Finite Group Databasebeta

← #21449215

Subgroups — #21449215

Order 7808.

814 conjugacy classes of subgroups.

The subgroup lattice has 352 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14519760C211yesmaximal, characteristic, complemented
2C2×#14519746C211yesmaximal, characteristic
3C22×C22⋊Dic61C211yesmaximal, characteristic, complemented
4#16839690C212yesmaximal, complemented
5#16839677C212yesmaximal, complemented
6#16839641C211yesmaximal, characteristic, complemented
7#16839639C212yesmaximal, complemented
8#16839635C211yesmaximal, characteristic, complemented
9#16839625C211yesmaximal, characteristic, complemented
10#16839620C212yesmaximal, complemented
11C22×C22⋊C4×C61C211yesmaximal, characteristic, complemented
12C22×C22⋊D61C2211yescharacteristic
13C22×C22⋊D61C2211yescharacteristic
14C22×C22⋊D61C2211yescharacteristic
15C23×Dic61C2212yes—
16#14519760—24no—
17#14519746—24no—
18C2×#11758196C2212yescomplemented
19C2×#11758196C2212yescomplemented
20C2×C22⋊Dic61—24no—
21C2×C22⋊Dic61C2211yescharacteristic
22C2×C22⋊Dic61C2212yes—
23C2×C22⋊Dic61C2211yescharacteristic
24C2×C22⋊Dic61C2211yescharacteristic
25C2×C22⋊Dic61C2211yescharacteristic
26C2×C22⋊Dic61C2211yescharacteristic
27C2×#11758198C2212yescomplemented
28C2×#11758198C2212yescomplemented
29#14519684C2212yescomplemented
30#14519684C2212yescomplemented
31#14519684C2212yescomplemented
32#14519684C2212yescomplemented
33C25×C61C2211yescharacteristic
34C23×C4×C61C2211yescharacteristic
35C23×C4×C61C2211yescharacteristic
36C2×C22⋊C4×C61—24no—
37C2×C22⋊C4×C61C2212yes—
38C2×C22⋊C4×C61C2212yes—
39C24×C61—22no—
40C24×C61—22no—
41C24×C61—24no—
42C24×C61—42no—
43C24×C61D414yes—
44C24×C61C2311yescharacteristic
45C24×C61C2311yescharacteristic
46C24×C61C2311yescharacteristic
47C23×D61C2311yescharacteristic
48C22×C4×C61—22no—
49C22×C4×C61—22no—
50C22×C4×C61—22no—
51C22×C4×C61—22no—
52C22×C4×C61—42no—
53C22×C4×C61C2312yes—
54C22×C4×C61C2312yes—
55C2×C22⋊D61—22no—
56C2×C22⋊D61—22no—
57C2×C22⋊D61—22no—
58C2×C22⋊D61—22no—
59C2×C22⋊D61—22no—
60C2×C22⋊D61—24no—
61C2×C22⋊D61—42no—
62C22×Dic61—24no—
63C22×Dic61—24no—
64C22×Dic61—42no—
65C22×Dic61C2312yes—
66C22×Dic61C2311yescharacteristic
67C22×Dic61C2311yescharacteristic
68C22×Dic61C2311yescharacteristic
69C22×Dic61C2312yes—
70C22⋊C4×C61—24no—
71C22⋊C4×C61—24no—
72C22⋊Dic61—22no—
73C22⋊Dic61—22no—
74C22⋊Dic61—22no—
75C22⋊Dic61—22no—
76C22⋊Dic61—24no—
77C22⋊Dic61D414yescomplemented
78#11758198—24no—
79#11758198—42no—
80#11758196—24no—
81#11758196—42no—
82C23×C61—21no—
83C23×C61—21no—
84C23×C61—22no—
85C23×C61—22no—
86C23×C61—22no—
87C23×C61—28no—
88C23×C61—28no—
89C23×C61—21no—
90C23×C61—21no—
91C23×C61—22no—
92C23×C61—22no—
93C23×C61—44no—
94C23×C61—48no—
95C23×C61—48no—
96C23×C61C2×D412yes—
97C23×C61C2×D412yes—
98C23×C61C2×D412yes—
99C23×C61C2×D412yes—
100C23×C61#4112yes—
101C23×C61#4114yes—
102C23×C61C2411yescharacteristic
103C22×D61—21no—
104C22×D61—21no—
105C22×D61—21no—
106C22×D61—22no—
107C22×D61—22no—
108C2×C4×C61—22no—
109C2×C4×C61—22no—
110C2×C4×C61—22no—
111C2×C4×C61—22no—
112C2×C4×C61—22no—
113C2×C4×C61—22no—
114C2×C4×C61—44no—
115C2×C4×C61—44no—
116C22⋊D61—44no—
117C22⋊D61—44no—
118C22⋊D61—44no—
119C2×Dic61—22no—
120C2×Dic61—22no—
121C2×Dic61—21no—
122C2×Dic61—22no—
123C2×Dic61—21no—
124C2×Dic61—21no—
125C2×Dic61—21no—
126C2×Dic61—22no—
127C2×Dic61—21no—
128C2×Dic61—22no—
129C2×Dic61—22no—
130C2×Dic61—22no—
131C2×Dic61—48no—
132C2×Dic61C2×D414yes—
133C22×C61—22no—
134C22×C61—22no—
135C22×C61—22no—
136C22×C61—22no—
137C22×C61—24no—
138C22×C61—24no—
139C22×C61—24no—
140C22×C61—24no—
141C22×C61—22no—
142C22×C61—22no—
143C22×C61—22no—
144C22×C61—416no—
145C22×C61—42no—
146C22×C61—42no—
147C22×C61#12114yes—
148C22×C61#12314yescomplemented
149C22×C61C22×D411yescharacteristic
150C22×C61C22×D411yescharacteristic
151C22×C61C2×#4111yescharacteristic
152C22×C61C2×#4112yes—
153C22×C61H(5,𝔽2)12yes—
154C2×D61—41no—
155C2×D61—41no—
156C2×D61—41no—
157C2×D61—42no—
158C2×D61—42no—
159C4×C61—42no—
160C4×C61—42no—
161Dic61—24no—
162Dic61—41no—
163Dic61—41no—
164Dic61—41no—
165Dic61—42no—
166#2412—611nomaximal, Sylow
167C2×C61—24no—
168C2×C61—24no—
169C2×C61—42no—
170C2×C61C2×#12111yescharacteristic
171C2×C61C2×#12311yescharacteristic
172C2×C61#53411yescharacteristic
173C2×C61#54612yes—
174C2×C61#55112yes—
175D61—81no—
176C2×#123—611no—
177C2×#120—611no—
178C22×C22⋊C4—611no—
179C22×C22⋊C4D6111yescharacteristic, complemented
180#397—612no—
181#394—612no—
182#386—611no—
183#386—612no—
184#385—611no—
185#381—611no—
186#380—612no—
187C61#241211yescharacteristic, complemented, Sylow
188C25C2×D6111yescharacteristic
189C22×D4—611no—
190C22×D4—611no—
191C22×D4—611no—
192C23×C4—612no—
193C23×C4C2×D6111yescharacteristic
194C23×C4C2×D6111yescharacteristic
195#123—1224no—
196#120—1224no—
197C2×C4⋊C4—612no—
198C2×C4⋊C4—612no—
199C2×C22⋊C4—24no—
200C2×C22⋊C4—611no—
201C2×C22⋊C4—611no—
202C2×C22⋊C4—612no—
203C2×C22⋊C4—611no—
204C2×C22⋊C4—611no—
205C2×C22⋊C4—611no—
206C2×C22⋊C4—612no—
207C2×C22⋊C4—612no—
208C2×C22⋊C4—1224no—
209C2×C22⋊C4C2×D6112yes—
210C2×C22⋊C4C2×D6112yes—
211#95—612no—
212#95—612no—
213#95—612no—
214#95—612no—
215C24—24no—
216C24—22no—
217C24—22no—
218C24—42no—
219C24—611no—
220C24C22⋊D6114yes—
221C24C22×D6111yescharacteristic
222C24C22×D6111yescharacteristic
223C24C22×D6111yescharacteristic
224C2×D4—1224no—
225C2×D4—1222no—
226C2×D4—1222no—
227C2×D4—1222no—
228C2×D4—1222no—
229C2×D4—1222no—
230C2×D4—2442no—
231C22×C4—22no—
232C22×C4—22no—
233C22×C4—22no—
234C22×C4—22no—
235C22×C4—42no—
236C22×C4—612no—
237C22×C4—611no—
238C22×C4—612no—
239C22×C4—611no—
240C22×C4—611no—
241C22×C4—1224no—
242C22×C4—1224no—
243C22×C4—2442no—
244C22×C4C22×D6112yes—
245C22×C4C22×D6112yes—
246C4⋊C4—1224no—
247C4⋊C4—2442no—
248C22⋊C4—24no—
249C22⋊C4—24no—
250C22⋊C4—614no—
251C22⋊C4—1224no—
252C22⋊C4—1224no—
253C22⋊C4—1222no—
254C22⋊C4—1222no—
255C22⋊C4—1222no—
256C22⋊C4—1222no—
257C22⋊C4—2442no—
258C23—21no—
259C23—21no—
260C23—22no—
261C23—22no—
262C23—22no—
263C23—21no—
264C23—21no—
265C23—22no—
266C23—22no—
267C23—28no—
268C23—28no—
269C23—44no—
270C23—48no—
271C23—48no—
272C23—1221no—
273C23—1221no—
274C23—1221no—
275C23—1222no—
276C23—1222no—
277C23#1175822214yes—
278C23D4×D6112yes—
279C23#1175822412yes—
280C23C2×C22⋊D6112yes—
281C23C2×C22⋊D6112yes—
282C23C2×C22⋊D6112yes—
283C23C23×D6111yescharacteristic
284D4—2444no—
285D4—2444no—
286D4—2444no—
287C2×C4—22no—
288C2×C4—22no—
289C2×C4—22no—
290C2×C4—22no—
291C2×C4—22no—
292C2×C4—22no—
293C2×C4—44no—
294C2×C4—44no—
295C2×C4—614no—
296C2×C4—1222no—
297C2×C4—1222no—
298C2×C4—1222no—
299C2×C4—1221no—
300C2×C4—1221no—
301C2×C4—1221no—
302C2×C4—1221no—
303C2×C4—1221no—
304C2×C4—1222no—
305C2×C4—1222no—
306C2×C4—1222no—
307C2×C4—1222no—
308C2×C4—2448no—
309C22—22no—
310C22—22no—
311C22—22no—
312C22—22no—
313C22—24no—
314C22—24no—
315C22—24no—
316C22—24no—
317C22—22no—
318C22—22no—
319C22—22no—
320C22—416no—
321C22—42no—
322C22—42no—
323C22—2441no—
324C22—2441no—
325C22—2441no—
326C22—2442no—
327C22—2442no—
328C22#1451974914yes—
329C22#1451976014yescomplemented
330C22C2×D4×D6111yescharacteristic
331C22C22×C22⋊D6111yescharacteristic
332C22C2×#1175822411yescharacteristic
333C22C2×#1175822212yes—
334C22#1451982212yes—
335C4—42no—
336C4—42no—
337C4—1224no—
338C4—2441no—
339C4—2441no—
340C4—2441no—
341C4—2442no—
342C2—24no—
343C2—24no—
344C2—42no—
345C2—4881no—
346C2C2×#1451974911yescharacteristic
347C2C2×#1451976011yescharacteristic
348C2#1684032111yescharacteristic
349C2#1684040212yes—
350C2#1684043812yes—
subgroupG/H
center, FrattiniC23C23×D61
commutator, socleC23×C61C24
FittingC22×C22⋊C4×C61C2
hypercenterC22×C22⋊C4D61
hypocenterC61#2412
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C23 ◁ C22×C22⋊C4

Complements

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

NH ≅ G/Ntype
1. C2×#14519760C2semidirect
3. C22×C22⋊Dic61C2semidirect
4. #16839690C2semidirect
5. #16839677C2semidirect
6. #16839641C2semidirect
7. #16839639C2semidirect
8. #16839635C2semidirect
9. #16839625C2semidirect
10. #16839620C2semidirect
11. C22×C22⋊C4×C61C2semidirect
18. C2×#11758196C22semidirect
19. C2×#11758196C22semidirect
27. C2×#11758198C22semidirect
28. C2×#11758198C22semidirect
29. #14519684C22semidirect
30. #14519684C22semidirect
31. #14519684C22semidirect
32. #14519684C22semidirect
77. C22⋊Dic61D4semidirect
148. C22×C61#123semidirect
179. C22×C22⋊C4D61semidirect
187. C61#2412semidirect
329. C22#14519760semidirect