Finite Group Databasebeta

← #21446829

Subgroups — #21446829

Order 7808.

392 conjugacy classes of subgroups; only the 93 normal subgroups are shown.

normal subgroups only

This group has 392 conjugacy classes of subgroups — too many to draw. Only its 93 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×Dic244C211yesmaximal, characteristic, complemented
2C2×#14519756C212yesmaximal
3C2×#14519702C212yesmaximal, complemented
4#16839525C211yesmaximal, characteristic, complemented
5C2×C22⋊C8×C61C211yesmaximal, characteristic
6C22×Dic122C2212yes—
7C2×Dic244—24no—
8C2×Dic244—22no—
9#14519756—24no—
10#14519756—24no—
11C2×C4⋊Dic61C2212yes—
12C2×#11758196—22no—
13C2×C22⋊Dic61—22no—
14#14519702—24no—
15C23×C4×C61C2211yescharacteristic
16C22×C8×C61C2211yescharacteristic
17C22×C8×C61C2211yescharacteristic
18C22⋊C8×C61—22no—
19C24×C61D411yescharacteristic
20C22×C4×C61—21no—
21C22×C4×C61—22no—
22C22×C4×C61—22no—
23C22×C4×C61—21no—
24C22×C4×C61D411yescharacteristic
25C22×C4×C61C2311yescharacteristic
26C22×Dic61—22no—
27C22×Dic61—22no—
28C2×Dic122—22no—
29C2×Dic122—22no—
30C2×Dic122—22no—
31C2×Dic122—22no—
32C2×Dic122—22no—
33C2×Dic122D414yes—
34C2×C8×C61—22no—
35C2×C8×C61—21no—
36C2×C8×C61—22no—
37C2×C8×C61D412yes—
38C22⋊Dic61—28no—
39C4⋊Dic61—22no—
40C4⋊Dic61D414yes—
41#11758196—28no—
42Dic244—28no—
43C23×C61—22no—
44C23×C61—21no—
45C23×C61—21no—
46C23×C61—22no—
47C23×C61Q1612yescomplemented
48C23×C61C2×D411yescharacteristic
49C2×C4×C61—22no—
50C2×C4×C61—21no—
51C2×C4×C61—41no—
52C2×C4×C61—42no—
53C2×C4×C61—41no—
54C2×C4×C61C2×D412yes—
55C2×C4×C61C2×D411yescharacteristic
56C2×C4×C61C2×D412yes—
57C2×C4×C61#4111yescharacteristic
58C2×Dic61—24no—
59C2×Dic61—24no—
60C2×Dic61—42no—
61C2×Dic61—42no—
62C2×Dic61—42no—
63C2×Dic61—42no—
64Dic122—24no—
65Dic122—24no—
66Dic122—42no—
67Dic122—42no—
68C8×C61—22no—
69C8×C61—41no—
70C22×C61—24no—
71C22×C61—22no—
72C22×C61—41no—
73C22×C61—42no—
74C22×C61—41no—
75C22×C61#12012yes—
76C22×C61#12111yescharacteristic
77C22×C61C2×Q1611yescharacteristic
78C22×C61#13511yescharacteristic
79C22×C61#13712yes—
80C4×C61—41no—
81C4×C61#12011yescharacteristic
82C4×C61#12112yes—
83C4×C61#12711yescharacteristic
84Dic61—44no—
85Dic61—44no—
86#2001—611nomaximal, Sylow
87C2×C61—42no—
88C2×C61#39211yescharacteristic
89C2×C61#45112yes—
90C2×C61#45212yes—
91C2×C61#46711yescharacteristic
92C2×C61#47011yescharacteristic
93C22×Q16—611no—
94C2×C22⋊Q8—612no—
95C2×#103—612no—
96C2×C22⋊C8D6111yescharacteristic
97#340—611no—
98C61#200111yescharacteristic, complemented, Sylow
99C22×Q8—612no—
100C23×C4C2×D6111yescharacteristic
101C2×Q16—1224no—
102C2×Q16—1222no—
103C22×C8C2×D6111yescharacteristic
104C22×C8C2×D6111yescharacteristic
105C22⋊Q8—1224no—
106C22⋊Q8—1224no—
107C2×C4⋊C4—612no—
108C2×C4⋊C4—1222no—
109C2×C22⋊C4—1222no—
110#103—1224no—
111C22⋊C8—22no—
112C24D24411yescharacteristic
113C2×Q8—614no—
114C2×Q8—1222no—
115C2×Q8—1222no—
116C2×Q8—1222no—
117C2×Q8—1222no—
118C2×Q8—1222no—
119C22×C4—21no—
120C22×C4—22no—
121C22×C4—22no—
122C22×C4—21no—
123C22×C4—1222no—
124C22×C4—1222no—
125C22×C4D24411yescharacteristic
126C22×C4C22×D6111yescharacteristic
127Q16—1228no—
128C2×C8—22no—
129C2×C8—22no—
130C2×C8—21no—
131C2×C8C22⋊D6112yes—
132C4⋊C4—614no—
133C4⋊C4—1228no—
134C4⋊C4—1222no—
135C22⋊C4—1228no—
136C23—22no—
137C23—22no—
138C23—21no—
139C23—21no—
140C23Dic24412yescomplemented
141C23C2×D24411yescharacteristic
142Q8—1224no—
143Q8—1224no—
144Q8—2442no—
145Q8—2442no—
146C2×C4—22no—
147C2×C4—21no—
148C2×C4—41no—
149C2×C4—42no—
150C2×C4—41no—
151C2×C4—1224no—
152C2×C4—1224no—
153C2×C4—2442no—
154C2×C4—2442no—
155C2×C4—2442no—
156C2×C4—2442no—
157C2×C4#1175822211yescharacteristic
158C2×C4D4×D6112yes—
159C2×C4D4×D6112yes—
160C2×C4C2×C22⋊D6111yescharacteristic
161C8—22no—
162C8—41no—
163C22—22no—
164C22—24no—
165C22—41no—
166C22—42no—
167C22—41no—
168C22#1451974712yes—
169C22#1451975111yescharacteristic
170C22C2×Dic24411yescharacteristic
171C22#1451979911yescharacteristic
172C22#1451981012yes—
173C4—41no—
174C4—2444no—
175C4—2444no—
176C4#1451974511yescharacteristic
177C4#1451975012yes—
178C4#1451977311yescharacteristic
179C2—42no—
180C2#1683967111yescharacteristic
181C2#1683992012yes—
182C2#1683992612yes—
183C2#1684000311yescharacteristic
184C2#1684002011yescharacteristic
subgroupG/H
centerC23C2×D244
commutatorC22×C4×C61C23
FrattiniC22×C4C22×D61
FittingC2×C22⋊C8×C61C2
socleC23×C61C2×D4
hypercenterC2×C22⋊C8D61
hypocenterC61#2001
LCSG ▷ C22×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×C22⋊C8

Complements

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

NH ≅ G/Ntype
1. C22×Dic244C2semidirect
3. C2×#14519702C2semidirect
4. #16839525C2semidirect
47. C23×C61Q16semidirect
98. C61#2001semidirect
140. C23Dic244semidirect