Finite Group Databasebeta

← #29604469

Subgroups — #29604469

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×#14519758C211yesmaximal, characteristic
2C2×#16839650C211yesmaximal, characteristic, complemented
3C2×C22⋊C4×Dic61C211yesmaximal, characteristic, complemented
4C2×C4×C22⋊Dic61C211yesmaximal, characteristic, complemented
5#21444085C211yesmaximal, characteristic, complemented
6#21444066C211yesmaximal, characteristic, complemented
7#21444062C211yesmaximal, characteristic, complemented
8#21444060C211yesmaximal, characteristic
9#21444056C211yesmaximal, characteristic, complemented
10#21444050C211yesmaximal, characteristic, complemented
11#21444050C211yesmaximal, characteristic, complemented
12#21444047C211yesmaximal, characteristic, complemented
13#21444042C211yesmaximal, characteristic, complemented
14#21444041C211yesmaximal, characteristic, complemented
15C2×C61×#386C211yesmaximal, characteristic
16C24×Dic61C2211yescharacteristic
17C2×#14519758—24no—
18C2×#14519758—24no—
19C2×#14519758C418yescomplemented
20C22×#11758196C2211yescharacteristic
21C22×#11758196C2211yescharacteristic
22C22×#11758196C2211yescharacteristic
23C22×C22⋊Dic61C2211yescharacteristic
24C22×C22⋊Dic61C2211yescharacteristic
25C22×C22⋊Dic61C2211yescharacteristic
26C22×C22⋊Dic61C2211yescharacteristic
27C22×C22⋊Dic61C2211yescharacteristic
28C22×C22⋊Dic61C2211yescharacteristic
29C22×C22⋊Dic61C2211yescharacteristic
30C22×C4×Dic61C2211yescharacteristic
31C22×C4×Dic61C2211yescharacteristic
32C22×C4×Dic61C2211yescharacteristic
33#16839650—24no—
34C22⋊C4×Dic61—24no—
35C4×C22⋊Dic61—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
50C23×D4×C61C2211yescharacteristic
51C24×C4×C61C2211yescharacteristic
52C22×C22⋊C4×C61C2211yescharacteristic
53C22×C22⋊C4×C61C2211yescharacteristic
54C22×C22⋊C4×C61C2211yescharacteristic
55C61×#386—24no—
56C2×#95×C61C2211yescharacteristic
57C2×#95×C61C2211yescharacteristic
58C23×Dic61—22no—
59C23×Dic61—22no—
60C23×Dic61—22no—
61C23×Dic61—22no—
62C23×Dic61—41no—
63C23×Dic61—41no—
64C23×Dic61C2×C414yescomplemented
65C23×Dic61C2311yescharacteristic
66C23×Dic61C2311yescharacteristic
67C23×Dic61C2311yescharacteristic
68C23×Dic61C2311yescharacteristic
69C23×Dic61C2311yescharacteristic
70C23×Dic61C2311yescharacteristic
71C23×Dic61C2311yescharacteristic
72C23×Dic61C2311yescharacteristic
73#14519758—232no—
74C2×#11758196—22no—
75C2×#11758196—22no—
76C2×#11758196—22no—
77C2×#11758196—22no—
78C2×#11758196—22no—
79C2×#11758196—22no—
80C2×#11758196—41no—
81C2×#11758196C2×C414yescomplemented
82C2×#11758196C2×C414yescomplemented
83C2×C22⋊Dic61—22no—
84C2×C22⋊Dic61—22no—
85C2×C22⋊Dic61—22no—
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—22no—
93C2×C22⋊Dic61—22no—
94C2×C22⋊Dic61—22no—
95C2×C22⋊Dic61—22no—
96C2×C22⋊Dic61—22no—
97C2×C22⋊Dic61—41no—
98C2×C22⋊Dic61—41no—
99C2×C22⋊Dic61C2×C414yes—
100C2×C22⋊Dic61C2×C414yes—
101C2×C22⋊Dic61C2×C414yescomplemented
102C2×C22⋊Dic61D414yes—
103C2×C22⋊Dic61D414yes—
104C2×C4×Dic61—22no—
105C2×C4×Dic61—22no—
106C2×C4×Dic61—22no—
107C2×C4×Dic61—22no—
108C2×C4×Dic61—22no—
109C2×C4×Dic61—22no—
110C2×C4×Dic61—41no—
111C2×C4×Dic61—41no—
112C2×C4×Dic61—41no—
113#14519684—22no—
114#14519684—22no—
115#14519684—22no—
116#14519684—22no—
117#14519684—22no—
118#14519684—22no—
119#14519684—22no—
120#14519684—22no—
121#14519684—22no—
122#14519684—22no—
123#14519684—41no—
124#14519684—41no—
125#14519684—41no—
126#14519684—41no—
127C25×C61C2311yescharacteristic
128C25×C61C2311yescharacteristic
129C22×D4×C61—22no—
130C22×D4×C61—22no—
131C22×D4×C61—22no—
132C22×D4×C61—22no—
133C22×D4×C61—41no—
134C22×D4×C61—41no—
135C22×D4×C61C2×C414yes—
136C23×C4×C61—22no—
137C23×C4×C61—22no—
138C23×C4×C61—22no—
139C23×C4×C61—22no—
140C23×C4×C61—22no—
141C23×C4×C61—41no—
142C23×C4×C61—41no—
143C23×C4×C61C2311yescharacteristic
144C23×C4×C61C2311yescharacteristic
145C23×C4×C61C2311yescharacteristic
146C23×C4×C61C2311yescharacteristic
147C23×C4×C61C2311yescharacteristic
148C2×C22⋊C4×C61—22no—
149C2×C22⋊C4×C61—22no—
150C2×C22⋊C4×C61—22no—
151C2×C22⋊C4×C61—22no—
152C2×C22⋊C4×C61—22no—
153C2×C22⋊C4×C61—22no—
154C2×C22⋊C4×C61—41no—
155C2×C22⋊C4×C61—41no—
156C2×C22⋊C4×C61D414yes—
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×C61—21no—
172C24×C61—21no—
173C24×C61—21no—
174C24×C61—21no—
175C24×C61—21no—
176C24×C61—21no—
177C24×C61—21no—
178C24×C61—21no—
179C24×C61—21no—
180C24×C61—21no—
181C24×C61—21no—
182C24×C61—21no—
183C24×C61C22×C412yes—
184C24×C61C22×C412yes—
185C24×C61C2×D412yes—
186C24×C61C2×D412yes—
187C24×C61C2×D412yes—
188C24×C61#4112yes—
189C24×C61C2411yescharacteristic
190C2×D4×C61—28no—
191C2×D4×C61—28no—
192C2×D4×C61—44no—
193C2×D4×C61—44no—
194C2×D4×C61—44no—
195C2×D4×C61—44no—
196C2×D4×C61—44no—
197C22×C4×C61—21no—
198C22×C4×C61—21no—
199C22×C4×C61—21no—
200C22×C4×C61—21no—
201C22×C4×C61—28no—
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—44no—
228C22×C4×C61—44no—
229C22×C4×C61—44no—
230C22×C4×C61—44no—
231C22×C4×C61—44no—
232C22×C4×C61—44no—
233C22×C4×C61C22×C412yes—
234C22×C4×C61C2×D412yes—
235C22×C4×C61C2×D412yes—
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—28no—
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—28no—
279C22×Dic61—21no—
280C22×Dic61—21no—
281C22×Dic61—21no—
282C22×Dic61—21no—
283C22×Dic61—21no—
284C22×Dic61—21no—
285C22×Dic61—21no—
286C22×Dic61—44no—
287C22×Dic61—44no—
288C22×Dic61—44no—
289C22×Dic61—44no—
290C22×Dic61—44no—
291C22×Dic61C22×C412yes—
292C22×Dic61C22×C412yes—
293C22×Dic61C22×C412yes—
294C22×Dic61C22×C412yes—
295C22×Dic61C2×D412yes—
296C22×Dic61C2×D412yes—
297C22×Dic61C2×D412yes—
298C22×Dic61C2×D412yes—
299C22×Dic61#4112yes—
300C22×Dic61#4112yes—
301C22×Dic61#4112yes—
302C22⋊C4×C61—28no—
303C22⋊C4×C61—44no—
304C22⋊C4×C61—44no—
305C22⋊Dic61—28no—
306C22⋊Dic61—28no—
307C22⋊Dic61—28no—
308C22⋊Dic61—28no—
309C22⋊Dic61—44no—
310C22⋊Dic61—44no—
311C22⋊Dic61C22⋊C4116yescomplemented
312#11758196—28no—
313#11758196—28no—
314#11758196—44no—
315C4×Dic61—44no—
316C4×Dic61—44no—
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—22no—
337C23×C61—22no—
338C23×C61—22no—
339C23×C61—22no—
340C23×C61—22no—
341C23×C61—22no—
342C23×C61—22no—
343C23×C61—22no—
344C23×C61—22no—
345C23×C61—22no—
346C23×C61—22no—
347C23×C61—22no—
348C23×C61—22no—
349C23×C61—22no—
350C23×C61—22no—
351C23×C61—22no—
352C23×C61—22no—
353C23×C61—22no—
354C23×C61—41no—
355C23×C61—41no—
356C23×C61—41no—
357C23×C61—41no—
358C23×C61—41no—
359C23×C61—41no—
360C23×C61—41no—
361C23×C61—41no—
362C23×C61—41no—
363C23×C61—41no—
364C23×C61—41no—
365C23×C61—41no—
366C23×C61—41no—
367C23×C61—41no—
368C23×C61—41no—
369C23×C61—41no—
370C23×C61—41no—
371C23×C61—41no—
372C23×C61—41no—
373C23×C61—41no—
374C23×C61—41no—
375C23×C61—41no—
376C23×C61—41no—
377C23×C61—41no—
378C23×C61—41no—
379C23×C61—41no—
380C23×C61—41no—
381C23×C61—41no—
382C23×C61—41no—
383C23×C61—41no—
384C23×C61—41no—
385C23×C61—41no—
386C23×C61C2×C22⋊C414yes—
387C23×C61C4×D414yes—
388C23×C61C23×C411yescharacteristic
389C23×C61C22×D411yescharacteristic
390C23×C61C22×D411yescharacteristic
391C23×C61C22×D411yescharacteristic
392C23×C61C2×#4111yescharacteristic
393C23×C61C2×#4111yescharacteristic
394C23×C61C2×#4111yescharacteristic
395C23×C61C2×#4111yescharacteristic
396C23×C61C2×#4111yescharacteristic
397C23×C61C2×#4111yescharacteristic
398C23×C61C2×#4111yescharacteristic
399C23×C61H(5,𝔽2)11yescharacteristic
400C23×C61H(5,𝔽2)11yescharacteristic
401C23×C61H(5,𝔽2)11yescharacteristic
402C23×C612−1+411yescharacteristic
403D4×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—416no—
420C2×C4×C61—41no—
421C2×C4×C61—41no—
422C2×C4×C61—41no—
423C2×C4×C61—41no—
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#12314yescomplemented
440C2×Dic61—22no—
441C2×Dic61—22no—
442C2×Dic61—22no—
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—22no—
465C2×Dic61—22no—
466C2×Dic61—22no—
467C2×Dic61—416no—
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×Dic61C2×C22⋊C414yes—
496C2×Dic61C2×C22⋊C414yes—
497#14096—611nomaximal, Sylow
498C22×C61—24no—
499C22×C61—24no—
500C22×C61—24no—
501C22×C61—24no—
502C22×C61—24no—
503C22×C61—24no—
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×C61—42no—
514C22×C61—42no—
515C22×C61—42no—
516C22×C61—42no—
517C22×C61—42no—
518C22×C61—42no—
519C22×C61—42no—
520C22×C61—42no—
521C22×C61—42no—
522C22×C61—42no—
523C22×C61—42no—
524C22×C61—42no—
525C22×C61—42no—
526C22×C61—42no—
527C22×C61—42no—
528C22×C61C22×C22⋊C411yescharacteristic
529C22×C61C2×C4×D411yescharacteristic
530C22×C61C4×#4111yescharacteristic
531C22×C61C4×#4111yescharacteristic
532C22×C61C4×#4111yescharacteristic
533C22×C61#51811yescharacteristic
534C22×C61#52011yescharacteristic
535C22×C61C2×#12311yescharacteristic
536C22×C61#52511yescharacteristic
537C22×C61#52511yescharacteristic
538C22×C61#52511yescharacteristic
539C22×C61#52911yescharacteristic
540C22×C61#52911yescharacteristic
541C22×C61#53211yescharacteristic
542C22×C61#53211yescharacteristic
543C22×C61#53811yescharacteristic
544C22×C61#53911yescharacteristic
545C22×C61#54011yescharacteristic
546C22×C61#54211yescharacteristic
547C22×C61D4211yescharacteristic
548C22×C61D4211yescharacteristic
549C22×C61#54611yescharacteristic
550C22×C61#54611yescharacteristic
551C22×C61#54611yescharacteristic
552C22×C61#54611yescharacteristic
553C22×C61#54611yescharacteristic
554C22×C61#54711yescharacteristic
555C22×C61#54711yescharacteristic
556C22×C61#54711yescharacteristic
557C22×C61#55111yescharacteristic
558C22×C61#55111yescharacteristic
559C22×C61#55211yescharacteristic
560C22×C61#55311yescharacteristic
561C22×C61#55311yescharacteristic
562C22×C61#55911yescharacteristic
563C4×C61—24no—
564C4×C61—42no—
565C4×C61—42no—
566C4×C61—42no—
567C4×C61—81no—
568Dic61—24no—
569Dic61—24no—
570Dic61—42no—
571Dic61—42no—
572Dic61—42no—
573Dic61—42no—
574Dic61—42no—
575Dic61—81no—
576C22×#123—611no—
577C2×#388—611no—
578C2×#386D6111yescharacteristic
579C2×C4×C22⋊C4—611no—
580C2×C4×C22⋊C4—611no—
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—44no—
593C2×C61#229711yescharacteristic
594C2×C61C4×#12311yescharacteristic
595C2×C61#233511yescharacteristic
596C2×C61D4×C22⋊C411yescharacteristic
597C2×C61#233911yescharacteristic
598C2×C61#235911yescharacteristic
599C2×C61#237411yescharacteristic
600C2×C61#241811yescharacteristic
601C2×C61#242211yescharacteristic
602C2×C61#245511yescharacteristic
603C2×C61#245711yescharacteristic
604C2×C61#246411yescharacteristic
605C2×C61#247011yescharacteristic
606C2×C61#255311yescharacteristic
607C2×C61#255711yescharacteristic
608C23×D4C2×D6111yescharacteristic
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⋊C4C2×D6111yescharacteristic
625C22×C22⋊C4C2×D6111yescharacteristic
626C22×C22⋊C4C2×D6111yescharacteristic
627C22×C42—611no—
628C22×C42—611no—
629C22×C42—611no—
630#388—1224no—
631#386—24no—
632C4×C22⋊C4—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×#95—611no—
647C2×#95—611no—
648C2×#95C2×D6111yescharacteristic
649C2×#95C2×D6111yescharacteristic
650C61#1409611yescharacteristic, complemented, Sylow
651C25C22×D6111yescharacteristic
652C25C22×D6111yescharacteristic
653C22×D4—22no—
654C22×D4—22no—
655C22×D4—22no—
656C22×D4—22no—
657C22×D4—41no—
658C22×D4—41no—
659C22×D4C4×D6114yes—
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—611no—
673C23×C4—611no—
674C23×C4—614no—
675C23×C4—611no—
676C23×C4—1222no—
677C23×C4—1222no—
678C23×C4—1222no—
679C23×C4—1222no—
680C23×C4—2441no—
681C23×C4—2441no—
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—22no—
701C2×C22⋊C4—22no—
702C2×C22⋊C4—22no—
703C2×C22⋊C4—41no—
704C2×C22⋊C4—41no—
705C2×C22⋊C4—614no—
706C2×C22⋊C4—614no—
707C2×C22⋊C4—614no—
708C2×C22⋊C4—614no—
709C2×C22⋊C4—614no—
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—1222no—
721C2×C22⋊C4—1222no—
722C2×C22⋊C4—1222no—
723C2×C22⋊C4—1222no—
724C2×C22⋊C4—2441no—
725C2×C22⋊C4—2441no—
726C2×C22⋊C4C22⋊D6114yes—
727C2×C42—1222no—
728C2×C42—1222no—
729C2×C42—1222no—
730C2×C42—1222no—
731C2×C42—1222no—
732C2×C42—1222no—
733C2×C42—2441no—
734C2×C42—2441no—
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—21no—
765C24—21no—
766C24—21no—
767C24—21no—
768C24—21no—
769C24—21no—
770C24—21no—
771C24—21no—
772C24—21no—
773C24—21no—
774C24—21no—
775C24—21no—
776C24C2×C4×D6112yes—
777C24C2×C4×D6112yes—
778C24#1175822212yes—
779C24D4×D6112yes—
780C24D4×D6112yes—
781C24C2×C22⋊D6112yes—
782C24C23×D6111yescharacteristic
783C2×D4—28no—
784C2×D4—28no—
785C2×D4—44no—
786C2×D4—44no—
787C2×D4—44no—
788C2×D4—44no—
789C2×D4—44no—
790C22×C4—21no—
791C22×C4—21no—
792C22×C4—21no—
793C22×C4—21no—
794C22×C4—28no—
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—21no—
820C22×C4—44no—
821C22×C4—44no—
822C22×C4—44no—
823C22×C4—44no—
824C22×C4—44no—
825C22×C4—44no—
826C22×C4—612no—
827C22×C4—612no—
828C22×C4—612no—
829C22×C4—612no—
830C22×C4—612no—
831C22×C4—612no—
832C22×C4—612no—
833C22×C4—612no—
834C22×C4—612no—
835C22×C4—612no—
836C22×C4—612no—
837C22×C4—1228no—
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×C4—1221no—
874C22×C4—1221no—
875C22×C4—1221no—
876C22×C4—1228no—
877C22×C4—1221no—
878C22×C4—1221no—
879C22×C4—1221no—
880C22×C4—1221no—
881C22×C4—1221no—
882C22×C4—1221no—
883C22×C4—1221no—
884C22×C4—2444no—
885C22×C4—2444no—
886C22×C4—2444no—
887C22×C4—2444no—
888C22×C4—2444no—
889C22×C4C2×C4×D6112yes—
890C22×C4#1175822412yes—
891C22×C4#1175822412yes—
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—44no—
900C22⋊C4—44no—
901C22⋊C4—6116no—
902C22⋊C4—1228no—
903C22⋊C4—1228no—
904C22⋊C4—1228no—
905C22⋊C4—1228no—
906C22⋊C4—2444no—
907C22⋊C4—2444no—
908C42—2444no—
909C42—2444no—
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—22no—
930C23—22no—
931C23—22no—
932C23—22no—
933C23—22no—
934C23—22no—
935C23—22no—
936C23—22no—
937C23—22no—
938C23—22no—
939C23—22no—
940C23—22no—
941C23—22no—
942C23—22no—
943C23—22no—
944C23—22no—
945C23—22no—
946C23—22no—
947C23—41no—
948C23—41no—
949C23—41no—
950C23—41no—
951C23—41no—
952C23—41no—
953C23—41no—
954C23—41no—
955C23—41no—
956C23—41no—
957C23—41no—
958C23—41no—
959C23—41no—
960C23—41no—
961C23—41no—
962C23—41no—
963C23—41no—
964C23—41no—
965C23—41no—
966C23—41no—
967C23—41no—
968C23—41no—
969C23—41no—
970C23—41no—
971C23—41no—
972C23—41no—
973C23—41no—
974C23—41no—
975C23—41no—
976C23—41no—
977C23—41no—
978C23—41no—
979C23C22⋊C4×D6114yes—
980C23C4×C22⋊D6114yes—
981C23C22×C4×D6111yescharacteristic
982C23C2×D4×D6111yescharacteristic
983C23C2×D4×D6111yescharacteristic
984C23C22×C22⋊D6111yescharacteristic
985C23#41×D6111yescharacteristic
986C23#41×D6111yescharacteristic
987C23#41×D6111yescharacteristic
988C23C2×#1175822411yescharacteristic
989C23C2×#1175822411yescharacteristic
990C23C2×#1175822411yescharacteristic
991C23C2×#1175822211yescharacteristic
992C23#1451982211yescharacteristic
993C23#1451982211yescharacteristic
994C23#1451982211yescharacteristic
995C23#1451982411yescharacteristic
996D4—416no—
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—41no—
1030C2×C4—41no—
1031C2×C4—41no—
1032C2×C4—614no—
1033C2×C4—614no—
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—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—24416no—
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×C4—2441no—
1088C2×C4—2441no—
1089C2×C4#1451975814yescomplemented
1090C22—24no—
1091C22—24no—
1092C22—24no—
1093C22—24no—
1094C22—24no—
1095C22—24no—
1096C22—42no—
1097C22—42no—
1098C22—42no—
1099C22—42no—
1100C22—42no—
1101C22—42no—
1102C22—42no—
1103C22—42no—
1104C22—42no—
1105C22—42no—
1106C22—42no—
1107C22—42no—
1108C22—42no—
1109C22—42no—
1110C22—42no—
1111C22—42no—
1112C22—42no—
1113C22—42no—
1114C22—42no—
1115C22—42no—
1116C22—42no—
1117C22—42no—
1118C22—42no—
1119C22—42no—
1120C22C2×C22⋊C4×D6111yescharacteristic
1121C22C2×C4×C22⋊D6111yescharacteristic
1122C22C4×#1175822411yescharacteristic
1123C22C4×#1175822411yescharacteristic
1124C22C4×#1175822411yescharacteristic
1125C22#1684023511yescharacteristic
1126C22#1684024111yescharacteristic
1127C22C2×#1451975811yescharacteristic
1128C22#1684026811yescharacteristic
1129C22#1684026911yescharacteristic
1130C22#1684027011yescharacteristic
1131C22#1684029211yescharacteristic
1132C22#1684029211yescharacteristic
1133C22#1684030711yescharacteristic
1134C22#1684030711yescharacteristic
1135C22#1684034711yescharacteristic
1136C22#1684035511yescharacteristic
1137C22#1684036211yescharacteristic
1138C22#1684037911yescharacteristic
1139C22D4×C22⋊D6111yescharacteristic
1140C22D4×C22⋊D6111yescharacteristic
1141C22#1684039911yescharacteristic
1142C22#1684040111yescharacteristic
1143C22#1684040211yescharacteristic
1144C22#1684040211yescharacteristic
1145C22#1684040611yescharacteristic
1146C22#1684041011yescharacteristic
1147C22#1684041111yescharacteristic
1148C22#1684041211yescharacteristic
1149C22#1684044111yescharacteristic
1150C22#1684044311yescharacteristic
1151C22#1684045211yescharacteristic
1152C22#1684045911yescharacteristic
1153C22#1684045911yescharacteristic
1154C22#1684049611yescharacteristic
1155C4—24no—
1156C4—42no—
1157C4—42no—
1158C4—42no—
1159C4—81no—
1160C4—1224no—
1161C4—1224no—
1162C4—4881no—
1163C4—2442no—
1164C4—2442no—
1165C4—2442no—
1166C4—2442no—
1167C4—2442no—
1168C2—44no—
1169C2—44no—
1170C2#2144830411yescharacteristic
1171C2C4×#1451975811yescharacteristic
1172C2#2144861011yescharacteristic
1173C2C22⋊C4×C22⋊D6111yescharacteristic
1174C2#2144864511yescharacteristic
1175C2#2144880511yescharacteristic
1176C2#2144895211yescharacteristic
1177C2#2144927711yescharacteristic
1178C2#2144932911yescharacteristic
1179C2#2144969811yescharacteristic
1180C2#2144972311yescharacteristic
1181C2#2144982111yescharacteristic
1182C2#2144991211yescharacteristic
1183C2#2145086111yescharacteristic
1184C2#2145091511yescharacteristic
subgroupG/H
center, FrattiniC24C23×D61
commutatorC23×C61C23×C4
FittingC2×C61×#386C2
socle, cosocleC24×C61C24
prime radicalC23×D4×C61C22
hypercenterC2×#386D61
hypocenterC61#14096
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C24 ◁ C2×#386

Complements

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

NH ≅ G/Ntype
2. C2×#16839650C2semidirect
3. C2×C22⋊C4×Dic61C2semidirect
4. C2×C4×C22⋊Dic61C2semidirect
5. #21444085C2semidirect
6. #21444066C2semidirect
7. #21444062C2semidirect
9. #21444056C2semidirect
10. #21444050C2semidirect
11. #21444050C2semidirect
12. #21444047C2semidirect
13. #21444042C2semidirect
14. #21444041C2semidirect
19. C2×#14519758C4semidirect
64. C23×Dic61C2×C4semidirect
81. C2×#11758196C2×C4semidirect
82. C2×#11758196C2×C4semidirect
101. C2×C22⋊Dic61C2×C4semidirect
311. C22⋊Dic61C22⋊C4semidirect
439. C2×C4×C61#123semidirect
650. C61#14096semidirect
1089. C2×C4#14519758semidirect

Maximal subgroups

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

subgroupindex
C22×#145197582
C2×#168396502
C2×C22⋊C4×Dic612
C2×C4×C22⋊Dic612
#214440852
#214440662
#214440622
#214440602
#214440562
#214440502
#214440472
#214440422
#214440412
C2×C61×#3862
#1409661