Finite Group Databasebeta

← #30550786

Subgroups — #30550786

Order 15616.

2362 conjugacy classes of subgroups.

The subgroup lattice has 1182 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840273C211yesmaximal, characteristic, complemented
2#21456656C214yesmaximal, complemented
3#21456645C212yesmaximal, complemented
4#21456629C212yesmaximal, complemented
5#21456607C214yesmaximal, complemented
6#21456596C212yesmaximal, complemented
7#21456580C212yesmaximal, complemented
8#21455763C211yesmaximal, characteristic, complemented
9#21455755C211yesmaximal, characteristic, complemented
10#21455750C212yesmaximal, complemented
11#21455445C212yesmaximal, complemented
12#21455434C212yesmaximal, complemented
13#21455077C211yesmaximal, characteristic, complemented
14#21455069C211yesmaximal, characteristic, complemented
15#21455061C212yesmaximal, complemented
16C2×#16839726C211yesmaximal, characteristic, complemented
17C2×C61×#525C211yesmaximal, characteristic, complemented
18C22×#11758222C2211yescharacteristic
19C2×#14519808C2212yescomplemented
20C2×#14519803C2212yescomplemented
21C22×#11758194C2212yescomplemented
22#16840273—21no—
23#16840273—21no—
24#16840273—21no—
25#16840273—21no—
26#16840273C2212yes—
27#16840273C2212yes—
28#16840273C2212yescomplemented
29#16840273C2212yescomplemented
30C2×#14519760—21no—
31C2×#14519756C2211yescharacteristic, complemented
32C2×#14519756C2211yescharacteristic, complemented
33C2×#14519751C2211yescharacteristic, complemented
34C2×#14519751C2211yescharacteristic, complemented
35C2×#14519746—21no—
36C2×C4×C22⋊D61—21no—
37C2×C4×C22⋊D61—21no—
38C2×#14519736C2211yescharacteristic
39#16840103C2214yescomplemented
40#16840103C2214yescomplemented
41#16840100C2214yescomplemented
42#16840095C2212yescomplemented
43#16840090C2212yescomplemented
44#16840086C2214yescomplemented
45#16840086C2214yescomplemented
46#16840083C2214yescomplemented
47#16840078C2212yescomplemented
48#16840073C2212yescomplemented
49#16840018C2214yescomplemented
50#16840013C2214yescomplemented
51#16840010C2214yescomplemented
52#16840006C2214yescomplemented
53#16840001C2214yescomplemented
54#16839996C2214yescomplemented
55#16839993C2214yescomplemented
56#16839989C2214yescomplemented
57#16839924C2214yescomplemented
58#16839924C2214yescomplemented
59#16839922C2214yescomplemented
60#16839917C2212yescomplemented
61#16839912C2212yescomplemented
62#16839907C2214yescomplemented
63#16839907C2214yescomplemented
64#16839905C2214yescomplemented
65#16839900C2212yescomplemented
66#16839895C2212yescomplemented
67#16839802C2212yescomplemented
68#16839802C2212yescomplemented
69#16839771C2212yescomplemented
70#16839767C2212yescomplemented
71#16839761C2212yescomplemented
72#16839761C2212yescomplemented
73#16839726C2211yescharacteristic
74#16839726C2211yescharacteristic
75#16839726C2212yescomplemented
76#16839726C2212yescomplemented
77#16839726C2212yescomplemented
78C2×C22⋊#92418C2212yescomplemented
79C2×C22⋊#92418C2212yescomplemented
80C22×#41×C61C2211yescharacteristic, complemented
81C24×C4×C61C2211yescharacteristic
82C61×#525—21no—
83C61×#525—21no—
84C61×#525—21no—
85C61×#525—21no—
86C61×#525C2212yes—
87C61×#525C2212yes—
88C61×#525C2212yescomplemented
89C61×#525C2212yescomplemented
90C2×#123×C61—21no—
91C2×C22⋊Q8×C61C2211yescharacteristic
92C2×C22⋊Q8×C61C2211yescharacteristic, complemented
93C2×#121×C61C2211yescharacteristic
94C2×#121×C61C2211yescharacteristic, complemented
95C2×#120×C61—21no—
96C2×C4×D4×C61—21no—
97C2×C4×D4×C61—21no—
98C2×#117×C61C2211yescharacteristic, complemented
99C2×#11758222—21no—
100C2×#11758222—21no—
101C2×#11758222—44no—
102C2×#11758222C2312yes—
103C2×#11758222C2312yes—
104C22×Dic122C2311yescharacteristic
105C22×D244C2311yescharacteristic
106C22×C22⋊D61—21no—
107C22×C22⋊D61—21no—
108C22×C22⋊D61—21no—
109C22×C4×D61—21no—
110#14519808—44no—
111#14519803—44no—
112C2×#11758202C2314yescomplemented
113C2×#11758200C2314yescomplemented
114C2×#11758201C2314yescomplemented
115C2×#11758199C2314yescomplemented
116C2×#11758194—44no—
117C2×#11758194C2312yes—
118C2×#11758194C2312yes—
119C2×#11758194C2314yes—
120C22×#92418C2314yes—
121#14519760—22no—
122#14519760—22no—
123#14519760—22no—
124#14519760—22no—
125#14519756—21no—
126#14519756—21no—
127#14519756—21no—
128#14519756—21no—
129#14519756C2312yes—
130#14519756C2312yes—
131#14519756C2312yes—
132#14519756C2312yes—
133#14519751—21no—
134#14519751—21no—
135#14519751—21no—
136#14519751—21no—
137#14519751C2312yes—
138#14519751C2312yes—
139#14519751C2312yes—
140#14519751C2312yes—
141#14519746—22no—
142#14519746—22no—
143#14519746—22no—
144#14519746—22no—
145C4×C22⋊D61—22no—
146C4×C22⋊D61—22no—
147C4×C22⋊D61—22no—
148C4×C22⋊D61—22no—
149C4×C22⋊D61—22no—
150C4×C22⋊D61—22no—
151C4×C22⋊D61—22no—
152C4×C22⋊D61—22no—
153#14519736—21no—
154#14519736—21no—
155#14519736C2312yes—
156#14519736C2312yes—
157C2×C4⋊Dic61C2311yescharacteristic
158C2×C4⋊Dic61C2311yescharacteristic
159C2×#11758196—21no—
160C2×#11758196—21no—
161C2×C22⋊Dic61—21no—
162C2×C22⋊Dic61—21no—
163C2×C22⋊Dic61—21no—
164C2×#11758198—21no—
165C2×#11758198—21no—
166C2×C4×Dic61—21no—
167#14519710C2314yescomplemented
168#14519710C2314yescomplemented
169#14519708C2314yescomplemented
170#14519708C2314yescomplemented
171#14519701C2314yescomplemented
172#14519701C2314yescomplemented
173#14519700C2314yescomplemented
174#14519700C2314yescomplemented
175#14519698C2314yescomplemented
176#14519698C2314yescomplemented
177#14519697C2314yescomplemented
178#14519697C2314yescomplemented
179C22⋊#92418C2312yes—
180C22⋊#92418C2312yes—
181C22⋊#92418C2312yes—
182C22⋊#92418C2312yes—
183C22⋊#92418C2314yes—
184C22⋊#92418C2314yes—
185C25×C61D411yescharacteristic
186C2×#41×C61—21no—
187C2×#41×C61—21no—
188C2×#41×C61—44no—
189C2×#41×C61C2312yes—
190C2×#41×C61C2312yes—
191C22×Q8×C61C2311yescharacteristic
192C22×D4×C61—21no—
193C22×D4×C61—21no—
194C22×D4×C61—21no—
195C22×D4×C61C2311yescharacteristic
196C23×C4×C61—21no—
197C23×C4×C61—44no—
198C23×C4×C61D411yescharacteristic
199C23×C4×C61D411yescharacteristic
200C23×C4×C61D411yescharacteristic
201C23×C4×C61D411yescharacteristic
202C23×C4×C61D411yescharacteristic
203C23×C4×C61D411yescharacteristic
204C23×C4×C61D411yescharacteristic
205C23×C4×C61C2311yescharacteristic
206C23×C4×C61C2311yescharacteristic
207C23×C4×C61C2311yescharacteristic
208C23×C4×C61C2311yescharacteristic
209C23×C4×C61C2311yescharacteristic
210C23×C4×C61C2311yescharacteristic
211C23×C4×C61C2311yescharacteristic
212#123×C61—22no—
213#123×C61—22no—
214#123×C61—22no—
215#123×C61—22no—
216C22⋊Q8×C61—21no—
217C22⋊Q8×C61—21no—
218C22⋊Q8×C61—21no—
219C22⋊Q8×C61—21no—
220C22⋊Q8×C61C2312yes—
221C22⋊Q8×C61C2312yes—
222C22⋊Q8×C61C2312yes—
223C22⋊Q8×C61C2312yes—
224#121×C61—21no—
225#121×C61—21no—
226#121×C61—21no—
227#121×C61—21no—
228#121×C61C2312yes—
229#121×C61C2312yes—
230#121×C61C2312yes—
231#121×C61C2312yes—
232#120×C61—22no—
233#120×C61—22no—
234#120×C61—22no—
235#120×C61—22no—
236C4×D4×C61—22no—
237C4×D4×C61—22no—
238C4×D4×C61—22no—
239C4×D4×C61—22no—
240C4×D4×C61—22no—
241C4×D4×C61—22no—
242C4×D4×C61—22no—
243C4×D4×C61—22no—
244#117×C61—21no—
245#117×C61—21no—
246#117×C61C2312yes—
247#117×C61C2312yes—
248C2×C4⋊C4×C61—21no—
249C2×C4⋊C4×C61—21no—
250C2×C4⋊C4×C61C2311yescharacteristic
251C2×C4⋊C4×C61C2311yescharacteristic
252C2×C22⋊C4×C61—21no—
253C2×C22⋊C4×C61—21no—
254C2×C22⋊C4×C61—21no—
255C2×C22⋊C4×C61—21no—
256C2×C22⋊C4×C61—21no—
257C2×C42×C61—21no—
258C24×C61—21no—
259C24×C61—42no—
260C24×C61—42no—
261C24×C61—42no—
262C24×C61C2×D411yescharacteristic
263C24×C61C2×D411yescharacteristic
264C24×C61C2×D411yescharacteristic
265C24×C61C2×D411yescharacteristic
266C24×C61C2×D411yescharacteristic
267C24×C61C2×D411yescharacteristic
268C24×C61C2×D411yescharacteristic
269C23×D61—21no—
270#41×C61—44no—
271#41×C61—44no—
272#41×C61—44no—
273#41×C61—44no—
274C2×Q8×C61—21no—
275C2×Q8×C61—24no—
276C2×Q8×C61C2412yes—
277C2×D4×C61—22no—
278C2×D4×C61—22no—
279C2×D4×C61—22no—
280C2×D4×C61—22no—
281C2×D4×C61—22no—
282C2×D4×C61—22no—
283C2×D4×C61—21no—
284C2×D4×C61—24no—
285C2×D4×C61—44no—
286C2×D4×C61—44no—
287C2×D4×C61—44no—
288C2×D4×C61C2412yes—
289C22×C4×C61—24no—
290C22×C4×C61—24no—
291C22×C4×C61—24no—
292C22×C4×C61—21no—
293C22×C4×C61—21no—
294C22×C4×C61—21no—
295C22×C4×C61—22no—
296C22×C4×C61—22no—
297C22×C4×C61—42no—
298C22×C4×C61—42no—
299C22×C4×C61—42no—
300C22×C4×C61—42no—
301C22×C4×C61—42no—
302C22×C4×C61—42no—
303C22×C4×C61—42no—
304C22×C4×C61—42no—
305C22×C4×C61—42no—
306C22×C4×C61—42no—
307C22×C4×C61—42no—
308C22×C4×C61—44no—
309C22×C4×C61C2×D411yescharacteristic
310C22×C4×C61C2×D411yescharacteristic
311C22×C4×C61C2×D411yescharacteristic
312C22×C4×C61C2×D411yescharacteristic
313C22×C4×C61C2×D411yescharacteristic
314C22×C4×C61C2×D411yescharacteristic
315C22×C4×C61C2×D411yescharacteristic
316C22×C4×C61C2×D411yescharacteristic
317C22×C4×C61C2×D411yescharacteristic
318C22×C4×C61C2×D411yescharacteristic
319C22×C4×C61C2×D411yescharacteristic
320C22×C4×C61C2×D411yescharacteristic
321C22×C4×C61C2×D411yescharacteristic
322C22×C4×C61C2×D411yescharacteristic
323C22×C4×C61C2×D411yescharacteristic
324C22×C4×C61C2×D411yescharacteristic
325C22×C4×C61C2×D411yescharacteristic
326C22×C4×C61C2×D411yescharacteristic
327C22×C4×C61C2×D411yescharacteristic
328C22×C4×C61C2×D411yescharacteristic
329C22×C4×C61C2×D411yescharacteristic
330C22×C4×C61C2411yescharacteristic
331C22×C4×C61C2411yescharacteristic
332C22×C4×C61C2411yescharacteristic
333C22×C4×C61C2411yescharacteristic
334C22×C4×C61C2411yescharacteristic
335C22×C4×C61C2411yescharacteristic
336C22×C4×C61C2411yescharacteristic
337C2×C22⋊D61—22no—
338C2×C22⋊D61—22no—
339C2×C22⋊D61—22no—
340C2×C22⋊D61—22no—
341C2×C22⋊D61—22no—
342C2×C22⋊D61—22no—
343C2×C22⋊D61—44no—
344C2×C22⋊D61—44no—
345C2×C22⋊D61—44no—
346C22×Dic61—21no—
347C22×Dic61—21no—
348C22×Dic61—21no—
349#11758222—24no—
350#11758222—24no—
351#11758222—42no—
352#11758222—42no—
353#11758222—44no—
354#11758222—44no—
355C2×D244—21no—
356C2×D244—42no—
357C2×D244C2412yes—
358C2×C4×D61—22no—
359C2×C4×D61—22no—
360C2×C4×D61—44no—
361C2×Dic122—21no—
362C2×Dic122—42no—
363C2×Dic122C2412yes—
364C4⋊C4×C61—22no—
365C4⋊C4×C61—22no—
366C4⋊C4×C61—22no—
367C4⋊C4×C61—22no—
368C4⋊C4×C61—21no—
369C4⋊C4×C61—21no—
370C4⋊C4×C61C2412yes—
371C4⋊C4×C61C2412yes—
372C22⋊C4×C61—22no—
373C22⋊C4×C61—22no—
374C22⋊C4×C61—22no—
375C22⋊C4×C61—22no—
376C22⋊C4×C61—22no—
377C22⋊C4×C61—22no—
378C22⋊C4×C61—22no—
379C22⋊C4×C61—22no—
380C22⋊C4×C61—22no—
381C22⋊C4×C61—22no—
382C42×C61—22no—
383C42×C61—22no—
384C22⋊Dic61—22no—
385C22⋊Dic61—22no—
386C22⋊Dic61—22no—
387C22⋊Dic61—22no—
388C22⋊Dic61—22no—
389C22⋊Dic61—22no—
390#11758202—44no—
391#11758201—44no—
392#11758200—44no—
393#11758199—44no—
394#11758198—22no—
395#11758198—22no—
396#11758198—22no—
397#11758198—22no—
398C4⋊Dic61—21no—
399C4⋊Dic61—21no—
400C4⋊Dic61C2412yes—
401C4⋊Dic61C2412yes—
402#11758196—22no—
403#11758196—22no—
404#11758196—22no—
405#11758196—22no—
406C4×Dic61—22no—
407C4×Dic61—22no—
408#11758194—24no—
409#11758194—24no—
410#11758194—44no—
411C2×#92418—44no—
412C2×#92418C2414yes—
413C2×#92418C2414yes—
414C23×C61—22no—
415C23×C61—22no—
416C23×C61—22no—
417C23×C61—22no—
418C23×C61—22no—
419C23×C61—22no—
420C23×C61—22no—
421C23×C61—22no—
422C23×C61—22no—
423C23×C61—22no—
424C23×C61—41no—
425C23×C61—41no—
426C23×C61—41no—
427C23×C61—41no—
428C23×C61—41no—
429C23×C61—41no—
430C23×C61—41no—
431C23×C61—41no—
432C23×C61—41no—
433C23×C61—41no—
434C23×C61—41no—
435C23×C61—41no—
436C23×C61—42no—
437C23×C61—42no—
438C23×C61—416no—
439C23×C61—42no—
440C23×C61C22×D411yescharacteristic
441C23×C61C22×D411yescharacteristic
442C23×C61C22×D411yescharacteristic
443C23×C61C22×D411yescharacteristic
444C23×C61C22×D411yescharacteristic
445C23×C61C22×D411yescharacteristic
446C23×C61C22×D411yescharacteristic
447C22×D61—22no—
448C22×D61—42no—
449C22×D61—42no—
450C22×D61—42no—
451Q8×C61—24no—
452Q8×C61—42no—
453D4×C61—24no—
454D4×C61—44no—
455D4×C61—44no—
456D4×C61—44no—
457D4×C61—44no—
458D4×C61—44no—
459D4×C61—44no—
460D4×C61—42no—
461C2×C4×C61—22no—
462C2×C4×C61—22no—
463C2×C4×C61—22no—
464C2×C4×C61—22no—
465C2×C4×C61—22no—
466C2×C4×C61—22no—
467C2×C4×C61—22no—
468C2×C4×C61—22no—
469C2×C4×C61—22no—
470C2×C4×C61—22no—
471C2×C4×C61—22no—
472C2×C4×C61—22no—
473C2×C4×C61—22no—
474C2×C4×C61—22no—
475C2×C4×C61—22no—
476C2×C4×C61—22no—
477C2×C4×C61—22no—
478C2×C4×C61—22no—
479C2×C4×C61—41no—
480C2×C4×C61—41no—
481C2×C4×C61—41no—
482C2×C4×C61—41no—
483C2×C4×C61—41no—
484C2×C4×C61—41no—
485C2×C4×C61—41no—
486C2×C4×C61—41no—
487C2×C4×C61—41no—
488C2×C4×C61—41no—
489C2×C4×C61—41no—
490C2×C4×C61—41no—
491C2×C4×C61—44no—
492C2×C4×C61—44no—
493C2×C4×C61—42no—
494C2×C4×C61—42no—
495C2×C4×C61—42no—
496C2×C4×C61C22×D411yescharacteristic
497C2×C4×C61C22×D411yescharacteristic
498C2×C4×C61C22×D411yescharacteristic
499C2×C4×C61C22×D411yescharacteristic
500C2×C4×C61C22×D411yescharacteristic
501C2×C4×C61C22×D411yescharacteristic
502C2×C4×C61C22×D411yescharacteristic
503C2×C4×C61H(5,𝔽2)14yes—
504C2×C4×C61C2511yescharacteristic
505C22⋊D61—44no—
506C22⋊D61—44no—
507C22⋊D61—44no—
508C22⋊D61—44no—
509C22⋊D61—44no—
510C22⋊D61—44no—
511C2×Dic61—22no—
512C2×Dic61—22no—
513C2×Dic61—22no—
514C2×Dic61—42no—
515C2×Dic61—42no—
516C2×Dic61—42no—
517D244—22no—
518D244—22no—
519D244—42no—
520C4×D61—44no—
521C4×D61—44no—
522Dic122—22no—
523Dic122—22no—
524Dic122—42no—
525#92418—24no—
526#92418—24no—
527#60752—611nomaximal, Sylow
528C22×C61—21no—
529C22×C61—21no—
530C22×C61—21no—
531C22×C61—21no—
532C22×C61—21no—
533C22×C61—21no—
534C22×C61—21no—
535C22×C61—21no—
536C22×C61—21no—
537C22×C61—21no—
538C22×C61—21no—
539C22×C61—21no—
540C22×C61—21no—
541C22×C61—21no—
542C22×C61—21no—
543C22×C61—21no—
544C22×C61—21no—
545C22×C61—21no—
546C22×C61—44no—
547C22×C61—44no—
548C22×C61—44no—
549C22×C61—44no—
550C22×C61—44no—
551C22×C61—44no—
552C22×C61—44no—
553C22×C61—42no—
554C22×C61—42no—
555C22×C61—42no—
556C22×C61—84no—
557C22×C61#53412yes—
558C22×C61#57512yes—
559C22×C61#57512yes—
560C22×C61C23×D411yescharacteristic
561C2×D61—42no—
562C2×D61—42no—
563C2×D61—42no—
564C2×D61—84no—
565C4×C61—21no—
566C4×C61—21no—
567C4×C61—21no—
568C4×C61—21no—
569C4×C61—21no—
570C4×C61—21no—
571C4×C61—42no—
572C4×C61—42no—
573C4×C61—42no—
574C4×C61#53412yes—
575C4×C61C2×H(5,𝔽2)12yes—
576Dic61—42no—
577Dic61—42no—
578Dic61—42no—
579C2×#525—611no—
580C2×#525D6111yescharacteristic, complemented
581#3197—614no—
582#3196—612no—
583#3194—612no—
584#3191—614no—
585#3190—612no—
586#3188—612no—
587#3095—611no—
588#3094—611no—
589#3093—612no—
590#3056—612no—
591#3055—612no—
592#3007—611no—
593#3006—611no—
594#3005—612no—
595C2×#407—611no—
596C2×C61—22no—
597C2×C61—22no—
598C2×C61—22no—
599C2×C61—41no—
600C2×C61—41no—
601C2×C61—41no—
602C2×C61—41no—
603C2×C61—82no—
604C2×C61C2×#53411yescharacteristic
605C2×C61C2×#57511yescharacteristic
606C2×C61C2×#57511yescharacteristic
607D61—82no—
608C22×#41—611no—
609C22×#41C2×D6111yescharacteristic, complemented
610C24×C4C2×D6111yescharacteristic
611C2×#137—612no—
612C2×AGL(1,ℤ/8)—612no—
613C22×M16—612no—
614#525—21no—
615#525—21no—
616#525—21no—
617#525—21no—
618#525—612no—
619#525—612no—
620#525—612no—
621#525—612no—
622#525—1221no—
623#525—1221no—
624#525—1221no—
625#525—1221no—
626#525C2×D6112yes—
627#525C2×D6112yes—
628#525C2×D6112yescomplemented
629#525C2×D6112yescomplemented
630C2×#123—21no—
631C2×#123—1221no—
632C2×C22⋊Q8—611no—
633C2×C22⋊Q8—611no—
634C2×C22⋊Q8C2×D6111yescharacteristic
635C2×C22⋊Q8C2×D6111yescharacteristic, complemented
636C2×#121—611no—
637C2×#121—611no—
638C2×#121C2×D6111yescharacteristic
639C2×#121C2×D6111yescharacteristic, complemented
640C2×#120—21no—
641C2×#120—1221no—
642C2×C4×D4—21no—
643C2×C4×D4—21no—
644C2×C4×D4—1221no—
645C2×C4×D4—1221no—
646C2×#117—611no—
647C2×#117C2×D6111yescharacteristic, complemented
648#485—614no—
649#485—614no—
650#485—614no—
651#484—612no—
652#483—612no—
653#482—614no—
654#482—614no—
655#482—614no—
656#481—612no—
657#480—612no—
658#470—614no—
659#469—614no—
660#468—614no—
661#468—614no—
662#467—614no—
663#466—614no—
664#465—614no—
665#465—614no—
666#452—614no—
667#452—614no—
668#452—614no—
669#451—612no—
670#450—612no—
671#449—614no—
672#449—614no—
673#449—614no—
674#448—612no—
675#447—612no—
676#428—612no—
677#428—612no—
678#419—612no—
679#418—612no—
680#417—612no—
681#417—612no—
682#407—612no—
683#407—611no—
684#407—611no—
685#407—612no—
686#407—612no—
687C2×C22⋊C8—612no—
688C2×C22⋊C8—612no—
689C61#6075211yescharacteristic, complemented, Sylow
690C25C22⋊D6111yescharacteristic
691C2×#41—21no—
692C2×#41—21no—
693C2×#41—44no—
694C2×#41—612no—
695C2×#41—612no—
696C2×#41—1221no—
697C2×#41—1221no—
698C2×#41—2444no—
699C2×#41C22×D6112yes—
700C2×#41C22×D6112yes—
701C22×Q8—611no—
702C22×Q8C22×D6111yescharacteristic
703C22×D4—21no—
704C22×D4—21no—
705C22×D4—21no—
706C22×D4—611no—
707C22×D4—1221no—
708C22×D4—1221no—
709C22×D4—1221no—
710C22×D4C22×D6111yescharacteristic
711C23×C4—21no—
712C23×C4—44no—
713C23×C4—1221no—
714C23×C4C22⋊D6111yescharacteristic
715C23×C4C22⋊D6111yescharacteristic
716C23×C4C22⋊D6111yescharacteristic
717C23×C4C22⋊D6111yescharacteristic
718C23×C4C22⋊D6111yescharacteristic
719C23×C4C22⋊D6111yescharacteristic
720C23×C4C22⋊D6111yescharacteristic
721C23×C4C22×D6111yescharacteristic
722C23×C4C22×D6111yescharacteristic
723C23×C4C22×D6111yescharacteristic
724C23×C4C22×D6111yescharacteristic
725C23×C4C22×D6111yescharacteristic
726C23×C4C22×D6111yescharacteristic
727C23×C4C22×D6111yescharacteristic
728#137—2444no—
729AGL(1,ℤ/8)—2444no—
730C2×Q16—614no—
731C2×SD16—614no—
732C2×SD16—614no—
733C2×D8—614no—
734C2×M16—612no—
735C2×M16—612no—
736C2×M16—614no—
737C2×M16—2444no—
738C22×C8—614no—
739#123—22no—
740#123—22no—
741#123—22no—
742#123—22no—
743#123—1222no—
744#123—1222no—
745#123—1222no—
746#123—1222no—
747C22⋊Q8—21no—
748C22⋊Q8—21no—
749C22⋊Q8—21no—
750C22⋊Q8—21no—
751C22⋊Q8—612no—
752C22⋊Q8—612no—
753C22⋊Q8—612no—
754C22⋊Q8—612no—
755C22⋊Q8—1221no—
756C22⋊Q8—1221no—
757C22⋊Q8—1221no—
758C22⋊Q8—1221no—
759C22⋊Q8C22×D6112yes—
760C22⋊Q8C22×D6112yes—
761C22⋊Q8C22×D6112yes—
762C22⋊Q8C22×D6112yes—
763#121—21no—
764#121—21no—
765#121—21no—
766#121—21no—
767#121—612no—
768#121—612no—
769#121—612no—
770#121—612no—
771#121—1221no—
772#121—1221no—
773#121—1221no—
774#121—1221no—
775#121C22×D6112yes—
776#121C22×D6112yes—
777#121C22×D6112yes—
778#121C22×D6112yes—
779#120—22no—
780#120—22no—
781#120—22no—
782#120—22no—
783#120—1222no—
784#120—1222no—
785#120—1222no—
786#120—1222no—
787C4×D4—22no—
788C4×D4—22no—
789C4×D4—22no—
790C4×D4—22no—
791C4×D4—22no—
792C4×D4—22no—
793C4×D4—22no—
794C4×D4—22no—
795C4×D4—1222no—
796C4×D4—1222no—
797C4×D4—1222no—
798C4×D4—1222no—
799C4×D4—1222no—
800C4×D4—1222no—
801C4×D4—1222no—
802C4×D4—1222no—
803#117—21no—
804#117—21no—
805#117—612no—
806#117—612no—
807#117—1221no—
808#117—1221no—
809#117C22×D6112yes—
810#117C22×D6112yes—
811C2×C4⋊C4—21no—
812C2×C4⋊C4—21no—
813C2×C4⋊C4—611no—
814C2×C4⋊C4—611no—
815C2×C4⋊C4—1221no—
816C2×C4⋊C4—1221no—
817C2×C4⋊C4C22×D6111yescharacteristic
818C2×C4⋊C4C22×D6111yescharacteristic
819C2×C22⋊C4—21no—
820C2×C22⋊C4—21no—
821C2×C22⋊C4—21no—
822C2×C22⋊C4—21no—
823C2×C22⋊C4—21no—
824C2×C22⋊C4—1221no—
825C2×C22⋊C4—1221no—
826C2×C22⋊C4—1221no—
827C2×C22⋊C4—1221no—
828C2×C22⋊C4—1221no—
829C2×C42—21no—
830C2×C42—1221no—
831#107—614no—
832#107—614no—
833#106—614no—
834#106—614no—
835#103—614no—
836#103—614no—
837#103—614no—
838#103—614no—
839#102—614no—
840#102—614no—
841#102—614no—
842#102—614no—
843C22⋊C8—612no—
844C22⋊C8—612no—
845C22⋊C8—614no—
846C22⋊C8—614no—
847C22⋊C8—612no—
848C22⋊C8—612no—
849C24—21no—
850C24—42no—
851C24—42no—
852C24—42no—
853C24—1221no—
854C24C2×C22⋊D6111yescharacteristic
855C24C2×C22⋊D6111yescharacteristic
856C24C2×C22⋊D6111yescharacteristic
857C24C2×C22⋊D6111yescharacteristic
858C24C2×C22⋊D6111yescharacteristic
859C24C2×C22⋊D6111yescharacteristic
860C24C2×C22⋊D6111yescharacteristic
861#41—44no—
862#41—44no—
863#41—44no—
864#41—44no—
865#41—1224no—
866#41—1224no—
867#41—2442no—
868#41—2442no—
869#41—2444no—
870#41—2444no—
871C2×Q8—21no—
872C2×Q8—24no—
873C2×Q8—612no—
874C2×Q8—1221no—
875C2×Q8—2442no—
876C2×Q8C23×D6112yes—
877C2×D4—22no—
878C2×D4—22no—
879C2×D4—22no—
880C2×D4—22no—
881C2×D4—22no—
882C2×D4—22no—
883C2×D4—21no—
884C2×D4—24no—
885C2×D4—44no—
886C2×D4—44no—
887C2×D4—44no—
888C2×D4—612no—
889C2×D4—1222no—
890C2×D4—1222no—
891C2×D4—1222no—
892C2×D4—1222no—
893C2×D4—1222no—
894C2×D4—1222no—
895C2×D4—1221no—
896C2×D4—2442no—
897C2×D4—2444no—
898C2×D4—2444no—
899C2×D4—2444no—
900C2×D4C23×D6112yes—
901C22×C4—24no—
902C22×C4—24no—
903C22×C4—24no—
904C22×C4—21no—
905C22×C4—21no—
906C22×C4—21no—
907C22×C4—22no—
908C22×C4—22no—
909C22×C4—42no—
910C22×C4—42no—
911C22×C4—42no—
912C22×C4—42no—
913C22×C4—42no—
914C22×C4—42no—
915C22×C4—42no—
916C22×C4—42no—
917C22×C4—42no—
918C22×C4—42no—
919C22×C4—42no—
920C22×C4—44no—
921C22×C4—1221no—
922C22×C4—1221no—
923C22×C4—1221no—
924C22×C4—1222no—
925C22×C4—1222no—
926C22×C4—2444no—
927C22×C4C2×C22⋊D6111yescharacteristic
928C22×C4C2×C22⋊D6111yescharacteristic
929C22×C4C2×C22⋊D6111yescharacteristic
930C22×C4C2×C22⋊D6111yescharacteristic
931C22×C4C2×C22⋊D6111yescharacteristic
932C22×C4C2×C22⋊D6111yescharacteristic
933C22×C4C2×C22⋊D6111yescharacteristic
934C22×C4C2×C22⋊D6111yescharacteristic
935C22×C4C2×C22⋊D6111yescharacteristic
936C22×C4C2×C22⋊D6111yescharacteristic
937C22×C4C2×C22⋊D6111yescharacteristic
938C22×C4C2×C22⋊D6111yescharacteristic
939C22×C4C2×C22⋊D6111yescharacteristic
940C22×C4C2×C22⋊D6111yescharacteristic
941C22×C4C2×C22⋊D6111yescharacteristic
942C22×C4C2×C22⋊D6111yescharacteristic
943C22×C4C2×C22⋊D6111yescharacteristic
944C22×C4C2×C22⋊D6111yescharacteristic
945C22×C4C2×C22⋊D6111yescharacteristic
946C22×C4C2×C22⋊D6111yescharacteristic
947C22×C4C2×C22⋊D6111yescharacteristic
948C22×C4C23×D6111yescharacteristic
949C22×C4C23×D6111yescharacteristic
950C22×C4C23×D6111yescharacteristic
951C22×C4C23×D6111yescharacteristic
952C22×C4C23×D6111yescharacteristic
953C22×C4C23×D6111yescharacteristic
954C22×C4C23×D6111yescharacteristic
955Q16—2444no—
956SD16—2444no—
957SD16—2444no—
958D8—2444no—
959M16—1224no—
960M16—1224no—
961M16—2444no—
962C2×C8—614no—
963C2×C8—614no—
964C2×C8—2444no—
965C4⋊C4—22no—
966C4⋊C4—22no—
967C4⋊C4—22no—
968C4⋊C4—22no—
969C4⋊C4—21no—
970C4⋊C4—21no—
971C4⋊C4—612no—
972C4⋊C4—612no—
973C4⋊C4—1221no—
974C4⋊C4—1221no—
975C4⋊C4—1222no—
976C4⋊C4—1222no—
977C4⋊C4—1222no—
978C4⋊C4—1222no—
979C4⋊C4C23×D6112yes—
980C4⋊C4C23×D6112yes—
981C22⋊C4—22no—
982C22⋊C4—22no—
983C22⋊C4—22no—
984C22⋊C4—22no—
985C22⋊C4—22no—
986C22⋊C4—22no—
987C22⋊C4—22no—
988C22⋊C4—22no—
989C22⋊C4—22no—
990C22⋊C4—22no—
991C22⋊C4—1222no—
992C22⋊C4—1222no—
993C22⋊C4—1222no—
994C22⋊C4—1222no—
995C22⋊C4—1222no—
996C22⋊C4—1222no—
997C22⋊C4—1222no—
998C22⋊C4—1222no—
999C22⋊C4—1222no—
1000C22⋊C4—1222no—
1001C42—22no—
1002C42—22no—
1003C42—1222no—
1004C42—1222no—
1005C23—22no—
1006C23—22no—
1007C23—22no—
1008C23—22no—
1009C23—22no—
1010C23—22no—
1011C23—22no—
1012C23—22no—
1013C23—22no—
1014C23—22no—
1015C23—41no—
1016C23—41no—
1017C23—41no—
1018C23—41no—
1019C23—41no—
1020C23—41no—
1021C23—41no—
1022C23—41no—
1023C23—41no—
1024C23—41no—
1025C23—41no—
1026C23—41no—
1027C23—42no—
1028C23—42no—
1029C23—416no—
1030C23—42no—
1031C23—1222no—
1032C23—2442no—
1033C23—2442no—
1034C23—2442no—
1035C23C22×C22⋊D6111yescharacteristic
1036C23C22×C22⋊D6111yescharacteristic
1037C23C22×C22⋊D6111yescharacteristic
1038C23C22×C22⋊D6111yescharacteristic
1039C23C22×C22⋊D6111yescharacteristic
1040C23C22×C22⋊D6111yescharacteristic
1041C23C22×C22⋊D6111yescharacteristic
1042Q8—24no—
1043Q8—42no—
1044Q8—1222no—
1045Q8—1222no—
1046Q8—2442no—
1047D4—24no—
1048D4—44no—
1049D4—44no—
1050D4—44no—
1051D4—44no—
1052D4—44no—
1053D4—44no—
1054D4—42no—
1055D4—1222no—
1056D4—1222no—
1057D4—2442no—
1058D4—2444no—
1059D4—2444no—
1060D4—2444no—
1061D4—2444no—
1062D4—2444no—
1063D4—2444no—
1064C2×C4—22no—
1065C2×C4—22no—
1066C2×C4—22no—
1067C2×C4—22no—
1068C2×C4—22no—
1069C2×C4—22no—
1070C2×C4—22no—
1071C2×C4—22no—
1072C2×C4—22no—
1073C2×C4—22no—
1074C2×C4—22no—
1075C2×C4—22no—
1076C2×C4—22no—
1077C2×C4—22no—
1078C2×C4—22no—
1079C2×C4—22no—
1080C2×C4—22no—
1081C2×C4—22no—
1082C2×C4—41no—
1083C2×C4—41no—
1084C2×C4—41no—
1085C2×C4—41no—
1086C2×C4—41no—
1087C2×C4—41no—
1088C2×C4—41no—
1089C2×C4—41no—
1090C2×C4—41no—
1091C2×C4—41no—
1092C2×C4—41no—
1093C2×C4—41no—
1094C2×C4—44no—
1095C2×C4—44no—
1096C2×C4—42no—
1097C2×C4—42no—
1098C2×C4—42no—
1099C2×C4—1222no—
1100C2×C4—1222no—
1101C2×C4—1222no—
1102C2×C4—2444no—
1103C2×C4—2442no—
1104C2×C4—2442no—
1105C2×C4—2442no—
1106C2×C4—2444no—
1107C2×C4C22×C22⋊D6111yescharacteristic
1108C2×C4C22×C22⋊D6111yescharacteristic
1109C2×C4C22×C22⋊D6111yescharacteristic
1110C2×C4C22×C22⋊D6111yescharacteristic
1111C2×C4C22×C22⋊D6111yescharacteristic
1112C2×C4C22×C22⋊D6111yescharacteristic
1113C2×C4C22×C22⋊D6111yescharacteristic
1114C2×C4#1451982214yes—
1115C2×C4C24×D6111yescharacteristic
1116C8—1224no—
1117C8—1224no—
1118C22—21no—
1119C22—21no—
1120C22—21no—
1121C22—21no—
1122C22—21no—
1123C22—21no—
1124C22—21no—
1125C22—21no—
1126C22—21no—
1127C22—21no—
1128C22—21no—
1129C22—21no—
1130C22—21no—
1131C22—21no—
1132C22—21no—
1133C22—21no—
1134C22—21no—
1135C22—21no—
1136C22—44no—
1137C22—44no—
1138C22—44no—
1139C22—44no—
1140C22—44no—
1141C22—44no—
1142C22—44no—
1143C22—42no—
1144C22—42no—
1145C22—42no—
1146C22—84no—
1147C22—4884no—
1148C22—2442no—
1149C22—2442no—
1150C22—2442no—
1151C22#1684032112yes—
1152C22#1684056012yes—
1153C22#1684056012yes—
1154C22C23×C22⋊D6111yescharacteristic
1155C4—21no—
1156C4—21no—
1157C4—21no—
1158C4—21no—
1159C4—21no—
1160C4—21no—
1161C4—42no—
1162C4—42no—
1163C4—42no—
1164C4—2442no—
1165C4—2442no—
1166C4—2442no—
1167C4#1684032112yes—
1168C4C2×#1451982212yes—
1169C2—22no—
1170C2—22no—
1171C2—22no—
1172C2—41no—
1173C2—41no—
1174C2—41no—
1175C2—41no—
1176C2—82no—
1177C2—4882no—
1178C2C2×#1684032111yescharacteristic
1179C2C2×#1684056011yescharacteristic
1180C2C2×#1684056011yescharacteristic
subgroupG/H
centerC22C23×C22⋊D61
commutator, cosocleC2×C4×C61C25
FrattiniC2×C4C24×D61
FittingC2×C61×#525C2
socleC22×C61C23×D4
hypercenterC2×#525D61
hypocenterC61#60752
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C24×C4 ◁ C2×#525

Complements

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

NH ≅ G/Ntype
1. C2×#16840273C2semidirect
2. #21456656C2semidirect
3. #21456645C2semidirect
4. #21456629C2semidirect
5. #21456607C2semidirect
6. #21456596C2semidirect
7. #21456580C2semidirect
8. #21455763C2semidirect
9. #21455755C2semidirect
10. #21455750C2semidirect
11. #21455445C2semidirect
12. #21455434C2semidirect
13. #21455077C2semidirect
14. #21455069C2semidirect
15. #21455061C2semidirect
16. C2×#16839726C2semidirect
17. C2×C61×#525C2semidirect
19. C2×#14519808C22semidirect
20. C2×#14519803C22semidirect
21. C22×#11758194C22semidirect
28. #16840273C22semidirect
29. #16840273C22semidirect
31. C2×#14519756C22semidirect
32. C2×#14519756C22semidirect
33. C2×#14519751C22semidirect
34. C2×#14519751C22semidirect
39. #16840103C22semidirect
40. #16840103C22semidirect
41. #16840100C22semidirect
42. #16840095C22semidirect
43. #16840090C22semidirect
44. #16840086C22semidirect
45. #16840086C22semidirect
46. #16840083C22semidirect
47. #16840078C22semidirect
48. #16840073C22semidirect
49. #16840018C22semidirect
50. #16840013C22semidirect
51. #16840010C22semidirect
52. #16840006C22semidirect
53. #16840001C22semidirect
54. #16839996C22semidirect
55. #16839993C22semidirect
56. #16839989C22semidirect
57. #16839924C22semidirect
58. #16839924C22semidirect
59. #16839922C22semidirect
60. #16839917C22semidirect
61. #16839912C22semidirect
62. #16839907C22semidirect
63. #16839907C22semidirect
64. #16839905C22semidirect
65. #16839900C22semidirect
66. #16839895C22semidirect
67. #16839802C22semidirect
68. #16839802C22semidirect
69. #16839771C22semidirect
70. #16839767C22semidirect
71. #16839761C22semidirect
72. #16839761C22semidirect
75. #16839726C22semidirect
76. #16839726C22semidirect
77. #16839726C22semidirect
78. C2×C22⋊#92418C22semidirect
79. C2×C22⋊#92418C22semidirect
80. C22×#41×C61C22semidirect
88. C61×#525C22semidirect
89. C61×#525C22semidirect
92. C2×C22⋊Q8×C61C22semidirect
94. C2×#121×C61C22semidirect
98. C2×#117×C61C22semidirect
112. C2×#11758202C23semidirect
113. C2×#11758200C23semidirect
114. C2×#11758201C23semidirect
115. C2×#11758199C23semidirect
167. #14519710C23semidirect
168. #14519710C23semidirect
169. #14519708C23semidirect
170. #14519708C23semidirect
171. #14519701C23semidirect
172. #14519701C23semidirect
173. #14519700C23semidirect
174. #14519700C23semidirect
175. #14519698C23semidirect
176. #14519698C23semidirect
177. #14519697C23semidirect
178. #14519697C23semidirect
580. C2×#525D61semidirect
609. C22×#41C2×D61semidirect
628. #525C2×D61semidirect
629. #525C2×D61semidirect
635. C2×C22⋊Q8C2×D61semidirect
639. C2×#121C2×D61semidirect
647. C2×#117C2×D61semidirect
689. C61#60752semidirect

Maximal subgroups

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

subgroupindex
C2×#168402732
#214566562
#214566452
#214566292
#214566072
#214565962
#214565802
#214557632
#214557552
#214557502
#214554452
#214554342
#214550772
#214550692
#214550612
C2×#168397262
C2×C61×#5252
#6075261