Finite Group Databasebeta

← #21458541

Subgroups — #21458541

Order 7808.

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

normal subgroups only

This group has 372 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#16840486C211yesmaximal, characteristic, complemented
2D4×Dic122C211yesmaximal, characteristic, complemented
3#16840123C212yesmaximal, complemented
4#16840112C211yesmaximal, characteristic, complemented
5#16840055C212yesmaximal, complemented
6#16840043C211yesmaximal, characteristic, complemented
7#16839979C212yesmaximal
8#16839889C211yesmaximal, characteristic, complemented
9#16839863C212yesmaximal, complemented
10C4×#11758199C211yesmaximal, characteristic
11C61×#461C211yesmaximal, characteristic, complemented
12C22×Dic122—21no—
13C2×#11758199C2211yescharacteristic
14#14519777C2211yescharacteristic
15#14519776C2212yes—
16#14519772—22no—
17#14519766C2212yes—
18#14519757—21no—
19#14519756—21no—
20#14519754—22no—
21Q8×Dic61C2212yes—
22C4×Dic122C2211yescharacteristic
23C4×D244C2211yescharacteristic
24D4×Dic61C2212yes—
25#14519735—21no—
26#14519711C2212yes—
27#14519710C2211yescharacteristic
28#14519706C2212yes—
29#14519701C2212yes—
30#14519701C2212yes—
31#14519699C2212yes—
32#14519698C2211yescharacteristic
33#14519697C2211yescharacteristic
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—
44C22×Dic61—22no—
45C2×D244C2311yescharacteristic
46C2×C4×D61—21no—
47C2×Dic122—21no—
48C2×Dic122—22no—
49C2×Dic122—44no—
50C2×Dic122D411yescharacteristic
51SD16×C61—24no—
52C2×C8×C61C2312yes—
53C4⋊C4×C61—21no—
54C4⋊C4×C61—21no—
55C4⋊C4×C61C2311yescharacteristic
56C22⋊C4×C61—21no—
57C42×C61C2311yescharacteristic
58C22⋊Dic61—22no—
59#11758199—22no—
60#11758198—21no—
61#11758198—22no—
62#11758198—22no—
63C4⋊Dic61—21no—
64C4⋊Dic61—22no—
65C4⋊Dic61D411yescharacteristic
66C4⋊Dic61C2311yescharacteristic
67C4⋊Dic61C2312yes—
68#11758196—22no—
69#11758196D412yes—
70C4×Dic61—22no—
71C4×Dic61C2312yes—
72C2×#92418C2311yescharacteristic
73C2×#92418C2311yescharacteristic
74C23×C61—21no—
75C22×D61—21no—
76Q8×C61—22no—
77Q8×C61—22no—
78D4×C61—21no—
79D4×C61#4112yes—
80C2×C4×C61—22no—
81C2×C4×C61—21no—
82C2×C4×C61—42no—
83C2×C4×C61C2×D411yescharacteristic
84C2×C4×C61C2×D411yescharacteristic
85C2×C4×C61C2411yescharacteristic
86C2×Dic61—21no—
87C2×Dic61—22no—
88C2×Dic61—44no—
89C2×Dic61C2×D412yes—
90C2×Dic61C2×D412yes—
91D244—21no—
92D244—21no—
93C4×D61—42no—
94Dic122—22no—
95Dic122—44no—
96Dic122—42no—
97C8×C61—22no—
98#92418—21no—
99#92418—21no—
100C22×C61—22no—
101C22×C61—41no—
102C22×C61—41no—
103C22×C61C22×D411yescharacteristic
104C2×D61—41no—
105C2×D61—41no—
106C2×D61—41no—
107C4×C61—21no—
108C4×C61—42no—
109C4×C61—41no—
110C4×C61AGL(1,ℤ/8)12yes—
111C4×C61C2×#4111yescharacteristic
112C4×C612−1+411yescharacteristic
113Dic61—22no—
114Dic61—22no—
115Dic61—42no—
116Dic61—41no—
117#3367—611nomaximal, Sylow
118C2×C61—42no—
119C2×C61#54811yescharacteristic
120C2×C61C2×AGL(1,ℤ/8)11yescharacteristic
121C2×C61#57811yescharacteristic
122D61—81no—
123#556—611no—
124D4×Q8—611no—
125#489—612no—
126#487—611no—
127#477—612no—
128#474—611no—
129#463—612no—
130#461D6111yescharacteristic, complemented
131#446—611no—
132#440—612no—
133C4×D8—611no—
134C61#336711yescharacteristic, complemented, Sylow
135C22×Q8—1221no—
136C2×SD16C2×D6112yes—
137C2×D8—611no—
138C4⋊Q8—612no—
139C4⋊Q8—611no—
140C4⋊Q8C2×D6111yescharacteristic
141#126—1222no—
142#124—612no—
143C22⋊Q8—1222no—
144C22⋊Q8—1221no—
145C22⋊Q8—1221no—
146C4×Q8—611no—
147C4×Q8—612no—
148C4×D4—612no—
149C4×D4—611no—
150C4×D4C2×D6111yescharacteristic
151#117—1221no—
152#107—612no—
153#107—611no—
154C4⋊C8—612no—
155C4⋊C8C2×D6111yescharacteristic
156#103—612no—
157#103—612no—
158#103C2×D6112yes—
159#102—611no—
160#102—612no—
161#102—611no—
162#97—612no—
163C4×C8—611no—
164C2×Q8—611no—
165C2×Q8—1222no—
166C2×Q8—1221no—
167C2×Q8—2444no—
168C2×Q8C22×D6112yes—
169C2×D4—611no—
170C2×D4C22×D6111yescharacteristic
171C22×C4—21no—
172C22×C4—1222no—
173C22×C4—1221no—
174SD16—24no—
175D8—1222no—
176C2×C8—611no—
177C2×C8—611no—
178C2×C8C22×D6112yes—
179C4⋊C4—21no—
180C4⋊C4—21no—
181C4⋊C4—612no—
182C4⋊C4—611no—
183C4⋊C4—612no—
184C4⋊C4—611no—
185C4⋊C4—1222no—
186C4⋊C4—1222no—
187C4⋊C4—1221no—
188C4⋊C4C22×D6111yescharacteristic
189C22⋊C4—21no—
190C22⋊C4—1222no—
191C22⋊C4—1222no—
192C22⋊C4—1222no—
193C22⋊C4—1221no—
194C42—612no—
195C42—1222no—
196C42C22×D6111yescharacteristic
197C23—21no—
198C23—1221no—
199Q8—22no—
200Q8—22no—
201Q8—1222no—
202Q8—2444no—
203Q8—2442no—
204D4—21no—
205D4—1221no—
206D4—1221no—
207D4#1175822412yes—
208C2×C4—22no—
209C2×C4—21no—
210C2×C4—42no—
211C2×C4—612no—
212C2×C4—612no—
213C2×C4—1221no—
214C2×C4—1222no—
215C2×C4—2444no—
216C2×C4—2442no—
217C2×C4D4×D6111yescharacteristic
218C2×C4D4×D6111yescharacteristic
219C2×C4C23×D6111yescharacteristic
220C8—22no—
221C8—1221no—
222C8—1221no—
223C22—22no—
224C22—41no—
225C22—41no—
226C22—2441no—
227C22—2441no—
228C22—2441no—
229C22C2×D4×D6111yescharacteristic
230C4—21no—
231C4—41no—
232C4—42no—
233C4—1222no—
234C4—1222no—
235C4—2441no—
236C4—2442no—
237C4#1451980412yes—
238C4C2×#1175822411yescharacteristic
239C4#1451982411yescharacteristic
240C2—42no—
241C2—4881no—
242C2#1684041811yescharacteristic
243C2C2×#1451980411yescharacteristic
244C2#1684057811yescharacteristic
subgroupG/H
centerC22C2×D4×D61
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC61×#461C2
socleC22×C61C22×D4
hypercenter#461D61
hypocenterC61#3367
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. #16840486C2semidirect
2. D4×Dic122C2semidirect
3. #16840123C2semidirect
4. #16840112C2semidirect
5. #16840055C2semidirect
6. #16840043C2semidirect
8. #16839889C2semidirect
9. #16839863C2semidirect
11. C61×#461C2semidirect
130. #461D61semidirect
134. C61#3367semidirect