Finite Group Databasebeta

← #21456370

Subgroups — #21456370

Order 7808.

348 conjugacy classes of subgroups; only the 137 normal subgroups are shown.

normal subgroups only

This group has 348 conjugacy classes of subgroups — too many to draw. Only its 137 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#16840317C211yesmaximal, characteristic
2#125×D61C211yesmaximal, characteristic
3#16840172C211yesmaximal, characteristic, complemented
4#16840171C211yesmaximal, characteristic, complemented
5#16840168C211yesmaximal, characteristic, complemented
6#16840163C212yesmaximal, complemented
7#16840162C212yesmaximal, complemented
8#16839803C212yesmaximal
9#16839801C212yesmaximal
10#16839714C211yesmaximal, characteristic
11C61×#501C211yesmaximal, characteristic, complemented
12C2×#11758189C2212yes—
13#14519777C2211yescharacteristic
14#14519769C2211yescharacteristic
15#14519768C2211yescharacteristic
16#14519768C2211yescharacteristic
17#14519768C2212yes—
18#14519767—21no—
19#14519767—21no—
20#14519757—21no—
21#14519753—21no—
22Q8×Dic61—21no—
23#14519742—21no—
24#14519735C2212yes—
25C4⋊C4×D61—21no—
26C4⋊C4×D61—21no—
27C4⋊C4×D61C2211yescharacteristic
28C4⋊C4×D61C2211yescharacteristic
29C42×D61C2211yescharacteristic
30#14519711C2212yes—
31#14519710C2212yes—
32#14519710C2212yes—
33#14519709C2212yes—
34#14519708C2212yes—
35#14519708C2212yes—
36#14519688C2211yescharacteristic
37C8×Dic61C2212yes—
38C4⋊Q8×C61C2211yescharacteristic
39#125×C61C2211yescharacteristic
40#107×C61C2212yes—
41#106×C61C2212yes—
42#97×C61C2211yescharacteristic
43C2×Q8×C61—21no—
44C2×C4×D61—21no—
45C2×C4×D61—21no—
46C2×C4×D61D411yescharacteristic
47C2×C4×D61D411yescharacteristic
48C2×C4×D61C2311yescharacteristic
49C2×Dic122—21no—
50C2×C8×C61C2312yes—
51C4⋊C4×C61—21no—
52C4⋊C4×C61—21no—
53C4⋊C4×C61—21no—
54C4⋊C4×C61C2311yescharacteristic
55C4⋊C4×C61C2312yes—
56C4⋊C4×C61C2311yescharacteristic
57C42×C61C2311yescharacteristic
58#11758198—22no—
59C4⋊Dic61—21no—
60C4⋊Dic61—21no—
61C4⋊Dic61—21no—
62C4⋊Dic61—22no—
63C4⋊Dic61C2311yescharacteristic
64C4⋊Dic61C2312yes—
65C4⋊Dic61C2311yescharacteristic
66#11758196—21no—
67#11758196—21no—
68#11758196—21no—
69#11758196—21no—
70#11758196—21no—
71#11758196—21no—
72#11758196—22no—
73C4×Dic61—22no—
74C4×Dic61D411yescharacteristic
75C4×Dic61D411yescharacteristic
76C4×Dic61C2311yescharacteristic
77C2×#92418C2312yes—
78#11758189Q818yescomplemented
79C22×D61C2×D411yescharacteristic
80Q8×C61—42no—
81C2×C4×C61—22no—
82C2×C4×C61—21no—
83C2×C4×C61—21no—
84C2×C4×C61C2×D411yescharacteristic
85C2×C4×C61C2×D411yescharacteristic
86C2×C4×C61C2411yescharacteristic
87C2×Dic61—22no—
88C2×Dic61—21no—
89C2×Dic61—21no—
90C2×Dic61C2×D411yescharacteristic
91C2×Dic61C2×D411yescharacteristic
92C2×Dic61C2×D411yescharacteristic
93C4×D61—41no—
94C4×D61—41no—
95C4×D61—42no—
96C4×D61—42no—
97C4×D61C2×Q814yes—
98Dic122—42no—
99C8×C61C2×Q814yes—
100#92418C2×Q814yes—
101C22×C61C22×D411yescharacteristic
102C2×D61—21no—
103C2×D61—21no—
104C2×D61C4⋊Q812yes—
105C4×C61—21no—
106C4×C61—21no—
107C4×C61—41no—
108C4×C61—41no—
109C4×C61—42no—
110C4×C61C22×Q812yes—
111Dic61—21no—
112Dic61—21no—
113Dic61—42no—
114Dic61—41no—
115Dic61—41no—
116Dic61C4⋊Q812yes—
117#3166—611nomaximal, Sylow
118C2×C61C2×C4⋊Q811yescharacteristic
119C2×C61#57511yescharacteristic
120C2×C61#57511yescharacteristic
121D61—22no—
122#533—611no—
123C2×#125—611no—
124#501—611no—
125#501—611no—
126#501—611no—
127#501D6111yescharacteristic, complemented
128#499—612no—
129#499—612no—
130#428—612no—
131#428—612no—
132C4×M16—611no—
133C61#316611yescharacteristic, complemented, Sylow
134C2×M16—612no—
135C4⋊Q8—611no—
136C4⋊Q8C2×D6111yescharacteristic
137#125—611no—
138#125—611no—
139#125—612no—
140#125—611no—
141#125—1221no—
142#125—1221no—
143#125C2×D6111yescharacteristic
144C22⋊Q8—1221no—
145C22⋊Q8—1221no—
146C4×Q8—1221no—
147C4×Q8—1221no—
148#117—612no—
149C2×C4⋊C4—611no—
150C2×C4⋊C4—611no—
151C2×C4⋊C4—1221no—
152C2×C4⋊C4—1221no—
153C2×C42—611no—
154#107—612no—
155#107—612no—
156#107—612no—
157#107C2×D6112yes—
158#106—612no—
159#106—612no—
160#106—612no—
161#106C2×D6112yes—
162#97—611no—
163#97C2×D6111yescharacteristic
164C4×C8—612no—
165C2×Q8—21no—
166C2×Q8—1221no—
167C22×C4—611no—
168C22×C4—611no—
169C22×C4—611no—
170C22×C4—1221no—
171C22×C4—1221no—
172M16—618no—
173C2×C8—612no—
174C2×C8C22×D6112yes—
175C4⋊C4—21no—
176C4⋊C4—21no—
177C4⋊C4—21no—
178C4⋊C4—611no—
179C4⋊C4—611no—
180C4⋊C4—612no—
181C4⋊C4—1221no—
182C4⋊C4—1221no—
183C4⋊C4—1221no—
184C4⋊C4—1221no—
185C4⋊C4—1221no—
186C4⋊C4—1221no—
187C4⋊C4—1222no—
188C4⋊C4—1222no—
189C4⋊C4—1221no—
190C4⋊C4—1221no—
191C4⋊C4—1221no—
192C4⋊C4C22×D6111yescharacteristic
193C4⋊C4C22×D6112yes—
194C4⋊C4C22×D6111yescharacteristic
195C22⋊C4—1222no—
196C42—611no—
197C42—611no—
198C42—611no—
199C42—1222no—
200C42C22×D6111yescharacteristic
201C23—611no—
202Q8—42no—
203Q8—2442no—
204C2×C4—22no—
205C2×C4—21no—
206C2×C4—21no—
207C2×C4—611no—
208C2×C4—614no—
209C2×C4—611no—
210C2×C4—611no—
211C2×C4—1222no—
212C2×C4—1221no—
213C2×C4—1221no—
214C2×C4—2441no—
215C2×C4—2441no—
216C2×C4—2442no—
217C2×C4—2442no—
218C2×C4D4×D6111yescharacteristic
219C2×C4D4×D6111yescharacteristic
220C2×C4C23×D6111yescharacteristic
221C8—614no—
222C8Q8×D6114yes—
223C22—612no—
224C22—1221no—
225C22—1221no—
226C22C2×D4×D6111yescharacteristic
227C4—21no—
228C4—21no—
229C4—41no—
230C4—42no—
231C4—41no—
232C4—612no—
233C4—1221no—
234C4—1221no—
235C4—2441no—
236C4—2441no—
237C4—2442no—
238C4C2×Q8×D6112yes—
239C2—1222no—
240C2C4⋊Q8×D6111yescharacteristic
241C2#1684055811yescharacteristic
242C2#1684056111yescharacteristic
subgroupG/H
centerC22C2×D4×D61
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC61×#501C2
socleC22×C61C22×D4
hypercenter#501D61
hypocenterC61#3166
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ #501

Complements

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

NH ≅ G/Ntype
3. #16840172C2semidirect
4. #16840171C2semidirect
5. #16840168C2semidirect
6. #16840163C2semidirect
7. #16840162C2semidirect
11. C61×#501C2semidirect
78. #11758189Q8semidirect
127. #501D61semidirect
133. C61#3166semidirect