Finite Group Databasebeta

← #21458877

Subgroups — #21458877

Order 7808.

362 conjugacy classes of subgroups; only the 117 normal subgroups are shown.

normal subgroups only

This group has 362 conjugacy classes of subgroups — too many to draw. Only its 117 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#16840498C211yesmaximal, characteristic
2#16840487C211yesmaximal, characteristic, complemented
3#16840153C212yesmaximal, complemented
4#16839982C212yesmaximal, complemented
5#16839969C211yesmaximal, characteristic, complemented
6#16839965C212yesmaximal, complemented
7#16839959C211yesmaximal, characteristic
8#16839892C211yesmaximal, characteristic, complemented
9#16839863C212yesmaximal, complemented
10C4×Dic244C211yesmaximal, characteristic, complemented
11C61×#492C211yesmaximal, characteristic
12C2×Dic244C2211yescharacteristic
13C2×#11758202C2212yes—
14C2×#11758200C2212yes—
15#14519775C2212yes—
16#14519768—21no—
17#14519767—22no—
18#14519764—21no—
19#14519764C2212yes—
20#14519758—22no—
21Q8×Dic61C2212yes—
22C4×Dic122C2211yescharacteristic
23C4×Dic122C2211yescharacteristic
24C4×Dic122C2211yescharacteristic
25#14519742—21no—
26D4×Dic61—21no—
27D4×Dic61C2212yes—
28#14519711C2211yescharacteristic
29C4⋊#92418C2211yescharacteristic
30#14519706C2212yes—
31#14519702C2211yescharacteristic
32#14519702C2211yescharacteristic
33#14519701C2212yes—
34#14519698C2212yes—
35#14519687C2212yes—
36C2×SD16×C61C2212yes—
37C2×SD16×C61C2212yes—
38C4⋊Q8×C61C2211yescharacteristic
39#127×C61C2211yescharacteristic
40C4×C8×C61C2211yescharacteristic
41C2×Q8×C61C2312yes—
42C2×D4×C61—21no—
43C2×D4×C61—21no—
44C2×D4×C61C2312yes—
45C22×Dic61—22no—
46C2×Dic122D411yescharacteristic
47C2×Dic122C2311yescharacteristic
48C2×Dic122C2311yescharacteristic
49SD16×C61—24no—
50SD16×C61—42no—
51C2×C8×C61C2311yescharacteristic
52C2×C8×C61C2311yescharacteristic
53C4⋊C4×C61—21no—
54C4⋊C4×C61—21no—
55C42×C61C2311yescharacteristic
56C22⋊Dic61—22no—
57C22⋊Dic61—22no—
58C22⋊Dic61—22no—
59#11758202—42no—
60#11758200—42no—
61C4⋊Dic61—22no—
62C4⋊Dic61D411yescharacteristic
63C4⋊Dic61C2311yescharacteristic
64C4⋊Dic61C2311yescharacteristic
65#11758196—21no—
66#11758196—21no—
67#11758196—22no—
68#11758196—22no—
69#11758196D412yes—
70C4×Dic61—21no—
71C4×Dic61—21no—
72C4×Dic61—22no—
73C4×Dic61C2312yes—
74C2×#92418C2312yes—
75Dic244—22no—
76C23×C61—22no—
77Q8×C61—22no—
78Q8×C61—22no—
79D4×C61—22no—
80D4×C61—22no—
81D4×C61—42no—
82D4×C61—81no—
83C2×C4×C61—22no—
84C2×C4×C61C2×D411yescharacteristic
85C2×C4×C61C2×D411yescharacteristic
86C2×C4×C61C2411yescharacteristic
87C2×Dic61—21no—
88C2×Dic61—21no—
89C2×Dic61—21no—
90C2×Dic61—21no—
91C2×Dic61—82no—
92C2×Dic61C2×D412yes—
93C2×Dic61C2×D412yes—
94Dic122—22no—
95Dic122—21no—
96Dic122—21no—
97Dic122—21no—
98Dic122—21no—
99C8×C61—21no—
100C8×C61#4112yes—
101#92418—22no—
102C22×C61—42no—
103C22×C61—42no—
104C22×C61—42no—
105C22×C61C22×D411yescharacteristic
106C4×C61—21no—
107C4×C61—42no—
108C4×C61#13712yes—
109C4×C61C2×#4111yescharacteristic
110C4×C61H(5,𝔽2)11yescharacteristic
111Dic61—22no—
112Dic61—22no—
113Dic61—41no—
114Dic61—41no—
115Dic61—41no—
116Dic61—41no—
117#3400—611nomaximal, Sylow
118C2×C61—82no—
119C2×C61#55011yescharacteristic
120C2×C61C2×#13711yescharacteristic
121C2×C61#57711yescharacteristic
122#559—611no—
123#557—611no—
124#497—612no—
125#492D6111yescharacteristic
126#464—612no—
127#462—611no—
128#461—612no—
129#460—611no—
130#446—611no—
131#440—612no—
132C4×Q16—611no—
133C61#340011yescharacteristic, complemented, Sylow
134C2×Q16—612no—
135C2×Q16—611no—
136C2×SD16—612no—
137C2×SD16C2×D6112yes—
138C2×SD16C2×D6112yes—
139C4⋊Q8—612no—
140C4⋊Q8C2×D6111yescharacteristic
141#127C2×D6111yescharacteristic
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—611no—
151C4×Q8—1221no—
152C4×D4—612no—
153C4×D4—1221no—
154#107—611no—
155C4⋊C8—612no—
156C4⋊C8—611no—
157#103—612no—
158#103—611no—
159#103—611no—
160#102—612no—
161#97—612no—
162C4×C8C2×D6111yescharacteristic
163C2×Q8—611no—
164C2×Q8—611no—
165C2×Q8—611no—
166C2×Q8C22×D6112yes—
167C2×D4—21no—
168C2×D4—21no—
169C2×D4C22×D6112yes—
170C22×C4—1222no—
171Q16—1222no—
172Q16—2442no—
173SD16—24no—
174SD16—42no—
175SD16—2442no—
176C2×C8—612no—
177C2×C8C22×D6111yescharacteristic
178C2×C8C22×D6111yescharacteristic
179C4⋊C4—21no—
180C4⋊C4—21no—
181C4⋊C4—612no—
182C4⋊C4—611no—
183C4⋊C4—611no—
184C4⋊C4—611no—
185C4⋊C4—1222no—
186C4⋊C4—1222no—
187C4⋊C4—1222no—
188C4⋊C4—1221no—
189C4⋊C4—1221no—
190C22⋊C4—1222no—
191C22⋊C4—1222no—
192C22⋊C4—1222no—
193C42—612no—
194C42—1222no—
195C42—1221no—
196C42—1221no—
197C42C22×D6111yescharacteristic
198C23—22no—
199Q8—22no—
200Q8—22no—
201Q8—1222no—
202Q8—1221no—
203Q8—1221no—
204Q8—1221no—
205Q8—1221no—
206D4—22no—
207D4—22no—
208D4—42no—
209D4—81no—
210C2×C4—22no—
211C2×C4—612no—
212C2×C4—612no—
213C2×C4—1221no—
214C2×C4—1221no—
215C2×C4—1221no—
216C2×C4—1221no—
217C2×C4—4882no—
218C2×C4D4×D6111yescharacteristic
219C2×C4D4×D6111yescharacteristic
220C2×C4C23×D6111yescharacteristic
221C8—21no—
222C8—1222no—
223C8#1175822412yes—
224C22—42no—
225C22—42no—
226C22—42no—
227C22C2×D4×D6111yescharacteristic
228C4—21no—
229C4—42no—
230C4—1222no—
231C4—1222no—
232C4—2441no—
233C4—2441no—
234C4—2441no—
235C4—2441no—
236C4#1451980612yes—
237C4C2×#1175822411yescharacteristic
238C4#1451982211yescharacteristic
239C2—82no—
240C2#1684043211yescharacteristic
241C2C2×#1451980611yescharacteristic
242C2#1684056811yescharacteristic
subgroupG/H
centerC22C2×D4×D61
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC61×#492C2
socleC22×C61C22×D4
hypercenter#492D61
hypocenterC61#3400
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ #492

Complements

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

NH ≅ G/Ntype
2. #16840487C2semidirect
3. #16840153C2semidirect
4. #16839982C2semidirect
5. #16839969C2semidirect
6. #16839965C2semidirect
8. #16839892C2semidirect
9. #16839863C2semidirect
10. C4×Dic244C2semidirect
133. C61#3400semidirect