Finite Group Databasebeta

← #21446806

Subgroups — #21446806

Order 7808.

260 conjugacy classes of subgroups; only the 87 normal subgroups are shown.

normal subgroups only

This group has 260 conjugacy classes of subgroups — too many to draw. Only its 87 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×#14519776C211yesmaximal, characteristic
2#16839785C211yesmaximal, characteristic
3M16×Dic61C211yesmaximal, characteristic
4#16839531C211yesmaximal, characteristic
5#16839530C211yesmaximal, characteristic
6#16839530C211yesmaximal, characteristic
7C61×#343C211yesmaximal, characteristic
8C22×Dic122C412yes—
9C2×#11758194C2211yescharacteristic
10C2×#11758194C2211yescharacteristic
11#14519776—21no—
12#14519776—21no—
13#14519776—21no—
14#14519776—21no—
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×C411yescharacteristic
28C22×Dic61C2×C411yescharacteristic
29C22×Dic61C2×C412yes—
30C2×Dic122—22no—
31C2×Dic122—22no—
32C2×Dic122—44no—
33M16×C61—21no—
34M16×C61—21no—
35M16×C61—21no—
36M16×C61Q812yescomplemented
37C2×C8×C61—21no—
38C2×C8×C61—21no—
39C4⋊C4×C61—21no—
40C4⋊C4×C61—21no—
41C4⋊Dic61—21no—
42C4⋊Dic61—21no—
43#11758196—22no—
44#11758196—22no—
45C4×Dic61D411yescharacteristic
46C4×Dic61D411yescharacteristic
47C4×Dic61D411yescharacteristic
48C4×Dic61D411yescharacteristic
49#11758194—21no—
50#11758194—21no—
51#11758194—21no—
52#11758194Q812yescomplemented
53C2×#92418—21no—
54C2×#92418—21no—
55C23×C61C22×C411yescharacteristic
56C2×C4×C61—22no—
57C2×C4×C61—42no—
58C2×C4×C61C2×D411yescharacteristic
59C2×C4×C61C2×D411yescharacteristic
60C2×C4×C61C2×Q811yescharacteristic
61C2×C4×C61C2×Q811yescharacteristic
62C2×C4×C61#4111yescharacteristic
63C2×C4×C61#4111yescharacteristic
64C2×Dic61—22no—
65C2×Dic61—22no—
66C2×Dic61—22no—
67C2×Dic61—42no—
68C2×Dic61C22⋊C411yescharacteristic
69C2×Dic61C22⋊C411yescharacteristic
70C2×Dic61C22⋊C411yescharacteristic
71C2×Dic61C22⋊C411yescharacteristic
72Dic122—44no—
73Dic122—44no—
74C8×C61—22no—
75C8×C61—41no—
76#92418—22no—
77#92418—41no—
78C22×C61—21no—
79C22×C61—21no—
80C22×C61C2×C22⋊C411yescharacteristic
81C22×C61C4×Q811yescharacteristic
82C22×C61C4×Q811yescharacteristic
83C4×C61—42no—
84C4×C61C22⋊Q811yescharacteristic
85C4×C61C22⋊Q811yescharacteristic
86C4×C61#12411yescharacteristic
87C4×C61C4⋊Q811yescharacteristic
88Dic61—21no—
89Dic61—21no—
90Dic61—42no—
91Dic61#10012yes—
92Dic61#10112yes—
93#1997—611nomaximal, Sylow
94C2×C61—21no—
95C2×C61—21no—
96C2×C61#39111yescharacteristic
97C2×C61C2×#10011yescharacteristic
98C2×C61C2×#10111yescharacteristic
99C2×C4⋊Q8—611no—
100#423—611no—
101C4×M16—611no—
102#343—611no—
103#343—611no—
104#343—611no—
105#343D6111yescharacteristic
106C61#199711yescharacteristic, complemented, Sylow
107C22×Q8—612no—
108C2×M16—611no—
109C2×M16—611no—
110C2×M16C2×D6111yescharacteristic
111C2×M16C2×D6111yescharacteristic
112C4⋊Q8—1221no—
113C4⋊Q8—1221no—
114C4⋊Q8—1221no—
115C4⋊Q8—1221no—
116C2×C4⋊C4—612no—
117C2×C4⋊C4—611no—
118C2×C4⋊C4C2×D6111yescharacteristic
119C2×C42—611no—
120C4⋊C8—1221no—
121C4⋊C8—1221no—
122#97—1221no—
123C4×C8—1221no—
124C2×Q8—1222no—
125C2×Q8—1222no—
126C2×Q8—2444no—
127C22×C4—611no—
128C22×C4—611no—
129C22×C4—612no—
130C22×C4C4×D6112yes—
131C22×C4C22×D6111yescharacteristic
132M16—21no—
133M16—21no—
134M16—21no—
135M16—612no—
136M16—1221no—
137M16—1221no—
138M16—1221no—
139M16Dic12212yescomplemented
140C2×C8—21no—
141C2×C8—21no—
142C2×C8—1221no—
143C2×C8—1221no—
144C4⋊C4—21no—
145C4⋊C4—21no—
146C4⋊C4—1222no—
147C4⋊C4—1222no—
148C4⋊C4—1221no—
149C4⋊C4—1221no—
150C42—611no—
151C42—611no—
152C42—611no—
153C42—611no—
154C23C2×C4×D6111yescharacteristic
155Q8—2444no—
156Q8—2444no—
157C2×C4—22no—
158C2×C4—42no—
159C2×C4—611no—
160C2×C4—611no—
161C2×C4—611no—
162C2×C4—611no—
163C2×C4—1222no—
164C2×C4—1222no—
165C2×C4—1222no—
166C2×C4—2442no—
167C2×C4C2×Dic12211yescharacteristic
168C2×C4#1175822211yescharacteristic
169C2×C4D4×D6111yescharacteristic
170C2×C4D4×D6111yescharacteristic
171C2×C4#1175822411yescharacteristic
172C2×C4Q8×D6111yescharacteristic
173C8—22no—
174C8—41no—
175C8—1222no—
176C8—2441no—
177C22—21no—
178C22—21no—
179C22C22⋊C4×D6111yescharacteristic
180C22#1451974211yescharacteristic
181C22C4×Dic12211yescharacteristic
182C4—42no—
183C4—612no—
184C4—612no—
185C4—1221no—
186C4—1221no—
187C4—2442no—
188C4#1451975411yescharacteristic
189C4#1451975511yescharacteristic
190C4#1451976311yescharacteristic
191C4#1451977611yescharacteristic
192C2—21no—
193C2—21no—
194C2#1683966611yescharacteristic
195C2#100×D6111yescharacteristic
196C2#101×D6111yescharacteristic
subgroupG/H
centerC22C22⋊C4×D61
commutatorC23×C61C22×C4
FrattiniC22×C4C22×D61
FittingC61×#343C2
socleC22×C61C2×C22⋊C4
hypercenter#343D61
hypocenterC61#1997
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
36. M16×C61Q8semidirect
52. #11758194Q8semidirect
106. C61#1997semidirect
139. M16Dic122semidirect