Finite Group Databasebeta

← #21445382

Subgroups — #21445382

Order 7808.

176 conjugacy classes of subgroups; only the 51 normal subgroups are shown.

normal subgroups only

This group has 176 conjugacy classes of subgroups — too many to draw. Only its 51 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#16840110C211yesmaximal, characteristic, complemented
2#16839957C211yesmaximal, characteristic
3#16839840C211yesmaximal, characteristic, complemented
4#16839512C211yesmaximal, characteristic, complemented
5#16839508C211yesmaximal, characteristic, complemented
6#16839505C211yesmaximal, characteristic, complemented
7C61×#461C211yesmaximal, characteristic, complemented
8C2×#11758199—21no—
9C2×#11758194—21no—
10#14519774C2211yescharacteristic
11C4⋊#92418C2211yescharacteristic
12C4⋊#92418C2211yescharacteristic
13#14519697—21no—
14#14519697—21no—
15#14519697—21no—
16C22⋊#92418—21no—
17C4×#92418C2211yescharacteristic
18C2×SD16×C61—21no—
19C4⋊Q8×C61C2211yescharacteristic
20C4×D4×C61C2211yescharacteristic
21C4⋊C8×C61C2211yescharacteristic
22#103×C61—21no—
23C2×Q8×C61—21no—
24C2×D4×C61D411yescharacteristic
25C22×C4×C61—21no—
26C2×D244—21no—
27C2×D244—21no—
28C2×D244—21no—
29SD16×C61—42no—
30C2×C8×C61—21no—
31C4⋊C4×C61—21no—
32C4⋊C4×C61—21no—
33C4⋊C4×C61D411yescharacteristic
34C22⋊C4×C61—21no—
35C42×C61C2311yescharacteristic
36#11758199—42no—
37#11758194—42no—
38C2×#92418—21no—
39C2×#92418—21no—
40C2×#92418D411yescharacteristic
41C2×#92418D411yescharacteristic
42C23×C61—21no—
43C22×D61—41no—
44Q8×C61—41no—
45Q8×C61—41no—
46D4×C61—21no—
47D4×C61—21no—
48C2×C4×C61—21no—
49C2×C4×C61—41no—
50C2×C4×C61—41no—
51C2×C4×C61—41no—
52C2×C4×C61C2×D411yescharacteristic
53C2×C4×C61C2×D411yescharacteristic
54C2×C4×C61#4111yescharacteristic
55D244—41no—
56D244—41no—
57D244—41no—
58D244—41no—
59D244—81no—
60C8×C61—41no—
61#92418—21no—
62#92418—21no—
63#92418—41no—
64#92418—41no—
65C22×C61—41no—
66C22×C61—41no—
67C22×C61—41no—
68C22×C61#12111yescharacteristic
69C2×D61—81no—
70C2×D61—81no—
71C2×D61—81no—
72C4×C61—21no—
73C4×C61—41no—
74C4×C61—81no—
75C4×C61#13511yescharacteristic
76C4×C61AGL(1,ℤ/8)11yescharacteristic
77C4×C61AGL(1,ℤ/8)11yescharacteristic
78C4×C61AGL(1,ℤ/8)11yescharacteristic
79#1701—611nomaximal, Sylow
80C2×C61—81no—
81C2×C61#46311yescharacteristic
82C2×C61#46911yescharacteristic
83C2×C61#47111yescharacteristic
84D61—161no—
85#486—611no—
86#461D6111yescharacteristic, complemented
87#459—611no—
88#436—611no—
89#334—611no—
90#332—611no—
91#331—611no—
92C61#170111yescharacteristic, complemented, Sylow
93C2×SD16—21no—
94C2×D8—1221no—
95C2×M16—1221no—
96C4⋊Q8C2×D6111yescharacteristic
97#127—611no—
98C4×D4C2×D6111yescharacteristic
99C4⋊C8—611no—
100C4⋊C8—611no—
101C4⋊C8C2×D6111yescharacteristic
102#103—21no—
103#102—1221no—
104#102—1221no—
105#102—1221no—
106C22⋊C8—1221no—
107C4×C8—611no—
108C2×Q8—21no—
109C2×D4—1221no—
110C2×D4—1221no—
111C2×D4—1221no—
112C2×D4C22⋊D6111yescharacteristic
113C22×C4—21no—
114SD16—42no—
115D8—2442no—
116M16—2442no—
117C2×C8—21no—
118C2×C8—611no—
119C2×C8—611no—
120C2×C8—1221no—
121C2×C8—1221no—
122C4⋊C4—21no—
123C4⋊C4—21no—
124C4⋊C4C22⋊D6111yescharacteristic
125C22⋊C4—21no—
126C42C22×D6111yescharacteristic
127C23—21no—
128C23—2441no—
129Q8—41no—
130Q8—41no—
131D4—21no—
132D4—21no—
133D4—4881no—
134D4—2441no—
135D4—2441no—
136D4—2441no—
137D4—2441no—
138C2×C4—21no—
139C2×C4—41no—
140C2×C4—41no—
141C2×C4—41no—
142C2×C4D4×D6111yescharacteristic
143C2×C4#1175822411yescharacteristic
144C2×C4C2×C22⋊D6111yescharacteristic
145C8—41no—
146C8—1221no—
147C8—1221no—
148C8—2441no—
149C8—2441no—
150C22—41no—
151C22—41no—
152C22—41no—
153C22—4881no—
154C22—4881no—
155C22—4881no—
156C22#1451974911yescharacteristic
157C4—21no—
158C4—41no—
159C4—81no—
160C4#1451979811yescharacteristic
161C4#1451980211yescharacteristic
162C4#1451980311yescharacteristic
163C4#1451980411yescharacteristic
164C2—81no—
165C2—9761no—
166C2#1683997911yescharacteristic
167C2#1684001311yescharacteristic
168C2#1684002711yescharacteristic
subgroupG/H
centerC22#14519749
commutatorC42×C61C23
FrattiniC42C22×D61
FittingC61×#461C2
socleC22×C61#121
hypercenter#461D61
hypocenterC61#1701
LCSG ▷ C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ #461

Complements

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

NH ≅ G/Ntype
1. #16840110C2semidirect
3. #16839840C2semidirect
4. #16839512C2semidirect
5. #16839508C2semidirect
6. #16839505C2semidirect
7. C61×#461C2semidirect
86. #461D61semidirect
92. C61#1701semidirect