Finite Group Databasebeta

← #29604493

Subgroups — #29604493

Order 15616.

2206 conjugacy classes of subgroups.

The subgroup lattice has 1186 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#14519766C211yesmaximal, characteristic
2C2×#16839652C211yesmaximal, characteristic, complemented
3C2×#16839640C211yesmaximal, characteristic
4C2×C4×#11758198C211yesmaximal, characteristic, complemented
5#21444090C211yesmaximal, characteristic, complemented
6#21444067C211yesmaximal, characteristic, complemented
7#21444061C211yesmaximal, characteristic, complemented
8#21444059C211yesmaximal, characteristic
9#21444057C211yesmaximal, characteristic, complemented
10#21444055C211yesmaximal, characteristic, complemented
11#21444055C211yesmaximal, characteristic, complemented
12#21444045C211yesmaximal, characteristic, complemented
13#21444040C211yesmaximal, characteristic, complemented
14#95×Dic61C211yesmaximal, characteristic, complemented
15C2×C61×#391C211yesmaximal, characteristic, complemented
16C23×D244C2211yescharacteristic
17C23×C4×D61C2211yescharacteristic
18C2×#14519766—24no—
19C2×#14519766—24no—
20C2×#14519766C418yescomplemented
21C22×#11758198C2211yescharacteristic
22C22×#11758198C2211yescharacteristic
23C22×#11758198C2211yescharacteristic
24C22×#11758198C2211yescharacteristic
25C22×#11758198C2211yescharacteristic
26C22×#11758198C2211yescharacteristic
27C22×#11758198C2211yescharacteristic
28C22×#11758198C2211yescharacteristic
29C22×#11758198C2211yescharacteristic
30C22×#11758198C2211yescharacteristic
31C22×#11758198C2211yescharacteristic
32C22×C4×Dic61C2211yescharacteristic
33C22×C4×Dic61C2211yescharacteristic
34C22×C4×Dic61C2211yescharacteristic
35#16839652—24no—
36#16839640—24no—
37C4×#11758198—24no—
38C2×#14519684C2211yescharacteristic
39C2×#14519684C2211yescharacteristic
40C2×#14519684C2211yescharacteristic
41C2×#14519684C2211yescharacteristic
42C2×#14519684C2211yescharacteristic
43C2×#14519684C2211yescharacteristic
44C2×#14519684C2211yescharacteristic
45C2×#14519684C2211yescharacteristic
46C2×#14519684C2211yescharacteristic
47C2×#14519684C2211yescharacteristic
48C2×#14519684C2211yescharacteristic
49C2×#14519684C2211yescharacteristic
50C23×Q8×C61C2211yescharacteristic
51C22×C4⋊C4×C61C2211yescharacteristic
52C22×C42×C61C2211yescharacteristic
53C61×#391—24no—
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—
80#14519766—232no—
81C2×#11758198—22no—
82C2×#11758198—22no—
83C2×#11758198—22no—
84C2×#11758198—22no—
85C2×#11758198—22no—
86C2×#11758198—22no—
87C2×#11758198—22no—
88C2×#11758198—22no—
89C2×#11758198—22no—
90C2×#11758198—22no—
91C2×#11758198—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—41no—
103C2×#11758198—41no—
104C2×#11758198—41no—
105C2×#11758198—41no—
106C2×#11758198—41no—
107C2×#11758198—41no—
108C2×#11758198C2×C414yes—
109C2×#11758198C2×C414yes—
110C2×#11758198C2×C414yescomplemented
111C2×#11758198C2×C414yescomplemented
112C2×#11758198D414yes—
113C2×#11758198D414yes—
114C2×C4×Dic61—22no—
115C2×C4×Dic61—22no—
116C2×C4×Dic61—22no—
117C2×C4×Dic61—22no—
118C2×C4×Dic61—22no—
119C2×C4×Dic61—22no—
120C2×C4×Dic61—41no—
121C2×C4×Dic61—41no—
122C2×C4×Dic61C2×C414yescomplemented
123#14519684—22no—
124#14519684—22no—
125#14519684—22no—
126#14519684—22no—
127#14519684—22no—
128#14519684—22no—
129#14519684—22no—
130#14519684—22no—
131#14519684—22no—
132#14519684—22no—
133#14519684—41no—
134#14519684—41no—
135C22×Q8×C61—22no—
136C22×Q8×C61—22no—
137C22×Q8×C61—22no—
138C22×Q8×C61—22no—
139C22×Q8×C61—41no—
140C22×Q8×C61—41no—
141C22×Q8×C61C2×C414yescomplemented
142C23×C4×C61C2311yescharacteristic
143C23×C4×C61C2311yescharacteristic
144C23×C4×C61C2311yescharacteristic
145C23×C4×C61C2311yescharacteristic
146C23×C4×C61C2311yescharacteristic
147C23×C4×C61C2311yescharacteristic
148C23×C4×C61C2311yescharacteristic
149C2×C4⋊C4×C61—22no—
150C2×C4⋊C4×C61—22no—
151C2×C4⋊C4×C61—41no—
152C2×C42×C61—22no—
153C2×C42×C61—22no—
154C2×C42×C61—41no—
155#95×C61—22no—
156#95×C61—22no—
157#95×C61—22no—
158#95×C61D414yes—
159C24×C61C2411yescharacteristic
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×D61—21no—
186C23×D61C22×C412yes—
187C23×D61C22×C412yes—
188C23×D61C2×D412yes—
189C23×D61C2×D412yes—
190C2×Q8×C61—28no—
191C2×Q8×C61—28no—
192C2×Q8×C61—44no—
193C2×Q8×C61—44no—
194C2×Q8×C61—44no—
195C2×Q8×C61—44no—
196C2×Q8×C61—44no—
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×C61—21no—
224C22×C4×C61—21no—
225C22×C4×C61—21no—
226C22×C4×C61—21no—
227C22×C4×C61—21no—
228C22×C4×C61—21no—
229C22×C4×C61—21no—
230C22×C4×C61—21no—
231C22×C4×C61—21no—
232C22×C4×C61—21no—
233C22×C4×C61—21no—
234C22×C4×C61C22×C412yes—
235C22×C4×C61C22×C412yes—
236C22×C4×C61C22×C412yes—
237C22×C4×C61C2×D412yes—
238C22×C4×C61C2×D412yes—
239C22×C4×C61C2×D412yes—
240C22×C4×C61C2×D412yes—
241C22×C4×C61C2×D412yes—
242C22×C4×C61#4112yes—
243C22×C4×C61#4112yes—
244C22×C4×C61#4112yes—
245C22×C4×C61#4112yes—
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×Dic61—21no—
277C22×Dic61—21no—
278C22×Dic61—21no—
279C22×Dic61—21no—
280C22×Dic61—21no—
281C22×Dic61C22×C412yes—
282C22×Dic61C22×C412yes—
283C22×Dic61C2×D412yes—
284C22×Dic61C2×D412yes—
285C22×Dic61#4112yes—
286C22×Dic61#4112yes—
287C22×Dic61#4112yes—
288C2×D244—28no—
289C2×D244—28no—
290C2×D244—44no—
291C2×D244—44no—
292C2×D244—44no—
293C2×D244—44no—
294C2×D244—44no—
295C2×C4×D61—28no—
296C2×C4×D61—44no—
297C2×C4×D61—44no—
298C2×C4×D61—44no—
299C2×C4×D61—44no—
300C2×C4×D61—44no—
301C2×C4×D61—44no—
302C4⋊C4×C61—44no—
303C42×C61—44no—
304#11758198—28no—
305#11758198—28no—
306#11758198—28no—
307#11758198—28no—
308#11758198—44no—
309#11758198—44no—
310#11758198—44no—
311#11758198—44no—
312#11758198—44no—
313#11758198—44no—
314#11758198C22⋊C4116yescomplemented
315C4×Dic61—28no—
316C4×Dic61—44no—
317C4×Dic61—44no—
318C23×C61C23×C411yescharacteristic
319C23×C61C22×D411yescharacteristic
320C23×C61C22×D411yescharacteristic
321C23×C61C22×D411yescharacteristic
322C23×C61C2×#4111yescharacteristic
323C23×C61C2×#4111yescharacteristic
324C23×C61C2×#4111yescharacteristic
325C23×C61C2×#4111yescharacteristic
326C23×C61C2×#4111yescharacteristic
327C23×C61C2×#4111yescharacteristic
328C23×C61C2×#4111yescharacteristic
329C23×C61H(5,𝔽2)11yescharacteristic
330C23×C61H(5,𝔽2)11yescharacteristic
331C23×C61H(5,𝔽2)11yescharacteristic
332C23×C612−1+411yescharacteristic
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—22no—
354C22×D61—22no—
355C22×D61—22no—
356C22×D61—22no—
357C22×D61—22no—
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—41no—
398C22×D61—41no—
399C22×D61—41no—
400C22×D61—41no—
401C22×D61—41no—
402C22×D61C2×C22⋊C414yes—
403Q8×C61—416no—
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×C61—41no—
444C2×C4×C61—41no—
445C2×C4×C61—41no—
446C2×C4×C61—41no—
447C2×C4×C61—41no—
448C2×C4×C61—41no—
449C2×C4×C61—41no—
450C2×C4×C61C2×C22⋊C414yes—
451C2×C4×C61C4×D414yes—
452C2×C4×C61#12414yescomplemented
453C2×Dic61—22no—
454C2×Dic61—22no—
455C2×Dic61—22no—
456C2×Dic61—22no—
457C2×Dic61—22no—
458C2×Dic61—22no—
459C2×Dic61—22no—
460C2×Dic61—22no—
461C2×Dic61—22no—
462C2×Dic61—22no—
463C2×Dic61—22no—
464C2×Dic61—22no—
465C2×Dic61—22no—
466C2×Dic61—22no—
467C2×Dic61—22no—
468C2×Dic61—22no—
469C2×Dic61—22no—
470C2×Dic61—22no—
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—
489C2×Dic61—41no—
490C2×Dic61—41no—
491C2×Dic61—41no—
492C2×Dic61—41no—
493C2×Dic61—41no—
494C2×Dic61C2×C22⋊C414yes—
495D244—416no—
496C4×D61—416no—
497#14098—611nomaximal, Sylow
498C22×C61C22×C22⋊C411yescharacteristic
499C22×C61C2×C4×D411yescharacteristic
500C22×C61C4×#4111yescharacteristic
501C22×C61C4×#4111yescharacteristic
502C22×C61C4×#4111yescharacteristic
503C22×C61#51811yescharacteristic
504C22×C61#52011yescharacteristic
505C22×C61#52511yescharacteristic
506C22×C61#52511yescharacteristic
507C22×C61C2×#12411yescharacteristic
508C22×C61#52911yescharacteristic
509C22×C61#52911yescharacteristic
510C22×C61#53211yescharacteristic
511C22×C61#53211yescharacteristic
512C22×C61#53211yescharacteristic
513C22×C61#53811yescharacteristic
514C22×C61#53811yescharacteristic
515C22×C61#54211yescharacteristic
516C22×C61#54211yescharacteristic
517C22×C61D4211yescharacteristic
518C22×C61D4211yescharacteristic
519C22×C61#54611yescharacteristic
520C22×C61#54611yescharacteristic
521C22×C61#54611yescharacteristic
522C22×C61#54611yescharacteristic
523C22×C61#54611yescharacteristic
524C22×C61#54711yescharacteristic
525C22×C61#54711yescharacteristic
526C22×C61#54811yescharacteristic
527C22×C61#55111yescharacteristic
528C22×C61#55111yescharacteristic
529C22×C61#55511yescharacteristic
530C22×C61#55511yescharacteristic
531C22×C61#55611yescharacteristic
532C22×C61#55911yescharacteristic
533C2×D61—24no—
534C2×D61—24no—
535C2×D61—24no—
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—42no—
550C2×D61—42no—
551C2×D61—42no—
552C2×D61—42no—
553C2×D61—42no—
554C2×D61—42no—
555C2×D61—81no—
556C2×D61—81no—
557C2×D61—81no—
558C2×D61—81no—
559C2×D61—81no—
560C2×D61—81no—
561C2×D61—81no—
562C2×D61—81no—
563C4×C61—24no—
564C4×C61—24no—
565C4×C61—24no—
566C4×C61—42no—
567C4×C61—42no—
568C4×C61—42no—
569C4×C61—81no—
570Dic61—24no—
571Dic61—42no—
572Dic61—42no—
573Dic61—42no—
574Dic61—42no—
575Dic61—81no—
576C22×#124—611no—
577C2×#391D6111yescharacteristic, complemented
578C2×#388—611no—
579C2×#386—611no—
580C2×C4×C22⋊C4—611no—
581#1446—611no—
582#1440—611no—
583#1439—611no—
584#1438—611no—
585#1437—611no—
586#1437—611no—
587#1437—611no—
588#1434—611no—
589C22⋊#95—611no—
590C4×#95—611no—
591C2×C61#229711yescharacteristic
592C2×C61C4×#12411yescharacteristic
593C2×C61#233711yescharacteristic
594C2×C61D4×C22⋊C411yescharacteristic
595C2×C61#233911yescharacteristic
596C2×C61#236711yescharacteristic
597C2×C61#237211yescharacteristic
598C2×C61#245911yescharacteristic
599C2×C61#246111yescharacteristic
600C2×C61#247211yescharacteristic
601C2×C61#247411yescharacteristic
602C2×C61#249111yescharacteristic
603C2×C61#252111yescharacteristic
604C2×C61#255511yescharacteristic
605C2×C61#255711yescharacteristic
606D61—44no—
607D61—82no—
608C23×Q8C2×D6111yescharacteristic
609C23×D4—611no—
610C24×C4—611no—
611C2×#124—618no—
612C2×#124—1224no—
613C2×#124—1224no—
614C22×C4⋊C4C2×D6111yescharacteristic
615C22×C22⋊C4—611no—
616C22×C22⋊C4—611no—
617C22×C22⋊C4—611no—
618C22×C22⋊C4—611no—
619C22×C22⋊C4—611no—
620C22×C22⋊C4—611no—
621C22×C22⋊C4—611no—
622C22×C22⋊C4—611no—
623C22×C22⋊C4—611no—
624C22×C22⋊C4—611no—
625C22×C22⋊C4—611no—
626C22×C42—611no—
627C22×C42—611no—
628C22×C42—611no—
629C22×C42C2×D6111yescharacteristic
630#391—24no—
631#388—1224no—
632#386—1224no—
633C4×C22⋊C4—1224no—
634C2×#95—611no—
635C2×#95—611no—
636C2×#95—611no—
637C2×#95—611no—
638C2×#95—611no—
639C2×#95—611no—
640C2×#95—611no—
641C2×#95—611no—
642C2×#95—611no—
643C2×#95—611no—
644C2×#95—611no—
645C2×#95—611no—
646C2×#95C2×D6111yescharacteristic
647C2×#95C2×D6111yescharacteristic
648C2×#95C2×D6111yescharacteristic
649C2×#95C2×D6111yescharacteristic
650C61#1409811yescharacteristic, complemented, Sylow
651C25—611no—
652C25—611no—
653C22×Q8—22no—
654C22×Q8—22no—
655C22×Q8—22no—
656C22×Q8—22no—
657C22×Q8—41no—
658C22×Q8—41no—
659C22×Q8C4×D6114yescomplemented
660C22×D4—614no—
661C22×D4—1222no—
662C22×D4—1222no—
663C22×D4—1222no—
664C22×D4—1222no—
665C22×D4—2441no—
666C22×D4—2441no—
667C23×C4—611no—
668C23×C4—611no—
669C23×C4—611no—
670C23×C4—611no—
671C23×C4—611no—
672C23×C4—611no—
673C23×C4—1222no—
674C23×C4—1222no—
675C23×C4—1222no—
676C23×C4—1222no—
677C23×C4—1222no—
678C23×C4—2441no—
679C23×C4—2441no—
680C23×C4C22×D6111yescharacteristic
681C23×C4C22×D6111yescharacteristic
682C23×C4C22×D6111yescharacteristic
683C23×C4C22×D6111yescharacteristic
684C23×C4C22×D6111yescharacteristic
685C23×C4C22×D6111yescharacteristic
686C23×C4C22×D6111yescharacteristic
687#124—12232no—
688C2×C4⋊C4—22no—
689C2×C4⋊C4—22no—
690C2×C4⋊C4—41no—
691C2×C22⋊C4—614no—
692C2×C22⋊C4—614no—
693C2×C22⋊C4—614no—
694C2×C22⋊C4—614no—
695C2×C22⋊C4—614no—
696C2×C22⋊C4—614no—
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—1222no—
714C2×C22⋊C4—1222no—
715C2×C22⋊C4—1222no—
716C2×C22⋊C4—1222no—
717C2×C22⋊C4—1222no—
718C2×C22⋊C4—2441no—
719C2×C22⋊C4—2441no—
720C2×C22⋊C4—2441no—
721C2×C22⋊C4—2441no—
722C2×C22⋊C4—2441no—
723C2×C22⋊C4—2441no—
724C2×C42—22no—
725C2×C42—22no—
726C2×C42—41no—
727C2×C42—614no—
728C2×C42—1222no—
729C2×C42—1222no—
730C2×C42—1222no—
731C2×C42—1222no—
732C2×C42—1222no—
733C2×C42—1222no—
734C2×C42—2441no—
735C2×C42—2441no—
736#95—22no—
737#95—22no—
738#95—22no—
739#95—1222no—
740#95—1222no—
741#95—1222no—
742#95—1222no—
743#95—1222no—
744#95—1222no—
745#95—1222no—
746#95—1222no—
747#95—1222no—
748#95—1222no—
749#95—2441no—
750#95—2441no—
751#95C22⋊D6114yes—
752C24—612no—
753C24—612no—
754C24—612no—
755C24—612no—
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—
775C24—1221no—
776C24—1221no—
777C24—1221no—
778C24—1221no—
779C24—1221no—
780C24—1221no—
781C24—1221no—
782C24C23×D6111yescharacteristic
783C2×Q8—28no—
784C2×Q8—28no—
785C2×Q8—44no—
786C2×Q8—44no—
787C2×Q8—44no—
788C2×Q8—44no—
789C2×Q8—44no—
790C2×D4—1228no—
791C2×D4—1228no—
792C2×D4—2444no—
793C2×D4—2444no—
794C2×D4—2444no—
795C2×D4—2444no—
796C2×D4—2444no—
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—21no—
818C22×C4—21no—
819C22×C4—21no—
820C22×C4—21no—
821C22×C4—21no—
822C22×C4—21no—
823C22×C4—21no—
824C22×C4—21no—
825C22×C4—21no—
826C22×C4—21no—
827C22×C4—21no—
828C22×C4—21no—
829C22×C4—21no—
830C22×C4—21no—
831C22×C4—21no—
832C22×C4—21no—
833C22×C4—21no—
834C22×C4—612no—
835C22×C4—612no—
836C22×C4—612no—
837C22×C4—612no—
838C22×C4—612no—
839C22×C4—612no—
840C22×C4—612no—
841C22×C4—1228no—
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—1221no—
861C22×C4—1221no—
862C22×C4—1221no—
863C22×C4—1221no—
864C22×C4—1221no—
865C22×C4—1221no—
866C22×C4—1221no—
867C22×C4—1221no—
868C22×C4—1221no—
869C22×C4—1221no—
870C22×C4—1221no—
871C22×C4—1221no—
872C22×C4—1221no—
873C22×C4—1221no—
874C22×C4—1221no—
875C22×C4—1221no—
876C22×C4—1221no—
877C22×C4—2444no—
878C22×C4—2444no—
879C22×C4—2444no—
880C22×C4—2444no—
881C22×C4—2444no—
882C22×C4—2444no—
883C22×C4C2×C4×D6112yes—
884C22×C4C2×C4×D6112yes—
885C22×C4C2×C4×D6112yes—
886C22×C4#1175822212yes—
887C22×C4D4×D6112yes—
888C22×C4D4×D6112yes—
889C22×C4#1175822612yes—
890C22×C4#1175822612yes—
891C22×C4#1175822612yes—
892C22×C4C2×C22⋊D6112yes—
893C22×C4C2×C22⋊D6112yes—
894C22×C4C2×C22⋊D6112yes—
895C4⋊C4—44no—
896C22⋊C4—6116no—
897C22⋊C4—1228no—
898C22⋊C4—1228no—
899C22⋊C4—1228no—
900C22⋊C4—1228no—
901C22⋊C4—2444no—
902C22⋊C4—2444no—
903C22⋊C4—2444no—
904C22⋊C4—2444no—
905C22⋊C4—2444no—
906C22⋊C4—2444no—
907C42—44no—
908C42—1228no—
909C42—2444no—
910C42—2444no—
911C23—614no—
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—1222no—
927C23—1222no—
928C23—1222no—
929C23—1222no—
930C23—1222no—
931C23—1222no—
932C23—1222no—
933C23—1222no—
934C23—1222no—
935C23—1222no—
936C23—1222no—
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—
970C23—2441no—
971C23—2441no—
972C23—2441no—
973C23—2441no—
974C23—2441no—
975C23—2441no—
976C23—2441no—
977C23—2441no—
978C23—2441no—
979C23—2441no—
980C23—2441no—
981C23C22×C4×D6111yescharacteristic
982C23C2×D4×D6111yescharacteristic
983C23C2×D4×D6111yescharacteristic
984C23C22×C22⋊D6111yescharacteristic
985C23#41×D6111yescharacteristic
986C23#41×D6111yescharacteristic
987C23#41×D6111yescharacteristic
988C23C2×#1175822211yescharacteristic
989C23C2×#1175822611yescharacteristic
990C23C2×#1175822611yescharacteristic
991C23C2×#1175822611yescharacteristic
992C23#1451982211yescharacteristic
993C23#1451982211yescharacteristic
994C23#1451982311yescharacteristic
995C23#1451982511yescharacteristic
996Q8—416no—
997D4—24416no—
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—22no—
1020C2×C4—22no—
1021C2×C4—22no—
1022C2×C4—22no—
1023C2×C4—22no—
1024C2×C4—22no—
1025C2×C4—41no—
1026C2×C4—41no—
1027C2×C4—41no—
1028C2×C4—41no—
1029C2×C4—41no—
1030C2×C4—41no—
1031C2×C4—41no—
1032C2×C4—41no—
1033C2×C4—41no—
1034C2×C4—41no—
1035C2×C4—41no—
1036C2×C4—41no—
1037C2×C4—41no—
1038C2×C4—41no—
1039C2×C4—41no—
1040C2×C4—41no—
1041C2×C4—41no—
1042C2×C4—41no—
1043C2×C4—41no—
1044C2×C4—614no—
1045C2×C4—1222no—
1046C2×C4—1222no—
1047C2×C4—1222no—
1048C2×C4—1222no—
1049C2×C4—1222no—
1050C2×C4—1222no—
1051C2×C4—1222no—
1052C2×C4—1222no—
1053C2×C4—1222no—
1054C2×C4—1222no—
1055C2×C4—1222no—
1056C2×C4—1222no—
1057C2×C4—1222no—
1058C2×C4—1222no—
1059C2×C4—1222no—
1060C2×C4—1222no—
1061C2×C4—1222no—
1062C2×C4—1222no—
1063C2×C4—24416no—
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×C4—2441no—
1075C2×C4—2441no—
1076C2×C4—2441no—
1077C2×C4—2441no—
1078C2×C4—2441no—
1079C2×C4—2441no—
1080C2×C4—2441no—
1081C2×C4—2441no—
1082C2×C4—2441no—
1083C2×C4—2441no—
1084C2×C4—2441no—
1085C2×C4—2441no—
1086C2×C4—2441no—
1087C2×C4C22⋊C4×D6114yes—
1088C2×C4C4×C22⋊D6114yes—
1089C2×C4#1451976614yescomplemented
1090C22—1224no—
1091C22—1224no—
1092C22—1224no—
1093C22—4881no—
1094C22—4881no—
1095C22—4881no—
1096C22—4881no—
1097C22—4881no—
1098C22—4881no—
1099C22—4881no—
1100C22—4881no—
1101C22—2442no—
1102C22—2442no—
1103C22—2442no—
1104C22—2442no—
1105C22—2442no—
1106C22—2442no—
1107C22—2442no—
1108C22—2442no—
1109C22—2442no—
1110C22—2442no—
1111C22—2442no—
1112C22—2442no—
1113C22—2442no—
1114C22—2442no—
1115C22—2442no—
1116C22—2442no—
1117C22—2442no—
1118C22—2442no—
1119C22—2442no—
1120C22C2×C22⋊C4×D6111yescharacteristic
1121C22C2×C4×C22⋊D6111yescharacteristic
1122C22C4×#1175822611yescharacteristic
1123C22C4×#1175822611yescharacteristic
1124C22C4×#1175822611yescharacteristic
1125C22#1684023511yescharacteristic
1126C22#1684024411yescharacteristic
1127C22#1684027511yescharacteristic
1128C22#1684027511yescharacteristic
1129C22C2×#1451976611yescharacteristic
1130C22#1684029911yescharacteristic
1131C22#1684029911yescharacteristic
1132C22#1684030811yescharacteristic
1133C22#1684031111yescharacteristic
1134C22#1684031311yescharacteristic
1135C22#1684034611yescharacteristic
1136C22#1684035211yescharacteristic
1137C22#1684038211yescharacteristic
1138C22#1684038611yescharacteristic
1139C22D4×C22⋊D6111yescharacteristic
1140C22D4×C22⋊D6111yescharacteristic
1141C22#1684040011yescharacteristic
1142C22#1684040211yescharacteristic
1143C22#1684040211yescharacteristic
1144C22#1684040311yescharacteristic
1145C22#1684040511yescharacteristic
1146C22#1684041411yescharacteristic
1147C22#1684041511yescharacteristic
1148C22#1684042311yescharacteristic
1149C22#1684043911yescharacteristic
1150C22#1684043911yescharacteristic
1151C22#1684047411yescharacteristic
1152C22#1684047811yescharacteristic
1153C22#1684048411yescharacteristic
1154C22#1684049711yescharacteristic
1155C4—24no—
1156C4—24no—
1157C4—24no—
1158C4—42no—
1159C4—42no—
1160C4—42no—
1161C4—81no—
1162C4—1224no—
1163C4—4881no—
1164C4—2442no—
1165C4—2442no—
1166C4—2442no—
1167C4—2442no—
1168C2—4882no—
1169C2—2444no—
1170C2#2144830811yescharacteristic
1171C2C4×#1451976611yescharacteristic
1172C2#2144863111yescharacteristic
1173C2C22⋊C4×C22⋊D6111yescharacteristic
1174C2#2144864811yescharacteristic
1175C2#2144888611yescharacteristic
1176C2#2144893011yescharacteristic
1177C2#2144976311yescharacteristic
1178C2#2144979311yescharacteristic
1179C2#2144995211yescharacteristic
1180C2#2144998211yescharacteristic
1181C2#2145018511yescharacteristic
1182C2#2145052811yescharacteristic
1183C2#2145089011yescharacteristic
1184C2#2145092511yescharacteristic
subgroupG/H
center, FrattiniC24C23×D61
commutatorC23×C61C23×C4
FittingC2×C61×#391C2
socle, cosocleC24×C61C24
prime radicalC23×D244C22
hypercenterC2×#391D61
hypocenterC61#14098
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C24 ◁ C2×#391

Complements

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

NH ≅ G/Ntype
2. C2×#16839652C2semidirect
4. C2×C4×#11758198C2semidirect
5. #21444090C2semidirect
6. #21444067C2semidirect
7. #21444061C2semidirect
9. #21444057C2semidirect
10. #21444055C2semidirect
11. #21444055C2semidirect
12. #21444045C2semidirect
13. #21444040C2semidirect
14. #95×Dic61C2semidirect
15. C2×C61×#391C2semidirect
20. C2×#14519766C4semidirect
110. C2×#11758198C2×C4semidirect
111. C2×#11758198C2×C4semidirect
122. C2×C4×Dic61C2×C4semidirect
141. C22×Q8×C61C2×C4semidirect
314. #11758198C22⋊C4semidirect
452. C2×C4×C61#124semidirect
577. C2×#391D61semidirect
650. C61#14098semidirect
659. C22×Q8C4×D61semidirect
1089. C2×C4#14519766semidirect

Maximal subgroups

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

subgroupindex
C22×#145197662
C2×#168396522
C2×#168396402
C2×C4×#117581982
#214440902
#214440672
#214440612
#214440592
#214440572
#214440552
#214440452
#214440402
#95×Dic612
C2×C61×#3912
#1409861