Finite Group Databasebeta

← #21445826

Subgroups — #21445826

Order 7808.

356 conjugacy classes of subgroups; only the 109 normal subgroups are shown.

normal subgroups only

This group has 356 conjugacy classes of subgroups — too many to draw. Only its 109 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×C4×D244C211yesmaximal, characteristic
2C2×C4⋊#92418C211yesmaximal, characteristic, complemented
3C2×#14519697C212yesmaximal
4#16839524C212yesmaximal, complemented
5C61×#382C211yesmaximal, characteristic, complemented
6C22×D244C2211yescharacteristic
7C22×C4×D61—21no—
8C22×#92418C2212yes—
9C4×D244—22no—
10C4×D244C414yescomplemented
11C2×C4⋊Dic61C2211yescharacteristic
12C2×#11758198—21no—
13C4⋊#92418—22no—
14#14519697—24no—
15C2×C4⋊C4×C61C2212yes—
16C2×C42×C61C2211yescharacteristic
17#95×C61—21no—
18#95×C61—21no—
19C23×D61—21no—
20C22×C4×C61—22no—
21C22×C4×C61D411yescharacteristic
22C22×C4×C61D411yescharacteristic
23C22×C4×C61C2311yescharacteristic
24C22×Dic61—21no—
25C2×D244—21no—
26C2×D244—21no—
27C2×D244—21no—
28C2×D244C2×C412yes—
29C2×D244D412yes—
30C2×D244Q812yes—
31C2×C4×D61—24no—
32C2×C4×D61—44no—
33C4⋊C4×C61—22no—
34C4⋊C4×C61—22no—
35C42×C61C2×C412yes—
36C42×C61D412yes—
37#11758198—24no—
38C4⋊Dic61—21no—
39C4⋊Dic61C2×C412yes—
40C2×#92418—22no—
41C2×#92418—22no—
42C2×#92418—22no—
43C23×C61C2×D411yescharacteristic
44C22×D61—22no—
45C22×D61—22no—
46C22×D61—22no—
47C22×D61—42no—
48C22×D61—42no—
49C2×C4×C61—22no—
50C2×C4×C61—22no—
51C2×C4×C61—42no—
52C2×C4×C61—42no—
53C2×C4×C61—42no—
54C2×C4×C61C22⋊C412yes—
55C2×C4×C61C22⋊C412yes—
56C2×C4×C61C22×C411yescharacteristic
57C2×C4×C61C2×D411yescharacteristic
58C2×C4×C61C2×D411yescharacteristic
59C2×C4×C61C2×Q811yescharacteristic
60C2×C4×C61#4111yescharacteristic
61C2×C4×C61#4111yescharacteristic
62C2×Dic61—22no—
63C2×Dic61—42no—
64D244—22no—
65D244—22no—
66D244—22no—
67D244C4⋊C414yes—
68C4×D61—48no—
69#92418—42no—
70C22×C61C2×C22⋊C411yescharacteristic
71C22×C61#12111yescharacteristic
72C22×C61C22⋊Q811yescharacteristic
73C22×C61#13512yes—
74C22×C61AGL(1,ℤ/8)12yes—
75C2×D61—24no—
76C2×D61—42no—
77C2×D61—42no—
78C2×D61—44no—
79C2×D61—44no—
80C4×C61—22no—
81C4×C61—22no—
82C4×C61—82no—
83C4×C61C2×C4⋊C411yescharacteristic
84C4×C61#11711yescharacteristic
85C4×C61#12111yescharacteristic
86C4×C61C22⋊Q811yescharacteristic
87Dic61—42no—
88#1804—611nomaximal, Sylow
89C2×C61#38011yescharacteristic
90C2×C61#41611yescharacteristic
91C2×C61#41811yescharacteristic
92C2×C61#46312yes—
93C2×C61#47812yes—
94D61—44no—
95C2×C4×D4—611no—
96C2×C4⋊C8—611no—
97C2×#102—612no—
98#382D6111yescharacteristic, complemented
99#340—612no—
100C61#180411yescharacteristic, complemented, Sylow
101C22×D4—611no—
102C23×C4—1221no—
103C22×C8—612no—
104C4×D4—614no—
105C4×D4—1222no—
106C2×C4⋊C4—611no—
107C2×C4⋊C4C2×D6112yes—
108C2×C22⋊C4—1221no—
109C2×C42C2×D6111yescharacteristic
110C4⋊C8—1222no—
111#102—1224no—
112#95—21no—
113#95—21no—
114C24—1221no—
115C2×D4—612no—
116C2×D4—612no—
117C2×D4—612no—
118C2×D4—1221no—
119C2×D4—1221no—
120C2×D4—1221no—
121C22×C4—22no—
122C22×C4—1221no—
123C22×C4—1224no—
124C22×C4—2444no—
125C22×C4C22⋊D6111yescharacteristic
126C22×C4C22⋊D6111yescharacteristic
127C22×C4C22×D6111yescharacteristic
128C2×C8—1222no—
129C2×C8—1222no—
130C2×C8—1222no—
131C4⋊C4—22no—
132C4⋊C4—22no—
133C4⋊C4—612no—
134C4⋊C4—1221no—
135C22⋊C4—1224no—
136C42C4×D6112yes—
137C42D24412yes—
138C23—1222no—
139C23—1222no—
140C23—1222no—
141C23—2442no—
142C23—2442no—
143C23C2×C22⋊D6111yescharacteristic
144D4—614no—
145D4—1222no—
146D4—1222no—
147D4—1222no—
148C2×C4—22no—
149C2×C4—22no—
150C2×C4—42no—
151C2×C4—42no—
152C2×C4—42no—
153C2×C4—1222no—
154C2×C4—2448no—
155C2×C4—2442no—
156C2×C4#1175819812yes—
157C2×C4#1175819812yes—
158C2×C4C2×C4×D6111yescharacteristic
159C2×C4C2×D24411yescharacteristic
160C2×C4D4×D6111yescharacteristic
161C2×C4#1175822411yescharacteristic
162C2×C4Q8×D6111yescharacteristic
163C2×C4#1175822611yescharacteristic
164C8—2442no—
165C22—1224no—
166C22—2444no—
167C22—2442no—
168C22—2442no—
169C22—2444no—
170C22C2×#1175819811yescharacteristic
171C22#1451974811yescharacteristic
172C22#1451975311yescharacteristic
173C22#1451979712yes—
174C22#1451980212yes—
175C4—22no—
176C4—22no—
177C4—82no—
178C4—2442no—
179C4C4⋊C4×D6111yescharacteristic
180C4#1451973511yescharacteristic
181C4#1451975211yescharacteristic
182C4#1451975711yescharacteristic
183C2—2444no—
184C2#1683961911yescharacteristic
185C2#1683975611yescharacteristic
186C2#1683976611yescharacteristic
187C2#1683997412yes—
188C2#1684005912yes—
subgroupG/H
centerC23C2×C22⋊D61
commutatorC2×C4×C61C22×C4
FrattiniC22×C4C22×D61
FittingC61×#382C2
socleC23×C61C2×D4
hypercenter#382D61
hypocenterC61#1804
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ #382

Complements

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

NH ≅ G/Ntype
2. C2×C4⋊#92418C2semidirect
4. #16839524C2semidirect
5. C61×#382C2semidirect
10. C4×D244C4semidirect
98. #382D61semidirect
100. C61#1804semidirect