Finite Group Databasebeta

← #28401450

Subgroups — #28401450

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#20299169C211yesmaximal, characteristic, complemented
2#20298936C211yesmaximal, characteristic, complemented
3#20298933C211yesmaximal, characteristic, complemented
4#20298928C211yesmaximal, characteristic, complemented
5#20298919C211yesmaximal, characteristic, complemented
6#20298854C211yesmaximal, characteristic, complemented
7#20298842C211yesmaximal, characteristic, complemented
8#20298837C211yesmaximal, characteristic, complemented
9#20298825C211yesmaximal, characteristic, complemented
10#20298760C211yesmaximal, characteristic, complemented
11#20298760C211yesmaximal, characteristic, complemented
12#20298753C211yesmaximal, characteristic, complemented
13#20298736C211yesmaximal, characteristic, complemented
14#20298565C211yesmaximal, characteristic, complemented
15#537×C113C211yesmaximal, characteristic
16C22×Dic226C2211yescharacteristic
17C2×#14268637C2211yescharacteristic
18C2×#14268637C2211yescharacteristic
19C2×#14268635C2211yescharacteristic
20C2×#14268635C2211yescharacteristic
21C2×#14268631C2211yescharacteristic
22C22×#11744751C2211yescharacteristic
23#16813620—21no—
24#16813609—21no—
25#16813603—21no—
26#16813603—21no—
27#16813601C2211yescharacteristic
28#16813601C2211yescharacteristic
29#16813601C2211yescharacteristic
30#16813601C2211yescharacteristic
31#16813581C2211yescharacteristic
32#16813555C2211yescharacteristic
33#16813555C2211yescharacteristic
34#16813553C2211yescharacteristic
35#16813553C2211yescharacteristic
36#16813546C2211yescharacteristic
37#16813546C2211yescharacteristic
38#16813545C2211yescharacteristic
39#16813545C2211yescharacteristic
40#16813545C2211yescharacteristic
41#16813545C2211yescharacteristic
42#16813543C2211yescharacteristic
43#16813543C2211yescharacteristic
44C22⋊#11744751C2211yescharacteristic
45C22⋊#11744751C2211yescharacteristic
46C22⋊#11744751C2211yescharacteristic
47C22⋊#11744751C2211yescharacteristic
48C2×#41×C113C2211yescharacteristic
49C2×#41×C113C2211yescharacteristic
50C22⋊Q8×C113—21no—
51C22⋊Q8×C113C2211yescharacteristic
52C22⋊Q8×C113C2211yescharacteristic
53#121×C113—21no—
54#121×C113—21no—
55#121×C113—21no—
56#121×C113C2211yescharacteristic
57#121×C113C2211yescharacteristic
58C2×C4⋊C4×C113C2211yescharacteristic
59C2×Dic226—21no—
60C2×Dic226—41no—
61C2×Dic226—41no—
62C2×Dic226C2311yescharacteristic
63C2×Dic226C2311yescharacteristic
64C22×Dic113—21no—
65#14268637—41no—
66#14268637—41no—
67#14268635—41no—
68#14268635—41no—
69#14268631—41no—
70C2×#11744751—41no—
71C2×#11744751C2311yescharacteristic
72C2×#11744751C2311yescharacteristic
73C2×#11744751C2311yescharacteristic
74C2×#11744751C2311yescharacteristic
75C4⋊Dic113C2311yescharacteristic
76C4⋊Dic113C2311yescharacteristic
77#14268626—21no—
78#14268626—21no—
79#14268626—21no—
80#14268626—21no—
81C22⋊Dic113—21no—
82C22⋊Dic113—21no—
83C22⋊Dic113—21no—
84C22⋊Dic113—21no—
85C22⋊Dic113—21no—
86C4×Dic113—21no—
87#41×C113—41no—
88#41×C113—41no—
89#41×C113—41no—
90#41×C113—41no—
91C2×Q8×C113D411yescharacteristic
92C2×Q8×C113C2311yescharacteristic
93C2×D4×C113—21no—
94C2×D4×C113—21no—
95C2×D4×C113—21no—
96C2×D4×C113D411yescharacteristic
97C2×D4×C113D411yescharacteristic
98C2×D4×C113D411yescharacteristic
99C2×D4×C113C2311yescharacteristic
100C22×C4×C113—21no—
101C22×C4×C113—21no—
102C22×C4×C113C2311yescharacteristic
103C22×C4×C113C2311yescharacteristic
104C22×C4×C113C2311yescharacteristic
105C4⋊C4×C113—21no—
106C4⋊C4×C113—21no—
107C4⋊C4×C113—21no—
108C4⋊C4×C113C2311yescharacteristic
109C4⋊C4×C113C2311yescharacteristic
110C22⋊C4×C113—21no—
111C22⋊C4×C113—21no—
112C22⋊C4×C113—21no—
113C22⋊C4×C113—21no—
114C23×C113—21no—
115C23×C113C2×D411yescharacteristic
116C23×C113C2×D411yescharacteristic
117C23×C113C2×D411yescharacteristic
118Q8×C113—21no—
119Q8×C113—21no—
120Q8×C113—41no—
121D4×C113—21no—
122D4×C113—21no—
123D4×C113—41no—
124D4×C113—41no—
125D4×C113—41no—
126D4×C113—42no—
127D4×C113—81no—
128D4×C113—81no—
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—21no—
138C2×C4×C113—42no—
139C2×C4×C113—81no—
140C2×C4×C113C2×D411yescharacteristic
141C2×C4×C113C2×D411yescharacteristic
142C2×C4×C113C2×D411yescharacteristic
143C2×C4×C113C2411yescharacteristic
144C2×Dic113—21no—
145C2×Dic113—21no—
146C2×Dic113—21no—
147C2×Dic113—21no—
148C2×Dic113—42no—
149Dic226—21no—
150Dic226—21no—
151Dic226—21no—
152Dic226—21no—
153Dic226—42no—
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×C113—41no—
168C22×C113—41no—
169C22×C113—41no—
170C22×C113C22×D411yescharacteristic
171C4×C113—21no—
172C4×C113—21no—
173C4×C113—21no—
174C4×C113—41no—
175C4×C113—41no—
176C4×C113—41no—
177C4×C113H(5,𝔽2)11yescharacteristic
178C4×C113H(5,𝔽2)11yescharacteristic
179Dic113—41no—
180Dic113—41no—
181Dic113—41no—
182Dic113—41no—
183C2×C113—41no—
184C2×C113—41no—
185C2×C113—41no—
186C2×C113—81no—
187C2×C113#53411yescharacteristic
188C2×C113#57711yescharacteristic
189C2×C113#57811yescharacteristic
190#3201—1131nomaximal, Sylow
191C113#320111yescharacteristic, complemented, Sylow
192#537D11311yescharacteristic
193#536—1131no—
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×#41C2×D11311yescharacteristic
208C2×#41C2×D11311yescharacteristic
209C22×Q8—1131no—
210C2×Q16—1131no—
211C2×Q16—1131no—
212C2×SD16—1131no—
213C2×SD16—1131no—
214C2×M16—1131no—
215C22×C8—1131no—
216C4⋊Q8—2261no—
217#124—2261no—
218#123—2261no—
219#123—2261no—
220C22⋊Q8—21no—
221C22⋊Q8—1131no—
222C22⋊Q8—1131no—
223C22⋊Q8—1131no—
224C22⋊Q8—1131no—
225C22⋊Q8C2×D11311yescharacteristic
226C22⋊Q8C2×D11311yescharacteristic
227#121—21no—
228#121—21no—
229#121—21no—
230#121C2×D11311yescharacteristic
231#121C2×D11311yescharacteristic
232#117—1131no—
233C2×C4⋊C4C2×D11311yescharacteristic
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—41no—
253#41—41no—
254C2×Q8—1131no—
255C2×Q8—1131no—
256C2×Q8—4521no—
257C2×Q8—4521no—
258C2×Q8—2261no—
259C2×Q8C22⋊D11311yescharacteristic
260C2×Q8C22×D11311yescharacteristic
261C2×D4—21no—
262C2×D4—21no—
263C2×D4—21no—
264C2×D4C22⋊D11311yescharacteristic
265C2×D4C22⋊D11311yescharacteristic
266C2×D4C22⋊D11311yescharacteristic
267C2×D4C22×D11311yescharacteristic
268C22×C4—21no—
269C22×C4—21no—
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—1131no—
288C4⋊C4—1131no—
289C4⋊C4—2261no—
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—2261no—
300C22⋊C4—2261no—
301C22⋊C4—2261no—
302C22⋊C4—2261no—
303C22⋊C4—2261no—
304C42—2261no—
305C23—21no—
306C23C2×C22⋊D11311yescharacteristic
307C23C2×C22⋊D11311yescharacteristic
308C23C2×C22⋊D11311yescharacteristic
309Q8—21no—
310Q8—21no—
311Q8—41no—
312Q8—4522no—
313Q8—2261no—
314Q8—2261no—
315Q8—2261no—
316Q8—2261no—
317D4—21no—
318D4—21no—
319D4—41no—
320D4—41no—
321D4—41no—
322D4—42no—
323D4—81no—
324D4—81no—
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—42no—
335C2×C4—81no—
336C2×C4—4522no—
337C2×C4—2261no—
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—41no—
359C22—41no—
360C22—41no—
361C22C22×C22⋊D11311yescharacteristic
362C4—21no—
363C4—21no—
364C4—21no—
365C4—41no—
366C4—41no—
367C4—41no—
368C4—4521no—
369C4—4521no—
370C4—4521no—
371C4—4521no—
372C4#1681366711yescharacteristic
373C4#1681366711yescharacteristic
374C2—41no—
375C2—41no—
376C2—41no—
377C2—81no—
378C2#2029915711yescharacteristic
379C2#2029940911yescharacteristic
380C2#2029941311yescharacteristic
subgroupG/H
centerC22C22×C22⋊D113
commutator, cosocleC2×C4×C113C24
FrattiniC2×C4C23×D113
Fitting, prime radical#537×C113C2
socleC22×C113C22×D4
hypercenter#537D113
hypocenterC113#3201
LCSG ▷ C2×C4×C113 ▷ C2×C113 ▷ C113
UCSC1 ◁ C22 ◁ C2×#41 ◁ #537

Complements

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

NH ≅ G/Ntype
1. #20299169C2semidirect
2. #20298936C2semidirect
3. #20298933C2semidirect
4. #20298928C2semidirect
5. #20298919C2semidirect
6. #20298854C2semidirect
7. #20298842C2semidirect
8. #20298837C2semidirect
9. #20298825C2semidirect
10. #20298760C2semidirect
11. #20298760C2semidirect
12. #20298753C2semidirect
13. #20298736C2semidirect
14. #20298565C2semidirect
191. C113#3201semidirect

Maximal subgroups

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

subgroupindex
#202991692
#202989362
#202989332
#202989282
#202989192
#202988542
#202988422
#202988372
#202988252
#202987602
#202987532
#202987362
#202985652
#537×C1132
#3201113