Finite Group Databasebeta

← #21458029

Subgroups — #21458029

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#16840408C211yesmaximal, characteristic
2#16840119C211yesmaximal, characteristic, complemented
3#16840103C211yesmaximal, characteristic, complemented
4#16840080C211yesmaximal, characteristic, complemented
5#16840059C211yesmaximal, characteristic, complemented
6#16840018C211yesmaximal, characteristic, complemented
7#16840010C211yesmaximal, characteristic, complemented
8#16839984C211yesmaximal, characteristic, complemented
9#16839922C211yesmaximal, characteristic, complemented
10#16839912C211yesmaximal, characteristic, complemented
11C4×#11758201C211yesmaximal, characteristic, complemented
12#16839840C211yesmaximal, characteristic, complemented
13#16839766C211yesmaximal, characteristic, complemented
14#16839761C211yesmaximal, characteristic, complemented
15C61×#552C211yesmaximal, characteristic, complemented
16C2×#11758222C2211yescharacteristic
17C22×D244C2211yescharacteristic
18C2×#11758202C2211yescharacteristic, complemented
19C2×#11758201C2211yescharacteristic
20C2×#11758201C2211yescharacteristic
21C2×#11758194C2211yescharacteristic
22C2×#11758194C2211yescharacteristic, complemented
23#14519765C2211yescharacteristic
24#14519762—21no—
25#14519756C2211yescharacteristic
26#14519751C2211yescharacteristic
27#14519750—21no—
28#14519745—21no—
29C4×D244C2211yescharacteristic
30C22⋊C4×D61—21no—
31#14519710C2211yescharacteristic, complemented
32#14519708C2211yescharacteristic, complemented
33#14519708C2211yescharacteristic, complemented
34C4⋊#92418C2211yescharacteristic, complemented
35#14519701C2211yescharacteristic, complemented
36#14519700C2211yescharacteristic, complemented
37#14519700C2211yescharacteristic, complemented
38#14519700C2211yescharacteristic, complemented
39#14519697C2211yescharacteristic
40#14519697C2211yescharacteristic
41#14519697C2211yescharacteristic
42#14519697C2211yescharacteristic
43#14519697C2211yescharacteristic
44#14519697C2211yescharacteristic
45C22⋊#92418C2211yescharacteristic
46C22⋊#92418C2211yescharacteristic, complemented
47C4×#92418C2211yescharacteristic, complemented
48#126×C61—21no—
49#125×C61—21no—
50#125×C61C2211yescharacteristic, complemented
51#123×C61—21no—
52C22⋊Q8×C61C2211yescharacteristic
53C22⋊Q8×C61C2211yescharacteristic, complemented
54C4×Q8×C61C2211yescharacteristic, complemented
55C4×D4×C61C2211yescharacteristic
56#117×C61—21no—
57#117×C61C2211yescharacteristic
58C2×C4⋊C4×C61C2211yescharacteristic, complemented
59C23×D61—21no—
60C2×Q8×C61C2311yescharacteristic
61C2×D4×C61D411yescharacteristic
62C22×C4×C61—21no—
63C22×C4×C61C2311yescharacteristic
64C22×C4×C61C2311yescharacteristic
65C2×C22⋊D61—21no—
66C2×C22⋊D61—21no—
67#11758222—22no—
68#11758222—41no—
69C2×D244—22no—
70C2×D244—21no—
71C2×D244—41no—
72C2×D244C2311yescharacteristic
73C2×D244C2311yescharacteristic
74C2×C4×D61—21no—
75C2×C4×D61—21no—
76C2×Dic122C2311yescharacteristic
77C4⋊C4×C61—21no—
78C4⋊C4×C61—21no—
79C4⋊C4×C61—21no—
80C4⋊C4×C61—21no—
81C4⋊C4×C61—21no—
82C4⋊C4×C61—21no—
83C4⋊C4×C61D411yescharacteristic
84C4⋊C4×C61C2311yescharacteristic
85C4⋊C4×C61C2311yescharacteristic
86C4⋊C4×C61C2311yescharacteristic
87C22⋊C4×C61—21no—
88C22⋊C4×C61—21no—
89C22⋊C4×C61—21no—
90C22⋊C4×C61D411yescharacteristic
91C22⋊C4×C61D411yescharacteristic
92C42×C61—21no—
93C42×C61—21no—
94C42×C61C2311yescharacteristic
95C22⋊Dic61—21no—
96#11758202—41no—
97#11758201—22no—
98#11758201—41no—
99#11758198—21no—
100#11758198—21no—
101#11758198—21no—
102#11758198—21no—
103C4⋊Dic61C2311yescharacteristic
104#11758196—21no—
105#11758194—41no—
106#11758194—41no—
107C2×#92418C2311yescharacteristic
108C2×#92418C2311yescharacteristic
109C2×#92418C2311yescharacteristic
110C2×#92418C2311yescharacteristic
111C23×C61C2×D411yescharacteristic
112C23×C61C2×D411yescharacteristic
113C22×D61—21no—
114C22×D61—21no—
115C22×D61—42no—
116C22×D61—42no—
117C22×D61—81no—
118Q8×C61—21no—
119Q8×C61—21no—
120D4×C61—41no—
121C2×C4×C61—21no—
122C2×C4×C61—21no—
123C2×C4×C61—21no—
124C2×C4×C61—21no—
125C2×C4×C61—21no—
126C2×C4×C61—21no—
127C2×C4×C61—21no—
128C2×C4×C61—21no—
129C2×C4×C61—42no—
130C2×C4×C61C2×D411yescharacteristic
131C2×C4×C61C2×D411yescharacteristic
132C2×C4×C61C2×D411yescharacteristic
133C2×C4×C61C2×D411yescharacteristic
134C2×C4×C61C2411yescharacteristic
135C22⋊D61—42no—
136C22⋊D61—81no—
137C2×Dic61—21no—
138C2×Dic61—21no—
139D244—21no—
140D244—21no—
141D244—21no—
142D244—42no—
143D244#4112yes—
144C4×D61—42no—
145C4×D61—81no—
146Dic122—21no—
147Dic122—21no—
148#92418—21no—
149#92418—21no—
150#92418—21no—
151#92418—21no—
152C22×C61—21no—
153C22×C61—21no—
154C22×C61—21no—
155C22×C61—21no—
156C22×C61—21no—
157C22×C61—21no—
158C22×C61C22×D411yescharacteristic
159C2×D61—22no—
160C2×D61—41no—
161C2×D61—41no—
162C2×D61—41no—
163C2×D61—41no—
164C2×D61—41no—
165C2×D61—84no—
166C4×C61—21no—
167C4×C61—21no—
168C4×C61—21no—
169C4×C61—21no—
170C4×C61—41no—
171C4×C61—41no—
172C4×C61—41no—
173C4×C61—41no—
174C4×C61C2×#4111yescharacteristic
175C4×C61H(5,𝔽2)11yescharacteristic
176Dic61—41no—
177Dic61—41no—
178#3323—611nomaximal, Sylow
179C2×C61—41no—
180C2×C61—41no—
181C2×C61#54611yescharacteristic
182C2×C61#57511yescharacteristic
183C2×C61#57711yescharacteristic
184D61—42no—
185D61—81no—
186#552D6111yescharacteristic, complemented
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#450—611no—
197C4×SD16—611no—
198#436—611no—
199#418—611no—
200#417—611no—
201C61#332311yescharacteristic, complemented, Sylow
202C2×#41—611no—
203C22×D4—611no—
204C2×Q16—611no—
205C2×SD16—611no—
206C2×SD16—611no—
207C2×M16—611no—
208C2×M16—611no—
209#126—21no—
210#125—21no—
211#125C2×D6111yescharacteristic, complemented
212#124—611no—
213#123—21no—
214#123—1221no—
215C22⋊Q8—611no—
216C22⋊Q8C2×D6111yescharacteristic
217C22⋊Q8C2×D6111yescharacteristic, complemented
218#121—611no—
219#121—1221no—
220#120—1221no—
221C4×Q8C2×D6111yescharacteristic, complemented
222C4×D4—611no—
223C4×D4C2×D6111yescharacteristic
224#117—21no—
225#117C2×D6111yescharacteristic
226C2×C4⋊C4C2×D6111yescharacteristic, complemented
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#102—611no—
241#102—611no—
242C22⋊C8—611no—
243C22⋊C8—611no—
244C4×C8—611no—
245C24—1221no—
246#41—1222no—
247#41—2441no—
248C2×Q8—611no—
249C2×Q8C22×D6111yescharacteristic
250C2×D4—611no—
251C2×D4—611no—
252C2×D4—1222no—
253C2×D4—1221no—
254C2×D4—1221no—
255C2×D4—1221no—
256C2×D4—2441no—
257C2×D4C22⋊D6111yescharacteristic
258C22×C4—21no—
259C22×C4—1221no—
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—21no—
274C4⋊C4—21no—
275C4⋊C4—21no—
276C4⋊C4—21no—
277C4⋊C4—21no—
278C4⋊C4—611no—
279C4⋊C4—1221no—
280C4⋊C4C22⋊D6111yescharacteristic
281C4⋊C4C22×D6111yescharacteristic
282C4⋊C4C22×D6111yescharacteristic
283C4⋊C4C22×D6111yescharacteristic
284C22⋊C4—21no—
285C22⋊C4—21no—
286C22⋊C4—21no—
287C22⋊C4—1221no—
288C22⋊C4—1221no—
289C22⋊C4—1221no—
290C22⋊C4—1221no—
291C22⋊C4—1221no—
292C22⋊C4C22⋊D6111yescharacteristic
293C22⋊C4C22⋊D6111yescharacteristic
294C42—21no—
295C42—21no—
296C42C22×D6111yescharacteristic
297C23—1221no—
298C23—1221no—
299C23—4881no—
300C23—2442no—
301C23—2442no—
302C23C2×C22⋊D6111yescharacteristic
303C23C2×C22⋊D6111yescharacteristic
304Q8—21no—
305Q8—21no—
306Q8—1221no—
307Q8—1221no—
308D4—41no—
309D4—612no—
310D4—1221no—
311D4—1221no—
312D4—1221no—
313D4—4881no—
314D4—2442no—
315D4—2442no—
316C2×C4—21no—
317C2×C4—21no—
318C2×C4—21no—
319C2×C4—21no—
320C2×C4—21no—
321C2×C4—21no—
322C2×C4—21no—
323C2×C4—21no—
324C2×C4—42no—
325C2×C4—1221no—
326C2×C4—1221no—
327C2×C4—4881no—
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—1222no—
345C22—4884no—
346C22—2441no—
347C22—2441no—
348C22—2441no—
349C22—2441no—
350C22—2441no—
351C22C22×C22⋊D6111yescharacteristic
352C4—21no—
353C4—21no—
354C4—21no—
355C4—21no—
356C4—41no—
357C4—41no—
358C4—41no—
359C4—41no—
360C4—2441no—
361C4—2441no—
362C4#41×D6111yescharacteristic
363C4#1451982311yescharacteristic
364C2—41no—
365C2—41no—
366C2—4881no—
367C2—2442no—
368C2#1684040011yescharacteristic
369C2#1684056011yescharacteristic
370C2#1684057011yescharacteristic
subgroupG/H
centerC22C22×C22⋊D61
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC61×#552C2
socleC22×C61C22×D4
hypercenter#552D61
hypocenterC61#3323
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C4×D4 ◁ #552

Complements

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

NH ≅ G/Ntype
2. #16840119C2semidirect
3. #16840103C2semidirect
4. #16840080C2semidirect
5. #16840059C2semidirect
6. #16840018C2semidirect
7. #16840010C2semidirect
8. #16839984C2semidirect
9. #16839922C2semidirect
10. #16839912C2semidirect
11. C4×#11758201C2semidirect
12. #16839840C2semidirect
13. #16839766C2semidirect
14. #16839761C2semidirect
15. C61×#552C2semidirect
18. C2×#11758202C22semidirect
22. C2×#11758194C22semidirect
31. #14519710C22semidirect
32. #14519708C22semidirect
33. #14519708C22semidirect
34. C4⋊#92418C22semidirect
35. #14519701C22semidirect
36. #14519700C22semidirect
37. #14519700C22semidirect
38. #14519700C22semidirect
46. C22⋊#92418C22semidirect
47. C4×#92418C22semidirect
50. #125×C61C22semidirect
53. C22⋊Q8×C61C22semidirect
54. C4×Q8×C61C22semidirect
58. C2×C4⋊C4×C61C22semidirect
186. #552D61semidirect
201. C61#3323semidirect
211. #125C2×D61semidirect
217. C22⋊Q8C2×D61semidirect
221. C4×Q8C2×D61semidirect
226. C2×C4⋊C4C2×D61semidirect