Finite Group Databasebeta

← #29783257

Subgroups — #29783257

Order 15616.

660 conjugacy classes of subgroups.

The subgroup lattice has 594 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21451779C211yesmaximal, characteristic
2#21447321C211yesmaximal, characteristic, complemented
3#21447214C211yesmaximal, characteristic, complemented
4#21447204C211yesmaximal, characteristic
5#21447134C211yesmaximal, characteristic
6#21446676C211yesmaximal, characteristic
7#21446549C211yesmaximal, characteristic, complemented
8#21446515C211yesmaximal, characteristic
9#21446512C211yesmaximal, characteristic, complemented
10#21446439C211yesmaximal, characteristic
11#21446397C211yesmaximal, characteristic, complemented
12#21446174C211yesmaximal, characteristic
13#21446073C211yesmaximal, characteristic, complemented
14#21445676C211yesmaximal, characteristic, complemented
15C61×#2320C211yesmaximal, characteristic, complemented
16C22×#11758201C2211yescharacteristic
17C2×#14519710C2211yescharacteristic
18C2×#14519710C2211yescharacteristic
19C2×#14519708C2211yescharacteristic
20C2×C4⋊#92418C2211yescharacteristic
21C2×C4⋊#92418C2211yescharacteristic
22C2×#14519701C2211yescharacteristic
23C2×#14519701C2211yescharacteristic
24C2×#14519701C2211yescharacteristic
25C2×#14519697C2211yescharacteristic
26C2×#14519697C2211yescharacteristic
27C2×#14519697C2211yescharacteristic
28C2×#14519688C2211yescharacteristic
29C2×C4×#92418C2211yescharacteristic
30#16839691—21no—
31#16839691—21no—
32#16839691—21no—
33#16839686—21no—
34#16839664C2211yescharacteristic
35#16839664C2211yescharacteristic
36#16839664C2211yescharacteristic
37#16839660C2211yescharacteristic
38#16839660C2211yescharacteristic
39#16839660C2211yescharacteristic
40#16839524C2211yescharacteristic
41#16839524C2211yescharacteristic
42#16839524C2211yescharacteristic
43#16839524C2211yescharacteristic
44#16839524C2211yescharacteristic
45#16839524C2211yescharacteristic
46#16839517C2211yescharacteristic
47#16839517C2211yescharacteristic
48C2×C4×Q8×C61C2211yescharacteristic
49C61×#391C2211yescharacteristic
50C61×#391C2211yescharacteristic
51C61×#389C2211yescharacteristic
52C61×#389C2211yescharacteristic
53C61×#387—21no—
54C61×#387—21no—
55C61×#383—21no—
56C61×#382—21no—
57C4×C4⋊C4×C61C2211yescharacteristic
58C61×#376C2211yescharacteristic
59C22×D244C2311yescharacteristic
60C2×#11758201—22no—
61C2×#11758201—22no—
62C2×#11758201—41no—
63C22×#92418C2311yescharacteristic
64C22×#92418C2311yescharacteristic
65C22×#92418C2311yescharacteristic
66C22×#92418C2311yescharacteristic
67C2×C4⋊Dic61C2311yescharacteristic
68C2×C4⋊Dic61C2311yescharacteristic
69C2×C4⋊Dic61C2311yescharacteristic
70C2×#11758196—21no—
71C2×#11758196—21no—
72C2×#11758196—21no—
73C2×#11758198—21no—
74C2×#11758198—21no—
75C2×#11758198—21no—
76C2×#11758198—21no—
77C2×#11758198—21no—
78C2×#11758198—21no—
79#14519710—22no—
80#14519710—41no—
81#14519708—22no—
82C4⋊#92418—22no—
83C4⋊#92418—22no—
84#14519701—22no—
85#14519701—22no—
86#14519701—41no—
87#14519697—22no—
88#14519697—22no—
89#14519697—41no—
90#14519688—41no—
91C4×#92418—41no—
92#14519684—21no—
93#14519684—21no—
94#14519684—21no—
95C22×Q8×C61C2311yescharacteristic
96C4×Q8×C61—22no—
97C4×Q8×C61—22no—
98C2×C4⋊C4×C61—21no—
99C2×C4⋊C4×C61—21no—
100C2×C4⋊C4×C61—21no—
101C2×C4⋊C4×C61C2311yescharacteristic
102C2×C4⋊C4×C61C2311yescharacteristic
103C2×C4⋊C4×C61C2311yescharacteristic
104C2×C42×C61—21no—
105C2×C42×C61—21no—
106C2×C42×C61C2311yescharacteristic
107C2×C42×C61C2311yescharacteristic
108C2×C42×C61C2311yescharacteristic
109#95×C61—21no—
110#95×C61—21no—
111#95×C61—21no—
112#95×C61—21no—
113#95×C61—21no—
114#95×C61—21no—
115#95×C61—21no—
116#95×C61D411yescharacteristic
117#95×C61D411yescharacteristic
118#95×C61D411yescharacteristic
119#95×C61D411yescharacteristic
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#4112yes—
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×C61C2×D411yescharacteristic
134C22×C4×C61C2×D411yescharacteristic
135C22×C4×C61C2×D411yescharacteristic
136C22×C4×C61C2×D411yescharacteristic
137C22×C4×C61C2411yescharacteristic
138C22×Dic61—21no—
139C22×Dic61—21no—
140C22×Dic61—21no—
141C2×D244—21no—
142C2×D244—21no—
143C2×D244—21no—
144C2×D244—21no—
145C2×D244—21no—
146C2×D244—21no—
147C4⋊C4×C61—24no—
148C4⋊C4×C61—21no—
149C4⋊C4×C61—21no—
150C4⋊C4×C61—21no—
151C4⋊C4×C61—21no—
152C4⋊C4×C61—21no—
153C4⋊C4×C61—81no—
154C4⋊C4×C61—81no—
155C4⋊C4×C61#4112yes—
156C42×C61—24no—
157C42×C61—21no—
158C42×C61—21no—
159C42×C61—21no—
160C42×C61—21no—
161C42×C61—21no—
162C42×C61—21no—
163C42×C61—81no—
164#11758201—44no—
165#11758198—81no—
166#11758198—81no—
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—
177#11758196—81no—
178#11758196—81no—
179#11758196—81no—
180C2×#92418—21no—
181C2×#92418—21no—
182C2×#92418—21no—
183C2×#92418—21no—
184C2×#92418—21no—
185C2×#92418—21no—
186C2×#92418—21no—
187C2×#92418—21no—
188C2×#92418—21no—
189C2×#92418—21no—
190C2×#92418#4112yes—
191C2×#92418#4112yes—
192C23×C61C22×D411yescharacteristic
193C22×D61—41no—
194C22×D61—41no—
195C22×D61—41no—
196C22×D61—41no—
197C22×D61—41no—
198C22×D61—41no—
199C22×D61—41no—
200Q8×C61—22no—
201Q8×C61—22no—
202Q8×C61—41no—
203Q8×C61—41no—
204C2×C4×C61—21no—
205C2×C4×C61—21no—
206C2×C4×C61—22no—
207C2×C4×C61—22no—
208C2×C4×C61—21no—
209C2×C4×C61—21no—
210C2×C4×C61—21no—
211C2×C4×C61—21no—
212C2×C4×C61—21no—
213C2×C4×C61—21no—
214C2×C4×C61—21no—
215C2×C4×C61—21no—
216C2×C4×C61—21no—
217C2×C4×C61—21no—
218C2×C4×C61—21no—
219C2×C4×C61—21no—
220C2×C4×C61—21no—
221C2×C4×C61—21no—
222C2×C4×C61—21no—
223C2×C4×C61—21no—
224C2×C4×C61—41no—
225C2×C4×C61—41no—
226C2×C4×C61—41no—
227C2×C4×C61—41no—
228C2×C4×C61—41no—
229C2×C4×C61—41no—
230C2×C4×C61—41no—
231C2×C4×C61—41no—
232C2×C4×C61—41no—
233C2×C4×C61—41no—
234C2×C4×C61C2×#4111yescharacteristic
235C2×C4×C61C2×#4111yescharacteristic
236C2×C4×C61C2×#4111yescharacteristic
237C2×C4×C61C2×#4111yescharacteristic
238C2×C4×C61H(5,𝔽2)11yescharacteristic
239C2×C4×C612−1+411yescharacteristic
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—41no—
250D244—41no—
251D244—41no—
252D244—41no—
253#92418—22no—
254#92418—22no—
255#92418—41no—
256#92418—41no—
257#29443—611nomaximal, Sylow
258C22×C61#52511yescharacteristic
259C22×C61#53211yescharacteristic
260C22×C61#53711yescharacteristic
261C22×C61#57611yescharacteristic
262C22×C61#57711yescharacteristic
263C22×C61#57711yescharacteristic
264C22×C61#57811yescharacteristic
265C2×D61—81no—
266C2×D61—81no—
267C2×D61—81no—
268C2×D61—81no—
269C2×D61—81no—
270C2×D61—81no—
271C2×D61—81no—
272C4×C61—42no—
273C4×C61—41no—
274C4×C61—42no—
275C4×C61—41no—
276C4×C61—41no—
277C4×C61—41no—
278C4×C61—41no—
279C4×C61—41no—
280C4×C61—81no—
281C4×C61—81no—
282C4×C61#55111yescharacteristic
283C4×C61#55211yescharacteristic
284C4×C61#55311yescharacteristic
285C4×C61#55611yescharacteristic
286Dic61—81no—
287Dic61—81no—
288Dic61—81no—
289#2644—611no—
290#2320D6111yescharacteristic, complemented
291#2088—611no—
292#2068—611no—
293#2067—611no—
294#2055—611no—
295#1968—611no—
296#1942—611no—
297#1936—611no—
298#1935—611no—
299#1925—611no—
300#1919—611no—
301#1880—611no—
302#1863—611no—
303#1768—611no—
304C2×C61#260111yescharacteristic
305C2×C61#311911yescharacteristic
306C2×C61#312111yescharacteristic
307C2×C61#317411yescharacteristic
308C2×C61#317511yescharacteristic
309C2×C61#325711yescharacteristic
310C2×C61#325811yescharacteristic
311D61—161no—
312C22×SD16—611no—
313C2×C4×Q8C2×D6111yescharacteristic
314C2×#107—611no—
315C2×#107—611no—
316C2×#106—611no—
317C2×C4⋊C8—611no—
318C2×C4⋊C8—611no—
319C2×#103—611no—
320C2×#103—611no—
321C2×#103—611no—
322C2×#102—611no—
323C2×#102—611no—
324C2×#102—611no—
325C2×#97—611no—
326C2×C4×C8—611no—
327#397—1221no—
328#397—1221no—
329#397—1221no—
330#396—1221no—
331#391C2×D6111yescharacteristic
332#391C2×D6111yescharacteristic
333#390—611no—
334#390—611no—
335#390—611no—
336#389—611no—
337#389—611no—
338#389—611no—
339#389C2×D6111yescharacteristic
340#389C2×D6111yescharacteristic
341#387—21no—
342#387—21no—
343#383—21no—
344#382—21no—
345C4×C4⋊C4C2×D6111yescharacteristic
346#376C2×D6111yescharacteristic
347#340—611no—
348#340—611no—
349#340—611no—
350#340—611no—
351#340—611no—
352#340—611no—
353#336—611no—
354#336—611no—
355C61#2944311yescharacteristic, complemented, Sylow
356C22×Q8C22×D6111yescharacteristic
357C22×D4—611no—
358C2×SD16—1222no—
359C2×SD16—1222no—
360C2×SD16—2441no—
361C22×C8—611no—
362C22×C8—611no—
363C22×C8—611no—
364C22×C8—611no—
365C4×Q8—22no—
366C4×Q8—22no—
367C2×C4⋊C4—21no—
368C2×C4⋊C4—21no—
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⋊C4C22×D6111yescharacteristic
377C2×C4⋊C4C22×D6111yescharacteristic
378C2×C4⋊C4C22×D6111yescharacteristic
379C2×C22⋊C4—1221no—
380C2×C22⋊C4—1221no—
381C2×C22⋊C4—1221no—
382C2×C22⋊C4—1221no—
383C2×C22⋊C4—1221no—
384C2×C22⋊C4—1221no—
385C2×C42—21no—
386C2×C42—21no—
387C2×C42C22×D6111yescharacteristic
388C2×C42C22×D6111yescharacteristic
389C2×C42C22×D6111yescharacteristic
390#107—1222no—
391#107—2441no—
392#106—1222no—
393C4⋊C8—1222no—
394C4⋊C8—1222no—
395#103—1222no—
396#103—1222no—
397#103—2441no—
398#102—1222no—
399#102—1222no—
400#102—2441no—
401#97—2441no—
402C4×C8—2441no—
403#95—21no—
404#95—21no—
405#95—21no—
406#95—21no—
407#95—21no—
408#95—21no—
409#95—21no—
410#95—1221no—
411#95—1221no—
412#95—1221no—
413#95C22⋊D6111yescharacteristic
414#95C22⋊D6111yescharacteristic
415#95C22⋊D6111yescharacteristic
416#95C22⋊D6111yescharacteristic
417C24—1221no—
418C2×Q8—21no—
419C2×Q8—21no—
420C2×Q8—21no—
421C2×Q8—21no—
422C2×Q8—21no—
423C2×Q8#1175822212yes—
424C2×D4—1221no—
425C2×D4—1221no—
426C2×D4—1221no—
427C2×D4—1221no—
428C2×D4—1221no—
429C2×D4—1221no—
430C22×C4—21no—
431C22×C4—21no—
432C22×C4—21no—
433C22×C4—21no—
434C22×C4—1221no—
435C22×C4—1221no—
436C22×C4—1221no—
437C22×C4C2×C22⋊D6111yescharacteristic
438C22×C4C2×C22⋊D6111yescharacteristic
439C22×C4C2×C22⋊D6111yescharacteristic
440C22×C4C2×C22⋊D6111yescharacteristic
441C22×C4C2×C22⋊D6111yescharacteristic
442C22×C4C2×C22⋊D6111yescharacteristic
443C22×C4C23×D6111yescharacteristic
444SD16—2444no—
445C2×C8—612no—
446C2×C8—612no—
447C2×C8—1221no—
448C2×C8—1221no—
449C2×C8—1221no—
450C2×C8—1221no—
451C2×C8—1221no—
452C2×C8—1221no—
453C2×C8—1221no—
454C2×C8—1221no—
455C2×C8—1221no—
456C2×C8—1221no—
457C4⋊C4—24no—
458C4⋊C4—21no—
459C4⋊C4—21no—
460C4⋊C4—21no—
461C4⋊C4—21no—
462C4⋊C4—21no—
463C4⋊C4—81no—
464C4⋊C4—81no—
465C4⋊C4—1221no—
466C4⋊C4—1221no—
467C4⋊C4—1221no—
468C4⋊C4—1221no—
469C4⋊C4—1221no—
470C4⋊C4—1221no—
471C4⋊C4—4881no—
472C4⋊C4—4881no—
473C4⋊C4—4881no—
474C4⋊C4#1175822212yes—
475C22⋊C4—4881no—
476C22⋊C4—4881no—
477C22⋊C4—4881no—
478C22⋊C4—4881no—
479C22⋊C4—4881no—
480C22⋊C4—4881no—
481C42—24no—
482C42—21no—
483C42—21no—
484C42—21no—
485C42—21no—
486C42—21no—
487C42—21no—
488C42—81no—
489C23—2441no—
490C23—2441no—
491C23—2441no—
492C23—2441no—
493C23—2441no—
494C23—2441no—
495C23—2441no—
496C23C22×C22⋊D6111yescharacteristic
497Q8—22no—
498Q8—22no—
499Q8—41no—
500Q8—41no—
501D4—2441no—
502D4—2441no—
503D4—2441no—
504D4—2441no—
505C2×C4—21no—
506C2×C4—21no—
507C2×C4—22no—
508C2×C4—22no—
509C2×C4—21no—
510C2×C4—21no—
511C2×C4—21no—
512C2×C4—21no—
513C2×C4—21no—
514C2×C4—21no—
515C2×C4—21no—
516C2×C4—21no—
517C2×C4—21no—
518C2×C4—21no—
519C2×C4—21no—
520C2×C4—21no—
521C2×C4—21no—
522C2×C4—21no—
523C2×C4—21no—
524C2×C4—21no—
525C2×C4—41no—
526C2×C4—41no—
527C2×C4—41no—
528C2×C4—41no—
529C2×C4—41no—
530C2×C4—41no—
531C2×C4—41no—
532C2×C4—41no—
533C2×C4—41no—
534C2×C4—41no—
535C2×C4—2441no—
536C2×C4—2441no—
537C2×C4—2441no—
538C2×C4—2441no—
539C2×C4—2441no—
540C2×C4—2441no—
541C2×C4—2441no—
542C2×C4—2441no—
543C2×C4—2441no—
544C2×C4#41×D6111yescharacteristic
545C2×C4#41×D6111yescharacteristic
546C2×C4C2×#1175822211yescharacteristic
547C2×C4C2×#1175822211yescharacteristic
548C2×C4#1451982311yescharacteristic
549C2×C4#1451982411yescharacteristic
550C8—1222no—
551C8—1222no—
552C8—2441no—
553C8—2441no—
554C22—4881no—
555C22—4881no—
556C22—4881no—
557C22—4881no—
558C22—4881no—
559C22—4881no—
560C22—4881no—
561C22#1684027311yescharacteristic
562C22#1684030811yescharacteristic
563C22#1684034011yescharacteristic
564C22#1684056511yescharacteristic
565C22#1684057011yescharacteristic
566C22#1684057011yescharacteristic
567C22#1684057711yescharacteristic
568C4—41no—
569C4—41no—
570C4—41no—
571C4—41no—
572C4—41no—
573C4—42no—
574C4—42no—
575C4—41no—
576C4—81no—
577C4—81no—
578C4—4881no—
579C4—4881no—
580C4—4881no—
581C4#1684043611yescharacteristic
582C4#1684044511yescharacteristic
583C4#1684045611yescharacteristic
584C4#1684048011yescharacteristic
585C2—9761no—
586C2#2145141611yescharacteristic
587C2#2145601811yescharacteristic
588C2#2145604811yescharacteristic
589C2#2145644811yescharacteristic
590C2#2145645211yescharacteristic
591C2#2145723011yescharacteristic
592C2#2145723911yescharacteristic
subgroupG/H
centerC23C22×C22⋊D61
commutator, cosocleC22×C4×C61C24
FrattiniC22×C4C23×D61
FittingC61×#2320C2
socleC23×C61C22×D4
prime radicalC22×D244C23
hypercenter#2320D61
hypocenterC61#29443
LCSG ▷ C22×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ #376 ◁ #2320

Complements

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

NH ≅ G/Ntype
2. #21447321C2semidirect
3. #21447214C2semidirect
7. #21446549C2semidirect
9. #21446512C2semidirect
11. #21446397C2semidirect
13. #21446073C2semidirect
14. #21445676C2semidirect
15. C61×#2320C2semidirect
290. #2320D61semidirect
355. C61#29443semidirect

Maximal subgroups

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

subgroupindex
#214517792
#214473212
#214472142
#214472042
#214471342
#214466762
#214465492
#214465152
#214465122
#214464392
#214463972
#214461742
#214460732
#214456762
C61×#23202
#2944361