Finite Group Databasebeta

← #21457032

Subgroups — #21457032

Order 7808.

322 conjugacy classes of subgroups; only the 113 normal subgroups are shown.

normal subgroups only

This group has 322 conjugacy classes of subgroups — too many to draw. Only its 113 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#16840317C211yesmaximal, characteristic
2#16840316C211yesmaximal, characteristic
3#16840169C212yesmaximal, complemented
4#16840129C212yesmaximal, complemented
5#16840106C212yesmaximal
6#16840102C212yesmaximal
7#16840058C211yesmaximal, characteristic, complemented
8#16840057C211yesmaximal, characteristic, complemented
9#16840044C211yesmaximal, characteristic, complemented
10#16839818C211yesmaximal, characteristic
11C61×#475C211yesmaximal, characteristic, complemented
12#14519777C2211yescharacteristic
13#14519776C2211yescharacteristic
14#14519775C2211yescharacteristic
15#14519768C2212yes—
16#14519767—21no—
17#14519757—21no—
18#14519757C2211yescharacteristic
19#14519755—21no—
20#14519753—21no—
21#14519753C2211yescharacteristic
22Q8×Dic61—21no—
23C4×Dic122—21no—
24C4×Dic122C2211yescharacteristic
25#14519742—21no—
26#14519735C2212yes—
27#14519734—21no—
28C42×D61C2211yescharacteristic
29#14519711C2212yes—
30#14519710C2212yes—
31#14519708C2212yes—
32C4⋊#92418C2211yescharacteristic
33#14519702C2212yes—
34#14519701C2212yes—
35#14519700C2212yes—
36#14519689C2212yes—
37#14519687C2212yes—
38C4⋊Q8×C61C2211yescharacteristic
39C4×Q8×C61C2211yescharacteristic
40#106×C61C2212yes—
41C4⋊C8×C61C2211yescharacteristic
42#103×C61C2212yes—
43C2×Q8×C61—21no—
44C2×Q8×C61C2311yescharacteristic
45C2×C4×D61D411yescharacteristic
46C2×C4×D61D411yescharacteristic
47C2×C4×D61C2311yescharacteristic
48C2×Dic122—21no—
49C2×Dic122—21no—
50C2×Dic122C2311yescharacteristic
51C2×C8×C61C2312yes—
52C4⋊C4×C61—21no—
53C4⋊C4×C61—21no—
54C4⋊C4×C61C2312yes—
55C4⋊C4×C61C2311yescharacteristic
56C42×C61—21no—
57C42×C61C2311yescharacteristic
58#11758198—21no—
59#11758198—21no—
60#11758198—22no—
61C4⋊Dic61—21no—
62C4⋊Dic61—21no—
63C4⋊Dic61—22no—
64C4⋊Dic61C2312yes—
65C4⋊Dic61C2311yescharacteristic
66#11758196—21no—
67#11758196—21no—
68#11758196—21no—
69#11758196—22no—
70#11758196—21no—
71#11758196—21no—
72C4×Dic61—21no—
73C4×Dic61—22no—
74C4×Dic61D411yescharacteristic
75C4×Dic61D411yescharacteristic
76C4×Dic61C2311yescharacteristic
77C2×#92418C2312yes—
78C22×D61C2×D411yescharacteristic
79Q8×C61—21no—
80Q8×C61—21no—
81Q8×C61—42no—
82C2×C4×C61—22no—
83C2×C4×C61—21no—
84C2×C4×C61—21no—
85C2×C4×C61C2×D411yescharacteristic
86C2×C4×C61C2×D411yescharacteristic
87C2×C4×C61C2411yescharacteristic
88C2×Dic61—21no—
89C2×Dic61—21no—
90C2×Dic61—22no—
91C2×Dic61C2×D411yescharacteristic
92C2×Dic61C2×D411yescharacteristic
93C2×Dic61C2×D411yescharacteristic
94C4×D61—22no—
95C4×D61—21no—
96C4×D61—21no—
97C4×D61—41no—
98Dic122—21no—
99Dic122—21no—
100Dic122—42no—
101Dic122—42no—
102C8×C61—22no—
103#92418—22no—
104C22×C61C22×D411yescharacteristic
105C2×D61—21no—
106C2×D61—21no—
107C2×D61—21no—
108C4×C61—21no—
109C4×C61—41no—
110C4×C61—42no—
111C4×C61—41no—
112C4×C61#13712yes—
113C4×C612−1+411yescharacteristic
114C4×C612−1+411yescharacteristic
115Dic61—21no—
116Dic61—21no—
117Dic61—21no—
118Dic61—41no—
119Dic61—41no—
120Dic61—42no—
121#3237—611nomaximal, Sylow
122C2×C61#53611yescharacteristic
123C2×C61C2×#13711yescharacteristic
124C2×C61#57511yescharacteristic
125D61—41no—
126#533—611no—
127#533—611no—
128#501—612no—
129#491—612no—
130#485—612no—
131#485—612no—
132#477—611no—
133#477—611no—
134#475—611no—
135#475D6111yescharacteristic, complemented
136#432—611no—
137C61#323711yescharacteristic, complemented, Sylow
138C4⋊Q8—611no—
139C4⋊Q8—611no—
140C4⋊Q8—611no—
141C4⋊Q8C2×D6111yescharacteristic
142#125—612no—
143#125—1221no—
144C22⋊Q8—611no—
145C22⋊Q8—611no—
146C22⋊Q8—1221no—
147C22⋊Q8—1221no—
148C22⋊Q8—1221no—
149C4×Q8—611no—
150C4×Q8—1221no—
151C4×Q8—1221no—
152C4×Q8—1221no—
153C4×Q8C2×D6111yescharacteristic
154#117—612no—
155#117—1221no—
156C2×C42—611no—
157#107—612no—
158#107—612no—
159#106—612no—
160#106C2×D6112yes—
161C4⋊C8—611no—
162C4⋊C8C2×D6111yescharacteristic
163#103—612no—
164#103—612no—
165#103—612no—
166#103C2×D6112yes—
167C22⋊C8—612no—
168#97—612no—
169C2×Q8—21no—
170C2×Q8—611no—
171C2×Q8—1221no—
172C2×Q8—1221no—
173C2×Q8C22×D6111yescharacteristic
174C22×C4—611no—
175C22×C4—611no—
176C22×C4—611no—
177C2×C8—612no—
178C2×C8C22×D6112yes—
179C4⋊C4—21no—
180C4⋊C4—21no—
181C4⋊C4—612no—
182C4⋊C4—611no—
183C4⋊C4—1221no—
184C4⋊C4—1221no—
185C4⋊C4—1221no—
186C4⋊C4—1222no—
187C4⋊C4—1221no—
188C4⋊C4—1221no—
189C4⋊C4—1222no—
190C4⋊C4—1221no—
191C4⋊C4—1221no—
192C4⋊C4C22×D6112yes—
193C4⋊C4C22×D6111yescharacteristic
194C22⋊C4—1222no—
195C22⋊C4—1221no—
196C22⋊C4—1221no—
197C42—21no—
198C42—611no—
199C42—611no—
200C42—611no—
201C42—1222no—
202C42—1221no—
203C42C22×D6111yescharacteristic
204C23—611no—
205Q8—21no—
206Q8—21no—
207Q8—42no—
208Q8—1221no—
209Q8—1221no—
210Q8—2442no—
211Q8—2442no—
212C2×C4—21no—
213C2×C4—21no—
214C2×C4—22no—
215C2×C4—611no—
216C2×C4—611no—
217C2×C4—611no—
218C2×C4—1221no—
219C2×C4—1221no—
220C2×C4—1222no—
221C2×C4—1221no—
222C2×C4—1222no—
223C2×C4—1221no—
224C2×C4—2441no—
225C2×C4D4×D6111yescharacteristic
226C2×C4D4×D6111yescharacteristic
227C2×C4C23×D6111yescharacteristic
228C8—22no—
229C8—1222no—
230C22—1221no—
231C22—1221no—
232C22—1221no—
233C22C2×D4×D6111yescharacteristic
234C4—21no—
235C4—42no—
236C4—41no—
237C4—41no—
238C4—1221no—
239C4—1221no—
240C4—1221no—
241C4—2442no—
242C4—2441no—
243C4—2441no—
244C4#1451980612yes—
245C4#1451982411yescharacteristic
246C4#1451982511yescharacteristic
247C2—2441no—
248C2#1684033511yescharacteristic
249C2C2×#1451980611yescharacteristic
250C2#1684056111yescharacteristic
subgroupG/H
centerC22C2×D4×D61
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC61×#475C2
socleC22×C61C22×D4
hypercenter#475D61
hypocenterC61#3237
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ #475

Complements

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

NH ≅ G/Ntype
3. #16840169C2semidirect
4. #16840129C2semidirect
7. #16840058C2semidirect
8. #16840057C2semidirect
9. #16840044C2semidirect
11. C61×#475C2semidirect
135. #475D61semidirect
137. C61#3237semidirect