Finite Group Databasebeta

← #21444498

Subgroups — #21444498

Order 7808.

240 conjugacy classes of subgroups; only the 75 normal subgroups are shown.

normal subgroups only

This group has 240 conjugacy classes of subgroups — too many to draw. Only its 75 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⋊Q8×D61C211yesmaximal, characteristic
2#16839814C211yesmaximal, characteristic
3#16839784C211yesmaximal, characteristic
4#16839511C211yesmaximal, characteristic, complemented
5#16839510C211yesmaximal, characteristic, complemented
6#16839510C211yesmaximal, characteristic, complemented
7C61×#333C211yesmaximal, characteristic, complemented
8C2×Q8×D61C412yes—
9C2×#11758189—21no—
10#14519777C2211yescharacteristic
11#14519776—21no—
12#14519776—21no—
13#14519775C412yes—
14C4⋊C4×D61—21no—
15C4⋊C4×D61—21no—
16C42×D61C2211yescharacteristic
17C4⋊#92418C2211yescharacteristic
18C4⋊#92418C2211yescharacteristic
19#14519706—21no—
20#14519689—21no—
21C8×Dic61—21no—
22C4⋊Q8×C61C2211yescharacteristic
23C4⋊C8×C61C2211yescharacteristic
24C4⋊C8×C61C2211yescharacteristic
25C2×Q8×C61C2×C412yes—
26Q8×D61—44no—
27C2×C4×D61—22no—
28C2×C4×D61C2×C411yescharacteristic
29C2×C4×D61D411yescharacteristic
30C2×C4×D61D411yescharacteristic
31C2×Dic122—22no—
32C2×Dic122C2×C412yes—
33C2×C8×C61—21no—
34C2×C8×C61—21no—
35C4⋊C4×C61—21no—
36C4⋊C4×C61—21no—
37C42×C61C2311yescharacteristic
38C4⋊Dic61—21no—
39C4⋊Dic61—21no—
40#11758196—22no—
41#11758196—22no—
42C4×Dic61C2×C411yescharacteristic
43C4×Dic61D411yescharacteristic
44C4×Dic61D411yescharacteristic
45C2×#92418—21no—
46C2×#92418—21no—
47#11758189—42no—
48C22×D61C22⋊C411yescharacteristic
49Q8×C61—42no—
50C2×C4×C61—22no—
51C2×C4×C61C22×C411yescharacteristic
52C2×C4×C61C2×D411yescharacteristic
53C2×C4×C61C2×D411yescharacteristic
54C2×Dic61—22no—
55C2×Dic61C22⋊C411yescharacteristic
56C2×Dic61C22⋊C411yescharacteristic
57C2×Dic61C22⋊C411yescharacteristic
58C4×D61—21no—
59C4×D61—21no—
60C4×D61—22no—
61C4×D61—44no—
62C4×D61SD1612yes—
63C4×D61Q1612yes—
64Dic122—44no—
65Dic122—42no—
66C8×C61—41no—
67C8×C61—41no—
68#92418—41no—
69#92418—41no—
70C22×C61C2×C22⋊C411yescharacteristic
71C2×D61—21no—
72C2×D61—21no—
73C2×D61#10312yes—
74C4×C61—21no—
75C4×C61—42no—
76C4×C61C2×SD1611yescharacteristic
77C4×C61C2×Q1611yescharacteristic
78C4×C61#13711yescharacteristic
79C4×C61#13711yescharacteristic
80Dic61—21no—
81Dic61—42no—
82Dic61#10012yes—
83Dic61#10312yes—
84#1548—611nomaximal, Sylow
85C2×C61C2×#10011yescharacteristic
86C2×C61C2×#10311yescharacteristic
87C2×C61#41911yescharacteristic
88D61—22no—
89C2×C4⋊Q8—611no—
90#431—611no—
91#423—611no—
92#333—611no—
93#333—611no—
94#333—611no—
95#333D6111yescharacteristic, complemented
96C61#154811yescharacteristic, complemented, Sylow
97C22×Q8—612no—
98C2×M16—1221no—
99C4⋊Q8—612no—
100C4⋊Q8—611no—
101C4⋊Q8—1221no—
102C4⋊Q8—1221no—
103C4⋊Q8C2×D6111yescharacteristic
104C2×C4⋊C4—1221no—
105C2×C4⋊C4—1221no—
106C2×C42—611no—
107C4⋊C8—611no—
108C4⋊C8—611no—
109C4⋊C8—1221no—
110C4⋊C8C2×D6111yescharacteristic
111C4⋊C8C2×D6111yescharacteristic
112C22⋊C8—1221no—
113C4×C8—1221no—
114C2×Q8—612no—
115C2×Q8—1222no—
116C2×Q8—2444no—
117C2×Q8C4×D6112yes—
118C22×C4—611no—
119C22×C4—611no—
120C22×C4—611no—
121C22×C4—1222no—
122M16—2442no—
123C2×C8—21no—
124C2×C8—21no—
125C2×C8—1221no—
126C2×C8—1221no—
127C4⋊C4—21no—
128C4⋊C4—21no—
129C4⋊C4—1222no—
130C4⋊C4—1222no—
131C4⋊C4—1221no—
132C4⋊C4—1221no—
133C42—611no—
134C42—611no—
135C42—611no—
136C42C22×D6111yescharacteristic
137C23—611no—
138Q8—42no—
139Q8—2442no—
140Q8—2444no—
141C2×C4—22no—
142C2×C4—611no—
143C2×C4—611no—
144C2×C4—612no—
145C2×C4—612no—
146C2×C4—611no—
147C2×C4—1222no—
148C2×C4—1221no—
149C2×C4—1221no—
150C2×C4—1222no—
151C2×C4—2444no—
152C2×C4C2×C4×D6111yescharacteristic
153C2×C4D4×D6111yescharacteristic
154C2×C4D4×D6111yescharacteristic
155C8—41no—
156C8—41no—
157C8—2441no—
158C8—2441no—
159C22—612no—
160C22—1221no—
161C22—1221no—
162C22C22⋊C4×D6111yescharacteristic
163C4—21no—
164C4—42no—
165C4—612no—
166C4—612no—
167C4—1221no—
168C4—2442no—
169C4SD16×D6111yescharacteristic
170C4Q16×D6111yescharacteristic
171C4#1451980611yescharacteristic
172C4#1451980911yescharacteristic
173C2—1222no—
174C2#100×D6111yescharacteristic
175C2#103×D6111yescharacteristic
176C2#1683976911yescharacteristic
subgroupG/H
centerC22C22⋊C4×D61
commutatorC2×C4×C61C22×C4
FrattiniC42C22×D61
FittingC61×#333C2
socleC22×C61C2×C22⋊C4
hypercenter#333D61
hypocenterC61#1548
LCSG ▷ C2×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ #333

Complements

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

NH ≅ G/Ntype
4. #16839511C2semidirect
5. #16839510C2semidirect
6. #16839510C2semidirect
7. C61×#333C2semidirect
95. #333D61semidirect
96. C61#1548semidirect