Finite Group Databasebeta

← #29783234

Subgroups — #29783234

Order 15616.

674 conjugacy classes of subgroups.

The subgroup lattice has 596 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21451785C211yesmaximal, characteristic, complemented
2#21448458C211yesmaximal, characteristic
3#21447323C211yesmaximal, characteristic, complemented
4#21447210C211yesmaximal, characteristic, complemented
5#21447208C211yesmaximal, characteristic
6#21447133C211yesmaximal, characteristic
7#21446676C211yesmaximal, characteristic
8#21446549C211yesmaximal, characteristic, complemented
9#21446516C211yesmaximal, characteristic
10#21446463C211yesmaximal, characteristic, complemented
11#21446407C211yesmaximal, characteristic, complemented
12#21446150C211yesmaximal, characteristic
13#21446067C211yesmaximal, characteristic
14#21445679C211yesmaximal, characteristic, complemented
15C61×#1935C211yesmaximal, characteristic, complemented
16C22×#11758201C2211yescharacteristic
17C2×#14519739C2211yescharacteristic
18C2×#14519710C2211yescharacteristic
19C2×#14519710C2211yescharacteristic
20C2×#14519708C2211yescharacteristic
21C2×#14519706C2211yescharacteristic
22C2×#14519706C2211yescharacteristic
23C2×#14519701C2211yescharacteristic
24C2×#14519699C2211yescharacteristic
25C2×#14519699C2211yescharacteristic
26C2×#14519697C2211yescharacteristic
27C2×C4×#92418C2211yescharacteristic
28C61⋊#401—21no—
29#16839704—21no—
30#16839703—21no—
31#16839702—21no—
32#16839669C2211yescharacteristic
33#16839669C2211yescharacteristic
34#16839664C2211yescharacteristic
35#16839663C2211yescharacteristic
36#16839661C2211yescharacteristic
37#16839661C2211yescharacteristic
38#16839660C2211yescharacteristic
39#16839658C2211yescharacteristic
40#16839654—21no—
41#16839652—21no—
42#16839624—21no—
43#16839619—21no—
44C4⋊C4×Dic61C2211yescharacteristic
45#16839608C2211yescharacteristic
46#16839525C2211yescharacteristic
47#16839525C2211yescharacteristic
48#16839524C2211yescharacteristic
49#16839524C2211yescharacteristic
50#16839516C2211yescharacteristic
51#16839516C2211yescharacteristic
52C2×#103×C61C2211yescharacteristic
53C2×#103×C61C2211yescharacteristic
54C2×#97×C61C2211yescharacteristic
55C61×#391C2211yescharacteristic
56C61×#389C2211yescharacteristic
57C61×#340C2211yescharacteristic
58C61×#340C2211yescharacteristic
59C22×D244C2311yescharacteristic
60C22×C4×D61—21no—
61C2×#11758201—22no—
62C2×#11758201—22no—
63C2×#11758201—41no—
64C22×#92418C2311yescharacteristic
65C22×#92418C2311yescharacteristic
66#14519739—22no—
67#14519739—22no—
68C2×C4⋊Dic61—21no—
69C2×C4⋊Dic61—21no—
70C2×C4⋊Dic61C2311yescharacteristic
71C2×C4⋊Dic61C2311yescharacteristic
72C2×C4⋊Dic61C2311yescharacteristic
73C2×#11758196—21no—
74C2×#11758196—21no—
75C2×#11758198—21no—
76C2×#11758198—21no—
77C2×#11758198—21no—
78C2×#11758198—21no—
79C2×#11758198—21no—
80C2×C4×Dic61—21no—
81C2×C4×Dic61C2311yescharacteristic
82C2×C4×Dic61C2311yescharacteristic
83#14519710—22no—
84#14519710—41no—
85#14519708—22no—
86#14519706—22no—
87#14519706—22no—
88#14519701—22no—
89#14519699—22no—
90#14519699—41no—
91#14519697—22no—
92C4×#92418—41no—
93#14519684—21no—
94#14519684—21no—
95#14519684—21no—
96#14519684—21no—
97#14519684—21no—
98#14519684—21no—
99#14519684—21no—
100#14519684—21no—
101#14519684—21no—
102#14519684D411yescharacteristic
103#14519684D411yescharacteristic
104#14519684D411yescharacteristic
105#14519684D411yescharacteristic
106C22×Q8×C61C2311yescharacteristic
107C22×C8×C61C2311yescharacteristic
108C22×C8×C61C2311yescharacteristic
109C2×C4⋊C4×C61—21no—
110C2×C4⋊C4×C61C2311yescharacteristic
111C2×C4⋊C4×C61C2311yescharacteristic
112C2×C4⋊C4×C61C2311yescharacteristic
113C2×C42×C61C2311yescharacteristic
114#103×C61—22no—
115#103×C61—41no—
116#97×C61—41no—
117#95×C61—21no—
118#95×C61—21no—
119#95×C61—21no—
120C23×D61—21no—
121C2×Q8×C61—21no—
122C2×Q8×C61—21no—
123C2×Q8×C61—21no—
124C2×Q8×C61—21no—
125C2×Q8×C61—21no—
126C2×Q8×C61—21no—
127C22×C4×C61—21no—
128C22×C4×C61—21no—
129C22×C4×C61—21no—
130C22×C4×C61—21no—
131C22×C4×C61C2×D411yescharacteristic
132C22×C4×C61C2×D411yescharacteristic
133C22×C4×C61C2411yescharacteristic
134C22×Dic61—21no—
135C22×Dic61—21no—
136C22×Dic61—21no—
137C22×Dic61C2×D411yescharacteristic
138C22×Dic61C2×D411yescharacteristic
139C22×Dic61C2×D411yescharacteristic
140C22×Dic61C2×D411yescharacteristic
141C2×D244—21no—
142C2×D244—21no—
143C2×D244—21no—
144C2×D244—21no—
145C2×D244—21no—
146C2×D244#4112yes—
147C2×C4×D61—24no—
148C2×C4×D61—81no—
149C2×C4×D61—81no—
150C2×C8×C61—21no—
151C2×C8×C61—21no—
152C2×C8×C61—21no—
153C2×C8×C61—21no—
154C2×C8×C61—21no—
155C2×C8×C61—21no—
156C4⋊C4×C61—21no—
157C4⋊C4×C61—21no—
158C4⋊C4×C61—21no—
159C4⋊C4×C61—21no—
160C4⋊C4×C61—21no—
161C4⋊C4×C61—81no—
162C4⋊C4×C61#4112yes—
163C42×C61—21no—
164C42×C61—21no—
165#11758201—44no—
166#11758198—24no—
167#11758198—81no—
168#11758198—81no—
169#11758198—81no—
170#11758198—81no—
171C4⋊Dic61—21no—
172C4⋊Dic61—21no—
173C4⋊Dic61—21no—
174C4⋊Dic61—21no—
175C4⋊Dic61—21no—
176C4⋊Dic61—21no—
177C4⋊Dic61—81no—
178C4⋊Dic61—81no—
179#11758196—81no—
180#11758196—81no—
181C4×Dic61—21no—
182C4×Dic61—21no—
183C4×Dic61—21no—
184C4×Dic61—21no—
185C4×Dic61—81no—
186C2×#92418—21no—
187C2×#92418—21no—
188C2×#92418—21no—
189C2×#92418—21no—
190C2×#92418#4112yes—
191C2×#92418#4112yes—
192C23×C61C22×D411yescharacteristic
193C22×D61—22no—
194C22×D61—41no—
195C22×D61—41no—
196C22×D61—41no—
197C22×D61—41no—
198C22×D61—41no—
199C22×D61—41no—
200Q8×C61—41no—
201Q8×C61—41no—
202Q8×C61—41no—
203Q8×C61—41no—
204C2×C4×C61—22no—
205C2×C4×C61—21no—
206C2×C4×C61—21no—
207C2×C4×C61—21no—
208C2×C4×C61—21no—
209C2×C4×C61—21no—
210C2×C4×C61—21no—
211C2×C4×C61—41no—
212C2×C4×C61—41no—
213C2×C4×C61—41no—
214C2×C4×C61—41no—
215C2×C4×C61—41no—
216C2×C4×C61—41no—
217C2×C4×C61—41no—
218C2×C4×C61—41no—
219C2×C4×C61—41no—
220C2×C4×C61—41no—
221C2×C4×C61—41no—
222C2×C4×C61C2×#4111yescharacteristic
223C2×C4×C61C2×#4111yescharacteristic
224C2×C4×C61C2×#4111yescharacteristic
225C2×C4×C61C2×#4111yescharacteristic
226C2×C4×C61H(5,𝔽2)11yescharacteristic
227C2×C4×C612−1+411yescharacteristic
228C2×Dic61—21no—
229C2×Dic61—21no—
230C2×Dic61—21no—
231C2×Dic61—21no—
232C2×Dic61—21no—
233C2×Dic61—21no—
234C2×Dic61—21no—
235C2×Dic61—21no—
236C2×Dic61—21no—
237C2×Dic61—21no—
238C2×Dic61—21no—
239C2×Dic61—21no—
240C2×Dic61—41no—
241C2×Dic61—41no—
242C2×Dic61—41no—
243C2×Dic61—41no—
244C2×Dic61—41no—
245C2×Dic61—41no—
246C2×Dic61—41no—
247C2×Dic61—41no—
248C2×Dic61—41no—
249D244—22no—
250D244—22no—
251D244—41no—
252D244—41no—
253C4×D61—84no—
254C8×C61—41no—
255C8×C61—41no—
256#92418—22no—
257#92418—22no—
258#29441—611nomaximal, Sylow
259C22×C61#52511yescharacteristic
260C22×C61#53211yescharacteristic
261C22×C61#53711yescharacteristic
262C22×C61#57611yescharacteristic
263C22×C61#57711yescharacteristic
264C22×C61#57711yescharacteristic
265C22×C61#57811yescharacteristic
266C2×D61—42no—
267C2×D61—42no—
268C2×D61—42no—
269C2×D61—81no—
270C2×D61—81no—
271C2×D61—81no—
272C2×D61—81no—
273C4×C61—42no—
274C4×C61—41no—
275C4×C61—41no—
276C4×C61—81no—
277C4×C61—81no—
278C4×C61—81no—
279C4×C61#55111yescharacteristic
280C4×C61#55211yescharacteristic
281C4×C61#55311yescharacteristic
282C4×C61#55611yescharacteristic
283Dic61—41no—
284Dic61—41no—
285Dic61—41no—
286Dic61—41no—
287Dic61—81no—
288Dic61—81no—
289Dic61—81no—
290#2645—611no—
291#2319—611no—
292#2088—611no—
293#2068—611no—
294#2067—611no—
295#2055—611no—
296#1968—611no—
297#1942—611no—
298#1936—611no—
299#1935D6111yescharacteristic, complemented
300#1928—611no—
301#1920—611no—
302#1877—611no—
303#1862—611no—
304#1768—611no—
305C2×C61#260111yescharacteristic
306C2×C61#311811yescharacteristic
307C2×C61#312011yescharacteristic
308C2×C61#317411yescharacteristic
309C2×C61#317511yescharacteristic
310C2×C61#325711yescharacteristic
311C2×C61#325811yescharacteristic
312D61—82no—
313C22×SD16—611no—
314C2×C4×D4—611no—
315C2×#107—611no—
316C2×#107—611no—
317C2×#106—611no—
318C2×C4⋊C8—611no—
319C2×C4⋊C8—611no—
320C2×#103—611no—
321C2×#103C2×D6111yescharacteristic
322C2×#103C2×D6111yescharacteristic
323C2×#102—611no—
324C2×#102—611no—
325C2×#102—611no—
326C2×#97C2×D6111yescharacteristic
327C2×C4×C8—611no—
328#401—1221no—
329#400—1221no—
330#400—1221no—
331#400—1221no—
332#391—611no—
333#391—611no—
334#391C2×D6111yescharacteristic
335#390—611no—
336#390—611no—
337#389—611no—
338#389—611no—
339#389—611no—
340#389—611no—
341#389C2×D6111yescharacteristic
342#388—1221no—
343#388—1221no—
344#381—1221no—
345#380—1221no—
346C4×C4⋊C4—611no—
347#376—611no—
348#340—611no—
349#340—611no—
350#340—611no—
351#340—611no—
352#340C2×D6111yescharacteristic
353#340C2×D6111yescharacteristic
354#336—611no—
355#336—611no—
356C61#2944111yescharacteristic, complemented, Sylow
357C22×Q8C22×D6111yescharacteristic
358C22×D4—611no—
359C23×C4—1221no—
360C2×SD16—1222no—
361C2×SD16—1222no—
362C2×SD16—2441no—
363C22×C8—611no—
364C22×C8—611no—
365C22×C8C22×D6111yescharacteristic
366C22×C8C22×D6111yescharacteristic
367C4×D4—1222no—
368C4×D4—1222no—
369C2×C4⋊C4—21no—
370C2×C4⋊C4—611no—
371C2×C4⋊C4—611no—
372C2×C4⋊C4—611no—
373C2×C4⋊C4—1221no—
374C2×C4⋊C4—1221no—
375C2×C4⋊C4—1221no—
376C2×C4⋊C4—1221no—
377C2×C4⋊C4C22×D6111yescharacteristic
378C2×C4⋊C4C22×D6111yescharacteristic
379C2×C4⋊C4C22×D6111yescharacteristic
380C2×C22⋊C4—1221no—
381C2×C22⋊C4—1221no—
382C2×C22⋊C4—1221no—
383C2×C22⋊C4—1221no—
384C2×C22⋊C4—1221no—
385C2×C42—611no—
386C2×C42—611no—
387C2×C42—1221no—
388C2×C42C22×D6111yescharacteristic
389#107—1222no—
390#107—2441no—
391#106—1222no—
392C4⋊C8—1222no—
393C4⋊C8—1222no—
394#103—22no—
395#103—41no—
396#103—1222no—
397#102—1222no—
398#102—1222no—
399#102—2441no—
400#97—41no—
401C4×C8—2441no—
402#95—21no—
403#95—21no—
404#95—21no—
405#95—611no—
406#95—611no—
407#95—611no—
408#95—611no—
409#95—1221no—
410#95—1221no—
411#95—1221no—
412#95—1221no—
413#95—1221no—
414#95—1221no—
415#95—1221no—
416#95—1221no—
417#95—1221no—
418C24—1221no—
419C2×Q8—21no—
420C2×Q8—21no—
421C2×Q8—21no—
422C2×Q8—21no—
423C2×Q8—21no—
424C2×Q8—21no—
425C2×D4—612no—
426C2×D4—1221no—
427C2×D4—1221no—
428C2×D4—1221no—
429C2×D4—1221no—
430C2×D4—1221no—
431C22×C4—21no—
432C22×C4—21no—
433C22×C4—21no—
434C22×C4—21no—
435C22×C4—611no—
436C22×C4—611no—
437C22×C4—611no—
438C22×C4—611no—
439C22×C4—1224no—
440C22×C4—1221no—
441C22×C4—1221no—
442C22×C4—1221no—
443C22×C4—4881no—
444C22×C4—4881no—
445C22×C4D4×D6111yescharacteristic
446C22×C4D4×D6111yescharacteristic
447C22×C4C23×D6111yescharacteristic
448SD16—2444no—
449C2×C8—21no—
450C2×C8—21no—
451C2×C8—21no—
452C2×C8—21no—
453C2×C8—21no—
454C2×C8—21no—
455C2×C8—612no—
456C2×C8—612no—
457C2×C8—1221no—
458C2×C8—1221no—
459C2×C8—1221no—
460C2×C8—1221no—
461C4⋊C4—21no—
462C4⋊C4—21no—
463C4⋊C4—21no—
464C4⋊C4—21no—
465C4⋊C4—21no—
466C4⋊C4—81no—
467C4⋊C4—1221no—
468C4⋊C4—1221no—
469C4⋊C4—1221no—
470C4⋊C4—1221no—
471C4⋊C4—1221no—
472C4⋊C4—1221no—
473C4⋊C4—4881no—
474C4⋊C4—4881no—
475C4⋊C4—4881no—
476C4⋊C4—4881no—
477C4⋊C4#1175822212yes—
478C22⋊C4—1224no—
479C22⋊C4—4881no—
480C22⋊C4—4881no—
481C22⋊C4—4881no—
482C22⋊C4—4881no—
483C42—21no—
484C42—21no—
485C42—1221no—
486C42—1221no—
487C42—1221no—
488C42—1221no—
489C42—4881no—
490C23—1222no—
491C23—2441no—
492C23—2441no—
493C23—2441no—
494C23—2441no—
495C23—2441no—
496C23—2441no—
497C23C2×D4×D6111yescharacteristic
498Q8—41no—
499Q8—41no—
500Q8—41no—
501Q8—41no—
502D4—1222no—
503D4—1222no—
504D4—2441no—
505D4—2441no—
506C2×C4—22no—
507C2×C4—21no—
508C2×C4—21no—
509C2×C4—21no—
510C2×C4—21no—
511C2×C4—21no—
512C2×C4—21no—
513C2×C4—41no—
514C2×C4—41no—
515C2×C4—41no—
516C2×C4—41no—
517C2×C4—41no—
518C2×C4—41no—
519C2×C4—41no—
520C2×C4—41no—
521C2×C4—41no—
522C2×C4—41no—
523C2×C4—41no—
524C2×C4—1221no—
525C2×C4—1221no—
526C2×C4—1221no—
527C2×C4—1221no—
528C2×C4—1221no—
529C2×C4—1221no—
530C2×C4—1221no—
531C2×C4—1221no—
532C2×C4—1221no—
533C2×C4—1221no—
534C2×C4—1221no—
535C2×C4—1221no—
536C2×C4—4884no—
537C2×C4—2441no—
538C2×C4—2441no—
539C2×C4—2441no—
540C2×C4—2441no—
541C2×C4—2441no—
542C2×C4—2441no—
543C2×C4—2441no—
544C2×C4—2441no—
545C2×C4—2441no—
546C2×C4#41×D6111yescharacteristic
547C2×C4#41×D6111yescharacteristic
548C2×C4#41×D6111yescharacteristic
549C2×C4C2×#1175822211yescharacteristic
550C2×C4#1451982211yescharacteristic
551C2×C4#1451982411yescharacteristic
552C8—41no—
553C8—41no—
554C8—1222no—
555C8—1222no—
556C22—4881no—
557C22—4881no—
558C22—4881no—
559C22—4881no—
560C22—2442no—
561C22—2442no—
562C22—2442no—
563C22#1684027111yescharacteristic
564C22#1684031111yescharacteristic
565C22#1684033911yescharacteristic
566C22#1684056611yescharacteristic
567C22#1684057111yescharacteristic
568C22#1684057111yescharacteristic
569C22#1684057811yescharacteristic
570C4—41no—
571C4—41no—
572C4—42no—
573C4—81no—
574C4—81no—
575C4—81no—
576C4—4881no—
577C4—4881no—
578C4—4881no—
579C4—2441no—
580C4—2441no—
581C4—2441no—
582C4—2441no—
583C4#1684044011yescharacteristic
584C4#1684044811yescharacteristic
585C4#1684046211yescharacteristic
586C4#1684048011yescharacteristic
587C2—4882no—
588C2#2145142311yescharacteristic
589C2#2145600711yescharacteristic
590C2#2145603111yescharacteristic
591C2#2145645011yescharacteristic
592C2#2145645711yescharacteristic
593C2#2145722511yescharacteristic
594C2#2145724011yescharacteristic
subgroupG/H
centerC23C2×D4×D61
commutator, cosocleC22×C4×C61C24
FrattiniC22×C4C23×D61
FittingC61×#1935C2
socleC23×C61C22×D4
prime radicalC22×D244C23
hypercenter#1935D61
hypocenterC61#29441
LCSG ▷ C22×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1935

Complements

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

NH ≅ G/Ntype
1. #21451785C2semidirect
3. #21447323C2semidirect
4. #21447210C2semidirect
8. #21446549C2semidirect
10. #21446463C2semidirect
11. #21446407C2semidirect
14. #21445679C2semidirect
15. C61×#1935C2semidirect
299. #1935D61semidirect
356. C61#29441semidirect

Maximal subgroups

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

subgroupindex
#214517852
#214484582
#214473232
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