Finite Group Databasebeta

← #28402424

Subgroups — #28402424

Order 14464.

420 conjugacy classes of subgroups.

The subgroup lattice has 384 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20299294C211yesmaximal, characteristic, complemented
2#20298952C211yesmaximal, characteristic, complemented
3#20298931C211yesmaximal, characteristic, complemented
4#20298919C211yesmaximal, characteristic, complemented
5#20298898C211yesmaximal, characteristic, complemented
6#20298832C211yesmaximal, characteristic, complemented
7#20298829C211yesmaximal, characteristic, complemented
8#20298810C211yesmaximal, characteristic, complemented
9#20298743C211yesmaximal, characteristic, complemented
10#20298732C211yesmaximal, characteristic, complemented
11C4×#14268632C211yesmaximal, characteristic, complemented
12D4×#11744751C211yesmaximal, characteristic, complemented
13#20298594C211yesmaximal, characteristic, complemented
14C2×#16813543C211yesmaximal, characteristic, complemented
15#546×C113C211yesmaximal, characteristic, complemented
16C2×#14268634C2211yescharacteristic, complemented
17C2×#14268632C2211yescharacteristic
18C2×#14268632C2211yescharacteristic
19C22×#11744751C2211yescharacteristic
20C22×#11744751C2211yescharacteristic, complemented
21#16813617—21no—
22#16813614C2211yescharacteristic, complemented
23#16813604—21no—
24#16813596C2211yescharacteristic
25#16813596C2211yescharacteristic, complemented
26#16813594—21no—
27C4×D452C2211yescharacteristic, complemented
28#16813582—21no—
29#16813581C2211yescharacteristic, complemented
30C2×C4⋊Dic113C2211yescharacteristic
31#16813555C2211yescharacteristic, complemented
32#16813555C2211yescharacteristic, complemented
33#16813553C2211yescharacteristic, complemented
34C4⋊#11744751C2211yescharacteristic, complemented
35#16813546C2211yescharacteristic, complemented
36#16813546C2211yescharacteristic, complemented
37#16813546C2211yescharacteristic, complemented
38#16813543C2211yescharacteristic
39#16813543C2211yescharacteristic
40#16813543C2211yescharacteristic
41#16813543C2211yescharacteristic
42#16813543C2211yescharacteristic
43#16813543C2211yescharacteristic
44#16813542C2211yescharacteristic, complemented
45C22⋊#11744751C2211yescharacteristic
46C22⋊#11744751C2211yescharacteristic, complemented
47C4×#11744751C2211yescharacteristic, complemented
48C2×#41×C113C2211yescharacteristic
49C22×D4×C113C2211yescharacteristic
50#124×C113C2211yescharacteristic
51#123×C113—21no—
52C22⋊Q8×C113C2211yescharacteristic
53#121×C113—21no—
54#121×C113C2211yescharacteristic
55#120×C113—21no—
56C4×D4×C113C2211yescharacteristic
57C4×D4×C113C2211yescharacteristic
58C2×C22⋊C4×C113—21no—
59C2×D452C2311yescharacteristic
60C2×C22⋊D113—21no—
61C2×C22⋊D113—21no—
62C22×Dic113—21no—
63C2×C4×D113—21no—
64#14268634—41no—
65#14268632—22no—
66#14268632—41no—
67C2×#11744751—41no—
68C2×#11744751—41no—
69C2×#11744751C2311yescharacteristic
70C2×#11744751C2311yescharacteristic
71C2×#11744751C2311yescharacteristic
72C2×#11744751C2311yescharacteristic
73C4⋊Dic113—21no—
74C4⋊Dic113C2311yescharacteristic
75C4⋊Dic113C2311yescharacteristic
76C4⋊Dic113C2311yescharacteristic
77#14268626—21no—
78#14268626—21no—
79C22⋊Dic113—21no—
80#14268624—21no—
81#14268624—21no—
82#14268624—21no—
83C4×Dic113—21no—
84C24×C113—21no—
85#41×C113—22no—
86#41×C113—41no—
87C2×Q8×C113C2311yescharacteristic
88C2×D4×C113—22no—
89C2×D4×C113—21no—
90C2×D4×C113—21no—
91C2×D4×C113—21no—
92C2×D4×C113—41no—
93C2×D4×C113D411yescharacteristic
94C2×D4×C113C2311yescharacteristic
95C2×D4×C113C2311yescharacteristic
96C22×C4×C113—21no—
97C22×C4×C113—21no—
98C22×C4×C113C2311yescharacteristic
99C22×C4×C113C2311yescharacteristic
100C4⋊C4×C113—21no—
101C4⋊C4×C113D411yescharacteristic
102C4⋊C4×C113C2311yescharacteristic
103C22⋊C4×C113—21no—
104C22⋊C4×C113—21no—
105C22⋊C4×C113—21no—
106C22⋊C4×C113—21no—
107C22⋊C4×C113—21no—
108C22⋊C4×C113D411yescharacteristic
109C22⋊C4×C113D411yescharacteristic
110C42×C113C2311yescharacteristic
111C23×C113—21no—
112C23×C113—21no—
113C23×C113—42no—
114C23×C113—42no—
115C23×C113—81no—
116C23×C113C2×D411yescharacteristic
117C23×C113C2×D411yescharacteristic
118C22×D113—21no—
119Q8×C113—21no—
120Q8×C113—21no—
121D4×C113—22no—
122D4×C113—21no—
123D4×C113—21no—
124D4×C113—21no—
125D4×C113—42no—
126D4×C113—42no—
127D4×C113—81no—
128D4×C113#4112yes—
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—42no—
136C2×C4×C113—81no—
137C2×C4×C113C2×D411yescharacteristic
138C2×C4×C113C2×D411yescharacteristic
139C2×C4×C113C2×D411yescharacteristic
140C2×C4×C113C2×D411yescharacteristic
141C2×C4×C113C2411yescharacteristic
142C22⋊D113—42no—
143C22⋊D113—81no—
144C2×Dic113—21no—
145C2×Dic113—21no—
146C2×Dic113—21no—
147C2×Dic113—81no—
148D452—21no—
149D452—21no—
150C4×D113—81no—
151#11744751—21no—
152#11744751—21no—
153#11744751—21no—
154#11744751—21no—
155C22×C113—21no—
156C22×C113—21no—
157C22×C113—21no—
158C22×C113—22no—
159C22×C113—21no—
160C22×C113—21no—
161C22×C113—41no—
162C22×C113—41no—
163C22×C113—41no—
164C22×C113—41no—
165C22×C113—41no—
166C22×C113—84no—
167C22×C113#13512yes—
168C22×C113C22×D411yescharacteristic
169C2×D113—41no—
170C2×D113—41no—
171C2×D113—41no—
172C4×C113—21no—
173C4×C113—21no—
174C4×C113—21no—
175C4×C113—21no—
176C4×C113—41no—
177C4×C113—41no—
178C4×C113C2×#4111yescharacteristic
179C4×C113H(5,𝔽2)11yescharacteristic
180Dic113—41no—
181Dic113—41no—
182Dic113—41no—
183C2×C113—22no—
184C2×C113—41no—
185C2×C113—42no—
186C2×C113—81no—
187C2×C113#54611yescharacteristic
188C2×C113C2×#13511yescharacteristic
189C2×C113#57611yescharacteristic
190D113—81no—
191#3297—1131nomaximal, Sylow
192C113#329711yescharacteristic, complemented, Sylow
193#553—1131no—
194#546D11311yescharacteristic, complemented
195#488—1131no—
196#484—1131no—
197#482—1131no—
198#478—1131no—
199#466—1131no—
200#465—1131no—
201#463—1131no—
202#449—1131no—
203#447—1131no—
204C4×D8—1131no—
205C8×D4—1131no—
206#416—1131no—
207C2×#102—1131no—
208C2×#41C2×D11311yescharacteristic
209C22×D4C2×D11311yescharacteristic
210C2×SD16—1131no—
211C2×D8—1131no—
212C2×D8—1131no—
213C22×C8—1131no—
214C22×C8—1131no—
215#126—2261no—
216#125—1131no—
217#124C2×D11311yescharacteristic
218#123—21no—
219#123—2261no—
220C22⋊Q8C2×D11311yescharacteristic
221#121—21no—
222#121—1131no—
223#121—1131no—
224#121—2261no—
225#121C2×D11311yescharacteristic
226#120—21no—
227C4×D4—1131no—
228C4×D4—2261no—
229C4×D4C2×D11311yescharacteristic
230C4×D4C2×D11311yescharacteristic
231#117—1131no—
232C2×C4⋊C4—1131no—
233C2×C22⋊C4—21no—
234#107—1131no—
235#107—1131no—
236#106—1131no—
237C4⋊C8—1131no—
238#103—1131no—
239#103—1131no—
240#103—1131no—
241#102—1131no—
242#102—1131no—
243#102—1131no—
244#102—1131no—
245#102—1131no—
246#102—1131no—
247#102—1131no—
248C22⋊C8—1131no—
249C22⋊C8—1131no—
250C4×C8—1131no—
251C24—21no—
252#41—22no—
253#41—41no—
254C2×Q8C22×D11311yescharacteristic
255C2×D4—22no—
256C2×D4—21no—
257C2×D4—21no—
258C2×D4—21no—
259C2×D4—41no—
260C2×D4—1131no—
261C2×D4—2261no—
262C2×D4—2261no—
263C2×D4C22⋊D11311yescharacteristic
264C2×D4C22×D11311yescharacteristic
265C2×D4C22×D11311yescharacteristic
266C22×C4—21no—
267C22×C4—21no—
268C22×C4—2261no—
269C22×C4—2261no—
270C22×C4C22×D11311yescharacteristic
271C22×C4C22×D11311yescharacteristic
272SD16—4521no—
273D8—4521no—
274D8—2262no—
275C2×C8—1131no—
276C2×C8—1131no—
277C2×C8—1131no—
278C2×C8—1131no—
279C2×C8—4521no—
280C2×C8—4521no—
281C4⋊C4—21no—
282C4⋊C4—1131no—
283C4⋊C4—1131no—
284C4⋊C4—1131no—
285C4⋊C4—2261no—
286C4⋊C4—2261no—
287C4⋊C4—2261no—
288C4⋊C4C22⋊D11311yescharacteristic
289C4⋊C4C22×D11311yescharacteristic
290C22⋊C4—21no—
291C22⋊C4—21no—
292C22⋊C4—21no—
293C22⋊C4—21no—
294C22⋊C4—21no—
295C22⋊C4—2261no—
296C22⋊C4—2261no—
297C22⋊C4—2261no—
298C22⋊C4—2261no—
299C22⋊C4C22⋊D11311yescharacteristic
300C22⋊C4C22⋊D11311yescharacteristic
301C42—2261no—
302C42C22×D11311yescharacteristic
303C23—21no—
304C23—21no—
305C23—42no—
306C23—42no—
307C23—81no—
308C23—2261no—
309C23C2×C22⋊D11311yescharacteristic
310C23C2×C22⋊D11311yescharacteristic
311Q8—21no—
312Q8—21no—
313D4—22no—
314D4—21no—
315D4—21no—
316D4—21no—
317D4—42no—
318D4—42no—
319D4—81no—
320D4—9041no—
321D4—4522no—
322D4—2261no—
323D4—2261no—
324D4#1426864612yes—
325C2×C4—21no—
326C2×C4—21no—
327C2×C4—21no—
328C2×C4—21no—
329C2×C4—21no—
330C2×C4—21no—
331C2×C4—42no—
332C2×C4—81no—
333C2×C4—9041no—
334C2×C4—9041no—
335C2×C4—2261no—
336C2×C4—2261no—
337C2×C4—2261no—
338C2×C4C2×C22⋊D11311yescharacteristic
339C2×C4C2×C22⋊D11311yescharacteristic
340C2×C4C2×C22⋊D11311yescharacteristic
341C2×C4C2×C22⋊D11311yescharacteristic
342C2×C4C23×D11311yescharacteristic
343C8—2261no—
344C8—2261no—
345C8—2261no—
346C8—2261no—
347C22—21no—
348C22—21no—
349C22—21no—
350C22—21no—
351C22—21no—
352C22—22no—
353C22—41no—
354C22—41no—
355C22—41no—
356C22—41no—
357C22—41no—
358C22—84no—
359C22—4521no—
360C22—4521no—
361C22—4521no—
362C22#1681364212yes—
363C22C22×C22⋊D11311yescharacteristic
364C4—21no—
365C4—21no—
366C4—21no—
367C4—21no—
368C4—41no—
369C4—41no—
370C4—4521no—
371C4—4521no—
372C4—4521no—
373C4C2×#1426864611yescharacteristic
374C4#1681366711yescharacteristic
375C2—22no—
376C2—41no—
377C2—42no—
378C2—81no—
379C2—9041no—
380C2#2029924211yescharacteristic
381C2C2×#1681364211yescharacteristic
382C2#2029940111yescharacteristic
subgroupG/H
centerC22C22×C22⋊D113
commutator, cosocleC2×C4×C113C24
FrattiniC2×C4C23×D113
Fitting#546×C113C2
socleC22×C113C22×D4
hypercenter#546D113
hypocenterC113#3297
LCSG ▷ C2×C4×C113 ▷ C2×C113 ▷ C113
UCSC1 ◁ C22 ◁ C4×D4 ◁ #546

Complements

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

NH ≅ G/Ntype
1. #20299294C2semidirect
2. #20298952C2semidirect
3. #20298931C2semidirect
4. #20298919C2semidirect
5. #20298898C2semidirect
6. #20298832C2semidirect
7. #20298829C2semidirect
8. #20298810C2semidirect
9. #20298743C2semidirect
10. #20298732C2semidirect
11. C4×#14268632C2semidirect
12. D4×#11744751C2semidirect
13. #20298594C2semidirect
14. C2×#16813543C2semidirect
15. #546×C113C2semidirect
16. C2×#14268634C22semidirect
20. C22×#11744751C22semidirect
22. #16813614C22semidirect
25. #16813596C22semidirect
27. C4×D452C22semidirect
29. #16813581C22semidirect
31. #16813555C22semidirect
32. #16813555C22semidirect
33. #16813553C22semidirect
34. C4⋊#11744751C22semidirect
35. #16813546C22semidirect
36. #16813546C22semidirect
37. #16813546C22semidirect
44. #16813542C22semidirect
46. C22⋊#11744751C22semidirect
47. C4×#11744751C22semidirect
192. C113#3297semidirect
194. #546D113semidirect

Maximal subgroups

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

subgroupindex
#202992942
#202989522
#202989312
#202989192
#202988982
#202988322
#202988292
#202988102
#202987432
#202987322
C4×#142686322
D4×#117447512
#202985942
C2×#168135432
#546×C1132
#3297113