Finite Group Databasebeta

← #29695977

Subgroups — #29695977

Order 15616.

1320 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#21454732C211yesmaximal, characteristic, complemented
3#21454587C211yesmaximal, characteristic, complemented
4#21454366C211yesmaximal, characteristic, complemented
5#21454365C211yesmaximal, characteristic, complemented
6#21446714C211yesmaximal, characteristic, complemented
7#21446706C211yesmaximal, characteristic, complemented
8#21446318C211yesmaximal, characteristic, complemented
9#21446317C211yesmaximal, characteristic, complemented
10#21446184C211yesmaximal, characteristic, complemented
11#21446179C211yesmaximal, characteristic, complemented
12#21445871C211yesmaximal, characteristic, complemented
13#21445784C211yesmaximal, characteristic, complemented
14#21445659C211yesmaximal, characteristic, complemented
15C61×#1794C211yesmaximal, 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#16840529C2211yescharacteristic, complemented
32#16840528C2211yescharacteristic, complemented
33C2×#14519784C2211yescharacteristic
34#41×Dic61C2211yescharacteristic, complemented
35#16840230C2211yescharacteristic, complemented
36#16839881—22no—
37#16839876—22no—
38#16839854—21no—
39#16839853—21no—
40#16839847—21no—
41#16839842—21no—
42C2×#14519712C2211yescharacteristic, complemented
43#16839798C2211yescharacteristic, complemented
44#16839780C2211yescharacteristic, complemented
45#16839780C2211yescharacteristic, complemented
46#16839779—22no—
47#16839779C2211yescharacteristic
48#16839779C2211yescharacteristic, complemented
49#16839777—22no—
50C2×#14519704—22no—
51C2×#14519704C2211yescharacteristic
52C2×#14519704C2211yescharacteristic, complemented
53C2×#14519703C2211yescharacteristic, complemented
54#104×D61—22no—
55#16839759C2211yescharacteristic, complemented
56#16839735C2211yescharacteristic, complemented
57#16839728C2211yescharacteristic, complemented
58#16839718C2211yescharacteristic, complemented
59C2×C8×Dic61C2211yescharacteristic, complemented
60#16839533C2211yescharacteristic, complemented
61#16839532C2211yescharacteristic, complemented
62#16839527C2211yescharacteristic, complemented
63#16839521C2211yescharacteristic, complemented
64C61×#585C2211yescharacteristic
65C61×#421C2211yescharacteristic
66C61×#421C2211yescharacteristic, complemented
67C61×#416C2211yescharacteristic
68C61×#416C2211yescharacteristic, complemented
69C61×#410C2211yescharacteristic, complemented
70C61×#408C2211yescharacteristic, 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—22no—
126#14519784—21no—
127#14519784—21no—
128#14519784—22no—
129#14519784—41no—
130#14519784C2×C412yescomplemented
131#14519784C2×C412yescomplemented
132#14519783—41no—
133C2×#11758194—21no—
134C2×#11758194—22no—
135C2×#11758194C2311yescharacteristic
136C2×#11758194C2311yescharacteristic
137C2×#11758194C2311yescharacteristic
138M16×D61—22no—
139C22×#92418—21no—
140C22×#92418C2311yescharacteristic
141Q8×Dic61—21no—
142#14519742—21no—
143D4×Dic61—21no—
144D4×Dic61—41no—
145#14519739—21no—
146#14519737—41no—
147#14519736—21no—
148#14519736C2311yescharacteristic
149#14519734—21no—
150C2×C4×Dic61—21no—
151C2×C4×Dic61C2311yescharacteristic
152C42×D61—21no—
153#14519712—21no—
154#14519712—21no—
155#14519710—21no—
156#14519708—21no—
157#14519705—22no—
158#14519705—22no—
159#14519704—22no—
160#14519704—21no—
161#14519704—21no—
162#14519704—22no—
163#14519704D412yes—
164#14519704D412yes—
165#14519703—21no—
166#14519703—21no—
167#14519702—21no—
168#14519699—21no—
169#14519691—41no—
170#14519689—41no—
171#14519688—21no—
172C4×#92418—21no—
173C8×Dic61—21no—
174C8×Dic61—21no—
1752−1+4×C61—21no—
1762−1+4×C61—21no—
1772−1+4×C61C2×C412yescomplemented
178H(5,𝔽2)×C61—21no—
179H(5,𝔽2)×C61—21no—
180H(5,𝔽2)×C61—41no—
181H(5,𝔽2)×C61C2×C412yescomplemented
182C2×#41×C61—22no—
183C2×#41×C61—22no—
184C2×#41×C61—41no—
185C2×#41×C61C2311yescharacteristic
186C2×#41×C61C2311yescharacteristic
187C2×#41×C61C2311yescharacteristic
188C2×M16×C61C2311yescharacteristic
189C22×C8×C61C2311yescharacteristic
190#117×C61C2311yescharacteristic
191#117×C61C2311yescharacteristic
192#104×C61—22no—
193#104×C61—22no—
194#103×C61—21no—
195#103×C61—21no—
196#102×C61—21no—
197#102×C61—21no—
198#99×C61—41no—
199C22⋊C8×C61—41no—
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—42no—
244C22×C4×C61C2411yescharacteristic
245C2×C22⋊D61—21no—
246C2×C22⋊D61—21no—
247C2×C22⋊D61—42no—
248C22×Dic61—21no—
249C22×Dic61—41no—
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—
286C2×C8×C61—21no—
287C2×C8×C61—21no—
288C2×C8×C61—21no—
289C2×C8×C61—21no—
290C4⋊C4×C61—21no—
291C4⋊C4×C61—21no—
292C22⋊C4×C61—21no—
293C22⋊C4×C61—21no—
294C42×C61—21no—
295C42×C61—21no—
296C22⋊Dic61—21no—
297C22⋊Dic61—41no—
298#11758202—22no—
299#11758202—22no—
300#11758202—21no—
301#11758202—21no—
302#11758202C22⋊C412yes—
303#11758202C22⋊C412yes—
304#11758201—22no—
305#11758201—22no—
306#11758201—21no—
307#11758201—21no—
308#11758201C22⋊C412yes—
309#11758201C22⋊C412yes—
310#11758200—22no—
311#11758200—22no—
312#11758200—21no—
313#11758200—21no—
314#11758200C22⋊C412yes—
315#11758200C22⋊C412yes—
316#11758199—22no—
317#11758199—22no—
318#11758199—21no—
319#11758199—21no—
320#11758199C22⋊C412yes—
321#11758199C22⋊C412yes—
322#11758198—41no—
323C4⋊Dic61—21no—
324C4⋊Dic61—41no—
325#11758196—41no—
326C4×Dic61—21no—
327C4×Dic61—21no—
328C4×Dic61—41no—
329C4×Dic61—41no—
330C4×Dic61C2×D411yescharacteristic
331C4×Dic61C2×D411yescharacteristic
332#11758194—21no—
333#11758194—21no—
334#11758194—22no—
335#11758194—22no—
336#11758194—21no—
337#11758194—21no—
338#11758194—42no—
339#11758194C22×C412yes—
340#11758194C2×D412yes—
341C2×#92418—21no—
342C2×#92418—21no—
343C2×#92418—22no—
344C2×#92418—22no—
345C2×#92418—21no—
346C2×#92418—42no—
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—42no—
393C2×C4×C61—42no—
394C2×C4×C61—42no—
395C2×C4×C61—41no—
396C2×C4×C61—41no—
397C2×C4×C61—41no—
398C2×C4×C61—41no—
399C2×C4×C61C23×C411yescharacteristic
400C2×C4×C61C22×D411yescharacteristic
401C2×C4×C61C22×D411yescharacteristic
402C2×C4×C61C22×D411yescharacteristic
403C2×C4×C61C2×#4111yescharacteristic
404C2×C4×C61H(5,𝔽2)11yescharacteristic
405C22⋊D61—22no—
406C22⋊D61—22no—
407C22⋊D61—42no—
408C22⋊D61—42no—
409C22⋊D61—41no—
410C22⋊D61—41no—
411C2×Dic61—21no—
412C2×Dic61—21no—
413C2×Dic61—21no—
414C2×Dic61—21no—
415C2×Dic61—42no—
416C2×Dic61—42no—
417C2×Dic61—41no—
418C2×Dic61—82no—
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—41no—
437C8×C61—41no—
438#92418—22no—
439#92418—22no—
440#92418—41no—
441#92418C2×C22⋊C411yescharacteristic
442#92418C2×C22⋊C411yescharacteristic
443#92418C2×C22⋊C411yescharacteristic
444#92418C2×C22⋊C411yescharacteristic
445#22462—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—81no—
466C4×C61—81no—
467C4×C61C22×C22⋊C411yescharacteristic
468C4×C61C2×C4×D411yescharacteristic
469C4×C61D4211yescharacteristic
470C4×C61#54611yescharacteristic
471Dic61—22no—
472Dic61—22no—
473Dic61—41no—
474Dic61—41no—
475Dic61—81no—
476#3584—611no—
477#2957—611no—
478C4×#135—611no—
479#2901—611no—
480#2901—611no—
481#1976—611no—
482#1974—611no—
483#1906—611no—
484#1906—611no—
485#1881—611no—
486#1881—611no—
487#1814—611no—
488#1794—611no—
489#1794D6111yescharacteristic, complemented
490#1764—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#568—611no—
518C2×#131—611no—
519C4×#41—611no—
520C4×#41—611no—
521#444—1222no—
522#443—1222no—
523C4×Q16—1221no—
524C4×SD16—1221no—
525C4×SD16—1221no—
526C4×D8—1221no—
527C2×#108—611no—
528#427—611no—
529#421—611no—
530#421—611no—
531#421—611no—
532#421—611no—
533#421—1222no—
534#421—1222no—
535#421C2×D6111yescharacteristic
536#421C2×D6111yescharacteristic, complemented
537C2×#104—611no—
538C2×#104—611no—
539C2×#104—611no—
540C2×#104—1222no—
541C2×#104—1222no—
542#416—611no—
543#416C2×D6111yescharacteristic
544#416C2×D6111yescharacteristic, complemented
545#410—611no—
546#410C2×D6111yescharacteristic, complemented
547#408—611no—
548#408C2×D6111yescharacteristic, complemented
549#405—611no—
550C2×C4×C8—611no—
551#344—611no—
552#344—611no—
553#341—611no—
554#339—611no—
555C61#2246211yescharacteristic, 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—612no—
624#131—612no—
625#131—1221no—
626#131—1221no—
627#131—1222no—
628#131—1222no—
629#131—2441no—
630#131—2441no—
631C2×M16—611no—
632C2×M16—611no—
633C2×M16—611no—
634C2×M16—1221no—
635C2×M16—1222no—
636C2×M16—1222no—
637C2×M16C22×D6111yescharacteristic
638C22×C8—611no—
639C22×C8—1221no—
640C22×C8C22×D6111yescharacteristic
641C4×Q8—1221no—
642C4×Q8—1221no—
643C4×D4—1221no—
644C4×D4—1221no—
645C4×D4—2441no—
646C4×D4—2441no—
647#117—611no—
648#117—1221no—
649#117—1221no—
650#117C22×D6111yescharacteristic
651#117C22×D6111yescharacteristic
652C2×C42—611no—
653C2×C42—1221no—
654C2×C42—1221no—
655#108—1221no—
656#108—1221no—
657#107—1221no—
658#106—1221no—
659#104—22no—
660#104—22no—
661#104—612no—
662#104—612no—
663#104—1222no—
664#104—1222no—
665#104—1221no—
666#104—1221no—
667#104—1221no—
668#104—1221no—
669#104—1222no—
670#104—1222no—
671#103—21no—
672#103—21no—
673#103—1221no—
674#102—21no—
675#102—21no—
676#102—1221no—
677#99—41no—
678#99—2441no—
679C22⋊C8—41no—
680C22⋊C8—2441no—
681#97—1221no—
682C4×C8—1221no—
683C4×C8—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#41D4×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×Q8D4×D6111yescharacteristic
735C2×Q8#1175822411yescharacteristic
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×D4D4×D6111yescharacteristic
757C2×D4#1175822411yescharacteristic
758C22×C4—21no—
759C22×C4—21no—
760C22×C4—21no—
761C22×C4—42no—
762C22×C4—1221no—
763C22×C4—1221no—
764C22×C4—1221no—
765C22×C4—2442no—
766C22×C4—2441no—
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—612no—
796M16—612no—
797M16—1222no—
798M16—1222no—
799M16—1221no—
800M16—1221no—
801M16—1221no—
802M16—1221no—
803M16—2442no—
804M16—2442no—
805C2×C8—21no—
806C2×C8—21no—
807C2×C8—21no—
808C2×C8—21no—
809C2×C8—611no—
810C2×C8—611no—
811C2×C8—611no—
812C2×C8—611no—
813C2×C8—611no—
814C2×C8—611no—
815C2×C8—1222no—
816C2×C8—1222no—
817C2×C8—1221no—
818C2×C8—1221no—
819C2×C8—1221no—
820C2×C8—2442no—
821C2×C8—2442no—
822C4⋊C4—21no—
823C4⋊C4—21no—
824C4⋊C4—1221no—
825C4⋊C4—2441no—
826C4⋊C4—2441no—
827C22⋊C4—21no—
828C22⋊C4—21no—
829C22⋊C4—1221no—
830C22⋊C4—2441no—
831C22⋊C4—2441no—
832C42—21no—
833C42—21no—
834C42—611no—
835C42—611no—
836C42—1221no—
837C42—1221no—
838C42—2441no—
839C42—2441no—
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—
859Q8#1451973712yes—
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—
885D4#1451973712yes—
886C2×C4—21no—
887C2×C4—21no—
888C2×C4—22no—
889C2×C4—22no—
890C2×C4—22no—
891C2×C4—22no—
892C2×C4—21no—
893C2×C4—42no—
894C2×C4—42no—
895C2×C4—42no—
896C2×C4—41no—
897C2×C4—41no—
898C2×C4—41no—
899C2×C4—41no—
900C2×C4—1221no—
901C2×C4—1221no—
902C2×C4—1222no—
903C2×C4—1222no—
904C2×C4—1221no—
905C2×C4—1221no—
906C2×C4—4882no—
907C2×C4—4882no—
908C2×C4—2442no—
909C2×C4—2442no—
910C2×C4—2442no—
911C2×C4—2442no—
912C2×C4—2441no—
913C2×C4—2441no—
914C2×C4—2441no—
915C2×C4C22×C4×D6111yescharacteristic
916C2×C4C2×D4×D6111yescharacteristic
917C2×C4C2×D4×D6111yescharacteristic
918C2×C4C2×D4×D6111yescharacteristic
919C2×C4C2×#1175822411yescharacteristic
920C2×C4#1451982211yescharacteristic
921C8—41no—
922C8—41no—
923C8—611no—
924C8—611no—
925C8—611no—
926C8—611no—
927C8—1222no—
928C8—1222no—
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
944C22#1684039411yescharacteristic
945C22#1684039911yescharacteristic
946C4—22no—
947C4—22no—
948C4—41no—
949C4—81no—
950C4—81no—
951C4—1222no—
952C4—1222no—
953C4—4881no—
954C4—2441no—
955C4—2441no—
956C4C2×C22⋊C4×D6111yescharacteristic
957C4C2×#1451973711yescharacteristic
958C4#1684039411yescharacteristic
959C4#1684039911yescharacteristic
960C2—21no—
961C2—21no—
962C2—21no—
963C2—42no—
964C2—42no—
965C2—81no—
966C2—4881no—
967C2—2442no—
968C2#2144863511yescharacteristic
subgroupG/H
centerC4#16840394
commutatorC2×C4×C61C23×C4
FrattiniC22×C4C23×D61
FittingC61×#1794C2
socleC2×C61D4×C22⋊C4
prime radical#21460590C2
cosocleC22×C4×C61C24
hypercenter#1794D61
hypocenterC61#22462
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C4 ◁ C22×C4 ◁ #1794

Complements

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

NH ≅ G/Ntype
2. #21454732C2semidirect
3. #21454587C2semidirect
4. #21454366C2semidirect
5. #21454365C2semidirect
6. #21446714C2semidirect
7. #21446706C2semidirect
8. #21446318C2semidirect
9. #21446317C2semidirect
10. #21446184C2semidirect
11. #21446179C2semidirect
12. #21445871C2semidirect
13. #21445784C2semidirect
14. #21445659C2semidirect
15. C61×#1794C2semidirect
18. #16840577C4semidirect
20. #16840573C4semidirect
22. #16840570C4semidirect
24. #16840565C4semidirect
31. #16840529C22semidirect
32. #16840528C22semidirect
34. #41×Dic61C22semidirect
35. #16840230C22semidirect
42. C2×#14519712C22semidirect
43. #16839798C22semidirect
44. #16839780C22semidirect
45. #16839780C22semidirect
48. #16839779C22semidirect
52. C2×#14519704C22semidirect
53. C2×#14519703C22semidirect
55. #16839759C22semidirect
56. #16839735C22semidirect
57. #16839728C22semidirect
58. #16839718C22semidirect
59. C2×C8×Dic61C22semidirect
60. #16839533C22semidirect
61. #16839532C22semidirect
62. #16839527C22semidirect
63. #16839521C22semidirect
66. C61×#421C22semidirect
68. C61×#416C22semidirect
69. C61×#410C22semidirect
70. C61×#408C22semidirect
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
130. #14519784C2×C4semidirect
131. #14519784C2×C4semidirect
177. 2−1+4×C61C2×C4semidirect
181. H(5,𝔽2)×C61C2×C4semidirect
489. #1794D61semidirect
536. #421C2×D61semidirect
544. #416C2×D61semidirect
546. #410C2×D61semidirect
548. #408C2×D61semidirect
555. C61#22462semidirect
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
#214547322
#214545872
#214543662
#214543652
#214467142
#214467062
#214463182
#214463172
#214461842
#214461792
#214458712
#214457842
#214456592
C61×#17942
#2246261