Finite Group Databasebeta

← #29699482

Subgroups — #29699482

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#21454484C211yesmaximal, characteristic, complemented
3#21446529C211yesmaximal, characteristic, complemented
4#21446522C211yesmaximal, characteristic, complemented
5#21446415C211yesmaximal, characteristic, complemented
6#21446415C211yesmaximal, characteristic, complemented
7#21446146C211yesmaximal, characteristic
8#21446146C211yesmaximal, characteristic
9#21445959C211yesmaximal, characteristic, complemented
10#21445839C211yesmaximal, characteristic, complemented
11#21445836C211yesmaximal, characteristic, complemented
12#21445696C211yesmaximal, characteristic, complemented
13#21445661C211yesmaximal, characteristic, complemented
14#21445654C211yesmaximal, characteristic, complemented
15C61×#2906C211yesmaximal, characteristic, complemented
16C2×#14519797C2211yescharacteristic
17C4×#11758222C2211yescharacteristic
18#16839872C411yescharacteristic, complemented
19#16839872C411yescharacteristic, complemented
20#16839867C411yescharacteristic, complemented
21#16839867C411yescharacteristic, complemented
22#16839862C411yescharacteristic, complemented
23#16839862C411yescharacteristic, complemented
24#16839860C411yescharacteristic, complemented
25#16839860C411yescharacteristic, complemented
26#16839822—21no—
27#16839822—21no—
28#16839818—21no—
29#16839814—21no—
30#16839798C2211yescharacteristic
31#16839786C2211yescharacteristic
32C2×#14519704C2211yescharacteristic
33C2×#14519704C2211yescharacteristic
34C2×#14519703C2211yescharacteristic
35C2×#14519703C2211yescharacteristic
36#16839758C2211yescharacteristic
37#16839756C2211yescharacteristic
38#16839728C2211yescharacteristic
39#16839728C2211yescharacteristic
40#16839717C2211yescharacteristic
41#16839717C2211yescharacteristic
42C2×#14519688C2211yescharacteristic
43C2×#14519687C2211yescharacteristic
44C2×C8×Dic61C2211yescharacteristic
45C4×C4⋊Dic61C2211yescharacteristic
46#16839526C2211yescharacteristic
47#16839526C2211yescharacteristic
48#16839526C2211yescharacteristic
49#16839526C2211yescharacteristic
50#16839523C2211yescharacteristic
51#16839523C2211yescharacteristic
52#16839521C2211yescharacteristic
53#16839521C2211yescharacteristic
54#16839516C2211yescharacteristic
55#16839516C2211yescharacteristic
56C2×#131×C61C2211yescharacteristic
57C2×#131×C61C2211yescharacteristic
58C4×#41×C61C2211yescharacteristic
59C61×#424—21no—
60C61×#424—21no—
61C61×#424C2211yescharacteristic
62C61×#424C2211yescharacteristic
63C61×#423—21no—
64C61×#423C2211yescharacteristic
65C2×C4⋊C8×C61—21no—
66C2×C4⋊C8×C61C2211yescharacteristic
67C2×#11758222C2311yescharacteristic
68#14519797—22no—
69#14519797—22no—
70C2×#11758202C2×C411yescharacteristic
71C2×#11758200C2×C411yescharacteristic
72C2×#11758201C2×C411yescharacteristic
73C2×#11758199C2×C411yescharacteristic
74C2×#11758194C2311yescharacteristic
75C2×#11758194C2311yescharacteristic
76C22×#92418C2311yescharacteristic
77C22×#92418C2311yescharacteristic
78C4×Dic122C2×C411yescharacteristic
79C4×Dic122C2×C411yescharacteristic
80C4×D244C2×C411yescharacteristic
81C4×D244C2×C411yescharacteristic
82C4×C22⋊D61—21no—
83C4×C22⋊D61—21no—
84#14519736C2311yescharacteristic
85#14519734—21no—
86C2×C4⋊Dic61—21no—
87C2×C4×Dic61C2311yescharacteristic
88C2×C4×Dic61C2311yescharacteristic
89C42×D61—21no—
90#14519710C2×C411yescharacteristic
91#14519710C2×C411yescharacteristic
92#14519708C2×C411yescharacteristic
93#14519708C2×C411yescharacteristic
94C4⋊#92418—21no—
95C4⋊#92418—21no—
96#14519704—22no—
97#14519704—22no—
98#14519703—41no—
99#14519703—41no—
100#14519701C2×C411yescharacteristic
101#14519701C2×C411yescharacteristic
102#14519700C2×C411yescharacteristic
103#14519700C2×C411yescharacteristic
104#14519698C2×C411yescharacteristic
105#14519698C2×C411yescharacteristic
106#14519697C2×C411yescharacteristic
107#14519697C2×C411yescharacteristic
108#14519689—21no—
109#14519689—21no—
110#14519689—21no—
111#14519689—21no—
112#14519688C2×C411yescharacteristic
113#14519688C2×C411yescharacteristic
114#14519688C2×C411yescharacteristic
115#14519688C2×C411yescharacteristic
116#14519687—21no—
117#14519687—21no—
118#14519687—41no—
119C8×Dic61—21no—
120C8×Dic61—21no—
121C8×Dic61—41no—
122#14519684—21no—
123C2×#41×C61C2311yescharacteristic
124#131×C61—22no—
125#131×C61—22no—
126#131×C61—41no—
127#131×C61—41no—
128C2×M16×C61—21no—
129C2×M16×C61—21no—
130C2×M16×C61C2311yescharacteristic
131C2×M16×C61C2311yescharacteristic
132C22×C8×C61—21no—
133C22×C8×C61—21no—
134C22×C8×C61C2311yescharacteristic
135C22×C8×C61C2311yescharacteristic
136C4×Q8×C61C2×C411yescharacteristic
137C4×Q8×C61C2×C411yescharacteristic
138C4×D4×C61—21no—
139C4×D4×C61—21no—
140C4×D4×C61C2×C411yescharacteristic
141C4×D4×C61C2×C411yescharacteristic
142#117×C61—21no—
143#117×C61C2311yescharacteristic
144C2×C42×C61—21no—
145C2×C42×C61C2311yescharacteristic
146C4⋊C8×C61—21no—
147C4⋊C8×C61—21no—
148C4⋊C8×C61—21no—
149C4⋊C8×C61—21no—
150C4⋊C8×C61—21no—
151C4⋊C8×C61—21no—
152C4⋊C8×C61D411yescharacteristic
153C4⋊C8×C61D411yescharacteristic
154C4⋊C8×C61D411yescharacteristic
155C4⋊C8×C61D411yescharacteristic
156#41×C61—21no—
157#41×C61—21no—
158#41×C61#4112yes—
159#41×C61#4112yes—
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#4111yescharacteristic
167C22×C4×C61#4111yescharacteristic
168C22×C4×C61C2411yescharacteristic
169C2×C22⋊D61—21no—
170C22×Dic61—21no—
171C22×Dic61—21no—
172#11758222—21no—
173#11758222—21no—
174#11758222—21no—
175#11758222—21no—
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—
185M16×C61—42no—
186M16×C61—42no—
187C2×C8×C61—21no—
188C2×C8×C61—21no—
189C2×C8×C61—21no—
190C2×C8×C61—21no—
191C2×C8×C61—21no—
192C2×C8×C61—21no—
193C2×C8×C61—42no—
194C2×C8×C61—42no—
195C2×C8×C61C2×D411yescharacteristic
196C2×C8×C61C2×D411yescharacteristic
197C2×C8×C61C2×D411yescharacteristic
198C2×C8×C61C2×D411yescharacteristic
199C4⋊C4×C61—21no—
200C4⋊C4×C61—21no—
201C4⋊C4×C61C22×C411yescharacteristic
202C4⋊C4×C61C22×C411yescharacteristic
203C22⋊C4×C61—21no—
204C22⋊C4×C61—21no—
205C22⋊C4×C61—21no—
206C42×C61—21no—
207C42×C61—21no—
208C42×C61—21no—
209C42×C61C22×C411yescharacteristic
210C42×C61C22×C411yescharacteristic
211C42×C61C2×D411yescharacteristic
212C42×C61C2×D411yescharacteristic
213C22⋊Dic61—21no—
214#11758202—22no—
215#11758201—22no—
216#11758200—22no—
217#11758199—22no—
218#11758198—21no—
219#11758198—21no—
220C4⋊Dic61—42no—
221C4⋊Dic61C22×C411yescharacteristic
222C4⋊Dic61C22×C411yescharacteristic
223#11758196—21no—
224#11758196—21no—
225C4×Dic61—21no—
226C4×Dic61—21no—
227C4×Dic61—21no—
228C4×Dic61—21no—
229C4×Dic61—21no—
230C4×Dic61—21no—
231C4×Dic61—21no—
232#11758194—21no—
233#11758194—21no—
234#11758194—21no—
235#11758194—21no—
236C2×#92418—21no—
237C2×#92418—21no—
238C2×#92418—21no—
239C2×#92418—21no—
240C2×#92418—21no—
241C2×#92418—21no—
242C2×#92418C22×C411yescharacteristic
243C2×#92418C22×C411yescharacteristic
244C2×#92418C22×C411yescharacteristic
245C2×#92418C22×C411yescharacteristic
246C23×C61—21no—
247C23×C61C2×#4111yescharacteristic
248C22×D61—21no—
249Q8×C61—21no—
250Q8×C61#11712yes—
251D4×C61—22no—
252D4×C61—22no—
253D4×C61—21no—
254D4×C61#11712yes—
255C2×C4×C61—21no—
256C2×C4×C61—22no—
257C2×C4×C61—22no—
258C2×C4×C61—21no—
259C2×C4×C61—21no—
260C2×C4×C61—41no—
261C2×C4×C61—41no—
262C2×C4×C61—42no—
263C2×C4×C61—81no—
264C2×C4×C61C4×D411yescharacteristic
265C2×C4×C61C4×D411yescharacteristic
266C2×C4×C61C4×D411yescharacteristic
267C2×C4×C61C4×D411yescharacteristic
268C2×C4×C61C23×C411yescharacteristic
269C2×C4×C61C22×D411yescharacteristic
270C2×C4×C61C2×#4111yescharacteristic
271C2×C4×C61C2×#4111yescharacteristic
272C2×C4×C61H(5,𝔽2)11yescharacteristic
273C2×C4×C612−1+411yescharacteristic
274C22⋊D61—41no—
275C22⋊D61—41no—
276C2×Dic61—22no—
277C2×Dic61—21no—
278C2×Dic61—21no—
279C2×Dic61—21no—
280C2×Dic61—41no—
281C2×Dic61—41no—
282C2×Dic61—41no—
283C2×Dic61—41no—
284C2×Dic61—41no—
285D244—21no—
286D244—21no—
287C4×D61—42no—
288C4×D61—41no—
289C4×D61—41no—
290C4×D61—81no—
291Dic122—21no—
292Dic122—21no—
293C8×C61—21no—
294C8×C61—21no—
295C8×C61—21no—
296C8×C61—21no—
297C8×C61—41no—
298C8×C61—41no—
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—22no—
309C22×C61—41no—
310C22×C61—41no—
311C22×C61C2×C4×D411yescharacteristic
312C22×C61#55211yescharacteristic
313C22×C61#55311yescharacteristic
314C2×D61—41no—
315C2×D61—41no—
316C2×D61—41no—
317C4×C61—22no—
318C4×C61—21no—
319C4×C61—21no—
320C4×C61—21no—
321C4×C61—21no—
322C4×C61—41no—
323C4×C61—41no—
324C4×C61C2×#11711yescharacteristic
325C4×C61#52011yescharacteristic
326C4×C61#54611yescharacteristic
327C4×C61#54811yescharacteristic
328Dic61—42no—
329Dic61—41no—
330Dic61—41no—
331Dic61—41no—
332Dic61—81no—
333#2943—611no—
334#2925—611no—
335#2906D6111yescharacteristic, complemented
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#1806—611no—
345#1771—611no—
346#1765—611no—
347#1764—611no—
348C2×C61—21no—
349C2×C61—21no—
350C2×C61—42no—
351C2×C61#235211yescharacteristic
352C2×C61#295511yescharacteristic
353C2×C61#295611yescharacteristic
354D61—81no—
355C2×#135—611no—
356C2×#131C2×D6111yescharacteristic
357C2×#131C2×D6111yescharacteristic
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—21no—
374#424—21no—
375#424C2×D6111yescharacteristic
376#424C2×D6111yescharacteristic
377#423—21no—
378#423—611no—
379#423C2×D6111yescharacteristic
380C2×C4⋊C8—21no—
381C2×C4⋊C8C2×D6111yescharacteristic
382C2×#104—611no—
383C2×#104—611no—
384C2×#104—611no—
385C2×#104—611no—
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⋊C4—611no—
396#341—611no—
397#341—611no—
398#341—611no—
399#341—611no—
400#339—611no—
401#339—611no—
402#339—611no—
403#339—611no—
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—22no—
416#131—22no—
417#131—41no—
418#131—41no—
419C2×M16—21no—
420C2×M16—21no—
421C2×M16—611no—
422C2×M16—611no—
423C2×M16C22×D6111yescharacteristic
424C2×M16C22×D6111yescharacteristic
425C22×C8—21no—
426C22×C8—21no—
427C22×C8—611no—
428C22×C8—611no—
429C22×C8C22×D6111yescharacteristic
430C22×C8C22×D6111yescharacteristic
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—1221no—
448C2×C42—21no—
449C2×C42—611no—
450C2×C42—611no—
451C2×C42—1221no—
452C2×C42C22×D6111yescharacteristic
453#107—611no—
454#107—611no—
455#106—611no—
456#106—611no—
457C4⋊C8—21no—
458C4⋊C8—21no—
459C4⋊C8—21no—
460C4⋊C8—21no—
461C4⋊C8—21no—
462C4⋊C8—21no—
463C4⋊C8—1221no—
464C4⋊C8—1221no—
465C4⋊C8C22⋊D6111yescharacteristic
466C4⋊C8C22⋊D6111yescharacteristic
467C4⋊C8C22⋊D6111yescharacteristic
468C4⋊C8C22⋊D6111yescharacteristic
469#104—1222no—
470#104—1222no—
471#104—2441no—
472#104—2441no—
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—1221no—
496#41—21no—
497#41—21no—
498#41—1221no—
499#41—1221no—
500#41—1221no—
501#41—1221no—
502#41#1175822412yes—
503#41#1175822612yes—
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—1221no—
514C22×C4—1221no—
515C22×C4—1221no—
516C22×C4—1221no—
517C22×C4—1221no—
518C22×C4#1175822211yescharacteristic
519C22×C4#1175822211yescharacteristic
520C22×C4C23×D6111yescharacteristic
521Q16—1222no—
522SD16—1222no—
523SD16—1222no—
524D8—1222no—
525M16—21no—
526M16—21no—
527M16—21no—
528M16—21no—
529M16—42no—
530M16—42no—
531M16—1221no—
532M16—1221no—
533M16—1221no—
534M16—1221no—
535C2×C8—21no—
536C2×C8—21no—
537C2×C8—21no—
538C2×C8—21no—
539C2×C8—21no—
540C2×C8—21no—
541C2×C8—42no—
542C2×C8—42no—
543C2×C8—611no—
544C2×C8—611no—
545C2×C8—611no—
546C2×C8—611no—
547C2×C8—1221no—
548C2×C8—1221no—
549C2×C8—1221no—
550C2×C8—1221no—
551C2×C8—1221no—
552C2×C8—1221no—
553C2×C8C2×C22⋊D6111yescharacteristic
554C2×C8C2×C22⋊D6111yescharacteristic
555C2×C8C2×C22⋊D6111yescharacteristic
556C2×C8C2×C22⋊D6111yescharacteristic
557C4⋊C4—21no—
558C4⋊C4—21no—
559C4⋊C4—611no—
560C4⋊C4—611no—
561C4⋊C4—1221no—
562C4⋊C4—1221no—
563C4⋊C4—2442no—
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—1221no—
576C42—1221no—
577C42—1221no—
578C42—1221no—
579C42—1221no—
580C42—1221no—
581C42—1221no—
582C42C2×C4×D6111yescharacteristic
583C42C2×C4×D6111yescharacteristic
584C42C2×C22⋊D6111yescharacteristic
585C42C2×C22⋊D6111yescharacteristic
586C23—21no—
587C23—1221no—
588C23C2×#1175822211yescharacteristic
589Q8—21no—
590Q8—1221no—
591Q8—1221no—
592Q8#1451973512yes—
593D4—22no—
594D4—22no—
595D4—21no—
596D4—1221no—
597D4—1221no—
598D4—2441no—
599D4—2441no—
600D4#1451973512yes—
601C2×C4—21no—
602C2×C4—22no—
603C2×C4—22no—
604C2×C4—21no—
605C2×C4—21no—
606C2×C4—41no—
607C2×C4—41no—
608C2×C4—42no—
609C2×C4—81no—
610C2×C4—1222no—
611C2×C4—1221no—
612C2×C4—1221no—
613C2×C4—1221no—
614C2×C4—4881no—
615C2×C4—2442no—
616C2×C4—2441no—
617C2×C4—2441no—
618C2×C4—2441no—
619C2×C4—2441no—
620C2×C4—2441no—
621C2×C4—2441no—
622C2×C4—2441no—
623C2×C4C4×C22⋊D6111yescharacteristic
624C2×C4C4×C22⋊D6111yescharacteristic
625C2×C4C4×C22⋊D6111yescharacteristic
626C2×C4C4×C22⋊D6111yescharacteristic
627C2×C4C22×C4×D6111yescharacteristic
628C2×C4C22×C22⋊D6111yescharacteristic
629C2×C4C2×#1175822411yescharacteristic
630C2×C4C2×#1175822611yescharacteristic
631C2×C4#1451982211yescharacteristic
632C2×C4#1451982511yescharacteristic
633C8—21no—
634C8—21no—
635C8—21no—
636C8—21no—
637C8—41no—
638C8—41no—
639C8—1221no—
640C8—1221no—
641C8—1221no—
642C8—1221no—
643C8—2441no—
644C8—2441no—
645C22—21no—
646C22—21no—
647C22—22no—
648C22—41no—
649C22—41no—
650C22—2441no—
651C22—2441no—
652C22—2441no—
653C22C2×C4×C22⋊D6111yescharacteristic
654C22#1684044711yescharacteristic
655C22#1684046011yescharacteristic
656C4—22no—
657C4—21no—
658C4—21no—
659C4—21no—
660C4—21no—
661C4—41no—
662C4—41no—
663C4—4881no—
664C4—2442no—
665C4—2441no—
666C4—2441no—
667C4—2441no—
668C4C2×#1451973511yescharacteristic
669C4#1684024311yescharacteristic
670C4#1684040611yescharacteristic
671C4#1684042311yescharacteristic
672C2—21no—
673C2—21no—
674C2—42no—
675C2—4881no—
676C2#2144874411yescharacteristic
677C2#2145472011yescharacteristic
678C2#2145472611yescharacteristic
subgroupG/H
centerC2×C4C22×C22⋊D61
commutatorC2×C4×C61C23×C4
FrattiniC22×C4C23×D61
FittingC61×#2906C2
socleC22×C61C2×C4×D4
prime radicalC2×#14519797C22
cosocleC22×C4×C61C24
hypercenter#2906D61
hypocenterC61#22784
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C2×C4⋊C8 ◁ #2906

Complements

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

NH ≅ G/Ntype
2. #21454484C2semidirect
3. #21446529C2semidirect
4. #21446522C2semidirect
5. #21446415C2semidirect
6. #21446415C2semidirect
9. #21445959C2semidirect
10. #21445839C2semidirect
11. #21445836C2semidirect
12. #21445696C2semidirect
13. #21445661C2semidirect
14. #21445654C2semidirect
15. C61×#2906C2semidirect
18. #16839872C4semidirect
19. #16839872C4semidirect
20. #16839867C4semidirect
21. #16839867C4semidirect
22. #16839862C4semidirect
23. #16839862C4semidirect
24. #16839860C4semidirect
25. #16839860C4semidirect
335. #2906D61semidirect
406. C61#22784semidirect

Maximal subgroups

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

subgroupindex
#214546172
#214544842
#214465292
#214465222
#214464152
#214461462
#214459592
#214458392
#214458362
#214456962
#214456612
#214456542
C61×#29062
#2278461