Finite Group Databasebeta

← #21453834

Subgroups — #21453834

Order 7808.

478 conjugacy classes of subgroups; only the 133 normal subgroups are shown.

normal subgroups only

This group has 478 conjugacy classes of subgroups — too many to draw. Only its 133 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×#14519760C211yesmaximal, characteristic
2C2×#14519756C211yesmaximal, characteristic, complemented
3#16839694C211yesmaximal, characteristic, complemented
4#16839692C212yesmaximal, complemented
5#16839689C211yesmaximal, characteristic, complemented
6#16839687C212yesmaximal, complemented
7#16839684C212yesmaximal, complemented
8#16839683C211yesmaximal, characteristic, complemented
9#16839678C212yesmaximal
10#16839675C211yesmaximal, characteristic, complemented
11C61×#380C211yesmaximal, characteristic, complemented
12C22×Dic122C2211yescharacteristic
13C22×C22⋊D61C2211yescharacteristic
14#14519760—24no—
15#14519756—24no—
16C2×C4⋊Dic61C2211yescharacteristic
17C2×C4⋊Dic61C2212yes—
18C2×C4⋊Dic61C2212yes—
19C2×#11758196C2211yescharacteristic
20C2×#11758196C2212yes—
21C2×#11758196C2211yescharacteristic
22C2×C22⋊Dic61C2211yescharacteristic
23C2×C22⋊Dic61C2212yes—
24C2×#11758198C2211yescharacteristic
25C2×#11758198C2211yescharacteristic
26C2×#11758198C2212yes—
27C2×#11758198C2212yes—
28#14519684C2212yes—
29#14519684C2212yes—
30#14519684C2212yes—
31#14519684C2212yes—
32C23×C4×C61C2211yescharacteristic
33C2×C4⋊C4×C61C2212yes—
34C2×C22⋊C4×C61C2212yes—
35#95×C61C2211yescharacteristic
36#95×C61C2211yescharacteristic
37C24×C61C2311yescharacteristic
38C23×D61C2311yescharacteristic
39C22×C4×C61—42no—
40C22×C4×C61D414yes—
41C22×C4×C61C2312yes—
42C22×C4×C61C2312yes—
43C22×C4×C61C2311yescharacteristic
44C22×C4×C61C2311yescharacteristic
45C2×C22⋊D61—22no—
46C2×C22⋊D61—42no—
47C22×Dic61C2311yescharacteristic
48C22×Dic61C2312yes—
49C22×Dic61C2311yescharacteristic
50C22×Dic61C2312yes—
51C22×Dic61C2311yescharacteristic
52C2×Dic122—22no—
53C2×Dic122—42no—
54C4⋊C4×C61—42no—
55C22⋊C4×C61—42no—
56C22⋊Dic61—24no—
57C22⋊Dic61—22no—
58#11758198—22no—
59#11758198—22no—
60#11758198—42no—
61#11758198—42no—
62C4⋊Dic61—22no—
63C4⋊Dic61—42no—
64C4⋊Dic61—42no—
65#11758196—24no—
66#11758196—22no—
67#11758196—22no—
68C23×C61—21no—
69C23×C61—22no—
70C23×C61—22no—
71C23×C61—21no—
72C23×C61C2×D412yes—
73C23×C61C2411yescharacteristic
74C22×D61—21no—
75C22×D61—21no—
76C22×D61—22no—
77C22×D61—22no—
78C22×D61—21no—
79C2×C4×C61—22no—
80C2×C4×C61—22no—
81C2×C4×C61—22no—
82C2×C4×C61—22no—
83C2×C4×C61—22no—
84C2×C4×C61—22no—
85C2×C4×C61—22no—
86C2×C4×C61—22no—
87C2×C4×C61—44no—
88C2×C4×C61C2×D412yes—
89C2×C4×C61C2×D412yes—
90C22⋊D61—44no—
91C2×Dic61—21no—
92C2×Dic61—22no—
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—21no—
104Dic122—44no—
105C22×C61—22no—
106C22×C61—22no—
107C22×C61—22no—
108C22×C61—42no—
109C22×C61—42no—
110C22×C61C22×D411yescharacteristic
111C22×C61H(5,𝔽2)12yes—
112C22×C61H(5,𝔽2)11yescharacteristic
113C22×C612−1+412yes—
114C22×C612−1+411yescharacteristic
115C2×D61—41no—
116C2×D61—41no—
117C2×D61—41no—
118C2×D61—42no—
119C2×D61—42no—
120C4×C61—22no—
121C4×C61—22no—
122C4×C61—42no—
123C4×C61—42no—
124Dic61—42no—
125Dic61—41no—
126Dic61—41no—
127Dic61—42no—
128Dic61—41no—
129#2814—611nomaximal, Sylow
130C2×C61—42no—
131C2×C61#53411yescharacteristic
132C2×C61#53611yescharacteristic
133C2×C61#53711yescharacteristic
134C2×C61#56212yes—
135C2×C61#56312yes—
136D61—81no—
137C2×#123—611no—
138C2×C22⋊Q8—611no—
139#398—612no—
140#398—611no—
141#397—612no—
142#397—611no—
143#396—612no—
144#395—611no—
145#394—612no—
146#393—611no—
147#380D6111yescharacteristic, complemented
148C61#281411yescharacteristic, complemented, Sylow
149C22×Q8—611no—
150C22×D4—611no—
151C23×C4C2×D6111yescharacteristic
152#123—1224no—
153C22⋊Q8—1224no—
154C2×C4⋊C4—612no—
155C2×C4⋊C4—611no—
156C2×C4⋊C4—611no—
157C2×C4⋊C4—611no—
158C2×C4⋊C4—612no—
159C2×C4⋊C4—612no—
160C2×C4⋊C4C2×D6112yes—
161C2×C22⋊C4—612no—
162C2×C22⋊C4—611no—
163C2×C22⋊C4—611no—
164C2×C22⋊C4—611no—
165C2×C22⋊C4—612no—
166C2×C22⋊C4—612no—
167C2×C22⋊C4C2×D6112yes—
168#95—612no—
169#95—612no—
170#95—612no—
171#95—612no—
172#95C2×D6111yescharacteristic
173#95C2×D6111yescharacteristic
174C24—611no—
175C24C22×D6111yescharacteristic
176C2×Q8—1222no—
177C2×Q8—2442no—
178C2×D4—1222no—
179C2×D4—2442no—
180C22×C4—42no—
181C22×C4—611no—
182C22×C4—611no—
183C22×C4—612no—
184C22×C4—612no—
185C22×C4—611no—
186C22×C4D24414yes—
187C22×C4C22×D6112yes—
188C22×C4C22×D6112yes—
189C22×C4C22×D6111yescharacteristic
190C22×C4C22×D6111yescharacteristic
191C4⋊C4—42no—
192C4⋊C4—1224no—
193C4⋊C4—1222no—
194C4⋊C4—1222no—
195C4⋊C4—1222no—
196C4⋊C4—2442no—
197C4⋊C4—2442no—
198C22⋊C4—42no—
199C22⋊C4—1224no—
200C22⋊C4—1222no—
201C22⋊C4—1222no—
202C22⋊C4—1222no—
203C22⋊C4—2442no—
204C22⋊C4—2442no—
205C23—21no—
206C23—22no—
207C23—22no—
208C23—21no—
209C23—1221no—
210C23—1221no—
211C23—1222no—
212C23—1222no—
213C23—1221no—
214C23C2×D24412yes—
215C23C23×D6111yescharacteristic
216Q8—2444no—
217D4—2444no—
218C2×C4—22no—
219C2×C4—22no—
220C2×C4—22no—
221C2×C4—22no—
222C2×C4—22no—
223C2×C4—22no—
224C2×C4—22no—
225C2×C4—22no—
226C2×C4—44no—
227C2×C4—1221no—
228C2×C4—1221no—
229C2×C4—1222no—
230C2×C4—1222no—
231C2×C4—1221no—
232C2×C4—1222no—
233C2×C4—1222no—
234C2×C4—1221no—
235C2×C4—1222no—
236C2×C4—1222no—
237C2×C4—1222no—
238C2×C4—1221no—
239C2×C4—1222no—
240C2×C4C2×D24412yes—
241C2×C4C2×D24412yes—
242C22—22no—
243C22—22no—
244C22—22no—
245C22—42no—
246C22—42no—
247C22—2442no—
248C22—2442no—
249C22—2441no—
250C22—2441no—
251C22—2441no—
252C22C22×D24411yescharacteristic
253C22#1451982211yescharacteristic
254C22#1451982212yes—
255C22#1451982412yes—
256C22#1451982511yescharacteristic
257C4—22no—
258C4—22no—
259C4—42no—
260C4—42no—
261C4—2441no—
262C4—2442no—
263C4—2441no—
264C4—2441no—
265C4—2442no—
266C2—42no—
267C2—4881no—
268C2#1684032411yescharacteristic
269C2#1684033811yescharacteristic
270C2#1684034311yescharacteristic
271C2#1684050712yes—
272C2#1684051312yes—
subgroupG/H
center, FrattiniC23C23×D61
commutator, socleC23×C61C24
FittingC61×#380C2
hypercenter#380D61
hypocenterC61#2814
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C23 ◁ #380

Complements

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

NH ≅ G/Ntype
2. C2×#14519756C2semidirect
3. #16839694C2semidirect
4. #16839692C2semidirect
5. #16839689C2semidirect
6. #16839687C2semidirect
7. #16839684C2semidirect
8. #16839683C2semidirect
10. #16839675C2semidirect
11. C61×#380C2semidirect
147. #380D61semidirect
148. C61#2814semidirect