Finite Group Databasebeta

← #21455053

Subgroups — #21455053

Order 7808.

738 conjugacy classes of subgroups; only the 173 normal subgroups are shown.

normal subgroups only

This group has 738 conjugacy classes of subgroups — too many to draw. Only its 173 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
1C2×#14519808C212yesmaximal, complemented
2#16840273C211yesmaximal, characteristic
3#16839918C214yesmaximal, complemented
4#16839901C214yesmaximal, complemented
5#16839771C212yesmaximal, complemented
6#16839726C211yesmaximal, characteristic, complemented
7C23×Q8×C61C211yesmaximal, characteristic, complemented
8C2×#11758222C2211yescharacteristic
9#14519808—28no—
10C2×#11758202C2214yescomplemented
11C2×#11758201C2214yescomplemented
12C2×#11758194C2212yes—
13#14519760—21no—
14#14519756C2212yes—
15#14519751C2212yes—
16#14519746—21no—
17C4×C22⋊D61—22no—
18#14519736C2211yescharacteristic
19#14519701C2218yescomplemented
20C22⋊#92418C2214yes—
21C22×Q8×C61—28no—
22C22×Q8×C61—22no—
23C22×Q8×C61—21no—
24C22×Q8×C61C2214yes—
25C22×Q8×C61C2212yes—
26C23×C4×C61—21no—
27C23×C4×C61C2211yescharacteristic
28C24×C61D411yescharacteristic
29C2×Q8×C61—216no—
30C2×Q8×C61—28no—
31C2×Q8×C61—216no—
32C2×Q8×C61—24no—
33C2×Q8×C61—24no—
34C2×Q8×C61—22no—
35C2×Q8×C61D418yescomplemented
36C2×Q8×C61C2314yes—
37C22×C4×C61—28no—
38C22×C4×C61—24no—
39C22×C4×C61—22no—
40C22×C4×C61—24no—
41C22×C4×C61D412yes—
42C22×C4×C61D411yescharacteristic
43C22×C4×C61C2312yes—
44C22×C4×C61C2311yescharacteristic
45C2×C22⋊D61—21no—
46C2×C22⋊D61—22no—
47#11758222—24no—
48C2×D244C2311yescharacteristic
49C2×C4×D61—21no—
50C2×Dic122C2311yescharacteristic
51C22⋊Dic61—21no—
52C22⋊Dic61—22no—
53#11758202—28no—
54#11758201—28no—
55#11758198—22no—
56C4⋊Dic61C2312yes—
57#11758196—22no—
58C4×Dic61—21no—
59#11758194—24no—
60C2×#92418C2314yes—
61C23×C61—22no—
62C23×C61—24no—
63C23×C61C2×D411yescharacteristic
64C23×C61C2×D412yes—
65C22×D61—21no—
66Q8×C61—216no—
67Q8×C61—28no—
68Q8×C61—24no—
69Q8×C61C2×D418yes—
70C2×C4×C61—216no—
71C2×C4×C61—28no—
72C2×C4×C61—22no—
73C2×C4×C61—24no—
74C2×C4×C61—24no—
75C2×C4×C61—24no—
76C2×C4×C61C2×D412yes—
77C2×C4×C61C2×D411yescharacteristic
78C2×C4×C61C2×D414yes—
79C2×C4×C61C2411yescharacteristic
80C22⋊D61—42no—
81C22⋊D61—44no—
82C2×Dic61—22no—
83C2×Dic61—21no—
84D244—22no—
85C4×D61—42no—
86Dic122—22no—
87#92418—24no—
88C22×C61—28no—
89C22×C61—22no—
90C22×C61—22no—
91C22×C61—22no—
92C22×C61#12012yes—
93C22×C61#13714yescomplemented
94C22×C61C22×D411yescharacteristic
95C2×D61—41no—
96C2×D61—42no—
97C4×C61—28no—
98C4×C61—22no—
99C4×C61#12012yes—
100C4×C61C22×D412yes—
101Dic61—41no—
102Dic61—42no—
103#3004—611nomaximal, Sylow
104C2×C61—22no—
105C2×C61—24no—
106C2×C61C2×#12011yescharacteristic
107C2×C61C2×#13712yes—
108D61—81no—
109C23×Q8D6111yescharacteristic, complemented
110C2×#137—612no—
111#525—611no—
112#451—614no—
113#448—614no—
114#419—612no—
115#407—611no—
116C61#300411yescharacteristic, complemented, Sylow
117C2×#41—611no—
118C22×Q8—28no—
119C22×Q8—22no—
120C22×Q8—21no—
121C22×Q8C2×D6114yes—
122C22×Q8C2×D6112yes—
123C23×C4—21no—
124C23×C4C2×D6111yescharacteristic
125#137—1228no—
126C2×Q16—614no—
127C2×SD16—614no—
128C2×M16—612no—
129#123—1221no—
130C22⋊Q8—612no—
131#121—612no—
132#120—1221no—
133C4×D4—1222no—
134#117—611no—
135#103—618no—
136C22⋊C8—614no—
137C24C22⋊D6111yescharacteristic
138#41—1224no—
139C2×Q8—216no—
140C2×Q8—28no—
141C2×Q8—216no—
142C2×Q8—24no—
143C2×Q8—22no—
144C2×Q8—24no—
145C2×Q8—611no—
146C2×Q8C22⋊D6118yescomplemented
147C2×Q8C22×D6114yes—
148C2×D4—611no—
149C2×D4—1222no—
150C2×D4—1221no—
151C22×C4—28no—
152C22×C4—24no—
153C22×C4—22no—
154C22×C4—24no—
155C22×C4—1221no—
156C22×C4C22⋊D6112yes—
157C22×C4C22⋊D6111yescharacteristic
158C22×C4C22×D6112yes—
159C22×C4C22×D6111yescharacteristic
160Q16—1228no—
161SD16—1228no—
162M16—1224no—
163C2×C8—614no—
164C4⋊C4—612no—
165C4⋊C4—1222no—
166C22⋊C4—1221no—
167C22⋊C4—1222no—
168C22⋊C4—1222no—
169C42—1221no—
170C23—24no—
171C23—22no—
172C23—1221no—
173C23C2×C22⋊D6112yes—
174C23C2×C22⋊D6111yescharacteristic
175Q8—216no—
176Q8—24no—
177Q8—28no—
178Q8—1222no—
179Q8C2×C22⋊D6118yes—
180D4—1222no—
181D4—2444no—
182D4—2442no—
183C2×C4—216no—
184C2×C4—24no—
185C2×C4—28no—
186C2×C4—22no—
187C2×C4—24no—
188C2×C4—24no—
189C2×C4—1222no—
190C2×C4—1221no—
191C2×C4—2442no—
192C2×C4C2×C22⋊D6112yes—
193C2×C4C2×C22⋊D6114yes—
194C2×C4C2×C22⋊D6111yescharacteristic
195C2×C4C23×D6111yescharacteristic
196C8—1224no—
197C22—28no—
198C22—22no—
199C22—22no—
200C22—22no—
201C22—2441no—
202C22—2442no—
203C22#1451974612yes—
204C22#1451980814yescomplemented
205C22C22×C22⋊D6111yescharacteristic
206C4—28no—
207C4—22no—
208C4—2441no—
209C4—2442no—
210C4#1451974612yes—
211C4C22×C22⋊D6112yes—
212C2—24no—
213C2—22no—
214C2—4881no—
215C2C2×#1451974611yescharacteristic
216C2C2×#1451980812yes—
subgroupG/H
centerC22C22×C22⋊D61
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC23×Q8×C61C2
socleC22×C61C22×D4
hypercenterC23×Q8D61
hypocenterC61#3004
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23×C4 ◁ C23×Q8

Complements

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

NH ≅ G/Ntype
1. C2×#14519808C2semidirect
3. #16839918C2semidirect
4. #16839901C2semidirect
5. #16839771C2semidirect
6. #16839726C2semidirect
7. C23×Q8×C61C2semidirect
10. C2×#11758202C22semidirect
11. C2×#11758201C22semidirect
19. #14519701C22semidirect
35. C2×Q8×C61D4semidirect
93. C22×C61#137semidirect
109. C23×Q8D61semidirect
116. C61#3004semidirect
146. C2×Q8C22⋊D61semidirect
204. C22#14519808semidirect