Finite Group Databasebeta

← #21456065

Subgroups — #21456065

Order 7808.

394 conjugacy classes of subgroups.

The subgroup lattice has 352 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#16840372C211yesmaximal, characteristic, complemented
2#16840237C211yesmaximal, characteristic
3#16840104C211yesmaximal, characteristic, complemented
4#16840100C211yesmaximal, characteristic, complemented
5#16840064C211yesmaximal, characteristic, complemented
6#16840060C211yesmaximal, characteristic, complemented
7#16839965C211yesmaximal, characteristic, complemented
8#16839965C211yesmaximal, characteristic, complemented
9#16839913C211yesmaximal, characteristic
10#16839863C211yesmaximal, characteristic, complemented
11#16839859C211yesmaximal, characteristic, complemented
12#16839853C211yesmaximal, characteristic, complemented
13SD16×Dic61C211yesmaximal, characteristic, complemented
14#16839820C211yesmaximal, characteristic, complemented
15C61×#450C211yesmaximal, characteristic
16C2×#11758200C2211yescharacteristic
17C2×#11758200C2211yescharacteristic
18#14519775C2211yescharacteristic, complemented
19#14519770—21no—
20#14519770—21no—
21#14519768—21no—
22#14519768C2211yescharacteristic, complemented
23#14519767—21no—
24#14519756C2211yescharacteristic
25Q8×Dic61C2211yescharacteristic, complemented
26#14519742C2211yescharacteristic, complemented
27D4×Dic61—21no—
28D4×Dic61—21no—
29D4×Dic61C2211yescharacteristic
30D4×Dic61C2211yescharacteristic
31D4×Dic61C2211yescharacteristic
32D4×Dic61C2211yescharacteristic
33#14519736C2211yescharacteristic
34#14519736C2211yescharacteristic
35C2×C22⋊Dic61—21no—
36C2×C22⋊Dic61—21no—
37#14519711C2211yescharacteristic, complemented
38#14519710C2211yescharacteristic, complemented
39#14519709C2211yescharacteristic, complemented
40#14519708C2211yescharacteristic, complemented
41#14519706C2211yescharacteristic, complemented
42#14519706C2211yescharacteristic, complemented
43#14519702C2211yescharacteristic, complemented
44#14519702C2211yescharacteristic, complemented
45#14519701C2211yescharacteristic, complemented
46#14519701C2211yescharacteristic, complemented
47#14519698C2211yescharacteristic
48#14519698C2211yescharacteristic
49C22⋊#92418C2211yescharacteristic
50#14519687C2211yescharacteristic, 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—22no—
63C2×D4×C61—21no—
64C2×D4×C61C2311yescharacteristic
65C2×D4×C61C2311yescharacteristic
66C22×C4×C61C2311yescharacteristic
67C22×Dic61—21no—
68C22×Dic61—21no—
69C22×Dic61—21no—
70C22×Dic61—21no—
71C2×Dic122C2311yescharacteristic
72SD16×C61—22no—
73SD16×C61—22no—
74C2×C8×C61C2311yescharacteristic
75C2×C8×C61C2311yescharacteristic
76C4⋊C4×C61—21no—
77C4⋊C4×C61C2311yescharacteristic
78C22⋊C4×C61—21no—
79C22⋊Dic61—21no—
80C22⋊Dic61—21no—
81C22⋊Dic61—21no—
82C22⋊Dic61—21no—
83C22⋊Dic61—21no—
84C22⋊Dic61—21no—
85C22⋊Dic61D411yescharacteristic
86C22⋊Dic61D411yescharacteristic
87#11758200—22no—
88#11758200—22no—
89C4⋊Dic61—21no—
90C4⋊Dic61—21no—
91C4⋊Dic61D411yescharacteristic
92C4⋊Dic61D411yescharacteristic
93C4⋊Dic61C2311yescharacteristic
94C4⋊Dic61C2311yescharacteristic
95C4⋊Dic61C2311yescharacteristic
96#11758196—21no—
97#11758196—21no—
98#11758196—21no—
99#11758196—21no—
100#11758196—21no—
101C4×Dic61—21no—
102C4×Dic61—21no—
103C4×Dic61—21no—
104C4×Dic61C2311yescharacteristic
105C4×Dic61C2311yescharacteristic
106C2×#92418C2311yescharacteristic
107C2×#92418C2311yescharacteristic
108C23×C61—24no—
109C23×C61—21no—
110C23×C61—21no—
111C23×C61—81no—
112C23×C61—81no—
113C23×C61C2×D411yescharacteristic
114Q8×C61—21no—
115Q8×C61—21no—
116D4×C61—24no—
117D4×C61—21no—
118D4×C61—21no—
119D4×C61#4112yes—
120D4×C61#4112yes—
121C2×C4×C61—21no—
122C2×C4×C61—21no—
123C2×C4×C61—21no—
124C2×C4×C61—21no—
125C2×C4×C61C2×D411yescharacteristic
126C2×C4×C61C2411yescharacteristic
127C2×Dic61—21no—
128C2×Dic61—21no—
129C2×Dic61—21no—
130C2×Dic61—21no—
131C2×Dic61—81no—
132C2×Dic61—81no—
133C2×Dic61—81no—
134C2×Dic61—81no—
135C2×Dic61C2×D411yescharacteristic
136C2×Dic61C2×D411yescharacteristic
137C2×Dic61C2×D411yescharacteristic
138C2×Dic61C2×D411yescharacteristic
139Dic122—21no—
140Dic122—21no—
141C8×C61—21no—
142C8×C61—21no—
143#92418—21no—
144#92418—21no—
145C22×C61—21no—
146C22×C61—22no—
147C22×C61—22no—
148C22×C61—21no—
149C22×C61—21no—
150C22×C61—41no—
151C22×C61—41no—
152C22×C61—41no—
153C22×C61—41no—
154C22×C61—84no—
155C22×C61C22×D411yescharacteristic
156C4×C61—21no—
157C4×C61—41no—
158C4×C61—41no—
159C4×C61C2×#4111yescharacteristic
160C4×C61C2×#4111yescharacteristic
161Dic61—21no—
162Dic61—21no—
163Dic61—21no—
164Dic61—21no—
165Dic61—41no—
166Dic61—41no—
167Dic61—41no—
168Dic61—41no—
169#3123—611nomaximal, Sylow
170C2×C61—41no—
171C2×C61—42no—
172C2×C61—42no—
173C2×C61#52511yescharacteristic
174C2×C61#57711yescharacteristic
175C2×C61#57711yescharacteristic
176#541—611no—
177#518—611no—
178#485—611no—
179#485—611no—
180#478—611no—
181#478—611no—
182#461—611no—
183#461—611no—
184#450—611no—
185#450D6111yescharacteristic
186#440—611no—
187#440—611no—
188C4×SD16—611no—
189C4×SD16—611no—
190#433—611no—
191C61#312311yescharacteristic, complemented, Sylow
192C22×D4C2×D6111yescharacteristic
193C2×SD16—611no—
194C2×SD16—611no—
195C2×SD16C2×D6111yescharacteristic
196C2×SD16C2×D6111yescharacteristic
197C4⋊Q8—611no—
198#126—1221no—
199#126—1221no—
200#125—611no—
201#125—1221no—
202#125—1221no—
203C22⋊Q8—611no—
204C22⋊Q8C2×D6111yescharacteristic
205C4×Q8—611no—
206C4×Q8—611no—
207C4×D4—611no—
208C4×D4—611no—
209C4×D4—611no—
210C4×D4—611no—
211C4×D4—1221no—
212C4×D4—1221no—
213#117—611no—
214#117—611no—
215C2×C22⋊C4—1221no—
216C2×C22⋊C4—1221no—
217#107—611no—
218#107—611no—
219#106—611no—
220#106—611no—
221C4⋊C8—611no—
222C4⋊C8—611no—
223#103—611no—
224#103—611no—
225#103—611no—
226#103—611no—
227#102—611no—
228#102—611no—
229#102C2×D6111yescharacteristic
230#102C2×D6111yescharacteristic
231C22⋊C8—611no—
232C22⋊C8C2×D6111yescharacteristic
233#97—611no—
234C4×C8—611no—
235C24—21no—
236C2×Q8—611no—
237C2×Q8C22×D6111yescharacteristic
238C2×D4—22no—
239C2×D4—22no—
240C2×D4—21no—
241C2×D4C22×D6111yescharacteristic
242C2×D4C22×D6111yescharacteristic
243C22×C4—1221no—
244C22×C4—1221no—
245C22×C4—1221no—
246C22×C4—1221no—
247C22×C4C22×D6111yescharacteristic
248SD16—22no—
249SD16—22no—
250SD16—1222no—
251SD16—1222no—
252C2×C8—611no—
253C2×C8—611no—
254C2×C8C22×D6111yescharacteristic
255C2×C8C22×D6111yescharacteristic
256C4⋊C4—21no—
257C4⋊C4—611no—
258C4⋊C4—611no—
259C4⋊C4—611no—
260C4⋊C4—611no—
261C4⋊C4—611no—
262C4⋊C4—1221no—
263C4⋊C4—1221no—
264C4⋊C4—1221no—
265C4⋊C4—1221no—
266C4⋊C4—1221no—
267C4⋊C4—1221no—
268C4⋊C4—1221no—
269C4⋊C4C22×D6111yescharacteristic
270C22⋊C4—21no—
271C22⋊C4—611no—
272C22⋊C4—611no—
273C22⋊C4—1221no—
274C22⋊C4—1221no—
275C22⋊C4—1221no—
276C22⋊C4—1221no—
277C22⋊C4—1221no—
278C22⋊C4—1221no—
279C42—611no—
280C42—611no—
281C42—1221no—
282C42—1221no—
283C42—1221no—
284C23—24no—
285C23—21no—
286C23—21no—
287C23—81no—
288C23—81no—
289C23D4×D6111yescharacteristic
290Q8—21no—
291Q8—21no—
292Q8—1221no—
293Q8—1221no—
294D4—24no—
295D4—21no—
296D4—21no—
297D4#1175822412yes—
298D4#1175822412yes—
299C2×C4—21no—
300C2×C4—21no—
301C2×C4—21no—
302C2×C4—21no—
303C2×C4—611no—
304C2×C4—611no—
305C2×C4—611no—
306C2×C4—611no—
307C2×C4—1221no—
308C2×C4—1221no—
309C2×C4—1221no—
310C2×C4—1221no—
311C2×C4—4881no—
312C2×C4—4881no—
313C2×C4—4881no—
314C2×C4—4881no—
315C2×C4D4×D6111yescharacteristic
316C2×C4C23×D6111yescharacteristic
317C8—21no—
318C8—21no—
319C8—1221no—
320C8—1221no—
321C22—21no—
322C22—22no—
323C22—22no—
324C22—21no—
325C22—21no—
326C22—41no—
327C22—41no—
328C22—41no—
329C22—41no—
330C22—84no—
331C22C2×D4×D6111yescharacteristic
332C4—21no—
333C4—41no—
334C4—41no—
335C4—1221no—
336C4—1221no—
337C4—1221no—
338C4—1221no—
339C4—2441no—
340C4—2441no—
341C4—2441no—
342C4—2441no—
343C4C2×#1175822411yescharacteristic
344C4C2×#1175822411yescharacteristic
345C2—41no—
346C2—42no—
347C2—42no—
348C2#1684026811yescharacteristic
349C2#1684056811yescharacteristic
350C2#1684057211yescharacteristic
subgroupG/H
centerC22C2×D4×D61
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC61×#450C2
socleC22×C61C22×D4
hypercenter#450D61
hypocenterC61#3123
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. #16840372C2semidirect
3. #16840104C2semidirect
4. #16840100C2semidirect
5. #16840064C2semidirect
6. #16840060C2semidirect
7. #16839965C2semidirect
8. #16839965C2semidirect
10. #16839863C2semidirect
11. #16839859C2semidirect
12. #16839853C2semidirect
13. SD16×Dic61C2semidirect
14. #16839820C2semidirect
18. #14519775C22semidirect
22. #14519768C22semidirect
25. Q8×Dic61C22semidirect
26. #14519742C22semidirect
37. #14519711C22semidirect
38. #14519710C22semidirect
39. #14519709C22semidirect
40. #14519708C22semidirect
41. #14519706C22semidirect
42. #14519706C22semidirect
43. #14519702C22semidirect
44. #14519702C22semidirect
45. #14519701C22semidirect
46. #14519701C22semidirect
50. #14519687C22semidirect
51. C8×Dic61C22semidirect
191. C61#3123semidirect