Finite Group Databasebeta

← #28402137

Subgroups — #28402137

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×#16813651C211yesmaximal, characteristic, complemented
2C22×#14268637C211yesmaximal, characteristic, complemented
3Q8×C22⋊D113C211yesmaximal, characteristic, complemented
4#20299254C211yesmaximal, characteristic
5#20298989C211yesmaximal, characteristic, complemented
6#20298855C211yesmaximal, characteristic, complemented
7#20298825C211yesmaximal, characteristic, complemented
8#20298818C211yesmaximal, characteristic, complemented
9#20298807C211yesmaximal, characteristic, complemented
10#20298757C211yesmaximal, characteristic, complemented
11#20298756C211yesmaximal, characteristic, complemented
12#20298755C211yesmaximal, characteristic, complemented
13#20298702C211yesmaximal, characteristic, complemented
14#20298666C211yesmaximal, characteristic, complemented
15#448×C113C211yesmaximal, characteristic, complemented
16C2×#14268646C2211yescharacteristic
17C22×Dic226C2211yescharacteristic
18C2×Q8×D113C2211yescharacteristic
19#16813651—24no—
20C2×Dic452C2211yescharacteristic
21C2×Dic452C2211yescharacteristic
22C2×#14268637—24no—
23C2×#14268637C2211yescharacteristic
24C2×#14268637C2211yescharacteristic
25C2×#14268637C2211yescharacteristic
26C2×#14268637C2211yescharacteristic
27C2×#14268635C2211yescharacteristic
28C2×#14268630C2211yescharacteristic
29C22×#11744751C2211yescharacteristic
30#16813620—21no—
31#16813620C2211yescharacteristic
32#16813609C2211yescharacteristic
33#16813608—21no—
34#16813602C2211yescharacteristic
35#16813601—21no—
36#16813601C2211yescharacteristic
37#16813599—21no—
38#16813598—21no—
39#16813598C2211yescharacteristic
40#16813594—21no—
41Q8×Dic113C2211yescharacteristic
42#16813587C2211yescharacteristic
43D4×Dic113—21no—
44C4×C22⋊D113—21no—
45C4×C22⋊D113C2211yescharacteristic
46#16813553C2211yescharacteristic
47#16813551C2211yescharacteristic
48#16813547C2211yescharacteristic
49#16813547C2211yescharacteristic
50#16813545C2211yescharacteristic
51#16813543C2211yescharacteristic
52#16813534C2211yescharacteristic
53#16813532C2211yescharacteristic
54C22×Q8×C113C2211yescharacteristic
55C2×SD16×C113C2211yescharacteristic
56C2×SD16×C113C2211yescharacteristic
57#121×C113C2211yescharacteristic
58#103×C113C2211yescharacteristic
59#103×C113C2211yescharacteristic
60C22⋊C8×C113C2211yescharacteristic
61#14268646—22no—
62#14268646—41no—
63C2×Dic226—22no—
64C2×Dic226—21no—
65C2×Dic226—21no—
66C2×Dic226—41no—
67C2×Dic226C2311yescharacteristic
68C2×Dic226C2311yescharacteristic
69C2×Dic226C2311yescharacteristic
70Q8×D113—22no—
71Q8×D113—41no—
72C2×C22⋊D113—21no—
73C2×C22⋊D113D411yescharacteristic
74C22×Dic113—21no—
75C22×Dic113—21no—
76C2×C4×D113—21no—
77C2×C4×D113C2311yescharacteristic
78Dic452—22no—
79Dic452—41no—
80#14268637—22no—
81#14268637—22no—
82#14268637—22no—
83#14268637D414yescomplemented
84#14268635—22no—
85#14268630—22no—
86C2×#11744751—22no—
87C2×#11744751C2311yescharacteristic
88C2×#11744751C2311yescharacteristic
89C4⋊Dic113—21no—
90C4⋊Dic113—21no—
91C4⋊Dic113C2311yescharacteristic
92#14268626—21no—
93#14268626—21no—
94#14268626—21no—
95#14268626—21no—
96#14268626—21no—
97#14268626D411yescharacteristic
98C22⋊Dic113—21no—
99C22⋊Dic113—21no—
100C22⋊Dic113—21no—
101C22⋊Dic113D411yescharacteristic
102#14268624—21no—
103#14268624—21no—
104#14268624D411yescharacteristic
105C4×Dic113—21no—
106C4×Dic113—21no—
107C4×Dic113C2311yescharacteristic
108C2×Q8×C113—21no—
109C2×Q8×C113—22no—
110C2×Q8×C113—41no—
111C2×Q8×C113C2311yescharacteristic
112C2×Q8×C113C2311yescharacteristic
113C2×D4×C113—21no—
114C2×D4×C113C2311yescharacteristic
115C22×C4×C113—21no—
116C22×C4×C113C2311yescharacteristic
117SD16×C113—22no—
118SD16×C113—41no—
119C2×C8×C113C2311yescharacteristic
120C2×C8×C113C2311yescharacteristic
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×C113—42no—
130Q8×C113C2×D412yes—
131D4×C113—21no—
132D4×C113—21no—
133D4×C113—42no—
134C2×C4×C113—21no—
135C2×C4×C113—21no—
136C2×C4×C113—21no—
137C2×C4×C113—21no—
138C2×C4×C113—21no—
139C2×C4×C113—42no—
140C2×C4×C113C2×D411yescharacteristic
141C2×C4×C113C2411yescharacteristic
142C22⋊D113—22no—
143C22⋊D113—42no—
144C2×Dic113—21no—
145C2×Dic113—21no—
146C2×Dic113—21no—
147C2×Dic113—21no—
148C2×Dic113—42no—
149C2×Dic113—42no—
150C2×Dic113C2×D411yescharacteristic
151C2×Dic113C2×D411yescharacteristic
152C2×Dic113C2×D411yescharacteristic
153C4×D113—21no—
154C4×D113—21no—
155C4×D113—42no—
156Dic226—21no—
157Dic226—21no—
158Dic226—21no—
159Dic226—21no—
160Dic226—21no—
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—41no—
171C22×C113—41no—
172C22×C113—41no—
173C22×C113#13712yescomplemented
174C22×C113C22×D411yescharacteristic
175C2×D113—21no—
176C2×D113—21no—
177C2×D113—21no—
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—22no—
192C2×C113—81no—
193C2×C113D4211yescharacteristic
194C2×C113C2×#13711yescharacteristic
195C2×C113#57811yescharacteristic
196D113—41no—
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#452—1131no—
209#451—1131no—
210#451—1131no—
211#448D11311yescharacteristic, complemented
212#441—1131no—
213#435—1131no—
214C2×#41—1131no—
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×SD16C2×D11311yescharacteristic
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—1131no—
238C22⋊Q8—2261no—
239C22⋊Q8—2261no—
240C22⋊Q8—2261no—
241#121—2261no—
242#121C2×D11311yescharacteristic
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#103C2×D11311yescharacteristic
254#103C2×D11311yescharacteristic
255#102—1131no—
256C22⋊C8—1131no—
257C22⋊C8C2×D11311yescharacteristic
258#97—1131no—
259#41—4521no—
260#41—2262no—
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—2261no—
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—1134no—
286Q16—4521no—
287Q16—2262no—
288Q16—2262no—
289Q16—2262no—
290Q16—2262no—
291SD16—22no—
292SD16—41no—
293SD16—2262no—
294M16—2262no—
295C2×C8—1131no—
296C2×C8—1131no—
297C2×C8—2262no—
298C2×C8C22×D11311yescharacteristic
299C2×C8C22×D11311yescharacteristic
300C4⋊C4—1131no—
301C4⋊C4—1131no—
302C4⋊C4—2261no—
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—42no—
328Q8—1132no—
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—41no—
369C22—41no—
370C22—41no—
371C22—2261no—
372C22—2261no—
373C22—2261no—
374C22#1681365112yescomplemented
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—22no—
390C2—81no—
391C2—4521no—
392C2#2029923011yescharacteristic
393C2C2×#1681365111yescharacteristic
394C2#2029941411yescharacteristic
subgroupG/H
centerC22C2×D4×D113
commutator, cosocleC2×C4×C113C24
FrattiniC2×C4C23×D113
Fitting#448×C113C2
socleC22×C113C22×D4
prime radical#20299254C2
hypercenter#448D113
hypocenterC113#3270
LCSG ▷ C2×C4×C113 ▷ C2×C113 ▷ C113
UCSC1 ◁ C22 ◁ C22×C4 ◁ #448

Complements

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

NH ≅ G/Ntype
1. C2×#16813651C2semidirect
2. C22×#14268637C2semidirect
3. Q8×C22⋊D113C2semidirect
5. #20298989C2semidirect
6. #20298855C2semidirect
7. #20298825C2semidirect
8. #20298818C2semidirect
9. #20298807C2semidirect
10. #20298757C2semidirect
11. #20298756C2semidirect
12. #20298755C2semidirect
13. #20298702C2semidirect
14. #20298666C2semidirect
15. #448×C113C2semidirect
83. #14268637D4semidirect
173. C22×C113#137semidirect
198. C113#3270semidirect
211. #448D113semidirect
374. C22#16813651semidirect

Maximal subgroups

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

subgroupindex
C2×#168136512
C22×#142686372
Q8×C22⋊D1132
#202992542
#202989892
#202988552
#202988252
#202988182
#202988072
#202987572
#202987562
#202987552
#202987022
#202986662
#448×C1132
#3270113