Finite Group Databasebeta

← #21461833

Subgroups — #21461833

Order 7808.

432 conjugacy classes of subgroups; only the 88 normal subgroups are shown.

normal subgroups only

This group has 432 conjugacy classes of subgroups — too many to draw. Only its 88 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
1C22×D61⋊C8C211yesmaximal, characteristic, complemented
2C2×#14519839C212yesmaximal, complemented
3#16840704C211yesmaximal, characteristic, complemented
4#16840635C212yesmaximal, complemented
5#121×D61C211yesmaximal, characteristic
6C2×D61⋊C8—21no—
7C2×D61⋊C8—24no—
8C2×D61⋊C8C2212yes—
9C22×#92420—21no—
10C2×C4⋊#6923C2212yes—
11C2×C22⋊#6923—21no—
12#14519839—24no—
13(C2×#6923)⋊C4—21no—
14C2×D4×D61—21no—
15C2×D4×D61C2211yescharacteristic
16C22×C4×D61C2211yescharacteristic
17#14519752C411yescharacteristic, complemented
18#14519751C411yescharacteristic, complemented
19#14519750—21no—
20#14519749—21no—
21#14519748C411yescharacteristic, complemented
22C4⋊C4×D61C2211yescharacteristic
23C22⋊C4×D61—21no—
24#121×C61C411yescharacteristic, complemented
25C23×D61—21no—
26C23×D61D411yescharacteristic
27C22×#6923—22no—
28C2×D4×C61—21no—
29C2×D4×C61C2×C411yescharacteristic
30C22×C4×C61C2×C411yescharacteristic
31C2×C22⋊D61—21no—
32C2×C22⋊D61—21no—
33C2×C22⋊D61—21no—
34C22×Dic61D411yescharacteristic
35D4×D61—22no—
36D4×D61—22no—
37D4×D61—42no—
38D4×D61—42no—
39C2×D244—21no—
40C2×D244C2×C411yescharacteristic
41C2×C4×D61—22no—
42C2×C4×D61—22no—
43C2×C4×D61—21no—
44C2×C4×D61C2×C411yescharacteristic
45C2×C4×D61D411yescharacteristic
46C2×C4×D61D411yescharacteristic
47C2×C4×D61C2311yescharacteristic
48C22⋊#6923—42no—
49C2×#92420—24no—
50C2×#92420—22no—
51C4⋊#6923—22no—
52C4⋊#6923—22no—
53D61⋊C8—24no—
54D61⋊C8—22no—
55D61⋊C8D414yescomplemented
56C4⋊C4×C61C2×C411yescharacteristic
57C22⋊C4×C61—21no—
58C22⋊Dic61—21no—
59#11758198—21no—
60#11758198—21no—
61C4⋊Dic61C2×C411yescharacteristic
62#11758196—21no—
63C23×C61—21no—
64C23×C61C22⋊C411yescharacteristic
65C22×D61—22no—
66C22×D61—22no—
67C22×D61—21no—
68C22×D61—42no—
69C22×D61—41no—
70C22×D61—41no—
71C22×D61—42no—
72C22×D61C22⋊C411yescharacteristic
73C22×D61D812yes—
74C22×D61SD1612yes—
75C22×D61C2×D411yescharacteristic
76C2×#6923—42no—
77C2×#6923—42no—
78C2×#6923—42no—
79D4×C61—22no—
80D4×C61—42no—
81C2×C4×C61—22no—
82C2×C4×C61—21no—
83C2×C4×C61C22⋊C411yescharacteristic
84C2×C4×C61C22×C411yescharacteristic
85C22⋊D61—42no—
86C22⋊D61—42no—
87C22⋊D61—41no—
88C22⋊D61—41no—
89C2×Dic61—21no—
90C2×Dic61—21no—
91C2×Dic61—21no—
92C2×Dic61C22⋊C411yescharacteristic
93C2×Dic61C2×D411yescharacteristic
94D244—22no—
95D244—42no—
96C4×D61—22no—
97C4×D61—22no—
98C4×D61—21no—
99C4×D61—21no—
100C4×D61—41no—
101C4×D61—41no—
102C4×D61C2×D412yes—
103C4×D61#4112yes—
104#92420—24no—
105C22×C61—21no—
106C22×C61—21no—
107C22×C61—41no—
108C22×C61—41no—
109C22×C61—41no—
110C22×C61#10212yescomplemented
111C22×C61C2×C22⋊C411yescharacteristic
112C2×D61—21no—
113C2×D61—21no—
114C2×D61—24no—
115C2×D61—24no—
116C2×D61—41no—
117C2×D61—41no—
118C2×D61—41no—
119C2×D61—82no—
120C2×D61—82no—
121C2×D61#10212yescomplemented
122C2×D61#12112yes—
123C2×D61C2×D811yescharacteristic
124C2×D61C2×SD1611yescharacteristic
125C2×D61#13512yes—
126#6923—82no—
127C4×C61—21no—
128C4×C61—41no—
129C4×C61C4×D412yes—
130Dic61—21no—
131Dic61—41no—
132Dic61#12011yescharacteristic
133Dic61#12311yescharacteristic
134#1893—611nomaximal, Sylow
135C2×C61—22no—
136C2×C61—81no—
137C2×C61#38611yescharacteristic
138C2×C61C2×#10211yescharacteristic
139C2×C61#41611yescharacteristic
140D61—22no—
141D61—81no—
142D61#46512yes—
143D61#46612yes—
144C23×C8—611no—
145C2×#121—611no—
146C2×#102—612no—
147#380—611no—
148#340—612no—
149C61#189311yescharacteristic, complemented, Sylow
150C22×D4—611no—
151C22×D4—1221no—
152C23×C4—611no—
153C22×C8—612no—
154C22×C8—1224no—
155C22×C8—1221no—
156C22×C8—1221no—
157#121—611no—
158#121—611no—
159#121—611no—
160#121—1221no—
161#121—1221no—
162#121#692311yescharacteristic, complemented
163C2×C4⋊C4—611no—
164C2×C4⋊C4—612no—
165C2×C22⋊C4—1221no—
166C2×C22⋊C4—1221no—
167#102—1224no—
168#95—1221no—
169C24—611no—
170C24—1221no—
171C2×D4—21no—
172C2×D4—611no—
173C2×D4—1221no—
174C2×D4—1222no—
175C2×D4—1222no—
176C2×D4—1221no—
177C2×D4—1221no—
178C2×D4—1221no—
179C2×D4—2442no—
180C2×D4—2442no—
181C2×D4C2×#692311yescharacteristic
182C22×C4—611no—
183C22×C4—611no—
184C22×C4—611no—
185C22×C4—611no—
186C22×C4—611no—
187C22×C4—1222no—
188C22×C4—1222no—
189C22×C4—1221no—
190C22×C4—1222no—
191C22×C4C2×#692311yescharacteristic
192C2×C8—614no—
193C2×C8—1222no—
194C2×C8—1222no—
195C2×C8—1224no—
196C2×C8—1224no—
197C4⋊C4—611no—
198C4⋊C4—1221no—
199C4⋊C4—1222no—
200C4⋊C4—1222no—
201C4⋊C4C2×#692311yescharacteristic
202C22⋊C4—21no—
203C22⋊C4—1221no—
204C22⋊C4—1221no—
205C22⋊C4—1221no—
206C22⋊C4—2442no—
207C23—21no—
208C23—611no—
209C23—612no—
210C23—612no—
211C23—611no—
212C23—1222no—
213C23—1222no—
214C23—1221no—
215C23—2442no—
216C23—2441no—
217C23—2441no—
218C23—2442no—
219C23C22⋊#692311yescharacteristic
220D4—22no—
221D4—42no—
222D4—1222no—
223D4—2442no—
224D4—2441no—
225D4—2441no—
226D4—2442no—
227D4—2442no—
228C2×C4—22no—
229C2×C4—21no—
230C2×C4—611no—
231C2×C4—612no—
232C2×C4—612no—
233C2×C4—611no—
234C2×C4—1221no—
235C2×C4—1221no—
236C2×C4—1222no—
237C2×C4—1221no—
238C2×C4—1221no—
239C2×C4—1222no—
240C2×C4—1221no—
241C2×C4—2441no—
242C2×C4—2441no—
243C2×C4—2442no—
244C2×C4—2442no—
245C2×C4—2442no—
246C2×C4C22⋊#692311yescharacteristic
247C2×C4C22×#692311yescharacteristic
248C8—1224no—
249C22—21no—
250C22—21no—
251C22—41no—
252C22—41no—
253C22—41no—
254C22—612no—
255C22—611no—
256C22—611no—
257C22—612no—
258C22—612no—
259C22—1224no—
260C22—1224no—
261C22—1221no—
262C22—1221no—
263C22—4882no—
264C22—4882no—
265C22—2441no—
266C22—2441no—
267C22—2441no—
268C22#1451983912yescomplemented
269C22C2×C22⋊#692311yescharacteristic
270C4—21no—
271C4—41no—
272C4—611no—
273C4—611no—
274C4—1221no—
275C4—4882no—
276C4—2441no—
277C4D4×#692312yes—
278C2—22no—
279C2—81no—
280C2—612no—
281C2—612no—
282C2—1222no—
283C2—4881no—
284C2#1684071011yescharacteristic
285C2C2×#1451983911yescharacteristic
286C2#1684075211yescharacteristic
subgroupG/H
centerC22C2×C22⋊#6923
commutatorC2×C4×C61C22×C4
FrattiniC2×C4C22×#6923
Fitting#121×C61C4
socleC22×C61C2×C22⋊C4
hypercenter#121#6923
hypocenterC61#1893
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ #121

Complements

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

NH ≅ G/Ntype
1. C22×D61⋊C8C2semidirect
2. C2×#14519839C2semidirect
3. #16840704C2semidirect
4. #16840635C2semidirect
17. #14519752C4semidirect
18. #14519751C4semidirect
21. #14519748C4semidirect
24. #121×C61C4semidirect
55. D61⋊C8D4semidirect
110. C22×C61#102semidirect
121. C2×D61#102semidirect
149. C61#1893semidirect
162. #121#6923semidirect
268. C22#14519839semidirect