Finite Group Databasebeta

← #21447458

Subgroups — #21447458

Order 7808.

264 conjugacy classes of subgroups; only the 65 normal subgroups are shown.

normal subgroups only

This group has 264 conjugacy classes of subgroups — too many to draw. Only its 65 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#16840269C211yesmaximal, characteristic
2#16839746C211yesmaximal, characteristic, complemented
3#16839551C212yesmaximal, complemented
4#16839548C212yesmaximal, complemented
5C61×#410C211yesmaximal, characteristic, complemented
6C22×C4×D61C411yescharacteristic, complemented
7C2×#11758194—21no—
8#14519758C411yescharacteristic, complemented
9#14519758C2211yescharacteristic
10#14519753—21no—
11#14519748—21no—
12#14519745C411yescharacteristic, complemented
13#14519745C2211yescharacteristic
14C4×C22⋊D61—21no—
15C4×C22⋊D61—21no—
16#14519736C411yescharacteristic, complemented
17#14519696—21no—
18#14519694C2212yes—
19C2×#41×C61C2211yescharacteristic
20#117×C61—21no—
21#99×C61—21no—
22#99×C61C2212yes—
23C23×D61C2×C411yescharacteristic
24#41×C61—41no—
25#41×C61—41no—
26C2×Q8×C61D411yescharacteristic
27C2×D4×C61C2×C411yescharacteristic
28C2×D4×C61D411yescharacteristic
29C2×D4×C61C2311yescharacteristic
30C22×C4×C61C2×C411yescharacteristic
31C22×C4×C61D411yescharacteristic
32C22×C4×C61D411yescharacteristic
33C2×C22⋊D61—21no—
34C2×C22⋊D61—21no—
35C22×Dic61C2×C411yescharacteristic
36C2×C4×D61—21no—
37C2×C4×D61—21no—
38C2×C4×D61—41no—
39C2×C4×D61—41no—
40C4⋊C4×C61—41no—
41C22⋊C4×C61—22no—
42C42×C61—41no—
43C22⋊Dic61—21no—
44C22⋊Dic61—21no—
45C22⋊Dic61C2×C411yescharacteristic
46C22⋊Dic61C2×C411yescharacteristic
47#11758198—21no—
48#11758198—21no—
49C4⋊Dic61—21no—
50#11758196—21no—
51#11758196—21no—
52C4×Dic61—21no—
53#11758194—22no—
54#11758194—41no—
55C2×#92418—41no—
56C23×C61C22⋊C411yescharacteristic
57C23×C61C22×C411yescharacteristic
58C23×C61C2×D411yescharacteristic
59C22×D61—21no—
60C22×D61—42no—
61C22×D61—41no—
62Q8×C61—41no—
63D4×C61—41no—
64D4×C61—41no—
65D4×C61—41no—
66C2×C4×C61—21no—
67C2×C4×C61—21no—
68C2×C4×C61—21no—
69C2×C4×C61—21no—
70C2×C4×C61—21no—
71C2×C4×C61—21no—
72C2×C4×C61—42no—
73C2×C4×C61C22⋊C411yescharacteristic
74C2×C4×C61C22⋊C411yescharacteristic
75C2×C4×C61C22⋊C411yescharacteristic
76C2×C4×C61C2×D411yescharacteristic
77C22⋊D61—42no—
78C22⋊D61—42no—
79C2×Dic61—21no—
80C2×Dic61—21no—
81C2×Dic61—21no—
82C2×Dic61—41no—
83C4×D61—42no—
84C4×D61—41no—
85C4×D61—41no—
86#92418—42no—
87C22×C61—21no—
88C22×C61—21no—
89C22×C61—21no—
90C22×C61—41no—
91C22×C61—41no—
92C22×C61—41no—
93C22×C61C2×C22⋊C411yescharacteristic
94C2×D61—22no—
95C2×D61—41no—
96C2×D61—42no—
97C2×D61—41no—
98C2×D61—42no—
99C4×C61—21no—
100C4×C61—21no—
101C4×C61—21no—
102C4×C61—82no—
103C4×C61#9911yescharacteristic
104C4×C61#9911yescharacteristic
105Dic61—41no—
106Dic61—41no—
107Dic61—41no—
108#2120—611nomaximal, Sylow
109C2×C61—21no—
110C2×C61—41no—
111C2×C61—41no—
112C2×C61—41no—
113C2×C61C2×#9911yescharacteristic
114D61—42no—
115#525—611no—
116#413—611no—
117#410D6111yescharacteristic, complemented
118#352—612no—
119AΣL(1,𝔽16)—612no—
120C61#212011yescharacteristic, complemented, Sylow
121C2×#41C2×D6111yescharacteristic
122C23×C4—611no—
123C2×M16—1221no—
124#123—611no—
125#123—611no—
126C22⋊Q8—1221no—
127#121—1221no—
128#120—611no—
129#120—611no—
130C4×D4—1221no—
131C4×D4—1221no—
132#117—21no—
133#117—611no—
134#101—1221no—
135#100—612no—
136#99—21no—
137#99C2×D6112yes—
138C24—611no—
139#41—41no—
140#41—41no—
141C2×Q8D24411yescharacteristic
142C2×D4—1221no—
143C2×D4—1221no—
144C2×D4C4×D6111yescharacteristic
145C2×D4C22⋊D6111yescharacteristic
146C2×D4C22×D6111yescharacteristic
147C22×C4—611no—
148C22×C4—1221no—
149C22×C4—1221no—
150C22×C4—2441no—
151C22×C4—2441no—
152C22×C4C4×D6111yescharacteristic
153C22×C4D24411yescharacteristic
154C22×C4C22⋊D6111yescharacteristic
155M16—1222no—
156M16—2441no—
157C2×C8—2441no—
158C4⋊C4—41no—
159C4⋊C4—1221no—
160C4⋊C4—1221no—
161C4⋊C4—1221no—
162C22⋊C4—22no—
163C22⋊C4—611no—
164C22⋊C4—611no—
165C22⋊C4—1221no—
166C22⋊C4—1221no—
167C22⋊C4—1221no—
168C22⋊C4—1221no—
169C42—41no—
170C42—1221no—
171C23—1221no—
172C23—2441no—
173C23—2442no—
174C23#1175819811yescharacteristic
175C23C2×C4×D6111yescharacteristic
176C23C2×C22⋊D6111yescharacteristic
177Q8—41no—
178D4—41no—
179D4—41no—
180D4—41no—
181D4—2442no—
182D4—2442no—
183C2×C4—21no—
184C2×C4—21no—
185C2×C4—21no—
186C2×C4—21no—
187C2×C4—21no—
188C2×C4—21no—
189C2×C4—42no—
190C2×C4—1221no—
191C2×C4—1221no—
192C2×C4—1221no—
193C2×C4—2442no—
194C2×C4—2441no—
195C2×C4—2441no—
196C2×C4—2441no—
197C2×C4#1175819811yescharacteristic
198C2×C4#1175819811yescharacteristic
199C2×C4#1175819811yescharacteristic
200C2×C4C2×D24411yescharacteristic
201C8—2442no—
202C22—21no—
203C22—21no—
204C22—21no—
205C22—41no—
206C22—41no—
207C22—41no—
208C22—1222no—
209C22—2441no—
210C22—2442no—
211C22—2442no—
212C22—2441no—
213C22C2×#1175819811yescharacteristic
214C4—21no—
215C4—21no—
216C4—21no—
217C4—82no—
218C4—2441no—
219C4—2441no—
220C4—2441no—
221C4#1451969111yescharacteristic
222C4#1451969111yescharacteristic
223C2—21no—
224C2—41no—
225C2—41no—
226C2—41no—
227C2—2442no—
228C2C2×#1451969111yescharacteristic
subgroupG/H
centerC4#14519691
commutatorC23×C61C22×C4
FrattiniC2×D4C22×D61
FittingC61×#410C2
socleC2×C61C2×#99
hypercenter#410D61
hypocenterC61#2120
LCSG ▷ C23×C61 ▷ C22×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C4 ◁ C2×C4 ◁ C2×#41 ◁ #410

Complements

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

NH ≅ G/Ntype
2. #16839746C2semidirect
3. #16839551C2semidirect
4. #16839548C2semidirect
5. C61×#410C2semidirect
6. C22×C4×D61C4semidirect
8. #14519758C4semidirect
12. #14519745C4semidirect
16. #14519736C4semidirect
117. #410D61semidirect
120. C61#2120semidirect