Finite Group Databasebeta

← #21455605

Subgroups — #21455605

Order 7808.

388 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#16840315C211yesmaximal, characteristic, complemented
2#16840230C211yesmaximal, characteristic
3#16840072C211yesmaximal, characteristic, complemented
4#16840068C211yesmaximal, characteristic, complemented
5#16840065C211yesmaximal, characteristic, complemented
6#16840061C211yesmaximal, characteristic, complemented
7#16840056C211yesmaximal, characteristic, complemented
8#16840051C211yesmaximal, characteristic, complemented
9#16840046C211yesmaximal, characteristic, complemented
10#16840041C211yesmaximal, characteristic, complemented
11#16839798C211yesmaximal, characteristic, complemented
12C2×#14519706C211yesmaximal, characteristic, complemented
13#16839759C211yesmaximal, characteristic
14#16839756C211yesmaximal, characteristic
15C61×#427C211yesmaximal, characteristic, complemented
16C2×#11758222C2211yescharacteristic
17C22×#92418C2211yescharacteristic
18#14519776C2211yescharacteristic
19#14519776C2211yescharacteristic
20#14519768C2211yescharacteristic
21#14519768C2211yescharacteristic
22#14519754—21no—
23#14519754—21no—
24C4×Dic122—21no—
25C4×Dic122—21no—
26#14519742C2211yescharacteristic
27#14519742C2211yescharacteristic
28#14519739C2211yescharacteristic
29#14519739C2211yescharacteristic
30#14519737—21no—
31#14519737—21no—
32#14519736C2211yescharacteristic
33#14519734—21no—
34C2×C4×Dic61C2211yescharacteristic
35C42×D61—21no—
36#14519710C2211yescharacteristic
37#14519710C2211yescharacteristic
38#14519708C2211yescharacteristic
39#14519708C2211yescharacteristic
40#14519706C2211yescharacteristic
41#14519706C2211yescharacteristic
42#14519706C2211yescharacteristic
43#14519706C2211yescharacteristic
44#14519702C2211yescharacteristic
45#14519702C2211yescharacteristic
46#14519700C2211yescharacteristic
47#14519700C2211yescharacteristic
48#14519699C2211yescharacteristic
49#14519699C2211yescharacteristic
50#14519697C2211yescharacteristic
51#14519697C2211yescharacteristic
52C22×C8×C61C2211yescharacteristic
53#117×C61C2211yescharacteristic
54#117×C61C2211yescharacteristic
55#107×C61C2211yescharacteristic
56#107×C61C2211yescharacteristic
57#106×C61C2211yescharacteristic
58#106×C61C2211yescharacteristic
59C22×C4×C61C2311yescharacteristic
60C2×C22⋊D61—21no—
61C22×Dic61D411yescharacteristic
62C22×Dic61D411yescharacteristic
63#11758222—22no—
64#11758222Q814yescomplemented
65C2×D244C2311yescharacteristic
66C2×C4×D61—21no—
67C2×C4×D61—21no—
68C2×C4×D61—21no—
69C2×Dic122—21no—
70C2×Dic122—21no—
71C2×Dic122C2311yescharacteristic
72C2×C8×C61—22no—
73C2×C8×C61C2311yescharacteristic
74C2×C8×C61C2311yescharacteristic
75C4⋊C4×C61C2311yescharacteristic
76C4⋊C4×C61C2311yescharacteristic
77C4⋊C4×C61C2311yescharacteristic
78C4⋊C4×C61C2311yescharacteristic
79C22⋊C4×C61—21no—
80C22⋊C4×C61—21no—
81C42×C61—21no—
82C42×C61—21no—
83C22⋊Dic61—21no—
84#11758198—21no—
85#11758198—21no—
86C4⋊Dic61—21no—
87C4⋊Dic61—21no—
88C4⋊Dic61C2311yescharacteristic
89C4⋊Dic61C2311yescharacteristic
90#11758196—21no—
91#11758196—21no—
92#11758196—21no—
93#11758196—21no—
94#11758196—21no—
95#11758196—21no—
96C4×Dic61—21no—
97C4×Dic61—21no—
98C4×Dic61—21no—
99C4×Dic61D411yescharacteristic
100C4×Dic61D411yescharacteristic
101C4×Dic61C2311yescharacteristic
102C4×Dic61C2311yescharacteristic
103C2×#92418—22no—
104C2×#92418C2311yescharacteristic
105C2×#92418C2311yescharacteristic
106C23×C61C2×D411yescharacteristic
107C22×D61—21no—
108C2×C4×C61—21no—
109C2×C4×C61—21no—
110C2×C4×C61—21no—
111C2×C4×C61—21no—
112C2×C4×C61C2×D411yescharacteristic
113C2×C4×C61C2×Q812yes—
114C2×C4×C61#4112yes—
115C2×C4×C61C2411yescharacteristic
116C22⋊D61—24no—
117C2×Dic61—21no—
118C2×Dic61—22no—
119C2×Dic61—21no—
120C2×Dic61—21no—
121C2×Dic61—41no—
122C2×Dic61C2×D411yescharacteristic
123C2×Dic61C2×D411yescharacteristic
124C2×Dic61C2×D411yescharacteristic
125C2×Dic61C2×D411yescharacteristic
126D244—21no—
127D244C2×Q812yes—
128C4×D61—24no—
129C4×D61—42no—
130C4×D61—42no—
131Dic122—21no—
132Dic122—42no—
133Dic122—42no—
134Dic122C2×Q812yes—
135C8×C61—21no—
136C8×C61—21no—
137#92418—21no—
138#92418—21no—
139C22×C61—21no—
140C22×C61—21no—
141C22×C61C22⋊Q812yes—
142C22×C61C22×D411yescharacteristic
143C2×D61—22no—
144C2×D61—41no—
145C2×D61—41no—
146C4×C61—41no—
147C4×C61—41no—
148C4×C61—41no—
149C4×C61—41no—
150C4×C61C22⋊Q812yes—
151C4×C61C22×Q811yescharacteristic
152C4×C61C2×#4111yescharacteristic
153Dic61—22no—
154Dic61—21no—
155Dic61—21no—
156Dic61—21no—
157Dic61—41no—
158Dic61—41no—
159Dic61#13512yes—
160#3076—611nomaximal, Sylow
161C2×C61—22no—
162C2×C61C2×C22⋊Q811yescharacteristic
163C2×C61C2×#13511yescharacteristic
164C2×C61#57511yescharacteristic
165D61—42no—
166#533—611no—
167C4×#41—611no—
168#479—611no—
169#479—611no—
170#478—611no—
171#478—611no—
172#477—611no—
173#476—611no—
174#475—611no—
175#474—611no—
176#427—611no—
177#427D6111yescharacteristic, complemented
178C2×C4⋊C8—611no—
179#416—611no—
180#416—611no—
181C61#307611yescharacteristic, complemented, Sylow
182C2×#41—611no—
183C22×C8—611no—
184C22×C8C2×D6111yescharacteristic
185C4⋊Q8—611no—
186C4⋊Q8—611no—
187#125—611no—
188#125—611no—
189C22⋊Q8—1221no—
190C22⋊Q8—1221no—
191C4×Q8—611no—
192C4×Q8—611no—
193C4×Q8—1221no—
194C4×Q8—1221no—
195C4×D4—611no—
196C4×D4—611no—
197C4×D4—1221no—
198C4×D4—1221no—
199#117—611no—
200#117—1221no—
201#117C2×D6111yescharacteristic
202#117C2×D6111yescharacteristic
203C2×C42—611no—
204C2×C42—1221no—
205#107—611no—
206#107—611no—
207#107C2×D6111yescharacteristic
208#107C2×D6111yescharacteristic
209#106—611no—
210#106—611no—
211#106C2×D6111yescharacteristic
212#106C2×D6111yescharacteristic
213C4⋊C8—611no—
214C4⋊C8—611no—
215C4⋊C8—611no—
216C4⋊C8—611no—
217#103—611no—
218#103—611no—
219#103—611no—
220#103—611no—
221#102—611no—
222#102—611no—
223#102—611no—
224#102—611no—
225#41—614no—
226#41—1222no—
227C2×Q8—611no—
228C2×Q8—1221no—
229C2×Q8—1221no—
230C2×D4—611no—
231C2×D4—1221no—
232C22×C4—611no—
233C22×C4—611no—
234C22×C4—1221no—
235C22×C4—1221no—
236C22×C4—1221no—
237C22×C4C22×D6111yescharacteristic
238C2×C8—22no—
239C2×C8—611no—
240C2×C8—611no—
241C2×C8—1222no—
242C2×C8C22×D6111yescharacteristic
243C2×C8C22×D6111yescharacteristic
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⋊C4C22×D6111yescharacteristic
255C4⋊C4C22×D6111yescharacteristic
256C4⋊C4C22×D6111yescharacteristic
257C4⋊C4C22×D6111yescharacteristic
258C22⋊C4—21no—
259C22⋊C4—21no—
260C22⋊C4—1221no—
261C22⋊C4—1221no—
262C22⋊C4—1221no—
263C42—21no—
264C42—21no—
265C42—611no—
266C42—611no—
267C42—611no—
268C42—611no—
269C42—1221no—
270C42—1221no—
271C42—1221no—
272C23—1221no—
273C23D4×D6111yescharacteristic
274Q8—612no—
275Q8—1221no—
276Q8—2442no—
277Q8—2442no—
278D4—612no—
279D4—1224no—
280D4—1221no—
281C2×C4—21no—
282C2×C4—21no—
283C2×C4—21no—
284C2×C4—21no—
285C2×C4—611no—
286C2×C4—611no—
287C2×C4—611no—
288C2×C4—611no—
289C2×C4—1222no—
290C2×C4—1221no—
291C2×C4—1224no—
292C2×C4—1221no—
293C2×C4—1221no—
294C2×C4—2442no—
295C2×C4—2442no—
296C2×C4—2441no—
297C2×C4#1175822212yes—
298C2×C4D4×D6111yescharacteristic
299C2×C4Q8×D6112yes—
300C2×C4C23×D6111yescharacteristic
301C8—21no—
302C8—21no—
303C8—1221no—
304C8—1221no—
305C22—21no—
306C22—21no—
307C22—1222no—
308C22—2441no—
309C22—2441no—
310C22#1451975512yes—
311C22C2×D4×D6111yescharacteristic
312C4—41no—
313C4—41no—
314C4—41no—
315C4—41no—
316C4—612no—
317C4—1222no—
318C4—1221no—
319C4—1221no—
320C4—1221no—
321C4—2441no—
322C4—2441no—
323C4#1451975512yes—
324C4C2×Q8×D6111yescharacteristic
325C4C2×#1175822211yescharacteristic
326C2—22no—
327C2—2442no—
328C2C2×#1451975511yescharacteristic
329C2#135×D6111yescharacteristic
330C2#1684055911yescharacteristic
subgroupG/H
centerC2×C4D4×D61
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC61×#427C2
socleC22×C61C22×D4
hypercenter#427D61
hypocenterC61#3076
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ #427

Complements

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

NH ≅ G/Ntype
1. #16840315C2semidirect
3. #16840072C2semidirect
4. #16840068C2semidirect
5. #16840065C2semidirect
6. #16840061C2semidirect
7. #16840056C2semidirect
8. #16840051C2semidirect
9. #16840046C2semidirect
10. #16840041C2semidirect
11. #16839798C2semidirect
12. C2×#14519706C2semidirect
15. C61×#427C2semidirect
64. #11758222Q8semidirect
177. #427D61semidirect
181. C61#3076semidirect