Finite Group Databasebeta

← #28401471

Subgroups — #28401471

Order 14464.

402 conjugacy classes of subgroups.

The subgroup lattice has 394 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20299176C211yesmaximal, characteristic, complemented
2#20298933C211yesmaximal, characteristic, complemented
3#20298931C211yesmaximal, characteristic, complemented
4#20298911C211yesmaximal, characteristic, complemented
5#20298909C211yesmaximal, characteristic, complemented
6#20298846C211yesmaximal, characteristic, complemented
7#20298842C211yesmaximal, characteristic, complemented
8#20298837C211yesmaximal, characteristic, complemented
9#20298832C211yesmaximal, characteristic, complemented
10#20298760C211yesmaximal, characteristic, complemented
11#20298758C211yesmaximal, characteristic, complemented
12#20298743C211yesmaximal, characteristic, complemented
13#20298741C211yesmaximal, characteristic, complemented
14#20298565C211yesmaximal, characteristic, complemented
15#537×C113C211yesmaximal, characteristic, complemented
16C2×#14268647C2211yescharacteristic
17C2×#14268637C2211yescharacteristic
18C2×#14268635C2211yescharacteristic
19C2×#14268634C2211yescharacteristic
20C2×#14268632C2211yescharacteristic
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#16813555C2211yescharacteristic
35#16813555C2211yescharacteristic
36#16813546C2211yescharacteristic
37#16813546C2211yescharacteristic
38#16813545C2211yescharacteristic
39#16813545C2211yescharacteristic
40#16813543C2211yescharacteristic
41#16813543C2211yescharacteristic
42#16813542C2211yescharacteristic
43#16813542C2211yescharacteristic
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
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#14268635—41no—
70#14268634—41no—
71#14268632—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—
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
118C22×D113—21no—
119Q8×C113—21no—
120Q8×C113—21no—
121Q8×C113—41no—
122D4×C113—21no—
123D4×C113—21no—
124D4×C113—41no—
125D4×C113—41no—
126D4×C113—41no—
127D4×C113—42no—
128D4×C113—81no—
129D4×C113—81no—
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—21no—
139C2×C4×C113—42no—
140C2×C4×C113—81no—
141C2×C4×C113C2×D411yescharacteristic
142C2×C4×C113C2×D411yescharacteristic
143C2×C4×C113C2×D411yescharacteristic
144C2×C4×C113C2411yescharacteristic
145C22⋊D113—42no—
146C22⋊D113—81no—
147C22⋊D113—81no—
148C2×Dic113—21no—
149C2×Dic113—21no—
150C2×Dic113—21no—
151C2×Dic113—81no—
152D452—21no—
153D452—21no—
154C4×D113—42no—
155Dic226—21no—
156Dic226—21no—
157#11744751—21no—
158#11744751—21no—
159#11744751—21no—
160#11744751—21no—
161C22×C113—21no—
162C22×C113—21no—
163C22×C113—21no—
164C22×C113—21no—
165C22×C113—21no—
166C22×C113—21no—
167C22×C113—21no—
168C22×C113—21no—
169C22×C113—21no—
170C22×C113—41no—
171C22×C113—41no—
172C22×C113—41no—
173C22×C113C22×D411yescharacteristic
174C2×D113—41no—
175C2×D113—41no—
176C2×D113—41no—
177C4×C113—21no—
178C4×C113—21no—
179C4×C113—21no—
180C4×C113—41no—
181C4×C113—41no—
182C4×C113—41no—
183C4×C113H(5,𝔽2)11yescharacteristic
184C4×C113H(5,𝔽2)11yescharacteristic
185Dic113—41no—
186Dic113—41no—
187Dic113—41no—
188C2×C113—41no—
189C2×C113—41no—
190C2×C113—41no—
191C2×C113—81no—
192C2×C113#53411yescharacteristic
193C2×C113#57611yescharacteristic
194C2×C113#57811yescharacteristic
195D113—81no—
196#3203—1131nomaximal, Sylow
197C113#320311yescharacteristic, complemented, Sylow
198#537—1131no—
199#537D11311yescharacteristic, complemented
200#484—1131no—
201#484—1131no—
202#480—1131no—
203#480—1131no—
204#468—1131no—
205#468—1131no—
206#467—1131no—
207#466—1131no—
208#452—1131no—
209#452—1131no—
210#449—1131no—
211#449—1131no—
212#408—1131no—
213C2×#41—1131no—
214C2×#41C2×D11311yescharacteristic
215C2×#41C2×D11311yescharacteristic
216C2×Q16—1131no—
217C2×SD16—1131no—
218C2×SD16—1131no—
219C2×D8—1131no—
220C2×M16—1131no—
221C22×C8—1131no—
222C22⋊Q8—21no—
223C22⋊Q8—1131no—
224C22⋊Q8—1131no—
225C22⋊Q8—2261no—
226C22⋊Q8C2×D11311yescharacteristic
227C22⋊Q8C2×D11311yescharacteristic
228#121—21no—
229#121—21no—
230#121—21no—
231#121—1131no—
232#121—1131no—
233#121—2261no—
234#121—2261no—
235#121—2261no—
236#121C2×D11311yescharacteristic
237#121C2×D11311yescharacteristic
238C2×C4⋊C4—1131no—
239C2×C4⋊C4C2×D11311yescharacteristic
240#107—1131no—
241#107—1131no—
242#107—1131no—
243#107—1131no—
244#103—1131no—
245#103—1131no—
246#103—1131no—
247#103—1131no—
248#102—1131no—
249#102—1131no—
250#102—1131no—
251#102—1131no—
252C22⋊C8—1131no—
253C22⋊C8—1131no—
254C22⋊C8—1131no—
255C22⋊C8—1131no—
256#41—41no—
257#41—41no—
258#41—41no—
259#41—41no—
260#41—4521no—
261#41—4521no—
262C2×Q8—1131no—
263C2×Q8C22⋊D11311yescharacteristic
264C2×Q8C22×D11311yescharacteristic
265C2×D4—21no—
266C2×D4—21no—
267C2×D4—21no—
268C2×D4—1131no—
269C2×D4—2261no—
270C2×D4—2261no—
271C2×D4—2261no—
272C2×D4C22⋊D11311yescharacteristic
273C2×D4C22⋊D11311yescharacteristic
274C2×D4C22⋊D11311yescharacteristic
275C2×D4C22×D11311yescharacteristic
276C22×C4—21no—
277C22×C4—21no—
278C22×C4—2261no—
279C22×C4—2261no—
280C22×C4C22×D11311yescharacteristic
281C22×C4C22×D11311yescharacteristic
282C22×C4C22×D11311yescharacteristic
283Q16—4521no—
284SD16—4521no—
285SD16—4521no—
286D8—4521no—
287M16—4521no—
288C2×C8—1131no—
289C2×C8—1131no—
290C2×C8—1131no—
291C2×C8—1131no—
292C2×C8—4521no—
293C4⋊C4—21no—
294C4⋊C4—21no—
295C4⋊C4—21no—
296C4⋊C4—1131no—
297C4⋊C4—1131no—
298C4⋊C4—2261no—
299C4⋊C4—2261no—
300C4⋊C4—2261no—
301C4⋊C4C22×D11311yescharacteristic
302C4⋊C4C22×D11311yescharacteristic
303C22⋊C4—21no—
304C22⋊C4—21no—
305C22⋊C4—21no—
306C22⋊C4—21no—
307C22⋊C4—2261no—
308C22⋊C4—2261no—
309C22⋊C4—2261no—
310C22⋊C4—2261no—
311C23—21no—
312C23—2261no—
313C23C2×C22⋊D11311yescharacteristic
314C23C2×C22⋊D11311yescharacteristic
315C23C2×C22⋊D11311yescharacteristic
316Q8—21no—
317Q8—21no—
318Q8—41no—
319Q8—2261no—
320Q8—2261no—
321D4—21no—
322D4—21no—
323D4—41no—
324D4—41no—
325D4—41no—
326D4—42no—
327D4—81no—
328D4—81no—
329D4—9041no—
330D4—9041no—
331D4—4522no—
332D4—2261no—
333D4—2261no—
334C2×C4—21no—
335C2×C4—21no—
336C2×C4—21no—
337C2×C4—21no—
338C2×C4—21no—
339C2×C4—21no—
340C2×C4—21no—
341C2×C4—21no—
342C2×C4—21no—
343C2×C4—42no—
344C2×C4—81no—
345C2×C4—9041no—
346C2×C4—4522no—
347C2×C4—2261no—
348C2×C4—2261no—
349C2×C4—2261no—
350C2×C4C2×C22⋊D11311yescharacteristic
351C2×C4C2×C22⋊D11311yescharacteristic
352C2×C4C2×C22⋊D11311yescharacteristic
353C2×C4C23×D11311yescharacteristic
354C8—2261no—
355C8—2261no—
356C8—2261no—
357C8—2261no—
358C22—21no—
359C22—21no—
360C22—21no—
361C22—21no—
362C22—21no—
363C22—21no—
364C22—21no—
365C22—21no—
366C22—21no—
367C22—41no—
368C22—41no—
369C22—41no—
370C22—4521no—
371C22—4521no—
372C22—4521no—
373C22C22×C22⋊D11311yescharacteristic
374C4—21no—
375C4—21no—
376C4—21no—
377C4—41no—
378C4—41no—
379C4—41no—
380C4—4521no—
381C4—4521no—
382C4—4521no—
383C4#1681366711yescharacteristic
384C4#1681366711yescharacteristic
385C2—41no—
386C2—41no—
387C2—41no—
388C2—81no—
389C2—9041no—
390C2#2029915711yescharacteristic
391C2#2029940111yescharacteristic
392C2#2029941311yescharacteristic
subgroupG/H
centerC22C22×C22⋊D113
commutator, cosocleC2×C4×C113C24
FrattiniC2×C4C23×D113
Fitting#537×C113C2
socleC22×C113C22×D4
hypercenter#537D113
hypocenterC113#3203
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. #20299176C2semidirect
2. #20298933C2semidirect
3. #20298931C2semidirect
4. #20298911C2semidirect
5. #20298909C2semidirect
6. #20298846C2semidirect
7. #20298842C2semidirect
8. #20298837C2semidirect
9. #20298832C2semidirect
10. #20298760C2semidirect
11. #20298758C2semidirect
12. #20298743C2semidirect
13. #20298741C2semidirect
14. #20298565C2semidirect
15. #537×C113C2semidirect
197. C113#3203semidirect
199. #537D113semidirect

Maximal subgroups

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

subgroupindex
#202991762
#202989332
#202989312
#202989112
#202989092
#202988462
#202988422
#202988372
#202988322
#202987602
#202987582
#202987432
#202987412
#202985652
#537×C1132
#3203113