Finite Group Databasebeta

← #28401281

Subgroups — #28401281

Order 14464.

366 conjugacy classes of subgroups.

The subgroup lattice has 338 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20299152C211yesmaximal, characteristic, complemented
2#20299135C211yesmaximal, characteristic
3#20299005C211yesmaximal, characteristic, complemented
4#20298991C211yesmaximal, characteristic, complemented
5#20298965C211yesmaximal, characteristic, complemented
6#20298959C211yesmaximal, characteristic, complemented
7#20298838C211yesmaximal, characteristic, complemented
8#20298836C211yesmaximal, characteristic, complemented
9#20298830C211yesmaximal, characteristic
10#20298828C211yesmaximal, characteristic
11#20298703C211yesmaximal, characteristic, complemented
12#20298700C211yesmaximal, characteristic, complemented
13#20298696C211yesmaximal, characteristic, complemented
14#97×D113C211yesmaximal, characteristic, complemented
15#441×C113C211yesmaximal, characteristic, complemented
16C2×#14268637C2211yescharacteristic
17C2×#14268636C2211yescharacteristic
18C2×#14268634C2211yescharacteristic
19C2×C8×D113C2211yescharacteristic
20C2×C8×D113C2211yescharacteristic
21#16813621C2211yescharacteristic
22#16813620C2211yescharacteristic
23#16813617—21no—
24#16813613C2211yescharacteristic
25#16813612—21no—
26#16813611C2211yescharacteristic
27#16813607—21no—
28#16813602C2211yescharacteristic
29#16813600—21no—
30#16813598C2211yescharacteristic
31#16813598C2211yescharacteristic
32#16813597C2211yescharacteristic
33C4×Dic226—21no—
34C4×Dic226C2211yescharacteristic
35C4×D452—21no—
36C4×D452C2211yescharacteristic
37#16813579—21no—
38#16813579—21no—
39C42×D113C2211yescharacteristic
40#16813556C2211yescharacteristic
41#16813555C2211yescharacteristic
42#16813553C2211yescharacteristic
43#16813547C2211yescharacteristic
44#16813546C2211yescharacteristic
45#16813546C2211yescharacteristic
46#16813545C2211yescharacteristic
47#16813544C2211yescharacteristic
48#16813542C2211yescharacteristic
49#16813533C2211yescharacteristic
50#16813532C2211yescharacteristic
51#16813532C2211yescharacteristic
52C2×Q16×C113C2211yescharacteristic
53C4×Q8×C113C2211yescharacteristic
54C4×Q8×C113C2211yescharacteristic
55#106×C113C2211yescharacteristic
56#103×C113C2211yescharacteristic
57#103×C113C2211yescharacteristic
58#97×C113C2211yescharacteristic
59C2×Dic226—21no—
60C2×Dic226C2311yescharacteristic
61C2×D452—21no—
62C2×D452C2311yescharacteristic
63C2×C4×D113—21no—
64C2×C4×D113D411yescharacteristic
65C2×C4×D113D411yescharacteristic
66C2×C4×D113C2311yescharacteristic
67#14268637—22no—
68#14268636—22no—
69#14268634—22no—
70C2×#11744751C2311yescharacteristic
71C2×#11744751C2311yescharacteristic
72C8×D113—22no—
73C8×D113—22no—
74C4⋊Dic113—21no—
75C4⋊Dic113—21no—
76C4⋊Dic113C2311yescharacteristic
77C4⋊Dic113C2311yescharacteristic
78#14268626—21no—
79#14268626—21no—
80#14268626—21no—
81#14268626—21no—
82#14268626—21no—
83#14268626—21no—
84#14268626—21no—
85#14268624—21no—
86#14268624—21no—
87#14268624—21no—
88#14268624—21no—
89#14268624—21no—
90#14268624—21no—
91#14268624—21no—
92C4×Dic113—21no—
93C4×Dic113D411yescharacteristic
94C4×Dic113D411yescharacteristic
95C4×Dic113C2311yescharacteristic
96C2×Q8×C113C2311yescharacteristic
97C2×Q8×C113C2311yescharacteristic
98Q16×C113—22no—
99C2×C8×C113C2311yescharacteristic
100C2×C8×C113C2311yescharacteristic
101C4⋊C4×C113—21no—
102C4⋊C4×C113—21no—
103C4⋊C4×C113C2311yescharacteristic
104C4⋊C4×C113C2311yescharacteristic
105C42×C113—21no—
106C42×C113—21no—
107C42×C113C2311yescharacteristic
108C22×D113—21no—
109C22×D113C2×D411yescharacteristic
110Q8×C113—21no—
111Q8×C113—21no—
112Q8×C113—21no—
113Q8×C113—21no—
114C2×C4×C113—21no—
115C2×C4×C113—21no—
116C2×C4×C113—21no—
117C2×C4×C113—21no—
118C2×C4×C113C2×D411yescharacteristic
119C2×C4×C113C2×D411yescharacteristic
120C2×C4×C113C2411yescharacteristic
121C2×Dic113—21no—
122C2×Dic113—21no—
123C2×Dic113—21no—
124C2×Dic113C2×D411yescharacteristic
125C2×Dic113C2×D411yescharacteristic
126C2×Dic113C2×D411yescharacteristic
127D452—21no—
128D452—21no—
129D452—42no—
130C4×D113—22no—
131C4×D113—21no—
132C4×D113—21no—
133C4×D113—41no—
134C4×D113—42no—
135Dic226—21no—
136Dic226—21no—
137Dic226—42no—
138C8×C113—21no—
139C8×C113#4112yes—
140#11744751—21no—
141#11744751#4112yes—
142C22×C113C22×D411yescharacteristic
143C2×D113—21no—
144C2×D113—21no—
145C2×D113—41no—
146C2×D113—41no—
147C2×D113—41no—
148C2×D113#13712yes—
149C4×C113—21no—
150C4×C113—21no—
151C4×C113—41no—
152C4×C113—41no—
153C4×C113—41no—
154C4×C113—41no—
155C4×C113C2×#4111yescharacteristic
156C4×C113C2×#4111yescharacteristic
157Dic113—21no—
158Dic113—21no—
159Dic113—21no—
160Dic113—41no—
161Dic113—41no—
162Dic113—41no—
163C2×C113#53211yescharacteristic
164C2×C113C2×#13711yescharacteristic
165C2×C113#57511yescharacteristic
166D113—22no—
167D113—81no—
168#3181—1131nomaximal, Sylow
169C113#318111yescharacteristic, complemented, Sylow
170#533—1131no—
171#529—1131no—
172#501—1131no—
173#497—1131no—
174#491—1131no—
175#489—1131no—
176#467—1131no—
177#467—1131no—
178#465—1131no—
179#465—1131no—
180#441—1131no—
181#441D11311yescharacteristic, complemented
182#440—1131no—
183#440—1131no—
184C2×#97—1131no—
185C2×Q16—1131no—
186C2×Q16C2×D11311yescharacteristic
187C2×SD16—1131no—
188C2×SD16—1131no—
189C22×C8—1131no—
190C22×C8—1131no—
191C4⋊Q8—1131no—
192C4⋊Q8—1131no—
193#126—2261no—
194#125—1131no—
195#125—2261no—
196#124—1131no—
197#123—2261no—
198C22⋊Q8—1131no—
199C22⋊Q8—1131no—
200C22⋊Q8—1131no—
201C22⋊Q8—2261no—
202#121—1131no—
203C4×Q8—1131no—
204C4×Q8—2261no—
205C4×Q8C2×D11311yescharacteristic
206C4×Q8C2×D11311yescharacteristic
207C4×D4—1131no—
208C4×D4—2261no—
209#117—2261no—
210#117—2261no—
211C2×C42—1131no—
212#107—1131no—
213#107—1131no—
214#106—1131no—
215#106C2×D11311yescharacteristic
216#103—1131no—
217#103—1131no—
218#103—1131no—
219#103—1131no—
220#103C2×D11311yescharacteristic
221#103C2×D11311yescharacteristic
222#102—1131no—
223#102—1131no—
224#97—1131no—
225#97—1131no—
226#97—1131no—
227#97C2×D11311yescharacteristic
228C2×Q8—1131no—
229C2×Q8—2261no—
230C2×Q8C22×D11311yescharacteristic
231C2×Q8C22×D11311yescharacteristic
232C2×D4—1131no—
233C2×D4—2261no—
234C22×C4—1131no—
235C22×C4—1131no—
236C22×C4—1131no—
237C22×C4—2261no—
238Q16—22no—
239Q16—2262no—
240SD16—2262no—
241SD16—2262no—
242C2×C8—1131no—
243C2×C8—1131no—
244C2×C8—2262no—
245C2×C8—2262no—
246C2×C8C22×D11311yescharacteristic
247C2×C8C22×D11311yescharacteristic
248C4⋊C4—21no—
249C4⋊C4—21no—
250C4⋊C4—1131no—
251C4⋊C4—1131no—
252C4⋊C4—2261no—
253C4⋊C4—2261no—
254C4⋊C4—2261no—
255C4⋊C4—2261no—
256C4⋊C4—2261no—
257C4⋊C4—2261no—
258C4⋊C4—2261no—
259C4⋊C4—2261no—
260C4⋊C4—2261no—
261C4⋊C4C22×D11311yescharacteristic
262C4⋊C4C22×D11311yescharacteristic
263C22⋊C4—2261no—
264C22⋊C4—2261no—
265C22⋊C4—2261no—
266C22⋊C4—2261no—
267C22⋊C4—2261no—
268C22⋊C4—2261no—
269C22⋊C4—2261no—
270C42—21no—
271C42—21no—
272C42—1131no—
273C42—1131no—
274C42—1131no—
275C42—2261no—
276C42C22×D11311yescharacteristic
277C23—1131no—
278C23—2261no—
279Q8—21no—
280Q8—21no—
281Q8—21no—
282Q8—21no—
283Q8—4522no—
284Q8—2261no—
285Q8—2261no—
286D4—4522no—
287D4—2261no—
288D4—2261no—
289C2×C4—21no—
290C2×C4—21no—
291C2×C4—21no—
292C2×C4—21no—
293C2×C4—1131no—
294C2×C4—1131no—
295C2×C4—1131no—
296C2×C4—4522no—
297C2×C4—4521no—
298C2×C4—2262no—
299C2×C4—2261no—
300C2×C4—2261no—
301C2×C4—2261no—
302C2×C4—2261no—
303C2×C4—2261no—
304C2×C4D4×D11311yescharacteristic
305C2×C4D4×D11311yescharacteristic
306C2×C4C23×D11311yescharacteristic
307C8—21no—
308C8—1132no—
309C8—2261no—
310C8#1426864712yes—
311C22—1132no—
312C22—4521no—
313C22—4521no—
314C22—4521no—
315C22—2261no—
316C22—2261no—
317C22C2×D4×D11311yescharacteristic
318C4—21no—
319C4—21no—
320C4—41no—
321C4—41no—
322C4—41no—
323C4—41no—
324C4—4521no—
325C4—4521no—
326C4—4521no—
327C4—2261no—
328C4—2261no—
329C4—2261no—
330C4#41×D11311yescharacteristic
331C4C2×#1426864711yescharacteristic
332C2—9041no—
333C2—2262no—
334C2#2029914511yescharacteristic
335C2#137×D11311yescharacteristic
336C2#2029939711yescharacteristic
subgroupG/H
centerC22C2×D4×D113
commutator, cosocleC2×C4×C113C24
FrattiniC2×C4C23×D113
Fitting#441×C113C2
socleC22×C113C22×D4
prime radical#16813597C22
hypercenter#441D113
hypocenterC113#3181
LCSG ▷ C2×C4×C113 ▷ C2×C113 ▷ C113
UCSC1 ◁ C22 ◁ C42 ◁ #441

Complements

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

NH ≅ G/Ntype
1. #20299152C2semidirect
3. #20299005C2semidirect
4. #20298991C2semidirect
5. #20298965C2semidirect
6. #20298959C2semidirect
7. #20298838C2semidirect
8. #20298836C2semidirect
11. #20298703C2semidirect
12. #20298700C2semidirect
13. #20298696C2semidirect
14. #97×D113C2semidirect
15. #441×C113C2semidirect
169. C113#3181semidirect
181. #441D113semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
#202991522
#202991352
#202990052
#202989912
#202989652
#202989592
#202988382
#202988362
#202988302
#202988282
#202987032
#202987002
#202986962
#97×D1132
#441×C1132
#3181113