Finite Group Databasebeta

← #28402520

Subgroups — #28402520

Order 14464.

408 conjugacy classes of subgroups.

The subgroup lattice has 382 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20299311C211yesmaximal, characteristic, complemented
2#20299267C211yesmaximal, characteristic, complemented
3#20298943C211yesmaximal, characteristic, complemented
4#20298922C211yesmaximal, characteristic, complemented
5#20298920C211yesmaximal, characteristic, complemented
6#20298891C211yesmaximal, characteristic, complemented
7#20298834C211yesmaximal, characteristic, complemented
8#20298833C211yesmaximal, characteristic, complemented
9#20298792C211yesmaximal, characteristic, complemented
10#20298746C211yesmaximal, characteristic, complemented
11#20298743C211yesmaximal, characteristic, complemented
12#20298683C211yesmaximal, characteristic, complemented
13C8×C22⋊D113C211yesmaximal, characteristic, complemented
14#20298593C211yesmaximal, characteristic, complemented
15#416×C113C211yesmaximal, characteristic, complemented
16C2×#14268648C2211yescharacteristic
17C2×#14268634C2211yescharacteristic
18C2×D904C2211yescharacteristic
19C2×#14268632C2211yescharacteristic
20C2×C8×D113C2211yescharacteristic
21#16813621C2211yescharacteristic
22#16813618—21no—
23#16813618C2211yescharacteristic
24#16813610—21no—
25#16813608—21no—
26#16813597C2211yescharacteristic
27#16813596—21no—
28#16813596C2211yescharacteristic
29#16813596C2211yescharacteristic
30#16813595—21no—
31#16813593—21no—
32#16813593C2211yescharacteristic
33Q8×Dic113C2211yescharacteristic
34#16813584C2211yescharacteristic
35C4×C22⋊D113—21no—
36C4×C22⋊D113C2211yescharacteristic
37#16813580C2211yescharacteristic
38#16813579—21no—
39#16813556C2211yescharacteristic
40#16813555C2211yescharacteristic
41#16813553C2211yescharacteristic
42#16813551C2211yescharacteristic
43#16813546C2211yescharacteristic
44#16813544C2211yescharacteristic
45#16813544C2211yescharacteristic
46#16813543C2211yescharacteristic
47#16813542C2211yescharacteristic
48#16813542C2211yescharacteristic
49C22⋊#11744751C2211yescharacteristic
50#16813534C2211yescharacteristic
51C8×Dic113C2211yescharacteristic
52C2×#41×C113C2211yescharacteristic
53C22×C8×C113C2211yescharacteristic
54#117×C113C2211yescharacteristic
55#103×C113C2211yescharacteristic
56#103×C113C2211yescharacteristic
57#102×C113C2211yescharacteristic
58#102×C113C2211yescharacteristic
59#14268648—22no—
60#14268648—41no—
61C2×Dic226—21no—
62C2×D452—21no—
63C2×D452—21no—
64C2×D452C2311yescharacteristic
65C2×D452C2311yescharacteristic
66C2×C22⋊D113—21no—
67C2×C22⋊D113—21no—
68C2×C22⋊D113—21no—
69C2×C22⋊D113—21no—
70C2×C22⋊D113—21no—
71C2×C22⋊D113D411yescharacteristic
72C2×C4×D113—21no—
73C2×C4×D113—21no—
74C2×C4×D113C2311yescharacteristic
75#14268634—22no—
76D904—41no—
77#14268632—41no—
78C2×#11744751C2311yescharacteristic
79C2×#11744751C2311yescharacteristic
80C8×D113—41no—
81C4⋊Dic113—21no—
82C4⋊Dic113C2311yescharacteristic
83C4⋊Dic113C2311yescharacteristic
84#14268626—21no—
85#14268626D411yescharacteristic
86C22⋊Dic113—21no—
87C22⋊Dic113D411yescharacteristic
88#14268624—21no—
89#14268624—21no—
90#14268624—21no—
91#14268624—21no—
92#14268624—21no—
93#14268624D411yescharacteristic
94C4×Dic113—21no—
95C4×Dic113—21no—
96C4×Dic113C2311yescharacteristic
97#41×C113—22no—
98#41×C113—41no—
99C2×Q8×C113C2311yescharacteristic
100C2×D4×C113—21no—
101C2×D4×C113C2311yescharacteristic
102C22×C4×C113—21no—
103C22×C4×C113C2311yescharacteristic
104C2×C8×C113—41no—
105C2×C8×C113C2311yescharacteristic
106C2×C8×C113C2311yescharacteristic
107C4⋊C4×C113C2311yescharacteristic
108C4⋊C4×C113C2311yescharacteristic
109C22⋊C4×C113—21no—
110C42×C113—21no—
111C23×C113—21no—
112C23×C113C2×D411yescharacteristic
113C22×D113—21no—
114C22×D113—21no—
115C22×D113C2×D411yescharacteristic
116Q8×C113—21no—
117Q8×C113#4112yes—
118D4×C113—21no—
119D4×C113—21no—
120D4×C113—42no—
121C2×C4×C113—21no—
122C2×C4×C113—21no—
123C2×C4×C113—21no—
124C2×C4×C113—21no—
125C2×C4×C113—21no—
126C2×C4×C113—42no—
127C2×C4×C113C2×D411yescharacteristic
128C2×C4×C113C2411yescharacteristic
129C22⋊D113—22no—
130C22⋊D113—42no—
131C22⋊D113—81no—
132C22⋊D113—81no—
133C22⋊D113—81no—
134C22⋊D113—81no—
135C2×Dic113—21no—
136C2×Dic113—21no—
137C2×Dic113C2×D411yescharacteristic
138C2×Dic113C2×D411yescharacteristic
139C2×Dic113C2×D411yescharacteristic
140D452—21no—
141D452—21no—
142D452—21no—
143D452—21no—
144D452—42no—
145D452—81no—
146C4×D113—21no—
147C4×D113—21no—
148C4×D113—42no—
149C4×D113—42no—
150Dic226—81no—
151C8×C113—21no—
152C8×C113—21no—
153#11744751—21no—
154#11744751—21no—
155C22×C113—21no—
156C22×C113—21no—
157C22×C113—21no—
158C22×C113—41no—
159C22×C113—41no—
160C22×C113—41no—
161C22×C113C22×D411yescharacteristic
162C2×D113—21no—
163C2×D113—21no—
164C2×D113—21no—
165C2×D113—41no—
166C2×D113—41no—
167C2×D113—41no—
168C2×D113—41no—
169C2×D113—41no—
170C2×D113—41no—
171C4×C113—22no—
172C4×C113—21no—
173C4×C113—41no—
174C4×C113—41no—
175C4×C113C2×#4111yescharacteristic
176C4×C113H(5,𝔽2)11yescharacteristic
177Dic113—21no—
178Dic113—21no—
179Dic113—41no—
180Dic113—41no—
181Dic113#13512yes—
182C2×C113—41no—
183C2×C113—81no—
184C2×C113#54611yescharacteristic
185C2×C113C2×#13511yescharacteristic
186C2×C113#57611yescharacteristic
187D113—41no—
188D113—81no—
189D113—81no—
190#3305—1131nomaximal, Sylow
191C113#330511yescharacteristic, complemented, Sylow
192#555—1131no—
193#550—1131no—
194#486—1131no—
195#482—1131no—
196#482—1131no—
197#477—1131no—
198#466—1131no—
199#466—1131no—
200#459—1131no—
201#449—1131no—
202#449—1131no—
203C4×SD16—1131no—
204C8×D4—1131no—
205#416—1131no—
206#416D11311yescharacteristic, complemented
207C2×#41—1131no—
208C2×#41C2×D11311yescharacteristic
209C2×SD16—1131no—
210C2×D8—1131no—
211C2×D8—1131no—
212C22×C8—1131no—
213C22×C8C2×D11311yescharacteristic
214C4⋊Q8—1131no—
215#127—1131no—
216#127—2261no—
217#124—2261no—
218#124—2261no—
219#121—1131no—
220#121—1131no—
221#121—1131no—
222#121—1131no—
223#121—2261no—
224#121—2261no—
225#121—2261no—
226C4×Q8—1131no—
227C4×D4—1131no—
228C4×D4—1131no—
229C4×D4—2261no—
230#117—1131no—
231#117—2261no—
232#117C2×D11311yescharacteristic
233#107—1131no—
234#107—1131no—
235#106—1131no—
236C4⋊C8—1131no—
237#103—1131no—
238#103C2×D11311yescharacteristic
239#103C2×D11311yescharacteristic
240#102—1131no—
241#102—1131no—
242#102—1131no—
243#102—1131no—
244#102—1131no—
245#102C2×D11311yescharacteristic
246#102C2×D11311yescharacteristic
247C22⋊C8—1131no—
248C22⋊C8—1131no—
249C4×C8—1131no—
250#41—22no—
251#41—41no—
252#41—4521no—
253#41—2262no—
254C2×Q8—2261no—
255C2×Q8C22×D11311yescharacteristic
256C2×D4—21no—
257C2×D4—1131no—
258C2×D4—1131no—
259C2×D4—1131no—
260C2×D4—2261no—
261C2×D4—2261no—
262C2×D4—2261no—
263C2×D4—2261no—
264C2×D4—2261no—
265C2×D4—2261no—
266C2×D4—2261no—
267C2×D4C22×D11311yescharacteristic
268C22×C4—21no—
269C22×C4—1131no—
270C22×C4—2261no—
271C22×C4—2261no—
272C22×C4C22×D11311yescharacteristic
273SD16—2262no—
274D8—4521no—
275D8—4521no—
276C2×C8—41no—
277C2×C8—1131no—
278C2×C8—1131no—
279C2×C8—4521no—
280C2×C8C22×D11311yescharacteristic
281C2×C8C22×D11311yescharacteristic
282C4⋊C4—1131no—
283C4⋊C4—1131no—
284C4⋊C4—1131no—
285C4⋊C4—2261no—
286C4⋊C4—2261no—
287C4⋊C4C22×D11311yescharacteristic
288C4⋊C4C22×D11311yescharacteristic
289C22⋊C4—21no—
290C22⋊C4—1131no—
291C22⋊C4—1131no—
292C22⋊C4—2261no—
293C22⋊C4—2261no—
294C22⋊C4—2261no—
295C22⋊C4—2261no—
296C22⋊C4—2261no—
297C22⋊C4—2261no—
298C42—21no—
299C42—1131no—
300C42—2261no—
301C42—2261no—
302C23—21no—
303C23—1131no—
304C23—2261no—
305C23—2261no—
306C23D4×D11311yescharacteristic
307Q8—21no—
308Q8—9041no—
309Q8#1426864712yes—
310D4—21no—
311D4—21no—
312D4—42no—
313D4—9041no—
314D4—9041no—
315D4—9041no—
316D4—9041no—
317D4—9041no—
318D4—4522no—
319D4—4522no—
320D4—2262no—
321D4—2261no—
322D4—2261no—
323D4—2261no—
324D4—2261no—
325C2×C4—21no—
326C2×C4—21no—
327C2×C4—21no—
328C2×C4—21no—
329C2×C4—21no—
330C2×C4—42no—
331C2×C4—1131no—
332C2×C4—1131no—
333C2×C4—1131no—
334C2×C4—4522no—
335C2×C4—4522no—
336C2×C4—2261no—
337C2×C4—2261no—
338C2×C4—2261no—
339C2×C4—2261no—
340C2×C4D4×D11311yescharacteristic
341C2×C4C23×D11311yescharacteristic
342C8—21no—
343C8—21no—
344C8—2261no—
345C8—2261no—
346C22—21no—
347C22—21no—
348C22—21no—
349C22—41no—
350C22—41no—
351C22—41no—
352C22—4521no—
353C22—4521no—
354C22—4521no—
355C22—4521no—
356C22—4521no—
357C22—4521no—
358C22—2261no—
359C22—2261no—
360C22—2261no—
361C22C2×D4×D11311yescharacteristic
362C4—21no—
363C4—22no—
364C4—41no—
365C4—41no—
366C4—1132no—
367C4—4521no—
368C4—4521no—
369C4—2261no—
370C4—2261no—
371C4C2×#1426864711yescharacteristic
372C4#1681366711yescharacteristic
373C2—41no—
374C2—81no—
375C2—9041no—
376C2—9041no—
377C2—4521no—
378C2#2029923811yescharacteristic
379C2#135×D11311yescharacteristic
380C2#2029940011yescharacteristic
subgroupG/H
centerC22C2×D4×D113
commutator, cosocleC2×C4×C113C24
FrattiniC2×C4C23×D113
Fitting#416×C113C2
socleC22×C113C22×D4
hypercenter#416D113
hypocenterC113#3305
LCSG ▷ C2×C4×C113 ▷ C2×C113 ▷ C113
UCSC1 ◁ C22 ◁ C22×C4 ◁ #416

Complements

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

NH ≅ G/Ntype
1. #20299311C2semidirect
2. #20299267C2semidirect
3. #20298943C2semidirect
4. #20298922C2semidirect
5. #20298920C2semidirect
6. #20298891C2semidirect
7. #20298834C2semidirect
8. #20298833C2semidirect
9. #20298792C2semidirect
10. #20298746C2semidirect
11. #20298743C2semidirect
12. #20298683C2semidirect
13. C8×C22⋊D113C2semidirect
14. #20298593C2semidirect
15. #416×C113C2semidirect
191. C113#3305semidirect
206. #416D113semidirect

Maximal subgroups

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

subgroupindex
#202993112
#202992672
#202989432
#202989222
#202989202
#202988912
#202988342
#202988332
#202987922
#202987462
#202987432
#202986832
C8×C22⋊D1132
#202985932
#416×C1132
#3305113