Finite Group Databasebeta

← #28400208

Subgroups — #28400208

Order 14464.

492 conjugacy classes of subgroups.

The subgroup lattice has 408 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×SD16×D113C211yesmaximal, characteristic, complemented
2C2×#16813628C211yesmaximal, characteristic, complemented
3#20299171C211yesmaximal, characteristic, complemented
4#20299164C211yesmaximal, characteristic
5#20298847C211yesmaximal, characteristic, complemented
6#20298846C211yesmaximal, characteristic, complemented
7#20298843C211yesmaximal, characteristic, complemented
8#20298842C211yesmaximal, characteristic, complemented
9#20298828C211yesmaximal, characteristic, complemented
10#20298827C211yesmaximal, characteristic, complemented
11#20298824C211yesmaximal, characteristic, complemented
12#20298633C211yesmaximal, characteristic, complemented
13#20298605C211yesmaximal, characteristic, complemented
14#20298601C211yesmaximal, characteristic, complemented
15#465×C113C211yesmaximal, characteristic, complemented
16C2×#14268647C2211yescharacteristic
17C2×Q8×D113C2211yescharacteristic
18C2×D4×D113C2211yescharacteristic
19C2×#14268636C2211yescharacteristic
20C2×#14268635C2211yescharacteristic
21C2×#14268634C2211yescharacteristic
22SD16×D113—24no—
23#16813628—24no—
24C2×#14268631C2211yescharacteristic, complemented
25C2×#14268630C2211yescharacteristic
26C2×#14268630C2211yescharacteristic, complemented
27C2×C8×D113C2211yescharacteristic
28C2×C8×D113C2211yescharacteristic, complemented
29#16813621—21no—
30#16813618—21no—
31#16813608—21no—
32#16813608—21no—
33#16813607—21no—
34#16813604—21no—
35#16813602C2211yescharacteristic, complemented
36#16813601C2211yescharacteristic, complemented
37#16813598C2211yescharacteristic, complemented
38#16813597C2211yescharacteristic
39#16813596C2211yescharacteristic
40#16813593C2211yescharacteristic
41#16813592—21no—
42#16813590—21no—
43#16813580C2211yescharacteristic
44#16813580C2211yescharacteristic
45#16813555C2211yescharacteristic, complemented
46#16813555C2211yescharacteristic, complemented
47#16813554C2211yescharacteristic, complemented
48#16813547C2211yescharacteristic, complemented
49#16813546C2211yescharacteristic, complemented
50#16813545C2211yescharacteristic, complemented
51#16813544C2211yescharacteristic
52#16813543C2211yescharacteristic
53#16813542C2211yescharacteristic
54C2×SD16×C113C2211yescharacteristic
55C22×C8×C113C2211yescharacteristic, complemented
56C22⋊Q8×C113C2211yescharacteristic, complemented
57#121×C113C2211yescharacteristic
58#106×C113C2211yescharacteristic, complemented
59#103×C113C2211yescharacteristic, complemented
60#102×C113C2211yescharacteristic
61C23×D113—21no—
62#14268647—22no—
63#14268647—22no—
64C2×Dic226—21no—
65C2×Dic226D411yescharacteristic
66C2×Dic226C2311yescharacteristic
67Q8×D113—22no—
68Q8×D113—22no—
69C2×D452—21no—
70C2×D452D411yescharacteristic
71C2×D452C2311yescharacteristic
72C2×C22⋊D113—21no—
73C2×C22⋊D113—21no—
74C2×C22⋊D113—21no—
75C2×C22⋊D113D411yescharacteristic
76C2×C22⋊D113D411yescharacteristic
77D4×D113—22no—
78D4×D113—22no—
79C2×C4×D113—21no—
80C2×C4×D113C2311yescharacteristic
81C2×C4×D113C2311yescharacteristic
82#14268636—22no—
83#14268635—22no—
84#14268634—22no—
85#14268631—22no—
86#14268630—22no—
87#14268630—22no—
88C2×#11744751C2311yescharacteristic
89C2×#11744751C2311yescharacteristic
90C8×D113—22no—
91C8×D113D414yescomplemented
92C4⋊Dic113—21no—
93C4⋊Dic113C2311yescharacteristic
94C4⋊Dic113C2311yescharacteristic
95#14268626—21no—
96#14268626—21no—
97C22⋊Dic113—21no—
98C22⋊Dic113—21no—
99#14268624—21no—
100#14268624—21no—
101#14268624—21no—
102#14268624—21no—
103#14268624—21no—
104#14268624—21no—
105C4×Dic113—21no—
106C4×Dic113—21no—
107C2×Q8×C113C2311yescharacteristic
108C2×D4×C113—21no—
109C2×D4×C113C2311yescharacteristic
110C22×C4×C113C2311yescharacteristic
111SD16×C113—22no—
112C2×C8×C113—22no—
113C2×C8×C113C2311yescharacteristic
114C2×C8×C113C2311yescharacteristic
115C4⋊C4×C113—21no—
116C4⋊C4×C113C2311yescharacteristic
117C4⋊C4×C113C2311yescharacteristic
118C22⋊C4×C113—21no—
119C22⋊C4×C113—21no—
120C23×C113—21no—
121C23×C113C2×D411yescharacteristic
122C22×D113—21no—
123C22×D113—42no—
124C22×D113—81no—
125C22×D113—81no—
126C22×D113C2×D411yescharacteristic
127C22×D113C2×D411yescharacteristic
128Q8×C113—21no—
129Q8×C113—21no—
130D4×C113—21no—
131D4×C113—21no—
132D4×C113—81no—
133C2×C4×C113—21no—
134C2×C4×C113—21no—
135C2×C4×C113—21no—
136C2×C4×C113—21no—
137C2×C4×C113—21no—
138C2×C4×C113C2×D411yescharacteristic
139C2×C4×C113C2411yescharacteristic
140C22⋊D113—22no—
141C22⋊D113—22no—
142C22⋊D113—42no—
143C22⋊D113—81no—
144C22⋊D113—81no—
145C2×Dic113—21no—
146C2×Dic113—21no—
147C2×Dic113—21no—
148C2×Dic113C2×D411yescharacteristic
149C2×Dic113C2×D411yescharacteristic
150D452—22no—
151D452—21no—
152D452—21no—
153D452—81no—
154C4×D113—21no—
155C4×D113—21no—
156C4×D113—42no—
157C4×D113C2×D412yes—
158C4×D113#4112yes—
159Dic226—22no—
160Dic226—21no—
161Dic226—21no—
162Dic226—42no—
163C8×C113—21no—
164C8×C113C2×D412yes—
165#11744751—21no—
166#11744751C2×D412yes—
167C22×C113—21no—
168C22×C113—21no—
169C22×C113—21no—
170C22×C113—41no—
171C22×C113—41no—
172C22×C113—41no—
173C22×C113C22×D411yescharacteristic
174C2×D113—21no—
175C2×D113—21no—
176C2×D113—21no—
177C2×D113—21no—
178C2×D113—21no—
179C2×D113—41no—
180C2×D113—41no—
181C2×D113—41no—
182C2×D113—84no—
183C2×D113#12112yes—
184C4×C113—21no—
185C4×C113—41no—
186C4×C113—41no—
187C4×C113—41no—
188C4×C113C22×D411yescharacteristic
189C4×C113C2×#4111yescharacteristic
190Dic113—21no—
191Dic113—41no—
192Dic113—41no—
193Dic113—41no—
194Dic113#12112yes—
195C2×C113—41no—
196C2×C113—81no—
197C2×C113C2×#12111yescharacteristic
198C2×C113#57711yescharacteristic
199C2×C113#57711yescharacteristic
200D113—22no—
201D113—41no—
202D113—81no—
203#3057—1131nomaximal, Sylow
204C113#305711yescharacteristic, complemented, Sylow
205C22×SD16—1131no—
206C2×#131—1131no—
207#536—1131no—
208#535—1131no—
209#468—1131no—
210#468—1131no—
211#468—1131no—
212#468—1131no—
213#465—1131no—
214#465—1131no—
215#465—1131no—
216#465D11311yescharacteristic, complemented
217#427—1131no—
218#419—1131no—
219#418—1131no—
220C2×#41—1131no—
221C22×Q8—1131no—
222C22×D4—1131no—
223C2×SD16—1131no—
224C2×SD16—1131no—
225C2×SD16—1131no—
226C2×SD16—2264no—
227C2×SD16C2×D11311yescharacteristic
228#131—2264no—
229C2×M16—1131no—
230C2×M16—1131no—
231C2×M16—1131no—
232C22×C8—1131no—
233C22×C8—1131no—
234C22×C8C2×D11311yescharacteristic, complemented
235C4⋊Q8—2261no—
236#127—2261no—
237#124—2261no—
238#124—2261no—
239#123—2261no—
240#123—2261no—
241C22⋊Q8—1131no—
242C22⋊Q8—1131no—
243C22⋊Q8—1131no—
244C22⋊Q8C2×D11311yescharacteristic, complemented
245#121—1131no—
246#121—1131no—
247#121—1131no—
248#121C2×D11311yescharacteristic
249#120—2261no—
250#120—2261no—
251#117—1131no—
252#117—1131no—
253#107—1131no—
254#107—1131no—
255#106—1131no—
256#106C2×D11311yescharacteristic, complemented
257#103—1131no—
258#103—1131no—
259#103—1131no—
260#103C2×D11311yescharacteristic, complemented
261#102—1131no—
262#102—1131no—
263#102—1131no—
264#102C2×D11311yescharacteristic
265C24—2261no—
266#41—2262no—
267#41—2262no—
268C2×Q8—1131no—
269C2×Q8—1131no—
270C2×Q8—2261no—
271C2×Q8—2262no—
272C2×Q8—2262no—
273C2×Q8C22×D11311yescharacteristic
274C2×D4—21no—
275C2×D4—1131no—
276C2×D4—1131no—
277C2×D4—1131no—
278C2×D4—1131no—
279C2×D4—2261no—
280C2×D4—2262no—
281C2×D4—2262no—
282C2×D4—2261no—
283C2×D4—2261no—
284C2×D4—2261no—
285C2×D4C22×D11311yescharacteristic
286C22×C4—1131no—
287C22×C4—1131no—
288C22×C4—2261no—
289C22×C4C22×D11311yescharacteristic
290SD16—22no—
291SD16—2262no—
292SD16—2262no—
293SD16—2262no—
294M16—2262no—
295M16—2262no—
296M16—2262no—
297C2×C8—22no—
298C2×C8—1131no—
299C2×C8—1134no—
300C2×C8—1131no—
301C2×C8—2262no—
302C2×C8C22×D11311yescharacteristic
303C2×C8C22×D11311yescharacteristic
304C4⋊C4—21no—
305C4⋊C4—1131no—
306C4⋊C4—1131no—
307C4⋊C4—2261no—
308C4⋊C4—2261no—
309C4⋊C4—2261no—
310C4⋊C4C22×D11311yescharacteristic
311C4⋊C4C22×D11311yescharacteristic
312C22⋊C4—21no—
313C22⋊C4—21no—
314C22⋊C4—2261no—
315C22⋊C4—2261no—
316C22⋊C4—2261no—
317C22⋊C4—2261no—
318C22⋊C4—2261no—
319C22⋊C4—2261no—
320C22⋊C4—2261no—
321C22⋊C4—2261no—
322C42—2261no—
323C42—2261no—
324C23—21no—
325C23—1131no—
326C23—1131no—
327C23—9041no—
328C23—9041no—
329C23—4522no—
330C23—2261no—
331C23D4×D11311yescharacteristic
332Q8—21no—
333Q8—21no—
334Q8—4522no—
335Q8—2262no—
336Q8—2261no—
337Q8—2261no—
338D4—21no—
339D4—21no—
340D4—81no—
341D4—9041no—
342D4—9041no—
343D4—9041no—
344D4—4522no—
345D4—2262no—
346D4—2262no—
347D4—2262no—
348D4—2261no—
349D4—2261no—
350C2×C4—21no—
351C2×C4—21no—
352C2×C4—21no—
353C2×C4—21no—
354C2×C4—21no—
355C2×C4—1131no—
356C2×C4—1132no—
357C2×C4—1132no—
358C2×C4—1131no—
359C2×C4—4522no—
360C2×C4—2261no—
361C2×C4—2261no—
362C2×C4—2261no—
363C2×C4—2261no—
364C2×C4—2261no—
365C2×C4D4×D11311yescharacteristic
366C2×C4C23×D11311yescharacteristic
367C8—21no—
368C8—1132no—
369C8—2261no—
370C8D4×D11312yes—
371C22—21no—
372C22—21no—
373C22—21no—
374C22—41no—
375C22—41no—
376C22—41no—
377C22—1132no—
378C22—9044no—
379C22—4521no—
380C22—4521no—
381C22—4521no—
382C22—2261no—
383C22—2261no—
384C22—2261no—
385C22—2261no—
386C22—2261no—
387C22C2×D4×D11311yescharacteristic
388C4—21no—
389C4—41no—
390C4—41no—
391C4—41no—
392C4—1132no—
393C4—4521no—
394C4—4521no—
395C4—4521no—
396C4—2261no—
397C4C2×D4×D11311yescharacteristic
398C4#41×D11311yescharacteristic
399C2—41no—
400C2—81no—
401C2—9041no—
402C2—4521no—
403C2—2262no—
404C2#121×D11311yescharacteristic
405C2#2029940411yescharacteristic
406C2#2029940511yescharacteristic
subgroupG/H
centerC22C2×D4×D113
commutator, cosocleC2×C4×C113C24
FrattiniC2×C4C23×D113
Fitting#465×C113C2
socleC22×C113C22×D4
prime radical#20299164C2
hypercenter#465D113
hypocenterC113#3057
LCSG ▷ C2×C4×C113 ▷ C2×C113 ▷ C113
UCSC1 ◁ C22 ◁ C22×C4 ◁ #465

Complements

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

NH ≅ G/Ntype
1. C2×SD16×D113C2semidirect
2. C2×#16813628C2semidirect
3. #20299171C2semidirect
5. #20298847C2semidirect
6. #20298846C2semidirect
7. #20298843C2semidirect
8. #20298842C2semidirect
9. #20298828C2semidirect
10. #20298827C2semidirect
11. #20298824C2semidirect
12. #20298633C2semidirect
13. #20298605C2semidirect
14. #20298601C2semidirect
15. #465×C113C2semidirect
24. C2×#14268631C22semidirect
26. C2×#14268630C22semidirect
28. C2×C8×D113C22semidirect
35. #16813602C22semidirect
36. #16813601C22semidirect
37. #16813598C22semidirect
45. #16813555C22semidirect
46. #16813555C22semidirect
47. #16813554C22semidirect
48. #16813547C22semidirect
49. #16813546C22semidirect
50. #16813545C22semidirect
55. C22×C8×C113C22semidirect
56. C22⋊Q8×C113C22semidirect
58. #106×C113C22semidirect
59. #103×C113C22semidirect
91. C8×D113D4semidirect
204. C113#3057semidirect
216. #465D113semidirect
234. C22×C8C2×D113semidirect
244. C22⋊Q8C2×D113semidirect
256. #106C2×D113semidirect
260. #103C2×D113semidirect

Maximal subgroups

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

subgroupindex
C2×SD16×D1132
C2×#168136282
#202991712
#202991642
#202988472
#202988462
#202988432
#202988422
#202988282
#202988272
#202988242
#202986332
#202986052
#202986012
#465×C1132
#3057113