Finite Group Databasebeta

← #28402535

Subgroups — #28402535

Order 14464.

442 conjugacy classes of subgroups.

The subgroup lattice has 390 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20299252C211yesmaximal, characteristic, complemented
2#20298957C211yesmaximal, characteristic, complemented
3#20298926C211yesmaximal, characteristic, complemented
4#20298914C211yesmaximal, characteristic, complemented
5#20298888C211yesmaximal, characteristic, complemented
6#20298849C211yesmaximal, characteristic, complemented
7#20298829C211yesmaximal, characteristic, complemented
8#20298810C211yesmaximal, characteristic, complemented
9#20298743C211yesmaximal, characteristic, complemented
10#20298732C211yesmaximal, characteristic, complemented
11#20298708C211yesmaximal, characteristic, complemented
12#20298670C211yesmaximal, characteristic, complemented
13#20298599C211yesmaximal, characteristic, complemented
14C2×#16813543C211yesmaximal, characteristic, complemented
15#546×C113C211yesmaximal, characteristic, complemented
16C2×#14268646—21no—
17C2×#14268634C2211yescharacteristic, complemented
18C2×#14268632C2211yescharacteristic
19C2×#14268632C2211yescharacteristic
20C2×#14268631C2211yescharacteristic, complemented
21C22×#11744751C2211yescharacteristic
22#16813622C2211yescharacteristic, complemented
23#16813606—21no—
24#16813606—21no—
25#16813602—21no—
26#16813596C2211yescharacteristic
27#16813596C2211yescharacteristic, complemented
28C4×D452C2211yescharacteristic, complemented
29C2×C4⋊Dic113C2211yescharacteristic
30C2×C4⋊Dic113C2211yescharacteristic, complemented
31#16813553C2211yescharacteristic, complemented
32#16813553C2211yescharacteristic, 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
47#16813533C2211yescharacteristic, 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—
59#14268646—44no—
60C2×Dic226—21no—
61C2×D452C2311yescharacteristic
62C2×C22⋊D113—21no—
63C2×C22⋊D113—21no—
64C22×Dic113—21no—
65C22×Dic113—21no—
66C2×C4×D113—21no—
67#14268634—41no—
68#14268632—22no—
69#14268632—41no—
70#14268631—41no—
71C2×#11744751—41no—
72C2×#11744751C2311yescharacteristic
73C2×#11744751C2311yescharacteristic
74C2×#11744751C2311yescharacteristic
75C2×#11744751C2311yescharacteristic
76C4⋊Dic113—21no—
77C4⋊Dic113—21no—
78C4⋊Dic113—21no—
79C4⋊Dic113C2311yescharacteristic
80C4⋊Dic113C2311yescharacteristic
81C4⋊Dic113C2311yescharacteristic
82#14268624—21no—
83#14268624—21no—
84#14268624—21no—
85C24×C113—21no—
86#41×C113—22no—
87#41×C113—41no—
88C2×Q8×C113C2311yescharacteristic
89C2×D4×C113—22no—
90C2×D4×C113—21no—
91C2×D4×C113—21no—
92C2×D4×C113—21no—
93C2×D4×C113—41no—
94C2×D4×C113D411yescharacteristic
95C2×D4×C113C2311yescharacteristic
96C2×D4×C113C2311yescharacteristic
97C22×C4×C113—21no—
98C22×C4×C113—21no—
99C22×C4×C113C2311yescharacteristic
100C22×C4×C113C2311yescharacteristic
101C4⋊C4×C113—21no—
102C4⋊C4×C113D411yescharacteristic
103C4⋊C4×C113C2311yescharacteristic
104C22⋊C4×C113—21no—
105C22⋊C4×C113—21no—
106C22⋊C4×C113—21no—
107C22⋊C4×C113—21no—
108C22⋊C4×C113—21no—
109C22⋊C4×C113D411yescharacteristic
110C22⋊C4×C113D411yescharacteristic
111C42×C113C2311yescharacteristic
112C23×C113—21no—
113C23×C113—21no—
114C23×C113—42no—
115C23×C113—42no—
116C23×C113—81no—
117C23×C113C2×D411yescharacteristic
118C23×C113C2×D411yescharacteristic
119C22×D113—21no—
120Q8×C113—21no—
121Q8×C113—21no—
122D4×C113—22no—
123D4×C113—21no—
124D4×C113—21no—
125D4×C113—21no—
126D4×C113—42no—
127D4×C113—42no—
128D4×C113—81no—
129D4×C113#4112yescomplemented
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—42no—
137C2×C4×C113—81no—
138C2×C4×C113C2×D411yescharacteristic
139C2×C4×C113C2×D411yescharacteristic
140C2×C4×C113C2×D411yescharacteristic
141C2×C4×C113C2×D411yescharacteristic
142C2×C4×C113C2411yescharacteristic
143C22⋊D113—42no—
144C22⋊D113—42no—
145C2×Dic113—21no—
146C2×Dic113—21no—
147C2×Dic113—21no—
148C2×Dic113—42no—
149C2×Dic113—42no—
150D452—21no—
151D452—21no—
152C4×D113—42no—
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—22no—
162C22×C113—21no—
163C22×C113—21no—
164C22×C113—41no—
165C22×C113—41no—
166C22×C113—41no—
167C22×C113—41no—
168C22×C113—41no—
169C22×C113—84no—
170C22×C113AGL(1,ℤ/8)12yes—
171C22×C113C22×D411yescharacteristic
172C2×D113—41no—
173C2×D113—41no—
174C2×D113—41no—
175C4×C113—21no—
176C4×C113—21no—
177C4×C113—21no—
178C4×C113—21no—
179C4×C113—41no—
180C4×C113—41no—
181C4×C113C2×#4111yescharacteristic
182C4×C113H(5,𝔽2)11yescharacteristic
183Dic113—41no—
184Dic113—41no—
185Dic113—41no—
186C2×C113—22no—
187C2×C113—41no—
188C2×C113—42no—
189C2×C113—81no—
190C2×C113#54611yescharacteristic
191C2×C113C2×AGL(1,ℤ/8)11yescharacteristic
192C2×C113#57711yescharacteristic
193D113—81no—
194#3306—1131nomaximal, Sylow
195C113#330611yescharacteristic, complemented, Sylow
196#547—1131no—
197#546D11311yescharacteristic, complemented
198#489—1131no—
199#483—1131no—
200#481—1131no—
201#476—1131no—
202#469—1131no—
203#465—1131no—
204#463—1131no—
205#449—1131no—
206#447—1131no—
207#442—1131no—
208#435—1131no—
209#417—1131no—
210C2×#102—1131no—
211C2×#41—2261no—
212C2×#41C2×D11311yescharacteristic
213C22×D4C2×D11311yescharacteristic
214C2×SD16—1131no—
215C2×D8—1131no—
216C2×D8—1131no—
217C2×M16—1131no—
218C22×C8—1131no—
219C4⋊Q8—1131no—
220#124C2×D11311yescharacteristic
221#123—21no—
222#123—2261no—
223#123—2261no—
224C22⋊Q8—2261no—
225C22⋊Q8C2×D11311yescharacteristic
226#121—21no—
227#121—1131no—
228#121—1131no—
229#121C2×D11311yescharacteristic
230#120—21no—
231C4×D4—1131no—
232C4×D4C2×D11311yescharacteristic
233C4×D4C2×D11311yescharacteristic
234C2×C4⋊C4—1131no—
235C2×C4⋊C4—1131no—
236C2×C22⋊C4—21no—
237#106—1131no—
238#106—1131no—
239#106—1131no—
240C4⋊C8—1131no—
241#103—1131no—
242#103—1131no—
243#103—1131no—
244#102—1131no—
245#102—1131no—
246#102—1131no—
247#102—1131no—
248#102—1131no—
249#102—1131no—
250#102—1131no—
251C22⋊C8—1131no—
252C22⋊C8—1131no—
253#97—1131no—
254C24—21no—
255#41—22no—
256#41—41no—
257#41—4524no—
258C2×Q8—2261no—
259C2×Q8C22×D11311yescharacteristic
260C2×D4—22no—
261C2×D4—21no—
262C2×D4—21no—
263C2×D4—21no—
264C2×D4—41no—
265C2×D4—1131no—
266C2×D4—2261no—
267C2×D4—2261no—
268C2×D4C22⋊D11311yescharacteristic
269C2×D4C22×D11311yescharacteristic
270C2×D4C22×D11311yescharacteristic
271C22×C4—21no—
272C22×C4—21no—
273C22×C4—2261no—
274C22×C4—2261no—
275C22×C4—2261no—
276C22×C4C22×D11311yescharacteristic
277C22×C4C22×D11311yescharacteristic
278SD16—4521no—
279D8—4521no—
280D8—2262no—
281M16—4521no—
282C2×C8—1131no—
283C2×C8—1131no—
284C2×C8—1131no—
285C2×C8—1131no—
286C2×C8—4521no—
287C4⋊C4—21no—
288C4⋊C4—1131no—
289C4⋊C4—1131no—
290C4⋊C4—1131no—
291C4⋊C4—2261no—
292C4⋊C4—2261no—
293C4⋊C4—2261no—
294C4⋊C4C22⋊D11311yescharacteristic
295C4⋊C4C22×D11311yescharacteristic
296C22⋊C4—21no—
297C22⋊C4—21no—
298C22⋊C4—21no—
299C22⋊C4—21no—
300C22⋊C4—21no—
301C22⋊C4—2261no—
302C22⋊C4—2261no—
303C22⋊C4—2261no—
304C22⋊C4C22⋊D11311yescharacteristic
305C22⋊C4C22⋊D11311yescharacteristic
306C42C22×D11311yescharacteristic
307C23—21no—
308C23—21no—
309C23—42no—
310C23—42no—
311C23—81no—
312C23—2261no—
313C23C2×C22⋊D11311yescharacteristic
314C23C2×C22⋊D11311yescharacteristic
315Q8—21no—
316Q8—21no—
317Q8—4522no—
318D4—22no—
319D4—21no—
320D4—21no—
321D4—21no—
322D4—42no—
323D4—42no—
324D4—81no—
325D4—4522no—
326D4—4522no—
327D4—2261no—
328D4—2261no—
329D4#1426864612yescomplemented
330C2×C4—21no—
331C2×C4—21no—
332C2×C4—21no—
333C2×C4—21no—
334C2×C4—21no—
335C2×C4—21no—
336C2×C4—42no—
337C2×C4—81no—
338C2×C4—4522no—
339C2×C4—4522no—
340C2×C4—4522no—
341C2×C4—2261no—
342C2×C4—2261no—
343C2×C4—2261no—
344C2×C4C2×C22⋊D11311yescharacteristic
345C2×C4C2×C22⋊D11311yescharacteristic
346C2×C4C2×C22⋊D11311yescharacteristic
347C2×C4C2×C22⋊D11311yescharacteristic
348C2×C4C23×D11311yescharacteristic
349C8—2261no—
350C8—2261no—
351C8—2261no—
352C8—2261no—
353C22—21no—
354C22—21no—
355C22—21no—
356C22—21no—
357C22—21no—
358C22—22no—
359C22—41no—
360C22—41no—
361C22—41no—
362C22—41no—
363C22—41no—
364C22—84no—
365C22—4521no—
366C22—4521no—
367C22—4521no—
368C22#1681364712yes—
369C22C22×C22⋊D11311yescharacteristic
370C4—21no—
371C4—21no—
372C4—21no—
373C4—21no—
374C4—41no—
375C4—41no—
376C4—4521no—
377C4—4521no—
378C4—4521no—
379C4C2×#1426864611yescharacteristic
380C4#1681366711yescharacteristic
381C2—22no—
382C2—41no—
383C2—42no—
384C2—81no—
385C2—9041no—
386C2#2029924211yescharacteristic
387C2C2×#1681364711yescharacteristic
388C2#2029940911yescharacteristic
subgroupG/H
centerC22C22×C22⋊D113
commutator, cosocleC2×C4×C113C24
FrattiniC2×C4C23×D113
Fitting#546×C113C2
socleC22×C113C22×D4
hypercenter#546D113
hypocenterC113#3306
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. #20299252C2semidirect
2. #20298957C2semidirect
3. #20298926C2semidirect
4. #20298914C2semidirect
5. #20298888C2semidirect
6. #20298849C2semidirect
7. #20298829C2semidirect
8. #20298810C2semidirect
9. #20298743C2semidirect
10. #20298732C2semidirect
11. #20298708C2semidirect
12. #20298670C2semidirect
13. #20298599C2semidirect
14. C2×#16813543C2semidirect
15. #546×C113C2semidirect
17. C2×#14268634C22semidirect
20. C2×#14268631C22semidirect
22. #16813622C22semidirect
27. #16813596C22semidirect
28. C4×D452C22semidirect
30. C2×C4⋊Dic113C22semidirect
31. #16813553C22semidirect
32. #16813553C22semidirect
33. #16813553C22semidirect
34. C4⋊#11744751C22semidirect
35. #16813546C22semidirect
36. #16813546C22semidirect
37. #16813546C22semidirect
44. #16813542C22semidirect
46. C22⋊#11744751C22semidirect
47. #16813533C22semidirect
129. D4×C113#41semidirect
195. C113#3306semidirect
197. #546D113semidirect
329. D4#14268646semidirect

Maximal subgroups

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

subgroupindex
#202992522
#202989572
#202989262
#202989142
#202988882
#202988492
#202988292
#202988102
#202987432
#202987322
#202987082
#202986702
#202985992
C2×#168135432
#546×C1132
#3306113