Finite Group Databasebeta

← #21461960

Subgroups — #21461960

Order 7808.

408 conjugacy classes of subgroups; only the 72 normal subgroups are shown.

normal subgroups only

This group has 408 conjugacy classes of subgroups — too many to draw. Only its 72 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
1C2×#14519836C212yesmaximal, complemented
2C2×#14519835C212yesmaximal, complemented
3#16840704C211yesmaximal, characteristic, complemented
4C4×C22⋊#6923C211yesmaximal, characteristic, complemented
5C2×#14519750C211yesmaximal, characteristic
6C2×C4⋊#6923—21no—
7C2×C22⋊#6923C2212yes—
8C2×C22⋊#6923C2212yes—
9C2×C4×#6923—21no—
10#14519836—24no—
11#14519835—24no—
12(C2×#6923)⋊C4—21no—
13(C2×#6923)⋊C4—21no—
14C22×D244C2211yescharacteristic
15C22×C22⋊D61C411yescharacteristic, complemented
16C22×C22⋊D61C2211yescharacteristic
17C22×C4×D61C2211yescharacteristic
18#14519750—21no—
19#14519750—21no—
20#14519750—21no—
21#14519750—21no—
22C2×#11758196C411yescharacteristic, complemented
23C2×#11758198C411yescharacteristic, complemented
24C2×C22⋊C4×C61C411yescharacteristic, complemented
25C24×C61C2×C411yescharacteristic
26C23×D61C2×C411yescharacteristic
27C23×D61C2311yescharacteristic
28C22×#6923—22no—
29C22×#6923—22no—
30C22×C4×C61C2×C411yescharacteristic
31C22×C4×C61C2×C411yescharacteristic
32C2×C22⋊D61—22no—
33C2×C22⋊D61—21no—
34C2×C22⋊D61—21no—
35C2×C22⋊D61—22no—
36C2×C22⋊D61—21no—
37C2×C22⋊D61—21no—
38C2×C22⋊D61—42no—
39C22×Dic61C2×C411yescharacteristic
40C22×Dic61C2×C411yescharacteristic
41C2×D244—22no—
42C2×D244—21no—
43C2×D244—21no—
44C2×D244—22no—
45C2×C4×D61—42no—
46C2×C4×D61D411yescharacteristic
47C2×C4×D61D411yescharacteristic
48C2×C4×D61D411yescharacteristic
49C2×C4×D61D411yescharacteristic
50C22⋊#6923—22no—
51C22⋊#6923—22no—
52C22⋊#6923—22no—
53C22⋊#6923D414yescomplemented
54C4⋊#6923—42no—
55C4×#6923—42no—
56C22⋊C4×C61—21no—
57C22⋊C4×C61—21no—
58#11758198—21no—
59#11758198—21no—
60#11758196—21no—
61#11758196—21no—
62C23×C61—21no—
63C23×C61—22no—
64C23×C61—41no—
65C23×C61—41no—
66C23×C61C22×C411yescharacteristic
67C22×D61—21no—
68C22×D61—22no—
69C22×D61—41no—
70C22×D61—41no—
71C22×D61—41no—
72C22×D61—41no—
73C22×D61C2×D411yescharacteristic
74C22×D61C2×D411yescharacteristic
75C22×D61C2×D412yes—
76C22×D61#4112yes—
77C2×#6923—24no—
78C2×#6923—42no—
79C2×#6923—42no—
80C2×#6923—42no—
81C2×#6923—42no—
82C2×#6923—42no—
83C2×C4×C61—21no—
84C2×C4×C61—22no—
85C2×C4×C61—41no—
86C2×C4×C61C22⋊C411yescharacteristic
87C2×C4×C61C22⋊C411yescharacteristic
88C22⋊D61—42no—
89C22⋊D61—42no—
90C22⋊D61—41no—
91C22⋊D61—41no—
92C22⋊D61—42no—
93C2×Dic61—22no—
94C2×Dic61—21no—
95C2×Dic61—22no—
96C2×Dic61C22⋊C411yescharacteristic
97C2×Dic61C22⋊C411yescharacteristic
98D244—42no—
99D244—41no—
100D244—41no—
101C4×D61—22no—
102C4×D61—22no—
103C4×D61—41no—
104C4×D61—41no—
105C22×C61—21no—
106C22×C61—21no—
107C22×C61—41no—
108C22×C61—41no—
109C22×C61—41no—
110C22×C61—82no—
111C22×C61C2×C22⋊C411yescharacteristic
112C22×C61C4×D412yes—
113C2×D61—21no—
114C2×D61—21no—
115C2×D61—21no—
116C2×D61—21no—
117C2×D61—42no—
118C2×D61—42no—
119C2×D61—41no—
120C2×D61—41no—
121C2×D61—41no—
122C2×D61—82no—
123C2×D61#12112yes—
124C2×D61#12411yescharacteristic
125C2×D61#12711yescharacteristic
126#6923—44no—
127#6923—82no—
128C4×C61—21no—
129C4×C61—21no—
130C4×C61—41no—
131Dic61—21no—
132Dic61—41no—
133Dic61#9912yescomplemented
134#1964—611nomaximal, Sylow
135C2×C61—22no—
136C2×C61—81no—
137C2×C61#39011yescharacteristic
138C2×C61C2×#9911yescharacteristic
139C2×C61#41011yescharacteristic
140D61—22no—
141D61—21no—
142D61—21no—
143D61—81no—
144C2×#121—611no—
145C2×#99—612no—
146C2×#99—612no—
147#380—611no—
148C4×C22⋊C4—611no—
149C61#196411yescharacteristic, complemented, Sylow
150C22×D4—611no—
151C22×D4—611no—
152C22×D4—611no—
153C23×C4—611no—
154#121—1221no—
155#121—1221no—
156#121—1221no—
157#121—1221no—
158C2×C4⋊C4—611no—
159C2×C4⋊C4—1221no—
160C2×C22⋊C4—612no—
161C2×C22⋊C4—611no—
162C2×C22⋊C4—612no—
163C2×C22⋊C4#692311yescharacteristic, complemented
164C2×C42—1221no—
165#99—1224no—
166#99—1224no—
167#95—1221no—
168#95—1221no—
169C24—611no—
170C24—611no—
171C24C2×#692311yescharacteristic
172C2×D4—1222no—
173C2×D4—1221no—
174C2×D4—1221no—
175C2×D4—1222no—
176C2×D4—1221no—
177C2×D4—1221no—
178C2×D4—1222no—
179C2×D4—1221no—
180C2×D4—1221no—
181C2×D4—1222no—
182C2×D4—2442no—
183C22×C4—611no—
184C22×C4—611no—
185C22×C4—611no—
186C22×C4—611no—
187C22×C4—611no—
188C22×C4—611no—
189C22×C4—1222no—
190C22×C4—1222no—
191C22×C4—2442no—
192C22×C4C2×#692311yescharacteristic
193C22×C4C2×#692311yescharacteristic
194C4⋊C4—1221no—
195C4⋊C4—1221no—
196C4⋊C4—2442no—
197C22⋊C4—21no—
198C22⋊C4—21no—
199C22⋊C4—614no—
200C22⋊C4—1222no—
201C22⋊C4—1221no—
202C22⋊C4—1221no—
203C22⋊C4—1222no—
204C22⋊C4—1222no—
205C42—2442no—
206C23—21no—
207C23—22no—
208C23—41no—
209C23—41no—
210C23—611no—
211C23—611no—
212C23—612no—
213C23—612no—
214C23—1222no—
215C23—1221no—
216C23—2441no—
217C23—2441no—
218C23—2441no—
219C23—2441no—
220C23C22×#692311yescharacteristic
221D4—2442no—
222D4—2441no—
223D4—2441no—
224D4—2442no—
225D4—2442no—
226D4—2442no—
227D4—2441no—
228D4—2441no—
229C2×C4—21no—
230C2×C4—22no—
231C2×C4—41no—
232C2×C4—611no—
233C2×C4—611no—
234C2×C4—1222no—
235C2×C4—1222no—
236C2×C4—1222no—
237C2×C4—1224no—
238C2×C4—1221no—
239C2×C4—1222no—
240C2×C4—2441no—
241C2×C4—2441no—
242C2×C4—2442no—
243C2×C4—2442no—
244C2×C4—2442no—
245C2×C4—2442no—
246C2×C4—2442no—
247C2×C4C22⋊#692311yescharacteristic
248C2×C4C22⋊#692311yescharacteristic
249C22—21no—
250C22—21no—
251C22—41no—
252C22—41no—
253C22—41no—
254C22—82no—
255C22—612no—
256C22—611no—
257C22—611no—
258C22—1221no—
259C22—1221no—
260C22—1221no—
261C22—1221no—
262C22—4882no—
263C22—2442no—
264C22—2442no—
265C22—2441no—
266C22—2441no—
267C22—2441no—
268C22C2×C22⋊#692311yescharacteristic
269C22D4×#692312yes—
270C4—21no—
271C4—21no—
272C4—41no—
273C4—612no—
274C4—1221no—
275C4—4882no—
276C4—2444no—
277C4—2441no—
278C2—22no—
279C2—81no—
280C2—1221no—
281C2—1222no—
282C2—1221no—
283C2—4881no—
284C2#1684071411yescharacteristic
285C2D61⋊#9911yescharacteristic
286C2#1684074111yescharacteristic
subgroupG/H
centerC22C2×C22⋊#6923
commutatorC23×C61C22×C4
FrattiniC23C22×#6923
FittingC2×C22⋊C4×C61C4
socleC22×C61C2×C22⋊C4
hypercenterC2×C22⋊C4#6923
hypocenterC61#1964
LCSG ▷ C23×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C22⋊C4

Complements

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

NH ≅ G/Ntype
1. C2×#14519836C2semidirect
2. C2×#14519835C2semidirect
3. #16840704C2semidirect
4. C4×C22⋊#6923C2semidirect
15. C22×C22⋊D61C4semidirect
22. C2×#11758196C4semidirect
23. C2×#11758198C4semidirect
24. C2×C22⋊C4×C61C4semidirect
53. C22⋊#6923D4semidirect
133. Dic61#99semidirect
149. C61#1964semidirect
163. C2×C22⋊C4#6923semidirect