Finite Group Databasebeta

← #21456590

Subgroups — #21456590

Order 7808.

416 conjugacy classes of subgroups; only the 121 normal subgroups are shown.

normal subgroups only

This group has 416 conjugacy classes of subgroups — too many to draw. Only its 121 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
1C22⋊Q8×D61C212yesmaximal
2#16840099C212yesmaximal, complemented
3#16840096C212yesmaximal, complemented
4#16840003C211yesmaximal, characteristic, complemented
5#16840001C212yesmaximal, complemented
6#16839919C212yesmaximal, complemented
7#16839916C212yesmaximal, complemented
8C2×#14519689C211yesmaximal, characteristic
9C61×#467C211yesmaximal, characteristic, complemented
10C2×Q8×D61C2212yes—
11C22×C4×D61C2211yescharacteristic
12C2×Dic244C2211yescharacteristic, complemented
13C2×#11758202C2212yescomplemented
14C22×#92418C2211yescharacteristic
15#14519757C2212yes—
16#14519756C2212yes—
17#14519755—22no—
18#14519754—22no—
19#14519753C2212yes—
20C4⋊C4×D61—22no—
21C4⋊C4×D61C2212yes—
22C22⋊C4×D61—22no—
23#14519711C2211yescharacteristic, complemented
24#14519710C2212yescomplemented
25#14519702C2212yescomplemented
26#14519701C2212yescomplemented
27#14519700C2212yescomplemented
28#14519689C2212yes—
29#14519689C2212yes—
30C2×Q16×C61C2211yescharacteristic, complemented
31C22×C8×C61C2211yescharacteristic
32C22⋊Q8×C61C2212yes—
33#107×C61C2211yescharacteristic, complemented
34#103×C61C2212yescomplemented
35C23×D61D411yescharacteristic
36C2×Q8×C61C2312yes—
37C22×C4×C61C2311yescharacteristic
38C22×Dic61D411yescharacteristic
39Q8×D61—42no—
40Q8×D61—42no—
41C2×C4×D61—22no—
42C2×C4×D61—22no—
43C2×C4×D61—41no—
44C2×C4×D61—41no—
45C2×C4×D61D412yes—
46C2×C4×D61C2312yes—
47C2×Dic122—22no—
48C2×Dic122C2312yes—
49Q16×C61—41no—
50C2×C8×C61—41no—
51C2×C8×C61C2311yescharacteristic
52C2×C8×C61C2311yescharacteristic
53C4⋊C4×C61—22no—
54C4⋊C4×C61C2312yes—
55C22⋊C4×C61—22no—
56C22⋊Dic61—22no—
57#11758202—42no—
58#11758198—22no—
59#11758198—22no—
60C4⋊Dic61—22no—
61C4⋊Dic61C2312yes—
62#11758196—22no—
63#11758196—22no—
64#11758196—22no—
65C2×#92418—41no—
66C2×#92418C2312yes—
67Dic244—41no—
68C23×C61C2×D411yescharacteristic
69C22×D61—41no—
70C22×D61—41no—
71C22×D61Q1614yescomplemented
72C22×D61C2×D412yes—
73Q8×C61—22no—
74Q8×C61—22no—
75C2×C4×C61—21no—
76C2×C4×C61—21no—
77C2×C4×C61—22no—
78C2×C4×C61—22no—
79C2×C4×C61C2×D411yescharacteristic
80C2×C4×C61C2411yescharacteristic
81C2×Dic61—22no—
82C2×Dic61—22no—
83C2×Dic61—41no—
84C2×Dic61C2×D412yes—
85C4×D61—22no—
86C4×D61—22no—
87C4×D61—42no—
88C4×D61—44no—
89C4×D61—44no—
90Dic122—22no—
91Dic122—22no—
92Dic122—44no—
93C8×C61—21no—
94C8×C61—21no—
95#92418—22no—
96C22×C61—21no—
97C22×C61—21no—
98C22×C61C2×Q1612yes—
99C22×C61C22×D411yescharacteristic
100C2×D61—22no—
101C2×D61—22no—
102C2×D61—44no—
103C2×D61C2×Q1614yes—
104C4×C61—21no—
105C4×C61—42no—
106C4×C61—42no—
107C4×C61H(5,𝔽2)11yescharacteristic
108C4×C61H(5,𝔽2)11yescharacteristic
109Dic61—22no—
110Dic61—42no—
111Dic61—42no—
112#3189—611nomaximal, Sylow
113C2×C61—22no—
114C2×C61#53411yescharacteristic
115C2×C61C22×Q1611yescharacteristic
116C2×C61#57511yescharacteristic
117D61—24no—
118C2×C22⋊Q8—612no—
119#484—612no—
120#484—612no—
121#467—611no—
122#467—612no—
123#467D6111yescharacteristic, complemented
124#451—612no—
125#451—612no—
126C2×C22⋊C8—611no—
127C61#318911yescharacteristic, complemented, Sylow
128C22×Q8—612no—
129C23×C4—611no—
130C2×Q16—612no—
131C2×Q16—611no—
132C2×Q16C2×D6111yescharacteristic, complemented
133C22×C8—611no—
134C22×C8C2×D6111yescharacteristic
135C22⋊Q8—612no—
136C22⋊Q8—612no—
137C22⋊Q8—612no—
138C22⋊Q8—1222no—
139C22⋊Q8—1222no—
140C22⋊Q8C2×D6112yes—
141C2×C4⋊C4—612no—
142C2×C4⋊C4—1222no—
143C2×C22⋊C4—1222no—
144#107—611no—
145#107—612no—
146#107C2×D6111yescharacteristic, complemented
147#103—612no—
148#103—612no—
149#103—612no—
150#103C2×D6112yescomplemented
151C22⋊C8—612no—
152C22⋊C8—612no—
153C24—611no—
154C2×Q8—612no—
155C2×Q8—1222no—
156C2×Q8—2442no—
157C2×Q8—2442no—
158C2×Q8C22×D6112yes—
159C22×C4—611no—
160C22×C4—612no—
161C22×C4—612no—
162C22×C4—1222no—
163C22×C4—1222no—
164C22×C4—2441no—
165C22×C4—2441no—
166C22×C4C22×D6111yescharacteristic
167Q16—41no—
168Q16—2441no—
169Q16—2442no—
170C2×C8—41no—
171C2×C8—612no—
172C2×C8—2441no—
173C2×C8C22×D6111yescharacteristic
174C2×C8C22×D6111yescharacteristic
175C4⋊C4—22no—
176C4⋊C4—612no—
177C4⋊C4—1222no—
178C4⋊C4—1222no—
179C4⋊C4—1222no—
180C4⋊C4—1222no—
181C4⋊C4C22×D6112yes—
182C22⋊C4—22no—
183C22⋊C4—1222no—
184C22⋊C4—1222no—
185C22⋊C4—1222no—
186C23—612no—
187C23—614no—
188C23—2441no—
189C23—2441no—
190C23D4×D6111yescharacteristic
191Q8—22no—
192Q8—22no—
193Q8—1222no—
194Q8—1222no—
195Q8—2444no—
196C2×C4—21no—
197C2×C4—21no—
198C2×C4—22no—
199C2×C4—22no—
200C2×C4—612no—
201C2×C4—1222no—
202C2×C4—1222no—
203C2×C4—1222no—
204C2×C4—1222no—
205C2×C4—2442no—
206C2×C4—2444no—
207C2×C4—2444no—
208C2×C4—2441no—
209C2×C4D4×D6111yescharacteristic
210C2×C4C23×D6111yescharacteristic
211C8—21no—
212C8—21no—
213C8—1222no—
214C22—21no—
215C22—21no—
216C22—614no—
217C22—1222no—
218C22—1222no—
219C22—2444no—
220C22Q16×D6112yes—
221C22C2×D4×D6111yescharacteristic
222C4—21no—
223C4—42no—
224C4—42no—
225C4—1222no—
226C4—2442no—
227C4—2442no—
228C4#1451982211yescharacteristic
229C4#1451982311yescharacteristic
230C2—22no—
231C2—1224no—
232C2#1684032011yescharacteristic
233C2C2×Q16×D6111yescharacteristic
234C2#1684055911yescharacteristic
subgroupG/H
centerC22C2×D4×D61
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC61×#467C2
socleC22×C61C22×D4
hypercenter#467D61
hypocenterC61#3189
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ #467

Complements

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

NH ≅ G/Ntype
2. #16840099C2semidirect
3. #16840096C2semidirect
4. #16840003C2semidirect
5. #16840001C2semidirect
6. #16839919C2semidirect
7. #16839916C2semidirect
9. C61×#467C2semidirect
12. C2×Dic244C22semidirect
13. C2×#11758202C22semidirect
23. #14519711C22semidirect
24. #14519710C22semidirect
25. #14519702C22semidirect
26. #14519701C22semidirect
27. #14519700C22semidirect
30. C2×Q16×C61C22semidirect
33. #107×C61C22semidirect
34. #103×C61C22semidirect
71. C22×D61Q16semidirect
123. #467D61semidirect
127. C61#3189semidirect
132. C2×Q16C2×D61semidirect
146. #107C2×D61semidirect
150. #103C2×D61semidirect