Finite Group Databasebeta

← #28401198

Subgroups — #28401198

Order 14464.

362 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#20299206C211yesmaximal, characteristic, complemented
2#20299199C211yesmaximal, characteristic
3#20298998C211yesmaximal, characteristic, complemented
4#20298969C211yesmaximal, characteristic, complemented
5#20298965C211yesmaximal, characteristic, complemented
6#20298961C211yesmaximal, characteristic, complemented
7#20298847C211yesmaximal, characteristic, complemented
8#20298843C211yesmaximal, characteristic, complemented
9#20298828C211yesmaximal, characteristic, complemented
10#20298824C211yesmaximal, characteristic, complemented
11#20298698C211yesmaximal, characteristic, complemented
12#20298696C211yesmaximal, characteristic, complemented
13C4×#14268636C211yesmaximal, characteristic, complemented
14#20298552C211yesmaximal, characteristic, complemented
15C4×SD16×C113C211yesmaximal, characteristic, complemented
16C2×#14268636C2211yescharacteristic
17C2×#14268635C2211yescharacteristic
18C2×#14268634C2211yescharacteristic
19C2×#14268630C2211yescharacteristic
20C2×C8×D113C2211yescharacteristic
21#16813620C2211yescharacteristic
22#16813618C2211yescharacteristic
23#16813617—21no—
24#16813616—21no—
25#16813614—21no—
26#16813613C2211yescharacteristic
27#16813613C2211yescharacteristic
28#16813612—21no—
29#16813605—21no—
30#16813604—21no—
31#16813602C2211yescharacteristic
32#16813598C2211yescharacteristic
33#16813597C2211yescharacteristic
34#16813596—21no—
35#16813595—21no—
36#16813593C2211yescharacteristic
37C4×Dic226C2211yescharacteristic
38C4×D452C2211yescharacteristic
39#16813579C2211yescharacteristic
40#16813555C2211yescharacteristic
41#16813555C2211yescharacteristic
42#16813554C2211yescharacteristic
43#16813547C2211yescharacteristic
44#16813546C2211yescharacteristic
45#16813545C2211yescharacteristic
46#16813544C2211yescharacteristic
47#16813543C2211yescharacteristic
48#16813542C2211yescharacteristic
49#16813533C2211yescharacteristic
50#16813532C2211yescharacteristic
51C8×Dic113C2211yescharacteristic
52C2×SD16×C113C2211yescharacteristic
53C4×Q8×C113C2211yescharacteristic
54C4×D4×C113C2211yescharacteristic
55#106×C113C2211yescharacteristic
56#103×C113C2211yescharacteristic
57#102×C113C2211yescharacteristic
58C4×C8×C113C2211yescharacteristic
59C2×Dic226C2311yescharacteristic
60C2×D452—21no—
61C2×D452C2311yescharacteristic
62C2×C22⋊D113—21no—
63C2×C22⋊D113—21no—
64C2×C22⋊D113—21no—
65C2×C4×D113—21no—
66C2×C4×D113C2311yescharacteristic
67#14268636—22no—
68#14268635—22no—
69#14268634—22no—
70#14268630—22no—
71C2×#11744751C2311yescharacteristic
72C2×#11744751C2311yescharacteristic
73C8×D113—22no—
74C4⋊Dic113—21no—
75C4⋊Dic113—21no—
76C4⋊Dic113—21no—
77C4⋊Dic113C2311yescharacteristic
78C4⋊Dic113C2311yescharacteristic
79#14268626—21no—
80#14268626—21no—
81#14268626—21no—
82#14268626—21no—
83#14268626—21no—
84#14268626—21no—
85#14268626D411yescharacteristic
86#14268626D411yescharacteristic
87C22⋊Dic113—21no—
88#14268624—21no—
89#14268624—21no—
90#14268624—21no—
91#14268624—21no—
92#14268624D411yescharacteristic
93#14268624D411yescharacteristic
94C4×Dic113—21no—
95C4×Dic113C2311yescharacteristic
96C2×Q8×C113C2311yescharacteristic
97C2×D4×C113C2311yescharacteristic
98C22×C4×C113—21no—
99SD16×C113—22no—
100C2×C8×C113C2311yescharacteristic
101C2×C8×C113C2311yescharacteristic
102C4⋊C4×C113—21no—
103C4⋊C4×C113C2311yescharacteristic
104C4⋊C4×C113C2311yescharacteristic
105C22⋊C4×C113—21no—
106C42×C113—21no—
107C42×C113C2311yescharacteristic
108C23×C113—21no—
109C22×D113—21no—
110C22×D113C2×D411yescharacteristic
111Q8×C113—21no—
112Q8×C113—21no—
113D4×C113—21no—
114D4×C113—21no—
115C2×C4×C113—21no—
116C2×C4×C113—21no—
117C2×C4×C113—21no—
118C2×C4×C113—81no—
119C2×C4×C113C2×D411yescharacteristic
120C2×C4×C113C2×D411yescharacteristic
121C2×C4×C113C2411yescharacteristic
122C22⋊D113—81no—
123C22⋊D113—81no—
124C22⋊D113—81no—
125C2×Dic113—21no—
126C2×Dic113—21no—
127C2×Dic113—21no—
128C2×Dic113C2×D411yescharacteristic
129C2×Dic113C2×D411yescharacteristic
130C2×Dic113C2×D411yescharacteristic
131D452—21no—
132D452—21no—
133D452—81no—
134C4×D113—21no—
135C4×D113—21no—
136C4×D113—81no—
137Dic226—21no—
138Dic226—21no—
139C8×C113—21no—
140C8×C113#4112yes—
141#11744751—21no—
142#11744751#4112yes—
143C22×C113—41no—
144C22×C113—41no—
145C22×C113—41no—
146C22×C113C22×D411yescharacteristic
147C2×D113—21no—
148C2×D113—21no—
149C2×D113—21no—
150C2×D113—41no—
151C2×D113—41no—
152C2×D113—41no—
153C4×C113—21no—
154C4×C113—21no—
155C4×C113—41no—
156C4×C113—41no—
157C4×C113—41no—
158C4×C113C2×#4111yescharacteristic
159C4×C113C2×#4111yescharacteristic
160Dic113—21no—
161Dic113—21no—
162Dic113—21no—
163Dic113—41no—
164Dic113—41no—
165Dic113—41no—
166C2×C113—81no—
167C2×C113#53211yescharacteristic
168C2×C113#57711yescharacteristic
169C2×C113#57711yescharacteristic
170D113—41no—
171D113—81no—
172#3174—1131nomaximal, Sylow
173C113#317411yescharacteristic, complemented, Sylow
174#541—1131no—
175#540—1131no—
176#499—1131no—
177#492—1131no—
178#491—1131no—
179#490—1131no—
180#468—1131no—
181#468—1131no—
182#465—1131no—
183#465—1131no—
184#440—1131no—
185#440—1131no—
186C4×SD16—1131no—
187C4×SD16D11311yescharacteristic, complemented
188#405—1131no—
189C2×SD16—1131no—
190C2×SD16—1131no—
191C2×SD16—1131no—
192C2×SD16C2×D11311yescharacteristic
193C2×M16—1131no—
194C22×C8—1131no—
195C4⋊Q8—1131no—
196#127—1131no—
197#126—2261no—
198#126—2261no—
199#125—1131no—
200#125—1131no—
201#125—2261no—
202#125—2261no—
203#123—2261no—
204#123—2261no—
205C22⋊Q8—1131no—
206C22⋊Q8—1131no—
207#121—1131no—
208#121—1131no—
209#121—2261no—
210#121—2261no—
211C4×Q8—1131no—
212C4×Q8C2×D11311yescharacteristic
213C4×D4—1131no—
214C4×D4C2×D11311yescharacteristic
215#117—1131no—
216#107—1131no—
217#107—1131no—
218#106—1131no—
219#106C2×D11311yescharacteristic
220#103—1131no—
221#103—1131no—
222#103—1131no—
223#103C2×D11311yescharacteristic
224#102—1131no—
225#102—1131no—
226#102—1131no—
227#102C2×D11311yescharacteristic
228#97—1131no—
229#97—1131no—
230C4×C8—1131no—
231C4×C8C2×D11311yescharacteristic
232C2×Q8—1131no—
233C2×Q8C22×D11311yescharacteristic
234C2×D4—1131no—
235C2×D4—2261no—
236C2×D4—2261no—
237C2×D4—2261no—
238C2×D4—2261no—
239C2×D4C22×D11311yescharacteristic
240C22×C4—21no—
241C22×C4—1131no—
242C22×C4—2261no—
243SD16—22no—
244SD16—2262no—
245SD16—2262no—
246SD16—2262no—
247M16—2262no—
248C2×C8—1131no—
249C2×C8—1131no—
250C2×C8—2262no—
251C2×C8C22×D11311yescharacteristic
252C2×C8C22×D11311yescharacteristic
253C4⋊C4—21no—
254C4⋊C4—1131no—
255C4⋊C4—1131no—
256C4⋊C4—1131no—
257C4⋊C4—1131no—
258C4⋊C4—2261no—
259C4⋊C4—2261no—
260C4⋊C4—2261no—
261C4⋊C4—2261no—
262C4⋊C4—2261no—
263C4⋊C4—2261no—
264C4⋊C4—2261no—
265C4⋊C4—2261no—
266C4⋊C4—2261no—
267C4⋊C4C22×D11311yescharacteristic
268C4⋊C4C22×D11311yescharacteristic
269C22⋊C4—21no—
270C22⋊C4—1131no—
271C22⋊C4—1131no—
272C22⋊C4—2261no—
273C22⋊C4—2261no—
274C22⋊C4—2261no—
275C22⋊C4—2261no—
276C22⋊C4—2261no—
277C42—21no—
278C42—1131no—
279C42—2261no—
280C42C22×D11311yescharacteristic
281C23—21no—
282C23—1131no—
283C23—2261no—
284Q8—21no—
285Q8—21no—
286Q8—2261no—
287Q8—2261no—
288D4—21no—
289D4—21no—
290D4—9041no—
291D4—9041no—
292D4—9041no—
293D4—9041no—
294D4—2261no—
295D4—2261no—
296C2×C4—21no—
297C2×C4—21no—
298C2×C4—21no—
299C2×C4—81no—
300C2×C4—1131no—
301C2×C4—1131no—
302C2×C4—1131no—
303C2×C4—9041no—
304C2×C4—2261no—
305C2×C4—2261no—
306C2×C4—2261no—
307C2×C4—2261no—
308C2×C4—2261no—
309C2×C4D4×D11311yescharacteristic
310C2×C4D4×D11311yescharacteristic
311C2×C4C23×D11311yescharacteristic
312C8—21no—
313C8—1132no—
314C8—2261no—
315C8#1426864712yes—
316C22—41no—
317C22—41no—
318C22—41no—
319C22—4521no—
320C22—4521no—
321C22—4521no—
322C22—2261no—
323C22—2261no—
324C22—2261no—
325C22C2×D4×D11311yescharacteristic
326C4—21no—
327C4—21no—
328C4—41no—
329C4—41no—
330C4—41no—
331C4—4521no—
332C4—4521no—
333C4—4521no—
334C4—2261no—
335C4—2261no—
336C4—2261no—
337C4#41×D11311yescharacteristic
338C4C2×#1426864711yescharacteristic
339C2—81no—
340C2—9041no—
341C2—4521no—
342C2#2029914511yescharacteristic
343C2#2029940411yescharacteristic
344C2#2029940511yescharacteristic
subgroupG/H
centerC22C2×D4×D113
commutator, cosocleC2×C4×C113C24
FrattiniC2×C4C23×D113
FittingC4×SD16×C113C2
socleC22×C113C22×D4
prime radical#20299199C2
hypercenterC4×SD16D113
hypocenterC113#3174
LCSG ▷ C2×C4×C113 ▷ C2×C113 ▷ C113
UCSC1 ◁ C22 ◁ C42 ◁ C4×SD16

Complements

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

NH ≅ G/Ntype
1. #20299206C2semidirect
3. #20298998C2semidirect
4. #20298969C2semidirect
5. #20298965C2semidirect
6. #20298961C2semidirect
7. #20298847C2semidirect
8. #20298843C2semidirect
9. #20298828C2semidirect
10. #20298824C2semidirect
11. #20298698C2semidirect
12. #20298696C2semidirect
13. C4×#14268636C2semidirect
14. #20298552C2semidirect
15. C4×SD16×C113C2semidirect
173. C113#3174semidirect
187. C4×SD16D113semidirect

Maximal subgroups

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

subgroupindex
#202992062
#202991992
#202989982
#202989692
#202989652
#202989612
#202988472
#202988432
#202988282
#202988242
#202986982
#202986962
C4×#142686362
#202985522
C4×SD16×C1132
#3174113