Finite Group Databasebeta

← #21446810

Subgroups — #21446810

Order 7808.

228 conjugacy classes of subgroups; only the 83 normal subgroups are shown.

normal subgroups only

This group has 228 conjugacy classes of subgroups — too many to draw. Only its 83 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×#14519768C211yesmaximal, characteristic
2#16839785C211yesmaximal, characteristic
3M16×Dic61C211yesmaximal, characteristic
4#16839531C211yesmaximal, characteristic
5#16839530C211yesmaximal, characteristic
6#16839530C211yesmaximal, characteristic
7C61×#343C211yesmaximal, characteristic
8C2×#11758194C2211yescharacteristic
9C2×#11758194C2211yescharacteristic
10#14519768—21no—
11#14519768—21no—
12#14519768—21no—
13#14519768—21no—
14C2×C4⋊Dic61C412yes—
15C2×C4⋊Dic61C2211yescharacteristic
16C2×#11758196C412yes—
17C2×C4×Dic61C2211yescharacteristic
18#14519706—21no—
19#14519706—21no—
20#14519687—21no—
21C8×Dic61—21no—
22C2×M16×C61C2211yescharacteristic
23C2×M16×C61C2211yescharacteristic
24C2×C4⋊C4×C61C2211yescharacteristic
25C22×C4×C61C2×C412yes—
26C22×C4×C61C2311yescharacteristic
27C22×Dic61C2×C412yes—
28C22×Dic61C2×C411yescharacteristic
29C22×Dic61C2×C411yescharacteristic
30M16×C61—21no—
31M16×C61—21no—
32M16×C61—21no—
33M16×C61Q812yes—
34C2×C8×C61—21no—
35C2×C8×C61—21no—
36C4⋊C4×C61—21no—
37C4⋊C4×C61—21no—
38C4⋊Dic61—21no—
39C4⋊Dic61—21no—
40C4⋊Dic61—22no—
41C4⋊Dic61—22no—
42#11758196—22no—
43#11758196—22no—
44C4×Dic61D411yescharacteristic
45C4×Dic61D411yescharacteristic
46C4×Dic61D411yescharacteristic
47C4×Dic61D411yescharacteristic
48#11758194—21no—
49#11758194—21no—
50#11758194—21no—
51#11758194Q812yes—
52C2×#92418—21no—
53C2×#92418—21no—
54C23×C61C22×C411yescharacteristic
55C2×C4×C61—22no—
56C2×C4×C61—42no—
57C2×C4×C61C2×D411yescharacteristic
58C2×C4×C61C2×D411yescharacteristic
59C2×C4×C61C2×Q811yescharacteristic
60C2×C4×C61C2×Q811yescharacteristic
61C2×C4×C61#4111yescharacteristic
62C2×C4×C61#4111yescharacteristic
63C2×Dic61—22no—
64C2×Dic61—41no—
65C2×Dic61—41no—
66C2×Dic61—42no—
67C2×Dic61C22⋊C411yescharacteristic
68C2×Dic61C22⋊C411yescharacteristic
69C2×Dic61C22⋊C411yescharacteristic
70C2×Dic61C22⋊C411yescharacteristic
71C8×C61—22no—
72C8×C61—41no—
73#92418—22no—
74#92418—41no—
75C22×C61—21no—
76C22×C61—21no—
77C22×C61C2×C22⋊C411yescharacteristic
78C22×C61C4×Q811yescharacteristic
79C22×C61C4×Q811yescharacteristic
80C4×C61—42no—
81C4×C61C22⋊Q811yescharacteristic
82C4×C61C22⋊Q811yescharacteristic
83C4×C61#12411yescharacteristic
84C4×C61C4⋊Q811yescharacteristic
85Dic61—21no—
86Dic61—21no—
87Dic61—21no—
88Dic61—21no—
89Dic61—42no—
90#1998—611nomaximal, Sylow
91C2×C61—21no—
92C2×C61—21no—
93C2×C61#39111yescharacteristic
94C2×C61#41311yescharacteristic
95C2×C61#41311yescharacteristic
96C2×#125—611no—
97#423—611no—
98C4×M16—611no—
99#343—611no—
100#343—611no—
101#343—611no—
102#343D6111yescharacteristic
103C61#199811yescharacteristic, complemented, Sylow
104C2×M16—611no—
105C2×M16—611no—
106C2×M16C2×D6111yescharacteristic
107C2×M16C2×D6111yescharacteristic
108#125—1221no—
109#125—1221no—
110#125—1221no—
111#125—1221no—
112C2×C4⋊C4—612no—
113C2×C4⋊C4—612no—
114C2×C4⋊C4—611no—
115C2×C4⋊C4C2×D6111yescharacteristic
116C2×C42—611no—
117C4⋊C8—1221no—
118C4⋊C8—1221no—
119#97—1221no—
120C4×C8—1221no—
121C22×C4—611no—
122C22×C4—611no—
123C22×C4—612no—
124C22×C4C4×D6112yes—
125C22×C4C22×D6111yescharacteristic
126M16—21no—
127M16—21no—
128M16—21no—
129M16—612no—
130M16—1221no—
131M16—1221no—
132M16—1221no—
133M16Dic12212yes—
134C2×C8—21no—
135C2×C8—21no—
136C2×C8—1221no—
137C2×C8—1221no—
138C4⋊C4—21no—
139C4⋊C4—21no—
140C4⋊C4—1222no—
141C4⋊C4—1222no—
142C4⋊C4—1222no—
143C4⋊C4—1222no—
144C4⋊C4—1221no—
145C4⋊C4—1221no—
146C42—611no—
147C42—611no—
148C42—611no—
149C42—611no—
150C23C2×C4×D6111yescharacteristic
151C2×C4—22no—
152C2×C4—42no—
153C2×C4—611no—
154C2×C4—611no—
155C2×C4—611no—
156C2×C4—611no—
157C2×C4—1222no—
158C2×C4—2441no—
159C2×C4—2441no—
160C2×C4—2442no—
161C2×C4C2×Dic12211yescharacteristic
162C2×C4#1175822211yescharacteristic
163C2×C4D4×D6111yescharacteristic
164C2×C4D4×D6111yescharacteristic
165C2×C4#1175822411yescharacteristic
166C2×C4Q8×D6111yescharacteristic
167C8—22no—
168C8—41no—
169C8—1222no—
170C8—2441no—
171C22—21no—
172C22—21no—
173C22C22⋊C4×D6111yescharacteristic
174C22#1451974211yescharacteristic
175C22C4×Dic12211yescharacteristic
176C4—42no—
177C4—1221no—
178C4—1221no—
179C4—1221no—
180C4—1221no—
181C4—2442no—
182C4#1451975411yescharacteristic
183C4#1451975511yescharacteristic
184C4#1451976311yescharacteristic
185C4#1451977611yescharacteristic
186C2—21no—
187C2—21no—
188C2#1683966611yescharacteristic
189C2#1683974311yescharacteristic
190C2#1683974511yescharacteristic
subgroupG/H
centerC22C22⋊C4×D61
commutatorC23×C61C22×C4
FrattiniC22×C4C22×D61
FittingC61×#343C2
socleC22×C61C2×C22⋊C4
hypercenter#343D61
hypocenterC61#1998
LCSG ▷ C23×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ #343

Complements

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

NH ≅ G/Ntype
103. C61#1998semidirect