Finite Group Databasebeta

← #21444230

Subgroups — #21444230

Order 7808.

234 conjugacy classes of subgroups; only the 77 normal subgroups are shown.

normal subgroups only

This group has 234 conjugacy classes of subgroups — too many to draw. Only its 77 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
2C4×#11758194C211yesmaximal, characteristic, complemented
3#16839492C212yesmaximal, complemented
4#16839489C212yesmaximal, complemented
5C2×C4⋊C8×C61C211yesmaximal, 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—
17#14519688—21no—
18C4×#92418C2212yes—
19C22×C8×C61—21no—
20C2×C42×C61C2211yescharacteristic
21C4⋊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—
31C2×C8×C61—42no—
32C42×C61C2×C411yescharacteristic
33C42×C61D411yescharacteristic
34C42×C61D411yescharacteristic
35C42×C61C2311yescharacteristic
36C22⋊Dic61—21no—
37#11758198—21no—
38#11758198—21no—
39#11758198—21no—
40#11758198—21no—
41C4⋊Dic61C2×C411yescharacteristic
42C4⋊Dic61C2×C411yescharacteristic
43#11758196—21no—
44#11758196—21no—
45#11758196—21no—
46#11758196—21no—
47C4×Dic61—21no—
48#11758194—24no—
49C2×#92418—22no—
50C23×C61C22⋊C411yescharacteristic
51C22×D61—21no—
52C2×C4×C61—22no—
53C2×C4×C61—22no—
54C2×C4×C61—21no—
55C2×C4×C61—21no—
56C2×C4×C61C22⋊C411yescharacteristic
57C2×C4×C61C22⋊C411yescharacteristic
58C2×C4×C61C22⋊C411yescharacteristic
59C2×C4×C61C22×C411yescharacteristic
60C2×C4×C61C2×D411yescharacteristic
61C2×C4×C61C2×D411yescharacteristic
62C22⋊D61—42no—
63C2×Dic61—21no—
64C2×Dic61—21no—
65C2×Dic61—21no—
66D244—22no—
67C4×D61—41no—
68C4×D61—41no—
69Dic122—22no—
70C8×C61—42no—
71#92418—24no—
72C22×C61—21no—
73C22×C61—21no—
74C22×C61#10412yes—
75C22×C61C2×C22⋊C411yescharacteristic
76C2×D61—41no—
77C2×D61—41no—
78C2×D61—41no—
79C4×C61—21no—
80C4×C61—21no—
81C4×C61—21no—
82C4×C61—21no—
83C4×C61#13112yes—
84C4×C61AGL(1,ℤ/8)11yescharacteristic
85C4×C61#13711yescharacteristic
86Dic61—41no—
87Dic61—41no—
88Dic61—41no—
89#1483—611nomaximal, Sylow
90C2×C61—22no—
91C2×C61#40811yescharacteristic
92C2×C61#41711yescharacteristic
93C2×C61C2×#10411yescharacteristic
94D61—81no—
95#529—611no—
96C2×C4⋊C8D6111yescharacteristic, complemented
97C4×M16—611no—
98Q8⋊C8—612no—
99D4⋊C8—612no—
100C61#148311yescharacteristic, complemented, Sylow
101C2×M16—1221no—
102C22×C8—21no—
103#126—1221no—
104#125—611no—
105#124—611no—
106#123—1221no—
107C22⋊Q8—611no—
108#121—611no—
109C4×Q8—611no—
110C4×D4—611no—
111C4×D4—1221no—
112#117—1221no—
113C2×C42C2×D6111yescharacteristic
114C4⋊C8—21no—
115C4⋊C8C2×D6112yes—
116#97—1221no—
117C4×C8—612no—
118C2×Q8—611no—
119C2×D4—611no—
120C2×D4—1221no—
121C22×C4—1221no—
122C22×C4C4×D6111yescharacteristic
123C22×C4D24411yescharacteristic
124C22×C4C22⋊D6111yescharacteristic
125M16—1224no—
126C2×C8—22no—
127C2×C8—42no—
128C2×C8—1222no—
129C4⋊C4—611no—
130C4⋊C4—611no—
131C4⋊C4—1221no—
132C4⋊C4—1221no—
133C4⋊C4—1221no—
134C4⋊C4—1221no—
135C22⋊C4—1221no—
136C22⋊C4—1221no—
137C22⋊C4—1221no—
138C22⋊C4—1221no—
139C22⋊C4—1221no—
140C42—1221no—
141C42C4×D6111yescharacteristic
142C42D24411yescharacteristic
143C42C22⋊D6111yescharacteristic
144C42C22×D6111yescharacteristic
145C23—1221no—
146C23#1175819811yescharacteristic
147Q8—1222no—
148D4—1222no—
149D4—2442no—
150C2×C4—22no—
151C2×C4—21no—
152C2×C4—22no—
153C2×C4—21no—
154C2×C4—1221no—
155C2×C4—1221no—
156C2×C4—1221no—
157C2×C4—2441no—
158C2×C4—2441no—
159C2×C4#1175819811yescharacteristic
160C2×C4#1175819811yescharacteristic
161C2×C4#1175819811yescharacteristic
162C2×C4C2×C4×D6111yescharacteristic
163C2×C4C2×D24411yescharacteristic
164C2×C4C2×C22⋊D6111yescharacteristic
165C8—42no—
166C8—1224no—
167C22—21no—
168C22—21no—
169C22—2441no—
170C22—2441no—
171C22—2441no—
172C22#1451970312yes—
173C22C2×#1175819811yescharacteristic
174C4—21no—
175C4—21no—
176C4—21no—
177C4—21no—
178C4—2441no—
179C4—2441no—
180C4—2441no—
181C4#1451978312yes—
182C4#1451980311yescharacteristic
183C4#1451980811yescharacteristic
184C2—22no—
185C2—4881no—
186C2#1683972811yescharacteristic
187C2#1683976111yescharacteristic
188C2C2×#1451970311yescharacteristic
subgroupG/H
centerC2×C4C2×C22⋊D61
commutatorC2×C4×C61C22×C4
FrattiniC42C22×D61
FittingC2×C4⋊C8×C61C2
socleC22×C61C2×C22⋊C4
hypercenterC2×C4⋊C8D61
hypocenterC61#1483
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ C2×C4⋊C8

Complements

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

NH ≅ G/Ntype
2. C4×#11758194C2semidirect
3. #16839492C2semidirect
4. #16839489C2semidirect
5. C2×C4⋊C8×C61C2semidirect
96. C2×C4⋊C8D61semidirect
100. C61#1483semidirect