Finite Group Databasebeta

← #21453878

Subgroups — #21453878

Order 7808.

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

normal subgroups only

This group has 430 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
1C2×#14519771C211yesmaximal, characteristic
2#16839700C212yesmaximal, complemented
3#16839697C212yesmaximal
4#16839693C212yesmaximal, complemented
5#16839688C212yesmaximal
6#16839681C212yesmaximal, complemented
7#16839673C212yesmaximal
8#16839630C211yesmaximal, characteristic, complemented
9C2×C4⋊Q8×C61C211yesmaximal, characteristic, complemented
10#14519771—24no—
11C2×#11758196C2211yescharacteristic
12C2×#11758196C2211yescharacteristic
13C2×#11758196C2211yescharacteristic
14C2×#11758196C2214yes—
15C2×#11758198C2211yescharacteristic
16C2×#11758198C2211yescharacteristic
17C2×#11758198C2211yescharacteristic
18C2×#11758198C2214yes—
19#14519684C2214yes—
20#14519684C2212yes—
21#14519684C2212yes—
22#14519684C2214yes—
23#14519684C2212yes—
24C22×Q8×C61C2212yes—
25C4⋊Q8×C61—24no—
26C2×C4⋊C4×C61C2212yes—
27C2×C4⋊C4×C61C2212yes—
28C2×C42×C61C2211yescharacteristic
29C23×D61C2311yescharacteristic
30C2×Q8×C61—24no—
31C2×Q8×C61—44no—
32C22×C4×C61C2314yes—
33C22×C4×C61C2311yescharacteristic
34C22×C4×C61C2311yescharacteristic
35C22×C4×C61C2311yescharacteristic
36C22×Dic61C2314yes—
37C22×Dic61C2311yescharacteristic
38C22×Dic61C2311yescharacteristic
39C22×Dic61C2311yescharacteristic
40C4⋊C4×C61—24no—
41C4⋊C4×C61—24no—
42C42×C61D414yes—
43#11758198—22no—
44#11758198—22no—
45#11758198—22no—
46#11758198—44no—
47#11758196—22no—
48#11758196—22no—
49#11758196—22no—
50#11758196—44no—
51C23×C61C2411yescharacteristic
52C22×D61—21no—
53C22×D61—22no—
54C22×D61—22no—
55C22×D61—22no—
56Q8×C61—48no—
57C2×C4×C61—22no—
58C2×C4×C61—22no—
59C2×C4×C61—22no—
60C2×C4×C61—24no—
61C2×C4×C61—24no—
62C2×C4×C61—24no—
63C2×C4×C61C2×D412yes—
64C2×C4×C61C2×D412yes—
65C2×C4×C61C2×D412yes—
66C2×Dic61—21no—
67C2×Dic61—21no—
68C2×Dic61—21no—
69C2×Dic61—22no—
70C2×Dic61—24no—
71C2×Dic61—22no—
72C2×Dic61—22no—
73C2×Dic61—24no—
74C2×Dic61—24no—
75C22×C61C22×D411yescharacteristic
76C22×C61H(5,𝔽2)12yes—
77C22×C612−1+412yes—
78C22×C612−1+412yes—
79C2×D61—41no—
80C2×D61—41no—
81C2×D61—41no—
82C2×D61—44no—
83C4×C61—22no—
84C4×C61—22no—
85C4×C61—22no—
86C4×C61—44no—
87Dic61—41no—
88Dic61—41no—
89Dic61—41no—
90Dic61—44no—
91#2821—611nomaximal, Sylow
92C2×C61#53511yescharacteristic
93C2×C61#53611yescharacteristic
94C2×C61#53611yescharacteristic
95C2×C61#56314yes—
96D61—81no—
97C2×C4⋊Q8D6111yescharacteristic, complemented
98C2×#126—611no—
99#400—612no—
100#399—612no—
101#398—612no—
102#397—612no—
103#395—612no—
104#393—612no—
105#383—611no—
106C61#282111yescharacteristic, complemented, Sylow
107C22×Q8C2×D6112yes—
108C4⋊Q8—24no—
109#126—1224no—
110C2×C4⋊C4—611no—
111C2×C4⋊C4—611no—
112C2×C4⋊C4—611no—
113C2×C4⋊C4—614no—
114C2×C4⋊C4C2×D6112yes—
115C2×C4⋊C4C2×D6112yes—
116C2×C22⋊C4—611no—
117C2×C22⋊C4—611no—
118C2×C22⋊C4—611no—
119C2×C22⋊C4—614no—
120C2×C42C2×D6111yescharacteristic
121#95—612no—
122#95—612no—
123#95—612no—
124#95—614no—
125#95—614no—
126C24—611no—
127C2×Q8—24no—
128C2×Q8—44no—
129C22×C4—614no—
130C22×C4—611no—
131C22×C4—611no—
132C22×C4—611no—
133C22×C4C22×D6114yes—
134C22×C4C22×D6111yescharacteristic
135C22×C4C22×D6111yescharacteristic
136C22×C4C22×D6111yescharacteristic
137C4⋊C4—24no—
138C4⋊C4—24no—
139C4⋊C4—1222no—
140C4⋊C4—1222no—
141C4⋊C4—1222no—
142C4⋊C4—2444no—
143C22⋊C4—1222no—
144C22⋊C4—1222no—
145C22⋊C4—1222no—
146C22⋊C4—2444no—
147C42C22⋊D6114yes—
148C23—1221no—
149C23—1222no—
150C23—1222no—
151C23—1222no—
152C23C23×D6111yescharacteristic
153Q8—48no—
154C2×C4—22no—
155C2×C4—22no—
156C2×C4—22no—
157C2×C4—24no—
158C2×C4—24no—
159C2×C4—24no—
160C2×C4—1221no—
161C2×C4—1221no—
162C2×C4—1221no—
163C2×C4—1224no—
164C2×C4—1222no—
165C2×C4—1224no—
166C2×C4—1224no—
167C2×C4—1222no—
168C2×C4—1222no—
169C2×C4C2×C22⋊D6112yes—
170C2×C4C2×C22⋊D6112yes—
171C2×C4C2×C22⋊D6112yes—
172C22—2444no—
173C22—2441no—
174C22—2441no—
175C22—2441no—
176C22C22×C22⋊D6111yescharacteristic
177C22#1451982212yes—
178C22#1451982512yes—
179C22#1451982512yes—
180C4—22no—
181C4—22no—
182C4—22no—
183C4—44no—
184C4—2444no—
185C4—2441no—
186C4—2441no—
187C4—2441no—
188C2—4881no—
189C2#1684032911yescharacteristic
190C2#1684033611yescharacteristic
191C2#1684033611yescharacteristic
192C2#1684051114yes—
subgroupG/H
center, FrattiniC23C23×D61
commutator, socleC23×C61C24
FittingC2×C4⋊Q8×C61C2
hypercenterC2×C4⋊Q8D61
hypocenterC61#2821
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C4⋊Q8

Complements

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

NH ≅ G/Ntype
2. #16839700C2semidirect
4. #16839693C2semidirect
6. #16839681C2semidirect
8. #16839630C2semidirect
9. C2×C4⋊Q8×C61C2semidirect
97. C2×C4⋊Q8D61semidirect
106. C61#2821semidirect