Finite Group Databasebeta

← #21447791

Subgroups — #21447791

Order 7808.

216 conjugacy classes of subgroups; only the 47 normal subgroups are shown.

normal subgroups only

This group has 216 conjugacy classes of subgroups — too many to draw. Only its 47 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#16840564C211yesmaximal, characteristic
2#16840202C211yesmaximal, characteristic, complemented
3C2×#14519722C211yesmaximal, characteristic, complemented
4#16840038C211yesmaximal, characteristic, complemented
5#16839574C211yesmaximal, characteristic, complemented
6#16839545C211yesmaximal, characteristic, complemented
7C61×#359C211yesmaximal, characteristic, complemented
8#14519823—21no—
9#14519810—21no—
10#14519804—22no—
11#14519802—21no—
12#14519800—21no—
13C2×Dic244C2211yescharacteristic, complemented
14C2×D488C2211yescharacteristic
15D8×D61—21no—
16#14519783C2211yescharacteristic
17#14519723—21no—
18#14519722—22no—
19#14519721—21no—
20#14519717C2211yescharacteristic, complemented
21#14519695—21no—
22#135×C61C2211yescharacteristic
23C2×C16×C61C2211yescharacteristic, complemented
24#108×C61C2211yescharacteristic, complemented
25#41×C61—21no—
26#11758226—22no—
27D4×D61—22no—
28D4×D61—42no—
29#11758222—41no—
30#11758222D411yescharacteristic
31C2×D244—21no—
32C2×D244—41no—
33C2×Dic122—21no—
34Q16×C61D411yescharacteristic
35SD16×C61—21no—
36D8×C61D411yescharacteristic
37M16×C61—21no—
38C2×C8×C61C2311yescharacteristic
39#11758201—22no—
40#11758199—22no—
41#11758194D411yescharacteristic
42Dic244—21no—
43Dic244—21no—
44Dic244—41no—
45D488—21no—
46D488D412yes—
47#11758190—41no—
48#11758189—21no—
49C8×D61—21no—
50C16×C61—21no—
51#11758185—21no—
52C22×D61—42no—
53C22×D61—41no—
54Q8×C61—21no—
55D4×C61—21no—
56D4×C61—41no—
57C2×C4×C61—41no—
58C2×C4×C61C2×D411yescharacteristic
59C22⋊D61—21no—
60C22⋊D61—42no—
61C2×Dic61—41no—
62D244—22no—
63D244—42no—
64D244—41no—
65D244D811yescharacteristic
66C4×D61—21no—
67C4×D61—42no—
68Dic122—41no—
69Dic122—41no—
70Dic122D811yescharacteristic
71C8×C61—41no—
72C8×C61C2×D411yescharacteristic
73C8×C61C2×D411yescharacteristic
74#92418—21no—
75C22×C61—41no—
76C22×C61AGL(1,ℤ/8)11yescharacteristic
77C2×D61—21no—
78C2×D61—42no—
79C2×D61—162no—
80C2×D61—161no—
81C4×C61—41no—
82C4×C61#12011yescharacteristic
83C4×C61C2×D811yescharacteristic
84Dic61—21no—
85Dic61—81no—
86#2194—611nomaximal, Sylow
87C2×C61—21no—
88C2×C61—81no—
89C2×C61#44711yescharacteristic
90D61—41no—
91D61—82no—
92#576—611no—
93#510—611no—
94C2×SD32—611no—
95#473—611no—
96#361—611no—
97#359D6111yescharacteristic, complemented
98#350—611no—
99C61#219411yescharacteristic, complemented, Sylow
100H(5,𝔽2)—1221no—
101#137—1221no—
102AGL(1,ℤ/8)—1221no—
103AGL(1,ℤ/8)—1222no—
104#135—1221no—
105#135C2×D6111yescharacteristic
106C2×Q16—611no—
107C2×D8—611no—
108C2×D8—1221no—
109#131—611no—
110Q32—1221no—
111SD32—1222no—
112SD32—1221no—
113M32—611no—
114C2×C16C2×D6111yescharacteristic, complemented
115#108C2×D6111yescharacteristic, complemented
116#101—1221no—
117#41—21no—
118#41—611no—
119#41—1222no—
120#41—2441no—
121C2×Q8—1221no—
122C2×D4—1222no—
123C2×D4—1221no—
124C2×D4—2441no—
125C2×D4—2442no—
126Q16—1221no—
127Q16—1221no—
128Q16—2441no—
129Q16D24411yescharacteristic
130SD16—21no—
131SD16—1222no—
132SD16—2441no—
133D8—612no—
134D8—1222no—
135D8—1221no—
136D8D24411yescharacteristic
137M16—21no—
138M16—611no—
139M16—1221no—
140C2×C8—1221no—
141C2×C8C22×D6111yescharacteristic
142C16—21no—
143C16—1221no—
144C23—2442no—
145C23—2441no—
146Q8—21no—
147Q8—611no—
148Q8—2441no—
149Q8—2441no—
150D4—21no—
151D4—41no—
152D4—611no—
153D4—1221no—
154D4—1222no—
155D4—2442no—
156D4—2442no—
157D4—2441no—
158C2×C4—41no—
159C2×C4—1221no—
160C2×C4—2442no—
161C2×C4—2441no—
162C2×C4D4×D6111yescharacteristic
163C8—41no—
164C8—1221no—
165C8C2×D24411yescharacteristic
166C8D4×D6111yescharacteristic
167C22—41no—
168C22—1221no—
169C22—9761no—
170C22—9762no—
171C22—2442no—
172C22#1451980411yescharacteristic
173C4—41no—
174C4—1221no—
175C4—4881no—
176C4#1451974711yescharacteristic
177C4D8×D6111yescharacteristic
178C2—21no—
179C2—81no—
180C2—4882no—
181C2—2441no—
182C2#1683989711yescharacteristic
subgroupG/H
centerC2#16839897
commutatorC2×C8×C61C23
FrattiniC2×C8C22×D61
FittingC61×#359C2
socleC2×C61#447
hypercenter#359D61
hypocenterC61#2194
LCSG ▷ C2×C8×C61 ▷ C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×C8 ◁ #359

Complements

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

NH ≅ G/Ntype
2. #16840202C2semidirect
3. C2×#14519722C2semidirect
4. #16840038C2semidirect
5. #16839574C2semidirect
6. #16839545C2semidirect
7. C61×#359C2semidirect
13. C2×Dic244C22semidirect
20. #14519717C22semidirect
23. C2×C16×C61C22semidirect
24. #108×C61C22semidirect
97. #359D61semidirect
99. C61#2194semidirect
114. C2×C16C2×D61semidirect
115. #108C2×D61semidirect