Finite Group Databasebeta

← #29601522

Subgroups — #29601522

Order 15616.

2298 conjugacy classes of subgroups.

The subgroup lattice has 1070 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16839635C211yesmaximal, characteristic
2C2×#16839634C211yesmaximal, characteristic
3C2×C4×#11758196C211yesmaximal, characteristic, complemented
4C2×C22⋊C4×Dic61C211yesmaximal, characteristic
5C2×C22⋊C4×Dic61C211yesmaximal, characteristic
6C22×#14519684C211yesmaximal, characteristic
7#21444052C211yesmaximal, characteristic, complemented
8#21444052C211yesmaximal, characteristic, complemented
9#21444050C211yesmaximal, characteristic, complemented
10#21444050C211yesmaximal, characteristic, complemented
11#21444047C211yesmaximal, characteristic, complemented
12#21444045C211yesmaximal, characteristic, complemented
13#21444041C211yesmaximal, characteristic
14C4×#14519684C211yesmaximal, characteristic, complemented
15C2×C4×C22⋊C4×C61C211yesmaximal, characteristic
16C24×Dic61C2211yescharacteristic
17C24×Dic61C2211yescharacteristic
18C22×#11758196C2211yescharacteristic
19C22×#11758196C2211yescharacteristic
20C22×#11758196C2211yescharacteristic
21C22×#11758196C2211yescharacteristic
22C22×C22⋊Dic61C2211yescharacteristic
23C22×C22⋊Dic61C2211yescharacteristic
24C22×C4×Dic61C2211yescharacteristic
25C22×C4×Dic61C2211yescharacteristic
26C22×C4×Dic61C2211yescharacteristic
27C22×C4×Dic61C2211yescharacteristic
28#16839635C418yescomplemented
29#16839634C418yescomplemented
30C4×#11758196—24no—
31C22⋊C4×Dic61—24no—
32C22⋊C4×Dic61C418yescomplemented
33C2×#14519684—24no—
34C2×#14519684C2211yescharacteristic
35C2×#14519684C2211yescharacteristic
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
58C23×Dic61—22no—
59C23×Dic61—22no—
60C23×Dic61—22no—
61C23×Dic61—22no—
62C23×Dic61—22no—
63C23×Dic61—22no—
64C23×Dic61—22no—
65C23×Dic61—22no—
66C23×Dic61—41no—
67C23×Dic61—41no—
68C23×Dic61—41no—
69C23×Dic61—41no—
70C23×Dic61C2×C414yes—
71C23×Dic61C2×C414yes—
72C23×Dic61C2311yescharacteristic
73C23×Dic61C2311yescharacteristic
74C23×Dic61C2311yescharacteristic
75C23×Dic61C2311yescharacteristic
76C23×Dic61C2311yescharacteristic
77C23×Dic61C2311yescharacteristic
78C23×Dic61C2311yescharacteristic
79C23×Dic61C2311yescharacteristic
80C2×#11758196—22no—
81C2×#11758196—22no—
82C2×#11758196—22no—
83C2×#11758196—22no—
84C2×#11758196—41no—
85C2×#11758196—41no—
86C2×#11758196—41no—
87C2×#11758196—41no—
88C2×#11758196C2×C414yescomplemented
89C2×#11758196C2×C414yescomplemented
90C2×#11758196C2×C414yescomplemented
91C2×#11758196C2×C414yescomplemented
92C2×C22⋊Dic61—22no—
93C2×C22⋊Dic61—22no—
94C2×C22⋊Dic61C2×C414yes—
95C2×C22⋊Dic61C2×C414yes—
96C2×C22⋊Dic61C2×C414yes—
97C2×C22⋊Dic61C2×C414yes—
98C2×C4×Dic61—22no—
99C2×C4×Dic61—22no—
100C2×C4×Dic61—22no—
101C2×C4×Dic61—22no—
102C2×C4×Dic61—22no—
103C2×C4×Dic61—22no—
104C2×C4×Dic61—41no—
105C2×C4×Dic61—41no—
106C2×C4×Dic61—41no—
107C2×C4×Dic61—41no—
108C2×C4×Dic61C2×C414yescomplemented
109C2×C4×Dic61C2×C414yescomplemented
110#14519684—22no—
111#14519684—22no—
112#14519684—22no—
113#14519684—22no—
114#14519684—22no—
115#14519684—22no—
116#14519684—22no—
117#14519684—41no—
118#14519684—41no—
119#14519684C2×C414yescomplemented
120#14519684C2×C414yescomplemented
121#14519684C2×C414yescomplemented
122#14519684C2×C414yescomplemented
123#14519684C2×C414yescomplemented
124#14519684C2×C414yescomplemented
125#14519684D414yes—
126C25×C61C2311yescharacteristic
127C23×C4×C61—22no—
128C23×C4×C61—22no—
129C23×C4×C61—22no—
130C23×C4×C61—22no—
131C23×C4×C61—41no—
132C23×C4×C61—41no—
133C23×C4×C61C2×C414yes—
134C23×C4×C61C2311yescharacteristic
135C23×C4×C61C2311yescharacteristic
136C23×C4×C61C2311yescharacteristic
137C23×C4×C61C2311yescharacteristic
138C23×C4×C61C2311yescharacteristic
139C23×C4×C61C2311yescharacteristic
140C2×C22⋊C4×C61—22no—
141C2×C22⋊C4×C61—22no—
142C2×C22⋊C4×C61C2×C414yes—
143C2×C22⋊C4×C61C2×C414yes—
144C2×C22⋊C4×C61D414yes—
145C2×C22⋊C4×C61Q814yes—
146C2×C42×C61—22no—
147C2×C42×C61—22no—
148C2×C42×C61—22no—
149C2×C42×C61—22no—
150C2×C42×C61—41no—
151C2×C42×C61—41no—
152#95×C61—22no—
153#95×C61—22no—
154C24×C61—21no—
155C24×C61—21no—
156C24×C61—21no—
157C24×C61—21no—
158C24×C61—21no—
159C24×C61—21no—
160C24×C61—21no—
161C24×C61—21no—
162C24×C61C22×C412yes—
163C24×C61C22×C412yes—
164C24×C61C22×C412yes—
165C24×C61C2×D412yes—
166C24×C61C2×Q812yes—
167C24×C61#4112yes—
168C24×C61#4112yes—
169C24×C61C2411yescharacteristic
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—28no—
183C22×C4×C61—21no—
184C22×C4×C61—21no—
185C22×C4×C61—21no—
186C22×C4×C61—21no—
187C22×C4×C61—21no—
188C22×C4×C61—21no—
189C22×C4×C61—21no—
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—28no—
202C22×C4×C61—44no—
203C22×C4×C61—44no—
204C22×C4×C61—44no—
205C22×C4×C61—44no—
206C22×C4×C61—44no—
207C22×C4×C61C22×C412yes—
208C22×C4×C61C22×C412yes—
209C22×C4×C61C22×C412yes—
210C22×C4×C61C22×C412yes—
211C22×C4×C61C22×C412yes—
212C22×C4×C61C22×C412yes—
213C22×C4×C61C2×D412yes—
214C22×C4×C61C2×D412yes—
215C22×C4×C61C2×D412yes—
216C22×C4×C61C2×Q812yes—
217C22×C4×C61C2×Q812yes—
218C22×C4×C61#4112yes—
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—28no—
236C22×Dic61—28no—
237C22×Dic61—21no—
238C22×Dic61—21no—
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—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—28no—
262C22×Dic61—28no—
263C22×Dic61—44no—
264C22×Dic61—44no—
265C22×Dic61—44no—
266C22×Dic61—44no—
267C22×Dic61—44no—
268C22×Dic61—44no—
269C22×Dic61—44no—
270C22×Dic61—44no—
271C22×Dic61—44no—
272C22×Dic61—44no—
273C22×Dic61C22×C412yes—
274C22×Dic61C22×C412yes—
275C22×Dic61C22×C412yes—
276C22×Dic61C22×C412yes—
277C22×Dic61C22×C412yes—
278C22×Dic61C22×C412yes—
279C22×Dic61C22×C412yes—
280C22×Dic61C22×C412yes—
281C22×Dic61C22×C412yes—
282C22×Dic61C22×C412yes—
283C22×Dic61C22×C412yes—
284C22×Dic61C22×C412yes—
285C22×Dic61C2×D412yes—
286C22×Dic61C2×D412yes—
287C22×Dic61#4112yes—
288C22×Dic61#4112yes—
289C22⋊C4×C61—28no—
290C22⋊C4×C61C4⋊C4116yescomplemented
291C42×C61—44no—
292C42×C61—44no—
293C22⋊Dic61—28no—
294C22⋊Dic61C42116yescomplemented
295#11758196—28no—
296#11758196—28no—
297#11758196—44no—
298#11758196—44no—
299C4×Dic61—28no—
300C4×Dic61—44no—
301C4×Dic61—44no—
302C4×Dic61—44no—
303C23×C61—22no—
304C23×C61—22no—
305C23×C61—22no—
306C23×C61—22no—
307C23×C61—22no—
308C23×C61—22no—
309C23×C61—22no—
310C23×C61—22no—
311C23×C61—22no—
312C23×C61—22no—
313C23×C61—22no—
314C23×C61—22no—
315C23×C61—22no—
316C23×C61—22no—
317C23×C61—22no—
318C23×C61—22no—
319C23×C61—22no—
320C23×C61—22no—
321C23×C61—22no—
322C23×C61—22no—
323C23×C61—22no—
324C23×C61—22no—
325C23×C61—22no—
326C23×C61—22no—
327C23×C61—22no—
328C23×C61—22no—
329C23×C61—22no—
330C23×C61—22no—
331C23×C61C2×C4214yes—
332C23×C61C2×C4⋊C414yes—
333C23×C61#11714yes—
334C23×C61C4×D414yes—
335C23×C61C4×D414yes—
336C23×C61C4×Q814yes—
337C23×C61C4×Q814yes—
338C23×C61C23×C411yescharacteristic
339C23×C61C23×C411yescharacteristic
340C23×C61C23×C411yescharacteristic
341C23×C61C22×D411yescharacteristic
342C23×C61C22×D411yescharacteristic
343C23×C61C22×Q811yescharacteristic
344C23×C61C2×#4111yescharacteristic
345C23×C61C2×#4111yescharacteristic
346C23×C61C2×#4111yescharacteristic
347C23×C61C2×#4111yescharacteristic
348C23×C61C2×#4111yescharacteristic
349C23×C61H(5,𝔽2)11yescharacteristic
350C23×C61H(5,𝔽2)11yescharacteristic
351C23×C61H(5,𝔽2)11yescharacteristic
352C23×C612−1+411yescharacteristic
353C2×C4×C61—22no—
354C2×C4×C61—22no—
355C2×C4×C61—22no—
356C2×C4×C61—22no—
357C2×C4×C61—22no—
358C2×C4×C61—22no—
359C2×C4×C61—22no—
360C2×C4×C61—22no—
361C2×C4×C61—22no—
362C2×C4×C61—22no—
363C2×C4×C61—22no—
364C2×C4×C61—22no—
365C2×C4×C61—22no—
366C2×C4×C61—22no—
367C2×C4×C61—22no—
368C2×C4×C61—22no—
369C2×C4×C61—22no—
370C2×C4×C61—22no—
371C2×C4×C61—22no—
372C2×C4×C61—22no—
373C2×C4×C61—22no—
374C2×C4×C61—22no—
375C2×C4×C61—22no—
376C2×C4×C61—22no—
377C2×C4×C61—22no—
378C2×C4×C61—22no—
379C2×C4×C61—22no—
380C2×C4×C61—416no—
381C2×C4×C61—41no—
382C2×C4×C61—41no—
383C2×C4×C61—41no—
384C2×C4×C61—41no—
385C2×C4×C61—41no—
386C2×C4×C61—41no—
387C2×C4×C61—41no—
388C2×C4×C61—41no—
389C2×C4×C61—41no—
390C2×C4×C61—41no—
391C2×C4×C61—41no—
392C2×C4×C61—41no—
393C2×C4×C61C2×C4⋊C414yes—
394C2×C4×C61C2×C4⋊C414yes—
395C2×C4×C61C4×D414yes—
396C2×Dic61—22no—
397C2×Dic61—22no—
398C2×Dic61—22no—
399C2×Dic61—22no—
400C2×Dic61—22no—
401C2×Dic61—22no—
402C2×Dic61—22no—
403C2×Dic61—22no—
404C2×Dic61—22no—
405C2×Dic61—22no—
406C2×Dic61—22no—
407C2×Dic61—22no—
408C2×Dic61—22no—
409C2×Dic61—22no—
410C2×Dic61—22no—
411C2×Dic61—22no—
412C2×Dic61—22no—
413C2×Dic61—22no—
414C2×Dic61—22no—
415C2×Dic61—22no—
416C2×Dic61—22no—
417C2×Dic61—22no—
418C2×Dic61—22no—
419C2×Dic61—22no—
420C2×Dic61—22no—
421C2×Dic61—22no—
422C2×Dic61—22no—
423C2×Dic61—22no—
424C2×Dic61—22no—
425C2×Dic61—22no—
426C2×Dic61—22no—
427C2×Dic61—22no—
428C2×Dic61—22no—
429C2×Dic61—22no—
430C2×Dic61—22no—
431C2×Dic61—22no—
432C2×Dic61—416no—
433C2×Dic61—416no—
434C2×Dic61—41no—
435C2×Dic61—41no—
436C2×Dic61—41no—
437C2×Dic61—41no—
438C2×Dic61—41no—
439C2×Dic61—41no—
440C2×Dic61—41no—
441C2×Dic61—41no—
442C2×Dic61—41no—
443C2×Dic61—41no—
444C2×Dic61—41no—
445C2×Dic61—41no—
446C2×Dic61—41no—
447C2×Dic61—41no—
448C2×Dic61—41no—
449C2×Dic61—41no—
450C2×Dic61C2×C4214yes—
451C2×Dic61C2×C4214yes—
452C2×Dic61C4×D414yes—
453C2×Dic61C4×D414yes—
454#13814—611nomaximal, Sylow
455C22×C61—24no—
456C22×C61—24no—
457C22×C61—24no—
458C22×C61—24no—
459C22×C61—24no—
460C22×C61—24no—
461C22×C61—24no—
462C22×C61—24no—
463C22×C61—24no—
464C22×C61—24no—
465C22×C61—24no—
466C22×C61—24no—
467C22×C61—24no—
468C22×C61—24no—
469C22×C61C4×C4⋊C418yescomplemented
470C22×C61C22×C4211yescharacteristic
471C22×C61C22×C4⋊C411yescharacteristic
472C22×C61C2×#11711yescharacteristic
473C22×C61C2×C4×D411yescharacteristic
474C22×C61C2×C4×D411yescharacteristic
475C22×C61C2×C4×D411yescharacteristic
476C22×C61C2×C4×D411yescharacteristic
477C22×C61C2×C4×D411yescharacteristic
478C22×C61C2×C4×Q811yescharacteristic
479C22×C61C2×C4×Q811yescharacteristic
480C22×C61C4×#4111yescharacteristic
481C22×C61C4×#4111yescharacteristic
482C22×C61C4×#4111yescharacteristic
483C22×C61#51811yescharacteristic
484C22×C61#51811yescharacteristic
485C22×C61#51811yescharacteristic
486C22×C61#52011yescharacteristic
487C22×C61#52011yescharacteristic
488C22×C61#52011yescharacteristic
489C22×C61D4211yescharacteristic
490C22×C61#54611yescharacteristic
491C22×C61#54611yescharacteristic
492C22×C61#54611yescharacteristic
493C22×C61#54611yescharacteristic
494C22×C61#54711yescharacteristic
495C22×C61D4×Q811yescharacteristic
496C22×C61#55111yescharacteristic
497C22×C61#55111yescharacteristic
498C22×C61#55111yescharacteristic
499C22×C61#55111yescharacteristic
500C22×C61#55211yescharacteristic
501C22×C61#55211yescharacteristic
502C22×C61#55411yescharacteristic
503C22×C61#55411yescharacteristic
504C22×C61#55411yescharacteristic
505C4×C61—24no—
506C4×C61—24no—
507C4×C61—24no—
508C4×C61—42no—
509C4×C61—42no—
510C4×C61—42no—
511Dic61—24no—
512Dic61—24no—
513Dic61—24no—
514Dic61—24no—
515Dic61—42no—
516Dic61—42no—
517Dic61—42no—
518Dic61—42no—
519C2×#385—611no—
520C2×#385—611no—
521C2×C4×C4⋊C4—611no—
522C2×C4×C22⋊C4—611no—
523C2×C4×C22⋊C4—611no—
524C2×C4×C22⋊C4D6111yescharacteristic
525C22×#95—611no—
526#1436—611no—
527#1436—611no—
528#1436—611no—
529#1436—611no—
530C4⋊#95—611no—
531#1434—611no—
532C22⋊#95—611no—
533C4×#95—611no—
534C2×C61—28no—
535C2×C61C2×C4×C4⋊C411yescharacteristic
536C2×C61C42×D411yescharacteristic
537C2×C61#227511yescharacteristic
538C2×C61#234211yescharacteristic
539C2×C61#234311yescharacteristic
540C2×C61D4×C4⋊C411yescharacteristic
541C2×C61#234911yescharacteristic
542C2×C61#235811yescharacteristic
543C2×C61#235811yescharacteristic
544C2×C61#235911yescharacteristic
545C2×C61#235911yescharacteristic
546C2×C61#236011yescharacteristic
547C2×C61#236011yescharacteristic
548C2×C61#236811yescharacteristic
549C2×C61#236811yescharacteristic
550C24×C4—611no—
551C24×C4—611no—
552C24×C4C2×D6111yescharacteristic
553C22×C4⋊C4—611no—
554C22×C4⋊C4—611no—
555C22×C4⋊C4—611no—
556C22×C4⋊C4—611no—
557C22×C22⋊C4—611no—
558C22×C22⋊C4—611no—
559C22×C22⋊C4C2×D6111yescharacteristic
560C22×C22⋊C4C2×D6111yescharacteristic
561C22×C42—611no—
562C22×C42—611no—
563C22×C42—611no—
564C22×C42—611no—
565C22×C42C2×D6111yescharacteristic
566C22×C42C2×D6111yescharacteristic
567#385—618no—
568#385—618no—
569C4×C4⋊C4—1224no—
570C4×C22⋊C4—24no—
571C4×C22⋊C4—618no—
572C4×C22⋊C4—1224no—
573C2×#95—611no—
574C2×#95—611no—
575C2×#95—611no—
576C2×#95—611no—
577C2×#95—611no—
578C2×#95—611no—
579C2×#95—611no—
580C2×#95—611no—
581C2×#95—611no—
582C2×#95—611no—
583C2×#95—611no—
584C2×#95—611no—
585C2×#95—611no—
586C2×#95—611no—
587C2×#95—611no—
588C2×#95—611no—
589C2×#95—1224no—
590C2×#95C2×D6111yescharacteristic
591C2×#95C2×D6111yescharacteristic
592C61#1381411yescharacteristic, complemented, Sylow
593C25C22×D6111yescharacteristic
594C23×C4—22no—
595C23×C4—22no—
596C23×C4—22no—
597C23×C4—22no—
598C23×C4—41no—
599C23×C4—41no—
600C23×C4—611no—
601C23×C4—611no—
602C23×C4—611no—
603C23×C4—611no—
604C23×C4—611no—
605C23×C4—611no—
606C23×C4—611no—
607C23×C4—611no—
608C23×C4—614no—
609C23×C4—614no—
610C23×C4—1222no—
611C23×C4—1222no—
612C23×C4—1222no—
613C23×C4—1222no—
614C23×C4—1222no—
615C23×C4—1222no—
616C23×C4—1222no—
617C23×C4—1222no—
618C23×C4—2441no—
619C23×C4—2441no—
620C23×C4—2441no—
621C23×C4—2441no—
622C23×C4C4×D6114yes—
623C23×C4C22×D6111yescharacteristic
624C23×C4C22×D6111yescharacteristic
625C23×C4C22×D6111yescharacteristic
626C23×C4C22×D6111yescharacteristic
627C23×C4C22×D6111yescharacteristic
628C23×C4C22×D6111yescharacteristic
629C2×C4⋊C4—614no—
630C2×C4⋊C4—614no—
631C2×C4⋊C4—614no—
632C2×C4⋊C4—614no—
633C2×C4⋊C4—1222no—
634C2×C4⋊C4—1222no—
635C2×C4⋊C4—1222no—
636C2×C4⋊C4—1222no—
637C2×C4⋊C4—2441no—
638C2×C4⋊C4—2441no—
639C2×C4⋊C4—2441no—
640C2×C4⋊C4—2441no—
641C2×C22⋊C4—22no—
642C2×C22⋊C4—22no—
643C2×C22⋊C4—614no—
644C2×C22⋊C4—614no—
645C2×C22⋊C4—614no—
646C2×C22⋊C4—614no—
647C2×C22⋊C4—1222no—
648C2×C22⋊C4—1222no—
649C2×C22⋊C4Dic12214yes—
650C2×C22⋊C4C4×D6114yes—
651C2×C22⋊C4C4×D6114yes—
652C2×C22⋊C4C22⋊D6114yes—
653C2×C42—22no—
654C2×C42—22no—
655C2×C42—22no—
656C2×C42—22no—
657C2×C42—41no—
658C2×C42—41no—
659C2×C42—614no—
660C2×C42—614no—
661C2×C42—1222no—
662C2×C42—1222no—
663C2×C42—1222no—
664C2×C42—1222no—
665C2×C42—1222no—
666C2×C42—1222no—
667C2×C42—2441no—
668C2×C42—2441no—
669C2×C42—2441no—
670C2×C42—2441no—
671#95—22no—
672#95—22no—
673#95—614no—
674#95—614no—
675#95—614no—
676#95—614no—
677#95—614no—
678#95—614no—
679#95—614no—
680#95—1222no—
681#95—1222no—
682#95—1222no—
683#95—1222no—
684#95—1222no—
685#95—1222no—
686#95—1222no—
687#95—2441no—
688#95—2441no—
689C24—21no—
690C24—21no—
691C24—21no—
692C24—21no—
693C24—21no—
694C24—21no—
695C24—21no—
696C24—21no—
697C24C2×Dic12212yes—
698C24C2×C4×D6112yes—
699C24C2×C4×D6112yes—
700C24C2×C4×D6112yes—
701C24#1175822212yes—
702C24#1175822212yes—
703C24C2×C22⋊D6112yes—
704C24C23×D6111yescharacteristic
705C22×C4—21no—
706C22×C4—21no—
707C22×C4—21no—
708C22×C4—21no—
709C22×C4—21no—
710C22×C4—21no—
711C22×C4—21no—
712C22×C4—21no—
713C22×C4—21no—
714C22×C4—21no—
715C22×C4—21no—
716C22×C4—21no—
717C22×C4—21no—
718C22×C4—21no—
719C22×C4—21no—
720C22×C4—21no—
721C22×C4—21no—
722C22×C4—21no—
723C22×C4—21no—
724C22×C4—21no—
725C22×C4—21no—
726C22×C4—21no—
727C22×C4—21no—
728C22×C4—21no—
729C22×C4—21no—
730C22×C4—21no—
731C22×C4—21no—
732C22×C4—21no—
733C22×C4—21no—
734C22×C4—21no—
735C22×C4—28no—
736C22×C4—28no—
737C22×C4—44no—
738C22×C4—44no—
739C22×C4—44no—
740C22×C4—44no—
741C22×C4—44no—
742C22×C4—612no—
743C22×C4—612no—
744C22×C4—612no—
745C22×C4—612no—
746C22×C4—612no—
747C22×C4—612no—
748C22×C4—612no—
749C22×C4—612no—
750C22×C4—612no—
751C22×C4—612no—
752C22×C4—612no—
753C22×C4—612no—
754C22×C4—612no—
755C22×C4—612no—
756C22×C4—612no—
757C22×C4—612no—
758C22×C4—1228no—
759C22×C4—1228no—
760C22×C4—1221no—
761C22×C4—1221no—
762C22×C4—1221no—
763C22×C4—1221no—
764C22×C4—1221no—
765C22×C4—1221no—
766C22×C4—1221no—
767C22×C4—1221no—
768C22×C4—1221no—
769C22×C4—1221no—
770C22×C4—1221no—
771C22×C4—1221no—
772C22×C4—1221no—
773C22×C4—1221no—
774C22×C4—1221no—
775C22×C4—1221no—
776C22×C4—1221no—
777C22×C4—1221no—
778C22×C4—1221no—
779C22×C4—1221no—
780C22×C4—1221no—
781C22×C4—1221no—
782C22×C4—1221no—
783C22×C4—1221no—
784C22×C4—1221no—
785C22×C4—1221no—
786C22×C4—1221no—
787C22×C4—1221no—
788C22×C4—1221no—
789C22×C4—1221no—
790C22×C4—1221no—
791C22×C4—1221no—
792C22×C4—1221no—
793C22×C4—1221no—
794C22×C4—1221no—
795C22×C4—1221no—
796C22×C4—1221no—
797C22×C4—1221no—
798C22×C4—1221no—
799C22×C4—1221no—
800C22×C4—1228no—
801C22×C4—1228no—
802C22×C4—2444no—
803C22×C4—2444no—
804C22×C4—2444no—
805C22×C4—2444no—
806C22×C4—2444no—
807C22×C4—2444no—
808C22×C4—2444no—
809C22×C4—2444no—
810C22×C4—2444no—
811C22×C4—2444no—
812C22×C4C2×Dic12212yes—
813C22×C4C2×Dic12212yes—
814C22×C4C2×C4×D6112yes—
815C22×C4C2×C4×D6112yes—
816C22×C4C2×C4×D6112yes—
817C22×C4C2×C4×D6112yes—
818C22×C4C2×C4×D6112yes—
819C22×C4C2×C4×D6112yes—
820C22×C4D4×D6112yes—
821C22×C4#1175822412yes—
822C22×C4C2×C22⋊D6112yes—
823C22×C4C2×C22⋊D6112yes—
824C4⋊C4—1228no—
825C4⋊C4—1228no—
826C4⋊C4—2444no—
827C4⋊C4—2444no—
828C22⋊C4—28no—
829C22⋊C4—6116no—
830C22⋊C4—1228no—
831C22⋊C4#11758196116yescomplemented
832C42—44no—
833C42—44no—
834C42—1228no—
835C42—2444no—
836C42—2444no—
837C42—2444no—
838C23—22no—
839C23—22no—
840C23—22no—
841C23—22no—
842C23—22no—
843C23—22no—
844C23—22no—
845C23—22no—
846C23—22no—
847C23—22no—
848C23—22no—
849C23—22no—
850C23—22no—
851C23—22no—
852C23—22no—
853C23—22no—
854C23—22no—
855C23—22no—
856C23—22no—
857C23—22no—
858C23—22no—
859C23—22no—
860C23—22no—
861C23—22no—
862C23—22no—
863C23—22no—
864C23—22no—
865C23—22no—
866C23C42×D6114yes—
867C23C2×#1175819614yes—
868C23#1451973414yes—
869C23C4×C22⋊D6114yes—
870C23C4×C22⋊D6114yes—
871C23C4×Dic12214yes—
872C23C4×Dic12214yes—
873C23C22×C4×D6111yescharacteristic
874C23C22×C4×D6111yescharacteristic
875C23C22×C4×D6111yescharacteristic
876C23C2×D4×D6111yescharacteristic
877C23C22×C22⋊D6111yescharacteristic
878C23C22×Dic12211yescharacteristic
879C23#41×D6111yescharacteristic
880C23#41×D6111yescharacteristic
881C23C2×#1175822411yescharacteristic
882C23C2×#1175822211yescharacteristic
883C23C2×#1175822211yescharacteristic
884C23#1451982211yescharacteristic
885C23#1451982211yescharacteristic
886C23#1451982311yescharacteristic
887C23#1451982411yescharacteristic
888C2×C4—22no—
889C2×C4—22no—
890C2×C4—22no—
891C2×C4—22no—
892C2×C4—22no—
893C2×C4—22no—
894C2×C4—22no—
895C2×C4—22no—
896C2×C4—22no—
897C2×C4—22no—
898C2×C4—22no—
899C2×C4—22no—
900C2×C4—22no—
901C2×C4—22no—
902C2×C4—22no—
903C2×C4—22no—
904C2×C4—22no—
905C2×C4—22no—
906C2×C4—22no—
907C2×C4—22no—
908C2×C4—22no—
909C2×C4—22no—
910C2×C4—22no—
911C2×C4—22no—
912C2×C4—22no—
913C2×C4—22no—
914C2×C4—22no—
915C2×C4—416no—
916C2×C4—41no—
917C2×C4—41no—
918C2×C4—41no—
919C2×C4—41no—
920C2×C4—41no—
921C2×C4—41no—
922C2×C4—41no—
923C2×C4—41no—
924C2×C4—41no—
925C2×C4—41no—
926C2×C4—41no—
927C2×C4—41no—
928C2×C4—614no—
929C2×C4—614no—
930C2×C4—614no—
931C2×C4—614no—
932C2×C4—1222no—
933C2×C4—1222no—
934C2×C4—1222no—
935C2×C4—1222no—
936C2×C4—1222no—
937C2×C4—1222no—
938C2×C4—1222no—
939C2×C4—1222no—
940C2×C4—1222no—
941C2×C4—1222no—
942C2×C4—1222no—
943C2×C4—1222no—
944C2×C4—1222no—
945C2×C4—1222no—
946C2×C4—1222no—
947C2×C4—1222no—
948C2×C4—1222no—
949C2×C4—1222no—
950C2×C4—1222no—
951C2×C4—1222no—
952C2×C4—1222no—
953C2×C4—1222no—
954C2×C4—1222no—
955C2×C4—1222no—
956C2×C4—1222no—
957C2×C4—1222no—
958C2×C4—1222no—
959C2×C4—1222no—
960C2×C4—1222no—
961C2×C4—1222no—
962C2×C4—1222no—
963C2×C4—1222no—
964C2×C4—1222no—
965C2×C4—1222no—
966C2×C4—1222no—
967C2×C4—1222no—
968C2×C4—24416no—
969C2×C4—24416no—
970C2×C4—2441no—
971C2×C4—2441no—
972C2×C4—2441no—
973C2×C4—2441no—
974C2×C4—2441no—
975C2×C4—2441no—
976C2×C4—2441no—
977C2×C4—2441no—
978C2×C4—2441no—
979C2×C4—2441no—
980C2×C4—2441no—
981C2×C4—2441no—
982C2×C4—2441no—
983C2×C4—2441no—
984C2×C4—2441no—
985C2×C4—2441no—
986C2×C4C2×#1175819614yes—
987C2×C4C2×#1175819614yes—
988C2×C4#1451973714yes—
989C22—24no—
990C22—24no—
991C22—24no—
992C22—24no—
993C22—24no—
994C22—24no—
995C22—24no—
996C22—24no—
997C22—24no—
998C22—24no—
999C22—24no—
1000C22—24no—
1001C22—24no—
1002C22—24no—
1003C22C4×#1175819618yescomplemented
1004C22C2×C42×D6111yescharacteristic
1005C22C22×#1175819611yescharacteristic
1006C22C2×#1451973411yescharacteristic
1007C22C4×D4×D6111yescharacteristic
1008C22C4×D4×D6111yescharacteristic
1009C22C2×#1451973711yescharacteristic
1010C22C2×C4×C22⋊D6111yescharacteristic
1011C22C2×C4×C22⋊D6111yescharacteristic
1012C22C2×C4×Dic12211yescharacteristic
1013C22C2×C4×Dic12211yescharacteristic
1014C22C4×#1175822411yescharacteristic
1015C22C4×#1175822411yescharacteristic
1016C22#1684023011yescharacteristic
1017C22#1684023411yescharacteristic
1018C22#1684023411yescharacteristic
1019C22#1684023511yescharacteristic
1020C22#1684024111yescharacteristic
1021C22#1684024111yescharacteristic
1022C22#1684024211yescharacteristic
1023C22D4×C22⋊D6111yescharacteristic
1024C22#1684040011yescharacteristic
1025C22#1684040211yescharacteristic
1026C22#1684040611yescharacteristic
1027C22#1684040811yescharacteristic
1028C22#1684041111yescharacteristic
1029C22D4×Dic12211yescharacteristic
1030C22#1684043611yescharacteristic
1031C22#1684043811yescharacteristic
1032C22#1684044111yescharacteristic
1033C22#1684044111yescharacteristic
1034C22#1684044511yescharacteristic
1035C22#1684045211yescharacteristic
1036C22#1684046911yescharacteristic
1037C22#1684047111yescharacteristic
1038C22#1684047111yescharacteristic
1039C4—24no—
1040C4—24no—
1041C4—24no—
1042C4—42no—
1043C4—42no—
1044C4—42no—
1045C4—1224no—
1046C4—1224no—
1047C4—1224no—
1048C4—1224no—
1049C4—2442no—
1050C4—2442no—
1051C4—2442no—
1052C4—2442no—
1053C2—28no—
1054C2C2×C4×#1175819611yescharacteristic
1055C2C4×#1451973711yescharacteristic
1056C2#2144817811yescharacteristic
1057C2#2144866211yescharacteristic
1058C2#2144867311yescharacteristic
1059C2D4×#1175819611yescharacteristic
1060C2#2144872411yescharacteristic
1061C2#2144879611yescharacteristic
1062C2#2144879811yescharacteristic
1063C2#2144880511yescharacteristic
1064C2#2144881111yescharacteristic
1065C2#2144882211yescharacteristic
1066C2#2144882511yescharacteristic
1067C2#2144889711yescharacteristic
1068C2#2144890211yescharacteristic
subgroupG/H
center, FrattiniC24C23×D61
commutatorC22×C61C22×C42
FittingC2×C4×C22⋊C4×C61C2
socle, cosocleC24×C61C24
prime radicalC25×C61C23
hypercenterC2×C4×C22⋊C4D61
hypocenterC61#13814
LCSG ▷ C22×C61 ▷ C61
UCSC1 ◁ C24 ◁ C2×C4×C22⋊C4

Complements

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

NH ≅ G/Ntype
3. C2×C4×#11758196C2semidirect
7. #21444052C2semidirect
8. #21444052C2semidirect
9. #21444050C2semidirect
10. #21444050C2semidirect
11. #21444047C2semidirect
12. #21444045C2semidirect
14. C4×#14519684C2semidirect
28. #16839635C4semidirect
29. #16839634C4semidirect
32. C22⋊C4×Dic61C4semidirect
88. C2×#11758196C2×C4semidirect
89. C2×#11758196C2×C4semidirect
90. C2×#11758196C2×C4semidirect
91. C2×#11758196C2×C4semidirect
108. C2×C4×Dic61C2×C4semidirect
109. C2×C4×Dic61C2×C4semidirect
119. #14519684C2×C4semidirect
120. #14519684C2×C4semidirect
121. #14519684C2×C4semidirect
122. #14519684C2×C4semidirect
123. #14519684C2×C4semidirect
124. #14519684C2×C4semidirect
290. C22⋊C4×C61C4⋊C4semidirect
294. C22⋊Dic61C42semidirect
469. C22×C61C4×C4⋊C4semidirect
592. C61#13814semidirect
831. C22⋊C4#11758196semidirect
1003. C22C4×#11758196semidirect

Maximal subgroups

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

subgroupindex
C2×#168396352
C2×#168396342
C2×C4×#117581962
C2×C22⋊C4×Dic612
C22×#145196842
#214440522
#214440502
#214440472
#214440452
#214440412
C4×#145196842
C2×C4×C22⋊C4×C612
#1381461