Finite Group Databasebeta

← #28401247

Subgroups — #28401247

Order 14464.

350 conjugacy classes of subgroups.

The subgroup lattice has 334 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20299222C211yesmaximal, characteristic
2#20299211C211yesmaximal, characteristic, complemented
3#20298992C211yesmaximal, characteristic, complemented
4#20298955C211yesmaximal, characteristic, complemented
5#20298950C211yesmaximal, characteristic, complemented
6#20298857C211yesmaximal, characteristic, complemented
7#20298845C211yesmaximal, characteristic
8#20298840C211yesmaximal, characteristic, complemented
9#20298828C211yesmaximal, characteristic
10#20298704C211yesmaximal, characteristic, complemented
11#20298697C211yesmaximal, characteristic, complemented
12#20298692C211yesmaximal, characteristic, complemented
13#20298685C211yesmaximal, characteristic, complemented
14#20298555C211yesmaximal, characteristic, complemented
15#501×C113C211yesmaximal, characteristic, complemented
16C2×Dic452C2211yescharacteristic
17C2×Dic452C2211yescharacteristic
18C2×#14268636C2211yescharacteristic
19C2×#14268636C2211yescharacteristic
20C2×#14268630C2211yescharacteristic
21C2×C8×D113C2211yescharacteristic
22#16813622C2211yescharacteristic
23#16813617—21no—
24#16813617—21no—
25#16813617—21no—
26#16813613—21no—
27#16813613—21no—
28#16813611—21no—
29#16813610C2211yescharacteristic
30#16813607—21no—
31#16813602C2211yescharacteristic
32#16813602C2211yescharacteristic
33#16813602C2211yescharacteristic
34#16813598—21no—
35#16813597C2211yescharacteristic
36#16813587C2211yescharacteristic
37#16813587C2211yescharacteristic
38#16813587C2211yescharacteristic
39#16813584C2211yescharacteristic
40#16813579C2211yescharacteristic
41#16813545C2211yescharacteristic
42#16813545C2211yescharacteristic
43#16813545C2211yescharacteristic
44#16813545C2211yescharacteristic
45#16813545C2211yescharacteristic
46#16813545C2211yescharacteristic
47#16813542C2211yescharacteristic
48#16813542C2211yescharacteristic
49#16813532C2211yescharacteristic
50C4×#11744751C2211yescharacteristic
51C8×Dic113C2211yescharacteristic
52C4⋊Q8×C113C2211yescharacteristic
53#125×C113C2211yescharacteristic
54#107×C113C2211yescharacteristic
55#107×C113C2211yescharacteristic
56#106×C113C2211yescharacteristic
57#106×C113C2211yescharacteristic
58#97×C113C2211yescharacteristic
59C2×Dic226C2311yescharacteristic
60C2×Dic226C2311yescharacteristic
61C2×Dic226C2311yescharacteristic
62C2×D452—21no—
63C2×D452C2311yescharacteristic
64C2×C4×D113—21no—
65C2×C4×D113C2311yescharacteristic
66Dic452—22no—
67Dic452—22no—
68#14268636—22no—
69#14268636—22no—
70#14268630—22no—
71C2×#11744751C2311yescharacteristic
72C2×#11744751C2311yescharacteristic
73C8×D113—22no—
74C4⋊Dic113—21no—
75C4⋊Dic113—21no—
76C4⋊Dic113—21no—
77C4⋊Dic113—21no—
78C4⋊Dic113—21no—
79#14268626—21no—
80#14268626—21no—
81#14268626—21no—
82#14268626D411yescharacteristic
83#14268626D411yescharacteristic
84#14268624—21no—
85#14268624—21no—
86#14268624—21no—
87#14268624—21no—
88#14268624—21no—
89#14268624—21no—
90#14268624—21no—
91#14268624D411yescharacteristic
92#14268624D411yescharacteristic
93C4×Dic113—21no—
94C4×Dic113—21no—
95C4×Dic113—21no—
96C4×Dic113C2311yescharacteristic
97C2×Q8×C113—21no—
98C2×C8×C113C2311yescharacteristic
99C2×C8×C113C2311yescharacteristic
100C4⋊C4×C113—21no—
101C4⋊C4×C113—21no—
102C4⋊C4×C113—21no—
103C4⋊C4×C113C2311yescharacteristic
104C4⋊C4×C113C2311yescharacteristic
105C4⋊C4×C113C2311yescharacteristic
106C4⋊C4×C113C2311yescharacteristic
107C42×C113C2311yescharacteristic
108C22×D113—21no—
109C22×D113C2×D411yescharacteristic
110Q8×C113—81no—
111C2×C4×C113—21no—
112C2×C4×C113—21no—
113C2×C4×C113—21no—
114C2×C4×C113—21no—
115C2×C4×C113C2×D411yescharacteristic
116C2×C4×C113C2×D411yescharacteristic
117C2×C4×C113C2411yescharacteristic
118C2×Dic113—21no—
119C2×Dic113—21no—
120C2×Dic113—21no—
121C2×Dic113C2×D411yescharacteristic
122C2×Dic113C2×D411yescharacteristic
123C2×Dic113C2×D411yescharacteristic
124D452—21no—
125D452—21no—
126D452—81no—
127C4×D113—21no—
128C4×D113—21no—
129C4×D113—81no—
130Dic226—21no—
131Dic226—21no—
132Dic226—21no—
133Dic226—21no—
134Dic226—21no—
135Dic226—21no—
136C8×C113#4112yes—
137C8×C113#4112yes—
138#11744751—21no—
139#11744751—21no—
140C22×C113C22×D411yescharacteristic
141C2×D113—21no—
142C2×D113—21no—
143C2×D113—21no—
144C2×D113—41no—
145C2×D113—41no—
146C2×D113—41no—
147C4×C113—21no—
148C4×C113—21no—
149C4×C113—41no—
150C4×C113—41no—
151C4×C113—41no—
152C4×C113—41no—
153C4×C113C2×#4111yescharacteristic
154C4×C113C2×#4111yescharacteristic
155Dic113—21no—
156Dic113—21no—
157Dic113—21no—
158Dic113—41no—
159Dic113—41no—
160Dic113—41no—
161C2×C113#53211yescharacteristic
162C2×C113#57711yescharacteristic
163C2×C113#57811yescharacteristic
164D113—41no—
165D113—81no—
166#3178—1131nomaximal, Sylow
167C113#317811yescharacteristic, complemented, Sylow
168#542—1131no—
169#541—1131no—
170#501D11311yescharacteristic, complemented
171#497—1131no—
172#488—1131no—
173#487—1131no—
174#470—1131no—
175#468—1131no—
176#467—1131no—
177#465—1131no—
178#441—1131no—
179#440—1131no—
180C4×Q16—1131no—
181C4×SD16—1131no—
182#405—1131no—
183C2×Q16—1131no—
184C2×Q16—1131no—
185C2×SD16—1131no—
186C2×SD16—1131no—
187C2×M16—1131no—
188C22×C8—1131no—
189C4⋊Q8—1131no—
190C4⋊Q8C2×D11311yescharacteristic
191#126—2261no—
192#126—2261no—
193#126—2261no—
194#125—2261no—
195#125—2261no—
196#125C2×D11311yescharacteristic
197#124—1131no—
198#124—2261no—
199#123—2261no—
200C22⋊Q8—1131no—
201C22⋊Q8—1131no—
202C22⋊Q8—1131no—
203C22⋊Q8—2261no—
204#121—1131no—
205C4×Q8—1131no—
206C4×Q8—1131no—
207C4×Q8—1131no—
208C4×D4—1131no—
209#117—1131no—
210#107C2×D11311yescharacteristic
211#107C2×D11311yescharacteristic
212#106C2×D11311yescharacteristic
213#106C2×D11311yescharacteristic
214#103—1131no—
215#103—1131no—
216#103—1131no—
217#103—1131no—
218#103—1131no—
219#103—1131no—
220#102—1131no—
221#102—1131no—
222#97—1131no—
223#97C2×D11311yescharacteristic
224C4×C8—1131no—
225C4×C8—1131no—
226C2×Q8—21no—
227C2×Q8—1131no—
228C2×Q8—1131no—
229C2×Q8—1131no—
230C2×D4—1131no—
231C2×D4—2261no—
232C22×C4—1131no—
233C22×C4—2261no—
234Q16—2262no—
235Q16—2262no—
236SD16—2262no—
237SD16—2262no—
238M16—2262no—
239C2×C8—1131no—
240C2×C8—1131no—
241C2×C8—2262no—
242C2×C8C22×D11311yescharacteristic
243C2×C8C22×D11311yescharacteristic
244C4⋊C4—21no—
245C4⋊C4—21no—
246C4⋊C4—21no—
247C4⋊C4—1131no—
248C4⋊C4—1131no—
249C4⋊C4—2261no—
250C4⋊C4—2261no—
251C4⋊C4—2261no—
252C4⋊C4—2261no—
253C4⋊C4—2261no—
254C4⋊C4—2261no—
255C4⋊C4—2261no—
256C4⋊C4—2261no—
257C4⋊C4C22×D11311yescharacteristic
258C4⋊C4C22×D11311yescharacteristic
259C4⋊C4C22×D11311yescharacteristic
260C4⋊C4C22×D11311yescharacteristic
261C22⋊C4—1131no—
262C22⋊C4—1131no—
263C22⋊C4—2261no—
264C22⋊C4—2261no—
265C22⋊C4—2261no—
266C22⋊C4—2261no—
267C22⋊C4—2261no—
268C22⋊C4—2261no—
269C22⋊C4—2261no—
270C42—1131no—
271C42—2261no—
272C42—2261no—
273C42—2261no—
274C42C22×D11311yescharacteristic
275C23—1131no—
276C23—2261no—
277Q8—81no—
278Q8—2261no—
279Q8—2261no—
280Q8—2261no—
281Q8—2261no—
282Q8—2261no—
283Q8—2261no—
284D4—9041no—
285D4—2261no—
286D4—2261no—
287C2×C4—21no—
288C2×C4—21no—
289C2×C4—21no—
290C2×C4—21no—
291C2×C4—1131no—
292C2×C4—1131no—
293C2×C4—1131no—
294C2×C4—9041no—
295C2×C4—2261no—
296C2×C4—2261no—
297C2×C4—2261no—
298C2×C4—2261no—
299C2×C4—2261no—
300C2×C4D4×D11311yescharacteristic
301C2×C4D4×D11311yescharacteristic
302C2×C4C23×D11311yescharacteristic
303C8—2261no—
304C8—2261no—
305C8#1426864812yes—
306C8#1426864812yes—
307C22—4521no—
308C22—4521no—
309C22—4521no—
310C22—2261no—
311C22—2261no—
312C22—2261no—
313C22C2×D4×D11311yescharacteristic
314C4—21no—
315C4—21no—
316C4—41no—
317C4—41no—
318C4—41no—
319C4—41no—
320C4—4521no—
321C4—4521no—
322C4—4521no—
323C4—2261no—
324C4—2261no—
325C4—2261no—
326C4C2×#1426864811yescharacteristic
327C4C2×#1426864811yescharacteristic
328C2—9041no—
329C2—4521no—
330C2#2029914911yescharacteristic
331C2#2029940811yescharacteristic
332C2#2029941411yescharacteristic
subgroupG/H
centerC22C2×D4×D113
commutator, cosocleC2×C4×C113C24
FrattiniC2×C4C23×D113
Fitting#501×C113C2
socleC22×C113C22×D4
prime radical#16813597C22
hypercenter#501D113
hypocenterC113#3178
LCSG ▷ C2×C4×C113 ▷ C2×C113 ▷ C113
UCSC1 ◁ C22 ◁ C42 ◁ #501

Complements

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

NH ≅ G/Ntype
2. #20299211C2semidirect
3. #20298992C2semidirect
4. #20298955C2semidirect
5. #20298950C2semidirect
6. #20298857C2semidirect
8. #20298840C2semidirect
10. #20298704C2semidirect
11. #20298697C2semidirect
12. #20298692C2semidirect
13. #20298685C2semidirect
14. #20298555C2semidirect
15. #501×C113C2semidirect
167. C113#3178semidirect
170. #501D113semidirect

Maximal subgroups

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

subgroupindex
#202992222
#202992112
#202989922
#202989552
#202989502
#202988572
#202988452
#202988402
#202988282
#202987042
#202986972
#202986922
#202986852
#202985552
#501×C1132
#3178113