Finite Group Databasebeta

← #29695969

Subgroups — #29695969

Order 15616.

1316 conjugacy classes of subgroups.

The subgroup lattice has 970 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21460590C211yesmaximal, characteristic
2#21454734C211yesmaximal, characteristic, complemented
3#21454617C211yesmaximal, characteristic, complemented
4#21454363C211yesmaximal, characteristic, complemented
5#21446716C211yesmaximal, characteristic, complemented
6#21446709C211yesmaximal, characteristic, complemented
7#21446323C211yesmaximal, characteristic, complemented
8#21446320C211yesmaximal, characteristic, complemented
9#21446181C211yesmaximal, characteristic, complemented
10#21446178C211yesmaximal, characteristic, complemented
11#21445871C211yesmaximal, characteristic, complemented
12#21445783C211yesmaximal, characteristic, complemented
13#21445781C211yesmaximal, characteristic, complemented
14#21445664C211yesmaximal, characteristic, complemented
15C61×#2901C211yesmaximal, characteristic, complemented
16#16840598C2211yescharacteristic
17#16840577—21no—
18#16840577C412yescomplemented
19#16840573—21no—
20#16840573C412yescomplemented
21#16840570—21no—
22#16840570C412yescomplemented
23#16840565—21no—
24#16840565C412yescomplemented
25#16840560—22no—
26#16840560C2211yescharacteristic
27#16840560C2211yescharacteristic
28C2×#14519797—22no—
29C2×#14519797C2211yescharacteristic
30C2×#14519797C2211yescharacteristic
31#16840528C2211yescharacteristic, complemented
32C2×#14519784C2211yescharacteristic
33C4×#11758222C2211yescharacteristic, complemented
34#16839882—22no—
35#16839877—22no—
36#16839872—21no—
37#16839867—21no—
38#16839862—21no—
39#16839860—21no—
40C2×#14519712C2211yescharacteristic, complemented
41#16839798C2211yescharacteristic, complemented
42#16839779C2211yescharacteristic
43#16839779C2211yescharacteristic, complemented
44#16839778C2211yescharacteristic, complemented
45#16839778C2211yescharacteristic, complemented
46#16839777—22no—
47C2×#14519705C2211yescharacteristic, complemented
48#104×D61—22no—
49#16839758C2211yescharacteristic
50#16839758C2211yescharacteristic, complemented
51#16839756C2211yescharacteristic, complemented
52#16839736C2211yescharacteristic, complemented
53#16839735C2211yescharacteristic, complemented
54#16839730C2211yescharacteristic, complemented
55#16839729C2211yescharacteristic, complemented
56#16839720C2211yescharacteristic, complemented
57C2×#14519688C2211yescharacteristic, complemented
58#16839533C2211yescharacteristic, complemented
59#16839532C2211yescharacteristic, complemented
60#16839526C2211yescharacteristic, complemented
61#16839522C2211yescharacteristic, complemented
62C61×#585C2211yescharacteristic
63C61×#568C2211yescharacteristic, complemented
64C4×#41×C61C2211yescharacteristic, complemented
65C61×#421—22no—
66C61×#421C2211yescharacteristic
67C61×#421C2211yescharacteristic, complemented
68C2×#104×C61—22no—
69C2×#104×C61C2211yescharacteristic
70C2×#104×C61C2211yescharacteristic, complemented
71#14519825—21no—
72#14519824—21no—
73#14519824C2×C412yescomplemented
74#14519823—21no—
75#14519823C2×C412yescomplemented
76#14519822—21no—
77#14519822—41no—
78C2×#11758222—22no—
79C2×#11758222C2311yescharacteristic
80C2×#11758222C2311yescharacteristic
81#41×D61—22no—
82#41×D61—41no—
83#14519808—21no—
84#14519808—22no—
85#14519808—22no—
86#14519808C2×C412yescomplemented
87#14519807—21no—
88#14519807—22no—
89#14519807—22no—
90#14519807C2×C412yescomplemented
91#14519803—21no—
92#14519803—22no—
93#14519803—22no—
94#14519803C2×C412yescomplemented
95#14519802—21no—
96#14519802—22no—
97#14519802—22no—
98#14519802C2×C412yescomplemented
99#14519797—22no—
100#14519797—22no—
101#14519797—22no—
102#14519797—22no—
103#14519797—22no—
104#14519797—22no—
105#14519797—21no—
106#14519797—21no—
107#14519797—21no—
108#14519797—21no—
109#14519797C2×C412yes—
110#14519797C2×C412yes—
111#14519797D412yes—
112#14519797D412yes—
113C2×#11758202—22no—
114C2×#11758202C2×C411yescharacteristic, complemented
115C2×#11758202D411yescharacteristic
116C2×#11758200—22no—
117C2×#11758200C2×C411yescharacteristic, complemented
118C2×#11758200D411yescharacteristic
119C2×#11758201—22no—
120C2×#11758201C2×C411yescharacteristic, complemented
121C2×#11758201D411yescharacteristic
122C2×#11758199—22no—
123C2×#11758199C2×C411yescharacteristic, complemented
124C2×#11758199D411yescharacteristic
125#14519785—41no—
126#14519784—21no—
127#14519784—21no—
128#14519784C2×C412yescomplemented
129#14519784C2×C412yescomplemented
130#14519783—22no—
131C2×#11758194—21no—
132C2×#11758194C2311yescharacteristic
133C2×#11758194C2311yescharacteristic
134M16×D61—22no—
135C22×#92418—21no—
136C22×#92418C2311yescharacteristic
137C22×#92418C2311yescharacteristic
138C4×Dic122—21no—
139C4×D244—21no—
140C4×C22⋊D61—41no—
141#14519736C2311yescharacteristic
142#14519736C2311yescharacteristic
143#14519734—21no—
144C42×D61—21no—
145#14519712—21no—
146#14519712—21no—
147#14519710—21no—
148#14519708—21no—
149#14519705—21no—
150#14519705—21no—
151#14519704—22no—
152#14519704—22no—
153#14519703—22no—
154#14519703—22no—
155#14519701—21no—
156#14519701—21no—
157#14519700—21no—
158#14519698—21no—
159#14519698—21no—
160#14519697—21no—
161#14519692—41no—
162#14519691—41no—
163C22⋊#92418—41no—
164#14519689—41no—
165#14519688—21no—
166#14519688—21no—
167#14519687—21no—
168C8×Dic61—21no—
1692−1+4×C61—21no—
1702−1+4×C61—21no—
1712−1+4×C61C2×C412yescomplemented
172H(5,𝔽2)×C61—21no—
173H(5,𝔽2)×C61—21no—
174H(5,𝔽2)×C61—41no—
175H(5,𝔽2)×C61C2×C412yescomplemented
176C2×#41×C61—22no—
177C2×#41×C61—22no—
178C2×#41×C61—41no—
179C2×#41×C61C2311yescharacteristic
180C2×#41×C61C2311yescharacteristic
181C2×#41×C61C2311yescharacteristic
182#131×C61—22no—
183#131×C61—41no—
184C2×M16×C61—22no—
185C2×M16×C61C2311yescharacteristic
186C2×M16×C61C2311yescharacteristic
187C4×Q8×C61—21no—
188C4×D4×C61—21no—
189C4×D4×C61—41no—
190#117×C61—21no—
191#117×C61C2311yescharacteristic
192C2×C42×C61—21no—
193C2×C42×C61C2311yescharacteristic
194#104×C61—22no—
195#104×C61—22no—
196#104×C61—21no—
197#104×C61—21no—
198#104×C61D412yes—
199#104×C61D412yes—
200#41×C61—21no—
201#41×C61—21no—
202#41×C61—21no—
203#41×C61—21no—
204#41×C61—22no—
205#41×C61—22no—
206#41×C61—22no—
207#41×C61—22no—
208#41×C61—21no—
209#41×C61—21no—
210#41×C61—21no—
211#41×C61—21no—
212#41×C61—42no—
213#41×C61—42no—
214#41×C61—42no—
215#41×C61—42no—
216#41×C61—41no—
217#41×C61—41no—
218#41×C61C22×C412yes—
219#41×C61C22×C412yes—
220#41×C61C2×D412yes—
221#41×C61C2×D412yes—
222C2×Q8×C61—22no—
223C2×Q8×C61—22no—
224C2×Q8×C61—41no—
225C2×Q8×C61C22×C411yescharacteristic
226C2×Q8×C61C2×D411yescharacteristic
227C2×Q8×C61#4111yescharacteristic
228C2×D4×C61—21no—
229C2×D4×C61—21no—
230C2×D4×C61—22no—
231C2×D4×C61—22no—
232C2×D4×C61—21no—
233C2×D4×C61—42no—
234C2×D4×C61—41no—
235C2×D4×C61—42no—
236C2×D4×C61—42no—
237C2×D4×C61C22×C411yescharacteristic
238C2×D4×C61C2×D411yescharacteristic
239C2×D4×C61#4111yescharacteristic
240C22×C4×C61—21no—
241C22×C4×C61—21no—
242C22×C4×C61—21no—
243C22×C4×C61—21no—
244C22×C4×C61—42no—
245C22×C4×C61—41no—
246C22×C4×C61C2411yescharacteristic
247C2×C22⋊D61—21no—
248C2×C22⋊D61—21no—
249C2×C22⋊D61—42no—
250#11758226—22no—
251#11758226—41no—
252Q8×D61—22no—
253Q8×D61—41no—
254#11758224—22no—
255#11758224—41no—
256#11758224—42no—
257#11758224—42no—
258D4×D61—22no—
259D4×D61—41no—
260D4×D61—42no—
261D4×D61—42no—
262#11758222—21no—
263#11758222—21no—
264#11758222—21no—
265#11758222—21no—
266#11758222—21no—
267#11758222—21no—
268#11758222—22no—
269#11758222—22no—
270#11758222—42no—
271#11758222—42no—
272#11758222C22×C412yes—
273#11758222C2×D412yes—
274C2×D244—22no—
275C2×D244C22×C411yescharacteristic
276C2×D244C2×D411yescharacteristic
277C2×C4×D61—21no—
278C2×C4×D61—21no—
279C2×C4×D61—42no—
280C2×C4×D61—41no—
281C2×Dic122—22no—
282C2×Dic122C22×C411yescharacteristic
283C2×Dic122C2×D411yescharacteristic
284M16×C61—21no—
285M16×C61—21no—
286M16×C61—21no—
287M16×C61—42no—
288M16×C61C2×D412yes—
289C2×C8×C61—21no—
290C2×C8×C61—21no—
291C2×C8×C61—42no—
292C4⋊C4×C61—21no—
293C4⋊C4×C61—41no—
294C22⋊C4×C61—21no—
295C22⋊C4×C61—41no—
296C42×C61—21no—
297C42×C61—21no—
298C42×C61—41no—
299C42×C61C2×D411yescharacteristic
300C42×C61C2×D411yescharacteristic
301C22⋊Dic61—21no—
302C22⋊Dic61—21no—
303#11758202—22no—
304#11758202—22no—
305#11758202—21no—
306#11758202—21no—
307#11758202C22⋊C412yes—
308#11758202C22⋊C412yes—
309#11758201—22no—
310#11758201—22no—
311#11758201—21no—
312#11758201—21no—
313#11758201C22⋊C412yes—
314#11758201C22⋊C412yes—
315#11758200—22no—
316#11758200—22no—
317#11758200—21no—
318#11758200—21no—
319#11758200C22⋊C412yes—
320#11758200C22⋊C412yes—
321#11758199—22no—
322#11758199—22no—
323#11758199—21no—
324#11758199—21no—
325#11758199C22⋊C412yes—
326#11758199C22⋊C412yes—
327#11758198—41no—
328C4⋊Dic61—21no—
329C4⋊Dic61—21no—
330#11758196—41no—
331C4×Dic61—21no—
332C4×Dic61—21no—
333C4×Dic61—41no—
334#11758194—21no—
335#11758194—22no—
336#11758194—22no—
337#11758194—21no—
338#11758194—21no—
339#11758194C22×C412yes—
340C2×#92418—21no—
341C2×#92418—22no—
342C2×#92418—22no—
343C2×#92418—21no—
344C2×#92418—21no—
345C2×#92418—21no—
346C2×#92418—21no—
347C2×#92418C22×C411yescharacteristic
348C2×#92418C22×C411yescharacteristic
349C2×#92418C2×D411yescharacteristic
350C2×#92418C2×D411yescharacteristic
351C2×#92418C2×D411yescharacteristic
352C2×#92418C2×D411yescharacteristic
353#11758189—42no—
354C8×D61—42no—
355C23×C61—21no—
356C23×C61—21no—
357C23×C61—21no—
358C23×C61—42no—
359C23×C61H(5,𝔽2)11yescharacteristic
360C22×D61—21no—
361C22×D61—21no—
362C22×D61—42no—
363Q8×C61—21no—
364Q8×C61—21no—
365Q8×C61—21no—
366Q8×C61—21no—
367Q8×C61—42no—
368Q8×C61C2×C22⋊C412yes—
369Q8×C61C4×D412yes—
370D4×C61—22no—
371D4×C61—22no—
372D4×C61—22no—
373D4×C61—22no—
374D4×C61—21no—
375D4×C61—21no—
376D4×C61—21no—
377D4×C61—21no—
378D4×C61—42no—
379D4×C61—42no—
380D4×C61—42no—
381D4×C61—41no—
382D4×C61—41no—
383D4×C61C2×C22⋊C412yes—
384D4×C61C4×D412yes—
385C2×C4×C61—21no—
386C2×C4×C61—21no—
387C2×C4×C61—22no—
388C2×C4×C61—22no—
389C2×C4×C61—22no—
390C2×C4×C61—22no—
391C2×C4×C61—21no—
392C2×C4×C61—21no—
393C2×C4×C61—21no—
394C2×C4×C61—42no—
395C2×C4×C61—42no—
396C2×C4×C61—42no—
397C2×C4×C61—41no—
398C2×C4×C61—41no—
399C2×C4×C61—41no—
400C2×C4×C61—81no—
401C2×C4×C61—82no—
402C2×C4×C61C23×C411yescharacteristic
403C2×C4×C61C22×D411yescharacteristic
404C2×C4×C61C22×D411yescharacteristic
405C2×C4×C61C22×D411yescharacteristic
406C2×C4×C61C2×#4111yescharacteristic
407C2×C4×C61H(5,𝔽2)11yescharacteristic
408C22⋊D61—22no—
409C22⋊D61—22no—
410C22⋊D61—42no—
411C22⋊D61—42no—
412C22⋊D61—41no—
413C22⋊D61—41no—
414C2×Dic61—21no—
415C2×Dic61—21no—
416C2×Dic61—42no—
417C2×Dic61—41no—
418C2×Dic61—41no—
419D244—21no—
420D244—21no—
421D244—21no—
422D244—42no—
423D244C2×C22⋊C412yes—
424C4×D61—22no—
425C4×D61—22no—
426C4×D61—42no—
427C4×D61—42no—
428C4×D61—41no—
429C4×D61—41no—
430C4×D61—82no—
431Dic122—21no—
432Dic122—21no—
433Dic122—21no—
434Dic122—42no—
435Dic122C2×C22⋊C412yes—
436C8×C61—22no—
437C8×C61—41no—
438#92418—22no—
439#92418—41no—
440#92418—41no—
441#92418C2×C22⋊C411yescharacteristic
442#92418C2×C22⋊C411yescharacteristic
443#92418C2×C22⋊C411yescharacteristic
444#92418C2×C22⋊C411yescharacteristic
445#22461—611nomaximal, Sylow
446C22×C61—22no—
447C22×C61—22no—
448C22×C61—41no—
449C22×C61—41no—
450C22×C61—81no—
451C22×C61—81no—
452C22×C61—81no—
453C22×C61—162no—
454C22×C61#51811yescharacteristic
455C22×C61D4211yescharacteristic
456C22×C61#54611yescharacteristic
457C2×D61—22no—
458C2×D61—41no—
459C2×D61—81no—
460C2×D61—81no—
461C2×D61—162no—
462C4×C61—22no—
463C4×C61—22no—
464C4×C61—41no—
465C4×C61—41no—
466C4×C61—41no—
467C4×C61—81no—
468C4×C61C22×C22⋊C411yescharacteristic
469C4×C61C2×C4×D411yescharacteristic
470C4×C61D4211yescharacteristic
471C4×C61#54611yescharacteristic
472Dic61—22no—
473Dic61—41no—
474Dic61—81no—
475Dic61—81no—
476#3584—611no—
477#2957—611no—
478#2943—611no—
479#2901—611no—
480#2901D6111yescharacteristic, complemented
481#1976—611no—
482#1975—611no—
483#1906—611no—
484#1906—611no—
485#1881—611no—
486#1881—611no—
487#1814—611no—
488#1794—611no—
489#1794—611no—
490#1765—611no—
491C2×C61—21no—
492C2×C61—21no—
493C2×C61—21no—
494C2×C61—42no—
495C2×C61—42no—
496C2×C61—81no—
497C2×C61D4×C22⋊C411yescharacteristic
498D61—42no—
499D61—81no—
500#585—611no—
501#585C2×D6111yescharacteristic
502#578—612no—
503#578—1221no—
504#577—612no—
505#577—612no—
506#577—1221no—
507#577—1221no—
508#576—612no—
509#576—1221no—
510#575—611no—
511#575—611no—
512#575—1222no—
513C2×#135—611no—
514C2×#135—611no—
515C2×#135—1222no—
516#568—611no—
517#568C2×D6111yescharacteristic, complemented
518C2×#131—611no—
519C4×#41—611no—
520C4×#41C2×D6111yescharacteristic, complemented
521#444—1222no—
522#443—1222no—
523#442—1221no—
524#441—1221no—
525#440—1221no—
526#440—1221no—
527C2×#108—611no—
528#427—611no—
529#421—22no—
530#421—611no—
531#421—611no—
532#421—611no—
533#421—611no—
534#421—1222no—
535#421C2×D6111yescharacteristic
536#421C2×D6111yescharacteristic, complemented
537C2×#104—22no—
538C2×#104—611no—
539C2×#104—1222no—
540C2×#104C2×D6111yescharacteristic
541C2×#104C2×D6111yescharacteristic, complemented
542#416—611no—
543#416—611no—
544#416—611no—
545#410—611no—
546#410—611no—
547#408—611no—
548#408—611no—
549#405—611no—
550C2×#97—611no—
551#344—611no—
552#344—611no—
553#341—611no—
554#339—611no—
555C61#2246111yescharacteristic, complemented, Sylow
5562−1+4—21no—
5572−1+4—21no—
5582−1+4—612no—
5592−1+4—1221no—
5602−1+4—1221no—
5612−1+4C4×D6112yescomplemented
562H(5,𝔽2)—21no—
563H(5,𝔽2)—21no—
564H(5,𝔽2)—41no—
565H(5,𝔽2)—612no—
566H(5,𝔽2)—1221no—
567H(5,𝔽2)—1221no—
568H(5,𝔽2)—2441no—
569H(5,𝔽2)C4×D6112yescomplemented
570C2×#41—22no—
571C2×#41—22no—
572C2×#41—41no—
573C2×#41—611no—
574C2×#41—611no—
575C2×#41—1222no—
576C2×#41—1222no—
577C2×#41—2441no—
578C2×#41C22×D6111yescharacteristic
579C2×#41C22×D6111yescharacteristic
580C2×#41C22×D6111yescharacteristic
581#137—612no—
582#137—612no—
583#137—1222no—
584#137—1222no—
585#137—1222no—
586#137—1222no—
587#137—1221no—
588#137—1221no—
589AGL(1,ℤ/8)—612no—
590AGL(1,ℤ/8)—612no—
591AGL(1,ℤ/8)—1222no—
592AGL(1,ℤ/8)—1222no—
593AGL(1,ℤ/8)—1222no—
594AGL(1,ℤ/8)—1222no—
595AGL(1,ℤ/8)—1221no—
596AGL(1,ℤ/8)—1221no—
597#135—612no—
598#135—612no—
599#135—612no—
600#135—612no—
601#135—1221no—
602#135—1221no—
603#135—1221no—
604#135—1221no—
605#135—1222no—
606#135—1222no—
607#135—1222no—
608#135—1222no—
609#135—1222no—
610#135—1222no—
611C2×Q16—611no—
612C2×Q16—611no—
613C2×Q16—1222no—
614C2×SD16—611no—
615C2×SD16—611no—
616C2×SD16—611no—
617C2×SD16—611no—
618C2×SD16—1222no—
619C2×SD16—1222no—
620C2×D8—611no—
621C2×D8—611no—
622C2×D8—1222no—
623#131—22no—
624#131—41no—
625#131—612no—
626#131—612no—
627#131—1222no—
628#131—1221no—
629#131—1221no—
630#131—2441no—
631C2×M16—22no—
632C2×M16—611no—
633C2×M16—611no—
634C2×M16—1221no—
635C2×M16—1222no—
636C2×M16C22×D6111yescharacteristic
637C2×M16C22×D6111yescharacteristic
638C22×C8—611no—
639C22×C8—611no—
640C22×C8—1221no—
641C4×Q8—21no—
642C4×Q8—1221no—
643C4×D4—21no—
644C4×D4—41no—
645C4×D4—1221no—
646C4×D4—2441no—
647#117—21no—
648#117—611no—
649#117—611no—
650#117—1221no—
651#117C22×D6111yescharacteristic
652C2×C42—21no—
653C2×C42—1221no—
654C2×C42C22×D6111yescharacteristic
655#108—1221no—
656#108—1221no—
657#107—1221no—
658#106—1221no—
659#104—22no—
660#104—22no—
661#104—21no—
662#104—21no—
663#104—1222no—
664#104—1222no—
665#104—1222no—
666#104—1222no—
667#104—1221no—
668#104—1221no—
669#104C22⋊D6112yes—
670#104C22⋊D6112yes—
671#103—1221no—
672#103—1221no—
673#103—1221no—
674#102—1221no—
675#102—1221no—
676#102—1221no—
677#99—2441no—
678#99—2441no—
679C22⋊C8—2441no—
680C22⋊C8—2441no—
681#97—1221no—
682#97—1221no—
683#97—1221no—
684C4×C8—1221no—
685#41—21no—
686#41—21no—
687#41—21no—
688#41—21no—
689#41—22no—
690#41—22no—
691#41—22no—
692#41—22no—
693#41—21no—
694#41—21no—
695#41—21no—
696#41—21no—
697#41—42no—
698#41—42no—
699#41—42no—
700#41—42no—
701#41—41no—
702#41—41no—
703#41—612no—
704#41—612no—
705#41—1222no—
706#41—1222no—
707#41—1221no—
708#41—1221no—
709#41—1222no—
710#41—1222no—
711#41—1221no—
712#41—1221no—
713#41—1221no—
714#41—1221no—
715#41—2442no—
716#41—2442no—
717#41—2442no—
718#41—2442no—
719#41—2441no—
720#41—2441no—
721#41C2×C4×D6112yes—
722#41C2×C4×D6112yes—
723#41D4×D6112yes—
724#41C2×C22⋊D6112yes—
725C2×Q8—22no—
726C2×Q8—22no—
727C2×Q8—41no—
728C2×Q8—611no—
729C2×Q8—611no—
730C2×Q8—1222no—
731C2×Q8—1222no—
732C2×Q8—2441no—
733C2×Q8C2×C4×D6111yescharacteristic
734C2×Q8#1175822211yescharacteristic
735C2×Q8D4×D6111yescharacteristic
736C2×D4—21no—
737C2×D4—21no—
738C2×D4—22no—
739C2×D4—22no—
740C2×D4—21no—
741C2×D4—42no—
742C2×D4—41no—
743C2×D4—42no—
744C2×D4—42no—
745C2×D4—611no—
746C2×D4—611no—
747C2×D4—1222no—
748C2×D4—1221no—
749C2×D4—1222no—
750C2×D4—1221no—
751C2×D4—2442no—
752C2×D4—2441no—
753C2×D4—2442no—
754C2×D4—2442no—
755C2×D4C2×C4×D6111yescharacteristic
756C2×D4#1175822211yescharacteristic
757C2×D4D4×D6111yescharacteristic
758C22×C4—21no—
759C22×C4—21no—
760C22×C4—21no—
761C22×C4—21no—
762C22×C4—42no—
763C22×C4—41no—
764C22×C4—1221no—
765C22×C4—1221no—
766C22×C4—2442no—
767C22×C4—2441no—
768C22×C4C23×D6111yescharacteristic
769Q16—612no—
770Q16—612no—
771Q16—1221no—
772Q16—1221no—
773Q16—1222no—
774Q16—1222no—
775SD16—612no—
776SD16—612no—
777SD16—612no—
778SD16—612no—
779SD16—1221no—
780SD16—1221no—
781SD16—1221no—
782SD16—1221no—
783SD16—1222no—
784SD16—1222no—
785SD16—1222no—
786SD16—1222no—
787D8—612no—
788D8—612no—
789D8—1221no—
790D8—1221no—
791D8—1222no—
792D8—1222no—
793M16—21no—
794M16—21no—
795M16—21no—
796M16—42no—
797M16—612no—
798M16—1222no—
799M16—1222no—
800M16—1221no—
801M16—1221no—
802M16—1221no—
803M16—2442no—
804M16C2×C22⋊D6112yes—
805C2×C8—21no—
806C2×C8—21no—
807C2×C8—42no—
808C2×C8—611no—
809C2×C8—611no—
810C2×C8—611no—
811C2×C8—611no—
812C2×C8—611no—
813C2×C8—611no—
814C2×C8—1222no—
815C2×C8—1222no—
816C2×C8—1221no—
817C2×C8—1221no—
818C2×C8—1221no—
819C2×C8—1221no—
820C2×C8—1221no—
821C2×C8—2442no—
822C4⋊C4—21no—
823C4⋊C4—41no—
824C4⋊C4—1221no—
825C4⋊C4—1221no—
826C4⋊C4—2441no—
827C22⋊C4—21no—
828C22⋊C4—41no—
829C22⋊C4—1221no—
830C22⋊C4—1221no—
831C22⋊C4—2441no—
832C42—21no—
833C42—21no—
834C42—41no—
835C42—1221no—
836C42—1221no—
837C42—2441no—
838C42C2×C22⋊D6111yescharacteristic
839C42C2×C22⋊D6111yescharacteristic
840C23—21no—
841C23—21no—
842C23—21no—
843C23—42no—
844C23—1221no—
845C23—1221no—
846C23—2442no—
847C23#1451982211yescharacteristic
848Q8—21no—
849Q8—21no—
850Q8—21no—
851Q8—21no—
852Q8—42no—
853Q8—612no—
854Q8—1221no—
855Q8—1221no—
856Q8—1221no—
857Q8—2442no—
858Q8C22⋊C4×D6112yes—
859Q8C4×C22⋊D6112yes—
860D4—22no—
861D4—22no—
862D4—22no—
863D4—22no—
864D4—21no—
865D4—21no—
866D4—21no—
867D4—21no—
868D4—42no—
869D4—42no—
870D4—42no—
871D4—41no—
872D4—41no—
873D4—612no—
874D4—1222no—
875D4—1222no—
876D4—1221no—
877D4—1221no—
878D4—1221no—
879D4—2442no—
880D4—2442no—
881D4—2442no—
882D4—2441no—
883D4—2441no—
884D4C22⋊C4×D6112yes—
885D4C4×C22⋊D6112yes—
886C2×C4—21no—
887C2×C4—21no—
888C2×C4—22no—
889C2×C4—22no—
890C2×C4—22no—
891C2×C4—22no—
892C2×C4—21no—
893C2×C4—21no—
894C2×C4—21no—
895C2×C4—42no—
896C2×C4—42no—
897C2×C4—42no—
898C2×C4—41no—
899C2×C4—41no—
900C2×C4—41no—
901C2×C4—81no—
902C2×C4—82no—
903C2×C4—1221no—
904C2×C4—1222no—
905C2×C4—1222no—
906C2×C4—1221no—
907C2×C4—4882no—
908C2×C4—2442no—
909C2×C4—2442no—
910C2×C4—2442no—
911C2×C4—2441no—
912C2×C4—2441no—
913C2×C4—2441no—
914C2×C4—2441no—
915C2×C4C22×C4×D6111yescharacteristic
916C2×C4C2×D4×D6111yescharacteristic
917C2×C4C2×D4×D6111yescharacteristic
918C2×C4C22×C22⋊D6111yescharacteristic
919C2×C4C2×#1175822211yescharacteristic
920C2×C4#1451982211yescharacteristic
921C8—22no—
922C8—41no—
923C8—611no—
924C8—611no—
925C8—611no—
926C8—611no—
927C8—1222no—
928C8—2441no—
929C8—2441no—
930C22—22no—
931C22—22no—
932C22—41no—
933C22—41no—
934C22—81no—
935C22—81no—
936C22—81no—
937C22—162no—
938C22—1222no—
939C22—9762no—
940C22—4881no—
941C22—4881no—
942C22—2441no—
943C22#1684023511yescharacteristic
944C22D4×C22⋊D6111yescharacteristic
945C22#1684040211yescharacteristic
946C4—22no—
947C4—22no—
948C4—41no—
949C4—41no—
950C4—41no—
951C4—81no—
952C4—1222no—
953C4—4881no—
954C4—4881no—
955C4—2441no—
956C4C2×C22⋊C4×D6111yescharacteristic
957C4C2×C4×C22⋊D6111yescharacteristic
958C4D4×C22⋊D6111yescharacteristic
959C4#1684040211yescharacteristic
960C2—21no—
961C2—21no—
962C2—21no—
963C2—42no—
964C2—42no—
965C2—81no—
966C2—4881no—
967C2—2442no—
968C2C22⋊C4×C22⋊D6111yescharacteristic
subgroupG/H
centerC4D4×C22⋊D61
commutatorC2×C4×C61C23×C4
FrattiniC22×C4C23×D61
FittingC61×#2901C2
socleC2×C61D4×C22⋊C4
prime radical#21460590C2
cosocleC22×C4×C61C24
hypercenter#2901D61
hypocenterC61#22461
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C4 ◁ C22×C4 ◁ #2901

Complements

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

NH ≅ G/Ntype
2. #21454734C2semidirect
3. #21454617C2semidirect
4. #21454363C2semidirect
5. #21446716C2semidirect
6. #21446709C2semidirect
7. #21446323C2semidirect
8. #21446320C2semidirect
9. #21446181C2semidirect
10. #21446178C2semidirect
11. #21445871C2semidirect
12. #21445783C2semidirect
13. #21445781C2semidirect
14. #21445664C2semidirect
15. C61×#2901C2semidirect
18. #16840577C4semidirect
20. #16840573C4semidirect
22. #16840570C4semidirect
24. #16840565C4semidirect
31. #16840528C22semidirect
33. C4×#11758222C22semidirect
40. C2×#14519712C22semidirect
41. #16839798C22semidirect
43. #16839779C22semidirect
44. #16839778C22semidirect
45. #16839778C22semidirect
47. C2×#14519705C22semidirect
50. #16839758C22semidirect
51. #16839756C22semidirect
52. #16839736C22semidirect
53. #16839735C22semidirect
54. #16839730C22semidirect
55. #16839729C22semidirect
56. #16839720C22semidirect
57. C2×#14519688C22semidirect
58. #16839533C22semidirect
59. #16839532C22semidirect
60. #16839526C22semidirect
61. #16839522C22semidirect
63. C61×#568C22semidirect
64. C4×#41×C61C22semidirect
67. C61×#421C22semidirect
70. C2×#104×C61C22semidirect
73. #14519824C2×C4semidirect
75. #14519823C2×C4semidirect
86. #14519808C2×C4semidirect
90. #14519807C2×C4semidirect
94. #14519803C2×C4semidirect
98. #14519802C2×C4semidirect
114. C2×#11758202C2×C4semidirect
117. C2×#11758200C2×C4semidirect
120. C2×#11758201C2×C4semidirect
123. C2×#11758199C2×C4semidirect
128. #14519784C2×C4semidirect
129. #14519784C2×C4semidirect
171. 2−1+4×C61C2×C4semidirect
175. H(5,𝔽2)×C61C2×C4semidirect
480. #2901D61semidirect
517. #568C2×D61semidirect
520. C4×#41C2×D61semidirect
536. #421C2×D61semidirect
541. C2×#104C2×D61semidirect
555. C61#22461semidirect
561. 2−1+4C4×D61semidirect
569. H(5,𝔽2)C4×D61semidirect

Maximal subgroups

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

subgroupindex
#214605902
#214547342
#214546172
#214543632
#214467162
#214467092
#214463232
#214463202
#214461812
#214461782
#214458712
#214457832
#214457812
#214456642
C61×#29012
#2246161