Finite Group Databasebeta

← #21461599

Subgroups — #21461599

Order 7808.

292 conjugacy classes of subgroups; only the 88 normal subgroups are shown.

normal subgroups only

This group has 292 conjugacy classes of subgroups — too many to draw. Only its 88 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1D61⋊#131C211yesmaximal, characteristic
2#16840752C211yesmaximal, characteristic
3#16840728C211yesmaximal, characteristic, complemented
4#16840721C211yesmaximal, characteristic, complemented
5#16840637C211yesmaximal, characteristic, complemented
6#16840633C211yesmaximal, characteristic, complemented
7#104×D61C211yesmaximal, characteristic
8#14519865C412yescomplemented
9#14519864—22no—
10#14519864C412yescomplemented
11D61⋊M16—21no—
12D61⋊M16C2211yescharacteristic
13C2×D61⋊C8—21no—
14C2×D61⋊C8C2211yescharacteristic
15C2×D61⋊C8C2211yescharacteristic
16#14519856C2211yescharacteristic
17#14519840C412yescomplemented
18#14519839C412yescomplemented
19#14519832—22no—
20#14519831—21no—
21C8×#6923—21no—
22#41×D61C2211yescharacteristic
23M16×D61C2211yescharacteristic
24C42×D61C2211yescharacteristic
25#14519705C411yescharacteristic, complemented
26#14519704C411yescharacteristic, complemented
27#14519703C411yescharacteristic, complemented
28#104×C61C411yescharacteristic, complemented
29#41×C61C2×C411yescharacteristic
30#11758226C2×C411yescharacteristic
31Q8×D61C2×C411yescharacteristic
32#11758224—21no—
33#11758224C2×C411yescharacteristic
34D4×D61—21no—
35D4×D61C2×C411yescharacteristic
36#11758222—21no—
37#11758222C2×C411yescharacteristic
38C2×C4×D61—21no—
39C2×C4×D61—21no—
40C2×C4×D61C2311yescharacteristic
41C22⋊#6923—21no—
42#11758217—21no—
43#11758217—22no—
44C2×#92420—21no—
45C2×#92420—22no—
46C2×#92420D412yes—
47C4⋊#6923C2×C412yes—
48C4×#6923—21no—
49#11758213—22no—
50#11758213C2×C412yes—
51D61⋊C8—21no—
52D61⋊C8—21no—
53D61⋊C8—22no—
54D61⋊C8C2×C412yes—
55D61⋊C8C2×C412yes—
56D61⋊C8D411yescharacteristic
57D61⋊C8D411yescharacteristic
58M16×C61C2×C411yescharacteristic
59C42×C61C2×C411yescharacteristic
60C4×Dic61—21no—
61C4×Dic61C2×C411yescharacteristic
62#11758194C2×C411yescharacteristic
63#11758189—21no—
64C8×D61—21no—
65C22×D61—21no—
66C22×D61#4111yescharacteristic
67C2×#6923—22no—
68Q8×C61C4211yescharacteristic
69D4×C61—21no—
70D4×C61C4211yescharacteristic
71C2×C4×C61—21no—
72C2×C4×C61—21no—
73C2×C4×C61C22×C411yescharacteristic
74C22⋊D61—21no—
75C22⋊D61—21no—
76C22⋊D61—21no—
77C2×Dic61—21no—
78C2×Dic61—21no—
79C2×Dic61C2×D411yescharacteristic
80D244—21no—
81D244C4211yescharacteristic
82C4×D61—21no—
83C4×D61—21no—
84C4×D61—21no—
85C4×D61—42no—
86C4×D61C22×C411yescharacteristic
87C4×D61C22×C411yescharacteristic
88C4×D61C2×D411yescharacteristic
89C4×D61#4111yescharacteristic
90Dic122—21no—
91Dic122C4211yescharacteristic
92#92420—22no—
93#92420—22no—
94#92420C22⋊C412yes—
95#92420C22⋊C412yes—
96C8×C61—21no—
97#92418—21no—
98C22×C61—21no—
99C22×C61C4×D411yescharacteristic
100C2×D61—22no—
101C2×D61—21no—
102C2×D61—42no—
103C2×D61#11711yescharacteristic
104C2×D61C4×D411yescharacteristic
105#6923—42no—
106C4×C61—21no—
107C4×C61—41no—
108C4×C61C2×C4211yescharacteristic
109C4×C61C4×D411yescharacteristic
110Dic61—21no—
111Dic61—41no—
112Dic61C2×C22⋊C411yescharacteristic
113Dic61C4×D411yescharacteristic
114#1765—611nomaximal, Sylow
115C2×C61—21no—
116C2×C61—41no—
117C2×C61C4×C22⋊C411yescharacteristic
118D61—21no—
119D61—41no—
120D61#44412yes—
121C2×#131—611no—
122C2×#104—611no—
123#416—611no—
124#405—611no—
125C2×#97—611no—
126#341—611no—
127#339—611no—
128C61#176511yescharacteristic, complemented, Sylow
129C2×#41—611no—
130#131—612no—
131#131—612no—
132#131—1222no—
133C2×M16—611no—
134C2×M16—611no—
135C2×M16—1221no—
136C22×C8—611no—
137C22×C8—611no—
138C22×C8—1221no—
139#117—611no—
140C2×C42—611no—
141#104—611no—
142#104—611no—
143#104—611no—
144#104#692311yescharacteristic, complemented
145#103—612no—
146#102—612no—
147#97—1221no—
148#97—1222no—
149C4×C8—1221no—
150#41—611no—
151#41—611no—
152#41—611no—
153#41—1221no—
154#41—1221no—
155#41C2×#692311yescharacteristic
156C2×Q8—611no—
157C2×D4—611no—
158C2×D4—1221no—
159C22×C4—611no—
160C22×C4—1221no—
161C22×C4—1221no—
162M16—612no—
163M16—611no—
164M16—1221no—
165M16—1222no—
166M16—1222no—
167M16—1221no—
168M16C2×#692311yescharacteristic
169C2×C8—611no—
170C2×C8—611no—
171C2×C8—612no—
172C2×C8—612no—
173C2×C8—612no—
174C2×C8—1221no—
175C2×C8—1222no—
176C2×C8—1222no—
177C2×C8—1221no—
178C2×C8—1221no—
179C2×C8—1221no—
180C4⋊C4—612no—
181C22⋊C4—1221no—
182C42—611no—
183C42—1221no—
184C42—1221no—
185C42C2×#692311yescharacteristic
186C23—611no—
187C23—1221no—
188Q8—611no—
189Q8—1221no—
190Q8C4×#692311yescharacteristic
191D4—21no—
192D4—611no—
193D4—1221no—
194D4—1221no—
195D4—1221no—
196D4—1221no—
197D4C4×#692311yescharacteristic
198C2×C4—21no—
199C2×C4—21no—
200C2×C4—611no—
201C2×C4—611no—
202C2×C4—611no—
203C2×C4—611no—
204C2×C4—611no—
205C2×C4—1221no—
206C2×C4—1221no—
207C2×C4—1221no—
208C2×C4—1221no—
209C2×C4—1222no—
210C2×C4—1221no—
211C2×C4—2442no—
212C2×C4C22×#692311yescharacteristic
213C8—21no—
214C8—612no—
215C8—612no—
216C8—1222no—
217C8—1222no—
218C8—1221no—
219C22—21no—
220C22—611no—
221C22—611no—
222C22—1222no—
223C22—1221no—
224C22—2442no—
225C22D4×#692311yescharacteristic
226C4—21no—
227C4—41no—
228C4—611no—
229C4—611no—
230C4—1221no—
231C4—2441no—
232C4—2442no—
233C4C2×C4×#692311yescharacteristic
234C4D4×#692311yescharacteristic
235C2—21no—
236C2—41no—
237C2—612no—
238C2—1221no—
239C2—2441no—
240C2C22⋊C4×#692311yescharacteristic
subgroupG/H
centerC4D4×#6923
commutatorC4×C61C2×C42
FrattiniC2×C4C22×#6923
Fitting#104×C61C4
socleC2×C61C4×C22⋊C4
hypercenter#104#6923
hypocenterC61#1765
LCSG ▷ C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C4 ◁ C2×C4 ◁ #104

Complements

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

NH ≅ G/Ntype
3. #16840728C2semidirect
4. #16840721C2semidirect
5. #16840637C2semidirect
6. #16840633C2semidirect
8. #14519865C4semidirect
10. #14519864C4semidirect
17. #14519840C4semidirect
18. #14519839C4semidirect
25. #14519705C4semidirect
26. #14519704C4semidirect
27. #14519703C4semidirect
28. #104×C61C4semidirect
128. C61#1765semidirect
144. #104#6923semidirect