Finite Group Databasebeta

← #30576225

Subgroups — #30576225

Order 15616.

1702 conjugacy classes of subgroups.

The subgroup lattice has 1234 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21459434C211yesmaximal, characteristic
2#21458782C212yesmaximal, complemented
3#21458661C212yesmaximal, complemented
4#21458343C212yesmaximal, complemented
5#21458259C212yesmaximal, complemented
6#21458181C212yesmaximal, complemented
7#21457879C212yesmaximal, complemented
8#21457864C212yesmaximal, complemented
9#21457700C212yesmaximal, complemented
10#21457186C211yesmaximal, characteristic, complemented
11#21457161C211yesmaximal, characteristic, complemented
12#21457150C211yesmaximal, characteristic, complemented
13#21457040C211yesmaximal, characteristic, complemented
14#21457033C211yesmaximal, characteristic, complemented
15#21456998C211yesmaximal, characteristic, complemented
16#21455975C211yesmaximal, characteristic, complemented
17#21455945C211yesmaximal, characteristic, complemented
18#21455854C211yesmaximal, characteristic, complemented
19#21455620C211yesmaximal, characteristic, complemented
20#21455601C211yesmaximal, characteristic, complemented
21C2×#16840054C211yesmaximal, characteristic, complemented
22#21454944C211yesmaximal, characteristic, complemented
23C61×#3509C211yesmaximal, characteristic, complemented
24#16840490C2211yescharacteristic
25#16840485C2211yescharacteristic
26#16840480—21no—
27#16840452C2211yescharacteristic
28#16840452C2211yescharacteristic
29#16840445—21no—
30#16840445—21no—
31D4×Dic122C2211yescharacteristic
32#16840421C2211yescharacteristic
33#16840421C2211yescharacteristic
34#16840416C2211yescharacteristic
35#16840411—21no—
36#16840319C2211yescharacteristic
37#16840316—21no—
38#16840296C2211yescharacteristic
39#16840296C2211yescharacteristic
40#16840292—21no—
41#16840292—21no—
42C4×#11758222C2211yescharacteristic
43C4×#11758224—21no—
44C2×C4×Dic122C2211yescharacteristic
45C2×C4×Dic122C2211yescharacteristic
46#16840172C2212yes—
47#16840168C2212yes—
48#16840161C2212yes—
49#16840132C2212yes—
50#16840124C2212yes—
51#16840119C2212yes—
52#16840103C2212yes—
53#16840103C2212yes—
54#16840103C2212yes—
55#16840100C2212yes—
56#16840095C2212yes—
57#16840092C2212yes—
58#16840090C2212yes—
59#16840086C2212yes—
60#16840075C2212yes—
61#16840069C2212yes—
62#16840069C2212yes—
63#16840066C2212yes—
64#16840066C2212yes—
65#16840066C2212yes—
66#16840059C2212yes—
67#16840057C2212yes—
68#16840054C2211yescharacteristic
69#16840054C2211yescharacteristic
70#16840054C2211yescharacteristic
71#16840054C2211yescharacteristic
72#16840054C2212yes—
73#16840054C2211yescharacteristic
74#16840054C2212yes—
75#16840054C2211yescharacteristic
76#16840049C2211yescharacteristic
77#16840049C2211yescharacteristic
78#16840044C2211yescharacteristic
79#16840044C2211yescharacteristic
80#16840044C2211yescharacteristic
81#16840039C2211yescharacteristic
82#16840018C2212yes—
83#16840010C2212yes—
84#16840001C2212yes—
85#16840001C2212yes—
86#16840001C2212yes—
87#16839993C2212yes—
88#16839984C2212yes—
89#16839984C2212yes—
90#16839972C2212yes—
91#16839969C2211yescharacteristic
92#16839969C2211yescharacteristic
93#16839969C2211yescharacteristic
94#16839964C2211yescharacteristic
95#16839922C2212yes—
96#16839917C2212yes—
97#16839917C2212yes—
98#16839893C2212yes—
99#16839867C2212yes—
100#16839867C2212yes—
101#16839867C2212yes—
102#16839860C2212yes—
103C4×#11758202C2212yes—
104C4×#11758202C2212yes—
105#16839834C2212yes—
106#16839834C2212yes—
107D4×#92418C2212yes—
108#16839819C2211yescharacteristic
109#16839819C2211yescharacteristic
110#16839815C2211yescharacteristic
111#16839805C2212yes—
112#16839798C2212yes—
113C2×#14519710C2212yes—
114#16839786C2211yescharacteristic
115C2×C4⋊#92418C2211yescharacteristic
116C2×C4⋊#92418C2211yescharacteristic
117#16839770C2212yes—
118#16839756C2212yes—
119C2×#14519700C2212yes—
120C61×#557—21no—
121C61×#557C2212yes—
122C61×#556—21no—
123C61×#556C2212yes—
124C61×#552—21no—
125C61×#552—21no—
126C61×#552C2212yes—
127C61×#552C2212yes—
128C61×#541—21no—
129C61×#541—21no—
130C61×#536—21no—
131C61×#533C2211yescharacteristic
132C61×#533C2211yescharacteristic
133C61×#533C2211yescharacteristic
134C61×#533C2211yescharacteristic
135C61×#533C2211yescharacteristic
136C2×C4⋊Q8×C61C2211yescharacteristic
137C61×#519—21no—
138C4×#41×C61C2211yescharacteristic
139C2×#11758222C2311yescharacteristic
140C2×#11758224—21no—
141C22×Dic122C2311yescharacteristic
142C22×Dic122C2311yescharacteristic
143C2×#11758202C2312yes—
144C2×#11758202C2312yes—
145C2×#11758202C2312yes—
146C2×#11758201C2312yes—
147C2×#11758194C2312yes—
148C22×#92418C2312yes—
149C22×#92418C2312yes—
150#14519777C2311yescharacteristic
151#14519777C2311yescharacteristic
152#14519776—21no—
153#14519775—21no—
154#14519772—21no—
155#14519772—21no—
156#14519771—21no—
157#14519771—21no—
158#14519770—21no—
159#14519770—21no—
160#14519769—21no—
161#14519769C2311yescharacteristic
162#14519769C2311yescharacteristic
163#14519767—21no—
164#14519767—21no—
165#14519767—21no—
166#14519767—21no—
167#14519765C2311yescharacteristic
168#14519765C2311yescharacteristic
169#14519763—21no—
170#14519763—21no—
171#14519761—21no—
172#14519761—21no—
173#14519760—21no—
174#14519760—21no—
175#14519758—21no—
176#14519758—21no—
177#14519757—21no—
178#14519756—21no—
179#14519756C2311yescharacteristic
180#14519756C2311yescharacteristic
181#14519756C2311yescharacteristic
182#14519756C2311yescharacteristic
183#14519755—21no—
184#14519755—21no—
185#14519754—21no—
186#14519754—21no—
187#14519753—21no—
188#14519751C2311yescharacteristic
189#14519751C2311yescharacteristic
190#14519749—21no—
191#14519749—21no—
192C4×Dic122—21no—
193C4×Dic122—21no—
194C4×Dic122—21no—
195C4×Dic122—21no—
196C4×Dic122—21no—
197C4×Dic122C2311yescharacteristic
198C4×Dic122C2311yescharacteristic
199C4×Dic122C2311yescharacteristic
200C4×Dic122C2311yescharacteristic
201C4×Dic122C2311yescharacteristic
202C4×Dic122C2311yescharacteristic
203C4×Dic122C2311yescharacteristic
204C4×Dic122C2311yescharacteristic
205#14519742—21no—
206C4×D244C2311yescharacteristic
207C4×D244C2311yescharacteristic
208D4×Dic61—21no—
209C4×C22⋊D61—21no—
210C4×C22⋊D61—21no—
211C4×C22⋊D61—21no—
212C4×C22⋊D61—21no—
213#14519737—21no—
214#14519737—21no—
215#14519736—21no—
216#14519736C2311yescharacteristic
217#14519735—21no—
218#14519734—21no—
219#14519734—21no—
220#14519734—21no—
221#14519733—21no—
222#14519733—21no—
223C2×C4⋊Dic61C2311yescharacteristic
224C2×C4⋊Dic61C2311yescharacteristic
225C2×#11758196—21no—
226C2×#11758196—21no—
227C2×C4×Dic61—21no—
228C2×C4×Dic61—21no—
229C42×D61—21no—
230#14519710C2312yes—
231#14519710C2312yes—
232#14519710C2312yes—
233#14519710C2312yes—
234#14519710C2312yes—
235#14519710C2312yes—
236#14519710C2312yes—
237#14519708C2312yes—
238#14519708C2312yes—
239#14519708C2312yes—
240#14519708C2312yes—
241#14519708C2312yes—
242C4⋊#92418C2311yescharacteristic
243C4⋊#92418C2311yescharacteristic
244C4⋊#92418C2311yescharacteristic
245C4⋊#92418C2311yescharacteristic
246C4⋊#92418C2312yes—
247C4⋊#92418C2312yes—
248C4⋊#92418C2312yes—
249#14519701C2312yes—
250#14519701C2312yes—
251#14519701C2312yes—
252#14519701C2312yes—
253#14519700C2312yes—
254#14519700C2312yes—
255#14519700C2312yes—
256#14519700C2312yes—
257#14519700C2312yes—
258#14519700C2312yes—
259#14519700C2312yes—
260#14519700C2312yes—
261#14519700C2312yes—
262#14519697C2312yes—
263#14519697C2312yes—
264#14519697C2312yes—
265C22⋊#92418C2312yes—
266C22⋊#92418C2312yes—
267C22⋊#92418C2312yes—
268#14519688C2312yes—
269#14519688C2312yes—
270C4×#92418C2312yes—
271C2×#41×C61D411yescharacteristic
272C22×Q8×C61—21no—
273C4⋊Q8×C61—22no—
274C4⋊Q8×C61—21no—
275C4⋊Q8×C61—21no—
276C4⋊Q8×C61C2311yescharacteristic
277C4⋊Q8×C61C2311yescharacteristic
278C4⋊Q8×C61C2311yescharacteristic
279C4⋊Q8×C61C2312yes—
280C4⋊Q8×C61C2311yescharacteristic
281#126×C61—22no—
282#126×C61—22no—
283#126×C61—22no—
284#126×C61—22no—
285#125×C61—22no—
286#125×C61—22no—
287#125×C61—22no—
288#125×C61—22no—
289#125×C61—21no—
290#125×C61—21no—
291#125×C61—21no—
292#125×C61C2312yes—
293#125×C61C2312yes—
294#124×C61—22no—
295#123×C61—22no—
296#123×C61—22no—
297C22⋊Q8×C61—21no—
298C22⋊Q8×C61—21no—
299C22⋊Q8×C61—21no—
300C22⋊Q8×C61—21no—
301C22⋊Q8×C61—21no—
302C22⋊Q8×C61—21no—
303C22⋊Q8×C61—21no—
304C22⋊Q8×C61C2312yes—
305C22⋊Q8×C61C2312yes—
306C22⋊Q8×C61C2312yes—
307C4×Q8×C61—22no—
308C4×Q8×C61—22no—
309C4×Q8×C61—21no—
310C4×Q8×C61—21no—
311C4×Q8×C61—21no—
312C4×Q8×C61—21no—
313C4×Q8×C61—21no—
314C4×Q8×C61—21no—
315C4×Q8×C61—21no—
316C4×Q8×C61D411yescharacteristic
317C4×Q8×C61C2312yes—
318C4×Q8×C61C2312yes—
319C4×Q8×C61C2312yes—
320C4×Q8×C61C2311yescharacteristic
321C4×D4×C61D411yescharacteristic
322C4×D4×C61D411yescharacteristic
323C4×D4×C61D411yescharacteristic
324C4×D4×C61C2311yescharacteristic
325C4×D4×C61C2311yescharacteristic
326C4×D4×C61C2311yescharacteristic
327#117×C61—21no—
328#117×C61—21no—
329#117×C61—21no—
330#117×C61—22no—
331#117×C61—22no—
332#117×C61D411yescharacteristic
333#117×C61D411yescharacteristic
334#117×C61D411yescharacteristic
335#117×C61C2312yes—
336#117×C61C2312yes—
337C2×C4⋊C4×C61—21no—
338C2×C4⋊C4×C61C2312yes—
339C2×C42×C61C2311yescharacteristic
340C2×C42×C61C2311yescharacteristic
341C2×C42×C61C2311yescharacteristic
342#41×C61—42no—
343C2×Q8×C61—21no—
344C2×Q8×C61—21no—
345C2×Q8×C61—21no—
346C2×Q8×C61—22no—
347C2×Q8×C61—44no—
348C2×Q8×C61C2×D411yescharacteristic
349C2×Q8×C61C2412yes—
350C2×D4×C61C2×D411yescharacteristic
351C2×D4×C61C2×D411yescharacteristic
352C2×D4×C61C2×D411yescharacteristic
353C22×C4×C61—22no—
354C22×C4×C61C2×D411yescharacteristic
355C22×C4×C61C2×D411yescharacteristic
356C22×C4×C61C2×D411yescharacteristic
357C22×C4×C61C2×D411yescharacteristic
358C22×C4×C61C2×D411yescharacteristic
359C22×C4×C61C2×D411yescharacteristic
360C22×C4×C61C2411yescharacteristic
361C22×C4×C61C2411yescharacteristic
362C22×C4×C61C2411yescharacteristic
363C2×C22⋊D61—21no—
364C2×C22⋊D61—21no—
365C2×C22⋊D61—21no—
366C22×Dic61—21no—
367C22×Dic61—21no—
368C22×Dic61—21no—
369C22×Dic61—21no—
370#11758224—44no—
371#11758222—22no—
372#11758222—41no—
373C2×D244C2411yescharacteristic
374C2×C4×D61—21no—
375C2×C4×D61—21no—
376C2×C4×D61—21no—
377C2×Dic122—22no—
378C2×Dic122—22no—
379C2×Dic122—21no—
380C2×Dic122—21no—
381C2×Dic122—21no—
382C2×Dic122—41no—
383C2×Dic122—41no—
384C2×Dic122C2411yescharacteristic
385C2×Dic122C2411yescharacteristic
386C2×Dic122C2411yescharacteristic
387C4⋊C4×C61—21no—
388C4⋊C4×C61—21no—
389C4⋊C4×C61—22no—
390C4⋊C4×C61—22no—
391C4⋊C4×C61—21no—
392C4⋊C4×C61—21no—
393C4⋊C4×C61—21no—
394C4⋊C4×C61—22no—
395C4⋊C4×C61—22no—
396C4⋊C4×C61—22no—
397C4⋊C4×C61—22no—
398C4⋊C4×C61—22no—
399C4⋊C4×C61—22no—
400C4⋊C4×C61—22no—
401C4⋊C4×C61—22no—
402C4⋊C4×C61—22no—
403C4⋊C4×C61—22no—
404C4⋊C4×C61C2×D411yescharacteristic
405C4⋊C4×C61C2×D411yescharacteristic
406C4⋊C4×C61C2×D411yescharacteristic
407C4⋊C4×C61C2×D411yescharacteristic
408C4⋊C4×C61C2×D411yescharacteristic
409C4⋊C4×C61C2×D411yescharacteristic
410C4⋊C4×C61C2412yes—
411C4⋊C4×C61C2412yes—
412C4⋊C4×C61C2412yes—
413C22⋊C4×C61—22no—
414C22⋊C4×C61—22no—
415C22⋊C4×C61—22no—
416C22⋊C4×C61—22no—
417C22⋊C4×C61—22no—
418C22⋊C4×C61C2×D411yescharacteristic
419C22⋊C4×C61C2×D411yescharacteristic
420C22⋊C4×C61C2×D411yescharacteristic
421C22⋊C4×C61C2×D411yescharacteristic
422C22⋊C4×C61C2×D411yescharacteristic
423C22⋊C4×C61C2×D411yescharacteristic
424C42×C61—22no—
425C42×C61—22no—
426C42×C61—22no—
427C42×C61—22no—
428C42×C61—22no—
429C42×C61C2×D411yescharacteristic
430C42×C61C2×D411yescharacteristic
431C42×C61C2×D411yescharacteristic
432C42×C61C2×D411yescharacteristic
433C42×C61C2×D411yescharacteristic
434C42×C61C2×D411yescharacteristic
435C42×C61C2411yescharacteristic
436C42×C61C2411yescharacteristic
437C42×C61C2411yescharacteristic
438C42×C61C2411yescharacteristic
439C22⋊Dic61—21no—
440C22⋊Dic61—21no—
441C22⋊Dic61—21no—
442C22⋊Dic61—21no—
443C22⋊Dic61—21no—
444#11758202—24no—
445#11758202—42no—
446#11758202—42no—
447#11758201—42no—
448#11758198—21no—
449#11758198—21no—
450#11758198—21no—
451#11758198—21no—
452#11758198—21no—
453#11758198—21no—
454#11758198—21no—
455#11758198—21no—
456C4⋊Dic61—21no—
457C4⋊Dic61—21no—
458C4⋊Dic61—21no—
459C4⋊Dic61—21no—
460C4⋊Dic61—21no—
461C4⋊Dic61C2411yescharacteristic
462C4⋊Dic61C2411yescharacteristic
463C4⋊Dic61C2411yescharacteristic
464C4⋊Dic61C2411yescharacteristic
465#11758196—21no—
466#11758196—21no—
467#11758196—21no—
468#11758196—21no—
469#11758196—21no—
470#11758196—21no—
471#11758196—21no—
472#11758196—21no—
473#11758196—21no—
474#11758196—21no—
475#11758196—21no—
476#11758196—21no—
477#11758196—21no—
478#11758196—21no—
479#11758196—21no—
480#11758196—21no—
481C4×Dic61—21no—
482C4×Dic61—21no—
483C4×Dic61—21no—
484C4×Dic61—21no—
485C4×Dic61—21no—
486C4×Dic61—21no—
487C4×Dic61—21no—
488C4×Dic61—21no—
489C4×Dic61—21no—
490#11758194—42no—
491C2×#92418—42no—
492C2×#92418—42no—
493C2×#92418C2412yes—
494C2×#92418C2412yes—
495C2×#92418C2412yes—
496C2×#92418C2412yes—
497C23×C61C22×D411yescharacteristic
498C23×C61C22×D411yescharacteristic
499C23×C61C22×D411yescharacteristic
500C22×D61—21no—
501Q8×C61—22no—
502Q8×C61—22no—
503Q8×C61—41no—
504Q8×C61—42no—
505Q8×C61—42no—
506Q8×C61—44no—
507Q8×C61—42no—
508D4×C61—22no—
509D4×C61—22no—
510D4×C61—41no—
511C2×C4×C61—22no—
512C2×C4×C61—22no—
513C2×C4×C61—22no—
514C2×C4×C61—22no—
515C2×C4×C61—21no—
516C2×C4×C61—21no—
517C2×C4×C61—21no—
518C2×C4×C61—21no—
519C2×C4×C61—21no—
520C2×C4×C61—21no—
521C2×C4×C61—22no—
522C2×C4×C61—22no—
523C2×C4×C61—22no—
524C2×C4×C61—22no—
525C2×C4×C61—41no—
526C2×C4×C61—41no—
527C2×C4×C61—44no—
528C2×C4×C61C22×D411yescharacteristic
529C2×C4×C61C22×D411yescharacteristic
530C2×C4×C61C22×D411yescharacteristic
531C2×C4×C61C22×D411yescharacteristic
532C2×C4×C61C22×D411yescharacteristic
533C2×C4×C61C22×D411yescharacteristic
534C2×C4×C61C22×D411yescharacteristic
535C2×C4×C61C22×D411yescharacteristic
536C2×C4×C61C22×D411yescharacteristic
537C2×C4×C61C22×D411yescharacteristic
538C2×C4×C61C22×D411yescharacteristic
539C2×C4×C61C2511yescharacteristic
540C22⋊D61—42no—
541C22⋊D61—42no—
542C22⋊D61—42no—
543C2×Dic61—21no—
544C2×Dic61—21no—
545C2×Dic61—21no—
546C2×Dic61—21no—
547C2×Dic61—21no—
548C2×Dic61—21no—
549C2×Dic61—21no—
550C2×Dic61—42no—
551C2×Dic61—42no—
552C2×Dic61—42no—
553C2×Dic61—42no—
554D244—21no—
555D244—21no—
556C4×D61—42no—
557C4×D61—42no—
558C4×D61—42no—
559Dic122—21no—
560Dic122—21no—
561Dic122—21no—
562Dic122—21no—
563Dic122—21no—
564Dic122—42no—
565Dic122—42no—
566Dic122—42no—
567Dic1222−1+412yes—
568#92418—22no—
569#92418—22no—
570#92418—22no—
571#92418—22no—
572#62130—611nomaximal, Sylow
573C22×C61—21no—
574C22×C61—21no—
575C22×C61—21no—
576C22×C61—21no—
577C22×C61—21no—
578C22×C61—21no—
579C22×C61—21no—
580C22×C61—21no—
581C22×C61#57512yes—
582C22×C61C23×D411yescharacteristic
583C2×D61—41no—
584C2×D61—41no—
585C2×D61—41no—
586C4×C61—21no—
587C4×C61—21no—
588C4×C61—21no—
589C4×C61—21no—
590C4×C61—21no—
591C4×C61—21no—
592C4×C61—21no—
593C4×C61—21no—
594C4×C61—21no—
595C4×C61—21no—
596C4×C61—42no—
597C4×C61—42no—
598C4×C61—42no—
599C4×C61—42no—
600C4×C61#57812yes—
601C4×C61C2×2−1+411yescharacteristic
602C4×C61#58511yescharacteristic
603Dic61—22no—
604Dic61—41no—
605Dic61—41no—
606Dic61—41no—
607Dic61—41no—
608Dic61—41no—
609Dic61—41no—
610#3509D6111yescharacteristic, complemented
611#3482—611no—
612#3390—612no—
613#3377—612no—
614#3349—612no—
615#3343—612no—
616#3336—612no—
617#3313—612no—
618#3312—612no—
619#3300—612no—
620#3252—611no—
621#3249—611no—
622#3248—611no—
623#3238—611no—
624#3237—611no—
625#3233—611no—
626#3116—611no—
627#3113—611no—
628#3104—611no—
629#3078—611no—
630#3076—611no—
631C2×#477—611no—
632#2990—611no—
633C2×C61—22no—
634C2×C61—41no—
635C2×C61—41no—
636C2×C61#348911yescharacteristic
637C2×C61C2×#57511yescharacteristic
638C2×C61C2×#57811yescharacteristic
639D61—81no—
640#557—21no—
641#557—611no—
642#557C2×D6112yes—
643#556—21no—
644#556—611no—
645#556—1221no—
646#556C2×D6112yes—
647#552—21no—
648#552—21no—
649#552—611no—
650#552—611no—
651#552—1221no—
652#552—1221no—
653#552C2×D6112yes—
654#552C2×D6112yes—
655D4×Q8—611no—
656#548—611no—
657#548—611no—
658#547—611no—
659#547—1221no—
660#541—21no—
661#541—21no—
662#536—21no—
663#533—611no—
664#533—1221no—
665#533C2×D6111yescharacteristic
666#533C2×D6111yescharacteristic
667#533C2×D6111yescharacteristic
668#533C2×D6111yescharacteristic
669#533C2×D6111yescharacteristic
670C2×C4⋊Q8C2×D6111yescharacteristic
671#529—611no—
672#529—611no—
673#529—1221no—
674#529—1221no—
675#519—21no—
676C4×#41—611no—
677C4×#41—1221no—
678C4×#41C2×D6111yescharacteristic
679C2×C4×Q8—611no—
680C2×C4×Q8—611no—
681#501—612no—
682#501—612no—
683#499—612no—
684#491—612no—
685#489—612no—
686#488—612no—
687#485—612no—
688#485—612no—
689#485—612no—
690#485—612no—
691#484—612no—
692#483—612no—
693#483—612no—
694#482—612no—
695#480—612no—
696#479—612no—
697#479—612no—
698#479—612no—
699#479—612no—
700#479—612no—
701#478—612no—
702#477—611no—
703#477—611no—
704#477—612no—
705#477—612no—
706#477—611no—
707#477—611no—
708#477—611no—
709#477—611no—
710#477—612no—
711#476—611no—
712#476—611no—
713#475—611no—
714#475—611no—
715#475—611no—
716#474—611no—
717#470—612no—
718#468—612no—
719#467—612no—
720#467—612no—
721#467—612no—
722#465—612no—
723#464—612no—
724#464—612no—
725#462—611no—
726#462—611no—
727#462—611no—
728#462—612no—
729#461—611no—
730#452—612no—
731#451—612no—
732#451—612no—
733#446—612no—
734#441—612no—
735#441—612no—
736#441—612no—
737#440—612no—
738C4×Q16—612no—
739C4×Q16—612no—
740#435—612no—
741#435—612no—
742C8×D4—612no—
743#432—611no—
744#432—611no—
745#431—611no—
746#428—612no—
747#427—612no—
748C2×#107—612no—
749#423—611no—
750C2×C4⋊C8—611no—
751C2×C4⋊C8—611no—
752#419—612no—
753#416—612no—
754C2×#103—612no—
755C61#6213011yescharacteristic, complemented, Sylow
756C2×#41—611no—
757C2×#41—1221no—
758C2×#41C22⋊D6111yescharacteristic
759C22×Q8—21no—
760C22×Q8—611no—
761C22×Q8—611no—
762C2×Q16—612no—
763C2×Q16—612no—
764C2×Q16—612no—
765C2×SD16—612no—
766C2×M16—612no—
767C22×C8—612no—
768C22×C8—612no—
769C4⋊Q8—22no—
770C4⋊Q8—21no—
771C4⋊Q8—21no—
772C4⋊Q8—611no—
773C4⋊Q8—611no—
774C4⋊Q8—1221no—
775C4⋊Q8—1221no—
776C4⋊Q8C22×D6111yescharacteristic
777C4⋊Q8C22×D6111yescharacteristic
778C4⋊Q8C22×D6111yescharacteristic
779C4⋊Q8C22×D6112yes—
780C4⋊Q8C22×D6111yescharacteristic
781#126—22no—
782#126—22no—
783#126—22no—
784#126—22no—
785#126—1221no—
786#126—1221no—
787#126—1221no—
788#126—1221no—
789#126—1221no—
790#126—1221no—
791#125—22no—
792#125—22no—
793#125—22no—
794#125—22no—
795#125—21no—
796#125—21no—
797#125—21no—
798#125—611no—
799#125—611no—
800#125—1221no—
801#125—1221no—
802#125—1221no—
803#125—1221no—
804#125—1221no—
805#125C22×D6112yes—
806#125C22×D6112yes—
807#124—22no—
808#124—611no—
809#124—611no—
810#124—1221no—
811#124—1221no—
812#123—22no—
813#123—22no—
814#123—1221no—
815#123—1221no—
816#123—1221no—
817#123—1221no—
818#123—1221no—
819#123—1221no—
820C22⋊Q8—21no—
821C22⋊Q8—21no—
822C22⋊Q8—21no—
823C22⋊Q8—21no—
824C22⋊Q8—21no—
825C22⋊Q8—21no—
826C22⋊Q8—21no—
827C22⋊Q8—611no—
828C22⋊Q8—611no—
829C22⋊Q8—611no—
830C22⋊Q8—611no—
831C22⋊Q8—1221no—
832C22⋊Q8—1221no—
833C22⋊Q8—1221no—
834C22⋊Q8—1221no—
835C22⋊Q8—1221no—
836C22⋊Q8—1221no—
837C22⋊Q8—1221no—
838C22⋊Q8C22×D6112yes—
839C22⋊Q8C22×D6112yes—
840C22⋊Q8C22×D6112yes—
841#121—611no—
842#121—611no—
843#121—1221no—
844#121—1221no—
845C4×Q8—22no—
846C4×Q8—22no—
847C4×Q8—21no—
848C4×Q8—21no—
849C4×Q8—21no—
850C4×Q8—21no—
851C4×Q8—21no—
852C4×Q8—21no—
853C4×Q8—21no—
854C4×Q8—611no—
855C4×Q8—611no—
856C4×Q8—611no—
857C4×Q8—611no—
858C4×Q8—611no—
859C4×Q8—611no—
860C4×Q8—611no—
861C4×Q8—611no—
862C4×Q8—1221no—
863C4×Q8—1221no—
864C4×Q8—1221no—
865C4×Q8—1221no—
866C4×Q8—1221no—
867C4×Q8—1221no—
868C4×Q8C22⋊D6111yescharacteristic
869C4×Q8C22×D6112yes—
870C4×Q8C22×D6112yes—
871C4×Q8C22×D6112yes—
872C4×Q8C22×D6111yescharacteristic
873C4×D4—611no—
874C4×D4—611no—
875C4×D4—1221no—
876C4×D4—1221no—
877C4×D4—1221no—
878C4×D4—1221no—
879C4×D4—1221no—
880C4×D4—1221no—
881C4×D4—1221no—
882C4×D4C22⋊D6111yescharacteristic
883C4×D4C22⋊D6111yescharacteristic
884C4×D4C22⋊D6111yescharacteristic
885C4×D4C22×D6111yescharacteristic
886C4×D4C22×D6111yescharacteristic
887C4×D4C22×D6111yescharacteristic
888#117—21no—
889#117—21no—
890#117—21no—
891#117—22no—
892#117—22no—
893#117—611no—
894#117—1221no—
895#117—1221no—
896#117—1221no—
897#117—1221no—
898#117—1221no—
899#117—1221no—
900#117—1221no—
901#117C22⋊D6111yescharacteristic
902#117C22⋊D6111yescharacteristic
903#117C22⋊D6111yescharacteristic
904#117C22×D6112yes—
905#117C22×D6112yes—
906C2×C4⋊C4—21no—
907C2×C4⋊C4—611no—
908C2×C4⋊C4—611no—
909C2×C4⋊C4—1221no—
910C2×C4⋊C4—1221no—
911C2×C4⋊C4C22×D6112yes—
912C2×C42—1221no—
913C2×C42—1221no—
914C2×C42—1221no—
915C2×C42C22×D6111yescharacteristic
916C2×C42C22×D6111yescharacteristic
917C2×C42C22×D6111yescharacteristic
918#107—612no—
919#107—612no—
920#107—612no—
921#107—612no—
922#107—612no—
923#107—612no—
924#107—612no—
925#106—612no—
926#106—612no—
927#106—612no—
928#106—612no—
929#106—612no—
930C4⋊C8—611no—
931C4⋊C8—611no—
932C4⋊C8—611no—
933C4⋊C8—612no—
934C4⋊C8—612no—
935C4⋊C8—612no—
936C4⋊C8—611no—
937#103—612no—
938#103—612no—
939#103—612no—
940#103—612no—
941#103—612no—
942#103—612no—
943#103—612no—
944#103—612no—
945#103—612no—
946#103—612no—
947#103—612no—
948#103—612no—
949#103—612no—
950#102—612no—
951#102—612no—
952#102—612no—
953C22⋊C8—612no—
954C22⋊C8—612no—
955C22⋊C8—612no—
956#97—612no—
957#97—612no—
958C4×C8—612no—
959#41—42no—
960#41—1222no—
961#41—2441no—
962#41—2444no—
963C2×Q8—21no—
964C2×Q8—21no—
965C2×Q8—21no—
966C2×Q8—22no—
967C2×Q8—44no—
968C2×Q8—611no—
969C2×Q8—611no—
970C2×Q8—611no—
971C2×Q8—1222no—
972C2×Q8—1222no—
973C2×Q8—1221no—
974C2×Q8—1221no—
975C2×Q8—1221no—
976C2×Q8—2441no—
977C2×Q8—2441no—
978C2×Q8C2×C22⋊D6111yescharacteristic
979C2×Q8C23×D6112yes—
980C2×D4—611no—
981C2×D4—1221no—
982C2×D4—1221no—
983C2×D4—1221no—
984C2×D4C2×C22⋊D6111yescharacteristic
985C2×D4C2×C22⋊D6111yescharacteristic
986C2×D4C2×C22⋊D6111yescharacteristic
987C22×C4—22no—
988C22×C4—1221no—
989C22×C4—1221no—
990C22×C4—1221no—
991C22×C4—1221no—
992C22×C4—1221no—
993C22×C4—1221no—
994C22×C4—1221no—
995C22×C4C2×C22⋊D6111yescharacteristic
996C22×C4C2×C22⋊D6111yescharacteristic
997C22×C4C2×C22⋊D6111yescharacteristic
998C22×C4C2×C22⋊D6111yescharacteristic
999C22×C4C2×C22⋊D6111yescharacteristic
1000C22×C4C2×C22⋊D6111yescharacteristic
1001C22×C4C23×D6111yescharacteristic
1002C22×C4C23×D6111yescharacteristic
1003C22×C4C23×D6111yescharacteristic
1004Q16—1224no—
1005Q16—2442no—
1006Q16—2442no—
1007SD16—2442no—
1008M16—2442no—
1009C2×C8—612no—
1010C2×C8—612no—
1011C2×C8—612no—
1012C2×C8—612no—
1013C2×C8—2442no—
1014C2×C8—2442no—
1015C4⋊C4—21no—
1016C4⋊C4—21no—
1017C4⋊C4—22no—
1018C4⋊C4—22no—
1019C4⋊C4—21no—
1020C4⋊C4—21no—
1021C4⋊C4—21no—
1022C4⋊C4—22no—
1023C4⋊C4—22no—
1024C4⋊C4—22no—
1025C4⋊C4—22no—
1026C4⋊C4—22no—
1027C4⋊C4—22no—
1028C4⋊C4—22no—
1029C4⋊C4—22no—
1030C4⋊C4—22no—
1031C4⋊C4—22no—
1032C4⋊C4—611no—
1033C4⋊C4—611no—
1034C4⋊C4—611no—
1035C4⋊C4—611no—
1036C4⋊C4—1221no—
1037C4⋊C4—1221no—
1038C4⋊C4—1221no—
1039C4⋊C4—1221no—
1040C4⋊C4—1221no—
1041C4⋊C4—1221no—
1042C4⋊C4—1221no—
1043C4⋊C4—1221no—
1044C4⋊C4—1221no—
1045C4⋊C4—1221no—
1046C4⋊C4—1221no—
1047C4⋊C4—1221no—
1048C4⋊C4—1221no—
1049C4⋊C4—1221no—
1050C4⋊C4—1221no—
1051C4⋊C4—1221no—
1052C4⋊C4—1221no—
1053C4⋊C4—1221no—
1054C4⋊C4—1221no—
1055C4⋊C4—1221no—
1056C4⋊C4—1221no—
1057C4⋊C4C2×C22⋊D6111yescharacteristic
1058C4⋊C4C2×C22⋊D6111yescharacteristic
1059C4⋊C4C2×C22⋊D6111yescharacteristic
1060C4⋊C4C2×C22⋊D6111yescharacteristic
1061C4⋊C4C2×C22⋊D6111yescharacteristic
1062C4⋊C4C2×C22⋊D6111yescharacteristic
1063C4⋊C4C23×D6112yes—
1064C4⋊C4C23×D6112yes—
1065C4⋊C4C23×D6112yes—
1066C22⋊C4—22no—
1067C22⋊C4—22no—
1068C22⋊C4—22no—
1069C22⋊C4—22no—
1070C22⋊C4—22no—
1071C22⋊C4—1221no—
1072C22⋊C4—1221no—
1073C22⋊C4—1221no—
1074C22⋊C4—1221no—
1075C22⋊C4—1221no—
1076C22⋊C4—1221no—
1077C22⋊C4—1221no—
1078C22⋊C4—1221no—
1079C22⋊C4—1221no—
1080C22⋊C4—1221no—
1081C22⋊C4—1221no—
1082C22⋊C4—1221no—
1083C22⋊C4—1221no—
1084C22⋊C4C2×C22⋊D6111yescharacteristic
1085C22⋊C4C2×C22⋊D6111yescharacteristic
1086C22⋊C4C2×C22⋊D6111yescharacteristic
1087C22⋊C4C2×C22⋊D6111yescharacteristic
1088C22⋊C4C2×C22⋊D6111yescharacteristic
1089C22⋊C4C2×C22⋊D6111yescharacteristic
1090C42—22no—
1091C42—22no—
1092C42—22no—
1093C42—22no—
1094C42—22no—
1095C42—1221no—
1096C42—1221no—
1097C42—1221no—
1098C42—1221no—
1099C42—1221no—
1100C42—1221no—
1101C42—1221no—
1102C42—1221no—
1103C42—1221no—
1104C42C2×C22⋊D6111yescharacteristic
1105C42C2×C22⋊D6111yescharacteristic
1106C42C2×C22⋊D6111yescharacteristic
1107C42C2×C22⋊D6111yescharacteristic
1108C42C2×C22⋊D6111yescharacteristic
1109C42C2×C22⋊D6111yescharacteristic
1110C42C23×D6111yescharacteristic
1111C42C23×D6111yescharacteristic
1112C42C23×D6111yescharacteristic
1113C42C23×D6111yescharacteristic
1114C23—1221no—
1115C23C22×C22⋊D6111yescharacteristic
1116C23C22×C22⋊D6111yescharacteristic
1117C23C22×C22⋊D6111yescharacteristic
1118Q8—22no—
1119Q8—22no—
1120Q8—41no—
1121Q8—42no—
1122Q8—42no—
1123Q8—44no—
1124Q8—42no—
1125Q8—612no—
1126Q8—1221no—
1127Q8—1221no—
1128Q8—1221no—
1129Q8—1221no—
1130Q8—1221no—
1131Q8—2442no—
1132Q8—2442no—
1133Q8—2442no—
1134D4—22no—
1135D4—22no—
1136D4—41no—
1137D4—1221no—
1138D4—1221no—
1139D4—2442no—
1140D4—2442no—
1141D4—2442no—
1142C2×C4—22no—
1143C2×C4—22no—
1144C2×C4—22no—
1145C2×C4—22no—
1146C2×C4—21no—
1147C2×C4—21no—
1148C2×C4—21no—
1149C2×C4—21no—
1150C2×C4—21no—
1151C2×C4—21no—
1152C2×C4—22no—
1153C2×C4—22no—
1154C2×C4—22no—
1155C2×C4—22no—
1156C2×C4—41no—
1157C2×C4—41no—
1158C2×C4—44no—
1159C2×C4—1221no—
1160C2×C4—1221no—
1161C2×C4—1221no—
1162C2×C4—1221no—
1163C2×C4—1221no—
1164C2×C4—1221no—
1165C2×C4—1221no—
1166C2×C4—2442no—
1167C2×C4—2442no—
1168C2×C4—2442no—
1169C2×C4—2442no—
1170C2×C4—2442no—
1171C2×C4—2442no—
1172C2×C4—2442no—
1173C2×C4C22×C22⋊D6111yescharacteristic
1174C2×C4C22×C22⋊D6111yescharacteristic
1175C2×C4C22×C22⋊D6111yescharacteristic
1176C2×C4C22×C22⋊D6111yescharacteristic
1177C2×C4C22×C22⋊D6111yescharacteristic
1178C2×C4C22×C22⋊D6111yescharacteristic
1179C2×C4C22×C22⋊D6111yescharacteristic
1180C2×C4C22×C22⋊D6111yescharacteristic
1181C2×C4C22×C22⋊D6111yescharacteristic
1182C2×C4C22×C22⋊D6111yescharacteristic
1183C2×C4C22×C22⋊D6111yescharacteristic
1184C2×C4C24×D6111yescharacteristic
1185C8—1222no—
1186C8—1222no—
1187C8—1222no—
1188C8—1222no—
1189C22—21no—
1190C22—21no—
1191C22—21no—
1192C22—21no—
1193C22—21no—
1194C22—21no—
1195C22—21no—
1196C22—21no—
1197C22—2441no—
1198C22—2441no—
1199C22—2441no—
1200C22#1684056012yes—
1201C22C23×C22⋊D6111yescharacteristic
1202C4—21no—
1203C4—21no—
1204C4—21no—
1205C4—21no—
1206C4—21no—
1207C4—21no—
1208C4—21no—
1209C4—21no—
1210C4—21no—
1211C4—21no—
1212C4—42no—
1213C4—42no—
1214C4—42no—
1215C4—42no—
1216C4—1222no—
1217C4—2441no—
1218C4—2441no—
1219C4—2441no—
1220C4—2441no—
1221C4—2441no—
1222C4—2441no—
1223C4#1684057712yes—
1224C42−1+4×D6111yescharacteristic
1225C4#1684059911yescharacteristic
1226C2—22no—
1227C2—41no—
1228C2—41no—
1229C2—4881no—
1230C2#2145949211yescharacteristic
1231C2C2×#1684056011yescharacteristic
1232C2C2×#1684057711yescharacteristic
subgroupG/H
centerC22C23×C22⋊D61
commutator, cosocleC2×C4×C61C25
FrattiniC2×C4C24×D61
FittingC61×#3509C2
socleC22×C61C23×D4
prime radical#21459434C2
hypercenter#3509D61
hypocenterC61#62130
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C4×#41 ◁ #3509

Complements

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

NH ≅ G/Ntype
2. #21458782C2semidirect
3. #21458661C2semidirect
4. #21458343C2semidirect
5. #21458259C2semidirect
6. #21458181C2semidirect
7. #21457879C2semidirect
8. #21457864C2semidirect
9. #21457700C2semidirect
10. #21457186C2semidirect
11. #21457161C2semidirect
12. #21457150C2semidirect
13. #21457040C2semidirect
14. #21457033C2semidirect
15. #21456998C2semidirect
16. #21455975C2semidirect
17. #21455945C2semidirect
18. #21455854C2semidirect
19. #21455620C2semidirect
20. #21455601C2semidirect
21. C2×#16840054C2semidirect
22. #21454944C2semidirect
23. C61×#3509C2semidirect
610. #3509D61semidirect
755. C61#62130semidirect

Maximal subgroups

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

subgroupindex
#214594342
#214587822
#214586612
#214583432
#214582592
#214581812
#214578792
#214578642
#214577002
#214571862
#214571612
#214571502
#214570402
#214570332
#214569982
#214559752
#214559452
#214558542
#214556202
#214556012
C2×#168400542
#214549442
C61×#35092
#6213061