Finite Group Databasebeta

← #21450129

Subgroups — #21450129

Order 7808.

584 conjugacy classes of subgroups; only the 151 normal subgroups are shown.

normal subgroups only

This group has 584 conjugacy classes of subgroups — too many to draw. Only its 151 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×#14519737C211yesmaximal, characteristic
2C2×C4⋊C4×D61C211yesmaximal, characteristic, complemented
3#16839702C211yesmaximal, characteristic, complemented
4#16839700C211yesmaximal, characteristic, complemented
5#16839698C211yesmaximal, characteristic, complemented
6#16839657C212yesmaximal, complemented
7#16839638C212yesmaximal
8#16839633C212yesmaximal, complemented
9#16839621C211yesmaximal, characteristic, complemented
10#16839620C212yesmaximal, complemented
11C61×#399C211yesmaximal, characteristic, complemented
12C22×C22⋊D61C2211yescharacteristic
13C23×Dic61C2211yescharacteristic
14C22×C4×D61C2211yescharacteristic
15C22×C4×D61C2212yes—
16#14519737—24no—
17C2×C4⋊Dic61C2211yescharacteristic
18C2×#11758196C2212yes—
19C2×#11758196C2211yescharacteristic
20C2×#11758196C2212yes—
21C2×#11758196C2212yes—
22C4⋊C4×D61—24no—
23C2×C22⋊Dic61C2212yes—
24C2×#11758198C2211yescharacteristic
25C2×#11758198C2212yes—
26C2×C4×Dic61C2211yescharacteristic
27#14519684C2211yescharacteristic
28#14519684C2212yes—
29#14519684C2212yes—
30#14519684C2212yes—
31#14519684C2212yes—
32C2×C4⋊C4×C61C2211yescharacteristic
33C2×C4⋊C4×C61C2212yes—
34C2×C22⋊C4×C61C2211yescharacteristic
35C2×C22⋊C4×C61C2212yes—
36#95×C61C2211yescharacteristic
37C24×C61C2311yescharacteristic
38C23×D61C2311yescharacteristic
39C22×C4×C61C2312yes—
40C22×C4×C61C2312yes—
41C22×C4×C61C2311yescharacteristic
42C22×C4×C61C2311yescharacteristic
43C2×C22⋊D61—22no—
44C2×C22⋊D61—22no—
45C2×C22⋊D61Q814yes—
46C22×Dic61—22no—
47C22×Dic61—24no—
48C22×Dic61C2312yes—
49C22×Dic61C2311yescharacteristic
50C22×Dic61C2312yes—
51C22×Dic61C2311yescharacteristic
52C22×Dic61C2311yescharacteristic
53C2×C4×D61—24no—
54C2×C4×D61—24no—
55C2×C4×D61—42no—
56C2×C4×D61—42no—
57C2×C4×D61D414yes—
58C4⋊C4×C61—22no—
59C4⋊C4×C61—42no—
60C22⋊C4×C61—22no—
61C22⋊C4×C61—42no—
62C22⋊Dic61—42no—
63#11758198—22no—
64#11758198—24no—
65C4⋊Dic61—22no—
66#11758196—22no—
67#11758196—24no—
68#11758196—24no—
69#11758196—42no—
70C4×Dic61—22no—
71C23×C61—21no—
72C23×C61—22no—
73C23×C61—21no—
74C23×C61—22no—
75C23×C61C2×Q812yes—
76C23×C61C2411yescharacteristic
77C22×D61—22no—
78C22×D61—22no—
79C22×D61C2×D412yes—
80C22×D61C2×Q812yes—
81C22×D61#4112yes—
82C2×C4×C61—22no—
83C2×C4×C61—21no—
84C2×C4×C61—22no—
85C2×C4×C61—22no—
86C2×C4×C61—22no—
87C2×C4×C61—22no—
88C2×C4×C61—22no—
89C2×C4×C61—22no—
90C2×C4×C61—22no—
91C2×C4×C61C2×D412yes—
92C22⋊D61—28no—
93C2×Dic61—21no—
94C2×Dic61—21no—
95C2×Dic61—22no—
96C2×Dic61—21no—
97C2×Dic61—22no—
98C2×Dic61—22no—
99C2×Dic61—22no—
100C2×Dic61—22no—
101C2×Dic61—22no—
102C2×Dic61—22no—
103C2×Dic61—44no—
104C2×Dic61C2×D412yes—
105C2×Dic61C2×Q812yes—
106C2×Dic61#4114yes—
107C4×D61—28no—
108C4×D61—48no—
109C22×C61—22no—
110C22×C61—24no—
111C22×C61—41no—
112C22×C61—41no—
113C22×C61—42no—
114C22×C61C22×D411yescharacteristic
115C22×C61C22×Q811yescharacteristic
116C22×C61C2×#4111yescharacteristic
117C22×C61C2×#4112yes—
118C22×C61H(5,𝔽2)12yes—
119C2×D61—22no—
120C2×D61—22no—
121C2×D61—24no—
122C2×D61—24no—
123C2×D61C22⋊Q814yes—
124C4×C61—22no—
125C4×C61—42no—
126C4×C61—41no—
127C4×C61—42no—
128Dic61—22no—
129Dic61—41no—
130Dic61—42no—
131Dic61—42no—
132Dic61#12314yes—
133#2487—611nomaximal, Sylow
134C2×C61—42no—
135C2×C61C2×C22⋊Q811yescharacteristic
136C2×C61C2×#12311yescharacteristic
137C2×C61#53511yescharacteristic
138C2×C61#55312yes—
139C2×C61#55412yes—
140D61—24no—
141C2×C4×D4—611no—
142C22×C4⋊C4—611no—
143#400—611no—
144#400—611no—
145#399—611no—
146#399D6111yescharacteristic, complemented
147#389—612no—
148#386—612no—
149#385—612no—
150#380—612no—
151#380—611no—
152C61#248711yescharacteristic, complemented, Sylow
153C22×D4—611no—
154C23×C4—611no—
155C23×C4—611no—
156C23×C4—612no—
157C4×D4—1224no—
158C2×C4⋊C4—612no—
159C2×C4⋊C4—611no—
160C2×C4⋊C4—611no—
161C2×C4⋊C4—612no—
162C2×C4⋊C4—612no—
163C2×C4⋊C4—1224no—
164C2×C4⋊C4C2×D6111yescharacteristic
165C2×C4⋊C4C2×D6112yes—
166C2×C22⋊C4—611no—
167C2×C22⋊C4—612no—
168C2×C22⋊C4—612no—
169C2×C22⋊C4C2×D6111yescharacteristic
170C2×C22⋊C4C2×D6112yes—
171C2×C42—611no—
172#95—612no—
173#95—612no—
174#95—611no—
175#95—612no—
176#95—612no—
177#95C2×D6111yescharacteristic
178C24—611no—
179C24C22×D6111yescharacteristic
180C2×D4—614no—
181C2×D4—1222no—
182C2×D4—1222no—
183C22×C4—611no—
184C22×C4—611no—
185C22×C4—614no—
186C22×C4—611no—
187C22×C4—612no—
188C22×C4—612no—
189C22×C4—1224no—
190C22×C4—1224no—
191C22×C4—1222no—
192C22×C4—1224no—
193C22×C4—2442no—
194C22×C4—2442no—
195C22×C4C22×D6112yes—
196C22×C4C22×D6112yes—
197C22×C4C22×D6111yescharacteristic
198C22×C4C22×D6111yescharacteristic
199C4⋊C4—22no—
200C4⋊C4—42no—
201C4⋊C4—1224no—
202C4⋊C4—1224no—
203C4⋊C4—1222no—
204C4⋊C4—1222no—
205C4⋊C4—2442no—
206C22⋊C4—22no—
207C22⋊C4—42no—
208C22⋊C4—1222no—
209C22⋊C4—1224no—
210C22⋊C4—2442no—
211C42—1222no—
212C23—21no—
213C23—22no—
214C23—21no—
215C23—22no—
216C23—612no—
217C23—612no—
218C23—612no—
219C23—1222no—
220C23—1222no—
221C23Q8×D6112yes—
222C23C23×D6111yescharacteristic
223D4—1228no—
224C2×C4—22no—
225C2×C4—21no—
226C2×C4—22no—
227C2×C4—22no—
228C2×C4—22no—
229C2×C4—22no—
230C2×C4—22no—
231C2×C4—22no—
232C2×C4—22no—
233C2×C4—612no—
234C2×C4—614no—
235C2×C4—612no—
236C2×C4—1228no—
237C2×C4—1221no—
238C2×C4—1221no—
239C2×C4—1221no—
240C2×C4—1222no—
241C2×C4—1222no—
242C2×C4—1222no—
243C2×C4—1222no—
244C2×C4—1222no—
245C2×C4—1222no—
246C2×C4—1222no—
247C2×C4—2448no—
248C2×C4—2444no—
249C2×C4D4×D6112yes—
250C22—24no—
251C22—22no—
252C22—42no—
253C22—41no—
254C22—41no—
255C22—614no—
256C22—1224no—
257C22—1224no—
258C22—1222no—
259C22—1222no—
260C22C2×D4×D6111yescharacteristic
261C22C2×Q8×D6111yescharacteristic
262C22#41×D6111yescharacteristic
263C22#41×D6112yes—
264C22#1451982212yes—
265C4—22no—
266C4—42no—
267C4—41no—
268C4—42no—
269C4—614no—
270C4—1222no—
271C4—2442no—
272C4—2441no—
273C4—2442no—
274C2—42no—
275C2—1224no—
276C2C22⋊Q8×D6111yescharacteristic
277C2#123×D6111yescharacteristic
278C2#1684032511yescharacteristic
279C2#1684045712yes—
280C2#1684046612yes—
subgroupG/H
center, FrattiniC23C23×D61
commutator, socleC23×C61C24
FittingC61×#399C2
hypercenter#399D61
hypocenterC61#2487
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C23 ◁ #399

Complements

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

NH ≅ G/Ntype
2. C2×C4⋊C4×D61C2semidirect
3. #16839702C2semidirect
4. #16839700C2semidirect
5. #16839698C2semidirect
6. #16839657C2semidirect
8. #16839633C2semidirect
9. #16839621C2semidirect
10. #16839620C2semidirect
11. C61×#399C2semidirect
146. #399D61semidirect
152. C61#2487semidirect