Finite Group Databasebeta

← #21461592

Subgroups — #21461592

Order 7808.

324 conjugacy classes of subgroups; only the 98 normal subgroups are shown.

normal subgroups only

This group has 324 conjugacy classes of subgroups — too many to draw. Only its 98 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
1C2×Q8×#6923C211yesmaximal, characteristic
2C2×#14519840C211yesmaximal, characteristic
3C2×#14519831C211yesmaximal, characteristic
4C4⋊C4×#6923C211yesmaximal, characteristic
5#16840636C211yesmaximal, characteristic
6#16840635C211yesmaximal, characteristic
7#103×D61C211yesmaximal, characteristic
8C2×D61⋊C8C2211yescharacteristic
9Q8×#6923—22no—
10Q8×#6923C414yescomplemented
11C2×C4⋊#6923—21no—
12C2×C4⋊#6923C2211yescharacteristic
13C2×C4⋊#6923C2211yescharacteristic
14C2×C4×#6923—21no—
15C2×C4×#6923—21no—
16C2×C4×#6923C2211yescharacteristic
17#14519840C414yescomplemented
18#14519831—22no—
19(C2×#6923)⋊C4—21no—
20C2×Q8×D61C2211yescharacteristic
21C2×C8×D61C2211yescharacteristic
22C4⋊C4×D61C2211yescharacteristic
23#14519702C411yescharacteristic, complemented
24#14519701C411yescharacteristic, complemented
25#14519700C411yescharacteristic, complemented
26#103×C61C411yescharacteristic, complemented
27C22×#6923—21no—
28C22×#6923—21no—
29C22×#6923D411yescharacteristic
30C22×#6923D411yescharacteristic
31C2×Q8×C61C2×C411yescharacteristic
32Q8×D61—21no—
33Q8×D61—21no—
34Q8×D61C2×C412yes—
35Q8×D61C2×C412yes—
36C2×C4×D61—21no—
37C2×C4×D61—21no—
38C2×C4×D61C2311yescharacteristic
39C2×Dic122—21no—
40C2×Dic122C2×C411yescharacteristic
41C2×#92420—21no—
42C4⋊#6923—24no—
43C4⋊#6923—21no—
44C4⋊#6923—21no—
45C4⋊#6923C2×C412yes—
46C4⋊#6923C2×C412yes—
47C4×#6923—24no—
48C4×#6923—42no—
49C4×#6923C2×C412yes—
50C4×#6923D412yes—
51D61⋊C8—21no—
52D61⋊C8C2×C412yes—
53C2×C8×C61C2×C411yescharacteristic
54C4⋊C4×C61C2×C411yescharacteristic
55C4⋊Dic61C2×C411yescharacteristic
56#11758196—21no—
57C2×#92418C2×C411yescharacteristic
58C8×D61—21no—
59C8×D61—21no—
60C22×D61C2×D411yescharacteristic
61C2×#6923—21no—
62C2×#6923—21no—
63C2×#6923—21no—
64C2×#6923—21no—
65C2×#6923—22no—
66C2×#6923—22no—
67C2×#6923—41no—
68C2×#6923—41no—
69C2×#6923—41no—
70C2×#6923—41no—
71C2×#6923C22⋊C412yes—
72C2×#6923C22⋊C412yes—
73Q8×C61—21no—
74Q8×C61C4212yescomplemented
75C2×C4×C61—21no—
76C2×C4×C61—21no—
77C2×C4×C61C22×C411yescharacteristic
78C2×Dic61—21no—
79C2×Dic61—21no—
80C2×Dic61#4111yescharacteristic
81C4×D61—22no—
82C4×D61—22no—
83C4×D61—41no—
84C4×D61—41no—
85C4×D61C22×C411yescharacteristic
86C4×D61C22×C411yescharacteristic
87C4×D61C2×D411yescharacteristic
88C4×D61#4111yescharacteristic
89Dic122—21no—
90Dic122—22no—
91Dic122—22no—
92Dic122C4212yescomplemented
93#92420—22no—
94C8×C61—21no—
95#92418—21no—
96C22×C61C4×D411yescharacteristic
97C2×D61C2×C22⋊C411yescharacteristic
98C2×D61C4×D411yescharacteristic
99C2×D61AGL(1,ℤ/8)11yescharacteristic
100C2×D61#13711yescharacteristic
101C2×D61#13711yescharacteristic
102C2×D61#13711yescharacteristic
103#6923—22no—
104#6923—22no—
105#6923—42no—
106#6923—42no—
107C4×C61—22no—
108C4×C61—41no—
109C4×C61C2×C4211yescharacteristic
110C4×C61C4×D411yescharacteristic
111Dic61—22no—
112Dic61—41no—
113Dic61#11711yescharacteristic
114Dic61C4×D411yescharacteristic
115#1763—611nomaximal, Sylow
116C2×C61C4×C22⋊C411yescharacteristic
117C2×C61#44011yescharacteristic
118C2×C61#44111yescharacteristic
119D61#41711yescharacteristic
120D61#41911yescharacteristic
121D61#44011yescharacteristic
122D61#44111yescharacteristic
123C2×C4×Q8—611no—
124C2×#103—611no—
125C2×#103—611no—
126C2×#97—611no—
127C4×C4⋊C4—611no—
128#340—611no—
129#340—611no—
130C61#176311yescharacteristic, complemented, Sylow
131C22×Q8—611no—
132C22×C8—611no—
133C22×C8—611no—
134C4×Q8—614no—
135C4×Q8—1222no—
136C2×C4⋊C4—611no—
137C2×C4⋊C4—611no—
138C2×C4⋊C4—611no—
139C2×C4⋊C4—1221no—
140C2×C42—611no—
141C2×C42—1221no—
142C2×C42—1221no—
143#103—614no—
144#103—611no—
145#103—611no—
146#103—611no—
147#103#692311yescharacteristic, complemented
148#97—1222no—
149#95—1221no—
150C2×Q8—612no—
151C2×Q8—612no—
152C2×Q8—611no—
153C2×Q8—1221no—
154C2×Q8—1221no—
155C2×Q8—1221no—
156C2×Q8C2×#692311yescharacteristic
157C22×C4—611no—
158C22×C4—611no—
159C22×C4—611no—
160C22×C4—1221no—
161C22×C4—1221no—
162C22×C4—1221no—
163C22×C4—1221no—
164C2×C8—612no—
165C2×C8—611no—
166C2×C8—1221no—
167C2×C8—1221no—
168C2×C8—1221no—
169C2×C8—1221no—
170C2×C8C2×#692311yescharacteristic
171C4⋊C4—612no—
172C4⋊C4—612no—
173C4⋊C4—611no—
174C4⋊C4—1221no—
175C4⋊C4—1221no—
176C4⋊C4—1221no—
177C4⋊C4—1224no—
178C4⋊C4C2×#692311yescharacteristic
179C42—612no—
180C42—612no—
181C42—1224no—
182C42—2442no—
183C23—611no—
184Q8—21no—
185Q8—612no—
186Q8—1222no—
187Q8—1222no—
188Q8—1221no—
189Q8C4×#692312yescomplemented
190C2×C4—21no—
191C2×C4—21no—
192C2×C4—611no—
193C2×C4—611no—
194C2×C4—611no—
195C2×C4—611no—
196C2×C4—611no—
197C2×C4—612no—
198C2×C4—612no—
199C2×C4—1222no—
200C2×C4—1222no—
201C2×C4—1221no—
202C2×C4—1221no—
203C2×C4—1221no—
204C2×C4—1221no—
205C2×C4—1221no—
206C2×C4—1222no—
207C2×C4—1222no—
208C2×C4—1221no—
209C2×C4—2441no—
210C2×C4—2441no—
211C2×C4—2441no—
212C2×C4—2441no—
213C2×C4—2441no—
214C2×C4—2441no—
215C2×C4C22×#692311yescharacteristic
216C8—21no—
217C8—1222no—
218C8—1221no—
219C22—611no—
220C22—611no—
221C22—611no—
222C22—611no—
223C22—611no—
224C22—611no—
225C22D4×#692311yescharacteristic
226C4—22no—
227C4—41no—
228C4—611no—
229C4—611no—
230C4—1222no—
231C4—1222no—
232C4—1222no—
233C4—2442no—
234C4—2442no—
235C4—2441no—
236C4C2×C4×#692311yescharacteristic
237C4D4×#692311yescharacteristic
238C2—611no—
239C2—611no—
240C2—611no—
241C2—611no—
242C2C22⋊C4×#692311yescharacteristic
243C2#1684080111yescharacteristic
244C2#1684080211yescharacteristic
subgroupG/H
centerC22D4×#6923
commutatorC4×C61C2×C42
FrattiniC2×C4C22×#6923
Fitting#103×C61C4
socleC22×C61C4×D4
hypercenter#103#6923
hypocenterC61#1763
LCSG ▷ C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C4 ◁ #103

Complements

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

NH ≅ G/Ntype
10. Q8×#6923C4semidirect
17. #14519840C4semidirect
23. #14519702C4semidirect
24. #14519701C4semidirect
25. #14519700C4semidirect
26. #103×C61C4semidirect
74. Q8×C61C42semidirect
92. Dic122C42semidirect
130. C61#1763semidirect
147. #103#6923semidirect
189. Q8C4×#6923semidirect