Finite Group Databasebeta

← #21444285

Subgroups — #21444285

Order 7808.

216 conjugacy classes of subgroups; only the 73 normal subgroups are shown.

normal subgroups only

This group has 216 conjugacy classes of subgroups — too many to draw. Only its 73 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#16840296C211yesmaximal, characteristic
2#16839786C211yesmaximal, characteristic, complemented
3#16839494C212yesmaximal, complemented
4#16839491C212yesmaximal, complemented
5C61×#431C211yesmaximal, characteristic, complemented
6C2×#11758194—21no—
7#14519771—21no—
8#14519769C411yescharacteristic
9#14519765C411yescharacteristic
10#14519760—21no—
11#14519756C411yescharacteristic
12#14519751C411yescharacteristic
13C4×Dic122C2211yescharacteristic
14C4×D244C2211yescharacteristic
15C4×C22⋊D61—21no—
16#14519734—21no—
17C4⋊#92418—21no—
18C4⋊#92418C2212yes—
19C2×C42×C61C2211yescharacteristic
20C4⋊C8×C61—21no—
21C22⋊C8×C61—21no—
22C4×C8×C61C2212yes—
23C22×C4×C61C2×C411yescharacteristic
24C22×C4×C61D411yescharacteristic
25C22×C4×C61D411yescharacteristic
26C2×C22⋊D61—21no—
27C2×D244C2×C411yescharacteristic
28C2×C4×D61—21no—
29C2×Dic122C2×C411yescharacteristic
30C2×C8×C61—22no—
31C42×C61C2×C411yescharacteristic
32C42×C61D411yescharacteristic
33C42×C61D411yescharacteristic
34C42×C61C2311yescharacteristic
35C22⋊Dic61—21no—
36#11758198—21no—
37#11758198—21no—
38#11758198—21no—
39#11758198—21no—
40C4⋊Dic61C2×C411yescharacteristic
41C4⋊Dic61C2×C411yescharacteristic
42#11758196—21no—
43#11758196—21no—
44#11758196—21no—
45#11758196—21no—
46C4×Dic61—21no—
47#11758194—42no—
48C2×#92418—22no—
49C23×C61C22⋊C411yescharacteristic
50C22×D61—21no—
51C2×C4×C61—22no—
52C2×C4×C61—21no—
53C2×C4×C61—21no—
54C2×C4×C61—41no—
55C2×C4×C61C22⋊C411yescharacteristic
56C2×C4×C61C22⋊C411yescharacteristic
57C2×C4×C61C22⋊C411yescharacteristic
58C2×C4×C61C22×C411yescharacteristic
59C2×C4×C61C2×D411yescharacteristic
60C2×C4×C61C2×D411yescharacteristic
61C22⋊D61—42no—
62C2×Dic61—21no—
63C2×Dic61—21no—
64C2×Dic61—21no—
65D244—22no—
66C4×D61—41no—
67C4×D61—41no—
68Dic122—22no—
69C8×C61—42no—
70#92418—42no—
71C22×C61—21no—
72C22×C61—21no—
73C22×C61—21no—
74C22×C61C2×C22⋊C411yescharacteristic
75C2×D61—41no—
76C2×D61—41no—
77C2×D61—41no—
78C4×C61—21no—
79C4×C61—21no—
80C4×C61—21no—
81C4×C61—21no—
82C4×C61#13112yes—
83C4×C61AGL(1,ℤ/8)11yescharacteristic
84C4×C61#13711yescharacteristic
85Dic61—41no—
86Dic61—41no—
87Dic61—41no—
88#1495—611nomaximal, Sylow
89C2×C61—41no—
90C2×C61#40811yescharacteristic
91C2×C61#41711yescharacteristic
92C2×C61#42111yescharacteristic
93D61—81no—
94#529—611no—
95#431D6111yescharacteristic, complemented
96#423—611no—
97Q8⋊C8—612no—
98D4⋊C8—612no—
99C61#149511yescharacteristic, complemented, Sylow
100C2×M16—1221no—
101#126—1221no—
102#125—611no—
103#124—611no—
104#123—1221no—
105C22⋊Q8—611no—
106#121—611no—
107C4×Q8—611no—
108C4×D4—611no—
109C4×D4—1221no—
110#117—1221no—
111C2×C42C2×D6111yescharacteristic
112C4⋊C8—21no—
113C4⋊C8—612no—
114C4⋊C8—1221no—
115C22⋊C8—21no—
116C4×C8C2×D6112yes—
117C2×Q8—611no—
118C2×D4—611no—
119C2×D4—1221no—
120C22×C4—1221no—
121C22×C4C4×D6111yescharacteristic
122C22×C4D24411yescharacteristic
123C22×C4C22⋊D6111yescharacteristic
124M16—2442no—
125C2×C8—22no—
126C2×C8—1222no—
127C4⋊C4—611no—
128C4⋊C4—611no—
129C4⋊C4—1221no—
130C4⋊C4—1221no—
131C4⋊C4—1221no—
132C4⋊C4—1221no—
133C22⋊C4—1221no—
134C22⋊C4—1221no—
135C22⋊C4—1221no—
136C22⋊C4—1221no—
137C22⋊C4—1221no—
138C42—1221no—
139C42C4×D6111yescharacteristic
140C42D24411yescharacteristic
141C42C22⋊D6111yescharacteristic
142C42C22×D6111yescharacteristic
143C23—1221no—
144C23#1175819811yescharacteristic
145Q8—1222no—
146D4—1222no—
147D4—2442no—
148C2×C4—21no—
149C2×C4—22no—
150C2×C4—21no—
151C2×C4—41no—
152C2×C4—1221no—
153C2×C4—1221no—
154C2×C4—1221no—
155C2×C4—2441no—
156C2×C4—2441no—
157C2×C4#1175819811yescharacteristic
158C2×C4#1175819811yescharacteristic
159C2×C4#1175819811yescharacteristic
160C2×C4C2×C4×D6111yescharacteristic
161C2×C4C2×D24411yescharacteristic
162C2×C4C2×C22⋊D6111yescharacteristic
163C8—42no—
164C8—2442no—
165C22—21no—
166C22—21no—
167C22—21no—
168C22—2441no—
169C22—2441no—
170C22—2441no—
171C22C2×#1175819811yescharacteristic
172C4—21no—
173C4—21no—
174C4—21no—
175C4—21no—
176C4—2441no—
177C4—2441no—
178C4—2441no—
179C4#1451978312yes—
180C4#1451980511yescharacteristic
181C4#1451981011yescharacteristic
182C2—41no—
183C2—4881no—
184C2#1683972811yescharacteristic
185C2#1683976411yescharacteristic
186C2#1683978011yescharacteristic
subgroupG/H
centerC2×C4C2×D244
commutatorC2×C4×C61C22×C4
FrattiniC42C22×D61
FittingC61×#431C2
socleC22×C61C2×C22⋊C4
hypercenter#431D61
hypocenterC61#1495
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #431

Complements

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

NH ≅ G/Ntype
2. #16839786C2semidirect
3. #16839494C2semidirect
4. #16839491C2semidirect
5. C61×#431C2semidirect
95. #431D61semidirect
99. C61#1495semidirect