Finite Group Databasebeta

← #21456848

Subgroups — #21456848

Order 7808.

386 conjugacy classes of subgroups; only the 125 normal subgroups are shown.

normal subgroups only

This group has 386 conjugacy classes of subgroups — too many to draw. Only its 125 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
1C2×#14519777C211yesmaximal, characteristic, complemented
2#16840296C211yesmaximal, characteristic
3#16840156C212yesmaximal, complemented
4#16840131C212yesmaximal, complemented
5#16839973C212yesmaximal, complemented
6#16839968C212yesmaximal, complemented
7#16839920C212yesmaximal, complemented
8#16839903C212yesmaximal
9C61×#432C211yesmaximal, characteristic, complemented
10C22×Dic122C2212yes—
11C2×Dic244C2214yes—
12C2×#11758190C2214yes—
13#14519777—21no—
14#14519777—21no—
15#14519777C2212yes—
16#14519777C2212yes—
17#14519771—21no—
18#14519769C2211yescharacteristic
19#14519765C2211yescharacteristic
20#14519760—21no—
21#14519756C2211yescharacteristic
22#14519751C2211yescharacteristic
23C4×Dic122C2211yescharacteristic
24C4×D244C2211yescharacteristic
25C4×C22⋊D61—21no—
26#14519734—21no—
27C2×C4⋊Dic61—21no—
28C2×C4⋊Dic61—21no—
29#14519702C2214yes—
30#14519702C2214yes—
31C2×C42×C61C2211yescharacteristic
32C4⋊C8×C61C2212yes—
33C22⋊C8×C61C2212yes—
34#97×C61C2212yes—
35C22×C4×C61D411yescharacteristic
36C22×C4×C61D411yescharacteristic
37C22×C4×C61C2311yescharacteristic
38C2×C22⋊D61—21no—
39C22×Dic61—22no—
40C2×D244C2311yescharacteristic
41C2×C4×D61—21no—
42C2×Dic122—22no—
43C2×Dic122—44no—
44C2×Dic122C2314yes—
45C2×Dic122C2311yescharacteristic
46C2×C8×C61C2314yes—
47C42×C61D411yescharacteristic
48C42×C61D411yescharacteristic
49C42×C61C2311yescharacteristic
50C42×C61C2311yescharacteristic
51C22⋊Dic61—21no—
52#11758198—21no—
53#11758198—21no—
54#11758198—21no—
55#11758198—21no—
56C4⋊Dic61—22no—
57C4⋊Dic61—22no—
58C4⋊Dic61—22no—
59C4⋊Dic61—22no—
60C4⋊Dic61C2311yescharacteristic
61C4⋊Dic61C2311yescharacteristic
62#11758196—21no—
63#11758196—21no—
64#11758196—21no—
65#11758196—21no—
66C4×Dic61—21no—
67Dic244—44no—
68#11758190—44no—
69C23×C61C2×D411yescharacteristic
70C22×D61—21no—
71C2×C4×C61—22no—
72C2×C4×C61—22no—
73C2×C4×C61—22no—
74C2×C4×C61C2×D411yescharacteristic
75C2×C4×C61C2×D411yescharacteristic
76C2×C4×C61C2×D411yescharacteristic
77C2×C4×C61C2×D411yescharacteristic
78C2×C4×C61C2×D411yescharacteristic
79C2×C4×C61C2411yescharacteristic
80C22⋊D61—42no—
81C2×Dic61—21no—
82C2×Dic61—21no—
83C2×Dic61—21no—
84C2×Dic61—24no—
85C2×Dic61—44no—
86D244—22no—
87C4×D61—42no—
88Dic122—24no—
89Dic122—22no—
90Dic122—24no—
91Dic122—44no—
92C8×C61—24no—
93C22×C61—21no—
94C22×C61—21no—
95C22×C61#13712yes—
96C22×C61C22×D411yescharacteristic
97C2×D61—41no—
98C2×D61—41no—
99C2×D61—41no—
100C4×C61—21no—
101C4×C61—21no—
102C4×C61—21no—
103C4×C61—21no—
104C4×C61#13712yes—
105C4×C61H(5,𝔽2)12yes—
106Dic61—44no—
107Dic61—41no—
108Dic61—41no—
109Dic61—41no—
110#3218—611nomaximal, Sylow
111C2×C61—22no—
112C2×C61#53511yescharacteristic
113C2×C61C2×#13711yescharacteristic
114C2×C61C2×#13711yescharacteristic
115D61—81no—
116C2×C4⋊Q8—611no—
117#529—611no—
118#497—612no—
119#491—612no—
120#462—612no—
121#461—612no—
122#451—612no—
123#448—612no—
124#432D6111yescharacteristic, complemented
125C61#321811yescharacteristic, complemented, Sylow
126C22×Q8—612no—
127C2×Q16—614no—
128C2×SD16—614no—
129C4⋊Q8—612no—
130C4⋊Q8—612no—
131C4⋊Q8—1221no—
132C4⋊Q8—1221no—
133#126—1221no—
134#125—611no—
135#124—611no—
136#123—1221no—
137C22⋊Q8—611no—
138#121—611no—
139C4×Q8—611no—
140C4×D4—611no—
141C4×D4—1221no—
142#117—1221no—
143C2×C4⋊C4—1221no—
144C2×C4⋊C4—1221no—
145C2×C42C2×D6111yescharacteristic
146C4⋊C8C2×D6112yes—
147#103—614no—
148#103—614no—
149C22⋊C8C2×D6112yes—
150#97C2×D6112yes—
151C2×Q8—614no—
152C2×Q8—611no—
153C2×Q8—1222no—
154C2×Q8—2444no—
155C2×D4—611no—
156C2×D4—1221no—
157C22×C4—1222no—
158C22×C4—1221no—
159C22×C4D24411yescharacteristic
160C22×C4D24411yescharacteristic
161C22×C4C22×D6111yescharacteristic
162Q16—2444no—
163SD16—2444no—
164C2×C8C22×D6114yes—
165C4⋊C4—611no—
166C4⋊C4—611no—
167C4⋊C4—1222no—
168C4⋊C4—1222no—
169C4⋊C4—1222no—
170C4⋊C4—1222no—
171C4⋊C4—1221no—
172C4⋊C4—1221no—
173C4⋊C4—1221no—
174C4⋊C4—1221no—
175C22⋊C4—1221no—
176C22⋊C4—1221no—
177C22⋊C4—1221no—
178C22⋊C4—1221no—
179C22⋊C4—1221no—
180C42—1221no—
181C42D24411yescharacteristic
182C42D24411yescharacteristic
183C42C22×D6111yescharacteristic
184C42C22×D6111yescharacteristic
185C23—1221no—
186C23C2×D24411yescharacteristic
187Q8—1224no—
188Q8—1222no—
189Q8—1224no—
190Q8—2444no—
191D4—1222no—
192D4—2442no—
193C2×C4—22no—
194C2×C4—22no—
195C2×C4—22no—
196C2×C4—1221no—
197C2×C4—1221no—
198C2×C4—1221no—
199C2×C4—1224no—
200C2×C4—2444no—
201C2×C4—2442no—
202C2×C4C2×D24411yescharacteristic
203C2×C4C2×D24411yescharacteristic
204C2×C4C2×D24411yescharacteristic
205C2×C4C2×D24411yescharacteristic
206C2×C4C2×D24411yescharacteristic
207C2×C4C23×D6111yescharacteristic
208C8—24no—
209C22—21no—
210C22—21no—
211C22—2441no—
212C22—2441no—
213C22—2441no—
214C22#1451981012yes—
215C22C22×D24411yescharacteristic
216C4—21no—
217C4—21no—
218C4—21no—
219C4—21no—
220C4—2441no—
221C4—2441no—
222C4—2444no—
223C4—2441no—
224C4#1451981012yes—
225C4#1451982312yes—
226C2—22no—
227C2—4881no—
228C2#1684033111yescharacteristic
229C2C2×#1451981011yescharacteristic
230C2C2×#1451981011yescharacteristic
subgroupG/H
centerC22C22×D244
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC61×#432C2
socleC22×C61C22×D4
hypercenter#432D61
hypocenterC61#3218
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C42 ◁ #432

Complements

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

NH ≅ G/Ntype
1. C2×#14519777C2semidirect
3. #16840156C2semidirect
4. #16840131C2semidirect
5. #16839973C2semidirect
6. #16839968C2semidirect
7. #16839920C2semidirect
9. C61×#432C2semidirect
124. #432D61semidirect
125. C61#3218semidirect