Finite Group Databasebeta

← #14736936

Subgroups — #14736936

Order 2816.

650 conjugacy classes of subgroups.

The subgroup lattice has 398 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13079744C211yesmaximal, characteristic
2#13079737C211yesmaximal, characteristic
3#13077329C211yesmaximal, characteristic
4#13068188C214yesmaximal, complemented
5#13068064C214yesmaximal, complemented
6#13067364C211yesmaximal, characteristic, complemented
7#13067297C211yesmaximal, characteristic, complemented
8#13067288C211yesmaximal, characteristic, complemented
9C2×C11×#487C211yesmaximal, characteristic, complemented
10C2×C11×C4⋊Q8C2211yescharacteristic
11C2×C11×C4⋊Q8C2211yescharacteristic
12C2×#66954—21no—
13#10623008C2211yescharacteristic
14C11×#487—21no—
15C11×#487—21no—
16C11×#487C2212yes—
17C11×#487C2212yes—
18C2×C11×#103—21no—
19C2×C11×#103—21no—
20C2×C4×C8×C11C2211yescharacteristic
21#10622723—21no—
22#10622701—21no—
23#10622701—21no—
24#10622700C2214yes—
25#10622697C2214yes—
26#10622692—21no—
27#10622691—21no—
28#10622581—22no—
29#10622580—22no—
30#10622538C2211yescharacteristic
31#10622538C2211yescharacteristic
32#10622537C2211yescharacteristic
33#10622301—21no—
34#10622301C2212yes—
35C8×D44—21no—
36C8×D44C2212yes—
37#10622185C2214yes—
38#10622184C2214yes—
39#10622096C2212yes—
40#10622095C2212yes—
41C22×Q8×C11—21no—
42C22×Q8×C11—21no—
43C2×#4339—21no—
44C22×C8×C11D411yescharacteristic
45C22×C8×C11D411yescharacteristic
46C11×C4⋊Q8—21no—
47C11×C4⋊Q8—21no—
48C11×C4⋊Q8—21no—
49C11×C4⋊Q8—21no—
50C11×C4⋊Q8—21no—
51C11×C4⋊Q8—21no—
52C11×C4⋊Q8C2312yes—
53C11×C4⋊Q8C2312yes—
54C2×C11×C4⋊C4—21no—
55C2×C11×C4⋊C4—21no—
56C2×C11×C4⋊C4—21no—
57C2×C11×C4⋊C4—21no—
58C2×C42×C11C2311yescharacteristic
59#66983—21no—
60#66983D412yes—
61C2×#4318—21no—
62#66954—44no—
63C2×#4313—22no—
64C2×C8×D11—22no—
65#66928—21no—
66#66927D411yescharacteristic
67C4×D44—21no—
68C4×D44C2312yes—
69#66922D411yescharacteristic
70C11×#103—22no—
71C11×#103—22no—
72C11×#103—22no—
73C11×#103—22no—
74C4×C8×C11D411yescharacteristic
75C4×C8×C11D411yescharacteristic
76C4×C8×C11C2311yescharacteristic
77C4×C8×C11C2311yescharacteristic
78C22⋊(C11⋊C8)—21no—
79C22⋊(C11⋊C8)—21no—
80(C2×D11)⋊C8—22no—
81(C2×D11)⋊C8—22no—
82#66873—24no—
83#66873—24no—
84#66872—24no—
85#66871—24no—
86C4⋊(C11⋊C8)—21no—
87C4⋊(C11⋊C8)C2312yes—
88C4⋊(C11⋊C8)C2312yes—
89C4⋊(C11⋊C8)C2312yes—
90C4×C11⋊C8—21no—
91C4×C11⋊C8—21no—
92#19199—111nomaximal, Sylow
93C2×Q8×C11—22no—
94C2×Q8×C11—22no—
95C2×Q8×C11—41no—
96C2×Q8×C11—41no—
97C2×Q8×C11—42no—
98C2×Q8×C11—42no—
99C2×Q8×C11—82no—
100C22×C4×C11—41no—
101C22×C4×C11—41no—
102C22×C4×C11C2×D411yescharacteristic
103C22×C4×C11C2×D411yescharacteristic
104C22×C4×C11#4111yescharacteristic
105C2×C22⋊D11—22no—
106#4339—42no—
107#4339—42no—
108C2×D44—21no—
109C2×D44—21no—
110C2×D44C2×D412yes—
111C2×C4×D11—22no—
112C2×Dic22—21no—
113C2×C8×C11—22no—
114C2×C8×C11—22no—
115C2×C8×C11C2×D411yescharacteristic
116C2×C8×C11C2×D411yescharacteristic
117C2×C8×C11C2×D411yescharacteristic
118C2×C8×C11C2×D411yescharacteristic
119C11×C4⋊C4—22no—
120C11×C4⋊C4—22no—
121C11×C4⋊C4—22no—
122C11×C4⋊C4—22no—
123C11×C4⋊C4—41no—
124C11×C4⋊C4—41no—
125C11×C4⋊C4—41no—
126C11×C4⋊C4—41no—
127C42×C11C2×D411yescharacteristic
128C42×C11C2×D411yescharacteristic
129C42×C11#4111yescharacteristic
130C42×C11C2411yescharacteristic
131(C2×D11)⋊C4—22no—
132(C2×D11)⋊C4—22no—
133C4⋊Dic11—21no—
134C4⋊Dic11C2×D412yes—
135#4318—42no—
136C2×C11⋊C8—22no—
137C2×C11⋊C8—22no—
138C2×C11⋊C8—22no—
139#4313—44no—
140C8×D11—44no—
141#3227—111no—
142#3226—111no—
143C2×#487D1111yescharacteristic, complemented
144#2931—111no—
145#1703—114no—
146#1683—114no—
147#1564—111no—
148#1548—111no—
149#1546—111no—
150C23×C11#12111yescharacteristic
151C22×D11—22no—
152Q8×C11—42no—
153Q8×C11—42no—
154Q8×C11—82no—
155Q8×C11—82no—
156Q8×C11—82no—
157C2×C4×C11—22no—
158C2×C4×C11—22no—
159C2×C4×C11—42no—
160C2×C4×C11—42no—
161C2×C4×C11—82no—
162C2×C4×C11—82no—
163C2×C4×C11#12111yescharacteristic
164C2×C4×C11#12111yescharacteristic
165C2×C4×C11#12111yescharacteristic
166C2×C4×C11#13512yes—
167C2×C4×C11AGL(1,ℤ/8)12yes—
168C2×C4×C11C22×D411yescharacteristic
169C2×C4×C11C22×D411yescharacteristic
170C2×C4×C11C2×#4111yescharacteristic
171C22⋊D11—44no—
172C2×Dic11—22no—
173D44—24no—
174D44—42no—
175D44—42no—
176C4×D11—42no—
177C4×D11—42no—
178Dic22—42no—
179C8×C11—21no—
180C8×C11—21no—
181C8×C11—21no—
182C8×C11—21no—
183C11⋊C8—42no—
184C11⋊C8—42no—
185C11⋊C8—42no—
186C2×#131—221no—
187#532—111no—
188C2×C4⋊Q8C2×D1111yescharacteristic
189C2×C4⋊Q8C2×D1111yescharacteristic
190#500—221no—
191#498—221no—
192#487—21no—
193#487—21no—
194#487C2×D1112yes—
195#487C2×D1112yes—
196#486—221no—
197#486—221no—
198#481—222no—
199#480—222no—
200#476—114no—
201#474—114no—
202#436—112no—
203#436—221no—
204C8×D4—112no—
205C8×D4—221no—
206#431—111no—
207#431—111no—
208#423—111no—
209C2×#103—21no—
210C2×#103—21no—
211#408—221no—
212C2×C4×C8C2×D1111yescharacteristic
213#335—112no—
214#334—112no—
215#333—114no—
216#332—114no—
217C22×C11—21no—
218C22×C11—21no—
219C22×C11#46312yes—
220C22×C11C2×#12111yescharacteristic
221C2×D11—42no—
222C2×D11—42no—
223C2×D11—42no—
224C4×C11—21no—
225C4×C11—21no—
226C4×C11—82no—
227C4×C11—82no—
228C4×C11#46312yes—
229C4×C11#47112yes—
230C4×C11C2×#13511yescharacteristic
231C4×C11C2×AGL(1,ℤ/8)11yescharacteristic
232C4×C11#57812yes—
233Dic11—42no—
234C2×#41—221no—
235C22×Q8—21no—
236C22×Q8—21no—
237#131—444no—
238C2×M16—221no—
239C2×M16—222no—
240C22×C8—222no—
241C22×C8C22⋊D1111yescharacteristic
242C22×C8C22⋊D1111yescharacteristic
243C4⋊Q8—21no—
244C4⋊Q8—21no—
245C4⋊Q8—21no—
246C4⋊Q8—21no—
247C4⋊Q8—21no—
248C4⋊Q8—21no—
249C4⋊Q8—111no—
250C4⋊Q8C22×D1112yes—
251C4⋊Q8C22×D1112yes—
252#127—111no—
253#124—221no—
254#121—112no—
255#121—221no—
256C4×D4—112no—
257C4×D4—221no—
258C2×C4⋊C4—21no—
259C2×C4⋊C4—21no—
260C2×C4⋊C4—21no—
261C2×C4⋊C4—21no—
262C2×C42C22×D1111yescharacteristic
263#107—224no—
264#106—224no—
265C4⋊C8—112no—
266C4⋊C8—112no—
267C4⋊C8—112no—
268C4⋊C8—221no—
269#103—22no—
270#103—22no—
271#103—22no—
272#103—22no—
273#102—224no—
274#102—224no—
275C22⋊C8—221no—
276C22⋊C8—221no—
277C22⋊C8—222no—
278C22⋊C8—222no—
279C4×C8—221no—
280C4×C8—221no—
281C4×C8C22⋊D1111yescharacteristic
282C4×C8C22⋊D1111yescharacteristic
283C4×C8C22×D1111yescharacteristic
284C4×C8C22×D1111yescharacteristic
285C2×C11—22no—
286C2×C11C2×#46311yescharacteristic
287C2×C11#305911yescharacteristic
288C2×C11C2×#47111yescharacteristic
289D11—82no—
290#41—442no—
291#41—442no—
292C2×Q8—22no—
293C2×Q8—22no—
294C2×Q8—41no—
295C2×Q8—41no—
296C2×Q8—42no—
297C2×Q8—42no—
298C2×Q8—82no—
299C2×Q8—221no—
300C2×D4—112no—
301C2×D4—222no—
302C2×D4—221no—
303C2×D4—221no—
304C22×C4—41no—
305C22×C4—41no—
306C22×C4—222no—
307C22×C4D4×D1111yescharacteristic
308C22×C4#434111yescharacteristic
309C22×C4C2×C22⋊D1111yescharacteristic
310M16—444no—
311M16—442no—
312C2×C8—22no—
313C2×C8—22no—
314C2×C8—222no—
315C2×C8—222no—
316C2×C8—222no—
317C2×C8—444no—
318C2×C8C2×C22⋊D1111yescharacteristic
319C2×C8C2×C22⋊D1111yescharacteristic
320C2×C8C2×C22⋊D1111yescharacteristic
321C2×C8C2×C22⋊D1111yescharacteristic
322C4⋊C4—22no—
323C4⋊C4—22no—
324C4⋊C4—22no—
325C4⋊C4—22no—
326C4⋊C4—41no—
327C4⋊C4—41no—
328C4⋊C4—41no—
329C4⋊C4—41no—
330C4⋊C4—112no—
331C4⋊C4—221no—
332C22⋊C4—222no—
333C22⋊C4—222no—
334C42D4×D1111yescharacteristic
335C42#434111yescharacteristic
336C42C2×C22⋊D1111yescharacteristic
337C42C23×D1111yescharacteristic
338C11#1919911yescharacteristic, complemented, Sylow
339C23—222no—
340C23#6699111yescharacteristic
341Q8—42no—
342Q8—42no—
343Q8—82no—
344Q8—82no—
345Q8—82no—
346Q8—442no—
347D4—224no—
348D4—444no—
349D4—442no—
350D4—442no—
351C2×C4—22no—
352C2×C4—22no—
353C2×C4—42no—
354C2×C4—42no—
355C2×C4—82no—
356C2×C4—82no—
357C2×C4—222no—
358C2×C4—442no—
359C2×C4—442no—
360C2×C4#6699111yescharacteristic
361C2×C4#6699111yescharacteristic
362C2×C4#6699111yescharacteristic
363C2×C4#6700212yes—
364C2×C4#6700312yes—
365C2×C4C2×D4×D1111yescharacteristic
366C2×C4C2×#434111yescharacteristic
367C2×C4C22×C22⋊D1111yescharacteristic
368C8—21no—
369C8—21no—
370C8—21no—
371C8—21no—
372C8—442no—
373C8—442no—
374C8—442no—
375C22—21no—
376C22—21no—
377C22—442no—
378C22—442no—
379C22—442no—
380C22#1062267012yes—
381C22C2×#6699111yescharacteristic
382C4—21no—
383C4—21no—
384C4—82no—
385C4—82no—
386C4—442no—
387C4#1062267012yes—
388C4#1062279012yes—
389C4#1062329712yes—
390C4C2×#6700211yescharacteristic
391C4C2×#6700311yescharacteristic
392C2—22no—
393C2—882no—
394C2C2×#1062267011yescharacteristic
395C2#1307826711yescharacteristic
396C2C2×#1062279011yescharacteristic
subgroupG/H
centerC22C2×#66991
commutator, cosocleC42×C11C24
FrattiniC42C23×D11
FittingC2×C11×#487C2
socleC22×C11C2×#121
prime radical#10623008C22
hypercenterC2×#487D11
hypocenterC11#19199
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ C2×#487

Complements

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

NH ≅ G/Ntype
4. #13068188C2semidirect
5. #13068064C2semidirect
6. #13067364C2semidirect
7. #13067297C2semidirect
8. #13067288C2semidirect
9. C2×C11×#487C2semidirect
143. C2×#487D11semidirect
338. C11#19199semidirect

Maximal subgroups

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

subgroupindex
#130797442
#130797372
#130773292
#130681882
#130680642
#130673642
#130672972
#130672882
C2×C11×#4872
#1919911