Finite Group Databasebeta

← #21458219

Subgroups — #21458219

Order 7808.

366 conjugacy classes of subgroups.

The subgroup lattice has 348 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#16840464C211yesmaximal, characteristic, complemented
2#16840460C211yesmaximal, characteristic, complemented
3#16840162C211yesmaximal, characteristic, complemented
4#16840088C211yesmaximal, characteristic, complemented
5#16840085C211yesmaximal, characteristic, complemented
6#16840081C211yesmaximal, characteristic, complemented
7#16840064C211yesmaximal, characteristic, complemented
8#16840061C211yesmaximal, characteristic, complemented
9#16839997C211yesmaximal, characteristic, complemented
10#16839996C211yesmaximal, characteristic, complemented
11#16839842C211yesmaximal, characteristic, complemented
12#16839825C211yesmaximal, characteristic, complemented
13#16839797C211yesmaximal, characteristic, complemented
14C2×#14519710C211yesmaximal, characteristic, complemented
15C61×#481C211yesmaximal, characteristic, complemented
16C2×#11758199C2211yescharacteristic
17C22×#92418C2211yescharacteristic
18C2×C8×D61C2211yescharacteristic
19#14519772—21no—
20#14519770—21no—
21#14519768C2211yescharacteristic
22#14519768C2211yescharacteristic
23#14519762—21no—
24#14519761—21no—
25#14519752C2211yescharacteristic
26#14519751—21no—
27#14519751C2211yescharacteristic
28#14519749—21no—
29#14519748C2211yescharacteristic
30D4×Dic61—21no—
31D4×Dic61C2211yescharacteristic
32#14519739C2211yescharacteristic
33C4×C22⋊D61—21no—
34C4×C22⋊D61C2211yescharacteristic
35#14519735C2211yescharacteristic
36#14519735C2211yescharacteristic
37C2×C4⋊Dic61C2211yescharacteristic
38#14519710C2211yescharacteristic
39#14519710C2211yescharacteristic
40#14519710C2211yescharacteristic
41#14519710C2211yescharacteristic
42#14519710C2211yescharacteristic
43#14519709C2211yescharacteristic
44#14519709C2211yescharacteristic
45#14519706C2211yescharacteristic
46#14519699C2211yescharacteristic
47#14519699C2211yescharacteristic
48#14519698C2211yescharacteristic
49#14519697C2211yescharacteristic
50#14519689C2211yescharacteristic
51C8×Dic61C2211yescharacteristic
52#121×C61C2211yescharacteristic
53C2×C4⋊C4×C61C2211yescharacteristic
54#106×C61C2211yescharacteristic
55#106×C61C2211yescharacteristic
56#102×C61C2211yescharacteristic
57#102×C61C2211yescharacteristic
58C22⋊C8×C61C2211yescharacteristic
59C2×D4×C61—21no—
60C2×D4×C61C2311yescharacteristic
61C22×C4×C61—21no—
62C22×C4×C61C2311yescharacteristic
63C2×C22⋊D61—21no—
64C2×C22⋊D61—21no—
65C2×C22⋊D61D411yescharacteristic
66C22×Dic61—21no—
67C22×Dic61—21no—
68C2×D244—21no—
69C2×D244C2311yescharacteristic
70C2×C4×D61—21no—
71C2×C4×D61C2311yescharacteristic
72C2×C8×C61C2311yescharacteristic
73C2×C8×C61C2311yescharacteristic
74C4⋊C4×C61—21no—
75C4⋊C4×C61C2311yescharacteristic
76C4⋊C4×C61C2311yescharacteristic
77C4⋊C4×C61C2311yescharacteristic
78C22⋊C4×C61—21no—
79C22⋊Dic61—21no—
80C22⋊Dic61—21no—
81C22⋊Dic61D411yescharacteristic
82#11758199—22no—
83#11758198—21no—
84#11758198—21no—
85#11758198—21no—
86#11758198—21no—
87#11758198—21no—
88#11758198D411yescharacteristic
89C4⋊Dic61—21no—
90C4⋊Dic61—21no—
91C4⋊Dic61—21no—
92C4⋊Dic61C2311yescharacteristic
93C4⋊Dic61C2311yescharacteristic
94C4⋊Dic61C2311yescharacteristic
95#11758196—21no—
96#11758196—21no—
97#11758196D411yescharacteristic
98C4×Dic61—21no—
99C4×Dic61—21no—
100C4×Dic61C2311yescharacteristic
101C2×#92418—22no—
102C2×#92418C2311yescharacteristic
103C2×#92418C2311yescharacteristic
104C8×D61—22no—
105C23×C61—21no—
106C23×C61C2×D411yescharacteristic
107C22×D61—21no—
108C22×D61C2×D411yescharacteristic
109D4×C61—21no—
110D4×C61—21no—
111D4×C61—42no—
112C2×C4×C61—21no—
113C2×C4×C61—21no—
114C2×C4×C61—21no—
115C2×C4×C61—21no—
116C2×C4×C61—21no—
117C2×C4×C61—81no—
118C2×C4×C61C2×D411yescharacteristic
119C2×C4×C61C2411yescharacteristic
120C22⋊D61—22no—
121C22⋊D61—42no—
122C22⋊D61—81no—
123C2×Dic61—21no—
124C2×Dic61—21no—
125C2×Dic61—21no—
126C2×Dic61—81no—
127C2×Dic61—81no—
128C2×Dic61C2×D411yescharacteristic
129C2×Dic61C2×D411yescharacteristic
130C2×Dic61C2×D411yescharacteristic
131D244—21no—
132D244—21no—
133D244—81no—
134C4×D61—21no—
135C4×D61—21no—
136C4×D61—81no—
137C8×C61—21no—
138C8×C61—21no—
139#92418—21no—
140#92418#4112yes—
141C22×C61—21no—
142C22×C61—21no—
143C22×C61—41no—
144C22×C61—41no—
145C22×C61—41no—
146C22×C61#13512yes—
147C22×C61C22×D411yescharacteristic
148C2×D61—21no—
149C2×D61—21no—
150C2×D61—21no—
151C2×D61—41no—
152C2×D61—41no—
153C2×D61—41no—
154C4×C61—21no—
155C4×C61—41no—
156C4×C61—41no—
157C4×C61—41no—
158C4×C61C2×#4111yescharacteristic
159C4×C612−1+411yescharacteristic
160Dic61—21no—
161Dic61—21no—
162Dic61—21no—
163Dic61—41no—
164Dic61—41no—
165Dic61—41no—
166#3339—611nomaximal, Sylow
167C2×C61—22no—
168C2×C61—81no—
169C2×C61#54711yescharacteristic
170C2×C61C2×#13511yescharacteristic
171C2×C61#57611yescharacteristic
172D61—41no—
173D61—81no—
174#553—611no—
175#553—611no—
176#499—611no—
177#482—611no—
178#482—611no—
179#481—611no—
180#481D6111yescharacteristic, complemented
181#478—611no—
182#478—611no—
183#466—611no—
184#466—611no—
185C4×D8—611no—
186C8×D4—611no—
187#427—611no—
188C2×#107—611no—
189C61#333911yescharacteristic, complemented, Sylow
190C2×D8—611no—
191C22×C8—611no—
192C22×C8—611no—
193#126—1221no—
194#126—1221no—
195#125—611no—
196#125—611no—
197#123—1221no—
198#123—1221no—
199#121—611no—
200#121—611no—
201#121—611no—
202#121—1221no—
203#121—1221no—
204#121C2×D6111yescharacteristic
205C4×D4—611no—
206C4×D4—611no—
207C4×D4—611no—
208C4×D4—1221no—
209C4×D4—1221no—
210#117—611no—
211#117—611no—
212C2×C4⋊C4—611no—
213C2×C4⋊C4C2×D6111yescharacteristic
214#107—611no—
215#107—611no—
216#107—611no—
217#107—611no—
218#107—611no—
219#106—611no—
220#106—611no—
221#106C2×D6111yescharacteristic
222#106C2×D6111yescharacteristic
223C4⋊C8—611no—
224#102—611no—
225#102—611no—
226#102—611no—
227#102—611no—
228#102C2×D6111yescharacteristic
229#102C2×D6111yescharacteristic
230C22⋊C8—611no—
231C22⋊C8C2×D6111yescharacteristic
232C4×C8—611no—
233C2×D4—21no—
234C2×D4—611no—
235C2×D4—611no—
236C2×D4—1221no—
237C2×D4—1221no—
238C2×D4—1221no—
239C2×D4C22×D6111yescharacteristic
240C22×C4—21no—
241C22×C4—611no—
242C22×C4—1221no—
243C22×C4—1221no—
244C22×C4—1221no—
245C22×C4C22×D6111yescharacteristic
246D8—1222no—
247C2×C8—611no—
248C2×C8—611no—
249C2×C8—1222no—
250C2×C8—1222no—
251C2×C8C22×D6111yescharacteristic
252C2×C8C22×D6111yescharacteristic
253C4⋊C4—21no—
254C4⋊C4—611no—
255C4⋊C4—611no—
256C4⋊C4—611no—
257C4⋊C4—611no—
258C4⋊C4—1221no—
259C4⋊C4—1221no—
260C4⋊C4—1221no—
261C4⋊C4—1221no—
262C4⋊C4—1221no—
263C4⋊C4C22×D6111yescharacteristic
264C4⋊C4C22×D6111yescharacteristic
265C4⋊C4C22×D6111yescharacteristic
266C22⋊C4—21no—
267C22⋊C4—611no—
268C22⋊C4—611no—
269C22⋊C4—1221no—
270C22⋊C4—1221no—
271C22⋊C4—1221no—
272C22⋊C4—1221no—
273C22⋊C4—1221no—
274C22⋊C4—1221no—
275C22⋊C4—1221no—
276C42—611no—
277C42—1221no—
278C42—1221no—
279C23—21no—
280C23—611no—
281C23—1221no—
282C23D4×D6111yescharacteristic
283D4—21no—
284D4—21no—
285D4—42no—
286D4—1222no—
287D4—1221no—
288D4—1221no—
289D4—4881no—
290D4—4881no—
291D4—2442no—
292C2×C4—21no—
293C2×C4—21no—
294C2×C4—21no—
295C2×C4—21no—
296C2×C4—21no—
297C2×C4—81no—
298C2×C4—611no—
299C2×C4—611no—
300C2×C4—611no—
301C2×C4—1221no—
302C2×C4—1221no—
303C2×C4—1221no—
304C2×C4—1221no—
305C2×C4—1221no—
306C2×C4—4881no—
307C2×C4—4881no—
308C2×C4—4881no—
309C2×C4D4×D6111yescharacteristic
310C2×C4C23×D6111yescharacteristic
311C8—21no—
312C8—21no—
313C8—612no—
314C8—1221no—
315C22—21no—
316C22—21no—
317C22—41no—
318C22—41no—
319C22—41no—
320C22—1221no—
321C22—1221no—
322C22—1221no—
323C22—2441no—
324C22—2441no—
325C22—2441no—
326C22#1451979812yes—
327C22C2×D4×D6111yescharacteristic
328C4—21no—
329C4—41no—
330C4—41no—
331C4—41no—
332C4—1221no—
333C4—1221no—
334C4—1221no—
335C4—2441no—
336C4—2441no—
337C4—2441no—
338C4#41×D6111yescharacteristic
339C4#1451982411yescharacteristic
340C2—22no—
341C2—81no—
342C2—4881no—
343C2—2441no—
344C2#1684041011yescharacteristic
345C2C2×#1451979811yescharacteristic
346C2#1684056611yescharacteristic
subgroupG/H
centerC22C2×D4×D61
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC61×#481C2
socleC22×C61C22×D4
hypercenter#481D61
hypocenterC61#3339
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ #481

Complements

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

NH ≅ G/Ntype
1. #16840464C2semidirect
2. #16840460C2semidirect
3. #16840162C2semidirect
4. #16840088C2semidirect
5. #16840085C2semidirect
6. #16840081C2semidirect
7. #16840064C2semidirect
8. #16840061C2semidirect
9. #16839997C2semidirect
10. #16839996C2semidirect
11. #16839842C2semidirect
12. #16839825C2semidirect
13. #16839797C2semidirect
14. C2×#14519710C2semidirect
15. C61×#481C2semidirect
180. #481D61semidirect
189. C61#3339semidirect