Finite Group Databasebeta

← #29601648

Subgroups — #29601648

Order 15616.

1630 conjugacy classes of subgroups.

The subgroup lattice has 1006 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16839655C211yesmaximal, characteristic
2C2×#16839637C211yesmaximal, characteristic
3#21444056C211yesmaximal, characteristic
4#21444056C211yesmaximal, characteristic
5#21444053C211yesmaximal, characteristic, complemented
6#21444053C211yesmaximal, characteristic, complemented
7#21444053C211yesmaximal, characteristic, complemented
8#21444051C211yesmaximal, characteristic, complemented
9#21444049C211yesmaximal, characteristic, complemented
10#21444048C211yesmaximal, characteristic, complemented
11#21444046C211yesmaximal, characteristic, complemented
12#21444044C211yesmaximal, characteristic, complemented
13#21444041C211yesmaximal, characteristic
14#21444041C211yesmaximal, characteristic
15C2×C61×#388C211yesmaximal, characteristic
16C24×Dic61C2211yescharacteristic
17C22×C4⋊Dic61C2211yescharacteristic
18C22×C4⋊Dic61C2211yescharacteristic
19C22×C4⋊Dic61C2211yescharacteristic
20C22×C22⋊Dic61C2211yescharacteristic
21C22×C22⋊Dic61C2211yescharacteristic
22C22×C22⋊Dic61C2211yescharacteristic
23C22×C4×Dic61C2211yescharacteristic
24C22×C4×Dic61C2211yescharacteristic
25C22×C4×Dic61C2211yescharacteristic
26#16839655C418yescomplemented
27#16839637C418yescomplemented
28C2×#14519684C2211yescharacteristic
29C2×#14519684C2211yescharacteristic
30C2×#14519684C2211yescharacteristic
31C2×#14519684C2211yescharacteristic
32C2×#14519684C2211yescharacteristic
33C2×#14519684C2211yescharacteristic
34C2×#14519684C2211yescharacteristic
35C2×#14519684C2211yescharacteristic
36C2×#14519684C2211yescharacteristic
37C2×#14519684C2211yescharacteristic
38C2×#14519684C2211yescharacteristic
39C2×#14519684C2211yescharacteristic
40C2×#14519684C2211yescharacteristic
41C2×#14519684C2211yescharacteristic
42C2×#14519684C2211yescharacteristic
43C2×#14519684C2211yescharacteristic
44C2×#14519684C2211yescharacteristic
45C2×#14519684C2211yescharacteristic
46C22×C4⋊C4×C61C2211yescharacteristic
47C22×C22⋊C4×C61C2211yescharacteristic
48C22×C22⋊C4×C61C2211yescharacteristic
49C22×C22⋊C4×C61C2211yescharacteristic
50C22×C42×C61C2211yescharacteristic
51C61×#388C418yescomplemented
52C2×#95×C61C2211yescharacteristic
53C2×#95×C61C2211yescharacteristic
54C23×Dic61—41no—
55C23×Dic61—41no—
56C23×Dic61—41no—
57C23×Dic61—41no—
58C23×Dic61—41no—
59C23×Dic61—41no—
60C23×Dic61C2×C414yes—
61C23×Dic61C2311yescharacteristic
62C23×Dic61C2311yescharacteristic
63C23×Dic61C2311yescharacteristic
64C23×Dic61C2311yescharacteristic
65C23×Dic61C2311yescharacteristic
66C23×Dic61C2311yescharacteristic
67C23×Dic61C2311yescharacteristic
68C23×Dic61C2311yescharacteristic
69C2×C4⋊Dic61—41no—
70C2×C4⋊Dic61—41no—
71C2×C4⋊Dic61—41no—
72C2×C4⋊Dic61—41no—
73C2×C4⋊Dic61—41no—
74C2×C4⋊Dic61—41no—
75C2×C4⋊Dic61C2×C414yes—
76C2×C4⋊Dic61C2×C414yes—
77C2×C4⋊Dic61C2×C414yescomplemented
78C2×C22⋊Dic61—41no—
79C2×C22⋊Dic61—41no—
80C2×C22⋊Dic61—41no—
81C2×C22⋊Dic61—41no—
82C2×C22⋊Dic61—41no—
83C2×C22⋊Dic61—41no—
84C2×C22⋊Dic61C2×C414yes—
85C2×C22⋊Dic61C2×C414yes—
86C2×C22⋊Dic61C2×C414yes—
87C2×C4×Dic61—41no—
88C2×C4×Dic61—41no—
89C2×C4×Dic61—41no—
90C2×C4×Dic61—41no—
91C2×C4×Dic61—41no—
92C2×C4×Dic61—41no—
93C2×C4×Dic61—41no—
94C2×C4×Dic61—41no—
95C2×C4×Dic61C2×C414yescomplemented
96#14519684—41no—
97#14519684—41no—
98#14519684—41no—
99#14519684—41no—
100#14519684—41no—
101#14519684—41no—
102#14519684—41no—
103#14519684—41no—
104#14519684—41no—
105#14519684—41no—
106#14519684—41no—
107#14519684—41no—
108#14519684—41no—
109#14519684—41no—
110#14519684C2×C414yes—
111#14519684C2×C414yes—
112#14519684C2×C414yescomplemented
113#14519684C2×C414yescomplemented
114C25×C61C2311yescharacteristic
115C23×C4×C61C2311yescharacteristic
116C23×C4×C61C2311yescharacteristic
117C23×C4×C61C2311yescharacteristic
118C23×C4×C61C2311yescharacteristic
119C23×C4×C61C2311yescharacteristic
120C23×C4×C61C2311yescharacteristic
121C2×C4⋊C4×C61—41no—
122C2×C4⋊C4×C61—41no—
123C2×C4⋊C4×C61C2×C414yescomplemented
124C2×C22⋊C4×C61—41no—
125C2×C22⋊C4×C61—41no—
126C2×C22⋊C4×C61—41no—
127C2×C22⋊C4×C61—41no—
128C2×C22⋊C4×C61C2×C414yes—
129C2×C22⋊C4×C61C2×C414yes—
130C2×C22⋊C4×C61C2×C414yes—
131C2×C22⋊C4×C61C2×C414yes—
132C2×C22⋊C4×C61C2×C414yes—
133C2×C42×C61—41no—
134C2×C42×C61—41no—
135C2×C42×C61C2×C414yescomplemented
136#95×C61C2×C414yescomplemented
137#95×C61C2×C414yescomplemented
138C24×C61—21no—
139C24×C61—21no—
140C24×C61—21no—
141C24×C61—21no—
142C24×C61—21no—
143C24×C61—21no—
144C24×C61—21no—
145C24×C61—21no—
146C24×C61—21no—
147C24×C61—21no—
148C24×C61—21no—
149C24×C61—21no—
150C24×C61C22×C412yes—
151C24×C61C22×C412yes—
152C24×C61C22×C412yes—
153C24×C61C2411yescharacteristic
154C22×C4×C61—21no—
155C22×C4×C61—21no—
156C22×C4×C61—21no—
157C22×C4×C61—21no—
158C22×C4×C61—21no—
159C22×C4×C61—21no—
160C22×C4×C61—21no—
161C22×C4×C61—21no—
162C22×C4×C61—21no—
163C22×C4×C61—21no—
164C22×C4×C61—21no—
165C22×C4×C61—21no—
166C22×C4×C61—21no—
167C22×C4×C61—21no—
168C22×C4×C61—21no—
169C22×C4×C61—21no—
170C22×C4×C61—21no—
171C22×C4×C61—21no—
172C22×C4×C61—21no—
173C22×C4×C61—21no—
174C22×C4×C61—21no—
175C22×C4×C61—21no—
176C22×C4×C61—21no—
177C22×C4×C61—21no—
178C22×C4×C61—21no—
179C22×C4×C61—21no—
180C22×C4×C61—21no—
181C22×C4×C61—21no—
182C22×C4×C61—21no—
183C22×C4×C61—21no—
184C22×C4×C61—21no—
185C22×C4×C61—21no—
186C22×C4×C61C22×C412yes—
187C22×C4×C61C22×C412yes—
188C22×C4×C61C22×C412yes—
189C22×C4×C61C22×C412yes—
190C22×C4×C61C22×C412yes—
191C22×C4×C61C22×C412yes—
192C22×C4×C61C22×C412yes—
193C22×C4×C61C22×C412yes—
194C22×C4×C61C22×C412yes—
195C22×C4×C61C22×C412yes—
196C22×Dic61—21no—
197C22×Dic61—21no—
198C22×Dic61—21no—
199C22×Dic61—21no—
200C22×Dic61—21no—
201C22×Dic61—21no—
202C22×Dic61—21no—
203C22×Dic61—21no—
204C22×Dic61—21no—
205C22×Dic61—21no—
206C22×Dic61—21no—
207C22×Dic61—21no—
208C22×Dic61—21no—
209C22×Dic61—21no—
210C22×Dic61—21no—
211C22×Dic61—21no—
212C22×Dic61—21no—
213C22×Dic61—21no—
214C22×Dic61—21no—
215C22×Dic61—21no—
216C22×Dic61—21no—
217C22×Dic61—21no—
218C22×Dic61—21no—
219C22×Dic61—21no—
220C22×Dic61—21no—
221C22×Dic61—21no—
222C22×Dic61—21no—
223C22×Dic61—21no—
224C22×Dic61—21no—
225C22×Dic61—21no—
226C22×Dic61—21no—
227C22×Dic61—21no—
228C22×Dic61—21no—
229C22×Dic61—21no—
230C22×Dic61—21no—
231C22×Dic61—21no—
232C22×Dic61—21no—
233C22×Dic61—21no—
234C22×Dic61—21no—
235C22×Dic61—21no—
236C22×Dic61—21no—
237C22×Dic61—21no—
238C22×Dic61—21no—
239C22×Dic61—21no—
240C22×Dic61—21no—
241C22×Dic61—21no—
242C22×Dic61—21no—
243C22×Dic61—21no—
244C22×Dic61—44no—
245C22×Dic61—44no—
246C22×Dic61—44no—
247C22×Dic61—44no—
248C22×Dic61—44no—
249C22×Dic61—44no—
250C22×Dic61—44no—
251C22×Dic61C22×C412yes—
252C22×Dic61C22×C412yes—
253C22×Dic61C22×C412yes—
254C22×Dic61C22×C412yes—
255C22×Dic61C22×C412yes—
256C22×Dic61C22×C412yes—
257C22×Dic61C22×C412yes—
258C22×Dic61C22×C412yes—
259C4⋊C4×C61—44no—
260C22⋊C4×C61—44no—
261C22⋊C4×C61—44no—
262C22⋊C4×C61C42116yescomplemented
263C42×C61—44no—
264C22⋊Dic61—44no—
265C22⋊Dic61—44no—
266C22⋊Dic61—44no—
267C4⋊Dic61—44no—
268C4⋊Dic61—44no—
269C4⋊Dic61—44no—
270C4×Dic61—44no—
271C4×Dic61—44no—
272C4×Dic61—44no—
273C23×C61—22no—
274C23×C61—22no—
275C23×C61—22no—
276C23×C61—22no—
277C23×C61—22no—
278C23×C61—22no—
279C23×C61—22no—
280C23×C61—22no—
281C23×C61—22no—
282C23×C61—22no—
283C23×C61—22no—
284C23×C61—22no—
285C23×C61—22no—
286C23×C61—22no—
287C23×C61—22no—
288C23×C61—22no—
289C23×C61—22no—
290C23×C61—22no—
291C23×C61—41no—
292C23×C61—41no—
293C23×C61—41no—
294C23×C61—41no—
295C23×C61—41no—
296C23×C61—41no—
297C23×C61—41no—
298C23×C61—41no—
299C23×C61—41no—
300C23×C61—41no—
301C23×C61—41no—
302C23×C61—41no—
303C23×C61—41no—
304C23×C61—41no—
305C23×C61—41no—
306C23×C61—41no—
307C23×C61C2×C4214yes—
308C23×C61C23×C411yescharacteristic
309C23×C61C23×C411yescharacteristic
310C23×C61C23×C411yescharacteristic
311C23×C61H(5,𝔽2)11yescharacteristic
312C23×C61H(5,𝔽2)11yescharacteristic
313C23×C61H(5,𝔽2)11yescharacteristic
314C23×C61H(5,𝔽2)11yescharacteristic
315C23×C61H(5,𝔽2)11yescharacteristic
316C23×C61H(5,𝔽2)11yescharacteristic
317C23×C61H(5,𝔽2)11yescharacteristic
318C23×C61H(5,𝔽2)11yescharacteristic
319C23×C612−1+411yescharacteristic
320C23×C612−1+411yescharacteristic
321C23×C612−1+411yescharacteristic
322C23×C612−1+411yescharacteristic
323C2×C4×C61—22no—
324C2×C4×C61—22no—
325C2×C4×C61—22no—
326C2×C4×C61—22no—
327C2×C4×C61—22no—
328C2×C4×C61—22no—
329C2×C4×C61—22no—
330C2×C4×C61—22no—
331C2×C4×C61—22no—
332C2×C4×C61—22no—
333C2×C4×C61—22no—
334C2×C4×C61—22no—
335C2×C4×C61—22no—
336C2×C4×C61—22no—
337C2×C4×C61—22no—
338C2×C4×C61—22no—
339C2×C4×C61—22no—
340C2×C4×C61—22no—
341C2×C4×C61—22no—
342C2×C4×C61—22no—
343C2×C4×C61—22no—
344C2×C4×C61—22no—
345C2×C4×C61—22no—
346C2×C4×C61—22no—
347C2×C4×C61—41no—
348C2×C4×C61—41no—
349C2×C4×C61—41no—
350C2×C4×C61—41no—
351C2×C4×C61—41no—
352C2×C4×C61—41no—
353C2×C4×C61—41no—
354C2×C4×C61—41no—
355C2×C4×C61—41no—
356C2×C4×C61—41no—
357C2×C4×C61—41no—
358C2×C4×C61—41no—
359C2×C4×C61—41no—
360C2×C4×C61—41no—
361C2×C4×C61—41no—
362C2×C4×C61—41no—
363C2×C4×C61C2×C4214yes—
364C2×C4×C61C2×C4214yes—
365C2×Dic61—22no—
366C2×Dic61—22no—
367C2×Dic61—22no—
368C2×Dic61—22no—
369C2×Dic61—22no—
370C2×Dic61—22no—
371C2×Dic61—22no—
372C2×Dic61—22no—
373C2×Dic61—22no—
374C2×Dic61—22no—
375C2×Dic61—22no—
376C2×Dic61—22no—
377C2×Dic61—22no—
378C2×Dic61—22no—
379C2×Dic61—22no—
380C2×Dic61—22no—
381C2×Dic61—22no—
382C2×Dic61—22no—
383C2×Dic61—22no—
384C2×Dic61—22no—
385C2×Dic61—22no—
386C2×Dic61—22no—
387C2×Dic61—22no—
388C2×Dic61—22no—
389C2×Dic61—416no—
390C2×Dic61—41no—
391C2×Dic61—41no—
392C2×Dic61—41no—
393C2×Dic61—41no—
394C2×Dic61—41no—
395C2×Dic61—41no—
396C2×Dic61—41no—
397C2×Dic61—41no—
398C2×Dic61—41no—
399C2×Dic61—41no—
400C2×Dic61—41no—
401C2×Dic61—41no—
402C2×Dic61—41no—
403C2×Dic61—41no—
404C2×Dic61—41no—
405C2×Dic61—41no—
406C2×Dic61—41no—
407C2×Dic61—41no—
408C2×Dic61—41no—
409C2×Dic61—41no—
410C2×Dic61—41no—
411C2×Dic61—41no—
412C2×Dic61—41no—
413C2×Dic61—41no—
414C2×Dic61—41no—
415C2×Dic61—41no—
416C2×Dic61—41no—
417C2×Dic61—41no—
418C2×Dic61—41no—
419C2×Dic61—41no—
420C2×Dic61—41no—
421C2×Dic61—41no—
422#13831—611nomaximal, Sylow
423C22×C61—24no—
424C22×C61—24no—
425C22×C61—24no—
426C22×C61—42no—
427C22×C61—42no—
428C22×C61—42no—
429C22×C61—42no—
430C22×C61—42no—
431C22×C61—42no—
432C22×C61—42no—
433C22×C61—42no—
434C22×C61—42no—
435C22×C61—42no—
436C22×C61—42no—
437C22×C61—42no—
438C22×C61C22×C4211yescharacteristic
439C22×C61#51811yescharacteristic
440C22×C61#51811yescharacteristic
441C22×C61#51811yescharacteristic
442C22×C61#51811yescharacteristic
443C22×C61#51811yescharacteristic
444C22×C61#51811yescharacteristic
445C22×C61#51811yescharacteristic
446C22×C61#51911yescharacteristic
447C22×C61#52011yescharacteristic
448C22×C61#52011yescharacteristic
449C22×C61#52011yescharacteristic
450C22×C61#52011yescharacteristic
451C22×C61#52011yescharacteristic
452C22×C61#52011yescharacteristic
453C22×C61#52011yescharacteristic
454C22×C61#52011yescharacteristic
455C22×C61#52011yescharacteristic
456C22×C61#52011yescharacteristic
457C22×C61#56011yescharacteristic
458C22×C61#56011yescharacteristic
459C22×C61#56011yescharacteristic
460C22×C61#56011yescharacteristic
461C22×C61H(3,𝔽4)11yescharacteristic
462C22×C61#56211yescharacteristic
463C22×C61#56211yescharacteristic
464C22×C61#56211yescharacteristic
465C22×C61#56211yescharacteristic
466C22×C61#56211yescharacteristic
467C22×C61#56211yescharacteristic
468C22×C61#56311yescharacteristic
469C22×C61#56311yescharacteristic
470C22×C61#56311yescharacteristic
471C22×C61#56311yescharacteristic
472C22×C61#56311yescharacteristic
473C4×C61—24no—
474C4×C61—24no—
475C4×C61—42no—
476C4×C61—42no—
477C4×C61—42no—
478C4×C61—42no—
479Dic61—42no—
480Dic61—42no—
481Dic61—42no—
482Dic61—42no—
483Dic61—42no—
484Dic61—42no—
485Dic61—42no—
486Dic61—42no—
487C2×#388—611no—
488C2×#388D6111yescharacteristic
489C2×#385—611no—
490#1437—611no—
491#1437—611no—
492#1436—611no—
493#1436—611no—
494#1436—611no—
495#1436—611no—
496C4⋊#95—611no—
497C4⋊#95—611no—
498#1434—611no—
499#1434—611no—
500C22⋊#95—611no—
501C22⋊#95—611no—
502C2×C61—44no—
503C2×C61#227411yescharacteristic
504C2×C61#227511yescharacteristic
505C2×C61#227511yescharacteristic
506C2×C61#237511yescharacteristic
507C2×C61#237611yescharacteristic
508C2×C61#237611yescharacteristic
509C2×C61#237611yescharacteristic
510C2×C61#237711yescharacteristic
511C2×C61#237711yescharacteristic
512C2×C61#237811yescharacteristic
513C2×C61#237811yescharacteristic
514C2×C61#237911yescharacteristic
515C2×C61#237911yescharacteristic
516C2×C61#238311yescharacteristic
517C2×C61#238311yescharacteristic
518C24×C4—611no—
519C22×C4⋊C4—611no—
520C22×C4⋊C4—611no—
521C22×C4⋊C4—611no—
522C22×C4⋊C4C2×D6111yescharacteristic
523C22×C22⋊C4—611no—
524C22×C22⋊C4—611no—
525C22×C22⋊C4—611no—
526C22×C22⋊C4C2×D6111yescharacteristic
527C22×C22⋊C4C2×D6111yescharacteristic
528C22×C22⋊C4C2×D6111yescharacteristic
529C22×C42—611no—
530C22×C42—611no—
531C22×C42—611no—
532C22×C42C2×D6111yescharacteristic
533#388—618no—
534#388Dic6118yescomplemented
535#385—618no—
536C2×#95—611no—
537C2×#95—611no—
538C2×#95—611no—
539C2×#95—611no—
540C2×#95—611no—
541C2×#95—611no—
542C2×#95—611no—
543C2×#95—611no—
544C2×#95—611no—
545C2×#95—611no—
546C2×#95—611no—
547C2×#95—611no—
548C2×#95—611no—
549C2×#95—611no—
550C2×#95—611no—
551C2×#95—611no—
552C2×#95—611no—
553C2×#95—611no—
554C2×#95C2×D6111yescharacteristic
555C2×#95C2×D6111yescharacteristic
556C61#1383111yescharacteristic, complemented, Sylow
557C25C22×D6111yescharacteristic
558C23×C4—611no—
559C23×C4—611no—
560C23×C4—611no—
561C23×C4—611no—
562C23×C4—611no—
563C23×C4—611no—
564C23×C4—611no—
565C23×C4—611no—
566C23×C4—614no—
567C23×C4—2441no—
568C23×C4—2441no—
569C23×C4—2441no—
570C23×C4—2441no—
571C23×C4—2441no—
572C23×C4—2441no—
573C23×C4C22×D6111yescharacteristic
574C23×C4C22×D6111yescharacteristic
575C23×C4C22×D6111yescharacteristic
576C23×C4C22×D6111yescharacteristic
577C23×C4C22×D6111yescharacteristic
578C23×C4C22×D6111yescharacteristic
579C2×C4⋊C4—41no—
580C2×C4⋊C4—41no—
581C2×C4⋊C4—614no—
582C2×C4⋊C4—614no—
583C2×C4⋊C4—614no—
584C2×C4⋊C4—2441no—
585C2×C4⋊C4—2441no—
586C2×C4⋊C4—2441no—
587C2×C4⋊C4—2441no—
588C2×C4⋊C4—2441no—
589C2×C4⋊C4—2441no—
590C2×C4⋊C4C2×Dic6114yescomplemented
591C2×C22⋊C4—41no—
592C2×C22⋊C4—41no—
593C2×C22⋊C4—41no—
594C2×C22⋊C4—41no—
595C2×C22⋊C4—614no—
596C2×C22⋊C4—614no—
597C2×C22⋊C4—614no—
598C2×C22⋊C4—2441no—
599C2×C22⋊C4—2441no—
600C2×C22⋊C4—2441no—
601C2×C22⋊C4—2441no—
602C2×C22⋊C4—2441no—
603C2×C22⋊C4—2441no—
604C2×C22⋊C4C4×D6114yes—
605C2×C22⋊C4C4×D6114yes—
606C2×C22⋊C4C2×Dic6114yes—
607C2×C22⋊C4C2×Dic6114yes—
608C2×C22⋊C4C2×Dic6114yes—
609C2×C42—41no—
610C2×C42—41no—
611C2×C42—614no—
612C2×C42—2441no—
613C2×C42—2441no—
614C2×C42—2441no—
615C2×C42—2441no—
616C2×C42—2441no—
617C2×C42—2441no—
618C2×C42—2441no—
619C2×C42—2441no—
620C2×C42C2×Dic6114yescomplemented
621#95—614no—
622#95—614no—
623#95—614no—
624#95—614no—
625#95—2441no—
626#95—2441no—
627#95—2441no—
628#95—2441no—
629#95—2441no—
630#95—2441no—
631#95—2441no—
632#95—2441no—
633#95—2441no—
634#95—2441no—
635#95—2441no—
636#95—2441no—
637#95—2441no—
638#95—2441no—
639#95C2×Dic6114yescomplemented
640#95C2×Dic6114yescomplemented
641C24—21no—
642C24—21no—
643C24—21no—
644C24—21no—
645C24—21no—
646C24—21no—
647C24—21no—
648C24—21no—
649C24—21no—
650C24—21no—
651C24—21no—
652C24—21no—
653C24C2×C4×D6112yes—
654C24C2×C4×D6112yes—
655C24C22×Dic6112yes—
656C24C23×D6111yescharacteristic
657C22×C4—21no—
658C22×C4—21no—
659C22×C4—21no—
660C22×C4—21no—
661C22×C4—21no—
662C22×C4—21no—
663C22×C4—21no—
664C22×C4—21no—
665C22×C4—21no—
666C22×C4—21no—
667C22×C4—21no—
668C22×C4—21no—
669C22×C4—21no—
670C22×C4—21no—
671C22×C4—21no—
672C22×C4—21no—
673C22×C4—21no—
674C22×C4—21no—
675C22×C4—21no—
676C22×C4—21no—
677C22×C4—21no—
678C22×C4—21no—
679C22×C4—21no—
680C22×C4—21no—
681C22×C4—21no—
682C22×C4—21no—
683C22×C4—21no—
684C22×C4—21no—
685C22×C4—21no—
686C22×C4—21no—
687C22×C4—21no—
688C22×C4—21no—
689C22×C4—612no—
690C22×C4—612no—
691C22×C4—612no—
692C22×C4—612no—
693C22×C4—612no—
694C22×C4—612no—
695C22×C4—612no—
696C22×C4—612no—
697C22×C4—1221no—
698C22×C4—1221no—
699C22×C4—1221no—
700C22×C4—1221no—
701C22×C4—1221no—
702C22×C4—1221no—
703C22×C4—1221no—
704C22×C4—1221no—
705C22×C4—1221no—
706C22×C4—1221no—
707C22×C4—1221no—
708C22×C4—1221no—
709C22×C4—1221no—
710C22×C4—1221no—
711C22×C4—1221no—
712C22×C4—1221no—
713C22×C4—1221no—
714C22×C4—1221no—
715C22×C4—1221no—
716C22×C4—1221no—
717C22×C4—1221no—
718C22×C4—1221no—
719C22×C4—1221no—
720C22×C4—1221no—
721C22×C4—1221no—
722C22×C4—1221no—
723C22×C4—1221no—
724C22×C4—1221no—
725C22×C4—1221no—
726C22×C4—1221no—
727C22×C4—1221no—
728C22×C4—1221no—
729C22×C4—1221no—
730C22×C4—1221no—
731C22×C4—1221no—
732C22×C4—1221no—
733C22×C4—1221no—
734C22×C4—1221no—
735C22×C4—1221no—
736C22×C4—1221no—
737C22×C4—1221no—
738C22×C4—1221no—
739C22×C4—1221no—
740C22×C4—1221no—
741C22×C4—1221no—
742C22×C4—1221no—
743C22×C4—1221no—
744C22×C4—1221no—
745C22×C4—2444no—
746C22×C4—2444no—
747C22×C4—2444no—
748C22×C4—2444no—
749C22×C4—2444no—
750C22×C4—2444no—
751C22×C4—2444no—
752C22×C4C2×C4×D6112yes—
753C22×C4C2×C4×D6112yes—
754C22×C4C2×C4×D6112yes—
755C22×C4C2×C4×D6112yes—
756C22×C4C22×Dic6112yes—
757C22×C4C22×Dic6112yes—
758C22×C4C22×Dic6112yes—
759C22×C4C22×Dic6112yes—
760C22×C4C22×Dic6112yes—
761C22×C4C22×Dic6112yes—
762C4⋊C4—44no—
763C4⋊C4—2444no—
764C4⋊C4—2444no—
765C4⋊C4—2444no—
766C22⋊C4—44no—
767C22⋊C4—44no—
768C22⋊C4—2444no—
769C22⋊C4—2444no—
770C22⋊C4—2444no—
771C22⋊C4C4×Dic61116yescomplemented
772C42—44no—
773C42—2444no—
774C42—2444no—
775C42—2444no—
776C23—22no—
777C23—22no—
778C23—22no—
779C23—22no—
780C23—22no—
781C23—22no—
782C23—22no—
783C23—22no—
784C23—22no—
785C23—22no—
786C23—22no—
787C23—22no—
788C23—22no—
789C23—22no—
790C23—22no—
791C23—22no—
792C23—22no—
793C23—22no—
794C23—41no—
795C23—41no—
796C23—41no—
797C23—41no—
798C23—41no—
799C23—41no—
800C23—41no—
801C23—41no—
802C23—41no—
803C23—41no—
804C23—41no—
805C23—41no—
806C23—41no—
807C23—41no—
808C23—41no—
809C23—41no—
810C23C2×C4×Dic6114yes—
811C23C22×C4×D6111yescharacteristic
812C23C22×C4×D6111yescharacteristic
813C23C23×Dic6111yescharacteristic
814C23#1451982211yescharacteristic
815C23#1451982211yescharacteristic
816C23#1451982211yescharacteristic
817C23#1451982211yescharacteristic
818C23#1451982311yescharacteristic
819C23#1451982311yescharacteristic
820C23#1451982311yescharacteristic
821C23#1451982311yescharacteristic
822C23#1451982411yescharacteristic
823C23#1451982411yescharacteristic
824C23#1451982411yescharacteristic
825C23#1451982411yescharacteristic
826C2×C4—22no—
827C2×C4—22no—
828C2×C4—22no—
829C2×C4—22no—
830C2×C4—22no—
831C2×C4—22no—
832C2×C4—22no—
833C2×C4—22no—
834C2×C4—22no—
835C2×C4—22no—
836C2×C4—22no—
837C2×C4—22no—
838C2×C4—22no—
839C2×C4—22no—
840C2×C4—22no—
841C2×C4—22no—
842C2×C4—22no—
843C2×C4—22no—
844C2×C4—22no—
845C2×C4—22no—
846C2×C4—22no—
847C2×C4—22no—
848C2×C4—22no—
849C2×C4—22no—
850C2×C4—41no—
851C2×C4—41no—
852C2×C4—41no—
853C2×C4—41no—
854C2×C4—41no—
855C2×C4—41no—
856C2×C4—41no—
857C2×C4—41no—
858C2×C4—41no—
859C2×C4—41no—
860C2×C4—41no—
861C2×C4—41no—
862C2×C4—41no—
863C2×C4—41no—
864C2×C4—41no—
865C2×C4—41no—
866C2×C4—1222no—
867C2×C4—1222no—
868C2×C4—1222no—
869C2×C4—1222no—
870C2×C4—1222no—
871C2×C4—1222no—
872C2×C4—1222no—
873C2×C4—1222no—
874C2×C4—1222no—
875C2×C4—1222no—
876C2×C4—1222no—
877C2×C4—1222no—
878C2×C4—1222no—
879C2×C4—1222no—
880C2×C4—1222no—
881C2×C4—1222no—
882C2×C4—1222no—
883C2×C4—1222no—
884C2×C4—1222no—
885C2×C4—1222no—
886C2×C4—1222no—
887C2×C4—1222no—
888C2×C4—1222no—
889C2×C4—1222no—
890C2×C4—24416no—
891C2×C4—2441no—
892C2×C4—2441no—
893C2×C4—2441no—
894C2×C4—2441no—
895C2×C4—2441no—
896C2×C4—2441no—
897C2×C4—2441no—
898C2×C4—2441no—
899C2×C4—2441no—
900C2×C4—2441no—
901C2×C4—2441no—
902C2×C4—2441no—
903C2×C4—2441no—
904C2×C4—2441no—
905C2×C4—2441no—
906C2×C4—2441no—
907C2×C4—2441no—
908C2×C4—2441no—
909C2×C4—2441no—
910C2×C4—2441no—
911C2×C4—2441no—
912C2×C4—2441no—
913C2×C4—2441no—
914C2×C4—2441no—
915C2×C4—2441no—
916C2×C4—2441no—
917C2×C4—2441no—
918C2×C4—2441no—
919C2×C4—2441no—
920C2×C4—2441no—
921C2×C4—2441no—
922C2×C4—2441no—
923C2×C4C2×C4×Dic6114yes—
924C2×C4C2×C4×Dic6114yes—
925C22—24no—
926C22—24no—
927C22—24no—
928C22—42no—
929C22—42no—
930C22—42no—
931C22—42no—
932C22—42no—
933C22—42no—
934C22—42no—
935C22—42no—
936C22—42no—
937C22—42no—
938C22—42no—
939C22—42no—
940C22C22×C4×Dic6111yescharacteristic
941C22#1684023411yescharacteristic
942C22#1684023411yescharacteristic
943C22#1684023411yescharacteristic
944C22#1684023411yescharacteristic
945C22#1684023611yescharacteristic
946C22#1684023711yescharacteristic
947C22#1684023711yescharacteristic
948C22#1684023911yescharacteristic
949C22#1684024111yescharacteristic
950C22#1684024111yescharacteristic
951C22#1684024111yescharacteristic
952C22#1684024111yescharacteristic
953C22#1684024211yescharacteristic
954C22#1684024211yescharacteristic
955C22#1684024511yescharacteristic
956C22#1684024511yescharacteristic
957C22#1684024511yescharacteristic
958C22#1684024511yescharacteristic
959C22#1684050011yescharacteristic
960C22#1684050011yescharacteristic
961C22#1684050211yescharacteristic
962C22#1684050311yescharacteristic
963C22#1684050411yescharacteristic
964C22#1684050611yescharacteristic
965C22#1684050611yescharacteristic
966C22#1684050711yescharacteristic
967C22#1684050711yescharacteristic
968C22#1684050911yescharacteristic
969C22#1684050911yescharacteristic
970C22#1684051211yescharacteristic
971C22#1684051411yescharacteristic
972C22#1684051411yescharacteristic
973C22#1684051411yescharacteristic
974C22#1684051511yescharacteristic
975C4—24no—
976C4—24no—
977C4—42no—
978C4—42no—
979C4—42no—
980C4—42no—
981C4—2442no—
982C4—2442no—
983C4—2442no—
984C4—2442no—
985C4—2442no—
986C4—2442no—
987C4—2442no—
988C4—2442no—
989C2—44no—
990C2#2144817511yescharacteristic
991C2#2144818011yescharacteristic
992C2#2144818011yescharacteristic
993C2#2144895911yescharacteristic
994C2#2144896111yescharacteristic
995C2#2144896511yescharacteristic
996C2#2144896711yescharacteristic
997C2#2144897211yescharacteristic
998C2#2144897611yescharacteristic
999C2#2144897911yescharacteristic
1000C2#2144898611yescharacteristic
1001C2#2144898811yescharacteristic
1002C2#2144899311yescharacteristic
1003C2#2144900611yescharacteristic
1004C2#2144901111yescharacteristic
subgroupG/H
center, FrattiniC24C23×D61
commutatorC22×C61C22×C42
FittingC2×C61×#388C2
socle, cosocleC24×C61C24
prime radicalC25×C61C23
hypercenterC2×#388D61
hypocenterC61#13831
LCSG ▷ C22×C61 ▷ C61
UCSC1 ◁ C24 ◁ C2×#388

Complements

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

NH ≅ G/Ntype
5. #21444053C2semidirect
6. #21444053C2semidirect
7. #21444053C2semidirect
8. #21444051C2semidirect
9. #21444049C2semidirect
10. #21444048C2semidirect
11. #21444046C2semidirect
12. #21444044C2semidirect
26. #16839655C4semidirect
27. #16839637C4semidirect
51. C61×#388C4semidirect
77. C2×C4⋊Dic61C2×C4semidirect
95. C2×C4×Dic61C2×C4semidirect
112. #14519684C2×C4semidirect
113. #14519684C2×C4semidirect
123. C2×C4⋊C4×C61C2×C4semidirect
135. C2×C42×C61C2×C4semidirect
136. #95×C61C2×C4semidirect
137. #95×C61C2×C4semidirect
262. C22⋊C4×C61C42semidirect
534. #388Dic61semidirect
556. C61#13831semidirect
590. C2×C4⋊C4C2×Dic61semidirect
620. C2×C42C2×Dic61semidirect
639. #95C2×Dic61semidirect
640. #95C2×Dic61semidirect
771. C22⋊C4C4×Dic61semidirect

Maximal subgroups

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

subgroupindex
C2×#168396552
C2×#168396372
#214440562
#214440532
#214440512
#214440492
#214440482
#214440462
#214440442
#214440412
C2×C61×#3882
#1383161