Finite Group Databasebeta

← #21455424

Subgroups — #21455424

Order 7808.

500 conjugacy classes of subgroups; only the 141 normal subgroups are shown.

normal subgroups only

This group has 500 conjugacy classes of subgroups — too many to draw. Only its 141 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
1C22×#11758189C211yesmaximal, characteristic, complemented
2#16840269C212yesmaximal, complemented
3#16840017C212yesmaximal, complemented
4#16840012C212yesmaximal, complemented
5#16840005C214yesmaximal, complemented
6#16839800C211yesmaximal, characteristic, complemented
7#16839758C212yesmaximal, complemented
8C2×#135×C61C211yesmaximal, characteristic, complemented
9C22×C4×D61C2211yescharacteristic
10C2×#11758189—24no—
11C2×#11758189C2212yes—
12C2×#11758189C2212yes—
13C22×#92418C2211yescharacteristic
14#14519758—22no—
15#14519753C2214yes—
16#14519748C2214yes—
17#14519745—22no—
18C4×C22⋊D61—24no—
19#14519736C2212yes—
20#14519711C2212yescomplemented
21#14519709C2212yescomplemented
22#14519701C2214yescomplemented
23#14519698C2214yescomplemented
24C2×#41×C61C2212yes—
25#135×C61—24no—
26C2×Q16×C61C2211yescharacteristic, complemented
27C2×SD16×C61C2212yescomplemented
28C2×D8×C61C2211yescharacteristic, complemented
29C22×C8×C61C2211yescharacteristic
30C23×D61D411yescharacteristic
31#41×C61—24no—
32#41×C61—24no—
33C2×Q8×C61C2312yes—
34C2×D4×C61—22no—
35C2×D4×C61C2312yes—
36C22×C4×C61—22no—
37C22×C4×C61C2311yescharacteristic
38C2×C22⋊D61—24no—
39C22×Dic61D411yescharacteristic
40C2×C4×D61—22no—
41C2×C4×D61—22no—
42C2×C4×D61D412yes—
43C2×C4×D61C2312yes—
44Q16×C61—22no—
45SD16×C61—24no—
46D8×C61—22no—
47C2×C8×C61D414yescomplemented
48C2×C8×C61C2311yescharacteristic
49C2×C8×C61C2311yescharacteristic
50C22⋊Dic61—22no—
51C22⋊Dic61—24no—
52#11758198—24no—
53C4⋊Dic61C2314yes—
54#11758196—24no—
55C4×Dic61—22no—
56C2×#92418—22no—
57C2×#92418C2312yes—
58#11758189—24no—
59#11758189—24no—
60C23×C61—22no—
61C23×C61C2×D411yescharacteristic
62C22×D61—22no—
63C22×D61—42no—
64C22×D61C2×D412yes—
65Q8×C61—22no—
66Q8×C61—22no—
67D4×C61—22no—
68D4×C61—22no—
69D4×C61—44no—
70C2×C4×C61—22no—
71C2×C4×C61—44no—
72C2×C4×C61C2×D411yescharacteristic
73C2×C4×C61C2×D412yes—
74C2×C4×C61#4112yes—
75C2×C4×C61C2411yescharacteristic
76C22⋊D61—48no—
77C2×Dic61—22no—
78C2×Dic61—24no—
79C2×Dic61C2×D412yes—
80C4×D61—24no—
81C4×D61—22no—
82C4×D61—22no—
83C8×C61C2×D412yes—
84C8×C61C2×D412yes—
85#92418—22no—
86C22×C61—22no—
87C22×C61—42no—
88C22×C61—44no—
89C22×C61#12112yes—
90C22×C61C22×D411yescharacteristic
91C2×D61—22no—
92C2×D61—24no—
93C2×D61—44no—
94C4×C61—42no—
95C4×C61#12112yes—
96C4×C61C22×D411yescharacteristic
97C4×C61C2×#4111yescharacteristic
98Dic61—22no—
99Dic61—44no—
100#3054—611nomaximal, Sylow
101C2×C61—22no—
102C2×C61—82no—
103C2×C61C2×#12111yescharacteristic
104C2×C61#57512yes—
105D61—42no—
106C2×#135D6111yescharacteristic, complemented
107C22×M16—611no—
108#525—612no—
109#470—612no—
110#469—612no—
111#468—614no—
112#427—611no—
113#416—612no—
114C61#305411yescharacteristic, complemented, Sylow
115C2×#41C2×D6112yes—
116C23×C4—611no—
117#135—24no—
118C2×Q16C2×D6111yescharacteristic, complemented
119C2×SD16C2×D6112yescomplemented
120C2×D8C2×D6111yescharacteristic, complemented
121C2×M16—612no—
122C2×M16—612no—
123C2×M16—1224no—
124C22×C8—611no—
125C22×C8C2×D6111yescharacteristic
126#123—1222no—
127C22⋊Q8—614no—
128#121—614no—
129#120—1222no—
130C4×D4—1224no—
131#117—612no—
132#107—612no—
133#106—612no—
134#103—614no—
135#102—614no—
136C24—611no—
137#41—24no—
138#41—24no—
139C2×Q8C22×D6112yes—
140C2×D4—22no—
141C2×D4—1224no—
142C2×D4C22×D6112yes—
143C22×C4—22no—
144C22×C4—611no—
145C22×C4—612no—
146C22×C4—612no—
147C22×C4—1222no—
148C22×C4—1222no—
149C22×C4C22×D6111yescharacteristic
150Q16—22no—
151SD16—24no—
152D8—22no—
153M16—1224no—
154M16—1224no—
155C2×C8—612no—
156C2×C8—1222no—
157C2×C8C22⋊D6114yescomplemented
158C2×C8C22×D6111yescharacteristic
159C2×C8C22×D6111yescharacteristic
160C4⋊C4—614no—
161C4⋊C4—1224no—
162C22⋊C4—1224no—
163C22⋊C4—1224no—
164C22⋊C4—1222no—
165C42—1222no—
166C23—22no—
167C23—612no—
168C23—1222no—
169C23—2442no—
170C23D4×D6111yescharacteristic
171Q8—22no—
172Q8—22no—
173D4—22no—
174D4—22no—
175D4—44no—
176D4—2448no—
177C2×C4—22no—
178C2×C4—44no—
179C2×C4—612no—
180C2×C4—1222no—
181C2×C4—1222no—
182C2×C4—1222no—
183C2×C4—1224no—
184C2×C4—1224no—
185C2×C4D4×D6111yescharacteristic
186C2×C4#1175822412yes—
187C2×C4C2×C22⋊D6112yes—
188C2×C4C23×D6111yescharacteristic
189C8—1222no—
190C8C2×C22⋊D6112yes—
191C8C2×C22⋊D6112yes—
192C22—22no—
193C22—42no—
194C22—44no—
195C22—1222no—
196C22—1224no—
197C22—2444no—
198C22#1451974812yes—
199C22C2×D4×D6111yescharacteristic
200C4—42no—
201C4—1222no—
202C4—2444no—
203C4#1451974812yes—
204C4C22×C22⋊D6111yescharacteristic
205C4C2×#1175822411yescharacteristic
206C2—22no—
207C2—82no—
208C2—2442no—
209C2C2×#1451974811yescharacteristic
210C2#1684055912yes—
subgroupG/H
centerC2×C4D4×D61
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC2×#135×C61C2
socleC22×C61C22×D4
hypercenterC2×#135D61
hypocenterC61#3054
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ C2×#135

Complements

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

NH ≅ G/Ntype
1. C22×#11758189C2semidirect
2. #16840269C2semidirect
3. #16840017C2semidirect
4. #16840012C2semidirect
5. #16840005C2semidirect
6. #16839800C2semidirect
7. #16839758C2semidirect
8. C2×#135×C61C2semidirect
20. #14519711C22semidirect
21. #14519709C22semidirect
22. #14519701C22semidirect
23. #14519698C22semidirect
26. C2×Q16×C61C22semidirect
27. C2×SD16×C61C22semidirect
28. C2×D8×C61C22semidirect
47. C2×C8×C61D4semidirect
106. C2×#135D61semidirect
114. C61#3054semidirect
118. C2×Q16C2×D61semidirect
119. C2×SD16C2×D61semidirect
120. C2×D8C2×D61semidirect
157. C2×C8C22⋊D61semidirect