Finite Group Databasebeta

← #21455396

Subgroups — #21455396

Order 7808.

520 conjugacy classes of subgroups; only the 145 normal subgroups are shown.

normal subgroups only

This group has 520 conjugacy classes of subgroups — too many to draw. Only its 145 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×C8×D61C211yesmaximal, characteristic, complemented
2#16840269C212yesmaximal, complemented
3#16840000C212yesmaximal, complemented
4#16839995C212yesmaximal, complemented
5#16839988C214yesmaximal, complemented
6#16839800C211yesmaximal, characteristic, complemented
7#16839758C212yesmaximal, complemented
8C2×#135×C61C211yesmaximal, characteristic, complemented
9C22×C4×D61C2211yescharacteristic
10C22×#92418C2211yescharacteristic
11C2×C8×D61—24no—
12C2×C8×D61C2212yes—
13C2×C8×D61C2212yes—
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—
58C8×D61—24no—
59C8×D61—24no—
60C23×C61—22no—
61C23×C61C2×D411yescharacteristic
62C22×D61—22no—
63C22×D61—24no—
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—28no—
92C2×D61—22no—
93C2×D61—22no—
94C2×D61#13514yescomplemented
95C4×C61—42no—
96C4×C61#12112yes—
97C4×C61C22×D411yescharacteristic
98C4×C61C2×#4111yescharacteristic
99Dic61—22no—
100Dic61—44no—
101#3050—611nomaximal, Sylow
102C2×C61—22no—
103C2×C61—82no—
104C2×C61C2×#12111yescharacteristic
105C2×C61C2×#13512yes—
106D61—24no—
107C2×#135D6111yescharacteristic, complemented
108C23×C8—611no—
109#525—612no—
110#467—612no—
111#466—612no—
112#465—614no—
113#427—611no—
114#416—612no—
115C61#305011yescharacteristic, complemented, Sylow
116C2×#41C2×D6112yes—
117C23×C4—611no—
118#135—24no—
119C2×Q16C2×D6111yescharacteristic, complemented
120C2×SD16C2×D6112yescomplemented
121C2×D8C2×D6111yescharacteristic, complemented
122C22×C8—611no—
123C22×C8—612no—
124C22×C8—612no—
125C22×C8—1224no—
126C22×C8C2×D6111yescharacteristic
127#123—1222no—
128C22⋊Q8—614no—
129#121—614no—
130#120—1222no—
131C4×D4—1224no—
132#117—612no—
133#107—612no—
134#106—612no—
135#103—614no—
136#102—614no—
137C24—611no—
138#41—24no—
139#41—24no—
140C2×Q8C22×D6112yes—
141C2×D4—22no—
142C2×D4—1224no—
143C2×D4C22×D6112yes—
144C22×C4—22no—
145C22×C4—611no—
146C22×C4—612no—
147C22×C4—612no—
148C22×C4—1222no—
149C22×C4—1222no—
150C22×C4C22×D6111yescharacteristic
151Q16—22no—
152SD16—24no—
153D8—22no—
154C2×C8—612no—
155C2×C8—1222no—
156C2×C8—1224no—
157C2×C8—1224no—
158C2×C8C22⋊D6114yescomplemented
159C2×C8C22×D6111yescharacteristic
160C2×C8C22×D6111yescharacteristic
161C4⋊C4—614no—
162C4⋊C4—1224no—
163C22⋊C4—1224no—
164C22⋊C4—1224no—
165C22⋊C4—1222no—
166C42—1222no—
167C23—22no—
168C23—612no—
169C23—1224no—
170C23—1222no—
171C23D4×D6111yescharacteristic
172Q8—22no—
173Q8—22no—
174D4—22no—
175D4—22no—
176D4—44no—
177D4—2448no—
178C2×C4—22no—
179C2×C4—44no—
180C2×C4—612no—
181C2×C4—1222no—
182C2×C4—1222no—
183C2×C4—1222no—
184C2×C4—1224no—
185C2×C4—1224no—
186C2×C4D4×D6111yescharacteristic
187C2×C4#1175822412yes—
188C2×C4C2×C22⋊D6112yes—
189C2×C4C23×D6111yescharacteristic
190C8—1222no—
191C8C2×C22⋊D6112yes—
192C8C2×C22⋊D6112yes—
193C22—22no—
194C22—42no—
195C22—44no—
196C22—614no—
197C22—1228no—
198C22—1222no—
199C22—1222no—
200C22#1451974812yes—
201C22C2×D4×D6111yescharacteristic
202C4—42no—
203C4—1222no—
204C4—2444no—
205C4#1451974812yes—
206C4C22×C22⋊D6111yescharacteristic
207C4C2×#1175822411yescharacteristic
208C2—22no—
209C2—82no—
210C2—1224no—
211C2C2×#1451974811yescharacteristic
212C2#135×D6112yes—
subgroupG/H
centerC2×C4D4×D61
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC2×#135×C61C2
socleC22×C61C22×D4
hypercenterC2×#135D61
hypocenterC61#3050
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×C8×D61C2semidirect
2. #16840269C2semidirect
3. #16840000C2semidirect
4. #16839995C2semidirect
5. #16839988C2semidirect
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
94. C2×D61#135semidirect
107. C2×#135D61semidirect
115. C61#3050semidirect
119. C2×Q16C2×D61semidirect
120. C2×SD16C2×D61semidirect
121. C2×D8C2×D61semidirect
158. C2×C8C22⋊D61semidirect