Finite Group Databasebeta

← #28402077

Subgroups — #28402077

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
2C22×#14268634C211yesmaximal, characteristic, complemented
3Q8×C22⋊D113C211yesmaximal, characteristic, complemented
4#20299239C211yesmaximal, characteristic
5#20298991C211yesmaximal, characteristic, complemented
6#20298847C211yesmaximal, characteristic, complemented
7#20298837C211yesmaximal, characteristic, complemented
8#20298822C211yesmaximal, characteristic, complemented
9#20298802C211yesmaximal, characteristic, complemented
10#20298759C211yesmaximal, characteristic, complemented
11#20298751C211yesmaximal, characteristic, complemented
12#20298738C211yesmaximal, characteristic, complemented
13#20298701C211yesmaximal, characteristic, complemented
14#20298666C211yesmaximal, characteristic, complemented
15#451×C113C211yesmaximal, characteristic, complemented
16C2×#14268648C2211yescharacteristic
17C2×Q8×D113C2211yescharacteristic, complemented
18C22×D452C2211yescharacteristic
19#16813654—24no—
20C2×#14268637C2211yescharacteristic, complemented
21C2×#14268636C2211yescharacteristic
22C2×#14268636C2211yescharacteristic
23C2×#14268634—24no—
24C2×#14268634C2211yescharacteristic
25C2×#14268634C2211yescharacteristic
26C2×#14268634C2211yescharacteristic
27C2×#14268634C2211yescharacteristic
28C2×#14268630C2211yescharacteristic, complemented
29C22×#11744751C2211yescharacteristic
30#16813620—21no—
31#16813620C2211yescharacteristic, complemented
32#16813611C2211yescharacteristic
33#16813607—21no—
34#16813601—21no—
35#16813601C2211yescharacteristic
36#16813598—21no—
37#16813598C2211yescharacteristic, complemented
38#16813597—21no—
39#16813597C2211yescharacteristic
40#16813592—21no—
41Q8×Dic113C2211yescharacteristic, complemented
42#16813584C2211yescharacteristic
43C4×C22⋊D113—21no—
44C4×C22⋊D113C2211yescharacteristic
45C22⋊C4×D113—21no—
46#16813555C2211yescharacteristic, complemented
47#16813551C2211yescharacteristic, complemented
48#16813546C2211yescharacteristic, complemented
49#16813545C2211yescharacteristic, complemented
50#16813544C2211yescharacteristic
51#16813544C2211yescharacteristic
52#16813534C2211yescharacteristic, complemented
53#16813532C2211yescharacteristic, complemented
54C22×Q8×C113C2211yescharacteristic
55C2×Q16×C113C2211yescharacteristic, complemented
56C2×Q16×C113C2211yescharacteristic, complemented
57C22⋊Q8×C113C2211yescharacteristic
58#103×C113C2211yescharacteristic, complemented
59#103×C113C2211yescharacteristic, complemented
60C22⋊C8×C113C2211yescharacteristic
61C23×D113—21no—
62#14268648—22no—
63#14268648—41no—
64C2×Dic226—21no—
65C2×Dic226C2311yescharacteristic
66Q8×D113—22no—
67Q8×D113—41no—
68C2×D452—22no—
69C2×D452—21no—
70C2×D452—21no—
71C2×D452—21no—
72C2×D452—41no—
73C2×D452C2311yescharacteristic
74C2×D452C2311yescharacteristic
75C2×C22⋊D113D411yescharacteristic
76C2×C4×D113—21no—
77C2×C4×D113—21no—
78C2×C4×D113—21no—
79C2×C4×D113C2311yescharacteristic
80#14268637—22no—
81#14268636—22no—
82#14268636—41no—
83#14268634—22no—
84#14268634—22no—
85#14268634—22no—
86#14268634D414yescomplemented
87#14268630—22no—
88C2×#11744751—22no—
89C2×#11744751C2311yescharacteristic
90C2×#11744751C2311yescharacteristic
91C4⋊Dic113—21no—
92C4⋊Dic113C2311yescharacteristic
93#14268626—21no—
94#14268626—21no—
95#14268626—21no—
96#14268626—21no—
97#14268626D411yescharacteristic
98C22⋊Dic113—21no—
99C22⋊Dic113D411yescharacteristic
100#14268624—21no—
101#14268624—21no—
102#14268624—21no—
103#14268624—21no—
104#14268624—21no—
105#14268624D411yescharacteristic
106C4×Dic113—21no—
107C4×Dic113C2311yescharacteristic
108C2×Q8×C113—21no—
109C2×Q8×C113—22no—
110C2×Q8×C113—41no—
111C2×Q8×C113C2311yescharacteristic
112C2×Q8×C113C2311yescharacteristic
113C2×Q8×C113C2311yescharacteristic
114C22×C4×C113—21no—
115C22×C4×C113C2311yescharacteristic
116Q16×C113—22no—
117Q16×C113—41no—
118C2×C8×C113C2311yescharacteristic
119C2×C8×C113C2311yescharacteristic
120C4⋊C4×C113—21no—
121C4⋊C4×C113C2311yescharacteristic
122C22⋊C4×C113—21no—
123C23×C113C2×D411yescharacteristic
124C22×D113—21no—
125C22×D113—21no—
126C22×D113—42no—
127C22×D113—42no—
128C22×D113—81no—
129C22×D113C2×D411yescharacteristic
130Q8×C113—21no—
131Q8×C113—21no—
132Q8×C113—21no—
133Q8×C113—21no—
134Q8×C113—21no—
135Q8×C113—42no—
136Q8×C113C2×D412yes—
137C2×C4×C113—21no—
138C2×C4×C113—21no—
139C2×C4×C113—21no—
140C2×C4×C113—21no—
141C2×C4×C113—21no—
142C2×C4×C113—21no—
143C2×C4×C113—42no—
144C2×C4×C113C2×D411yescharacteristic
145C2×C4×C113C2411yescharacteristic
146C22⋊D113—22no—
147C2×Dic113—21no—
148C2×Dic113—21no—
149C2×Dic113C2×D411yescharacteristic
150C2×Dic113C2×D411yescharacteristic
151C2×Dic113C2×D411yescharacteristic
152D452—21no—
153D452—21no—
154D452—21no—
155D452—42no—
156D452—42no—
157D452—81no—
158D452C2×D412yes—
159C4×D113—21no—
160C4×D113—21no—
161C4×D113—42no—
162C4×D113—42no—
163C4×D113—81no—
164Dic226—21no—
165Dic226—21no—
166Dic226—42no—
167C8×C113—21no—
168C8×C113—21no—
169#11744751—21no—
170#11744751C2×D412yes—
171C22×C113—21no—
172C22×C113—21no—
173C22×C113#13712yescomplemented
174C22×C113C22×D411yescharacteristic
175C2×D113—21no—
176C2×D113—22no—
177C2×D113—21no—
178C2×D113—21no—
179C2×D113—41no—
180C2×D113—41no—
181C2×D113—41no—
182C2×D113—41no—
183C2×D113—41no—
184C2×D113—84no—
185C4×C113—22no—
186C4×C113—21no—
187C4×C113—41no—
188C4×C113—41no—
189C4×C113—41no—
190C4×C113C22×D411yescharacteristic
191C4×C113H(5,𝔽2)11yescharacteristic
192Dic113—21no—
193Dic113—21no—
194Dic113—21no—
195Dic113—41no—
196Dic113—41no—
197C2×C113—22no—
198C2×C113D4211yescharacteristic
199C2×C113C2×#13711yescharacteristic
200C2×C113#57711yescharacteristic
201D113—41no—
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#451D11311yescharacteristic, complemented
217#450—1131no—
218#448—1131no—
219#440—1131no—
220#435—1131no—
221C2×#41—1131no—
222C22×Q8—1131no—
223C22×Q8C2×D11311yescharacteristic
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—1131no—
234C2×SD16—1131no—
235C2×SD16—2264no—
236C2×M16—1131no—
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
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#103C2×D11311yescharacteristic, complemented
260#103C2×D11311yescharacteristic, complemented
261#102—1131no—
262#102—1131no—
263C22⋊C8—1131no—
264C22⋊C8C2×D11311yescharacteristic
265#97—1131no—
266C24—2261no—
267#41—4521no—
268#41—2262no—
269C2×Q8—21no—
270C2×Q8—22no—
271C2×Q8—41no—
272C2×Q8—1131no—
273C2×Q8—4521no—
274C2×Q8—2261no—
275C2×Q8—2262no—
276C2×Q8C22×D11311yescharacteristic
277C2×Q8C22×D11311yescharacteristic
278C2×Q8C22×D11311yescharacteristic
279C2×D4—1131no—
280C2×D4—1131no—
281C2×D4—1131no—
282C2×D4—4521no—
283C2×D4—2262no—
284C2×D4—2261no—
285C2×D4—2261no—
286C2×D4—2261no—
287C22×C4—21no—
288C22×C4—1131no—
289C22×C4—2261no—
290C22×C4—2261no—
291C22×C4—2261no—
292C22×C4C22×D11311yescharacteristic
293Q16—22no—
294Q16—41no—
295Q16—2262no—
296SD16—1134no—
297SD16—4521no—
298SD16—2262no—
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—1131no—
310C4⋊C4—1131no—
311C4⋊C4—2261no—
312C4⋊C4—2261no—
313C4⋊C4—2261no—
314C4⋊C4—2261no—
315C4⋊C4—2261no—
316C4⋊C4C22×D11311yescharacteristic
317C22⋊C4—21no—
318C22⋊C4—1131no—
319C22⋊C4—1131no—
320C22⋊C4—2261no—
321C22⋊C4—2261no—
322C22⋊C4—2261no—
323C22⋊C4—2261no—
324C22⋊C4—2261no—
325C22⋊C4—2261no—
326C42—1131no—
327C42—2261no—
328C23—1131no—
329C23—9041no—
330C23—4522no—
331C23—4522no—
332C23—2261no—
333C23—2261no—
334C23D4×D11311yescharacteristic
335Q8—21no—
336Q8—21no—
337Q8—21no—
338Q8—21no—
339Q8—21no—
340Q8—42no—
341Q8—4522no—
342Q8—2261no—
343Q8—2261no—
344Q8D4×D11312yes—
345D4—1132no—
346D4—9041no—
347D4—4522no—
348D4—4522no—
349D4—2262no—
350D4—2261no—
351D4—2261no—
352D4—2261no—
353C2×C4—21no—
354C2×C4—21no—
355C2×C4—21no—
356C2×C4—21no—
357C2×C4—21no—
358C2×C4—21no—
359C2×C4—42no—
360C2×C4—1131no—
361C2×C4—1131no—
362C2×C4—1131no—
363C2×C4—9041no—
364C2×C4—4522no—
365C2×C4—4522no—
366C2×C4—2261no—
367C2×C4—2261no—
368C2×C4—2261no—
369C2×C4—2261no—
370C2×C4D4×D11311yescharacteristic
371C2×C4C23×D11311yescharacteristic
372C8—21no—
373C8—21no—
374C8—1132no—
375C8—2261no—
376C22—21no—
377C22—21no—
378C22—9044no—
379C22—4521no—
380C22—4521no—
381C22—4521no—
382C22—4521no—
383C22—4521no—
384C22—2261no—
385C22—2261no—
386C22—2261no—
387C22—2262no—
388C22#1681365412yescomplemented
389C22C2×D4×D11311yescharacteristic
390C4—21no—
391C4—22no—
392C4—41no—
393C4—41no—
394C4—41no—
395C4—4521no—
396C4—4521no—
397C4—2261no—
398C4—2261no—
399C4—2261no—
400C4C2×D4×D11311yescharacteristic
401C4#1681366711yescharacteristic
402C2—22no—
403C2—9041no—
404C2—4522no—
405C2—4521no—
406C2#2029923011yescharacteristic
407C2C2×#1681365411yescharacteristic
408C2#2029940711yescharacteristic
subgroupG/H
centerC22C2×D4×D113
commutator, cosocleC2×C4×C113C24
FrattiniC2×C4C23×D113
Fitting#451×C113C2
socleC22×C113C22×D4
prime radical#20299239C2
hypercenter#451D113
hypocenterC113#3266
LCSG ▷ C2×C4×C113 ▷ C2×C113 ▷ C113
UCSC1 ◁ C22 ◁ C22×C4 ◁ #451

Complements

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

NH ≅ G/Ntype
1. C2×#16813654C2semidirect
2. C22×#14268634C2semidirect
3. Q8×C22⋊D113C2semidirect
5. #20298991C2semidirect
6. #20298847C2semidirect
7. #20298837C2semidirect
8. #20298822C2semidirect
9. #20298802C2semidirect
10. #20298759C2semidirect
11. #20298751C2semidirect
12. #20298738C2semidirect
13. #20298701C2semidirect
14. #20298666C2semidirect
15. #451×C113C2semidirect
17. C2×Q8×D113C22semidirect
20. C2×#14268637C22semidirect
28. C2×#14268630C22semidirect
31. #16813620C22semidirect
37. #16813598C22semidirect
41. Q8×Dic113C22semidirect
46. #16813555C22semidirect
47. #16813551C22semidirect
48. #16813546C22semidirect
49. #16813545C22semidirect
52. #16813534C22semidirect
53. #16813532C22semidirect
55. C2×Q16×C113C22semidirect
56. C2×Q16×C113C22semidirect
58. #103×C113C22semidirect
59. #103×C113C22semidirect
86. #14268634D4semidirect
173. C22×C113#137semidirect
205. C113#3266semidirect
216. #451D113semidirect
227. C2×Q16C2×D113semidirect
228. C2×Q16C2×D113semidirect
259. #103C2×D113semidirect
260. #103C2×D113semidirect
388. C22#16813654semidirect

Maximal subgroups

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

subgroupindex
C2×#168136542
C22×#142686342
Q8×C22⋊D1132
#202992392
#202989912
#202988472
#202988372
#202988222
#202988022
#202987592
#202987512
#202987382
#202987012
#202986662
#451×C1132
#3266113