Finite Group Databasebeta

← #21458149

Subgroups — #21458149

Order 7808.

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

normal subgroups only

This group has 430 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#16840432C211yesmaximal, characteristic, complemented
2#16840417C211yesmaximal, characteristic, complemented
3#16840108C211yesmaximal, characteristic, complemented
4#16840079C212yesmaximal, complemented
5#16840048C211yesmaximal, characteristic, complemented
6#16840012C212yesmaximal, complemented
7#16839904C212yesmaximal, complemented
8C4×#11758200C211yesmaximal, characteristic, complemented
9#16839839C211yesmaximal, characteristic, complemented
10#16839760C212yesmaximal, complemented
11C61×#459C211yesmaximal, characteristic, complemented
12C2×#11758222—21no—
13C2×#11758224C2212yes—
14C2×#11758200C2211yescharacteristic
15C2×#11758189C2212yes—
16#14519777C2211yescharacteristic
17#14519773—21no—
18#14519759—22no—
19#14519756—21no—
20#14519749—22no—
21#14519748C2212yes—
22#14519748C2212yes—
23C4×Dic122C2211yescharacteristic
24C4×D244C2211yescharacteristic
25D4×Dic61—21no—
26C4⋊C4×D61C2212yes—
27#14519709C2212yes—
28#14519708C2211yescharacteristic
29#14519702C2212yes—
30#14519700C2211yescharacteristic
31#14519698C2211yescharacteristic
32#14519698C2212yes—
33#14519698C2212yes—
34#14519689C2212yes—
35C4×#92418C2211yescharacteristic
36C2×D8×C61C2212yes—
37#127×C61C2211yescharacteristic
38C4×D4×C61C2211yescharacteristic
39C4⋊C8×C61C2211yescharacteristic
40#102×C61C2212yes—
41C2×D4×C61—21no—
42C2×D4×C61—21no—
43C2×D4×C61C2312yes—
44C2×D4×C61C2311yescharacteristic
45C22×C4×C61—21no—
46C2×C22⋊D61—22no—
47C2×C22⋊D61—22no—
48C2×C22⋊D61—22no—
49C22×Dic61—22no—
50#11758224—24no—
51#11758224—42no—
52#11758222—44no—
53C2×D244D411yescharacteristic
54C2×C4×D61—22no—
55C2×C4×D61C2312yes—
56C2×Dic122—21no—
57C2×Dic122C2311yescharacteristic
58D8×C61—42no—
59C2×C8×C61C2312yes—
60C4⋊C4×C61C2311yescharacteristic
61C22⋊C4×C61—21no—
62C42×C61C2311yescharacteristic
63C22⋊Dic61—22no—
64C22⋊Dic61—22no—
65#11758200—22no—
66#11758198D412yes—
67C4⋊Dic61—21no—
68C4⋊Dic61D411yescharacteristic
69C4⋊Dic61C2312yes—
70C4⋊Dic61C2311yescharacteristic
71#11758196—21no—
72#11758196—22no—
73C4×Dic61—21no—
74C2×#92418C2311yescharacteristic
75C2×#92418C2311yescharacteristic
76#11758189—42no—
77C23×C61—21no—
78C23×C61—22no—
79C22×D61C2×D412yes—
80D4×C61—21no—
81D4×C61—22no—
82D4×C61—21no—
83D4×C61—22no—
84D4×C61—42no—
85D4×C61—81no—
86C2×C4×C61—21no—
87C2×C4×C61—42no—
88C2×C4×C61C2×D411yescharacteristic
89C2×C4×C61C2×D411yescharacteristic
90C2×C4×C61C2411yescharacteristic
91C22⋊D61—44no—
92C22⋊D61—44no—
93C22⋊D61—82no—
94C2×Dic61—21no—
95C2×Dic61—21no—
96C2×Dic61—22no—
97C2×Dic61—44no—
98C2×Dic61C2×D412yes—
99D244—22no—
100C4×D61—22no—
101C4×D61—22no—
102C4×D61—44no—
103Dic122—21no—
104Dic122—42no—
105Dic122#4112yescomplemented
106C8×C61—22no—
107#92418—21no—
108#92418—21no—
109C22×C61—42no—
110C22×C61—41no—
111C22×C61—41no—
112C22×C61—42no—
113C22×C61—42no—
114C22×C61—41no—
115C22×C61C22×D411yescharacteristic
116C2×D61—22no—
117C2×D61—22no—
118C2×D61—22no—
119C4×C61—21no—
120C4×C61—41no—
121C4×C61AGL(1,ℤ/8)12yes—
122C4×C61C2×#4111yescharacteristic
123C4×C61H(5,𝔽2)11yescharacteristic
124Dic61—22no—
125Dic61—22no—
126Dic61—42no—
127Dic61—41no—
128#3332—611nomaximal, Sylow
129C2×C61—82no—
130C2×C61—81no—
131C2×C61#54611yescharacteristic
132C2×C61C2×AGL(1,ℤ/8)11yescharacteristic
133C2×C61#57711yescharacteristic
134D61—42no—
135#550—611no—
136#547—611no—
137#486—611no—
138#481—612no—
139#475—611no—
140#469—612no—
141#459D6111yescharacteristic, complemented
142#449—612no—
143C4×SD16—611no—
144#436—611no—
145#417—612no—
146C61#333211yescharacteristic, complemented, Sylow
147C2×#41—612no—
148C2×#41—1221no—
149C2×SD16—611no—
150C2×D8C2×D6112yes—
151C2×M16—612no—
152C4⋊Q8—611no—
153#127—1221no—
154#127C2×D6111yescharacteristic
155#123—1222no—
156C22⋊Q8—1221no—
157#121—612no—
158#121—612no—
159#121—1222no—
160C4×Q8—611no—
161C4×D4—611no—
162C4×D4—1221no—
163C4×D4C2×D6111yescharacteristic
164C2×C4⋊C4—612no—
165#106—612no—
166#106—611no—
167C4⋊C8C2×D6111yescharacteristic
168#103—612no—
169#103—611no—
170#102—612no—
171#102—611no—
172#102—612no—
173#102C2×D6112yes—
174C22⋊C8—612no—
175C4×C8—611no—
176#41—1224no—
177#41—2444no—
178#41—2442no—
179C2×Q8—611no—
180C2×Q8—1221no—
181C2×D4—21no—
182C2×D4—21no—
183C2×D4—611no—
184C2×D4—1222no—
185C2×D4—1222no—
186C2×D4—1222no—
187C2×D4C22×D6112yes—
188C2×D4C22×D6111yescharacteristic
189C22×C4—21no—
190C22×C4—612no—
191C22×C4—1222no—
192C22×C4—1222no—
193SD16—1222no—
194D8—42no—
195M16—2442no—
196C2×C8—611no—
197C2×C8—611no—
198C2×C8C22×D6112yes—
199C4⋊C4—611no—
200C4⋊C4—612no—
201C4⋊C4—611no—
202C4⋊C4—1222no—
203C4⋊C4—1221no—
204C4⋊C4—1221no—
205C4⋊C4C22×D6111yescharacteristic
206C22⋊C4—21no—
207C22⋊C4—612no—
208C22⋊C4—1222no—
209C22⋊C4—1222no—
210C42—1221no—
211C42C22×D6111yescharacteristic
212C23—21no—
213C23—22no—
214C23—612no—
215Q8—612no—
216Q8—1221no—
217Q8—2442no—
218D4—21no—
219D4—22no—
220D4—21no—
221D4—22no—
222D4—42no—
223D4—81no—
224D4—1222no—
225D4—4882no—
226D4—2444no—
227D4—2444no—
228C2×C4—21no—
229C2×C4—42no—
230C2×C4—612no—
231C2×C4—1221no—
232C2×C4—1222no—
233C2×C4—1222no—
234C2×C4—1221no—
235C2×C4—1222no—
236C2×C4—2444no—
237C2×C4—2444no—
238C2×C4D4×D6111yescharacteristic
239C2×C4D4×D6111yescharacteristic
240C2×C4C23×D6111yescharacteristic
241C8—22no—
242C8—1221no—
243C8—1221no—
244C22—41no—
245C22—42no—
246C22—42no—
247C22—41no—
248C22—42no—
249C22—41no—
250C22—1222no—
251C22—1222no—
252C22—1222no—
253C22C2×D4×D6111yescharacteristic
254C4—21no—
255C4—41no—
256C4—1222no—
257C4—1222no—
258C4—2442no—
259C4—2441no—
260C4#1451980112yes—
261C4#41×D6111yescharacteristic
262C4#1451982211yescharacteristic
263C2—81no—
264C2—82no—
265C2—2442no—
266C2#1684040911yescharacteristic
267C2C2×#1451980111yescharacteristic
268C2#1684057211yescharacteristic
subgroupG/H
centerC22C2×D4×D61
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC61×#459C2
socleC22×C61C22×D4
hypercenter#459D61
hypocenterC61#3332
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ #459

Complements

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

NH ≅ G/Ntype
1. #16840432C2semidirect
2. #16840417C2semidirect
3. #16840108C2semidirect
4. #16840079C2semidirect
5. #16840048C2semidirect
6. #16840012C2semidirect
7. #16839904C2semidirect
8. C4×#11758200C2semidirect
9. #16839839C2semidirect
10. #16839760C2semidirect
11. C61×#459C2semidirect
105. Dic122#41semidirect
141. #459D61semidirect
146. C61#3332semidirect