Finite Group Databasebeta

← #21446044

Subgroups — #21446044

Order 7808.

302 conjugacy classes of subgroups; only the 83 normal subgroups are shown.

normal subgroups only

This group has 302 conjugacy classes of subgroups — too many to draw. Only its 83 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#16840243C211yesmaximal, characteristic
2#16839802C211yesmaximal, characteristic, complemented
3C2×#14519705C211yesmaximal, characteristic
4#16839761C211yesmaximal, characteristic
5#16839531C211yesmaximal, characteristic, complemented
6#16839522C211yesmaximal, characteristic, complemented
7C61×#384C211yesmaximal, characteristic, complemented
8C2×#11758222C2211yescharacteristic
9C2×#11758194C2211yescharacteristic
10C2×#11758194C2211yescharacteristic
11#14519742—21no—
12#14519739—21no—
13C4×C22⋊D61—22no—
14#14519736C2211yescharacteristic
15#14519735—21no—
16C4⋊C4×D61—21no—
17#14519710—21no—
18#14519708—21no—
19#14519705C414yescomplemented
20#14519700—21no—
21#14519697—21no—
22C2×C4⋊C4×C61—22no—
23C2×C4⋊C4×C61C2211yescharacteristic
24C2×C4⋊C4×C61C2211yescharacteristic
25C2×C42×C61C2211yescharacteristic
26C22×C4×C61—21no—
27C22×C4×C61—21no—
28C22×C4×C61D412yes—
29C22×C4×C61C2311yescharacteristic
30C2×C22⋊D61—21no—
31#11758222—21no—
32#11758222—21no—
33#11758222C2×C412yes—
34#11758222Q812yes—
35C2×D244D411yescharacteristic
36C2×C4×D61—21no—
37C2×C4×D61—22no—
38C2×Dic122D411yescharacteristic
39C4⋊C4×C61—21no—
40C4⋊C4×C61—21no—
41C4⋊C4×C61—21no—
42C4⋊C4×C61—21no—
43C4⋊C4×C61—44no—
44C42×C61—21no—
45C42×C61C2×C412yescomplemented
46C22⋊Dic61—21no—
47#11758198—22no—
48C4⋊Dic61D411yescharacteristic
49C4⋊Dic61D411yescharacteristic
50#11758196—22no—
51C4×Dic61—22no—
52C4×Dic61—21no—
53#11758194—21no—
54#11758194—21no—
55#11758194—21no—
56#11758194C2×C412yescomplemented
57C2×#92418—21no—
58C2×#92418—21no—
59C23×C61C2×D411yescharacteristic
60C22×D61—21no—
61C2×C4×C61—22no—
62C2×C4×C61—22no—
63C2×C4×C61—22no—
64C2×C4×C61—22no—
65C2×C4×C61—42no—
66C2×C4×C61—42no—
67C2×C4×C61—41no—
68C2×C4×C61C22×C411yescharacteristic
69C2×C4×C61C2×D411yescharacteristic
70C2×C4×C61C2×D411yescharacteristic
71C2×C4×C61C2×Q811yescharacteristic
72C2×C4×C61#4111yescharacteristic
73C2×C4×C61#4111yescharacteristic
74C22⋊D61—22no—
75C22⋊D61—22no—
76C2×Dic61—21no—
77C2×Dic61—21no—
78C2×Dic61—21no—
79D244—21no—
80D244C4⋊C412yescomplemented
81C4×D61—22no—
82C4×D61—22no—
83C4×D61—82no—
84Dic122—21no—
85Dic122C4⋊C412yescomplemented
86#92418—22no—
87#92418—41no—
88C22×C61—21no—
89C22×C61—21no—
90C22×C61C4×D411yescharacteristic
91C22×C61#12011yescharacteristic
92C22×C61C22⋊Q811yescharacteristic
93C2×D61—22no—
94C2×D61—41no—
95C2×D61—41no—
96C4×C61—24no—
97C4×C61—42no—
98C4×C61—81no—
99C4×C61C2×C4⋊C411yescharacteristic
100C4×C61C4×D411yescharacteristic
101C4×C61C22⋊Q811yescharacteristic
102C4×C61#12311yescharacteristic
103Dic61—22no—
104Dic61—41no—
105Dic61—41no—
106#1859—611nomaximal, Sylow
107C2×C61—21no—
108C2×C61—21no—
109C2×C61#38511yescharacteristic
110C2×C61#45311yescharacteristic
111C2×C61#45611yescharacteristic
112D61—42no—
113#520—611no—
114#428—611no—
115C2×#104—611no—
116#417—611no—
117#384D6111yescharacteristic, complemented
118#343—611no—
119#339—611no—
120C61#185911yescharacteristic, complemented, Sylow
121C2×#41—611no—
122C2×M16—611no—
123C2×M16—611no—
124C4×Q8—1221no—
125C4×D4—1221no—
126C4×D4—1222no—
127#117—611no—
128#117—1221no—
129C2×C4⋊C4—22no—
130C2×C4⋊C4—1221no—
131C2×C4⋊C4C2×D6111yescharacteristic
132C2×C4⋊C4C2×D6111yescharacteristic
133C2×C42C2×D6111yescharacteristic
134#107—1221no—
135#106—1221no—
136#104—614no—
137#103—1221no—
138#102—1221no—
139#41—612no—
140#41—612no—
141#41—1221no—
142#41—1221no—
143C2×Q8—611no—
144C2×D4—611no—
145C2×D4—1221no—
146C22×C4—21no—
147C22×C4—21no—
148C22×C4—1222no—
149C22×C4—1221no—
150C22×C4C22⋊D6112yes—
151C22×C4C22×D6111yescharacteristic
152M16—612no—
153M16—1221no—
154M16—1221no—
155M16—1221no—
156C2×C8—1221no—
157C2×C8—1221no—
158C4⋊C4—21no—
159C4⋊C4—21no—
160C4⋊C4—21no—
161C4⋊C4—21no—
162C4⋊C4—44no—
163C4⋊C4—611no—
164C4⋊C4—611no—
165C4⋊C4—1222no—
166C22⋊C4—1222no—
167C22⋊C4—1221no—
168C42—21no—
169C42—1222no—
170C42—1221no—
171C42C4×D6112yescomplemented
172C23—1221no—
173C23C2×C22⋊D6111yescharacteristic
174Q8—612no—
175Q8—1221no—
176D4—612no—
177D4—1222no—
178D4—1222no—
179D4—1221no—
180C2×C4—22no—
181C2×C4—22no—
182C2×C4—22no—
183C2×C4—22no—
184C2×C4—42no—
185C2×C4—42no—
186C2×C4—41no—
187C2×C4—1221no—
188C2×C4—1222no—
189C2×C4—1222no—
190C2×C4—1221no—
191C2×C4—1221no—
192C2×C4—4882no—
193C2×C4C2×C4×D6111yescharacteristic
194C2×C4#1175822211yescharacteristic
195C2×C4D4×D6111yescharacteristic
196C2×C4D4×D6111yescharacteristic
197C2×C4Q8×D6111yescharacteristic
198C2×C4#1175822611yescharacteristic
199C8—1222no—
200C8—2441no—
201C22—21no—
202C22—21no—
203C22—1222no—
204C22—2441no—
205C22—2441no—
206C22C4×C22⋊D6111yescharacteristic
207C22#1451974511yescharacteristic
208C22#1451975311yescharacteristic
209C4—24no—
210C4—42no—
211C4—81no—
212C4—1222no—
213C4—2441no—
214C4—2441no—
215C4C4⋊C4×D6111yescharacteristic
216C4#1451973911yescharacteristic
217C4#1451975511yescharacteristic
218C4#1451976211yescharacteristic
219C2—21no—
220C2—21no—
221C2—2442no—
222C2#1683963311yescharacteristic
223C2#1683992911yescharacteristic
224C2#1683994411yescharacteristic
subgroupG/H
centerC22#14519745
commutatorC2×C4×C61C22×C4
FrattiniC22×C4C22×D61
FittingC61×#384C2
socleC22×C61#120
hypercenter#384D61
hypocenterC61#1859
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ #384

Complements

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

NH ≅ G/Ntype
2. #16839802C2semidirect
5. #16839531C2semidirect
6. #16839522C2semidirect
7. C61×#384C2semidirect
19. #14519705C4semidirect
45. C42×C61C2×C4semidirect
56. #11758194C2×C4semidirect
80. D244C4⋊C4semidirect
85. Dic122C4⋊C4semidirect
117. #384D61semidirect
120. C61#1859semidirect
171. C42C4×D61semidirect