Finite Group Databasebeta

← #21456006

Subgroups — #21456006

Order 7808.

406 conjugacy classes of subgroups.

The subgroup lattice has 364 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#16840385C211yesmaximal, characteristic, complemented
2#16840236C211yesmaximal, characteristic, complemented
3#16840086C211yesmaximal, characteristic, complemented
4#16840051C211yesmaximal, characteristic, complemented
5#16840041C211yesmaximal, characteristic, complemented
6#16839980C211yesmaximal, characteristic, complemented
7#16839980C211yesmaximal, characteristic, complemented
8#16839912C211yesmaximal, characteristic, complemented
9#16839898C211yesmaximal, characteristic
10#16839873C211yesmaximal, characteristic, complemented
11#16839865C211yesmaximal, characteristic, complemented
12#16839847C211yesmaximal, characteristic, complemented
13#16839844C211yesmaximal, characteristic, complemented
14#16839820C211yesmaximal, characteristic, complemented
15C61×#485C211yesmaximal, characteristic, complemented
16C22×D244C2211yescharacteristic
17C2×#11758201C2211yescharacteristic
18C2×#11758201C2211yescharacteristic
19C2×D488C2211yescharacteristic
20C2×D488C2211yescharacteristic
21#14519776C2211yescharacteristic, complemented
22#14519772—21no—
23#14519766C2211yescharacteristic, complemented
24#14519763—21no—
25#14519759—21no—
26#14519757—21no—
27#14519751C2211yescharacteristic
28Q8×Dic61C2211yescharacteristic, complemented
29C4×D244—21no—
30C4×D244—21no—
31#14519739C2211yescharacteristic
32#14519739C2211yescharacteristic
33#14519739C2211yescharacteristic
34#14519739C2211yescharacteristic
35#14519739C2211yescharacteristic, complemented
36#14519736C2211yescharacteristic
37C22⋊C4×D61—21no—
38C22⋊C4×D61—21no—
39#14519710C2211yescharacteristic, complemented
40#14519708C2211yescharacteristic, complemented
41#14519706C2211yescharacteristic, complemented
42#14519706C2211yescharacteristic, complemented
43#14519699C2211yescharacteristic
44#14519699C2211yescharacteristic
45#14519697C2211yescharacteristic
46#14519697C2211yescharacteristic
47#14519697C2211yescharacteristic, complemented
48#14519697C2211yescharacteristic, complemented
49C22⋊#92418C2211yescharacteristic
50#14519687C2211yescharacteristic, complemented
51C8×Dic61C2211yescharacteristic, complemented
52C22⋊Q8×C61C2211yescharacteristic
53#117×C61C2211yescharacteristic
54#107×C61C2211yescharacteristic, complemented
55#106×C61C2211yescharacteristic, complemented
56#103×C61C2211yescharacteristic, complemented
57#103×C61C2211yescharacteristic, complemented
58C22⋊C8×C61C2211yescharacteristic
59C23×D61—21no—
60C2×Q8×C61C2311yescharacteristic
61C22×C4×C61C2311yescharacteristic
62C2×C22⋊D61—21no—
63C2×D244—21no—
64C2×D244—22no—
65C2×D244—22no—
66C2×D244C2311yescharacteristic
67C2×D244C2311yescharacteristic
68C2×D244C2311yescharacteristic
69C2×C4×D61—21no—
70C2×C4×D61—21no—
71C2×C4×D61—21no—
72C2×C4×D61—21no—
73C2×C4×D61—21no—
74C2×Dic122—21no—
75C2×C8×C61C2311yescharacteristic
76C2×C8×C61C2311yescharacteristic
77C4⋊C4×C61—21no—
78C4⋊C4×C61C2311yescharacteristic
79C4⋊C4×C61C2311yescharacteristic
80C4⋊C4×C61C2311yescharacteristic
81C22⋊C4×C61—21no—
82C22⋊C4×C61—21no—
83C42×C61—21no—
84C22⋊Dic61D411yescharacteristic
85C22⋊Dic61D411yescharacteristic
86#11758201—22no—
87#11758201—22no—
88#11758198—21no—
89#11758198—21no—
90#11758198—21no—
91#11758198—21no—
92#11758198—21no—
93#11758198—21no—
94#11758198—21no—
95#11758198—21no—
96C4⋊Dic61—21no—
97C4⋊Dic61D411yescharacteristic
98C4⋊Dic61D411yescharacteristic
99C4⋊Dic61C2311yescharacteristic
100#11758196—21no—
101C4×Dic61—21no—
102C4×Dic61C2311yescharacteristic
103C4×Dic61C2311yescharacteristic
104C2×#92418C2311yescharacteristic
105C2×#92418C2311yescharacteristic
106D488—22no—
107D488—22no—
108C23×C61C2×D411yescharacteristic
109C22×D61—21no—
110C22×D61—21no—
111C22×D61—24no—
112C22×D61—21no—
113C22×D61—81no—
114C22×D61—81no—
115Q8×C61—21no—
116Q8×C61—21no—
117C2×C4×C61—21no—
118C2×C4×C61—21no—
119C2×C4×C61—21no—
120C2×C4×C61—21no—
121C2×C4×C61—21no—
122C2×C4×C61—21no—
123C2×C4×C61C2×D411yescharacteristic
124C2×C4×C61C2411yescharacteristic
125C22⋊D61—81no—
126C2×Dic61—21no—
127C2×Dic61C2×D411yescharacteristic
128C2×Dic61C2×D411yescharacteristic
129C2×Dic61C2×D411yescharacteristic
130C2×Dic61C2×D411yescharacteristic
131D244—24no—
132D244—21no—
133D244—21no—
134D244—21no—
135D244—21no—
136D244#4112yes—
137D244#4112yes—
138C4×D61—81no—
139C4×D61—81no—
140C4×D61—81no—
141C4×D61—81no—
142C4×D61—81no—
143Dic122—81no—
144C8×C61—21no—
145C8×C61—21no—
146#92418—21no—
147#92418—21no—
148C22×C61—21no—
149C22×C61—21no—
150C22×C61—21no—
151C22×C61C22×D411yescharacteristic
152C2×D61—22no—
153C2×D61—22no—
154C2×D61—41no—
155C2×D61—41no—
156C2×D61—41no—
157C2×D61—41no—
158C2×D61—41no—
159C2×D61—41no—
160C2×D61—41no—
161C2×D61—84no—
162C4×C61—21no—
163C4×C61—41no—
164C4×C61—41no—
165C4×C61—41no—
166C4×C61—41no—
167C4×C61C2×#4111yescharacteristic
168C4×C61C2×#4111yescharacteristic
169Dic61—21no—
170Dic61—21no—
171Dic61—21no—
172Dic61—21no—
173Dic61—41no—
174#3118—611nomaximal, Sylow
175C2×C61—41no—
176C2×C61#52511yescharacteristic
177C2×C61#57611yescharacteristic
178C2×C61#57711yescharacteristic
179D61—42no—
180D61—42no—
181D61—81no—
182#542—611no—
183#518—611no—
184#485D6111yescharacteristic, complemented
185#482—611no—
186#476—611no—
187#474—611no—
188#463—611no—
189#463—611no—
190#450—611no—
191#447—611no—
192#442—611no—
193#440—611no—
194C4×SD16—611no—
195C4×D8—611no—
196#433—611no—
197C61#311811yescharacteristic, complemented, Sylow
198C22×D4—611no—
199C2×SD16—611no—
200C2×SD16—611no—
201C2×D8—611no—
202C2×D8—611no—
203C4⋊Q8—611no—
204#126—1221no—
205#124—611no—
206#124—1221no—
207#123—1221no—
208C22⋊Q8—1221no—
209C22⋊Q8C2×D6111yescharacteristic
210#121—611no—
211C4×Q8—611no—
212C4×D4—611no—
213C4×D4—611no—
214C4×D4—611no—
215C4×D4—611no—
216C4×D4—611no—
217C4×D4—1221no—
218C4×D4—1221no—
219#117—611no—
220#117C2×D6111yescharacteristic
221C2×C22⋊C4—1221no—
222C2×C22⋊C4—1221no—
223#107—611no—
224#107C2×D6111yescharacteristic, complemented
225#106—611no—
226#106C2×D6111yescharacteristic, complemented
227C4⋊C8—611no—
228C4⋊C8—611no—
229#103C2×D6111yescharacteristic, complemented
230#103C2×D6111yescharacteristic, complemented
231#102—611no—
232#102—611no—
233#102—611no—
234#102—611no—
235#102—611no—
236#102—611no—
237C22⋊C8—611no—
238C22⋊C8C2×D6111yescharacteristic
239#97—611no—
240C4×C8—611no—
241C24—1221no—
242C2×Q8—1221no—
243C2×Q8C22×D6111yescharacteristic
244C2×D4—611no—
245C2×D4—611no—
246C2×D4—611no—
247C2×D4—1222no—
248C2×D4—1222no—
249C2×D4—1221no—
250C2×D4—1221no—
251C22×C4—1221no—
252C22×C4—1221no—
253C22×C4—1221no—
254C22×C4—1221no—
255C22×C4—1221no—
256C22×C4C22×D6111yescharacteristic
257SD16—1222no—
258SD16—1222no—
259D8—1222no—
260D8—1222no—
261C2×C8—611no—
262C2×C8—611no—
263C2×C8C22×D6111yescharacteristic
264C2×C8C22×D6111yescharacteristic
265C4⋊C4—21no—
266C4⋊C4—611no—
267C4⋊C4—611no—
268C4⋊C4—611no—
269C4⋊C4—1221no—
270C4⋊C4—1221no—
271C4⋊C4C22×D6111yescharacteristic
272C4⋊C4C22×D6111yescharacteristic
273C4⋊C4C22×D6111yescharacteristic
274C22⋊C4—21no—
275C22⋊C4—21no—
276C22⋊C4—611no—
277C22⋊C4—611no—
278C22⋊C4—1221no—
279C22⋊C4—1221no—
280C22⋊C4—1221no—
281C22⋊C4—1221no—
282C22⋊C4—1221no—
283C22⋊C4—1221no—
284C22⋊C4—1221no—
285C22⋊C4—1221no—
286C42—21no—
287C42—611no—
288C42—611no—
289C42—1221no—
290C23—1224no—
291C23—1221no—
292C23—1221no—
293C23—1221no—
294C23—4881no—
295C23—4881no—
296C23D4×D6111yescharacteristic
297Q8—21no—
298Q8—21no—
299Q8—4881no—
300D4—612no—
301D4—612no—
302D4—1224no—
303D4—1221no—
304D4—1221no—
305D4—1221no—
306D4—1221no—
307D4—4881no—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—21no—
311C2×C4—21no—
312C2×C4—21no—
313C2×C4—21no—
314C2×C4—611no—
315C2×C4—611no—
316C2×C4—611no—
317C2×C4—611no—
318C2×C4—1221no—
319C2×C4—4881no—
320C2×C4—4881no—
321C2×C4—4881no—
322C2×C4—4881no—
323C2×C4—4881no—
324C2×C4D4×D6111yescharacteristic
325C2×C4C23×D6111yescharacteristic
326C8—21no—
327C8—21no—
328C8—1221no—
329C8—1221no—
330C22—21no—
331C22—21no—
332C22—21no—
333C22—1222no—
334C22—1222no—
335C22—4884no—
336C22—2441no—
337C22—2441no—
338C22—2441no—
339C22—2441no—
340C22—2441no—
341C22—2441no—
342C22—2441no—
343C22C2×D4×D6111yescharacteristic
344C4—21no—
345C4—41no—
346C4—41no—
347C4—41no—
348C4—41no—
349C4—1221no—
350C4—1221no—
351C4—1221no—
352C4—1221no—
353C4—2441no—
354C4#41×D6111yescharacteristic
355C4#41×D6111yescharacteristic
356C2—41no—
357C2—4881no—
358C2—2442no—
359C2—2442no—
360C2#1684027011yescharacteristic
361C2#1684056411yescharacteristic
362C2#1684057111yescharacteristic
subgroupG/H
centerC22C2×D4×D61
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC61×#485C2
socleC22×C61C22×D4
hypercenter#485D61
hypocenterC61#3118
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ #485

Complements

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

NH ≅ G/Ntype
1. #16840385C2semidirect
2. #16840236C2semidirect
3. #16840086C2semidirect
4. #16840051C2semidirect
5. #16840041C2semidirect
6. #16839980C2semidirect
7. #16839980C2semidirect
8. #16839912C2semidirect
10. #16839873C2semidirect
11. #16839865C2semidirect
12. #16839847C2semidirect
13. #16839844C2semidirect
14. #16839820C2semidirect
15. C61×#485C2semidirect
21. #14519776C22semidirect
23. #14519766C22semidirect
28. Q8×Dic61C22semidirect
35. #14519739C22semidirect
39. #14519710C22semidirect
40. #14519708C22semidirect
41. #14519706C22semidirect
42. #14519706C22semidirect
47. #14519697C22semidirect
48. #14519697C22semidirect
50. #14519687C22semidirect
51. C8×Dic61C22semidirect
54. #107×C61C22semidirect
55. #106×C61C22semidirect
56. #103×C61C22semidirect
57. #103×C61C22semidirect
184. #485D61semidirect
197. C61#3118semidirect
224. #107C2×D61semidirect
226. #106C2×D61semidirect
229. #103C2×D61semidirect
230. #103C2×D61semidirect