Finite Group Databasebeta

← #21457022

Subgroups — #21457022

Order 7808.

324 conjugacy classes of subgroups; only the 113 normal subgroups are shown.

normal subgroups only

This group has 324 conjugacy classes of subgroups — too many to draw. Only its 113 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#16840314C211yesmaximal, characteristic
2C2×#14519768C211yesmaximal, characteristic
3#16840169C212yesmaximal, complemented
4#16840129C212yesmaximal, complemented
5#16840098C211yesmaximal, characteristic
6#16840095C211yesmaximal, characteristic
7#16840092C211yesmaximal, characteristic
8#16840072C212yesmaximal, complemented
9#16840071C212yesmaximal, complemented
10#16839816C211yesmaximal, characteristic
11C61×#483C211yesmaximal, characteristic
12#14519776C2211yescharacteristic
13#14519775C2211yescharacteristic
14#14519768—21no—
15#14519768—21no—
16#14519768C2212yes—
17#14519768C2212yes—
18#14519767—21no—
19#14519756C2211yescharacteristic
20#14519754—21no—
21Q8×Dic61C2211yescharacteristic
22#14519742—21no—
23#14519742C2211yescharacteristic
24#14519733—21no—
25C2×C4⋊Dic61—21no—
26C2×C4⋊Dic61C2211yescharacteristic
27C2×#11758196—21no—
28C2×C4×Dic61C2211yescharacteristic
29#14519711C2212yes—
30#14519710C2212yes—
31#14519708C2212yes—
32#14519706C2212yes—
33#14519702C2212yes—
34#14519701C2212yes—
35#14519700C2212yes—
36C22⋊#92418C2211yescharacteristic
37#14519687C2212yes—
38C22⋊Q8×C61C2211yescharacteristic
39C2×C4⋊C4×C61C2211yescharacteristic
40#106×C61C2212yes—
41#103×C61C2212yes—
42C22⋊C8×C61C2211yescharacteristic
43C2×Q8×C61C2311yescharacteristic
44C22×C4×C61—21no—
45C22×C4×C61C2311yescharacteristic
46C22×Dic61—21no—
47C22×Dic61D411yescharacteristic
48C22×Dic61D411yescharacteristic
49C2×Dic122—21no—
50C2×Dic122C2311yescharacteristic
51C2×C8×C61C2312yes—
52C4⋊C4×C61—21no—
53C4⋊C4×C61—21no—
54C4⋊C4×C61C2312yes—
55C4⋊C4×C61C2311yescharacteristic
56C22⋊C4×C61—21no—
57C22⋊Dic61—21no—
58C4⋊Dic61—21no—
59C4⋊Dic61—22no—
60C4⋊Dic61—22no—
61C4⋊Dic61—21no—
62C4⋊Dic61C2312yes—
63C4⋊Dic61C2311yescharacteristic
64#11758196—21no—
65#11758196—22no—
66#11758196—22no—
67#11758196—21no—
68#11758196—21no—
69#11758196—21no—
70#11758196—21no—
71C4×Dic61—21no—
72C4×Dic61—21no—
73C4×Dic61D411yescharacteristic
74C4×Dic61D411yescharacteristic
75C4×Dic61C2311yescharacteristic
76C4×Dic61C2311yescharacteristic
77C2×#92418C2312yes—
78C23×C61C2×D411yescharacteristic
79Q8×C61—22no—
80C2×C4×C61—22no—
81C2×C4×C61—21no—
82C2×C4×C61—21no—
83C2×C4×C61—22no—
84C2×C4×C61—42no—
85C2×C4×C61C2×D411yescharacteristic
86C2×C4×C61C2411yescharacteristic
87C2×Dic61—22no—
88C2×Dic61—21no—
89C2×Dic61—21no—
90C2×Dic61—22no—
91C2×Dic61—41no—
92C2×Dic61—42no—
93C2×Dic61C2×D411yescharacteristic
94C2×Dic61C2×D411yescharacteristic
95C2×Dic61C2×D411yescharacteristic
96C2×Dic61C2×D411yescharacteristic
97Dic122—22no—
98Dic122—42no—
99C8×C61—22no—
100#92418—22no—
101C22×C61—21no—
102C22×C61—21no—
103C22×C61#13712yes—
104C22×C61C22×D411yescharacteristic
105C4×C61—21no—
106C4×C61—41no—
107C4×C61—42no—
108C4×C61—41no—
109C4×C612−1+412yes—
110Dic61—21no—
111Dic61—21no—
112Dic61—21no—
113Dic61—21no—
114Dic61—41no—
115Dic61—41no—
116Dic61—42no—
117#3236—611nomaximal, Sylow
118C2×C61—22no—
119C2×C61#53611yescharacteristic
120C2×C61C2×#13711yescharacteristic
121C2×C61#57511yescharacteristic
122#533—611no—
123C2×#125—611no—
124#501—612no—
125#491—612no—
126#484—611no—
127#484—611no—
128#483—611no—
129#483D6111yescharacteristic
130#479—612no—
131#479—612no—
132#432—611no—
133C61#323611yescharacteristic, complemented, Sylow
134C4⋊Q8—611no—
135C4⋊Q8—611no—
136#125—612no—
137#125—612no—
138#125—1221no—
139#125—1221no—
140#125—1221no—
141C22⋊Q8—611no—
142C22⋊Q8—1221no—
143C22⋊Q8C2×D6111yescharacteristic
144C4×Q8—611no—
145C4×Q8—611no—
146C4×Q8—1221no—
147#117—1221no—
148C2×C4⋊C4—611no—
149C2×C4⋊C4—1221no—
150C2×C4⋊C4—1221no—
151C2×C4⋊C4C2×D6111yescharacteristic
152C2×C42—611no—
153#107—612no—
154#107—612no—
155#106—612no—
156#106C2×D6112yes—
157C4⋊C8—612no—
158#103—612no—
159#103—612no—
160#103—612no—
161#103C2×D6112yes—
162C22⋊C8—611no—
163C22⋊C8C2×D6111yescharacteristic
164#97—612no—
165C2×Q8—611no—
166C2×Q8—1221no—
167C2×Q8C22×D6111yescharacteristic
168C22×C4—21no—
169C22×C4—611no—
170C22×C4—611no—
171C22×C4—1221no—
172C22×C4C22×D6111yescharacteristic
173C2×C8—612no—
174C2×C8C22×D6112yes—
175C4⋊C4—21no—
176C4⋊C4—21no—
177C4⋊C4—612no—
178C4⋊C4—611no—
179C4⋊C4—1222no—
180C4⋊C4—1222no—
181C4⋊C4—1222no—
182C4⋊C4—1222no—
183C4⋊C4—1221no—
184C4⋊C4—1221no—
185C4⋊C4—1221no—
186C4⋊C4—1221no—
187C4⋊C4—1221no—
188C4⋊C4—1221no—
189C4⋊C4—1221no—
190C4⋊C4C22×D6112yes—
191C4⋊C4C22×D6111yescharacteristic
192C22⋊C4—21no—
193C22⋊C4—1221no—
194C42—611no—
195C42—611no—
196C42—611no—
197C42—611no—
198C42—1221no—
199C42—1221no—
200C23D4×D6111yescharacteristic
201Q8—22no—
202Q8—1222no—
203Q8—2442no—
204C2×C4—22no—
205C2×C4—21no—
206C2×C4—21no—
207C2×C4—22no—
208C2×C4—42no—
209C2×C4—611no—
210C2×C4—611no—
211C2×C4—611no—
212C2×C4—611no—
213C2×C4—1222no—
214C2×C4—1221no—
215C2×C4—1221no—
216C2×C4—1222no—
217C2×C4—2441no—
218C2×C4—2442no—
219C2×C4D4×D6111yescharacteristic
220C2×C4C23×D6111yescharacteristic
221C8—22no—
222C8—1222no—
223C22—21no—
224C22—21no—
225C22#1451980612yes—
226C22C2×D4×D6111yescharacteristic
227C4—21no—
228C4—42no—
229C4—41no—
230C4—41no—
231C4—1221no—
232C4—1221no—
233C4—1221no—
234C4—1221no—
235C4—2442no—
236C4—2441no—
237C4—2441no—
238C4#1451982412yes—
239C2—22no—
240C2#1684033411yescharacteristic
241C2C2×#1451980611yescharacteristic
242C2#1684056111yescharacteristic
subgroupG/H
centerC22C2×D4×D61
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC61×#483C2
socleC22×C61C22×D4
hypercenter#483D61
hypocenterC61#3236
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ #483

Complements

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

NH ≅ G/Ntype
3. #16840169C2semidirect
4. #16840129C2semidirect
8. #16840072C2semidirect
9. #16840071C2semidirect
133. C61#3236semidirect