Finite Group Databasebeta

← #21449235

Subgroups — #21449235

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×#14519752C211yesmaximal, characteristic, complemented
2C2×#14519752C211yesmaximal, characteristic, complemented
3C2×C4×D244C211yesmaximal, characteristic, complemented
4C2×#14519735C211yesmaximal, characteristic, complemented
5#16839679C212yesmaximal, complemented
6#16839672C212yesmaximal, complemented
7#16839664C211yesmaximal, characteristic, complemented
8#16839663C212yesmaximal, complemented
9#16839654C212yesmaximal, complemented
10#16839619C211yesmaximal, characteristic, complemented
11C61×#389C211yesmaximal, characteristic, complemented
12C22×D244C2211yescharacteristic
13C22×D244C2211yescharacteristic
14C22×D244C2212yes—
15C22×D244C2212yes—
16C22×C4×D61C2211yescharacteristic
17C22×C4×D61C2211yescharacteristic
18#14519752—24no—
19#14519752—24no—
20C4×D244—24no—
21#14519735—24no—
22C2×C4⋊Dic61C2211yescharacteristic
23C2×C4⋊Dic61C2211yescharacteristic
24C2×#11758198C2212yes—
25C2×#11758198C2211yescharacteristic
26C2×#11758198C2211yescharacteristic
27C2×#11758198C2212yes—
28C2×#11758198C2212yes—
29C2×#11758198C2212yes—
30C2×#11758198C2212yes—
31C2×#11758198C2212yes—
32C2×C4×Dic61C2212yes—
33#14519684C2212yes—
34C2×C4⋊C4×C61C2211yescharacteristic
35C2×C4⋊C4×C61C2212yes—
36C2×C4⋊C4×C61C2211yescharacteristic
37C2×C42×C61C2211yescharacteristic
38#95×C61C2212yes—
39C23×D61C2312yes—
40C23×D61C2311yescharacteristic
41C23×D61C2311yescharacteristic
42C22×C4×C61C2312yes—
43C22×C4×C61C2311yescharacteristic
44C22×C4×C61C2312yes—
45C22×C4×C61C2311yescharacteristic
46C22×C4×C61C2311yescharacteristic
47C22×Dic61C2311yescharacteristic
48C22×Dic61C2312yes—
49C22×Dic61C2311yescharacteristic
50C2×D244—22no—
51C2×D244—22no—
52C2×D244—22no—
53C2×D244—24no—
54C2×D244—24no—
55C2×D244—24no—
56C2×D244—22no—
57C2×D244—22no—
58C2×D244—22no—
59C2×D244—42no—
60C2×D244—42no—
61C2×D244—42no—
62C2×C4×D61—22no—
63C2×C4×D61—22no—
64C2×C4×D61—22no—
65C2×C4×D61—22no—
66C2×C4×D61—22no—
67C2×C4×D61D414yescomplemented
68C4⋊C4×C61—22no—
69C4⋊C4×C61—42no—
70C4⋊C4×C61D414yescomplemented
71C42×C61—22no—
72#11758198—22no—
73#11758198—24no—
74#11758198—24no—
75#11758198—24no—
76#11758198—22no—
77#11758198—24no—
78#11758198—42no—
79#11758198—42no—
80C4⋊Dic61—22no—
81C4⋊Dic61—22no—
82C4×Dic61—24no—
83C23×C61C2411yescharacteristic
84C22×D61—21no—
85C22×D61—21no—
86C22×D61—21no—
87C22×D61—21no—
88C22×D61—21no—
89C22×D61—21no—
90C22×D61—21no—
91C22×D61—21no—
92C22×D61—21no—
93C22×D61—21no—
94C22×D61—21no—
95C22×D61—21no—
96C22×D61—22no—
97C22×D61—22no—
98C22×D61—22no—
99C22×D61—22no—
100C22×D61—22no—
101C22×D61—22no—
102C22×D61—22no—
103C22×D61C2×D412yes—
104C22×D61#4112yes—
105C2×C4×C61—21no—
106C2×C4×C61—21no—
107C2×C4×C61—22no—
108C2×C4×C61—22no—
109C2×C4×C61—21no—
110C2×C4×C61—22no—
111C2×C4×C61—21no—
112C2×C4×C61—22no—
113C2×C4×C61—21no—
114C2×C4×C61—22no—
115C2×C4×C61C2×D414yes—
116C2×C4×C61C2×D412yes—
117C2×C4×C61C2×D412yes—
118C2×C4×C61#4112yes—
119C2×C4×C61#4112yes—
120C2×Dic61—21no—
121C2×Dic61—21no—
122C2×Dic61—22no—
123C2×Dic61—21no—
124C2×Dic61—21no—
125C2×Dic61—22no—
126C2×Dic61—21no—
127C2×Dic61—22no—
128C2×Dic61C2×D412yes—
129D244—28no—
130D244—48no—
131D244—48no—
132D244—44no—
133C4×D61—28no—
134C4×D61—44no—
135C22×C61C22×D411yescharacteristic
136C22×C61C22×D411yescharacteristic
137C22×C61C2×#4111yescharacteristic
138C22×C61C2×#4111yescharacteristic
139C22×C61C2×#4111yescharacteristic
140C22×C61H(5,𝔽2)11yescharacteristic
141C22×C61H(5,𝔽2)11yescharacteristic
142C2×D61—22no—
143C2×D61—22no—
144C2×D61—22no—
145C2×D61—22no—
146C2×D61—22no—
147C2×D61—22no—
148C2×D61—41no—
149C2×D61—41no—
150C2×D61—41no—
151C2×D61—41no—
152C2×D61—41no—
153C2×D61—41no—
154C2×D61—41no—
155C2×D61—41no—
156C2×D61—42no—
157C2×D61—42no—
158C2×D61—42no—
159C2×D61—42no—
160C2×D61—42no—
161C2×D61—42no—
162C2×D61—42no—
163C4×C61—22no—
164C4×C61—24no—
165C4×C61—42no—
166C4×C61—41no—
167C4×C61#12114yes—
168Dic61—22no—
169Dic61—41no—
170Dic61—42no—
171#2414—611nomaximal, Sylow
172C2×C61C2×#12111yescharacteristic
173C2×C61#52511yescharacteristic
174C2×C61#53511yescharacteristic
175C2×C61#54611yescharacteristic
176C2×C61#55011yescharacteristic
177C2×C61#55311yescharacteristic
178C2×C61#55511yescharacteristic
179D61—42no—
180D61—42no—
181D61—82no—
182C2×#121—611no—
183C2×#121—611no—
184C2×C4×D4—611no—
185C2×#117—611no—
186#394—612no—
187#392—612no—
188#390—612no—
189#390—611no—
190#389D6111yescharacteristic, complemented
191#388—612no—
192#380—611no—
193C61#241411yescharacteristic, complemented, Sylow
194C22×D4—611no—
195C22×D4—611no—
196C22×D4—612no—
197C22×D4—612no—
198C23×C4—611no—
199C23×C4—611no—
200#121—1224no—
201#121—1224no—
202C4×D4—1224no—
203#117—1224no—
204C2×C4⋊C4—611no—
205C2×C4⋊C4—611no—
206C2×C4⋊C4C2×D6111yescharacteristic
207C2×C4⋊C4C2×D6112yes—
208C2×C4⋊C4C2×D6111yescharacteristic
209C2×C22⋊C4—612no—
210C2×C22⋊C4—611no—
211C2×C22⋊C4—611no—
212C2×C22⋊C4—612no—
213C2×C22⋊C4—612no—
214C2×C22⋊C4—612no—
215C2×C22⋊C4—612no—
216C2×C22⋊C4—612no—
217C2×C42—612no—
218C2×C42C2×D6111yescharacteristic
219#95—612no—
220#95C2×D6112yes—
221C24—611no—
222C24—611no—
223C24—612no—
224C2×D4—1222no—
225C2×D4—1222no—
226C2×D4—1224no—
227C2×D4—1224no—
228C2×D4—1224no—
229C2×D4—1222no—
230C2×D4—1222no—
231C2×D4—1222no—
232C2×D4—1222no—
233C2×D4—2442no—
234C2×D4—2442no—
235C2×D4—2442no—
236C22×C4—611no—
237C22×C4—614no—
238C22×C4—611no—
239C22×C4—612no—
240C22×C4—1222no—
241C22×C4—1222no—
242C22×C4—1222no—
243C22×C4—1222no—
244C22×C4—1222no—
245C22×C4C22×D6112yes—
246C22×C4C22×D6111yescharacteristic
247C22×C4C22×D6112yes—
248C22×C4C22×D6111yescharacteristic
249C22×C4C22×D6111yescharacteristic
250C4⋊C4—22no—
251C4⋊C4—42no—
252C4⋊C4—1222no—
253C4⋊C4—1222no—
254C4⋊C4D24414yescomplemented
255C22⋊C4—1222no—
256C22⋊C4—1224no—
257C22⋊C4—1222no—
258C22⋊C4—1224no—
259C22⋊C4—1224no—
260C22⋊C4—1224no—
261C22⋊C4—2442no—
262C22⋊C4—2442no—
263C42—22no—
264C42—1224no—
265C23—612no—
266C23—612no—
267C23—1221no—
268C23—1221no—
269C23—1221no—
270C23—1221no—
271C23—1221no—
272C23—1221no—
273C23—1221no—
274C23—1221no—
275C23—1221no—
276C23—1221no—
277C23—1221no—
278C23—1221no—
279C23—1222no—
280C23—1222no—
281C23—1222no—
282C23—1222no—
283C23—1222no—
284C23—1222no—
285C23—1222no—
286C23C23×D6111yescharacteristic
287D4—1228no—
288D4—2448no—
289D4—2448no—
290D4—2444no—
291C2×C4—21no—
292C2×C4—21no—
293C2×C4—22no—
294C2×C4—22no—
295C2×C4—21no—
296C2×C4—22no—
297C2×C4—21no—
298C2×C4—22no—
299C2×C4—21no—
300C2×C4—22no—
301C2×C4—612no—
302C2×C4—1221no—
303C2×C4—1221no—
304C2×C4—1228no—
305C2×C4—1221no—
306C2×C4—1222no—
307C2×C4—1221no—
308C2×C4—1222no—
309C2×C4—1221no—
310C2×C4—1222no—
311C2×C4—2444no—
312C2×C4C2×D24414yes—
313C2×C4C2×D24412yes—
314C2×C4D4×D6112yes—
315C2×C4#1175822612yes—
316C2×C4#1175822612yes—
317C22—1222no—
318C22—1222no—
319C22—1222no—
320C22—1222no—
321C22—1222no—
322C22—1222no—
323C22—2442no—
324C22—2442no—
325C22—2442no—
326C22—2442no—
327C22—2442no—
328C22—2442no—
329C22—2442no—
330C22—2441no—
331C22—2441no—
332C22—2441no—
333C22—2441no—
334C22—2441no—
335C22—2441no—
336C22—2441no—
337C22—2441no—
338C22C2×D4×D6111yescharacteristic
339C22C22×D24411yescharacteristic
340C22#41×D6111yescharacteristic
341C22C2×#1175822611yescharacteristic
342C22C2×#1175822611yescharacteristic
343C22#1451982211yescharacteristic
344C22#1451982311yescharacteristic
345C4—22no—
346C4—24no—
347C4—41no—
348C4—42no—
349C4—1222no—
350C4—2441no—
351C4—2442no—
352C4#1451975214yes—
353C2—4882no—
354C2—2442no—
355C2—2442no—
356C2C2×#1451975211yescharacteristic
357C2#1684027511yescharacteristic
358C2#1684032811yescharacteristic
359C2#1684040711yescharacteristic
360C2#1684043411yescharacteristic
361C2#1684046511yescharacteristic
362C2#1684047811yescharacteristic
subgroupG/H
center, FrattiniC23C23×D61
commutator, socleC23×C61C24
FittingC61×#389C2
hypercenter#389D61
hypocenterC61#2414
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C23 ◁ #389

Complements

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

NH ≅ G/Ntype
1. C2×#14519752C2semidirect
2. C2×#14519752C2semidirect
3. C2×C4×D244C2semidirect
4. C2×#14519735C2semidirect
5. #16839679C2semidirect
6. #16839672C2semidirect
7. #16839664C2semidirect
8. #16839663C2semidirect
9. #16839654C2semidirect
10. #16839619C2semidirect
11. C61×#389C2semidirect
67. C2×C4×D61D4semidirect
70. C4⋊C4×C61D4semidirect
190. #389D61semidirect
193. C61#2414semidirect
254. C4⋊C4D244semidirect