Finite Group Databasebeta

← #21447788

Subgroups — #21447788

Order 7808.

216 conjugacy classes of subgroups; only the 49 normal subgroups are shown.

normal subgroups only

This group has 216 conjugacy classes of subgroups — too many to draw. Only its 49 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#16840567C211yesmaximal, characteristic
2#16840203C211yesmaximal, characteristic, complemented
3C2×#14519720C211yesmaximal, characteristic, complemented
4#16839574C211yesmaximal, characteristic, complemented
5#16839568C211yesmaximal, characteristic, complemented
6#16839546C211yesmaximal, characteristic, complemented
7C61×#473C211yesmaximal, characteristic, complemented
8#14519823—21no—
9#14519805—21no—
10#14519805—22no—
11#14519799—21no—
12#14519799C2211yescharacteristic
13C2×D488—21no—
14C2×D488C2211yescharacteristic
15#14519723—21no—
16#14519720—21no—
17#14519720—22no—
18#14519717C2211yescharacteristic, complemented
19C2×#11758185C2211yescharacteristic, complemented
20#137×C61—21no—
21C2×Q16×C61C2211yescharacteristic, complemented
22#131×C61C2211yescharacteristic
23#108×C61C2211yescharacteristic, complemented
24#101×C61—21no—
25#41×C61D411yescharacteristic
26C2×Q8×C61—21no—
27#11758226—41no—
28D4×D61—42no—
29D4×D61—41no—
30#11758222—22no—
31#11758222—21no—
32C2×D244—22no—
33C2×D244—21no—
34Q16×C61—21no—
35Q16×C61—21no—
36Q16×C61—41no—
37SD16×C61—41no—
38M16×C61—21no—
39M16×C61—21no—
40M16×C61D411yescharacteristic
41C2×C8×C61—21no—
42C2×C8×C61C2311yescharacteristic
43Dic244D411yescharacteristic
44D488—22no—
45D488—21no—
46D488D411yescharacteristic
47D488D412yes—
48#11758190—22no—
49#11758190—21no—
50#11758185—21no—
51#11758185—21no—
52C22×D61—42no—
53C22×D61—41no—
54Q8×C61—41no—
55Q8×C61—41no—
56Q8×C61D811yescharacteristic
57D4×C61—21no—
58D4×C61D811yescharacteristic
59C2×C4×C61—21no—
60C2×C4×C61—41no—
61C2×C4×C61C2×D411yescharacteristic
62C22⋊D61—42no—
63C22⋊D61—41no—
64D244—22no—
65D244—21no—
66D244—42no—
67D244—41no—
68C4×D61—42no—
69C4×D61—41no—
70Dic122—21no—
71C8×C61—21no—
72C8×C61—41no—
73C8×C61C2×D411yescharacteristic
74C8×C61C2×D411yescharacteristic
75C22×C61—21no—
76C22×C61AGL(1,ℤ/8)11yescharacteristic
77C2×D61—42no—
78C2×D61—41no—
79C2×D61—161no—
80C2×D61—162no—
81C4×C61—21no—
82C4×C61—81no—
83C4×C61#12011yescharacteristic
84C4×C61C2×D811yescharacteristic
85Dic61—41no—
86#2194—611nomaximal, Sylow
87C2×C61—21no—
88C2×C61—41no—
89C2×C61#44711yescharacteristic
90D61—82no—
91D61—81no—
92#576—611no—
93#510—611no—
94C2×SD32—611no—
95#473D6111yescharacteristic, complemented
96#361—611no—
97#359—611no—
98#350—611no—
99C61#219411yescharacteristic, complemented, Sylow
100H(5,𝔽2)—1221no—
101#137—21no—
102AGL(1,ℤ/8)—1222no—
103AGL(1,ℤ/8)—1221no—
104#135—611no—
105#135—1221no—
106C2×Q16C2×D6111yescharacteristic, complemented
107C2×D8—611no—
108C2×D8—1221no—
109#131C2×D6111yescharacteristic
110Q32—1221no—
111SD32—1222no—
112SD32—1221no—
113M32—611no—
114C2×C16—611no—
115#108C2×D6111yescharacteristic, complemented
116#101—21no—
117#41—1222no—
118#41—1221no—
119#41—2441no—
120#41C22⋊D6111yescharacteristic
121C2×Q8—21no—
122C2×D4—1222no—
123C2×D4—1221no—
124C2×D4—2442no—
125C2×D4—2441no—
126Q16—21no—
127Q16—21no—
128Q16—41no—
129Q16—611no—
130SD16—41no—
131SD16—1222no—
132SD16—1221no—
133D8—612no—
134D8—611no—
135D8—1222no—
136D8—1221no—
137M16—21no—
138M16—21no—
139M16C22⋊D6111yescharacteristic
140C2×C8—21no—
141C2×C8C22×D6111yescharacteristic
142C16—1221no—
143C16—1221no—
144C23—2442no—
145C23—2441no—
146Q8—41no—
147Q8—41no—
148Q8—1221no—
149Q8#1175819911yescharacteristic
150D4—21no—
151D4—1222no—
152D4—1221no—
153D4—2442no—
154D4—2442no—
155D4—2441no—
156D4—2441no—
157D4#1175819911yescharacteristic
158C2×C4—21no—
159C2×C4—41no—
160C2×C4—2442no—
161C2×C4—2441no—
162C2×C4C2×C22⋊D6111yescharacteristic
163C8—21no—
164C8—41no—
165C8D4×D6111yescharacteristic
166C8D4×D6111yescharacteristic
167C22—21no—
168C22—9761no—
169C22—9762no—
170C22—2442no—
171C22—2441no—
172C22#1451980211yescharacteristic
173C4—21no—
174C4—81no—
175C4—2441no—
176C4#1451974511yescharacteristic
177C4C2×#1175819911yescharacteristic
178C2—21no—
179C2—41no—
180C2—4882no—
181C2—4881no—
182C2#1683989511yescharacteristic
subgroupG/H
centerC2#16839895
commutatorC2×C8×C61C23
FrattiniC2×C8C22×D61
FittingC61×#473C2
socleC2×C61#447
hypercenter#473D61
hypocenterC61#2194
LCSG ▷ C2×C8×C61 ▷ C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2 ◁ C2×C4 ◁ #131 ◁ #473

Complements

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

NH ≅ G/Ntype
2. #16840203C2semidirect
3. C2×#14519720C2semidirect
4. #16839574C2semidirect
5. #16839568C2semidirect
6. #16839546C2semidirect
7. C61×#473C2semidirect
18. #14519717C22semidirect
19. C2×#11758185C22semidirect
21. C2×Q16×C61C22semidirect
23. #108×C61C22semidirect
95. #473D61semidirect
99. C61#2194semidirect
106. C2×Q16C2×D61semidirect
115. #108C2×D61semidirect