Finite Group Databasebeta

← #14642349

Subgroups — #14642349

Order 2816.

500 conjugacy classes of subgroups; only the 97 normal subgroups are shown.

normal subgroups only

This group has 500 conjugacy classes of subgroups — too many to draw. Only its 97 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#13076967C211yesmaximal, characteristic
2#13068683C211yesmaximal, characteristic
3#13068377C211yesmaximal, characteristic
4#13066440C211yesmaximal, characteristic, complemented
5#13066439C211yesmaximal, characteristic, complemented
6#13066438C211yesmaximal, characteristic, complemented
7C11×#1271C211yesmaximal, characteristic, complemented
8C2×#66949—21no—
9C2×#66941C411yescharacteristic
10C2×C42×D11C2211yescharacteristic
11C11×#389C2211yescharacteristic
12C2×(C2×D11)⋊C8—21no—
13C2×(C2×D11)⋊C8—21no—
14C2×#66879—21no—
15#10622600C411yescharacteristic
16#10622600C411yescharacteristic
17#10622589C411yescharacteristic
18#10622585—21no—
19#10622541C2211yescharacteristic
20#10622280—21no—
21#10622259—21no—
22C11×#336C2211yescharacteristic
23C11×#336C2211yescharacteristic
24#10622188—21no—
25#10622162C2211yescharacteristic
26#10622162C2211yescharacteristic
27C22×C4×D11C2×C411yescharacteristic
28C22×C4×D11D411yescharacteristic
29C22×C4×D11D411yescharacteristic
30C22×Dic22—21no—
31C22×C8×C11—21no—
32C22×C8×C11—21no—
33C2×C11×C4⋊C4—21no—
34C2×C11×C4⋊C4C2×C411yescharacteristic
35C2×C11×C4⋊C4C2×C411yescharacteristic
36C2×C42×C11C2311yescharacteristic
37C2×(C2×D11)⋊C4—21no—
38C2×(C2×D11)⋊C4—21no—
39C2×C4⋊Dic11C2×C411yescharacteristic
40C2×C4⋊Dic11C2×C411yescharacteristic
41C2×Dic11⋊C4—21no—
42C2×Dic11⋊C4—21no—
43C2×Dic11⋊C4—21no—
44C2×Dic11⋊C4—21no—
45C2×C4×Dic11C2×C411yescharacteristic
46C2×C4×Dic11D411yescharacteristic
47C2×C4×Dic11D411yescharacteristic
48C22×C11⋊C8—21no—
49C22×C11⋊C8—21no—
50#66949—42no—
51#66949—42no—
52#66941—42no—
53C42×D11—42no—
54C11×#95—21no—
55C11⋊#95—21no—
56C11⋊#95—21no—
57C11⋊#95—21no—
58(C2×D11)⋊C8—24no—
59(C2×D11)⋊C8—42no—
60#66879—42no—
61#7708—111nomaximal, Sylow
62C23×D11C22⋊C411yescharacteristic
63C22×C4×C11—21no—
64C22×C4×C11—21no—
65C22×C4×C11C22×C411yescharacteristic
66C22×C4×C11C2×D411yescharacteristic
67C22×C4×C11C2×D411yescharacteristic
68C22×Dic11—21no—
69C22×Dic11—21no—
70C22×Dic11C22⋊C411yescharacteristic
71C22×Dic11C22⋊C411yescharacteristic
72C22×Dic11C22⋊C411yescharacteristic
73C2×C4×D11—22no—
74C2×C4×D11—22no—
75C2×C4×D11—22no—
76C2×C4×D11—21no—
77C2×C4×D11—21no—
78C2×C4×D11—21no—
79C2×C4×D11—21no—
80C2×C4×D11—21no—
81C2×C4×D11—21no—
82C2×C4×D11—41no—
83C2×C4×D11—41no—
84C2×C4×D11—41no—
85C2×Dic22—42no—
86C2×Dic22—42no—
87C2×Dic22—42no—
88C2×C8×C11—22no—
89C2×C8×C11—41no—
90C2×C8×C11—41no—
91C2×C8×C11—41no—
92C2×C8×C11—41no—
93C2×C8×C11—41no—
94C11×C4⋊C4—21no—
95C11×C4⋊C4—21no—
96C11×C4⋊C4—41no—
97C11×C4⋊C4—41no—
98C11×C4⋊C4—41no—
99C42×C11—41no—
100(C2×D11)⋊C4—42no—
101(C2×D11)⋊C4—42no—
102C4⋊Dic11—21no—
103C4⋊Dic11—21no—
104C4⋊Dic11—41no—
105Dic11⋊C4—42no—
106Dic11⋊C4—42no—
107Dic11⋊C4—42no—
108Dic11⋊C4—41no—
109Dic11⋊C4—41no—
110C4×Dic11—22no—
111C4×Dic11—22no—
112C4×Dic11—41no—
113C2×C11⋊C8—22no—
114C2×C11⋊C8—41no—
115C2×C11⋊C8—41no—
116C2×C11⋊C8—41no—
117C2×C11⋊C8—41no—
118C2×C11⋊C8—41no—
119#2857—111no—
120#1817—111no—
121#1749—111no—
122#1271—111no—
123#1271—111no—
124#1271—111no—
125#1271D1111yescharacteristic, complemented
126C23×C11C2×C22⋊C411yescharacteristic
127C22×D11—21no—
128C22×D11—21no—
129C22×D11—21no—
130C22×D11—21no—
131C22×D11—21no—
132C22×D11—21no—
133C22×D11#10112yes—
134C2×C4×C11—21no—
135C2×C4×C11—21no—
136C2×C4×C11—21no—
137C2×C4×C11—21no—
138C2×C4×C11—21no—
139C2×C4×C11—21no—
140C2×C4×C11—41no—
141C2×C4×C11—41no—
142C2×C4×C11—41no—
143C2×C4×C11—41no—
144C2×C4×C11—41no—
145C2×C4×C11—41no—
146C2×C4×C11#13111yescharacteristic
147C2×C4×C11#13111yescharacteristic
148C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
149C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
150C2×C4×C11#13711yescharacteristic
151C2×C4×C11#13711yescharacteristic
152C2×Dic11—21no—
153C2×Dic11—21no—
154C2×Dic11—21no—
155C2×Dic11—21no—
156C2×Dic11—21no—
157C2×Dic11—21no—
158C2×Dic11—21no—
159C2×Dic11—41no—
160C2×Dic11—41no—
161C2×Dic11—41no—
162C2×Dic11—41no—
163C2×Dic11—41no—
164C2×Dic11—41no—
165C2×Dic11#9912yes—
166C2×Dic11#10412yes—
167C4×D11—42no—
168C4×D11—42no—
169C4×D11—42no—
170C4×D11—42no—
171C4×D11—42no—
172C4×D11—42no—
173Dic22—84no—
174C8×C11—42no—
175C8×C11—81no—
176C11⋊C8—42no—
177C11⋊C8—81no—
178C2×C4⋊Q8—111no—
179C2×C22⋊Q8—221no—
180C22×C42—111no—
181C2×C22⋊C8—221no—
182C2×C22⋊C8—221no—
183C2×#97—221no—
184#391—221no—
185#389—111no—
186#389—221no—
187#389C2×D1111yescharacteristic
188#384—111no—
189#380—111no—
190#380—111no—
191#380—221no—
192#336—111no—
193#336—111no—
194#336—221no—
195#336C2×D1111yescharacteristic
196#336C2×D1111yescharacteristic
197C22×C11#40811yescharacteristic
198C22×C11C2×#9911yescharacteristic
199C22×C11C2×#10111yescharacteristic
200C22×C11#41811yescharacteristic
201C22×C11#41911yescharacteristic
202C22×C11C2×#10411yescharacteristic
203C22×C11#42111yescharacteristic
204C2×D11—22no—
205C2×D11—22no—
206C2×D11—22no—
207C2×D11—41no—
208C2×D11—41no—
209C2×D11—41no—
210C2×D11—41no—
211C4×C11—21no—
212C4×C11—21no—
213C4×C11—21no—
214C4×C11—21no—
215C4×C11—21no—
216C4×C11—21no—
217C4×C11—81no—
218C4×C11—81no—
219Dic11—22no—
220Dic11—22no—
221Dic11—41no—
222Dic11—81no—
223Dic11—81no—
224C22×Q8—221no—
225C23×C4—111no—
226C23×C4—111no—
227C23×C4—111no—
228C22×C8—21no—
229C22×C8—21no—
230C22×C8—221no—
231C22×C8—221no—
232C4⋊Q8—442no—
233C22⋊Q8—442no—
234C22⋊Q8—442no—
235C2×C4⋊C4—21no—
236C2×C4⋊C4—111no—
237C2×C4⋊C4—111no—
238C2×C4⋊C4—221no—
239C2×C4⋊C4—221no—
240C2×C4⋊C4—221no—
241C2×C4⋊C4—221no—
242C2×C4⋊C4C4×D1111yescharacteristic
243C2×C4⋊C4C4×D1111yescharacteristic
244C2×C22⋊C4—221no—
245C2×C22⋊C4—221no—
246C2×C42—111no—
247C2×C42—111no—
248C2×C42—111no—
249C2×C42—442no—
250C2×C42C22×D1111yescharacteristic
251C22⋊C8—224no—
252C22⋊C8—442no—
253#97—442no—
254#95—21no—
255#95—221no—
256#95—221no—
257#95—221no—
258C2×C11#147211yescharacteristic
259C2×C11#148411yescharacteristic
260C2×C11#149711yescharacteristic
261C2×C11#150811yescharacteristic
262C2×C11#151011yescharacteristic
263C2×C11#153111yescharacteristic
264C2×C11#155611yescharacteristic
265D11—42no—
266C24—111no—
267C2×Q8—442no—
268C2×Q8—442no—
269C2×Q8—442no—
270C22×C4—21no—
271C22×C4—21no—
272C22×C4—111no—
273C22×C4—111no—
274C22×C4—111no—
275C22×C4—222no—
276C22×C4—222no—
277C22×C4—222no—
278C22×C4—221no—
279C22×C4—221no—
280C22×C4—221no—
281C22×C4—221no—
282C22×C4—221no—
283C22×C4—221no—
284C22×C4—221no—
285C22×C4—221no—
286C22×C4—441no—
287C22×C4—441no—
288C22×C4—441no—
289C22×C4C2×C4×D1111yescharacteristic
290C22×C4D4×D1111yescharacteristic
291C22×C4D4×D1111yescharacteristic
292C2×C8—22no—
293C2×C8—41no—
294C2×C8—41no—
295C2×C8—41no—
296C2×C8—41no—
297C2×C8—41no—
298C2×C8—222no—
299C2×C8—441no—
300C2×C8—441no—
301C2×C8—441no—
302C2×C8—441no—
303C2×C8—441no—
304C4⋊C4—21no—
305C4⋊C4—21no—
306C4⋊C4—41no—
307C4⋊C4—41no—
308C4⋊C4—41no—
309C4⋊C4—221no—
310C4⋊C4—221no—
311C4⋊C4—441no—
312C4⋊C4—442no—
313C4⋊C4—442no—
314C4⋊C4—442no—
315C4⋊C4—441no—
316C4⋊C4—441no—
317C22⋊C4—442no—
318C22⋊C4—442no—
319C42—41no—
320C42—222no—
321C42—222no—
322C42—441no—
323C11#770811yescharacteristic, complemented, Sylow
324C23—112no—
325C23—221no—
326C23—221no—
327C23—221no—
328C23—221no—
329C23—221no—
330C23—221no—
331C23C22⋊C4×D1111yescharacteristic
332Q8—884no—
333C2×C4—21no—
334C2×C4—21no—
335C2×C4—21no—
336C2×C4—21no—
337C2×C4—21no—
338C2×C4—21no—
339C2×C4—41no—
340C2×C4—41no—
341C2×C4—41no—
342C2×C4—41no—
343C2×C4—41no—
344C2×C4—41no—
345C2×C4—112no—
346C2×C4—112no—
347C2×C4—221no—
348C2×C4—221no—
349C2×C4—221no—
350C2×C4—221no—
351C2×C4—221no—
352C2×C4—221no—
353C2×C4—221no—
354C2×C4—442no—
355C2×C4—442no—
356C2×C4—442no—
357C2×C4—442no—
358C2×C4—442no—
359C2×C4—442no—
360C2×C4—441no—
361C2×C4—441no—
362C2×C4—441no—
363C2×C4—441no—
364C2×C4—441no—
365C2×C4—441no—
366C2×C4#6695411yescharacteristic
367C2×C4#6696011yescharacteristic
368C2×C4#6696411yescharacteristic
369C2×C4#6696711yescharacteristic
370C2×C4#6696811yescharacteristic
371C2×C4#6697111yescharacteristic
372C8—42no—
373C8—81no—
374C8—442no—
375C8—881no—
376C22—222no—
377C22—222no—
378C22—222no—
379C22—441no—
380C22—441no—
381C22—441no—
382C22—441no—
383C22#1062234011yescharacteristic
384C22D11×#9911yescharacteristic
385C22D11×#10111yescharacteristic
386C22#1062238311yescharacteristic
387C22#1062241511yescharacteristic
388C22D11×#10411yescharacteristic
389C22#1062243411yescharacteristic
390C4—21no—
391C4—21no—
392C4—21no—
393C4—21no—
394C4—21no—
395C4—21no—
396C4—81no—
397C4—81no—
398C4—222no—
399C4—222no—
400C4—441no—
401C4—881no—
402C4—881no—
403C2—442no—
404C2#1306697811yescharacteristic
405C2#1306703111yescharacteristic
406C2#1306708711yescharacteristic
407C2#1306713411yescharacteristic
408C2#1306714311yescharacteristic
409C2#1306722911yescharacteristic
410C2#1306733111yescharacteristic
subgroupG/H
centerC23C22⋊C4×D11
commutatorC22×C4×C11C22×C4
FrattiniC2×C42C22×D11
FittingC11×#1271C2
socleC23×C11C2×C22⋊C4
prime radicalC23×D11C22⋊C4
cosocleC2×C42×C11C23
hypercenter#1271D11
hypocenterC11#7708
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1271

Complements

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

NH ≅ G/Ntype
4. #13066440C2semidirect
5. #13066439C2semidirect
6. #13066438C2semidirect
7. C11×#1271C2semidirect
125. #1271D11semidirect
323. C11#7708semidirect

Maximal subgroups

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

subgroupindex
#130769672
#130686832
#130683772
#130664402
#130664392
#130664382
C11×#12712
#770811