Finite Group Databasebeta

← #21449458

Subgroups — #21449458

Order 7808.

800 conjugacy classes of subgroups; only the 181 normal subgroups are shown.

normal subgroups only

This group has 800 conjugacy classes of subgroups — too many to draw. Only its 181 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×Q8×D61C211yesmaximal, characteristic
2C2×#14519776C212yesmaximal, complemented
3C2×#14519755C211yesmaximal, characteristic
4#16839683C211yesmaximal, characteristic, complemented
5#16839682C211yesmaximal, characteristic, complemented
6#16839681C211yesmaximal, characteristic, complemented
7#16839666C212yesmaximal, complemented
8#16839636C212yesmaximal
9#16839633C212yesmaximal
10#16839609C211yesmaximal, characteristic
11C61×#395C211yesmaximal, characteristic, complemented
12C22×Dic122C2211yescharacteristic
13C22×Dic122C2211yescharacteristic
14C22×Dic122C2212yes—
15C2×Q8×D61—24no—
16C2×Q8×D61—28no—
17C22×C4×D61C2212yes—
18C22×C4×D61C2211yescharacteristic
19#14519776—28no—
20#14519755—24no—
21C2×C4⋊Dic61C2212yes—
22C2×#11758196C2211yescharacteristic
23C2×#11758196C2212yes—
24C2×#11758196C2212yes—
25C2×#11758196C2211yescharacteristic
26C2×#11758198C2211yescharacteristic
27C2×#11758198C2211yescharacteristic
28C2×#11758198C2212yes—
29C2×C4×Dic61C2212yes—
30#14519684C2211yescharacteristic
31#14519684C2212yes—
32#14519684C2212yes—
33#14519684C2212yes—
34C22×Q8×C61C2211yescharacteristic
35C2×C4⋊C4×C61C2211yescharacteristic
36C2×C4⋊C4×C61C2212yes—
37#95×C61C2211yescharacteristic
38#95×C61C2212yes—
39C23×D61C2311yescharacteristic
40C2×Q8×C61—22no—
41C2×Q8×C61—24no—
42C22×C4×C61C2311yescharacteristic
43C22×C4×C61C2311yescharacteristic
44C22×C4×C61C2311yescharacteristic
45C22×C4×C61C2312yes—
46C22×C4×C61C2312yes—
47C22×Dic61C2311yescharacteristic
48C22×Dic61C2311yescharacteristic
49C22×Dic61C2312yes—
50C22×Dic61C2312yes—
51C22×Dic61C2311yescharacteristic
52Q8×D61—232no—
53C2×C4×D61—24no—
54C2×C4×D61—24no—
55C2×C4×D61—24no—
56C2×C4×D61—24no—
57C2×C4×D61D414yes—
58C2×Dic122—22no—
59C2×Dic122—24no—
60C2×Dic122—24no—
61C2×Dic122—24no—
62C2×Dic122—22no—
63C2×Dic122—24no—
64C2×Dic122D418yes—
65C4⋊C4×C61—22no—
66C4⋊C4×C61—24no—
67#11758198—22no—
68#11758198—22no—
69#11758198Q818yescomplemented
70C4⋊Dic61—24no—
71#11758196—22no—
72#11758196—24no—
73#11758196—22no—
74#11758196—24no—
75C4×Dic61—24no—
76C23×C61C2411yescharacteristic
77C22×D61—22no—
78C22×D61—21no—
79C22×D61—21no—
80C22×D61C2×D412yes—
81C22×D61C2×Q814yes—
82Q8×C61—28no—
83C2×C4×C61—22no—
84C2×C4×C61—22no—
85C2×C4×C61—22no—
86C2×C4×C61—22no—
87C2×C4×C61—22no—
88C2×C4×C61—21no—
89C2×C4×C61—22no—
90C2×C4×C61—21no—
91C2×C4×C61—21no—
92C2×C4×C61—21no—
93C2×C4×C61C2×D412yes—
94C2×C4×C61C2×D414yes—
95C2×C4×C61C2×Q814yescomplemented
96C2×Dic61—22no—
97C2×Dic61—22no—
98C2×Dic61—22no—
99C2×Dic61—22no—
100C2×Dic61—21no—
101C2×Dic61—22no—
102C2×Dic61—21no—
103C2×Dic61—21no—
104C2×Dic61—21no—
105C2×Dic61C2×D414yes—
106C2×Dic61C2×D414yes—
107C2×Dic61C2×D412yes—
108C2×Dic61C2×Q814yescomplemented
109C4×D61—216no—
110C4×D61—28no—
111Dic122—28no—
112Dic122—216no—
113Dic122—44no—
114C22×C61C22×D411yescharacteristic
115C22×C61C22×D412yes—
116C22×C61C22×Q812yes—
117C22×C612−1+411yescharacteristic
118C22×C612−1+411yescharacteristic
119C2×D61—22no—
120C2×D61—22no—
121C2×D61—24no—
122C2×D61—24no—
123C2×D61C4⋊Q814yescomplemented
124C4×C61—22no—
125C4×C61—24no—
126C4×C61—24no—
127C4×C61—41no—
128C4×C61—41no—
129Dic61—24no—
130Dic61—24no—
131Dic61—41no—
132Dic61—41no—
133Dic61#12014yes—
134#2434—611nomaximal, Sylow
135C2×C61C2×#12011yescharacteristic
136C2×C61C2×C4⋊Q811yescharacteristic
137C2×C61#53611yescharacteristic
138C2×C61D4×Q812yes—
139C2×C61D4×Q812yes—
140D61—24no—
141C23×Q8—611no—
142C2×C4⋊Q8—612no—
143C2×C22⋊Q8—611no—
144#395—611no—
145#395—611no—
146#395—611no—
147#395D6111yescharacteristic, complemented
148#391—612no—
149#385—612no—
150#385—612no—
151C4×C22⋊C4—611no—
152C61#243411yescharacteristic, complemented, Sylow
153C22×Q8—612no—
154C22×Q8—611no—
155C22×Q8—611no—
156C22×Q8—1224no—
157C22×Q8—1228no—
158C22×Q8C2×D6111yescharacteristic
159C23×C4—611no—
160C23×C4—612no—
161C4⋊Q8—1228no—
162C22⋊Q8—1224no—
163C2×C4⋊C4—611no—
164C2×C4⋊C4—611no—
165C2×C4⋊C4—612no—
166C2×C4⋊C4—612no—
167C2×C4⋊C4—612no—
168C2×C4⋊C4C2×D6111yescharacteristic
169C2×C4⋊C4C2×D6112yes—
170C2×C22⋊C4—612no—
171C2×C22⋊C4—611no—
172C2×C22⋊C4—611no—
173C2×C42—612no—
174#95—611no—
175#95—612no—
176#95—612no—
177#95—612no—
178#95C2×D6111yescharacteristic
179#95C2×D6112yes—
180C24—611no—
181C2×Q8—22no—
182C2×Q8—24no—
183C2×Q8—618no—
184C2×Q8—1224no—
185C2×Q8—1224no—
186C2×Q8—1224no—
187C2×Q8—1222no—
188C2×Q8—1224no—
189C2×Q8—12232no—
190C2×Q8—1222no—
191C22×C4—611no—
192C22×C4—612no—
193C22×C4—612no—
194C22×C4—614no—
195C22×C4—611no—
196C22×C4—611no—
197C22×C4—1224no—
198C22×C4—1224no—
199C22×C4—1224no—
200C22×C4—1224no—
201C22×C4C22×D6111yescharacteristic
202C22×C4C22×D6111yescharacteristic
203C22×C4C22×D6111yescharacteristic
204C22×C4C22×D6112yes—
205C22×C4C22×D6112yes—
206C4⋊C4—22no—
207C4⋊C4—24no—
208C4⋊C4—1222no—
209C4⋊C4—1224no—
210C4⋊C4—1224no—
211C4⋊C4—1222no—
212C4⋊C4—1224no—
213C22⋊C4—618no—
214C22⋊C4—1222no—
215C22⋊C4—1222no—
216C42—1224no—
217C23—612no—
218C23—614no—
219C23—1222no—
220C23—1221no—
221C23—1221no—
222C23C23×D6111yescharacteristic
223Q8—28no—
224Q8—12216no—
225Q8—1228no—
226Q8—2444no—
227C2×C4—22no—
228C2×C4—22no—
229C2×C4—22no—
230C2×C4—22no—
231C2×C4—22no—
232C2×C4—21no—
233C2×C4—21no—
234C2×C4—22no—
235C2×C4—21no—
236C2×C4—21no—
237C2×C4—614no—
238C2×C4—612no—
239C2×C4—614no—
240C2×C4—614no—
241C2×C4—1228no—
242C2×C4—12216no—
243C2×C4—1222no—
244C2×C4—1222no—
245C2×C4—1222no—
246C2×C4—1222no—
247C2×C4—1221no—
248C2×C4—1221no—
249C2×C4—1222no—
250C2×C4—1221no—
251C2×C4—1221no—
252C2×C4D4×D6112yes—
253C2×C4D4×D6114yes—
254C2×C4Q8×D6114yescomplemented
255C22—614no—
256C22—1222no—
257C22—1222no—
258C22—1224no—
259C22—1224no—
260C22C2×D4×D6111yescharacteristic
261C22C2×D4×D6112yes—
262C22C2×Q8×D6112yes—
263C22#1451982411yescharacteristic
264C22#1451982511yescharacteristic
265C4—22no—
266C4—24no—
267C4—24no—
268C4—41no—
269C4—41no—
270C4—614no—
271C4—1224no—
272C4—1224no—
273C4—2441no—
274C4—2441no—
275C2—1224no—
276C2#120×D6111yescharacteristic
277C2C4⋊Q8×D6111yescharacteristic
278C2#1684033511yescharacteristic
279C2#1684042512yes—
280C2#1684042712yes—
subgroupG/H
center, FrattiniC23C23×D61
commutator, socleC23×C61C24
FittingC61×#395C2
hypercenter#395D61
hypocenterC61#2434
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C23 ◁ #395

Complements

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

NH ≅ G/Ntype
2. C2×#14519776C2semidirect
4. #16839683C2semidirect
5. #16839682C2semidirect
6. #16839681C2semidirect
7. #16839666C2semidirect
11. C61×#395C2semidirect
69. #11758198Q8semidirect
95. C2×C4×C61C2×Q8semidirect
108. C2×Dic61C2×Q8semidirect
123. C2×D61C4⋊Q8semidirect
147. #395D61semidirect
152. C61#2434semidirect
254. C2×C4Q8×D61semidirect