Finite Group Databasebeta

← #21444425

Subgroups — #21444425

Order 7808.

216 conjugacy classes of subgroups; only the 59 normal subgroups are shown.

normal subgroups only

This group has 216 conjugacy classes of subgroups — too many to draw. Only its 59 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#16840297C211yesmaximal, characteristic
2#16839817C211yesmaximal, characteristic, complemented
3#16839714C211yesmaximal, characteristic, complemented
4#16839504C211yesmaximal, characteristic, complemented
5#16839501C211yesmaximal, characteristic, complemented
6#16839501C211yesmaximal, characteristic, complemented
7C61×#330C211yesmaximal, characteristic, complemented
8C2×#11758189—21no—
9#14519772—21no—
10#14519765C2211yescharacteristic
11#14519762—21no—
12#14519757C411yescharacteristic
13#14519752C411yescharacteristic
14#14519742C411yescharacteristic
15#14519739—21no—
16#14519739C411yescharacteristic
17#14519735—21no—
18C42×D61C2211yescharacteristic
19#14519706—21no—
20#14519689—21no—
21#14519688C2211yescharacteristic
22#14519688C2211yescharacteristic
23C8×Dic61—21no—
24#125×C61C2211yescharacteristic
25#97×C61C2211yescharacteristic
26#97×C61C2211yescharacteristic
27C2×D244—21no—
28C2×D244C2×C411yescharacteristic
29C2×C4×D61—21no—
30C2×C4×D61C2×C411yescharacteristic
31C2×C4×D61D411yescharacteristic
32C2×C4×D61D411yescharacteristic
33C2×Dic122C2×C411yescharacteristic
34C2×C8×C61—21no—
35C2×C8×C61—21no—
36C4⋊C4×C61—21no—
37C4⋊C4×C61—21no—
38C4⋊C4×C61C2×C411yescharacteristic
39C4⋊C4×C61C2×C411yescharacteristic
40C42×C61C2311yescharacteristic
41#11758198—21no—
42#11758198—21no—
43#11758198—21no—
44#11758198—21no—
45#11758198—21no—
46C4⋊Dic61—21no—
47#11758196—21no—
48C4×Dic61—21no—
49C4×Dic61C2×C411yescharacteristic
50C4×Dic61D411yescharacteristic
51C4×Dic61D411yescharacteristic
52C2×#92418—21no—
53C2×#92418—21no—
54#11758189—24no—
55C22×D61—21no—
56C22×D61C22⋊C411yescharacteristic
57C2×C4×C61—21no—
58C2×C4×C61—21no—
59C2×C4×C61C22×C411yescharacteristic
60C2×C4×C61C2×D411yescharacteristic
61C2×C4×C61C2×D411yescharacteristic
62C2×Dic61—21no—
63C2×Dic61C22⋊C411yescharacteristic
64C2×Dic61C22⋊C411yescharacteristic
65C2×Dic61C22⋊C411yescharacteristic
66D244—41no—
67D244—42no—
68C4×D61—22no—
69C4×D61—41no—
70C4×D61—41no—
71C4×D61—42no—
72Dic122—41no—
73C8×C61—22no—
74C8×C61—41no—
75#92418—22no—
76#92418—41no—
77C22×C61C2×C22⋊C411yescharacteristic
78C2×D61—21no—
79C2×D61—21no—
80C2×D61—21no—
81C2×D61—41no—
82C2×D61—41no—
83C2×D61—41no—
84C4×C61—21no—
85C4×C61—21no—
86C4×C61—21no—
87C4×C61—41no—
88C4×C61—41no—
89Dic61—21no—
90Dic61—21no—
91Dic61—41no—
92Dic61#10412yes—
93#1529—611nomaximal, Sylow
94C2×C61#41311yescharacteristic
95C2×C61C2×#10411yescharacteristic
96C2×C61#42111yescharacteristic
97D61—41no—
98D61—81no—
99#529—611no—
100#432—611no—
101C4×M16—611no—
102#330—611no—
103#330D6111yescharacteristic, complemented
104#329—611no—
105#329—611no—
106C61#152911yescharacteristic, complemented, Sylow
107C2×M16—1221no—
108#126—1221no—
109#125C2×D6111yescharacteristic
110#124—611no—
111#123—1221no—
112C22⋊Q8—611no—
113#121—611no—
114C4×Q8—611no—
115C4×D4—611no—
116C4×D4—1221no—
117#117—1221no—
118C2×C42—611no—
119C4⋊C8—1221no—
120C22⋊C8—1221no—
121#97—611no—
122#97—611no—
123#97C2×D6111yescharacteristic
124#97C2×D6111yescharacteristic
125C4×C8—1221no—
126C2×Q8—611no—
127C2×D4—611no—
128C2×D4—1221no—
129C22×C4—611no—
130C22×C4—611no—
131C22×C4—611no—
132C22×C4—1221no—
133M16—1224no—
134C2×C8—21no—
135C2×C8—21no—
136C2×C8—1221no—
137C2×C8—1221no—
138C4⋊C4—21no—
139C4⋊C4—21no—
140C4⋊C4—1221no—
141C4⋊C4—1221no—
142C4⋊C4C4×D6111yescharacteristic
143C4⋊C4C4×D6111yescharacteristic
144C22⋊C4—1221no—
145C22⋊C4—1221no—
146C22⋊C4—1221no—
147C22⋊C4—1221no—
148C22⋊C4—1221no—
149C42—611no—
150C42—611no—
151C42—611no—
152C42—1221no—
153C42C22×D6111yescharacteristic
154C23—611no—
155C23—1221no—
156Q8—2441no—
157D4—2441no—
158D4—2442no—
159C2×C4—21no—
160C2×C4—21no—
161C2×C4—611no—
162C2×C4—611no—
163C2×C4—611no—
164C2×C4—1222no—
165C2×C4—1221no—
166C2×C4—2441no—
167C2×C4—2441no—
168C2×C4—2442no—
169C2×C4C2×C4×D6111yescharacteristic
170C2×C4D4×D6111yescharacteristic
171C2×C4D4×D6111yescharacteristic
172C8—22no—
173C8—41no—
174C8—1222no—
175C8—2441no—
176C22—1221no—
177C22—1221no—
178C22—1221no—
179C22—2441no—
180C22—2441no—
181C22—2441no—
182C22C22⋊C4×D6111yescharacteristic
183C4—21no—
184C4—21no—
185C4—21no—
186C4—41no—
187C4—41no—
188C4—612no—
189C4—1221no—
190C4—1221no—
191C4—2441no—
192C2—4881no—
193C2—2441no—
194C2#1683974511yescharacteristic
195C2#104×D6111yescharacteristic
196C2#1683977711yescharacteristic
subgroupG/H
centerC22C22⋊C4×D61
commutatorC2×C4×C61C22×C4
FrattiniC42C22×D61
FittingC61×#330C2
socleC22×C61C2×C22⋊C4
hypercenter#330D61
hypocenterC61#1529
LCSG ▷ C2×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ #330

Complements

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

NH ≅ G/Ntype
2. #16839817C2semidirect
3. #16839714C2semidirect
4. #16839504C2semidirect
5. #16839501C2semidirect
6. #16839501C2semidirect
7. C61×#330C2semidirect
103. #330D61semidirect
106. C61#1529semidirect