Finite Group Databasebeta

← #21444251

Subgroups — #21444251

Order 7808.

246 conjugacy classes of subgroups; only the 77 normal subgroups are shown.

normal subgroups only

This group has 246 conjugacy classes of subgroups — too many to draw. Only its 77 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
1C4×#11758222C211yesmaximal, characteristic
2#16839815C211yesmaximal, characteristic, complemented
3#16839492C212yesmaximal, complemented
4#16839489C212yesmaximal, complemented
5C61×#432C211yesmaximal, characteristic, complemented
6C2×#11758222C411yescharacteristic
7C4×Dic122C411yescharacteristic
8C4×Dic122C2211yescharacteristic
9C4×D244C411yescharacteristic
10C4×D244C2211yescharacteristic
11C4×C22⋊D61—21no—
12C4×C22⋊D61—21no—
13#14519736C411yescharacteristic
14#14519734—21no—
15C42×D61—21no—
16C4⋊#92418—21no—
17C22⋊#92418—21no—
18C4×#92418C2212yes—
19C2×C42×C61C2211yescharacteristic
20C4⋊C8×C61C2212yes—
21C22⋊C8×C61—21no—
22#97×C61—21no—
23C22×C4×C61C2×C411yescharacteristic
24C22×C4×C61D411yescharacteristic
25C22×C4×C61D411yescharacteristic
26C2×C22⋊D61—21no—
27#11758222—22no—
28#11758222—22no—
29C2×D244C2×C411yescharacteristic
30C2×C4×D61—21no—
31C2×C4×D61—21no—
32C2×C4×D61—21no—
33C2×Dic122C2×C411yescharacteristic
34C2×C8×C61—22no—
35C42×C61C2×C411yescharacteristic
36C42×C61D411yescharacteristic
37C42×C61D411yescharacteristic
38C42×C61C2311yescharacteristic
39C22⋊Dic61—21no—
40#11758198—21no—
41#11758198—21no—
42C4⋊Dic61C2×C411yescharacteristic
43C4⋊Dic61C2×C411yescharacteristic
44#11758196—21no—
45#11758196—21no—
46C4×Dic61—21no—
47C4×Dic61—21no—
48C4×Dic61—21no—
49C2×#92418—22no—
50C23×C61C22⋊C411yescharacteristic
51C22×D61—21no—
52C2×C4×C61—21no—
53C2×C4×C61—21no—
54C2×C4×C61—22no—
55C2×C4×C61—41no—
56C2×C4×C61C22⋊C411yescharacteristic
57C2×C4×C61C22⋊C411yescharacteristic
58C2×C4×C61C22⋊C411yescharacteristic
59C2×C4×C61C22×C411yescharacteristic
60C2×C4×C61C2×D411yescharacteristic
61C2×C4×C61C2×D411yescharacteristic
62C22⋊D61—24no—
63C2×Dic61—21no—
64C2×Dic61—21no—
65C2×Dic61—21no—
66D244—21no—
67D244M1612yes—
68C4×D61—24no—
69C4×D61—42no—
70C4×D61—42no—
71Dic122—21no—
72Dic122M1612yes—
73C8×C61—42no—
74#92418—42no—
75C22×C61—21no—
76C22×C61—21no—
77C22×C61—21no—
78C22×C61C2×C22⋊C411yescharacteristic
79C2×D61—22no—
80C2×D61—41no—
81C2×D61—41no—
82C4×C61—21no—
83C4×C61—21no—
84C4×C61—21no—
85C4×C61—21no—
86C4×C61C2×M1611yescharacteristic
87C4×C61C2×M1611yescharacteristic
88C4×C61#13512yes—
89Dic61—22no—
90Dic61—41no—
91Dic61—41no—
92#1488—611nomaximal, Sylow
93C2×C61—41no—
94C2×C61#40711yescharacteristic
95C2×C61#41611yescharacteristic
96C2×C61#42111yescharacteristic
97D61—42no—
98C4×#41—611no—
99#432D6111yescharacteristic, complemented
100#431—611no—
101Q8⋊C8—612no—
102D4⋊C8—612no—
103C61#148811yescharacteristic, complemented, Sylow
104C2×#41—611no—
105C4×Q8—611no—
106C4×Q8—611no—
107C4×D4—611no—
108C4×D4—611no—
109C4×D4—1221no—
110C4×D4—1221no—
111#117—611no—
112#117—1221no—
113C2×C42—1221no—
114C2×C42C2×D6111yescharacteristic
115C4⋊C8—1221no—
116C4⋊C8C2×D6112yes—
117C22⋊C8—21no—
118C22⋊C8—1221no—
119#97—21no—
120C4×C8—612no—
121#41—1222no—
122#41—1222no—
123C2×Q8—611no—
124C2×D4—611no—
125C2×D4—1221no—
126C22×C4—1221no—
127C22×C4—1221no—
128C22×C4—1221no—
129C22×C4C4×D6111yescharacteristic
130C22×C4D24411yescharacteristic
131C22×C4C22⋊D6111yescharacteristic
132C2×C8—22no—
133C2×C8—1222no—
134C4⋊C4—611no—
135C4⋊C4—611no—
136C4⋊C4—1221no—
137C4⋊C4—1221no—
138C22⋊C4—1221no—
139C22⋊C4—1221no—
140C22⋊C4—1221no—
141C42—1221no—
142C42—1221no—
143C42—1221no—
144C42C4×D6111yescharacteristic
145C42D24411yescharacteristic
146C42C22⋊D6111yescharacteristic
147C42C22×D6111yescharacteristic
148C23—1221no—
149C23#1175819811yescharacteristic
150Q8—612no—
151Q8—1221no—
152D4—612no—
153D4—1224no—
154D4—1221no—
155C2×C4—21no—
156C2×C4—21no—
157C2×C4—22no—
158C2×C4—41no—
159C2×C4—1224no—
160C2×C4—1221no—
161C2×C4—1221no—
162C2×C4—1221no—
163C2×C4—2442no—
164C2×C4—2442no—
165C2×C4#1175819811yescharacteristic
166C2×C4#1175819811yescharacteristic
167C2×C4#1175819811yescharacteristic
168C2×C4C2×C4×D6111yescharacteristic
169C2×C4C2×D24411yescharacteristic
170C2×C4C2×C22⋊D6111yescharacteristic
171C8—42no—
172C8—2442no—
173C22—21no—
174C22—21no—
175C22—21no—
176C22—1222no—
177C22—2441no—
178C22—2441no—
179C22C2×#1175819811yescharacteristic
180C4—21no—
181C4—21no—
182C4—21no—
183C4—21no—
184C4—1222no—
185C4—2441no—
186C4—2441no—
187C4M16×D6111yescharacteristic
188C4M16×D6111yescharacteristic
189C4#1451979712yes—
190C2—41no—
191C2—2442no—
192C2#1683972511yescharacteristic
193C2#1683975611yescharacteristic
194C2#1683977811yescharacteristic
subgroupG/H
centerC2×C4C2×C22⋊D61
commutatorC2×C4×C61C22×C4
FrattiniC42C22×D61
FittingC61×#432C2
socleC22×C61C2×C22⋊C4
hypercenter#432D61
hypocenterC61#1488
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #432

Complements

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

NH ≅ G/Ntype
2. #16839815C2semidirect
3. #16839492C2semidirect
4. #16839489C2semidirect
5. C61×#432C2semidirect
99. #432D61semidirect
103. C61#1488semidirect