Finite Group Databasebeta

← #28400044

Subgroups — #28400044

Order 14464.

484 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
1C2×#16813654C211yesmaximal, characteristic, complemented
2C2×#16813651C211yesmaximal, characteristic, complemented
3#20299147C211yesmaximal, characteristic
4C4×Q8×D113C211yesmaximal, characteristic, complemented
5#20298821C211yesmaximal, characteristic, complemented
6#20298820C211yesmaximal, characteristic, complemented
7#20298817C211yesmaximal, characteristic, complemented
8#20298807C211yesmaximal, characteristic, complemented
9#20298806C211yesmaximal, characteristic, complemented
10#20298797C211yesmaximal, characteristic, complemented
11#20298796C211yesmaximal, characteristic, complemented
12#20298620C211yesmaximal, characteristic, complemented
13#20298598C211yesmaximal, characteristic, complemented
14#20298596C211yesmaximal, characteristic, complemented
15#464×C113C211yesmaximal, characteristic, complemented
16C2×#14268648C2211yescharacteristic
17C2×#14268646C2211yescharacteristic
18C2×Q8×D113C2211yescharacteristic
19#16813654—24no—
20#16813651—24no—
21C2×Dic452C2211yescharacteristic
22C2×#14268637C2211yescharacteristic
23C2×#14268637C2211yescharacteristic
24C2×#14268636C2211yescharacteristic
25C2×#14268635C2211yescharacteristic
26C2×#14268634C2211yescharacteristic
27C2×#14268630C2211yescharacteristic
28C2×#14268630C2211yescharacteristic
29#16813620C2211yescharacteristic
30#16813618C2211yescharacteristic
31#16813610C2211yescharacteristic
32#16813595—21no—
33#16813595—21no—
34Q8×Dic113C2211yescharacteristic
35C4×Dic226—21no—
36C4×Dic226C2211yescharacteristic
37#16813587—21no—
38#16813587C2211yescharacteristic
39#16813582—21no—
40#16813582—21no—
41C4⋊C4×D113—21no—
42C4⋊C4×D113C2211yescharacteristic
43C42×D113—21no—
44C42×D113C2211yescharacteristic
45C4⋊#11744751C2211yescharacteristic
46#16813551C2211yescharacteristic
47#16813551C2211yescharacteristic
48#16813547C2211yescharacteristic
49#16813546C2211yescharacteristic
50#16813545C2211yescharacteristic
51#16813544C2211yescharacteristic
52#16813543C2211yescharacteristic
53#16813542C2211yescharacteristic
54C2×Q16×C113C2211yescharacteristic
55C2×SD16×C113C2211yescharacteristic
56#124×C113C2211yescharacteristic
57C4×Q8×C113C2211yescharacteristic
58C4⋊C8×C113C2211yescharacteristic
59#103×C113C2211yescharacteristic
60#102×C113C2211yescharacteristic
61#14268648—22no—
62#14268648—22no—
63#14268646—22no—
64#14268646—22no—
65C2×Dic226—21no—
66C2×Dic226C2311yescharacteristic
67C2×Dic226C2311yescharacteristic
68Q8×D113—22no—
69Q8×D113D414yescomplemented
70C2×D452—21no—
71C2×D452C2311yescharacteristic
72C2×C22⋊D113—21no—
73C2×C22⋊D113—21no—
74C2×C22⋊D113—21no—
75C22×Dic113—21no—
76C2×C4×D113—21no—
77C2×C4×D113—21no—
78C2×C4×D113—21no—
79C2×C4×D113D411yescharacteristic
80C2×C4×D113D411yescharacteristic
81C2×C4×D113C2311yescharacteristic
82Dic452—22no—
83#14268637—22no—
84#14268637—22no—
85#14268636—22no—
86#14268635—22no—
87#14268634—22no—
88#14268630—22no—
89#14268630—22no—
90C2×#11744751C2311yescharacteristic
91C2×#11744751C2311yescharacteristic
92C4⋊Dic113—21no—
93C4⋊Dic113C2311yescharacteristic
94#14268626—21no—
95#14268626—21no—
96#14268626—21no—
97#14268626—21no—
98#14268626—21no—
99#14268624—21no—
100#14268624—21no—
101C4×Dic113—21no—
102C4×Dic113—21no—
103C4×Dic113—21no—
104C4×Dic113D411yescharacteristic
105C4×Dic113D411yescharacteristic
106C4×Dic113C2311yescharacteristic
107C2×Q8×C113C2311yescharacteristic
108C2×Q8×C113C2311yescharacteristic
109C2×D4×C113C2311yescharacteristic
110Q16×C113—22no—
111SD16×C113—22no—
112C2×C8×C113C2311yescharacteristic
113C2×C8×C113C2311yescharacteristic
114C4⋊C4×C113—21no—
115C4⋊C4×C113C2311yescharacteristic
116C22⋊C4×C113—21no—
117C22⋊C4×C113—21no—
118C42×C113—21no—
119C42×C113C2311yescharacteristic
120C23×C113—21no—
121C22×D113—21no—
122C22×D113C2×D411yescharacteristic
123Q8×C113—21no—
124Q8×C113—21no—
125Q8×C113—21no—
126Q8×C113C2×D412yes—
127D4×C113—21no—
128D4×C113—21no—
129C2×C4×C113—21no—
130C2×C4×C113—21no—
131C2×C4×C113—21no—
132C2×C4×C113C2×D411yescharacteristic
133C2×C4×C113C2×D411yescharacteristic
134C2×C4×C113C2411yescharacteristic
135C22⋊D113—42no—
136C22⋊D113—42no—
137C22⋊D113—42no—
138C2×Dic113—21no—
139C2×Dic113—21no—
140C2×Dic113—21no—
141C2×Dic113—42no—
142C2×Dic113C2×D411yescharacteristic
143C2×Dic113C2×D411yescharacteristic
144C2×Dic113C2×D411yescharacteristic
145D452—21no—
146D452—21no—
147D452—42no—
148C4×D113—24no—
149C4×D113—22no—
150C4×D113—41no—
151C4×D113—42no—
152C4×D113—42no—
153C4×D113C2×D412yes—
154C4×D113#4112yes—
155Dic226—21no—
156Dic226—24no—
157Dic226—21no—
158Dic226—21no—
159Dic226C2×D412yes—
160C8×C113—21no—
161C8×C113—21no—
162#11744751—21no—
163#11744751—21no—
164C22×C113—41no—
165C22×C113—41no—
166C22×C113—41no—
167C22×C113C22×D411yescharacteristic
168C2×D113—21no—
169C2×D113—21no—
170C2×D113—41no—
171C2×D113—41no—
172C2×D113—41no—
173C2×D113#12112yes—
174C4×C113—22no—
175C4×C113—21no—
176C4×C113—21no—
177C4×C113—41no—
178C4×C113—41no—
179C4×C113C22×D411yescharacteristic
180C4×C113C2×#4111yescharacteristic
181Dic113—22no—
182Dic113—21no—
183Dic113—41no—
184Dic113—41no—
185Dic113#12112yes—
186Dic113#13712yescomplemented
187C2×C113—81no—
188C2×C113C2×#12111yescharacteristic
189C2×C113C2×#13711yescharacteristic
190C2×C113#57511yescharacteristic
191D113—22no—
192D113—81no—
193#3037—1131nomaximal, Sylow
194C113#303711yescharacteristic, complemented, Sylow
195C2×#137—1131no—
196C2×#137—1131no—
197#532—1131no—
198C2×C4×Q8—1131no—
199#464—1131no—
200#464—1131no—
201#464—1131no—
202#464D11311yescharacteristic, complemented
203#462—1131no—
204#462—1131no—
205#460—1131no—
206#460—1131no—
207#423—1131no—
208#417—1131no—
209#417—1131no—
210C2×#41—1131no—
211C2×#41—1131no—
212C22×Q8—1131no—
213#137—2264no—
214#137—2264no—
215C2×Q16—1131no—
216C2×Q16—1131no—
217C2×Q16—1131no—
218C2×Q16C2×D11311yescharacteristic
219C2×SD16—1131no—
220C2×SD16—1131no—
221C2×SD16—1131no—
222C2×SD16C2×D11311yescharacteristic
223C2×M16—1131no—
224C2×M16—1131no—
225C4⋊Q8—1131no—
226#127—1131no—
227#124—1131no—
228#124C2×D11311yescharacteristic
229#121—2261no—
230#121—2261no—
231C4×Q8—1131no—
232C4×Q8—1131no—
233C4×Q8—1131no—
234C4×Q8—2261no—
235C4×Q8—2261no—
236C4×Q8C2×D11311yescharacteristic
237C4×D4—2261no—
238C4×D4—2261no—
239C2×C4⋊C4—1131no—
240C2×C4⋊C4—2261no—
241C2×C42—1131no—
242C2×C42—2261no—
243C4⋊C8—1131no—
244C4⋊C8—1131no—
245C4⋊C8—1131no—
246C4⋊C8C2×D11311yescharacteristic
247#103—1131no—
248#103—1131no—
249#103—1131no—
250#103C2×D11311yescharacteristic
251#102—1131no—
252#102—1131no—
253#102—1131no—
254#102C2×D11311yescharacteristic
255#41—2262no—
256#41—2262no—
257#41—2262no—
258#41—2262no—
259C2×Q8—1134no—
260C2×Q8—1131no—
261C2×Q8—1131no—
262C2×Q8—2261no—
263C2×Q8—2262no—
264C2×Q8C22×D11311yescharacteristic
265C2×Q8C22×D11311yescharacteristic
266C2×D4—1131no—
267C2×D4—2261no—
268C2×D4—2261no—
269C2×D4—2261no—
270C2×D4—2261no—
271C2×D4C22×D11311yescharacteristic
272C22×C4—1131no—
273C22×C4—1131no—
274C22×C4—1131no—
275C22×C4—2261no—
276C22×C4—2261no—
277C22×C4—2261no—
278C22×C4—2261no—
279Q16—22no—
280Q16—2262no—
281Q16—2262no—
282Q16—2262no—
283SD16—22no—
284SD16—2262no—
285SD16—2262no—
286SD16—2262no—
287M16—2262no—
288M16—2262no—
289C2×C8—1131no—
290C2×C8—1131no—
291C2×C8C22×D11311yescharacteristic
292C2×C8C22×D11311yescharacteristic
293C4⋊C4—21no—
294C4⋊C4—1131no—
295C4⋊C4—2261no—
296C4⋊C4—2261no—
297C4⋊C4—2261no—
298C4⋊C4—2261no—
299C4⋊C4—2261no—
300C4⋊C4—2261no—
301C4⋊C4C22×D11311yescharacteristic
302C22⋊C4—21no—
303C22⋊C4—21no—
304C22⋊C4—2261no—
305C22⋊C4—2261no—
306C42—21no—
307C42—1131no—
308C42—1131no—
309C42—1131no—
310C42—2261no—
311C42—2261no—
312C42—2261no—
313C42C22×D11311yescharacteristic
314C23—21no—
315C23—1131no—
316C23—2261no—
317Q8—21no—
318Q8—21no—
319Q8—21no—
320Q8—1132no—
321Q8—2264no—
322Q8—2261no—
323Q8—2261no—
324Q8—2261no—
325Q8D4×D11312yes—
326D4—21no—
327D4—21no—
328D4—4522no—
329D4—4522no—
330D4—4522no—
331D4—4522no—
332D4—2261no—
333D4—2261no—
334C2×C4—21no—
335C2×C4—21no—
336C2×C4—21no—
337C2×C4—1131no—
338C2×C4—1131no—
339C2×C4—1132no—
340C2×C4—1132no—
341C2×C4—1131no—
342C2×C4—4521no—
343C2×C4—4522no—
344C2×C4—4522no—
345C2×C4—4522no—
346C2×C4—2262no—
347C2×C4—2264no—
348C2×C4—2261no—
349C2×C4—2261no—
350C2×C4—2261no—
351C2×C4D4×D11311yescharacteristic
352C2×C4D4×D11311yescharacteristic
353C2×C4C23×D11311yescharacteristic
354C8—21no—
355C8—21no—
356C8—2261no—
357C8—2261no—
358C22—41no—
359C22—41no—
360C22—41no—
361C22—1132no—
362C22—4521no—
363C22—4521no—
364C22—4521no—
365C22—2261no—
366C22—2261no—
367C22C2×D4×D11311yescharacteristic
368C4—22no—
369C4—21no—
370C4—21no—
371C4—41no—
372C4—41no—
373C4—1132no—
374C4—1132no—
375C4—4521no—
376C4—4521no—
377C4—2262no—
378C4—2261no—
379C4C2×D4×D11311yescharacteristic
380C4#41×D11311yescharacteristic
381C2—81no—
382C2—9041no—
383C2—2262no—
384C2#121×D11311yescharacteristic
385C2#137×D11311yescharacteristic
386C2#2029939511yescharacteristic
subgroupG/H
centerC22C2×D4×D113
commutator, cosocleC2×C4×C113C24
FrattiniC2×C4C23×D113
Fitting#464×C113C2
socleC22×C113C22×D4
prime radical#20299147C2
hypercenter#464D113
hypocenterC113#3037
LCSG ▷ C2×C4×C113 ▷ C2×C113 ▷ C113
UCSC1 ◁ C22 ◁ C42 ◁ #464

Complements

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

NH ≅ G/Ntype
1. C2×#16813654C2semidirect
2. C2×#16813651C2semidirect
4. C4×Q8×D113C2semidirect
5. #20298821C2semidirect
6. #20298820C2semidirect
7. #20298817C2semidirect
8. #20298807C2semidirect
9. #20298806C2semidirect
10. #20298797C2semidirect
11. #20298796C2semidirect
12. #20298620C2semidirect
13. #20298598C2semidirect
14. #20298596C2semidirect
15. #464×C113C2semidirect
69. Q8×D113D4semidirect
186. Dic113#137semidirect
194. C113#3037semidirect
202. #464D113semidirect

Maximal subgroups

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

subgroupindex
C2×#168136542
C2×#168136512
#202991472
C4×Q8×D1132
#202988212
#202988202
#202988172
#202988072
#202988062
#202987972
#202987962
#202986202
#202985982
#202985962
#464×C1132
#3037113