Finite Group Databasebeta

← #28400836

Subgroups — #28400836

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#20299219C211yesmaximal, characteristic, complemented
2#20298933C211yesmaximal, characteristic, complemented
3#20298911C211yesmaximal, characteristic, complemented
4#20298893C211yesmaximal, characteristic, complemented
5#20298878C211yesmaximal, characteristic, complemented
6#20298820C211yesmaximal, characteristic, complemented
7#20298813C211yesmaximal, characteristic, complemented
8#20298760C211yesmaximal, characteristic, complemented
9#20298743C211yesmaximal, characteristic
10#20298698C211yesmaximal, characteristic, complemented
11#20298696C211yesmaximal, characteristic, complemented
12C4×#14268637C211yesmaximal, characteristic, complemented
13C4×#14268632C211yesmaximal, characteristic, complemented
14#20298659C211yesmaximal, characteristic, complemented
15#520×C113C211yesmaximal, characteristic, complemented
16C2×#14268637C2211yescharacteristic
17C2×#14268635C2211yescharacteristic
18C2×#14268634C2211yescharacteristic
19C2×#14268632C2211yescharacteristic
20#16813622C2211yescharacteristic
21#16813617—21no—
22#16813610C2211yescharacteristic
23#16813608—21no—
24#16813604—21no—
25#16813601C2211yescharacteristic
26#16813600—21no—
27#16813596C2211yescharacteristic
28C4×Dic226C2211yescharacteristic
29C4×D452C2211yescharacteristic
30#16813555C2211yescharacteristic
31#16813555C2211yescharacteristic
32#16813555C2211yescharacteristic
33#16813555C2211yescharacteristic
34C4⋊#11744751C2211yescharacteristic
35C4⋊#11744751C2211yescharacteristic
36#16813546C2211yescharacteristic
37#16813546C2211yescharacteristic
38#16813545C2211yescharacteristic
39#16813545C2211yescharacteristic
40#16813543C2211yescharacteristic
41#16813543C2211yescharacteristic
42#16813542C2211yescharacteristic
43#16813542C2211yescharacteristic
44C22⋊#11744751C2211yescharacteristic
45C22⋊#11744751C2211yescharacteristic
46#16813533C2211yescharacteristic
47C4×#11744751C2211yescharacteristic
48C2×#41×C113C2211yescharacteristic
49C4×Q8×C113C2211yescharacteristic
50C4×Q8×C113C2211yescharacteristic
51C4×D4×C113—21no—
52C4×D4×C113—21no—
53C4×D4×C113C2211yescharacteristic
54C4×D4×C113C2211yescharacteristic
55#117×C113—21no—
56#117×C113C2211yescharacteristic
57C2×C4⋊C4×C113—21no—
58C2×C4⋊C4×C113C2211yescharacteristic
59C2×Dic226—21no—
60C2×Dic226C2311yescharacteristic
61C2×D452C2311yescharacteristic
62C2×C22⋊D113—21no—
63C2×C4×D113—21no—
64#14268637—22no—
65#14268635—22no—
66#14268634—22no—
67#14268632—22no—
68C2×#11744751C2311yescharacteristic
69C2×#11744751C2311yescharacteristic
70C2×#11744751C2311yescharacteristic
71C2×#11744751C2311yescharacteristic
72C4⋊Dic113—21no—
73C4⋊Dic113C2311yescharacteristic
74C4⋊Dic113C2311yescharacteristic
75#14268626—21no—
76#14268626—21no—
77C22⋊Dic113—21no—
78#14268624—21no—
79#14268624—21no—
80#14268624—21no—
81#14268624—21no—
82C4×Dic113—21no—
83#41×C113—22no—
84#41×C113—22no—
85C2×Q8×C113C2311yescharacteristic
86C2×D4×C113—21no—
87C2×D4×C113C2311yescharacteristic
88C22×C4×C113—21no—
89C22×C4×C113—21no—
90C22×C4×C113—21no—
91C22×C4×C113—21no—
92C22×C4×C113C2311yescharacteristic
93C4⋊C4×C113—21no—
94C4⋊C4×C113—21no—
95C4⋊C4×C113—21no—
96C4⋊C4×C113D411yescharacteristic
97C4⋊C4×C113D411yescharacteristic
98C4⋊C4×C113C2311yescharacteristic
99C4⋊C4×C113C2311yescharacteristic
100C22⋊C4×C113—21no—
101C22⋊C4×C113—21no—
102C22⋊C4×C113D411yescharacteristic
103C22⋊C4×C113D411yescharacteristic
104C42×C113—21no—
105C42×C113—21no—
106C42×C113C2311yescharacteristic
107C42×C113C2311yescharacteristic
108C23×C113—21no—
109C23×C113C2×D411yescharacteristic
110C22×D113—21no—
111Q8×C113—21no—
112Q8×C113#4112yes—
113D4×C113—24no—
114D4×C113—21no—
115D4×C113#4112yes—
116C2×C4×C113—24no—
117C2×C4×C113—21no—
118C2×C4×C113—21no—
119C2×C4×C113—21no—
120C2×C4×C113—21no—
121C2×C4×C113—21no—
122C2×C4×C113—81no—
123C2×C4×C113—81no—
124C2×C4×C113—81no—
125C2×C4×C113C2×D411yescharacteristic
126C2×C4×C113C2×D411yescharacteristic
127C2×C4×C113C2×D411yescharacteristic
128C2×C4×C113C2×D411yescharacteristic
129C2×C4×C113C2×D411yescharacteristic
130C2×C4×C113C2411yescharacteristic
131C22⋊D113—81no—
132C2×Dic113—21no—
133C2×Dic113—21no—
134C2×Dic113—21no—
135D452—21no—
136D452—21no—
137C4×D113—81no—
138Dic226—21no—
139Dic226—21no—
140Dic226—81no—
141#11744751—21no—
142#11744751—21no—
143#11744751—21no—
144#11744751—21no—
145C22×C113—21no—
146C22×C113—22no—
147C22×C113—21no—
148C22×C113—21no—
149C22×C113—41no—
150C22×C113—41no—
151C22×C113C22×D411yescharacteristic
152C2×D113—41no—
153C2×D113—41no—
154C2×D113—41no—
155C4×C113—21no—
156C4×C113—22no—
157C4×C113—21no—
158C4×C113—21no—
159C4×C113—21no—
160C4×C113—21no—
161C4×C113—41no—
162C4×C113—41no—
163C4×C113C2×#4111yescharacteristic
164C4×C113C2×#4111yescharacteristic
165Dic113—41no—
166Dic113—41no—
167Dic113—41no—
168C2×C113—41no—
169C2×C113—42no—
170C2×C113#52511yescharacteristic
171C2×C113#57611yescharacteristic
172C2×C113#57811yescharacteristic
173D113—81no—
174#3124—1131nomaximal, Sylow
175C113#312411yescharacteristic, complemented, Sylow
176#542—1131no—
177#520D11311yescharacteristic, complemented
178#484—1131no—
179#480—1131no—
180#477—1131no—
181#474—1131no—
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×#41C2×D11311yescharacteristic
192C2×Q16—1131no—
193C2×SD16—1131no—
194C2×SD16—1131no—
195C2×D8—1131no—
196C4⋊Q8—1131no—
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×Q8C2×D11311yescharacteristic
206C4×Q8C2×D11311yescharacteristic
207C4×D4—21no—
208C4×D4—21no—
209C4×D4—1131no—
210C4×D4C2×D11311yescharacteristic
211C4×D4C2×D11311yescharacteristic
212#117—21no—
213#117C2×D11311yescharacteristic
214C2×C4⋊C4—21no—
215C2×C4⋊C4C2×D11311yescharacteristic
216#107—1131no—
217#107—1131no—
218#107—1131no—
219#107—1131no—
220C4⋊C8—1131no—
221C4⋊C8—1131no—
222#103—1131no—
223#103—1131no—
224#103—1131no—
225#103—1131no—
226#102—1131no—
227#102—1131no—
228#102—1131no—
229#102—1131no—
230C22⋊C8—1131no—
231C22⋊C8—1131no—
232#97—1131no—
233C4×C8—1131no—
234#41—22no—
235#41—22no—
236C2×Q8—1131no—
237C2×Q8—2261no—
238C2×Q8C22×D11311yescharacteristic
239C2×D4—21no—
240C2×D4—1131no—
241C2×D4—2261no—
242C2×D4C22×D11311yescharacteristic
243C22×C4—21no—
244C22×C4—21no—
245C22×C4—21no—
246C22×C4—21no—
247C22×C4—2261no—
248C22×C4C22×D11311yescharacteristic
249Q16—2262no—
250SD16—2262no—
251SD16—2262no—
252D8—2262no—
253C2×C8—1131no—
254C2×C8—1131no—
255C2×C8—1131no—
256C2×C8—1131no—
257C4⋊C4—21no—
258C4⋊C4—21no—
259C4⋊C4—21no—
260C4⋊C4—1131no—
261C4⋊C4—1131no—
262C4⋊C4—2261no—
263C4⋊C4—2261no—
264C4⋊C4—2261no—
265C4⋊C4C22⋊D11311yescharacteristic
266C4⋊C4C22⋊D11311yescharacteristic
267C4⋊C4C22×D11311yescharacteristic
268C4⋊C4C22×D11311yescharacteristic
269C22⋊C4—21no—
270C22⋊C4—21no—
271C22⋊C4—2261no—
272C22⋊C4—2261no—
273C22⋊C4—2261no—
274C22⋊C4—2261no—
275C22⋊C4—2261no—
276C22⋊C4C22⋊D11311yescharacteristic
277C22⋊C4C22⋊D11311yescharacteristic
278C42—21no—
279C42—21no—
280C42—2261no—
281C42C22×D11311yescharacteristic
282C42C22×D11311yescharacteristic
283C23—21no—
284C23—2261no—
285C23C2×C22⋊D11311yescharacteristic
286Q8—21no—
287Q8—9041no—
288Q8—2261no—
289Q8—2261no—
290Q8#1426864712yes—
291D4—24no—
292D4—21no—
293D4—9041no—
294D4—2261no—
295D4—2261no—
296D4#1426864712yes—
297C2×C4—24no—
298C2×C4—21no—
299C2×C4—21no—
300C2×C4—21no—
301C2×C4—21no—
302C2×C4—21no—
303C2×C4—81no—
304C2×C4—81no—
305C2×C4—81no—
306C2×C4—9041no—
307C2×C4—2261no—
308C2×C4—2261no—
309C2×C4—2261no—
310C2×C4C2×C22⋊D11311yescharacteristic
311C2×C4C2×C22⋊D11311yescharacteristic
312C2×C4C2×C22⋊D11311yescharacteristic
313C2×C4C2×C22⋊D11311yescharacteristic
314C2×C4C2×C22⋊D11311yescharacteristic
315C2×C4C23×D11311yescharacteristic
316C8—2261no—
317C8—2261no—
318C8—2261no—
319C8—2261no—
320C22—21no—
321C22—22no—
322C22—21no—
323C22—21no—
324C22—41no—
325C22—41no—
326C22—4521no—
327C22—4521no—
328C22—4521no—
329C22C22×C22⋊D11311yescharacteristic
330C4—21no—
331C4—22no—
332C4—21no—
333C4—21no—
334C4—21no—
335C4—21no—
336C4—41no—
337C4—41no—
338C4—4521no—
339C4—4521no—
340C4—4521no—
341C4C2×#1426864711yescharacteristic
342C4C2×#1426864711yescharacteristic
343C2—41no—
344C2—42no—
345C2—9041no—
346C2#2029910911yescharacteristic
347C2#2029940111yescharacteristic
348C2#2029941311yescharacteristic
subgroupG/H
centerC22C22×C22⋊D113
commutator, cosocleC2×C4×C113C24
FrattiniC2×C4C23×D113
Fitting#520×C113C2
socleC22×C113C22×D4
prime radical#20298743C2
hypercenter#520D113
hypocenterC113#3124
LCSG ▷ C2×C4×C113 ▷ C2×C113 ▷ C113
UCSC1 ◁ C22 ◁ #117 ◁ #520

Complements

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

NH ≅ G/Ntype
1. #20299219C2semidirect
2. #20298933C2semidirect
3. #20298911C2semidirect
4. #20298893C2semidirect
5. #20298878C2semidirect
6. #20298820C2semidirect
7. #20298813C2semidirect
8. #20298760C2semidirect
10. #20298698C2semidirect
11. #20298696C2semidirect
12. C4×#14268637C2semidirect
13. C4×#14268632C2semidirect
14. #20298659C2semidirect
15. #520×C113C2semidirect
175. C113#3124semidirect
177. #520D113semidirect

Maximal subgroups

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

subgroupindex
#202992192
#202989332
#202989112
#202988932
#202988782
#202988202
#202988132
#202987602
#202987432
#202986982
#202986962
C4×#142686372
C4×#142686322
#202986592
#520×C1132
#3124113