Finite Group Databasebeta

← #21456969

Subgroups — #21456969

Order 7808.

360 conjugacy classes of subgroups; only the 123 normal subgroups are shown.

normal subgroups only

This group has 360 conjugacy classes of subgroups — too many to draw. Only its 123 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#16840316C211yesmaximal, characteristic
2C4⋊Q8×D61C211yesmaximal, characteristic
3#16840166C212yesmaximal, complemented
4#16840111C212yesmaximal, complemented
5#16840099C212yesmaximal
6#16840096C212yesmaximal
7#16840058C211yesmaximal, characteristic, complemented
8#16840057C211yesmaximal, characteristic, complemented
9#16840054C211yesmaximal, characteristic, complemented
10#16839814C211yesmaximal, characteristic
11C61×#477C211yesmaximal, characteristic, complemented
12C2×Q8×D61—21no—
13#14519777C2211yescharacteristic
14#14519776—21no—
15#14519776C2212yes—
16#14519776C2211yescharacteristic
17#14519775—21no—
18#14519775C2211yescharacteristic
19#14519767—21no—
20#14519757C2211yescharacteristic
21#14519755—21no—
22#14519753C2211yescharacteristic
23C4×Dic122—21no—
24C4×Dic122C2211yescharacteristic
25#14519734—21no—
26C4⋊C4×D61—21no—
27C4⋊C4×D61C2212yes—
28C42×D61C2211yescharacteristic
29#14519711C2212yes—
30#14519710C2212yes—
31#14519710C2212yes—
32C4⋊#92418C2211yescharacteristic
33#14519702C2212yes—
34#14519701C2212yes—
35#14519700C2212yes—
36#14519689C2212yes—
37C8×Dic61C2212yes—
38C4⋊Q8×C61C2211yescharacteristic
39C4×Q8×C61C2211yescharacteristic
40#107×C61C2212yes—
41C4⋊C8×C61C2211yescharacteristic
42#103×C61C2212yes—
43C2×Q8×C61—21no—
44C2×Q8×C61C2311yescharacteristic
45Q8×D61—44no—
46C2×C4×D61—22no—
47C2×C4×D61D411yescharacteristic
48C2×C4×D61D411yescharacteristic
49C2×C4×D61C2311yescharacteristic
50C2×Dic122—21no—
51C2×Dic122—22no—
52C2×Dic122—21no—
53C2×Dic122C2311yescharacteristic
54C2×C8×C61C2312yes—
55C4⋊C4×C61—21no—
56C4⋊C4×C61—21no—
57C4⋊C4×C61C2312yes—
58C4⋊C4×C61C2311yescharacteristic
59C42×C61—21no—
60C42×C61C2311yescharacteristic
61#11758198—21no—
62#11758198—21no—
63C4⋊Dic61—21no—
64C4⋊Dic61—21no—
65C4⋊Dic61C2312yes—
66C4⋊Dic61C2311yescharacteristic
67#11758196—21no—
68#11758196—22no—
69#11758196—22no—
70#11758196—21no—
71#11758196—21no—
72#11758196—21no—
73#11758196—21no—
74C4×Dic61—21no—
75C4×Dic61D411yescharacteristic
76C4×Dic61D411yescharacteristic
77C4×Dic61C2311yescharacteristic
78C2×#92418C2312yes—
79C22×D61C2×D411yescharacteristic
80Q8×C61—21no—
81Q8×C61—21no—
82Q8×C61—42no—
83C2×C4×C61—21no—
84C2×C4×C61—22no—
85C2×C4×C61—21no—
86C2×C4×C61C2×D411yescharacteristic
87C2×C4×C61C2×D411yescharacteristic
88C2×C4×C61C2411yescharacteristic
89C2×Dic61—21no—
90C2×Dic61—21no—
91C2×Dic61—22no—
92C2×Dic61C2×D411yescharacteristic
93C2×Dic61C2×D411yescharacteristic
94C2×Dic61C2×D411yescharacteristic
95C4×D61—21no—
96C4×D61—21no—
97C4×D61—22no—
98C4×D61—44no—
99C4×D61Q1614yes—
100Dic122—21no—
101Dic122—21no—
102Dic122—42no—
103Dic122—42no—
104Dic122—44no—
105C8×C61—22no—
106#92418—22no—
107C22×C61C22×D411yescharacteristic
108C2×D61—21no—
109C2×D61—21no—
110C2×D61C2×Q1612yes—
111C4×C61—21no—
112C4×C61—41no—
113C4×C61—42no—
114C4×C61—41no—
115C4×C61C2×Q1612yes—
116C4×C612−1+411yescharacteristic
117C4×C612−1+411yescharacteristic
118Dic61—21no—
119Dic61—41no—
120Dic61—42no—
121Dic61—41no—
122Dic61C2×Q1612yes—
123Dic61AGL(1,ℤ/8)12yes—
124#3230—611nomaximal, Sylow
125C2×C61#53611yescharacteristic
126C2×C61C22×Q1611yescharacteristic
127C2×C61C2×AGL(1,ℤ/8)11yescharacteristic
128D61—22no—
129#533—611no—
130C2×C4⋊Q8—611no—
131#500—612no—
132#487—612no—
133#484—612no—
134#484—612no—
135#477—611no—
136#477—611no—
137#477—611no—
138#477D6111yescharacteristic, complemented
139#431—611no—
140C61#323011yescharacteristic, complemented, Sylow
141C22×Q8—1221no—
142C4⋊Q8—612no—
143C4⋊Q8—611no—
144C4⋊Q8—611no—
145C4⋊Q8—611no—
146C4⋊Q8—1221no—
147C4⋊Q8—1221no—
148C4⋊Q8C2×D6111yescharacteristic
149#125—1221no—
150C22⋊Q8—611no—
151C22⋊Q8—611no—
152C22⋊Q8—1221no—
153C4×Q8—611no—
154C4×Q8—1221no—
155C4×Q8C2×D6111yescharacteristic
156#117—1221no—
157C2×C4⋊C4—612no—
158C2×C4⋊C4—1221no—
159C2×C42—611no—
160#107—612no—
161#107—612no—
162#107—612no—
163#107C2×D6112yes—
164C4⋊C8—611no—
165C4⋊C8C2×D6111yescharacteristic
166#103—612no—
167#103—612no—
168#103—612no—
169#103C2×D6112yes—
170C22⋊C8—612no—
171C4×C8—612no—
172C2×Q8—21no—
173C2×Q8—611no—
174C2×Q8—1221no—
175C2×Q8—1222no—
176C2×Q8—1221no—
177C2×Q8—2444no—
178C2×Q8C22×D6111yescharacteristic
179C22×C4—611no—
180C22×C4—611no—
181C22×C4—611no—
182C22×C4—1222no—
183C2×C8—612no—
184C2×C8C22×D6112yes—
185C4⋊C4—21no—
186C4⋊C4—21no—
187C4⋊C4—612no—
188C4⋊C4—611no—
189C4⋊C4—1222no—
190C4⋊C4—1222no—
191C4⋊C4—1221no—
192C4⋊C4—1221no—
193C4⋊C4—1221no—
194C4⋊C4—1221no—
195C4⋊C4—1221no—
196C4⋊C4—1221no—
197C4⋊C4—1221no—
198C4⋊C4C22×D6112yes—
199C4⋊C4C22×D6111yescharacteristic
200C22⋊C4—1221no—
201C22⋊C4—1221no—
202C42—21no—
203C42—611no—
204C42—611no—
205C42—611no—
206C42—1221no—
207C42C22×D6111yescharacteristic
208C23—611no—
209Q8—21no—
210Q8—21no—
211Q8—42no—
212Q8—1221no—
213Q8—1221no—
214Q8—2442no—
215Q8—2442no—
216Q8—2444no—
217C2×C4—21no—
218C2×C4—21no—
219C2×C4—22no—
220C2×C4—611no—
221C2×C4—611no—
222C2×C4—614no—
223C2×C4—611no—
224C2×C4—1222no—
225C2×C4—1221no—
226C2×C4—1221no—
227C2×C4—1221no—
228C2×C4—1221no—
229C2×C4—1222no—
230C2×C4—2444no—
231C2×C4D4×D6111yescharacteristic
232C2×C4D4×D6111yescharacteristic
233C2×C4C23×D6111yescharacteristic
234C8—22no—
235C8—1222no—
236C22—612no—
237C22—1221no—
238C22—1221no—
239C22C2×D4×D6111yescharacteristic
240C4—21no—
241C4—42no—
242C4—41no—
243C4—41no—
244C4—612no—
245C4—612no—
246C4—1221no—
247C4—2442no—
248C4—2441no—
249C4—2441no—
250C4Q16×D6112yes—
251C4#1451982411yescharacteristic
252C4#1451982511yescharacteristic
253C2—1222no—
254C2#1684033511yescharacteristic
255C2C2×Q16×D6111yescharacteristic
256C2AGL(1,ℤ/8)×D6111yescharacteristic
subgroupG/H
centerC22C2×D4×D61
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC61×#477C2
socleC22×C61C22×D4
hypercenter#477D61
hypocenterC61#3230
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ #477

Complements

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

NH ≅ G/Ntype
3. #16840166C2semidirect
4. #16840111C2semidirect
7. #16840058C2semidirect
8. #16840057C2semidirect
9. #16840054C2semidirect
11. C61×#477C2semidirect
138. #477D61semidirect
140. C61#3230semidirect