Finite Group Databasebeta

← #21457070

Subgroups — #21457070

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#16840390C211yesmaximal, characteristic, complemented
2#16840365C211yesmaximal, characteristic
3#16840170C211yesmaximal, characteristic, complemented
4#16840162C211yesmaximal, characteristic, complemented
5#16840125C211yesmaximal, characteristic, complemented
6#16840107C211yesmaximal, characteristic, complemented
7#16840086C211yesmaximal, characteristic, complemented
8#16840081C211yesmaximal, characteristic, complemented
9#16840073C211yesmaximal, characteristic, complemented
10#16840064C211yesmaximal, characteristic, complemented
11#16840061C211yesmaximal, characteristic, complemented
12#16840050C211yesmaximal, characteristic, complemented
13#16840041C211yesmaximal, characteristic, complemented
14#16839820C211yesmaximal, characteristic, complemented
15C61×#482C211yesmaximal, characteristic, complemented
16#14519777—21no—
17#14519776C2211yescharacteristic
18#14519776C2211yescharacteristic
19#14519773C2211yescharacteristic
20#14519769—21no—
21#14519768C2211yescharacteristic
22#14519768C2211yescharacteristic
23#14519768C2211yescharacteristic
24#14519761—21no—
25#14519759—21no—
26#14519754—21no—
27#14519754—21no—
28#14519751C2211yescharacteristic
29#14519749—21no—
30#14519748—21no—
31D4×Dic61C2211yescharacteristic
32#14519739C2211yescharacteristic
33#14519736C2211yescharacteristic
34C2×C4⋊Dic61C2211yescharacteristic
35#14519710C2211yescharacteristic
36#14519710C2211yescharacteristic
37#14519710C2211yescharacteristic
38#14519709C2211yescharacteristic
39#14519709C2211yescharacteristic
40#14519708C2211yescharacteristic
41#14519706C2211yescharacteristic
42#14519706C2211yescharacteristic
43#14519699C2211yescharacteristic
44#14519699C2211yescharacteristic
45#14519698C2211yescharacteristic
46#14519698C2211yescharacteristic
47#14519697C2211yescharacteristic
48#14519697C2211yescharacteristic
49C22⋊#92418C2211yescharacteristic
50#14519687C2211yescharacteristic
51C8×Dic61C2211yescharacteristic
52#121×C61C2211yescharacteristic
53#117×C61C2211yescharacteristic
54#107×C61C2211yescharacteristic
55#106×C61C2211yescharacteristic
56#102×C61C2211yescharacteristic
57#102×C61C2211yescharacteristic
58C22⋊C8×C61C2211yescharacteristic
59C2×D4×C61—21no—
60C2×D4×C61C2311yescharacteristic
61C22×C4×C61C2311yescharacteristic
62C2×C22⋊D61—21no—
63C2×C22⋊D61—21no—
64C2×C22⋊D61—21no—
65C22×Dic61—21no—
66C22×Dic61—21no—
67C2×D244C2311yescharacteristic
68C2×C4×D61—21no—
69C2×Dic122—21no—
70C2×Dic122—21no—
71C2×C8×C61C2311yescharacteristic
72C2×C8×C61C2311yescharacteristic
73C4⋊C4×C61C2311yescharacteristic
74C4⋊C4×C61C2311yescharacteristic
75C4⋊C4×C61C2311yescharacteristic
76C22⋊C4×C61—21no—
77C22⋊C4×C61—21no—
78C42×C61—21no—
79C22⋊Dic61—21no—
80C22⋊Dic61D411yescharacteristic
81C22⋊Dic61D411yescharacteristic
82#11758198—21no—
83#11758198—21no—
84C4⋊Dic61—21no—
85C4⋊Dic61—21no—
86C4⋊Dic61—21no—
87C4⋊Dic61—21no—
88C4⋊Dic61D411yescharacteristic
89C4⋊Dic61D411yescharacteristic
90C4⋊Dic61C2311yescharacteristic
91C4⋊Dic61C2311yescharacteristic
92C4⋊Dic61C2311yescharacteristic
93#11758196—21no—
94#11758196—21no—
95#11758196—21no—
96#11758196—21no—
97#11758196—21no—
98C4×Dic61C2311yescharacteristic
99C4×Dic61C2311yescharacteristic
100C2×#92418C2311yescharacteristic
101C2×#92418C2311yescharacteristic
102C23×C61—21no—
103C23×C61C2×D411yescharacteristic
104C22×D61—21no—
105D4×C61—21no—
106D4×C61—21no—
107D4×C61—81no—
108C2×C4×C61—21no—
109C2×C4×C61—21no—
110C2×C4×C61—21no—
111C2×C4×C61—21no—
112C2×C4×C61—21no—
113C2×C4×C61C2×D411yescharacteristic
114C2×C4×C61C2411yescharacteristic
115C22⋊D61—81no—
116C22⋊D61—81no—
117C22⋊D61—81no—
118C2×Dic61—21no—
119C2×Dic61—21no—
120C2×Dic61—21no—
121C2×Dic61—81no—
122C2×Dic61—81no—
123C2×Dic61C2×D411yescharacteristic
124C2×Dic61C2×D411yescharacteristic
125C2×Dic61C2×D411yescharacteristic
126C2×Dic61C2×D411yescharacteristic
127D244—21no—
128D244—21no—
129C4×D61—81no—
130Dic122—81no—
131Dic122—81no—
132C8×C61—21no—
133C8×C61—21no—
134#92418—21no—
135#92418—21no—
136C22×C61—21no—
137C22×C61—21no—
138C22×C61—21no—
139C22×C61—41no—
140C22×C61—41no—
141C22×C61—41no—
142C22×C61C22×D411yescharacteristic
143C2×D61—41no—
144C2×D61—41no—
145C2×D61—41no—
146C4×C61—21no—
147C4×C61—41no—
148C4×C61—41no—
149C4×C61—41no—
150C4×C612−1+411yescharacteristic
151C4×C612−1+411yescharacteristic
152Dic61—21no—
153Dic61—21no—
154Dic61—21no—
155Dic61—21no—
156Dic61—41no—
157Dic61—41no—
158Dic61—41no—
159#3241—611nomaximal, Sylow
160C2×C61—41no—
161C2×C61—81no—
162C2×C61#53611yescharacteristic
163C2×C61#57611yescharacteristic
164C2×C61#57711yescharacteristic
165D61—81no—
166#544—611no—
167#540—611no—
168#501—611no—
169#499—611no—
170#490—611no—
171#486—611no—
172#482—611no—
173#482D6111yescharacteristic, complemented
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—611no—
184C4⋊Q8—1221no—
185#127—611no—
186#125—611no—
187#125—611no—
188#125—611no—
189#125—1221no—
190#123—1221no—
191#123—1221no—
192C22⋊Q8—1221no—
193C22⋊Q8—1221no—
194#121—611no—
195#121—1221no—
196#121—1221no—
197#121C2×D6111yescharacteristic
198C4×D4—611no—
199C4×D4—611no—
200#117—611no—
201#117C2×D6111yescharacteristic
202C2×C4⋊C4—611no—
203#107—611no—
204#107—611no—
205#107—611no—
206#107C2×D6111yescharacteristic
207#106—611no—
208#106—611no—
209#106—611no—
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#102C2×D6111yescharacteristic
220#102C2×D6111yescharacteristic
221C22⋊C8—611no—
222C22⋊C8C2×D6111yescharacteristic
223#97—611no—
224C4×C8—611no—
225C2×Q8—1221no—
226C2×Q8—1221no—
227C2×D4—21no—
228C2×D4—611no—
229C2×D4—1221no—
230C2×D4—1221no—
231C2×D4—1221no—
232C2×D4C22×D6111yescharacteristic
233C22×C4—1221no—
234C22×C4—1221no—
235C22×C4—1221no—
236C22×C4C22×D6111yescharacteristic
237C2×C8—611no—
238C2×C8—611no—
239C2×C8C22×D6111yescharacteristic
240C2×C8C22×D6111yescharacteristic
241C4⋊C4—611no—
242C4⋊C4—611no—
243C4⋊C4—611no—
244C4⋊C4—611no—
245C4⋊C4—611no—
246C4⋊C4—1221no—
247C4⋊C4—1221no—
248C4⋊C4—1221no—
249C4⋊C4—1221no—
250C4⋊C4—1221no—
251C4⋊C4—1221no—
252C4⋊C4—1221no—
253C4⋊C4—1221no—
254C4⋊C4—1221no—
255C4⋊C4C22×D6111yescharacteristic
256C4⋊C4C22×D6111yescharacteristic
257C4⋊C4C22×D6111yescharacteristic
258C22⋊C4—21no—
259C22⋊C4—21no—
260C22⋊C4—611no—
261C22⋊C4—611no—
262C22⋊C4—1221no—
263C22⋊C4—1221no—
264C22⋊C4—1221no—
265C42—21no—
266C42—611no—
267C42—611no—
268C23—21no—
269C23—1221no—
270C23D4×D6111yescharacteristic
271Q8—4881no—
272Q8—4881no—
273D4—21no—
274D4—21no—
275D4—81no—
276D4—1221no—
277D4—1221no—
278D4—4881no—
279D4—4881no—
280D4—4881no—
281C2×C4—21no—
282C2×C4—21no—
283C2×C4—21no—
284C2×C4—21no—
285C2×C4—21no—
286C2×C4—611no—
287C2×C4—611no—
288C2×C4—611no—
289C2×C4—611no—
290C2×C4—1221no—
291C2×C4—1221no—
292C2×C4—1221no—
293C2×C4—4881no—
294C2×C4—4881no—
295C2×C4—4881no—
296C2×C4D4×D6111yescharacteristic
297C2×C4C23×D6111yescharacteristic
298C8—21no—
299C8—21no—
300C8—1221no—
301C8—1221no—
302C22—21no—
303C22—21no—
304C22—21no—
305C22—41no—
306C22—41no—
307C22—41no—
308C22—2441no—
309C22—2441no—
310C22—2441no—
311C22C2×D4×D6111yescharacteristic
312C4—21no—
313C4—41no—
314C4—41no—
315C4—41no—
316C4—1221no—
317C4—1221no—
318C4—1221no—
319C4—1221no—
320C4—2441no—
321C4—2441no—
322C4—2441no—
323C4#1451982411yescharacteristic
324C4#1451982411yescharacteristic
325C2—41no—
326C2—81no—
327C2—4881no—
328C2#1684033411yescharacteristic
329C2#1684056611yescharacteristic
330C2#1684056911yescharacteristic
subgroupG/H
centerC22C2×D4×D61
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC61×#482C2
socleC22×C61C22×D4
hypercenter#482D61
hypocenterC61#3241
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ #482

Complements

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

NH ≅ G/Ntype
1. #16840390C2semidirect
3. #16840170C2semidirect
4. #16840162C2semidirect
5. #16840125C2semidirect
6. #16840107C2semidirect
7. #16840086C2semidirect
8. #16840081C2semidirect
9. #16840073C2semidirect
10. #16840064C2semidirect
11. #16840061C2semidirect
12. #16840050C2semidirect
13. #16840041C2semidirect
14. #16839820C2semidirect
15. C61×#482C2semidirect
173. #482D61semidirect
181. C61#3241semidirect