Finite Group Databasebeta

← #21458171

Subgroups — #21458171

Order 7808.

388 conjugacy classes of subgroups.

The subgroup lattice has 346 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#16840470C211yesmaximal, characteristic, complemented
2#16840412C211yesmaximal, characteristic
3#16840159C211yesmaximal, characteristic, complemented
4#16840091C211yesmaximal, characteristic, complemented
5#16840090C211yesmaximal, characteristic, complemented
6#16840079C211yesmaximal, characteristic, complemented
7#16840078C211yesmaximal, characteristic, complemented
8#16840050C211yesmaximal, characteristic, complemented
9#16840045C211yesmaximal, characteristic, complemented
10#16839988C211yesmaximal, characteristic, complemented
11SD16×Dic61C211yesmaximal, characteristic, complemented
12C8×C22⋊D61C211yesmaximal, characteristic, complemented
13C2×#14519709C211yesmaximal, characteristic, complemented
14#106×D61C211yesmaximal, characteristic, complemented
15C61×#465C211yesmaximal, characteristic, complemented
16C2×#11758224—21no—
17C2×C8×D61C2211yescharacteristic
18#14519776C2211yescharacteristic
19#14519776C2211yescharacteristic
20#14519767—21no—
21#14519759—21no—
22#14519758—21no—
23#14519757—21no—
24#14519754—21no—
25#14519754—21no—
26#14519753C2211yescharacteristic
27#14519748C2211yescharacteristic
28Q8×Dic61C2211yescharacteristic
29D4×Dic61C2211yescharacteristic
30C4×C22⋊D61C2211yescharacteristic
31#14519737—21no—
32C2×C4⋊Dic61C2211yescharacteristic
33C2×C4⋊Dic61C2211yescharacteristic
34C4⋊C4×D61C2211yescharacteristic
35C4⋊C4×D61C2211yescharacteristic
36#14519709C2211yescharacteristic
37#14519709C2211yescharacteristic
38#14519709C2211yescharacteristic
39#14519709C2211yescharacteristic
40#14519708C2211yescharacteristic
41#14519708C2211yescharacteristic
42#14519708C2211yescharacteristic
43#14519708C2211yescharacteristic
44#14519706C2211yescharacteristic
45#14519701C2211yescharacteristic
46#14519701C2211yescharacteristic
47#14519698C2211yescharacteristic
48#14519698C2211yescharacteristic
49C22⋊#92418C2211yescharacteristic
50#14519689C2211yescharacteristic
51C8×Dic61C2211yescharacteristic
52C2×SD16×C61C2211yescharacteristic
53C22×C8×C61C2211yescharacteristic
54C22⋊Q8×C61C2211yescharacteristic
55#121×C61C2211yescharacteristic
56#106×C61C2211yescharacteristic
57#103×C61C2211yescharacteristic
58#102×C61C2211yescharacteristic
59C2×Q8×C61C2311yescharacteristic
60C2×D4×C61—21no—
61C2×D4×C61C2311yescharacteristic
62C22×C4×C61C2311yescharacteristic
63C2×C22⋊D61—21no—
64C2×C22⋊D61D411yescharacteristic
65C22×Dic61—21no—
66C22×Dic61—21no—
67C22×Dic61—21no—
68#11758224—44no—
69C2×C4×D61—21no—
70C2×C4×D61—21no—
71C2×C4×D61C2311yescharacteristic
72C2×Dic122—21no—
73C2×Dic122—21no—
74SD16×C61—22no—
75C2×C8×C61—22no—
76C2×C8×C61C2311yescharacteristic
77C2×C8×C61C2311yescharacteristic
78C4⋊C4×C61—21no—
79C4⋊C4×C61C2311yescharacteristic
80C4⋊C4×C61C2311yescharacteristic
81C22⋊C4×C61—21no—
82C22⋊C4×C61—21no—
83C22⋊Dic61—21no—
84C22⋊Dic61—21no—
85C22⋊Dic61D411yescharacteristic
86#11758198—21no—
87#11758198D411yescharacteristic
88C4⋊Dic61—21no—
89C4⋊Dic61—21no—
90C4⋊Dic61—21no—
91C4⋊Dic61C2311yescharacteristic
92C4⋊Dic61C2311yescharacteristic
93C4⋊Dic61C2311yescharacteristic
94C4⋊Dic61C2311yescharacteristic
95#11758196—21no—
96#11758196—21no—
97#11758196—21no—
98#11758196—21no—
99#11758196—21no—
100#11758196D411yescharacteristic
101C4×Dic61—21no—
102C4×Dic61C2311yescharacteristic
103C2×#92418C2311yescharacteristic
104C2×#92418C2311yescharacteristic
105C8×D61—22no—
106C23×C61—21no—
107C23×C61C2×D411yescharacteristic
108C22×D61C2×D411yescharacteristic
109Q8×C61—21no—
110Q8×C61—21no—
111D4×C61—21no—
112D4×C61—21no—
113D4×C61—42no—
114C2×C4×C61—21no—
115C2×C4×C61—21no—
116C2×C4×C61—21no—
117C2×C4×C61—21no—
118C2×C4×C61—21no—
119C2×C4×C61C2×D411yescharacteristic
120C2×C4×C61C2411yescharacteristic
121C22⋊D61—42no—
122C22⋊D61SD1614yescomplemented
123C2×Dic61—21no—
124C2×Dic61—21no—
125C2×Dic61—21no—
126C2×Dic61—21no—
127C2×Dic61—42no—
128C2×Dic61—42no—
129C2×Dic61—81no—
130C2×Dic61C2×D411yescharacteristic
131C2×Dic61C2×D411yescharacteristic
132C2×Dic61C2×D411yescharacteristic
133C4×D61—21no—
134C4×D61—21no—
135C4×D61—42no—
136C4×D61—81no—
137Dic122—42no—
138Dic122—81no—
139C8×C61—21no—
140C8×C61#4112yescomplemented
141#92418—21no—
142#92418—21no—
143C22×C61—21no—
144C22×C61—21no—
145C22×C61—41no—
146C22×C61—41no—
147C22×C61—41no—
148C22×C61C2×SD1612yes—
149C22×C61C22×D411yescharacteristic
150C2×D61—21no—
151C2×D61—21no—
152C2×D61C2×SD1612yes—
153C4×C61—21no—
154C4×C61—41no—
155C4×C61—41no—
156C4×C61—41no—
157C4×C61C2×#4111yescharacteristic
158C4×C612−1+411yescharacteristic
159Dic61—21no—
160Dic61—21no—
161Dic61—41no—
162Dic61—41no—
163Dic61—41no—
164Dic61—41no—
165Dic61C2×SD1612yes—
166#3335—611nomaximal, Sylow
167C2×C61—22no—
168C2×C61—81no—
169C2×C61#54711yescharacteristic
170C2×C61C22×SD1611yescharacteristic
171C2×C61#57711yescharacteristic
172D61—22no—
173#554—611no—
174#547—611no—
175#498—611no—
176#483—611no—
177#483—611no—
178#481—611no—
179#481—611no—
180#476—611no—
181#475—611no—
182#465—611no—
183#465D6111yescharacteristic, complemented
184C4×SD16—611no—
185C8×D4—611no—
186C2×#106—611no—
187C2×#106—611no—
188C61#333511yescharacteristic, complemented, Sylow
189C2×#41—1221no—
190C2×SD16C2×D6111yescharacteristic
191C22×C8—611no—
192C22×C8C2×D6111yescharacteristic
193C4⋊Q8—611no—
194C4⋊Q8—611no—
195#125—1221no—
196#123—1221no—
197#123—1221no—
198C22⋊Q8—611no—
199C22⋊Q8—1221no—
200C22⋊Q8—1221no—
201C22⋊Q8—1221no—
202C22⋊Q8C2×D6111yescharacteristic
203#121—611no—
204#121C2×D6111yescharacteristic
205C4×Q8—611no—
206C4×D4—611no—
207C4×D4—611no—
208C4×D4—1221no—
209C2×C4⋊C4—611no—
210C2×C4⋊C4—611no—
211C2×C4⋊C4—611no—
212C2×C4⋊C4—611no—
213#106—611no—
214#106—611no—
215#106—611no—
216#106—611no—
217#106—611no—
218#106—611no—
219#106—611no—
220#106—611no—
221#106C2×D6111yescharacteristic
222C4⋊C8—611no—
223#103—611no—
224#103—611no—
225#103C2×D6111yescharacteristic
226#102—611no—
227#102—611no—
228#102C2×D6111yescharacteristic
229C22⋊C8—611no—
230C22⋊C8—611no—
231C4×C8—611no—
232#41—2444no—
233C2×Q8—1221no—
234C2×Q8—1221no—
235C2×Q8C22×D6111yescharacteristic
236C2×D4—21no—
237C2×D4—611no—
238C2×D4—1221no—
239C2×D4C22×D6111yescharacteristic
240C22×C4—611no—
241C22×C4—1221no—
242C22×C4—1221no—
243C22×C4—1221no—
244C22×C4—1221no—
245C22×C4—1221no—
246C22×C4C22×D6111yescharacteristic
247SD16—22no—
248C2×C8—22no—
249C2×C8—611no—
250C2×C8—611no—
251C2×C8—1222no—
252C2×C8C22×D6111yescharacteristic
253C2×C8C22×D6111yescharacteristic
254C4⋊C4—21no—
255C4⋊C4—611no—
256C4⋊C4—611no—
257C4⋊C4—611no—
258C4⋊C4—611no—
259C4⋊C4—611no—
260C4⋊C4—1221no—
261C4⋊C4—1221no—
262C4⋊C4—1221no—
263C4⋊C4—1221no—
264C4⋊C4—1221no—
265C4⋊C4—1221no—
266C4⋊C4—1221no—
267C4⋊C4—1221no—
268C4⋊C4C22×D6111yescharacteristic
269C4⋊C4C22×D6111yescharacteristic
270C22⋊C4—21no—
271C22⋊C4—21no—
272C22⋊C4—611no—
273C22⋊C4—611no—
274C22⋊C4—1221no—
275C22⋊C4—1221no—
276C22⋊C4—1221no—
277C42—611no—
278C42—1221no—
279C23—21no—
280C23—611no—
281C23D4×D6111yescharacteristic
282Q8—21no—
283Q8—21no—
284Q8—4881no—
285Q8—2442no—
286D4—21no—
287D4—21no—
288D4—42no—
289D4—614no—
290D4—2442no—
291C2×C4—21no—
292C2×C4—21no—
293C2×C4—21no—
294C2×C4—21no—
295C2×C4—21no—
296C2×C4—611no—
297C2×C4—611no—
298C2×C4—611no—
299C2×C4—1221no—
300C2×C4—1221no—
301C2×C4—1221no—
302C2×C4—1221no—
303C2×C4—1221no—
304C2×C4—1221no—
305C2×C4—4881no—
306C2×C4—4881no—
307C2×C4—2442no—
308C2×C4—2442no—
309C2×C4—2442no—
310C2×C4D4×D6111yescharacteristic
311C2×C4C23×D6111yescharacteristic
312C8—21no—
313C8—1221no—
314C8—1221no—
315C8#1175822412yescomplemented
316C22—21no—
317C22—21no—
318C22—41no—
319C22—41no—
320C22—41no—
321C22—612no—
322C22—1221no—
323C22—1221no—
324C22SD16×D6112yes—
325C22C2×D4×D6111yescharacteristic
326C4—21no—
327C4—41no—
328C4—41no—
329C4—41no—
330C4—612no—
331C4—1221no—
332C4—1221no—
333C4—2441no—
334C4—2441no—
335C4—2441no—
336C4—2441no—
337C4C2×#1175822411yescharacteristic
338C4#1451982411yescharacteristic
339C2—22no—
340C2—81no—
341C2—1222no—
342C2#1684041211yescharacteristic
343C2C2×SD16×D6111yescharacteristic
344C2#1684056911yescharacteristic
subgroupG/H
centerC22C2×D4×D61
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC61×#465C2
socleC22×C61C22×D4
hypercenter#465D61
hypocenterC61#3335
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ #465

Complements

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

NH ≅ G/Ntype
1. #16840470C2semidirect
3. #16840159C2semidirect
4. #16840091C2semidirect
5. #16840090C2semidirect
6. #16840079C2semidirect
7. #16840078C2semidirect
8. #16840050C2semidirect
9. #16840045C2semidirect
10. #16839988C2semidirect
11. SD16×Dic61C2semidirect
12. C8×C22⋊D61C2semidirect
13. C2×#14519709C2semidirect
14. #106×D61C2semidirect
15. C61×#465C2semidirect
122. C22⋊D61SD16semidirect
140. C8×C61#41semidirect
183. #465D61semidirect
188. C61#3335semidirect
315. C8#11758224semidirect