Finite Group Databasebeta

← #30575945

Subgroups — #30575945

Order 15616.

1706 conjugacy classes of subgroups.

The subgroup lattice has 1250 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21459412C211yesmaximal, characteristic
2#21458782C212yesmaximal, complemented
3#21458587C212yesmaximal, complemented
4#21458379C212yesmaximal, complemented
5#21458364C212yesmaximal, complemented
6#21458349C212yesmaximal, complemented
7#21458081C212yesmaximal, complemented
8#21457939C212yesmaximal, complemented
9#21457879C212yesmaximal, complemented
10#21457202C211yesmaximal, characteristic, complemented
11#21457186C211yesmaximal, characteristic, complemented
12#21457150C211yesmaximal, characteristic, complemented
13#21457049C211yesmaximal, characteristic, complemented
14#21457017C211yesmaximal, characteristic, complemented
15#21456998C211yesmaximal, characteristic, complemented
16#21455975C211yesmaximal, characteristic, complemented
17#21455945C211yesmaximal, characteristic, complemented
18#21455884C211yesmaximal, characteristic, complemented
19#21455628C211yesmaximal, characteristic, complemented
20#21455620C211yesmaximal, characteristic, complemented
21#21455601C211yesmaximal, characteristic, complemented
22#21454936C211yesmaximal, characteristic, complemented
23C61×#3509C211yesmaximal, characteristic, complemented
24#16840497C2211yescharacteristic
25#16840495—21no—
26#16840490C2211yescharacteristic
27#16840484—21no—
28#16840482C2211yescharacteristic
29#16840461—21no—
30#16840461—21no—
31#16840458C2211yescharacteristic
32#16840458C2211yescharacteristic
33#16840433C2211yescharacteristic
34#16840421C2211yescharacteristic
35#16840421C2211yescharacteristic
36#16840312C2211yescharacteristic
37#16840308—21no—
38#16840296C2211yescharacteristic
39#16840296C2211yescharacteristic
40#16840290—21no—
41#16840290—21no—
42C4×#11758222C2211yescharacteristic
43C4×#11758222C2211yescharacteristic
44#16840230—21no—
45C2×C4×Dic122C2211yescharacteristic
46#16840172C2212yes—
47#16840168C2212yes—
48#16840161C2212yes—
49#16840128C2212yes—
50#16840124C2212yes—
51#16840119C2212yes—
52#16840103C2212yes—
53#16840100C2212yes—
54#16840100C2212yes—
55#16840097C2212yes—
56#16840090C2212yes—
57#16840086C2212yes—
58#16840086C2212yes—
59#16840086C2212yes—
60#16840080C2212yes—
61#16840069C2212yes—
62#16840069C2212yes—
63#16840066C2212yes—
64#16840066C2212yes—
65#16840066C2212yes—
66#16840059C2212yes—
67#16840057C2212yes—
68#16840054C2211yescharacteristic
69#16840054C2211yescharacteristic
70#16840054C2212yes—
71#16840049C2212yes—
72#16840049C2211yescharacteristic
73#16840049C2211yescharacteristic
74#16840044C2211yescharacteristic
75#16840044C2211yescharacteristic
76#16840044C2211yescharacteristic
77#16840044C2211yescharacteristic
78#16840039C2211yescharacteristic
79#16840039C2211yescharacteristic
80#16840039C2211yescharacteristic
81#16840039C2211yescharacteristic
82#16840018C2212yes—
83#16840010C2212yes—
84#16840010C2212yes—
85#16840010C2212yes—
86#16840001C2212yes—
87#16839993C2212yes—
88#16839984C2212yes—
89#16839984C2212yes—
90#16839969C2211yescharacteristic
91#16839969C2211yescharacteristic
92#16839964C2211yescharacteristic
93#16839964C2211yescharacteristic
94#16839962C2212yes—
95#16839922C2212yes—
96#16839922C2212yes—
97#16839917C2212yes—
98#16839893C2212yes—
99#16839867C2212yes—
100#16839867C2212yes—
101#16839867C2212yes—
102#16839860C2212yes—
103C4×#11758202C2212yes—
104C4×#11758201C2212yes—
105#16839840C2212yes—
106#16839834C2212yes—
107#16839834C2212yes—
108#16839819C2211yescharacteristic
109#16839819C2211yescharacteristic
110#16839815C2211yescharacteristic
111#16839805C2212yes—
112#16839802C2212yes—
113#16839798C2212yes—
114#16839786C2211yescharacteristic
115#16839786C2211yescharacteristic
116C2×C4⋊#92418C2211yescharacteristic
117#16839770C2212yes—
118#16839761C2212yes—
119#16839756C2212yes—
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×#11758222—21no—
140C2×#11758222C2311yescharacteristic
141C2×#11758222C2311yescharacteristic
142C22×Dic122C2311yescharacteristic
143C2×#11758202C2312yes—
144C2×#11758202C2312yes—
145C2×#11758201C2312yes—
146C2×#11758201C2312yes—
147C2×#11758194C2312yes—
148C2×#11758194C2312yes—
149C22×#92418C2312yes—
150#14519777C2311yescharacteristic
151#14519775—21no—
152#14519774C2311yescharacteristic
153#14519773—21no—
154#14519772—21no—
155#14519772—21no—
156#14519771—21no—
157#14519771—21no—
158#14519770—21no—
159#14519770—21no—
160#14519769C2311yescharacteristic
161#14519769C2311yescharacteristic
162#14519767—21no—
163#14519767—21no—
164#14519766—21no—
165#14519765—21no—
166#14519765C2311yescharacteristic
167#14519765C2311yescharacteristic
168#14519764—21no—
169#14519763—21no—
170#14519763—21no—
171#14519762—21no—
172#14519762—21no—
173#14519760—21no—
174#14519760—21no—
175#14519759—21no—
176#14519759—21no—
177#14519756C2311yescharacteristic
178#14519756C2311yescharacteristic
179#14519755—21no—
180#14519755—21no—
181#14519751—21no—
182#14519751C2311yescharacteristic
183#14519751C2311yescharacteristic
184#14519751C2311yescharacteristic
185#14519751C2311yescharacteristic
186#14519750—21no—
187#14519750—21no—
188#14519749—21no—
189#14519749—21no—
190#14519749—21no—
191#14519749—21no—
192C4×Dic122—21no—
193C4×Dic122—21no—
194C4×Dic122C2311yescharacteristic
195C4×Dic122C2311yescharacteristic
196C4×Dic122C2311yescharacteristic
197C4×Dic122C2311yescharacteristic
198C4×Dic122C2311yescharacteristic
199C4×Dic122C2311yescharacteristic
200#14519742—21no—
201#14519742—21no—
202C4×D244—21no—
203C4×D244C2311yescharacteristic
204C4×D244C2311yescharacteristic
205C4×D244C2311yescharacteristic
206C4×D244C2311yescharacteristic
207#14519739—21no—
208#14519739—21no—
209C4×C22⋊D61—21no—
210C4×C22⋊D61—21no—
211C4×C22⋊D61—21no—
212C4×C22⋊D61—21no—
213C4×C22⋊D61—21no—
214C4×C22⋊D61—21no—
215#14519737—21no—
216#14519737—21no—
217#14519737—21no—
218#14519737—21no—
219#14519736C2311yescharacteristic
220#14519736C2311yescharacteristic
221#14519734—21no—
222#14519734—21no—
223#14519734—21no—
224#14519734—21no—
225C2×C4⋊Dic61C2311yescharacteristic
226C2×#11758196—21no—
227C2×C4×Dic61—21no—
228C42×D61—21no—
229C42×D61—21no—
230#14519710C2312yes—
231#14519710C2312yes—
232#14519710C2312yes—
233#14519710C2312yes—
234#14519710C2312yes—
235#14519710C2312yes—
236#14519708C2312yes—
237#14519708C2312yes—
238#14519708C2312yes—
239#14519708C2312yes—
240#14519708C2312yes—
241#14519708C2312yes—
242C4⋊#92418C2312yes—
243C4⋊#92418C2311yescharacteristic
244C4⋊#92418C2311yescharacteristic
245C4⋊#92418C2311yescharacteristic
246C4⋊#92418C2311yescharacteristic
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#14519697C2312yes—
260#14519697C2312yes—
261#14519697C2312yes—
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—
366C2×C22⋊D61—21no—
367C2×C22⋊D61—21no—
368C2×C22⋊D61—21no—
369C22×Dic61—21no—
370C22×Dic61—21no—
371#11758222—22no—
372#11758222—22no—
373#11758222—41no—
374#11758222—41no—
375#11758222—44no—
376C2×D244—21no—
377C2×D244—21no—
378C2×D244C2411yescharacteristic
379C2×D244C2411yescharacteristic
380C2×C4×D61—21no—
381C2×C4×D61—21no—
382C2×C4×D61—21no—
383C2×C4×D61—21no—
384C2×C4×D61—21no—
385C2×C4×D61—21no—
386C2×Dic122—22no—
387C2×Dic122—21no—
388C2×Dic122—21no—
389C2×Dic122—41no—
390C2×Dic122C2411yescharacteristic
391C2×Dic122C2411yescharacteristic
392C4⋊C4×C61—21no—
393C4⋊C4×C61—21no—
394C4⋊C4×C61—22no—
395C4⋊C4×C61—22no—
396C4⋊C4×C61—21no—
397C4⋊C4×C61—21no—
398C4⋊C4×C61—21no—
399C4⋊C4×C61—22no—
400C4⋊C4×C61—22no—
401C4⋊C4×C61—22no—
402C4⋊C4×C61—22no—
403C4⋊C4×C61—22no—
404C4⋊C4×C61—22no—
405C4⋊C4×C61—22no—
406C4⋊C4×C61—22no—
407C4⋊C4×C61—22no—
408C4⋊C4×C61—22no—
409C4⋊C4×C61C2×D411yescharacteristic
410C4⋊C4×C61C2×D411yescharacteristic
411C4⋊C4×C61C2×D411yescharacteristic
412C4⋊C4×C61C2×D411yescharacteristic
413C4⋊C4×C61C2×D411yescharacteristic
414C4⋊C4×C61C2×D411yescharacteristic
415C4⋊C4×C61C2412yes—
416C4⋊C4×C61C2412yes—
417C4⋊C4×C61C2412yes—
418C22⋊C4×C61—22no—
419C22⋊C4×C61—22no—
420C22⋊C4×C61—22no—
421C22⋊C4×C61—22no—
422C22⋊C4×C61—22no—
423C22⋊C4×C61C2×D411yescharacteristic
424C22⋊C4×C61C2×D411yescharacteristic
425C22⋊C4×C61C2×D411yescharacteristic
426C22⋊C4×C61C2×D411yescharacteristic
427C22⋊C4×C61C2×D411yescharacteristic
428C22⋊C4×C61C2×D411yescharacteristic
429C42×C61—22no—
430C42×C61—22no—
431C42×C61—22no—
432C42×C61—22no—
433C42×C61—22no—
434C42×C61C2×D411yescharacteristic
435C42×C61C2×D411yescharacteristic
436C42×C61C2×D411yescharacteristic
437C42×C61C2×D411yescharacteristic
438C42×C61C2×D411yescharacteristic
439C42×C61C2×D411yescharacteristic
440C42×C61C2411yescharacteristic
441C42×C61C2411yescharacteristic
442C42×C61C2411yescharacteristic
443C42×C61C2411yescharacteristic
444C22⋊Dic61—21no—
445C22⋊Dic61—21no—
446C22⋊Dic61—21no—
447C22⋊Dic61—21no—
448#11758202—24no—
449#11758202—42no—
450#11758201—42no—
451#11758201—42no—
452#11758198—21no—
453#11758198—21no—
454#11758198—21no—
455#11758198—21no—
456#11758198—21no—
457#11758198—21no—
458#11758198—21no—
459#11758198—21no—
460#11758198—21no—
461#11758198—21no—
462#11758198—21no—
463#11758198—21no—
464C4⋊Dic61—21no—
465C4⋊Dic61—21no—
466C4⋊Dic61C2411yescharacteristic
467C4⋊Dic61C2411yescharacteristic
468C4⋊Dic61C2411yescharacteristic
469C4⋊Dic61C2411yescharacteristic
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—
481#11758196—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—
491#11758194—42no—
492C2×#92418—42no—
493C2×#92418C2412yes—
494C2×#92418C2412yes—
495C2×#92418C2412yes—
496C2×#92418C2412yes—
497C23×C61C22×D411yescharacteristic
498C23×C61C22×D411yescharacteristic
499C23×C61C22×D411yescharacteristic
500C22×D61—21no—
501C22×D61—21no—
502Q8×C61—22no—
503Q8×C61—22no—
504Q8×C61—41no—
505Q8×C61—42no—
506Q8×C61—44no—
507Q8×C61—42no—
508Q8×C61—42no—
509D4×C61—41no—
510D4×C61—41no—
511D4×C61—41no—
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—41no—
528C2×C4×C61—44no—
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×C61C22×D411yescharacteristic
540C2×C4×C61C2511yescharacteristic
541C22⋊D61—42no—
542C22⋊D61—42no—
543C22⋊D61—42no—
544C22⋊D61—42no—
545C22⋊D61—81no—
546C22⋊D61—81no—
547C2×Dic61—21no—
548C2×Dic61—21no—
549C2×Dic61—21no—
550C2×Dic61—21no—
551C2×Dic61—21no—
552C2×Dic61—21no—
553C2×Dic61—42no—
554C2×Dic61—81no—
555D244—21no—
556D244—21no—
557D244—21no—
558D244—21no—
559D244—42no—
560D244—81no—
561C4×D61—42no—
562C4×D61—42no—
563C4×D61—42no—
564C4×D61—42no—
565C4×D61—81no—
566C4×D61—81no—
567Dic122—21no—
568Dic122—21no—
569Dic122—21no—
570Dic122—42no—
571Dic122—42no—
572Dic1222−1+412yes—
573#92418—22no—
574#92418—22no—
575#92418—22no—
576#92418—22no—
577#62118—611nomaximal, Sylow
578C22×C61—21no—
579C22×C61—21no—
580C22×C61—21no—
581C22×C61—21no—
582C22×C61—21no—
583C22×C61—21no—
584C22×C61—21no—
585C22×C61—21no—
586C22×C61—21no—
587C22×C61C23×D411yescharacteristic
588C2×D61—41no—
589C2×D61—41no—
590C2×D61—41no—
591C2×D61—41no—
592C2×D61—41no—
593C2×D61—41no—
594C4×C61—21no—
595C4×C61—21no—
596C4×C61—21no—
597C4×C61—21no—
598C4×C61—21no—
599C4×C61—21no—
600C4×C61—21no—
601C4×C61—21no—
602C4×C61—21no—
603C4×C61—21no—
604C4×C61—42no—
605C4×C61—42no—
606C4×C61—42no—
607C4×C61—42no—
608C4×C61#57512yes—
609C4×C61C2×2−1+411yescharacteristic
610C4×C61#58511yescharacteristic
611Dic61—22no—
612Dic61—41no—
613Dic61—41no—
614Dic61—41no—
615Dic61—41no—
616Dic61—41no—
617#3509D6111yescharacteristic, complemented
618#3480—611no—
619#3390—612no—
620#3371—612no—
621#3351—612no—
622#3350—612no—
623#3349—612no—
624#3327—612no—
625#3317—612no—
626#3313—612no—
627#3254—611no—
628#3252—611no—
629#3248—611no—
630#3239—611no—
631#3235—611no—
632#3233—611no—
633#3116—611no—
634#3113—611no—
635#3107—611no—
636#3079—611no—
637#3078—611no—
638#3076—611no—
639#2989—611no—
640C2×C61—41no—
641C2×C61—41no—
642C2×C61—41no—
643C2×C61#348911yescharacteristic
644C2×C61C2×#57511yescharacteristic
645C2×C61#358611yescharacteristic
646D61—81no—
647D61—81no—
648#559—611no—
649#559—1221no—
650#557—21no—
651#557—611no—
652#557C2×D6112yes—
653#556—21no—
654#556—611no—
655#556—1221no—
656#556C2×D6112yes—
657#553—611no—
658#553—611no—
659#553—1221no—
660#553—1221no—
661#552—21no—
662#552—21no—
663#552C2×D6112yes—
664#552C2×D6112yes—
665#550—611no—
666#548—611no—
667#548—611no—
668#541—21no—
669#541—21no—
670#536—21no—
671#533C2×D6111yescharacteristic
672#533C2×D6111yescharacteristic
673#533C2×D6111yescharacteristic
674#533C2×D6111yescharacteristic
675#533C2×D6111yescharacteristic
676#532—611no—
677#532—1221no—
678C2×C4⋊Q8C2×D6111yescharacteristic
679#529—611no—
680#529—611no—
681#529—1221no—
682#529—1221no—
683#519—21no—
684C4×#41—611no—
685C4×#41—611no—
686C4×#41—1221no—
687C4×#41C2×D6111yescharacteristic
688C2×C4×Q8—611no—
689#501—612no—
690#501—612no—
691#499—612no—
692#490—612no—
693#489—612no—
694#488—612no—
695#485—612no—
696#485—612no—
697#485—612no—
698#484—612no—
699#483—612no—
700#482—612no—
701#482—612no—
702#482—612no—
703#481—612no—
704#479—612no—
705#479—612no—
706#479—612no—
707#479—612no—
708#479—612no—
709#478—612no—
710#477—611no—
711#477—611no—
712#477—612no—
713#477—612no—
714#476—611no—
715#476—612no—
716#476—611no—
717#475—611no—
718#475—611no—
719#475—611no—
720#475—611no—
721#474—611no—
722#474—611no—
723#474—611no—
724#474—611no—
725#470—612no—
726#468—612no—
727#468—612no—
728#468—612no—
729#467—612no—
730#465—612no—
731#464—612no—
732#464—612no—
733#462—611no—
734#462—611no—
735#461—611no—
736#461—611no—
737#460—612no—
738#452—612no—
739#452—612no—
740#451—612no—
741#446—612no—
742#441—612no—
743#441—612no—
744#441—612no—
745#440—612no—
746C4×Q16—612no—
747C4×SD16—612no—
748#436—612no—
749#435—612no—
750#435—612no—
751#432—611no—
752#432—611no—
753#431—611no—
754#428—612no—
755#428—612no—
756#427—612no—
757#423—611no—
758#423—611no—
759C2×C4⋊C8—611no—
760#419—612no—
761#417—612no—
762#416—612no—
763C61#6211811yescharacteristic, complemented, Sylow
764C2×#41—611no—
765C2×#41—611no—
766C2×#41—1221no—
767C2×#41C22⋊D6111yescharacteristic
768C22×Q8—21no—
769C22×Q8—611no—
770C2×Q16—612no—
771C2×Q16—612no—
772C2×SD16—612no—
773C2×SD16—612no—
774C2×M16—612no—
775C2×M16—612no—
776C22×C8—612no—
777C4⋊Q8—22no—
778C4⋊Q8—21no—
779C4⋊Q8—21no—
780C4⋊Q8—611no—
781C4⋊Q8—1221no—
782C4⋊Q8C22×D6111yescharacteristic
783C4⋊Q8C22×D6111yescharacteristic
784C4⋊Q8C22×D6111yescharacteristic
785C4⋊Q8C22×D6112yes—
786C4⋊Q8C22×D6111yescharacteristic
787#127—611no—
788#127—1221no—
789#126—22no—
790#126—22no—
791#126—22no—
792#126—22no—
793#126—1221no—
794#126—1221no—
795#126—1221no—
796#126—1221no—
797#126—1221no—
798#126—1221no—
799#125—22no—
800#125—22no—
801#125—22no—
802#125—22no—
803#125—21no—
804#125—21no—
805#125—21no—
806#125—611no—
807#125—611no—
808#125—1221no—
809#125—1221no—
810#125C22×D6112yes—
811#125C22×D6112yes—
812#124—22no—
813#124—611no—
814#124—611no—
815#124—1221no—
816#124—1221no—
817#124—1221no—
818#124—1221no—
819#124—1221no—
820#123—22no—
821#123—22no—
822#123—1221no—
823#123—1221no—
824#123—1221no—
825#123—1221no—
826#123—1221no—
827#123—1221no—
828C22⋊Q8—21no—
829C22⋊Q8—21no—
830C22⋊Q8—21no—
831C22⋊Q8—21no—
832C22⋊Q8—21no—
833C22⋊Q8—21no—
834C22⋊Q8—21no—
835C22⋊Q8—611no—
836C22⋊Q8—611no—
837C22⋊Q8—1221no—
838C22⋊Q8—1221no—
839C22⋊Q8C22×D6112yes—
840C22⋊Q8C22×D6112yes—
841C22⋊Q8C22×D6112yes—
842#121—611no—
843#121—611no—
844#121—611no—
845#121—611no—
846#121—1221no—
847#121—1221no—
848#121—1221no—
849#121—1221no—
850#121—1221no—
851#121—1221no—
852#121—1221no—
853C4×Q8—22no—
854C4×Q8—22no—
855C4×Q8—21no—
856C4×Q8—21no—
857C4×Q8—21no—
858C4×Q8—21no—
859C4×Q8—21no—
860C4×Q8—21no—
861C4×Q8—21no—
862C4×Q8—611no—
863C4×Q8—611no—
864C4×Q8—611no—
865C4×Q8—611no—
866C4×Q8—611no—
867C4×Q8—611no—
868C4×Q8—1221no—
869C4×Q8—1221no—
870C4×Q8—1221no—
871C4×Q8—1221no—
872C4×Q8C22⋊D6111yescharacteristic
873C4×Q8C22×D6112yes—
874C4×Q8C22×D6112yes—
875C4×Q8C22×D6112yes—
876C4×Q8C22×D6111yescharacteristic
877C4×D4—611no—
878C4×D4—611no—
879C4×D4—611no—
880C4×D4—611no—
881C4×D4—1221no—
882C4×D4—1221no—
883C4×D4—1221no—
884C4×D4—1221no—
885C4×D4—1221no—
886C4×D4—1221no—
887C4×D4—1221no—
888C4×D4—1221no—
889C4×D4—1221no—
890C4×D4—1221no—
891C4×D4—1221no—
892C4×D4—1221no—
893C4×D4—1221no—
894C4×D4C22⋊D6111yescharacteristic
895C4×D4C22⋊D6111yescharacteristic
896C4×D4C22⋊D6111yescharacteristic
897C4×D4C22×D6111yescharacteristic
898C4×D4C22×D6111yescharacteristic
899C4×D4C22×D6111yescharacteristic
900#117—21no—
901#117—21no—
902#117—21no—
903#117—22no—
904#117—22no—
905#117—611no—
906#117—611no—
907#117—1221no—
908#117—1221no—
909#117—1221no—
910#117—1221no—
911#117C22⋊D6111yescharacteristic
912#117C22⋊D6111yescharacteristic
913#117C22⋊D6111yescharacteristic
914#117C22×D6112yes—
915#117C22×D6112yes—
916C2×C4⋊C4—21no—
917C2×C4⋊C4—611no—
918C2×C4⋊C4—1221no—
919C2×C4⋊C4C22×D6112yes—
920C2×C42—1221no—
921C2×C42—1221no—
922C2×C42—1221no—
923C2×C42C22×D6111yescharacteristic
924C2×C42C22×D6111yescharacteristic
925C2×C42C22×D6111yescharacteristic
926#107—612no—
927#107—612no—
928#107—612no—
929#107—612no—
930#107—612no—
931#107—612no—
932#106—612no—
933#106—612no—
934#106—612no—
935#106—612no—
936#106—612no—
937#106—612no—
938C4⋊C8—611no—
939C4⋊C8—611no—
940C4⋊C8—612no—
941C4⋊C8—611no—
942C4⋊C8—612no—
943C4⋊C8—612no—
944C4⋊C8—611no—
945#103—612no—
946#103—612no—
947#103—612no—
948#103—612no—
949#103—612no—
950#103—612no—
951#103—612no—
952#103—612no—
953#103—612no—
954#103—612no—
955#102—612no—
956#102—612no—
957#102—612no—
958#102—612no—
959#102—612no—
960#102—612no—
961C22⋊C8—612no—
962C22⋊C8—612no—
963C22⋊C8—612no—
964#97—612no—
965#97—612no—
966C4×C8—612no—
967#41—42no—
968#41—1222no—
969#41—1222no—
970#41—2441no—
971#41—2441no—
972#41—2444no—
973C2×Q8—21no—
974C2×Q8—21no—
975C2×Q8—21no—
976C2×Q8—22no—
977C2×Q8—44no—
978C2×Q8—611no—
979C2×Q8—611no—
980C2×Q8—1222no—
981C2×Q8—1221no—
982C2×Q8—1221no—
983C2×Q8—2441no—
984C2×Q8C2×C22⋊D6111yescharacteristic
985C2×Q8C23×D6112yes—
986C2×D4—611no—
987C2×D4—611no—
988C2×D4—1221no—
989C2×D4—1221no—
990C2×D4—1221no—
991C2×D4—1221no—
992C2×D4—1221no—
993C2×D4—1221no—
994C2×D4—1221no—
995C2×D4—1221no—
996C2×D4C2×C22⋊D6111yescharacteristic
997C2×D4C2×C22⋊D6111yescharacteristic
998C2×D4C2×C22⋊D6111yescharacteristic
999C22×C4—22no—
1000C22×C4—1221no—
1001C22×C4—1221no—
1002C22×C4—1221no—
1003C22×C4—1221no—
1004C22×C4—1221no—
1005C22×C4—1221no—
1006C22×C4—1221no—
1007C22×C4—1221no—
1008C22×C4C2×C22⋊D6111yescharacteristic
1009C22×C4C2×C22⋊D6111yescharacteristic
1010C22×C4C2×C22⋊D6111yescharacteristic
1011C22×C4C2×C22⋊D6111yescharacteristic
1012C22×C4C2×C22⋊D6111yescharacteristic
1013C22×C4C2×C22⋊D6111yescharacteristic
1014C22×C4C23×D6111yescharacteristic
1015C22×C4C23×D6111yescharacteristic
1016C22×C4C23×D6111yescharacteristic
1017Q16—1224no—
1018Q16—2442no—
1019SD16—2442no—
1020SD16—2442no—
1021M16—2442no—
1022M16—2442no—
1023C2×C8—612no—
1024C2×C8—612no—
1025C2×C8—612no—
1026C2×C8—612no—
1027C2×C8—2442no—
1028C4⋊C4—21no—
1029C4⋊C4—21no—
1030C4⋊C4—22no—
1031C4⋊C4—22no—
1032C4⋊C4—21no—
1033C4⋊C4—21no—
1034C4⋊C4—21no—
1035C4⋊C4—22no—
1036C4⋊C4—22no—
1037C4⋊C4—22no—
1038C4⋊C4—22no—
1039C4⋊C4—22no—
1040C4⋊C4—22no—
1041C4⋊C4—22no—
1042C4⋊C4—22no—
1043C4⋊C4—22no—
1044C4⋊C4—22no—
1045C4⋊C4—611no—
1046C4⋊C4—611no—
1047C4⋊C4—611no—
1048C4⋊C4—611no—
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⋊C4—1221no—
1058C4⋊C4—1221no—
1059C4⋊C4—1221no—
1060C4⋊C4—1221no—
1061C4⋊C4—1221no—
1062C4⋊C4—1221no—
1063C4⋊C4C2×C22⋊D6111yescharacteristic
1064C4⋊C4C2×C22⋊D6111yescharacteristic
1065C4⋊C4C2×C22⋊D6111yescharacteristic
1066C4⋊C4C2×C22⋊D6111yescharacteristic
1067C4⋊C4C2×C22⋊D6111yescharacteristic
1068C4⋊C4C2×C22⋊D6111yescharacteristic
1069C4⋊C4C23×D6112yes—
1070C4⋊C4C23×D6112yes—
1071C4⋊C4C23×D6112yes—
1072C22⋊C4—22no—
1073C22⋊C4—22no—
1074C22⋊C4—22no—
1075C22⋊C4—22no—
1076C22⋊C4—22no—
1077C22⋊C4—1221no—
1078C22⋊C4—1221no—
1079C22⋊C4—1221no—
1080C22⋊C4—1221no—
1081C22⋊C4—1221no—
1082C22⋊C4—1221no—
1083C22⋊C4—1221no—
1084C22⋊C4—1221no—
1085C22⋊C4—1221no—
1086C22⋊C4—1221no—
1087C22⋊C4—1221no—
1088C22⋊C4—1221no—
1089C22⋊C4—1221no—
1090C22⋊C4—1221no—
1091C22⋊C4—1221no—
1092C22⋊C4—1221no—
1093C22⋊C4C2×C22⋊D6111yescharacteristic
1094C22⋊C4C2×C22⋊D6111yescharacteristic
1095C22⋊C4C2×C22⋊D6111yescharacteristic
1096C22⋊C4C2×C22⋊D6111yescharacteristic
1097C22⋊C4C2×C22⋊D6111yescharacteristic
1098C22⋊C4C2×C22⋊D6111yescharacteristic
1099C42—22no—
1100C42—22no—
1101C42—22no—
1102C42—22no—
1103C42—22no—
1104C42—1221no—
1105C42—1221no—
1106C42—1221no—
1107C42—1221no—
1108C42—1221no—
1109C42—1221no—
1110C42—1221no—
1111C42—1221no—
1112C42C2×C22⋊D6111yescharacteristic
1113C42C2×C22⋊D6111yescharacteristic
1114C42C2×C22⋊D6111yescharacteristic
1115C42C2×C22⋊D6111yescharacteristic
1116C42C2×C22⋊D6111yescharacteristic
1117C42C2×C22⋊D6111yescharacteristic
1118C42C23×D6111yescharacteristic
1119C42C23×D6111yescharacteristic
1120C42C23×D6111yescharacteristic
1121C42C23×D6111yescharacteristic
1122C23—1221no—
1123C23—1221no—
1124C23C22×C22⋊D6111yescharacteristic
1125C23C22×C22⋊D6111yescharacteristic
1126C23C22×C22⋊D6111yescharacteristic
1127Q8—22no—
1128Q8—22no—
1129Q8—41no—
1130Q8—42no—
1131Q8—44no—
1132Q8—42no—
1133Q8—42no—
1134Q8—612no—
1135Q8—1221no—
1136Q8—1221no—
1137Q8—1221no—
1138Q8—2442no—
1139Q8—2442no—
1140D4—41no—
1141D4—41no—
1142D4—41no—
1143D4—1221no—
1144D4—1221no—
1145D4—1221no—
1146D4—1221no—
1147D4—4881no—
1148D4—4881no—
1149D4—4881no—
1150D4—2442no—
1151D4—2442no—
1152D4—2442no—
1153D4—2442no—
1154D4—2442no—
1155C2×C4—22no—
1156C2×C4—22no—
1157C2×C4—22no—
1158C2×C4—21no—
1159C2×C4—21no—
1160C2×C4—21no—
1161C2×C4—21no—
1162C2×C4—21no—
1163C2×C4—21no—
1164C2×C4—22no—
1165C2×C4—22no—
1166C2×C4—22no—
1167C2×C4—22no—
1168C2×C4—41no—
1169C2×C4—41no—
1170C2×C4—41no—
1171C2×C4—44no—
1172C2×C4—1221no—
1173C2×C4—1221no—
1174C2×C4—1221no—
1175C2×C4—1221no—
1176C2×C4—1221no—
1177C2×C4—1221no—
1178C2×C4—4881no—
1179C2×C4—4881no—
1180C2×C4—4881no—
1181C2×C4—2442no—
1182C2×C4—2442no—
1183C2×C4—2442no—
1184C2×C4—2442no—
1185C2×C4—2442no—
1186C2×C4C22×C22⋊D6111yescharacteristic
1187C2×C4C22×C22⋊D6111yescharacteristic
1188C2×C4C22×C22⋊D6111yescharacteristic
1189C2×C4C22×C22⋊D6111yescharacteristic
1190C2×C4C22×C22⋊D6111yescharacteristic
1191C2×C4C22×C22⋊D6111yescharacteristic
1192C2×C4C22×C22⋊D6111yescharacteristic
1193C2×C4C22×C22⋊D6111yescharacteristic
1194C2×C4C22×C22⋊D6111yescharacteristic
1195C2×C4C22×C22⋊D6111yescharacteristic
1196C2×C4C22×C22⋊D6111yescharacteristic
1197C2×C4C24×D6111yescharacteristic
1198C8—1222no—
1199C8—1222no—
1200C8—1222no—
1201C8—1222no—
1202C22—21no—
1203C22—21no—
1204C22—21no—
1205C22—21no—
1206C22—21no—
1207C22—21no—
1208C22—21no—
1209C22—21no—
1210C22—21no—
1211C22—2441no—
1212C22—2441no—
1213C22—2441no—
1214C22—2441no—
1215C22—2441no—
1216C22—2441no—
1217C22C23×C22⋊D6111yescharacteristic
1218C4—21no—
1219C4—21no—
1220C4—21no—
1221C4—21no—
1222C4—21no—
1223C4—21no—
1224C4—21no—
1225C4—21no—
1226C4—21no—
1227C4—21no—
1228C4—42no—
1229C4—42no—
1230C4—42no—
1231C4—42no—
1232C4—1222no—
1233C4—2441no—
1234C4—2441no—
1235C4—2441no—
1236C4—2441no—
1237C4—2441no—
1238C4#1684056012yes—
1239C42−1+4×D6111yescharacteristic
1240C4#1684059911yescharacteristic
1241C2—41no—
1242C2—41no—
1243C2—41no—
1244C2—4881no—
1245C2—4881no—
1246C2#2145949211yescharacteristic
1247C2C2×#1684056011yescharacteristic
1248C2#2146060611yescharacteristic
subgroupG/H
centerC22C23×C22⋊D61
commutator, cosocleC2×C4×C61C25
FrattiniC2×C4C24×D61
FittingC61×#3509C2
socleC22×C61C23×D4
prime radical#21459412C2
hypercenter#3509D61
hypocenterC61#62118
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. #21458587C2semidirect
4. #21458379C2semidirect
5. #21458364C2semidirect
6. #21458349C2semidirect
7. #21458081C2semidirect
8. #21457939C2semidirect
9. #21457879C2semidirect
10. #21457202C2semidirect
11. #21457186C2semidirect
12. #21457150C2semidirect
13. #21457049C2semidirect
14. #21457017C2semidirect
15. #21456998C2semidirect
16. #21455975C2semidirect
17. #21455945C2semidirect
18. #21455884C2semidirect
19. #21455628C2semidirect
20. #21455620C2semidirect
21. #21455601C2semidirect
22. #21454936C2semidirect
23. C61×#3509C2semidirect
617. #3509D61semidirect
763. C61#62118semidirect

Maximal subgroups

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

subgroupindex
#214594122
#214587822
#214585872
#214583792
#214583642
#214583492
#214580812
#214579392
#214578792
#214572022
#214571862
#214571502
#214570492
#214570172
#214569982
#214559752
#214559452
#214558842
#214556282
#214556202
#214556012
#214549362
C61×#35092
#6211861