Finite Group Databasebeta

← #14649727

Subgroups — #14649727

Order 2816.

500 conjugacy classes of subgroups; only the 111 normal subgroups are shown.

normal subgroups only

This group has 500 conjugacy classes of subgroups — too many to draw. Only its 111 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13078088C211yesmaximal, characteristic
2#13071581C211yesmaximal, characteristic, complemented
3#13067177C211yesmaximal, characteristic
4#13067112C211yesmaximal, characteristic
5#13066518C211yesmaximal, characteristic, complemented
6#13066475C211yesmaximal, characteristic, complemented
7C11×#1479C211yesmaximal, characteristic, complemented
8C2×C4×Q8×C11C2211yescharacteristic
9C2×#66995—21no—
10#10623008C2211yescharacteristic
11C11×#431C2211yescharacteristic
12C11×#431C2211yescharacteristic
13#10622843—21no—
14#10622644C412yescomplemented
15#10622641—22no—
16#10622640C412yescomplemented
17#10622594—22no—
18C4⋊C4×Dic11—21no—
19#10622579—21no—
20#10622550—21no—
21#10622549C2211yescharacteristic
22C4×C4⋊Dic11C2211yescharacteristic
23#10622545—21no—
24#10622537C2211yescharacteristic
25C11×Q8⋊C8—22no—
26#10622108—21no—
27#10622108—21no—
28#10622108—22no—
29C22×Q8×C11D411yescharacteristic
30C2×#4339—21no—
31C4×Q8×C11—21no—
32C4×Q8×C11—21no—
33C4×Q8×C11C2×C412yes—
34C4×Q8×C11D412yes—
35C2×C11×C4⋊C4—21no—
36C2×C11×C4⋊C4D411yescharacteristic
37C2×C42×C11—21no—
38C2×C42×C11C2311yescharacteristic
39C2×#4326—22no—
40#66995—42no—
41#66995—42no—
42C2×#4325—22no—
43#66983—21no—
44#66983—21no—
45C2×C4⋊Dic11—21no—
46C2×C4⋊Dic11—21no—
47C2×C4×Dic11—22no—
48C2×C4×Dic11—21no—
49C2×#4318—21no—
50#66928—21no—
51#66927C2×C411yescharacteristic
52C4×D44—21no—
53C4×D44—21no—
54#66922C2×C411yescharacteristic
55C11×C4⋊C8—21no—
56C11×C4⋊C8—21no—
57C11×C22⋊C8—21no—
58C11×C22⋊C8—21no—
59C4×C8×C11—21no—
60C4×C8×C11—21no—
61C11⋊#95—22no—
62C11⋊#95—22no—
63C11⋊#95—22no—
64C11⋊#95—21no—
65C11⋊#95D411yescharacteristic
66C11⋊#95D411yescharacteristic
67C11⋊#95D412yes—
68#66874—22no—
69#66873—22no—
70C4⋊(C11⋊C8)—21no—
71C4⋊(C11⋊C8)C2×C412yes—
72#9182—111nomaximal, Sylow
73C2×Q8×C11—21no—
74C2×Q8×C11—21no—
75C2×Q8×C11—21no—
76C2×Q8×C11—21no—
77C2×Q8×C11—21no—
78C2×Q8×C11C22⋊C412yes—
79C22×C4×C11—21no—
80C22×C4×C11—21no—
81C22×C4×C11C2×D411yescharacteristic
82C22×C4×C11C2×D411yescharacteristic
83C22×C4×C11C2×D411yescharacteristic
84C2×C22⋊D11—41no—
85C22×Dic11—21no—
86C22×Dic11—22no—
87C22×Dic11—21no—
88#4339—41no—
89#4339—41no—
90#4339—41no—
91#4339—41no—
92C2×D44—21no—
93C2×D44—21no—
94C2×D44—21no—
95C2×C4×D11—41no—
96C2×Dic22—21no—
97C2×C8×C11—41no—
98C2×C8×C11—41no—
99C11×C4⋊C4—22no—
100C11×C4⋊C4—22no—
101C11×C4⋊C4—21no—
102C11×C4⋊C4C22⋊C412yes—
103C42×C11—22no—
104C42×C11—22no—
105C42×C11C22×C411yescharacteristic
106C42×C11C2×D411yescharacteristic
107C42×C11#4111yescharacteristic
108C42×C11#4111yescharacteristic
109#4326—44no—
110#4325—44no—
111(C2×D11)⋊C4—41no—
112(C2×D11)⋊C4—41no—
113C4⋊Dic11—21no—
114C4⋊Dic11—21no—
115C4⋊Dic11—42no—
116C4⋊Dic11—41no—
117C4⋊Dic11—41no—
118C4×Dic11—44no—
119C4×Dic11—41no—
120C4×Dic11—41no—
121#4318—41no—
122#4318—41no—
123C2×C11⋊C8—22no—
124#3037—111no—
125#2356—111no—
126#1517—111no—
127#1502—111no—
128#1479D1111yescharacteristic, complemented
129#1303—111no—
130#1286—111no—
131C23×C11#12011yescharacteristic
132C22×D11—41no—
133Q8×C11—22no—
134Q8×C11—22no—
135Q8×C11—41no—
136Q8×C11—41no—
137C2×C4×C11—22no—
138C2×C4×C11—22no—
139C2×C4×C11—41no—
140C2×C4×C11—41no—
141C2×C4×C11—42no—
142C2×C4×C11—41no—
143C2×C4×C11—41no—
144C2×C4×C11C2×C22⋊C411yescharacteristic
145C2×C4×C11C4×D411yescharacteristic
146C2×C4×C11C4×D411yescharacteristic
147C2×C4×C11#12111yescharacteristic
148C2×C4×C11#12111yescharacteristic
149C2×C4×C11#12311yescharacteristic
150C2×C4×C11#13511yescharacteristic
151C2×C4×C11#13511yescharacteristic
152C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
153C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
154C22⋊D11—81no—
155C22⋊D11—81no—
156C2×Dic11—22no—
157C2×Dic11—41no—
158C2×Dic11—41no—
159C2×Dic11—42no—
160C2×Dic11—41no—
161C2×Dic11—41no—
162C2×Dic11—42no—
163C2×Dic11—41no—
164C2×Dic11—41no—
165C2×Dic11—42no—
166D44—41no—
167D44—41no—
168D44—81no—
169D44—81no—
170C4×D11—81no—
171C4×D11—81no—
172Dic22—41no—
173Dic22—41no—
174C8×C11—81no—
175C8×C11—81no—
176C11⋊C8—42no—
177C2×#137—221no—
178#532—111no—
179C2×C4×Q8C2×D1111yescharacteristic
180#464—222no—
181#462—112no—
182#460—112no—
183#431C2×D1111yescharacteristic
184#431C2×D1111yescharacteristic
185#423—111no—
186#417—221no—
187#391—221no—
188#387—222no—
189#383—221no—
190#382—111no—
191C4×C4⋊C4—111no—
192C4×C4⋊C4—221no—
193#376—221no—
194#327—221no—
195#327—221no—
196#327—222no—
197Q8⋊C8—22no—
198C22×C11—21no—
199C22×C11—21no—
200C22×C11#38611yescharacteristic
201C22×C11#44911yescharacteristic
202C22×C11#44911yescharacteristic
203C2×D11—81no—
204C2×D11—81no—
205C2×D11—81no—
206C4×C11—21no—
207C4×C11—21no—
208C4×C11—21no—
209C4×C11—21no—
210C4×C11—42no—
211C4×C11—42no—
212C4×C11#41611yescharacteristic
213C4×C11#41811yescharacteristic
214C4×C11#48211yescharacteristic
215C4×C11#48211yescharacteristic
216Dic11—42no—
217Dic11—81no—
218Dic11—82no—
219Dic11—81no—
220C2×#41—221no—
221C22×Q8D4411yescharacteristic
222#137—442no—
223#137—442no—
224C2×Q16—222no—
225C2×SD16—222no—
226C2×M16—221no—
227C4⋊Q8—111no—
228#127—111no—
229#124—221no—
230#121—221no—
231#121—221no—
232C4×Q8—21no—
233C4×Q8—21no—
234C4×Q8C4×D1112yes—
235C4×Q8C22⋊D1112yes—
236C4×D4—221no—
237C4×D4—221no—
238C2×C4⋊C4—21no—
239C2×C4⋊C4—221no—
240C2×C4⋊C4—221no—
241C2×C4⋊C4D4411yescharacteristic
242C2×C42—21no—
243C2×C42—222no—
244C2×C42—221no—
245C2×C42C22×D1111yescharacteristic
246C4⋊C8—21no—
247C4⋊C8—21no—
248C4⋊C8—112no—
249C4⋊C8—221no—
250#103—222no—
251#102—222no—
252C22⋊C8—21no—
253C22⋊C8—21no—
254C4×C8—21no—
255C4×C8—21no—
256#95—111no—
257#95—111no—
258#95—112no—
259#95—222no—
260#95—222no—
261#95—222no—
262#95—221no—
263C2×C11—21no—
264C2×C11—21no—
265C2×C11#187511yescharacteristic
266C2×C11#190511yescharacteristic
267C2×C11#190611yescharacteristic
268D11—161no—
269#41—441no—
270#41—441no—
271#41—441no—
272#41—441no—
273C2×Q8—21no—
274C2×Q8—21no—
275C2×Q8—21no—
276C2×Q8—21no—
277C2×Q8—21no—
278C2×Q8—221no—
279C2×Q8(C2×D11)⋊C412yes—
280C2×D4—221no—
281C2×D4—221no—
282C2×D4—221no—
283C2×D4—441no—
284C22×C4—21no—
285C22×C4—21no—
286C22×C4—221no—
287C22×C4—222no—
288C22×C4—221no—
289C22×C4—441no—
290C22×C4C2×D4411yescharacteristic
291C22×C4D4×D1111yescharacteristic
292C22×C4D4×D1111yescharacteristic
293Q16—444no—
294SD16—444no—
295M16—441no—
296M16—441no—
297C2×C8—41no—
298C2×C8—41no—
299C2×C8—222no—
300C4⋊C4—22no—
301C4⋊C4—21no—
302C4⋊C4—22no—
303C4⋊C4—221no—
304C4⋊C4—221no—
305C4⋊C4—442no—
306C4⋊C4—441no—
307C4⋊C4—441no—
308C4⋊C4(C2×D11)⋊C412yes—
309C22⋊C4—441no—
310C22⋊C4—441no—
311C42—22no—
312C42—22no—
313C42—444no—
314C42—441no—
315C42—441no—
316C42C2×C4×D1111yescharacteristic
317C42#434111yescharacteristic
318C42#434111yescharacteristic
319C42C2×C22⋊D1111yescharacteristic
320C11#918211yescharacteristic, complemented, Sylow
321C23—441no—
322C23#6693511yescharacteristic
323Q8—22no—
324Q8—22no—
325Q8—41no—
326Q8—41no—
327Q8—441no—
328Q8—441no—
329D4—441no—
330D4—441no—
331D4—881no—
332D4—881no—
333D4—881no—
334D4—881no—
335C2×C4—22no—
336C2×C4—22no—
337C2×C4—41no—
338C2×C4—41no—
339C2×C4—42no—
340C2×C4—41no—
341C2×C4—41no—
342C2×C4—222no—
343C2×C4—441no—
344C2×C4—441no—
345C2×C4—442no—
346C2×C4—441no—
347C2×C4—441no—
348C2×C4—442no—
349C2×C4—441no—
350C2×C4—441no—
351C2×C4—442no—
352C2×C4—881no—
353C2×C4—881no—
354C2×C4(C22⋊D11)⋊C411yescharacteristic
355C2×C4(C22⋊D11)⋊C411yescharacteristic
356C2×C4#6693911yescharacteristic
357C2×C4#6695711yescharacteristic
358C2×C4#6695711yescharacteristic
359C2×C4#6696111yescharacteristic
360C2×C4#6696111yescharacteristic
361C2×C4C2×(C2×D11)⋊C411yescharacteristic
362C2×C4#6699211yescharacteristic
363C2×C4#6699211yescharacteristic
364C8—81no—
365C8—81no—
366C8—442no—
367C22—21no—
368C22—21no—
369C22—881no—
370C22—881no—
371C22—881no—
372C22#1062234711yescharacteristic
373C22#1062234711yescharacteristic
374C22#1062257111yescharacteristic
375C4—21no—
376C4—21no—
377C4—21no—
378C4—21no—
379C4—42no—
380C4—42no—
381C4—442no—
382C4—881no—
383C4—882no—
384C4—881no—
385C4#1062235011yescharacteristic
386C4#1062235011yescharacteristic
387C4#1062272611yescharacteristic
388C4#1062274411yescharacteristic
389C2—21no—
390C2—21no—
391C2—1761no—
392C2#1306893611yescharacteristic
393C2#1306910811yescharacteristic
394C2#1306911511yescharacteristic
subgroupG/H
centerC22#10622571
commutatorC42×C11C22×C4
FrattiniC2×C42C22×D11
FittingC11×#1479C2
socleC22×C11#386
prime radical#10623008C22
cosocleC2×C42×C11C23
hypercenter#1479D11
hypocenterC11#9182
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1479

Complements

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

NH ≅ G/Ntype
2. #13071581C2semidirect
5. #13066518C2semidirect
6. #13066475C2semidirect
7. C11×#1479C2semidirect
14. #10622644C4semidirect
16. #10622640C4semidirect
128. #1479D11semidirect
320. C11#9182semidirect

Maximal subgroups

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

subgroupindex
#130780882
#130715812
#130671772
#130671122
#130665182
#130664752
C11×#14792
#918211