Finite Group Databasebeta

← #21444415

Subgroups — #21444415

Order 7808.

264 conjugacy classes of subgroups; only the 61 normal subgroups are shown.

normal subgroups only

This group has 264 conjugacy classes of subgroups — too many to draw. Only its 61 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#124×D61C211yesmaximal, characteristic
2#16839817C211yesmaximal, characteristic, complemented
3#16839714C211yesmaximal, characteristic, complemented
4#16839502C211yesmaximal, characteristic, complemented
5#16839501C211yesmaximal, characteristic, complemented
6#16839501C211yesmaximal, characteristic, complemented
7C61×#329C211yesmaximal, characteristic, complemented
8C2×Q8×D61C411yescharacteristic
9C2×D4×D61C411yescharacteristic
10C2×#11758189—21no—
11#14519766C411yescharacteristic
12#14519765C2211yescharacteristic
13#14519764C411yescharacteristic
14#14519763—21no—
15#14519763—21no—
16C22⋊C4×D61—21no—
17C22⋊C4×D61—21no—
18C42×D61C2211yescharacteristic
19#14519706—21no—
20#14519689—21no—
21#14519688C2211yescharacteristic, complemented
22#14519688C2211yescharacteristic, complemented
23C8×Dic61—21no—
24#124×C61C2211yescharacteristic
25#97×C61C2211yescharacteristic, complemented
26#97×C61C2211yescharacteristic, complemented
27C23×D61—21no—
28C2×Q8×C61C2×C411yescharacteristic
29C2×D4×C61C2×C411yescharacteristic
30C2×C22⋊D61—21no—
31Q8×D61—42no—
32D4×D61—42no—
33C2×D244C2×C411yescharacteristic
34C2×C4×D61—21no—
35C2×C4×D61C2×C411yescharacteristic
36C2×C4×D61D411yescharacteristic
37C2×C4×D61D411yescharacteristic
38C2×Dic122—21no—
39C2×Dic122C2×C411yescharacteristic
40C2×C8×C61—21no—
41C2×C8×C61—21no—
42C22⋊C4×C61—21no—
43C22⋊C4×C61—21no—
44C42×C61C2311yescharacteristic
45C22⋊Dic61—21no—
46C22⋊Dic61—21no—
47#11758198—21no—
48#11758198—21no—
49#11758198—21no—
50#11758198—21no—
51C4×Dic61C2×C411yescharacteristic
52C4×Dic61D411yescharacteristic
53C4×Dic61D411yescharacteristic
54C2×#92418—21no—
55C2×#92418—21no—
56#11758189—24no—
57C23×C61—21no—
58C22×D61—21no—
59C22×D61—42no—
60C22×D61—42no—
61C22×D61—42no—
62C22×D61C22⋊C411yescharacteristic
63Q8×C61—41no—
64D4×C61—41no—
65C2×C4×C61—21no—
66C2×C4×C61C22×C411yescharacteristic
67C2×C4×C61C2×D411yescharacteristic
68C2×C4×C61C2×D411yescharacteristic
69C22⋊D61—42no—
70C2×Dic61—21no—
71C2×Dic61C22⋊C411yescharacteristic
72C2×Dic61C22⋊C411yescharacteristic
73C2×Dic61C22⋊C411yescharacteristic
74D244—41no—
75C4×D61—22no—
76C4×D61—22no—
77C4×D61—41no—
78C4×D61—42no—
79Dic122—42no—
80Dic122—41no—
81C8×C61—22no—
82C8×C61—41no—
83#92418—22no—
84#92418—41no—
85C22×C61—41no—
86C22×C61—41no—
87C22×C61—41no—
88C22×C61C2×C22⋊C411yescharacteristic
89C2×D61—21no—
90C2×D61—21no—
91C2×D61—41no—
92C2×D61—41no—
93C2×D61—41no—
94C2×D61—84no—
95C2×D61#10412yes—
96C4×C61—21no—
97C4×C61—21no—
98C4×C61—21no—
99C4×C61—41no—
100Dic61—21no—
101Dic61—21no—
102Dic61—41no—
103Dic61#10012yes—
104#1527—611nomaximal, Sylow
105C2×C61—81no—
106C2×C61C2×#10011yescharacteristic
107C2×C61C2×#10411yescharacteristic
108C2×C61#42111yescharacteristic
109D61—22no—
110D61—81no—
111C2×#124—611no—
112#432—611no—
113C4×M16—611no—
114#329—611no—
115#329—611no—
116#329—611no—
117#329D6111yescharacteristic, complemented
118C61#152711yescharacteristic, complemented, Sylow
119C22×Q8—611no—
120C22×D4—611no—
121C2×M16—1221no—
122#124—611no—
123#124—611no—
124#124—611no—
125#124—1221no—
126#124—1221no—
127#124C2×D6111yescharacteristic
128C2×C22⋊C4—1221no—
129C2×C22⋊C4—1221no—
130C2×C42—611no—
131C4⋊C8—1221no—
132C22⋊C8—1221no—
133#97—611no—
134#97—611no—
135#97C2×D6111yescharacteristic, complemented
136#97C2×D6111yescharacteristic, complemented
137C4×C8—1221no—
138C24—1221no—
139C2×Q8—611no—
140C2×Q8—1221no—
141C2×Q8—2442no—
142C2×Q8C4×D6111yescharacteristic
143C2×D4—611no—
144C2×D4—1221no—
145C2×D4—2442no—
146C2×D4C4×D6111yescharacteristic
147C22×C4—611no—
148C22×C4—611no—
149C22×C4—611no—
150C22×C4—1221no—
151M16—1224no—
152C2×C8—21no—
153C2×C8—21no—
154C2×C8—1221no—
155C2×C8—1221no—
156C22⋊C4—21no—
157C22⋊C4—21no—
158C22⋊C4—1221no—
159C22⋊C4—1221no—
160C22⋊C4—1221no—
161C22⋊C4—1221no—
162C22⋊C4—1221no—
163C22⋊C4—1221no—
164C42—611no—
165C42—611no—
166C42—611no—
167C42C22×D6111yescharacteristic
168C23—21no—
169C23—611no—
170C23—1221no—
171C23—2442no—
172C23—2442no—
173C23—2442no—
174Q8—41no—
175Q8—2441no—
176Q8—2442no—
177D4—41no—
178D4—2441no—
179D4—2442no—
180C2×C4—21no—
181C2×C4—611no—
182C2×C4—611no—
183C2×C4—611no—
184C2×C4—1222no—
185C2×C4—1222no—
186C2×C4—1221no—
187C2×C4—2441no—
188C2×C4—2442no—
189C2×C4C2×C4×D6111yescharacteristic
190C2×C4D4×D6111yescharacteristic
191C2×C4D4×D6111yescharacteristic
192C8—22no—
193C8—41no—
194C8—1222no—
195C8—2441no—
196C22—41no—
197C22—41no—
198C22—41no—
199C22—612no—
200C22—1221no—
201C22—1221no—
202C22—4884no—
203C22—2441no—
204C22—2441no—
205C22—2441no—
206C22C22⋊C4×D6111yescharacteristic
207C4—21no—
208C4—21no—
209C4—21no—
210C4—41no—
211C4—612no—
212C4—1221no—
213C4—1221no—
214C4—2441no—
215C2—81no—
216C2—1222no—
217C2—4881no—
218C2#100×D6111yescharacteristic
219C2#104×D6111yescharacteristic
220C2#1683977711yescharacteristic
subgroupG/H
centerC22C22⋊C4×D61
commutatorC2×C4×C61C22×C4
FrattiniC42C22×D61
FittingC61×#329C2
socleC22×C61C2×C22⋊C4
hypercenter#329D61
hypocenterC61#1527
LCSG ▷ C2×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ #329

Complements

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

NH ≅ G/Ntype
2. #16839817C2semidirect
3. #16839714C2semidirect
4. #16839502C2semidirect
5. #16839501C2semidirect
6. #16839501C2semidirect
7. C61×#329C2semidirect
21. #14519688C22semidirect
22. #14519688C22semidirect
25. #97×C61C22semidirect
26. #97×C61C22semidirect
117. #329D61semidirect
118. C61#1527semidirect
135. #97C2×D61semidirect
136. #97C2×D61semidirect