Finite Group Databasebeta

← #21450321

Subgroups — #21450321

Order 7808.

456 conjugacy classes of subgroups.

The subgroup lattice has 362 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#16839704C211yesmaximal, characteristic, complemented
2#16839702C211yesmaximal, characteristic, complemented
3#16839700C211yesmaximal, characteristic, complemented
4#16839657C211yesmaximal, characteristic, complemented
5#16839645C211yesmaximal, characteristic, complemented
6#16839643C211yesmaximal, characteristic, complemented
7#16839636C211yesmaximal, characteristic
8#16839633C211yesmaximal, characteristic
9#16839633C211yesmaximal, characteristic
10#16839633C211yesmaximal, characteristic
11#16839627C211yesmaximal, characteristic, complemented
12#16839619C211yesmaximal, characteristic
13#16839609C211yesmaximal, characteristic
14#95×D61C211yesmaximal, characteristic
15C61×#398C211yesmaximal, characteristic, complemented
16C22×C4×D61C2211yescharacteristic
17C22×C4×D61C2211yescharacteristic
18C22×C4×D61C2211yescharacteristic
19C2×C4⋊Dic61C2211yescharacteristic
20C2×C4⋊Dic61C2211yescharacteristic
21C2×#11758196C2211yescharacteristic
22C2×#11758196C2211yescharacteristic
23C2×#11758196C2211yescharacteristic
24C2×#11758196C2211yescharacteristic
25C2×#11758198C2211yescharacteristic
26C2×#11758198C2211yescharacteristic
27C2×#11758198C2211yescharacteristic
28C2×#11758198C2211yescharacteristic
29C2×C4×Dic61C2211yescharacteristic
30C2×C4×Dic61C2211yescharacteristic
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×C4⋊C4×C61C2211yescharacteristic
47C2×C4⋊C4×C61C2211yescharacteristic
48#95×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—22no—
69C2×C4×D61—22no—
70C2×C4×D61—22no—
71C2×C4×D61—41no—
72C2×C4×D61—41no—
73C2×C4×D61—41no—
74C2×C4×D61—41no—
75C4⋊C4×C61—41no—
76C4⋊C4×C61—41no—
77C4⋊C4×C61—41no—
78C4⋊C4×C61—41no—
79#11758198—22no—
80#11758198—22no—
81#11758198—22no—
82#11758198Q814yes—
83C4⋊Dic61—22no—
84C4⋊Dic61—41no—
85#11758196—22no—
86#11758196—22no—
87#11758196—41no—
88#11758196—41no—
89C4×Dic61—22no—
90C4×Dic61—41no—
91C23×C61C2411yescharacteristic
92C22×D61—21no—
93C22×D61—21no—
94C22×D61—21no—
95C22×D61—21no—
96C22×D61C2×Q812yes—
97C22×D61#4112yes—
98C22×D61#4112yes—
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—21no—
115C2×C4×C61—21no—
116C2×C4×C61—21no—
117C2×C4×C61—21no—
118C2×C4×C61C2×Q812yes—
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×Dic61C2×Q812yes—
140C2×Dic61#4112yes—
141C4×D61—44no—
142C4×D61—44no—
143C4×D61—44no—
144C22×C61C22×Q811yescharacteristic
145C22×C61C2×#4111yescharacteristic
146C22×C61C2×#4111yescharacteristic
147C22×C61C2×#4111yescharacteristic
148C22×C61C2×#4111yescharacteristic
149C22×C61H(5,𝔽2)11yescharacteristic
150C22×C61H(5,𝔽2)11yescharacteristic
151C2×D61—22no—
152C2×D61—22no—
153C2×D61—22no—
154C2×D61—22no—
155C2×D61—22no—
156C2×D61—22no—
157C2×D61#12514yes—
158C4×C61—22no—
159C4×C61—22no—
160C4×C61—41no—
161C4×C61—41no—
162C4×C61—41no—
163C4×C61—41no—
164C4×C61—41no—
165Dic61—22no—
166Dic61—22no—
167Dic61—41no—
168Dic61—41no—
169Dic61—41no—
170Dic61—41no—
171Dic61—41no—
172#2505—611nomaximal, Sylow
173C2×C61C2×#12511yescharacteristic
174C2×C61#52911yescharacteristic
175C2×C61#53811yescharacteristic
176C2×C61#55111yescharacteristic
177C2×C61#55111yescharacteristic
178C2×C61#55411yescharacteristic
179C2×C61#55411yescharacteristic
180D61—24no—
181#400—611no—
182#400—611no—
183#400—611no—
184#398D6111yescharacteristic, complemented
185#389—611no—
186#387—611no—
187#387—611no—
188#385—611no—
189#385—611no—
190#385—611no—
191#385—611no—
192#382—611no—
193#380—611no—
194C4×C22⋊C4—611no—
195C2×#95—611no—
196C61#250511yescharacteristic, complemented, Sylow
197C23×C4—611no—
198C23×C4—611no—
199C23×C4—611no—
200C2×C4⋊C4—611no—
201C2×C4⋊C4—611no—
202C2×C4⋊C4—611no—
203C2×C4⋊C4—611no—
204C2×C4⋊C4—611no—
205C2×C4⋊C4—611no—
206C2×C4⋊C4C2×D6111yescharacteristic
207C2×C4⋊C4C2×D6111yescharacteristic
208C2×C4⋊C4C2×D6111yescharacteristic
209C2×C4⋊C4C2×D6111yescharacteristic
210C2×C22⋊C4—611no—
211C2×C22⋊C4—611no—
212C2×C22⋊C4—611no—
213C2×C22⋊C4—611no—
214C2×C42—611no—
215C2×C42—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#95—611no—
225#95—611no—
226#95—611no—
227#95—611no—
228#95—611no—
229#95C2×D6111yescharacteristic
230#95C2×D6111yescharacteristic
231#95C2×D6111yescharacteristic
232C24—611no—
233C22×C4—611no—
234C22×C4—611no—
235C22×C4—611no—
236C22×C4—611no—
237C22×C4—611no—
238C22×C4—611no—
239C22×C4—611no—
240C22×C4—1222no—
241C22×C4—1222no—
242C22×C4—1222no—
243C22×C4—1222no—
244C22×C4—1222no—
245C22×C4—2441no—
246C22×C4—2441no—
247C22×C4—2441no—
248C22×C4—2441no—
249C22×C4C22×D6111yescharacteristic
250C22×C4C22×D6111yescharacteristic
251C22×C4C22×D6111yescharacteristic
252C22×C4C22×D6111yescharacteristic
253C22×C4C22×D6111yescharacteristic
254C22×C4C22×D6111yescharacteristic
255C22×C4C22×D6111yescharacteristic
256C4⋊C4—41no—
257C4⋊C4—41no—
258C4⋊C4—41no—
259C4⋊C4—41no—
260C4⋊C4—1222no—
261C4⋊C4—1222no—
262C4⋊C4—1222no—
263C4⋊C4—2441no—
264C4⋊C4—2441no—
265C4⋊C4—2441no—
266C22⋊C4—614no—
267C22⋊C4—1222no—
268C22⋊C4—1222no—
269C22⋊C4—1222no—
270C42—1222no—
271C42—2441no—
272C23—612no—
273C23—612no—
274C23—612no—
275C23—1221no—
276C23—1221no—
277C23—1221no—
278C23—1221no—
279C23C23×D6111yescharacteristic
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—21no—
294C2×C4—21no—
295C2×C4—21no—
296C2×C4—21no—
297C2×C4—21no—
298C2×C4—21no—
299C2×C4—612no—
300C2×C4—612no—
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—1221no—
318C2×C4—1221no—
319C2×C4—1221no—
320C2×C4—2444no—
321C2×C4—2444no—
322C2×C4—2444no—
323C2×C4Q8×D6112yes—
324C2×C4#1175822612yes—
325C22—614no—
326C22—1222no—
327C22—1222no—
328C22—1222no—
329C22—1222no—
330C22—1222no—
331C22—1222no—
332C22C2×Q8×D6111yescharacteristic
333C22#41×D6111yescharacteristic
334C22#41×D6111yescharacteristic
335C22#41×D6111yescharacteristic
336C22C2×#1175822611yescharacteristic
337C22#1451982211yescharacteristic
338C22#1451982211yescharacteristic
339C4—22no—
340C4—22no—
341C4—41no—
342C4—41no—
343C4—41no—
344C4—41no—
345C4—41no—
346C4—1222no—
347C4—1222no—
348C4—2441no—
349C4—2441no—
350C4—2441no—
351C4—2441no—
352C4—2441no—
353C2—1224no—
354C2#125×D6111yescharacteristic
355C2#1684029711yescharacteristic
356C2#1684034411yescharacteristic
357C2#1684043911yescharacteristic
358C2#1684044011yescharacteristic
359C2#1684046611yescharacteristic
360C2#1684047311yescharacteristic
subgroupG/H
center, FrattiniC23C23×D61
commutator, socleC23×C61C24
FittingC61×#398C2
hypercenter#398D61
hypocenterC61#2505
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C23 ◁ #398

Complements

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

NH ≅ G/Ntype
1. #16839704C2semidirect
2. #16839702C2semidirect
3. #16839700C2semidirect
4. #16839657C2semidirect
5. #16839645C2semidirect
6. #16839643C2semidirect
11. #16839627C2semidirect
15. C61×#398C2semidirect
184. #398D61semidirect
196. C61#2505semidirect