Finite Group Databasebeta

← #28401456

Subgroups — #28401456

Order 14464.

390 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#20299176C211yesmaximal, characteristic
2#20298939C211yesmaximal, characteristic, complemented
3#20298931C211yesmaximal, characteristic, complemented
4#20298926C211yesmaximal, characteristic, complemented
5#20298922C211yesmaximal, characteristic, complemented
6#20298854C211yesmaximal, characteristic, complemented
7#20298846C211yesmaximal, characteristic, complemented
8#20298837C211yesmaximal, characteristic, complemented
9#20298829C211yesmaximal, characteristic, complemented
10#20298758C211yesmaximal, characteristic, complemented
11#20298758C211yesmaximal, characteristic, complemented
12#20298754C211yesmaximal, characteristic, complemented
13#20298737C211yesmaximal, characteristic, complemented
14#20298565C211yesmaximal, characteristic, complemented
15#536×C113C211yesmaximal, characteristic, complemented
16C2×#14268647C2211yescharacteristic
17C2×#14268637C2211yescharacteristic
18C2×#14268637C2211yescharacteristic
19C2×#14268634C2211yescharacteristic
20C2×#14268634C2211yescharacteristic
21C2×#14268631C2211yescharacteristic
22C22×#11744751C2211yescharacteristic
23#16813601C2211yescharacteristic
24#16813601C2211yescharacteristic
25#16813598—21no—
26#16813596C2211yescharacteristic
27#16813596C2211yescharacteristic
28#16813594—21no—
29#16813594—21no—
30#16813593—21no—
31C2×C4⋊Dic113C2211yescharacteristic
32#16813555C2211yescharacteristic
33#16813555C2211yescharacteristic
34#16813553C2211yescharacteristic
35#16813553C2211yescharacteristic
36#16813546C2211yescharacteristic
37#16813546C2211yescharacteristic
38#16813546C2211yescharacteristic
39#16813546C2211yescharacteristic
40#16813545C2211yescharacteristic
41#16813545C2211yescharacteristic
42#16813542C2211yescharacteristic
43#16813542C2211yescharacteristic
44C22⋊#11744751C2211yescharacteristic
45C22⋊#11744751C2211yescharacteristic
46C22⋊#11744751C2211yescharacteristic
47C22⋊#11744751C2211yescharacteristic
48C2×#41×C113C2211yescharacteristic
49C22×Q8×C113C2211yescharacteristic
50C4⋊Q8×C113—21no—
51#124×C113—21no—
52#123×C113—21no—
53#123×C113—21no—
54C22⋊Q8×C113C2211yescharacteristic
55C22⋊Q8×C113C2211yescharacteristic
56C22⋊Q8×C113C2211yescharacteristic
57C22⋊Q8×C113C2211yescharacteristic
58#117×C113C2211yescharacteristic
59#14268647—41no—
60#14268647—41no—
61C2×Dic226C2311yescharacteristic
62C2×D452C2311yescharacteristic
63C2×C22⋊D113—21no—
64C2×C22⋊D113—21no—
65C2×C22⋊D113—21no—
66C22×Dic113—21no—
67C2×C4×D113—21no—
68#14268637—41no—
69#14268637—41no—
70#14268634—41no—
71#14268634—41no—
72#14268631—41no—
73C2×#11744751—41no—
74C2×#11744751C2311yescharacteristic
75C2×#11744751C2311yescharacteristic
76C2×#11744751C2311yescharacteristic
77C2×#11744751C2311yescharacteristic
78C4⋊Dic113—21no—
79C4⋊Dic113C2311yescharacteristic
80C4⋊Dic113C2311yescharacteristic
81#14268626—21no—
82#14268626—21no—
83C22⋊Dic113—21no—
84C22⋊Dic113—21no—
85#14268624—21no—
86#14268624—21no—
87#41×C113—41no—
88#41×C113—41no—
89C2×Q8×C113—21no—
90C2×Q8×C113—41no—
91C2×Q8×C113—41no—
92C2×Q8×C113D411yescharacteristic
93C2×Q8×C113C2311yescharacteristic
94C2×Q8×C113C2311yescharacteristic
95C2×D4×C113D411yescharacteristic
96C2×D4×C113D411yescharacteristic
97C2×D4×C113D411yescharacteristic
98C22×C4×C113—21no—
99C22×C4×C113C2311yescharacteristic
100C22×C4×C113C2311yescharacteristic
101C22×C4×C113C2311yescharacteristic
102C4⋊C4×C113—21no—
103C4⋊C4×C113—21no—
104C4⋊C4×C113—21no—
105C4⋊C4×C113—21no—
106C4⋊C4×C113C2311yescharacteristic
107C4⋊C4×C113C2311yescharacteristic
108C22⋊C4×C113—21no—
109C22⋊C4×C113—21no—
110C22⋊C4×C113—21no—
111C22⋊C4×C113—21no—
112C22⋊C4×C113—21no—
113C42×C113—21no—
114C23×C113C2×D411yescharacteristic
115C23×C113C2×D411yescharacteristic
116C23×C113C2×D411yescharacteristic
117C22×D113—21no—
118Q8×C113—21no—
119Q8×C113—21no—
120Q8×C113—21no—
121Q8×C113—21no—
122Q8×C113—41no—
123Q8×C113—42no—
124D4×C113—41no—
125D4×C113—41no—
126D4×C113—41no—
127C2×C4×C113—21no—
128C2×C4×C113—21no—
129C2×C4×C113—21no—
130C2×C4×C113—21no—
131C2×C4×C113—21no—
132C2×C4×C113—21no—
133C2×C4×C113—21no—
134C2×C4×C113—21no—
135C2×C4×C113—21no—
136C2×C4×C113—21no—
137C2×C4×C113—42no—
138C2×C4×C113C2×D411yescharacteristic
139C2×C4×C113C2×D411yescharacteristic
140C2×C4×C113C2×D411yescharacteristic
141C2×C4×C113C2411yescharacteristic
142C22⋊D113—42no—
143C22⋊D113—81no—
144C22⋊D113—81no—
145C2×Dic113—21no—
146C2×Dic113—21no—
147C2×Dic113—21no—
148C2×Dic113—81no—
149D452—21no—
150D452—21no—
151C4×D113—42no—
152Dic226—21no—
153Dic226—21no—
154#11744751—21no—
155#11744751—21no—
156#11744751—21no—
157#11744751—21no—
158C22×C113—21no—
159C22×C113—21no—
160C22×C113—21no—
161C22×C113—21no—
162C22×C113—21no—
163C22×C113—21no—
164C22×C113—21no—
165C22×C113—21no—
166C22×C113—21no—
167C22×C113C22×D411yescharacteristic
168C2×D113—41no—
169C2×D113—41no—
170C2×D113—41no—
171C4×C113—21no—
172C4×C113—21no—
173C4×C113—21no—
174C4×C113—41no—
175C4×C113—41no—
176C4×C113—41no—
177C4×C113—41no—
178C4×C113H(5,𝔽2)11yescharacteristic
179C4×C113H(5,𝔽2)11yescharacteristic
180Dic113—41no—
181Dic113—41no—
182Dic113—41no—
183C2×C113—41no—
184C2×C113—41no—
185C2×C113—41no—
186C2×C113#53411yescharacteristic
187C2×C113#57711yescharacteristic
188C2×C113#57811yescharacteristic
189D113—81no—
190#3201—1131nomaximal, Sylow
191C113#320111yescharacteristic, complemented, Sylow
192#537—1131no—
193#536D11311yescharacteristic, complemented
194#485—1131no—
195#484—1131no—
196#483—1131no—
197#482—1131no—
198#470—1131no—
199#468—1131no—
200#467—1131no—
201#465—1131no—
202#452—1131no—
203#452—1131no—
204#451—1131no—
205#448—1131no—
206#408—1131no—
207C2×#41—1131no—
208C2×#41C2×D11311yescharacteristic
209C22×Q8C2×D11311yescharacteristic
210C2×Q16—1131no—
211C2×Q16—1131no—
212C2×SD16—1131no—
213C2×SD16—1131no—
214C2×M16—1131no—
215C22×C8—1131no—
216C4⋊Q8—21no—
217#124—21no—
218#123—21no—
219#123—21no—
220C22⋊Q8—1131no—
221C22⋊Q8—1131no—
222C22⋊Q8—2261no—
223C22⋊Q8C2×D11311yescharacteristic
224C22⋊Q8C2×D11311yescharacteristic
225C22⋊Q8C2×D11311yescharacteristic
226C22⋊Q8C2×D11311yescharacteristic
227#121—1131no—
228#121—1131no—
229#121—2261no—
230#121—2261no—
231#121—2261no—
232#117C2×D11311yescharacteristic
233C2×C4⋊C4—1131no—
234#107—1131no—
235#107—1131no—
236#106—1131no—
237#106—1131no—
238#103—1131no—
239#103—1131no—
240#103—1131no—
241#103—1131no—
242#103—1131no—
243#103—1131no—
244#102—1131no—
245#102—1131no—
246C22⋊C8—1131no—
247C22⋊C8—1131no—
248C22⋊C8—1131no—
249C22⋊C8—1131no—
250#41—41no—
251#41—41no—
252#41—4521no—
253#41—4521no—
254C2×Q8—21no—
255C2×Q8—41no—
256C2×Q8—41no—
257C2×Q8—1131no—
258C2×Q8C22⋊D11311yescharacteristic
259C2×Q8C22×D11311yescharacteristic
260C2×Q8C22×D11311yescharacteristic
261C2×D4—1131no—
262C2×D4—2261no—
263C2×D4—2261no—
264C2×D4—2261no—
265C2×D4C22⋊D11311yescharacteristic
266C2×D4C22⋊D11311yescharacteristic
267C2×D4C22⋊D11311yescharacteristic
268C22×C4—21no—
269C22×C4—2261no—
270C22×C4—2261no—
271C22×C4C22×D11311yescharacteristic
272C22×C4C22×D11311yescharacteristic
273C22×C4C22×D11311yescharacteristic
274Q16—4521no—
275Q16—4521no—
276SD16—4521no—
277SD16—4521no—
278M16—4521no—
279C2×C8—1131no—
280C2×C8—1131no—
281C2×C8—1131no—
282C2×C8—1131no—
283C2×C8—4521no—
284C4⋊C4—21no—
285C4⋊C4—21no—
286C4⋊C4—21no—
287C4⋊C4—21no—
288C4⋊C4—1131no—
289C4⋊C4—1131no—
290C4⋊C4—2261no—
291C4⋊C4—2261no—
292C4⋊C4—2261no—
293C4⋊C4C22×D11311yescharacteristic
294C4⋊C4C22×D11311yescharacteristic
295C22⋊C4—21no—
296C22⋊C4—21no—
297C22⋊C4—21no—
298C22⋊C4—21no—
299C22⋊C4—21no—
300C22⋊C4—2261no—
301C22⋊C4—2261no—
302C22⋊C4—2261no—
303C22⋊C4—2261no—
304C42—21no—
305C23—2261no—
306C23C2×C22⋊D11311yescharacteristic
307C23C2×C22⋊D11311yescharacteristic
308C23C2×C22⋊D11311yescharacteristic
309Q8—21no—
310Q8—21no—
311Q8—21no—
312Q8—21no—
313Q8—41no—
314Q8—42no—
315Q8—2261no—
316Q8—2261no—
317D4—41no—
318D4—41no—
319D4—41no—
320D4—9041no—
321D4—9041no—
322D4—4522no—
323D4—2261no—
324D4—2261no—
325C2×C4—21no—
326C2×C4—21no—
327C2×C4—21no—
328C2×C4—21no—
329C2×C4—21no—
330C2×C4—21no—
331C2×C4—21no—
332C2×C4—21no—
333C2×C4—21no—
334C2×C4—21no—
335C2×C4—42no—
336C2×C4—9041no—
337C2×C4—4522no—
338C2×C4—2261no—
339C2×C4—2261no—
340C2×C4—2261no—
341C2×C4C2×C22⋊D11311yescharacteristic
342C2×C4C2×C22⋊D11311yescharacteristic
343C2×C4C2×C22⋊D11311yescharacteristic
344C2×C4C23×D11311yescharacteristic
345C8—2261no—
346C8—2261no—
347C8—2261no—
348C8—2261no—
349C22—21no—
350C22—21no—
351C22—21no—
352C22—21no—
353C22—21no—
354C22—21no—
355C22—21no—
356C22—21no—
357C22—21no—
358C22—4521no—
359C22—4521no—
360C22—4521no—
361C22C22×C22⋊D11311yescharacteristic
362C4—21no—
363C4—21no—
364C4—21no—
365C4—41no—
366C4—41no—
367C4—41no—
368C4—41no—
369C4—4521no—
370C4—4521no—
371C4—4521no—
372C4#1681366711yescharacteristic
373C4#1681366711yescharacteristic
374C2—41no—
375C2—41no—
376C2—41no—
377C2—9041no—
378C2#2029915711yescharacteristic
379C2#2029940611yescharacteristic
380C2#2029941311yescharacteristic
subgroupG/H
centerC22C22×C22⋊D113
commutator, cosocleC2×C4×C113C24
FrattiniC2×C4C23×D113
Fitting#536×C113C2
socleC22×C113C22×D4
prime radical#20299176C2
hypercenter#536D113
hypocenterC113#3201
LCSG ▷ C2×C4×C113 ▷ C2×C113 ▷ C113
UCSC1 ◁ C22 ◁ C2×#41 ◁ #536

Complements

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

NH ≅ G/Ntype
2. #20298939C2semidirect
3. #20298931C2semidirect
4. #20298926C2semidirect
5. #20298922C2semidirect
6. #20298854C2semidirect
7. #20298846C2semidirect
8. #20298837C2semidirect
9. #20298829C2semidirect
10. #20298758C2semidirect
11. #20298758C2semidirect
12. #20298754C2semidirect
13. #20298737C2semidirect
14. #20298565C2semidirect
15. #536×C113C2semidirect
191. C113#3201semidirect
193. #536D113semidirect

Maximal subgroups

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

subgroupindex
#202991762
#202989392
#202989312
#202989262
#202989222
#202988542
#202988462
#202988372
#202988292
#202987582
#202987542
#202987372
#202985652
#536×C1132
#3201113