109C22C2×C4×D24411yescharacteristic
1110C22C2×C4×D24411yescharacteristic
1111C22C2×C4×D24411yescharacteristic
1112C22#1684023011yescharacteristic
1113C22#1684023511yescharacteristic
1114C22#1684024311yescharacteristic
1115C22#1684027411yescharacteristic
1116C22#1684027411yescharacteristic
1117C22#1684029011yescharacteristic
1118C22#1684029011yescharacteristic
1119C22C2×#1451977411yescharacteristic
1120C22#1684031211yescharacteristic
1121C22#1684031211yescharacteristic
1122C22#1684031211yescharacteristic
1123C22#1684032411yescharacteristic
1124C22#1684034311yescharacteristic
1125C22#1684035011yescharacteristic
1126C22#1684035911yescharacteristic
1127C22#1684040711yescharacteristic
1128C22#1684040711yescharacteristic
1129C22#1684040711yescharacteristic
1130C22#1684040711yescharacteristic
1131C22#1684040711yescharacteristic
1132C22#1684040711yescharacteristic
1133C22#1684042411yescharacteristic
1134C22#1684042411yescharacteristic
1135C22#1684044111yescharacteristic
1136C22#1684044111yescharacteristic
1137C22#1684045311yescharacteristic
1138C22#1684046111yescharacteristic
1139C22#1684046111yescharacteristic
1140C22#1684046211yescharacteristic
1141C22#1684048411yescharacteristic
1142C22#1684049511yescharacteristic
1143C4—24no—
1144C4—24no—
1145C4—24no—
1146C4—24no—
1147C4—42no—
1148C4—42no—
1149C4—42no—
1150C4—4881no—
1151C4—4881no—
1152C4—2442no—
1153C4—2442no—
1154C4—2442no—
1155C4—2442no—
1156C2—4882no—
1157C2—2444no—
1158C2#2144826311yescharacteristic
1159C2C4×#1451977411yescharacteristic
1160C2#2144852211yescharacteristic
1161C2#2144867111yescharacteristic
1162C2#2144875111yescharacteristic
1163C2#2144886911yescharacteristic
1164C2#2144889011yescharacteristic
1165C2#2145074511yescharacteristic
1166C2#2145075311yescharacteristic
1167C2#2145091211yescharacteristic
1168C2#2145092711yescharacteristic
1169C2#2145094211yescharacteristic
1170C2#2145095711yescharacteristic
1171C2#2145141011yescharacteristic
1172C2#2145142511yescharacteristic
subgroupG/H
center, FrattiniC24C23×D61
commutatorC23×C61C23×C4
FittingC4×#95×C61C2
socle, cosocleC24×C61C24
prime radicalC23×D244C22
hypercenterC4×#95D61
hypocenterC61#14084
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C24 ◁ C4×#95

Complements

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

NH ≅ G/Ntype
2. C2×#16839654C2semidirect
3. C2×#16839653C2semidirect
4. C2×#16839647C2semidirect
6. C2×#16839636C2semidirect
7. C2×C4×#11758198C2semidirect
8. #21444086C2semidirect
9. #21444065C2semidirect
10. #21444065C2semidirect
12. #21444057C2semidirect
13. #21444057C2semidirect
14. #21444049C2semidirect
15. C4×#95×C61C2semidirect
34. #16839664C4semidirect
88. C2×C4⋊Dic61C2×C4semidirect
123. C2×#11758198C2×C4semidirect
124. C2×#11758198C2×C4semidirect
152. C2×C42×C61C2×C4semidirect
153. C2×C42×C61D4semidirect
157. #95×C61D4semidirect
584. C4×#95D61semidirect
644. C61#14084semidirect
729. C2×C42C4×D61semidirect
730. C2×C42D244semidirect
744. #95D244semidirect

Maximal subgroups

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

subgroupindex
C2×#168396642
C2×#168396542
C2×#168396532
C2×#168396472
C2×#168396402
C2×#168396362
C2×C4×#117581982
#214440862
#214440652
#214440592
#214440572
#214440492
C4×#95×C612
#1408461