Finite Group Databasebeta

← #21461868

Subgroups — #21461868

Order 7808.

380 conjugacy classes of subgroups; only the 66 normal subgroups are shown.

normal subgroups only

This group has 380 conjugacy classes of subgroups — too many to draw. Only its 66 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#16840829C211yesmaximal, characteristic, complemented
2D61⋊#99C211yesmaximal, characteristic, complemented
3C2×#14519835C212yesmaximal, complemented
4#16840639C212yesmaximal, complemented
5#16840322C211yesmaximal, characteristic
6D4×#6923—24no—
7#14519856—21no—
8C2×C22⋊#6923—21no—
9C2×C22⋊#6923C2212yes—
10C2×C22⋊#6923C2212yes—
11#14519836—21no—
12#14519835—21no—
13#14519835—24no—
14C22×C22⋊D61C2211yescharacteristic
15C2×D4×D61C2211yescharacteristic
16#14519761C411yescharacteristic, complemented
17#14519759—21no—
18#14519758C411yescharacteristic, complemented
19#14519750—21no—
20#14519748—21no—
21#14519746C411yescharacteristic, complemented
22#14519745—21no—
23C22⋊C4×D61C2211yescharacteristic
24#120×C61C411yescharacteristic, complemented
25C24×C61C2×C411yescharacteristic, complemented
26C23×D61D411yescharacteristic
27C23×D61C2311yescharacteristic
28C22×#6923—22no—
29C22×#6923—22no—
30C22×#6923—22no—
31C2×D4×C61—21no—
32C2×D4×C61C2×C411yescharacteristic
33C2×C22⋊D61—22no—
34C2×C22⋊D61—21no—
35C2×C22⋊D61—21no—
36C2×C22⋊D61—22no—
37C2×C22⋊D61—21no—
38C2×C22⋊D61C2×C411yescharacteristic
39C2×C22⋊D61D411yescharacteristic
40C22×Dic61C2×C411yescharacteristic, complemented
41D4×D61—22no—
42D4×D61—22no—
43C2×D244D411yescharacteristic
44C2×C4×D61—21no—
45C2×C4×D61D411yescharacteristic
46C22⋊#6923—22no—
47C22⋊#6923—22no—
48C22⋊#6923—22no—
49C22⋊#6923—22no—
50C22⋊#6923D414yescomplemented
51C4⋊#6923—22no—
52C4×#6923—22no—
53C22⋊C4×C61—21no—
54C22⋊C4×C61C2×C411yescharacteristic, complemented
55C22⋊Dic61—21no—
56C22⋊Dic61—21no—
57C22⋊Dic61C2×C411yescharacteristic, complemented
58#11758198—21no—
59#11758198—21no—
60C4⋊Dic61—21no—
61#11758196—21no—
62C23×C61—21no—
63C23×C61—22no—
64C23×C61—81no—
65C23×C61C22⋊C411yescharacteristic
66C23×C61C22×C411yescharacteristic
67C22×D61—21no—
68C22×D61—21no—
69C22×D61—81no—
70C22×D61—81no—
71C22×D61C22⋊C411yescharacteristic
72C22×D61C2×D412yes—
73C22×D61C2×D411yescharacteristic
74C22×D61C2×D411yescharacteristic
75C22×D61#4112yes—
76C2×#6923—24no—
77C2×#6923—42no—
78C2×#6923—82no—
79C2×#6923—82no—
80C2×#6923—82no—
81D4×C61—22no—
82D4×C61—81no—
83C2×C4×C61—21no—
84C2×C4×C61C22⋊C411yescharacteristic
85C22⋊D61—22no—
86C22⋊D61—22no—
87C22⋊D61—41no—
88C22⋊D61—42no—
89C22⋊D61—41no—
90C22⋊D61—81no—
91C2×Dic61—21no—
92C2×Dic61—21no—
93C2×Dic61—22no—
94C2×Dic61C22⋊C411yescharacteristic
95D244—22no—
96C4×D61—21no—
97C4×D61—21no—
98C4×D61—81no—
99C22×C61—21no—
100C22×C61—41no—
101C22×C61—41no—
102C22×C61—41no—
103C22×C61—41no—
104C22×C61—41no—
105C22×C61—82no—
106C22×C61C2×C22⋊C411yescharacteristic
107C22×C61C4×D412yes—
108C2×D61—21no—
109C2×D61—41no—
110C2×D61—42no—
111C2×D61—42no—
112C2×D61—41no—
113C2×D61—42no—
114C2×D61—41no—
115C2×D61—81no—
116C2×D61#12011yescharacteristic
117C2×D61#12112yes—
118C2×D61#12311yescharacteristic
119#6923—44no—
120#6923—82no—
121C4×C61—21no—
122C4×C61—41no—
123Dic61—21no—
124Dic61—41no—
125Dic61—41no—
126#1913—611nomaximal, Sylow
127C2×C61—21no—
128C2×C61—22no—
129C2×C61—41no—
130C2×C61—81no—
131C2×C61#38611yescharacteristic
132D61—21no—
133D61—22no—
134D61—21no—
135D61—41no—
136#534—611no—
137#518—611no—
138C2×#99—612no—
139C2×#99—611no—
140#342—612no—
141C61#191311yescharacteristic, complemented, Sylow
142C22×D4—611no—
143C22×D4—611no—
144#123—611no—
145#123—611no—
146#123—1221no—
147#121—1221no—
148#121—1221no—
149#120—611no—
150#120—1221no—
151#120#692311yescharacteristic, complemented
152C4×D4—1224no—
153#117—1221no—
154C2×C22⋊C4—612no—
155C2×C22⋊C4—611no—
156C2×C22⋊C4—612no—
157C2×C22⋊C4—1221no—
158#99—1224no—
159#99—1221no—
160#99—1221no—
161C24—611no—
162C24—611no—
163C24C2×#692311yescharacteristic, complemented
164C2×D4—21no—
165C2×D4—611no—
166C2×D4—611no—
167C2×D4—611no—
168C2×D4—1222no—
169C2×D4—1222no—
170C2×D4—1221no—
171C2×D4—1222no—
172C2×D4—1221no—
173C2×D4—1221no—
174C2×D4—1222no—
175C2×D4C2×#692311yescharacteristic
176C22×C4—611no—
177C22×C4—611no—
178C22×C4—1221no—
179C22×C4—1222no—
180C22×C4—1222no—
181C22×C4—1222no—
182C4⋊C4—1221no—
183C4⋊C4—1222no—
184C4⋊C4—1221no—
185C22⋊C4—21no—
186C22⋊C4—614no—
187C22⋊C4—611no—
188C22⋊C4—1221no—
189C22⋊C4—1221no—
190C22⋊C4—1221no—
191C22⋊C4—1222no—
192C22⋊C4—1222no—
193C22⋊C4—1221no—
194C22⋊C4—1222no—
195C22⋊C4—1222no—
196C22⋊C4C2×#692311yescharacteristic, complemented
197C42—1222no—
198C23—21no—
199C23—22no—
200C23—81no—
201C23—611no—
202C23—611no—
203C23—612no—
204C23—612no—
205C23—611no—
206C23—1221no—
207C23—1221no—
208C23—4881no—
209C23—4881no—
210C23C22⋊#692311yescharacteristic
211C23C22×#692311yescharacteristic
212D4—22no—
213D4—81no—
214D4—1222no—
215D4—1222no—
216D4—1222no—
217D4—4881no—
218D4—2441no—
219D4—2441no—
220D4—2442no—
221C2×C4—21no—
222C2×C4—611no—
223C2×C4—1221no—
224C2×C4—1221no—
225C2×C4—1224no—
226C2×C4—1221no—
227C2×C4—1221no—
228C2×C4—1222no—
229C2×C4—4881no—
230C2×C4—4882no—
231C2×C4—4882no—
232C2×C4—4882no—
233C2×C4—2442no—
234C2×C4C22⋊#692311yescharacteristic
235C22—21no—
236C22—41no—
237C22—41no—
238C22—41no—
239C22—41no—
240C22—41no—
241C22—82no—
242C22—611no—
243C22—611no—
244C22—612no—
245C22—1221no—
246C22—4881no—
247C22—2441no—
248C22—2442no—
249C22—2442no—
250C22—2441no—
251C22—2441no—
252C22—2442no—
253C22C2×C22⋊#692311yescharacteristic
254C22D4×#692312yes—
255C4—21no—
256C4—41no—
257C4—1221no—
258C4—4882no—
259C4—2441no—
260C4—2444no—
261C4—2441no—
262C2—21no—
263C2—22no—
264C2—41no—
265C2—81no—
266C2—1222no—
267C2—1221no—
268C2—1221no—
269C2—2441no—
270C2#1684071011yescharacteristic
subgroupG/H
centerC2#16840710
commutatorC23×C61C22×C4
FrattiniC23C22×#6923
Fitting#120×C61C4
socleC2×C61#386
hypercenter#120#6923
hypocenterC61#1913
LCSG ▷ C23×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2 ◁ C23 ◁ #120

Complements

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

NH ≅ G/Ntype
1. #16840829C2semidirect
2. D61⋊#99C2semidirect
3. C2×#14519835C2semidirect
4. #16840639C2semidirect
16. #14519761C4semidirect
18. #14519758C4semidirect
21. #14519746C4semidirect
24. #120×C61C4semidirect
25. C24×C61C2×C4semidirect
40. C22×Dic61C2×C4semidirect
50. C22⋊#6923D4semidirect
54. C22⋊C4×C61C2×C4semidirect
57. C22⋊Dic61C2×C4semidirect
141. C61#1913semidirect
151. #120#6923semidirect
163. C24C2×#6923semidirect
196. C22⋊C4C2×#6923semidirect