Finite Group Databasebeta

← #29604458

Subgroups — #29604458

Order 15616.

2266 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×#14519759C211yesmaximal, characteristic
2C2×#16839655C211yesmaximal, characteristic, complemented
3C2×#16839641C211yesmaximal, characteristic
4C2×C4×#11758198C211yesmaximal, characteristic, complemented
5#21444088C211yesmaximal, characteristic, complemented
6#21444066C211yesmaximal, characteristic, complemented
7#21444065C211yesmaximal, characteristic, complemented
8#21444058C211yesmaximal, characteristic
9#21444057C211yesmaximal, characteristic, complemented
10#21444054C211yesmaximal, characteristic, complemented
11#21444052C211yesmaximal, characteristic, complemented
12#21444049C211yesmaximal, characteristic, complemented
13#21444042C211yesmaximal, characteristic, complemented
14#21444040C211yesmaximal, characteristic, complemented
15C2×C4×C22⋊C4×C61C211yesmaximal, characteristic, complemented
16C23×C22⋊D61C2211yescharacteristic
17C23×C4×D61C2211yescharacteristic
18C2×#14519759—24no—
19C2×#14519759—24no—
20C2×#14519759C418yescomplemented
21C22×C4⋊Dic61C2211yescharacteristic
22C22×C4⋊Dic61C2211yescharacteristic
23C22×#11758196C2211yescharacteristic
24C22×C22⋊Dic61C2211yescharacteristic
25C22×C22⋊Dic61C2211yescharacteristic
26C22×C22⋊Dic61C2211yescharacteristic
27C22×#11758198C2211yescharacteristic
28C22×#11758198C2211yescharacteristic
29C22×#11758198C2211yescharacteristic
30C22×#11758198C2211yescharacteristic
31C22×#11758198C2211yescharacteristic
32C22×C4×Dic61C2211yescharacteristic
33#16839655—24no—
34#16839641—24no—
35C4×#11758198—24no—
36C2×#14519684C2211yescharacteristic
37C2×#14519684C2211yescharacteristic
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
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×C414yescomplemented
80#14519759—232no—
81C2×C4⋊Dic61—22no—
82C2×C4⋊Dic61—22no—
83C2×C4⋊Dic61—22no—
84C2×C4⋊Dic61—22no—
85C2×C4⋊Dic61—41no—
86C2×C4⋊Dic61C2×C414yescomplemented
87C2×#11758196—22no—
88C2×#11758196—22no—
89C2×#11758196C2×C414yescomplemented
90C2×C22⋊Dic61—22no—
91C2×C22⋊Dic61—22no—
92C2×C22⋊Dic61—22no—
93C2×C22⋊Dic61—22no—
94C2×C22⋊Dic61—22no—
95C2×C22⋊Dic61—22no—
96C2×C22⋊Dic61—41no—
97C2×C22⋊Dic61—41no—
98C2×C22⋊Dic61C2×C414yes—
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×#11758198C2×C414yescomplemented
113C2×#11758198D414yes—
114C2×C4×Dic61—22no—
115C2×C4×Dic61—22no—
116C2×C4×Dic61—41no—
117#14519684—22no—
118#14519684—22no—
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—22no—
137C23×C4×C61—41no—
138C23×C4×C61—41no—
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×C61C2×C414yes—
149C2×C22⋊C4×C61D414yes—
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×C61C2×D412yes—
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×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—28no—
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—44no—
222C22×C4×C61—44no—
223C22×C4×C61—44no—
224C22×C4×C61—44no—
225C22×C4×C61—44no—
226C22×C4×C61—44no—
227C22×C4×C61C22×C412yes—
228C22×C4×C61C22×C412yes—
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—
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×Dic61—21no—
287C22×Dic61—21no—
288C22×Dic61—21no—
289C22×Dic61—21no—
290C22×Dic61C22×C412yes—
291C22×Dic61C22×C412yes—
292C22×Dic61C22×C412yes—
293C22×Dic61C2×D412yes—
294C22×Dic61#4112yes—
295C2×C4×D61—28no—
296C2×C4×D61—28no—
297C2×C4×D61—44no—
298C2×C4×D61—44no—
299C2×C4×D61—44no—
300C2×C4×D61—44no—
301C2×C4×D61—44no—
302C22⋊C4×C61—28no—
303C22⋊C4×C61C22⋊C4116yescomplemented
304C42×C61—44no—
305C42×C61—44no—
306C22⋊Dic61—28no—
307C22⋊Dic61—44no—
308C22⋊Dic61—44no—
309#11758198—28no—
310#11758198—28no—
311#11758198—28no—
312#11758198—44no—
313#11758198—44no—
314C4⋊Dic61—28no—
315C4⋊Dic61—44no—
316#11758196—28no—
317C4×Dic61—44no—
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—22no—
333C23×C61—22no—
334C23×C61—22no—
335C23×C61—22no—
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×C61—41no—
349C23×C61—41no—
350C23×C61—41no—
351C23×C61—41no—
352C23×C61C2×C22⋊C414yes—
353C23×C61C23×C411yescharacteristic
354C23×C61C22×D411yescharacteristic
355C23×C61C22×D411yescharacteristic
356C23×C61C22×D411yescharacteristic
357C23×C61C2×#4111yescharacteristic
358C23×C61C2×#4111yescharacteristic
359C23×C61C2×#4111yescharacteristic
360C23×C61C2×#4111yescharacteristic
361C23×C61C2×#4111yescharacteristic
362C23×C61C2×#4111yescharacteristic
363C23×C61C2×#4111yescharacteristic
364C23×C61H(5,𝔽2)11yescharacteristic
365C23×C61H(5,𝔽2)11yescharacteristic
366C23×C61H(5,𝔽2)11yescharacteristic
367C23×C612−1+411yescharacteristic
368C22×D61—22no—
369C22×D61—22no—
370C22×D61—22no—
371C22×D61—22no—
372C22×D61—22no—
373C22×D61—22no—
374C22×D61—22no—
375C22×D61—22no—
376C22×D61—22no—
377C22×D61—22no—
378C22×D61—22no—
379C22×D61—22no—
380C22×D61—22no—
381C22×D61—22no—
382C22×D61—22no—
383C22×D61—22no—
384C22×D61—22no—
385C22×D61—22no—
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×D61C4×D414yes—
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—416no—
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×C61C2×C22⋊C414yes—
444C2×C4×C61C2×C22⋊C414yes—
445C2×C4×C61#12314yescomplemented
446C22⋊D61—416no—
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—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—
490C2×Dic61—41no—
491C2×Dic61—41no—
492C2×Dic61—41no—
493C2×Dic61—41no—
494C2×Dic61—41no—
495C2×Dic61—41no—
496C4×D61—416no—
497#14096—611nomaximal, Sylow
498C22×C61—24no—
499C22×C61—24no—
500C22×C61—24no—
501C22×C61—42no—
502C22×C61—42no—
503C22×C61—42no—
504C22×C61—42no—
505C22×C61—42no—
506C22×C61—42no—
507C22×C61—42no—
508C22×C61—42no—
509C22×C61—42no—
510C22×C61—42no—
511C22×C61—42no—
512C22×C61—42no—
513C22×C61C22×C22⋊C411yescharacteristic
514C22×C61C2×C4×D411yescharacteristic
515C22×C61C4×#4111yescharacteristic
516C22×C61C4×#4111yescharacteristic
517C22×C61C4×#4111yescharacteristic
518C22×C61#51811yescharacteristic
519C22×C61#52011yescharacteristic
520C22×C61C2×#12311yescharacteristic
521C22×C61#52511yescharacteristic
522C22×C61#52511yescharacteristic
523C22×C61#52511yescharacteristic
524C22×C61#52911yescharacteristic
525C22×C61#52911yescharacteristic
526C22×C61#53211yescharacteristic
527C22×C61#53211yescharacteristic
528C22×C61#53811yescharacteristic
529C22×C61#53911yescharacteristic
530C22×C61#54011yescharacteristic
531C22×C61#54211yescharacteristic
532C22×C61D4211yescharacteristic
533C22×C61D4211yescharacteristic
534C22×C61#54611yescharacteristic
535C22×C61#54611yescharacteristic
536C22×C61#54611yescharacteristic
537C22×C61#54611yescharacteristic
538C22×C61#54611yescharacteristic
539C22×C61#54711yescharacteristic
540C22×C61#54711yescharacteristic
541C22×C61#54711yescharacteristic
542C22×C61#55111yescharacteristic
543C22×C61#55111yescharacteristic
544C22×C61#55211yescharacteristic
545C22×C61#55311yescharacteristic
546C22×C61#55311yescharacteristic
547C22×C61#55911yescharacteristic
548C2×D61—24no—
549C2×D61—24no—
550C2×D61—24no—
551C2×D61—42no—
552C2×D61—42no—
553C2×D61—42no—
554C2×D61—42no—
555C2×D61—42no—
556C2×D61—42no—
557C2×D61—42no—
558C2×D61—42no—
559C2×D61—42no—
560C2×D61—42no—
561C2×D61—42no—
562C2×D61—42no—
563C4×C61—24no—
564C4×C61—24no—
565C4×C61—24no—
566C4×C61—42no—
567C4×C61—42no—
568C4×C61—42no—
569Dic61—42no—
570Dic61—42no—
571Dic61—42no—
572Dic61—42no—
573Dic61—42no—
574Dic61—81no—
575Dic61—81no—
576C22×#123—611no—
577C2×#388—611no—
578C2×#386—611no—
579C2×C4×C22⋊C4—611no—
580C2×C4×C22⋊C4D6111yescharacteristic, complemented
581#1445—611no—
582#1440—611no—
583#1439—611no—
584#1438—611no—
585#1437—611no—
586#1436—611no—
587#1436—611no—
588C4⋊#95—611no—
589C22⋊#95—611no—
590C22⋊#95—611no—
591C2×C61—44no—
592C2×C61#229711yescharacteristic
593C2×C61C4×#12311yescharacteristic
594C2×C61#233511yescharacteristic
595C2×C61D4×C22⋊C411yescharacteristic
596C2×C61#233911yescharacteristic
597C2×C61#235911yescharacteristic
598C2×C61#237411yescharacteristic
599C2×C61#241811yescharacteristic
600C2×C61#242211yescharacteristic
601C2×C61#245511yescharacteristic
602C2×C61#245711yescharacteristic
603C2×C61#246411yescharacteristic
604C2×C61#247011yescharacteristic
605C2×C61#255311yescharacteristic
606C2×C61#255711yescharacteristic
607D61—44no—
608C23×D4—611no—
609C24×C4—611no—
610C24×C4C2×D6111yescharacteristic
611C2×#123—618no—
612C2×#123—1224no—
613C2×#123—1224no—
614C22×C4⋊C4—611no—
615C22×C4⋊C4—611no—
616C22×C4⋊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⋊C4C2×D6111yescharacteristic
626C22×C22⋊C4C2×D6111yescharacteristic
627C22×C42—611no—
628C22×C42C2×D6111yescharacteristic
629C22×C42C2×D6111yescharacteristic
630#388—1224no—
631#386—1224no—
632C4×C22⋊C4—24no—
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×#95—611no—
647C2×#95—611no—
648C2×#95C2×D6111yescharacteristic
649C2×#95C2×D6111yescharacteristic
650C61#1409611yescharacteristic, complemented, Sylow
651C25—611no—
652C25C22×D6111yescharacteristic
653C22×D4—614no—
654C22×D4—1222no—
655C22×D4—1222no—
656C22×D4—1222no—
657C22×D4—1222no—
658C22×D4—2441no—
659C22×D4—2441no—
660C23×C4—22no—
661C23×C4—22no—
662C23×C4—22no—
663C23×C4—22no—
664C23×C4—22no—
665C23×C4—41no—
666C23×C4—41no—
667C23×C4—611no—
668C23×C4—611no—
669C23×C4—611no—
670C23×C4—611no—
671C23×C4—611no—
672C23×C4—614no—
673C23×C4—611no—
674C23×C4—611no—
675C23×C4—1222no—
676C23×C4—1222no—
677C23×C4—1222no—
678C23×C4—1222no—
679C23×C4—2441no—
680C23×C4—2441no—
681C23×C4C22×D6111yescharacteristic
682C23×C4C22×D6111yescharacteristic
683C23×C4C22×D6111yescharacteristic
684C23×C4C22×D6111yescharacteristic
685C23×C4C22×D6111yescharacteristic
686C23×C4C22×D6111yescharacteristic
687#123—12232no—
688C2×C4⋊C4—614no—
689C2×C4⋊C4—614no—
690C2×C4⋊C4—1222no—
691C2×C4⋊C4—1222no—
692C2×C4⋊C4—1222no—
693C2×C4⋊C4—1222no—
694C2×C4⋊C4—1222no—
695C2×C4⋊C4—1222no—
696C2×C4⋊C4—2441no—
697C2×C22⋊C4—22no—
698C2×C22⋊C4—22no—
699C2×C22⋊C4—22no—
700C2×C22⋊C4—614no—
701C2×C22⋊C4—614no—
702C2×C22⋊C4—614no—
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—1222no—
719C2×C22⋊C4—1222no—
720C2×C22⋊C4—2441no—
721C2×C22⋊C4—2441no—
722C2×C22⋊C4—2441no—
723C2×C22⋊C4—2441no—
724C2×C22⋊C4C4×D6114yes—
725C2×C22⋊C4D24414yes—
726C2×C22⋊C4C22⋊D6114yes—
727C2×C42—22no—
728C2×C42—22no—
729C2×C42—22no—
730C2×C42—22no—
731C2×C42—41no—
732C2×C42—41no—
733C2×C42—1222no—
734C2×C42—1222no—
735C2×C42—2441no—
736#95—22no—
737#95—22no—
738#95—1222no—
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—2441no—
749#95—2441no—
750#95—2441no—
751#95—2441no—
752C24—21no—
753C24—21no—
754C24—21no—
755C24—21no—
756C24—21no—
757C24—21no—
758C24—21no—
759C24—21no—
760C24—21no—
761C24—21no—
762C24—21no—
763C24—21no—
764C24—612no—
765C24—612no—
766C24—612no—
767C24—1221no—
768C24—1221no—
769C24—1221no—
770C24—1221no—
771C24—1221no—
772C24—1221no—
773C24—1221no—
774C24—1221no—
775C24—1221no—
776C24—1221no—
777C24—1221no—
778C24—1221no—
779C24C2×C4×D6112yes—
780C24C2×D24412yes—
781C24C2×C22⋊D6112yes—
782C24C23×D6111yescharacteristic
783C2×D4—1228no—
784C2×D4—1228no—
785C2×D4—2444no—
786C2×D4—2444no—
787C2×D4—2444no—
788C2×D4—2444no—
789C2×D4—2444no—
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—28no—
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—44no—
822C22×C4—44no—
823C22×C4—44no—
824C22×C4—44no—
825C22×C4—44no—
826C22×C4—44no—
827C22×C4—612no—
828C22×C4—612no—
829C22×C4—612no—
830C22×C4—612no—
831C22×C4—612no—
832C22×C4—1228no—
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—1228no—
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—1221no—
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×D24412yes—
886C22×C4C2×D24412yes—
887C22×C4#1175822212yes—
888C22×C4#1175822212yes—
889C22×C4#1175822212yes—
890C22×C4#1175822212yes—
891C22×C4D4×D6112yes—
892C22×C4#1175822412yes—
893C22×C4C2×C22⋊D6112yes—
894C22×C4C2×C22⋊D6112yes—
895C4⋊C4—1228no—
896C4⋊C4—1228no—
897C4⋊C4—2444no—
898C22⋊C4—28no—
899C22⋊C4—1228no—
900C22⋊C4—1228no—
901C22⋊C4—1228no—
902C22⋊C4—1228no—
903C22⋊C4—2444no—
904C22⋊C4—2444no—
905C22⋊C4—2444no—
906C22⋊C4—2444no—
907C22⋊C4#11758198116yescomplemented
908C42—44no—
909C42—44no—
910C42—2444no—
911C23—22no—
912C23—22no—
913C23—22no—
914C23—22no—
915C23—22no—
916C23—22no—
917C23—22no—
918C23—22no—
919C23—22no—
920C23—22no—
921C23—22no—
922C23—22no—
923C23—22no—
924C23—22no—
925C23—22no—
926C23—22no—
927C23—22no—
928C23—22no—
929C23—41no—
930C23—41no—
931C23—41no—
932C23—41no—
933C23—41no—
934C23—41no—
935C23—41no—
936C23—41no—
937C23—41no—
938C23—41no—
939C23—41no—
940C23—41no—
941C23—41no—
942C23—41no—
943C23—41no—
944C23—41no—
945C23—614no—
946C23—1222no—
947C23—1222no—
948C23—1222no—
949C23—1222no—
950C23—1222no—
951C23—1222no—
952C23—1222no—
953C23—1222no—
954C23—1222no—
955C23—1222no—
956C23—1222no—
957C23—1222no—
958C23—1222no—
959C23—1222no—
960C23—1222no—
961C23—1222no—
962C23—1222no—
963C23—1222no—
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—
980C23C2×#1175819814yes—
981C23C22×C4×D6111yescharacteristic
982C23C2×D4×D6111yescharacteristic
983C23C22×C22⋊D6111yescharacteristic
984C23C22×D24411yescharacteristic
985C23#41×D6111yescharacteristic
986C23#41×D6111yescharacteristic
987C23C2×#1175822411yescharacteristic
988C23C2×#1175822211yescharacteristic
989C23C2×#1175822211yescharacteristic
990C23C2×#1175822211yescharacteristic
991C23C2×#1175822211yescharacteristic
992C23#1451982211yescharacteristic
993C23#1451982211yescharacteristic
994C23#1451982311yescharacteristic
995C23#1451982411yescharacteristic
996D4—24416no—
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—22no—
1022C2×C4—22no—
1023C2×C4—22no—
1024C2×C4—416no—
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—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—24416no—
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×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×C4C2×#1175819814yes—
1088C2×C4C2×#1175819814yes—
1089C2×C4#1451975914yescomplemented
1090C22—24no—
1091C22—24no—
1092C22—24no—
1093C22—42no—
1094C22—42no—
1095C22—42no—
1096C22—42no—
1097C22—42no—
1098C22—42no—
1099C22—42no—
1100C22—42no—
1101C22—42no—
1102C22—42no—
1103C22—42no—
1104C22—42no—
1105C22—1224no—
1106C22—1224no—
1107C22—1224no—
1108C22—2442no—
1109C22—2442no—
1110C22—2442no—
1111C22—2442no—
1112C22—2442no—
1113C22—2442no—
1114C22—2442no—
1115C22—2442no—
1116C22—2442no—
1117C22—2442no—
1118C22—2442no—
1119C22—2442no—
1120C22C22×#1175819811yescharacteristic
1121C22C4×D4×D6111yescharacteristic
1122C22C4×#1175822411yescharacteristic
1123C22C4×#1175822211yescharacteristic
1124C22C4×#1175822211yescharacteristic
1125C22#1684023411yescharacteristic
1126C22#1684024111yescharacteristic
1127C22C2×#1451975911yescharacteristic
1128C22#1684027111yescharacteristic
1129C22#1684027311yescharacteristic
1130C22#1684027311yescharacteristic
1131C22#1684029011yescharacteristic
1132C22#1684029411yescharacteristic
1133C22#1684031211yescharacteristic
1134C22#1684031211yescharacteristic
1135C22#1684035011yescharacteristic
1136C22#1684035411yescharacteristic
1137C22#1684036311yescharacteristic
1138C22#1684038311yescharacteristic
1139C22D4×C22⋊D6111yescharacteristic
1140C22D4×D24411yescharacteristic
1141C22#1684040011yescharacteristic
1142C22#1684040211yescharacteristic
1143C22#1684040611yescharacteristic
1144C22#1684040711yescharacteristic
1145C22#1684040711yescharacteristic
1146C22#1684041111yescharacteristic
1147C22#1684041611yescharacteristic
1148C22#1684041711yescharacteristic
1149C22#1684043811yescharacteristic
1150C22#1684044111yescharacteristic
1151C22#1684045111yescharacteristic
1152C22#1684045611yescharacteristic
1153C22#1684045811yescharacteristic
1154C22#1684049511yescharacteristic
1155C4—24no—
1156C4—24no—
1157C4—24no—
1158C4—42no—
1159C4—42no—
1160C4—42no—
1161C4—4881no—
1162C4—4881no—
1163C4—2442no—
1164C4—2442no—
1165C4—2442no—
1166C4—2442no—
1167C4—2442no—
1168C2—44no—
1169C2—2444no—
1170C2#2144830911yescharacteristic
1171C2C4×#1451975911yescharacteristic
1172C2#2144861111yescharacteristic
1173C2D4×#1175819811yescharacteristic
1174C2#2144864411yescharacteristic
1175C2#2144881211yescharacteristic
1176C2#2144895311yescharacteristic
1177C2#2144928111yescharacteristic
1178C2#2144933311yescharacteristic
1179C2#2144969611yescharacteristic
1180C2#2144972011yescharacteristic
1181C2#2144982511yescharacteristic
1182C2#2144990911yescharacteristic
1183C2#2145085811yescharacteristic
1184C2#2145091211yescharacteristic
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#14096
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C24 ◁ C2×C4×C22⋊C4

Complements

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

NH ≅ G/Ntype
2. C2×#16839655C2semidirect
4. C2×C4×#11758198C2semidirect
5. #21444088C2semidirect
6. #21444066C2semidirect
7. #21444065C2semidirect
9. #21444057C2semidirect
10. #21444054C2semidirect
11. #21444052C2semidirect
12. #21444049C2semidirect
13. #21444042C2semidirect
14. #21444040C2semidirect
15. C2×C4×C22⋊C4×C61C2semidirect
20. C2×#14519759C4semidirect
79. C22×C4×D61C2×C4semidirect
86. C2×C4⋊Dic61C2×C4semidirect
89. C2×#11758196C2×C4semidirect
112. C2×#11758198C2×C4semidirect
303. C22⋊C4×C61C22⋊C4semidirect
445. C2×C4×C61#123semidirect
580. C2×C4×C22⋊C4D61semidirect
650. C61#14096semidirect
907. C22⋊C4#11758198semidirect
1089. C2×C4#14519759semidirect

Maximal subgroups

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

subgroupindex
C22×#145197592
C2×#168396552
C2×#168396412
C2×C4×#117581982
#214440882
#214440662
#214440652
#214440582
#214440572
#214440542
#214440522
#214440492
#214440422
#214440402
C2×C4×C22⋊C4×C612
#1409661