Finite Group Databasebeta

← #21444205

Subgroups — #21444205

Order 7808.

264 conjugacy classes of subgroups; only the 83 normal subgroups are shown.

normal subgroups only

This group has 264 conjugacy classes of subgroups — too many to draw. Only its 83 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
1C4×#11758226C211yesmaximal, characteristic
2#16839813C211yesmaximal, characteristic, complemented
3C4⋊C8×D61C211yesmaximal, characteristic, complemented
4Q8⋊#92418C211yesmaximal, characteristic, complemented
5#16839491C211yesmaximal, characteristic, complemented
6#16839489C211yesmaximal, characteristic, complemented
7C61×Q8⋊C8C211yesmaximal, characteristic, complemented
8C2×#11758226C411yescharacteristic
9C2×C8×D61—21no—
10Q8×Dic61C411yescharacteristic
11C4×D244—21no—
12C4×D244C2211yescharacteristic
13#14519739—21no—
14#14519739C411yescharacteristic
15#14519735—21no—
16#14519735C411yescharacteristic
17C42×D61—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
28#11758226—22no—
29#11758226C814yescomplemented
30C2×D244—21no—
31C2×D244C2×C411yescharacteristic
32C2×C4×D61—21no—
33C2×C4×D61—21no—
34C2×C4×D61—21no—
35C2×C4×D61C2×C411yescharacteristic
36C2×C4×D61D411yescharacteristic
37C2×C4×D61D411yescharacteristic
38C2×C8×C61—21no—
39C2×C8×C61—21no—
40C4⋊C4×C61—21no—
41C4⋊C4×C61C2×C411yescharacteristic
42C42×C61—21no—
43C42×C61C2311yescharacteristic
44#11758198—21no—
45#11758198—21no—
46#11758198—21no—
47C4⋊Dic61—21no—
48C4⋊Dic61C2×C411yescharacteristic
49C4×Dic61—21no—
50C4×Dic61—21no—
51C4×Dic61C2×C411yescharacteristic
52C4×Dic61D411yescharacteristic
53C4×Dic61D411yescharacteristic
54C2×#92418—21no—
55C2×#92418—21no—
56C8×D61—42no—
57C22×D61—21no—
58C22×D61C22⋊C411yescharacteristic
59Q8×C61—21no—
60Q8×C61C2×C812yescomplemented
61C2×C4×C61—21no—
62C2×C4×C61—21no—
63C2×C4×C61C22×C411yescharacteristic
64C2×C4×C61C2×D411yescharacteristic
65C2×C4×C61C2×D411yescharacteristic
66C2×Dic61—21no—
67C2×Dic61C22⋊C411yescharacteristic
68C2×Dic61C22⋊C411yescharacteristic
69C2×Dic61C22⋊C411yescharacteristic
70D244—24no—
71D244—21no—
72D244C2×C812yescomplemented
73C4×D61—21no—
74C4×D61—21no—
75C4×D61—24no—
76C4×D61—41no—
77C4×D61—42no—
78C4×D61—41no—
79C4×D61—41no—
80C4×D61C2×C812yes—
81C4×D61M1612yes—
82C8×C61—41no—
83C8×C61—41no—
84#92418—41no—
85#92418—41no—
86C22×C61C2×C22⋊C411yescharacteristic
87C2×D61—21no—
88C2×D61—21no—
89C2×D61—22no—
90C2×D61—41no—
91C2×D61—41no—
92C2×D61C22⋊C812yes—
93C4×C61—22no—
94C4×C61—21no—
95C4×C61—41no—
96C4×C61C22×C811yescharacteristic
97C4×C61C2×M1611yescharacteristic
98C4×C61AGL(1,ℤ/8)11yescharacteristic
99C4×C61#13711yescharacteristic
100Dic61—21no—
101Dic61—21no—
102Dic61—41no—
103Dic61C22⋊C812yes—
104#1477—611nomaximal, Sylow
105C2×C61C2×C22⋊C811yescharacteristic
106C2×C61#41711yescharacteristic
107C2×C61#42111yescharacteristic
108D61—22no—
109D61—42no—
110C4×#41—611no—
111#431—611no—
112C2×C4⋊C8—611no—
113Q8⋊C8—611no—
114Q8⋊C8D6111yescharacteristic, complemented
115D4⋊C8—611no—
116D4⋊C8—611no—
117C61#147711yescharacteristic, complemented, Sylow
118C2×#41—611no—
119C22×C8—1221no—
120C4×Q8—611no—
121C4×Q8C2×D6111yescharacteristic
122C4×D4—611no—
123C4×D4—611no—
124C4×D4—1221no—
125C4×D4—1221no—
126#117—611no—
127#117—1221no—
128C2×C42—611no—
129C2×C42—1221no—
130C4⋊C8—611no—
131C4⋊C8—1221no—
132C4⋊C8—1221no—
133C4⋊C8C2×D6111yescharacteristic
134C22⋊C8—1221no—
135C4×C8—611no—
136C4×C8C2×D6111yescharacteristic
137#41—614no—
138#41—1222no—
139C2×Q8C4×D6111yescharacteristic
140C2×D4—611no—
141C2×D4—1221no—
142C22×C4—611no—
143C22×C4—611no—
144C22×C4—611no—
145C22×C4—1221no—
146C22×C4—1221no—
147C22×C4—1221no—
148C2×C8—21no—
149C2×C8—21no—
150C2×C8—1221no—
151C2×C8—1221no—
152C2×C8—2442no—
153C4⋊C4—21no—
154C4⋊C4—611no—
155C4⋊C4—1221no—
156C4⋊C4C4×D6111yescharacteristic
157C22⋊C4—1221no—
158C22⋊C4—1221no—
159C22⋊C4—1221no—
160C42—21no—
161C42—611no—
162C42—611no—
163C42—611no—
164C42—1221no—
165C42—1221no—
166C42C22×D6111yescharacteristic
167C23—611no—
168C23—1221no—
169Q8—21no—
170Q8C8×D6112yescomplemented
171D4—612no—
172D4—1224no—
173D4—1221no—
174C2×C4—21no—
175C2×C4—21no—
176C2×C4—611no—
177C2×C4—612no—
178C2×C4—612no—
179C2×C4—611no—
180C2×C4—611no—
181C2×C4—1224no—
182C2×C4—1221no—
183C2×C4—1221no—
184C2×C4—1221no—
185C2×C4—2441no—
186C2×C4—2442no—
187C2×C4—2441no—
188C2×C4—2441no—
189C2×C4C2×C4×D6111yescharacteristic
190C2×C4D4×D6111yescharacteristic
191C2×C4D4×D6111yescharacteristic
192C8—41no—
193C8—41no—
194C8—2441no—
195C8—2441no—
196C22—612no—
197C22—1221no—
198C22—1221no—
199C22—1222no—
200C22—2441no—
201C22—2441no—
202C22C22⋊C4×D6111yescharacteristic
203C4—22no—
204C4—21no—
205C4—41no—
206C4—612no—
207C4—1221no—
208C4—1221no—
209C4—2441no—
210C4C2×C8×D6111yescharacteristic
211C4M16×D6111yescharacteristic
212C4#1451980411yescharacteristic
213C4#1451980911yescharacteristic
214C2—1222no—
215C2—2442no—
216C2C22⋊C8×D6111yescharacteristic
217C2#1683976211yescharacteristic
218C2#1683977711yescharacteristic
subgroupG/H
centerC2×C4D4×D61
commutatorC4×C61C22×C8
FrattiniC42C22×D61
FittingC61×Q8⋊C8C2
socleC22×C61C2×C22⋊C4
hypercenterQ8⋊C8D61
hypocenterC61#1477
LCSG ▷ 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. C4⋊C8×D61C2semidirect
4. Q8⋊#92418C2semidirect
5. #16839491C2semidirect
6. #16839489C2semidirect
7. C61×Q8⋊C8C2semidirect
29. #11758226C8semidirect
60. Q8×C61C2×C8semidirect
72. D244C2×C8semidirect
114. Q8⋊C8D61semidirect
117. C61#1477semidirect
170. Q8C8×D61semidirect