Finite Group Databasebeta

← #21446106

Subgroups — #21446106

Order 7808.

260 conjugacy classes of subgroups; only the 79 normal subgroups are shown.

normal subgroups only

This group has 260 conjugacy classes of subgroups — too many to draw. Only its 79 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#16840528C211yesmaximal, characteristic
2#16839790C211yesmaximal, characteristic, complemented
3#16839789C211yesmaximal, characteristic, complemented
4#16839735C211yesmaximal, characteristic
5#16839730C211yesmaximal, characteristic
6#16839534C211yesmaximal, characteristic, complemented
7C61×#344C211yesmaximal, characteristic, complemented
8C2×#11758222C2211yescharacteristic
9#14519785—22no—
10#14519783—22no—
11C2×#11758194C2211yescharacteristic
12M16×D61—22no—
13C22×#92418C2211yescharacteristic
14#14519736C2211yescharacteristic
15C4⋊#92418—22no—
16#14519706—22no—
17#14519691C414yes—
18#14519689—22no—
19C2×M16×C61C2211yescharacteristic
20C2×M16×C61C2211yescharacteristic
21#117×C61C2211yescharacteristic
22C22×C4×C61C2311yescharacteristic
23C2×C22⋊D61C2×C412yes—
24#11758222—21no—
25#11758222—21no—
26#11758222—21no—
27#11758222—21no—
28C2×D244Q811yescharacteristic
29C2×C4×D61D412yes—
30C2×Dic122Q811yescharacteristic
31M16×C61—21no—
32M16×C61—21no—
33M16×C61—21no—
34M16×C61—21no—
35C2×C8×C61—21no—
36C2×C8×C61D412yes—
37C4⋊C4×C61—21no—
38C22⋊C4×C61C2×C412yes—
39C42×C61—21no—
40C22⋊Dic61C2×C412yes—
41C4⋊Dic61—21no—
42C4×Dic61—21no—
43#11758194—21no—
44#11758194—21no—
45C2×#92418—21no—
46C2×#92418—21no—
47C2×#92418—21no—
48C2×#92418D412yes—
49#11758189—24no—
50C8×D61—24no—
51C23×C61C22×C411yescharacteristic
52C22×D61C4⋊C412yes—
53C2×C4×C61—22no—
54C2×C4×C61C2×D411yescharacteristic
55C2×C4×C61C2×D411yescharacteristic
56C2×C4×C61C2×D411yescharacteristic
57C2×C4×C61C2×Q811yescharacteristic
58C2×C4×C61#4111yescharacteristic
59C2×C4×C61#4111yescharacteristic
60C22⋊D61—22no—
61C22⋊D61—22no—
62C2×Dic61—22no—
63C2×Dic61C4⋊C412yes—
64D244—21no—
65D244—21no—
66C4×D61—22no—
67C4×D61—22no—
68Dic122—21no—
69Dic122—21no—
70C8×C61—22no—
71C8×C61—41no—
72#92418—22no—
73#92418—41no—
74C22×C61—41no—
75C22×C61C2×C4⋊C411yescharacteristic
76C22×C61C4×D411yescharacteristic
77C22×C61C4×D411yescharacteristic
78C2×D61—22no—
79C2×D61—42no—
80C4×C61—42no—
81C4×C61#12011yescharacteristic
82C4×C61C22⋊Q811yescharacteristic
83C4×C61C22⋊Q811yescharacteristic
84C4×C61#12311yescharacteristic
85Dic61—22no—
86Dic61—42no—
87#1868—611nomaximal, Sylow
88C2×C61—21no—
89C2×C61—21no—
90C2×C61—21no—
91C2×C61#38511yescharacteristic
92D61—42no—
93#568—611no—
94#424—611no—
95#424—611no—
96#410—611no—
97#408—611no—
98#344—611no—
99#344D6111yescharacteristic, complemented
100C61#186811yescharacteristic, complemented, Sylow
101C2×#41—611no—
102#131—1222no—
103#131—1222no—
104C2×M16—611no—
105C2×M16—1222no—
106C2×M16C2×D6111yescharacteristic
107C2×M16C2×D6111yescharacteristic
108C22×C8—611no—
109#117—611no—
110#117C2×D6111yescharacteristic
111C4⋊C8—1222no—
112C4⋊C8—1222no—
113#99—614no—
114C22⋊C8—1222no—
115#41—1221no—
116#41—1221no—
117#41—1221no—
118#41—1221no—
119C2×Q8—611no—
120C2×D4—612no—
121C2×D4—611no—
122C22×C4—612no—
123C22×C4C22×D6111yescharacteristic
124M16—21no—
125M16—21no—
126M16—21no—
127M16—21no—
128M16—1224no—
129M16—1221no—
130M16—1221no—
131C2×C8—21no—
132C2×C8—612no—
133C2×C8—1224no—
134C2×C8—1221no—
135C2×C8—1221no—
136C2×C8—1221no—
137C2×C8D24412yes—
138C4⋊C4—21no—
139C4⋊C4—1221no—
140C22⋊C4—612no—
141C22⋊C4C4×D6112yes—
142C42—21no—
143C42—1221no—
144C23—612no—
145C23C2×C4×D6111yescharacteristic
146Q8—1221no—
147Q8—1221no—
148D4—1222no—
149D4—1222no—
150D4—1221no—
151D4—1221no—
152C2×C4—22no—
153C2×C4—612no—
154C2×C4—1222no—
155C2×C4—1222no—
156C2×C4—1222no—
157C2×C4C2×D24411yescharacteristic
158C2×C4#1175822211yescharacteristic
159C2×C4D4×D6111yescharacteristic
160C2×C4D4×D6111yescharacteristic
161C2×C4#1175822411yescharacteristic
162C2×C4Q8×D6111yescharacteristic
163C8—22no—
164C8—41no—
165C8—1222no—
166C8—2441no—
167C22—41no—
168C22—1222no—
169C22—2442no—
170C22C4⋊C4×D6111yescharacteristic
171C22#1451973711yescharacteristic
172C22C4×D24411yescharacteristic
173C4—42no—
174C4—1222no—
175C4—2442no—
176C4#1451974711yescharacteristic
177C4#1451975511yescharacteristic
178C4#1451975711yescharacteristic
179C4#1451975911yescharacteristic
180C2—21no—
181C2—21no—
182C2—21no—
183C2—2442no—
184C2#1683963611yescharacteristic
subgroupG/H
centerC4#14519747
commutatorC23×C61C22×C4
FrattiniC22×C4C22×D61
FittingC61×#344C2
socleC2×C61#385
hypercenter#344D61
hypocenterC61#1868
LCSG ▷ C23×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C4 ◁ C22×C4 ◁ #344

Complements

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

NH ≅ G/Ntype
2. #16839790C2semidirect
3. #16839789C2semidirect
6. #16839534C2semidirect
7. C61×#344C2semidirect
99. #344D61semidirect
100. C61#1868semidirect