Finite Group Databasebeta

← #30552757

Subgroups — #30552757

Order 15616.

1736 conjugacy classes of subgroups.

The subgroup lattice has 1274 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21459631C211yesmaximal, characteristic, complemented
2#21459240C211yesmaximal, characteristic
3#21457123C212yesmaximal, complemented
4#21457110C212yesmaximal, complemented
5#21457075C212yesmaximal, complemented
6#21457070C212yesmaximal, complemented
7#21457044C211yesmaximal, characteristic, complemented
8#21457037C211yesmaximal, characteristic, complemented
9#21457017C211yesmaximal, characteristic, complemented
10#21457016C211yesmaximal, characteristic, complemented
11#21457002C211yesmaximal, characteristic, complemented
12#21456949C211yesmaximal, characteristic, complemented
13#21456946C211yesmaximal, characteristic, complemented
14#21456348C212yesmaximal, complemented
15#21456172C212yesmaximal, complemented
16#21455805C212yesmaximal, complemented
17#21455772C212yesmaximal, complemented
18#21455633C211yesmaximal, characteristic, complemented
19#21455611C211yesmaximal, characteristic, complemented
20#21455602C211yesmaximal, characteristic, complemented
21#476×D61C211yesmaximal, characteristic, complemented
22#21454480C211yesmaximal, characteristic, complemented
23C61×#3233C211yesmaximal, characteristic, complemented
24Q8×Dic122—21no—
25#16840490—21no—
26#16840472—21no—
27#16840470—21no—
28#16840470—21no—
29Q8×D244—21no—
30#16840425—21no—
31#16840425—21no—
32#16840392C2211yescharacteristic
33#16840392C2212yes—
34#16840392C2212yescomplemented
35#16840390C2212yescomplemented
36#16840385C2211yescharacteristic
37#16840381C2211yescharacteristic
38#16840378—21no—
39#16840368C2211yescharacteristic
40#16840365C2211yescharacteristic
41#16840364—21no—
42#16840351—21no—
43#16840348—21no—
44#16840342C2211yescharacteristic
45#16840330C2211yescharacteristic
46#16840328C2211yescharacteristic
47#16840317C2211yescharacteristic
48#16840317C2211yescharacteristic, complemented
49#16840312C2211yescharacteristic
50#16840309—21no—
51#16840309C2211yescharacteristic
52C2×#14519777C2211yescharacteristic, complemented
53C4⋊Q8×D61C2211yescharacteristic
54C4⋊Q8×D61C2211yescharacteristic, complemented
55#16840299C2211yescharacteristic
56#16840290—21no—
57#16840274—21no—
58#16840271—21no—
59#16840242C2212yes—
60C4×#11758226C2211yescharacteristic
61C4×#11758222C2211yescharacteristic
62C4×D4×D61C2211yescharacteristic
63#16840172C2212yescomplemented
64#16840172C2212yescomplemented
65#16840170C2212yescomplemented
66#16840170C2212yescomplemented
67#16840162C2212yescomplemented
68#16840160C2212yescomplemented
69#16840159C2212yescomplemented
70#16840128C2212yes—
71#16840125C2212yes—
72#16840123C2212yes—
73#16840121C2212yes—
74#16840118C2212yes—
75#16840109C2212yes—
76#16840107C2212yes—
77#16840101C2212yescomplemented
78#16840091C2212yescomplemented
79#16840090C2212yescomplemented
80#16840089C2212yescomplemented
81#16840088C2212yes—
82#16840086C2212yes—
83#16840086C2212yescomplemented
84#16840085C2212yes—
85#16840082C2212yescomplemented
86#16840081C2212yes—
87#16840081C2212yescomplemented
88#16840079C2212yes—
89#16840077C2212yes—
90#16840073C2212yes—
91#16840067C2212yescomplemented
92#16840065C2212yes—
93#16840064C2212yes—
94#16840061C2212yescomplemented
95#16840057C2211yescharacteristic, complemented
96#16840057C2211yescharacteristic, complemented
97#16840053C2211yescharacteristic
98#16840053C2211yescharacteristic
99#16840053C2211yescharacteristic, complemented
100#16840053C2211yescharacteristic, complemented
101#16840052C2211yescharacteristic
102#16840052C2211yescharacteristic
103#16840051C2212yes—
104#16840050C2212yes—
105#16840049C2211yescharacteristic
106#16840049C2211yescharacteristic, complemented
107#16840045C2212yescomplemented
108#16840041C2212yescomplemented
109#16840039C2211yescharacteristic
110#16840039C2211yescharacteristic, complemented
111#16839821C2212yescomplemented
112#16839820C2212yescomplemented
113#16839819C2211yescharacteristic, complemented
114#16839818C2211yescharacteristic, complemented
115#16839814C2211yescharacteristic, complemented
116#16839803C2212yes—
117#16839803C2212yes—
118#16839797C2212yes—
119#106×D61C2212yes—
120#16839784C2211yescharacteristic
121C4⋊C8×D61C2211yescharacteristic
122#16839765C2212yes—
123#16839762C2212yes—
124#16839757C2212yes—
125#102×D61C2212yes—
126#16839727C2212yes—
127#16839716C2212yes—
128C61×#533C2211yescharacteristic, complemented
129C61×#529C2211yescharacteristic
130C61×#499C2212yescomplemented
131C61×#488C2212yes—
132C61×#485C2212yescomplemented
133C61×#482C2212yes—
134C61×#477C2211yescharacteristic, complemented
135C61×#476C2211yescharacteristic
136C61×#475C2211yescharacteristic, complemented
137C61×#474C2211yescharacteristic
138C61×#431C2211yescharacteristic, complemented
139C2×#11758226C2311yescharacteristic
140C2×#11758222—21no—
141C2×#11758222—21no—
142C2×#11758222C2311yescharacteristic
143C22×Dic122—21no—
144C2×Q8×D61—21no—
145C2×Q8×D61—21no—
146C2×D4×D61C2311yescharacteristic
147C22×C4×D61—21no—
148C2×#11758189C2312yes—
149C2×C8×D61C2312yes—
150#14519777—21no—
151#14519777—21no—
152#14519777—22no—
153#14519777C2311yescharacteristic
154#14519777C2311yescharacteristic
155#14519777C2312yes—
156#14519777C2311yescharacteristic
157#14519776—22no—
158#14519776—22no—
159#14519776—21no—
160#14519776—21no—
161#14519776—21no—
162#14519776C2312yes—
163#14519776C2312yes—
164#14519776C2311yescharacteristic
165#14519775—21no—
166#14519775—21no—
167#14519774C2311yescharacteristic
168#14519773—21no—
169#14519773C2311yescharacteristic
170#14519772—21no—
171#14519772—21no—
172#14519770—21no—
173#14519769—22no—
174#14519768C2311yescharacteristic
175#14519768C2312yes—
176#14519768C2312yes—
177#14519767—22no—
178#14519767—22no—
179#14519767—21no—
180#14519766C2311yescharacteristic
181#14519765—21no—
182#14519763—21no—
183#14519763—21no—
184#14519763—21no—
185#14519763—21no—
186#14519762—21no—
187#14519762—21no—
188#14519762—21no—
189#14519761—21no—
190#14519761—21no—
191#14519759—21no—
192#14519759—21no—
193#14519757—21no—
194#14519757—21no—
195#14519757—22no—
196#14519757—22no—
197#14519757—21no—
198#14519757—21no—
199#14519755—21no—
200#14519755—22no—
201#14519755—22no—
202#14519755—21no—
203#14519754—22no—
204#14519754—22no—
205#14519754—21no—
206#14519753—21no—
207#14519753—21no—
208#14519753C2311yescharacteristic
209#14519752—21no—
210#14519752—21no—
211#14519752—21no—
212#14519752C2311yescharacteristic
213#14519752C2311yescharacteristic
214#14519751—21no—
215#14519751C2311yescharacteristic
216#14519751C2311yescharacteristic
217#14519750—21no—
218#14519750—21no—
219#14519750—21no—
220#14519750—21no—
221#14519750—21no—
222#14519749—21no—
223#14519748—21no—
224#14519748C2311yescharacteristic
225#14519747—21no—
226#14519747—21no—
227#14519747—21no—
228#14519745—21no—
229Q8×Dic61—21no—
230Q8×Dic61—21no—
231Q8×Dic61C2311yescharacteristic
232C4×Dic122—22no—
233C4×Dic122D411yescharacteristic
234C4×Dic122D411yescharacteristic
235#14519742—21no—
236#14519742—21no—
237C4×D244—22no—
238C4×D244—21no—
239C4×D244—21no—
240C4×D244—21no—
241C4×D244D411yescharacteristic
242C4×D244D411yescharacteristic
243C4×D244C2311yescharacteristic
244C4×D244C2311yescharacteristic
245D4×Dic61C2311yescharacteristic
246#14519739—21no—
247#14519739C2311yescharacteristic
248#14519739C2311yescharacteristic
249C4×C22⋊D61—21no—
250C4×C22⋊D61—21no—
251C4×C22⋊D61D411yescharacteristic
252C4×C22⋊D61D411yescharacteristic
253C4×C22⋊D61D411yescharacteristic
254C4×C22⋊D61D411yescharacteristic
255#14519737—22no—
256#14519737—22no—
257#14519737—21no—
258#14519736C2311yescharacteristic
259#14519735—21no—
260#14519735C2311yescharacteristic
261#14519735C2312yes—
262#14519735C2312yes—
263#14519734—21no—
264#14519734C2311yescharacteristic
265#14519734C2311yescharacteristic
266C2×C4⋊Dic61—21no—
267C2×C4⋊Dic61C2312yes—
268C4⋊C4×D61—21no—
269C4⋊C4×D61—21no—
270C4⋊C4×D61C2311yescharacteristic
271C4⋊C4×D61C2312yes—
272C4⋊C4×D61C2312yes—
273C22⋊C4×D61—21no—
274C42×D61—21no—
275C42×D61C2311yescharacteristic
276C42×D61C2311yescharacteristic
277#14519710C2312yes—
278#14519710C2312yes—
279#14519710C2312yes—
280#14519710C2312yes—
281#14519709C2312yes—
282#14519709C2312yes—
283#14519709C2312yes—
284#14519709C2312yes—
285#14519708C2312yes—
286#14519708C2312yes—
287#14519708C2312yes—
288#14519708C2312yes—
289C4⋊#92418C2311yescharacteristic
290C4⋊#92418C2311yescharacteristic
291#14519706C2312yes—
292#14519706C2312yes—
293#14519701C2312yes—
294#14519701C2312yes—
295#14519699C2312yes—
296#14519699C2312yes—
297#14519699C2312yes—
298#14519699C2312yes—
299#14519698C2312yes—
300#14519698C2312yes—
301#14519697C2312yes—
302#14519697C2312yes—
303#14519697C2312yes—
304#14519697C2312yes—
305C22⋊#92418C2312yes—
306#14519689C2312yes—
307#14519689C2312yes—
308#14519688C2312yes—
309#14519687C2312yes—
310C8×Dic61C2312yes—
311C4⋊Q8×C61C2311yescharacteristic
312C4⋊Q8×C61C2311yescharacteristic
313#126×C61—21no—
314#125×C61C2312yes—
315#125×C61C2311yescharacteristic
316#124×C61C2311yescharacteristic
317#123×C61—21no—
318C22⋊Q8×C61—21no—
319C22⋊Q8×C61—21no—
320C22⋊Q8×C61C2311yescharacteristic
321#121×C61C2311yescharacteristic
322C4×Q8×C61—21no—
323C4×Q8×C61—21no—
324C4×Q8×C61C2311yescharacteristic
325C4×D4×C61—21no—
326C4×D4×C61C2311yescharacteristic
327#117×C61—21no—
328#117×C61C2312yes—
329C2×C42×C61C2311yescharacteristic
330#107×C61C2312yes—
331#107×C61C2312yes—
332#106×C61C2312yes—
333#106×C61C2312yes—
334C4⋊C8×C61C2311yescharacteristic
335C4⋊C8×C61C2311yescharacteristic
336#103×C61C2312yes—
337#103×C61C2312yes—
338#102×C61C2312yes—
339#102×C61C2312yes—
340C22⋊C8×C61C2312yes—
341C4×C8×C61C2312yes—
342C23×D61—21no—
343C2×Q8×C61—21no—
344C2×Q8×C61—21no—
345C2×Q8×C61C2411yescharacteristic
346C2×D4×C61—21no—
347C2×D4×C61C2411yescharacteristic
348C22×C4×C61—21no—
349C22×C4×C61C2×D411yescharacteristic
350C22×C4×C61C2×D411yescharacteristic
351C22×C4×C61C2411yescharacteristic
352C2×C22⋊D61—21no—
353C2×C22⋊D61—21no—
354C2×C22⋊D61—21no—
355C2×C22⋊D61—21no—
356C2×C22⋊D61—21no—
357C2×C22⋊D61—21no—
358C2×C22⋊D61C2×D411yescharacteristic
359C2×C22⋊D61C2×D411yescharacteristic
360C22×Dic61—22no—
361C22×Dic61—21no—
362#11758226—22no—
363#11758226—22no—
364Q8×D61—82no—
365Q8×D61—82no—
366D4×D61—22no—
367D4×D61—22no—
368#11758222—22no—
369#11758222—22no—
370#11758222—82no—
371#11758222—82no—
372C2×D244—21no—
373C2×D244—21no—
374C2×D244—21no—
375C2×D244—21no—
376C2×D244—21no—
377C2×D244C2×D411yescharacteristic
378C2×D244C2411yescharacteristic
379C2×D244C2411yescharacteristic
380C2×C4×D61—21no—
381C2×C4×D61—21no—
382C2×C4×D61—21no—
383C2×C4×D61—21no—
384C2×C4×D61—22no—
385C2×C4×D61—22no—
386C2×C4×D61—21no—
387C2×C4×D61—21no—
388C2×C4×D61—82no—
389C2×C4×D61C2×D411yescharacteristic
390C2×C4×D61C2×D411yescharacteristic
391C2×C4×D61C2×D411yescharacteristic
392C2×C4×D61C2×D411yescharacteristic
393C2×C4×D61C2411yescharacteristic
394C2×C4×D61C2411yescharacteristic
395C2×Dic122—21no—
396C2×Dic122—21no—
397C2×Dic122—22no—
398C2×Dic122—21no—
399C2×Dic122—22no—
400C2×Dic122—22no—
401C2×Dic122—21no—
402C2×Dic122—82no—
403C2×Dic122C2×D411yescharacteristic
404C2×C8×C61C2412yes—
405C2×C8×C61C2412yes—
406C4⋊C4×C61—21no—
407C4⋊C4×C61—21no—
408C4⋊C4×C61—21no—
409C4⋊C4×C61—22no—
410C4⋊C4×C61—22no—
411C4⋊C4×C61—21no—
412C4⋊C4×C61—21no—
413C4⋊C4×C61—21no—
414C4⋊C4×C61C2412yes—
415C4⋊C4×C61C2412yes—
416C4⋊C4×C61C2411yescharacteristic
417C4⋊C4×C61C2411yescharacteristic
418C22⋊C4×C61—22no—
419C22⋊C4×C61—21no—
420C22⋊C4×C61—21no—
421C22⋊C4×C61—21no—
422C22⋊C4×C61—21no—
423C22⋊C4×C61—21no—
424C42×C61—21no—
425C42×C61—22no—
426C42×C61C2×D411yescharacteristic
427C42×C61C2×D411yescharacteristic
428C42×C61C2411yescharacteristic
429C42×C61C2411yescharacteristic
430C22⋊Dic61—21no—
431C22⋊Dic61—21no—
432C22⋊Dic61C2×D411yescharacteristic
433C22⋊Dic61C2×D411yescharacteristic
434#11758198—22no—
435#11758198—22no—
436#11758198—21no—
437#11758198—21no—
438#11758198—21no—
439#11758198—21no—
440#11758198—21no—
441#11758198—21no—
442#11758198—21no—
443#11758198—21no—
444#11758198—21no—
445#11758198—21no—
446#11758198—21no—
447#11758198—21no—
448#11758198C2×D411yescharacteristic
449#11758198C2×D411yescharacteristic
450#11758198C2×D411yescharacteristic
451#11758198C2×D411yescharacteristic
452C4⋊Dic61—21no—
453C4⋊Dic61—21no—
454C4⋊Dic61—22no—
455C4⋊Dic61—22no—
456C4⋊Dic61—21no—
457C4⋊Dic61—21no—
458C4⋊Dic61—21no—
459C4⋊Dic61—22no—
460C4⋊Dic61—22no—
461C4⋊Dic61C2×D411yescharacteristic
462C4⋊Dic61C2×D411yescharacteristic
463C4⋊Dic61C2412yes—
464C4⋊Dic61C2412yes—
465C4⋊Dic61C2411yescharacteristic
466C4⋊Dic61C2411yescharacteristic
467#11758196—22no—
468#11758196—22no—
469#11758196—21no—
470#11758196—22no—
471#11758196—22no—
472#11758196—21no—
473#11758196—21no—
474#11758196—21no—
475#11758196—22no—
476#11758196—22no—
477#11758196C2×D411yescharacteristic
478#11758196C2×D411yescharacteristic
479#11758196C2×D411yescharacteristic
480#11758196C2×D411yescharacteristic
481C4×Dic61—21no—
482C4×Dic61—21no—
483C4×Dic61—22no—
484C4×Dic61—22no—
485C4×Dic61C2×D411yescharacteristic
486C4×Dic61C2×D411yescharacteristic
487C4×Dic61C2×D411yescharacteristic
488C4×Dic61C2×D411yescharacteristic
489C4×Dic61C2411yescharacteristic
490C4×Dic61C2411yescharacteristic
491C2×#92418C2412yes—
492C2×#92418C2412yes—
493#11758189—24no—
494C8×D61—24no—
495C23×C61—21no—
496C23×C61C22×D411yescharacteristic
497C22×D61—21no—
498C22×D61—21no—
499C22×D61—42no—
500C22×D61—81no—
501C22×D61—81no—
502C22×D61C22×D411yescharacteristic
503C22×D61C22×D411yescharacteristic
504Q8×C61—21no—
505Q8×C61—21no—
506Q8×C61—42no—
507Q8×C61—42no—
508D4×C61—21no—
509D4×C61—21no—
510D4×C61—81no—
511C2×C4×C61—22no—
512C2×C4×C61—21no—
513C2×C4×C61—21no—
514C2×C4×C61—22no—
515C2×C4×C61—21no—
516C2×C4×C61—21no—
517C2×C4×C61—22no—
518C2×C4×C61—21no—
519C2×C4×C61—41no—
520C2×C4×C61—42no—
521C2×C4×C61C22×D411yescharacteristic
522C2×C4×C61C22×D411yescharacteristic
523C2×C4×C61C22×D411yescharacteristic
524C2×C4×C61C22×D411yescharacteristic
525C2×C4×C61C22×D411yescharacteristic
526C2×C4×C61C2511yescharacteristic
527C22⋊D61—22no—
528C22⋊D61—22no—
529C22⋊D61—42no—
530C22⋊D61—81no—
531C22⋊D61—81no—
532C22⋊D61—81no—
533C22⋊D61—81no—
534C22⋊D61—81no—
535C2×Dic61—21no—
536C2×Dic61—22no—
537C2×Dic61—22no—
538C2×Dic61—21no—
539C2×Dic61—81no—
540C2×Dic61—82no—
541C2×Dic61C22×D411yescharacteristic
542C2×Dic61C22×D411yescharacteristic
543C2×Dic61C22×D411yescharacteristic
544C2×Dic61C22×D411yescharacteristic
545C2×Dic61C22×D411yescharacteristic
546C2×Dic61C22×D411yescharacteristic
547D244—22no—
548D244—21no—
549D244—21no—
550D244—21no—
551D244—21no—
552D244—42no—
553D244—81no—
554D244—81no—
555D244—81no—
556D244—81no—
557C4×D61—22no—
558C4×D61—22no—
559C4×D61—21no—
560C4×D61—21no—
561C4×D61—41no—
562C4×D61—41no—
563C4×D61—42no—
564C4×D61—42no—
565C4×D61—42no—
566C4×D61—81no—
567C4×D61—81no—
568C4×D61—81no—
569C4×D61—82no—
570C4×D61—82no—
571C4×D612−1+412yes—
572C4×D612−1+412yes—
573Dic122—22no—
574Dic122—42no—
575Dic122—42no—
576Dic122—81no—
577Dic122—82no—
578Dic122—82no—
579Dic122—82no—
580Dic122—81no—
581C8×C61—22no—
582C8×C61—22no—
583#92418—22no—
584#92418—22no—
585#60892—611nomaximal, Sylow
586C22×C61—21no—
587C22×C61—21no—
588C22×C61—21no—
589C22×C61—41no—
590C22×C61—41no—
591C22×C61—41no—
592C22×C61C23×D411yescharacteristic
593C2×D61—21no—
594C2×D61—21no—
595C2×D61—21no—
596C2×D61—21no—
597C2×D61—21no—
598C2×D61—41no—
599C2×D61—41no—
600C2×D61—41no—
601C2×D61—41no—
602C2×D61—41no—
603C2×D61—41no—
604C2×D61—84no—
605C2×D61#53612yes—
606C4×C61—21no—
607C4×C61—21no—
608C4×C61—21no—
609C4×C61—21no—
610C4×C61—42no—
611C4×C61—41no—
612C4×C61—41no—
613C4×C61—41no—
614C4×C61—42no—
615C4×C61#57712yes—
616C4×C61C2×2−1+411yescharacteristic
617C4×C61C2×2−1+411yescharacteristic
618Dic61—21no—
619Dic61—21no—
620Dic61—21no—
621Dic61—21no—
622Dic61—21no—
623Dic61—42no—
624Dic61—42no—
625Dic61—41no—
626Dic61—41no—
627Dic61#53612yes—
628#3503—611no—
629#3460—611no—
630#3244—612no—
631#3244—612no—
632#3241—612no—
633#3241—612no—
634#3238—611no—
635#3238—611no—
636#3235—611no—
637#3235—611no—
638#3233—611no—
639#3233D6111yescharacteristic, complemented
640#3227—611no—
641#3227—611no—
642#3163—612no—
643#3136—612no—
644#3099—612no—
645#3096—612no—
646#3079—611no—
647#3077—611no—
648#3076—611no—
649C2×#476—611no—
650#2925—611no—
651C2×C61—41no—
652C2×C61—81no—
653C2×C61C2×#53611yescharacteristic
654C2×C61C2×#57711yescharacteristic
655C2×C61#358511yescharacteristic
656D61—22no—
657D61—41no—
658D61—81no—
659D61—81no—
660Q82—1221no—
661#557—1221no—
662#554—1221no—
663#554—1221no—
664#554—1221no—
665D4×Q8—1221no—
666D4×Q8—1221no—
667D4×Q8—1221no—
668#544—612no—
669#544—611no—
670#544—612no—
671#544—612no—
672#542—611no—
673#542—611no—
674#542—1221no—
675#540—611no—
676#540—611no—
677#540—1221no—
678#538—1221no—
679#538—1221no—
680#537—611no—
681#535—611no—
682#535—611no—
683#533—611no—
684#533—611no—
685#533C2×D6111yescharacteristic, complemented
686#532—611no—
687#532—611no—
688#532—1221no—
689C2×C4⋊Q8—611no—
690C2×C4⋊Q8—611no—
691C2×C4⋊Q8—611no—
692#529—611no—
693#529—1221no—
694#529C2×D6111yescharacteristic
695#525—1221no—
696#525—1221no—
697#520—612no—
698C4×#41—611no—
699C4×#41—611no—
700C2×C4×D4—611no—
701#501—612no—
702#501—612no—
703#501—612no—
704#501—612no—
705#499—612no—
706#499C2×D6112yescomplemented
707#498—612no—
708#498—612no—
709#490—612no—
710#490—612no—
711#489—612no—
712#489—612no—
713#488—612no—
714#488C2×D6112yes—
715#486—612no—
716#486—612no—
717#485—612no—
718#485C2×D6112yescomplemented
719#483—612no—
720#483—612no—
721#482—612no—
722#482—612no—
723#482—612no—
724#482—612no—
725#482—612no—
726#482C2×D6112yes—
727#481—612no—
728#481—612no—
729#481—612no—
730#481—612no—
731#480—612no—
732#480—612no—
733#479—612no—
734#478—612no—
735#478—612no—
736#478—612no—
737#477—611no—
738#477—611no—
739#477C2×D6111yescharacteristic, complemented
740#476—611no—
741#476—611no—
742#476—611no—
743#476—611no—
744#476—612no—
745#476—611no—
746#476—611no—
747#476—611no—
748#476—611no—
749#476—612no—
750#476C2×D6111yescharacteristic
751#475—612no—
752#475C2×D6111yescharacteristic, complemented
753#474—611no—
754#474—611no—
755#474—612no—
756#474C2×D6111yescharacteristic
757#433—612no—
758#433—612no—
759#432—611no—
760#432—611no—
761#431—611no—
762#431C2×D6111yescharacteristic, complemented
763#428—612no—
764#428—612no—
765#427—612no—
766C2×#106—612no—
767#423—611no—
768C2×C4⋊C8—611no—
769#418—612no—
770#417—612no—
771#416—612no—
772C2×#102—612no—
773#408—612no—
774#405—612no—
775C61#6089211yescharacteristic, complemented, Sylow
776C2×#41—611no—
777C2×#41—611no—
778C2×#41—1221no—
779C2×#41—1221no—
780C22×Q8—1221no—
781C22×Q8—1221no—
782C22×Q8—1221no—
783C22×D4—611no—
784C23×C4—1221no—
785C2×M16—612no—
786C22×C8—612no—
787C4⋊Q8—612no—
788C4⋊Q8—612no—
789C4⋊Q8—611no—
790C4⋊Q8—611no—
791C4⋊Q8—611no—
792C4⋊Q8—612no—
793C4⋊Q8—611no—
794C4⋊Q8—1222no—
795C4⋊Q8—1221no—
796C4⋊Q8—1221no—
797C4⋊Q8—1221no—
798C4⋊Q8—1221no—
799C4⋊Q8—1221no—
800C4⋊Q8—1222no—
801C4⋊Q8—1222no—
802C4⋊Q8—1221no—
803C4⋊Q8—1221no—
804C4⋊Q8C22×D6111yescharacteristic
805C4⋊Q8C22×D6111yescharacteristic
806#127—611no—
807#127—611no—
808#127—1221no—
809#126—21no—
810#126—1221no—
811#126—1221no—
812#126—1221no—
813#125—611no—
814#125—612no—
815#125—612no—
816#125—1222no—
817#125—1221no—
818#125—1222no—
819#125—1222no—
820#125C22×D6111yescharacteristic
821#125C22×D6112yes—
822#124—611no—
823#124—1221no—
824#124—1221no—
825#124—1221no—
826#124—1221no—
827#124—1221no—
828#124C22×D6111yescharacteristic
829#123—21no—
830#123—1221no—
831#123—1221no—
832#123—1221no—
833#123—1221no—
834#123—1221no—
835#123—1221no—
836#123—1221no—
837C22⋊Q8—21no—
838C22⋊Q8—21no—
839C22⋊Q8—611no—
840C22⋊Q8—1222no—
841C22⋊Q8—1222no—
842C22⋊Q8—1221no—
843C22⋊Q8—1221no—
844C22⋊Q8—1221no—
845C22⋊Q8—1222no—
846C22⋊Q8—1222no—
847C22⋊Q8—1222no—
848C22⋊Q8—1222no—
849C22⋊Q8—1221no—
850C22⋊Q8—1221no—
851C22⋊Q8—1221no—
852C22⋊Q8—1221no—
853C22⋊Q8—1221no—
854C22⋊Q8—1221no—
855C22⋊Q8C22×D6111yescharacteristic
856#121—611no—
857#121—611no—
858#121—611no—
859#121—611no—
860#121—611no—
861#121—1221no—
862#121—1221no—
863#121—1221no—
864#121—1221no—
865#121—1221no—
866#121—1221no—
867#121—1221no—
868#121—1221no—
869#121—1221no—
870#121—1221no—
871#121—1221no—
872#121C22×D6111yescharacteristic
873#120—1221no—
874#120—1221no—
875#120—1221no—
876#120—1221no—
877C4×Q8—21no—
878C4×Q8—21no—
879C4×Q8—611no—
880C4×Q8—611no—
881C4×Q8—611no—
882C4×Q8—1222no—
883C4×Q8—1221no—
884C4×Q8—1221no—
885C4×Q8—1221no—
886C4×Q8—1221no—
887C4×Q8C22×D6111yescharacteristic
888C4×D4—21no—
889C4×D4—611no—
890C4×D4—611no—
891C4×D4—611no—
892C4×D4—611no—
893C4×D4—611no—
894C4×D4—611no—
895C4×D4—611no—
896C4×D4—611no—
897C4×D4—611no—
898C4×D4—611no—
899C4×D4—611no—
900C4×D4—1221no—
901C4×D4—1221no—
902C4×D4—1222no—
903C4×D4—1221no—
904C4×D4—1221no—
905C4×D4—1221no—
906C4×D4—1222no—
907C4×D4—1222no—
908C4×D4—1221no—
909C4×D4—1221no—
910C4×D4C22×D6111yescharacteristic
911#117—21no—
912#117—611no—
913#117—611no—
914#117—611no—
915#117—611no—
916#117—612no—
917#117—612no—
918#117—1221no—
919#117—1221no—
920#117C22×D6112yes—
921C2×C4⋊C4—612no—
922C2×C4⋊C4—611no—
923C2×C4⋊C4—612no—
924C2×C4⋊C4—612no—
925C2×C4⋊C4—1221no—
926C2×C4⋊C4—1221no—
927C2×C4⋊C4—1221no—
928C2×C22⋊C4—1221no—
929C2×C42—611no—
930C2×C42—611no—
931C2×C42—1221no—
932C2×C42C22×D6111yescharacteristic
933#107—612no—
934#107—612no—
935#107—612no—
936#107—612no—
937#107C22×D6112yes—
938#107C22×D6112yes—
939#106—612no—
940#106—612no—
941#106—612no—
942#106—612no—
943#106—612no—
944#106—612no—
945#106—612no—
946#106—612no—
947#106C22×D6112yes—
948#106C22×D6112yes—
949C4⋊C8—612no—
950C4⋊C8—612no—
951C4⋊C8—611no—
952C4⋊C8—611no—
953C4⋊C8C22×D6111yescharacteristic
954C4⋊C8C22×D6111yescharacteristic
955#103—612no—
956#103—612no—
957#103C22×D6112yes—
958#103C22×D6112yes—
959#102—612no—
960#102—612no—
961#102—612no—
962#102—612no—
963#102—612no—
964#102—612no—
965#102—612no—
966#102—612no—
967#102—612no—
968#102—612no—
969#102C22×D6112yes—
970#102C22×D6112yes—
971C22⋊C8—612no—
972C22⋊C8—612no—
973C22⋊C8—612no—
974C22⋊C8C22×D6112yes—
975#97—612no—
976#97—612no—
977C4×C8—612no—
978C4×C8C22×D6112yes—
979C24—1221no—
980#41—1222no—
981#41—1222no—
982#41—1222no—
983#41—1222no—
984#41—4882no—
985#41—4882no—
986C2×Q8—21no—
987C2×Q8—21no—
988C2×Q8—611no—
989C2×Q8—1221no—
990C2×Q8—1222no—
991C2×Q8—1222no—
992C2×Q8—1221no—
993C2×Q8—1222no—
994C2×Q8—1221no—
995C2×Q8—1221no—
996C2×Q8—4882no—
997C2×Q8—4882no—
998C2×Q8—4882no—
999C2×Q8C23×D6111yescharacteristic
1000C2×D4—21no—
1001C2×D4—611no—
1002C2×D4—611no—
1003C2×D4—611no—
1004C2×D4—611no—
1005C2×D4—611no—
1006C2×D4—1221no—
1007C2×D4—1221no—
1008C2×D4—1221no—
1009C2×D4—1222no—
1010C2×D4—1222no—
1011C2×D4—1221no—
1012C2×D4—1221no—
1013C2×D4—1221no—
1014C2×D4—1221no—
1015C2×D4—1221no—
1016C2×D4—1221no—
1017C2×D4—1221no—
1018C2×D4—1221no—
1019C2×D4C23×D6111yescharacteristic
1020C22×C4—21no—
1021C22×C4—611no—
1022C22×C4—611no—
1023C22×C4—611no—
1024C22×C4—611no—
1025C22×C4—611no—
1026C22×C4—611no—
1027C22×C4—1221no—
1028C22×C4—1221no—
1029C22×C4—1221no—
1030C22×C4—1221no—
1031C22×C4—1222no—
1032C22×C4—1222no—
1033C22×C4—1221no—
1034C22×C4—1222no—
1035C22×C4—1221no—
1036C22×C4—1221no—
1037C22×C4—4882no—
1038C22×C4D4×D6111yescharacteristic
1039C22×C4D4×D6111yescharacteristic
1040C22×C4C23×D6111yescharacteristic
1041M16—1224no—
1042C2×C8—612no—
1043C2×C8—612no—
1044C2×C8—1224no—
1045C2×C8C23×D6112yes—
1046C2×C8C23×D6112yes—
1047C4⋊C4—21no—
1048C4⋊C4—21no—
1049C4⋊C4—21no—
1050C4⋊C4—21no—
1051C4⋊C4—21no—
1052C4⋊C4—21no—
1053C4⋊C4—22no—
1054C4⋊C4—22no—
1055C4⋊C4—611no—
1056C4⋊C4—611no—
1057C4⋊C4—611no—
1058C4⋊C4—611no—
1059C4⋊C4—611no—
1060C4⋊C4—611no—
1061C4⋊C4—612no—
1062C4⋊C4—612no—
1063C4⋊C4—611no—
1064C4⋊C4—611no—
1065C4⋊C4—1221no—
1066C4⋊C4—1222no—
1067C4⋊C4—1222no—
1068C4⋊C4—1222no—
1069C4⋊C4—1222no—
1070C4⋊C4—1221no—
1071C4⋊C4—1221no—
1072C4⋊C4—1221no—
1073C4⋊C4—1222no—
1074C4⋊C4—1222no—
1075C4⋊C4—1221no—
1076C4⋊C4—1221no—
1077C4⋊C4—1222no—
1078C4⋊C4—1222no—
1079C4⋊C4—1222no—
1080C4⋊C4—1221no—
1081C4⋊C4—1221no—
1082C4⋊C4—1222no—
1083C4⋊C4—1221no—
1084C4⋊C4C23×D6112yes—
1085C4⋊C4C23×D6112yes—
1086C4⋊C4C23×D6111yescharacteristic
1087C4⋊C4C23×D6111yescharacteristic
1088C22⋊C4—22no—
1089C22⋊C4—21no—
1090C22⋊C4—21no—
1091C22⋊C4—21no—
1092C22⋊C4—21no—
1093C22⋊C4—21no—
1094C22⋊C4—611no—
1095C22⋊C4—611no—
1096C22⋊C4—611no—
1097C22⋊C4—611no—
1098C22⋊C4—611no—
1099C22⋊C4—611no—
1100C22⋊C4—1221no—
1101C22⋊C4—1221no—
1102C22⋊C4—1221no—
1103C22⋊C4—1221no—
1104C22⋊C4—1221no—
1105C22⋊C4—1221no—
1106C22⋊C4—1221no—
1107C22⋊C4—1222no—
1108C22⋊C4—1222no—
1109C22⋊C4—1221no—
1110C22⋊C4—1221no—
1111C22⋊C4—1221no—
1112C22⋊C4—1221no—
1113C22⋊C4—1221no—
1114C22⋊C4—1221no—
1115C22⋊C4—1221no—
1116C42—21no—
1117C42—22no—
1118C42—611no—
1119C42—611no—
1120C42—611no—
1121C42—611no—
1122C42—611no—
1123C42—611no—
1124C42—1221no—
1125C42—1221no—
1126C42—1222no—
1127C42—1222no—
1128C42D4×D6111yescharacteristic
1129C42D4×D6111yescharacteristic
1130C42C23×D6111yescharacteristic
1131C42C23×D6111yescharacteristic
1132C23—21no—
1133C23—611no—
1134C23—611no—
1135C23—1221no—
1136C23—1221no—
1137C23—4881no—
1138C23—4881no—
1139C23—2442no—
1140C23C2×D4×D6111yescharacteristic
1141Q8—21no—
1142Q8—21no—
1143Q8—42no—
1144Q8—42no—
1145Q8—1222no—
1146Q8—4882no—
1147Q8—4881no—
1148Q8—4882no—
1149Q8—4882no—
1150Q8—4881no—
1151Q8—2442no—
1152Q8—2442no—
1153D4—21no—
1154D4—21no—
1155D4—81no—
1156D4—1222no—
1157D4—1222no—
1158D4—1222no—
1159D4—1221no—
1160D4—1221no—
1161D4—1221no—
1162D4—1221no—
1163D4—4881no—
1164D4—4881no—
1165D4—4881no—
1166D4—4881no—
1167D4—4881no—
1168D4—4881no—
1169D4—4881no—
1170D4—4881no—
1171D4—4881no—
1172D4—2442no—
1173D4—2442no—
1174C2×C4—22no—
1175C2×C4—21no—
1176C2×C4—21no—
1177C2×C4—22no—
1178C2×C4—21no—
1179C2×C4—21no—
1180C2×C4—22no—
1181C2×C4—21no—
1182C2×C4—41no—
1183C2×C4—42no—
1184C2×C4—611no—
1185C2×C4—612no—
1186C2×C4—612no—
1187C2×C4—611no—
1188C2×C4—611no—
1189C2×C4—611no—
1190C2×C4—611no—
1191C2×C4—611no—
1192C2×C4—1222no—
1193C2×C4—1222no—
1194C2×C4—1221no—
1195C2×C4—1221no—
1196C2×C4—1221no—
1197C2×C4—1222no—
1198C2×C4—1222no—
1199C2×C4—1221no—
1200C2×C4—4881no—
1201C2×C4—4881no—
1202C2×C4—4881no—
1203C2×C4—4882no—
1204C2×C4—4882no—
1205C2×C4—4881no—
1206C2×C4—4882no—
1207C2×C4—2441no—
1208C2×C4—2441no—
1209C2×C4—2442no—
1210C2×C4—2442no—
1211C2×C4—2442no—
1212C2×C4C2×D4×D6111yescharacteristic
1213C2×C4C2×D4×D6111yescharacteristic
1214C2×C4C2×D4×D6111yescharacteristic
1215C2×C4C2×D4×D6111yescharacteristic
1216C2×C4C2×D4×D6111yescharacteristic
1217C2×C4C24×D6111yescharacteristic
1218C8—22no—
1219C8—22no—
1220C8—1222no—
1221C8—1222no—
1222C22—21no—
1223C22—21no—
1224C22—21no—
1225C22—41no—
1226C22—41no—
1227C22—41no—
1228C22—612no—
1229C22—1221no—
1230C22—1221no—
1231C22—1221no—
1232C22—1221no—
1233C22—1221no—
1234C22—4884no—
1235C22—2441no—
1236C22—2441no—
1237C22—2441no—
1238C22—2441no—
1239C22—2441no—
1240C22—2441no—
1241C22C22×D4×D6111yescharacteristic
1242C4—21no—
1243C4—21no—
1244C4—21no—
1245C4—21no—
1246C4—41no—
1247C4—42no—
1248C4—42no—
1249C4—41no—
1250C4—41no—
1251C4—612no—
1252C4—1221no—
1253C4—1221no—
1254C4—1221no—
1255C4—1221no—
1256C4—1221no—
1257C4—2441no—
1258C4—2441no—
1259C4—2442no—
1260C4—2442no—
1261C4#1684056912yes—
1262C42−1+4×D6111yescharacteristic
1263C42−1+4×D6111yescharacteristic
1264C2—41no—
1265C2—81no—
1266C2—1222no—
1267C2—4881no—
1268C2—4881no—
1269C2—2441no—
1270C2#536×D6111yescharacteristic
1271C2C2×#1684056911yescharacteristic
1272C2#2146059611yescharacteristic
subgroupG/H
centerC22C22×D4×D61
commutator, cosocleC2×C4×C61C25
FrattiniC2×C4C24×D61
FittingC61×#3233C2
socleC22×C61C23×D4
prime radical#21459240C2
hypercenter#3233D61
hypocenterC61#60892
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3233

Complements

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

NH ≅ G/Ntype
1. #21459631C2semidirect
3. #21457123C2semidirect
4. #21457110C2semidirect
5. #21457075C2semidirect
6. #21457070C2semidirect
7. #21457044C2semidirect
8. #21457037C2semidirect
9. #21457017C2semidirect
10. #21457016C2semidirect
11. #21457002C2semidirect
12. #21456949C2semidirect
13. #21456946C2semidirect
14. #21456348C2semidirect
15. #21456172C2semidirect
16. #21455805C2semidirect
17. #21455772C2semidirect
18. #21455633C2semidirect
19. #21455611C2semidirect
20. #21455602C2semidirect
21. #476×D61C2semidirect
22. #21454480C2semidirect
23. C61×#3233C2semidirect
34. #16840392C22semidirect
35. #16840390C22semidirect
48. #16840317C22semidirect
52. C2×#14519777C22semidirect
54. C4⋊Q8×D61C22semidirect
63. #16840172C22semidirect
64. #16840172C22semidirect
65. #16840170C22semidirect
66. #16840170C22semidirect
67. #16840162C22semidirect
68. #16840160C22semidirect
69. #16840159C22semidirect
77. #16840101C22semidirect
78. #16840091C22semidirect
79. #16840090C22semidirect
80. #16840089C22semidirect
83. #16840086C22semidirect
85. #16840082C22semidirect
87. #16840081C22semidirect
91. #16840067C22semidirect
94. #16840061C22semidirect
95. #16840057C22semidirect
96. #16840057C22semidirect
99. #16840053C22semidirect
100. #16840053C22semidirect
106. #16840049C22semidirect
107. #16840045C22semidirect
108. #16840041C22semidirect
110. #16840039C22semidirect
111. #16839821C22semidirect
112. #16839820C22semidirect
113. #16839819C22semidirect
114. #16839818C22semidirect
115. #16839814C22semidirect
128. C61×#533C22semidirect
130. C61×#499C22semidirect
132. C61×#485C22semidirect
134. C61×#477C22semidirect
136. C61×#475C22semidirect
138. C61×#431C22semidirect
639. #3233D61semidirect
685. #533C2×D61semidirect
706. #499C2×D61semidirect
718. #485C2×D61semidirect
739. #477C2×D61semidirect
752. #475C2×D61semidirect
762. #431C2×D61semidirect
775. C61#60892semidirect

Maximal subgroups

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

subgroupindex
#214596312
#214592402
#214571232
#214571102
#214570752
#214570702
#214570442
#214570372
#214570172
#214570162
#214570022
#214569492
#214569462
#214563482
#214561722
#214558052
#214557722
#214556332
#214556112
#214556022
#476×D612
#214544802
C61×#32332
#6089261