Finite Group Databasebeta

← #21444538

Subgroups — #21444538

Order 7808.

246 conjugacy classes of subgroups; only the 65 normal subgroups are shown.

normal subgroups only

This group has 246 conjugacy classes of subgroups — too many to draw. Only its 65 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#16840310C211yesmaximal, characteristic
2#16839818C211yesmaximal, characteristic, complemented
3#16839784C211yesmaximal, characteristic, complemented
4#16839509C211yesmaximal, characteristic, complemented
5#16839507C211yesmaximal, characteristic, complemented
6#16839506C211yesmaximal, characteristic, complemented
7C61×#331C211yesmaximal, characteristic, complemented
8C2×#11758224—21no—
9C2×#11758189—21no—
10#14519777C2211yescharacteristic
11#14519764—21no—
12#14519748—21no—
13#14519748C412yes—
14D4×Dic61—21no—
15D4×Dic61C412yes—
16C42×D61C2211yescharacteristic
17C4⋊#92418C2211yescharacteristic
18C4⋊#92418C2211yescharacteristic
19#14519706—21no—
20#14519689—21no—
21#14519687—21no—
22#127×C61C2211yescharacteristic
23C4⋊C8×C61C2211yescharacteristic
24C4⋊C8×C61C2211yescharacteristic
25C2×D4×C61—21no—
26C2×D4×C61—21no—
27C2×D4×C61C2×C412yes—
28C2×C22⋊D61—22no—
29C22×Dic61—22no—
30#11758224—42no—
31#11758224—42no—
32C2×C4×D61C2×C411yescharacteristic
33C2×C4×D61D411yescharacteristic
34C2×C4×D61D411yescharacteristic
35C2×Dic122—21no—
36C2×C8×C61—21no—
37C2×C8×C61—21no—
38C42×C61C2311yescharacteristic
39C22⋊Dic61—22no—
40C22⋊Dic61—22no—
41C4⋊Dic61—21no—
42C4⋊Dic61C2×C412yes—
43C4×Dic61C2×C411yescharacteristic
44C4×Dic61D411yescharacteristic
45C4×Dic61D411yescharacteristic
46C2×#92418—21no—
47C2×#92418—21no—
48#11758189—42no—
49C23×C61—22no—
50C22×D61C22⋊C411yescharacteristic
51D4×C61—42no—
52D4×C61—41no—
53D4×C61—41no—
54D4×C61—41no—
55D4×C61—41no—
56C2×C4×C61C22×C411yescharacteristic
57C2×C4×C61C2×D411yescharacteristic
58C2×C4×C61C2×D411yescharacteristic
59C22⋊D61—44no—
60C2×Dic61—22no—
61C2×Dic61—44no—
62C2×Dic61C22⋊C411yescharacteristic
63C2×Dic61C22⋊C411yescharacteristic
64C2×Dic61C22⋊C411yescharacteristic
65C4×D61—21no—
66C4×D61—21no—
67C4×D61—21no—
68C4×D61—21no—
69C4×D61—41no—
70Dic122—41no—
71Dic122—41no—
72C8×C61—41no—
73C8×C61—41no—
74#92418—41no—
75#92418—41no—
76C22×C61—42no—
77C22×C61—42no—
78C22×C61—42no—
79C22×C61C2×C22⋊C411yescharacteristic
80C2×D61—21no—
81C2×D61—21no—
82C2×D61—21no—
83C4×C61—21no—
84C4×C61AGL(1,ℤ/8)11yescharacteristic
85C4×C61AGL(1,ℤ/8)11yescharacteristic
86C4×C61AGL(1,ℤ/8)11yescharacteristic
87C4×C61#13711yescharacteristic
88Dic61—21no—
89Dic61—21no—
90Dic61—21no—
91Dic61—42no—
92#1557—611nomaximal, Sylow
93C2×C61—82no—
94C2×C61#41311yescharacteristic
95C2×C61#41711yescharacteristic
96C2×C61#41811yescharacteristic
97D61—41no—
98#532—611no—
99#432—611no—
100#423—611no—
101#332—611no—
102#332—611no—
103#331—611no—
104#331D6111yescharacteristic, complemented
105C61#155711yescharacteristic, complemented, Sylow
106C2×#41—1221no—
107C2×M16—1221no—
108C4⋊Q8—611no—
109#127C2×D6111yescharacteristic
110#124—1221no—
111#121—612no—
112#121—1221no—
113C4×D4—612no—
114C4×D4—1221no—
115C2×C42—611no—
116C4⋊C8—611no—
117C4⋊C8—611no—
118C4⋊C8—1221no—
119C4⋊C8C2×D6111yescharacteristic
120C4⋊C8C2×D6111yescharacteristic
121C22⋊C8—1221no—
122#97—1221no—
123#41—2442no—
124#41—2442no—
125C2×Q8—1221no—
126C2×D4—21no—
127C2×D4—21no—
128C2×D4—1222no—
129C2×D4C4×D6112yes—
130C22×C4—611no—
131C22×C4—611no—
132C22×C4—611no—
133C22×C4—1222no—
134M16—2442no—
135C2×C8—21no—
136C2×C8—21no—
137C2×C8—1221no—
138C2×C8—1221no—
139C4⋊C4—612no—
140C4⋊C4—1221no—
141C22⋊C4—1222no—
142C22⋊C4—1222no—
143C42—611no—
144C42—611no—
145C42—611no—
146C42C22×D6111yescharacteristic
147C23—22no—
148C23—611no—
149Q8—2441no—
150Q8—2441no—
151D4—42no—
152D4—41no—
153D4—41no—
154D4—41no—
155D4—41no—
156D4—2444no—
157C2×C4—611no—
158C2×C4—611no—
159C2×C4—611no—
160C2×C4—1221no—
161C2×C4—1221no—
162C2×C4—1221no—
163C2×C4—1221no—
164C2×C4—1222no—
165C2×C4—2441no—
166C2×C4—2444no—
167C2×C4C2×C4×D6111yescharacteristic
168C2×C4D4×D6111yescharacteristic
169C2×C4D4×D6111yescharacteristic
170C8—41no—
171C8—41no—
172C8—2441no—
173C8—2441no—
174C22—42no—
175C22—42no—
176C22—42no—
177C22—1221no—
178C22—1221no—
179C22—1221no—
180C22C22⋊C4×D6111yescharacteristic
181C4—21no—
182C4—1221no—
183C4—1221no—
184C4—1221no—
185C4—2442no—
186C4#1451980111yescharacteristic
187C4#1451980111yescharacteristic
188C4#1451980411yescharacteristic
189C4#1451980611yescharacteristic
190C2—82no—
191C2—2441no—
192C2#1683974311yescharacteristic
193C2#1683976011yescharacteristic
194C2#1683976511yescharacteristic
subgroupG/H
centerC22C22⋊C4×D61
commutatorC2×C4×C61C22×C4
FrattiniC42C22×D61
FittingC61×#331C2
socleC22×C61C2×C22⋊C4
hypercenter#331D61
hypocenterC61#1557
LCSG ▷ C2×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ #331

Complements

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

NH ≅ G/Ntype
2. #16839818C2semidirect
3. #16839784C2semidirect
4. #16839509C2semidirect
5. #16839507C2semidirect
6. #16839506C2semidirect
7. C61×#331C2semidirect
104. #331D61semidirect
105. C61#1557semidirect