Finite Group Databasebeta

← #21449233

Subgroups — #21449233

Order 7808.

704 conjugacy classes of subgroups.

The subgroup lattice has 364 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14519748C211yesmaximal, characteristic, complemented
2C2×C4×C22⋊D61C211yesmaximal, characteristic, complemented
3C2×#14519735C211yesmaximal, characteristic, complemented
4#16839678C212yesmaximal, complemented
5#16839670C212yesmaximal, complemented
6#16839665C211yesmaximal, characteristic, complemented
7#16839665C212yesmaximal, complemented
8#16839661C211yesmaximal, characteristic, complemented
9#16839650C212yesmaximal, complemented
10#16839622C211yesmaximal, characteristic, complemented
11C2×#121×C61C211yesmaximal, characteristic, complemented
12C22×C22⋊D61C2211yescharacteristic
13C22×C22⋊D61C2212yes—
14C22×C4×D61C2211yescharacteristic
15#14519748—24no—
16C4×C22⋊D61—24no—
17#14519735—24no—
18C2×C4⋊Dic61C2211yescharacteristic
19C2×C4⋊Dic61C2211yescharacteristic
20C2×C4⋊Dic61C2212yes—
21C2×#11758196C2211yescharacteristic
22C2×C22⋊Dic61C2211yescharacteristic
23C2×C22⋊Dic61C2212yes—
24C2×C22⋊Dic61C2212yes—
25C2×C22⋊Dic61C2212yes—
26C2×C22⋊Dic61C2212yes—
27C2×#11758198C2212yes—
28C2×#11758198C2211yescharacteristic
29C2×C4×Dic61C2212yes—
30C2×C4×Dic61C2211yescharacteristic
31#14519684C2212yes—
32#14519684C2212yes—
33C22×D4×C61C2211yescharacteristic
34C22×D4×C61C2212yes—
35C23×C4×C61C2211yescharacteristic
36#121×C61—24no—
37C2×C4⋊C4×C61C2211yescharacteristic
38C2×C22⋊C4×C61C2212yes—
39C24×C61C2312yes—
40C24×C61C2311yescharacteristic
41C23×D61C2311yescharacteristic
42C2×D4×C61—24no—
43C2×D4×C61—24no—
44C2×D4×C61—22no—
45C2×D4×C61—22no—
46C2×D4×C61—22no—
47C2×D4×C61—42no—
48C22×C4×C61—22no—
49C22×C4×C61—22no—
50C22×C4×C61—22no—
51C22×C4×C61C2311yescharacteristic
52C22×C4×C61C2312yes—
53C22×C4×C61C2311yescharacteristic
54C2×C22⋊D61—22no—
55C2×C22⋊D61—22no—
56C2×C22⋊D61—24no—
57C2×C22⋊D61—22no—
58C2×C22⋊D61—42no—
59C2×C22⋊D61—42no—
60C22×Dic61C2312yes—
61C22×Dic61C2312yes—
62C22×Dic61C2311yescharacteristic
63C22×Dic61C2311yescharacteristic
64C22×Dic61C2311yescharacteristic
65C2×C4×D61—22no—
66C2×C4×D61—22no—
67C2×C4×D61D414yescomplemented
68C4⋊C4×C61D414yescomplemented
69C22⋊C4×C61—24no—
70C22⋊Dic61—22no—
71C22⋊Dic61—24no—
72C22⋊Dic61—24no—
73C22⋊Dic61—42no—
74C22⋊Dic61—42no—
75#11758198—22no—
76#11758198—24no—
77C4⋊Dic61—22no—
78C4⋊Dic61—22no—
79C4⋊Dic61—42no—
80#11758196—22no—
81C4×Dic61—24no—
82C4×Dic61—22no—
83C23×C61—21no—
84C23×C61—21no—
85C23×C61—21no—
86C23×C61—21no—
87C23×C61—21no—
88C23×C61—21no—
89C23×C61—22no—
90C23×C61—22no—
91C23×C61—22no—
92C23×C61—22no—
93C23×C61—22no—
94C23×C61—22no—
95C23×C61—22no—
96C23×C61#4112yes—
97C23×C61C2411yescharacteristic
98C22×D61—21no—
99C22×D61—21no—
100C22×D61—21no—
101C22×D61—21no—
102C22×D61—21no—
103C22×D61—21no—
104C22×D61C2×D412yes—
105D4×C61—48no—
106D4×C61—44no—
107C2×C4×C61—22no—
108C2×C4×C61—22no—
109C2×C4×C61—21no—
110C2×C4×C61—21no—
111C2×C4×C61—21no—
112C2×C4×C61—44no—
113C2×C4×C61C2×D414yes—
114C2×C4×C61C2×D412yes—
115C2×C4×C61C2×D412yes—
116C2×C4×C61#4112yes—
117C22⋊D61—28no—
118C22⋊D61—48no—
119C2×Dic61—21no—
120C2×Dic61—21no—
121C2×Dic61—21no—
122C2×Dic61—21no—
123C2×Dic61—22no—
124C2×Dic61—21no—
125C2×Dic61—22no—
126C2×Dic61—22no—
127C2×Dic61—21no—
128C2×Dic61—22no—
129C2×Dic61—21no—
130C2×Dic61—22no—
131C2×Dic61—22no—
132C2×Dic61C2×D412yes—
133C2×Dic61#4112yes—
134C4×D61—28no—
135C22×C61—22no—
136C22×C61—22no—
137C22×C61—22no—
138C22×C61—41no—
139C22×C61—41no—
140C22×C61—41no—
141C22×C61—41no—
142C22×C61—42no—
143C22×C61—42no—
144C22×C61—42no—
145C22×C61—42no—
146C22×C61—42no—
147C22×C61—42no—
148C22×C61—42no—
149C22×C61C22×D411yescharacteristic
150C22×C61C22×D411yescharacteristic
151C22×C61C2×#4111yescharacteristic
152C22×C61C2×#4111yescharacteristic
153C22×C61C2×#4111yescharacteristic
154C22×C61H(5,𝔽2)11yescharacteristic
155C22×C61H(5,𝔽2)11yescharacteristic
156C2×D61—22no—
157C2×D61—22no—
158C2×D61—22no—
159C2×D61—41no—
160C2×D61—41no—
161C2×D61—41no—
162C2×D61—41no—
163C4×C61—24no—
164C4×C61—41no—
165C4×C61#12114yes—
166Dic61—22no—
167Dic61—22no—
168Dic61—41no—
169Dic61—42no—
170Dic61—42no—
171#2414—611nomaximal, Sylow
172C2×C61—42no—
173C2×C61—82no—
174C2×C61C2×#12111yescharacteristic
175C2×C61#52511yescharacteristic
176C2×C61#53511yescharacteristic
177C2×C61#54611yescharacteristic
178C2×C61#55011yescharacteristic
179C2×C61#55311yescharacteristic
180C2×C61#55511yescharacteristic
181D61—42no—
182C2×#121—611no—
183C2×#121D6111yescharacteristic, complemented
184C2×C4×D4—611no—
185C2×#117—611no—
186#394—612no—
187#392—612no—
188#390—612no—
189#390—611no—
190#389—611no—
191#388—612no—
192#380—611no—
193C61#241411yescharacteristic, complemented, Sylow
194C22×D4—611no—
195C22×D4—612no—
196C22×D4C2×D6111yescharacteristic
197C22×D4C2×D6112yes—
198C23×C4—611no—
199C23×C4C2×D6111yescharacteristic
200#121—24no—
201#121—1224no—
202C4×D4—1224no—
203#117—1224no—
204C2×C4⋊C4—611no—
205C2×C4⋊C4—611no—
206C2×C4⋊C4—611no—
207C2×C4⋊C4—612no—
208C2×C4⋊C4C2×D6111yescharacteristic
209C2×C22⋊C4—611no—
210C2×C22⋊C4—612no—
211C2×C22⋊C4—612no—
212C2×C22⋊C4—612no—
213C2×C22⋊C4—611no—
214C2×C22⋊C4—612no—
215C2×C22⋊C4—612no—
216C2×C22⋊C4C2×D6112yes—
217C2×C42—612no—
218C2×C42—611no—
219#95—612no—
220#95—612no—
221C24—611no—
222C24C22×D6112yes—
223C24C22×D6111yescharacteristic
224C2×D4—24no—
225C2×D4—22no—
226C2×D4—22no—
227C2×D4—24no—
228C2×D4—22no—
229C2×D4—42no—
230C2×D4—1222no—
231C2×D4—1222no—
232C2×D4—1222no—
233C2×D4—1224no—
234C2×D4—2442no—
235C2×D4—2442no—
236C22×C4—22no—
237C22×C4—22no—
238C22×C4—22no—
239C22×C4—611no—
240C22×C4—611no—
241C22×C4—614no—
242C22×C4—612no—
243C22×C4—612no—
244C22×C4—611no—
245C22×C4—1222no—
246C22×C4—1222no—
247C22×C4C22×D6111yescharacteristic
248C22×C4C22×D6112yes—
249C22×C4C22×D6111yescharacteristic
250C4⋊C4—1222no—
251C4⋊C4—1222no—
252C4⋊C4—1222no—
253C4⋊C4—2442no—
254C4⋊C4C22⋊D6114yescomplemented
255C22⋊C4—24no—
256C22⋊C4—1222no—
257C22⋊C4—1222no—
258C22⋊C4—1224no—
259C22⋊C4—1224no—
260C22⋊C4—1224no—
261C22⋊C4—2442no—
262C22⋊C4—2442no—
263C42—1222no—
264C42—1224no—
265C23—21no—
266C23—21no—
267C23—21no—
268C23—21no—
269C23—21no—
270C23—21no—
271C23—22no—
272C23—22no—
273C23—22no—
274C23—22no—
275C23—22no—
276C23—22no—
277C23—22no—
278C23—612no—
279C23—1221no—
280C23—1221no—
281C23—1221no—
282C23—1221no—
283C23—1221no—
284C23—1221no—
285C23#1175822412yes—
286C23C23×D6111yescharacteristic
287D4—48no—
288D4—44no—
289D4—1228no—
290D4—2448no—
291C2×C4—22no—
292C2×C4—22no—
293C2×C4—21no—
294C2×C4—21no—
295C2×C4—21no—
296C2×C4—44no—
297C2×C4—612no—
298C2×C4—612no—
299C2×C4—1221no—
300C2×C4—1221no—
301C2×C4—1221no—
302C2×C4—1221no—
303C2×C4—1228no—
304C2×C4—1221no—
305C2×C4—1222no—
306C2×C4—1222no—
307C2×C4—1222no—
308C2×C4—1221no—
309C2×C4—1222no—
310C2×C4—1221no—
311C2×C4—1222no—
312C2×C4—1222no—
313C2×C4D4×D6112yes—
314C2×C4#1175822412yes—
315C2×C4C2×C22⋊D6114yes—
316C2×C4C2×C22⋊D6112yes—
317C22—22no—
318C22—22no—
319C22—22no—
320C22—41no—
321C22—41no—
322C22—41no—
323C22—41no—
324C22—42no—
325C22—42no—
326C22—42no—
327C22—42no—
328C22—42no—
329C22—42no—
330C22—42no—
331C22—1222no—
332C22—1222no—
333C22—1222no—
334C22—2441no—
335C22—2441no—
336C22—2441no—
337C22—2441no—
338C22C2×D4×D6111yescharacteristic
339C22C22×C22⋊D6111yescharacteristic
340C22#41×D6111yescharacteristic
341C22C2×#1175822411yescharacteristic
342C22C2×#1175822411yescharacteristic
343C22#1451982211yescharacteristic
344C22#1451982311yescharacteristic
345C4—24no—
346C4—41no—
347C4—1222no—
348C4—1222no—
349C4—2441no—
350C4—2442no—
351C4—2442no—
352C4#1451974814yes—
353C2—42no—
354C2—82no—
355C2—2442no—
356C2C2×#1451974811yescharacteristic
357C2#1684027211yescharacteristic
358C2#1684032811yescharacteristic
359C2#1684040611yescharacteristic
360C2#1684043111yescharacteristic
361C2#1684046411yescharacteristic
362C2#1684047611yescharacteristic
subgroupG/H
center, FrattiniC23C23×D61
commutator, socleC23×C61C24
FittingC2×#121×C61C2
hypercenterC2×#121D61
hypocenterC61#2414
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×#121

Complements

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

NH ≅ G/Ntype
1. C2×#14519748C2semidirect
2. C2×C4×C22⋊D61C2semidirect
3. C2×#14519735C2semidirect
4. #16839678C2semidirect
5. #16839670C2semidirect
6. #16839665C2semidirect
7. #16839665C2semidirect
8. #16839661C2semidirect
9. #16839650C2semidirect
10. #16839622C2semidirect
11. C2×#121×C61C2semidirect
67. C2×C4×D61D4semidirect
68. C4⋊C4×C61D4semidirect
183. C2×#121D61semidirect
193. C61#2414semidirect
254. C4⋊C4C22⋊D61semidirect