Finite Group Databasebeta

← #21461690

Subgroups — #21461690

Order 7808.

292 conjugacy classes of subgroups; only the 84 normal subgroups are shown.

normal subgroups only

This group has 292 conjugacy classes of subgroups — too many to draw. Only its 84 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⋊(C4⋊C8)C211yesmaximal, characteristic
2C2×#14519840C212yesmaximal
3#16840706C211yesmaximal, characteristic
4#16840635C212yesmaximal
5C4×Q8×D61C211yesmaximal, characteristic
6C2×D61⋊C8C2212yes—
7C2×C4⋊#6923C2212yes—
8#14519844—21no—
9C4⋊#92420—21no—
10#14519840—24no—
11(C2×#6923)⋊C4—21no—
12(C2×#6923)⋊C4—21no—
13C2×Q8×D61C2211yescharacteristic
14Q8×Dic61C411yescharacteristic, complemented
15C4×Dic122—21no—
16C4×Dic122C411yescharacteristic, complemented
17#14519742—21no—
18#14519742C411yescharacteristic, complemented
19C4⋊C4×D61—21no—
20C4⋊C4×D61C2211yescharacteristic
21C42×D61—21no—
22C42×D61C2211yescharacteristic
23C4×Q8×C61C411yescharacteristic, complemented
24C22×#6923—22no—
25C2×Q8×C61C2×C411yescharacteristic
26Q8×D61—21no—
27Q8×D61—21no—
28Q8×D61D412yes—
29Q8×D61Q812yes—
30C2×C4×D61—21no—
31C2×C4×D61—21no—
32C2×C4×D61D411yescharacteristic
33C2×C4×D61D411yescharacteristic
34C2×C4×D61C2311yescharacteristic
35C2×Dic122—21no—
36C2×Dic122C2×C411yescharacteristic
37C2×#92420—22no—
38C4⋊#6923—22no—
39C4⋊#6923—22no—
40D61⋊C8—22no—
41D61⋊C8—22no—
42C4⋊C4×C61—21no—
43C4⋊C4×C61C2×C411yescharacteristic
44C42×C61—21no—
45C42×C61C2×C411yescharacteristic
46C4⋊Dic61—21no—
47C4⋊Dic61C2×C411yescharacteristic
48#11758196—21no—
49#11758196—21no—
50#11758196—21no—
51C4×Dic61—21no—
52C4×Dic61—21no—
53C4×Dic61—21no—
54C4×Dic61C2×C411yescharacteristic
55C4×Dic61D411yescharacteristic
56C4×Dic61D411yescharacteristic
57C22×D61C2×D411yescharacteristic
58C2×#6923—42no—
59C2×#6923—42no—
60C2×#6923—42no—
61Q8×C61—21no—
62Q8×C61C4⋊C412yes—
63C2×C4×C61—21no—
64C2×C4×C61—21no—
65C2×C4×C61C22⋊C411yescharacteristic
66C2×C4×C61C22⋊C411yescharacteristic
67C2×C4×C61C22×C411yescharacteristic
68C2×Dic61—21no—
69C2×Dic61—21no—
70C2×Dic61C22⋊C411yescharacteristic
71C2×Dic61C22⋊C411yescharacteristic
72C2×Dic61C2×D411yescharacteristic
73C4×D61—22no—
74C4×D61—22no—
75C4×D61—22no—
76C4×D61—22no—
77C4×D61—42no—
78C4×D61C2×D411yescharacteristic
79C4×D61C2×Q811yescharacteristic
80C4×D61#4111yescharacteristic
81C4×D61#4111yescharacteristic
82Dic122—21no—
83Dic122—22no—
84Dic122—22no—
85Dic122C4⋊C412yes—
86#92420—42no—
87C22×C61C2×C22⋊C411yescharacteristic
88C2×D61#12111yescharacteristic
89C2×D61C22⋊Q811yescharacteristic
90C2×D61#13512yes—
91C2×D61#13712yes—
92#6923—82no—
93C4×C61—22no—
94C4×C61—21no—
95C4×C61—21no—
96C4×C61—41no—
97C4×C61C2×C4⋊C411yescharacteristic
98C4×C61#11711yescharacteristic
99Dic61—22no—
100Dic61—21no—
101Dic61—21no—
102Dic61—41no—
103Dic61#12111yescharacteristic
104Dic61C22⋊Q811yescharacteristic
105#1805—611nomaximal, Sylow
106C2×C61#38011yescharacteristic
107C2×C61#41611yescharacteristic
108C2×C61#41911yescharacteristic
109D61#46412yes—
110D61#47912yes—
111C2×C4×Q8—611no—
112C2×C4⋊C8—611no—
113C2×#103—612no—
114#382—611no—
115#340—612no—
116C61#180511yescharacteristic, complemented, Sylow
117C22×Q8—611no—
118C22×C8—612no—
119C4×Q8—611no—
120C4×Q8—611no—
121C4×Q8—611no—
122C4×Q8—1221no—
123C4×Q8—1221no—
124C4×Q8#692311yescharacteristic, complemented
125C2×C4⋊C4—611no—
126C2×C4⋊C4—612no—
127C2×C4⋊C4—1221no—
128C2×C42—611no—
129C2×C42—1221no—
130C4⋊C8—1221no—
131C4⋊C8—1221no—
132#103—1224no—
133#95—1221no—
134#95—1221no—
135C2×Q8—612no—
136C2×Q8—612no—
137C2×Q8—611no—
138C2×Q8—1221no—
139C2×Q8—1221no—
140C2×Q8—1221no—
141C2×Q8C2×#692311yescharacteristic
142C22×C4—611no—
143C22×C4—611no—
144C22×C4—611no—
145C22×C4—1221no—
146C22×C4—1221no—
147C22×C4—1222no—
148C2×C8—1222no—
149C2×C8—1222no—
150C2×C8—1222no—
151C4⋊C4—21no—
152C4⋊C4—611no—
153C4⋊C4—1221no—
154C4⋊C4—1221no—
155C4⋊C4—1221no—
156C4⋊C4—1222no—
157C4⋊C4—1222no—
158C4⋊C4—1221no—
159C4⋊C4C2×#692311yescharacteristic
160C42—21no—
161C42—611no—
162C42—611no—
163C42—611no—
164C42—1221no—
165C42—1221no—
166C42—1221no—
167C42C2×#692311yescharacteristic
168C23—611no—
169Q8—21no—
170Q8—612no—
171Q8—1222no—
172Q8—1222no—
173Q8—1221no—
174Q8C4⋊#692312yes—
175C2×C4—21no—
176C2×C4—21no—
177C2×C4—611no—
178C2×C4—611no—
179C2×C4—611no—
180C2×C4—611no—
181C2×C4—611no—
182C2×C4—611no—
183C2×C4—611no—
184C2×C4—1222no—
185C2×C4—1222no—
186C2×C4—1222no—
187C2×C4—1222no—
188C2×C4—1221no—
189C2×C4—1221no—
190C2×C4—2442no—
191C2×C4—2442no—
192C2×C4—2442no—
193C2×C4—2442no—
194C2×C4C22⋊#692311yescharacteristic
195C2×C4C22⋊#692311yescharacteristic
196C2×C4C22×#692311yescharacteristic
197C8—2442no—
198C22—611no—
199C22—611no—
200C22—612no—
201C22—612no—
202C22C2×C22⋊#692311yescharacteristic
203C4—22no—
204C4—21no—
205C4—21no—
206C4—41no—
207C4—611no—
208C4—611no—
209C4—1222no—
210C4—1221no—
211C4—1221no—
212C4—4882no—
213C4—2441no—
214C4C2×C4⋊#692311yescharacteristic
215C4#1451985611yescharacteristic
216C2—612no—
217C2—612no—
218C2#1684070411yescharacteristic
219C2#1684075211yescharacteristic
220C2#1684075511yescharacteristic
subgroupG/H
centerC22C2×C22⋊#6923
commutatorC2×C4×C61C22×C4
FrattiniC2×C4C22×#6923
FittingC4×Q8×C61C4
socleC22×C61C2×C22⋊C4
hypercenterC4×Q8#6923
hypocenterC61#1805
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ C4×Q8

Complements

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

NH ≅ G/Ntype
14. Q8×Dic61C4semidirect
16. C4×Dic122C4semidirect
18. #14519742C4semidirect
23. C4×Q8×C61C4semidirect
116. C61#1805semidirect
124. C4×Q8#6923semidirect