Finite Group Databasebeta

← #29699479

Subgroups — #29699479

Order 15616.

740 conjugacy classes of subgroups.

The subgroup lattice has 680 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21454617C211yesmaximal, characteristic
2#21454485C211yesmaximal, characteristic, complemented
3#21454388C211yesmaximal, characteristic, complemented
4#21446527C211yesmaximal, characteristic, complemented
5#21446520C211yesmaximal, characteristic, complemented
6#21446416C211yesmaximal, characteristic, complemented
7#21446416C211yesmaximal, characteristic, complemented
8#21446143C211yesmaximal, characteristic
9#21446143C211yesmaximal, characteristic
10#21445959C211yesmaximal, characteristic, complemented
11#21445840C211yesmaximal, characteristic, complemented
12#21445694C211yesmaximal, characteristic, complemented
13#21445660C211yesmaximal, characteristic, complemented
14#21445653C211yesmaximal, characteristic, complemented
15C61×#1806C211yesmaximal, characteristic, complemented
16C2×#14519797C2211yescharacteristic
17C2×#14519785C2211yescharacteristic
18C2×#14519785C2211yescharacteristic
19C4×#11758222C2211yescharacteristic
20#16839872C411yescharacteristic, complemented
21#16839872C411yescharacteristic, complemented
22#16839867C411yescharacteristic, complemented
23#16839867C411yescharacteristic, complemented
24#16839862C411yescharacteristic, complemented
25#16839862C411yescharacteristic, complemented
26#16839860C411yescharacteristic, complemented
27#16839860C411yescharacteristic, complemented
28#16839823—21no—
29#16839823—21no—
30#16839819—21no—
31#16839815—21no—
32#16839798C2211yescharacteristic
33#16839790C2211yescharacteristic
34#16839790C2211yescharacteristic
35#16839787—21no—
36#16839787—21no—
37#16839786C2211yescharacteristic
38#16839784—21no—
39C2×C4⋊#92418C2211yescharacteristic
40C4⋊C8×D61—21no—
41C2×#14519705C2211yescharacteristic
42C2×#14519705C2211yescharacteristic
43#16839758C2211yescharacteristic
44#16839756C2211yescharacteristic
45#16839729C2211yescharacteristic
46#16839729C2211yescharacteristic
47#16839718C2211yescharacteristic
48#16839718C2211yescharacteristic
49C2×#14519688C2211yescharacteristic
50C2×#14519688C2211yescharacteristic
51C2×C4×#92418C2211yescharacteristic
52#16839526C2211yescharacteristic
53#16839526C2211yescharacteristic
54#16839526C2211yescharacteristic
55#16839526C2211yescharacteristic
56#16839522C2211yescharacteristic
57#16839522C2211yescharacteristic
58#16839517C2211yescharacteristic
59#16839517C2211yescharacteristic
60C4×#41×C61C2211yescharacteristic
61C61×#423C2211yescharacteristic
62C2×#104×C61C2211yescharacteristic
63C2×#104×C61C2211yescharacteristic
64C4×C4⋊C4×C61C2211yescharacteristic
65C61×#339C2211yescharacteristic
66C61×#339C2211yescharacteristic
67C2×#11758222C2311yescharacteristic
68#14519797—22no—
69#14519797—22no—
70C2×#11758202C2×C411yescharacteristic
71C2×#11758200C2×C411yescharacteristic
72C2×#11758201C2×C411yescharacteristic
73C2×#11758199C2×C411yescharacteristic
74#14519785—22no—
75#14519785—22no—
76#14519785—41no—
77#14519785—41no—
78C2×#11758194C2311yescharacteristic
79C2×#11758194C2311yescharacteristic
80C2×#11758189—21no—
81C2×#11758189—21no—
82C22×#92418C2311yescharacteristic
83C22×#92418C2311yescharacteristic
84C22×#92418C2311yescharacteristic
85C22×#92418C2311yescharacteristic
86C2×C8×D61—21no—
87C2×C8×D61—21no—
88C4×Dic122C2×C411yescharacteristic
89C4×Dic122C2×C411yescharacteristic
90C4×D244C2×C411yescharacteristic
91C4×D244C2×C411yescharacteristic
92C4×C22⋊D61—21no—
93C4×C22⋊D61—21no—
94#14519736C2311yescharacteristic
95#14519734—21no—
96C42×D61—21no—
97#14519710C2×C411yescharacteristic
98#14519710C2×C411yescharacteristic
99#14519708C2×C411yescharacteristic
100#14519708C2×C411yescharacteristic
101C4⋊#92418—21no—
102C4⋊#92418—21no—
103C4⋊#92418D411yescharacteristic
104C4⋊#92418D411yescharacteristic
105C4⋊#92418D411yescharacteristic
106C4⋊#92418D411yescharacteristic
107#14519706—21no—
108#14519706—21no—
109#14519706—21no—
110#14519706—21no—
111#14519705—22no—
112#14519705—22no—
113#14519701C2×C411yescharacteristic
114#14519701C2×C411yescharacteristic
115#14519700C2×C411yescharacteristic
116#14519700C2×C411yescharacteristic
117#14519698C2×C411yescharacteristic
118#14519698C2×C411yescharacteristic
119#14519697C2×C411yescharacteristic
120#14519697C2×C411yescharacteristic
121C22⋊#92418—21no—
122C22⋊#92418—21no—
123C22⋊#92418—21no—
124C22⋊#92418—21no—
125#14519688—21no—
126#14519688—21no—
127#14519688—41no—
128#14519688C2×C411yescharacteristic
129#14519688C2×C411yescharacteristic
130#14519688C2×C411yescharacteristic
131#14519688C2×C411yescharacteristic
132C4×#92418—21no—
133C4×#92418—21no—
134C4×#92418—41no—
135C2×#41×C61C2311yescharacteristic
136C2×M16×C61C2311yescharacteristic
137C2×M16×C61C2311yescharacteristic
138C4×Q8×C61C2×C411yescharacteristic
139C4×Q8×C61C2×C411yescharacteristic
140C4×D4×C61—21no—
141C4×D4×C61—21no—
142C4×D4×C61C2×C411yescharacteristic
143C4×D4×C61C2×C411yescharacteristic
144#117×C61—21no—
145#117×C61C2311yescharacteristic
146C2×C4⋊C4×C61—21no—
147C2×C42×C61—21no—
148C2×C42×C61C2311yescharacteristic
149C2×C42×C61C2311yescharacteristic
150C2×C42×C61C2311yescharacteristic
151C4⋊C8×C61—21no—
152C4⋊C8×C61—21no—
153#104×C61—41no—
154#104×C61—41no—
155#95×C61—21no—
156#41×C61—21no—
157#41×C61—21no—
158#41×C61—21no—
159#41×C61—21no—
160C2×Q8×C61C22×C411yescharacteristic
161C2×D4×C61—21no—
162C2×D4×C61C22×C411yescharacteristic
163C22×C4×C61—21no—
164C22×C4×C61—21no—
165C22×C4×C61—21no—
166C22×C4×C61—21no—
167C22×C4×C61—21no—
168C22×C4×C61#4111yescharacteristic
169C22×C4×C61#4111yescharacteristic
170C22×C4×C61C2411yescharacteristic
171C2×C22⋊D61—21no—
172#11758222—21no—
173#11758222—21no—
174#11758222#4112yes—
175#11758222#4112yes—
176C2×D244C22×C411yescharacteristic
177C2×C4×D61—21no—
178C2×C4×D61—21no—
179C2×C4×D61—21no—
180C2×Dic122C22×C411yescharacteristic
181M16×C61—21no—
182M16×C61—21no—
183M16×C61—21no—
184M16×C61—21no—
185C2×C8×C61—21no—
186C2×C8×C61—21no—
187C4⋊C4×C61—21no—
188C4⋊C4×C61—21no—
189C4⋊C4×C61—42no—
190C4⋊C4×C61C22×C411yescharacteristic
191C4⋊C4×C61C22×C411yescharacteristic
192C22⋊C4×C61—21no—
193C22⋊C4×C61—21no—
194C22⋊C4×C61—21no—
195C42×C61—21no—
196C42×C61—21no—
197C42×C61—21no—
198C42×C61—21no—
199C42×C61—21no—
200C42×C61—21no—
201C42×C61—21no—
202C42×C61C22×C411yescharacteristic
203C42×C61C22×C411yescharacteristic
204C42×C61C2×D411yescharacteristic
205C42×C61C2×D411yescharacteristic
206C22⋊Dic61—21no—
207#11758202—22no—
208#11758201—22no—
209#11758200—22no—
210#11758199—22no—
211#11758198—21no—
212#11758198—21no—
213C4⋊Dic61C22×C411yescharacteristic
214C4⋊Dic61C22×C411yescharacteristic
215#11758196—21no—
216#11758196—21no—
217C4×Dic61—21no—
218C4×Dic61—21no—
219C4×Dic61—21no—
220#11758194—21no—
221#11758194—21no—
222#11758194—21no—
223#11758194—21no—
224C2×#92418—21no—
225C2×#92418—21no—
226C2×#92418—21no—
227C2×#92418—21no—
228C2×#92418—21no—
229C2×#92418—21no—
230C2×#92418—21no—
231C2×#92418—21no—
232C2×#92418—21no—
233C2×#92418—21no—
234C2×#92418C22×C411yescharacteristic
235C2×#92418C22×C411yescharacteristic
236C2×#92418C22×C411yescharacteristic
237C2×#92418C22×C411yescharacteristic
238C2×#92418C2×D411yescharacteristic
239C2×#92418C2×D411yescharacteristic
240C2×#92418C2×D411yescharacteristic
241C2×#92418C2×D411yescharacteristic
242#11758189—42no—
243#11758189—42no—
244C8×D61—42no—
245C8×D61—42no—
246C23×C61—21no—
247C23×C61C2×#4111yescharacteristic
248C22×D61—21no—
249Q8×C61—21no—
250Q8×C61—21no—
251D4×C61—21no—
252D4×C61—21no—
253D4×C61—41no—
254D4×C61—41no—
255C2×C4×C61—22no—
256C2×C4×C61—21no—
257C2×C4×C61—21no—
258C2×C4×C61—21no—
259C2×C4×C61—41no—
260C2×C4×C61—41no—
261C2×C4×C61—42no—
262C2×C4×C61—41no—
263C2×C4×C61—41no—
264C2×C4×C61—41no—
265C2×C4×C61—41no—
266C2×C4×C61—41no—
267C2×C4×C61—41no—
268C2×C4×C61—41no—
269C2×C4×C61—81no—
270C2×C4×C61C4×D411yescharacteristic
271C2×C4×C61C4×D411yescharacteristic
272C2×C4×C61C4×D411yescharacteristic
273C2×C4×C61C4×D411yescharacteristic
274C2×C4×C61C23×C411yescharacteristic
275C2×C4×C61C22×D411yescharacteristic
276C2×C4×C61C2×#4111yescharacteristic
277C2×C4×C61C2×#4111yescharacteristic
278C2×C4×C61H(5,𝔽2)11yescharacteristic
279C2×C4×C612−1+411yescharacteristic
280C22⋊D61—22no—
281C22⋊D61—22no—
282C2×Dic61—21no—
283C2×Dic61—21no—
284C2×Dic61—21no—
285D244—21no—
286D244#11712yes—
287C4×D61—22no—
288C4×D61—22no—
289C4×D61—42no—
290C4×D61—81no—
291Dic122—21no—
292Dic122#11712yes—
293C8×C61—41no—
294C8×C61—41no—
295#92418—21no—
296#92418—21no—
297#92418—21no—
298#92418—21no—
299#92418—21no—
300#92418—21no—
301#92418—21no—
302#92418—21no—
303#92418—41no—
304#92418—41no—
305#22784—611nomaximal, Sylow
306C22×C61—21no—
307C22×C61—21no—
308C22×C61—41no—
309C22×C61—41no—
310C22×C61—41no—
311C22×C61C2×C4×D411yescharacteristic
312C22×C61#55211yescharacteristic
313C22×C61#55311yescharacteristic
314C2×D61—22no—
315C2×D61—41no—
316C2×D61—41no—
317C4×C61—21no—
318C4×C61—21no—
319C4×C61—21no—
320C4×C61—21no—
321C4×C61—42no—
322C4×C61—41no—
323C4×C61—41no—
324C4×C61—41no—
325C4×C61—81no—
326C4×C61C2×#11711yescharacteristic
327C4×C61#52011yescharacteristic
328C4×C61#54611yescharacteristic
329C4×C61#54811yescharacteristic
330Dic61—22no—
331Dic61—41no—
332Dic61—41no—
333#2943—611no—
334#2925—611no—
335#2906—611no—
336#1938—611no—
337#1937—611no—
338#1922—611no—
339#1922—611no—
340#1876—611no—
341#1876—611no—
342#1838—611no—
343#1806—611no—
344#1806D6111yescharacteristic, complemented
345#1771—611no—
346#1765—611no—
347#1764—611no—
348C2×C61—21no—
349C2×C61—21no—
350C2×C61—81no—
351C2×C61#235211yescharacteristic
352C2×C61#295511yescharacteristic
353C2×C61#295611yescharacteristic
354D61—42no—
355C2×#135—611no—
356C2×#131—611no—
357C2×#131—611no—
358C4×#41—611no—
359C4×#41C2×D6111yescharacteristic
360#442—611no—
361#442—611no—
362#441—611no—
363#441—611no—
364#440—611no—
365#440—611no—
366#440—611no—
367#440—611no—
368#433—1221no—
369#433—1221no—
370#432—1221no—
371#431—1221no—
372#427—611no—
373#424—611no—
374#424—611no—
375#424—1221no—
376#424—1221no—
377#423—611no—
378#423—1221no—
379#423C2×D6111yescharacteristic
380C2×C4⋊C8—611no—
381C2×C4⋊C8—1221no—
382C2×#104—611no—
383C2×#104—611no—
384C2×#104C2×D6111yescharacteristic
385C2×#104C2×D6111yescharacteristic
386#416—611no—
387#416—611no—
388#408—611no—
389#408—611no—
390#405—611no—
391#405—611no—
392C2×#97—611no—
393C2×#97—611no—
394C2×C4×C8—611no—
395C4×C4⋊C4C2×D6111yescharacteristic
396#341—611no—
397#341—611no—
398#341—611no—
399#341—611no—
400#339—611no—
401#339—611no—
402#339C2×D6111yescharacteristic
403#339C2×D6111yescharacteristic
404#336—611no—
405#336—611no—
406C61#2278411yescharacteristic, complemented, Sylow
407C2×#41—611no—
408C2×#41C22×D6111yescharacteristic
409#135—1222no—
410#135—1222no—
411C2×Q16—611no—
412C2×SD16—611no—
413C2×SD16—611no—
414C2×D8—611no—
415#131—1222no—
416#131—1222no—
417#131—2441no—
418#131—2441no—
419C2×M16—611no—
420C2×M16—611no—
421C2×M16—1221no—
422C2×M16—1221no—
423C2×M16C22×D6111yescharacteristic
424C2×M16C22×D6111yescharacteristic
425C22×C8—611no—
426C22×C8—611no—
427C22×C8—611no—
428C22×C8—611no—
429C22×C8—1221no—
430C22×C8—1221no—
431C4×Q8—611no—
432C4×Q8—611no—
433C4×Q8C4×D6111yescharacteristic
434C4×Q8C4×D6111yescharacteristic
435C4×D4—21no—
436C4×D4—21no—
437C4×D4—611no—
438C4×D4—611no—
439C4×D4—1221no—
440C4×D4—1221no—
441C4×D4C4×D6111yescharacteristic
442C4×D4C4×D6111yescharacteristic
443#117—21no—
444#117—611no—
445#117—1221no—
446#117C22×D6111yescharacteristic
447C2×C4⋊C4—21no—
448C2×C42—21no—
449C2×C42—1221no—
450C2×C42C22×D6111yescharacteristic
451C2×C42C22×D6111yescharacteristic
452C2×C42C22×D6111yescharacteristic
453#107—611no—
454#107—611no—
455#106—611no—
456#106—611no—
457C4⋊C8—21no—
458C4⋊C8—21no—
459C4⋊C8—611no—
460C4⋊C8—611no—
461C4⋊C8—611no—
462C4⋊C8—611no—
463C4⋊C8—1221no—
464C4⋊C8—1221no—
465C4⋊C8—1221no—
466C4⋊C8—1221no—
467C4⋊C8—1221no—
468C4⋊C8—1221no—
469#104—41no—
470#104—41no—
471#104—1222no—
472#104—1222no—
473#103—611no—
474#103—611no—
475#103—611no—
476#103—611no—
477#102—611no—
478#102—611no—
479#102—611no—
480#102—611no—
481C22⋊C8—1221no—
482C22⋊C8—1221no—
483C22⋊C8—1221no—
484C22⋊C8—1221no—
485#97—611no—
486#97—611no—
487#97—611no—
488#97—611no—
489#97—1221no—
490#97—1221no—
491#97—2441no—
492C4×C8—1221no—
493C4×C8—1221no—
494C4×C8—2441no—
495#95—21no—
496#41—21no—
497#41—21no—
498#41—21no—
499#41—21no—
500#41—612no—
501#41—612no—
502#41—1221no—
503#41—1221no—
504C2×Q8—611no—
505C2×Q8C2×C4×D6111yescharacteristic
506C2×D4—21no—
507C2×D4—611no—
508C2×D4—1221no—
509C2×D4C2×C4×D6111yescharacteristic
510C22×C4—21no—
511C22×C4—21no—
512C22×C4—21no—
513C22×C4—21no—
514C22×C4—21no—
515C22×C4—1221no—
516C22×C4—1221no—
517C22×C4—1221no—
518C22×C4#1175822411yescharacteristic
519C22×C4#1175822411yescharacteristic
520C22×C4C23×D6111yescharacteristic
521Q16—1222no—
522SD16—1222no—
523SD16—1222no—
524D8—1222no—
525M16—21no—
526M16—21no—
527M16—21no—
528M16—21no—
529M16—1221no—
530M16—1221no—
531M16—1221no—
532M16—1221no—
533M16—2442no—
534M16—2442no—
535C2×C8—21no—
536C2×C8—21no—
537C2×C8—611no—
538C2×C8—611no—
539C2×C8—611no—
540C2×C8—611no—
541C2×C8—611no—
542C2×C8—611no—
543C2×C8—611no—
544C2×C8—611no—
545C2×C8—1221no—
546C2×C8—1221no—
547C2×C8—1221no—
548C2×C8—1221no—
549C2×C8—1221no—
550C2×C8—1221no—
551C2×C8—1221no—
552C2×C8—1221no—
553C2×C8—1221no—
554C2×C8—1221no—
555C2×C8—2442no—
556C2×C8—2442no—
557C4⋊C4—21no—
558C4⋊C4—21no—
559C4⋊C4—42no—
560C4⋊C4—611no—
561C4⋊C4—611no—
562C4⋊C4—1221no—
563C4⋊C4—1221no—
564C4⋊C4C2×C4×D6111yescharacteristic
565C4⋊C4C2×C4×D6111yescharacteristic
566C22⋊C4—21no—
567C22⋊C4—21no—
568C22⋊C4—21no—
569C22⋊C4—1221no—
570C22⋊C4—1221no—
571C22⋊C4—1221no—
572C42—21no—
573C42—21no—
574C42—21no—
575C42—21no—
576C42—21no—
577C42—21no—
578C42—21no—
579C42—1221no—
580C42—1221no—
581C42—1221no—
582C42C2×C4×D6111yescharacteristic
583C42C2×C4×D6111yescharacteristic
584C42D4×D6111yescharacteristic
585C42D4×D6111yescharacteristic
586C23—21no—
587C23—1221no—
588C23C2×#1175822411yescharacteristic
589Q8—21no—
590Q8—21no—
591Q8—612no—
592Q8—1221no—
593D4—21no—
594D4—21no—
595D4—41no—
596D4—41no—
597D4—612no—
598D4—1222no—
599D4—1222no—
600D4—1221no—
601C2×C4—22no—
602C2×C4—21no—
603C2×C4—21no—
604C2×C4—21no—
605C2×C4—41no—
606C2×C4—41no—
607C2×C4—42no—
608C2×C4—41no—
609C2×C4—41no—
610C2×C4—41no—
611C2×C4—41no—
612C2×C4—41no—
613C2×C4—41no—
614C2×C4—41no—
615C2×C4—81no—
616C2×C4—1221no—
617C2×C4—1222no—
618C2×C4—1222no—
619C2×C4—1221no—
620C2×C4—1221no—
621C2×C4—4881no—
622C2×C4—2442no—
623C2×C4#1451973711yescharacteristic
624C2×C4#1451973711yescharacteristic
625C2×C4#1451973711yescharacteristic
626C2×C4#1451973711yescharacteristic
627C2×C4C22×C4×D6111yescharacteristic
628C2×C4C2×D4×D6111yescharacteristic
629C2×C4#41×D6111yescharacteristic
630C2×C4#41×D6111yescharacteristic
631C2×C4#1451982211yescharacteristic
632C2×C4#1451982511yescharacteristic
633C8—41no—
634C8—41no—
635C8—1221no—
636C8—1221no—
637C8—1221no—
638C8—1221no—
639C8—1221no—
640C8—1221no—
641C8—1221no—
642C8—1221no—
643C8—2441no—
644C8—2441no—
645C22—21no—
646C22—21no—
647C22—41no—
648C22—41no—
649C22—41no—
650C22—1222no—
651C22—2441no—
652C22—2441no—
653C22C2×#1451973711yescharacteristic
654C22#1684044611yescharacteristic
655C22#1684045911yescharacteristic
656C4—21no—
657C4—21no—
658C4—21no—
659C4—21no—
660C4—42no—
661C4—41no—
662C4—41no—
663C4—41no—
664C4—81no—
665C4—1222no—
666C4—2441no—
667C4—2441no—
668C4#117×D6111yescharacteristic
669C4#1684024311yescharacteristic
670C4#1684040911yescharacteristic
671C4#1684042211yescharacteristic
672C2—21no—
673C2—21no—
674C2—81no—
675C2—2442no—
676C2#2144874111yescharacteristic
677C2#2145471811yescharacteristic
678C2#2145472511yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D61
commutatorC2×C4×C61C23×C4
FrattiniC22×C4C23×D61
FittingC61×#1806C2
socleC22×C61C2×C4×D4
prime radicalC2×#14519797C22
cosocleC22×C4×C61C24
hypercenter#1806D61
hypocenterC61#22784
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1806

Complements

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

NH ≅ G/Ntype
2. #21454485C2semidirect
3. #21454388C2semidirect
4. #21446527C2semidirect
5. #21446520C2semidirect
6. #21446416C2semidirect
7. #21446416C2semidirect
10. #21445959C2semidirect
11. #21445840C2semidirect
12. #21445694C2semidirect
13. #21445660C2semidirect
14. #21445653C2semidirect
15. C61×#1806C2semidirect
20. #16839872C4semidirect
21. #16839872C4semidirect
22. #16839867C4semidirect
23. #16839867C4semidirect
24. #16839862C4semidirect
25. #16839862C4semidirect
26. #16839860C4semidirect
27. #16839860C4semidirect
344. #1806D61semidirect
406. C61#22784semidirect

Maximal subgroups

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

subgroupindex
#214546172
#214544852
#214543882
#214465272
#214465202
#214464162
#214461432
#214459592
#214458402
#214456942
#214456602
#214456532
C61×#18062
#2278461