Finite Group Databasebeta

← #21457073

Subgroups — #21457073

Order 7808.

332 conjugacy classes of subgroups.

The subgroup lattice has 332 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#16840389C211yesmaximal, characteristic, complemented
2#16840368C211yesmaximal, characteristic
3#16840161C211yesmaximal, characteristic, complemented
4#16840127C211yesmaximal, characteristic, complemented
5#16840110C211yesmaximal, characteristic, complemented
6#16840089C211yesmaximal, characteristic, complemented
7#16840088C211yesmaximal, characteristic, complemented
8#16840082C211yesmaximal, characteristic, complemented
9#16840077C211yesmaximal, characteristic, complemented
10#16840065C211yesmaximal, characteristic, complemented
11#16840061C211yesmaximal, characteristic, complemented
12#16840051C211yesmaximal, characteristic, complemented
13#16840041C211yesmaximal, characteristic, complemented
14#16839824C211yesmaximal, characteristic, complemented
15C61×#501C211yesmaximal, characteristic, complemented
16#14519776C2211yescharacteristic
17#14519775—21no—
18#14519774C2211yescharacteristic
19#14519769C2211yescharacteristic
20#14519768C2211yescharacteristic
21#14519767—21no—
22#14519762—21no—
23#14519762—21no—
24#14519755—21no—
25#14519753—21no—
26#14519752—21no—
27#14519752—21no—
28#14519752C2211yescharacteristic
29#14519752C2211yescharacteristic
30#14519739C2211yescharacteristic
31#14519739C2211yescharacteristic
32#14519735C2211yescharacteristic
33#14519734C2211yescharacteristic
34C4⋊C4×D61C2211yescharacteristic
35#14519710C2211yescharacteristic
36#14519710C2211yescharacteristic
37#14519708C2211yescharacteristic
38#14519708C2211yescharacteristic
39#14519706C2211yescharacteristic
40#14519706C2211yescharacteristic
41#14519699C2211yescharacteristic
42#14519699C2211yescharacteristic
43#14519699C2211yescharacteristic
44#14519699C2211yescharacteristic
45#14519697C2211yescharacteristic
46#14519697C2211yescharacteristic
47#14519697C2211yescharacteristic
48#14519697C2211yescharacteristic
49#14519689C2211yescharacteristic
50#14519689C2211yescharacteristic
51C4×#92418C2211yescharacteristic
52C4⋊Q8×C61C2211yescharacteristic
53#125×C61C2211yescharacteristic
54#107×C61C2211yescharacteristic
55#107×C61C2211yescharacteristic
56#106×C61C2211yescharacteristic
57#106×C61C2211yescharacteristic
58#97×C61C2211yescharacteristic
59C2×Q8×C61—21no—
60C2×D244—21no—
61C2×D244—21no—
62C2×D244—21no—
63C2×D244—21no—
64C2×D244C2311yescharacteristic
65C2×D244C2311yescharacteristic
66C2×C4×D61—21no—
67C2×C4×D61—21no—
68C2×C4×D61—21no—
69C2×C4×D61C2311yescharacteristic
70C2×Dic122—21no—
71C2×C8×C61C2311yescharacteristic
72C2×C8×C61C2311yescharacteristic
73C4⋊C4×C61—21no—
74C4⋊C4×C61—21no—
75C4⋊C4×C61—21no—
76C4⋊C4×C61C2311yescharacteristic
77C4⋊C4×C61C2311yescharacteristic
78C4⋊C4×C61C2311yescharacteristic
79C4⋊C4×C61C2311yescharacteristic
80C42×C61C2311yescharacteristic
81#11758198—21no—
82#11758198—21no—
83#11758198—21no—
84#11758198—21no—
85#11758198—21no—
86#11758198D411yescharacteristic
87#11758198D411yescharacteristic
88C4⋊Dic61—21no—
89C4⋊Dic61C2311yescharacteristic
90C4⋊Dic61C2311yescharacteristic
91#11758196—21no—
92#11758196—21no—
93#11758196—21no—
94#11758196—21no—
95#11758196—21no—
96#11758196D411yescharacteristic
97#11758196D411yescharacteristic
98C4×Dic61—21no—
99C4×Dic61C2311yescharacteristic
100C2×#92418C2311yescharacteristic
101C2×#92418C2311yescharacteristic
102C22×D61—21no—
103C22×D61—21no—
104C22×D61C2×D411yescharacteristic
105Q8×C61—81no—
106C2×C4×C61—21no—
107C2×C4×C61—21no—
108C2×C4×C61—21no—
109C2×C4×C61—21no—
110C2×C4×C61C2×D411yescharacteristic
111C2×C4×C61C2×D411yescharacteristic
112C2×C4×C61C2411yescharacteristic
113C2×Dic61—21no—
114C2×Dic61—21no—
115C2×Dic61C2×D411yescharacteristic
116C2×Dic61C2×D411yescharacteristic
117C2×Dic61C2×D411yescharacteristic
118D244—21no—
119D244—21no—
120D244—21no—
121D244—21no—
122D244—81no—
123D244—81no—
124D244—81no—
125D244—81no—
126C4×D61—21no—
127C4×D61—21no—
128C4×D61—81no—
129C4×D61—81no—
130C4×D61—81no—
131Dic122—81no—
132C8×C61—21no—
133C8×C61—21no—
134#92418—21no—
135#92418—21no—
136C22×C61C22×D411yescharacteristic
137C2×D61—21no—
138C2×D61—21no—
139C2×D61—21no—
140C2×D61—41no—
141C2×D61—41no—
142C2×D61—41no—
143C2×D61—41no—
144C2×D61—41no—
145C2×D61—41no—
146C4×C61—21no—
147C4×C61—21no—
148C4×C61—41no—
149C4×C61—41no—
150C4×C61—41no—
151C4×C61—41no—
152C4×C612−1+411yescharacteristic
153C4×C612−1+411yescharacteristic
154Dic61—21no—
155Dic61—21no—
156Dic61—21no—
157Dic61—41no—
158Dic61—41no—
159#3241—611nomaximal, Sylow
160C2×C61#53611yescharacteristic
161C2×C61#57611yescharacteristic
162C2×C61#57711yescharacteristic
163D61—41no—
164D61—81no—
165D61—81no—
166#544—611no—
167#540—611no—
168#501D6111yescharacteristic, complemented
169#499—611no—
170#490—611no—
171#486—611no—
172#482—611no—
173#482—611no—
174#481—611no—
175#480—611no—
176#478—611no—
177#478—611no—
178#476—611no—
179#474—611no—
180#433—611no—
181C61#324111yescharacteristic, complemented, Sylow
182C4⋊Q8—611no—
183C4⋊Q8—1221no—
184C4⋊Q8C2×D6111yescharacteristic
185#127—611no—
186#125—611no—
187#125—611no—
188#125—1221no—
189#125C2×D6111yescharacteristic
190#123—1221no—
191#123—1221no—
192C22⋊Q8—1221no—
193C22⋊Q8—1221no—
194#121—611no—
195#121—611no—
196#121—1221no—
197#121—1221no—
198C4×D4—611no—
199C4×D4—611no—
200#117—611no—
201#117—611no—
202C2×C4⋊C4—611no—
203#107—611no—
204#107—611no—
205#107C2×D6111yescharacteristic
206#107C2×D6111yescharacteristic
207#106—611no—
208#106—611no—
209#106C2×D6111yescharacteristic
210#106C2×D6111yescharacteristic
211C4⋊C8—611no—
212C4⋊C8—611no—
213#102—611no—
214#102—611no—
215#102—611no—
216#102—611no—
217#102—611no—
218#102—611no—
219#102—611no—
220#102—611no—
221C22⋊C8—611no—
222C22⋊C8—611no—
223#97C2×D6111yescharacteristic
224C4×C8—611no—
225C2×Q8—21no—
226C2×Q8—1221no—
227C2×D4—611no—
228C2×D4—611no—
229C2×D4—1221no—
230C2×D4—1221no—
231C2×D4—1221no—
232C2×D4—1221no—
233C22×C4—611no—
234C22×C4—1221no—
235C22×C4—1221no—
236C22×C4—1221no—
237C2×C8—611no—
238C2×C8—611no—
239C2×C8C22×D6111yescharacteristic
240C2×C8C22×D6111yescharacteristic
241C4⋊C4—21no—
242C4⋊C4—21no—
243C4⋊C4—21no—
244C4⋊C4—611no—
245C4⋊C4—611no—
246C4⋊C4—611no—
247C4⋊C4—611no—
248C4⋊C4—1221no—
249C4⋊C4—1221no—
250C4⋊C4—1221no—
251C4⋊C4—1221no—
252C4⋊C4—1221no—
253C4⋊C4—1221no—
254C4⋊C4C22×D6111yescharacteristic
255C4⋊C4C22×D6111yescharacteristic
256C4⋊C4C22×D6111yescharacteristic
257C4⋊C4C22×D6111yescharacteristic
258C22⋊C4—611no—
259C22⋊C4—611no—
260C22⋊C4—1221no—
261C22⋊C4—1221no—
262C22⋊C4—1221no—
263C22⋊C4—1221no—
264C22⋊C4—1221no—
265C42—611no—
266C42—1221no—
267C42C22×D6111yescharacteristic
268C23—611no—
269C23—1221no—
270C23—1221no—
271Q8—81no—
272Q8—4881no—
273D4—1221no—
274D4—1221no—
275D4—1221no—
276D4—1221no—
277D4—4881no—
278D4—4881no—
279D4—4881no—
280D4—4881no—
281C2×C4—21no—
282C2×C4—21no—
283C2×C4—21no—
284C2×C4—21no—
285C2×C4—611no—
286C2×C4—611no—
287C2×C4—611no—
288C2×C4—1221no—
289C2×C4—1221no—
290C2×C4—1221no—
291C2×C4—1221no—
292C2×C4—4881no—
293C2×C4—4881no—
294C2×C4—4881no—
295C2×C4D4×D6111yescharacteristic
296C2×C4D4×D6111yescharacteristic
297C2×C4C23×D6111yescharacteristic
298C8—21no—
299C8—21no—
300C8—1221no—
301C8—1221no—
302C22—1221no—
303C22—1221no—
304C22—1221no—
305C22—2441no—
306C22—2441no—
307C22—2441no—
308C22—2441no—
309C22—2441no—
310C22—2441no—
311C22C2×D4×D6111yescharacteristic
312C4—21no—
313C4—21no—
314C4—41no—
315C4—41no—
316C4—41no—
317C4—41no—
318C4—1221no—
319C4—1221no—
320C4—1221no—
321C4—2441no—
322C4—2441no—
323C4#1451982511yescharacteristic
324C4#1451982511yescharacteristic
325C2—4881no—
326C2—4881no—
327C2—2441no—
328C2#1684033711yescharacteristic
329C2#1684056611yescharacteristic
330C2#1684057111yescharacteristic
subgroupG/H
centerC22C2×D4×D61
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC61×#501C2
socleC22×C61C22×D4
hypercenter#501D61
hypocenterC61#3241
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ #501

Complements

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

NH ≅ G/Ntype
1. #16840389C2semidirect
3. #16840161C2semidirect
4. #16840127C2semidirect
5. #16840110C2semidirect
6. #16840089C2semidirect
7. #16840088C2semidirect
8. #16840082C2semidirect
9. #16840077C2semidirect
10. #16840065C2semidirect
11. #16840061C2semidirect
12. #16840051C2semidirect
13. #16840041C2semidirect
14. #16839824C2semidirect
15. C61×#501C2semidirect
168. #501D61semidirect
181. C61#3241semidirect