Finite Group Databasebeta

← #21447459

Subgroups — #21447459

Order 7808.

264 conjugacy classes of subgroups; only the 55 normal subgroups are shown.

normal subgroups only

This group has 264 conjugacy classes of subgroups — too many to draw. Only its 55 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#16840270C211yesmaximal, characteristic
2#16839743C211yesmaximal, characteristic, complemented
3#16839734C211yesmaximal, characteristic, complemented
4#16839552C211yesmaximal, characteristic, complemented
5#16839550C211yesmaximal, characteristic, complemented
6#16839548C211yesmaximal, characteristic, complemented
7C61×#352C211yesmaximal, characteristic, complemented
8C2×#11758224C2211yescharacteristic
9C22×C4×D61C411yescharacteristic, complemented
10M16×D61—21no—
11#14519760C411yescharacteristic, complemented
12#14519755—21no—
13#14519750—21no—
14#14519747C411yescharacteristic, complemented
15#14519745C2211yescharacteristic
16#14519739—21no—
17#14519737—21no—
18#14519733—21no—
19#14519733C411yescharacteristic, complemented
20#14519695—21no—
21#14519694C2211yescharacteristic
22#14519692C2211yescharacteristic
23#14519691—21no—
24#123×C61C2211yescharacteristic
25#100×C61C2211yescharacteristic
26#99×C61C2211yescharacteristic
27C23×D61C2×C411yescharacteristic
28C2×D4×C61C2311yescharacteristic
29C22×C4×C61C2×C411yescharacteristic
30C2×C22⋊D61—21no—
31C2×C22⋊D61C2×C411yescharacteristic
32C2×C22⋊D61D411yescharacteristic
33C22×Dic61C2×C411yescharacteristic
34C22×Dic61D411yescharacteristic
35#11758224—41no—
36#11758224—41no—
37C2×D244—21no—
38C2×C4×D61—21no—
39C2×C4×D61—21no—
40C2×C4×D61—41no—
41C2×C4×D61—41no—
42C2×C4×D61D411yescharacteristic
43C2×Dic122D411yescharacteristic
44M16×C61—21no—
45C4⋊C4×C61—21no—
46C22⋊C4×C61—21no—
47C22⋊C4×C61—21no—
48C22⋊C4×C61C2×C411yescharacteristic
49C22⋊Dic61—21no—
50C22⋊Dic61C2×C411yescharacteristic
51#11758198—21no—
52#11758198—21no—
53#11758198—21no—
54#11758196—21no—
55#11758196—21no—
56#11758196—41no—
57C4×Dic61—21no—
58C4×Dic61—41no—
59#11758194—21no—
60#11758189—41no—
61C8×D61—41no—
62C23×C61C22×C411yescharacteristic
63C23×C61C2×D411yescharacteristic
64C22×D61—21no—
65C22×D61—42no—
66C22×D61—41no—
67C22×D61C22⋊C411yescharacteristic
68D4×C61—41no—
69C2×C4×C61—21no—
70C2×C4×C61—21no—
71C2×C4×C61—41no—
72C2×C4×C61—41no—
73C2×C4×C61C2×D411yescharacteristic
74C22⋊D61—41no—
75C22⋊D61—41no—
76C22⋊D61—42no—
77C2×Dic61—21no—
78C2×Dic61—21no—
79C2×Dic61—21no—
80C2×Dic61—21no—
81C2×Dic61—21no—
82C2×Dic61—41no—
83C2×Dic61C22⋊C411yescharacteristic
84C2×Dic61C22⋊C411yescharacteristic
85C2×Dic61C22⋊C411yescharacteristic
86D244—42no—
87C4×D61—21no—
88C4×D61—21no—
89C4×D61—42no—
90C4×D61—41no—
91C4×D61—41no—
92Dic122—41no—
93C8×C61—41no—
94#92418—41no—
95C22×C61—21no—
96C22×C61—21no—
97C22×C61—41no—
98C22×C61—41no—
99C22×C61C2×C22⋊C411yescharacteristic
100C2×D61—22no—
101C2×D61—21no—
102C2×D61—41no—
103C2×D61—42no—
104C2×D61—41no—
105C2×D61—41no—
106C2×D61—42no—
107C4×C61—21no—
108C4×C61—41no—
109C4×C61—41no—
110C4×C61—81no—
111Dic61—21no—
112Dic61—21no—
113Dic61—41no—
114Dic61—81no—
115Dic61#9911yescharacteristic
116Dic61#9911yescharacteristic
117#2120—611nomaximal, Sylow
118C2×C61—21no—
119C2×C61—41no—
120C2×C61—41no—
121C2×C61C2×#9911yescharacteristic
122D61—41no—
123D61—42no—
124#525—611no—
125#413—611no—
126#410—611no—
127#352—611no—
128#352D6111yescharacteristic, complemented
129AΣL(1,𝔽16)—611no—
130AΣL(1,𝔽16)—611no—
131C61#212011yescharacteristic, complemented, Sylow
132C2×#41—611no—
133C23×C4—611no—
134C2×M16—1221no—
135#123—611no—
136#123C2×D6111yescharacteristic
137C22⋊Q8—1221no—
138#121—1221no—
139#120—611no—
140#120—611no—
141C4×D4—1221no—
142C4×D4—1221no—
143#117—611no—
144#117—1221no—
145#101—1221no—
146#100—611no—
147#100C2×D6111yescharacteristic
148#99—611no—
149#99—1221no—
150#99C2×D6111yescharacteristic
151C24—611no—
152#41—2441no—
153#41—2441no—
154C2×Q8—611no—
155C2×D4—611no—
156C2×D4—611no—
157C2×D4—1221no—
158C2×D4—1221no—
159C2×D4C22×D6111yescharacteristic
160C22×C4—611no—
161C22×C4—611no—
162C22×C4—611no—
163C22×C4—1221no—
164C22×C4—1221no—
165C22×C4—2441no—
166C22×C4—2441no—
167C22×C4C4×D6111yescharacteristic
168M16—21no—
169M16—1221no—
170M16—2441no—
171C2×C8—2441no—
172C4⋊C4—21no—
173C4⋊C4—1221no—
174C4⋊C4—1221no—
175C4⋊C4—2441no—
176C22⋊C4—21no—
177C22⋊C4—21no—
178C22⋊C4—611no—
179C22⋊C4—1221no—
180C22⋊C4—1221no—
181C22⋊C4—1221no—
182C22⋊C4—1221no—
183C22⋊C4C4×D6111yescharacteristic
184C42—1221no—
185C42—2441no—
186C23—611no—
187C23—1221no—
188C23—2441no—
189C23—2442no—
190C23C2×C4×D6111yescharacteristic
191C23D4×D6111yescharacteristic
192Q8—2441no—
193D4—41no—
194D4—2442no—
195D4—2441no—
196D4—2441no—
197D4—2442no—
198C2×C4—21no—
199C2×C4—21no—
200C2×C4—41no—
201C2×C4—41no—
202C2×C4—611no—
203C2×C4—611no—
204C2×C4—611no—
205C2×C4—1221no—
206C2×C4—1221no—
207C2×C4—1221no—
208C2×C4—1221no—
209C2×C4—1221no—
210C2×C4—1221no—
211C2×C4—1221no—
212C2×C4—2441no—
213C2×C4—2441no—
214C2×C4—2442no—
215C2×C4—2441no—
216C2×C4D4×D6111yescharacteristic
217C8—41no—
218C8—2441no—
219C22—21no—
220C22—21no—
221C22—41no—
222C22—41no—
223C22—1222no—
224C22—1221no—
225C22—2441no—
226C22—2441no—
227C22—2442no—
228C22—2442no—
229C22—2441no—
230C22C22⋊C4×D6111yescharacteristic
231C4—21no—
232C4—41no—
233C4—41no—
234C4—81no—
235C4—611no—
236C4—611no—
237C4—1221no—
238C4—1221no—
239C4—4881no—
240C4—2441no—
241C2—21no—
242C2—41no—
243C2—41no—
244C2—2442no—
245C2—2441no—
246C2#99×D6111yescharacteristic
subgroupG/H
centerC2#99×D61
commutatorC23×C61C22×C4
FrattiniC2×D4C22×D61
FittingC61×#352C2
socleC2×C61C2×#99
hypercenter#352D61
hypocenterC61#2120
LCSG ▷ C23×C61 ▷ C22×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2 ◁ C22 ◁ C2×D4 ◁ #352

Complements

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

NH ≅ G/Ntype
2. #16839743C2semidirect
3. #16839734C2semidirect
4. #16839552C2semidirect
5. #16839550C2semidirect
6. #16839548C2semidirect
7. C61×#352C2semidirect
9. C22×C4×D61C4semidirect
11. #14519760C4semidirect
14. #14519747C4semidirect
19. #14519733C4semidirect
128. #352D61semidirect
131. C61#2120semidirect