Finite Group Databasebeta

← #21455949

Subgroups — #21455949

Order 7808.

380 conjugacy classes of subgroups; only the 133 normal subgroups are shown.

normal subgroups only

This group has 380 conjugacy classes of subgroups — too many to draw. Only its 133 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
1#16840319C211yesmaximal, characteristic
2#16840092C212yesmaximal
3#16840047C212yesmaximal, complemented
4#16839972C212yesmaximal, complemented
5#16839918C212yesmaximal
6#16839867C214yesmaximal, complemented
7#16839819C211yesmaximal, characteristic
8C2×C4×Q8×C61C211yesmaximal, characteristic
9C2×#11758202C2214yes—
10#14519777C2211yescharacteristic
11#14519777C2211yescharacteristic
12#14519769—21no—
13#14519756—21no—
14#14519756C2212yes—
15C4×Dic122—21no—
16C4×Dic122C2212yes—
17#14519736—21no—
18#14519708C2214yes—
19C4⋊#92418C2212yes—
20#14519701C2214yes—
21#14519700C2214yes—
22C22⋊#92418C2212yes—
23#14519688C2212yes—
24C22×Q8×C61C2211yescharacteristic
25C4×Q8×C61—21no—
26C4×Q8×C61—21no—
27C4×Q8×C61C2212yes—
28C4×Q8×C61C2212yes—
29C2×C4⋊C4×C61—21no—
30C2×C4⋊C4×C61C2211yescharacteristic
31C2×C42×C61—21no—
32C2×C42×C61C2211yescharacteristic
33C2×Q8×C61—24no—
34C2×Q8×C61—21no—
35C2×Q8×C61C2312yes—
36C22×C4×C61—21no—
37C22×C4×C61—21no—
38C22×C4×C61D411yescharacteristic
39C22×C4×C61D411yescharacteristic
40C22×C4×C61C2311yescharacteristic
41C2×Dic122—21no—
42C2×Dic122C2312yes—
43C4⋊C4×C61—22no—
44C4⋊C4×C61—22no—
45C4⋊C4×C61—21no—
46C4⋊C4×C61C2312yes—
47C42×C61—22no—
48C42×C61—22no—
49C42×C61D411yescharacteristic
50C42×C61D411yescharacteristic
51C42×C61C2311yescharacteristic
52C42×C61C2311yescharacteristic
53C22⋊Dic61—22no—
54#11758202—28no—
55C4⋊Dic61—21no—
56C4⋊Dic61—21no—
57C4⋊Dic61—21no—
58C4⋊Dic61C2312yes—
59#11758196—22no—
60#11758196—22no—
61C4×Dic61—22no—
62C2×#92418C2314yes—
63C23×C61C2×D411yescharacteristic
64Q8×C61—24no—
65Q8×C61—22no—
66Q8×C61#4114yes—
67C2×C4×C61—24no—
68C2×C4×C61—22no—
69C2×C4×C61—22no—
70C2×C4×C61—22no—
71C2×C4×C61—22no—
72C2×C4×C61—22no—
73C2×C4×C61—42no—
74C2×C4×C61C2×D411yescharacteristic
75C2×C4×C61C2×D411yescharacteristic
76C2×C4×C61C2×D411yescharacteristic
77C2×C4×C61C2×D411yescharacteristic
78C2×C4×C61C2×D411yescharacteristic
79C2×C4×C61C2411yescharacteristic
80C2×Dic61—22no—
81C2×Dic61—22no—
82Dic122—24no—
83Dic122—42no—
84#92418—24no—
85C22×C61—21no—
86C22×C61—21no—
87C22×C61#13712yes—
88C22×C61C22×D411yescharacteristic
89C4×C61—24no—
90C4×C61—21no—
91C4×C61—21no—
92C4×C61—21no—
93C4×C61—21no—
94C4×C61—42no—
95C4×C61#13712yes—
96C4×C61C2×#4112yes—
97Dic61—42no—
98Dic61—42no—
99#3113—611nomaximal, Sylow
100C2×C61—22no—
101C2×C61#52511yescharacteristic
102C2×C61C2×#13711yescharacteristic
103C2×C61C2×#13711yescharacteristic
104#533—611no—
105C2×C4×Q8D6111yescharacteristic
106#483—612no—
107#475—612no—
108#462—612no—
109#451—612no—
110#441—614no—
111#432—611no—
112C61#311311yescharacteristic, complemented, Sylow
113C22×Q8C2×D6111yescharacteristic
114C2×Q16—614no—
115C4⋊Q8—611no—
116C4⋊Q8—611no—
117#125—1221no—
118C22⋊Q8—612no—
119C22⋊Q8—1221no—
120C4×Q8—21no—
121C4×Q8—21no—
122C4×Q8—612no—
123C4×Q8—1221no—
124C4×Q8C2×D6112yes—
125C4×Q8C2×D6112yes—
126#117—1221no—
127C2×C4⋊C4—21no—
128C2×C4⋊C4C2×D6111yescharacteristic
129C2×C42—21no—
130C2×C42C2×D6111yescharacteristic
131#106—614no—
132C4⋊C8—612no—
133#103—614no—
134#103—614no—
135C22⋊C8—612no—
136#97—612no—
137C2×Q8—24no—
138C2×Q8—21no—
139C2×Q8—612no—
140C2×Q8—1221no—
141C2×Q8C22×D6112yes—
142C22×C4—21no—
143C22×C4—21no—
144C22×C4C22⋊D6111yescharacteristic
145C22×C4C22⋊D6111yescharacteristic
146C22×C4C22×D6111yescharacteristic
147Q16—1228no—
148C2×C8—614no—
149C4⋊C4—22no—
150C4⋊C4—22no—
151C4⋊C4—21no—
152C4⋊C4—612no—
153C4⋊C4—1222no—
154C4⋊C4—1222no—
155C4⋊C4—1221no—
156C4⋊C4—1221no—
157C4⋊C4—1221no—
158C4⋊C4C22×D6112yes—
159C22⋊C4—1222no—
160C42—22no—
161C42—22no—
162C42—1222no—
163C42C22⋊D6111yescharacteristic
164C42C22⋊D6111yescharacteristic
165C42C22×D6111yescharacteristic
166C42C22×D6111yescharacteristic
167C23C2×C22⋊D6111yescharacteristic
168Q8—24no—
169Q8—22no—
170Q8—1224no—
171Q8—2442no—
172Q8#1175822214yes—
173C2×C4—24no—
174C2×C4—22no—
175C2×C4—22no—
176C2×C4—22no—
177C2×C4—22no—
178C2×C4—22no—
179C2×C4—42no—
180C2×C4—1222no—
181C2×C4—1222no—
182C2×C4C2×C22⋊D6111yescharacteristic
183C2×C4C2×C22⋊D6111yescharacteristic
184C2×C4C2×C22⋊D6111yescharacteristic
185C2×C4C2×C22⋊D6111yescharacteristic
186C2×C4C2×C22⋊D6111yescharacteristic
187C2×C4C23×D6111yescharacteristic
188C8—1224no—
189C22—21no—
190C22—21no—
191C22#1451980712yes—
192C22C22×C22⋊D6111yescharacteristic
193C4—24no—
194C4—21no—
195C4—21no—
196C4—21no—
197C4—21no—
198C4—42no—
199C4—2442no—
200C4—2442no—
201C4#1451980812yes—
202C4C2×#1175822212yes—
203C2—22no—
204C2#1684027311yescharacteristic
205C2C2×#1451980711yescharacteristic
206C2C2×#1451980811yescharacteristic
subgroupG/H
centerC22C22×C22⋊D61
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC2×C4×Q8×C61C2
socleC22×C61C22×D4
hypercenterC2×C4×Q8D61
hypocenterC61#3113
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C42 ◁ C2×C4×Q8

Complements

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

NH ≅ G/Ntype
3. #16840047C2semidirect
4. #16839972C2semidirect
6. #16839867C2semidirect
112. C61#3113semidirect