Finite Group Databasebeta

← #21445838

Subgroups — #21445838

Order 7808.

312 conjugacy classes of subgroups; only the 87 normal subgroups are shown.

normal subgroups only

This group has 312 conjugacy classes of subgroups — too many to draw. Only its 87 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#16840230C211yesmaximal, characteristic
2#16839785C211yesmaximal, characteristic, complemented
3C2×#14519705C211yesmaximal, characteristic
4C2×#14519703C211yesmaximal, characteristic
5C4×#11758196C211yesmaximal, characteristic, complemented
6#16839521C211yesmaximal, characteristic, complemented
7C61×#339C211yesmaximal, characteristic, complemented
8C2×#11758222C2211yescharacteristic
9C2×#11758194C2211yescharacteristic
10#14519742C411yescharacteristic, complemented
11#14519742C411yescharacteristic, complemented
12#14519739C411yescharacteristic, complemented
13#14519739C411yescharacteristic, complemented
14#14519737—21no—
15#14519737—21no—
16#14519734—21no—
17C2×#11758196—21no—
18C2×C4×Dic61C2211yescharacteristic
19C2×C4×Dic61C2211yescharacteristic
20C42×D61—21no—
21#14519706—21no—
22#14519706—21no—
23#14519705—22no—
24#14519703—22no—
25#14519684—21no—
26C2×M16×C61C2211yescharacteristic
27#117×C61C2211yescharacteristic
28C2×C42×C61C2211yescharacteristic
29C22×C4×C61—21no—
30C22×C4×C61C2311yescharacteristic
31C2×C22⋊D61—21no—
32C22×Dic61—21no—
33C22×Dic61D411yescharacteristic
34C22×Dic61D411yescharacteristic
35#11758222—21no—
36#11758222—21no—
37#11758222D412yes—
38#11758222Q812yes—
39C2×D244C2×C411yescharacteristic
40C2×C4×D61—21no—
41C2×C4×D61—21no—
42C2×C4×D61—21no—
43C2×Dic122C2×C411yescharacteristic
44M16×C61—21no—
45M16×C61—21no—
46C2×C8×C61—21no—
47C4⋊C4×C61C2×C411yescharacteristic
48C4⋊C4×C61C2×C411yescharacteristic
49C22⋊C4×C61—21no—
50C42×C61—21no—
51C42×C61—21no—
52C42×C61—21no—
53#11758198—21no—
54#11758198—21no—
55#11758196—24no—
56#11758196—21no—
57#11758196—21no—
58C4×Dic61—21no—
59C4×Dic61—21no—
60C4×Dic61—21no—
61C4×Dic61—21no—
62C4×Dic61C2×C411yescharacteristic
63C4×Dic61C2×C411yescharacteristic
64C4×Dic61D411yescharacteristic
65C4×Dic61D411yescharacteristic
66#11758194—21no—
67#11758194—21no—
68C2×#92418—21no—
69C23×C61C2×D411yescharacteristic
70C22×D61—21no—
71C2×C4×C61—22no—
72C2×C4×C61—21no—
73C2×C4×C61—21no—
74C2×C4×C61—41no—
75C2×C4×C61—41no—
76C2×C4×C61C22×C411yescharacteristic
77C2×C4×C61C2×D411yescharacteristic
78C2×C4×C61C2×D411yescharacteristic
79C2×C4×C61C2×Q811yescharacteristic
80C2×C4×C61#4111yescharacteristic
81C2×C4×C61#4111yescharacteristic
82C22⋊D61—22no—
83C22⋊D61—22no—
84C2×Dic61—21no—
85C2×Dic61—22no—
86C2×Dic61—22no—
87C2×Dic61—41no—
88C2×Dic61—41no—
89C2×Dic61—41no—
90C2×Dic61C22⋊C411yescharacteristic
91C2×Dic61C22⋊C411yescharacteristic
92C2×Dic61C22⋊C411yescharacteristic
93C2×Dic61C22⋊C411yescharacteristic
94D244—21no—
95D244C4⋊C412yescomplemented
96C4×D61—22no—
97C4×D61—22no—
98C4×D61—42no—
99C4×D61—42no—
100Dic122—21no—
101Dic122C4⋊C412yescomplemented
102C8×C61—41no—
103#92418—41no—
104C22×C61—21no—
105C22×C61—21no—
106C22×C61C2×C22⋊C411yescharacteristic
107C22×C61#12111yescharacteristic
108C22×C61C22⋊Q811yescharacteristic
109C2×D61—22no—
110C2×D61—41no—
111C2×D61—41no—
112C4×C61—42no—
113C4×C61—41no—
114C4×C61—41no—
115C4×C61C2×C4⋊C411yescharacteristic
116C4×C61#11711yescharacteristic
117C4×C61#12111yescharacteristic
118C4×C61C22⋊Q811yescharacteristic
119Dic61—22no—
120Dic61—21no—
121Dic61—21no—
122Dic61—21no—
123Dic61—42no—
124Dic61#10412yescomplemented
125#1806—611nomaximal, Sylow
126C2×C61—21no—
127C2×C61—21no—
128C2×C61#38011yescharacteristic
129C2×C61C2×#10411yescharacteristic
130C2×C61#42111yescharacteristic
131D61—42no—
132C4×#41—611no—
133#423—611no—
134C2×#104—611no—
135C2×#104—611no—
136C4×C4⋊C4—611no—
137#339—611no—
138#339D6111yescharacteristic, complemented
139C61#180611yescharacteristic, complemented, Sylow
140C2×#41—611no—
141C2×M16—611no—
142C2×M16C2×D6111yescharacteristic
143C4×Q8—611no—
144C4×Q8—611no—
145C4×D4—611no—
146C4×D4—611no—
147C4×D4—1221no—
148C4×D4—1221no—
149#117—1221no—
150#117C2×D6111yescharacteristic
151C2×C4⋊C4—1221no—
152C2×C42—611no—
153C2×C42—611no—
154C2×C42—1221no—
155C2×C42C2×D6111yescharacteristic
156C4⋊C8—1221no—
157C4⋊C8—1221no—
158#104—1222no—
159#104—1222no—
160#95—1221no—
161#41—612no—
162#41—612no—
163#41—1221no—
164#41—1221no—
165C2×Q8—611no—
166C2×D4—611no—
167C2×D4—1221no—
168C22×C4—21no—
169C22×C4—611no—
170C22×C4—611no—
171C22×C4—1221no—
172C22×C4—1221no—
173C22×C4—1221no—
174C22×C4—1221no—
175C22×C4C22×D6111yescharacteristic
176M16—21no—
177M16—21no—
178M16—1221no—
179M16—1221no—
180C2×C8—21no—
181C2×C8—1221no—
182C4⋊C4—1221no—
183C4⋊C4—1221no—
184C4⋊C4—1224no—
185C4⋊C4C4×D6111yescharacteristic
186C4⋊C4C4×D6111yescharacteristic
187C22⋊C4—21no—
188C22⋊C4—1221no—
189C22⋊C4—1221no—
190C42—21no—
191C42—21no—
192C42—21no—
193C42—611no—
194C42—611no—
195C42—611no—
196C42—611no—
197C42—1221no—
198C42—1221no—
199C42—1221no—
200C42—1221no—
201C23—1221no—
202C23D4×D6111yescharacteristic
203Q8—612no—
204Q8—1221no—
205D4—612no—
206D4—1222no—
207D4—1222no—
208D4—1221no—
209C2×C4—22no—
210C2×C4—21no—
211C2×C4—21no—
212C2×C4—41no—
213C2×C4—41no—
214C2×C4—611no—
215C2×C4—611no—
216C2×C4—611no—
217C2×C4—611no—
218C2×C4—1222no—
219C2×C4—1221no—
220C2×C4—1222no—
221C2×C4—1222no—
222C2×C4—1222no—
223C2×C4—2442no—
224C2×C4—2442no—
225C2×C4—2441no—
226C2×C4—2441no—
227C2×C4—2441no—
228C2×C4C2×C4×D6111yescharacteristic
229C2×C4#1175822211yescharacteristic
230C2×C4#1175822211yescharacteristic
231C2×C4D4×D6111yescharacteristic
232C2×C4D4×D6111yescharacteristic
233C2×C4Q8×D6111yescharacteristic
234C8—41no—
235C8—2441no—
236C22—21no—
237C22—21no—
238C22—1222no—
239C22—2441no—
240C22—2441no—
241C22C22⋊C4×D6111yescharacteristic
242C22#1451975011yescharacteristic
243C22#1451975511yescharacteristic
244C4—42no—
245C4—41no—
246C4—41no—
247C4—612no—
248C4—1221no—
249C4—1221no—
250C4—1221no—
251C4—1222no—
252C4—2442no—
253C4C4⋊C4×D6111yescharacteristic
254C4#1451973411yescharacteristic
255C4#1451975011yescharacteristic
256C4#1451975511yescharacteristic
257C2—21no—
258C2—21no—
259C2—2442no—
260C2#1683962111yescharacteristic
261C2#104×D6111yescharacteristic
262C2#1683977711yescharacteristic
subgroupG/H
centerC2×C4D4×D61
commutatorC2×C4×C61C22×C4
FrattiniC22×C4C22×D61
FittingC61×#339C2
socleC22×C61C2×C22⋊C4
hypercenter#339D61
hypocenterC61#1806
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ #339

Complements

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

NH ≅ G/Ntype
2. #16839785C2semidirect
5. C4×#11758196C2semidirect
6. #16839521C2semidirect
7. C61×#339C2semidirect
10. #14519742C4semidirect
11. #14519742C4semidirect
12. #14519739C4semidirect
13. #14519739C4semidirect
95. D244C4⋊C4semidirect
101. Dic122C4⋊C4semidirect
124. Dic61#104semidirect
138. #339D61semidirect
139. C61#1806semidirect