Finite Group Databasebeta

← #28400841

Subgroups — #28400841

Order 14464.

384 conjugacy classes of subgroups.

The subgroup lattice has 350 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20299222C211yesmaximal, characteristic, complemented
2#20299077C211yesmaximal, characteristic, complemented
3#20298935C211yesmaximal, characteristic, complemented
4#20298913C211yesmaximal, characteristic, complemented
5#20298890C211yesmaximal, characteristic, complemented
6#20298821C211yesmaximal, characteristic, complemented
7#20298813C211yesmaximal, characteristic, complemented
8#20298761C211yesmaximal, characteristic, complemented
9#20298744C211yesmaximal, characteristic
10#20298697C211yesmaximal, characteristic, complemented
11#20298695C211yesmaximal, characteristic, complemented
12#20298692C211yesmaximal, characteristic, complemented
13#20298678C211yesmaximal, characteristic, complemented
14#20298658C211yesmaximal, characteristic, complemented
15#474×C113C211yesmaximal, characteristic, complemented
16C2×#14268646C2211yescharacteristic
17C2×Dic452C2211yescharacteristic
18C2×#14268636C2211yescharacteristic
19C2×#14268635C2211yescharacteristic
20C2×#14268632C2211yescharacteristic
21#16813617—21no—
22#16813611—21no—
23#16813610C2211yescharacteristic
24#16813607—21no—
25#16813602C2211yescharacteristic
26#16813598—21no—
27#16813597C2211yescharacteristic
28C4×Dic226C2211yescharacteristic
29#16813587C2211yescharacteristic
30#16813587C2211yescharacteristic
31D4×Dic113C2211yescharacteristic
32#16813584C2211yescharacteristic
33C4×C22⋊D113—21no—
34#16813582—21no—
35#16813579C2211yescharacteristic
36#16813578—21no—
37C2×#14268626—21no—
38C4⋊C4×D113C2211yescharacteristic
39#16813555C2211yescharacteristic
40#16813555C2211yescharacteristic
41C4⋊#11744751C2211yescharacteristic
42#16813547C2211yescharacteristic
43#16813545C2211yescharacteristic
44#16813545C2211yescharacteristic
45#16813545C2211yescharacteristic
46#16813544C2211yescharacteristic
47#16813542C2211yescharacteristic
48#16813534C2211yescharacteristic
49#16813534C2211yescharacteristic
50#16813532C2211yescharacteristic
51C8×Dic113C2211yescharacteristic
52C4⋊Q8×C113C2211yescharacteristic
53C4×D4×C113C2211yescharacteristic
54#107×C113C2211yescharacteristic
55#107×C113C2211yescharacteristic
56C4⋊C8×C113C2211yescharacteristic
57#102×C113C2211yescharacteristic
58#102×C113C2211yescharacteristic
59#14268646—22no—
60#14268646—22no—
61C2×Dic226C2311yescharacteristic
62C2×Dic226C2311yescharacteristic
63C2×D452—21no—
64C2×D452C2311yescharacteristic
65C2×C22⋊D113—21no—
66C22×Dic113—21no—
67C22×Dic113—21no—
68C2×C4×D113—21no—
69C2×C4×D113—21no—
70C2×C4×D113C2311yescharacteristic
71Dic452—22no—
72#14268636—22no—
73#14268635—22no—
74#14268632—22no—
75C2×#11744751C2311yescharacteristic
76C2×#11744751C2311yescharacteristic
77C4⋊Dic113—21no—
78C4⋊Dic113C2311yescharacteristic
79#14268626—21no—
80#14268626—21no—
81#14268626—21no—
82#14268626—21no—
83#14268626D411yescharacteristic
84#14268626D411yescharacteristic
85C22⋊Dic113—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×D4×C113C2311yescharacteristic
99C22×C4×C113—21no—
100C2×C8×C113C2311yescharacteristic
101C2×C8×C113C2311yescharacteristic
102C4⋊C4×C113—21no—
103C4⋊C4×C113C2311yescharacteristic
104C4⋊C4×C113C2311yescharacteristic
105C4⋊C4×C113C2311yescharacteristic
106C22⋊C4×C113—21no—
107C42×C113C2311yescharacteristic
108C23×C113—21no—
109C22×D113—21no—
110C22×D113C2×D411yescharacteristic
111Q8×C113—81no—
112D4×C113—21no—
113D4×C113#4112yes—
114C2×C4×C113—21no—
115C2×C4×C113—21no—
116C2×C4×C113—21no—
117C2×C4×C113—81no—
118C2×C4×C113C2×D411yescharacteristic
119C2×C4×C113C2×D411yescharacteristic
120C2×C4×C113C2411yescharacteristic
121C22⋊D113—24no—
122C2×Dic113—24no—
123C2×Dic113—21no—
124C2×Dic113—21no—
125C2×Dic113—21no—
126C2×Dic113—81no—
127C2×Dic113C2×D411yescharacteristic
128C2×Dic113C2×D411yescharacteristic
129C2×Dic113C2×D411yescharacteristic
130D452—21no—
131D452—21no—
132D452—81no—
133C4×D113—21no—
134C4×D113—21no—
135C4×D113—81no—
136C4×D113—81no—
137Dic226—21no—
138Dic226—21no—
139Dic226—21no—
140Dic226#4112yes—
141C8×C113—21no—
142C8×C113—21no—
143#11744751—21no—
144#11744751—21no—
145C22×C113—22no—
146C22×C113—41no—
147C22×C113—41no—
148C22×C113C22×D411yescharacteristic
149C2×D113—21no—
150C2×D113—21no—
151C2×D113—21no—
152C2×D113—41no—
153C2×D113—41no—
154C2×D113—41no—
155C4×C113—21no—
156C4×C113—21no—
157C4×C113—41no—
158C4×C113—41no—
159C4×C113—41no—
160C4×C113C2×#4111yescharacteristic
161C4×C113C2×#4111yescharacteristic
162Dic113—22no—
163Dic113—21no—
164Dic113—21no—
165Dic113—21no—
166Dic113—41no—
167Dic113—41no—
168C2×C113—42no—
169C2×C113#52511yescharacteristic
170C2×C113#57611yescharacteristic
171C2×C113#57811yescharacteristic
172D113—41no—
173D113—81no—
174#3124—1131nomaximal, Sylow
175C113#312411yescharacteristic, complemented, Sylow
176#542—1131no—
177#520—1131no—
178#484—1131no—
179#480—1131no—
180#477—1131no—
181#474D11311yescharacteristic, complemented
182#464—1131no—
183#463—1131no—
184#452—1131no—
185#449—1131no—
186#440—1131no—
187#440—1131no—
188C4×Q16—1131no—
189C4×D8—1131no—
190#433—1131no—
191C2×#41—1131no—
192C2×Q16—1131no—
193C2×SD16—1131no—
194C2×SD16—1131no—
195C2×D8—1131no—
196C4⋊Q8C2×D11311yescharacteristic
197#126—2261no—
198#124—1131no—
199#124—2261no—
200#123—2261no—
201C22⋊Q8—1131no—
202C22⋊Q8—2261no—
203#121—1131no—
204C4×Q8—1131no—
205C4×Q8—1131no—
206C4×Q8—1131no—
207C4×D4—1131no—
208C4×D4—1131no—
209C4×D4—2261no—
210C4×D4—2261no—
211C4×D4C2×D11311yescharacteristic
212#117—1131no—
213#117—2261no—
214C2×C4⋊C4—1131no—
215C2×C4⋊C4—2261no—
216#107—1131no—
217#107—1131no—
218#107C2×D11311yescharacteristic
219#107C2×D11311yescharacteristic
220C4⋊C8—1131no—
221C4⋊C8C2×D11311yescharacteristic
222#103—1131no—
223#103—1131no—
224#103—1131no—
225#103—1131no—
226#102—1131no—
227#102—1131no—
228#102C2×D11311yescharacteristic
229#102C2×D11311yescharacteristic
230C22⋊C8—1131no—
231C22⋊C8—1131no—
232#97—1131no—
233C4×C8—1131no—
234#41—2262no—
235#41—2262no—
236C2×Q8—21no—
237C2×Q8—1131no—
238C2×Q8—1131no—
239C2×D4—1131no—
240C2×D4—2261no—
241C2×D4—2261no—
242C2×D4C22×D11311yescharacteristic
243C22×C4—21no—
244C22×C4—1131no—
245C22×C4—2261no—
246C22×C4—2261no—
247C22×C4—2261no—
248C22×C4—2261no—
249Q16—2262no—
250SD16—2262no—
251SD16—2262no—
252D8—2262no—
253C2×C8—1131no—
254C2×C8—1131no—
255C2×C8C22×D11311yescharacteristic
256C2×C8C22×D11311yescharacteristic
257C4⋊C4—21no—
258C4⋊C4—1131no—
259C4⋊C4—1131no—
260C4⋊C4—1131no—
261C4⋊C4—2261no—
262C4⋊C4—2261no—
263C4⋊C4—2261no—
264C4⋊C4—2261no—
265C4⋊C4—2261no—
266C4⋊C4C22×D11311yescharacteristic
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—
277C22⋊C4—2261no—
278C42—1131no—
279C42—2261no—
280C42—2261no—
281C42—2261no—
282C42C22×D11311yescharacteristic
283C23—21no—
284C23—1131no—
285C23—2261no—
286Q8—81no—
287Q8—1132no—
288Q8—2261no—
289Q8—2261no—
290Q8—2261no—
291D4—21no—
292D4—9041no—
293D4—2264no—
294D4—2261no—
295D4—2261no—
296D4#1426864812yes—
297C2×C4—21no—
298C2×C4—21no—
299C2×C4—21no—
300C2×C4—81no—
301C2×C4—1131no—
302C2×C4—1131no—
303C2×C4—1131no—
304C2×C4—9041no—
305C2×C4—9041no—
306C2×C4—9041no—
307C2×C4—2261no—
308C2×C4—2261no—
309C2×C4—2264no—
310C2×C4—2261no—
311C2×C4—2261no—
312C2×C4—2261no—
313C2×C4D4×D11311yescharacteristic
314C2×C4D4×D11311yescharacteristic
315C2×C4C23×D11311yescharacteristic
316C8—21no—
317C8—21no—
318C8—2261no—
319C8—2261no—
320C22—22no—
321C22—41no—
322C22—41no—
323C22—4521no—
324C22—4521no—
325C22—4521no—
326C22—2261no—
327C22—2261no—
328C22—2261no—
329C22C2×D4×D11311yescharacteristic
330C4—21no—
331C4—21no—
332C4—41no—
333C4—41no—
334C4—41no—
335C4—4521no—
336C4—4521no—
337C4—2261no—
338C4—2262no—
339C4—2261no—
340C4—2261no—
341C4#41×D11311yescharacteristic
342C4C2×#1426864811yescharacteristic
343C2—42no—
344C2—9041no—
345C2—4521no—
346C2#2029911111yescharacteristic
347C2#2029939911yescharacteristic
348C2#2029941411yescharacteristic
subgroupG/H
centerC22C2×D4×D113
commutator, cosocleC2×C4×C113C24
FrattiniC2×C4C23×D113
Fitting#474×C113C2
socleC22×C113C22×D4
prime radical#20298744C2
hypercenter#474D113
hypocenterC113#3124
LCSG ▷ C2×C4×C113 ▷ C2×C113 ▷ C113
UCSC1 ◁ C22 ◁ C42 ◁ #474

Complements

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

NH ≅ G/Ntype
1. #20299222C2semidirect
2. #20299077C2semidirect
3. #20298935C2semidirect
4. #20298913C2semidirect
5. #20298890C2semidirect
6. #20298821C2semidirect
7. #20298813C2semidirect
8. #20298761C2semidirect
10. #20298697C2semidirect
11. #20298695C2semidirect
12. #20298692C2semidirect
13. #20298678C2semidirect
14. #20298658C2semidirect
15. #474×C113C2semidirect
175. C113#3124semidirect
181. #474D113semidirect

Maximal subgroups

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

subgroupindex
#202992222
#202990772
#202989352
#202989132
#202988902
#202988212
#202988132
#202987612
#202987442
#202986972
#202986952
#202986922
#202986782
#202986582
#474×C1132
#3124113