Finite Group Databasebeta

← #21455662

Subgroups — #21455662

Order 7808.

362 conjugacy classes of subgroups; only the 141 normal subgroups are shown.

normal subgroups only

This group has 362 conjugacy classes of subgroups — too many to draw. Only its 141 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#16840390C211yesmaximal, characteristic
2#16840239C211yesmaximal, characteristic
3#16840070C212yesmaximal, complemented
4#16840070C212yesmaximal, complemented
5#16840058C212yesmaximal, complemented
6#16840048C212yesmaximal, complemented
7#16839804C211yesmaximal, characteristic
8#16839800C211yesmaximal, characteristic
9#16839772C211yesmaximal, characteristic
10C2×#14519702C211yesmaximal, characteristic
11C61×#424C211yesmaximal, characteristic
12C22×Dic122C2211yescharacteristic
13#14519777C2212yes—
14#14519776—21no—
15#14519769C2212yes—
16#14519768—21no—
17#14519754—22no—
18C4×Dic122C2212yes—
19C4×Dic122C2212yes—
20#14519742—21no—
21#14519742—21no—
22#14519736C2211yescharacteristic
23#14519736C2211yescharacteristic
24#14519733—22no—
25C2×C4⋊Dic61C2211yescharacteristic
26#14519711C2211yescharacteristic
27#14519711C2211yescharacteristic
28#14519711C2212yes—
29#14519709C2211yescharacteristic
30#14519709C2212yes—
31#14519709C2211yescharacteristic
32#14519702C2212yes—
33#14519702C2212yes—
34#14519702C2212yes—
35#14519702C2212yes—
36C2×M16×C61C2211yescharacteristic
37C22×C8×C61C2211yescharacteristic
38#117×C61C2211yescharacteristic
39C4⋊C8×C61C2212yes—
40C4⋊C8×C61C2212yes—
41C22×C4×C61C2311yescharacteristic
42C22×Dic61—21no—
43C22×Dic61—21no—
44C2×Dic122—21no—
45C2×Dic122—22no—
46C2×Dic122—22no—
47C2×Dic122Q814yescomplemented
48C2×Dic122C2312yes—
49M16×C61—22no—
50C2×C8×C61—22no—
51C2×C8×C61C2311yescharacteristic
52C2×C8×C61C2311yescharacteristic
53C2×C8×C61C2312yes—
54C4⋊C4×C61D411yescharacteristic
55C4⋊C4×C61D411yescharacteristic
56C22⋊C4×C61D412yes—
57C42×C61C2312yes—
58C22⋊Dic61—21no—
59C22⋊Dic61—21no—
60C4⋊Dic61—21no—
61C4⋊Dic61—22no—
62C4⋊Dic61C2312yes—
63C4⋊Dic61C2311yescharacteristic
64C4⋊Dic61C2311yescharacteristic
65C4⋊Dic61C2311yescharacteristic
66C4⋊Dic61C2311yescharacteristic
67#11758196—22no—
68#11758196—22no—
69#11758196—22no—
70#11758196—22no—
71C4×Dic61—22no—
72C4×Dic61—22no—
73C4×Dic61—21no—
74C4×Dic61—21no—
75C23×C61C2×D411yescharacteristic
76C2×C4×C61C2×D412yes—
77C2×C4×C61C2×D412yes—
78C2×C4×C61C2×D411yescharacteristic
79C2×C4×C61C2×Q812yes—
80C2×C4×C61#4112yes—
81C2×C4×C61C2411yescharacteristic
82C2×Dic61—24no—
83C2×Dic61—22no—
84C2×Dic61—21no—
85C2×Dic61—21no—
86C2×Dic61—21no—
87C2×Dic61—21no—
88C2×Dic61—22no—
89C2×Dic61—81no—
90Dic122—24no—
91Dic122—22no—
92Dic122—82no—
93Dic122C2×Q814yes—
94C8×C61—21no—
95C8×C61—21no—
96C8×C61—22no—
97C22×C61—21no—
98C22×C61—21no—
99C22×C61C22⋊Q812yes—
100C22×C61C22×D411yescharacteristic
101C4×C61—22no—
102C4×C61—22no—
103C4×C61C22⋊Q812yes—
104C4×C61C22×Q811yescharacteristic
105C4×C61C2×#4111yescharacteristic
106Dic61—24no—
107Dic61—41no—
108Dic61—42no—
109Dic61—41no—
110Dic61—41no—
111Dic61—41no—
112#3082—611nomaximal, Sylow
113C2×C61—22no—
114C2×C61C2×C22⋊Q811yescharacteristic
115C2×C61#57711yescharacteristic
116C2×C61#57811yescharacteristic
117#544—611no—
118#519—611no—
119#479—612no—
120#479—612no—
121#477—612no—
122#475—612no—
123#428—611no—
124#427—611no—
125#424D6111yescharacteristic
126#419—611no—
127C2×#103—611no—
128C61#308211yescharacteristic, complemented, Sylow
129C22×Q8—611no—
130C2×M16C2×D6111yescharacteristic
131C22×C8C2×D6111yescharacteristic
132C4⋊Q8—612no—
133C4⋊Q8—1221no—
134#125—612no—
135#125—1221no—
136C22⋊Q8—1222no—
137C4×Q8—612no—
138C4×Q8—612no—
139C4×Q8—1221no—
140C4×Q8—1221no—
141#117—611no—
142#117—611no—
143#117—1222no—
144#117C2×D6111yescharacteristic
145C2×C4⋊C4—611no—
146#107—611no—
147#107—611no—
148#107—612no—
149#106—611no—
150#106—611no—
151#106—612no—
152C4⋊C8C2×D6112yes—
153C4⋊C8C2×D6112yes—
154#103—612no—
155#103—612no—
156#103—612no—
157#103—612no—
158C2×Q8—614no—
159C2×Q8—612no—
160C2×Q8—1221no—
161C2×Q8—1222no—
162C2×Q8—1222no—
163C22×C4—1221no—
164C22×C4—1221no—
165C22×C4C22×D6111yescharacteristic
166M16—22no—
167C2×C8—22no—
168C2×C8C22×D6111yescharacteristic
169C2×C8C22×D6112yes—
170C2×C8C22×D6111yescharacteristic
171C4⋊C4—612no—
172C4⋊C4—611no—
173C4⋊C4—611no—
174C4⋊C4—611no—
175C4⋊C4—611no—
176C4⋊C4—1221no—
177C4⋊C4—1222no—
178C4⋊C4—1222no—
179C4⋊C4—1222no—
180C4⋊C4—1222no—
181C4⋊C4—1222no—
182C4⋊C4D24411yescharacteristic
183C4⋊C4D24411yescharacteristic
184C22⋊C4—1221no—
185C22⋊C4—1221no—
186C22⋊C4D24412yes—
187C42—1221no—
188C42—1221no—
189C42—1222no—
190C42—1222no—
191C42C22×D6112yes—
192C23C2×D24411yescharacteristic
193Q8—614no—
194Q8—1222no—
195Q8—1224no—
196Q8—4882no—
197C2×C4—1222no—
198C2×C4—1224no—
199C2×C4—1221no—
200C2×C4—1221no—
201C2×C4—1221no—
202C2×C4—1221no—
203C2×C4—1222no—
204C2×C4—4881no—
205C2×C4C2×D24412yes—
206C2×C4C2×D24412yes—
207C2×C4C2×D24411yescharacteristic
208C2×C4#1175822412yes—
209C2×C4Q8×D6112yes—
210C2×C4C23×D6111yescharacteristic
211C8—21no—
212C8—21no—
213C8—22no—
214C22—21no—
215C22—21no—
216C22#1451975712yes—
217C22C22×D24411yescharacteristic
218C4—22no—
219C4—22no—
220C4—1224no—
221C4—2441no—
222C4—2442no—
223C4—2441no—
224C4—2441no—
225C4—2441no—
226C4#1451975712yes—
227C4C2×Q8×D6111yescharacteristic
228C4C2×#1175822411yescharacteristic
229C2—22no—
230C2C2×#1451975711yescharacteristic
231C2#1684057411yescharacteristic
232C2#1684057911yescharacteristic
subgroupG/H
centerC22C22×D244
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC61×#424C2
socleC22×C61C22×D4
hypercenter#424D61
hypocenterC61#3082
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ #117 ◁ #424

Complements

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

NH ≅ G/Ntype
3. #16840070C2semidirect
4. #16840070C2semidirect
5. #16840058C2semidirect
6. #16840048C2semidirect
47. C2×Dic122Q8semidirect
128. C61#3082semidirect