Finite Group Databasebeta

← #28402083

Subgroups — #28402083

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×#16813654C211yesmaximal, characteristic, complemented
2C2×SD16×D113C211yesmaximal, characteristic, complemented
3#20299263C211yesmaximal, characteristic, complemented
4#20299241C211yesmaximal, characteristic
5#20298841C211yesmaximal, characteristic, complemented
6#20298836C211yesmaximal, characteristic, complemented
7#20298817C211yesmaximal, characteristic, complemented
8#20298800C211yesmaximal, characteristic, complemented
9#20298759C211yesmaximal, characteristic, complemented
10#20298752C211yesmaximal, characteristic, complemented
11#20298747C211yesmaximal, characteristic, complemented
12#20298735C211yesmaximal, characteristic, complemented
13#20298700C211yesmaximal, characteristic, complemented
14#20298671C211yesmaximal, characteristic, complemented
15#497×C113C211yesmaximal, characteristic, complemented
16C2×#14268648C2211yescharacteristic
17C2×Q8×D113C2211yescharacteristic
18C2×Q8×D113C2211yescharacteristic, complemented
19C2×D4×D113C2211yescharacteristic
20#16813654—24no—
21C2×#14268637C2211yescharacteristic, complemented
22C2×#14268636C2211yescharacteristic
23C2×#14268635C2211yescharacteristic
24C2×#14268634C2211yescharacteristic
25C2×#14268634C2211yescharacteristic
26SD16×D113—24no—
27C2×#14268630C2211yescharacteristic, complemented
28C2×C8×D113C2211yescharacteristic
29#16813621—21no—
30#16813604—21no—
31#16813600—21no—
32#16813600—21no—
33#16813598C2211yescharacteristic
34#16813598C2211yescharacteristic
35#16813598C2211yescharacteristic, complemented
36#16813595—21no—
37#16813593C2211yescharacteristic
38#16813592—21no—
39C4×Dic226C2211yescharacteristic, complemented
40C4×D452C2211yescharacteristic
41C4×D452C2211yescharacteristic
42#16813584—21no—
43C22⋊C4×D113—21no—
44#16813556C2211yescharacteristic, complemented
45C4⋊#11744751C2211yescharacteristic, complemented
46#16813547C2211yescharacteristic, complemented
47#16813546C2211yescharacteristic, complemented
48#16813546C2211yescharacteristic, complemented
49#16813546C2211yescharacteristic, complemented
50#16813544C2211yescharacteristic
51#16813543C2211yescharacteristic
52#16813534C2211yescharacteristic
53#16813534C2211yescharacteristic, complemented
54C2×Q16×C113C2211yescharacteristic, complemented
55C2×Q16×C113C2211yescharacteristic, complemented
56C2×SD16×C113C2211yescharacteristic
57C2×SD16×C113C2211yescharacteristic
58C4⋊Q8×C113C2211yescharacteristic, complemented
59#124×C113C2211yescharacteristic
60#97×C113C2211yescharacteristic, complemented
61C23×D113—21no—
62#14268648—22no—
63#14268648—41no—
64C2×Dic226—21no—
65C2×Dic226—21no—
66C2×Dic226C2311yescharacteristic
67Q8×D113—22no—
68Q8×D113—22no—
69Q8×D113—41no—
70Q8×D113—41no—
71C2×D452—21no—
72C2×D452D411yescharacteristic
73C2×D452C2311yescharacteristic
74C2×C22⋊D113—21no—
75C2×C22⋊D113—21no—
76D4×D113—22no—
77D4×D113—41no—
78C2×C4×D113—21no—
79C2×C4×D113—21no—
80C2×C4×D113—21no—
81C2×C4×D113—21no—
82C2×C4×D113C2311yescharacteristic
83C2×C4×D113C2311yescharacteristic
84#14268637—22no—
85#14268636D414yescomplemented
86#14268635—22no—
87#14268634—22no—
88#14268634—22no—
89#14268630—22no—
90C2×#11744751C2311yescharacteristic
91C2×#11744751C2311yescharacteristic
92C8×D113—22no—
93C4⋊Dic113D411yescharacteristic
94C4⋊Dic113C2311yescharacteristic
95C4⋊Dic113C2311yescharacteristic
96#14268626—21no—
97#14268626—21no—
98#14268626—21no—
99#14268626—21no—
100C22⋊Dic113—21no—
101#14268624—21no—
102#14268624—21no—
103#14268624—21no—
104#14268624—21no—
105#14268624D411yescharacteristic
106#14268624D411yescharacteristic
107C4×Dic113—21no—
108C2×Q8×C113C2311yescharacteristic
109C2×Q8×C113C2311yescharacteristic
110C2×Q8×C113C2311yescharacteristic
111C2×D4×C113C2311yescharacteristic
112Q16×C113—22no—
113Q16×C113—41no—
114SD16×C113—22no—
115SD16×C113—41no—
116C2×C8×C113C2311yescharacteristic
117C2×C8×C113C2311yescharacteristic
118C4⋊C4×C113—21no—
119C4⋊C4×C113—21no—
120C22⋊C4×C113—21no—
121C22⋊C4×C113—21no—
122C42×C113C2311yescharacteristic
123C23×C113—21no—
124C22×D113—21no—
125C22×D113—42no—
126C22×D113—42no—
127C22×D113—81no—
128C22×D113C2×D411yescharacteristic
129C22×D113C2×D411yescharacteristic
130Q8×C113—21no—
131Q8×C113—21no—
132Q8×C113—21no—
133Q8×C113—21no—
134Q8×C113—21no—
135Q8×C113—21no—
136D4×C113—21no—
137D4×C113—21no—
138C2×C4×C113—21no—
139C2×C4×C113—21no—
140C2×C4×C113—21no—
141C2×C4×C113C2×D411yescharacteristic
142C2×C4×C113C2×D411yescharacteristic
143C2×C4×C113C2411yescharacteristic
144C22⋊D113—42no—
145C22⋊D113—81no—
146C2×Dic113—21no—
147C2×Dic113—21no—
148C2×Dic113—21no—
149C2×Dic113C2×D411yescharacteristic
150C2×Dic113C2×D411yescharacteristic
151D452—22no—
152D452—21no—
153D452—42no—
154D452C2×D412yes—
155C4×D113—21no—
156C4×D113—21no—
157C4×D113—21no—
158C4×D113—21no—
159C4×D113—42no—
160C4×D113—42no—
161C4×D113—42no—
162C4×D113—81no—
163Dic226—21no—
164Dic226—42no—
165Dic226—42no—
166Dic226C2×D412yes—
167C8×C113—21no—
168C8×C113C2×D412yes—
169#11744751—21no—
170#11744751—21no—
171C22×C113—41no—
172C22×C113—41no—
173C22×C113—41no—
174C22×C113C22×D411yescharacteristic
175C2×D113—21no—
176C2×D113—21no—
177C2×D113—21no—
178C2×D113—22no—
179C2×D113—21no—
180C2×D113—21no—
181C2×D113—41no—
182C2×D113—41no—
183C2×D113—84no—
184C2×D113#13712yescomplemented
185C4×C113—21no—
186C4×C113—21no—
187C4×C113—41no—
188C4×C113—41no—
189C4×C113—41no—
190C4×C113C22×D411yescharacteristic
191C4×C113H(5,𝔽2)11yescharacteristic
192Dic113—22no—
193Dic113—21no—
194Dic113—21no—
195Dic113—41no—
196Dic113—41no—
197C2×C113—81no—
198C2×C113D4211yescharacteristic
199C2×C113C2×#13711yescharacteristic
200C2×C113#57711yescharacteristic
201D113—22no—
202D113—41no—
203D113—42no—
204#3266—1131nomaximal, Sylow
205C113#326611yescharacteristic, complemented, Sylow
206C2×#137—1131no—
207C22×SD16—1131no—
208D4×Q8—1131no—
209#546—1131no—
210#497D11311yescharacteristic, complemented
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#435—1131no—
221C2×#41—1131no—
222C22×Q8—1131no—
223C22×Q8—1131no—
224C22×D4—1131no—
225#137—2264no—
226C2×Q16—1131no—
227C2×Q16C2×D11311yescharacteristic, complemented
228C2×Q16C2×D11311yescharacteristic, complemented
229C2×SD16—1131no—
230C2×SD16—1131no—
231C2×SD16—1131no—
232C2×SD16—1131no—
233C2×SD16—2264no—
234C2×SD16C2×D11311yescharacteristic
235C2×SD16C2×D11311yescharacteristic
236C2×M16—1131no—
237C22×C8—1131no—
238C4⋊Q8—2261no—
239C4⋊Q8C2×D11311yescharacteristic, complemented
240#124C2×D11311yescharacteristic
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—1131no—
253C4×D4—2261no—
254C2×C22⋊C4—2261no—
255#107—1131no—
256C4⋊C8—1131no—
257#103—1131no—
258#103—1131no—
259#103—1131no—
260#103—1131no—
261#102—1131no—
262#102—1131no—
263C22⋊C8—1131no—
264C22⋊C8—1131no—
265#97C2×D11311yescharacteristic, complemented
266C24—2261no—
267#41—4521no—
268#41—2262no—
269C2×Q8—1131no—
270C2×Q8—4521no—
271C2×Q8—4521no—
272C2×Q8—2261no—
273C2×Q8—2261no—
274C2×Q8—2262no—
275C2×Q8—2262no—
276C2×Q8C22×D11311yescharacteristic
277C2×Q8C22×D11311yescharacteristic
278C2×Q8C22×D11311yescharacteristic
279C2×D4—1131no—
280C2×D4—1131no—
281C2×D4—4521no—
282C2×D4—2261no—
283C2×D4—2261no—
284C2×D4—2262no—
285C2×D4—2261no—
286C2×D4C22×D11311yescharacteristic
287C22×C4—1131no—
288C22×C4—1131no—
289C22×C4—2261no—
290C22×C4—2261no—
291C22×C4—2261no—
292C22×C4—2261no—
293Q16—22no—
294Q16—41no—
295Q16—2262no—
296SD16—22no—
297SD16—41no—
298SD16—1134no—
299SD16—2262no—
300SD16—2262no—
301SD16—2262no—
302M16—2262no—
303C2×C8—1131no—
304C2×C8—1131no—
305C2×C8—2262no—
306C2×C8C22×D11311yescharacteristic
307C2×C8C22×D11311yescharacteristic
308C4⋊C4—21no—
309C4⋊C4—21no—
310C4⋊C4—1131no—
311C4⋊C4—1131no—
312C4⋊C4—1131no—
313C4⋊C4—2261no—
314C4⋊C4—2261no—
315C4⋊C4—2261no—
316C4⋊C4—2261no—
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—2261no—
327C42C22×D11311yescharacteristic
328C23—21no—
329C23—1131no—
330C23—1131no—
331C23—9041no—
332C23—4522no—
333C23—4522no—
334C23—2261no—
335Q8—21no—
336Q8—21no—
337Q8—21no—
338Q8—21no—
339Q8—21no—
340Q8—21no—
341Q8—1132no—
342Q8—4522no—
343Q8—4522no—
344Q8—2261no—
345D4—21no—
346D4—21no—
347D4—1132no—
348D4—9041no—
349D4—4522no—
350D4—4522no—
351D4—2262no—
352D4—2261no—
353C2×C4—21no—
354C2×C4—21no—
355C2×C4—21no—
356C2×C4—1131no—
357C2×C4—1131no—
358C2×C4—9041no—
359C2×C4—4522no—
360C2×C4—4522no—
361C2×C4—4522no—
362C2×C4—2261no—
363C2×C4—2261no—
364C2×C4—2261no—
365C2×C4—2261no—
366C2×C4—2261no—
367C2×C4—2261no—
368C2×C4—2261no—
369C2×C4D4×D11311yescharacteristic
370C2×C4D4×D11311yescharacteristic
371C2×C4C23×D11311yescharacteristic
372C8—21no—
373C8—2261no—
374C8—2261no—
375C8D4×D11312yes—
376C22—41no—
377C22—41no—
378C22—41no—
379C22—1132no—
380C22—9044no—
381C22—4521no—
382C22—4521no—
383C22—2261no—
384C22—2261no—
385C22—2261no—
386C22—2262no—
387C22—2261no—
388C22—2261no—
389C22C2×D4×D11311yescharacteristic
390C4—21no—
391C4—21no—
392C4—41no—
393C4—41no—
394C4—41no—
395C4—4521no—
396C4—4521no—
397C4—2261no—
398C4—2261no—
399C4—2262no—
400C4C2×D4×D11311yescharacteristic
401C4#1681366711yescharacteristic
402C2—81no—
403C2—4522no—
404C2—4521no—
405C2—2262no—
406C2#2029923311yescharacteristic
407C2#137×D11311yescharacteristic
408C2#2029940711yescharacteristic
subgroupG/H
centerC22C2×D4×D113
commutator, cosocleC2×C4×C113C24
FrattiniC2×C4C23×D113
Fitting#497×C113C2
socleC22×C113C22×D4
prime radical#20299241C2
hypercenter#497D113
hypocenterC113#3266
LCSG ▷ C2×C4×C113 ▷ C2×C113 ▷ C113
UCSC1 ◁ C22 ◁ C42 ◁ #497

Complements

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

NH ≅ G/Ntype
1. C2×#16813654C2semidirect
2. C2×SD16×D113C2semidirect
3. #20299263C2semidirect
5. #20298841C2semidirect
6. #20298836C2semidirect
7. #20298817C2semidirect
8. #20298800C2semidirect
9. #20298759C2semidirect
10. #20298752C2semidirect
11. #20298747C2semidirect
12. #20298735C2semidirect
13. #20298700C2semidirect
14. #20298671C2semidirect
15. #497×C113C2semidirect
18. C2×Q8×D113C22semidirect
21. C2×#14268637C22semidirect
27. C2×#14268630C22semidirect
35. #16813598C22semidirect
39. C4×Dic226C22semidirect
44. #16813556C22semidirect
45. C4⋊#11744751C22semidirect
46. #16813547C22semidirect
47. #16813546C22semidirect
48. #16813546C22semidirect
49. #16813546C22semidirect
53. #16813534C22semidirect
54. C2×Q16×C113C22semidirect
55. C2×Q16×C113C22semidirect
58. C4⋊Q8×C113C22semidirect
60. #97×C113C22semidirect
85. #14268636D4semidirect
184. C2×D113#137semidirect
205. C113#3266semidirect
210. #497D113semidirect
227. C2×Q16C2×D113semidirect
228. C2×Q16C2×D113semidirect
239. C4⋊Q8C2×D113semidirect
265. #97C2×D113semidirect

Maximal subgroups

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

subgroupindex
C2×#168136542
C2×SD16×D1132
#202992632
#202992412
#202988412
#202988362
#202988172
#202988002
#202987592
#202987522
#202987472
#202987352
#202987002
#202986712
#497×C1132
#3266113