Finite Group Databasebeta

← #21457751

Subgroups — #21457751

Order 7808.

396 conjugacy classes of subgroups.

The subgroup lattice has 370 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#16840483C211yesmaximal, characteristic, complemented
2#16840431C211yesmaximal, characteristic
3#16840107C211yesmaximal, characteristic, complemented
4#16840087C211yesmaximal, characteristic, complemented
5#16840084C211yesmaximal, characteristic, complemented
6#16840045C211yesmaximal, characteristic, complemented
7#16839993C211yesmaximal, characteristic, complemented
8#16839988C211yesmaximal, characteristic, complemented
9#16839960C211yesmaximal, characteristic, complemented
10#16839923C211yesmaximal, characteristic, complemented
11Q16×Dic61C211yesmaximal, characteristic, complemented
12#16839825C211yesmaximal, characteristic, complemented
13#16839758C211yesmaximal, characteristic, complemented
14#16839757C211yesmaximal, characteristic, complemented
15C61×#452C211yesmaximal, characteristic, complemented
16C2×#11758226C2211yescharacteristic
17C2×#11758201C2211yescharacteristic
18C22×#92418C2211yescharacteristic
19C2×C8×D61C2211yescharacteristic
20#14519776C2211yescharacteristic
21#14519773—21no—
22#14519773C2211yescharacteristic
23#14519772—21no—
24#14519770—21no—
25#14519763—21no—
26#14519753C2211yescharacteristic
27#14519751—21no—
28#14519751C2211yescharacteristic
29#14519748—21no—
30#14519748C2211yescharacteristic
31Q8×Dic61C2211yescharacteristic
32Q8×Dic61C2211yescharacteristic
33#14519742—21no—
34C4×C22⋊D61—21no—
35C4×C22⋊D61C2211yescharacteristic
36#14519736C2211yescharacteristic
37#14519735C2211yescharacteristic
38#14519711C2211yescharacteristic
39#14519709C2211yescharacteristic
40#14519708C2211yescharacteristic
41#14519706C2211yescharacteristic
42#14519701C2211yescharacteristic
43#14519701C2211yescharacteristic
44#14519701C2211yescharacteristic
45#14519699C2211yescharacteristic
46#14519699C2211yescharacteristic
47#14519698C2211yescharacteristic
48#14519698C2211yescharacteristic
49#14519697C2211yescharacteristic
50#14519689C2211yescharacteristic
51C8×Dic61C2211yescharacteristic
52C2×#41×C61C2211yescharacteristic
53C2×Q16×C61C2211yescharacteristic
54C2×SD16×C61C2211yescharacteristic
55C22⋊Q8×C61C2211yescharacteristic
56#103×C61C2211yescharacteristic
57#102×C61C2211yescharacteristic
58C22⋊C8×C61C2211yescharacteristic
59#41×C61—22no—
60#41×C61—41no—
61C2×Q8×C61C2311yescharacteristic
62C2×Q8×C61C2311yescharacteristic
63C2×D4×C61—21no—
64C2×D4×C61C2311yescharacteristic
65C22×C4×C61—21no—
66C22×C4×C61C2311yescharacteristic
67C2×C22⋊D61—21no—
68C2×C22⋊D61—21no—
69C2×C22⋊D61—21no—
70C2×C22⋊D61—21no—
71C2×C22⋊D61D411yescharacteristic
72#11758226—22no—
73#11758226—41no—
74C2×D244—21no—
75C2×D244C2311yescharacteristic
76C2×C4×D61—21no—
77C2×C4×D61C2311yescharacteristic
78C2×Dic122—21no—
79Q16×C61—22no—
80SD16×C61—41no—
81C2×C8×C61C2311yescharacteristic
82C2×C8×C61C2311yescharacteristic
83C4⋊C4×C61—21no—
84C4⋊C4×C61C2311yescharacteristic
85C22⋊C4×C61—21no—
86C22⋊Dic61—21no—
87C22⋊Dic61—21no—
88C22⋊Dic61D411yescharacteristic
89#11758201—41no—
90#11758198—21no—
91#11758198—21no—
92#11758198—21no—
93#11758198D411yescharacteristic
94C4⋊Dic61—21no—
95C4⋊Dic61—21no—
96C4⋊Dic61C2311yescharacteristic
97C4⋊Dic61C2311yescharacteristic
98C4⋊Dic61C2311yescharacteristic
99#11758196—21no—
100#11758196—21no—
101#11758196D411yescharacteristic
102C4×Dic61—21no—
103C4×Dic61—21no—
104C4×Dic61—21no—
105C4×Dic61—21no—
106C4×Dic61C2311yescharacteristic
107C2×#92418—41no—
108C2×#92418C2311yescharacteristic
109C2×#92418C2311yescharacteristic
110C8×D61—41no—
111C23×C61—21no—
112C23×C61C2×D411yescharacteristic
113C22×D61—21no—
114C22×D61C2×D411yescharacteristic
115Q8×C61—21no—
116Q8×C61—21no—
117Q8×C61—21no—
118Q8×C61#4112yes—
119D4×C61—21no—
120D4×C61—21no—
121D4×C61—42no—
122C2×C4×C61—21no—
123C2×C4×C61—21no—
124C2×C4×C61—21no—
125C2×C4×C61—21no—
126C2×C4×C61—21no—
127C2×C4×C61—42no—
128C2×C4×C61C2×D411yescharacteristic
129C2×C4×C61C2411yescharacteristic
130C22⋊D61—22no—
131C22⋊D61—42no—
132C22⋊D61—81no—
133C22⋊D61—81no—
134C22⋊D61—81no—
135C2×Dic61—21no—
136C2×Dic61—21no—
137C2×Dic61—21no—
138C2×Dic61C2×D411yescharacteristic
139C2×Dic61C2×D411yescharacteristic
140C2×Dic61C2×D411yescharacteristic
141D244—21no—
142D244—21no—
143D244—42no—
144C4×D61—21no—
145C4×D61—21no—
146C4×D61—42no—
147Dic122—42no—
148C8×C61—21no—
149C8×C61—21no—
150#92418—21no—
151#92418—21no—
152C22×C61—21no—
153C22×C61—21no—
154C22×C61—21no—
155C22×C61—41no—
156C22×C61—41no—
157C22×C61—41no—
158C22×C61C22×D411yescharacteristic
159C2×D61—21no—
160C2×D61—21no—
161C2×D61—21no—
162C2×D61—41no—
163C2×D61—41no—
164C2×D61—41no—
165C4×C61—22no—
166C4×C61—21no—
167C4×C61—41no—
168C4×C61—41no—
169C4×C61C2×#4111yescharacteristic
170C4×C61H(5,𝔽2)11yescharacteristic
171Dic61—21no—
172Dic61—21no—
173Dic61—41no—
174Dic61—41no—
175Dic61—41no—
176Dic61#13512yes—
177#3304—611nomaximal, Sylow
178C2×C61—41no—
179C2×C61—81no—
180C2×C61#54611yescharacteristic
181C2×C61C2×#13511yescharacteristic
182C2×C61#57711yescharacteristic
183D61—41no—
184D61—81no—
185#556—611no—
186#550—611no—
187#486—611no—
188#482—611no—
189#482—611no—
190#475—611no—
191#465—611no—
192#465—611no—
193#460—611no—
194#452—611no—
195#452D6111yescharacteristic, complemented
196C4×Q16—611no—
197C8×D4—611no—
198#416—611no—
199#416—611no—
200C61#330411yescharacteristic, complemented, Sylow
201C2×#41—611no—
202C2×#41C2×D6111yescharacteristic
203C2×Q16C2×D6111yescharacteristic
204C2×SD16—611no—
205C2×SD16C2×D6111yescharacteristic
206C22×C8—611no—
207C22×C8—611no—
208C4⋊Q8—611no—
209#127—611no—
210#127—1221no—
211#126—1221no—
212#126—1221no—
213#124—1221no—
214C22⋊Q8—611no—
215C22⋊Q8C2×D6111yescharacteristic
216#121—611no—
217#121—611no—
218#121—1221no—
219#121—1221no—
220C4×Q8—611no—
221C4×Q8—611no—
222C4×Q8—1221no—
223C4×D4—611no—
224C4×D4—1221no—
225#117—611no—
226#117—611no—
227#107—611no—
228#106—611no—
229#106—611no—
230C4⋊C8—611no—
231#103—611no—
232#103—611no—
233#103—611no—
234#103C2×D6111yescharacteristic
235#102—611no—
236#102—611no—
237#102—611no—
238#102—611no—
239#102—611no—
240#102C2×D6111yescharacteristic
241C22⋊C8—611no—
242C22⋊C8C2×D6111yescharacteristic
243C4×C8—611no—
244#41—22no—
245#41—41no—
246#41—1222no—
247#41—2441no—
248C2×Q8—1221no—
249C2×Q8C22×D6111yescharacteristic
250C2×Q8C22×D6111yescharacteristic
251C2×D4—21no—
252C2×D4—611no—
253C2×D4—611no—
254C2×D4—1221no—
255C2×D4—1221no—
256C2×D4—1221no—
257C2×D4—1221no—
258C2×D4—1221no—
259C2×D4C22×D6111yescharacteristic
260C22×C4—21no—
261C22×C4—611no—
262C22×C4—1221no—
263C22×C4C22×D6111yescharacteristic
264Q16—22no—
265SD16—41no—
266SD16—2441no—
267C2×C8—611no—
268C2×C8—611no—
269C2×C8—2441no—
270C2×C8—2441no—
271C2×C8C22×D6111yescharacteristic
272C2×C8C22×D6111yescharacteristic
273C4⋊C4—21no—
274C4⋊C4—611no—
275C4⋊C4—611no—
276C4⋊C4—611no—
277C4⋊C4—611no—
278C4⋊C4—1221no—
279C4⋊C4—1221no—
280C4⋊C4—1221no—
281C4⋊C4—1221no—
282C4⋊C4C22×D6111yescharacteristic
283C22⋊C4—21no—
284C22⋊C4—611no—
285C22⋊C4—611no—
286C22⋊C4—1221no—
287C22⋊C4—1221no—
288C22⋊C4—1221no—
289C22⋊C4—1221no—
290C22⋊C4—1221no—
291C42—611no—
292C42—1221no—
293C42—1221no—
294C42—1221no—
295C42—1221no—
296C23—21no—
297C23—611no—
298C23—1221no—
299C23D4×D6111yescharacteristic
300Q8—21no—
301Q8—21no—
302Q8—21no—
303Q8—2442no—
304Q8#1175822412yes—
305D4—21no—
306D4—21no—
307D4—42no—
308D4—1222no—
309D4—1221no—
310D4—1221no—
311D4—4881no—
312D4—4881no—
313D4—4881no—
314D4—2442no—
315D4—2442no—
316C2×C4—21no—
317C2×C4—21no—
318C2×C4—21no—
319C2×C4—21no—
320C2×C4—21no—
321C2×C4—42no—
322C2×C4—611no—
323C2×C4—611no—
324C2×C4—611no—
325C2×C4—1221no—
326C2×C4—1221no—
327C2×C4—1221no—
328C2×C4—1221no—
329C2×C4—1221no—
330C2×C4—2442no—
331C2×C4D4×D6111yescharacteristic
332C2×C4C23×D6111yescharacteristic
333C8—21no—
334C8—21no—
335C8—1221no—
336C8—1221no—
337C22—21no—
338C22—21no—
339C22—21no—
340C22—41no—
341C22—41no—
342C22—41no—
343C22—1221no—
344C22—1221no—
345C22—1221no—
346C22—2441no—
347C22—2441no—
348C22—2441no—
349C22C2×D4×D6111yescharacteristic
350C4—21no—
351C4—22no—
352C4—41no—
353C4—41no—
354C4—612no—
355C4—1221no—
356C4—1221no—
357C4—2441no—
358C4—2441no—
359C4—2441no—
360C4C2×#1175822411yescharacteristic
361C4#1451982211yescharacteristic
362C2—41no—
363C2—81no—
364C2—4881no—
365C2—2441no—
366C2#1684039911yescharacteristic
367C2#135×D6111yescharacteristic
368C2#1684057111yescharacteristic
subgroupG/H
centerC22C2×D4×D61
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC61×#452C2
socleC22×C61C22×D4
hypercenter#452D61
hypocenterC61#3304
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ #452

Complements

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

NH ≅ G/Ntype
1. #16840483C2semidirect
3. #16840107C2semidirect
4. #16840087C2semidirect
5. #16840084C2semidirect
6. #16840045C2semidirect
7. #16839993C2semidirect
8. #16839988C2semidirect
9. #16839960C2semidirect
10. #16839923C2semidirect
11. Q16×Dic61C2semidirect
12. #16839825C2semidirect
13. #16839758C2semidirect
14. #16839757C2semidirect
15. C61×#452C2semidirect
195. #452D61semidirect
200. C61#3304semidirect