Finite Group Databasebeta

← #21461004

Subgroups — #21461004

Order 7808.

564 conjugacy classes of subgroups; only the 140 normal subgroups are shown.

normal subgroups only

This group has 564 conjugacy classes of subgroups — too many to draw. Only its 140 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×C4⋊#6923C211yesmaximal, characteristic
2C2×(C2×#6923)⋊C4C212yesmaximal
3C2×(C2×#6923)⋊C4C211yesmaximal, characteristic
4C2×(C2×#6923)⋊C4C212yesmaximal
5C2×C4⋊C4×D61C211yesmaximal, characteristic
6C23×#6923C2212yes—
7C23×#6923C2212yes—
8C2×C4⋊#6923—24no—
9C2×C4⋊#6923—22no—
10(C2×#6923)⋊C4—24no—
11(C2×#6923)⋊C4—22no—
12(C2×#6923)⋊C4—24no—
13C22×C4×D61C2211yescharacteristic
14C22×C4×D61C2211yescharacteristic
15C22×C4×D61C2211yescharacteristic
16C2×C4⋊Dic61C411yescharacteristic, complemented
17C2×#11758196C411yescharacteristic, complemented
18C2×#11758196C411yescharacteristic, complemented
19C4⋊C4×D61—22no—
20C4⋊C4×D61—22no—
21C2×C4⋊C4×C61C411yescharacteristic, complemented
22C23×D61C2311yescharacteristic
23C22×#6923—22no—
24C22×#6923—22no—
25C22×#6923—22no—
26C22×#6923—22no—
27C22×#6923—22no—
28C22×#6923—22no—
29C22×#6923—22no—
30C22×#6923—22no—
31C22×#6923—22no—
32C22×#6923—22no—
33C22×#6923—22no—
34C22×#6923—22no—
35C22×#6923D414yes—
36C22×#6923Q814yes—
37C22×C4×C61C2×C411yescharacteristic
38C22×C4×C61C2×C411yescharacteristic
39C22×C4×C61C2×C411yescharacteristic
40C22×Dic61C2×C411yescharacteristic
41C22×Dic61C2×C411yescharacteristic
42C22×Dic61C2×C411yescharacteristic
43C2×C4×D61—22no—
44C2×C4×D61—21no—
45C2×C4×D61—21no—
46C2×C4×D61—21no—
47C2×C4×D61—21no—
48C2×C4×D61—22no—
49C2×C4×D61—22no—
50C2×C4×D61—21no—
51C2×C4×D61—21no—
52C2×C4×D61—22no—
53C2×C4×D61D412yes—
54C2×C4×D61D412yes—
55C2×C4×D61D412yes—
56C2×C4×D61Q812yes—
57C4⋊#6923—28no—
58C4⋊C4×C61—22no—
59C4⋊Dic61—22no—
60#11758196—22no—
61#11758196—22no—
62C23×C61C22×C411yescharacteristic
63C22×D61C2×D412yes—
64C22×D61C2×D411yescharacteristic
65C22×D61C2×D411yescharacteristic
66C22×D61C2×D411yescharacteristic
67C22×D61C2×Q812yes—
68C22×D61C2×Q811yescharacteristic
69C22×D61#4111yescharacteristic
70C22×D61#4111yescharacteristic
71C22×D61#4112yes—
72C22×D61#4112yes—
73C2×#6923—24no—
74C2×#6923—24no—
75C2×#6923—24no—
76C2×#6923—24no—
77C2×#6923—24no—
78C2×#6923—24no—
79C2×#6923—42no—
80C2×#6923—42no—
81C2×#6923—42no—
82C2×#6923—42no—
83C2×#6923—42no—
84C2×#6923—42no—
85C2×#6923—42no—
86C2×#6923—42no—
87C2×C4×C61—21no—
88C2×C4×C61—21no—
89C2×C4×C61—22no—
90C2×C4×C61—21no—
91C2×C4×C61—22no—
92C2×C4×C61C22⋊C412yes—
93C2×C4×C61C4⋊C412yescomplemented
94C2×Dic61—21no—
95C2×Dic61—21no—
96C2×Dic61—22no—
97C2×Dic61—21no—
98C2×Dic61—22no—
99C2×Dic61C22⋊C412yes—
100C2×Dic61C4⋊C412yescomplemented
101C4×D61—22no—
102C4×D61—22no—
103C4×D61—22no—
104C4×D61—24no—
105C4×D61—22no—
106C4×D61—22no—
107C4×D61—22no—
108C4×D61—41no—
109C4×D61—42no—
110C4×D61—41no—
111C22×C61C2×C22⋊C411yescharacteristic
112C22×C61C2×C4⋊C411yescharacteristic
113C22×C61#11711yescharacteristic
114C22×C61C4×D412yes—
115C22×C61C4×Q812yes—
116C2×D61#12011yescharacteristic
117C2×D61#12112yes—
118C2×D61#12111yescharacteristic
119C2×D61#12111yescharacteristic
120C2×D61#12112yes—
121C2×D61C22⋊Q812yes—
122C2×D61C22⋊Q811yescharacteristic
123C2×D61C22⋊Q812yes—
124C2×D61C22⋊Q812yes—
125C2×D61C22⋊Q811yescharacteristic
126C2×D61#12312yes—
127C2×D61#12311yescharacteristic
128C2×D61#12411yescharacteristic
129C2×D61#12512yes—
130C2×D61#12512yes—
131C2×D61#12612yes—
132C2×D61C4⋊Q812yes—
133C2×D61C4⋊Q811yescharacteristic
134#6923—44no—
135#6923—44no—
136C4×C61—22no—
137C4×C61—22no—
138C4×C61—41no—
139Dic61—22no—
140Dic61—22no—
141Dic61—41no—
142#1441—611nomaximal, Sylow
143C2×C61#38011yescharacteristic
144C2×C61#38611yescharacteristic
145C2×C61#38712yes—
146C2×C61#38912yes—
147C2×C61#39111yescharacteristic
148D61#39411yescharacteristic
149D61#39511yescharacteristic
150D61#39612yes—
151D61#39811yescharacteristic
152D61#39812yes—
153D61#40011yescharacteristic
154C22×C4⋊C4—611no—
155C22×C4⋊C4—611no—
156C2×#95—611no—
157C2×#95—612no—
158C2×#95—612no—
159C61#144111yescharacteristic, complemented, Sylow
160C23×C4—611no—
161C23×C4—611no—
162C23×C4—612no—
163C23×C4—612no—
164C23×C4—611no—
165C2×C4⋊C4—611no—
166C2×C4⋊C4—611no—
167C2×C4⋊C4—611no—
168C2×C4⋊C4—1222no—
169C2×C4⋊C4—1222no—
170C2×C4⋊C4—1222no—
171C2×C4⋊C4—1224no—
172C2×C4⋊C4#692311yescharacteristic, complemented
173#95—1224no—
174#95—1222no—
175#95—1224no—
176C24—611no—
177C22×C4—611no—
178C22×C4—611no—
179C22×C4—612no—
180C22×C4—612no—
181C22×C4—612no—
182C22×C4—612no—
183C22×C4—614no—
184C22×C4—614no—
185C22×C4—611no—
186C22×C4—1221no—
187C22×C4—1221no—
188C22×C4—1222no—
189C22×C4—1221no—
190C22×C4—1221no—
191C22×C4—1222no—
192C22×C4—1222no—
193C22×C4—1221no—
194C22×C4—1221no—
195C22×C4—1222no—
196C22×C4—1222no—
197C22×C4—1222no—
198C22×C4—1222no—
199C22×C4—1222no—
200C22×C4—1222no—
201C22×C4—1222no—
202C22×C4—1222no—
203C22×C4—1222no—
204C22×C4—1222no—
205C22×C4—1222no—
206C22×C4—1222no—
207C22×C4—1222no—
208C22×C4C2×#692311yescharacteristic
209C22×C4C2×#692311yescharacteristic
210C22×C4C2×#692311yescharacteristic
211C4⋊C4—22no—
212C4⋊C4—1222no—
213C4⋊C4—1222no—
214C4⋊C4—1228no—
215C4⋊C4—1222no—
216C23—611no—
217C23—611no—
218C23—611no—
219C23—611no—
220C23—611no—
221C23—611no—
222C23—612no—
223C23—612no—
224C23—612no—
225C23—612no—
226C23C22×#692311yescharacteristic
227C2×C4—21no—
228C2×C4—21no—
229C2×C4—22no—
230C2×C4—21no—
231C2×C4—22no—
232C2×C4—612no—
233C2×C4—612no—
234C2×C4—1222no—
235C2×C4—1222no—
236C2×C4—1222no—
237C2×C4—1222no—
238C2×C4—1222no—
239C2×C4—1224no—
240C2×C4—1222no—
241C2×C4—1221no—
242C2×C4—1221no—
243C2×C4—1222no—
244C2×C4—1224no—
245C2×C4—1224no—
246C2×C4—1224no—
247C2×C4—1224no—
248C2×C4—1224no—
249C2×C4—1224no—
250C2×C4—1221no—
251C2×C4—1222no—
252C2×C4—2441no—
253C2×C4—2442no—
254C2×C4—2441no—
255C2×C4—2442no—
256C2×C4—2442no—
257C2×C4—2442no—
258C2×C4—2442no—
259C2×C4—2442no—
260C2×C4—2442no—
261C2×C4—2442no—
262C2×C4—2442no—
263C2×C4C4⋊#692312yescomplemented
264C2×C4C22⋊#692312yes—
265C22—611no—
266C22—611no—
267C22—611no—
268C22—611no—
269C22—611no—
270C22—612no—
271C22—611no—
272C22—612no—
273C22—612no—
274C22—612no—
275C22—612no—
276C22—612no—
277C22—612no—
278C22—612no—
279C22—612no—
280C22—612no—
281C22—611no—
282C22—611no—
283C22C2×C22⋊#692311yescharacteristic
284C22C2×C4⋊#692311yescharacteristic
285C22#1451985611yescharacteristic
286C22D4×#692312yes—
287C22Q8×#692312yes—
288C4—22no—
289C4—22no—
290C4—41no—
291C4—1222no—
292C4—1222no—
293C4—2444no—
294C4—2444no—
295C4—2441no—
296C2—611no—
297C2—612no—
298C2—611no—
299C2—611no—
300C2—612no—
301C2—611no—
302C2#1684070411yescharacteristic
303C2#1684071011yescharacteristic
304C2#1684071112yes—
305C2#1684071312yes—
306C2(C2×#6923)⋊Q811yescharacteristic
subgroupG/H
center, FrattiniC23C22×#6923
commutator, socleC23×C61C22×C4
FittingC2×C4⋊C4×C61C4
hypercenterC2×C4⋊C4#6923
hypocenterC61#1441
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C4⋊C4

Complements

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

NH ≅ G/Ntype
16. C2×C4⋊Dic61C4semidirect
17. C2×#11758196C4semidirect
18. C2×#11758196C4semidirect
21. C2×C4⋊C4×C61C4semidirect
93. C2×C4×C61C4⋊C4semidirect
100. C2×Dic61C4⋊C4semidirect
159. C61#1441semidirect
172. C2×C4⋊C4#6923semidirect
263. C2×C4C4⋊#6923semidirect