Finite Group Databasebeta

← #28402897

Subgroups — #28402897

Order 14464.

430 conjugacy classes of subgroups.

The subgroup lattice has 388 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20299267C211yesmaximal, characteristic, complemented
2#20299249C211yesmaximal, characteristic, complemented
3#20298943C211yesmaximal, characteristic, complemented
4#20298916C211yesmaximal, characteristic, complemented
5#20298915C211yesmaximal, characteristic, complemented
6#20298881C211yesmaximal, characteristic, complemented
7#20298851C211yesmaximal, characteristic, complemented
8#20298850C211yesmaximal, characteristic, complemented
9#20298792C211yesmaximal, characteristic, complemented
10#20298746C211yesmaximal, characteristic, complemented
11#20298743C211yesmaximal, characteristic, complemented
12#20298683C211yesmaximal, characteristic, complemented
13#20298674C211yesmaximal, characteristic, complemented
14#20298598C211yesmaximal, characteristic, complemented
15#417×C113C211yesmaximal, characteristic, complemented
16C2×#14268648C2211yescharacteristic
17C2×#14268647—21no—
18C2×#14268634C2211yescharacteristic
19C2×D904C2211yescharacteristic
20C2×#14268632C2211yescharacteristic
21C2×#14268630C2211yescharacteristic
22#16813621C2211yescharacteristic
23#16813618—21no—
24#16813618C2211yescharacteristic
25#16813607—21no—
26#16813605—21no—
27#16813600—21no—
28#16813597C2211yescharacteristic
29#16813596—21no—
30#16813596C2211yescharacteristic
31#16813596C2211yescharacteristic
32#16813593—21no—
33#16813593C2211yescharacteristic
34Q8×Dic113C2211yescharacteristic
35#16813584C2211yescharacteristic
36C4×C22⋊D113—21no—
37C4×C22⋊D113C2211yescharacteristic
38C4⋊C4×D113C2211yescharacteristic
39#16813554C2211yescharacteristic
40#16813553C2211yescharacteristic
41#16813553C2211yescharacteristic
42#16813551C2211yescharacteristic
43#16813546C2211yescharacteristic
44#16813544C2211yescharacteristic
45#16813544C2211yescharacteristic
46#16813543C2211yescharacteristic
47#16813542C2211yescharacteristic
48#16813542C2211yescharacteristic
49C22⋊#11744751C2211yescharacteristic
50#16813534C2211yescharacteristic
51C8×Dic113C2211yescharacteristic
52C2×#41×C113C2211yescharacteristic
53C2×M16×C113C2211yescharacteristic
54C2×C4⋊C4×C113C2211yescharacteristic
55#103×C113C2211yescharacteristic
56#103×C113C2211yescharacteristic
57#102×C113C2211yescharacteristic
58#102×C113C2211yescharacteristic
59#14268648—22no—
60#14268648—41no—
61#14268647—44no—
62C2×Dic226—21no—
63C2×D452—21no—
64C2×D452—21no—
65C2×D452C2311yescharacteristic
66C2×D452C2311yescharacteristic
67C2×C22⋊D113—21no—
68C2×C22⋊D113—21no—
69C2×C22⋊D113—21no—
70C2×C22⋊D113—21no—
71C2×C22⋊D113—21no—
72C2×C22⋊D113D411yescharacteristic
73C2×C4×D113—21no—
74C2×C4×D113—21no—
75C2×C4×D113—21no—
76C2×C4×D113C2311yescharacteristic
77#14268634—22no—
78D904—41no—
79#14268632—41no—
80#14268630—41no—
81C2×#11744751C2311yescharacteristic
82C2×#11744751C2311yescharacteristic
83C4⋊Dic113—21no—
84C4⋊Dic113C2311yescharacteristic
85C4⋊Dic113C2311yescharacteristic
86#14268626—21no—
87#14268626—21no—
88#14268626D411yescharacteristic
89C22⋊Dic113—21no—
90C22⋊Dic113D411yescharacteristic
91#14268624—21no—
92#14268624—21no—
93#14268624—21no—
94#14268624—21no—
95#14268624D411yescharacteristic
96C4×Dic113—21no—
97C4×Dic113C2311yescharacteristic
98#41×C113—22no—
99#41×C113—41no—
100C2×Q8×C113C2311yescharacteristic
101C2×D4×C113—21no—
102C2×D4×C113C2311yescharacteristic
103C22×C4×C113—21no—
104C22×C4×C113—21no—
105C22×C4×C113C2311yescharacteristic
106M16×C113—41no—
107C2×C8×C113C2311yescharacteristic
108C2×C8×C113C2311yescharacteristic
109C4⋊C4×C113—21no—
110C4⋊C4×C113C2311yescharacteristic
111C4⋊C4×C113C2311yescharacteristic
112C23×C113—21no—
113C23×C113C2×D411yescharacteristic
114C22×D113—21no—
115C22×D113—21no—
116C22×D113C2×D411yescharacteristic
117Q8×C113—21no—
118Q8×C113#4112yescomplemented
119D4×C113—21no—
120D4×C113—21no—
121D4×C113—42no—
122C2×C4×C113—21no—
123C2×C4×C113—21no—
124C2×C4×C113—21no—
125C2×C4×C113—21no—
126C2×C4×C113—21no—
127C2×C4×C113—42no—
128C2×C4×C113—42no—
129C2×C4×C113C2×D411yescharacteristic
130C2×C4×C113C2411yescharacteristic
131C22⋊D113—22no—
132C22⋊D113—42no—
133C22⋊D113—42no—
134C22⋊D113—81no—
135C22⋊D113—81no—
136C22⋊D113—81no—
137C2×Dic113—21no—
138C2×Dic113—21no—
139C2×Dic113C2×D411yescharacteristic
140C2×Dic113C2×D411yescharacteristic
141C2×Dic113C2×D411yescharacteristic
142D452—21no—
143D452—21no—
144D452—21no—
145D452—21no—
146D452—42no—
147D452—42no—
148C4×D113—21no—
149C4×D113—21no—
150C4×D113—42no—
151C4×D113—42no—
152C4×D113—42no—
153Dic226—42no—
154C8×C113—21no—
155C8×C113—21no—
156#11744751—21no—
157#11744751—21no—
158C22×C113—21no—
159C22×C113—21no—
160C22×C113—21no—
161C22×C113—41no—
162C22×C113—41no—
163C22×C113—41no—
164C22×C113C22×D411yescharacteristic
165C2×D113—21no—
166C2×D113—21no—
167C2×D113—21no—
168C2×D113—41no—
169C2×D113—41no—
170C2×D113—41no—
171C2×D113—41no—
172C2×D113—41no—
173C2×D113—41no—
174C4×C113—22no—
175C4×C113—21no—
176C4×C113—41no—
177C4×C113—41no—
178C4×C113C2×#4111yescharacteristic
179C4×C113H(5,𝔽2)11yescharacteristic
180Dic113—21no—
181Dic113—21no—
182Dic113—41no—
183Dic113—41no—
184Dic113AGL(1,ℤ/8)12yes—
185C2×C113—41no—
186C2×C113—81no—
187C2×C113#54611yescharacteristic
188C2×C113C2×AGL(1,ℤ/8)11yescharacteristic
189C2×C113#57711yescharacteristic
190D113—41no—
191D113—81no—
192D113—81no—
193#3332—1131nomaximal, Sylow
194C113#333211yescharacteristic, complemented, Sylow
195#550—1131no—
196#547—1131no—
197#486—1131no—
198#481—1131no—
199#481—1131no—
200#475—1131no—
201#469—1131no—
202#469—1131no—
203#459—1131no—
204#449—1131no—
205#449—1131no—
206C4×SD16—1131no—
207#436—1131no—
208#417—1131no—
209#417D11311yescharacteristic, complemented
210C2×#41—1131no—
211C2×#41—2261no—
212C2×#41C2×D11311yescharacteristic
213C2×SD16—1131no—
214C2×D8—1131no—
215C2×D8—1131no—
216C2×M16—1131no—
217C2×M16C2×D11311yescharacteristic
218C4⋊Q8—1131no—
219#127—1131no—
220#127—2261no—
221#123—2261no—
222#123—2261no—
223C22⋊Q8—2261no—
224#121—1131no—
225#121—1131no—
226#121—1131no—
227#121—1131no—
228#121—2261no—
229#121—2261no—
230C4×Q8—1131no—
231C4×D4—1131no—
232C4×D4—1131no—
233C4×D4—2261no—
234C2×C4⋊C4—1131no—
235C2×C4⋊C4C2×D11311yescharacteristic
236#106—1131no—
237#106—1131no—
238#106—1131no—
239C4⋊C8—1131no—
240#103—1131no—
241#103C2×D11311yescharacteristic
242#103C2×D11311yescharacteristic
243#102—1131no—
244#102—1131no—
245#102—1131no—
246#102—1131no—
247#102—1131no—
248#102C2×D11311yescharacteristic
249#102C2×D11311yescharacteristic
250C22⋊C8—1131no—
251C22⋊C8—1131no—
252C4×C8—1131no—
253#41—22no—
254#41—41no—
255#41—4524no—
256#41—4521no—
257#41—2262no—
258C2×Q8—2261no—
259C2×Q8C22×D11311yescharacteristic
260C2×D4—21no—
261C2×D4—1131no—
262C2×D4—1131no—
263C2×D4—1131no—
264C2×D4—2261no—
265C2×D4—2261no—
266C2×D4—2261no—
267C2×D4—2261no—
268C2×D4—2261no—
269C2×D4—2261no—
270C2×D4—2261no—
271C2×D4C22×D11311yescharacteristic
272C22×C4—21no—
273C22×C4—21no—
274C22×C4—1131no—
275C22×C4—2261no—
276C22×C4—2261no—
277C22×C4—2261no—
278C22×C4C22×D11311yescharacteristic
279SD16—2262no—
280D8—4521no—
281D8—4521no—
282M16—41no—
283M16—4521no—
284C2×C8—1131no—
285C2×C8—1131no—
286C2×C8C22×D11311yescharacteristic
287C2×C8C22×D11311yescharacteristic
288C4⋊C4—21no—
289C4⋊C4—1131no—
290C4⋊C4—1131no—
291C4⋊C4—1131no—
292C4⋊C4—2261no—
293C4⋊C4—2261no—
294C4⋊C4—2261no—
295C4⋊C4C22×D11311yescharacteristic
296C4⋊C4C22×D11311yescharacteristic
297C22⋊C4—1131no—
298C22⋊C4—1131no—
299C22⋊C4—2261no—
300C22⋊C4—2261no—
301C22⋊C4—2261no—
302C22⋊C4—2261no—
303C22⋊C4—2261no—
304C42—1131no—
305C42—2261no—
306C23—21no—
307C23—1131no—
308C23—2261no—
309C23—2261no—
310C23D4×D11311yescharacteristic
311Q8—21no—
312Q8—4522no—
313Q8#1426864712yescomplemented
314D4—21no—
315D4—21no—
316D4—42no—
317D4—9041no—
318D4—9041no—
319D4—9041no—
320D4—4522no—
321D4—4522no—
322D4—4522no—
323D4—4522no—
324D4—2262no—
325D4—2261no—
326D4—2261no—
327D4—2261no—
328D4—2261no—
329C2×C4—21no—
330C2×C4—21no—
331C2×C4—21no—
332C2×C4—21no—
333C2×C4—21no—
334C2×C4—42no—
335C2×C4—42no—
336C2×C4—1131no—
337C2×C4—1131no—
338C2×C4—1131no—
339C2×C4—4522no—
340C2×C4—4522no—
341C2×C4—4522no—
342C2×C4—2261no—
343C2×C4—2261no—
344C2×C4—2261no—
345C2×C4—2261no—
346C2×C4D4×D11311yescharacteristic
347C2×C4C23×D11311yescharacteristic
348C8—21no—
349C8—21no—
350C8—2261no—
351C8—2261no—
352C22—21no—
353C22—21no—
354C22—21no—
355C22—41no—
356C22—41no—
357C22—41no—
358C22—4521no—
359C22—4521no—
360C22—4521no—
361C22—4521no—
362C22—4521no—
363C22—4521no—
364C22—2261no—
365C22—2261no—
366C22—2261no—
367C22C2×D4×D11311yescharacteristic
368C4—21no—
369C4—22no—
370C4—41no—
371C4—41no—
372C4—1132no—
373C4—4521no—
374C4—4521no—
375C4—2261no—
376C4—2261no—
377C4C2×#1426864711yescharacteristic
378C4#1681366711yescharacteristic
379C2—41no—
380C2—81no—
381C2—9041no—
382C2—9041no—
383C2—4521no—
384C2#2029923811yescharacteristic
385C2AGL(1,ℤ/8)×D11311yescharacteristic
386C2#2029940711yescharacteristic
subgroupG/H
centerC22C2×D4×D113
commutator, cosocleC2×C4×C113C24
FrattiniC2×C4C23×D113
Fitting#417×C113C2
socleC22×C113C22×D4
hypercenter#417D113
hypocenterC113#3332
LCSG ▷ C2×C4×C113 ▷ C2×C113 ▷ C113
UCSC1 ◁ C22 ◁ C22×C4 ◁ #417

Complements

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

NH ≅ G/Ntype
1. #20299267C2semidirect
2. #20299249C2semidirect
3. #20298943C2semidirect
4. #20298916C2semidirect
5. #20298915C2semidirect
6. #20298881C2semidirect
7. #20298851C2semidirect
8. #20298850C2semidirect
9. #20298792C2semidirect
10. #20298746C2semidirect
11. #20298743C2semidirect
12. #20298683C2semidirect
13. #20298674C2semidirect
14. #20298598C2semidirect
15. #417×C113C2semidirect
118. Q8×C113#41semidirect
194. C113#3332semidirect
209. #417D113semidirect
313. Q8#14268647semidirect

Maximal subgroups

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

subgroupindex
#202992672
#202992492
#202989432
#202989162
#202989152
#202988812
#202988512
#202988502
#202987922
#202987462
#202987432
#202986832
#202986742
#202985982
#417×C1132
#3332113