Finite Group Databasebeta

← #21458039

Subgroups — #21458039

Order 7808.

402 conjugacy classes of subgroups.

The subgroup lattice has 372 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#16840446C211yesmaximal, characteristic, complemented
2#16840406C211yesmaximal, characteristic
3#16840115C211yesmaximal, characteristic, complemented
4#16840104C211yesmaximal, characteristic, complemented
5#16840079C211yesmaximal, characteristic, complemented
6#16840060C211yesmaximal, characteristic, complemented
7#16840018C211yesmaximal, characteristic, complemented
8#16840005C211yesmaximal, characteristic, complemented
9#16839982C211yesmaximal, characteristic, complemented
10#16839921C211yesmaximal, characteristic, complemented
11SD16×Dic61C211yesmaximal, characteristic, complemented
12#16839837C211yesmaximal, characteristic, complemented
13#16839767C211yesmaximal, characteristic, complemented
14#16839760C211yesmaximal, characteristic, complemented
15C61×#450C211yesmaximal, characteristic, complemented
16C2×#11758224C2211yescharacteristic
17C2×#11758202C2211yescharacteristic, complemented
18C2×#11758194C2211yescharacteristic
19C2×#11758189C2211yescharacteristic, complemented
20#14519770—21no—
21#14519768C2211yescharacteristic, complemented
22#14519767—21no—
23#14519764C2211yescharacteristic
24#14519759—21no—
25#14519758—21no—
26#14519756C2211yescharacteristic
27#14519753C2211yescharacteristic, complemented
28#14519749—21no—
29#14519748C2211yescharacteristic
30#14519746—21no—
31Q8×Dic61C2211yescharacteristic, complemented
32D4×Dic61C2211yescharacteristic
33C4×C22⋊D61C2211yescharacteristic
34#14519736C2211yescharacteristic
35#14519735—21no—
36C4⋊C4×D61C2211yescharacteristic, complemented
37C2×C22⋊Dic61—21no—
38#14519711C2211yescharacteristic, complemented
39#14519709C2211yescharacteristic, complemented
40#14519708C2211yescharacteristic, complemented
41#14519706C2211yescharacteristic, complemented
42#14519702C2211yescharacteristic, complemented
43#14519702C2211yescharacteristic, complemented
44#14519701C2211yescharacteristic, complemented
45#14519700C2211yescharacteristic, complemented
46#14519698C2211yescharacteristic
47#14519698C2211yescharacteristic
48#14519698C2211yescharacteristic
49#14519698C2211yescharacteristic
50#14519689C2211yescharacteristic, complemented
51C8×Dic61C2211yescharacteristic, complemented
52C22×D4×C61C2211yescharacteristic
53C2×SD16×C61C2211yescharacteristic
54C2×SD16×C61C2211yescharacteristic
55C22⋊Q8×C61C2211yescharacteristic
56#102×C61C2211yescharacteristic
57#102×C61C2211yescharacteristic
58C22⋊C8×C61C2211yescharacteristic
59C24×C61—21no—
60C2×Q8×C61C2311yescharacteristic
61C2×D4×C61—22no—
62C2×D4×C61—21no—
63C2×D4×C61—41no—
64C2×D4×C61C2311yescharacteristic
65C2×D4×C61C2311yescharacteristic
66C22×C4×C61C2311yescharacteristic
67C2×C22⋊D61—21no—
68C2×C22⋊D61—21no—
69C2×C22⋊D61D411yescharacteristic
70C22×Dic61—21no—
71C22×Dic61—21no—
72#11758224—22no—
73#11758224—41no—
74C2×C4×D61—21no—
75C2×C4×D61C2311yescharacteristic
76C2×Dic122C2311yescharacteristic
77SD16×C61—22no—
78SD16×C61—41no—
79C2×C8×C61C2311yescharacteristic
80C2×C8×C61C2311yescharacteristic
81C4⋊C4×C61—21no—
82C4⋊C4×C61C2311yescharacteristic
83C22⋊C4×C61—21no—
84C22⋊Dic61—21no—
85C22⋊Dic61—21no—
86C22⋊Dic61—21no—
87C22⋊Dic61—21no—
88C22⋊Dic61—21no—
89C22⋊Dic61—21no—
90C22⋊Dic61D411yescharacteristic
91#11758202—41no—
92#11758198—21no—
93#11758198D411yescharacteristic
94C4⋊Dic61—21no—
95C4⋊Dic61—21no—
96C4⋊Dic61C2311yescharacteristic
97C4⋊Dic61C2311yescharacteristic
98C4⋊Dic61C2311yescharacteristic
99#11758196—21no—
100#11758196—21no—
101#11758196—21no—
102#11758196—21no—
103#11758196D411yescharacteristic
104C4×Dic61—21no—
105C4×Dic61—21no—
106C4×Dic61C2311yescharacteristic
107#11758194—41no—
108C2×#92418C2311yescharacteristic
109C2×#92418C2311yescharacteristic
110#11758189—41no—
111C23×C61—21no—
112C23×C61—21no—
113C23×C61—42no—
114C23×C61—42no—
115C23×C61—81no—
116C23×C61C2×D411yescharacteristic
117C22×D61C2×D411yescharacteristic
118Q8×C61—21no—
119Q8×C61—21no—
120D4×C61—21no—
121D4×C61—21no—
122D4×C61—21no—
123D4×C61—42no—
124D4×C61#4112yes—
125C2×C4×C61—21no—
126C2×C4×C61—21no—
127C2×C4×C61—21no—
128C2×C4×C61—21no—
129C2×C4×C61C2×D411yescharacteristic
130C2×C4×C61C2411yescharacteristic
131C22⋊D61—41no—
132C22⋊D61—42no—
133C22⋊D61—81no—
134C2×Dic61—21no—
135C2×Dic61—21no—
136C2×Dic61—21no—
137C2×Dic61—21no—
138C2×Dic61—42no—
139C2×Dic61—81no—
140C2×Dic61C2×D411yescharacteristic
141C2×Dic61C2×D411yescharacteristic
142C2×Dic61C2×D411yescharacteristic
143C4×D61—21no—
144C4×D61—21no—
145C4×D61—42no—
146Dic122—21no—
147Dic122—21no—
148C8×C61—21no—
149C8×C61—21no—
150#92418—21no—
151#92418—21no—
152C22×C61—22no—
153C22×C61—21no—
154C22×C61—21no—
155C22×C61—21no—
156C22×C61—41no—
157C22×C61—41no—
158C22×C61—41no—
159C22×C61—41no—
160C22×C61—41no—
161C22×C61—84no—
162C22×C61C22×D411yescharacteristic
163C2×D61—21no—
164C2×D61—21no—
165C2×D61—21no—
166C4×C61—21no—
167C4×C61—41no—
168C4×C61—41no—
169C4×C61C2×#4111yescharacteristic
170C4×C61H(5,𝔽2)11yescharacteristic
171Dic61—21no—
172Dic61—21no—
173Dic61—21no—
174Dic61—41no—
175Dic61—41no—
176Dic61—41no—
177Dic61—41no—
178#3323—611nomaximal, Sylow
179C2×C61—41no—
180C2×C61—42no—
181C2×C61—81no—
182C2×C61#54611yescharacteristic
183C2×C61#57511yescharacteristic
184C2×C61#57711yescharacteristic
185D61—41no—
186#552—611no—
187#546—611no—
188#488—611no—
189#485—611no—
190#481—611no—
191#478—611no—
192#470—611no—
193#468—611no—
194#464—611no—
195#452—611no—
196#450D6111yescharacteristic, complemented
197C4×SD16—611no—
198#436—611no—
199#418—611no—
200#417—611no—
201C61#332311yescharacteristic, complemented, Sylow
202C2×#41—611no—
203C22×D4C2×D6111yescharacteristic
204C2×Q16—611no—
205C2×SD16C2×D6111yescharacteristic
206C2×SD16C2×D6111yescharacteristic
207C2×M16—611no—
208C2×M16—611no—
209#126—1221no—
210#125—611no—
211#125—1221no—
212#124—611no—
213#123—1221no—
214#123—1221no—
215C22⋊Q8—611no—
216C22⋊Q8—611no—
217C22⋊Q8C2×D6111yescharacteristic
218#121—611no—
219#121—1221no—
220#120—1221no—
221C4×Q8—611no—
222C4×D4—611no—
223C4×D4—611no—
224#117—611no—
225#117—1221no—
226C2×C4⋊C4—611no—
227C2×C22⋊C4—1221no—
228#107—611no—
229#106—611no—
230#106—611no—
231C4⋊C8—611no—
232#103—611no—
233#103—611no—
234#103—611no—
235#103—611no—
236#102—611no—
237#102—611no—
238#102—611no—
239#102—611no—
240#102C2×D6111yescharacteristic
241#102C2×D6111yescharacteristic
242C22⋊C8—611no—
243C22⋊C8C2×D6111yescharacteristic
244C4×C8—611no—
245C24—21no—
246#41—1222no—
247#41—2441no—
248C2×Q8—611no—
249C2×Q8C22×D6111yescharacteristic
250C2×D4—22no—
251C2×D4—21no—
252C2×D4—41no—
253C2×D4—611no—
254C2×D4—1221no—
255C2×D4—1221no—
256C2×D4C22×D6111yescharacteristic
257C2×D4C22×D6111yescharacteristic
258C22×C4—611no—
259C22×C4—1221no—
260C22×C4—1221no—
261C22×C4—1221no—
262C22×C4C22×D6111yescharacteristic
263Q16—2441no—
264SD16—22no—
265SD16—41no—
266M16—2441no—
267M16—2441no—
268C2×C8—611no—
269C2×C8—611no—
270C2×C8C22×D6111yescharacteristic
271C2×C8C22×D6111yescharacteristic
272C4⋊C4—21no—
273C4⋊C4—611no—
274C4⋊C4—611no—
275C4⋊C4—611no—
276C4⋊C4—611no—
277C4⋊C4—1221no—
278C4⋊C4—1221no—
279C4⋊C4—1221no—
280C4⋊C4—1221no—
281C4⋊C4—1221no—
282C4⋊C4—1221no—
283C4⋊C4C22×D6111yescharacteristic
284C22⋊C4—21no—
285C22⋊C4—611no—
286C22⋊C4—611no—
287C22⋊C4—1221no—
288C22⋊C4—1221no—
289C22⋊C4—1221no—
290C22⋊C4—1221no—
291C22⋊C4—1221no—
292C22⋊C4—1221no—
293C22⋊C4—1221no—
294C42—611no—
295C42—1221no—
296C42—1221no—
297C23—21no—
298C23—21no—
299C23—42no—
300C23—42no—
301C23—81no—
302C23—611no—
303C23D4×D6111yescharacteristic
304Q8—21no—
305Q8—21no—
306Q8—1221no—
307Q8—1221no—
308D4—21no—
309D4—21no—
310D4—21no—
311D4—42no—
312D4—4881no—
313D4—2441no—
314D4—2442no—
315D4#1175822412yes—
316C2×C4—21no—
317C2×C4—21no—
318C2×C4—21no—
319C2×C4—21no—
320C2×C4—611no—
321C2×C4—611no—
322C2×C4—611no—
323C2×C4—1221no—
324C2×C4—1221no—
325C2×C4—1221no—
326C2×C4—1221no—
327C2×C4—1221no—
328C2×C4—1221no—
329C2×C4—4881no—
330C2×C4—2442no—
331C2×C4—2442no—
332C2×C4D4×D6111yescharacteristic
333C2×C4C23×D6111yescharacteristic
334C8—21no—
335C8—21no—
336C8—1221no—
337C8—1221no—
338C22—21no—
339C22—21no—
340C22—21no—
341C22—22no—
342C22—41no—
343C22—41no—
344C22—41no—
345C22—41no—
346C22—41no—
347C22—84no—
348C22—1221no—
349C22—1221no—
350C22—1221no—
351C22C2×D4×D6111yescharacteristic
352C4—21no—
353C4—41no—
354C4—41no—
355C4—1221no—
356C4—1221no—
357C4—1221no—
358C4—2441no—
359C4—2441no—
360C4—2441no—
361C4—2441no—
362C4C2×#1175822411yescharacteristic
363C4#1451982211yescharacteristic
364C2—41no—
365C2—42no—
366C2—81no—
367C2—2441no—
368C2#1684039911yescharacteristic
369C2#1684055811yescharacteristic
370C2#1684056811yescharacteristic
subgroupG/H
centerC22C2×D4×D61
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC61×#450C2
socleC22×C61C22×D4
hypercenter#450D61
hypocenterC61#3323
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ #450

Complements

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

NH ≅ G/Ntype
1. #16840446C2semidirect
3. #16840115C2semidirect
4. #16840104C2semidirect
5. #16840079C2semidirect
6. #16840060C2semidirect
7. #16840018C2semidirect
8. #16840005C2semidirect
9. #16839982C2semidirect
10. #16839921C2semidirect
11. SD16×Dic61C2semidirect
12. #16839837C2semidirect
13. #16839767C2semidirect
14. #16839760C2semidirect
15. C61×#450C2semidirect
17. C2×#11758202C22semidirect
19. C2×#11758189C22semidirect
21. #14519768C22semidirect
27. #14519753C22semidirect
31. Q8×Dic61C22semidirect
36. C4⋊C4×D61C22semidirect
38. #14519711C22semidirect
39. #14519709C22semidirect
40. #14519708C22semidirect
41. #14519706C22semidirect
42. #14519702C22semidirect
43. #14519702C22semidirect
44. #14519701C22semidirect
45. #14519700C22semidirect
50. #14519689C22semidirect
51. C8×Dic61C22semidirect
196. #450D61semidirect
201. C61#3323semidirect