Finite Group Databasebeta

← #21455631

Subgroups — #21455631

Order 7808.

416 conjugacy classes of subgroups; only the 133 normal subgroups are shown.

normal subgroups only

This group has 416 conjugacy classes of subgroups — too many to draw. Only its 133 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
1C4⋊Q8×D61C211yesmaximal, characteristic, complemented
2C4×#11758224C211yesmaximal, characteristic
3#16840058C211yesmaximal, characteristic, complemented
4#16840054C211yesmaximal, characteristic, complemented
5#16840052C211yesmaximal, characteristic, complemented
6#16840046C212yesmaximal, complemented
7#16840040C212yesmaximal, complemented
8#16839801C212yesmaximal, complemented
9#16839784C211yesmaximal, characteristic, complemented
10#16839760C212yesmaximal
11C61×#476C211yesmaximal, characteristic, complemented
12C2×#11758224C2211yescharacteristic
13C2×Q8×D61—21no—
14C2×#11758189C2212yes—
15#14519777C2211yescharacteristic
16#14519776—21no—
17#14519776C2212yes—
18#14519775—21no—
19C4×Dic122C2211yescharacteristic
20#14519742C2211yescharacteristic
21D4×Dic61C2211yescharacteristic
22C4×C22⋊D61—21no—
23#14519737—21no—
24#14519735C2211yescharacteristic
25#14519733—21no—
26C4⋊C4×D61—21no—
27C4⋊C4×D61C2212yes—
28C2×C4×Dic61—21no—
29C42×D61C2211yescharacteristic
30#14519711C2212yes—
31#14519710C2212yes—
32#14519708C2212yes—
33C4⋊#92418C2211yescharacteristic
34#14519706C2212yes—
35#14519702C2212yes—
36#14519700C2212yes—
37#14519698C2212yes—
38C4⋊Q8×C61C2211yescharacteristic
39C4×D4×C61C2211yescharacteristic
40#106×C61C2212yes—
41C4⋊C8×C61C2211yescharacteristic
42#102×C61C2212yes—
43C2×Q8×C61—21no—
44C2×D4×C61C2311yescharacteristic
45C22×C4×C61—21no—
46C2×C22⋊D61—21no—
47C22×Dic61—21no—
48C22×Dic61—21no—
49Q8×D61—44no—
50#11758224—22no—
51#11758224Q814yescomplemented
52C2×C4×D61—22no—
53C2×C4×D61D411yescharacteristic
54C2×C4×D61D411yescharacteristic
55C2×C4×D61C2311yescharacteristic
56C2×Dic122—21no—
57C2×Dic122—22no—
58C2×Dic122C2311yescharacteristic
59C2×C8×C61C2312yes—
60C4⋊C4×C61—21no—
61C4⋊C4×C61C2312yes—
62C4⋊C4×C61C2311yescharacteristic
63C22⋊C4×C61—21no—
64C42×C61C2311yescharacteristic
65C22⋊Dic61—21no—
66#11758198—21no—
67C4⋊Dic61—21no—
68C4⋊Dic61C2312yes—
69C4⋊Dic61C2311yescharacteristic
70#11758196—21no—
71#11758196—22no—
72#11758196—22no—
73#11758196—21no—
74C4×Dic61—21no—
75C4×Dic61—21no—
76C4×Dic61—21no—
77C4×Dic61D411yescharacteristic
78C4×Dic61D411yescharacteristic
79C4×Dic61C2311yescharacteristic
80C2×#92418C2312yes—
81#11758189—24no—
82C23×C61—21no—
83C22×D61C2×D411yescharacteristic
84Q8×C61—42no—
85D4×C61—21no—
86D4×C61C2×Q812yescomplemented
87C2×C4×C61—21no—
88C2×C4×C61—22no—
89C2×C4×C61—42no—
90C2×C4×C61C2×D411yescharacteristic
91C2×C4×C61C2×D411yescharacteristic
92C2×C4×C61C2411yescharacteristic
93C22⋊D61—24no—
94C2×Dic61—21no—
95C2×Dic61—24no—
96C2×Dic61—21no—
97C2×Dic61—22no—
98C2×Dic61—42no—
99C2×Dic61C2×D411yescharacteristic
100C2×Dic61C2×D411yescharacteristic
101C2×Dic61C2×D411yescharacteristic
102C4×D61—22no—
103C4×D61—22no—
104C4×D61—44no—
105C4×D61C2×Q812yes—
106C4×D61#4112yes—
107Dic122—21no—
108Dic122—42no—
109Dic122—44no—
110Dic122C2×Q812yescomplemented
111C8×C61—22no—
112#92418—22no—
113C22×C61—22no—
114C22×C61—41no—
115C22×C61—41no—
116C22×C61C22×D411yescharacteristic
117C2×D61—21no—
118C2×D61—21no—
119C2×D61C22⋊Q812yes—
120C4×C61—21no—
121C4×C61—42no—
122C4×C61—41no—
123C4×C61#13712yes—
124C4×C61C22×Q811yescharacteristic
125C4×C61C2×#4111yescharacteristic
126Dic61—22no—
127Dic61—21no—
128Dic61—42no—
129Dic61—41no—
130Dic61C22⋊Q812yes—
131Dic61AGL(1,ℤ/8)12yes—
132#3079—611nomaximal, Sylow
133C2×C61—42no—
134C2×C61C2×C22⋊Q811yescharacteristic
135C2×C61C2×AGL(1,ℤ/8)11yescharacteristic
136C2×C61C2×#13711yescharacteristic
137D61—22no—
138C2×C4⋊Q8—611no—
139C4×#41—611no—
140#477—611no—
141#477—611no—
142#476—611no—
143#476D6111yescharacteristic, complemented
144#475—612no—
145#474—612no—
146#428—612no—
147#423—611no—
148#417—612no—
149C61#307911yescharacteristic, complemented, Sylow
150C2×#41—611no—
151C22×Q8—1221no—
152C2×M16—612no—
153C4⋊Q8—612no—
154C4⋊Q8—611no—
155C4⋊Q8—1221no—
156C4⋊Q8—1221no—
157C4⋊Q8C2×D6111yescharacteristic
158C4×Q8—611no—
159C4×Q8—611no—
160C4×D4—611no—
161C4×D4—1221no—
162C4×D4—1221no—
163C4×D4C2×D6111yescharacteristic
164#117—611no—
165#117—1221no—
166C2×C4⋊C4—612no—
167C2×C4⋊C4—1221no—
168C2×C42—611no—
169C2×C42—1221no—
170#107—612no—
171#107—612no—
172#106—612no—
173#106C2×D6112yes—
174C4⋊C8—612no—
175C4⋊C8—611no—
176C4⋊C8C2×D6111yescharacteristic
177#103—612no—
178#103—612no—
179#102—612no—
180#102C2×D6112yes—
181#41—614no—
182#41—1222no—
183C2×Q8—21no—
184C2×Q8—611no—
185C2×Q8—1222no—
186C2×Q8—1221no—
187C2×Q8—2444no—
188C2×D4—1221no—
189C2×D4C22×D6111yescharacteristic
190C22×C4—21no—
191C22×C4—611no—
192C22×C4—611no—
193C22×C4—611no—
194C22×C4—1222no—
195C22×C4—1221no—
196C22×C4—1221no—
197M16—1224no—
198C2×C8—612no—
199C2×C8C22×D6112yes—
200C4⋊C4—21no—
201C4⋊C4—612no—
202C4⋊C4—611no—
203C4⋊C4—1222no—
204C4⋊C4—1222no—
205C4⋊C4—1221no—
206C4⋊C4—1221no—
207C4⋊C4—1221no—
208C4⋊C4C22×D6112yes—
209C4⋊C4C22×D6111yescharacteristic
210C22⋊C4—21no—
211C22⋊C4—1221no—
212C22⋊C4—1221no—
213C42—611no—
214C42—611no—
215C42—611no—
216C42—1221no—
217C42—1221no—
218C42—1221no—
219C42C22×D6111yescharacteristic
220C23—21no—
221C23—611no—
222Q8—42no—
223Q8—612no—
224Q8—1221no—
225Q8—2442no—
226Q8—2444no—
227D4—21no—
228D4—1224no—
229D4Q8×D6112yescomplemented
230C2×C4—21no—
231C2×C4—22no—
232C2×C4—42no—
233C2×C4—611no—
234C2×C4—611no—
235C2×C4—612no—
236C2×C4—612no—
237C2×C4—611no—
238C2×C4—1222no—
239C2×C4—1224no—
240C2×C4—1221no—
241C2×C4—1222no—
242C2×C4—1221no—
243C2×C4—1222no—
244C2×C4—2444no—
245C2×C4—2442no—
246C2×C4D4×D6111yescharacteristic
247C2×C4D4×D6111yescharacteristic
248C2×C4C23×D6111yescharacteristic
249C8—22no—
250C8—1222no—
251C22—22no—
252C22—41no—
253C22—41no—
254C22—612no—
255C22—1221no—
256C22—1221no—
257C22C2×D4×D6111yescharacteristic
258C4—21no—
259C4—42no—
260C4—41no—
261C4—612no—
262C4—612no—
263C4—1222no—
264C4—1221no—
265C4—2441no—
266C4—2442no—
267C4#1451980612yes—
268C4C2×Q8×D6111yescharacteristic
269C4#41×D6111yescharacteristic
270C2—42no—
271C2—1222no—
272C2C22⋊Q8×D6111yescharacteristic
273C2AGL(1,ℤ/8)×D6111yescharacteristic
274C2C2×#1451980611yescharacteristic
subgroupG/H
centerC22C2×D4×D61
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC61×#476C2
socleC22×C61C22×D4
hypercenter#476D61
hypocenterC61#3079
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ #476

Complements

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

NH ≅ G/Ntype
1. C4⋊Q8×D61C2semidirect
3. #16840058C2semidirect
4. #16840054C2semidirect
5. #16840052C2semidirect
6. #16840046C2semidirect
7. #16840040C2semidirect
8. #16839801C2semidirect
9. #16839784C2semidirect
11. C61×#476C2semidirect
51. #11758224Q8semidirect
86. D4×C61C2×Q8semidirect
110. Dic122C2×Q8semidirect
143. #476D61semidirect
149. C61#3079semidirect
229. D4Q8×D61semidirect