Finite Group Databasebeta

← #355×D61 #21447495

Subgroups — #355×D61 #21447495

Order 7808.

260 conjugacy classes of subgroups; only the 57 normal subgroups are shown.

normal subgroups only

This group has 260 conjugacy classes of subgroups — too many to draw. Only its 57 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#101×D61C212yesmaximal, complemented
3#16839559C211yesmaximal, characteristic, complemented
4#16839558C212yesmaximal, complemented
5C61×#355C211yesmaximal, characteristic, complemented
6C2×Q8×D61C2211yescharacteristic
7C2×D4×D61C411yescharacteristic
8M16×D61—22no—
9#14519766C2211yescharacteristic
10#14519765C411yescharacteristic
11#14519764C411yescharacteristic
12#14519763—22no—
13C22⋊C4×D61—22no—
14C42×D61C411yescharacteristic
15#14519696C2212yescomplemented
16#14519695—22no—
17#124×C61C2211yescharacteristic
18#101×C61C2212yescomplemented
19C23×D61—21no—
20C2×Q8×C61C2311yescharacteristic
21C2×D4×C61C2×C411yescharacteristic
22C2×C22⋊D61—21no—
23Q8×D61—41no—
24Q8×D61—41no—
25D4×D61—41no—
26D4×D61—41no—
27C2×D244C2×C411yescharacteristic
28C2×C4×D61—21no—
29C2×C4×D61C2×C411yescharacteristic
30C2×C4×D61D412yes—
31C2×Dic122C2×C411yescharacteristic
32C2×Dic122D412yes—
33M16×C61—22no—
34C22⋊C4×C61—22no—
35C42×C61C2×C411yescharacteristic
36C22⋊Dic61—22no—
37#11758198—22no—
38#11758198—22no—
39C4×Dic61—21no—
40C4×Dic61C2×C411yescharacteristic
41#11758194—22no—
42#11758189—42no—
43C8×D61—42no—
44C23×C61—21no—
45C22×D61—21no—
46C22×D61—44no—
47C22×D61—41no—
48C22×D61—41no—
49C22×D61C22⋊C411yescharacteristic
50Q8×C61—41no—
51D4×C61—41no—
52C2×C4×C61—21no—
53C2×C4×C61C22×C411yescharacteristic
54C2×C4×C61C2×D412yes—
55C22⋊D61—42no—
56C2×Dic61—21no—
57C2×Dic61C22⋊C411yescharacteristic
58C2×Dic61C22⋊C412yes—
59D244—41no—
60C4×D61—22no—
61C4×D61—22no—
62C4×D61—21no—
63C4×D61—21no—
64C4×D61—42no—
65Dic122—41no—
66Dic122—42no—
67C8×C61—42no—
68#92418—42no—
69C22×C61—42no—
70C22×C61—41no—
71C22×C61C2×C22⋊C411yescharacteristic
72C2×D61—22no—
73C2×D61—42no—
74C2×D61—41no—
75C2×D61—82no—
76C2×D61—82no—
77C2×D61#9911yescharacteristic
78C2×D61#9911yescharacteristic
79C4×C61—22no—
80C4×C61—21no—
81C4×C61—41no—
82Dic61—22no—
83Dic61—21no—
84Dic61—41no—
85C2×#355—611nomaximal, Sylow
86C2×C61—21no—
87C2×C61—81no—
88C2×C61C2×#9911yescharacteristic
89D61—21no—
90D61—81no—
91D61#35512yesdirect product factor
92C2×#124—611no—
93C2×#101—612no—
94#355—611no—
95#355—612no—
96#355D6111yescharacteristic, direct product factor
97C61C2×#35511yescharacteristic, complemented, Sylow
98C22×Q8—611no—
99C22×D4—611no—
100C2×M16—1222no—
101#124—611no—
102#124—611no—
103#124—611no—
104#124—1222no—
105#124C2×D6111yescharacteristic
106C2×C22⋊C4—1222no—
107C2×C42—611no—
108#101—612no—
109#101—1222no—
110#101C2×D6112yescomplemented
111C24—1221no—
112C2×Q8—611no—
113C2×Q8—612no—
114C2×Q8—2441no—
115C2×Q8—2441no—
116C2×Q8C22×D6111yescharacteristic
117C2×D4—611no—
118C2×D4—1221no—
119C2×D4—2441no—
120C2×D4—2441no—
121C2×D4C4×D6111yescharacteristic
122C22×C4—611no—
123C22×C4—612no—
124C22×C4—1221no—
125M16—22no—
126M16—1222no—
127M16—2442no—
128C2×C8—2442no—
129C22⋊C4—22no—
130C22⋊C4—1222no—
131C22⋊C4—1222no—
132C22⋊C4—1222no—
133C42—611no—
134C42—1221no—
135C42C4×D6111yescharacteristic
136C23—21no—
137C23—611no—
138C23—1221no—
139C23—2441no—
140C23—2441no—
141C23—2444no—
142Q8—41no—
143Q8—2442no—
144Q8—2441no—
145D4—41no—
146D4—2441no—
147D4—2442no—
148C2×C4—21no—
149C2×C4—611no—
150C2×C4—612no—
151C2×C4—1222no—
152C2×C4—1222no—
153C2×C4—1221no—
154C2×C4—1221no—
155C2×C4—1221no—
156C2×C4—2442no—
157C2×C4C2×C4×D6111yescharacteristic
158C2×C4D4×D6112yes—
159C8—42no—
160C8—2442no—
161C22—42no—
162C22—41no—
163C22—611no—
164C22—611no—
165C22—1222no—
166C22—4882no—
167C22—4882no—
168C22—2442no—
169C22—2441no—
170C22C22⋊C4×D6111yescharacteristic
171C4—22no—
172C4—21no—
173C4—41no—
174C4—1221no—
175C4—1222no—
176C4—2441no—
177C2—21no—
178C2—81no—
179C2—612no—
180C2—1221no—
181C2—4881no—
182C2#99×D6111yescharacteristic
subgroupG/H
centerC2#99×D61
commutatorC2×C4×C61C22×C4
FrattiniC2×Q8C22×D61
FittingC61×#355C2
socleC2×C61C2×#99
hypercenter#355D61
hypocenterC61C2×#355
LCSG ▷ C2×C4×C61 ▷ C22×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2 ◁ C22 ◁ C2×Q8 ◁ #355

Complements

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

NH ≅ G/Ntype
2. #101×D61C2semidirect
3. #16839559C2semidirect
4. #16839558C2semidirect
5. C61×#355C2semidirect
15. #14519696C22semidirect
18. #101×C61C22semidirect
91. D61#355direct (N × H)
96. #355D61direct (N × H)
97. C61C2×#355semidirect
110. #101C2×D61semidirect