Finite Group Databasebeta

← #21447793

Subgroups — #21447793

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#16840563C211yesmaximal, characteristic
2#16840205C211yesmaximal, characteristic, complemented
3C2×#14519721C211yesmaximal, characteristic, complemented
4#16840038C211yesmaximal, characteristic, complemented
5#16839568C211yesmaximal, characteristic, complemented
6#16839547C211yesmaximal, characteristic, complemented
7C61×#361C211yesmaximal, characteristic, complemented
8#14519822—21no—
9#14519810—21no—
10#14519803—21no—
11#14519801—22no—
12#14519799C2211yescharacteristic
13#14519796—21no—
14C2×Dic244C2211yescharacteristic, complemented
15D8×D61—21no—
16#14519783C2211yescharacteristic
17Dic488—21no—
18#14519722—21no—
19#14519721—22no—
20C2×#11758185C2211yescharacteristic, complemented
21#14519695—21no—
22C2×D8×C61C2211yescharacteristic
23M32×C61C2211yescharacteristic, complemented
24#108×C61C2211yescharacteristic, complemented
25C2×D4×C61—21no—
26C2×C22⋊D61—42no—
27#11758224—22no—
28#11758224—41no—
29D4×D61—22no—
30D4×D61—41no—
31#11758222—21no—
32#11758222D411yescharacteristic
33C2×Dic122—21no—
34D8×C61—21no—
35D8×C61D412yes—
36M16×C61—21no—
37C2×C8×C61C2311yescharacteristic
38#11758200—22no—
39#11758199—22no—
40#11758194D411yescharacteristic
41Dic244—21no—
42Dic244—21no—
43Dic244—41no—
44Dic244D411yescharacteristic
45D488D411yescharacteristic
46#11758190—21no—
47#11758190—41no—
48#11758189—21no—
49C8×D61—21no—
50C16×C61—21no—
51#11758185—21no—
52C23×C61—41no—
53C22×D61—42no—
54D4×C61—22no—
55D4×C61—41no—
56C2×C4×C61C2×D411yescharacteristic
57C22⋊D61—21no—
58C22⋊D61—42no—
59C22⋊D61—42no—
60C22⋊D61—41no—
61C2×Dic61—42no—
62C2×Dic61—41no—
63D244—21no—
64D244D811yescharacteristic
65C4×D61—21no—
66C4×D61—41no—
67Dic122—21no—
68Dic122—41no—
69Dic122—41no—
70Dic122D811yescharacteristic
71C8×C61—41no—
72C8×C61C2×D411yescharacteristic
73C8×C61C2×D411yescharacteristic
74#92418—21no—
75C22×C61—42no—
76C22×C61—161no—
77C22×C61AGL(1,ℤ/8)11yescharacteristic
78C2×D61—21no—
79C2×D61—41no—
80C2×D61—162no—
81C4×C61#12011yescharacteristic
82C4×C61C2×D811yescharacteristic
83Dic61—21no—
84Dic61—41no—
85Dic61—81no—
86#2194—611nomaximal, Sylow
87C2×C61—21no—
88C2×C61—82no—
89C2×C61#44711yescharacteristic
90D61—41no—
91D61—81no—
92#576—611no—
93#510—611no—
94C2×SD32—611no—
95#473—611no—
96#361D6111yescharacteristic, complemented
97#359—611no—
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—611no—
105#135—1221no—
106C2×Q16—611no—
107C2×D8—1221no—
108C2×D8C2×D6111yescharacteristic
109#131—611no—
110Q32—1221no—
111SD32—1221no—
112SD32—1222no—
113M32C2×D6111yescharacteristic, complemented
114C2×C16—611no—
115#108C2×D6111yescharacteristic, complemented
116#101—1221no—
117#41—611no—
118#41—1222no—
119#41—1221no—
120#41—2441no—
121C2×Q8—1221no—
122C2×D4—21no—
123C2×D4—1222no—
124C2×D4—2441no—
125C2×D4—2442no—
126Q16—611no—
127Q16—1221no—
128Q16—1221no—
129Q16—2441no—
130SD16—1222no—
131SD16—1221no—
132SD16—2441no—
133D8—21no—
134D8—611no—
135D8—1222no—
136D8D24412yes—
137M16—21no—
138M16—611no—
139M16—1221no—
140C2×C8—1221no—
141C2×C8C22×D6111yescharacteristic
142C16—21no—
143C16—1221no—
144C23—41no—
145C23—2442no—
146Q8—611no—
147Q8—1221no—
148Q8—2441no—
149Q8—2441no—
150D4—22no—
151D4—41no—
152D4—611no—
153D4—1221no—
154D4—1221no—
155D4—2442no—
156D4—2442no—
157D4—2441no—
158C2×C4—1221no—
159C2×C4—2442no—
160C2×C4—2441no—
161C2×C4—2441no—
162C2×C4D4×D6111yescharacteristic
163C8—41no—
164C8—1221no—
165C8C2×D24411yescharacteristic
166C8D4×D6111yescharacteristic
167C22—42no—
168C22—161no—
169C22—1221no—
170C22—9762no—
171C22—2441no—
172C22#1451980411yescharacteristic
173C4—1221no—
174C4—4881no—
175C4—2441no—
176C4#1451974711yescharacteristic
177C4D8×D6111yescharacteristic
178C2—21no—
179C2—82no—
180C2—4881no—
181C2—2441no—
182C2#1683989711yescharacteristic
subgroupG/H
centerC2#16839897
commutatorC2×C8×C61C23
FrattiniC2×C8C22×D61
FittingC61×#361C2
socleC2×C61#447
hypercenter#361D61
hypocenterC61#2194
LCSG ▷ C2×C8×C61 ▷ C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×C8 ◁ #361

Complements

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

NH ≅ G/Ntype
2. #16840205C2semidirect
3. C2×#14519721C2semidirect
4. #16840038C2semidirect
5. #16839568C2semidirect
6. #16839547C2semidirect
7. C61×#361C2semidirect
14. C2×Dic244C22semidirect
20. C2×#11758185C22semidirect
23. M32×C61C22semidirect
24. #108×C61C22semidirect
96. #361D61semidirect
99. C61#2194semidirect
113. M32C2×D61semidirect
115. #108C2×D61semidirect