Finite Group Databasebeta

← #21451233

Subgroups — #21451233

Order 7808.

428 conjugacy classes of subgroups.

The subgroup lattice has 358 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#16839702C211yesmaximal, characteristic, complemented
2#16839695C211yesmaximal, characteristic, complemented
3#16839685C211yesmaximal, characteristic
4#16839661C211yesmaximal, characteristic, complemented
5#16839661C211yesmaximal, characteristic, complemented
6#16839657C211yesmaximal, characteristic, complemented
7#16839656C211yesmaximal, characteristic
8#16839650C211yesmaximal, characteristic
9#16839647C211yesmaximal, characteristic, complemented
10#16839643C211yesmaximal, characteristic, complemented
11#16839637C211yesmaximal, characteristic
12#16839637C211yesmaximal, characteristic
13C4⋊C4×Dic61C211yesmaximal, characteristic, complemented
14C22⋊C4×Dic61C211yesmaximal, characteristic
15C61×#396C211yesmaximal, characteristic
16C23×Dic61C2211yescharacteristic
17C2×C4⋊Dic61C2211yescharacteristic
18C2×C4⋊Dic61C2211yescharacteristic
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×C4×Dic61C2211yescharacteristic
30C2×C4×Dic61C2211yescharacteristic
31C2×C4×Dic61C2211yescharacteristic
32C2×C4×Dic61C2211yescharacteristic
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×C4⋊C4×C61C2211yescharacteristic
47C2×C22⋊C4×C61C2211yescharacteristic
48C2×C22⋊C4×C61C2211yescharacteristic
49C2×C22⋊C4×C61C2211yescharacteristic
50#95×C61C2211yescharacteristic
51C24×C61C2311yescharacteristic
52C22×C4×C61C2311yescharacteristic
53C22×C4×C61C2311yescharacteristic
54C22×C4×C61C2311yescharacteristic
55C22×C4×C61C2311yescharacteristic
56C22×C4×C61C2311yescharacteristic
57C22×C4×C61C2311yescharacteristic
58C22×Dic61—22no—
59C22×Dic61—41no—
60C22×Dic61—41no—
61C22×Dic61C2311yescharacteristic
62C22×Dic61C2311yescharacteristic
63C22×Dic61C2311yescharacteristic
64C22×Dic61C2311yescharacteristic
65C22×Dic61C2311yescharacteristic
66C22×Dic61C2311yescharacteristic
67C22×Dic61C2311yescharacteristic
68C22×Dic61C2311yescharacteristic
69C4⋊C4×C61—22no—
70C4⋊C4×C61—22no—
71C4⋊C4×C61—22no—
72C22⋊C4×C61—22no—
73C22⋊C4×C61—22no—
74C22⋊C4×C61—22no—
75C22⋊Dic61—41no—
76C22⋊Dic61—41no—
77C22⋊Dic61Q814yes—
78C4⋊Dic61—22no—
79C4⋊Dic61—22no—
80C4⋊Dic61—41no—
81C4⋊Dic61—41no—
82C4⋊Dic61—41no—
83#11758196—22no—
84#11758196—22no—
85#11758196—41no—
86#11758196—41no—
87C4×Dic61—22no—
88C4×Dic61—41no—
89C4×Dic61—41no—
90C4×Dic61—41no—
91C23×C61—21no—
92C23×C61—21no—
93C23×C61—21no—
94C23×C61—21no—
95C23×C61—21no—
96C23×C61—21no—
97C23×C61C2×Q812yes—
98C23×C61C2411yescharacteristic
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—21no—
113C2×C4×C61—21no—
114C2×C4×C61#4112yes—
115C2×C4×C61#4112yes—
116C2×C4×C61#4112yes—
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—
137C2×Dic61—21no—
138C2×Dic61—44no—
139C2×Dic61C2×Q812yes—
140C2×Dic61C2×Q812yes—
141C2×Dic61#4112yes—
142C22×C61—22no—
143C22×C61—22no—
144C22×C61—22no—
145C22×C61—41no—
146C22×C61—41no—
147C22×C61—41no—
148C22×C61—41no—
149C22×C61C22×Q811yescharacteristic
150C22×C61C2×#4111yescharacteristic
151C22×C61C2×#4111yescharacteristic
152C22×C61C2×#4111yescharacteristic
153C22×C61C2×#4111yescharacteristic
154C22×C61H(5,𝔽2)11yescharacteristic
155C22×C61H(5,𝔽2)11yescharacteristic
156C4×C61—22no—
157C4×C61—22no—
158C4×C61—22no—
159C4×C61—41no—
160C4×C61—41no—
161C4×C61—41no—
162Dic61—22no—
163Dic61—22no—
164Dic61—22no—
165Dic61—41no—
166Dic61—41no—
167Dic61—41no—
168Dic61—41no—
169Dic61—41no—
170#2587—611nomaximal, Sylow
171C2×C61—42no—
172C2×C61#52911yescharacteristic
173C2×C61#53311yescharacteristic
174C2×C61#53811yescharacteristic
175C2×C61#55311yescharacteristic
176C2×C61#55311yescharacteristic
177C2×C61#55411yescharacteristic
178C2×C61#55411yescharacteristic
179#400—611no—
180#398—611no—
181#396—611no—
182#396D6111yescharacteristic
183#389—611no—
184#389—611no—
185#389—611no—
186#388—611no—
187#388—611no—
188#387—611no—
189#387—611no—
190#385—611no—
191#385—611no—
192C4×C4⋊C4—611no—
193C4×C22⋊C4—611no—
194C61#258711yescharacteristic, complemented, Sylow
195C23×C4—611no—
196C2×C4⋊C4—611no—
197C2×C4⋊C4—611no—
198C2×C4⋊C4—611no—
199C2×C4⋊C4—611no—
200C2×C4⋊C4—611no—
201C2×C4⋊C4—611no—
202C2×C4⋊C4—611no—
203C2×C4⋊C4—611no—
204C2×C4⋊C4—611no—
205C2×C4⋊C4C2×D6111yescharacteristic
206C2×C4⋊C4C2×D6111yescharacteristic
207C2×C4⋊C4C2×D6111yescharacteristic
208C2×C22⋊C4—611no—
209C2×C22⋊C4—611no—
210C2×C22⋊C4—611no—
211C2×C22⋊C4C2×D6111yescharacteristic
212C2×C22⋊C4C2×D6111yescharacteristic
213C2×C22⋊C4C2×D6111yescharacteristic
214C2×C42—611no—
215C2×C42—611no—
216C2×C42—611no—
217C2×C42—611no—
218#95—611no—
219#95—611no—
220#95—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#95C2×D6111yescharacteristic
230C24C22×D6111yescharacteristic
231C22×C4—611no—
232C22×C4—611no—
233C22×C4—611no—
234C22×C4—611no—
235C22×C4—611no—
236C22×C4—611no—
237C22×C4—611no—
238C22×C4—611no—
239C22×C4—1222no—
240C22×C4—2441no—
241C22×C4—2441no—
242C22×C4C22×D6111yescharacteristic
243C22×C4C22×D6111yescharacteristic
244C22×C4C22×D6111yescharacteristic
245C22×C4C22×D6111yescharacteristic
246C22×C4C22×D6111yescharacteristic
247C22×C4C22×D6111yescharacteristic
248C4⋊C4—22no—
249C4⋊C4—22no—
250C4⋊C4—22no—
251C4⋊C4—1222no—
252C4⋊C4—1222no—
253C4⋊C4—1222no—
254C4⋊C4—1222no—
255C4⋊C4—2441no—
256C4⋊C4—2441no—
257C4⋊C4—2441no—
258C4⋊C4—2441no—
259C4⋊C4—2441no—
260C22⋊C4—22no—
261C22⋊C4—22no—
262C22⋊C4—22no—
263C22⋊C4—614no—
264C22⋊C4—2441no—
265C22⋊C4—2441no—
266C42—1222no—
267C42—2441no—
268C42—2441no—
269C42—2441no—
270C23—21no—
271C23—21no—
272C23—21no—
273C23—21no—
274C23—21no—
275C23—21no—
276C23Q8×D6112yes—
277C23C23×D6111yescharacteristic
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—21no—
288C2×C4—21no—
289C2×C4—21no—
290C2×C4—21no—
291C2×C4—21no—
292C2×C4—21no—
293C2×C4—612no—
294C2×C4—612no—
295C2×C4—612no—
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—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—2444no—
318C2×C4#1175822412yes—
319C2×C4#1175822412yes—
320C2×C4#1175822412yes—
321C22—22no—
322C22—22no—
323C22—22no—
324C22—41no—
325C22—41no—
326C22—41no—
327C22—41no—
328C22C2×Q8×D6111yescharacteristic
329C22#41×D6111yescharacteristic
330C22C2×#1175822411yescharacteristic
331C22C2×#1175822411yescharacteristic
332C22C2×#1175822411yescharacteristic
333C22#1451982311yescharacteristic
334C22#1451982311yescharacteristic
335C4—22no—
336C4—22no—
337C4—22no—
338C4—41no—
339C4—41no—
340C4—41no—
341C4—1222no—
342C4—1222no—
343C4—1222no—
344C4—2441no—
345C4—2441no—
346C4—2441no—
347C4—2441no—
348C4—2441no—
349C2—42no—
350C2#1684029311yescharacteristic
351C2#1684031411yescharacteristic
352C2#1684035111yescharacteristic
353C2#1684046411yescharacteristic
354C2#1684046411yescharacteristic
355C2#1684047011yescharacteristic
356C2#1684047011yescharacteristic
subgroupG/H
center, FrattiniC23C23×D61
commutator, socleC23×C61C24
FittingC61×#396C2
hypercenter#396D61
hypocenterC61#2587
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C23 ◁ #396

Complements

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

NH ≅ G/Ntype
1. #16839702C2semidirect
2. #16839695C2semidirect
4. #16839661C2semidirect
5. #16839661C2semidirect
6. #16839657C2semidirect
9. #16839647C2semidirect
10. #16839643C2semidirect
13. C4⋊C4×Dic61C2semidirect
194. C61#2587semidirect