Finite Group Databasebeta

← #21447501

Subgroups — #21447501

Order 7808.

250 conjugacy classes of subgroups; only the 55 normal subgroups are shown.

normal subgroups only

This group has 250 conjugacy classes of subgroups — too many to draw. Only its 55 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#16840311C211yesmaximal, characteristic
2#16839745C212yesmaximal, complemented
3#16839560C212yesmaximal, complemented
4#16839559C211yesmaximal, characteristic, complemented
5C61×#355C211yesmaximal, characteristic, complemented
6C2×#11758226C2211yescharacteristic
7C2×#11758224C411yescharacteristic
8M16×D61—22no—
9#14519775C2211yescharacteristic
10#14519773C411yescharacteristic
11#14519765C411yescharacteristic
12#14519750—22no—
13#14519737—22no—
14C42×D61C411yescharacteristic
15#14519696C2212yes—
16#14519693—22no—
17#124×C61C2211yescharacteristic
18#101×C61C2212yes—
19C2×Q8×C61C2311yescharacteristic
20C2×D4×C61C2×C411yescharacteristic
21C2×C22⋊D61—21no—
22C2×C22⋊D61—22no—
23C22×Dic61—21no—
24#11758226—41no—
25#11758226—41no—
26#11758224—41no—
27#11758224—41no—
28C2×D244C2×C411yescharacteristic
29C2×D244D412yes—
30C2×C4×D61—21no—
31C2×C4×D61C2×C411yescharacteristic
32C2×C4×D61D412yes—
33C2×Dic122C2×C411yescharacteristic
34M16×C61—22no—
35C22⋊C4×C61—22no—
36C42×C61C2×C411yescharacteristic
37#11758198—22no—
38#11758196—22no—
39C4×Dic61—21no—
40C4×Dic61C2×C411yescharacteristic
41#11758194—22no—
42#11758189—42no—
43C8×D61—42no—
44C23×C61—21no—
45C22×D61C22⋊C412yes—
46C22×D61C22⋊C411yescharacteristic
47Q8×C61—41no—
48D4×C61—41no—
49C2×C4×C61—21no—
50C2×C4×C61C22×C411yescharacteristic
51C2×C4×C61C2×D412yes—
52C22⋊D61—44no—
53C22⋊D61—42no—
54C2×Dic61—21no—
55C2×Dic61—21no—
56C2×Dic61—41no—
57C2×Dic61—41no—
58C2×Dic61C22⋊C411yescharacteristic
59D244—41no—
60D244—42no—
61C4×D61—22no—
62C4×D61—22no—
63C4×D61—21no—
64C4×D61—21no—
65C4×D61—42no—
66Dic122—41no—
67C8×C61—42no—
68#92418—42no—
69C22×C61—42no—
70C22×C61—41no—
71C22×C61C2×C22⋊C411yescharacteristic
72C2×D61—21no—
73C2×D61—22no—
74C2×D61—41no—
75C2×D61—42no—
76C4×C61—22no—
77C4×C61—21no—
78C4×C61—41no—
79Dic61—22no—
80Dic61—41no—
81Dic61#9911yescharacteristic
82Dic61#9911yescharacteristic
83#2132—611nomaximal, Sylow
84C2×C61—21no—
85C2×C61—81no—
86C2×C61C2×#9911yescharacteristic
87D61—41no—
88D61—42no—
89#532—611no—
90#413—612no—
91#356—612no—
92#355—611no—
93#355D6111yescharacteristic, complemented
94C61#213211yescharacteristic, complemented, Sylow
95C2×#41—611no—
96C2×#41—611no—
97C2×M16—1222no—
98C4⋊Q8—611no—
99#127—611no—
100#124—611no—
101#124C2×D6111yescharacteristic
102#121—1222no—
103C4×D4—1222no—
104C2×C42—611no—
105#101—612no—
106#101C2×D6112yes—
107#100—1222no—
108#41—2441no—
109#41—2441no—
110#41—2441no—
111#41—2441no—
112C2×Q8—611no—
113C2×Q8C22×D6111yescharacteristic
114C2×D4—611no—
115C2×D4—612no—
116C2×D4—1222no—
117C2×D4—1221no—
118C2×D4C4×D6111yescharacteristic
119C22×C4—611no—
120C22×C4—612no—
121C22×C4—1221no—
122C22×C4—1221no—
123M16—22no—
124M16—1222no—
125M16—2442no—
126C2×C8—2442no—
127C4⋊C4—1222no—
128C22⋊C4—22no—
129C22⋊C4—1222no—
130C42—611no—
131C42—1221no—
132C42C4×D6111yescharacteristic
133C23—21no—
134C23—612no—
135C23—611no—
136Q8—41no—
137Q8—2441no—
138D4—41no—
139D4—2442no—
140D4—2441no—
141D4—2444no—
142D4—2442no—
143C2×C4—21no—
144C2×C4—611no—
145C2×C4—1222no—
146C2×C4—1222no—
147C2×C4—1221no—
148C2×C4—1221no—
149C2×C4—1221no—
150C2×C4—1221no—
151C2×C4—2442no—
152C2×C4—2441no—
153C2×C4—2441no—
154C2×C4C2×C4×D6111yescharacteristic
155C2×C4D4×D6112yes—
156C8—42no—
157C8—2442no—
158C22—42no—
159C22—41no—
160C22—1221no—
161C22—1222no—
162C22—2441no—
163C22—2442no—
164C22C22⋊C4×D6111yescharacteristic
165C4—22no—
166C4—21no—
167C4—41no—
168C4—611no—
169C4—611no—
170C4—1222no—
171C4—2441no—
172C2—21no—
173C2—81no—
174C2—2441no—
175C2—2442no—
176C2#99×D6111yescharacteristic
subgroupG/H
centerC2#99×D61
commutatorC2×C4×C61C22×C4
FrattiniC2×Q8C22×D61
FittingC61×#355C2
socleC2×C61C2×#99
hypercenter#355D61
hypocenterC61#2132
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. #16839745C2semidirect
3. #16839560C2semidirect
4. #16839559C2semidirect
5. C61×#355C2semidirect
93. #355D61semidirect
94. C61#2132semidirect