Finite Group Databasebeta

← #29604443

Subgroups — #29604443

Order 15616.

2158 conjugacy classes of subgroups.

The subgroup lattice has 1176 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#14519762C211yesmaximal, characteristic
2C2×#16839664C211yesmaximal, characteristic
3C2×#16839648C211yesmaximal, characteristic, complemented
4C2×C4×#11758198C211yesmaximal, characteristic, complemented
5#21444073C211yesmaximal, characteristic, complemented
6#21444061C211yesmaximal, characteristic, complemented
7#21444061C211yesmaximal, characteristic, complemented
8#21444059C211yesmaximal, characteristic
9#21444057C211yesmaximal, characteristic, complemented
10#21444057C211yesmaximal, characteristic, complemented
11#21444057C211yesmaximal, characteristic, complemented
12#21444055C211yesmaximal, characteristic, complemented
13#21444052C211yesmaximal, characteristic, complemented
14#21444040C211yesmaximal, characteristic, complemented
15C2×C4×C4⋊C4×C61C211yesmaximal, characteristic, complemented
16C23×D244C2211yescharacteristic
17C23×C4×D61C2211yescharacteristic
18C2×#14519762—24no—
19C2×#14519762—24no—
20C2×#14519762C418yescomplemented
21C22×C4⋊Dic61C2211yescharacteristic
22C22×#11758196C2211yescharacteristic
23C22×#11758198C2211yescharacteristic
24C22×#11758198C2211yescharacteristic
25C22×#11758198C2211yescharacteristic
26C22×#11758198C2211yescharacteristic
27C22×#11758198C2211yescharacteristic
28C22×#11758198C2211yescharacteristic
29C22×#11758198C2211yescharacteristic
30C22×#11758198C2211yescharacteristic
31C22×#11758198C2211yescharacteristic
32C22×#11758198C2211yescharacteristic
33C22×#11758198C2211yescharacteristic
34C22×C4×Dic61C2211yescharacteristic
35#16839664—24no—
36#16839648—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
50C22×C4⋊C4×C61C2211yescharacteristic
51C22×C4⋊C4×C61C2211yescharacteristic
52C22×C42×C61C2211yescharacteristic
53C22×C42×C61C2211yescharacteristic
54C22×C42×C61C2211yescharacteristic
55C4×C4⋊C4×C61—24no—
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—41no—
78C22×C4×D61—41no—
79C22×C4×D61C2×C414yes—
80#14519762—232no—
81C2×C4⋊Dic61—22no—
82C2×C4⋊Dic61—22no—
83C2×C4⋊Dic61—41no—
84C2×#11758196—22no—
85C2×#11758196—22no—
86C2×#11758196C2×C414yes—
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—22no—
103C2×#11758198—22no—
104C2×#11758198—22no—
105C2×#11758198—22no—
106C2×#11758198—22no—
107C2×#11758198—22no—
108C2×#11758198—22no—
109C2×#11758198—22no—
110C2×#11758198—41no—
111C2×#11758198—41no—
112C2×#11758198—41no—
113C2×#11758198—41no—
114C2×#11758198—41no—
115C2×#11758198—41no—
116C2×#11758198C2×C414yes—
117C2×#11758198C2×C414yes—
118C2×#11758198C2×C414yes—
119C2×#11758198D414yes—
120C2×C4×Dic61—22no—
121C2×C4×Dic61—22no—
122C2×C4×Dic61—41no—
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—41no—
132#14519684—41no—
133#14519684—41no—
134#14519684—41no—
135C23×C4×C61C2311yescharacteristic
136C23×C4×C61C2311yescharacteristic
137C23×C4×C61C2311yescharacteristic
138C23×C4×C61C2311yescharacteristic
139C23×C4×C61C2311yescharacteristic
140C23×C4×C61C2311yescharacteristic
141C23×C4×C61C2311yescharacteristic
142C2×C4⋊C4×C61—22no—
143C2×C4⋊C4×C61—22no—
144C2×C4⋊C4×C61—22no—
145C2×C4⋊C4×C61C2×C414yes—
146C2×C4⋊C4×C61D414yes—
147C2×C4⋊C4×C61D414yes—
148C2×C42×C61—22no—
149C2×C42×C61—22no—
150C2×C42×C61—22no—
151C2×C42×C61—22no—
152C2×C42×C61—22no—
153C2×C42×C61—22no—
154C2×C42×C61—22no—
155C2×C42×C61—41no—
156C2×C42×C61—41no—
157#95×C61—22no—
158#95×C61—22no—
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×D61#4112yes—
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×C61—21no—
224C22×C4×C61C22×C412yes—
225C22×C4×C61C22×C412yes—
226C22×C4×C61C22×C412yes—
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×C61#4112yes—
235C22×C4×C61#4112yes—
236C22×C4×C61#4112yes—
237C22×C4×C61#4112yes—
238C22×C4×C61#4112yes—
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×Dic61—21no—
277C22×Dic61C22×C412yes—
278C22×Dic61C22×C412yes—
279C22×Dic61C2×D412yes—
280C22×Dic61#4112yes—
281C2×D244—28no—
282C2×D244—28no—
283C2×D244—44no—
284C2×D244—44no—
285C2×D244—44no—
286C2×D244—44no—
287C2×D244—44no—
288C2×C4×D61—28no—
289C2×C4×D61—28no—
290C2×C4×D61—44no—
291C2×C4×D61—44no—
292C2×C4×D61—44no—
293C2×C4×D61—44no—
294C2×C4×D61—44no—
295C4⋊C4×C61—28no—
296C4⋊C4×C61C22⋊C4116yescomplemented
297C42×C61—28no—
298C42×C61—44no—
299C42×C61—44no—
300#11758198—28no—
301#11758198—28no—
302#11758198—28no—
303#11758198—28no—
304#11758198—28no—
305#11758198—44no—
306#11758198—44no—
307#11758198—44no—
308#11758198—44no—
309#11758198—44no—
310#11758198—44no—
311C4⋊Dic61—44no—
312#11758196—28no—
313C4×Dic61—44no—
314C23×C61C23×C411yescharacteristic
315C23×C61C22×D411yescharacteristic
316C23×C61C22×D411yescharacteristic
317C23×C61C22×D411yescharacteristic
318C23×C61C2×#4111yescharacteristic
319C23×C61C2×#4111yescharacteristic
320C23×C61C2×#4111yescharacteristic
321C23×C61C2×#4111yescharacteristic
322C23×C61C2×#4111yescharacteristic
323C23×C61C2×#4111yescharacteristic
324C23×C61C2×#4111yescharacteristic
325C23×C61H(5,𝔽2)11yescharacteristic
326C23×C61H(5,𝔽2)11yescharacteristic
327C23×C61H(5,𝔽2)11yescharacteristic
328C23×C612−1+411yescharacteristic
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—22no—
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—41no—
398C22×D61C4×D414yes—
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—22no—
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×C61C2×C22⋊C414yes—
445C2×C4×C61C2×C22⋊C414yes—
446C2×C4×C61C2×C22⋊C414yes—
447C2×C4×C61#12314yescomplemented
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—22no—
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—
489C2×Dic61—41no—
490D244—416no—
491C4×D61—416no—
492#14095—611nomaximal, Sylow
493C22×C61C22×C22⋊C411yescharacteristic
494C22×C61C2×C4×D411yescharacteristic
495C22×C61C4×#4111yescharacteristic
496C22×C61C4×#4111yescharacteristic
497C22×C61C4×#4111yescharacteristic
498C22×C61#51811yescharacteristic
499C22×C61#52011yescharacteristic
500C22×C61C2×#12311yescharacteristic
501C22×C61#52511yescharacteristic
502C22×C61#52511yescharacteristic
503C22×C61#52511yescharacteristic
504C22×C61#52911yescharacteristic
505C22×C61#52911yescharacteristic
506C22×C61#53211yescharacteristic
507C22×C61#53211yescharacteristic
508C22×C61#53811yescharacteristic
509C22×C61#53911yescharacteristic
510C22×C61#54011yescharacteristic
511C22×C61#54211yescharacteristic
512C22×C61D4211yescharacteristic
513C22×C61D4211yescharacteristic
514C22×C61#54611yescharacteristic
515C22×C61#54611yescharacteristic
516C22×C61#54611yescharacteristic
517C22×C61#54711yescharacteristic
518C22×C61#54811yescharacteristic
519C22×C61#54811yescharacteristic
520C22×C61#55011yescharacteristic
521C22×C61#55011yescharacteristic
522C22×C61#55111yescharacteristic
523C22×C61#55111yescharacteristic
524C22×C61#55211yescharacteristic
525C22×C61#55311yescharacteristic
526C22×C61#55311yescharacteristic
527C22×C61#55911yescharacteristic
528C2×D61—24no—
529C2×D61—24no—
530C2×D61—24no—
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—42no—
550C2×D61—81no—
551C2×D61—81no—
552C2×D61—81no—
553C2×D61—81no—
554C2×D61—81no—
555C2×D61—81no—
556C2×D61—81no—
557C2×D61—81no—
558C4×C61—24no—
559C4×C61—24no—
560C4×C61—24no—
561C4×C61—24no—
562C4×C61—42no—
563C4×C61—42no—
564C4×C61—42no—
565Dic61—42no—
566Dic61—42no—
567Dic61—42no—
568Dic61—42no—
569Dic61—81no—
570Dic61—81no—
571C22×#123—611no—
572C2×#390—611no—
573C2×#387—611no—
574C2×C4×C4⋊C4D6111yescharacteristic, complemented
575C2×C4×C22⋊C4—611no—
576#1441—611no—
577#1439—611no—
578#1439—611no—
579#1438—611no—
580#1437—611no—
581#1437—611no—
582#1437—611no—
583#1437—611no—
584#1436—611no—
585C22⋊#95—611no—
586C2×C61#229711yescharacteristic
587C2×C61C4×#12311yescharacteristic
588C2×C61#233511yescharacteristic
589C2×C61D4×C22⋊C411yescharacteristic
590C2×C61#234111yescharacteristic
591C2×C61#235911yescharacteristic
592C2×C61#237411yescharacteristic
593C2×C61#244311yescharacteristic
594C2×C61#244511yescharacteristic
595C2×C61#245611yescharacteristic
596C2×C61#245811yescharacteristic
597C2×C61#246111yescharacteristic
598C2×C61#247111yescharacteristic
599C2×C61#255411yescharacteristic
600C2×C61#255811yescharacteristic
601D61—44no—
602D61—82no—
603C23×D4—611no—
604C24×C4—611no—
605C2×#123—618no—
606C2×#123—1224no—
607C2×#123—1224no—
608C22×C4⋊C4—611no—
609C22×C4⋊C4—611no—
610C22×C4⋊C4C2×D6111yescharacteristic
611C22×C4⋊C4C2×D6111yescharacteristic
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×C22⋊C4—611no—
620C22×C22⋊C4—611no—
621C22×C22⋊C4—611no—
622C22×C22⋊C4—611no—
623C22×C42—611no—
624C22×C42C2×D6111yescharacteristic
625C22×C42C2×D6111yescharacteristic
626C22×C42C2×D6111yescharacteristic
627#390—1224no—
628#387—1224no—
629C4×C4⋊C4—24no—
630C4×C22⋊C4—1224no—
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×#95—611no—
641C2×#95—611no—
642C2×#95—611no—
643C2×#95C2×D6111yescharacteristic
644C2×#95C2×D6111yescharacteristic
645C61#1409511yescharacteristic, complemented, Sylow
646C25—611no—
647C25—611no—
648C22×D4—614no—
649C22×D4—1222no—
650C22×D4—1222no—
651C22×D4—1222no—
652C22×D4—1222no—
653C22×D4—2441no—
654C22×D4—2441no—
655C23×C4—611no—
656C23×C4—611no—
657C23×C4—611no—
658C23×C4—611no—
659C23×C4—614no—
660C23×C4—611no—
661C23×C4—611no—
662C23×C4—1222no—
663C23×C4—1222no—
664C23×C4—1222no—
665C23×C4—1222no—
666C23×C4—2441no—
667C23×C4—2441no—
668C23×C4C22×D6111yescharacteristic
669C23×C4C22×D6111yescharacteristic
670C23×C4C22×D6111yescharacteristic
671C23×C4C22×D6111yescharacteristic
672C23×C4C22×D6111yescharacteristic
673C23×C4C22×D6111yescharacteristic
674C23×C4C22×D6111yescharacteristic
675#123—12232no—
676C2×C4⋊C4—22no—
677C2×C4⋊C4—22no—
678C2×C4⋊C4—22no—
679C2×C4⋊C4—614no—
680C2×C4⋊C4—1222no—
681C2×C4⋊C4—1222no—
682C2×C4⋊C4—1222no—
683C2×C4⋊C4—1222no—
684C2×C4⋊C4—2441no—
685C2×C4⋊C4C4×D6114yes—
686C2×C4⋊C4D24414yes—
687C2×C4⋊C4C22⋊D6114yes—
688C2×C22⋊C4—614no—
689C2×C22⋊C4—614no—
690C2×C22⋊C4—614no—
691C2×C22⋊C4—614no—
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—1222no—
714C2×C22⋊C4—1222no—
715C2×C22⋊C4—2441no—
716C2×C22⋊C4—2441no—
717C2×C22⋊C4—2441no—
718C2×C22⋊C4—2441no—
719C2×C22⋊C4—2441no—
720C2×C22⋊C4—2441no—
721C2×C42—22no—
722C2×C42—22no—
723C2×C42—22no—
724C2×C42—22no—
725C2×C42—22no—
726C2×C42—22no—
727C2×C42—22no—
728C2×C42—41no—
729C2×C42—41no—
730C2×C42—1222no—
731C2×C42—1222no—
732C2×C42—2441no—
733#95—22no—
734#95—22no—
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#95—2441no—
744#95—2441no—
745#95—2441no—
746#95—2441no—
747C24—612no—
748C24—612no—
749C24—612no—
750C24—612no—
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—
775C24—1221no—
776C24—1221no—
777C24C23×D6111yescharacteristic
778C2×D4—1228no—
779C2×D4—1228no—
780C2×D4—2444no—
781C2×D4—2444no—
782C2×D4—2444no—
783C2×D4—2444no—
784C2×D4—2444no—
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—21no—
818C22×C4—21no—
819C22×C4—612no—
820C22×C4—612no—
821C22×C4—612no—
822C22×C4—612no—
823C22×C4—1228no—
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—1228no—
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—2444no—
864C22×C4—2444no—
865C22×C4—2444no—
866C22×C4—2444no—
867C22×C4—2444no—
868C22×C4C2×C4×D6112yes—
869C22×C4C2×C4×D6112yes—
870C22×C4C2×C4×D6112yes—
871C22×C4C2×D24412yes—
872C22×C4C2×D24412yes—
873C22×C4C2×D24412yes—
874C22×C4#1175822212yes—
875C22×C4#1175822212yes—
876C22×C4#1175822212yes—
877C22×C4#1175822212yes—
878C22×C4D4×D6112yes—
879C22×C4#1175822612yes—
880C22×C4C2×C22⋊D6112yes—
881C22×C4C2×C22⋊D6112yes—
882C22×C4C2×C22⋊D6112yes—
883C4⋊C4—28no—
884C4⋊C4—1228no—
885C4⋊C4—2444no—
886C4⋊C4#11758198116yescomplemented
887C22⋊C4—1228no—
888C22⋊C4—1228no—
889C22⋊C4—1228no—
890C22⋊C4—1228no—
891C22⋊C4—1228no—
892C22⋊C4—2444no—
893C22⋊C4—2444no—
894C22⋊C4—2444no—
895C22⋊C4—2444no—
896C22⋊C4—2444no—
897C22⋊C4—2444no—
898C42—28no—
899C42—44no—
900C42—44no—
901C42—2444no—
902C23—614no—
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—1222no—
927C23—1222no—
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—
970C23—2441no—
971C23—2441no—
972C23C22×C4×D6111yescharacteristic
973C23C2×D4×D6111yescharacteristic
974C23C22×C22⋊D6111yescharacteristic
975C23C22×D24411yescharacteristic
976C23#41×D6111yescharacteristic
977C23#41×D6111yescharacteristic
978C23C2×#1175822211yescharacteristic
979C23C2×#1175822211yescharacteristic
980C23C2×#1175822211yescharacteristic
981C23C2×#1175822211yescharacteristic
982C23C2×#1175822611yescharacteristic
983C23#1451982211yescharacteristic
984C23#1451982311yescharacteristic
985C23#1451982311yescharacteristic
986C23#1451982511yescharacteristic
987D4—24416no—
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—22no—
1020C2×C4—22no—
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—41no—
1032C2×C4—41no—
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—1222no—
1044C2×C4—1222no—
1045C2×C4—24416no—
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×C4—2441no—
1075C2×C4—2441no—
1076C2×C4C2×#1175819814yes—
1077C2×C4C2×#1175819814yes—
1078C2×C4C2×#1175819814yes—
1079C2×C4#1451976214yescomplemented
1080C22—1224no—
1081C22—1224no—
1082C22—1224no—
1083C22—4881no—
1084C22—4881no—
1085C22—4881no—
1086C22—4881no—
1087C22—4881no—
1088C22—4881no—
1089C22—4881no—
1090C22—4881no—
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—2442no—
1109C22—2442no—
1110C22C22×#1175819811yescharacteristic
1111C22C4×D4×D6111yescharacteristic
1112C22C4×#1175822211yescharacteristic
1113C22C4×#1175822211yescharacteristic
1114C22C4×#1175822611yescharacteristic
1115C22#1684023411yescharacteristic
1116C22#1684024411yescharacteristic
1117C22C2×#1451976211yescharacteristic
1118C22#1684027111yescharacteristic
1119C22#1684027311yescharacteristic
1120C22#1684027311yescharacteristic
1121C22#1684029011yescharacteristic
1122C22#1684029911yescharacteristic
1123C22#1684031211yescharacteristic
1124C22#1684031211yescharacteristic
1125C22#1684034511yescharacteristic
1126C22#1684035911yescharacteristic
1127C22#1684036711yescharacteristic
1128C22#1684038411yescharacteristic
1129C22D4×C22⋊D6111yescharacteristic
1130C22D4×D24411yescharacteristic
1131C22#1684040011yescharacteristic
1132C22#1684040711yescharacteristic
1133C22#1684040811yescharacteristic
1134C22#1684041311yescharacteristic
1135C22#1684042311yescharacteristic
1136C22#1684042411yescharacteristic
1137C22#1684043111yescharacteristic
1138C22#1684043411yescharacteristic
1139C22#1684043611yescharacteristic
1140C22#1684043611yescharacteristic
1141C22#1684045311yescharacteristic
1142C22#1684046011yescharacteristic
1143C22#1684046111yescharacteristic
1144C22#1684049711yescharacteristic
1145C4—24no—
1146C4—24no—
1147C4—24no—
1148C4—24no—
1149C4—42no—
1150C4—42no—
1151C4—42no—
1152C4—4881no—
1153C4—4881no—
1154C4—2442no—
1155C4—2442no—
1156C4—2442no—
1157C4—2442no—
1158C2—4882no—
1159C2—2444no—
1160C2#2144830911yescharacteristic
1161C2C4×#1451976211yescharacteristic
1162C2#2144860311yescharacteristic
1163C2D4×#1175819811yescharacteristic
1164C2#2144865711yescharacteristic
1165C2#2144881611yescharacteristic
1166C2#2144894811yescharacteristic
1167C2#2144955411yescharacteristic
1168C2#2144958411yescharacteristic
1169C2#2144970511yescharacteristic
1170C2#2144973511yescharacteristic
1171C2#2144978611yescharacteristic
1172C2#2144992411yescharacteristic
1173C2#2145087311yescharacteristic
1174C2#2145092711yescharacteristic
subgroupG/H
center, FrattiniC24C23×D61
commutatorC23×C61C23×C4
FittingC2×C4×C4⋊C4×C61C2
socle, cosocleC24×C61C24
prime radicalC23×D244C22
hypercenterC2×C4×C4⋊C4D61
hypocenterC61#14095
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C24 ◁ C2×C4×C4⋊C4

Complements

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

NH ≅ G/Ntype
3. C2×#16839648C2semidirect
4. C2×C4×#11758198C2semidirect
5. #21444073C2semidirect
6. #21444061C2semidirect
7. #21444061C2semidirect
9. #21444057C2semidirect
10. #21444057C2semidirect
11. #21444057C2semidirect
12. #21444055C2semidirect
13. #21444052C2semidirect
14. #21444040C2semidirect
15. C2×C4×C4⋊C4×C61C2semidirect
20. C2×#14519762C4semidirect
296. C4⋊C4×C61C22⋊C4semidirect
447. C2×C4×C61#123semidirect
574. C2×C4×C4⋊C4D61semidirect
645. C61#14095semidirect
886. C4⋊C4#11758198semidirect
1079. C2×C4#14519762semidirect

Maximal subgroups

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

subgroupindex
C22×#145197622
C2×#168396642
C2×#168396482
C2×C4×#117581982
#214440732
#214440612
#214440592
#214440572
#214440552
#214440522
#214440402
C2×C4×C4⋊C4×C612
#1409561