Finite Group Databasebeta

← #21458185

Subgroups — #21458185

Order 7808.

342 conjugacy classes of subgroups.

The subgroup lattice has 324 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#16840454C211yesmaximal, characteristic
2#16840447C211yesmaximal, characteristic
3#16840162C211yesmaximal, characteristic, complemented
4#16840106C211yesmaximal, characteristic, complemented
5#16840101C211yesmaximal, characteristic, complemented
6#16840093C211yesmaximal, characteristic, complemented
7#16840072C211yesmaximal, characteristic, complemented
8#16840067C211yesmaximal, characteristic, complemented
9#16840002C211yesmaximal, characteristic, complemented
10#16840001C211yesmaximal, characteristic, complemented
11#16839854C211yesmaximal, characteristic, complemented
12#16839825C211yesmaximal, characteristic
13#16839797C211yesmaximal, characteristic, complemented
14C2×#14519710C211yesmaximal, characteristic, complemented
15C61×#483C211yesmaximal, characteristic, complemented
16C2×#11758202C2211yescharacteristic
17C22×#92418C2211yescharacteristic
18C2×C8×D61C2211yescharacteristic
19#14519772—21no—
20#14519772—21no—
21#14519768—21no—
22#14519768C2211yescharacteristic
23#14519768C2211yescharacteristic
24#14519767—21no—
25#14519761—21no—
26#14519760—21no—
27#14519757C2211yescharacteristic
28#14519756C2211yescharacteristic
29#14519753C2211yescharacteristic
30Q8×Dic61C2211yescharacteristic
31#14519742C2211yescharacteristic
32C4×C22⋊D61C2211yescharacteristic
33#14519736—21no—
34#14519735C2211yescharacteristic
35#14519735C2211yescharacteristic
36#14519733—21no—
37C2×C4⋊Dic61C2211yescharacteristic
38#14519710C2211yescharacteristic
39#14519710C2211yescharacteristic
40#14519710C2211yescharacteristic
41#14519710C2211yescharacteristic
42#14519710C2211yescharacteristic
43#14519709C2211yescharacteristic
44#14519709C2211yescharacteristic
45#14519706C2211yescharacteristic
46#14519702C2211yescharacteristic
47#14519702C2211yescharacteristic
48#14519701C2211yescharacteristic
49#14519700C2211yescharacteristic
50#14519689C2211yescharacteristic
51C8×Dic61C2211yescharacteristic
52C22⋊Q8×C61C2211yescharacteristic
53C2×C4⋊C4×C61C2211yescharacteristic
54#106×C61C2211yescharacteristic
55#106×C61C2211yescharacteristic
56#103×C61C2211yescharacteristic
57#103×C61C2211yescharacteristic
58C22⋊C8×C61C2211yescharacteristic
59C2×Q8×C61C2311yescharacteristic
60C22×C4×C61—21no—
61C22×C4×C61C2311yescharacteristic
62C2×C22⋊D61D411yescharacteristic
63C22×Dic61—21no—
64C2×C4×D61C2311yescharacteristic
65C2×Dic122C2311yescharacteristic
66C2×C8×C61C2311yescharacteristic
67C2×C8×C61C2311yescharacteristic
68C4⋊C4×C61—21no—
69C4⋊C4×C61—21no—
70C4⋊C4×C61C2311yescharacteristic
71C4⋊C4×C61C2311yescharacteristic
72C4⋊C4×C61C2311yescharacteristic
73C22⋊C4×C61—21no—
74C22⋊Dic61—21no—
75C22⋊Dic61D411yescharacteristic
76#11758202—22no—
77#11758198—21no—
78#11758198—21no—
79#11758198—21no—
80#11758198—21no—
81#11758198D411yescharacteristic
82C4⋊Dic61—21no—
83C4⋊Dic61—21no—
84C4⋊Dic61—21no—
85C4⋊Dic61—21no—
86C4⋊Dic61—21no—
87C4⋊Dic61C2311yescharacteristic
88C4⋊Dic61C2311yescharacteristic
89C4⋊Dic61C2311yescharacteristic
90#11758196—21no—
91#11758196—21no—
92#11758196—21no—
93#11758196—21no—
94#11758196—21no—
95#11758196D411yescharacteristic
96C4×Dic61—21no—
97C4×Dic61—21no—
98C4×Dic61—21no—
99C4×Dic61—21no—
100C4×Dic61C2311yescharacteristic
101C2×#92418—22no—
102C2×#92418C2311yescharacteristic
103C2×#92418C2311yescharacteristic
104C8×D61—22no—
105C23×C61C2×D411yescharacteristic
106C22×D61C2×D411yescharacteristic
107Q8×C61—21no—
108Q8×C61—21no—
109C2×C4×C61—21no—
110C2×C4×C61—21no—
111C2×C4×C61—21no—
112C2×C4×C61—21no—
113C2×C4×C61—21no—
114C2×C4×C61—21no—
115C2×C4×C61—42no—
116C2×C4×C61C2×D411yescharacteristic
117C2×C4×C61C2411yescharacteristic
118C22⋊D61—22no—
119C2×Dic61—21no—
120C2×Dic61—21no—
121C2×Dic61—21no—
122C2×Dic61—21no—
123C2×Dic61—42no—
124C2×Dic61C2×D411yescharacteristic
125C2×Dic61C2×D411yescharacteristic
126C2×Dic61C2×D411yescharacteristic
127C4×D61—21no—
128C4×D61—21no—
129Dic122—21no—
130Dic122—21no—
131C8×C61—21no—
132C8×C61—21no—
133#92418—21no—
134#92418#4112yes—
135C22×C61—21no—
136C22×C61—21no—
137C22×C61#13512yes—
138C22×C61C22×D411yescharacteristic
139C2×D61—21no—
140C2×D61—21no—
141C2×D61—21no—
142C4×C61—21no—
143C4×C61—41no—
144C4×C61—41no—
145C4×C61—41no—
146C4×C61—41no—
147C4×C61C2×#4111yescharacteristic
148C4×C612−1+411yescharacteristic
149Dic61—21no—
150Dic61—21no—
151Dic61—21no—
152Dic61—41no—
153Dic61—41no—
154Dic61—41no—
155Dic61—41no—
156#3336—611nomaximal, Sylow
157C2×C61—22no—
158C2×C61#54711yescharacteristic
159C2×C61C2×#13511yescharacteristic
160C2×C61#57811yescharacteristic
161D61—41no—
162#552—611no—
163#552—611no—
164#499—611no—
165#485—611no—
166#485—611no—
167#483—611no—
168#483D6111yescharacteristic, complemented
169#479—611no—
170#479—611no—
171#467—611no—
172#467—611no—
173C4×Q16—611no—
174C8×D4—611no—
175#427—611no—
176C2×#107—611no—
177C61#333611yescharacteristic, complemented, Sylow
178C2×Q16—611no—
179C22×C8—611no—
180C22×C8—611no—
181#126—1221no—
182#126—1221no—
183#125—611no—
184#125—611no—
185#125—1221no—
186#125—1221no—
187#123—1221no—
188#123—1221no—
189C22⋊Q8—611no—
190C22⋊Q8—611no—
191C22⋊Q8—611no—
192C22⋊Q8C2×D6111yescharacteristic
193C4×Q8—611no—
194C4×Q8—611no—
195C4×D4—611no—
196#117—611no—
197#117—611no—
198#117—1221no—
199#117—1221no—
200C2×C4⋊C4—611no—
201C2×C4⋊C4C2×D6111yescharacteristic
202#107—611no—
203#107—611no—
204#107—611no—
205#107—611no—
206#107—611no—
207#106—611no—
208#106—611no—
209#106C2×D6111yescharacteristic
210#106C2×D6111yescharacteristic
211C4⋊C8—611no—
212#103—611no—
213#103—611no—
214#103—611no—
215#103—611no—
216#103C2×D6111yescharacteristic
217#103C2×D6111yescharacteristic
218C22⋊C8—611no—
219C22⋊C8C2×D6111yescharacteristic
220C4×C8—611no—
221C2×Q8—611no—
222C2×Q8C22×D6111yescharacteristic
223C2×D4—611no—
224C22×C4—21no—
225C22×C4—611no—
226C22×C4—1221no—
227C22×C4C22×D6111yescharacteristic
228Q16—1222no—
229C2×C8—611no—
230C2×C8—611no—
231C2×C8—1222no—
232C2×C8—1222no—
233C2×C8C22×D6111yescharacteristic
234C2×C8C22×D6111yescharacteristic
235C4⋊C4—21no—
236C4⋊C4—21no—
237C4⋊C4—611no—
238C4⋊C4—611no—
239C4⋊C4—611no—
240C4⋊C4—611no—
241C4⋊C4—1221no—
242C4⋊C4—1221no—
243C4⋊C4—1221no—
244C4⋊C4—1221no—
245C4⋊C4—1221no—
246C4⋊C4—1221no—
247C4⋊C4—1221no—
248C4⋊C4—1221no—
249C4⋊C4—1221no—
250C4⋊C4—1221no—
251C4⋊C4C22×D6111yescharacteristic
252C4⋊C4C22×D6111yescharacteristic
253C4⋊C4C22×D6111yescharacteristic
254C22⋊C4—21no—
255C22⋊C4—611no—
256C22⋊C4—611no—
257C22⋊C4—1221no—
258C22⋊C4—1221no—
259C22⋊C4—1221no—
260C22⋊C4—1221no—
261C22⋊C4—1221no—
262C42—611no—
263C42—1221no—
264C42—1221no—
265C42—1221no—
266C42—1221no—
267C23—611no—
268C23D4×D6111yescharacteristic
269Q8—21no—
270Q8—21no—
271Q8—1221no—
272Q8—1221no—
273D4—1222no—
274C2×C4—21no—
275C2×C4—21no—
276C2×C4—21no—
277C2×C4—21no—
278C2×C4—21no—
279C2×C4—21no—
280C2×C4—42no—
281C2×C4—611no—
282C2×C4—611no—
283C2×C4—611no—
284C2×C4—1221no—
285C2×C4—1221no—
286C2×C4—1221no—
287C2×C4—1221no—
288C2×C4—1221no—
289C2×C4—1221no—
290C2×C4—2442no—
291C2×C4D4×D6111yescharacteristic
292C2×C4C23×D6111yescharacteristic
293C8—21no—
294C8—21no—
295C8—612no—
296C8—1221no—
297C22—21no—
298C22—21no—
299C22—1221no—
300C22—1221no—
301C22—1221no—
302C22#1451979812yes—
303C22C2×D4×D6111yescharacteristic
304C4—21no—
305C4—41no—
306C4—41no—
307C4—41no—
308C4—41no—
309C4—1221no—
310C4—1221no—
311C4—1221no—
312C4—2441no—
313C4—2441no—
314C4—2441no—
315C4—2441no—
316C4#41×D6111yescharacteristic
317C4#1451982411yescharacteristic
318C2—22no—
319C2—2441no—
320C2#1684041011yescharacteristic
321C2C2×#1451979811yescharacteristic
322C2#1684057811yescharacteristic
subgroupG/H
centerC22C2×D4×D61
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC61×#483C2
socleC22×C61C22×D4
hypercenter#483D61
hypocenterC61#3336
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ #483

Complements

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

NH ≅ G/Ntype
3. #16840162C2semidirect
4. #16840106C2semidirect
5. #16840101C2semidirect
6. #16840093C2semidirect
7. #16840072C2semidirect
8. #16840067C2semidirect
9. #16840002C2semidirect
10. #16840001C2semidirect
11. #16839854C2semidirect
13. #16839797C2semidirect
14. C2×#14519710C2semidirect
15. C61×#483C2semidirect
168. #483D61semidirect
177. C61#3336semidirect