Finite Group Databasebeta

← #21447740

Subgroups — #21447740

Order 7808.

230 conjugacy classes of subgroups; only the 53 normal subgroups are shown.

normal subgroups only

This group has 230 conjugacy classes of subgroups — too many to draw. Only its 53 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
1C2×#14519799C211yesmaximal, characteristic, complemented
2C2×#14519721C211yesmaximal, characteristic, complemented
3C2×#14519718C211yesmaximal, characteristic, complemented
4#16839565C211yesmaximal, characteristic, complemented
5#16839562C211yesmaximal, characteristic, complemented
6C22⋊#11758185C211yesmaximal, characteristic, complemented
7C61×#466C211yesmaximal, characteristic, complemented
8C2×#11758222—21no—
9#14519799—22no—
10#14519799—22no—
11C2×Dic244C2211yescharacteristic
12C2×#11758190—21no—
13C2×D488C2211yescharacteristic
14#14519721—22no—
15#14519718—22no—
16C2×#11758185C2211yescharacteristic
17C2×#11758185C2211yescharacteristic
18C2×D8×C61C2211yescharacteristic
19C22×C8×C61C2211yescharacteristic
20#121×C61—21no—
21#107×C61C2211yescharacteristic
22#102×C61—21no—
23C2×D4×C61—21no—
24C2×D4×C61—41no—
25C22×C4×C61D411yescharacteristic
26C2×C22⋊D61—41no—
27#11758222—24no—
28#11758222—42no—
29C2×D244—21no—
30C2×C4×D61—41no—
31C2×Dic122—21no—
32D8×C61—21no—
33D8×C61—21no—
34C2×C8×C61—21no—
35C2×C8×C61—21no—
36C2×C8×C61D411yescharacteristic
37C2×C8×C61C2311yescharacteristic
38C4⋊C4×C61—21no—
39C22⋊C4×C61—41no—
40Dic244—21no—
41Dic244D412yescomplemented
42D488—21no—
43D488D412yescomplemented
44#11758190—24no—
45#11758185—21no—
46#11758185—21no—
47C23×C61—41no—
48C23×C61D811yescharacteristic
49C22×D61—41no—
50D4×C61—41no—
51D4×C61—41no—
52D4×C61—82no—
53C2×C4×C61—21no—
54C2×C4×C61—21no—
55C2×C4×C61—41no—
56C2×C4×C61D811yescharacteristic
57C2×C4×C61C2×D411yescharacteristic
58C22⋊D61—44no—
59C2×Dic61—41no—
60D244—22no—
61D244—41no—
62C4×D61—44no—
63Dic122—22no—
64Dic122—41no—
65C8×C61—21no—
66C8×C61C2×D411yescharacteristic
67C8×C61C2×D411yescharacteristic
68C22×C61—21no—
69C22×C61—21no—
70C22×C61—21no—
71C22×C61—81no—
72C22×C61—81no—
73C22×C61—81no—
74C22×C61C2×D811yescharacteristic
75C2×D61—42no—
76C2×D61—81no—
77C2×D61—81no—
78C4×C61—21no—
79C4×C61—81no—
80C4×C61#12011yescharacteristic
81C4×C61AGL(1,ℤ/8)11yescharacteristic
82Dic61—42no—
83#2186—611nomaximal, Sylow
84C2×C61—41no—
85C2×C61—161no—
86C2×C61#44711yescharacteristic
87C2×C61#50811yescharacteristic
88C2×C61#50911yescharacteristic
89D61—82no—
90C2×#135—611no—
91C2×SD32—611no—
92C2×D16—611no—
93#466D6111yescharacteristic, complemented
94#358—611no—
95#357—611no—
96C22⋊C16—611no—
97C61#218611yescharacteristic, complemented, Sylow
98C2×#41—1221no—
99#135—1222no—
100#135—1222no—
101C2×Q16—611no—
102C2×SD16—1221no—
103C2×D8—611no—
104C2×D8C2×D6111yescharacteristic
105C22×C8C2×D6111yescharacteristic
106#121—21no—
107SD32—1222no—
108D16—1222no—
109C2×C16—611no—
110C2×C16—611no—
111#107C2×D6111yescharacteristic
112#102—21no—
113#41—1224no—
114#41—2442no—
115C2×Q8—1221no—
116C2×D4—21no—
117C2×D4—41no—
118C2×D4—1221no—
119C2×D4—2441no—
120C22×C4—2441no—
121C22×C4C22⋊D6111yescharacteristic
122Q16—612no—
123Q16—1221no—
124SD16—1224no—
125D8—21no—
126D8—21no—
127D8—612no—
128D8—1221no—
129C2×C8—21no—
130C2×C8—21no—
131C2×C8C22⋊D6111yescharacteristic
132C2×C8C22×D6111yescharacteristic
133C4⋊C4—21no—
134C22⋊C4—41no—
135C16—1221no—
136C16—1221no—
137C23—41no—
138C23—2441no—
139C23#1175819911yescharacteristic
140Q8—1222no—
141Q8—2441no—
142D4—41no—
143D4—41no—
144D4—82no—
145D4—1222no—
146D4—2444no—
147D4—2441no—
148C2×C4—21no—
149C2×C4—21no—
150C2×C4—41no—
151C2×C4—2444no—
152C2×C4—2441no—
153C2×C4#1175819911yescharacteristic
154C2×C4C2×C22⋊D6111yescharacteristic
155C8—21no—
156C8D4×D6111yescharacteristic
157C8D4×D6111yescharacteristic
158C22—21no—
159C22—21no—
160C22—21no—
161C22—81no—
162C22—81no—
163C22—81no—
164C22—4881no—
165C22—4881no—
166C22—2442no—
167C22C2×#1175819911yescharacteristic
168C4—21no—
169C4—81no—
170C4—2442no—
171C4#1451974511yescharacteristic
172C4#1451980211yescharacteristic
173C2—41no—
174C2—161no—
175C2—4882no—
176C2#1683989511yescharacteristic
177C2#1684019211yescharacteristic
178C2#1684019811yescharacteristic
subgroupG/H
centerC22C2×#11758199
commutatorC2×C8×C61C23
FrattiniC2×C8C22×D61
FittingC61×#466C2
socleC22×C61C2×D8
hypercenter#466D61
hypocenterC61#2186
LCSG ▷ C2×C8×C61 ▷ C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8 ◁ #466

Complements

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

NH ≅ G/Ntype
1. C2×#14519799C2semidirect
2. C2×#14519721C2semidirect
3. C2×#14519718C2semidirect
4. #16839565C2semidirect
5. #16839562C2semidirect
6. C22⋊#11758185C2semidirect
7. C61×#466C2semidirect
41. Dic244D4semidirect
43. D488D4semidirect
93. #466D61semidirect
97. C61#2186semidirect