Finite Group Databasebeta

← #28402089

Subgroups — #28402089

Order 14464.

494 conjugacy classes of subgroups.

The subgroup lattice has 410 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16813655C211yesmaximal, characteristic, complemented
2C22×#14268636C211yesmaximal, characteristic, complemented
3D4×Dic226C211yesmaximal, characteristic, complemented
4#20299244C211yesmaximal, characteristic
5#20298992C211yesmaximal, characteristic, complemented
6#20298844C211yesmaximal, characteristic, complemented
7#20298839C211yesmaximal, characteristic, complemented
8#20298821C211yesmaximal, characteristic, complemented
9#20298804C211yesmaximal, characteristic, complemented
10#20298762C211yesmaximal, characteristic, complemented
11#20298756C211yesmaximal, characteristic, complemented
12#20298751C211yesmaximal, characteristic, complemented
13#20298739C211yesmaximal, characteristic, complemented
14#20298700C211yesmaximal, characteristic, complemented
15#435×C113C211yesmaximal, characteristic, complemented
16C2×#14268647C2211yescharacteristic
17C22×Dic226C2211yescharacteristic
18C22×Dic226C2211yescharacteristic, complemented
19C22×D452C2211yescharacteristic
20#16813655—24no—
21C2×Dic452C2211yescharacteristic, complemented
22C2×Dic452C2211yescharacteristic, complemented
23C2×Dic452C2211yescharacteristic, complemented
24C2×#14268636—24no—
25C2×#14268636C2211yescharacteristic
26C2×#14268636C2211yescharacteristic
27C2×#14268636C2211yescharacteristic
28C2×#14268636C2211yescharacteristic
29C2×#14268636C2211yescharacteristic
30C2×#14268636C2211yescharacteristic
31#16813622C2211yescharacteristic, complemented
32#16813621—21no—
33#16813610C2211yescharacteristic
34#16813607—21no—
35#16813601C2211yescharacteristic
36#16813601C2211yescharacteristic
37#16813601C2211yescharacteristic, complemented
38#16813599—21no—
39#16813599—21no—
40#16813596C2211yescharacteristic
41#16813595—21no—
42#16813590—21no—
43C4×Dic226C2211yescharacteristic, complemented
44C4×D452C2211yescharacteristic
45D4×Dic113—21no—
46C22⋊C4×D113—21no—
47#16813556C2211yescharacteristic, complemented
48#16813547C2211yescharacteristic, complemented
49#16813547C2211yescharacteristic, complemented
50#16813547C2211yescharacteristic, complemented
51#16813547C2211yescharacteristic, complemented
52#16813544C2211yescharacteristic
53#16813544C2211yescharacteristic
54C2×M16×C113C2211yescharacteristic, complemented
55C22×C8×C113C2211yescharacteristic
56C4×D4×C113C2211yescharacteristic
57C4⋊C8×C113C2211yescharacteristic, complemented
58C22⋊C8×C113C2211yescharacteristic
59C22⋊C8×C113C2211yescharacteristic, complemented
60#97×C113C2211yescharacteristic, complemented
61C23×D113—21no—
62#14268647—22no—
63#14268647—41no—
64C2×Dic226—22no—
65C2×Dic226—22no—
66C2×Dic226—21no—
67C2×Dic226—21no—
68C2×Dic226—41no—
69C2×Dic226—41no—
70C2×Dic226C2311yescharacteristic
71C2×Dic226C2311yescharacteristic
72C2×Dic226C2311yescharacteristic
73C2×Dic226C2311yescharacteristic
74C2×D452—22no—
75C2×D452—21no—
76C2×D452—41no—
77C2×D452C2311yescharacteristic
78C2×D452C2311yescharacteristic
79C2×C22⋊D113—21no—
80C2×C22⋊D113—21no—
81C22×Dic113—21no—
82C22×Dic113—21no—
83C2×C4×D113—21no—
84C2×C4×D113—21no—
85Dic452—22no—
86Dic452—22no—
87Dic452—41no—
88#14268636—22no—
89#14268636—22no—
90#14268636—22no—
91#14268636—22no—
92#14268636—41no—
93#14268636D414yescomplemented
94C4⋊Dic113—21no—
95C4⋊Dic113—21no—
96C4⋊Dic113C2311yescharacteristic
97C4⋊Dic113C2311yescharacteristic
98#14268626—21no—
99#14268626—21no—
100#14268626—21no—
101#14268626—21no—
102C22⋊Dic113—21no—
103C22⋊Dic113—21no—
104C22⋊Dic113—21no—
105#14268624—21no—
106#14268624—21no—
107#14268624—21no—
108#14268624—21no—
109C4×Dic113—21no—
110C2×D4×C113D411yescharacteristic
111C22×C4×C113C2311yescharacteristic
112C22×C4×C113C2311yescharacteristic
113M16×C113—22no—
114C2×C8×C113—22no—
115C2×C8×C113C2311yescharacteristic
116C2×C8×C113C2311yescharacteristic
117C2×C8×C113C2311yescharacteristic
118C2×C8×C113C2311yescharacteristic
119C4⋊C4×C113D411yescharacteristic
120C22⋊C4×C113D411yescharacteristic
121C22⋊C4×C113D411yescharacteristic
122C42×C113C2311yescharacteristic
123C23×C113C2×D411yescharacteristic
124C23×C113C2×D411yescharacteristic
125C22×D113—21no—
126C22×D113—21no—
127C22×D113—42no—
128C22×D113—42no—
129C22×D113—81no—
130D4×C113—22no—
131C2×C4×C113—21no—
132C2×C4×C113—21no—
133C2×C4×C113—21no—
134C2×C4×C113—21no—
135C2×C4×C113C2×D411yescharacteristic
136C2×C4×C113C2×D411yescharacteristic
137C2×C4×C113C2×D411yescharacteristic
138C2×C4×C113C2×D411yescharacteristic
139C2×C4×C113C2411yescharacteristic
140C22⋊D113—42no—
141C22⋊D113—81no—
142C2×Dic113—21no—
143C2×Dic113—21no—
144C2×Dic113—21no—
145C2×Dic113—21no—
146C2×Dic113—21no—
147C2×Dic113—21no—
148C2×Dic113—42no—
149C2×Dic113—42no—
150D452—21no—
151D452—21no—
152D452—21no—
153D452—42no—
154D452C2×D412yes—
155C4×D113—42no—
156C4×D113—81no—
157Dic226—21no—
158Dic226—21no—
159Dic226—21no—
160Dic226—21no—
161Dic226—21no—
162Dic226—21no—
163Dic226—21no—
164Dic226—42no—
165Dic226—42no—
166Dic226C2×D412yes—
167C8×C113—21no—
168C8×C113—21no—
169C8×C113—21no—
170C8×C113C2×D412yes—
171C22×C113—21no—
172C22×C113—21no—
173C22×C113—21no—
174C22×C113—21no—
175C22×C113—21no—
176C22×C113#13712yescomplemented
177C22×C113C22×D411yescharacteristic
178C2×D113—22no—
179C2×D113—41no—
180C2×D113—41no—
181C2×D113—41no—
182C2×D113—41no—
183C2×D113—41no—
184C2×D113—84no—
185C4×C113—21no—
186C4×C113—21no—
187C4×C113—21no—
188C4×C113—21no—
189C4×C113C22×D411yescharacteristic
190C4×C113H(5,𝔽2)11yescharacteristic
191Dic113—22no—
192Dic113—41no—
193Dic113—41no—
194Dic113—41no—
195Dic113—41no—
196Dic113—41no—
197C2×C113—22no—
198C2×C113—41no—
199C2×C113D4211yescharacteristic
200C2×C113C2×#13711yescharacteristic
201C2×C113#57711yescharacteristic
202D113—42no—
203D113—81no—
204#3266—1131nomaximal, Sylow
205C113#326611yescharacteristic, complemented, Sylow
206C2×#137—1131no—
207C22×SD16—1131no—
208D4×Q8—1131no—
209#546—1131no—
210#497—1131no—
211#468—1131no—
212#467—1131no—
213#464—1131no—
214#461—1131no—
215#452—1131no—
216#451—1131no—
217#450—1131no—
218#448—1131no—
219#440—1131no—
220#435D11311yescharacteristic, complemented
221C2×#41—1131no—
222C22×Q8—1131no—
223C22×Q8—1131no—
224C22×D4—1131no—
225#137—2264no—
226C2×Q16—1131no—
227C2×Q16—1131no—
228C2×Q16—1131no—
229C2×SD16—1131no—
230C2×SD16—1131no—
231C2×SD16—1131no—
232C2×SD16—1131no—
233C2×SD16—1131no—
234C2×SD16—1131no—
235C2×SD16—2264no—
236C2×M16C2×D11311yescharacteristic, complemented
237C22×C8C2×D11311yescharacteristic
238C4⋊Q8—1131no—
239C4⋊Q8—2261no—
240#124—1131no—
241#123—2261no—
242C22⋊Q8—1131no—
243C22⋊Q8—1131no—
244C22⋊Q8—1131no—
245C22⋊Q8—2261no—
246C22⋊Q8—2261no—
247#121—1131no—
248#121—2261no—
249#120—2261no—
250C4×Q8—1131no—
251C4×D4—1131no—
252C4×D4—2261no—
253C4×D4C2×D11311yescharacteristic
254C2×C22⋊C4—2261no—
255#107—1131no—
256C4⋊C8C2×D11311yescharacteristic, complemented
257#103—1131no—
258#103—1131no—
259#103—1131no—
260#103—1131no—
261#102—1131no—
262#102—1131no—
263C22⋊C8C2×D11311yescharacteristic
264C22⋊C8C2×D11311yescharacteristic, complemented
265#97C2×D11311yescharacteristic, complemented
266C24—2261no—
267#41—4521no—
268#41—2262no—
269C2×Q8—1131no—
270C2×Q8—1131no—
271C2×Q8—1131no—
272C2×Q8—1131no—
273C2×Q8—4521no—
274C2×Q8—4521no—
275C2×Q8—2262no—
276C2×Q8—2262no—
277C2×Q8—2261no—
278C2×Q8—2261no—
279C2×D4—1131no—
280C2×D4—1131no—
281C2×D4—4521no—
282C2×D4—2262no—
283C2×D4—2261no—
284C2×D4—2261no—
285C2×D4—2261no—
286C2×D4D45211yescharacteristic
287C22×C4—2261no—
288C22×C4—2261no—
289C22×C4—2261no—
290C22×C4—2261no—
291C22×C4C22×D11311yescharacteristic
292C22×C4C22×D11311yescharacteristic
293Q16—4521no—
294Q16—2262no—
295Q16—2262no—
296SD16—1134no—
297SD16—4521no—
298SD16—2262no—
299SD16—2262no—
300SD16—2262no—
301SD16—2262no—
302M16—22no—
303C2×C8—22no—
304C2×C8C22×D11311yescharacteristic
305C2×C8C22×D11311yescharacteristic
306C2×C8C22×D11311yescharacteristic
307C2×C8C22×D11311yescharacteristic
308C4⋊C4—1131no—
309C4⋊C4—1131no—
310C4⋊C4—2261no—
311C4⋊C4—2261no—
312C4⋊C4—2261no—
313C4⋊C4—2261no—
314C4⋊C4—2261no—
315C4⋊C4—2261no—
316C4⋊C4D45211yescharacteristic
317C22⋊C4—2261no—
318C22⋊C4—2261no—
319C22⋊C4—2261no—
320C22⋊C4—2261no—
321C22⋊C4—2261no—
322C22⋊C4—2261no—
323C22⋊C4—2261no—
324C22⋊C4D45211yescharacteristic
325C22⋊C4D45211yescharacteristic
326C42—2261no—
327C42C22×D11311yescharacteristic
328C23—9041no—
329C23—4522no—
330C23—4522no—
331C23—2261no—
332C23—2261no—
333C23C2×D45211yescharacteristic
334C23C2×D45211yescharacteristic
335Q8—1132no—
336Q8—4522no—
337Q8—4522no—
338Q8—2261no—
339Q8—2261no—
340Q8—2261no—
341Q8—2261no—
342Q8—2261no—
343Q8—2261no—
344Q8—2261no—
345D4—22no—
346D4—1132no—
347D4—9041no—
348D4—4522no—
349D4—4522no—
350D4—2261no—
351D4—2261no—
352D4—2261no—
353C2×C4—21no—
354C2×C4—21no—
355C2×C4—21no—
356C2×C4—21no—
357C2×C4—9041no—
358C2×C4—4522no—
359C2×C4—4522no—
360C2×C4—4522no—
361C2×C4—2261no—
362C2×C4—2261no—
363C2×C4—2261no—
364C2×C4—2261no—
365C2×C4—2261no—
366C2×C4—2261no—
367C2×C4C2×D45211yescharacteristic
368C2×C4C2×D45211yescharacteristic
369C2×C4C2×D45211yescharacteristic
370C2×C4C2×D45211yescharacteristic
371C2×C4C23×D11311yescharacteristic
372C8—21no—
373C8—21no—
374C8—21no—
375C8D4×D11312yes—
376C22—21no—
377C22—21no—
378C22—21no—
379C22—21no—
380C22—21no—
381C22—9044no—
382C22—4521no—
383C22—4521no—
384C22—4521no—
385C22—4521no—
386C22—4521no—
387C22—2262no—
388C22#1681365512yescomplemented
389C22C22×D45211yescharacteristic
390C4—21no—
391C4—21no—
392C4—21no—
393C4—21no—
394C4—4521no—
395C4—4521no—
396C4—4521no—
397C4—4521no—
398C4—4521no—
399C4—2262no—
400C4C2×D4×D11311yescharacteristic
401C4#1681366811yescharacteristic
402C2—22no—
403C2—41no—
404C2—9041no—
405C2—4522no—
406C2D4×D45211yescharacteristic
407C2C2×#1681365511yescharacteristic
408C2#2029941011yescharacteristic
subgroupG/H
centerC22C22×D452
commutator, cosocleC2×C4×C113C24
FrattiniC2×C4C23×D113
Fitting#435×C113C2
socleC22×C113C22×D4
prime radical#20299244C2
hypercenter#435D113
hypocenterC113#3266
LCSG ▷ C2×C4×C113 ▷ C2×C113 ▷ C113
UCSC1 ◁ C22 ◁ C4×D4 ◁ #435

Complements

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

NH ≅ G/Ntype
1. C2×#16813655C2semidirect
2. C22×#14268636C2semidirect
3. D4×Dic226C2semidirect
5. #20298992C2semidirect
6. #20298844C2semidirect
7. #20298839C2semidirect
8. #20298821C2semidirect
9. #20298804C2semidirect
10. #20298762C2semidirect
11. #20298756C2semidirect
12. #20298751C2semidirect
13. #20298739C2semidirect
14. #20298700C2semidirect
15. #435×C113C2semidirect
18. C22×Dic226C22semidirect
21. C2×Dic452C22semidirect
22. C2×Dic452C22semidirect
23. C2×Dic452C22semidirect
31. #16813622C22semidirect
37. #16813601C22semidirect
43. C4×Dic226C22semidirect
47. #16813556C22semidirect
48. #16813547C22semidirect
49. #16813547C22semidirect
50. #16813547C22semidirect
51. #16813547C22semidirect
54. C2×M16×C113C22semidirect
57. C4⋊C8×C113C22semidirect
59. C22⋊C8×C113C22semidirect
60. #97×C113C22semidirect
93. #14268636D4semidirect
176. C22×C113#137semidirect
205. C113#3266semidirect
220. #435D113semidirect
236. C2×M16C2×D113semidirect
256. C4⋊C8C2×D113semidirect
264. C22⋊C8C2×D113semidirect
265. #97C2×D113semidirect
388. C22#16813655semidirect

Maximal subgroups

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

subgroupindex
C2×#168136552
C22×#142686362
D4×Dic2262
#202992442
#202989922
#202988442
#202988392
#202988212
#202988042
#202987622
#202987562
#202987512
#202987392
#202987002
#435×C1132
#3266113