Finite Group Databasebeta

← #28402142

Subgroups — #28402142

Order 14464.

472 conjugacy classes of subgroups.

The subgroup lattice has 396 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16813652C211yesmaximal, characteristic, complemented
2C2×Q16×D113C211yesmaximal, characteristic, complemented
3#20299261C211yesmaximal, characteristic, complemented
4#20299255C211yesmaximal, characteristic
5#20298989C211yesmaximal, characteristic, complemented
6#20298854C211yesmaximal, characteristic, complemented
7#20298826C211yesmaximal, characteristic, complemented
8#20298819C211yesmaximal, characteristic, complemented
9#20298806C211yesmaximal, characteristic, complemented
10#20298756C211yesmaximal, characteristic, complemented
11#20298755C211yesmaximal, characteristic, complemented
12#20298735C211yesmaximal, characteristic, complemented
13#20298702C211yesmaximal, characteristic, complemented
14#20298672C211yesmaximal, characteristic, complemented
15#452×C113C211yesmaximal, characteristic, complemented
16C22×Dic226C2211yescharacteristic
17C2×Q8×D113C2211yescharacteristic
18C2×Q8×D113C2211yescharacteristic
19#16813652—24no—
20C2×Dic452C2211yescharacteristic
21C2×Dic452C2211yescharacteristic
22C2×#14268637C2211yescharacteristic
23C2×#14268637C2211yescharacteristic
24C2×#14268637C2211yescharacteristic
25Q16×D113—24no—
26C2×#14268635C2211yescharacteristic
27C2×#14268635C2211yescharacteristic
28C2×#14268631C2211yescharacteristic
29C2×C8×D113C2211yescharacteristic
30#16813621—21no—
31#16813620C2211yescharacteristic
32#16813609—21no—
33#16813609C2211yescharacteristic
34#16813602C2211yescharacteristic
35#16813601—21no—
36#16813601C2211yescharacteristic
37#16813600—21no—
38#16813599—21no—
39#16813593—21no—
40#16813593C2211yescharacteristic
41Q8×Dic113C2211yescharacteristic
42#16813587C2211yescharacteristic
43C4×C22⋊D113—21no—
44C4×C22⋊D113C2211yescharacteristic
45#16813582—21no—
46#16813553C2211yescharacteristic
47#16813551C2211yescharacteristic
48#16813547C2211yescharacteristic
49#16813547C2211yescharacteristic
50#16813546C2211yescharacteristic
51#16813545C2211yescharacteristic
52#16813534C2211yescharacteristic
53#16813532C2211yescharacteristic
54C2×#41×C113C2211yescharacteristic
55C2×Q16×C113C2211yescharacteristic
56C2×SD16×C113C2211yescharacteristic
57C22⋊Q8×C113C2211yescharacteristic
58#103×C113C2211yescharacteristic
59#102×C113C2211yescharacteristic
60C22⋊C8×C113C2211yescharacteristic
61C2×Dic226—22no—
62C2×Dic226—21no—
63C2×Dic226—21no—
64C2×Dic226—21no—
65C2×Dic226—41no—
66C2×Dic226C2311yescharacteristic
67C2×Dic226C2311yescharacteristic
68C2×Dic226C2311yescharacteristic
69Q8×D113—22no—
70Q8×D113—22no—
71Q8×D113—41no—
72Q8×D113—41no—
73C2×C22⋊D113—21no—
74C2×C22⋊D113D411yescharacteristic
75C22×Dic113—21no—
76C2×C4×D113—21no—
77C2×C4×D113—21no—
78C2×C4×D113C2311yescharacteristic
79Dic452—22no—
80Dic452—41no—
81#14268637—22no—
82#14268637—22no—
83#14268637D414yescomplemented
84#14268635—22no—
85#14268635—22no—
86#14268631—22no—
87C2×#11744751C2311yescharacteristic
88C2×#11744751C2311yescharacteristic
89C8×D113—22no—
90C4⋊Dic113—21no—
91C4⋊Dic113—21no—
92C4⋊Dic113C2311yescharacteristic
93#14268626—21no—
94#14268626—21no—
95#14268626—21no—
96#14268626—21no—
97#14268626D411yescharacteristic
98C22⋊Dic113—21no—
99C22⋊Dic113—21no—
100C22⋊Dic113—21no—
101C22⋊Dic113—21no—
102C22⋊Dic113D411yescharacteristic
103#14268624—21no—
104#14268624D411yescharacteristic
105C4×Dic113—21no—
106C4×Dic113—21no—
107C4×Dic113C2311yescharacteristic
108#41×C113—22no—
109#41×C113—41no—
110C2×Q8×C113C2311yescharacteristic
111C2×Q8×C113C2311yescharacteristic
112C2×D4×C113—21no—
113C2×D4×C113C2311yescharacteristic
114C22×C4×C113—21no—
115C22×C4×C113C2311yescharacteristic
116Q16×C113—22no—
117SD16×C113—41no—
118C2×C8×C113C2311yescharacteristic
119C2×C8×C113C2311yescharacteristic
120C4⋊C4×C113—21no—
121C4⋊C4×C113C2311yescharacteristic
122C22⋊C4×C113—21no—
123C23×C113—21no—
124C23×C113C2×D411yescharacteristic
125C22×D113C2×D411yescharacteristic
126Q8×C113—21no—
127Q8×C113—21no—
128Q8×C113—21no—
129Q8×C113C2×D412yes—
130D4×C113—21no—
131D4×C113—21no—
132D4×C113—42no—
133C2×C4×C113—21no—
134C2×C4×C113—21no—
135C2×C4×C113—21no—
136C2×C4×C113—21no—
137C2×C4×C113—21no—
138C2×C4×C113—42no—
139C2×C4×C113C2×D411yescharacteristic
140C2×C4×C113C2411yescharacteristic
141C22⋊D113—22no—
142C22⋊D113—42no—
143C2×Dic113—21no—
144C2×Dic113—21no—
145C2×Dic113—21no—
146C2×Dic113—21no—
147C2×Dic113—42no—
148C2×Dic113C2×D411yescharacteristic
149C2×Dic113C2×D411yescharacteristic
150C2×Dic113C2×D411yescharacteristic
151C4×D113—21no—
152C4×D113—21no—
153C4×D113—42no—
154C4×D113—42no—
155Dic226—21no—
156Dic226—21no—
157Dic226—21no—
158Dic226—21no—
159Dic226—21no—
160Dic226—42no—
161Dic226—42no—
162Dic226—42no—
163Dic226C2×D412yes—
164C8×C113—21no—
165C8×C113—21no—
166#11744751—21no—
167#11744751C2×D412yes—
168C22×C113—21no—
169C22×C113—21no—
170C22×C113—21no—
171C22×C113—41no—
172C22×C113—41no—
173C22×C113—41no—
174C22×C113C22×D411yescharacteristic
175C2×D113—21no—
176C2×D113—21no—
177C2×D113#13712yescomplemented
178C4×C113—21no—
179C4×C113—22no—
180C4×C113—41no—
181C4×C113—41no—
182C4×C113C22×D411yescharacteristic
183C4×C113H(5,𝔽2)11yescharacteristic
184Dic113—22no—
185Dic113—21no—
186Dic113—21no—
187Dic113—21no—
188Dic113—41no—
189Dic113—41no—
190Dic113—41no—
191C2×C113—41no—
192C2×C113—81no—
193C2×C113D4211yescharacteristic
194C2×C113C2×#13711yescharacteristic
195C2×C113#57811yescharacteristic
196D113—22no—
197#3270—1131nomaximal, Sylow
198C113#327011yescharacteristic, complemented, Sylow
199C2×#137—1131no—
200C22×Q16—1131no—
201D4×Q8—1131no—
202#548—1131no—
203#497—1131no—
204#470—1131no—
205#465—1131no—
206#464—1131no—
207#462—1131no—
208#452D11311yescharacteristic, complemented
209#451—1131no—
210#451—1131no—
211#448—1131no—
212#441—1131no—
213#435—1131no—
214C2×#41C2×D11311yescharacteristic
215C22×Q8—1131no—
216C22×Q8—1131no—
217C22×Q8—1131no—
218#137—2264no—
219C2×Q16—1131no—
220C2×Q16—1131no—
221C2×Q16—1131no—
222C2×Q16—1131no—
223C2×Q16—1131no—
224C2×Q16—2264no—
225C2×Q16C2×D11311yescharacteristic
226C2×SD16—1131no—
227C2×SD16—1131no—
228C2×SD16C2×D11311yescharacteristic
229C2×M16—1131no—
230C22×C8—1131no—
231C4⋊Q8—1131no—
232C4⋊Q8—2261no—
233#124—1131no—
234#124—2261no—
235C22⋊Q8—1131no—
236C22⋊Q8—1131no—
237C22⋊Q8—2261no—
238C22⋊Q8—2261no—
239C22⋊Q8—2261no—
240C22⋊Q8C2×D11311yescharacteristic
241#121—1131no—
242#121—2261no—
243C4×Q8—1131no—
244C4×Q8—1131no—
245C4×D4—1131no—
246C4×D4—2261no—
247C4×D4—2261no—
248#106—1131no—
249C4⋊C8—1131no—
250#103—1131no—
251#103—1131no—
252#103—1131no—
253#103—1131no—
254#103C2×D11311yescharacteristic
255#102C2×D11311yescharacteristic
256C22⋊C8—1131no—
257C22⋊C8C2×D11311yescharacteristic
258#97—1131no—
259#41—22no—
260#41—41no—
261C2×Q8—1131no—
262C2×Q8—1131no—
263C2×Q8—1131no—
264C2×Q8—4521no—
265C2×Q8—4521no—
266C2×Q8—4521no—
267C2×Q8—2261no—
268C2×Q8—2261no—
269C2×Q8—2262no—
270C2×Q8—2262no—
271C2×Q8—2262no—
272C2×Q8—2261no—
273C2×Q8C22×D11311yescharacteristic
274C2×Q8C22×D11311yescharacteristic
275C2×D4—21no—
276C2×D4—1131no—
277C2×D4—2261no—
278C2×D4C22×D11311yescharacteristic
279C22×C4—21no—
280C22×C4—1131no—
281C22×C4—2261no—
282C22×C4—2261no—
283C22×C4—2261no—
284C22×C4C22×D11311yescharacteristic
285Q16—22no—
286Q16—1134no—
287Q16—4521no—
288Q16—2262no—
289Q16—2262no—
290Q16—2262no—
291SD16—41no—
292SD16—2262no—
293SD16—2262no—
294M16—2262no—
295C2×C8—1131no—
296C2×C8—1131no—
297C2×C8—2262no—
298C2×C8C22×D11311yescharacteristic
299C2×C8C22×D11311yescharacteristic
300C4⋊C4—21no—
301C4⋊C4—1131no—
302C4⋊C4—1131no—
303C4⋊C4—2261no—
304C4⋊C4—2261no—
305C4⋊C4—2261no—
306C4⋊C4—2261no—
307C4⋊C4—2261no—
308C4⋊C4—2261no—
309C4⋊C4C22×D11311yescharacteristic
310C22⋊C4—21no—
311C22⋊C4—1131no—
312C22⋊C4—1131no—
313C22⋊C4—2261no—
314C22⋊C4—2261no—
315C22⋊C4—2261no—
316C22⋊C4—2261no—
317C22⋊C4—2261no—
318C42—1131no—
319C42—2261no—
320C42—2261no—
321C23—21no—
322C23—1131no—
323C23D4×D11311yescharacteristic
324Q8—21no—
325Q8—21no—
326Q8—21no—
327Q8—1132no—
328Q8—4522no—
329Q8—4522no—
330Q8—4522no—
331Q8—2261no—
332Q8—2261no—
333Q8—2261no—
334Q8—2261no—
335Q8—2261no—
336Q8D4×D11312yes—
337D4—21no—
338D4—21no—
339D4—42no—
340D4—4522no—
341D4—2262no—
342C2×C4—21no—
343C2×C4—21no—
344C2×C4—21no—
345C2×C4—21no—
346C2×C4—21no—
347C2×C4—42no—
348C2×C4—1131no—
349C2×C4—1131no—
350C2×C4—1131no—
351C2×C4—4522no—
352C2×C4—4522no—
353C2×C4—4522no—
354C2×C4—2261no—
355C2×C4—2261no—
356C2×C4—2261no—
357C2×C4—2261no—
358C2×C4—2261no—
359C2×C4—2261no—
360C2×C4D4×D11311yescharacteristic
361C2×C4C23×D11311yescharacteristic
362C8—21no—
363C8—21no—
364C8—1132no—
365C8—2261no—
366C22—21no—
367C22—21no—
368C22—21no—
369C22—41no—
370C22—41no—
371C22—41no—
372C22—1132no—
373C22—2261no—
374C22—2261no—
375C22C2×D4×D11311yescharacteristic
376C4—21no—
377C4—22no—
378C4—41no—
379C4—41no—
380C4—4521no—
381C4—4521no—
382C4—4521no—
383C4—2261no—
384C4—2261no—
385C4—2261no—
386C4—2262no—
387C4C2×D4×D11311yescharacteristic
388C4#1681366711yescharacteristic
389C2—41no—
390C2—81no—
391C2—2262no—
392C2#2029923011yescharacteristic
393C2#137×D11311yescharacteristic
394C2#2029941211yescharacteristic
subgroupG/H
centerC22C2×D4×D113
commutator, cosocleC2×C4×C113C24
FrattiniC2×C4C23×D113
Fitting#452×C113C2
socleC22×C113C22×D4
prime radical#20299255C2
hypercenter#452D113
hypocenterC113#3270
LCSG ▷ C2×C4×C113 ▷ C2×C113 ▷ C113
UCSC1 ◁ C22 ◁ C22×C4 ◁ #452

Complements

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

NH ≅ G/Ntype
1. C2×#16813652C2semidirect
2. C2×Q16×D113C2semidirect
3. #20299261C2semidirect
5. #20298989C2semidirect
6. #20298854C2semidirect
7. #20298826C2semidirect
8. #20298819C2semidirect
9. #20298806C2semidirect
10. #20298756C2semidirect
11. #20298755C2semidirect
12. #20298735C2semidirect
13. #20298702C2semidirect
14. #20298672C2semidirect
15. #452×C113C2semidirect
83. #14268637D4semidirect
177. C2×D113#137semidirect
198. C113#3270semidirect
208. #452D113semidirect

Maximal subgroups

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

subgroupindex
C2×#168136522
C2×Q16×D1132
#202992612
#202992552
#202989892
#202988542
#202988262
#202988192
#202988062
#202987562
#202987552
#202987352
#202987022
#202986722
#452×C1132
#3270113