Finite Group Databasebeta

← #14739431

Subgroups — #14739431

Order 2816.

666 conjugacy classes of subgroups.

The subgroup lattice has 388 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13079554C211yesmaximal, characteristic
2C2×#10622640C211yesmaximal, characteristic
3#13077701C211yesmaximal, characteristic, complemented
4#13068158C214yesmaximal, complemented
5#13068090C214yesmaximal, complemented
6#13067392C211yesmaximal, characteristic, complemented
7#13067285C211yesmaximal, characteristic
8#13067273C211yesmaximal, characteristic, complemented
9C11×#3078C211yesmaximal, characteristic, complemented
10C11×#533C2211yescharacteristic
11C2×C4×Q8×C11C2211yescharacteristic
12C22×#4325—21no—
13C2×#66927C2211yescharacteristic
14C11×#479—22no—
15C11×#477C2212yescomplemented
16C11×#475C2212yescomplemented
17C11×#428—21no—
18C11×#423C2211yescharacteristic
19C11×#419—21no—
20#10622701C2212yes—
21#10622698C2212yes—
22#10622659—22no—
23#10622640—22no—
24#10622640—22no—
25#10622640C2214yes—
26#10622637—22no—
27#10622637C2214yescomplemented
28C2×#66873—21no—
29#10622539—22no—
30#10622538C2211yescharacteristic
31#10622538C2211yescharacteristic
32C2×C4⋊(C11⋊C8)C2211yescharacteristic
33#10622185C2212yescomplemented
34#10622184C2212yescomplemented
35#10622123C2214yes—
36#10622117C2214yescomplemented
37C22×Q8×C11D411yescharacteristic
38C22×D44—21no—
39C22×D44—21no—
40C22×D44—21no—
41C2×C11×M16—21no—
42C11×C4⋊Q8C2311yescharacteristic
43C11×C4⋊Q8C2311yescharacteristic
44C11×#125—21no—
45C11×C22⋊Q8—21no—
46C11×C22⋊Q8—21no—
47C4×Q8×C11—21no—
48C4×Q8×C11—21no—
49C4×Q8×C11—21no—
50C4×Q8×C11—21no—
51C4×Q8×C11D412yes—
52C4×Q8×C11C2312yes—
53C11×#117—21no—
54C2×C11×C4⋊C4—21no—
55C2×C11×C4⋊C4D411yescharacteristic
56C2×C42×C11—21no—
57C2×C42×C11C2311yescharacteristic
58C2×#4325—24no—
59C2×#4325—24no—
60C2×#4325—44no—
61C22×C11⋊C8—21no—
62#66927—21no—
63#66927—21no—
64#66927—21no—
65#66927C2312yes—
66C11×#107—22no—
67C11×#106—22no—
68C11×C4⋊C8—21no—
69C11×C4⋊C8C2312yes—
70C11×#103—22no—
71C11×#103—22no—
72C22⋊(C11⋊C8)—21no—
73C22⋊(C11⋊C8)D412yes—
74#66873—24no—
75#66873—24no—
76C4⋊(C11⋊C8)—21no—
77C4⋊(C11⋊C8)—24no—
78C4⋊(C11⋊C8)D412yes—
79C4⋊(C11⋊C8)C2312yes—
80C4⋊(C11⋊C8)C2312yes—
81#66867—24no—
82C4×C11⋊C8—21no—
83C4×C11⋊C8C2312yes—
84#19432—111nomaximal, Sylow
85C23×D11—41no—
86C2×Q8×C11—21no—
87C2×Q8×C11—22no—
88C2×Q8×C11—22no—
89C2×Q8×C11—21no—
90C2×Q8×C11—21no—
91C2×Q8×C11C2×D412yes—
92C22×C4×C11—21no—
93C22×C4×C11—21no—
94C22×C4×C11C2×D411yescharacteristic
95C22×C4×C11C2×D411yescharacteristic
96C22×C4×C11#4111yescharacteristic
97C2×D44—22no—
98C2×D44—22no—
99C2×D44—22no—
100C2×D44—41no—
101C2×D44—41no—
102C2×D44—41no—
103C2×D44—42no—
104C2×D44—42no—
105C2×D44—82no—
106C2×D44—82no—
107C11×M16—42no—
108C2×C8×C11—22no—
109C11×C4⋊C4—22no—
110C11×C4⋊C4—21no—
111C11×C4⋊C4—22no—
112C11×C4⋊C4—21no—
113C11×C4⋊C4—21no—
114C11×C4⋊C4—21no—
115C11×C4⋊C4—21no—
116C11×C4⋊C4—41no—
117C11×C4⋊C4—41no—
118C11×C4⋊C4C2×D412yes—
119C11×C22⋊C4—41no—
120C42×C11—22no—
121C42×C11—22no—
122C42×C11—41no—
123C42×C11C2×D411yescharacteristic
124C42×C11C2×D411yescharacteristic
125C42×C11#4111yescharacteristic
126C42×C11C2411yescharacteristic
127#4325—48no—
128#4325—84no—
129C2×C11⋊C8—22no—
130C2×C11⋊C8—22no—
131C2×C11⋊C8—42no—
132C2×C11⋊C8C2×D414yes—
133#3208—111no—
134#3078D1111yescharacteristic, complemented
135C2×#460—111no—
136#2983—111no—
137#1698—114no—
138#1686—114no—
139#1571—111no—
140#1545—111no—
141#1542—111no—
142C23×C11#12111yescharacteristic
143C22×D11—42no—
144C22×D11—82no—
145C22×D11—82no—
146C22×D11—82no—
147Q8×C11—22no—
148Q8×C11—22no—
149Q8×C11—42no—
150Q8×C11—42no—
151Q8×C11—81no—
152C2×C4×C11—22no—
153C2×C4×C11—22no—
154C2×C4×C11—22no—
155C2×C4×C11—41no—
156C2×C4×C11—42no—
157C2×C4×C11—41no—
158C2×C4×C11—41no—
159C2×C4×C11—81no—
160C2×C4×C11#12111yescharacteristic
161C2×C4×C11#12111yescharacteristic
162C2×C4×C11#12111yescharacteristic
163C2×C4×C11AGL(1,ℤ/8)12yes—
164C2×C4×C11#13712yes—
165C2×C4×C11C22×D411yescharacteristic
166C2×C4×C11C22×D411yescharacteristic
167C2×C4×C11C2×#4111yescharacteristic
168D44—42no—
169D44—42no—
170D44—44no—
171D44—82no—
172D44—82no—
173D44—82no—
174D44—82no—
175C8×C11—42no—
176C11⋊C8—24no—
177C11⋊C8—42no—
178C11⋊C8—42no—
179C22×SD16—221no—
180#533C2×D1111yescharacteristic
181C2×#127—111no—
182C2×C4×Q8C2×D1111yescharacteristic
183#492—112no—
184#486—112no—
185#479—22no—
186#477C2×D1112yescomplemented
187#475C2×D1112yescomplemented
188#460—114no—
189#460—222no—
190#460—222no—
191#450—222no—
192#446—114no—
193#446—222no—
194#432—222no—
195#431—111no—
196#431—111no—
197#428—21no—
198#423C2×D1111yescharacteristic
199C2×C4⋊C8—111no—
200#419—21no—
201C2×#102—221no—
202#335—114no—
203#333—112no—
204#332—112no—
205#331—114no—
206C22×C11—21no—
207C22×C11—21no—
208C22×C11#46812yes—
209C22×C11C2×#12111yescharacteristic
210C2×D11—82no—
211C2×D11—82no—
212C2×D11—82no—
213C2×D11—164no—
214C4×C11—21no—
215C4×C11—21no—
216C4×C11—21no—
217C4×C11—42no—
218C4×C11—42no—
219C4×C11—81no—
220C4×C11—81no—
221C4×C11#46812yes—
222C4×C11C2×AGL(1,ℤ/8)11yescharacteristic
223C4×C11C2×#13711yescharacteristic
224C4×C11#57712yes—
225C22×Q8C22⋊D1111yescharacteristic
226C22×D4—221no—
227C22×D4—221no—
228C22×D4—221no—
229C2×SD16—224no—
230C2×SD16—224no—
231C2×SD16—444no—
232C2×M16—21no—
233C22×C8—221no—
234C4⋊Q8C22×D1111yescharacteristic
235C4⋊Q8C22×D1111yescharacteristic
236#127—112no—
237#127—221no—
238#127—221no—
239#127—221no—
240#125—21no—
241C22⋊Q8—21no—
242C22⋊Q8—21no—
243C4×Q8—21no—
244C4×Q8—21no—
245C4×Q8—21no—
246C4×Q8—21no—
247C4×Q8C22⋊D1112yes—
248C4×Q8C22×D1112yes—
249#117—21no—
250C2×C4⋊C4—21no—
251C2×C4⋊C4C22⋊D1111yescharacteristic
252C2×C42—21no—
253C2×C42C22×D1111yescharacteristic
254#107—22no—
255#106—22no—
256C4⋊C8—21no—
257C4⋊C8—112no—
258C4⋊C8—112no—
259C4⋊C8—112no—
260C4⋊C8—224no—
261C4⋊C8—221no—
262C4⋊C8C22×D1112yes—
263#103—22no—
264#103—22no—
265#102—224no—
266#102—224no—
267C22⋊C8—112no—
268C22⋊C8—221no—
269#97—224no—
270C4×C8—112no—
271C4×C8—221no—
272C2×C11—22no—
273C2×C11#304311yescharacteristic
274C2×C11C2×#46811yescharacteristic
275C2×C11#306811yescharacteristic
276D11—162no—
277C24—441no—
278C2×Q8—21no—
279C2×Q8—22no—
280C2×Q8—22no—
281C2×Q8—21no—
282C2×Q8—21no—
283C2×Q8C2×C22⋊D1112yes—
284C2×D4—222no—
285C2×D4—222no—
286C2×D4—222no—
287C2×D4—441no—
288C2×D4—441no—
289C2×D4—441no—
290C2×D4—442no—
291C2×D4—442no—
292C2×D4—882no—
293C2×D4—882no—
294C22×C4—21no—
295C22×C4—21no—
296C22×C4D4×D1111yescharacteristic
297C22×C4#434111yescharacteristic
298C22×C4C2×C22⋊D1111yescharacteristic
299SD16—448no—
300SD16—884no—
301M16—42no—
302C2×C8—22no—
303C2×C8—114no—
304C2×C8—222no—
305C2×C8—222no—
306C2×C8—442no—
307C4⋊C4—22no—
308C4⋊C4—21no—
309C4⋊C4—22no—
310C4⋊C4—21no—
311C4⋊C4—21no—
312C4⋊C4—21no—
313C4⋊C4—21no—
314C4⋊C4—41no—
315C4⋊C4—41no—
316C4⋊C4C2×C22⋊D1112yes—
317C22⋊C4—41no—
318C42—22no—
319C42—22no—
320C42—41no—
321C42D4×D1111yescharacteristic
322C42#434111yescharacteristic
323C42C2×C22⋊D1111yescharacteristic
324C42C23×D1111yescharacteristic
325C11#1943211yescharacteristic, complemented, Sylow
326C23—442no—
327C23—882no—
328C23—882no—
329C23—882no—
330C23#6699211yescharacteristic
331Q8—22no—
332Q8—22no—
333Q8—42no—
334Q8—42no—
335Q8—81no—
336D4—444no—
337D4—442no—
338D4—442no—
339D4—882no—
340D4—882no—
341D4—882no—
342D4—882no—
343C2×C4—22no—
344C2×C4—22no—
345C2×C4—22no—
346C2×C4—41no—
347C2×C4—42no—
348C2×C4—41no—
349C2×C4—41no—
350C2×C4—81no—
351C2×C4#6699211yescharacteristic
352C2×C4#6699211yescharacteristic
353C2×C4#6699211yescharacteristic
354C2×C4#6699512yes—
355C2×C4#6700212yes—
356C2×C4C2×D4×D1111yescharacteristic
357C2×C4C2×#434111yescharacteristic
358C2×C4C22×C22⋊D1111yescharacteristic
359C8—42no—
360C8—224no—
361C8—442no—
362C8—442no—
363C22—21no—
364C22—21no—
365C22—882no—
366C22—882no—
367C22—882no—
368C22—1764no—
369C22#1062266212yes—
370C22C2×#6699211yescharacteristic
371C4—21no—
372C4—21no—
373C4—21no—
374C4—42no—
375C4—42no—
376C4—81no—
377C4—81no—
378C4#1062266212yes—
379C4#1062330912yes—
380C4C2×#6699511yescharacteristic
381C4C2×#6700211yescharacteristic
382C2—22no—
383C2—1762no—
384C2#1307813911yescharacteristic
385C2C2×#1062266211yescharacteristic
386C2#1307834611yescharacteristic
subgroupG/H
centerC22C2×#66992
commutator, cosocleC42×C11C24
FrattiniC42C23×D11
FittingC11×#3078C2
socleC22×C11C2×#121
prime radicalC2×#66927C22
hypercenter#3078D11
hypocenterC11#19432
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3078

Complements

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

NH ≅ G/Ntype
3. #13077701C2semidirect
4. #13068158C2semidirect
5. #13068090C2semidirect
6. #13067392C2semidirect
8. #13067273C2semidirect
9. C11×#3078C2semidirect
15. C11×#477C22semidirect
16. C11×#475C22semidirect
27. #10622637C22semidirect
33. #10622185C22semidirect
34. #10622184C22semidirect
36. #10622117C22semidirect
134. #3078D11semidirect
186. #477C2×D11semidirect
187. #475C2×D11semidirect
325. C11#19432semidirect

Maximal subgroups

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

subgroupindex
#130795542
C2×#106226402
#130777012
#130681582
#130680902
#130673922
#130672852
#130672732
C11×#30782
#1943211