Finite Group Databasebeta

← #29602055

Subgroups — #29602055

Order 15616.

2330 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×#14519737C211yesmaximal, characteristic
2C2×#16839655C211yesmaximal, characteristic, complemented
3C2×#16839623C211yesmaximal, characteristic, complemented
4C2×C4×#11758198C211yesmaximal, characteristic, complemented
5#21444065C211yesmaximal, characteristic, complemented
6#21444061C211yesmaximal, characteristic, complemented
7#21444058C211yesmaximal, characteristic
8#21444058C211yesmaximal, characteristic
9#21444054C211yesmaximal, characteristic, complemented
10#21444052C211yesmaximal, characteristic, complemented
11#21444048C211yesmaximal, characteristic, complemented
12#21444043C211yesmaximal, characteristic, complemented
13#21444041C211yesmaximal, characteristic, complemented
14#21444040C211yesmaximal, characteristic, complemented
15C2×C61×#388C211yesmaximal, characteristic, complemented
16C23×C22⋊D61C2211yescharacteristic
17C24×Dic61C2211yescharacteristic
18C23×C4×D61C2211yescharacteristic
19C2×#14519737—24no—
20C2×#14519737—24no—
21C2×#14519737C418yescomplemented
22C22×C4⋊Dic61C2211yescharacteristic
23C22×#11758196C2211yescharacteristic
24C22×C22⋊Dic61C2211yescharacteristic
25C22×C22⋊Dic61C2211yescharacteristic
26C22×#11758198C2211yescharacteristic
27C22×#11758198C2211yescharacteristic
28C22×#11758198C2211yescharacteristic
29C22×#11758198C2211yescharacteristic
30C22×#11758198C2211yescharacteristic
31C22×C4×Dic61C2211yescharacteristic
32C22×C4×Dic61C2211yescharacteristic
33#16839655—24no—
34#16839623—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
50C22×C4⋊C4×C61C2211yescharacteristic
51C22×C22⋊C4×C61C2211yescharacteristic
52C22×C22⋊C4×C61C2211yescharacteristic
53C22×C22⋊C4×C61C2211yescharacteristic
54C22×C42×C61C2211yescharacteristic
55C61×#388—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—22no—
64C22×C22⋊D61—22no—
65C22×C22⋊D61C2×C414yes—
66C23×Dic61—22no—
67C23×Dic61—22no—
68C23×Dic61—22no—
69C23×Dic61—22no—
70C23×Dic61—41no—
71C23×Dic61—41no—
72C23×Dic61C2×C414yes—
73C23×Dic61C2311yescharacteristic
74C23×Dic61C2311yescharacteristic
75C23×Dic61C2311yescharacteristic
76C23×Dic61C2311yescharacteristic
77C23×Dic61C2311yescharacteristic
78C23×Dic61C2311yescharacteristic
79C23×Dic61C2311yescharacteristic
80C22×C4×D61—22no—
81C22×C4×D61—22no—
82C22×C4×D61—22no—
83C22×C4×D61—22no—
84C22×C4×D61—41no—
85C22×C4×D61—41no—
86C22×C4×D61C2×C414yes—
87#14519737—232no—
88C2×C4⋊Dic61—22no—
89C2×C4⋊Dic61—22no—
90C2×C4⋊Dic61—41no—
91C2×#11758196—22no—
92C2×#11758196—22no—
93C2×#11758196C2×C414yes—
94C2×C22⋊Dic61—22no—
95C2×C22⋊Dic61—22no—
96C2×C22⋊Dic61—22no—
97C2×C22⋊Dic61—22no—
98C2×C22⋊Dic61—41no—
99C2×C22⋊Dic61—41no—
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×#11758198C2×C414yes—
115C2×C4×Dic61—22no—
116C2×C4×Dic61—22no—
117C2×C4×Dic61—22no—
118C2×C4×Dic61—22no—
119C2×C4×Dic61—41no—
120C2×C4×Dic61C2×C414yes—
121#14519684—22no—
122#14519684—22no—
123#14519684—22no—
124#14519684—22no—
125#14519684—22no—
126#14519684—22no—
127#14519684—22no—
128#14519684—22no—
129#14519684—22no—
130#14519684—22no—
131#14519684—22no—
132#14519684—41no—
133#14519684—41no—
134#14519684D414yescomplemented
135C25×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—41no—
145C2×C22⋊C4×C61—22no—
146C2×C22⋊C4×C61—22no—
147C2×C22⋊C4×C61—22no—
148C2×C22⋊C4×C61—22no—
149C2×C22⋊C4×C61—41no—
150C2×C22⋊C4×C61—41no—
151C2×C22⋊C4×C61C2×C414yes—
152C2×C22⋊C4×C61D414yes—
153C2×C22⋊C4×C61D414yes—
154C2×C42×C61—22no—
155C2×C42×C61—22no—
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×D61#4112yes—
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×C61C2×D412yes—
227C22×C4×C61C2×D412yes—
228C22×C4×C61C2×D412yes—
229C22×C4×C61C2×D412yes—
230C22×C4×C61C2×D412yes—
231C22×C4×C61#4112yes—
232C2×C22⋊D61—28no—
233C2×C22⋊D61—28no—
234C2×C22⋊D61—28no—
235C2×C22⋊D61—28no—
236C2×C22⋊D61—28no—
237C2×C22⋊D61—28no—
238C2×C22⋊D61—28no—
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—28no—
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—44no—
282C22×Dic61—44no—
283C22×Dic61—44no—
284C22×Dic61—44no—
285C22×Dic61—44no—
286C22×Dic61C22×C412yes—
287C22×Dic61C22×C412yes—
288C22×Dic61C22×C412yes—
289C22×Dic61C2×D412yes—
290C22×Dic61C2×D412yes—
291C22×Dic61#4112yes—
292C22×Dic61#4112yes—
293C22×Dic61#4112yes—
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—
302C4⋊C4×C61—44no—
303C22⋊C4×C61—44no—
304C22⋊C4×C61—44no—
305C22⋊C4×C61C22⋊C4116yescomplemented
306C42×C61—44no—
307C22⋊Dic61—44no—
308C22⋊Dic61—44no—
309#11758198—28no—
310#11758198—28no—
311#11758198—28no—
312#11758198—44no—
313#11758198—44no—
314C4⋊Dic61—44no—
315#11758196—28no—
316C4×Dic61—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×D61#11714yes—
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—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—41no—
440C2×C4×C61—41no—
441C2×C4×C61—41no—
442C2×C4×C61—41no—
443C2×C4×C61C2×C22⋊C414yes—
444C2×C4×C61C2×C22⋊C414yes—
445C22⋊D61—232no—
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#11714yes—
495C2×Dic61C4×D414yes—
496C4×D61—416no—
497#13886—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×#11711yescharacteristic
515C22×C61C2×#11711yescharacteristic
516C22×C61C2×C4×D411yescharacteristic
517C22×C61C4×#4111yescharacteristic
518C22×C61#51811yescharacteristic
519C22×C61#52011yescharacteristic
520C22×C61#52511yescharacteristic
521C22×C61#52511yescharacteristic
522C22×C61#52511yescharacteristic
523C22×C61#52511yescharacteristic
524C22×C61#52511yescharacteristic
525C22×C61#52511yescharacteristic
526C22×C61#52911yescharacteristic
527C22×C61#52911yescharacteristic
528C22×C61#53811yescharacteristic
529C22×C61#53811yescharacteristic
530C22×C61#53911yescharacteristic
531C22×C61#53911yescharacteristic
532C22×C61D4211yescharacteristic
533C22×C61D4211yescharacteristic
534C22×C61#54611yescharacteristic
535C22×C61#54611yescharacteristic
536C22×C61#54611yescharacteristic
537C22×C61#54611yescharacteristic
538C22×C61#54711yescharacteristic
539C22×C61#54711yescharacteristic
540C22×C61#54711yescharacteristic
541C22×C61#55011yescharacteristic
542C22×C61#55311yescharacteristic
543C22×C61#55311yescharacteristic
544C22×C61#55511yescharacteristic
545C22×C61#55611yescharacteristic
546C22×C61#55911yescharacteristic
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—42no—
566C4×C61—42no—
567C4×C61—81no—
568C4×C61—81no—
569Dic61—24no—
570Dic61—24no—
571Dic61—42no—
572Dic61—42no—
573Dic61—42no—
574Dic61—81no—
575Dic61—81no—
576C22×C4×D4—611no—
577C2×#388—611no—
578C2×#388D6111yescharacteristic, complemented
579C2×#381—611no—
580C2×C4×C22⋊C4—611no—
581#1439—611no—
582#1439—611no—
583#1438—611no—
584#1438—611no—
585#1436—611no—
586#1436—611no—
587C4⋊#95—611no—
588#1434—611no—
589C22⋊#95—611no—
590C22⋊#95—611no—
591C2×C61—44no—
592C2×C61#228011yescharacteristic
593C2×C61#229011yescharacteristic
594C2×C61#231811yescharacteristic
595C2×C61D4×C22⋊C411yescharacteristic
596C2×C61#233911yescharacteristic
597C2×C61#235411yescharacteristic
598C2×C61#235711yescharacteristic
599C2×C61#245511yescharacteristic
600C2×C61#245511yescharacteristic
601C2×C61#245611yescharacteristic
602C2×C61#245611yescharacteristic
603C2×C61#245911yescharacteristic
604C2×C61#245911yescharacteristic
605C2×C61#246611yescharacteristic
606C2×C61#246611yescharacteristic
607D61—44no—
608C23×D4—611no—
609C24×C4—611no—
610C24×C4—611no—
611C2×C4×D4—618no—
612C2×C4×D4—1224no—
613C2×C4×D4—1224no—
614C22×C4⋊C4—611no—
615C22×C4⋊C4—611no—
616C22×C4⋊C4C2×D6111yescharacteristic
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×C42C2×D6111yescharacteristic
630#388—24no—
631#388—1224no—
632#381—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#1388611yescharacteristic, complemented, Sylow
651C25—611no—
652C25C22×D6111yescharacteristic
653C22×D4—614no—
654C22×D4—1222no—
655C22×D4—1222no—
656C22×D4—1222no—
657C22×D4—1222no—
658C22×D4—1222no—
659C22×D4—1222no—
660C23×C4—611no—
661C23×C4—611no—
662C23×C4—611no—
663C23×C4—611no—
664C23×C4—611no—
665C23×C4—614no—
666C23×C4—614no—
667C23×C4—611no—
668C23×C4—611no—
669C23×C4—1222no—
670C23×C4—1222no—
671C23×C4—1222no—
672C23×C4—1222no—
673C23×C4—1222no—
674C23×C4—1222no—
675C23×C4—1222no—
676C23×C4—1222no—
677C23×C4—2441no—
678C23×C4—2441no—
679C23×C4—2441no—
680C23×C4—2441no—
681C23×C4C22×D6111yescharacteristic
682C23×C4C22×D6111yescharacteristic
683C23×C4C22×D6111yescharacteristic
684C23×C4C22×D6111yescharacteristic
685C23×C4C22×D6111yescharacteristic
686C23×C4C22×D6111yescharacteristic
687C4×D4—12232no—
688C2×C4⋊C4—22no—
689C2×C4⋊C4—22no—
690C2×C4⋊C4—41no—
691C2×C4⋊C4—614no—
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—41no—
702C2×C22⋊C4—41no—
703C2×C22⋊C4—614no—
704C2×C22⋊C4—1222no—
705C2×C22⋊C4—1222no—
706C2×C22⋊C4—1222no—
707C2×C22⋊C4—1222no—
708C2×C22⋊C4—1222no—
709C2×C22⋊C4—1222no—
710C2×C22⋊C4—1222no—
711C2×C22⋊C4—1222no—
712C2×C22⋊C4—1222no—
713C2×C22⋊C4—1222no—
714C2×C22⋊C4—1222no—
715C2×C22⋊C4—1222no—
716C2×C22⋊C4—1222no—
717C2×C22⋊C4—1222no—
718C2×C22⋊C4—2441no—
719C2×C22⋊C4—2441no—
720C2×C22⋊C4—2441no—
721C2×C22⋊C4—2441no—
722C2×C22⋊C4—2441no—
723C2×C22⋊C4—2441no—
724C2×C22⋊C4C4×D6114yes—
725C2×C22⋊C4D24414yes—
726C2×C22⋊C4C22⋊D6114yes—
727C2×C42—22no—
728C2×C42—22no—
729C2×C42—41no—
730C2×C42—614no—
731C2×C42—1222no—
732C2×C42—1222no—
733C2×C42—1222no—
734C2×C42—1222no—
735C2×C42—2441no—
736#95—22no—
737#95—22no—
738#95—614no—
739#95—1222no—
740#95—1222no—
741#95—1222no—
742#95—1222no—
743#95—1222no—
744#95—1222no—
745#95—1222no—
746#95—1222no—
747#95—1222no—
748#95—1222no—
749#95—1222no—
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—1228no—
786C2×D4—1228no—
787C2×D4—1228no—
788C2×D4—1228no—
789C2×D4—1228no—
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—21no—
820C22×C4—21no—
821C22×C4—21no—
822C22×C4—21no—
823C22×C4—21no—
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—1228no—
834C22×C4—1228no—
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—1228no—
862C22×C4—1228no—
863C22×C4—1221no—
864C22×C4—1221no—
865C22×C4—1221no—
866C22×C4—1221no—
867C22×C4—1221no—
868C22×C4—1221no—
869C22×C4—1221no—
870C22×C4—1221no—
871C22×C4—1221no—
872C22×C4—1221no—
873C22×C4—1221no—
874C22×C4—1221no—
875C22×C4—1221no—
876C22×C4—1221no—
877C22×C4—2444no—
878C22×C4—2444no—
879C22×C4—2444no—
880C22×C4—2444no—
881C22×C4—2444no—
882C22×C4—2444no—
883C22×C4—2444no—
884C22×C4—2444no—
885C22×C4—2444no—
886C22×C4—2444no—
887C22×C4C2×C4×D6112yes—
888C22×C4C2×C4×D6112yes—
889C22×C4C2×D24412yes—
890C22×C4C2×D24412yes—
891C22×C4D4×D6112yes—
892C22×C4#1175822412yes—
893C22×C4C2×C22⋊D6112yes—
894C22×C4C2×C22⋊D6112yes—
895C4⋊C4—44no—
896C4⋊C4—1228no—
897C4⋊C4—2444no—
898C22⋊C4—44no—
899C22⋊C4—44no—
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—1228no—
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
987C23#41×D6111yescharacteristic
988C23#41×D6111yescharacteristic
989C23#41×D6111yescharacteristic
990C23#41×D6111yescharacteristic
991C23C2×#1175822411yescharacteristic
992C23#1451982211yescharacteristic
993C23#1451982211yescharacteristic
994C23#1451982311yescharacteristic
995C23#1451982411yescharacteristic
996D4—12232no—
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—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—41no—
1033C2×C4—41no—
1034C2×C4—41no—
1035C2×C4—41no—
1036C2×C4—41no—
1037C2×C4—614no—
1038C2×C4—614no—
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—24416no—
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×C4C2×#1175819814yes—
1089C2×C4C2×#1175819814yes—
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
1121C22#117×D6111yescharacteristic
1122C22#117×D6111yescharacteristic
1123C22C4×D4×D6111yescharacteristic
1124C22C4×#1175822411yescharacteristic
1125C22#1684023411yescharacteristic
1126C22#1684024111yescharacteristic
1127C22#1684026911yescharacteristic
1128C22#1684026911yescharacteristic
1129C22#1684027011yescharacteristic
1130C22#1684027211yescharacteristic
1131C22#1684027411yescharacteristic
1132C22#1684027411yescharacteristic
1133C22#1684029111yescharacteristic
1134C22#1684029511yescharacteristic
1135C22#1684034411yescharacteristic
1136C22#1684034611yescharacteristic
1137C22#1684035311yescharacteristic
1138C22#1684035511yescharacteristic
1139C22D4×C22⋊D6111yescharacteristic
1140C22D4×D24411yescharacteristic
1141C22#1684040011yescharacteristic
1142C22#1684040611yescharacteristic
1143C22#1684040711yescharacteristic
1144C22#1684040711yescharacteristic
1145C22#1684041011yescharacteristic
1146C22#1684041111yescharacteristic
1147C22#1684041611yescharacteristic
1148C22#1684043011yescharacteristic
1149C22#1684045511yescharacteristic
1150C22#1684046311yescharacteristic
1151C22#1684047411yescharacteristic
1152C22#1684047911yescharacteristic
1153C22#1684049411yescharacteristic
1154C22#1684049611yescharacteristic
1155C4—24no—
1156C4—24no—
1157C4—42no—
1158C4—42no—
1159C4—81no—
1160C4—81no—
1161C4—1224no—
1162C4—1224no—
1163C4—4881no—
1164C4—4881no—
1165C4—2442no—
1166C4—2442no—
1167C4—2442no—
1168C2—44no—
1169C2—2444no—
1170C2#2144819811yescharacteristic
1171C2#2144826111yescharacteristic
1172C2#2144844911yescharacteristic
1173C2D4×#1175819811yescharacteristic
1174C2#2144864411yescharacteristic
1175C2#2144876511yescharacteristic
1176C2#2144878911yescharacteristic
1177C2#2144969811yescharacteristic
1178C2#2144969911yescharacteristic
1179C2#2144970811yescharacteristic
1180C2#2144971611yescharacteristic
1181C2#2144975211yescharacteristic
1182C2#2144975411yescharacteristic
1183C2#2144985111yescharacteristic
1184C2#2144985311yescharacteristic
subgroupG/H
center, FrattiniC24C23×D61
commutatorC23×C61C23×C4
FittingC2×C61×#388C2
socle, cosocleC24×C61C24
prime radicalC23×C22⋊D61C22
hypercenterC2×#388D61
hypocenterC61#13886
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C24 ◁ C2×#388

Complements

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

NH ≅ G/Ntype
2. C2×#16839655C2semidirect
3. C2×#16839623C2semidirect
4. C2×C4×#11758198C2semidirect
5. #21444065C2semidirect
6. #21444061C2semidirect
9. #21444054C2semidirect
10. #21444052C2semidirect
11. #21444048C2semidirect
12. #21444043C2semidirect
13. #21444041C2semidirect
14. #21444040C2semidirect
15. C2×C61×#388C2semidirect
21. C2×#14519737C4semidirect
134. #14519684D4semidirect
305. C22⋊C4×C61C22⋊C4semidirect
578. C2×#388D61semidirect
650. C61#13886semidirect
907. C22⋊C4#11758198semidirect

Maximal subgroups

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

subgroupindex
C22×#145197372
C2×#168396552
C2×#168396232
C2×C4×#117581982
#214440652
#214440612
#214440582
#214440542
#214440522
#214440482
#214440432
#214440412
#214440402
C2×C61×#3882
#1388661