Finite Group Databasebeta

← #29604449

Subgroups — #29604449

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×#14519760C211yesmaximal, characteristic
2C2×#16839662C211yesmaximal, characteristic
3C2×#16839646C211yesmaximal, characteristic, complemented
4C2×C4×#11758196C211yesmaximal, characteristic, complemented
5#21444070C211yesmaximal, characteristic, complemented
6#21444063C211yesmaximal, characteristic, complemented
7#21444062C211yesmaximal, characteristic, complemented
8#21444058C211yesmaximal, characteristic
9#21444057C211yesmaximal, characteristic, complemented
10#21444057C211yesmaximal, characteristic, complemented
11#21444056C211yesmaximal, characteristic, complemented
12#21444055C211yesmaximal, characteristic, complemented
13#21444050C211yesmaximal, characteristic, complemented
14#21444042C211yesmaximal, characteristic, complemented
15C2×C4×C22⋊C4×C61C211yesmaximal, characteristic, complemented
16C23×C22⋊D61C2211yescharacteristic
17C2×#14519760—24no—
18C2×#14519760—24no—
19C2×#14519760C418yescomplemented
20C22×#11758196C2211yescharacteristic
21C22×#11758196C2211yescharacteristic
22C22×#11758196C2211yescharacteristic
23C22×#11758196C2211yescharacteristic
24C22×C22⋊Dic61C2211yescharacteristic
25C22×C22⋊Dic61C2211yescharacteristic
26C22×C22⋊Dic61C2211yescharacteristic
27C22×#11758198C2211yescharacteristic
28C22×#11758198C2211yescharacteristic
29C22×#11758198C2211yescharacteristic
30C22×#11758198C2211yescharacteristic
31C22×#11758198C2211yescharacteristic
32C22×#11758198C2211yescharacteristic
33C22×C4×Dic61C2211yescharacteristic
34C22×C4×Dic61C2211yescharacteristic
35#16839662—24no—
36#16839646—24no—
37C4×#11758196—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
50C24×C4×C61C2211yescharacteristic
51C22×C22⋊C4×C61C2211yescharacteristic
52C22×C22⋊C4×C61C2211yescharacteristic
53C22×C42×C61C2211yescharacteristic
54C22×C42×C61C2211yescharacteristic
55C4×C22⋊C4×C61—24no—
56C2×#95×C61C2211yescharacteristic
57C2×#95×C61C2211yescharacteristic
58C24×D61C2311yescharacteristic
59C22×C22⋊D61—22no—
60C22×C22⋊D61—22no—
61C22×C22⋊D61—22no—
62C22×C22⋊D61—22no—
63C22×C22⋊D61—41no—
64C22×C22⋊D61—41no—
65C22×C22⋊D61C2×C414yes—
66C23×Dic61C2311yescharacteristic
67C23×Dic61C2311yescharacteristic
68C23×Dic61C2311yescharacteristic
69C23×Dic61C2311yescharacteristic
70C23×Dic61C2311yescharacteristic
71C23×Dic61C2311yescharacteristic
72C23×Dic61C2311yescharacteristic
73#14519760—232no—
74C2×#11758196—22no—
75C2×#11758196—22no—
76C2×#11758196—22no—
77C2×#11758196—22no—
78C2×#11758196—22no—
79C2×#11758196—22no—
80C2×#11758196—22no—
81C2×#11758196—41no—
82C2×#11758196C2×C414yes—
83C2×#11758196C2×C414yes—
84C2×#11758196D414yes—
85C2×#11758196D414yes—
86C2×C22⋊Dic61—22no—
87C2×C22⋊Dic61—22no—
88C2×C22⋊Dic61—22no—
89C2×C22⋊Dic61—22no—
90C2×C22⋊Dic61—22no—
91C2×C22⋊Dic61—22no—
92C2×C22⋊Dic61—41no—
93C2×C22⋊Dic61—41no—
94C2×C22⋊Dic61C2×C414yes—
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—41no—
108C2×#11758198—41no—
109C2×#11758198—41no—
110C2×#11758198—41no—
111C2×#11758198C2×C414yes—
112C2×#11758198C2×C414yes—
113C2×C4×Dic61—22no—
114C2×C4×Dic61—22no—
115C2×C4×Dic61—22no—
116C2×C4×Dic61—22no—
117C2×C4×Dic61—22no—
118C2×C4×Dic61—41no—
119#14519684—22no—
120#14519684—22no—
121#14519684—22no—
122#14519684—22no—
123#14519684—22no—
124#14519684—22no—
125#14519684—22no—
126#14519684—22no—
127#14519684—41no—
128#14519684—41no—
129#14519684—41no—
130#14519684—41no—
131C25×C61C2311yescharacteristic
132C23×C4×C61—22no—
133C23×C4×C61—22no—
134C23×C4×C61—22no—
135C23×C4×C61—22no—
136C23×C4×C61—41no—
137C23×C4×C61—41no—
138C23×C4×C61C2×C414yes—
139C23×C4×C61C2311yescharacteristic
140C23×C4×C61C2311yescharacteristic
141C23×C4×C61C2311yescharacteristic
142C23×C4×C61C2311yescharacteristic
143C23×C4×C61C2311yescharacteristic
144C23×C4×C61C2311yescharacteristic
145C2×C22⋊C4×C61—22no—
146C2×C22⋊C4×C61—22no—
147C2×C22⋊C4×C61—22no—
148C2×C22⋊C4×C61—22no—
149C2×C22⋊C4×C61—22no—
150C2×C22⋊C4×C61D414yes—
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×C61—21no—
160C24×C61—21no—
161C24×C61—21no—
162C24×C61—21no—
163C24×C61—21no—
164C24×C61—21no—
165C24×C61—21no—
166C24×C61—21no—
167C24×C61—21no—
168C24×C61—21no—
169C24×C61—21no—
170C24×C61—21no—
171C24×C61C22×C412yes—
172C24×C61C2×D412yes—
173C24×C61#4112yes—
174C24×C61C2411yescharacteristic
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×D61—21no—
187C23×D61—21no—
188C23×D61—21no—
189C23×D61C22×C412yes—
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—28no—
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—28no—
224C22×C4×C61—44no—
225C22×C4×C61—44no—
226C22×C4×C61—44no—
227C22×C4×C61—44no—
228C22×C4×C61—44no—
229C22×C4×C61C22×C412yes—
230C22×C4×C61C22×C412yes—
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×C4×C61#4112yes—
239C2×C22⋊D61—28no—
240C2×C22⋊D61—28no—
241C2×C22⋊D61—44no—
242C2×C22⋊D61—44no—
243C2×C22⋊D61—44no—
244C2×C22⋊D61—44no—
245C2×C22⋊D61—44no—
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×Dic61—21no—
282C22×Dic61—21no—
283C22×Dic61—21no—
284C22×Dic61—21no—
285C22×Dic61—21no—
286C22×Dic61C22×C412yes—
287C22×Dic61C22×C412yes—
288C22×Dic61C22×C412yes—
289C22×Dic61C2×D412yes—
290C22×Dic61C2×D412yes—
291C22×Dic61C2×D412yes—
292C22×Dic61C2×D412yes—
293C22×Dic61#4112yes—
294C22×Dic61#4112yes—
295C22⋊C4×C61—28no—
296C22⋊C4×C61—28no—
297C42×C61—44no—
298C42×C61—44no—
299C22⋊Dic61—28no—
300C22⋊Dic61—44no—
301C22⋊Dic61—44no—
302#11758198—28no—
303#11758198—28no—
304#11758198—44no—
305#11758198—44no—
306#11758198—44no—
307#11758198—44no—
308#11758196—28no—
309#11758196—28no—
310#11758196—44no—
311#11758196C22⋊C4116yescomplemented
312C4×Dic61—28no—
313C4×Dic61—44no—
314C23×C61—22no—
315C23×C61—22no—
316C23×C61—22no—
317C23×C61—22no—
318C23×C61—22no—
319C23×C61—22no—
320C23×C61—22no—
321C23×C61—22no—
322C23×C61—22no—
323C23×C61—22no—
324C23×C61—22no—
325C23×C61—22no—
326C23×C61—22no—
327C23×C61—22no—
328C23×C61—22no—
329C23×C61—22no—
330C23×C61—22no—
331C23×C61—22no—
332C23×C61—41no—
333C23×C61—41no—
334C23×C61—41no—
335C23×C61—41no—
336C23×C61—41no—
337C23×C61—41no—
338C23×C61—41no—
339C23×C61—41no—
340C23×C61—41no—
341C23×C61—41no—
342C23×C61—41no—
343C23×C61—41no—
344C23×C61—41no—
345C23×C61—41no—
346C23×C61—41no—
347C23×C61—41no—
348C23×C61C4×D414yes—
349C23×C61C23×C411yescharacteristic
350C23×C61C22×D411yescharacteristic
351C23×C61C22×D411yescharacteristic
352C23×C61C22×D411yescharacteristic
353C23×C61C2×#4111yescharacteristic
354C23×C61C2×#4111yescharacteristic
355C23×C61C2×#4111yescharacteristic
356C23×C61C2×#4111yescharacteristic
357C23×C61C2×#4111yescharacteristic
358C23×C61C2×#4111yescharacteristic
359C23×C61C2×#4111yescharacteristic
360C23×C61H(5,𝔽2)11yescharacteristic
361C23×C61H(5,𝔽2)11yescharacteristic
362C23×C61H(5,𝔽2)11yescharacteristic
363C23×C612−1+411yescharacteristic
364C22×D61—22no—
365C22×D61—22no—
366C22×D61—22no—
367C22×D61—22no—
368C22×D61—22no—
369C22×D61—22no—
370C22×D61—22no—
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—
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—416no—
424C2×C4×C61—41no—
425C2×C4×C61—41no—
426C2×C4×C61—41no—
427C2×C4×C61—41no—
428C2×C4×C61—41no—
429C2×C4×C61—41no—
430C2×C4×C61—41no—
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×C61C2×C22⋊C414yes—
441C2×C4×C61#12314yescomplemented
442C22⋊D61—416no—
443C2×Dic61—22no—
444C2×Dic61—22no—
445C2×Dic61—22no—
446C2×Dic61—22no—
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—22no—
460C2×Dic61—22no—
461C2×Dic61—22no—
462C2×Dic61—22no—
463C2×Dic61—22no—
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—
490C2×Dic61C2×C22⋊C414yes—
491C2×Dic61C2×C22⋊C414yes—
492#14095—611nomaximal, Sylow
493C22×C61—24no—
494C22×C61—24no—
495C22×C61—24no—
496C22×C61—42no—
497C22×C61—42no—
498C22×C61—42no—
499C22×C61—42no—
500C22×C61—42no—
501C22×C61—42no—
502C22×C61—42no—
503C22×C61—42no—
504C22×C61—42no—
505C22×C61—42no—
506C22×C61—42no—
507C22×C61—42no—
508C22×C61C22×C22⋊C411yescharacteristic
509C22×C61C2×C4×D411yescharacteristic
510C22×C61C4×#4111yescharacteristic
511C22×C61C4×#4111yescharacteristic
512C22×C61C4×#4111yescharacteristic
513C22×C61#51811yescharacteristic
514C22×C61#52011yescharacteristic
515C22×C61C2×#12311yescharacteristic
516C22×C61#52511yescharacteristic
517C22×C61#52511yescharacteristic
518C22×C61#52511yescharacteristic
519C22×C61#52911yescharacteristic
520C22×C61#52911yescharacteristic
521C22×C61#53211yescharacteristic
522C22×C61#53211yescharacteristic
523C22×C61#53811yescharacteristic
524C22×C61#53911yescharacteristic
525C22×C61#54011yescharacteristic
526C22×C61#54211yescharacteristic
527C22×C61D4211yescharacteristic
528C22×C61D4211yescharacteristic
529C22×C61#54611yescharacteristic
530C22×C61#54611yescharacteristic
531C22×C61#54611yescharacteristic
532C22×C61#54711yescharacteristic
533C22×C61#54811yescharacteristic
534C22×C61#54811yescharacteristic
535C22×C61#55011yescharacteristic
536C22×C61#55011yescharacteristic
537C22×C61#55111yescharacteristic
538C22×C61#55111yescharacteristic
539C22×C61#55211yescharacteristic
540C22×C61#55311yescharacteristic
541C22×C61#55311yescharacteristic
542C22×C61#55911yescharacteristic
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—42no—
561C4×C61—42no—
562C4×C61—42no—
563C4×C61—42no—
564Dic61—24no—
565Dic61—24no—
566Dic61—42no—
567Dic61—42no—
568Dic61—42no—
569Dic61—81no—
570Dic61—81no—
571C22×#123—611no—
572C2×#390—611no—
573C2×#387—611no—
574C2×C4×C4⋊C4—611no—
575C2×C4×C22⋊C4D6111yescharacteristic, complemented
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—44no—
587C2×C61#229711yescharacteristic
588C2×C61C4×#12311yescharacteristic
589C2×C61#233511yescharacteristic
590C2×C61D4×C22⋊C411yescharacteristic
591C2×C61#234111yescharacteristic
592C2×C61#235911yescharacteristic
593C2×C61#237411yescharacteristic
594C2×C61#244311yescharacteristic
595C2×C61#244511yescharacteristic
596C2×C61#245611yescharacteristic
597C2×C61#245811yescharacteristic
598C2×C61#246111yescharacteristic
599C2×C61#247111yescharacteristic
600C2×C61#255411yescharacteristic
601C2×C61#255811yescharacteristic
602D61—82no—
603C23×D4—611no—
604C24×C4C2×D6111yescharacteristic
605C2×#123—618no—
606C2×#123—1224no—
607C2×#123—1224no—
608C22×C4⋊C4—611no—
609C22×C4⋊C4—611no—
610C22×C4⋊C4—611no—
611C22×C4⋊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×C22⋊C4—611no—
620C22×C22⋊C4—611no—
621C22×C22⋊C4C2×D6111yescharacteristic
622C22×C22⋊C4C2×D6111yescharacteristic
623C22×C42—611no—
624C22×C42—611no—
625C22×C42C2×D6111yescharacteristic
626C22×C42C2×D6111yescharacteristic
627#390—1224no—
628#387—1224no—
629C4×C4⋊C4—1224no—
630C4×C22⋊C4—24no—
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—
647C25C22×D6111yescharacteristic
648C22×D4—614no—
649C22×D4—1222no—
650C22×D4—1222no—
651C22×D4—1222no—
652C22×D4—1222no—
653C22×D4—2441no—
654C22×D4—2441no—
655C23×C4—22no—
656C23×C4—22no—
657C23×C4—22no—
658C23×C4—22no—
659C23×C4—41no—
660C23×C4—41no—
661C23×C4—611no—
662C23×C4—611no—
663C23×C4—611no—
664C23×C4—611no—
665C23×C4—611no—
666C23×C4—611no—
667C23×C4—611no—
668C23×C4C4×D6114yes—
669C23×C4C22×D6111yescharacteristic
670C23×C4C22×D6111yescharacteristic
671C23×C4C22×D6111yescharacteristic
672C23×C4C22×D6111yescharacteristic
673C23×C4C22×D6111yescharacteristic
674C23×C4C22×D6111yescharacteristic
675#123—12232no—
676C2×C4⋊C4—614no—
677C2×C4⋊C4—614no—
678C2×C4⋊C4—614no—
679C2×C4⋊C4—614no—
680C2×C4⋊C4—1222no—
681C2×C4⋊C4—1222no—
682C2×C4⋊C4—1222no—
683C2×C4⋊C4—1222no—
684C2×C4⋊C4—1222no—
685C2×C4⋊C4—1222no—
686C2×C4⋊C4—1222no—
687C2×C4⋊C4—2441no—
688C2×C22⋊C4—22no—
689C2×C22⋊C4—22no—
690C2×C22⋊C4—22no—
691C2×C22⋊C4—22no—
692C2×C22⋊C4—22no—
693C2×C22⋊C4—614no—
694C2×C22⋊C4—614no—
695C2×C22⋊C4—614no—
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—2441no—
715C2×C22⋊C4—2441no—
716C2×C22⋊C4—2441no—
717C2×C22⋊C4—2441no—
718C2×C22⋊C4—2441no—
719C2×C22⋊C4—2441no—
720C2×C22⋊C4C22⋊D6114yes—
721C2×C42—22no—
722C2×C42—22no—
723C2×C42—22no—
724C2×C42—22no—
725C2×C42—41no—
726C2×C42—41no—
727C2×C42—1222no—
728C2×C42—1222no—
729C2×C42—1222no—
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—21no—
748C24—21no—
749C24—21no—
750C24—21no—
751C24—21no—
752C24—21no—
753C24—21no—
754C24—21no—
755C24—21no—
756C24—21no—
757C24—21no—
758C24—21no—
759C24—612no—
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—
774C24C2×C4×D6112yes—
775C24#1175822212yes—
776C24C2×C22⋊D6112yes—
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—28no—
818C22×C4—28no—
819C22×C4—44no—
820C22×C4—44no—
821C22×C4—44no—
822C22×C4—44no—
823C22×C4—44no—
824C22×C4—612no—
825C22×C4—612no—
826C22×C4—612no—
827C22×C4—612no—
828C22×C4—612no—
829C22×C4—612no—
830C22×C4—612no—
831C22×C4—612no—
832C22×C4—612no—
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—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×C4C2×C4×D6112yes—
874C22×C4C2×C4×D6112yes—
875C22×C4#1175822212yes—
876C22×C4#1175822212yes—
877C22×C4#1175822212yes—
878C22×C4#1175822212yes—
879C22×C4D4×D6112yes—
880C22×C4D4×D6112yes—
881C22×C4C2×C22⋊D6112yes—
882C22×C4C2×C22⋊D6112yes—
883C4⋊C4—6116no—
884C4⋊C4—1228no—
885C4⋊C4—1228no—
886C4⋊C4—2444no—
887C22⋊C4—28no—
888C22⋊C4—28no—
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—44no—
899C42—44no—
900C42—1228no—
901C42—2444no—
902C23—22no—
903C23—22no—
904C23—22no—
905C23—22no—
906C23—22no—
907C23—22no—
908C23—22no—
909C23—22no—
910C23—22no—
911C23—22no—
912C23—22no—
913C23—22no—
914C23—22no—
915C23—22no—
916C23—22no—
917C23—22no—
918C23—22no—
919C23—22no—
920C23—41no—
921C23—41no—
922C23—41no—
923C23—41no—
924C23—41no—
925C23—41no—
926C23—41no—
927C23—41no—
928C23—41no—
929C23—41no—
930C23—41no—
931C23—41no—
932C23—41no—
933C23—41no—
934C23—41no—
935C23—41no—
936C23—1222no—
937C23—1222no—
938C23—1222no—
939C23—1222no—
940C23—1222no—
941C23—1222no—
942C23—1222no—
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—
971C23C4×C22⋊D6114yes—
972C23C22×C4×D6111yescharacteristic
973C23C2×D4×D6111yescharacteristic
974C23C2×D4×D6111yescharacteristic
975C23C22×C22⋊D6111yescharacteristic
976C23#41×D6111yescharacteristic
977C23#41×D6111yescharacteristic
978C23C2×#1175822211yescharacteristic
979C23C2×#1175822211yescharacteristic
980C23C2×#1175822211yescharacteristic
981C23C2×#1175822211yescharacteristic
982C23C2×#1175822211yescharacteristic
983C23#1451982211yescharacteristic
984C23#1451982211yescharacteristic
985C23#1451982311yescharacteristic
986C23#1451982411yescharacteristic
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—416no—
1013C2×C4—41no—
1014C2×C4—41no—
1015C2×C4—41no—
1016C2×C4—41no—
1017C2×C4—41no—
1018C2×C4—41no—
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—614no—
1030C2×C4—614no—
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—1222no—
1044C2×C4—1222no—
1045C2×C4—1222no—
1046C2×C4—1222no—
1047C2×C4—1222no—
1048C2×C4—1222no—
1049C2×C4—1222no—
1050C2×C4—1222no—
1051C2×C4—1222no—
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×C4—2441no—
1077C2×C4—2441no—
1078C2×C4C22⋊C4×D6114yes—
1079C2×C4#1451976014yescomplemented
1080C22—24no—
1081C22—24no—
1082C22—24no—
1083C22—42no—
1084C22—42no—
1085C22—42no—
1086C22—42no—
1087C22—42no—
1088C22—42no—
1089C22—42no—
1090C22—42no—
1091C22—42no—
1092C22—42no—
1093C22—42no—
1094C22—42no—
1095C22—4881no—
1096C22—4881no—
1097C22—4881no—
1098C22—4881no—
1099C22—4881no—
1100C22—4881no—
1101C22—4881no—
1102C22—4881no—
1103C22—2442no—
1104C22—2442no—
1105C22—2442no—
1106C22—2442no—
1107C22—2442no—
1108C22—2442no—
1109C22—2442no—
1110C22C2×C22⋊C4×D6111yescharacteristic
1111C22C2×C4×C22⋊D6111yescharacteristic
1112C22#1684023011yescharacteristic
1113C22C4×#1175822211yescharacteristic
1114C22C4×#1175822211yescharacteristic
1115C22#1684023511yescharacteristic
1116C22#1684024211yescharacteristic
1117C22C2×#1451976011yescharacteristic
1118C22#1684027111yescharacteristic
1119C22#1684027111yescharacteristic
1120C22#1684027311yescharacteristic
1121C22#1684029611yescharacteristic
1122C22#1684029611yescharacteristic
1123C22#1684030911yescharacteristic
1124C22#1684030911yescharacteristic
1125C22#1684034511yescharacteristic
1126C22#1684035411yescharacteristic
1127C22#1684036311yescharacteristic
1128C22#1684037711yescharacteristic
1129C22D4×C22⋊D6111yescharacteristic
1130C22D4×C22⋊D6111yescharacteristic
1131C22#1684040011yescharacteristic
1132C22#1684040211yescharacteristic
1133C22#1684040211yescharacteristic
1134C22#1684041111yescharacteristic
1135C22#1684042111yescharacteristic
1136C22#1684042111yescharacteristic
1137C22#1684043311yescharacteristic
1138C22#1684043311yescharacteristic
1139C22#1684043611yescharacteristic
1140C22#1684044111yescharacteristic
1141C22#1684044511yescharacteristic
1142C22#1684046111yescharacteristic
1143C22#1684046211yescharacteristic
1144C22#1684049511yescharacteristic
1145C4—24no—
1146C4—24no—
1147C4—42no—
1148C4—42no—
1149C4—42no—
1150C4—42no—
1151C4—1224no—
1152C4—1224no—
1153C4—4881no—
1154C4—4881no—
1155C4—2442no—
1156C4—2442no—
1157C4—2442no—
1158C2—44no—
1159C2—4882no—
1160C2#2144830511yescharacteristic
1161C2C4×#1451976011yescharacteristic
1162C2#2144860911yescharacteristic
1163C2C22⋊C4×C22⋊D6111yescharacteristic
1164C2#2144865911yescharacteristic
1165C2#2144881111yescharacteristic
1166C2#2144895011yescharacteristic
1167C2#2144954811yescharacteristic
1168C2#2144957811yescharacteristic
1169C2#2144971111yescharacteristic
1170C2#2144974111yescharacteristic
1171C2#2144978011yescharacteristic
1172C2#2144993011yescharacteristic
1173C2#2145087911yescharacteristic
1174C2#2145093311yescharacteristic
subgroupG/H
center, FrattiniC24C23×D61
commutatorC23×C61C23×C4
FittingC2×C4×C22⋊C4×C61C2
socle, cosocleC24×C61C24
prime radicalC23×C22⋊D61C22
hypercenterC2×C4×C22⋊C4D61
hypocenterC61#14095
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C24 ◁ C2×C4×C22⋊C4

Complements

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

NH ≅ G/Ntype
3. C2×#16839646C2semidirect
4. C2×C4×#11758196C2semidirect
5. #21444070C2semidirect
6. #21444063C2semidirect
7. #21444062C2semidirect
9. #21444057C2semidirect
10. #21444057C2semidirect
11. #21444056C2semidirect
12. #21444055C2semidirect
13. #21444050C2semidirect
14. #21444042C2semidirect
15. C2×C4×C22⋊C4×C61C2semidirect
19. C2×#14519760C4semidirect
311. #11758196C22⋊C4semidirect
441. C2×C4×C61#123semidirect
575. C2×C4×C22⋊C4D61semidirect
645. C61#14095semidirect
1079. C2×C4#14519760semidirect

Maximal subgroups

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

subgroupindex
C22×#145197602
C2×#168396622
C2×#168396462
C2×C4×#117581962
#214440702
#214440632
#214440622
#214440582
#214440572
#214440562
#214440552
#214440502
#214440422
C2×C4×C22⋊C4×C612
#1409561