Finite Group Databasebeta

← #21458437

Subgroups — #21458437

Order 7808.

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

normal subgroups only

This group has 342 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#16840485C211yesmaximal, characteristic
2#16840473C211yesmaximal, characteristic
3#16840158C211yesmaximal, characteristic, complemented
4#16840105C212yesmaximal, complemented
5#16840091C212yesmaximal, complemented
6#16840048C211yesmaximal, characteristic, complemented
7#16840019C212yesmaximal, complemented
8C4×#11758202C211yesmaximal, characteristic, complemented
9#16839839C211yesmaximal, characteristic
10#16839803C212yesmaximal, complemented
11C61×#477C211yesmaximal, characteristic, complemented
12C2×#11758202C2211yescharacteristic
13C2×#11758189C2212yes—
14#14519777C2211yescharacteristic
15#14519772—22no—
16#14519768—21no—
17#14519765—21no—
18#14519757C2212yes—
19#14519753—22no—
20#14519753C2212yes—
21C4×Dic122—21no—
22C4×Dic122C2211yescharacteristic
23C4×D244C2211yescharacteristic
24#14519739—21no—
25#14519735C2212yes—
26C4⋊C4×D61C2212yes—
27#14519710C2211yescharacteristic
28#14519709C2212yes—
29#14519708C2212yes—
30#14519708C2212yes—
31#14519702C2212yes—
32#14519701C2211yescharacteristic
33#14519700C2211yescharacteristic
34#14519689C2212yes—
35C4×#92418C2211yescharacteristic
36C4⋊Q8×C61C2211yescharacteristic
37C4×Q8×C61C2211yescharacteristic
38#107×C61C2212yes—
39C4⋊C8×C61C2211yescharacteristic
40#103×C61C2212yes—
41C2×Q8×C61—21no—
42C2×Q8×C61C2311yescharacteristic
43C2×D244D411yescharacteristic
44C2×C4×D61—22no—
45C2×C4×D61C2312yes—
46C2×Dic122—21no—
47C2×Dic122C2311yescharacteristic
48C2×C8×C61C2312yes—
49C4⋊C4×C61—21no—
50C4⋊C4×C61—21no—
51C4⋊C4×C61C2312yes—
52C4⋊C4×C61C2311yescharacteristic
53C42×C61—21no—
54C42×C61C2311yescharacteristic
55#11758202—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—
67#11758196—22no—
68C4×Dic61—21no—
69C4×Dic61—22no—
70C2×#92418C2311yescharacteristic
71C2×#92418C2311yescharacteristic
72#11758189—24no—
73C22×D61C2×D412yes—
74Q8×C61—21no—
75Q8×C61—21no—
76Q8×C61—81no—
77C2×C4×C61—21no—
78C2×C4×C61—21no—
79C2×C4×C61—22no—
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—
90C4×D61—82no—
91Dic122—21no—
92Dic122—21no—
93Dic122—42no—
94C8×C61—22no—
95#92418—21no—
96#92418#4112yes—
97C22×C61C22×D411yescharacteristic
98C2×D61—22no—
99C2×D61—22no—
100C2×D61—22no—
101C4×C61—21no—
102C4×C61—41no—
103C4×C61—42no—
104C4×C61—41no—
105C4×C61#13712yes—
106C4×C61C2×#4111yescharacteristic
107C4×C612−1+411yescharacteristic
108Dic61—22no—
109Dic61—41no—
110Dic61—42no—
111Dic61—41no—
112#3356—611nomaximal, Sylow
113C2×C61#54711yescharacteristic
114C2×C61C2×#13711yescharacteristic
115C2×C61#57711yescharacteristic
116D61—42no—
117#556—611no—
118#554—611no—
119#498—611no—
120#485—612no—
121#483—612no—
122#477D6111yescharacteristic, complemented
123#475—611no—
124#470—612no—
125C4×Q16—611no—
126#436—611no—
127#428—612no—
128C61#335611yescharacteristic, complemented, Sylow
129C2×Q16—611no—
130C2×M16—612no—
131C4⋊Q8—611no—
132C4⋊Q8C2×D6111yescharacteristic
133#126—1222no—
134#125—1221no—
135#124—1221no—
136C22⋊Q8—612no—
137C22⋊Q8—612no—
138C22⋊Q8—1222no—
139C4×Q8—611no—
140C4×Q8—1221no—
141C4×Q8C2×D6111yescharacteristic
142C4×D4—611no—
143C4×D4—1221no—
144#117—612no—
145C2×C4⋊C4—612no—
146#107—611no—
147#107C2×D6112yes—
148#106—612no—
149#106—612no—
150#106—612no—
151C4⋊C8C2×D6111yescharacteristic
152#103—611no—
153#103—612no—
154#103—611no—
155#103C2×D6112yes—
156C22⋊C8—612no—
157C4×C8—611no—
158C2×Q8—21no—
159C2×Q8—611no—
160C2×Q8—1221no—
161C2×Q8C22×D6111yescharacteristic
162C2×D4—611no—
163C22×C4—612no—
164C22×C4—1222no—
165Q16—1222no—
166M16—1224no—
167C2×C8—611no—
168C2×C8—611no—
169C2×C8C22×D6112yes—
170C4⋊C4—21no—
171C4⋊C4—21no—
172C4⋊C4—611no—
173C4⋊C4—612no—
174C4⋊C4—611no—
175C4⋊C4—1222no—
176C4⋊C4—1222no—
177C4⋊C4—1222no—
178C4⋊C4—1221no—
179C4⋊C4—1221no—
180C4⋊C4C22×D6111yescharacteristic
181C4⋊C4C22×D6112yes—
182C22⋊C4—612no—
183C22⋊C4—1222no—
184C22⋊C4—1222no—
185C22⋊C4—1222no—
186C42—21no—
187C42—1222no—
188C42—1221no—
189C42C22×D6111yescharacteristic
190C23—612no—
191Q8—21no—
192Q8—21no—
193Q8—81no—
194Q8—1221no—
195Q8—1221no—
196Q8—2442no—
197D4—1222no—
198C2×C4—21no—
199C2×C4—21no—
200C2×C4—22no—
201C2×C4—612no—
202C2×C4—1222no—
203C2×C4—1222no—
204C2×C4—1222no—
205C2×C4—1221no—
206C2×C4—1221no—
207C2×C4—4882no—
208C2×C4D4×D6111yescharacteristic
209C2×C4D4×D6111yescharacteristic
210C2×C4C23×D6111yescharacteristic
211C8—22no—
212C8—612no—
213C8—1221no—
214C22—1222no—
215C22—1222no—
216C22—1222no—
217C22C2×D4×D6111yescharacteristic
218C4—21no—
219C4—41no—
220C4—42no—
221C4—41no—
222C4—1222no—
223C4—2442no—
224C4—2441no—
225C4—2441no—
226C4#1451980912yes—
227C4#41×D6111yescharacteristic
228C4#1451982511yescharacteristic
229C2—2442no—
230C2#1684041411yescharacteristic
231C2C2×#1451980911yescharacteristic
232C2#1684057211yescharacteristic
subgroupG/H
centerC22C2×D4×D61
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC61×#477C2
socleC22×C61C22×D4
hypercenter#477D61
hypocenterC61#3356
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ #477

Complements

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

NH ≅ G/Ntype
3. #16840158C2semidirect
4. #16840105C2semidirect
5. #16840091C2semidirect
6. #16840048C2semidirect
7. #16840019C2semidirect
8. C4×#11758202C2semidirect
10. #16839803C2semidirect
11. C61×#477C2semidirect
122. #477D61semidirect
128. C61#3356semidirect