Finite Group Databasebeta

← #21458876

Subgroups — #21458876

Order 7808.

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

normal subgroups only

This group has 362 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#16840497C211yesmaximal, characteristic
2#16840487C211yesmaximal, characteristic, complemented
3#16840155C212yesmaximal, complemented
4#16840136C211yesmaximal, characteristic
5#16839986C212yesmaximal, complemented
6#16839966C212yesmaximal, complemented
7#16839963C211yesmaximal, characteristic
8#16839889C211yesmaximal, characteristic, complemented
9#16839865C212yesmaximal, complemented
10C4×#11758202C211yesmaximal, characteristic, complemented
11C61×#462C211yesmaximal, characteristic, complemented
12C2×#11758202C2211yescharacteristic
13C2×#11758190C2212yes—
14C2×#11758201C2212yes—
15C2×#11758201C2212yes—
16#14519775C2212yes—
17#14519774C2211yescharacteristic
18#14519768—21no—
19#14519767—22no—
20#14519766C2212yes—
21#14519765—21no—
22#14519762—22no—
23Q8×Dic61C2212yes—
24C4×Dic122C2211yescharacteristic
25C4×Dic122C2211yescharacteristic
26#14519742—21no—
27C4×D244—21no—
28#14519739C2212yes—
29#14519710C2211yescharacteristic
30#14519706C2212yes—
31#14519701C2211yescharacteristic
32#14519700C2211yescharacteristic
33#14519699C2212yes—
34#14519687C2212yes—
35C4×#92418C2211yescharacteristic
36C2×Q16×C61C2212yes—
37C4⋊Q8×C61C2211yescharacteristic
38C4×Q8×C61C2211yescharacteristic
39C4⋊C8×C61C2211yescharacteristic
40#103×C61C2212yes—
41C2×Q8×C61C2312yes—
42C2×Q8×C61C2311yescharacteristic
43C2×D244—21no—
44C2×D244—21no—
45C2×D244C2312yes—
46C2×C4×D61—22no—
47C2×Dic122D411yescharacteristic
48C2×Dic122C2311yescharacteristic
49Q16×C61—42no—
50C2×C8×C61C2312yes—
51C4⋊C4×C61—21no—
52C4⋊C4×C61—21no—
53C4⋊C4×C61—21no—
54C4⋊C4×C61C2311yescharacteristic
55C42×C61—21no—
56C42×C61C2311yescharacteristic
57#11758202—22no—
58#11758201—24no—
59#11758201—42no—
60#11758198—22no—
61#11758198—22no—
62#11758198—22no—
63C4⋊Dic61—22no—
64C4⋊Dic61D411yescharacteristic
65C4⋊Dic61C2311yescharacteristic
66#11758196—21no—
67#11758196—22no—
68#11758196—22no—
69#11758196D412yes—
70C4×Dic61—21no—
71C4×Dic61—22no—
72C4×Dic61C2312yes—
73C2×#92418C2311yescharacteristic
74C2×#92418C2311yescharacteristic
75#11758190—42no—
76C22×D61—22no—
77Q8×C61—22no—
78Q8×C61—21no—
79Q8×C61—22no—
80Q8×C61—21no—
81C2×C4×C61—22no—
82C2×C4×C61—21no—
83C2×C4×C61—21no—
84C2×C4×C61C2×D411yescharacteristic
85C2×C4×C61C2×D411yescharacteristic
86C2×C4×C61C2411yescharacteristic
87C2×Dic61—21no—
88C2×Dic61—21no—
89C2×Dic61C2×D412yes—
90C2×Dic61C2×D412yes—
91D244—22no—
92D244—22no—
93D244—42no—
94D244—81no—
95C4×D61—82no—
96Dic122—22no—
97Dic122—21no—
98Dic122—21no—
99C8×C61—22no—
100#92418—21no—
101#92418#4112yes—
102C22×C61C22×D411yescharacteristic
103C2×D61—42no—
104C2×D61—42no—
105C2×D61—42no—
106C4×C61—21no—
107C4×C61—42no—
108C4×C61—41no—
109C4×C61—41no—
110C4×C61#13712yes—
111C4×C61C2×#4111yescharacteristic
112C4×C61H(5,𝔽2)11yescharacteristic
113Dic61—22no—
114Dic61—22no—
115Dic61—41no—
116Dic61—41no—
117#3400—611nomaximal, Sylow
118C2×C61#55011yescharacteristic
119C2×C61C2×#13711yescharacteristic
120C2×C61#57711yescharacteristic
121D61—82no—
122#559—611no—
123#557—611no—
124#497—612no—
125#492—611no—
126#464—612no—
127#462D6111yescharacteristic, complemented
128#461—612no—
129#460—611no—
130#446—611no—
131#440—612no—
132C4×Q16—611no—
133C61#340011yescharacteristic, complemented, Sylow
134C2×Q16—611no—
135C2×Q16C2×D6112yes—
136C2×SD16—612no—
137C2×SD16—612no—
138C2×SD16—612no—
139C4⋊Q8—612no—
140C4⋊Q8C2×D6111yescharacteristic
141#127—611no—
142#125—1222no—
143#125—1221no—
144#124—612no—
145#124—1221no—
146#123—1222no—
147C4×Q8—611no—
148C4×Q8—612no—
149C4×Q8—611no—
150C4×Q8—1221no—
151C4×Q8C2×D6111yescharacteristic
152C4×D4—612no—
153C4×D4—1221no—
154#107—611no—
155C4⋊C8—612no—
156C4⋊C8C2×D6111yescharacteristic
157#103—611no—
158#103—611no—
159#103C2×D6112yes—
160#102—612no—
161#97—612no—
162C4×C8—611no—
163C2×Q8—611no—
164C2×Q8—611no—
165C2×Q8C22×D6111yescharacteristic
166C2×Q8C22×D6112yes—
167C2×D4—612no—
168C2×D4—1221no—
169C2×D4—1221no—
170C22×C4—1222no—
171Q16—42no—
172Q16—1222no—
173SD16—1224no—
174SD16—2442no—
175SD16—2442no—
176C2×C8—611no—
177C2×C8—611no—
178C2×C8C22×D6112yes—
179C4⋊C4—21no—
180C4⋊C4—21no—
181C4⋊C4—21no—
182C4⋊C4—612no—
183C4⋊C4—611no—
184C4⋊C4—611no—
185C4⋊C4—1222no—
186C4⋊C4—1222no—
187C4⋊C4—1222no—
188C4⋊C4—1221no—
189C4⋊C4C22×D6111yescharacteristic
190C22⋊C4—1222no—
191C22⋊C4—1222no—
192C22⋊C4—1222no—
193C42—21no—
194C42—612no—
195C42—1222no—
196C42—1221no—
197C42C22×D6111yescharacteristic
198C23—1222no—
199Q8—22no—
200Q8—21no—
201Q8—22no—
202Q8—21no—
203Q8—1222no—
204Q8—1221no—
205Q8—1221no—
206D4—1222no—
207D4—1222no—
208D4—4881no—
209D4—2442no—
210C2×C4—21no—
211C2×C4—21no—
212C2×C4—22no—
213C2×C4—612no—
214C2×C4—612no—
215C2×C4—1221no—
216C2×C4—1221no—
217C2×C4—4882no—
218C2×C4D4×D6111yescharacteristic
219C2×C4D4×D6111yescharacteristic
220C2×C4C23×D6111yescharacteristic
221C8—22no—
222C8—612no—
223C8—1221no—
224C22—2442no—
225C22—2442no—
226C22—2442no—
227C22C2×D4×D6111yescharacteristic
228C4—21no—
229C4—41no—
230C4—41no—
231C4—42no—
232C4—1222no—
233C4—1222no—
234C4—2441no—
235C4—2441no—
236C4#1451980912yes—
237C4#41×D6111yescharacteristic
238C4#1451982211yescharacteristic
239C2—4882no—
240C2#1684043011yescharacteristic
241C2C2×#1451980911yescharacteristic
242C2#1684057111yescharacteristic
subgroupG/H
centerC22C2×D4×D61
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC61×#462C2
socleC22×C61C22×D4
hypercenter#462D61
hypocenterC61#3400
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ #462

Complements

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

NH ≅ G/Ntype
2. #16840487C2semidirect
3. #16840155C2semidirect
5. #16839986C2semidirect
6. #16839966C2semidirect
8. #16839889C2semidirect
9. #16839865C2semidirect
10. C4×#11758202C2semidirect
11. C61×#462C2semidirect
127. #462D61semidirect
133. C61#3400semidirect