Finite Group Databasebeta

← #21450124

Subgroups — #21450124

Order 7808.

624 conjugacy classes of subgroups.

The subgroup lattice has 294 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14519758C211yesmaximal, characteristic
2C2×D4×Dic61C211yesmaximal, characteristic
3C22×#11758196C211yesmaximal, characteristic, complemented
4#16839695C212yesmaximal, complemented
5#16839690C212yesmaximal, complemented
6#16839657C212yesmaximal, complemented
7#16839625C211yesmaximal, characteristic, complemented
8#16839623C211yesmaximal, characteristic, complemented
9#16839620C212yesmaximal, complemented
10#16839620C211yesmaximal, characteristic, complemented
11C2×#123×C61C211yesmaximal, characteristic
12C23×Dic61C2211yescharacteristic
13C23×Dic61C2211yescharacteristic
14C23×Dic61C2211yescharacteristic
15#14519758—24no—
16D4×Dic61—24no—
17C2×C4⋊Dic61C2211yescharacteristic
18C2×#11758196—24no—
19C2×#11758196C2212yes—
20C2×#11758196C2212yes—
21C2×#11758196C2212yes—
22C2×#11758196C2212yes—
23C2×C22⋊Dic61C2211yescharacteristic
24C2×C22⋊Dic61C2212yes—
25C2×C22⋊Dic61C2211yescharacteristic
26C2×C22⋊Dic61C2211yescharacteristic
27C2×C4×Dic61C2211yescharacteristic
28#14519684C2212yes—
29#14519684C2212yes—
30#14519684C2212yes—
31#14519684C2212yes—
32#14519684C2212yes—
33C22×D4×C61C2211yescharacteristic
34C23×C4×C61C2211yescharacteristic
35#123×C61—24no—
36C2×C4⋊C4×C61C2212yes—
37C2×C22⋊C4×C61C2212yes—
38C2×C22⋊C4×C61C2211yescharacteristic
39C24×C61C2311yescharacteristic
40C24×C61C2311yescharacteristic
41C2×D4×C61—22no—
42C2×D4×C61—22no—
43C2×D4×C61D414yes—
44C22×C4×C61—22no—
45C22×C4×C61—22no—
46C22×C4×C61—22no—
47C22×C4×C61C2312yes—
48C22×C4×C61C2312yes—
49C22×C4×C61C2311yescharacteristic
50C22×Dic61—24no—
51C22×Dic61—22no—
52C22×Dic61—22no—
53C22×Dic61—22no—
54C22×Dic61—22no—
55C22×Dic61—24no—
56C22×Dic61D414yes—
57C22×Dic61C2311yescharacteristic
58C22×Dic61C2312yes—
59C22×Dic61C2311yescharacteristic
60C22×Dic61C2312yes—
61C22×Dic61C2311yescharacteristic
62C22×Dic61C2311yescharacteristic
63C4⋊C4×C61—24no—
64C22⋊C4×C61—22no—
65C22⋊C4×C61—24no—
66C22⋊Dic61—22no—
67C22⋊Dic61—22no—
68C22⋊Dic61—24no—
69C22⋊Dic61—22no—
70C4⋊Dic61—22no—
71#11758196—24no—
72#11758196—24no—
73#11758196—24no—
74#11758196—24no—
75C4×Dic61—22no—
76C23×C61—22no—
77C23×C61—22no—
78C23×C61—21no—
79C23×C61—22no—
80C23×C61—21no—
81C23×C61—22no—
82C23×C61C2×D412yes—
83C23×C61C2×D412yes—
84C23×C61C2×D412yes—
85C23×C61#4112yes—
86C23×C61C2411yescharacteristic
87D4×C61—28no—
88C2×C4×C61—21no—
89C2×C4×C61—21no—
90C2×C4×C61—22no—
91C2×C4×C61—22no—
92C2×C4×C61—22no—
93C2×C4×C61—22no—
94C2×C4×C61—22no—
95C2×C4×C61—22no—
96C2×C4×C61—44no—
97C2×C4×C61C2×D412yes—
98C2×Dic61—22no—
99C2×Dic61—28no—
100C2×Dic61—21no—
101C2×Dic61—22no—
102C2×Dic61—22no—
103C2×Dic61—22no—
104C2×Dic61—21no—
105C2×Dic61—22no—
106C2×Dic61—22no—
107C2×Dic61—22no—
108C2×Dic61—22no—
109C2×Dic61—22no—
110C2×Dic61—44no—
111C2×Dic61—44no—
112C2×Dic61C2×D412yes—
113C2×Dic61C2×D412yes—
114C2×Dic61#4114yes—
115C22×C61—22no—
116C22×C61—22no—
117C22×C61—24no—
118C22×C61—24no—
119C22×C61—22no—
120C22×C61—24no—
121C22×C61—41no—
122C22×C61—41no—
123C22×C61—42no—
124C22×C61#12114yes—
125C22×C61C22×D411yescharacteristic
126C22×C61C22×D411yescharacteristic
127C22×C61C2×#4112yes—
128C22×C61C2×#4111yescharacteristic
129C22×C612−1+412yes—
130C4×C61—22no—
131C4×C61—42no—
132C4×C61—42no—
133Dic61—22no—
134Dic61—42no—
135Dic61—41no—
136Dic61—41no—
137Dic61—42no—
138Dic61#12314yescomplemented
139#2486—611nomaximal, Sylow
140C2×C61—24no—
141C2×C61—42no—
142C2×C61C2×#12111yescharacteristic
143C2×C61C2×#12311yescharacteristic
144C2×C61#53611yescharacteristic
145C2×C61#54712yes—
146C2×C61#55212yes—
147C2×#123—611no—
148C2×#123D6111yescharacteristic
149C2×C4×D4—611no—
150C22×C4⋊C4—611no—
151#398—612no—
152#397—612no—
153#389—612no—
154#381—611no—
155#381—611no—
156#380—612no—
157#380—611no—
158C61#248611yescharacteristic, complemented, Sylow
159C22×D4C2×D6111yescharacteristic
160C23×C4—611no—
161C23×C4—611no—
162C23×C4—611no—
163C23×C4C2×D6111yescharacteristic
164#123—24no—
165#123—1224no—
166C4×D4—1224no—
167C2×C4⋊C4—612no—
168C2×C4⋊C4—612no—
169C2×C4⋊C4—611no—
170C2×C4⋊C4—612no—
171C2×C4⋊C4—612no—
172C2×C4⋊C4—1224no—
173C2×C4⋊C4C2×D6112yes—
174C2×C22⋊C4—611no—
175C2×C22⋊C4—611no—
176C2×C22⋊C4—611no—
177C2×C22⋊C4—612no—
178C2×C22⋊C4C2×D6111yescharacteristic
179C2×C22⋊C4C2×D6112yes—
180C2×C42—611no—
181#95—612no—
182#95—612no—
183#95—612no—
184#95—612no—
185#95—612no—
186C24C22×D6111yescharacteristic
187C24C22×D6111yescharacteristic
188C2×D4—22no—
189C2×D4—22no—
190C2×D4C22⋊D6114yes—
191C22×C4—22no—
192C22×C4—22no—
193C22×C4—22no—
194C22×C4—611no—
195C22×C4—614no—
196C22×C4—611no—
197C22×C4—611no—
198C22×C4—611no—
199C22×C4—612no—
200C22×C4—612no—
201C22×C4—1224no—
202C22×C4—1222no—
203C22×C4—1224no—
204C22×C4—1222no—
205C22×C4—1222no—
206C22×C4—1222no—
207C22×C4C22×D6112yes—
208C22×C4C22×D6112yes—
209C22×C4C22×D6111yescharacteristic
210C4⋊C4—24no—
211C4⋊C4—1224no—
212C4⋊C4—1224no—
213C4⋊C4—1224no—
214C4⋊C4—1222no—
215C4⋊C4—1224no—
216C22⋊C4—22no—
217C22⋊C4—24no—
218C22⋊C4—1222no—
219C22⋊C4—1222no—
220C22⋊C4—1222no—
221C22⋊C4—1224no—
222C42—1222no—
223C23—22no—
224C23—22no—
225C23—21no—
226C23—22no—
227C23—21no—
228C23—22no—
229C23D4×D6112yes—
230C23#1175822412yes—
231C23C2×C22⋊D6112yes—
232C23C2×C22⋊D6112yes—
233C23C23×D6111yescharacteristic
234D4—28no—
235C2×C4—21no—
236C2×C4—21no—
237C2×C4—22no—
238C2×C4—22no—
239C2×C4—22no—
240C2×C4—22no—
241C2×C4—22no—
242C2×C4—22no—
243C2×C4—44no—
244C2×C4—612no—
245C2×C4—614no—
246C2×C4—612no—
247C2×C4—1228no—
248C2×C4—1222no—
249C2×C4—1221no—
250C2×C4—1221no—
251C2×C4—1222no—
252C2×C4—1222no—
253C2×C4—1222no—
254C2×C4—1222no—
255C2×C4—1222no—
256C2×C4—1222no—
257C2×C4—1222no—
258C2×C4—1222no—
259C2×C4—2444no—
260C2×C4—2444no—
261C2×C4C2×C22⋊D6112yes—
262C22—24no—
263C22—22no—
264C22—22no—
265C22—24no—
266C22—22no—
267C22—24no—
268C22—42no—
269C22—41no—
270C22—41no—
271C22#1451974914yes—
272C22C2×D4×D6111yescharacteristic
273C22C22×C22⋊D6111yescharacteristic
274C22#41×D6112yes—
275C22C2×#1175822411yescharacteristic
276C22#1451982412yes—
277C4—22no—
278C4—42no—
279C4—42no—
280C4—614no—
281C4—1222no—
282C4—2442no—
283C4—2441no—
284C4—2441no—
285C4—2442no—
286C2—24no—
287C2—42no—
288C2C2×#1451974911yescharacteristic
289C2#123×D6111yescharacteristic
290C2#1684033411yescharacteristic
291C2#1684041112yes—
292C2#1684044912yes—
subgroupG/H
center, FrattiniC23C23×D61
commutator, socleC23×C61C24
FittingC2×#123×C61C2
hypercenterC2×#123D61
hypocenterC61#2486
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×#123

Complements

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

NH ≅ G/Ntype
3. C22×#11758196C2semidirect
4. #16839695C2semidirect
5. #16839690C2semidirect
6. #16839657C2semidirect
7. #16839625C2semidirect
8. #16839623C2semidirect
9. #16839620C2semidirect
10. #16839620C2semidirect
138. Dic61#123semidirect
158. C61#2486semidirect