Finite Group Databasebeta

← #21458035

Subgroups — #21458035

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#16840452C211yesmaximal, characteristic, complemented
2#16840116C211yesmaximal, characteristic, complemented
3#16840100C211yesmaximal, characteristic, complemented
4#16840078C211yesmaximal, characteristic, complemented
5#16840062C211yesmaximal, characteristic, complemented
6#16840018C211yesmaximal, characteristic, complemented
7#16840006C211yesmaximal, characteristic, complemented
8#16839981C211yesmaximal, characteristic, complemented
9#16839924C211yesmaximal, characteristic, complemented
10#16839913C211yesmaximal, characteristic, complemented
11C4×#11758200C211yesmaximal, characteristic, complemented
12#16839840C211yesmaximal, characteristic, complemented
13#16839767C211yesmaximal, characteristic, complemented
14#16839763C211yesmaximal, characteristic, complemented
15C61×#546C211yesmaximal, characteristic
16C2×#11758202C2211yescharacteristic, complemented
17C2×#11758200C2211yescharacteristic
18C2×#11758200C2211yescharacteristic
19C2×#11758194C2211yescharacteristic
20C2×#11758194C2211yescharacteristic, complemented
21#14519770—21no—
22#14519769C2211yescharacteristic, complemented
23#14519767—21no—
24#14519758—21no—
25#14519756C2211yescharacteristic
26#14519756C2211yescharacteristic, complemented
27C4×Dic122C2211yescharacteristic, complemented
28#14519736C2211yescharacteristic
29#14519733—21no—
30C2×C4⋊Dic61C2211yescharacteristic, complemented
31#14519710C2211yescharacteristic, complemented
32#14519708C2211yescharacteristic, complemented
33#14519708C2211yescharacteristic, complemented
34C4⋊#92418C2211yescharacteristic, complemented
35#14519701C2211yescharacteristic, complemented
36#14519701C2211yescharacteristic, complemented
37#14519701C2211yescharacteristic, complemented
38#14519700C2211yescharacteristic, complemented
39#14519698C2211yescharacteristic
40#14519698C2211yescharacteristic
41#14519698C2211yescharacteristic
42#14519698C2211yescharacteristic
43#14519698C2211yescharacteristic
44#14519698C2211yescharacteristic
45C22⋊#92418C2211yescharacteristic
46C22⋊#92418C2211yescharacteristic, complemented
47C4×#92418C2211yescharacteristic, complemented
48C2×#41×C61C2211yescharacteristic
49C22×D4×C61C2211yescharacteristic
50#124×C61C2211yescharacteristic
51#123×C61—21no—
52C22⋊Q8×C61C2211yescharacteristic
53#121×C61—21no—
54#121×C61C2211yescharacteristic
55#120×C61—21no—
56C4×D4×C61C2211yescharacteristic
57C4×D4×C61C2211yescharacteristic
58C2×C22⋊C4×C61—21no—
59C24×C61—21no—
60#41×C61—22no—
61#41×C61—41no—
62C2×Q8×C61C2311yescharacteristic
63C2×D4×C61—22no—
64C2×D4×C61—21no—
65C2×D4×C61—21no—
66C2×D4×C61—21no—
67C2×D4×C61—41no—
68C2×D4×C61D411yescharacteristic
69C2×D4×C61C2311yescharacteristic
70C2×D4×C61C2311yescharacteristic
71C22×C4×C61—21no—
72C22×C4×C61—21no—
73C22×C4×C61C2311yescharacteristic
74C22×C4×C61C2311yescharacteristic
75C22×Dic61—21no—
76C2×Dic122C2311yescharacteristic
77C4⋊C4×C61—21no—
78C4⋊C4×C61D411yescharacteristic
79C4⋊C4×C61C2311yescharacteristic
80C22⋊C4×C61—21no—
81C22⋊C4×C61—21no—
82C22⋊C4×C61—21no—
83C22⋊C4×C61—21no—
84C22⋊C4×C61—21no—
85C22⋊C4×C61D411yescharacteristic
86C22⋊C4×C61D411yescharacteristic
87C42×C61C2311yescharacteristic
88C22⋊Dic61—21no—
89C22⋊Dic61—21no—
90C22⋊Dic61—21no—
91#11758202—41no—
92#11758200—22no—
93#11758200—41no—
94C4⋊Dic61—21no—
95C4⋊Dic61C2311yescharacteristic
96C4⋊Dic61C2311yescharacteristic
97C4⋊Dic61C2311yescharacteristic
98#11758196—21no—
99#11758196—21no—
100#11758196—21no—
101#11758196—21no—
102#11758196—21no—
103C4×Dic61—21no—
104C4×Dic61—21no—
105#11758194—41no—
106#11758194—41no—
107C2×#92418C2311yescharacteristic
108C2×#92418C2311yescharacteristic
109C2×#92418C2311yescharacteristic
110C2×#92418C2311yescharacteristic
111C23×C61—21no—
112C23×C61—21no—
113C23×C61—42no—
114C23×C61—42no—
115C23×C61—81no—
116C23×C61C2×D411yescharacteristic
117C23×C61C2×D411yescharacteristic
118Q8×C61—21no—
119Q8×C61—21no—
120D4×C61—21no—
121D4×C61—21no—
122D4×C61—21no—
123D4×C61—41no—
124D4×C61—42no—
125D4×C61—42no—
126D4×C61—81no—
127D4×C61#4112yes—
128C2×C4×C61—21no—
129C2×C4×C61—21no—
130C2×C4×C61—21no—
131C2×C4×C61—21no—
132C2×C4×C61—21no—
133C2×C4×C61—21no—
134C2×C4×C61—42no—
135C2×C4×C61—81no—
136C2×C4×C61C2×D411yescharacteristic
137C2×C4×C61C2×D411yescharacteristic
138C2×C4×C61C2×D411yescharacteristic
139C2×C4×C61C2×D411yescharacteristic
140C2×C4×C61C2411yescharacteristic
141C2×Dic61—21no—
142C2×Dic61—21no—
143C2×Dic61—21no—
144C2×Dic61—21no—
145C2×Dic61—42no—
146Dic122—21no—
147Dic122—21no—
148#92418—21no—
149#92418—21no—
150#92418—21no—
151#92418—21no—
152C22×C61—21no—
153C22×C61—21no—
154C22×C61—22no—
155C22×C61—21no—
156C22×C61—21no—
157C22×C61—21no—
158C22×C61—21no—
159C22×C61—41no—
160C22×C61—41no—
161C22×C61—41no—
162C22×C61—41no—
163C22×C61—41no—
164C22×C61—84no—
165C22×C61C22×D411yescharacteristic
166C4×C61—21no—
167C4×C61—21no—
168C4×C61—21no—
169C4×C61—21no—
170C4×C61—41no—
171C4×C61—41no—
172C4×C61C2×#4111yescharacteristic
173C4×C61H(5,𝔽2)11yescharacteristic
174Dic61—41no—
175Dic61—41no—
176Dic61—41no—
177Dic61—41no—
178#3323—611nomaximal, Sylow
179C2×C61—41no—
180C2×C61—41no—
181C2×C61—42no—
182C2×C61—81no—
183C2×C61#54611yescharacteristic
184C2×C61#57511yescharacteristic
185C2×C61#57711yescharacteristic
186#552—611no—
187#546D6111yescharacteristic
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#450—611no—
197C4×SD16—611no—
198#436—611no—
199#418—611no—
200#417—611no—
201C61#332311yescharacteristic, complemented, Sylow
202C2×#41C2×D6111yescharacteristic
203C22×D4C2×D6111yescharacteristic
204C2×Q16—611no—
205C2×SD16—611no—
206C2×SD16—611no—
207C2×M16—611no—
208C2×M16—611no—
209#126—1221no—
210#125—611no—
211#125—1221no—
212#124C2×D6111yescharacteristic
213#123—21no—
214#123—1221no—
215C22⋊Q8—611no—
216C22⋊Q8—611no—
217C22⋊Q8C2×D6111yescharacteristic
218#121—21no—
219#121C2×D6111yescharacteristic
220#120—21no—
221C4×Q8—611no—
222C4×D4C2×D6111yescharacteristic
223C4×D4C2×D6111yescharacteristic
224#117—611no—
225#117—1221no—
226C2×C4⋊C4—611no—
227C2×C22⋊C4—21no—
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#102—611no—
241#102—611no—
242C22⋊C8—611no—
243C22⋊C8—611no—
244C4×C8—611no—
245C24—21no—
246#41—22no—
247#41—41no—
248C2×Q8—611no—
249C2×Q8C22×D6111yescharacteristic
250C2×D4—22no—
251C2×D4—21no—
252C2×D4—21no—
253C2×D4—21no—
254C2×D4—41no—
255C2×D4C22⋊D6111yescharacteristic
256C2×D4C22×D6111yescharacteristic
257C2×D4C22×D6111yescharacteristic
258C22×C4—21no—
259C22×C4—21no—
260C22×C4—1221no—
261C22×C4C22×D6111yescharacteristic
262C22×C4C22×D6111yescharacteristic
263Q16—2441no—
264SD16—1222no—
265SD16—2441no—
266M16—2441no—
267M16—2441no—
268C2×C8—611no—
269C2×C8—611no—
270C2×C8—611no—
271C2×C8—611no—
272C4⋊C4—21no—
273C4⋊C4—611no—
274C4⋊C4—611no—
275C4⋊C4—611no—
276C4⋊C4—1221no—
277C4⋊C4—1221no—
278C4⋊C4—1221no—
279C4⋊C4—1221no—
280C4⋊C4—1221no—
281C4⋊C4—1221no—
282C4⋊C4C22⋊D6111yescharacteristic
283C4⋊C4C22×D6111yescharacteristic
284C22⋊C4—21no—
285C22⋊C4—21no—
286C22⋊C4—21no—
287C22⋊C4—21no—
288C22⋊C4—21no—
289C22⋊C4—1221no—
290C22⋊C4—1221no—
291C22⋊C4—1221no—
292C22⋊C4C22⋊D6111yescharacteristic
293C22⋊C4C22⋊D6111yescharacteristic
294C42—1221no—
295C42—1221no—
296C42C22×D6111yescharacteristic
297C23—21no—
298C23—21no—
299C23—42no—
300C23—42no—
301C23—81no—
302C23C2×C22⋊D6111yescharacteristic
303C23C2×C22⋊D6111yescharacteristic
304Q8—21no—
305Q8—21no—
306Q8—1221no—
307Q8—1221no—
308D4—21no—
309D4—21no—
310D4—21no—
311D4—41no—
312D4—42no—
313D4—42no—
314D4—81no—
315D4#1175822412yes—
316C2×C4—21no—
317C2×C4—21no—
318C2×C4—21no—
319C2×C4—21no—
320C2×C4—21no—
321C2×C4—21no—
322C2×C4—42no—
323C2×C4—81no—
324C2×C4—1221no—
325C2×C4—1221no—
326C2×C4—1221no—
327C2×C4—1221no—
328C2×C4—2442no—
329C2×C4C2×C22⋊D6111yescharacteristic
330C2×C4C2×C22⋊D6111yescharacteristic
331C2×C4C2×C22⋊D6111yescharacteristic
332C2×C4C2×C22⋊D6111yescharacteristic
333C2×C4C23×D6111yescharacteristic
334C8—1221no—
335C8—1221no—
336C8—1221no—
337C8—1221no—
338C22—21no—
339C22—21no—
340C22—21no—
341C22—21no—
342C22—21no—
343C22—21no—
344C22—22no—
345C22—41no—
346C22—41no—
347C22—41no—
348C22—41no—
349C22—41no—
350C22—84no—
351C22C22×C22⋊D6111yescharacteristic
352C4—21no—
353C4—21no—
354C4—21no—
355C4—21no—
356C4—41no—
357C4—41no—
358C4—2441no—
359C4—2441no—
360C4—2441no—
361C4—2441no—
362C4C2×#1175822411yescharacteristic
363C4#1451982211yescharacteristic
364C2—41no—
365C2—41no—
366C2—42no—
367C2—81no—
368C2#1684040611yescharacteristic
369C2#1684056011yescharacteristic
370C2#1684057311yescharacteristic
subgroupG/H
centerC22C22×C22⋊D61
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC61×#546C2
socleC22×C61C22×D4
hypercenter#546D61
hypocenterC61#3323
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C4×D4 ◁ #546

Complements

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

NH ≅ G/Ntype
1. #16840452C2semidirect
2. #16840116C2semidirect
3. #16840100C2semidirect
4. #16840078C2semidirect
5. #16840062C2semidirect
6. #16840018C2semidirect
7. #16840006C2semidirect
8. #16839981C2semidirect
9. #16839924C2semidirect
10. #16839913C2semidirect
11. C4×#11758200C2semidirect
12. #16839840C2semidirect
13. #16839767C2semidirect
14. #16839763C2semidirect
16. C2×#11758202C22semidirect
20. C2×#11758194C22semidirect
22. #14519769C22semidirect
26. #14519756C22semidirect
27. C4×Dic122C22semidirect
30. C2×C4⋊Dic61C22semidirect
31. #14519710C22semidirect
32. #14519708C22semidirect
33. #14519708C22semidirect
34. C4⋊#92418C22semidirect
35. #14519701C22semidirect
36. #14519701C22semidirect
37. #14519701C22semidirect
38. #14519700C22semidirect
46. C22⋊#92418C22semidirect
47. C4×#92418C22semidirect
201. C61#3323semidirect