Finite Group Databasebeta

← #29837776

Subgroups — #29837776

Order 15616.

494 conjugacy classes of subgroups.

The subgroup lattice has 476 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21458832C211yesmaximal, characteristic, complemented
2#21448062C211yesmaximal, characteristic, complemented
3#21448058C211yesmaximal, characteristic, complemented
4#21448053C211yesmaximal, characteristic, complemented
5#21447980C211yesmaximal, characteristic, complemented
6#21447973C211yesmaximal, characteristic, complemented
7#21447953C211yesmaximal, characteristic, complemented
8#21447874C211yesmaximal, characteristic, complemented
9#21447874C211yesmaximal, characteristic, complemented
10#21447854C211yesmaximal, characteristic
11#21447728C211yesmaximal, characteristic, complemented
12#21447693C211yesmaximal, characteristic, complemented
13#21447683C211yesmaximal, characteristic, complemented
14C4×#14519718C211yesmaximal, characteristic, complemented
15C61×#3380C211yesmaximal, characteristic, complemented
16#16840497—21no—
17C2×#14519721C2211yescharacteristic
18C2×#14519718C2211yescharacteristic
19C2×#14519718C2211yescharacteristic
20#16840146C2211yescharacteristic
21#16840146C2211yescharacteristic
22#16840139C2211yescharacteristic
23#16839978—21no—
24#16839978—21no—
25#16839963—21no—
26C4×Dic244C2211yescharacteristic
27C4×D488C2211yescharacteristic
28C4×D488C2211yescharacteristic
29#16839589C2211yescharacteristic
30#16839587C2211yescharacteristic
31#16839587C2211yescharacteristic
32C4⋊#11758185C2211yescharacteristic
33C4⋊#11758185C2211yescharacteristic
34C4⋊#11758185C2211yescharacteristic
35#16839565C2211yescharacteristic
36#16839565C2211yescharacteristic
37#16839565C2211yescharacteristic
38#16839563C2211yescharacteristic
39#16839562C2211yescharacteristic
40#16839562C2211yescharacteristic
41#16839562C2211yescharacteristic
42#16839562C2211yescharacteristic
43#16839562C2211yescharacteristic
44#16839562C2211yescharacteristic
45#16839538C2211yescharacteristic
46#16839538C2211yescharacteristic
47C4×#11758185C2211yescharacteristic
48C61×#554—21no—
49C61×#500C2211yescharacteristic
50C61×#499C2211yescharacteristic
51C61×#499C2211yescharacteristic
52C61×#478—21no—
53C61×#478—21no—
54C61×#476—21no—
55C8×Q8×C61C2211yescharacteristic
56C4×D8×C61C2211yescharacteristic
57C4×D8×C61C2211yescharacteristic
58C4×D8×C61C2211yescharacteristic
59C2×Dic244C2311yescharacteristic
60C2×#11758190—21no—
61C2×#11758190—21no—
62C2×D488—21no—
63C2×D488C2311yescharacteristic
64C2×D488C2311yescharacteristic
65#14519774—21no—
66#14519766—41no—
67#14519765—21no—
68#14519765—21no—
69#14519762—41no—
70#14519762—41no—
71C4×Dic122—21no—
72C4×D244—21no—
73C4×D244—21no—
74#14519739—41no—
75#14519721—22no—
76#14519718—22no—
77#14519718—22no—
78C2×#11758185C2311yescharacteristic
79C2×#11758185C2311yescharacteristic
80C2×#11758185C2311yescharacteristic
81C2×#11758185C2311yescharacteristic
82#14519711C2311yescharacteristic
83#14519702—21no—
84#14519699—21no—
85#14519699—21no—
86C2×D8×C61C2311yescharacteristic
87C4⋊Q8×C61—21no—
88#125×C61—21no—
89#125×C61—21no—
90C22⋊Q8×C61—41no—
91C22⋊Q8×C61—41no—
92C22⋊Q8×C61—41no—
93C4×Q8×C61D411yescharacteristic
94C4×D4×C61—21no—
95C4×D4×C61—21no—
96C4×D4×C61—21no—
97C2×C4⋊C4×C61—41no—
98#107×C61—21no—
99#107×C61C2311yescharacteristic
100#107×C61C2311yescharacteristic
101#107×C61C2311yescharacteristic
102#106×C61—21no—
103#106×C61—21no—
104C4⋊C8×C61D411yescharacteristic
105C4⋊C8×C61D411yescharacteristic
106C4⋊C8×C61D411yescharacteristic
107#102×C61—21no—
108#102×C61—21no—
109#102×C61—21no—
110C4×C8×C61C2311yescharacteristic
111C4×C8×C61C2311yescharacteristic
112C4×C8×C61C2311yescharacteristic
113C2×Q8×C61—41no—
114C2×Q8×C61D811yescharacteristic
115C2×D4×C61—21no—
116C22×C4×C61—41no—
117C22×C4×C61—41no—
118C22×C4×C61—41no—
119C2×D244—21no—
120C2×D244—21no—
121C2×D244—41no—
122C2×D244—41no—
123C2×C4×D61—41no—
124C2×C4×D61—41no—
125C2×Dic122—21no—
126D8×C61—21no—
127D8×C61#4112yes—
128C2×C8×C61C2×D411yescharacteristic
129C2×C8×C61C2×D411yescharacteristic
130C2×C8×C61C2×D411yescharacteristic
131C2×C8×C61C2411yescharacteristic
132C4⋊C4×C61—21no—
133C4⋊C4×C61—21no—
134C4⋊C4×C61—21no—
135C4⋊C4×C61—41no—
136C4⋊C4×C61—41no—
137C4⋊C4×C61—41no—
138C4⋊C4×C61—41no—
139C4⋊C4×C61—41no—
140C4⋊C4×C61D811yescharacteristic
141C4⋊C4×C61D811yescharacteristic
142C4⋊C4×C61D811yescharacteristic
143C22⋊C4×C61—41no—
144C22⋊C4×C61—41no—
145C22⋊C4×C61—41no—
146C42×C61C2×D411yescharacteristic
147C42×C61C2×D411yescharacteristic
148C42×C61C2×D411yescharacteristic
149#11758198—41no—
150#11758198—41no—
151#11758198—41no—
152#11758198—41no—
153#11758198—41no—
154#11758198—41no—
155C4⋊Dic61—21no—
156#11758196—41no—
157C4×Dic61—41no—
158Dic244—21no—
159Dic244—21no—
160D488—21no—
161D488—21no—
162D488—21no—
163D488—21no—
164D488—81no—
165#11758190—81no—
166#11758190—81no—
167#11758185—21no—
168#11758185—21no—
169#11758185—21no—
170#11758185—21no—
171C23×C61—41no—
172C22×D61—41no—
173C22×D61—41no—
174Q8×C61—41no—
175Q8×C61—161no—
176D4×C61—22no—
177D4×C61—41no—
178C2×C4×C61—41no—
179C2×C4×C61—41no—
180C2×C4×C61—41no—
181C2×C4×C61—82no—
182C2×C4×C61—161no—
183C2×C4×C61—161no—
184C2×C4×C61C2×D811yescharacteristic
185C2×C4×C61C2×D811yescharacteristic
186C2×C4×C61C2×D811yescharacteristic
187C2×C4×C61C2×D811yescharacteristic
188C2×C4×C61C2×D811yescharacteristic
189C2×C4×C61C2×D811yescharacteristic
190C2×C4×C61C22×D411yescharacteristic
191C2×Dic61—41no—
192C2×Dic61—41no—
193D244—41no—
194D244—41no—
195D244—41no—
196D244—41no—
197D244—82no—
198D244—161no—
199C4×D61—161no—
200C4×D61—161no—
201Dic122—41no—
202Dic122—41no—
203C8×C61—21no—
204C8×C61—21no—
205C8×C61—21no—
206C8×C61C2×#4111yescharacteristic
207C8×C612−1+411yescharacteristic
208#33937—611nomaximal, Sylow
209C22×C61—42no—
210C22×C61—81no—
211C22×C61—81no—
212C22×C61C22×D811yescharacteristic
213C2×D61—81no—
214C2×D61—81no—
215C2×D61—81no—
216C2×D61—81no—
217C2×D61—81no—
218C2×D61—81no—
219C4×C61—21no—
220C4×C61—21no—
221C4×C61—21no—
222C4×C61—21no—
223C4×C61—21no—
224C4×C61—21no—
225C4×C61—81no—
226C4×C61—81no—
227C4×C61—81no—
228C4×C61#54811yescharacteristic
229C4×C61#57711yescharacteristic
230Dic61—81no—
231Dic61—81no—
232#3396—611no—
233#3380D6111yescharacteristic, complemented
234#2244—611no—
235#2243—611no—
236#2242—611no—
237#2229—611no—
238#2228—611no—
239#2224—611no—
240#2210—611no—
241#2210—611no—
242#2206—611no—
243#2183—611no—
244#2177—611no—
245#2175—611no—
246C4×D16—611no—
247C2×C61—82no—
248C2×C61#335811yescharacteristic
249C2×C61#341411yescharacteristic
250C2×C61#341511yescharacteristic
251D61—161no—
252D61—161no—
253#559—1221no—
254#554—21no—
255C2×SD32—611no—
256C2×D16—611no—
257C2×D16—611no—
258#500C2×D6111yescharacteristic
259#499C2×D6111yescharacteristic
260#499C2×D6111yescharacteristic
261#495—611no—
262#495—611no—
263#493—611no—
264#478—21no—
265#478—21no—
266#476—21no—
267#463—1221no—
268#463—1221no—
269#460—1221no—
270C8×Q8C2×D6111yescharacteristic
271C4×Q16—611no—
272C4×D8—611no—
273C4×D8—611no—
274C4×D8C2×D6111yescharacteristic
275C4×D8C2×D6111yescharacteristic
276C4×D8C2×D6111yescharacteristic
277#367—611no—
278#366—611no—
279#366—611no—
280C4⋊C16—611no—
281C4⋊C16—611no—
282C4⋊C16—611no—
283#358—611no—
284#358—611no—
285#358—611no—
286#357—611no—
287#357—611no—
288#357—611no—
289#357—611no—
290#357—611no—
291#357—611no—
292#357—611no—
293#346—611no—
294#346—611no—
295C4×C16—611no—
296C61#3393711yescharacteristic, complemented, Sylow
297C2×Q16—611no—
298C2×SD16—1221no—
299C2×SD16—1221no—
300C2×D8—611no—
301C2×D8—611no—
302C2×D8—1221no—
303C2×D8C22×D6111yescharacteristic
304C4⋊Q8—21no—
305#127—1221no—
306#125—21no—
307#125—21no—
308#124—1221no—
309#124—1221no—
310#124—2441no—
311#123—2441no—
312#123—2441no—
313C22⋊Q8—41no—
314C22⋊Q8—41no—
315C22⋊Q8—41no—
316C4×Q8—1221no—
317C4×Q8C22⋊D6111yescharacteristic
318C4×D4—21no—
319C4×D4—21no—
320C4×D4—21no—
321C4×D4—1221no—
322C4×D4—1221no—
323C4×D4—2441no—
324C2×C4⋊C4—41no—
325SD32—1222no—
326D16—1222no—
327D16—1222no—
328C2×C16—611no—
329C2×C16—611no—
330C2×C16—611no—
331C2×C16—611no—
332#107—21no—
333#107—611no—
334#107C22×D6111yescharacteristic
335#107C22×D6111yescharacteristic
336#107C22×D6111yescharacteristic
337#106—21no—
338#106—21no—
339C4⋊C8C22⋊D6111yescharacteristic
340C4⋊C8C22⋊D6111yescharacteristic
341C4⋊C8C22⋊D6111yescharacteristic
342#103—1221no—
343#102—21no—
344#102—21no—
345#102—21no—
346#102—1221no—
347#102—1221no—
348C4×C8C22×D6111yescharacteristic
349C4×C8C22×D6111yescharacteristic
350C4×C8C22×D6111yescharacteristic
351C2×Q8—41no—
352C2×Q8—1221no—
353C2×Q8#1175819911yescharacteristic
354C2×D4—21no—
355C2×D4—1221no—
356C2×D4—1221no—
357C2×D4—2441no—
358C2×D4—2441no—
359C22×C4—41no—
360C22×C4—41no—
361C22×C4—41no—
362C22×C4—2441no—
363C22×C4—2441no—
364Q16—1221no—
365Q16—1221no—
366SD16—4881no—
367SD16—4881no—
368D8—21no—
369D8—1221no—
370D8—1221no—
371D8—1221no—
372D8—1221no—
373D8—4881no—
374D8#1175822612yes—
375C2×C8C2×C22⋊D6111yescharacteristic
376C2×C8C2×C22⋊D6111yescharacteristic
377C2×C8C2×C22⋊D6111yescharacteristic
378C2×C8C23×D6111yescharacteristic
379C4⋊C4—21no—
380C4⋊C4—21no—
381C4⋊C4—21no—
382C4⋊C4—41no—
383C4⋊C4—41no—
384C4⋊C4—41no—
385C4⋊C4—41no—
386C4⋊C4—41no—
387C4⋊C4—1221no—
388C4⋊C4—2441no—
389C4⋊C4#1175819911yescharacteristic
390C4⋊C4#1175819911yescharacteristic
391C4⋊C4#1175819911yescharacteristic
392C22⋊C4—41no—
393C22⋊C4—41no—
394C22⋊C4—41no—
395C22⋊C4—2441no—
396C22⋊C4—2441no—
397C22⋊C4—2441no—
398C22⋊C4—2441no—
399C22⋊C4—2441no—
400C22⋊C4—2441no—
401C42—2441no—
402C42C2×C22⋊D6111yescharacteristic
403C42C2×C22⋊D6111yescharacteristic
404C42C2×C22⋊D6111yescharacteristic
405C16—1221no—
406C16—1221no—
407C16—1221no—
408C16—1221no—
409C23—41no—
410C23—2441no—
411C23—2441no—
412Q8—41no—
413Q8—161no—
414Q8—2441no—
415Q8—2441no—
416D4—22no—
417D4—41no—
418D4—9761no—
419D4—4882no—
420D4—2441no—
421D4—2441no—
422D4—2441no—
423D4—2441no—
424C2×C4—41no—
425C2×C4—41no—
426C2×C4—41no—
427C2×C4—82no—
428C2×C4—161no—
429C2×C4—161no—
430C2×C4—9761no—
431C2×C4—9761no—
432C2×C4—2441no—
433C2×C4—2441no—
434C2×C4C2×#1175819911yescharacteristic
435C2×C4C2×#1175819911yescharacteristic
436C2×C4C2×#1175819911yescharacteristic
437C2×C4C2×#1175819911yescharacteristic
438C2×C4C2×#1175819911yescharacteristic
439C2×C4C2×#1175819911yescharacteristic
440C2×C4C22×C22⋊D6111yescharacteristic
441C8—21no—
442C8—21no—
443C8—21no—
444C8C2×#1175822611yescharacteristic
445C8#1451982511yescharacteristic
446C22—42no—
447C22—81no—
448C22—81no—
449C22—4881no—
450C22—4881no—
451C22—4881no—
452C22—4881no—
453C22—4881no—
454C22—4881no—
455C22C22×#1175819911yescharacteristic
456C4—21no—
457C4—21no—
458C4—21no—
459C4—21no—
460C4—21no—
461C4—21no—
462C4—81no—
463C4—81no—
464C4—81no—
465C4—4881no—
466C4—4881no—
467C4#1684042311yescharacteristic
468C4#1684057011yescharacteristic
469C2—82no—
470C2—9761no—
471C2—9761no—
472C2#2145845411yescharacteristic
473C2#2145895311yescharacteristic
474C2#2145895811yescharacteristic
subgroupG/H
centerC22C22×#11758199
commutator, cosocleC2×C8×C61C24
FrattiniC2×C8C23×D61
FittingC61×#3380C2
socleC22×C61C22×D8
prime radical#21447854C2
hypercenter#3380D61
hypocenterC61#33937
LCSG ▷ C2×C8×C61 ▷ C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C4×Q8 ◁ C8×Q8 ◁ #3380

Complements

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

NH ≅ G/Ntype
1. #21458832C2semidirect
2. #21448062C2semidirect
3. #21448058C2semidirect
4. #21448053C2semidirect
5. #21447980C2semidirect
6. #21447973C2semidirect
7. #21447953C2semidirect
8. #21447874C2semidirect
9. #21447874C2semidirect
11. #21447728C2semidirect
12. #21447693C2semidirect
13. #21447683C2semidirect
14. C4×#14519718C2semidirect
15. C61×#3380C2semidirect
233. #3380D61semidirect
296. C61#33937semidirect

Maximal subgroups

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

subgroupindex
#214588322
#214480622
#214480582
#214480532
#214479802
#214479732
#214479532
#214478742
#214478542
#214477282
#214476932
#214476832
C4×#145197182
C61×#33802
#3393761