Finite Group Databasebeta

← #21461853

Subgroups — #21461853

Order 7808.

346 conjugacy classes of subgroups; only the 66 normal subgroups are shown.

normal subgroups only

This group has 346 conjugacy classes of subgroups — too many to draw. Only its 66 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#16840829C211yesmaximal, characteristic, complemented
2#16840760C211yesmaximal, characteristic, complemented
3#16840754C211yesmaximal, characteristic, complemented
4#16840742C211yesmaximal, characteristic, complemented
5#16840644C211yesmaximal, characteristic, complemented
6#16840630C211yesmaximal, characteristic, complemented
7C2×#14519801C211yesmaximal, characteristic
8D61⋊M16C2211yescharacteristic
9D4×#6923—22no—
10D4×#6923—22no—
11#14519856C2211yescharacteristic
12#14519856C2211yescharacteristic
13#14519856C2211yescharacteristic
14C2×C22⋊#6923—22no—
15#14519841—22no—
16#14519839—22no—
17#14519835—22no—
18C2×#11758224C2211yescharacteristic
19C2×D4×D61C2211yescharacteristic
20#14519801—22no—
21#14519801—22no—
22C2×#11758190C411yescharacteristic, complemented
23C2×#11758200C411yescharacteristic, complemented
24C2×#11758199C411yescharacteristic, complemented
25C2×#11758189C2211yescharacteristic
26C2×D8×C61C411yescharacteristic, complemented
27C23×D61—21no—
28C22×#6923—24no—
29C2×D4×C61C2×C411yescharacteristic
30C2×D4×C61C2×C411yescharacteristic, complemented
31C2×C22⋊D61—21no—
32C2×C22⋊D61—21no—
33C22×Dic61—21no—
34#11758224—21no—
35#11758224—21no—
36#11758224—21no—
37#11758224—21no—
38D4×D61—21no—
39D4×D61—21no—
40D4×D61D412yes—
41D4×D61D412yes—
42C2×D244C2×C411yescharacteristic
43C2×C4×D61C2311yescharacteristic
44C2×Dic122C2×C411yescharacteristic, complemented
45C22⋊#6923—24no—
46C22⋊#6923—21no—
47C22⋊#6923—21no—
48C22⋊#6923D412yes—
49#11758217—21no—
50C4⋊#6923—21no—
51C4⋊#6923—21no—
52C4⋊#6923—21no—
53C4×#6923—21no—
54C4×#6923—21no—
55C4×#6923D412yes—
56#11758213—21no—
57D61⋊C8—21no—
58D8×C61—22no—
59C2×C8×C61C2×C411yescharacteristic, complemented
60#11758200—22no—
61#11758199—22no—
62C2×#92418C2×C411yescharacteristic, complemented
63#11758190—22no—
64#11758189—21no—
65#11758189—21no—
66C23×C61—21no—
67C23×C61—21no—
68C22×D61—21no—
69C22×D61—22no—
70C22×D61—22no—
71C22×D61—82no—
72C22×D61C2×D411yescharacteristic
73C2×#6923—22no—
74C2×#6923—22no—
75C2×#6923—41no—
76C2×#6923—84no—
77D4×C61—21no—
78D4×C61—21no—
79D4×C61—21no—
80D4×C61C22⋊C412yes—
81C2×C4×C61C22×C411yescharacteristic
82C22⋊D61—22no—
83C22⋊D61—22no—
84C22⋊D61—41no—
85C22⋊D61—41no—
86C2×Dic61—21no—
87C2×Dic61—41no—
88C2×Dic61—41no—
89C2×Dic61#4111yescharacteristic
90D244—21no—
91D244C22⋊C412yes—
92C4×D61C2×D411yescharacteristic
93C4×D61C2×D411yescharacteristic
94C4×D61C2×D411yescharacteristic
95C4×D61#4111yescharacteristic
96Dic122—21no—
97Dic122—21no—
98#92420—41no—
99C8×C61—21no—
100#92418—21no—
101C22×C61—22no—
102C22×C61—41no—
103C22×C61—81no—
104C22×C61—81no—
105C22×C61C4×D411yescharacteristic
106C2×D61—22no—
107C2×D61—41no—
108C2×D61—44no—
109C2×D61—82no—
110C2×D61—81no—
111C2×D61#12011yescharacteristic
112C2×D61#12111yescharacteristic
113#6923—42no—
114#6923—42no—
115#6923—81no—
116C4×C61C2×C22⋊C411yescharacteristic
117C4×C61C4×D411yescharacteristic
118Dic61—41no—
119Dic61#12111yescharacteristic
120Dic61#12311yescharacteristic
121#1904—611nomaximal, Sylow
122C2×C61—21no—
123C2×C61—42no—
124C2×C61—81no—
125C2×C61#38611yescharacteristic
126D61—21no—
127D61—21no—
128D61—42no—
129C2×AGL(1,ℤ/8)—611no—
130#518—611no—
131#421—611no—
132#418—611no—
133#410—611no—
134#344—611no—
135H(3,ℤ/4)—611no—
136C61#190411yescharacteristic, complemented, Sylow
137C2×#41—611no—
138C22×D4—611no—
139AGL(1,ℤ/8)—1222no—
140AGL(1,ℤ/8)—1222no—
141C2×SD16—611no—
142C2×SD16—611no—
143C2×D8—611no—
144C2×D8#692311yescharacteristic, complemented
145C2×M16—611no—
146C2×M16—611no—
147C4×D4—1222no—
148C4×D4—1222no—
149#117—611no—
150#117—611no—
151#117—611no—
152C2×C22⋊C4—1222no—
153#104—1222no—
154#102—1222no—
155#99—1222no—
156C24—1221no—
157#41—1221no—
158#41—1221no—
159#41—1221no—
160#41—1221no—
161C2×Q8—611no—
162C2×D4—612no—
163C2×D4—612no—
164C2×D4—611no—
165C2×D4—1221no—
166C2×D4—1221no—
167C2×D4—1221no—
168C2×D4—1221no—
169C2×D4C2×#692311yescharacteristic
170C2×D4C2×#692311yescharacteristic, complemented
171C22×C4—611no—
172C22×C4—1221no—
173C22×C4—1224no—
174SD16—1222no—
175SD16—1222no—
176D8—22no—
177D8—1222no—
178M16—1221no—
179M16—1221no—
180M16—1221no—
181M16—1221no—
182C2×C8—611no—
183C2×C8—1221no—
184C2×C8C2×#692311yescharacteristic, complemented
185C4⋊C4—1221no—
186C4⋊C4—1221no—
187C4⋊C4—1221no—
188C22⋊C4—612no—
189C22⋊C4—1221no—
190C22⋊C4—1224no—
191C22⋊C4—1221no—
192C42—612no—
193C42—1221no—
194C42—1221no—
195C23—21no—
196C23—21no—
197C23—611no—
198C23—1222no—
199C23—1222no—
200C23—1221no—
201C23—4882no—
202Q8—1221no—
203Q8—1221no—
204D4—21no—
205D4—21no—
206D4—21no—
207D4—612no—
208D4—1222no—
209D4—1222no—
210D4—1221no—
211D4—2441no—
212D4—2441no—
213D4C22⋊#692312yes—
214C2×C4—611no—
215C2×C4—611no—
216C2×C4—611no—
217C2×C4—611no—
218C2×C4—611no—
219C2×C4—1222no—
220C2×C4—1222no—
221C2×C4—1221no—
222C2×C4—4884no—
223C2×C4—2441no—
224C2×C4—2441no—
225C2×C4—2441no—
226C2×C4C22×#692311yescharacteristic
227C8—21no—
228C8—1221no—
229C8—2441no—
230C22—22no—
231C22—41no—
232C22—81no—
233C22—81no—
234C22—611no—
235C22—611no—
236C22—1222no—
237C22—4881no—
238C22—4882no—
239C22—2441no—
240C22—2444no—
241C22D4×#692311yescharacteristic
242C4—611no—
243C4—611no—
244C4—4881no—
245C4—2442no—
246C4—2442no—
247C4—2441no—
248C4C2×C22⋊#692311yescharacteristic
249C4D4×#692311yescharacteristic
250C2—21no—
251C2—42no—
252C2—81no—
253C2—1221no—
254C2—1221no—
255C2—2442no—
256C2#1684071011yescharacteristic
subgroupG/H
centerC2#16840710
commutatorC2×C4×C61C22×C4
FrattiniC2×C4C22×#6923
FittingC2×D8×C61C4
socleC2×C61#386
hypercenterC2×D8#6923
hypocenterC61#1904
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×D8

Complements

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

NH ≅ G/Ntype
1. #16840829C2semidirect
2. #16840760C2semidirect
3. #16840754C2semidirect
4. #16840742C2semidirect
5. #16840644C2semidirect
6. #16840630C2semidirect
22. C2×#11758190C4semidirect
23. C2×#11758200C4semidirect
24. C2×#11758199C4semidirect
26. C2×D8×C61C4semidirect
30. C2×D4×C61C2×C4semidirect
44. C2×Dic122C2×C4semidirect
59. C2×C8×C61C2×C4semidirect
62. C2×#92418C2×C4semidirect
136. C61#1904semidirect
144. C2×D8#6923semidirect
170. C2×D4C2×#6923semidirect
184. C2×C8C2×#6923semidirect