Finite Group Databasebeta

← #21445812

Subgroups — #21445812

Order 7808.

272 conjugacy classes of subgroups; only the 97 normal subgroups are shown.

normal subgroups only

This group has 272 conjugacy classes of subgroups — too many to draw. Only its 97 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×Dic122C211yesmaximal, characteristic
2#16839786C211yesmaximal, characteristic
3C2×#14519695C212yesmaximal
4#16839530C212yesmaximal
5C61×#423C211yesmaximal, characteristic
6C22×Dic122C2211yescharacteristic
7C2×#11758194C2212yes—
8C4×Dic122—21no—
9C4×Dic122—21no—
10C4×Dic122—21no—
11C4×Dic122—21no—
12C2×C4⋊Dic61C2211yescharacteristic
13C2×#11758196C412yes—
14C2×C4×Dic61C412yes—
15C4⋊#92418—21no—
16C4⋊#92418—21no—
17#14519695—24no—
18C2×M16×C61C2212yes—
19C2×C42×C61C2211yescharacteristic
20C4⋊C8×C61—21no—
21C4⋊C8×C61—21no—
22C22×C4×C61C2×C411yescharacteristic
23C22×C4×C61C2×C411yescharacteristic
24C22×C4×C61C2311yescharacteristic
25C22×Dic61C2×C412yes—
26C22×Dic61C2×C412yes—
27C2×Dic122—21no—
28C2×Dic122—21no—
29C2×Dic122—21no—
30C2×Dic122—21no—
31C2×Dic122D412yes—
32C2×Dic122Q812yes—
33M16×C61—22no—
34M16×C61—22no—
35C2×C8×C61—22no—
36C42×C61D411yescharacteristic
37C42×C61D411yescharacteristic
38C42×C61D411yescharacteristic
39C42×C61D411yescharacteristic
40C4⋊Dic61—21no—
41C4⋊Dic61—21no—
42#11758196—22no—
43#11758196—22no—
44C4×Dic61—22no—
45C4×Dic61—22no—
46#11758194—22no—
47#11758194—22no—
48C2×#92418—22no—
49C23×C61C22×C411yescharacteristic
50C2×C4×C61—22no—
51C2×C4×C61—41no—
52C2×C4×C61C22⋊C411yescharacteristic
53C2×C4×C61C22⋊C411yescharacteristic
54C2×C4×C61C22⋊C411yescharacteristic
55C2×C4×C61C22⋊C411yescharacteristic
56C2×C4×C61C2×D411yescharacteristic
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—22no—
64C2×Dic61—22no—
65C2×Dic61—42no—
66C2×Dic61C4⋊C414yes—
67Dic122—22no—
68Dic122—22no—
69Dic122—22no—
70Dic122—22no—
71C8×C61—42no—
72#92418—42no—
73C22×C61—21no—
74C22×C61—21no—
75C22×C61C2×C22⋊C411yescharacteristic
76C22×C61C2×C4⋊C411yescharacteristic
77C22×C61#11711yescharacteristic
78C4×C61—21no—
79C4×C61—21no—
80C4×C61—21no—
81C4×C61#10112yescomplemented
82C4×C61#12111yescharacteristic
83C4×C61#12111yescharacteristic
84C4×C61C22⋊Q811yescharacteristic
85C4×C61C22⋊Q811yescharacteristic
86Dic61—24no—
87Dic61—42no—
88#1801—611nomaximal, Sylow
89C2×C61—21no—
90C2×C61—21no—
91C2×C61#38011yescharacteristic
92C2×C61C2×#10111yescharacteristic
93C2×C61#41311yescharacteristic
94C2×C4×Q8—611no—
95#423—611no—
96#423D6111yescharacteristic
97C2×#101—612no—
98#343—612no—
99C61#180111yescharacteristic, complemented, Sylow
100C22×Q8—611no—
101C2×M16—612no—
102C2×M16C2×D6112yes—
103C4×Q8—1221no—
104C4×Q8—1221no—
105C4×Q8—1221no—
106C4×Q8—1221no—
107C2×C4⋊C4—612no—
108C2×C4⋊C4—611no—
109C2×C42—612no—
110C2×C42C2×D6111yescharacteristic
111C4⋊C8—21no—
112C4⋊C8—21no—
113C4⋊C8—1221no—
114C4⋊C8—1221no—
115#101—1224no—
116C2×Q8—612no—
117C2×Q8—612no—
118C2×Q8—1221no—
119C2×Q8—1221no—
120C2×Q8—1221no—
121C2×Q8—1221no—
122C22×C4—612no—
123C22×C4—612no—
124C22×C4C4×D6111yescharacteristic
125C22×C4C4×D6111yescharacteristic
126C22×C4C22×D6111yescharacteristic
127M16—22no—
128M16—22no—
129M16—1222no—
130M16—1222no—
131C2×C8—22no—
132C2×C8—1222no—
133C4⋊C4—1222no—
134C4⋊C4—1222no—
135C4⋊C4—1221no—
136C4⋊C4—1221no—
137C42—1222no—
138C42—1222no—
139C42D24411yescharacteristic
140C42D24411yescharacteristic
141C42C22⋊D6111yescharacteristic
142C42C22⋊D6111yescharacteristic
143C23C2×C4×D6111yescharacteristic
144Q8—1222no—
145Q8—1222no—
146Q8—1222no—
147Q8—1222no—
148C2×C4—22no—
149C2×C4—41no—
150C2×C4—614no—
151C2×C4—1222no—
152C2×C4—1222no—
153C2×C4—1222no—
154C2×C4—2442no—
155C2×C4#1175819811yescharacteristic
156C2×C4#1175819811yescharacteristic
157C2×C4#1175819811yescharacteristic
158C2×C4#1175819811yescharacteristic
159C2×C4C2×D24411yescharacteristic
160C2×C4D4×D6111yescharacteristic
161C2×C4#1175822411yescharacteristic
162C2×C4Q8×D6111yescharacteristic
163C2×C4#1175822611yescharacteristic
164C2×C4C2×C22⋊D6111yescharacteristic
165C8—42no—
166C8—2442no—
167C22—21no—
168C22—21no—
169C22C2×#1175819811yescharacteristic
170C22C4⋊C4×D6111yescharacteristic
171C22#1451973511yescharacteristic
172C4—21no—
173C4—21no—
174C4—21no—
175C4—1224no—
176C4—2442no—
177C4#1451969512yescomplemented
178C4#1451974811yescharacteristic
179C4#1451975211yescharacteristic
180C4#1451975311yescharacteristic
181C4#1451975711yescharacteristic
182C2—21no—
183C2—21no—
184C2#1683961911yescharacteristic
185C2C2×#1451969511yescharacteristic
186C2#1683974411yescharacteristic
subgroupG/H
centerC22C2×#11758198
commutatorC23×C61C22×C4
FrattiniC22×C4C22×D61
FittingC61×#423C2
socleC22×C61C2×C22⋊C4
hypercenter#423D61
hypocenterC61#1801
LCSG ▷ C23×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C42 ◁ #423

Complements

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

NH ≅ G/Ntype
81. C4×C61#101semidirect
99. C61#1801semidirect
177. C4#14519695semidirect