Finite Group Databasebeta

← #21462082

Subgroups — #21462082

Order 7808.

234 conjugacy classes of subgroups; only the 52 normal subgroups are shown.

normal subgroups only

This group has 234 conjugacy classes of subgroups — too many to draw. Only its 52 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
1#16840749C211yesmaximal, characteristic
2#16840742C211yesmaximal, characteristic
3#16840665C212yesmaximal, complemented
4#16840664C212yesmaximal, complemented
5#16840334C211yesmaximal, characteristic
6C2×#11758217—21no—
7#14519856—21no—
8#14519838—21no—
9#14519837C2212yes—
10#14519835—21no—
11#14519835C2212yes—
12C2×#11758224C2211yescharacteristic
13C22×Dic122C411yescharacteristic, complemented
14#14519776—21no—
15#14519763—21no—
16#14519761C2211yescharacteristic
17#14519760C2211yescharacteristic
18#14519758C411yescharacteristic, complemented
19#14519755—21no—
20#14519754—21no—
21#14519733C411yescharacteristic, complemented
22#123×C61C411yescharacteristic, complemented
23C2×D4×C61C2×C411yescharacteristic
24C22×C4×C61C2×C411yescharacteristic
25C2×C22⋊D61D411yescharacteristic
26C2×C22⋊D61C2311yescharacteristic
27C22×Dic61C2×C411yescharacteristic
28C22×Dic61C2×C411yescharacteristic
29C22×Dic61D411yescharacteristic
30#11758224—41no—
31#11758224—41no—
32C2×C4×D61D411yescharacteristic
33C2×Dic122—21no—
34C2×Dic122—21no—
35C2×Dic122—41no—
36C2×Dic122—41no—
37C2×Dic122D411yescharacteristic
38C22⋊#6923—22no—
39#11758217—22no—
40#11758217—41no—
41C2×#92420—41no—
42C4⋊#6923—41no—
43C4×#6923—41no—
44C4⋊C4×C61—21no—
45C22⋊C4×C61—21no—
46C22⋊C4×C61C2×C411yescharacteristic
47C22⋊Dic61—21no—
48C22⋊Dic61C2×C411yescharacteristic
49#11758198—21no—
50#11758198—21no—
51C4⋊Dic61—21no—
52#11758196—21no—
53#11758196—21no—
54#11758196—21no—
55C4×Dic61—21no—
56C23×C61C22⋊C411yescharacteristic
57C23×C61C22×C411yescharacteristic
58C22×D61C2×D411yescharacteristic
59C2×#6923—42no—
60D4×C61—41no—
61C2×C4×C61—21no—
62C2×C4×C61—21no—
63C2×C4×C61—41no—
64C2×C4×C61C22⋊C411yescharacteristic
65C22⋊D61—41no—
66C22⋊D61—41no—
67C2×Dic61—21no—
68C2×Dic61—21no—
69C2×Dic61—21no—
70C2×Dic61—21no—
71C2×Dic61—21no—
72C2×Dic61—21no—
73C2×Dic61—41no—
74C2×Dic61C22⋊C411yescharacteristic
75C2×Dic61C22⋊C411yescharacteristic
76C2×Dic61C2×D411yescharacteristic
77C4×D61—21no—
78C4×D61—21no—
79Dic122—41no—
80Dic122—42no—
81Dic122—41no—
82Dic122—41no—
83#92420—42no—
84C22×C61—21no—
85C22×C61—21no—
86C22×C61—41no—
87C22×C61—41no—
88C22×C61C2×C22⋊C411yescharacteristic
89C2×D61—21no—
90C2×D61—41no—
91#6923—82no—
92C4×C61—21no—
93C4×C61—41no—
94C4×C61—41no—
95Dic61—21no—
96Dic61—21no—
97Dic61—41no—
98Dic61—41no—
99Dic61#9911yescharacteristic
100Dic61#9911yescharacteristic
101#2123—611nomaximal, Sylow
102C2×C61—21no—
103C2×C61—41no—
104C2×C61—41no—
105C2×C61C2×#9911yescharacteristic
106D61—41no—
107#536—611no—
108#413—611no—
109#410—611no—
110#352—612no—
111#352—612no—
112C61#212311yescharacteristic, complemented, Sylow
113C2×#41—611no—
114C22×Q8—611no—
115C2×M16—1221no—
116C4⋊Q8—1221no—
117#124—1221no—
118#123—611no—
119#123—611no—
120#123—611no—
121#123#692311yescharacteristic, complemented
122C22⋊Q8—1221no—
123C22⋊Q8—1221no—
124#117—611no—
125#117—1221no—
126#101—1221no—
127#100—612no—
128#99—612no—
129#99—1221no—
130#41—2441no—
131#41—2441no—
132C2×Q8—611no—
133C2×Q8—1221no—
134C2×Q8—1221no—
135C2×Q8—2441no—
136C2×Q8—2441no—
137C2×D4—611no—
138C2×D4—611no—
139C2×D4C2×#692311yescharacteristic
140C22×C4—611no—
141C22×C4—611no—
142C22×C4—611no—
143C22×C4—611no—
144C22×C4C2×#692311yescharacteristic
145M16—1222no—
146M16—2441no—
147C2×C8—2441no—
148C4⋊C4—21no—
149C4⋊C4—1221no—
150C4⋊C4—1221no—
151C4⋊C4—1221no—
152C4⋊C4—1221no—
153C4⋊C4—2441no—
154C22⋊C4—21no—
155C22⋊C4—611no—
156C22⋊C4—1221no—
157C22⋊C4—1221no—
158C22⋊C4—1221no—
159C22⋊C4—1222no—
160C22⋊C4C2×#692311yescharacteristic
161C42—1221no—
162C42—2441no—
163C23—611no—
164C23C22⋊#692311yescharacteristic
165C23C22×#692311yescharacteristic
166Q8—2441no—
167Q8—2441no—
168Q8—2441no—
169Q8—2442no—
170D4—41no—
171D4—2441no—
172D4—2441no—
173C2×C4—21no—
174C2×C4—21no—
175C2×C4—41no—
176C2×C4—611no—
177C2×C4—611no—
178C2×C4—611no—
179C2×C4—1221no—
180C2×C4—1221no—
181C2×C4—1221no—
182C2×C4—1221no—
183C2×C4—1221no—
184C2×C4—1221no—
185C2×C4—1221no—
186C2×C4—1221no—
187C2×C4—2442no—
188C2×C4—2441no—
189C2×C4C22⋊#692311yescharacteristic
190C8—2442no—
191C22—21no—
192C22—21no—
193C22—41no—
194C22—41no—
195C22—1221no—
196C22—2441no—
197C22C2×C22⋊#692311yescharacteristic
198C4—21no—
199C4—41no—
200C4—41no—
201C4—611no—
202C4—611no—
203C4—1221no—
204C4—1221no—
205C4—4882no—
206C4—2441no—
207C4—2441no—
208C2—21no—
209C2—41no—
210C2—41no—
211C2—2441no—
212C2D61⋊#9911yescharacteristic
subgroupG/H
centerC2D61⋊#99
commutatorC23×C61C22×C4
FrattiniC23C22×#6923
Fitting#123×C61C4
socleC2×C61C2×#99
hypercenter#123#6923
hypocenterC61#2123
LCSG ▷ C23×C61 ▷ C22×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2 ◁ C22 ◁ C2×D4 ◁ #123

Complements

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

NH ≅ G/Ntype
3. #16840665C2semidirect
4. #16840664C2semidirect
13. C22×Dic122C4semidirect
18. #14519758C4semidirect
21. #14519733C4semidirect
22. #123×C61C4semidirect
112. C61#2123semidirect
121. #123#6923semidirect