Finite Group Databasebeta

← #21458549

Subgroups — #21458549

Order 7808.

382 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#16840488C211yesmaximal, characteristic, complemented
2#16840433C211yesmaximal, characteristic
3#16840127C211yesmaximal, characteristic, complemented
4#16840125C211yesmaximal, characteristic, complemented
5#16840107C211yesmaximal, characteristic, complemented
6#16840065C211yesmaximal, characteristic, complemented
7#16840062C211yesmaximal, characteristic, complemented
8#16840041C211yesmaximal, characteristic, complemented
9#16839962C211yesmaximal, characteristic, complemented
10#16839960C211yesmaximal, characteristic, complemented
11#16839960C211yesmaximal, characteristic, complemented
12#16839890C211yesmaximal, characteristic, complemented
13#16839865C211yesmaximal, characteristic, complemented
14#16839847C211yesmaximal, characteristic, complemented
15C61×#440C211yesmaximal, characteristic, complemented
16C2×#11758222—21no—
17C2×#11758201C2211yescharacteristic
18C2×#11758201C2211yescharacteristic
19#14519776—21no—
20#14519776C2211yescharacteristic
21#14519774C2211yescharacteristic
22#14519773C2211yescharacteristic
23#14519773C2211yescharacteristic
24#14519769—21no—
25#14519769C2211yescharacteristic
26#14519768—21no—
27#14519768C2211yescharacteristic
28#14519751—21no—
29#14519750—21no—
30#14519750—21no—
31Q8×Dic61C2211yescharacteristic
32Q8×Dic61C2211yescharacteristic
33C4×Dic122—21no—
34C4×Dic122C2211yescharacteristic
35#14519739C2211yescharacteristic
36#14519739C2211yescharacteristic
37#14519710C2211yescharacteristic
38#14519708C2211yescharacteristic
39C4⋊#92418C2211yescharacteristic
40#14519706C2211yescharacteristic
41#14519706C2211yescharacteristic
42#14519699C2211yescharacteristic
43#14519699C2211yescharacteristic
44#14519699C2211yescharacteristic
45#14519699C2211yescharacteristic
46#14519698C2211yescharacteristic
47#14519698C2211yescharacteristic
48#14519697C2211yescharacteristic
49#14519697C2211yescharacteristic
50#14519687C2211yescharacteristic
51C8×Dic61C2211yescharacteristic
52C2×SD16×C61C2211yescharacteristic
53C4×Q8×C61C2211yescharacteristic
54C4×D4×C61C2211yescharacteristic
55#107×C61C2211yescharacteristic
56#103×C61C2211yescharacteristic
57#102×C61C2211yescharacteristic
58#97×C61C2211yescharacteristic
59C2×Q8×C61C2311yescharacteristic
60C2×D4×C61C2311yescharacteristic
61C22×C4×C61—21no—
62C2×C22⋊D61—21no—
63C2×C22⋊D61—21no—
64C2×C22⋊D61—21no—
65C2×C22⋊D61—21no—
66#11758222—44no—
67C2×D244—21no—
68C2×D244—21no—
69C2×D244C2311yescharacteristic
70C2×D244C2311yescharacteristic
71C2×C4×D61—21no—
72C2×C4×D61—21no—
73C2×Dic122—21no—
74C2×Dic122D411yescharacteristic
75SD16×C61—22no—
76C2×C8×C61C2311yescharacteristic
77C2×C8×C61C2311yescharacteristic
78C4⋊C4×C61—21no—
79C4⋊C4×C61C2311yescharacteristic
80C4⋊C4×C61C2311yescharacteristic
81C22⋊C4×C61—21no—
82C42×C61—21no—
83C42×C61C2311yescharacteristic
84#11758201—22no—
85#11758201—22no—
86#11758198—21no—
87#11758198—21no—
88C4⋊Dic61—21no—
89C4⋊Dic61—21no—
90C4⋊Dic61—21no—
91C4⋊Dic61D411yescharacteristic
92C4⋊Dic61C2311yescharacteristic
93C4⋊Dic61C2311yescharacteristic
94#11758196—21no—
95#11758196—21no—
96#11758196—21no—
97#11758196—21no—
98#11758196D411yescharacteristic
99#11758196D411yescharacteristic
100C4×Dic61—21no—
101C4×Dic61—21no—
102C4×Dic61C2311yescharacteristic
103C4×Dic61C2311yescharacteristic
104C2×#92418C2311yescharacteristic
105C2×#92418C2311yescharacteristic
106C23×C61—21no—
107C22×D61—21no—
108C22×D61—21no—
109Q8×C61—21no—
110Q8×C61#4112yescomplemented
111D4×C61—21no—
112D4×C61—21no—
113C2×C4×C61—21no—
114C2×C4×C61—21no—
115C2×C4×C61—21no—
116C2×C4×C61—42no—
117C2×C4×C61C2×D411yescharacteristic
118C2×C4×C61C2×D411yescharacteristic
119C2×C4×C61C2411yescharacteristic
120C22⋊D61—42no—
121C22⋊D61—42no—
122C22⋊D61—81no—
123C22⋊D61—81no—
124C2×Dic61—21no—
125C2×Dic61—21no—
126C2×Dic61C2×D411yescharacteristic
127C2×Dic61C2×D411yescharacteristic
128C2×Dic61C2×D411yescharacteristic
129C2×Dic61C2×D411yescharacteristic
130D244—21no—
131D244—21no—
132D244—21no—
133D244—21no—
134D244—42no—
135D244—81no—
136C4×D61—42no—
137C4×D61—42no—
138Dic122—22no—
139Dic122—42no—
140C8×C61—21no—
141C8×C61—21no—
142#92418—21no—
143#92418—21no—
144C22×C61—41no—
145C22×C61—41no—
146C22×C61—41no—
147C22×C61C22×D411yescharacteristic
148C2×D61—41no—
149C2×D61—41no—
150C2×D61—41no—
151C2×D61—41no—
152C2×D61—41no—
153C2×D61—41no—
154C4×C61—22no—
155C4×C61—21no—
156C4×C61—21no—
157C4×C61—41no—
158C4×C61—41no—
159C4×C61C2×#4111yescharacteristic
160C4×C612−1+411yescharacteristic
161Dic61—21no—
162Dic61—21no—
163Dic61—21no—
164Dic61—41no—
165Dic61—41no—
166Dic61AGL(1,ℤ/8)12yes—
167#3368—611nomaximal, Sylow
168C2×C61—81no—
169C2×C61#54811yescharacteristic
170C2×C61C2×AGL(1,ℤ/8)11yescharacteristic
171C2×C61#57711yescharacteristic
172D61—81no—
173D61—81no—
174#557—611no—
175#550—611no—
176#490—611no—
177#490—611no—
178#486—611no—
179#478—611no—
180#478—611no—
181#474—611no—
182#460—611no—
183#460—611no—
184#460—611no—
185#446—611no—
186#440—611no—
187#440D6111yescharacteristic, complemented
188C4×SD16—611no—
189C61#336811yescharacteristic, complemented, Sylow
190C2×#41—1221no—
191C2×SD16—611no—
192C2×SD16—611no—
193C2×SD16C2×D6111yescharacteristic
194C4⋊Q8—611no—
195C4⋊Q8—1221no—
196#127—611no—
197#127—611no—
198#127—611no—
199#125—611no—
200#125—611no—
201#125—1221no—
202#125—1221no—
203#121—1221no—
204#121—1221no—
205#121—1221no—
206C4×Q8—611no—
207C4×Q8—611no—
208C4×Q8—611no—
209C4×Q8—1221no—
210C4×Q8C2×D6111yescharacteristic
211C4×D4—611no—
212C4×D4—611no—
213C4×D4C2×D6111yescharacteristic
214#107—611no—
215#107C2×D6111yescharacteristic
216#106—611no—
217C4⋊C8—611no—
218C4⋊C8—611no—
219C4⋊C8—611no—
220#103C2×D6111yescharacteristic
221#102—611no—
222#102—611no—
223#102—611no—
224#102—611no—
225#102—611no—
226#102—611no—
227#102—611no—
228#102—611no—
229#102C2×D6111yescharacteristic
230#97—611no—
231#97C2×D6111yescharacteristic
232C4×C8—611no—
233#41—2444no—
234C2×Q8—611no—
235C2×Q8—1221no—
236C2×Q8C22×D6111yescharacteristic
237C2×D4—611no—
238C2×D4—611no—
239C2×D4—1221no—
240C2×D4—1221no—
241C2×D4—1221no—
242C2×D4—1221no—
243C2×D4—1221no—
244C2×D4—1221no—
245C2×D4C22×D6111yescharacteristic
246C22×C4—21no—
247C22×C4—1221no—
248C22×C4—1221no—
249SD16—22no—
250SD16—1222no—
251SD16—1222no—
252C2×C8—611no—
253C2×C8—611no—
254C2×C8C22×D6111yescharacteristic
255C2×C8C22×D6111yescharacteristic
256C4⋊C4—21no—
257C4⋊C4—611no—
258C4⋊C4—611no—
259C4⋊C4—611no—
260C4⋊C4—611no—
261C4⋊C4—611no—
262C4⋊C4—1221no—
263C4⋊C4—1221no—
264C4⋊C4—1221no—
265C4⋊C4—1221no—
266C4⋊C4—1221no—
267C4⋊C4—1221no—
268C4⋊C4—1221no—
269C4⋊C4C22×D6111yescharacteristic
270C4⋊C4C22×D6111yescharacteristic
271C22⋊C4—21no—
272C22⋊C4—1221no—
273C22⋊C4—1221no—
274C42—21no—
275C42—611no—
276C42—611no—
277C42—1221no—
278C42—1221no—
279C42C22×D6111yescharacteristic
280C23—21no—
281C23—1221no—
282C23—1221no—
283Q8—21no—
284Q8—1222no—
285Q8—2442no—
286Q8#1175822212yescomplemented
287D4—21no—
288D4—21no—
289D4—1221no—
290D4—1221no—
291D4—1221no—
292D4—1221no—
293D4—4881no—
294D4—4881no—
295D4—4881no—
296D4—2442no—
297D4—2442no—
298D4—2442no—
299C2×C4—21no—
300C2×C4—21no—
301C2×C4—21no—
302C2×C4—42no—
303C2×C4—611no—
304C2×C4—611no—
305C2×C4—611no—
306C2×C4—611no—
307C2×C4—1221no—
308C2×C4—1221no—
309C2×C4—2442no—
310C2×C4—2442no—
311C2×C4D4×D6111yescharacteristic
312C2×C4D4×D6111yescharacteristic
313C2×C4C23×D6111yescharacteristic
314C8—21no—
315C8—21no—
316C8—1221no—
317C8—1221no—
318C22—41no—
319C22—41no—
320C22—41no—
321C22—2441no—
322C22—2441no—
323C22—2441no—
324C22—2441no—
325C22—2441no—
326C22—2441no—
327C22C2×D4×D6111yescharacteristic
328C4—21no—
329C4—21no—
330C4—22no—
331C4—41no—
332C4—41no—
333C4—612no—
334C4—1221no—
335C4—1221no—
336C4—1221no—
337C4—2441no—
338C4—2441no—
339C4C2×#1175822211yescharacteristic
340C4#1451982411yescharacteristic
341C2—81no—
342C2—4881no—
343C2—4881no—
344C2#1684042111yescharacteristic
345C2AGL(1,ℤ/8)×D6111yescharacteristic
346C2#1684057111yescharacteristic
subgroupG/H
centerC22C2×D4×D61
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC61×#440C2
socleC22×C61C22×D4
hypercenter#440D61
hypocenterC61#3368
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ #440

Complements

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

NH ≅ G/Ntype
1. #16840488C2semidirect
3. #16840127C2semidirect
4. #16840125C2semidirect
5. #16840107C2semidirect
6. #16840065C2semidirect
7. #16840062C2semidirect
8. #16840041C2semidirect
9. #16839962C2semidirect
10. #16839960C2semidirect
11. #16839960C2semidirect
12. #16839890C2semidirect
13. #16839865C2semidirect
14. #16839847C2semidirect
15. C61×#440C2semidirect
110. Q8×C61#41semidirect
187. #440D61semidirect
189. C61#3368semidirect
286. Q8#11758222semidirect