Finite Group Databasebeta

← #28402140

Subgroups — #28402140

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
2C22×#14268637C211yesmaximal, characteristic, complemented
3D4×Dic226C211yesmaximal, characteristic, complemented
4#20298993C211yesmaximal, characteristic, complemented
5#20298854C211yesmaximal, characteristic, complemented
6#20298825C211yesmaximal, characteristic, complemented
7#20298817C211yesmaximal, characteristic, complemented
8#20298808C211yesmaximal, characteristic, complemented
9#20298760C211yesmaximal, characteristic, complemented
10#20298754C211yesmaximal, characteristic, complemented
11#20298753C211yesmaximal, characteristic, complemented
12#20298736C211yesmaximal, characteristic, complemented
13#20298703C211yesmaximal, characteristic, complemented
14#20298670C211yesmaximal, characteristic, complemented
15#548×C113C211yesmaximal, characteristic
16C22×Dic226C2211yescharacteristic
17C22×Dic226C2211yescharacteristic
18#16813652—24no—
19C2×#14268637—24no—
20C2×#14268637C2211yescharacteristic
21C2×#14268637C2211yescharacteristic
22C2×#14268637C2211yescharacteristic
23C2×#14268637C2211yescharacteristic
24C2×#14268637C2211yescharacteristic
25C2×#14268637C2211yescharacteristic
26C2×#14268635C2211yescharacteristic
27C2×#14268635C2211yescharacteristic
28C2×#14268635C2211yescharacteristic
29C2×#14268631C2211yescharacteristic
30C22×#11744751C2211yescharacteristic
31#16813622C2211yescharacteristic
32#16813621—21no—
33#16813601C2211yescharacteristic
34#16813601C2211yescharacteristic
35#16813599—21no—
36#16813599—21no—
37C4×Dic226C2211yescharacteristic
38D4×Dic113—21no—
39#16813553C2211yescharacteristic
40C4⋊#11744751C2211yescharacteristic
41#16813546C2211yescharacteristic
42#16813546C2211yescharacteristic
43#16813545C2211yescharacteristic
44#16813545C2211yescharacteristic
45#16813545C2211yescharacteristic
46#16813543C2211yescharacteristic
47C22⋊#11744751C2211yescharacteristic
48C22⋊#11744751C2211yescharacteristic
49#16813533C2211yescharacteristic
50C2×#41×C113C2211yescharacteristic
51C22×Q8×C113C2211yescharacteristic
52#124×C113—21no—
53#124×C113C2211yescharacteristic
54C22⋊Q8×C113—21no—
55C22⋊Q8×C113C2211yescharacteristic
56#121×C113—21no—
57#121×C113C2211yescharacteristic
58C4×Q8×C113C2211yescharacteristic
59C4×D4×C113—21no—
60C4×D4×C113C2211yescharacteristic
61C2×Dic226—22no—
62C2×Dic226—22no—
63C2×Dic226—21no—
64C2×Dic226—21no—
65C2×Dic226—41no—
66C2×Dic226—41no—
67C2×Dic226C2311yescharacteristic
68C2×Dic226C2311yescharacteristic
69C2×Dic226C2311yescharacteristic
70C22×Dic113—21no—
71C22×Dic113—21no—
72#14268637—22no—
73#14268637—22no—
74#14268637—22no—
75#14268637—22no—
76#14268637—41no—
77#14268637D414yescomplemented
78#14268635—22no—
79#14268635—22no—
80#14268635—41no—
81#14268631—22no—
82C2×#11744751—22no—
83C2×#11744751C2311yescharacteristic
84C2×#11744751C2311yescharacteristic
85C2×#11744751C2311yescharacteristic
86C2×#11744751C2311yescharacteristic
87C4⋊Dic113—21no—
88C4⋊Dic113—21no—
89C4⋊Dic113C2311yescharacteristic
90#14268626—21no—
91#14268626—21no—
92#14268626—21no—
93C22⋊Dic113—21no—
94C22⋊Dic113—21no—
95C4×Dic113—21no—
96#41×C113—22no—
97#41×C113—41no—
98C2×Q8×C113—21no—
99C2×Q8×C113—22no—
100C2×Q8×C113—41no—
101C2×Q8×C113C2311yescharacteristic
102C2×Q8×C113C2311yescharacteristic
103C2×D4×C113—21no—
104C2×D4×C113—21no—
105C2×D4×C113D411yescharacteristic
106C2×D4×C113C2311yescharacteristic
107C22×C4×C113—21no—
108C22×C4×C113—21no—
109C22×C4×C113C2311yescharacteristic
110C22×C4×C113C2311yescharacteristic
111C4⋊C4×C113—21no—
112C4⋊C4×C113—21no—
113C4⋊C4×C113D411yescharacteristic
114C4⋊C4×C113C2311yescharacteristic
115C22⋊C4×C113—21no—
116C22⋊C4×C113—21no—
117C22⋊C4×C113—21no—
118C22⋊C4×C113—21no—
119C22⋊C4×C113D411yescharacteristic
120C22⋊C4×C113D411yescharacteristic
121C42×C113—21no—
122C42×C113C2311yescharacteristic
123C23×C113—21no—
124C23×C113C2×D411yescharacteristic
125C23×C113C2×D411yescharacteristic
126Q8×C113—21no—
127Q8×C113—21no—
128Q8×C113—21no—
129Q8×C113—42no—
130Q8×C113C2×D412yes—
131D4×C113—22no—
132D4×C113—21no—
133D4×C113—21no—
134D4×C113—42no—
135D4×C113—42no—
136C2×C4×C113—21no—
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×C113—42no—
145C2×C4×C113C2×D411yescharacteristic
146C2×C4×C113C2×D411yescharacteristic
147C2×C4×C113C2×D411yescharacteristic
148C2×C4×C113C2×D411yescharacteristic
149C2×C4×C113C2411yescharacteristic
150C2×Dic113—21no—
151C2×Dic113—21no—
152C2×Dic113—21no—
153C2×Dic113—21no—
154C2×Dic113—42no—
155C2×Dic113—42no—
156Dic226—21no—
157Dic226—21no—
158Dic226—21no—
159Dic226—21no—
160Dic226—21no—
161Dic226—42no—
162Dic226—42no—
163Dic226C2×D412yes—
164#11744751—21no—
165#11744751—21no—
166#11744751—21no—
167#11744751C2×D412yes—
168C22×C113—21no—
169C22×C113—21no—
170C22×C113—21no—
171C22×C113—21no—
172C22×C113—21no—
173C22×C113—41no—
174C22×C113—41no—
175C22×C113—41no—
176C22×C113#13712yescomplemented
177C22×C113C22×D411yescharacteristic
178C4×C113—21no—
179C4×C113—21no—
180C4×C113—22no—
181C4×C113—21no—
182C4×C113—21no—
183C4×C113—41no—
184C4×C113—41no—
185C4×C113C22×D411yescharacteristic
186C4×C113H(5,𝔽2)11yescharacteristic
187Dic113—22no—
188Dic113—41no—
189Dic113—41no—
190Dic113—41no—
191C2×C113—22no—
192C2×C113—41no—
193C2×C113—81no—
194C2×C113D4211yescharacteristic
195C2×C113C2×#13711yescharacteristic
196C2×C113#57811yescharacteristic
197#3270—1131nomaximal, Sylow
198C113#327011yescharacteristic, complemented, Sylow
199C2×#137—1131no—
200C22×Q16—1131no—
201D4×Q8—1131no—
202#548D11311yescharacteristic
203#497—1131no—
204#470—1131no—
205#465—1131no—
206#464—1131no—
207#462—1131no—
208#452—1131no—
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×Q8C2×D11311yescharacteristic
218#137—2264no—
219C2×Q16—1131no—
220C2×Q16—1131no—
221C2×Q16—1131no—
222C2×Q16—1131no—
223C2×Q16—1131no—
224C2×Q16—1131no—
225C2×Q16—2264no—
226C2×SD16—1131no—
227C2×SD16—1131no—
228C2×SD16—1131no—
229C2×M16—1131no—
230C22×C8—1131no—
231C4⋊Q8—1131no—
232C4⋊Q8—2261no—
233#124—21no—
234#124C2×D11311yescharacteristic
235C22⋊Q8—21no—
236C22⋊Q8—1131no—
237C22⋊Q8—1131no—
238C22⋊Q8—2261no—
239C22⋊Q8—2261no—
240C22⋊Q8C2×D11311yescharacteristic
241#121—21no—
242#121C2×D11311yescharacteristic
243C4×Q8—1131no—
244C4×Q8C2×D11311yescharacteristic
245C4×D4—21no—
246C4×D4—2261no—
247C4×D4C2×D11311yescharacteristic
248#106—1131no—
249C4⋊C8—1131no—
250#103—1131no—
251#103—1131no—
252#103—1131no—
253#103—1131no—
254#103—1131no—
255#102—1131no—
256C22⋊C8—1131no—
257C22⋊C8—1131no—
258#97—1131no—
259#41—22no—
260#41—41no—
261C2×Q8—21no—
262C2×Q8—22no—
263C2×Q8—41no—
264C2×Q8—1131no—
265C2×Q8—1131no—
266C2×Q8—1131no—
267C2×Q8—4521no—
268C2×Q8—4521no—
269C2×Q8—2262no—
270C2×Q8—2262no—
271C2×Q8—2261no—
272C2×Q8—2261no—
273C2×Q8C22×D11311yescharacteristic
274C2×Q8C22×D11311yescharacteristic
275C2×D4—21no—
276C2×D4—21no—
277C2×D4C22⋊D11311yescharacteristic
278C2×D4C22×D11311yescharacteristic
279C22×C4—21no—
280C22×C4—21no—
281C22×C4—2261no—
282C22×C4—2261no—
283C22×C4C22×D11311yescharacteristic
284C22×C4C22×D11311yescharacteristic
285Q16—1134no—
286Q16—4521no—
287Q16—2262no—
288Q16—2262no—
289Q16—2262no—
290Q16—2262no—
291SD16—4521no—
292SD16—2262no—
293SD16—2262no—
294M16—2262no—
295C2×C8—1131no—
296C2×C8—1131no—
297C2×C8—1131no—
298C2×C8—1131no—
299C2×C8—2262no—
300C4⋊C4—21no—
301C4⋊C4—21no—
302C4⋊C4—1131no—
303C4⋊C4—2261no—
304C4⋊C4—2261no—
305C4⋊C4—2261no—
306C4⋊C4—2261no—
307C4⋊C4—2261no—
308C4⋊C4C22⋊D11311yescharacteristic
309C4⋊C4C22×D11311yescharacteristic
310C22⋊C4—21no—
311C22⋊C4—21no—
312C22⋊C4—21no—
313C22⋊C4—21no—
314C22⋊C4—2261no—
315C22⋊C4—2261no—
316C22⋊C4C22⋊D11311yescharacteristic
317C22⋊C4C22⋊D11311yescharacteristic
318C42—21no—
319C42—2261no—
320C42C22×D11311yescharacteristic
321C23—21no—
322C23C2×C22⋊D11311yescharacteristic
323C23C2×C22⋊D11311yescharacteristic
324Q8—21no—
325Q8—21no—
326Q8—21no—
327Q8—42no—
328Q8—1132no—
329Q8—4522no—
330Q8—4522no—
331Q8—2261no—
332Q8—2261no—
333Q8—2261no—
334Q8—2261no—
335Q8—2261no—
336Q8D4×D11312yes—
337D4—22no—
338D4—21no—
339D4—21no—
340D4—42no—
341D4—42no—
342C2×C4—21no—
343C2×C4—21no—
344C2×C4—21no—
345C2×C4—21no—
346C2×C4—21no—
347C2×C4—21no—
348C2×C4—21no—
349C2×C4—42no—
350C2×C4—42no—
351C2×C4—4522no—
352C2×C4—4522no—
353C2×C4—2261no—
354C2×C4—2261no—
355C2×C4—2261no—
356C2×C4—2261no—
357C2×C4C2×C22⋊D11311yescharacteristic
358C2×C4C2×C22⋊D11311yescharacteristic
359C2×C4C2×C22⋊D11311yescharacteristic
360C2×C4C2×C22⋊D11311yescharacteristic
361C2×C4C23×D11311yescharacteristic
362C8—1132no—
363C8—2261no—
364C8—2261no—
365C8—2261no—
366C22—21no—
367C22—21no—
368C22—21no—
369C22—21no—
370C22—21no—
371C22—41no—
372C22—41no—
373C22—41no—
374C22#1681365212yescomplemented
375C22C22×C22⋊D11311yescharacteristic
376C4—21no—
377C4—21no—
378C4—21no—
379C4—21no—
380C4—22no—
381C4—41no—
382C4—41no—
383C4—4521no—
384C4—4521no—
385C4—4521no—
386C4—2262no—
387C4C2×D4×D11311yescharacteristic
388C4#1681366711yescharacteristic
389C2—22no—
390C2—41no—
391C2—81no—
392C2D4×C22⋊D11311yescharacteristic
393C2C2×#1681365211yescharacteristic
394C2#2029941311yescharacteristic
subgroupG/H
centerC22C22×C22⋊D113
commutator, cosocleC2×C4×C113C24
FrattiniC2×C4C23×D113
Fitting, prime radical#548×C113C2
socleC22×C113C22×D4
hypercenter#548D113
hypocenterC113#3270
LCSG ▷ C2×C4×C113 ▷ C2×C113 ▷ C113
UCSC1 ◁ C22 ◁ C4×D4 ◁ #548

Complements

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

NH ≅ G/Ntype
1. C2×#16813652C2semidirect
2. C22×#14268637C2semidirect
3. D4×Dic226C2semidirect
4. #20298993C2semidirect
5. #20298854C2semidirect
6. #20298825C2semidirect
7. #20298817C2semidirect
8. #20298808C2semidirect
9. #20298760C2semidirect
10. #20298754C2semidirect
11. #20298753C2semidirect
12. #20298736C2semidirect
13. #20298703C2semidirect
14. #20298670C2semidirect
77. #14268637D4semidirect
176. C22×C113#137semidirect
198. C113#3270semidirect
374. C22#16813652semidirect

Maximal subgroups

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

subgroupindex
C2×#168136522
C22×#142686372
D4×Dic2262
#202989932
#202988542
#202988252
#202988172
#202988082
#202987602
#202987542
#202987532
#202987362
#202987032
#202986702
#548×C1132
#3270113