Finite Group Databasebeta

← #21451072

Subgroups — #21451072

Order 7808.

412 conjugacy classes of subgroups.

The subgroup lattice has 350 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#16839704C211yesmaximal, characteristic, complemented
2#16839701C211yesmaximal, characteristic, complemented
3#16839689C211yesmaximal, characteristic
4#16839684C211yesmaximal, characteristic
5#16839660C211yesmaximal, characteristic, complemented
6#16839653C211yesmaximal, characteristic
7#16839653C211yesmaximal, characteristic
8#16839646C211yesmaximal, characteristic, complemented
9#16839646C211yesmaximal, characteristic, complemented
10#16839643C211yesmaximal, characteristic, complemented
11#16839633C211yesmaximal, characteristic
12#16839629C211yesmaximal, characteristic, complemented
13#16839624C211yesmaximal, characteristic
14C4×#11758198C211yesmaximal, characteristic
15C4×C4⋊C4×C61C211yesmaximal, characteristic, complemented
16C22×C4×D61C2211yescharacteristic
17C2×C4⋊Dic61C2211yescharacteristic
18C2×C4⋊Dic61C2211yescharacteristic
19C2×#11758196C2211yescharacteristic
20C2×#11758196C2211yescharacteristic
21C2×#11758196C2211yescharacteristic
22C2×#11758196C2211yescharacteristic
23C2×#11758198C2211yescharacteristic
24C2×#11758198C2211yescharacteristic
25C2×#11758198C2211yescharacteristic
26C2×#11758198C2211yescharacteristic
27C2×#11758198C2211yescharacteristic
28C2×#11758198C2211yescharacteristic
29C2×C4×Dic61C2211yescharacteristic
30#14519684C2211yescharacteristic
31#14519684C2211yescharacteristic
32#14519684C2211yescharacteristic
33#14519684C2211yescharacteristic
34#14519684C2211yescharacteristic
35#14519684C2211yescharacteristic
36#14519684C2211yescharacteristic
37#14519684C2211yescharacteristic
38#14519684C2211yescharacteristic
39#14519684C2211yescharacteristic
40#14519684C2211yescharacteristic
41#14519684C2211yescharacteristic
42#14519684C2211yescharacteristic
43#14519684C2211yescharacteristic
44C2×C4⋊C4×C61C2211yescharacteristic
45C2×C4⋊C4×C61C2211yescharacteristic
46C2×C42×C61C2211yescharacteristic
47C2×C42×C61C2211yescharacteristic
48C2×C42×C61C2211yescharacteristic
49#95×C61C2211yescharacteristic
50#95×C61C2211yescharacteristic
51C23×D61C2311yescharacteristic
52C22×C4×C61C2311yescharacteristic
53C22×C4×C61C2311yescharacteristic
54C22×C4×C61C2311yescharacteristic
55C22×C4×C61C2311yescharacteristic
56C22×C4×C61C2311yescharacteristic
57C22×C4×C61C2311yescharacteristic
58C22×C4×C61C2311yescharacteristic
59C22×Dic61C2311yescharacteristic
60C22×Dic61C2311yescharacteristic
61C22×Dic61C2311yescharacteristic
62C22×Dic61C2311yescharacteristic
63C22×Dic61C2311yescharacteristic
64C22×Dic61C2311yescharacteristic
65C22×Dic61C2311yescharacteristic
66C2×C4×D61—22no—
67C2×C4×D61—22no—
68C2×C4×D61—41no—
69C4⋊C4×C61—22no—
70C4⋊C4×C61—22no—
71C42×C61—22no—
72C42×C61—41no—
73C42×C61—41no—
74#11758198—22no—
75#11758198—22no—
76#11758198—22no—
77#11758198—22no—
78#11758198—22no—
79#11758198—41no—
80C4⋊Dic61—22no—
81C4⋊Dic61—41no—
82#11758196—22no—
83#11758196—22no—
84#11758196—22no—
85#11758196—41no—
86C4×Dic61—22no—
87C23×C61C2411yescharacteristic
88C22×D61—21no—
89C22×D61—21no—
90C22×D61—21no—
91C22×D61—21no—
92C22×D61—21no—
93C22×D61—21no—
94C22×D61#4112yes—
95C2×C4×C61—21no—
96C2×C4×C61—21no—
97C2×C4×C61—21no—
98C2×C4×C61—21no—
99C2×C4×C61—21no—
100C2×C4×C61—21no—
101C2×C4×C61—21no—
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#4112yes—
113C2×C4×C61#4112yes—
114C2×C4×C61#4112yes—
115C2×C4×C61#4112yes—
116C2×Dic61—21no—
117C2×Dic61—21no—
118C2×Dic61—21no—
119C2×Dic61—21no—
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—
137C4×D61—44no—
138C22×C61C2×#4111yescharacteristic
139C22×C61C2×#4111yescharacteristic
140C22×C61C2×#4111yescharacteristic
141C22×C61C2×#4111yescharacteristic
142C22×C61C2×#4111yescharacteristic
143C22×C61H(5,𝔽2)11yescharacteristic
144C22×C612−1+411yescharacteristic
145C2×D61—22no—
146C2×D61—22no—
147C2×D61—22no—
148C2×D61—41no—
149C2×D61—41no—
150C2×D61—41no—
151C2×D61—41no—
152C4×C61—22no—
153C4×C61—22no—
154C4×C61—22no—
155C4×C61—22no—
156C4×C61—41no—
157C4×C61—41no—
158C4×C61—41no—
159Dic61—41no—
160Dic61—41no—
161Dic61—41no—
162Dic61—41no—
163Dic61—41no—
164Dic61—41no—
165Dic61—41no—
166#2573—611nomaximal, Sylow
167C2×C61#52911yescharacteristic
168C2×C61#52911yescharacteristic
169C2×C61#53911yescharacteristic
170C2×C61#55111yescharacteristic
171C2×C61#55211yescharacteristic
172C2×C61#55311yescharacteristic
173C2×C61#55611yescharacteristic
174D61—42no—
175#400—611no—
176#400—611no—
177#397—611no—
178#396—611no—
179#389—611no—
180#388—611no—
181#388—611no—
182#387—611no—
183#387—611no—
184#387—611no—
185#385—611no—
186#383—611no—
187#381—611no—
188C4×C4⋊C4D6111yescharacteristic, complemented
189C4×C22⋊C4—611no—
190C61#257311yescharacteristic, complemented, Sylow
191C23×C4—611no—
192C2×C4⋊C4—611no—
193C2×C4⋊C4—611no—
194C2×C4⋊C4—611no—
195C2×C4⋊C4—611no—
196C2×C4⋊C4—611no—
197C2×C4⋊C4—611no—
198C2×C4⋊C4C2×D6111yescharacteristic
199C2×C4⋊C4C2×D6111yescharacteristic
200C2×C22⋊C4—611no—
201C2×C22⋊C4—611no—
202C2×C22⋊C4—611no—
203C2×C22⋊C4—611no—
204C2×C22⋊C4—611no—
205C2×C22⋊C4—611no—
206C2×C42—611no—
207C2×C42C2×D6111yescharacteristic
208C2×C42C2×D6111yescharacteristic
209C2×C42C2×D6111yescharacteristic
210#95—611no—
211#95—611no—
212#95—611no—
213#95—611no—
214#95—611no—
215#95—611no—
216#95—611no—
217#95—611no—
218#95—611no—
219#95—611no—
220#95—611no—
221#95—611no—
222#95—611no—
223#95—611no—
224#95C2×D6111yescharacteristic
225#95C2×D6111yescharacteristic
226C24—611no—
227C22×C4—611no—
228C22×C4—611no—
229C22×C4—611no—
230C22×C4—611no—
231C22×C4—611no—
232C22×C4—611no—
233C22×C4—611no—
234C22×C4—1222no—
235C22×C4—1222no—
236C22×C4—2441no—
237C22×C4C22×D6111yescharacteristic
238C22×C4C22×D6111yescharacteristic
239C22×C4C22×D6111yescharacteristic
240C22×C4C22×D6111yescharacteristic
241C22×C4C22×D6111yescharacteristic
242C22×C4C22×D6111yescharacteristic
243C22×C4C22×D6111yescharacteristic
244C4⋊C4—22no—
245C4⋊C4—22no—
246C4⋊C4—1222no—
247C4⋊C4—1222no—
248C4⋊C4—1222no—
249C4⋊C4—1222no—
250C4⋊C4—2441no—
251C4⋊C4—2441no—
252C22⋊C4—1222no—
253C22⋊C4—1222no—
254C22⋊C4—1222no—
255C22⋊C4—1222no—
256C22⋊C4—1222no—
257C22⋊C4—2441no—
258C42—22no—
259C42—41no—
260C42—41no—
261C42—1222no—
262C23—612no—
263C23—1221no—
264C23—1221no—
265C23—1221no—
266C23—1221no—
267C23—1221no—
268C23—1221no—
269C23C23×D6111yescharacteristic
270C2×C4—21no—
271C2×C4—21no—
272C2×C4—21no—
273C2×C4—21no—
274C2×C4—21no—
275C2×C4—21no—
276C2×C4—21no—
277C2×C4—21no—
278C2×C4—21no—
279C2×C4—21no—
280C2×C4—21no—
281C2×C4—21no—
282C2×C4—21no—
283C2×C4—21no—
284C2×C4—21no—
285C2×C4—21no—
286C2×C4—21no—
287C2×C4—1221no—
288C2×C4—1221no—
289C2×C4—1221no—
290C2×C4—1221no—
291C2×C4—1221no—
292C2×C4—1221no—
293C2×C4—1221no—
294C2×C4—1221no—
295C2×C4—1221no—
296C2×C4—1221no—
297C2×C4—1221no—
298C2×C4—1221no—
299C2×C4—1221no—
300C2×C4—1221no—
301C2×C4—1221no—
302C2×C4—1221no—
303C2×C4—1221no—
304C2×C4—1221no—
305C2×C4—1221no—
306C2×C4—1221no—
307C2×C4—1221no—
308C2×C4—2444no—
309C2×C4#1175822212yes—
310C2×C4#1175822212yes—
311C2×C4#1175822212yes—
312C2×C4#1175822612yes—
313C22—1222no—
314C22—1222no—
315C22—1222no—
316C22—2441no—
317C22—2441no—
318C22—2441no—
319C22—2441no—
320C22#41×D6111yescharacteristic
321C22C2×#1175822211yescharacteristic
322C22C2×#1175822211yescharacteristic
323C22C2×#1175822211yescharacteristic
324C22C2×#1175822611yescharacteristic
325C22#1451982211yescharacteristic
326C22#1451982411yescharacteristic
327C4—22no—
328C4—22no—
329C4—22no—
330C4—22no—
331C4—41no—
332C4—41no—
333C4—41no—
334C4—2441no—
335C4—2441no—
336C4—2441no—
337C4—2441no—
338C4—2441no—
339C4—2441no—
340C4—2441no—
341C2—2442no—
342C2#1684029611yescharacteristic
343C2#1684029911yescharacteristic
344C2#1684035411yescharacteristic
345C2#1684044111yescharacteristic
346C2#1684045111yescharacteristic
347C2#1684046011yescharacteristic
348C2#1684048511yescharacteristic
subgroupG/H
center, FrattiniC23C23×D61
commutator, socleC23×C61C24
FittingC4×C4⋊C4×C61C2
hypercenterC4×C4⋊C4D61
hypocenterC61#2573
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C23 ◁ C4×C4⋊C4

Complements

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

NH ≅ G/Ntype
1. #16839704C2semidirect
2. #16839701C2semidirect
5. #16839660C2semidirect
8. #16839646C2semidirect
9. #16839646C2semidirect
10. #16839643C2semidirect
12. #16839629C2semidirect
15. C4×C4⋊C4×C61C2semidirect
188. C4×C4⋊C4D61semidirect
190. C61#2573semidirect