Finite Group Databasebeta

← #21458854

Subgroups — #21458854

Order 7808.

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

normal subgroups only

This group has 350 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#16840487C211yesmaximal, characteristic, complemented
2#16840482C211yesmaximal, characteristic
3#16840153C212yesmaximal
4#16840141C211yesmaximal, characteristic, complemented
5#16839982C212yesmaximal
6#16839973C211yesmaximal, characteristic, complemented
7#16839971C212yesmaximal, complemented
8#16839889C211yesmaximal, characteristic, complemented
9#16839866C212yesmaximal, complemented
10C4×#11758200C211yesmaximal, characteristic
11C61×#461C211yesmaximal, characteristic
12C2×Dic244C2212yes—
13C2×#11758202C2212yes—
14C2×#11758202C2212yes—
15C2×#11758200C2211yescharacteristic
16#14519777C2211yescharacteristic
17#14519775C2212yes—
18#14519770—22no—
19#14519768—21no—
20#14519767—22no—
21#14519764C2212yes—
22#14519756—21no—
23Q8×Dic61C2212yes—
24C4×Dic122C2211yescharacteristic
25C4×Dic122C2211yescharacteristic
26#14519742—21no—
27#14519742C2212yes—
28#14519736—21no—
29#14519708C2211yescharacteristic
30#14519706C2212yes—
31#14519702C2212yes—
32#14519700C2211yescharacteristic
33#14519698C2211yescharacteristic
34#14519687C2212yes—
35C4×#92418C2211yescharacteristic
36C2×SD16×C61C2212yes—
37C4⋊Q8×C61C2211yescharacteristic
38C4×D4×C61C2211yescharacteristic
39C4⋊C8×C61C2211yescharacteristic
40#103×C61C2212yes—
41C2×Q8×C61C2312yes—
42C2×D4×C61C2311yescharacteristic
43C22×C4×C61—21no—
44C2×Dic122D411yescharacteristic
45C2×Dic122C2311yescharacteristic
46C2×Dic122C2312yes—
47SD16×C61—42no—
48C2×C8×C61C2312yes—
49C4⋊C4×C61—21no—
50C4⋊C4×C61—21no—
51C4⋊C4×C61C2311yescharacteristic
52C22⋊C4×C61—21no—
53C42×C61C2311yescharacteristic
54C22⋊Dic61—22no—
55C22⋊Dic61—22no—
56#11758202—24no—
57#11758202—42no—
58#11758200—22no—
59C4⋊Dic61—21no—
60C4⋊Dic61—21no—
61C4⋊Dic61—22no—
62C4⋊Dic61D411yescharacteristic
63C4⋊Dic61C2311yescharacteristic
64#11758196—21no—
65#11758196—22no—
66#11758196—22no—
67#11758196—22no—
68#11758196D412yes—
69C4×Dic61—21no—
70C4×Dic61—22no—
71C4×Dic61—22no—
72C4×Dic61C2312yes—
73C2×#92418C2311yescharacteristic
74C2×#92418C2311yescharacteristic
75Dic244—42no—
76C23×C61—21no—
77Q8×C61—22no—
78Q8×C61—22no—
79D4×C61—21no—
80D4×C61—21no—
81C2×C4×C61—21no—
82C2×C4×C61—22no—
83C2×C4×C61—42no—
84C2×C4×C61C2×D411yescharacteristic
85C2×C4×C61C2×D411yescharacteristic
86C2×C4×C61C2411yescharacteristic
87C2×Dic61—21no—
88C2×Dic61—21no—
89C2×Dic61—22no—
90C2×Dic61C2×D412yes—
91C2×Dic61C2×D412yes—
92Dic122—22no—
93Dic122—21no—
94Dic122—22no—
95Dic122—21no—
96Dic122—22no—
97C8×C61—22no—
98#92418—21no—
99#92418#4112yes—
100C22×C61—41no—
101C22×C61—41no—
102C22×C61—41no—
103C22×C61C22×D411yescharacteristic
104C4×C61—21no—
105C4×C61—42no—
106C4×C61—41no—
107C4×C61#13712yes—
108C4×C61C2×#4111yescharacteristic
109C4×C61H(5,𝔽2)11yescharacteristic
110Dic61—22no—
111Dic61—22no—
112Dic61—41no—
113Dic61—42no—
114Dic61—41no—
115#3398—611nomaximal, Sylow
116C2×C61—81no—
117C2×C61#55011yescharacteristic
118C2×C61C2×#13711yescharacteristic
119C2×C61#57811yescharacteristic
120#557—611no—
121#556—611no—
122#497—612no—
123#494—611no—
124#464—612no—
125#462—611no—
126#462—612no—
127#461D6111yescharacteristic
128#446—611no—
129#441—612no—
130C4×SD16—611no—
131C61#339811yescharacteristic, complemented, Sylow
132C2×Q16—612no—
133C2×Q16—612no—
134C2×Q16—612no—
135C2×SD16—611no—
136C2×SD16C2×D6112yes—
137C4⋊Q8—612no—
138C4⋊Q8—611no—
139C4⋊Q8C2×D6111yescharacteristic
140#126—1222no—
141#125—1222no—
142#125—1221no—
143#124—612no—
144C22⋊Q8—1221no—
145C4×Q8—611no—
146C4×Q8—612no—
147C4×Q8—612no—
148C4×Q8—611no—
149C4×Q8—1221no—
150C4×D4C2×D6111yescharacteristic
151#117—1221no—
152#106—611no—
153C4⋊C8—612no—
154C4⋊C8C2×D6111yescharacteristic
155#103—612no—
156#103—611no—
157#103C2×D6112yes—
158#102—611no—
159#97—612no—
160C4×C8—611no—
161C2×Q8—611no—
162C2×Q8—612no—
163C2×Q8—611no—
164C2×Q8C22×D6112yes—
165C2×D4C22×D6111yescharacteristic
166C22×C4—21no—
167Q16—1224no—
168Q16—2442no—
169Q16—2442no—
170SD16—42no—
171SD16—1222no—
172C2×C8—611no—
173C2×C8—611no—
174C2×C8C22×D6112yes—
175C4⋊C4—21no—
176C4⋊C4—21no—
177C4⋊C4—612no—
178C4⋊C4—611no—
179C4⋊C4—611no—
180C4⋊C4—1222no—
181C4⋊C4—1222no—
182C4⋊C4—1222no—
183C4⋊C4—1222no—
184C4⋊C4—1221no—
185C4⋊C4—1221no—
186C4⋊C4—1221no—
187C4⋊C4C22×D6111yescharacteristic
188C22⋊C4—21no—
189C22⋊C4—1222no—
190C22⋊C4—1222no—
191C42—612no—
192C42—1222no—
193C42—1222no—
194C42—1221no—
195C42C22×D6111yescharacteristic
196C23—21no—
197Q8—22no—
198Q8—22no—
199Q8—1222no—
200Q8—1221no—
201Q8—1222no—
202Q8—1221no—
203Q8—1222no—
204D4—21no—
205D4—21no—
206C2×C4—21no—
207C2×C4—22no—
208C2×C4—42no—
209C2×C4—612no—
210C2×C4—612no—
211C2×C4—1221no—
212C2×C4—1222no—
213C2×C4—1221no—
214C2×C4D4×D6111yescharacteristic
215C2×C4D4×D6111yescharacteristic
216C2×C4C23×D6111yescharacteristic
217C8—22no—
218C8—612no—
219C8—1221no—
220C22—41no—
221C22—41no—
222C22—41no—
223C22C2×D4×D6111yescharacteristic
224C4—21no—
225C4—41no—
226C4—42no—
227C4—1222no—
228C4—1222no—
229C4—2441no—
230C4—2442no—
231C4—2441no—
232C4#1451980612yes—
233C4#41×D6111yescharacteristic
234C4#1451982211yescharacteristic
235C2—81no—
236C2#1684043011yescharacteristic
237C2C2×#1451980611yescharacteristic
238C2#1684057811yescharacteristic
subgroupG/H
centerC22C2×D4×D61
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC61×#461C2
socleC22×C61C22×D4
hypercenter#461D61
hypocenterC61#3398
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ #461

Complements

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

NH ≅ G/Ntype
1. #16840487C2semidirect
4. #16840141C2semidirect
6. #16839973C2semidirect
7. #16839971C2semidirect
8. #16839889C2semidirect
9. #16839866C2semidirect
131. C61#3398semidirect