Finite Group Databasebeta

← #21450292

Subgroups — #21450292

Order 7808.

544 conjugacy classes of subgroups; only the 161 normal subgroups are shown.

normal subgroups only

This group has 544 conjugacy classes of subgroups — too many to draw. Only its 161 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×#14519755C211yesmaximal, characteristic
2C2×C4⋊C4×D61C211yesmaximal, characteristic
3#16839694C211yesmaximal, characteristic, complemented
4#16839693C211yesmaximal, characteristic, complemented
5#16839692C211yesmaximal, characteristic, complemented
6#16839666C212yesmaximal, complemented
7#16839636C212yesmaximal
8#16839633C212yesmaximal
9#16839631C212yesmaximal, complemented
10#16839609C211yesmaximal, characteristic
11C61×#398C211yesmaximal, characteristic, complemented
12C22×Dic122C2211yescharacteristic
13C22×C4×D61C2211yescharacteristic
14C22×C4×D61C2212yes—
15#14519755—24no—
16C2×C4⋊Dic61C2211yescharacteristic
17C2×C4⋊Dic61C2212yes—
18C2×#11758196C2211yescharacteristic
19C2×#11758196C2212yes—
20C2×#11758196C2211yescharacteristic
21C2×#11758196C2212yes—
22C2×#11758196C2212yes—
23C4⋊C4×D61—24no—
24C2×#11758198C2211yescharacteristic
25C2×#11758198C2211yescharacteristic
26C2×#11758198C2212yes—
27C2×C4×Dic61C2212yes—
28#14519684C2211yescharacteristic
29#14519684C2212yes—
30#14519684C2212yes—
31#14519684C2212yes—
32C2×C4⋊C4×C61C2211yescharacteristic
33C2×C4⋊C4×C61C2211yescharacteristic
34C2×C4⋊C4×C61C2212yes—
35#95×C61C2211yescharacteristic
36#95×C61C2212yes—
37C23×D61C2311yescharacteristic
38C22×C4×C61C2312yes—
39C22×C4×C61C2311yescharacteristic
40C22×C4×C61C2311yescharacteristic
41C22×C4×C61C2311yescharacteristic
42C22×C4×C61C2312yes—
43C22×Dic61C2312yes—
44C22×Dic61C2311yescharacteristic
45C22×Dic61C2311yescharacteristic
46C22×Dic61C2312yes—
47C22×Dic61C2311yescharacteristic
48C2×C4×D61—24no—
49C2×C4×D61—24no—
50C2×C4×D61—42no—
51C2×C4×D61—42no—
52C2×C4×D61D414yes—
53C2×Dic122—22no—
54C2×Dic122—24no—
55C4⋊C4×C61—22no—
56C4⋊C4×C61—22no—
57C4⋊C4×C61—42no—
58#11758198—22no—
59#11758198—22no—
60#11758198Q818yescomplemented
61C4⋊Dic61—22no—
62C4⋊Dic61—42no—
63#11758196—22no—
64#11758196—24no—
65#11758196—22no—
66#11758196—42no—
67#11758196—42no—
68C4×Dic61—24no—
69C23×C61C2411yescharacteristic
70C22×D61—22no—
71C22×D61—21no—
72C22×D61—21no—
73C22×D61C2×D412yes—
74C22×D61C2×Q814yes—
75C2×C4×C61—22no—
76C2×C4×C61—22no—
77C2×C4×C61—22no—
78C2×C4×C61—21no—
79C2×C4×C61—22no—
80C2×C4×C61—21no—
81C2×C4×C61—22no—
82C2×C4×C61—21no—
83C2×C4×C61—22no—
84C2×C4×C61—21no—
85C2×C4×C61—22no—
86C2×C4×C61C2×D412yes—
87C2×C4×C61C2×Q814yes—
88C2×Dic61—22no—
89C2×Dic61—22no—
90C2×Dic61—21no—
91C2×Dic61—22no—
92C2×Dic61—21no—
93C2×Dic61—22no—
94C2×Dic61—21no—
95C2×Dic61—22no—
96C2×Dic61—21no—
97C2×Dic61—22no—
98C2×Dic61C2×D412yes—
99C2×Dic61C2×Q814yes—
100C2×Dic61#4114yes—
101C4×D61—28no—
102C4×D61—48no—
103Dic122—44no—
104C22×C61C22×D411yescharacteristic
105C22×C61C22×Q812yes—
106C22×C61C2×#4112yes—
107C22×C61H(5,𝔽2)11yescharacteristic
108C22×C61H(5,𝔽2)11yescharacteristic
109C2×D61—22no—
110C2×D61—22no—
111C2×D61—24no—
112C2×D61—24no—
113C2×D61C4⋊Q814yes—
114C4×C61—22no—
115C4×C61—24no—
116C4×C61—41no—
117C4×C61—42no—
118C4×C61—41no—
119Dic61—24no—
120Dic61—41no—
121Dic61—42no—
122Dic61—41no—
123Dic61#12314yes—
124#2502—611nomaximal, Sylow
125C2×C61C2×#12311yescharacteristic
126C2×C61C2×C4⋊Q811yescharacteristic
127C2×C61#53511yescharacteristic
128C2×C61#55412yes—
129C2×C61#55412yes—
130D61—24no—
131C2×C22⋊Q8—611no—
132C22×C4⋊C4—611no—
133#398—611no—
134#398—611no—
135#398—611no—
136#398D6111yescharacteristic, complemented
137#391—612no—
138#385—612no—
139#385—612no—
140#384—612no—
141C4×C22⋊C4—611no—
142C61#250211yescharacteristic, complemented, Sylow
143C22×Q8—611no—
144C23×C4—611no—
145C23×C4—612no—
146C22⋊Q8—1224no—
147C2×C4⋊C4—612no—
148C2×C4⋊C4—611no—
149C2×C4⋊C4—611no—
150C2×C4⋊C4—611no—
151C2×C4⋊C4—612no—
152C2×C4⋊C4—612no—
153C2×C4⋊C4—612no—
154C2×C4⋊C4—1224no—
155C2×C4⋊C4C2×D6111yescharacteristic
156C2×C4⋊C4C2×D6111yescharacteristic
157C2×C4⋊C4C2×D6112yes—
158C2×C22⋊C4—612no—
159C2×C22⋊C4—611no—
160C2×C22⋊C4—611no—
161C2×C42—612no—
162#95—611no—
163#95—612no—
164#95—612no—
165#95—612no—
166#95C2×D6111yescharacteristic
167#95C2×D6112yes—
168C24—611no—
169C2×Q8—1222no—
170C2×Q8—1224no—
171C22×C4—611no—
172C22×C4—612no—
173C22×C4—614no—
174C22×C4—611no—
175C22×C4—612no—
176C22×C4—611no—
177C22×C4—1224no—
178C22×C4—1224no—
179C22×C4—2442no—
180C22×C4—2442no—
181C22×C4C22×D6111yescharacteristic
182C22×C4C22×D6112yes—
183C22×C4C22×D6111yescharacteristic
184C22×C4C22×D6111yescharacteristic
185C22×C4C22×D6112yes—
186C4⋊C4—22no—
187C4⋊C4—22no—
188C4⋊C4—42no—
189C4⋊C4—1224no—
190C4⋊C4—1222no—
191C4⋊C4—1222no—
192C4⋊C4—1222no—
193C4⋊C4—2442no—
194C4⋊C4—2442no—
195C4⋊C4—2442no—
196C22⋊C4—618no—
197C22⋊C4—1222no—
198C22⋊C4—1222no—
199C42—1224no—
200C23—612no—
201C23—614no—
202C23—1222no—
203C23—1221no—
204C23—1221no—
205C23C23×D6111yescharacteristic
206Q8—2444no—
207C2×C4—22no—
208C2×C4—22no—
209C2×C4—22no—
210C2×C4—21no—
211C2×C4—21no—
212C2×C4—22no—
213C2×C4—22no—
214C2×C4—21no—
215C2×C4—22no—
216C2×C4—21no—
217C2×C4—22no—
218C2×C4—612no—
219C2×C4—614no—
220C2×C4—614no—
221C2×C4—1228no—
222C2×C4—1222no—
223C2×C4—1222no—
224C2×C4—1221no—
225C2×C4—1221no—
226C2×C4—1222no—
227C2×C4—1222no—
228C2×C4—1221no—
229C2×C4—1222no—
230C2×C4—1221no—
231C2×C4—1222no—
232C2×C4—2448no—
233C2×C4D4×D6112yes—
234C2×C4Q8×D6114yes—
235C22—614no—
236C22—1224no—
237C22—1224no—
238C22—1222no—
239C22—1222no—
240C22C2×D4×D6111yescharacteristic
241C22C2×Q8×D6112yes—
242C22#41×D6112yes—
243C22#1451982211yescharacteristic
244C22#1451982311yescharacteristic
245C4—24no—
246C4—22no—
247C4—41no—
248C4—41no—
249C4—42no—
250C4—614no—
251C4—1224no—
252C4—2441no—
253C4—2441no—
254C4—2442no—
255C2—1224no—
256C2#123×D6111yescharacteristic
257C2C4⋊Q8×D6111yescharacteristic
258C2#1684032811yescharacteristic
259C2#1684046612yes—
260C2#1684046812yes—
subgroupG/H
center, FrattiniC23C23×D61
commutator, socleC23×C61C24
FittingC61×#398C2
hypercenter#398D61
hypocenterC61#2502
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C23 ◁ #398

Complements

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

NH ≅ G/Ntype
3. #16839694C2semidirect
4. #16839693C2semidirect
5. #16839692C2semidirect
6. #16839666C2semidirect
9. #16839631C2semidirect
11. C61×#398C2semidirect
60. #11758198Q8semidirect
136. #398D61semidirect
142. C61#2502semidirect