Finite Group Databasebeta

← #21458720

Subgroups — #21458720

Order 7808.

374 conjugacy classes of subgroups; only the 133 normal subgroups are shown.

normal subgroups only

This group has 374 conjugacy classes of subgroups — too many to draw. Only its 133 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#16840472C211yesmaximal, characteristic, complemented
2Q8×D244C211yesmaximal, characteristic, complemented
3#16840171C212yesmaximal, complemented
4#16840160C211yesmaximal, characteristic, complemented
5#16840063C212yesmaximal, complemented
6#16840053C211yesmaximal, characteristic, complemented
7#16840053C212yesmaximal, complemented
8#16840043C211yesmaximal, characteristic, complemented
9#16839875C212yesmaximal
10C4×D488C211yesmaximal, characteristic
11C61×#446C211yesmaximal, characteristic, complemented
12C2×Q8×D61—21no—
13C2×D488C2211yescharacteristic
14#14519777C2211yescharacteristic
15#14519777C2211yescharacteristic
16#14519777C2212yes—
17#14519769C2212yes—
18#14519757—21no—
19#14519757—22no—
20#14519755—22no—
21#14519753—21no—
22C4×D244C2211yescharacteristic
23C4×D244C2212yes—
24C4×D244C2211yescharacteristic
25C4×D244C2212yes—
26C4⋊C4×D61—21no—
27#14519711C2212yes—
28#14519711C2211yescharacteristic
29#14519709C2212yes—
30#14519709C2212yes—
31#14519709C2212yes—
32#14519699C2212yes—
33#14519699C2211yescharacteristic
34#14519699C2212yes—
35#14519699C2211yescharacteristic
36C4×Q8×C61C2211yescharacteristic
37C4⋊C8×C61C2211yescharacteristic
38C4⋊C8×C61C2212yes—
39#97×C61C2212yes—
40C4×C8×C61C2211yescharacteristic
41C2×Q8×C61D411yescharacteristic
42Q8×D61—44no—
43C2×D244C2311yescharacteristic
44C2×D244C2311yescharacteristic
45C2×C4×D61—22no—
46C2×C4×D61—21no—
47C2×C4×D61—21no—
48C2×C4×D61—22no—
49C2×Dic122—22no—
50C2×Dic122—21no—
51C2×Dic122—21no—
52C2×C8×C61C2311yescharacteristic
53C2×C8×C61C2312yes—
54C2×C8×C61C2311yescharacteristic
55C4⋊C4×C61D411yescharacteristic
56C4⋊C4×C61D412yes—
57C42×C61C2311yescharacteristic
58C42×C61C2312yes—
59#11758198—22no—
60#11758198—21no—
61#11758198—22no—
62#11758198—21no—
63C4⋊Dic61—21no—
64C4⋊Dic61—22no—
65C4⋊Dic61—21no—
66C4⋊Dic61C2312yes—
67C4⋊Dic61C2312yes—
68C4⋊Dic61C2311yescharacteristic
69C4⋊Dic61C2311yescharacteristic
70#11758196—22no—
71#11758196—22no—
72D488Q814yescomplemented
73C22×D61—21no—
74C22×D61—21no—
75Q8×C61—22no—
76C2×C4×C61C2×D412yes—
77C2×C4×C61C2×D412yes—
78C2×C4×C61C2×D411yescharacteristic
79C2×C4×C61C2×D411yescharacteristic
80C2×C4×C61C2411yescharacteristic
81C2×Dic61—21no—
82C2×Dic61—22no—
83C2×Dic61—21no—
84C2×Dic61—22no—
85D244—21no—
86D244—21no—
87D244C2×Q812yes—
88D244C2×Q812yescomplemented
89C4×D61—44no—
90C4×D61—42no—
91C4×D61—42no—
92C4×D61—82no—
93Dic122—44no—
94Dic122—42no—
95Dic122—81no—
96C8×C61—21no—
97C8×C61—22no—
98C8×C61C2×Q812yescomplemented
99C22×C61C22×D411yescharacteristic
100C2×D61—22no—
101C2×D61—22no—
102C2×D61—41no—
103C2×D61—41no—
104C2×D61—41no—
105C2×D61—41no—
106C4×C61—22no—
107C4×C61—21no—
108C4×C61—22no—
109C4×C61AGL(1,ℤ/8)12yes—
110C4×C61C22×Q811yescharacteristic
111C4×C612−1+411yescharacteristic
112Dic61—41no—
113Dic61—42no—
114Dic61—41no—
115Dic61—42no—
116#3384—611nomaximal, Sylow
117C2×C61D4×Q811yescharacteristic
118C2×C61C2×AGL(1,ℤ/8)11yescharacteristic
119C2×C61#57711yescharacteristic
120D61—42no—
121D61—42no—
122#554—611no—
123D4×Q8—611no—
124#501—612no—
125#498—611no—
126#478—612no—
127#476—612no—
128#476—611no—
129#474—611no—
130#446D6111yescharacteristic, complemented
131#442—612no—
132C4×D8—611no—
133C61#338411yescharacteristic, complemented, Sylow
134C22×Q8—1221no—
135C2×D8—611no—
136C4⋊Q8—611no—
137C4⋊Q8—612no—
138C4⋊Q8—611no—
139#125—612no—
140C22⋊Q8—1221no—
141C22⋊Q8—1221no—
142C22⋊Q8—1222no—
143C22⋊Q8—1222no—
144C4×Q8C2×D6111yescharacteristic
145C4×D4—611no—
146C4×D4—612no—
147C4×D4—611no—
148C4×D4—612no—
149C2×C4⋊C4—1221no—
150#107—611no—
151#107—612no—
152#106—612no—
153#106—612no—
154#106—612no—
155C4⋊C8C2×D6111yescharacteristic
156C4⋊C8C2×D6112yes—
157#102—611no—
158#102—611no—
159#102—612no—
160#102—612no—
161#97C2×D6112yes—
162C4×C8C2×D6111yescharacteristic
163C2×Q8—1221no—
164C2×Q8—1222no—
165C2×Q8—1221no—
166C2×Q8—2444no—
167C2×Q8D24411yescharacteristic
168C2×D4—611no—
169C2×D4—611no—
170C22×C4—1222no—
171C22×C4—1221no—
172C22×C4—1222no—
173C22×C4—1221no—
174D8—614no—
175C2×C8C22×D6111yescharacteristic
176C2×C8C22×D6112yes—
177C2×C8C22×D6111yescharacteristic
178C4⋊C4—612no—
179C4⋊C4—611no—
180C4⋊C4—612no—
181C4⋊C4—611no—
182C4⋊C4—1222no—
183C4⋊C4—1221no—
184C4⋊C4—1222no—
185C4⋊C4—1221no—
186C4⋊C4—1222no—
187C4⋊C4D24411yescharacteristic
188C4⋊C4D24412yes—
189C22⋊C4—1221no—
190C22⋊C4—1222no—
191C22⋊C4—1221no—
192C22⋊C4—1222no—
193C42C22×D6111yescharacteristic
194C42C22×D6112yes—
195C23—1221no—
196C23—1221no—
197Q8—22no—
198Q8—4881no—
199Q8—2444no—
200Q8—2442no—
201D4—612no—
202D4—612no—
203D4—1221no—
204D4—1221no—
205C2×C4—1221no—
206C2×C4—1222no—
207C2×C4—1222no—
208C2×C4—1221no—
209C2×C4—4882no—
210C2×C4—2444no—
211C2×C4—2442no—
212C2×C4—2442no—
213C2×C4C2×D24411yescharacteristic
214C2×C4C2×D24412yes—
215C2×C4C2×D24412yes—
216C2×C4C2×D24411yescharacteristic
217C2×C4C23×D6111yescharacteristic
218C8—21no—
219C8—22no—
220C8Q8×D6112yescomplemented
221C22—1222no—
222C22—1222no—
223C22—2441no—
224C22—2441no—
225C22—2441no—
226C22—2441no—
227C22C22×D24411yescharacteristic
228C4—22no—
229C4—22no—
230C4—21no—
231C4—2441no—
232C4—2442no—
233C4—2441no—
234C4—2442no—
235C4#1451980512yes—
236C4C2×Q8×D6111yescharacteristic
237C4#1451982411yescharacteristic
238C2—2442no—
239C2—2442no—
240C2Q8×D24411yescharacteristic
241C2C2×#1451980511yescharacteristic
242C2#1684057411yescharacteristic
subgroupG/H
centerC22C22×D244
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC61×#446C2
socleC22×C61C22×D4
hypercenter#446D61
hypocenterC61#3384
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C4×Q8 ◁ #446

Complements

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

NH ≅ G/Ntype
1. #16840472C2semidirect
2. Q8×D244C2semidirect
3. #16840171C2semidirect
4. #16840160C2semidirect
5. #16840063C2semidirect
6. #16840053C2semidirect
7. #16840053C2semidirect
8. #16840043C2semidirect
11. C61×#446C2semidirect
72. D488Q8semidirect
88. D244C2×Q8semidirect
98. C8×C61C2×Q8semidirect
130. #446D61semidirect
133. C61#3384semidirect
220. C8Q8×D61semidirect