Finite Group Databasebeta

← #21456904

Subgroups — #21456904

Order 7808.

364 conjugacy classes of subgroups; only the 117 normal subgroups are shown.

normal subgroups only

This group has 364 conjugacy classes of subgroups — too many to draw. Only its 117 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#16840374C211yesmaximal, characteristic, complemented
2#16840338C211yesmaximal, characteristic
3#16840156C211yesmaximal, characteristic, complemented
4#16840142C211yesmaximal, characteristic, complemented
5#16840131C211yesmaximal, characteristic, complemented
6#16840117C211yesmaximal, characteristic, complemented
7#16839985C212yesmaximal, complemented
8#16839973C212yesmaximal, complemented
9#16839926C212yesmaximal
10#16839920C212yesmaximal, complemented
11C61×#433C211yesmaximal, characteristic, complemented
12C2×#11758222C2211yescharacteristic
13C22×Dic122C2211yescharacteristic
14C2×Dic244C2212yes—
15C2×Dic244C2212yes—
16C2×Dic244C2212yes—
17C2×#11758190C2212yes—
18#14519777C2211yescharacteristic
19#14519777C2211yescharacteristic
20#14519777C2211yescharacteristic
21#14519770—22no—
22#14519769C2211yescharacteristic
23#14519767—22no—
24#14519765C2211yescharacteristic
25#14519765C2211yescharacteristic
26#14519761—22no—
27#14519757—22no—
28#14519756C2212yes—
29C4×Dic122C2212yes—
30#14519702C2212yes—
31#14519702C2212yes—
32#14519702C2212yes—
33#14519699C2212yes—
34#117×C61C2211yescharacteristic
35C4⋊C8×C61C2212yes—
36C22⋊C8×C61C2212yes—
37#97×C61C2211yescharacteristic
38C4×C8×C61C2211yescharacteristic
39C22×C4×C61C2311yescharacteristic
40C2×C22⋊D61—21no—
41C22×Dic61—21no—
42#11758222—42no—
43C2×D244C2311yescharacteristic
44C2×C4×D61—21no—
45C2×Dic122—21no—
46C2×Dic122—42no—
47C2×Dic122C2311yescharacteristic
48C2×Dic122C2311yescharacteristic
49C2×Dic122C2311yescharacteristic
50C2×Dic122C2312yes—
51C2×C8×C61C2312yes—
52C2×C8×C61C2312yes—
53C4⋊C4×C61D412yes—
54C22⋊C4×C61D412yes—
55C42×C61C2311yescharacteristic
56C42×C61C2311yescharacteristic
57C22⋊Dic61—22no—
58#11758198—22no—
59#11758198—22no—
60C4⋊Dic61—22no—
61C4⋊Dic61—22no—
62C4⋊Dic61—22no—
63C4⋊Dic61C2312yes—
64#11758196—22no—
65#11758196—22no—
66#11758196—22no—
67C4×Dic61—22no—
68Dic244—42no—
69Dic244—42no—
70Dic244—42no—
71#11758190—42no—
72C23×C61C2×D411yescharacteristic
73C22×D61—21no—
74C2×C4×C61—22no—
75C2×C4×C61C2×D412yes—
76C2×C4×C61C2×D411yescharacteristic
77C2×C4×C61C2×D412yes—
78C2×C4×C61C2411yescharacteristic
79C22⋊D61—42no—
80C2×Dic61—22no—
81C2×Dic61—22no—
82C2×Dic61—21no—
83C2×Dic61—21no—
84C2×Dic61—21no—
85C2×Dic61—42no—
86D244—22no—
87C4×D61—42no—
88Dic122—22no—
89Dic122—22no—
90Dic122—22no—
91Dic122—22no—
92Dic122—22no—
93Dic122—42no—
94C8×C61—22no—
95C8×C61—22no—
96C22×C61—21no—
97C22×C61—22no—
98C22×C61C22×D411yescharacteristic
99C2×D61—41no—
100C2×D61—42no—
101C4×C61—21no—
102C4×C61—22no—
103C4×C61—22no—
104C4×C61H(5,𝔽2)12yes—
105Dic61—41no—
106Dic61—41no—
107Dic61—41no—
108Dic61—42no—
109Dic61—42no—
110#3223—611nomaximal, Sylow
111C2×C61—41no—
112C2×C61#53511yescharacteristic
113C2×C61#57812yes—
114D61—81no—
115#541—611no—
116#536—611no—
117#497—611no—
118#494—611no—
119#491—611no—
120#488—611no—
121#464—612no—
122#462—612no—
123#452—612no—
124#451—612no—
125#433D6111yescharacteristic, complemented
126C61#322311yescharacteristic, complemented, Sylow
127C2×#41—611no—
128C22×Q8—611no—
129C2×Q16—612no—
130C2×Q16—612no—
131C2×Q16—612no—
132C2×SD16—612no—
133C4⋊Q8—611no—
134C4⋊Q8—611no—
135C4⋊Q8—611no—
136#126—1222no—
137#125—611no—
138#125—1222no—
139#124—611no—
140#124—611no—
141#123—1222no—
142C22⋊Q8—612no—
143C22⋊Q8—1222no—
144C4×Q8—612no—
145#117C2×D6111yescharacteristic
146C4⋊C8C2×D6112yes—
147#103—612no—
148#103—612no—
149#103—612no—
150#102—612no—
151C22⋊C8C2×D6112yes—
152#97C2×D6111yescharacteristic
153C4×C8C2×D6111yescharacteristic
154#41—2442no—
155C2×Q8—611no—
156C2×Q8—611no—
157C2×Q8—611no—
158C2×Q8—612no—
159C2×Q8—1221no—
160C2×Q8—2442no—
161C2×D4—611no—
162C2×D4—1221no—
163C22×C4—1221no—
164C22×C4—1221no—
165C22×C4C22×D6111yescharacteristic
166Q16—2442no—
167Q16—2442no—
168Q16—2442no—
169SD16—2442no—
170C2×C8C22×D6112yes—
171C2×C8C22×D6112yes—
172C4⋊C4—612no—
173C4⋊C4—1222no—
174C4⋊C4—1222no—
175C4⋊C4—1222no—
176C4⋊C4—1222no—
177C4⋊C4—1222no—
178C4⋊C4—1222no—
179C4⋊C4D24412yes—
180C22⋊C4—1222no—
181C22⋊C4—1222no—
182C22⋊C4—1222no—
183C22⋊C4D24412yes—
184C42—1222no—
185C42C22×D6111yescharacteristic
186C42C22×D6111yescharacteristic
187C23—1221no—
188C23C2×D24411yescharacteristic
189Q8—1222no—
190Q8—1222no—
191Q8—1222no—
192Q8—1222no—
193Q8—1222no—
194Q8—2442no—
195D4—1222no—
196D4—2442no—
197C2×C4—22no—
198C2×C4—1222no—
199C2×C4—1222no—
200C2×C4—1221no—
201C2×C4—1221no—
202C2×C4—1221no—
203C2×C4—2442no—
204C2×C4—2442no—
205C2×C4C2×D24412yes—
206C2×C4C2×D24412yes—
207C2×C4C2×D24411yescharacteristic
208C2×C4C23×D6111yescharacteristic
209C8—22no—
210C8—22no—
211C22—22no—
212C22—21no—
213C22—2442no—
214C22—2441no—
215C22C22×D24411yescharacteristic
216C4—22no—
217C4—22no—
218C4—21no—
219C4—2442no—
220C4—2441no—
221C4—2441no—
222C4—2441no—
223C4—2442no—
224C4#1451982312yes—
225C2—41no—
226C2—4881no—
227C2#1684033111yescharacteristic
228C2#1684057912yes—
subgroupG/H
centerC22C22×D244
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC61×#433C2
socleC22×C61C22×D4
hypercenter#433D61
hypocenterC61#3223
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ #117 ◁ #433

Complements

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

NH ≅ G/Ntype
1. #16840374C2semidirect
3. #16840156C2semidirect
4. #16840142C2semidirect
5. #16840131C2semidirect
6. #16840117C2semidirect
7. #16839985C2semidirect
8. #16839973C2semidirect
10. #16839920C2semidirect
11. C61×#433C2semidirect
125. #433D61semidirect
126. C61#3223semidirect