Finite Group Databasebeta

← #21455664

Subgroups — #21455664

Order 7808.

362 conjugacy classes of subgroups; only the 133 normal subgroups are shown.

normal subgroups only

This group has 362 conjugacy classes of subgroups — too many to draw. Only its 133 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#16840072C212yesmaximal, complemented
4#16840068C212yesmaximal, complemented
5#16840056C212yesmaximal, complemented
6#16840046C212yesmaximal, complemented
7#16839805C211yesmaximal, characteristic
8#16839788C211yesmaximal, characteristic
9#16839770C211yesmaximal, characteristic
10C2×#14519702C211yesmaximal, characteristic
11C61×#427C211yesmaximal, characteristic
12C22×Dic122C2211yescharacteristic
13C2×#11758194C2211yescharacteristic
14#14519777—21no—
15#14519776C2212yes—
16#14519769—21no—
17#14519768C2212yes—
18#14519754—22no—
19C4×Dic122—21no—
20C4×Dic122—21no—
21#14519742C2212yes—
22#14519742C2212yes—
23#14519736C2211yescharacteristic
24#14519733—22no—
25C2×C4⋊Dic61C2211yescharacteristic
26#14519710C2212yes—
27#14519708C2212yes—
28#14519706C2212yes—
29#14519706C2212yes—
30#14519702C2212yes—
31#14519702C2212yes—
32#14519700C2212yes—
33#14519700C2212yes—
34C22×C8×C61C2211yescharacteristic
35#117×C61C2211yescharacteristic
36#117×C61C2211yescharacteristic
37#107×C61C2211yescharacteristic
38#107×C61C2211yescharacteristic
39#106×C61C2211yescharacteristic
40#106×C61C2211yescharacteristic
41C22×C4×C61C2311yescharacteristic
42C22×Dic61—21no—
43C22×Dic61—21no—
44C2×Dic122—21no—
45C2×Dic122—22no—
46C2×Dic122—22no—
47C2×Dic122Q814yescomplemented
48C2×Dic122C2312yes—
49C2×C8×C61—22no—
50C2×C8×C61C2311yescharacteristic
51C2×C8×C61C2311yescharacteristic
52C4⋊C4×C61C2311yescharacteristic
53C4⋊C4×C61C2311yescharacteristic
54C4⋊C4×C61C2311yescharacteristic
55C4⋊C4×C61C2311yescharacteristic
56C22⋊C4×C61—21no—
57C22⋊C4×C61—21no—
58C42×C61—21no—
59C42×C61—21no—
60C22⋊Dic61D412yes—
61C4⋊Dic61—21no—
62C4⋊Dic61—22no—
63C4⋊Dic61D411yescharacteristic
64C4⋊Dic61D411yescharacteristic
65C4⋊Dic61C2312yes—
66#11758196—22no—
67#11758196—22no—
68#11758196—22no—
69#11758196—22no—
70C4×Dic61—22no—
71C4×Dic61—22no—
72C4×Dic61C2312yes—
73#11758194—22no—
74C2×#92418C2312yes—
75C23×C61C2×D411yescharacteristic
76C2×C4×C61—21no—
77C2×C4×C61—21no—
78C2×C4×C61—21no—
79C2×C4×C61—21no—
80C2×C4×C61C2×D411yescharacteristic
81C2×C4×C61C2×Q812yes—
82C2×C4×C61#4112yes—
83C2×C4×C61C2411yescharacteristic
84C2×Dic61—24no—
85C2×Dic61—22no—
86C2×Dic61—22no—
87C2×Dic61—81no—
88C2×Dic61C2×D412yes—
89C2×Dic61C2×D412yes—
90Dic122—24no—
91Dic122—22no—
92Dic122—82no—
93Dic122C2×Q814yes—
94C8×C61—21no—
95C8×C61—21no—
96#92418—22no—
97C22×C61—21no—
98C22×C61—21no—
99C22×C61C22⋊Q812yes—
100C22×C61C22×D411yescharacteristic
101C4×C61—41no—
102C4×C61—41no—
103C4×C61—41no—
104C4×C61—41no—
105C4×C61C22⋊Q812yes—
106C4×C61C22×Q811yescharacteristic
107C4×C61C2×#4111yescharacteristic
108Dic61—24no—
109Dic61—22no—
110Dic61—22no—
111Dic61—42no—
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#427D6111yescharacteristic
125#424—611no—
126#419—611no—
127C2×#103—611no—
128C61#308211yescharacteristic, complemented, Sylow
129C22×Q8—611no—
130C2×M16—611no—
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—1222no—
143#117C2×D6111yescharacteristic
144#117C2×D6111yescharacteristic
145C2×C4⋊C4—611no—
146#107—612no—
147#107C2×D6111yescharacteristic
148#107C2×D6111yescharacteristic
149#106—612no—
150#106C2×D6111yescharacteristic
151#106C2×D6111yescharacteristic
152C4⋊C8—612no—
153C4⋊C8—612no—
154#103—612no—
155#103—612no—
156#103—612no—
157#103—612no—
158C2×Q8—614no—
159C2×Q8—612no—
160C2×Q8—1222no—
161C2×Q8—1222no—
162C2×Q8—1221no—
163C22×C4—1221no—
164C22×C4—1221no—
165C22×C4C22×D6111yescharacteristic
166M16—1222no—
167C2×C8—22no—
168C2×C8—612no—
169C2×C8C22×D6111yescharacteristic
170C2×C8C22×D6111yescharacteristic
171C4⋊C4—611no—
172C4⋊C4—611no—
173C4⋊C4—612no—
174C4⋊C4—1222no—
175C4⋊C4—1222no—
176C4⋊C4—1222no—
177C4⋊C4—1222no—
178C4⋊C4—1222no—
179C4⋊C4—1221no—
180C4⋊C4C22×D6111yescharacteristic
181C4⋊C4C22×D6111yescharacteristic
182C4⋊C4C22×D6111yescharacteristic
183C4⋊C4C22×D6111yescharacteristic
184C22⋊C4—21no—
185C22⋊C4—21no—
186C22⋊C4—612no—
187C42—21no—
188C42—21no—
189C42—612no—
190C42—1222no—
191C42—1222no—
192C23D4×D6111yescharacteristic
193Q8—614no—
194Q8—1222no—
195Q8—1224no—
196Q8—4882no—
197C2×C4—21no—
198C2×C4—21no—
199C2×C4—21no—
200C2×C4—21no—
201C2×C4—612no—
202C2×C4—612no—
203C2×C4—1222no—
204C2×C4—1224no—
205C2×C4—1222no—
206C2×C4—4881no—
207C2×C4#1175822212yes—
208C2×C4D4×D6111yescharacteristic
209C2×C4Q8×D6112yes—
210C2×C4C23×D6111yescharacteristic
211C8—21no—
212C8—21no—
213C8—1222no—
214C22—21no—
215C22—21no—
216C22#1451975512yes—
217C22C2×D4×D6111yescharacteristic
218C4—41no—
219C4—41no—
220C4—41no—
221C4—41no—
222C4—1224no—
223C4—1222no—
224C4—1222no—
225C4—2442no—
226C4#1451975512yes—
227C4C2×Q8×D6111yescharacteristic
228C4C2×#1175822211yescharacteristic
229C2—22no—
230C2C2×#1451975511yescharacteristic
231C2#1684056911yescharacteristic
232C2#1684057611yescharacteristic
subgroupG/H
centerC22C2×D4×D61
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC61×#427C2
socleC22×C61C22×D4
hypercenter#427D61
hypocenterC61#3082
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ #427

Complements

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

NH ≅ G/Ntype
3. #16840072C2semidirect
4. #16840068C2semidirect
5. #16840056C2semidirect
6. #16840046C2semidirect
47. C2×Dic122Q8semidirect
128. C61#3082semidirect