Finite Group Databasebeta

← #21451392

Subgroups — #21451392

Order 7808.

492 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×#14519742C211yesmaximal, characteristic, complemented
2C2×#14519736C211yesmaximal, characteristic
3#16839695C211yesmaximal, characteristic, complemented
4#16839690C211yesmaximal, characteristic
5#16839683C211yesmaximal, characteristic, complemented
6#16839674C211yesmaximal, characteristic
7#16839656C211yesmaximal, characteristic
8#16839655C211yesmaximal, characteristic
9#16839649C211yesmaximal, characteristic, complemented
10#16839648C211yesmaximal, characteristic, complemented
11#16839647C211yesmaximal, characteristic, complemented
12#16839643C211yesmaximal, characteristic, complemented
13#16839635C211yesmaximal, characteristic
14#16839629C211yesmaximal, characteristic, complemented
15C61×#385C211yesmaximal, characteristic
16C22×Dic122C2211yescharacteristic
17#14519742—24no—
18#14519736—24no—
19C2×C4⋊Dic61C2211yescharacteristic
20C2×C4⋊Dic61C2211yescharacteristic
21C2×C4⋊Dic61C2211yescharacteristic
22C2×#11758196C2211yescharacteristic
23C2×#11758196C2211yescharacteristic
24C2×#11758196C2211yescharacteristic
25C2×#11758196C2211yescharacteristic
26C2×C22⋊Dic61C2211yescharacteristic
27C2×C22⋊Dic61C2211yescharacteristic
28C2×C22⋊Dic61C2211yescharacteristic
29C2×C22⋊Dic61C2211yescharacteristic
30C2×C4×Dic61C2211yescharacteristic
31C2×C4×Dic61C2211yescharacteristic
32C2×C4×Dic61C2211yescharacteristic
33C2×C4×Dic61C2211yescharacteristic
34#14519684C2211yescharacteristic
35#14519684C2211yescharacteristic
36#14519684C2211yescharacteristic
37#14519684C2211yescharacteristic
38#14519684C2211yescharacteristic
39#14519684C2211yescharacteristic
40#14519684C2211yescharacteristic
41#14519684C2211yescharacteristic
42#14519684C2211yescharacteristic
43#14519684C2211yescharacteristic
44#14519684C2211yescharacteristic
45#14519684C2211yescharacteristic
46C23×C4×C61C2211yescharacteristic
47C2×C4⋊C4×C61C2211yescharacteristic
48C2×C4⋊C4×C61C2211yescharacteristic
49C2×C22⋊C4×C61C2211yescharacteristic
50C2×C22⋊C4×C61C2211yescharacteristic
51#95×C61C2211yescharacteristic
52#95×C61C2211yescharacteristic
53C24×C61C2311yescharacteristic
54C22×C4×C61—22no—
55C22×C4×C61—22no—
56C22×C4×C61—22no—
57C22×C4×C61C2311yescharacteristic
58C22×C4×C61C2311yescharacteristic
59C22×C4×C61C2311yescharacteristic
60C22×C4×C61C2311yescharacteristic
61C22×C4×C61C2311yescharacteristic
62C22×C4×C61C2311yescharacteristic
63C22×Dic61C2311yescharacteristic
64C22×Dic61C2311yescharacteristic
65C22×Dic61C2311yescharacteristic
66C22×Dic61C2311yescharacteristic
67C22×Dic61C2311yescharacteristic
68C22×Dic61C2311yescharacteristic
69C22×Dic61C2311yescharacteristic
70C22×Dic61C2311yescharacteristic
71C2×Dic122—22no—
72C2×Dic122—22no—
73C2×Dic122—22no—
74C4⋊C4×C61—22no—
75C4⋊C4×C61—22no—
76C22⋊C4×C61—22no—
77C22⋊C4×C61—22no—
78C22⋊Dic61—22no—
79C22⋊Dic61—22no—
80C22⋊Dic61—22no—
81C22⋊Dic61—22no—
82C4⋊Dic61—22no—
83C4⋊Dic61—22no—
84C4⋊Dic61—22no—
85#11758196—22no—
86#11758196—22no—
87#11758196—22no—
88#11758196—22no—
89C4×Dic61—22no—
90C4×Dic61—22no—
91C4×Dic61—22no—
92C4×Dic61D414yes—
93C23×C61—21no—
94C23×C61—21no—
95C23×C61—21no—
96C23×C61—21no—
97C23×C61—21no—
98C23×C61—21no—
99C23×C61#4112yes—
100C23×C61C2411yescharacteristic
101C2×C4×C61—28no—
102C2×C4×C61—21no—
103C2×C4×C61—21no—
104C2×C4×C61—21no—
105C2×C4×C61—21no—
106C2×C4×C61—21no—
107C2×C4×C61—21no—
108C2×C4×C61—21no—
109C2×C4×C61—21no—
110C2×C4×C61—21no—
111C2×C4×C61—21no—
112C2×C4×C61—21no—
113C2×C4×C61—21no—
114C2×C4×C61—21no—
115C2×C4×C61—21no—
116C2×C4×C61—21no—
117C2×C4×C61C2×D412yes—
118C2×C4×C61#4112yes—
119C2×C4×C61#4112yes—
120C2×Dic61—21no—
121C2×Dic61—21no—
122C2×Dic61—21no—
123C2×Dic61—21no—
124C2×Dic61—21no—
125C2×Dic61—21no—
126C2×Dic61—21no—
127C2×Dic61—21no—
128C2×Dic61—21no—
129C2×Dic61—21no—
130C2×Dic61—21no—
131C2×Dic61—21no—
132C2×Dic61—21no—
133C2×Dic61—21no—
134C2×Dic61—21no—
135C2×Dic61—21no—
136C2×Dic61—21no—
137C2×Dic61—21no—
138C2×Dic61—21no—
139C2×Dic61—21no—
140C2×Dic61—21no—
141C2×Dic61C2×D412yes—
142C2×Dic61C2×D412yes—
143C2×Dic61#4112yes—
144Dic122—28no—
145C22×C61—22no—
146C22×C61—22no—
147C22×C61—22no—
148C22×C61—41no—
149C22×C61—41no—
150C22×C61—41no—
151C22×C61—41no—
152C22×C61C22×D411yescharacteristic
153C22×C61C2×#4111yescharacteristic
154C22×C61C2×#4111yescharacteristic
155C22×C61C2×#4111yescharacteristic
156C22×C61C2×#4111yescharacteristic
157C22×C612−1+411yescharacteristic
158C22×C612−1+411yescharacteristic
159C4×C61—22no—
160C4×C61—22no—
161C4×C61—22no—
162C4×C61—41no—
163C4×C61—41no—
164C4×C61—41no—
165Dic61—22no—
166Dic61—22no—
167Dic61—22no—
168Dic61—41no—
169Dic61—41no—
170Dic61—41no—
171Dic61—41no—
172Dic61—41no—
173#2599—611nomaximal, Sylow
174C2×C61—42no—
175C2×C61#52511yescharacteristic
176C2×C61#52511yescharacteristic
177C2×C61#53611yescharacteristic
178C2×C61#55211yescharacteristic
179C2×C61#55211yescharacteristic
180C2×C61#55611yescharacteristic
181C2×C61#55611yescharacteristic
182C2×C4×Q8—611no—
183C2×#117—611no—
184#398—611no—
185#397—611no—
186#395—611no—
187#393—611no—
188#388—611no—
189#388—611no—
190#387—611no—
191#387—611no—
192#387—611no—
193#387—611no—
194#385—611no—
195#385D6111yescharacteristic
196#383—611no—
197C61#259911yescharacteristic, complemented, Sylow
198C22×Q8—611no—
199C23×C4C2×D6111yescharacteristic
200C4×Q8—1224no—
201#117—1224no—
202C2×C4⋊C4—611no—
203C2×C4⋊C4—611no—
204C2×C4⋊C4—611no—
205C2×C4⋊C4—611no—
206C2×C4⋊C4—611no—
207C2×C4⋊C4—611no—
208C2×C4⋊C4—611no—
209C2×C4⋊C4C2×D6111yescharacteristic
210C2×C4⋊C4C2×D6111yescharacteristic
211C2×C22⋊C4—611no—
212C2×C22⋊C4—611no—
213C2×C22⋊C4—611no—
214C2×C22⋊C4—611no—
215C2×C22⋊C4C2×D6111yescharacteristic
216C2×C22⋊C4C2×D6111yescharacteristic
217C2×C42—611no—
218C2×C42—611no—
219C2×C42—611no—
220C2×C42—611no—
221#95—611no—
222#95—611no—
223#95—611no—
224#95—611no—
225#95—611no—
226#95—611no—
227#95—611no—
228#95—611no—
229#95—611no—
230#95—611no—
231#95—611no—
232#95—611no—
233#95C2×D6111yescharacteristic
234#95C2×D6111yescharacteristic
235C24C22×D6111yescharacteristic
236C2×Q8—1222no—
237C2×Q8—1222no—
238C2×Q8—1222no—
239C22×C4—22no—
240C22×C4—22no—
241C22×C4—22no—
242C22×C4—611no—
243C22×C4—611no—
244C22×C4—611no—
245C22×C4—611no—
246C22×C4—611no—
247C22×C4—611no—
248C22×C4—611no—
249C22×C4—611no—
250C22×C4C22×D6111yescharacteristic
251C22×C4C22×D6111yescharacteristic
252C22×C4C22×D6111yescharacteristic
253C22×C4C22×D6111yescharacteristic
254C22×C4C22×D6111yescharacteristic
255C22×C4C22×D6111yescharacteristic
256C4⋊C4—22no—
257C4⋊C4—22no—
258C4⋊C4—1222no—
259C4⋊C4—1222no—
260C4⋊C4—1222no—
261C4⋊C4—1222no—
262C4⋊C4—1222no—
263C4⋊C4—1222no—
264C4⋊C4—1222no—
265C22⋊C4—22no—
266C22⋊C4—22no—
267C22⋊C4—1222no—
268C22⋊C4—1222no—
269C22⋊C4—1222no—
270C22⋊C4—1222no—
271C42—614no—
272C42—1222no—
273C42—1222no—
274C42—1222no—
275C23—21no—
276C23—21no—
277C23—21no—
278C23—21no—
279C23—21no—
280C23—21no—
281C23#1175822412yes—
282C23C23×D6111yescharacteristic
283Q8—1228no—
284C2×C4—28no—
285C2×C4—21no—
286C2×C4—21no—
287C2×C4—21no—
288C2×C4—21no—
289C2×C4—21no—
290C2×C4—21no—
291C2×C4—21no—
292C2×C4—21no—
293C2×C4—21no—
294C2×C4—21no—
295C2×C4—21no—
296C2×C4—21no—
297C2×C4—21no—
298C2×C4—21no—
299C2×C4—21no—
300C2×C4—612no—
301C2×C4—612no—
302C2×C4—612no—
303C2×C4—1221no—
304C2×C4—1221no—
305C2×C4—1221no—
306C2×C4—1221no—
307C2×C4—1221no—
308C2×C4—1221no—
309C2×C4—1221no—
310C2×C4—1221no—
311C2×C4—1221no—
312C2×C4—1221no—
313C2×C4—1221no—
314C2×C4—1221no—
315C2×C4—1221no—
316C2×C4—1221no—
317C2×C4—1221no—
318C2×C4—1221no—
319C2×C4—1221no—
320C2×C4—1221no—
321C2×C4—1221no—
322C2×C4—1221no—
323C2×C4—1221no—
324C2×C4#1175822212yes—
325C2×C4D4×D6112yes—
326C2×C4#1175822412yes—
327C22—22no—
328C22—22no—
329C22—22no—
330C22—41no—
331C22—41no—
332C22—41no—
333C22—41no—
334C22C2×D4×D6111yescharacteristic
335C22#41×D6111yescharacteristic
336C22C2×#1175822411yescharacteristic
337C22C2×#1175822411yescharacteristic
338C22C2×#1175822211yescharacteristic
339C22#1451982411yescharacteristic
340C22#1451982511yescharacteristic
341C4—22no—
342C4—22no—
343C4—22no—
344C4—41no—
345C4—41no—
346C4—41no—
347C4—1222no—
348C4—1222no—
349C4—1222no—
350C4—2441no—
351C4—2441no—
352C4—2441no—
353C4—2441no—
354C4—2441no—
355C2—42no—
356C2#1684026811yescharacteristic
357C2#1684027111yescharacteristic
358C2#1684033511yescharacteristic
359C2#1684044711yescharacteristic
360C2#1684044911yescharacteristic
361C2#1684048211yescharacteristic
362C2#1684048311yescharacteristic
subgroupG/H
center, FrattiniC23C23×D61
commutator, socleC23×C61C24
FittingC61×#385C2
hypercenter#385D61
hypocenterC61#2599
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C23 ◁ #385

Complements

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

NH ≅ G/Ntype
1. C2×#14519742C2semidirect
3. #16839695C2semidirect
5. #16839683C2semidirect
9. #16839649C2semidirect
10. #16839648C2semidirect
11. #16839647C2semidirect
12. #16839643C2semidirect
14. #16839629C2semidirect
197. C61#2599semidirect