Finite Group Databasebeta

← #21456364

Subgroups — #21456364

Order 7808.

380 conjugacy classes of subgroups; only the 141 normal subgroups are shown.

normal subgroups only

This group has 380 conjugacy classes of subgroups — too many to draw. Only its 141 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#16840318C211yesmaximal, characteristic
2C4⋊Q8×D61C211yesmaximal, characteristic
3#16840172C211yesmaximal, characteristic, complemented
4#16840171C211yesmaximal, characteristic, complemented
5#16840168C211yesmaximal, characteristic, complemented
6#16840166C212yesmaximal, complemented
7#16840159C212yesmaximal, complemented
8#16839803C212yesmaximal
9#16839801C212yesmaximal
10#16839714C211yesmaximal, characteristic
11C61×#501C211yesmaximal, characteristic, complemented
12C2×Q8×D61—21no—
13C2×#11758189C2212yes—
14#14519777C2211yescharacteristic
15#14519776—21no—
16#14519776C2212yes—
17#14519776C2211yescharacteristic
18#14519776C2211yescharacteristic
19#14519775—21no—
20#14519769C2211yescharacteristic
21#14519755—21no—
22#14519755—21no—
23#14519742—21no—
24#14519742—21no—
25#14519735C2211yescharacteristic
26#14519735C2211yescharacteristic
27C4⋊C4×D61—21no—
28C4⋊C4×D61C2212yes—
29C42×D61C2211yescharacteristic
30#14519711C2212yes—
31#14519710C2212yes—
32#14519710C2212yes—
33#14519709C2212yes—
34#14519708C2212yes—
35#14519708C2212yes—
36#14519688C2211yescharacteristic
37C8×Dic61C2212yes—
38C4⋊Q8×C61C2211yescharacteristic
39#125×C61C2211yescharacteristic
40#107×C61C2212yes—
41#106×C61C2212yes—
42#97×C61C2211yescharacteristic
43C2×Q8×C61—21no—
44Q8×D61—44no—
45C2×C4×D61—22no—
46C2×C4×D61D411yescharacteristic
47C2×C4×D61D411yescharacteristic
48C2×C4×D61C2311yescharacteristic
49C2×Dic122—21no—
50C2×Dic122—22no—
51C2×Dic122—21no—
52C2×Dic122—21no—
53C2×C8×C61C2312yes—
54C4⋊C4×C61—21no—
55C4⋊C4×C61—21no—
56C4⋊C4×C61—21no—
57C4⋊C4×C61C2311yescharacteristic
58C4⋊C4×C61C2312yes—
59C4⋊C4×C61C2311yescharacteristic
60C42×C61C2311yescharacteristic
61#11758198—21no—
62#11758198—21no—
63C4⋊Dic61—21no—
64C4⋊Dic61C2311yescharacteristic
65C4⋊Dic61C2312yes—
66C4⋊Dic61C2311yescharacteristic
67#11758196—21no—
68#11758196—21no—
69#11758196—22no—
70#11758196—22no—
71#11758196—21no—
72#11758196—21no—
73C4×Dic61—21no—
74C4×Dic61—21no—
75C4×Dic61D411yescharacteristic
76C4×Dic61D411yescharacteristic
77C4×Dic61C2311yescharacteristic
78C2×#92418C2312yes—
79#11758189Q818yescomplemented
80C22×D61C2×D411yescharacteristic
81Q8×C61—42no—
82C2×C4×C61—21no—
83C2×C4×C61—21no—
84C2×C4×C61—22no—
85C2×C4×C61C2×D411yescharacteristic
86C2×C4×C61C2×D411yescharacteristic
87C2×C4×C61C2411yescharacteristic
88C2×Dic61—21no—
89C2×Dic61—21no—
90C2×Dic61—22no—
91C2×Dic61C2×D411yescharacteristic
92C2×Dic61C2×D411yescharacteristic
93C2×Dic61C2×D411yescharacteristic
94C4×D61—22no—
95C4×D61—22no—
96C4×D61—44no—
97C4×D61C2×Q814yes—
98Dic122—42no—
99Dic122—42no—
100Dic122—44no—
101Dic122—42no—
102C8×C61C2×Q814yescomplemented
103#92418C2×Q814yescomplemented
104C22×C61C22×D411yescharacteristic
105C2×D61—21no—
106C2×D61—21no—
107C2×D61C4⋊Q812yes—
108C4×C61—21no—
109C4×C61—21no—
110C4×C61—42no—
111C4×C61—41no—
112C4×C61—41no—
113C4×C61C22×Q812yes—
114Dic61—42no—
115Dic61—41no—
116Dic61—41no—
117Dic61C4⋊Q812yes—
118Dic61AGL(1,ℤ/8)12yes—
119Dic61#13712yes—
120#3165—611nomaximal, Sylow
121C2×C61C2×C4⋊Q811yescharacteristic
122C2×C61C2×AGL(1,ℤ/8)11yescharacteristic
123C2×C61C2×#13711yescharacteristic
124D61—22no—
125#533—611no—
126C2×C4⋊Q8—611no—
127#501—611no—
128#501—611no—
129#501—611no—
130#501D6111yescharacteristic, complemented
131#500—612no—
132#498—612no—
133#428—612no—
134#428—612no—
135C4×M16—611no—
136C61#316511yescharacteristic, complemented, Sylow
137C22×Q8—1221no—
138C2×M16—612no—
139C4⋊Q8—612no—
140C4⋊Q8—611no—
141C4⋊Q8—611no—
142C4⋊Q8—611no—
143C4⋊Q8—1221no—
144C4⋊Q8—1221no—
145C4⋊Q8C2×D6111yescharacteristic
146#125—611no—
147#125C2×D6111yescharacteristic
148C22⋊Q8—1221no—
149C22⋊Q8—1221no—
150C4×Q8—1221no—
151C4×Q8—1221no—
152#117—611no—
153#117—611no—
154C2×C4⋊C4—612no—
155C2×C4⋊C4—1221no—
156C2×C42—611no—
157#107—612no—
158#107—612no—
159#107—612no—
160#107C2×D6112yes—
161#106—612no—
162#106—612no—
163#106—612no—
164#106C2×D6112yes—
165#97—611no—
166#97C2×D6111yescharacteristic
167C4×C8—612no—
168C2×Q8—21no—
169C2×Q8—1221no—
170C2×Q8—1221no—
171C2×Q8—1222no—
172C2×Q8—1221no—
173C2×Q8—2444no—
174C22×C4—611no—
175C22×C4—611no—
176C22×C4—611no—
177C22×C4—1222no—
178M16—618no—
179C2×C8—612no—
180C2×C8C22×D6112yes—
181C4⋊C4—21no—
182C4⋊C4—21no—
183C4⋊C4—21no—
184C4⋊C4—611no—
185C4⋊C4—612no—
186C4⋊C4—611no—
187C4⋊C4—1222no—
188C4⋊C4—1222no—
189C4⋊C4—1221no—
190C4⋊C4—1221no—
191C4⋊C4—1221no—
192C4⋊C4—1221no—
193C4⋊C4—1221no—
194C4⋊C4C22×D6111yescharacteristic
195C4⋊C4C22×D6112yes—
196C4⋊C4C22×D6111yescharacteristic
197C22⋊C4—1221no—
198C22⋊C4—1221no—
199C42—611no—
200C42—611no—
201C42—611no—
202C42—1221no—
203C42—1221no—
204C42C22×D6111yescharacteristic
205C23—611no—
206Q8—42no—
207Q8—2442no—
208Q8—2442no—
209Q8—2442no—
210Q8—2444no—
211C2×C4—21no—
212C2×C4—21no—
213C2×C4—22no—
214C2×C4—611no—
215C2×C4—611no—
216C2×C4—611no—
217C2×C4—614no—
218C2×C4—1222no—
219C2×C4—1222no—
220C2×C4—1221no—
221C2×C4—1221no—
222C2×C4—1222no—
223C2×C4—2444no—
224C2×C4D4×D6111yescharacteristic
225C2×C4D4×D6111yescharacteristic
226C2×C4C23×D6111yescharacteristic
227C8—614no—
228C8Q8×D6114yescomplemented
229C22—612no—
230C22—1221no—
231C22—1221no—
232C22C2×D4×D6111yescharacteristic
233C4—21no—
234C4—21no—
235C4—42no—
236C4—41no—
237C4—41no—
238C4—612no—
239C4—612no—
240C4—612no—
241C4—2442no—
242C4—2441no—
243C4—2441no—
244C4C2×Q8×D6112yes—
245C2—1222no—
246C2C4⋊Q8×D6111yescharacteristic
247C2AGL(1,ℤ/8)×D6111yescharacteristic
248C2#137×D6111yescharacteristic
subgroupG/H
centerC22C2×D4×D61
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC61×#501C2
socleC22×C61C22×D4
hypercenter#501D61
hypocenterC61#3165
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ #501

Complements

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

NH ≅ G/Ntype
3. #16840172C2semidirect
4. #16840171C2semidirect
5. #16840168C2semidirect
6. #16840166C2semidirect
7. #16840159C2semidirect
11. C61×#501C2semidirect
79. #11758189Q8semidirect
102. C8×C61C2×Q8semidirect
103. #92418C2×Q8semidirect
130. #501D61semidirect
136. C61#3165semidirect
228. C8Q8×D61semidirect