Finite Group Databasebeta

← #21444253

Subgroups — #21444253

Order 7808.

246 conjugacy classes of subgroups; only the 89 normal subgroups are shown.

normal subgroups only

This group has 246 conjugacy classes of subgroups — too many to draw. Only its 89 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#16839819C211yesmaximal, characteristic, complemented
2#16839815C211yesmaximal, characteristic, complemented
3Q8⋊#92418C212yesmaximal, complemented
4D4⋊#92418C212yesmaximal, complemented
5C4×#41×C61C211yesmaximal, characteristic
6C4⋊#92418—21no—
7C4⋊#92418C2212yes—
8C22⋊#92418—21no—
9C22⋊#92418—21no—
10#14519688—21no—
11C4×#92418C2212yes—
12C2×#41×C61C411yescharacteristic
13C4×Q8×C61C411yescharacteristic
14C4×Q8×C61C2211yescharacteristic
15C4×D4×C61—21no—
16C4×D4×C61—21no—
17C4×D4×C61C411yescharacteristic
18C4×D4×C61C2211yescharacteristic
19#117×C61—21no—
20#117×C61C411yescharacteristic
21C2×C42×C61—21no—
22C2×C42×C61C2211yescharacteristic
23#41×C61—22no—
24#41×C61—22no—
25C2×Q8×C61C2×C411yescharacteristic
26C2×D4×C61—21no—
27C2×D4×C61C2×C411yescharacteristic
28C22×C4×C61—21no—
29C22×C4×C61—21no—
30C22×C4×C61—21no—
31C22×C4×C61C2×C411yescharacteristic
32C22×C4×C61D411yescharacteristic
33C22×C4×C61D411yescharacteristic
34C4⋊C4×C61—21no—
35C4⋊C4×C61—21no—
36C4⋊C4×C61C2×C411yescharacteristic
37C4⋊C4×C61C2×C411yescharacteristic
38C22⋊C4×C61—21no—
39C22⋊C4×C61—21no—
40C22⋊C4×C61—21no—
41C42×C61—21no—
42C42×C61—21no—
43C42×C61—21no—
44C42×C61C2×C411yescharacteristic
45C42×C61D411yescharacteristic
46C42×C61D411yescharacteristic
47C42×C61C2311yescharacteristic
48C2×#92418—22no—
49C2×#92418—22no—
50C23×C61—21no—
51C23×C61C22⋊C411yescharacteristic
52Q8×C61—21no—
53Q8×C61M1612yes—
54D4×C61—24no—
55D4×C61—21no—
56D4×C61M1612yes—
57C2×C4×C61—24no—
58C2×C4×C61—21no—
59C2×C4×C61—21no—
60C2×C4×C61—21no—
61C2×C4×C61—22no—
62C2×C4×C61—21no—
63C2×C4×C61—21no—
64C2×C4×C61—41no—
65C2×C4×C61—42no—
66C2×C4×C61—42no—
67C2×C4×C61C22⋊C411yescharacteristic
68C2×C4×C61C22⋊C411yescharacteristic
69C2×C4×C61C22⋊C411yescharacteristic
70C2×C4×C61C22×C411yescharacteristic
71C2×C4×C61C2×D411yescharacteristic
72C2×C4×C61C2×D411yescharacteristic
73#92418—42no—
74#92418—42no—
75C22×C61—21no—
76C22×C61—22no—
77C22×C61—21no—
78C22×C61—21no—
79C22×C61—41no—
80C22×C61—41no—
81C22×C61C2×C22⋊C411yescharacteristic
82C4×C61—21no—
83C4×C61—22no—
84C4×C61—21no—
85C4×C61—21no—
86C4×C61—21no—
87C4×C61—41no—
88C4×C61—41no—
89C4×C61C2×M1611yescharacteristic
90C4×C61C2×M1611yescharacteristic
91C4×C61#13512yes—
92#1488—611nomaximal, Sylow
93C2×C61—41no—
94C2×C61—42no—
95C2×C61#40711yescharacteristic
96C2×C61#41611yescharacteristic
97C2×C61#42111yescharacteristic
98C4×#41D6111yescharacteristic
99#432—611no—
100#431—611no—
101Q8⋊C8—612no—
102D4⋊C8—612no—
103C61#148811yescharacteristic, complemented, Sylow
104C2×#41Dic6111yescharacteristic
105C4×Q8Dic6111yescharacteristic
106C4×Q8C2×D6111yescharacteristic
107C4×D4—21no—
108C4×D4—21no—
109C4×D4Dic6111yescharacteristic
110C4×D4C2×D6111yescharacteristic
111#117—21no—
112#117Dic6111yescharacteristic
113C2×C42—21no—
114C2×C42C2×D6111yescharacteristic
115C4⋊C8—612no—
116C4⋊C8—1221no—
117C22⋊C8—1221no—
118C22⋊C8—1221no—
119#97—1221no—
120C4×C8—612no—
121#41—22no—
122#41—22no—
123C2×Q8C2×Dic6111yescharacteristic
124C2×D4—21no—
125C2×D4C2×Dic6111yescharacteristic
126C22×C4—21no—
127C22×C4—21no—
128C22×C4—21no—
129C22×C4C2×Dic6111yescharacteristic
130C22×C4C22⋊D6111yescharacteristic
131C22×C4C22⋊D6111yescharacteristic
132C2×C8—1222no—
133C2×C8—1222no—
134C4⋊C4—21no—
135C4⋊C4—21no—
136C4⋊C4C2×Dic6111yescharacteristic
137C4⋊C4C2×Dic6111yescharacteristic
138C22⋊C4—21no—
139C22⋊C4—21no—
140C22⋊C4—21no—
141C42—21no—
142C42—21no—
143C42—21no—
144C42C2×Dic6111yescharacteristic
145C42C22⋊D6111yescharacteristic
146C42C22⋊D6111yescharacteristic
147C42C22×D6111yescharacteristic
148C23—21no—
149C23C22⋊Dic6111yescharacteristic
150Q8—21no—
151Q8#1175819412yes—
152D4—24no—
153D4—21no—
154D4#1175819412yes—
155C2×C4—24no—
156C2×C4—21no—
157C2×C4—21no—
158C2×C4—21no—
159C2×C4—22no—
160C2×C4—21no—
161C2×C4—21no—
162C2×C4—41no—
163C2×C4—42no—
164C2×C4—42no—
165C2×C4C22⋊Dic6111yescharacteristic
166C2×C4C22⋊Dic6111yescharacteristic
167C2×C4C22⋊Dic6111yescharacteristic
168C2×C4C22×Dic6111yescharacteristic
169C2×C4C2×C22⋊D6111yescharacteristic
170C2×C4C2×C22⋊D6111yescharacteristic
171C8—2442no—
172C8—2442no—
173C22—21no—
174C22—22no—
175C22—21no—
176C22—21no—
177C22—41no—
178C22—41no—
179C22C2×C22⋊Dic6111yescharacteristic
180C4—21no—
181C4—22no—
182C4—21no—
183C4—21no—
184C4—21no—
185C4—41no—
186C4—41no—
187C4C2×#1175819411yescharacteristic
188C4C2×#1175819411yescharacteristic
189C4#1451979712yes—
190C2—41no—
191C2—42no—
192C2#1683972611yescharacteristic
193C2#1683975811yescharacteristic
194C2#1683977911yescharacteristic
subgroupG/H
centerC2×C4C2×C22⋊D61
commutatorC2×C4×C61C22×C4
FrattiniC42C22×D61
FittingC4×#41×C61C2
socleC22×C61C2×C22⋊C4
hypercenterC4×#41D61
hypocenterC61#1488
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ C4×#41

Complements

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

NH ≅ G/Ntype
1. #16839819C2semidirect
2. #16839815C2semidirect
3. Q8⋊#92418C2semidirect
4. D4⋊#92418C2semidirect
103. C61#1488semidirect