Finite Group Databasebeta

← #21444283

Subgroups — #21444283

Order 7808.

216 conjugacy classes of subgroups; only the 65 normal subgroups are shown.

normal subgroups only

This group has 216 conjugacy classes of subgroups — too many to draw. Only its 65 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#16840299C211yesmaximal, characteristic
2#16839813C211yesmaximal, characteristic, complemented
3#16839784C211yesmaximal, characteristic, complemented
4Q8⋊#92418C211yesmaximal, characteristic, complemented
5#16839491C211yesmaximal, characteristic, complemented
6#16839489C211yesmaximal, characteristic, complemented
7C61×Q8⋊C8C211yesmaximal, characteristic, complemented
8C2×#11758189—21no—
9#14519772—21no—
10#14519768C411yescharacteristic
11#14519766C411yescharacteristic
12#14519762—21no—
13#14519753C411yescharacteristic
14#14519752C411yescharacteristic
15C4×D244—21no—
16C4×D244C2211yescharacteristic
17#14519734—21no—
18C42×D61C2211yescharacteristic
19C4⋊#92418C2211yescharacteristic
20#14519706—21no—
21#14519706—21no—
22#14519689—21no—
23C4×#92418C2211yescharacteristic
24C4×Q8×C61C2211yescharacteristic
25C4⋊C8×C61C2211yescharacteristic
26C4×C8×C61C2211yescharacteristic
27C2×Q8×C61C2×C411yescharacteristic
28C2×D244—21no—
29C2×D244C2×C411yescharacteristic
30C2×C4×D61—21no—
31C2×C4×D61C2×C411yescharacteristic
32C2×C4×D61D411yescharacteristic
33C2×C4×D61D411yescharacteristic
34C2×C8×C61—21no—
35C2×C8×C61—21no—
36C4⋊C4×C61—21no—
37C4⋊C4×C61C2×C411yescharacteristic
38C42×C61—21no—
39C42×C61C2311yescharacteristic
40#11758198—21no—
41#11758198—21no—
42#11758198—21no—
43#11758198—21no—
44#11758198—21no—
45C4⋊Dic61—21no—
46C4⋊Dic61C2×C411yescharacteristic
47#11758196—21no—
48#11758196—21no—
49C4×Dic61C2×C411yescharacteristic
50C4×Dic61D411yescharacteristic
51C4×Dic61D411yescharacteristic
52C2×#92418—21no—
53C2×#92418—21no—
54#11758189—42no—
55C22×D61—21no—
56C22×D61C22⋊C411yescharacteristic
57Q8×C61—21no—
58Q8×C61—21no—
59C2×C4×C61—21no—
60C2×C4×C61—21no—
61C2×C4×C61C22×C411yescharacteristic
62C2×C4×C61C2×D411yescharacteristic
63C2×C4×C61C2×D411yescharacteristic
64C2×Dic61—21no—
65C2×Dic61C22⋊C411yescharacteristic
66C2×Dic61C22⋊C411yescharacteristic
67C2×Dic61C22⋊C411yescharacteristic
68D244—21no—
69D244—21no—
70D244—42no—
71C4×D61—21no—
72C4×D61—21no—
73C4×D61—21no—
74C4×D61—21no—
75C4×D61—41no—
76C4×D61—41no—
77C4×D61—41no—
78C8×C61—41no—
79C8×C61—41no—
80#92418—41no—
81#92418—41no—
82C22×C61C2×C22⋊C411yescharacteristic
83C2×D61—21no—
84C2×D61—21no—
85C2×D61—21no—
86C2×D61—41no—
87C2×D61—41no—
88C2×D61—41no—
89C4×C61—21no—
90C4×C61—41no—
91C4×C61—41no—
92C4×C61#13111yescharacteristic
93C4×C61#13111yescharacteristic
94C4×C61AGL(1,ℤ/8)11yescharacteristic
95C4×C61#13711yescharacteristic
96Dic61—21no—
97Dic61—21no—
98Dic61—21no—
99Dic61—41no—
100#1495—611nomaximal, Sylow
101C2×C61#40811yescharacteristic
102C2×C61#41711yescharacteristic
103C2×C61#42111yescharacteristic
104D61—41no—
105D61—81no—
106#529—611no—
107#431—611no—
108#423—611no—
109Q8⋊C8—611no—
110Q8⋊C8D6111yescharacteristic, complemented
111D4⋊C8—611no—
112D4⋊C8—611no—
113C61#149511yescharacteristic, complemented, Sylow
114C2×M16—1221no—
115#126—1221no—
116#125—611no—
117#124—611no—
118#123—1221no—
119C22⋊Q8—611no—
120#121—611no—
121C4×Q8C2×D6111yescharacteristic
122C4×D4—611no—
123C4×D4—1221no—
124#117—1221no—
125C2×C42—611no—
126C4⋊C8—611no—
127C4⋊C8—1221no—
128C4⋊C8—1221no—
129C4⋊C8C2×D6111yescharacteristic
130C22⋊C8—1221no—
131C4×C8—611no—
132C4×C8C2×D6111yescharacteristic
133C2×Q8C4×D6111yescharacteristic
134C2×D4—611no—
135C2×D4—1221no—
136C22×C4—611no—
137C22×C4—611no—
138C22×C4—611no—
139C22×C4—1221no—
140M16—2442no—
141C2×C8—21no—
142C2×C8—21no—
143C2×C8—1221no—
144C2×C8—1221no—
145C4⋊C4—21no—
146C4⋊C4—611no—
147C4⋊C4—1221no—
148C4⋊C4—1221no—
149C4⋊C4—1221no—
150C4⋊C4C4×D6111yescharacteristic
151C22⋊C4—1221no—
152C22⋊C4—1221no—
153C22⋊C4—1221no—
154C22⋊C4—1221no—
155C22⋊C4—1221no—
156C42—21no—
157C42—611no—
158C42—611no—
159C42—611no—
160C42C22×D6111yescharacteristic
161C23—611no—
162C23—1221no—
163Q8—21no—
164Q8—21no—
165D4—1221no—
166D4—1221no—
167D4—2442no—
168C2×C4—21no—
169C2×C4—21no—
170C2×C4—611no—
171C2×C4—611no—
172C2×C4—611no—
173C2×C4—1221no—
174C2×C4—1221no—
175C2×C4—1221no—
176C2×C4—1221no—
177C2×C4—1221no—
178C2×C4—2441no—
179C2×C4—2441no—
180C2×C4—2441no—
181C2×C4C2×C4×D6111yescharacteristic
182C2×C4D4×D6111yescharacteristic
183C2×C4D4×D6111yescharacteristic
184C8—41no—
185C8—41no—
186C8—2441no—
187C8—2441no—
188C22—1221no—
189C22—1221no—
190C22—1221no—
191C22—2441no—
192C22—2441no—
193C22—2441no—
194C22C22⋊C4×D6111yescharacteristic
195C4—21no—
196C4—41no—
197C4—41no—
198C4—1221no—
199C4—1221no—
200C4—1221no—
201C4—2441no—
202C4#1451978311yescharacteristic
203C4#1451978511yescharacteristic
204C4#1451980411yescharacteristic
205C4#1451980911yescharacteristic
206C2—4881no—
207C2—2441no—
208C2#1683972711yescharacteristic
209C2#1683976211yescharacteristic
210C2#1683977711yescharacteristic
subgroupG/H
centerC2×C4D4×D61
commutatorC2×C4×C61C22×C4
FrattiniC42C22×D61
FittingC61×Q8⋊C8C2
socleC22×C61C2×C22⋊C4
hypercenterQ8⋊C8D61
hypocenterC61#1495
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C42 ◁ Q8⋊C8

Complements

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

NH ≅ G/Ntype
2. #16839813C2semidirect
3. #16839784C2semidirect
4. Q8⋊#92418C2semidirect
5. #16839491C2semidirect
6. #16839489C2semidirect
7. C61×Q8⋊C8C2semidirect
110. Q8⋊C8D61semidirect
113. C61#1495semidirect