Finite Group Databasebeta

← #21458248

Subgroups — #21458248

Order 7808.

340 conjugacy classes of subgroups; only the 115 normal subgroups are shown.

normal subgroups only

This group has 340 conjugacy classes of subgroups — too many to draw. Only its 115 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#16840486C211yesmaximal, characteristic
2#16840485C211yesmaximal, characteristic
3#16840165C211yesmaximal, characteristic, complemented
4#16840106C212yesmaximal, complemented
5#16840101C212yesmaximal, complemented
6#16840048C211yesmaximal, characteristic, complemented
7#16840002C212yesmaximal, complemented
8C4×#11758202C211yesmaximal, characteristic, complemented
9#16839827C211yesmaximal, characteristic
10#16839797C212yesmaximal, complemented
11C61×#475C211yesmaximal, characteristic, complemented
12C2×#11758202C2211yescharacteristic
13C2×C8×D61C2212yes—
14#14519777C2211yescharacteristic
15#14519772—22no—
16#14519772—22no—
17#14519766—21no—
18#14519765—21no—
19#14519757C2212yes—
20#14519753C2212yes—
21Q8×Dic61—21no—
22C4×Dic122—21no—
23C4×Dic122C2211yescharacteristic
24C4×D244C2211yescharacteristic
25#14519735C2212yes—
26#14519735C2212yes—
27#14519710C2212yes—
28#14519710C2211yescharacteristic
29#14519710C2212yes—
30#14519709C2212yes—
31#14519702C2212yes—
32#14519701C2211yescharacteristic
33#14519700C2211yescharacteristic
34#14519689C2212yes—
35C4×#92418C2211yescharacteristic
36C4⋊Q8×C61C2211yescharacteristic
37C4×Q8×C61C2211yescharacteristic
38#106×C61C2212yes—
39C4⋊C8×C61C2211yescharacteristic
40#103×C61C2212yes—
41C2×Q8×C61—21no—
42C2×Q8×C61C2311yescharacteristic
43C2×D244D411yescharacteristic
44C2×C4×D61C2312yes—
45C2×Dic122—21no—
46C2×Dic122C2311yescharacteristic
47C2×C8×C61C2312yes—
48C4⋊C4×C61—21no—
49C4⋊C4×C61—21no—
50C4⋊C4×C61C2312yes—
51C4⋊C4×C61C2311yescharacteristic
52C42×C61—21no—
53C42×C61C2311yescharacteristic
54#11758202—22no—
55#11758198—22no—
56#11758198—22no—
57#11758198—22no—
58#11758198—22no—
59#11758198D412yes—
60C4⋊Dic61—21no—
61C4⋊Dic61—22no—
62C4⋊Dic61D411yescharacteristic
63C4⋊Dic61C2311yescharacteristic
64C4⋊Dic61C2312yes—
65#11758196—21no—
66#11758196—22no—
67C4×Dic61—21no—
68C4×Dic61—22no—
69C4×Dic61—22no—
70C2×#92418C2311yescharacteristic
71C2×#92418C2311yescharacteristic
72C8×D61—24no—
73C22×D61C2×D412yes—
74Q8×C61—21no—
75Q8×C61—21no—
76Q8×C61—42no—
77C2×C4×C61—21no—
78C2×C4×C61—22no—
79C2×C4×C61—21no—
80C2×C4×C61C2×D411yescharacteristic
81C2×C4×C61C2×D411yescharacteristic
82C2×C4×C61C2411yescharacteristic
83C2×Dic61—21no—
84C2×Dic61—21no—
85C2×Dic61—22no—
86C2×Dic61C2×D412yes—
87D244—22no—
88C4×D61—22no—
89C4×D61—22no—
90Dic122—21no—
91Dic122—21no—
92Dic122—42no—
93C8×C61—22no—
94#92418—21no—
95#92418#4112yes—
96C22×C61C22×D411yescharacteristic
97C2×D61—22no—
98C2×D61—22no—
99C2×D61—22no—
100C4×C61—21no—
101C4×C61—41no—
102C4×C61—42no—
103C4×C61—41no—
104C4×C61#13512yes—
105C4×C61C2×#4111yescharacteristic
106C4×C612−1+411yescharacteristic
107Dic61—22no—
108Dic61—41no—
109Dic61—42no—
110Dic61—41no—
111#3342—611nomaximal, Sylow
112C2×C61#54711yescharacteristic
113C2×C61C2×#13511yescharacteristic
114C2×C61#57811yescharacteristic
115D61—42no—
116#556—611no—
117#556—611no—
118#500—611no—
119#485—612no—
120#485—612no—
121#475—611no—
122#475D6111yescharacteristic, complemented
123#467—612no—
124C4×Q16—611no—
125C8×D4—611no—
126#427—612no—
127C61#334211yescharacteristic, complemented, Sylow
128C2×Q16—611no—
129C22×C8—612no—
130C4⋊Q8—611no—
131C4⋊Q8C2×D6111yescharacteristic
132#126—1222no—
133#126—1222no—
134#124—1221no—
135#124—1221no—
136C22⋊Q8—612no—
137C22⋊Q8—612no—
138C4×Q8—611no—
139C4×Q8—1221no—
140C4×Q8—1221no—
141C4×Q8C2×D6111yescharacteristic
142C4×D4—611no—
143#117—612no—
144#117—612no—
145#107—611no—
146#107—612no—
147#107—612no—
148#106—612no—
149#106C2×D6112yes—
150C4⋊C8C2×D6111yescharacteristic
151#103—611no—
152#103—612no—
153#103—611no—
154#103C2×D6112yes—
155C22⋊C8—612no—
156C4×C8—611no—
157C2×Q8—21no—
158C2×Q8—611no—
159C2×Q8—1221no—
160C2×Q8C22×D6111yescharacteristic
161C2×D4—611no—
162C22×C4—612no—
163Q16—1222no—
164C2×C8—611no—
165C2×C8—611no—
166C2×C8—1224no—
167C2×C8C22×D6112yes—
168C4⋊C4—21no—
169C4⋊C4—21no—
170C4⋊C4—611no—
171C4⋊C4—611no—
172C4⋊C4—612no—
173C4⋊C4—1222no—
174C4⋊C4—1222no—
175C4⋊C4—1221no—
176C4⋊C4—1221no—
177C4⋊C4C22×D6111yescharacteristic
178C4⋊C4C22×D6112yes—
179C22⋊C4—612no—
180C22⋊C4—1222no—
181C22⋊C4—1222no—
182C22⋊C4—1222no—
183C22⋊C4—1222no—
184C42—21no—
185C42—1222no—
186C42—1222no—
187C42—1221no—
188C42C22×D6111yescharacteristic
189C23—612no—
190Q8—21no—
191Q8—21no—
192Q8—42no—
193Q8—1221no—
194Q8—1221no—
195Q8—2442no—
196D4—1222no—
197C2×C4—21no—
198C2×C4—21no—
199C2×C4—22no—
200C2×C4—612no—
201C2×C4—1222no—
202C2×C4—1222no—
203C2×C4—1221no—
204C2×C4—1222no—
205C2×C4—1221no—
206C2×C4D4×D6111yescharacteristic
207C2×C4D4×D6111yescharacteristic
208C2×C4C23×D6111yescharacteristic
209C8—22no—
210C8—612no—
211C8—1221no—
212C22—1222no—
213C22—1222no—
214C22—1222no—
215C22C2×D4×D6111yescharacteristic
216C4—21no—
217C4—42no—
218C4—41no—
219C4—41no—
220C4—1222no—
221C4—2442no—
222C4—2441no—
223C4—2441no—
224C4#1451979812yes—
225C4#41×D6111yescharacteristic
226C4#1451982511yescharacteristic
227C2—2442no—
228C2#1684041411yescharacteristic
229C2C2×#1451979811yescharacteristic
230C2#1684057811yescharacteristic
subgroupG/H
centerC22C2×D4×D61
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC61×#475C2
socleC22×C61C22×D4
hypercenter#475D61
hypocenterC61#3342
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. #16840165C2semidirect
4. #16840106C2semidirect
5. #16840101C2semidirect
6. #16840048C2semidirect
7. #16840002C2semidirect
8. C4×#11758202C2semidirect
10. #16839797C2semidirect
11. C61×#475C2semidirect
122. #475D61semidirect
127. C61#3342semidirect