Finite Group Databasebeta

← #28402091

Subgroups — #28402091

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
2C2×SD16×D113C211yesmaximal, characteristic, complemented
3#20299261C211yesmaximal, characteristic, complemented
4#20299245C211yesmaximal, characteristic
5#20298989C211yesmaximal, characteristic, complemented
6#20298840C211yesmaximal, characteristic, complemented
7#20298819C211yesmaximal, characteristic, complemented
8#20298802C211yesmaximal, characteristic, complemented
9#20298758C211yesmaximal, characteristic, complemented
10#20298755C211yesmaximal, characteristic, complemented
11#20298750C211yesmaximal, characteristic, complemented
12#20298736C211yesmaximal, characteristic, complemented
13#20298697C211yesmaximal, characteristic, complemented
14#20298667C211yesmaximal, characteristic, complemented
15#468×C113C211yesmaximal, characteristic, complemented
16C2×#14268647C2211yescharacteristic
17C22×Dic226C2211yescharacteristic, complemented
18C2×Q8×D113C2211yescharacteristic
19C2×D4×D113C2211yescharacteristic
20#16813655—24no—
21C2×Dic452C2211yescharacteristic, complemented
22C2×Dic452C2211yescharacteristic, complemented
23C2×#14268637C2211yescharacteristic, complemented
24C2×#14268636C2211yescharacteristic
25C2×#14268636C2211yescharacteristic
26C2×#14268635C2211yescharacteristic
27C2×#14268635C2211yescharacteristic
28C2×#14268634C2211yescharacteristic
29SD16×D113—24no—
30C2×C8×D113C2211yescharacteristic
31#16813621—21no—
32#16813620C2211yescharacteristic, complemented
33#16813609C2211yescharacteristic
34#16813604—21no—
35#16813602C2211yescharacteristic
36#16813602C2211yescharacteristic
37#16813600—21no—
38#16813599—21no—
39#16813593—21no—
40#16813590—21no—
41#16813587C2211yescharacteristic, complemented
42#16813584C2211yescharacteristic
43C4×C22⋊D113C2211yescharacteristic
44#16813582—21no—
45C22⋊C4×D113—21no—
46#16813551C2211yescharacteristic, complemented
47#16813545C2211yescharacteristic, complemented
48#16813545C2211yescharacteristic, complemented
49#16813545C2211yescharacteristic, complemented
50#16813542C2211yescharacteristic
51C22⋊#11744751C2211yescharacteristic, complemented
52#16813534C2211yescharacteristic
53#16813532C2211yescharacteristic, complemented
54C2×SD16×C113C2211yescharacteristic
55C2×M16×C113C2211yescharacteristic, complemented
56C22⋊Q8×C113C2211yescharacteristic, complemented
57#121×C113C2211yescharacteristic
58#107×C113C2211yescharacteristic, complemented
59#103×C113C2211yescharacteristic, complemented
60#102×C113C2211yescharacteristic
61C23×D113—21no—
62#14268647—22no—
63#14268647—41no—
64C2×Dic226—22no—
65C2×Dic226—21no—
66C2×Dic226—21no—
67C2×Dic226—41no—
68C2×Dic226C2311yescharacteristic
69C2×Dic226C2311yescharacteristic
70C2×Dic226C2311yescharacteristic
71Q8×D113—22no—
72Q8×D113—41no—
73C2×D452C2311yescharacteristic
74C2×C22⋊D113—21no—
75C2×C22⋊D113—21no—
76C2×C22⋊D113D411yescharacteristic
77D4×D113—22no—
78D4×D113—41no—
79C22×Dic113—21no—
80C2×C4×D113—21no—
81C2×C4×D113—21no—
82C2×C4×D113—21no—
83C2×C4×D113C2311yescharacteristic
84Dic452—22no—
85Dic452—22no—
86#14268637—41no—
87#14268636—22no—
88#14268636D414yescomplemented
89#14268635—22no—
90#14268635—41no—
91#14268634—22no—
92C2×#11744751C2311yescharacteristic
93C2×#11744751C2311yescharacteristic
94C8×D113—22no—
95C4⋊Dic113—21no—
96C4⋊Dic113—21no—
97#14268626—21no—
98#14268626—21no—
99#14268626—21no—
100#14268626D411yescharacteristic
101C22⋊Dic113—21no—
102C22⋊Dic113—21no—
103C22⋊Dic113D411yescharacteristic
104#14268624—21no—
105#14268624—21no—
106#14268624—21no—
107#14268624D411yescharacteristic
108C4×Dic113—21no—
109C4×Dic113C2311yescharacteristic
110C2×Q8×C113C2311yescharacteristic
111C2×D4×C113—21no—
112C2×D4×C113C2311yescharacteristic
113C22×C4×C113C2311yescharacteristic
114SD16×C113—22no—
115M16×C113—22no—
116C2×C8×C113C2311yescharacteristic
117C2×C8×C113C2311yescharacteristic
118C4⋊C4×C113—21no—
119C4⋊C4×C113C2311yescharacteristic
120C4⋊C4×C113C2311yescharacteristic
121C22⋊C4×C113—21no—
122C22⋊C4×C113—21no—
123C23×C113—21no—
124C23×C113C2×D411yescharacteristic
125C22×D113—21no—
126C22×D113—42no—
127C22×D113—42no—
128C22×D113—81no—
129C22×D113C2×D411yescharacteristic
130Q8×C113—21no—
131Q8×C113—21no—
132D4×C113—21no—
133D4×C113—21no—
134D4×C113—81no—
135C2×C4×C113—21no—
136C2×C4×C113—21no—
137C2×C4×C113—21no—
138C2×C4×C113—21no—
139C2×C4×C113—21no—
140C2×C4×C113C2×D411yescharacteristic
141C2×C4×C113C2411yescharacteristic
142C22⋊D113—22no—
143C22⋊D113—42no—
144C22⋊D113—42no—
145C2×Dic113—21no—
146C2×Dic113—21no—
147C2×Dic113—21no—
148C2×Dic113—42no—
149C2×Dic113C2×D411yescharacteristic
150C2×Dic113C2×D411yescharacteristic
151C2×Dic113C2×D411yescharacteristic
152D452—21no—
153D452C2×D412yes—
154C4×D113—21no—
155C4×D113—21no—
156C4×D113—42no—
157C4×D113—42no—
158C4×D113—81no—
159Dic226—21no—
160Dic226—21no—
161Dic226—21no—
162Dic226—21no—
163Dic226—21no—
164Dic226—42no—
165Dic226—42no—
166Dic226C2×D412yes—
167C8×C113—21no—
168C8×C113C2×D412yes—
169#11744751—21no—
170#11744751—21no—
171C22×C113—21no—
172C22×C113—21no—
173C22×C113—21no—
174C22×C113—41no—
175C22×C113—41no—
176C22×C113—41no—
177C22×C113C22×D411yescharacteristic
178C2×D113—21no—
179C2×D113—21no—
180C2×D113—22no—
181C2×D113—41no—
182C2×D113—41no—
183C2×D113—84no—
184C2×D113#13712yescomplemented
185C4×C113—21no—
186C4×C113—41no—
187C4×C113—41no—
188C4×C113—41no—
189C4×C113C22×D411yescharacteristic
190C4×C113H(5,𝔽2)11yescharacteristic
191Dic113—22no—
192Dic113—21no—
193Dic113—21no—
194Dic113—21no—
195Dic113—41no—
196Dic113—41no—
197C2×C113—41no—
198C2×C113—81no—
199C2×C113D4211yescharacteristic
200C2×C113C2×#13711yescharacteristic
201C2×C113#57711yescharacteristic
202D113—22no—
203D113—42no—
204#3266—1131nomaximal, Sylow
205C113#326611yescharacteristic, complemented, Sylow
206C2×#137—1131no—
207C22×SD16—1131no—
208D4×Q8—1131no—
209#546—1131no—
210#497—1131no—
211#468D11311yescharacteristic, complemented
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#435—1131no—
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—2264no—
235C2×SD16C2×D11311yescharacteristic
236C2×M16C2×D11311yescharacteristic, complemented
237C22×C8—1131no—
238C4⋊Q8—1131no—
239C4⋊Q8—2261no—
240#124—1131no—
241#123—2261no—
242C22⋊Q8—1131no—
243C22⋊Q8—1131no—
244C22⋊Q8—2261no—
245C22⋊Q8—2261no—
246C22⋊Q8C2×D11311yescharacteristic, complemented
247#121—2261no—
248#121C2×D11311yescharacteristic
249#120—2261no—
250C4×Q8—1131no—
251C4×D4—1131no—
252C4×D4—1131no—
253C4×D4—2261no—
254C2×C22⋊C4—2261no—
255#107C2×D11311yescharacteristic, complemented
256C4⋊C8—1131no—
257#103—1131no—
258#103—1131no—
259#103—1131no—
260#103C2×D11311yescharacteristic, complemented
261#102—1131no—
262#102C2×D11311yescharacteristic
263C22⋊C8—1131no—
264C22⋊C8—1131no—
265#97—1131no—
266C24—2261no—
267#41—4521no—
268#41—2262no—
269C2×Q8—1131no—
270C2×Q8—1131no—
271C2×Q8—1131no—
272C2×Q8—4521no—
273C2×Q8—4521no—
274C2×Q8—2261no—
275C2×Q8—2262no—
276C2×Q8—2262no—
277C2×Q8—2261no—
278C2×Q8C22×D11311yescharacteristic
279C2×D4—21no—
280C2×D4—1131no—
281C2×D4—1131no—
282C2×D4—4521no—
283C2×D4—2261no—
284C2×D4—2262no—
285C2×D4—2261no—
286C2×D4C22×D11311yescharacteristic
287C22×C4—1131no—
288C22×C4—2261no—
289C22×C4—2261no—
290C22×C4—2261no—
291C22×C4—2261no—
292C22×C4C22×D11311yescharacteristic
293Q16—4521no—
294Q16—2262no—
295Q16—2262no—
296SD16—22no—
297SD16—1134no—
298SD16—4521no—
299SD16—2262no—
300SD16—2262no—
301SD16—2262no—
302M16—22no—
303C2×C8—1131no—
304C2×C8—1131no—
305C2×C8—2262no—
306C2×C8C22×D11311yescharacteristic
307C2×C8C22×D11311yescharacteristic
308C4⋊C4—21no—
309C4⋊C4—1131no—
310C4⋊C4—2261no—
311C4⋊C4—2261no—
312C4⋊C4—2261no—
313C4⋊C4—2261no—
314C4⋊C4—2261no—
315C4⋊C4C22×D11311yescharacteristic
316C4⋊C4C22×D11311yescharacteristic
317C22⋊C4—21no—
318C22⋊C4—21no—
319C22⋊C4—1131no—
320C22⋊C4—1131no—
321C22⋊C4—2261no—
322C22⋊C4—2261no—
323C22⋊C4—2261no—
324C22⋊C4—2261no—
325C22⋊C4—2261no—
326C42—1131no—
327C42—2261no—
328C23—21no—
329C23—1131no—
330C23—9041no—
331C23—4522no—
332C23—4522no—
333C23—2261no—
334C23D4×D11311yescharacteristic
335Q8—21no—
336Q8—21no—
337Q8—1132no—
338Q8—4522no—
339Q8—4522no—
340Q8—2261no—
341Q8—2261no—
342Q8—2261no—
343Q8—2261no—
344Q8—2261no—
345D4—21no—
346D4—21no—
347D4—81no—
348D4—1132no—
349D4—4522no—
350D4—4522no—
351D4—2262no—
352D4—2261no—
353C2×C4—21no—
354C2×C4—21no—
355C2×C4—21no—
356C2×C4—21no—
357C2×C4—21no—
358C2×C4—1131no—
359C2×C4—1131no—
360C2×C4—1131no—
361C2×C4—9041no—
362C2×C4—4522no—
363C2×C4—4522no—
364C2×C4—4522no—
365C2×C4—2261no—
366C2×C4—2261no—
367C2×C4—2261no—
368C2×C4—2261no—
369C2×C4—2261no—
370C2×C4D4×D11311yescharacteristic
371C2×C4C23×D11311yescharacteristic
372C8—21no—
373C8—2261no—
374C8—2261no—
375C8D4×D11312yes—
376C22—21no—
377C22—21no—
378C22—21no—
379C22—41no—
380C22—41no—
381C22—41no—
382C22—1132no—
383C22—9044no—
384C22—4521no—
385C22—4521no—
386C22—2262no—
387C22—2261no—
388C22—2261no—
389C22C2×D4×D11311yescharacteristic
390C4—21no—
391C4—41no—
392C4—41no—
393C4—41no—
394C4—4521no—
395C4—4521no—
396C4—2261no—
397C4—2261no—
398C4—2261no—
399C4—2262no—
400C4C2×D4×D11311yescharacteristic
401C4#1681366811yescharacteristic
402C2—41no—
403C2—81no—
404C2—4522no—
405C2—2262no—
406C2#2029923211yescharacteristic
407C2#137×D11311yescharacteristic
408C2#2029940811yescharacteristic
subgroupG/H
centerC22C2×D4×D113
commutator, cosocleC2×C4×C113C24
FrattiniC2×C4C23×D113
Fitting#468×C113C2
socleC22×C113C22×D4
prime radical#20299245C2
hypercenter#468D113
hypocenterC113#3266
LCSG ▷ C2×C4×C113 ▷ C2×C113 ▷ C113
UCSC1 ◁ C22 ◁ C22×C4 ◁ #468

Complements

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

NH ≅ G/Ntype
1. C2×#16813655C2semidirect
2. C2×SD16×D113C2semidirect
3. #20299261C2semidirect
5. #20298989C2semidirect
6. #20298840C2semidirect
7. #20298819C2semidirect
8. #20298802C2semidirect
9. #20298758C2semidirect
10. #20298755C2semidirect
11. #20298750C2semidirect
12. #20298736C2semidirect
13. #20298697C2semidirect
14. #20298667C2semidirect
15. #468×C113C2semidirect
17. C22×Dic226C22semidirect
21. C2×Dic452C22semidirect
22. C2×Dic452C22semidirect
23. C2×#14268637C22semidirect
32. #16813620C22semidirect
41. #16813587C22semidirect
46. #16813551C22semidirect
47. #16813545C22semidirect
48. #16813545C22semidirect
49. #16813545C22semidirect
51. C22⋊#11744751C22semidirect
53. #16813532C22semidirect
55. C2×M16×C113C22semidirect
56. C22⋊Q8×C113C22semidirect
58. #107×C113C22semidirect
59. #103×C113C22semidirect
88. #14268636D4semidirect
184. C2×D113#137semidirect
205. C113#3266semidirect
211. #468D113semidirect
236. C2×M16C2×D113semidirect
246. C22⋊Q8C2×D113semidirect
255. #107C2×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×#168136552
C2×SD16×D1132
#202992612
#202992452
#202989892
#202988402
#202988192
#202988022
#202987582
#202987552
#202987502
#202987362
#202986972
#202986672
#468×C1132
#3266113