Finite Group Databasebeta

← #14641981

Subgroups — #14641981

Order 2816.

506 conjugacy classes of subgroups; only the 101 normal subgroups are shown.

normal subgroups only

This group has 506 conjugacy classes of subgroups — too many to draw. Only its 101 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#13071154C211yesmaximal, characteristic
2#13068683C211yesmaximal, characteristic
3#13068377C211yesmaximal, characteristic
4#13066442C211yesmaximal, characteristic, complemented
5#13066440C211yesmaximal, characteristic, complemented
6#13066438C211yesmaximal, characteristic, complemented
7C11×#1272C211yesmaximal, characteristic, complemented
8C2×#66999C411yescharacteristic
9C2×Q8×Dic11C411yescharacteristic
10C2×C42×D11C2211yescharacteristic
11C11×#391C2211yescharacteristic
12C2×(C2×D11)⋊C8—21no—
13C2×(C2×D11)⋊C8—21no—
14C2×#66879—21no—
15#10622600C411yescharacteristic
16C4⋊C4×Dic11C411yescharacteristic
17#10622541C2211yescharacteristic
18#10622281—21no—
19#10622279—21no—
20#10622268—21no—
21#10622262—21no—
22C11×#336C2211yescharacteristic
23C11×#336C2211yescharacteristic
24#10622188—21no—
25#10622162C2211yescharacteristic
26#10622162C2211yescharacteristic
27C22×Q8×C11C2×C411yescharacteristic
28C22×C4×D11C2×C411yescharacteristic
29C22×C4×D11D411yescharacteristic
30C22×C4×D11D411yescharacteristic
31C22×C8×C11—21no—
32C22×C8×C11—21no—
33C2×C11×C4⋊C4C2×C411yescharacteristic
34C2×C42×C11C2311yescharacteristic
35#66999—22no—
36#66999—22no—
37Q8×Dic11—42no—
38C2×(C2×D11)⋊C4—21no—
39C2×(C2×D11)⋊C4—21no—
40C2×C4⋊Dic11—21no—
41C2×C4⋊Dic11C2×C411yescharacteristic
42C2×C4⋊Dic11C2×C411yescharacteristic
43C2×Dic11⋊C4—21no—
44C2×Dic11⋊C4—21no—
45C2×C4×Dic11—21no—
46C2×C4×Dic11—21no—
47C2×C4×Dic11C2×C411yescharacteristic
48C2×C4×Dic11D411yescharacteristic
49C2×C4×Dic11D411yescharacteristic
50C22×C11⋊C8—21no—
51C22×C11⋊C8—21no—
52C42×D11—42no—
53C11×#95—21no—
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#7623—111nomaximal, Sylow
62C23×D11C22⋊C411yescharacteristic
63C2×Q8×C11—21no—
64C2×Q8×C11—41no—
65C2×Q8×C11—41no—
66C2×Q8×C11M1612yes—
67C22×C4×C11—21no—
68C22×C4×C11—21no—
69C22×C4×C11C22×C411yescharacteristic
70C22×C4×C11C2×D411yescharacteristic
71C22×C4×C11C2×D411yescharacteristic
72C22×Dic11—21no—
73C22×Dic11—21no—
74C22×Dic11C22⋊C411yescharacteristic
75C22×Dic11C22⋊C411yescharacteristic
76C22×Dic11C22⋊C411yescharacteristic
77C2×C4×D11—22no—
78C2×C4×D11—22no—
79C2×C4×D11—21no—
80C2×C4×D11—21no—
81C2×C4×D11—21no—
82C2×C4×D11—21no—
83C2×C4×D11—21no—
84C2×C4×D11—21no—
85C2×C4×D11—41no—
86C2×C4×D11—41no—
87C2×C4×D11—41no—
88C2×C4×D11—41no—
89C2×C8×C11—22no—
90C2×C8×C11—41no—
91C2×C8×C11—41no—
92C2×C8×C11—41no—
93C2×C8×C11—41no—
94C2×C8×C11—41no—
95C11×C4⋊C4—41no—
96C42×C11—41no—
97(C2×D11)⋊C4—24no—
98(C2×D11)⋊C4—42no—
99C4⋊Dic11—21no—
100C4⋊Dic11—41no—
101C4⋊Dic11—42no—
102C4⋊Dic11M1612yes—
103Dic11⋊C4—24no—
104Dic11⋊C4—41no—
105Dic11⋊C4—41no—
106C4×Dic11—22no—
107C4×Dic11—22no—
108C4×Dic11—41no—
109C4×Dic11—42no—
110C4×Dic11—42no—
111C2×C11⋊C8—22no—
112C2×C11⋊C8—41no—
113C2×C11⋊C8—41no—
114C2×C11⋊C8—41no—
115C2×C11⋊C8—41no—
116C2×C11⋊C8—41no—
117C4×C22⋊Q8—111no—
118#1817—111no—
119#1749—111no—
120#1272—111no—
121#1272D1111yescharacteristic, complemented
122#1271—111no—
123#1271—111no—
124C23×C11C2×C22⋊C411yescharacteristic
125C22×D11—21no—
126C22×D11—21no—
127C22×D11—21no—
128C22×D11—21no—
129C22×D11—21no—
130C22×D11—21no—
131C22×D11#10412yes—
132Q8×C11—42no—
133Q8×C11—42no—
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—22no—
141C2×C4×C11—41no—
142C2×C4×C11—41no—
143C2×C4×C11—41no—
144C2×C4×C11—41no—
145C2×C4×C11—41no—
146C2×C4×C11C2×M1611yescharacteristic
147C2×C4×C11C2×M1611yescharacteristic
148C2×C4×C11#13511yescharacteristic
149C2×C4×C11#13511yescharacteristic
150C2×C4×C11#13711yescharacteristic
151C2×C4×C11#13711yescharacteristic
152C2×Dic11—21no—
153C2×Dic11—21no—
154C2×Dic11—21no—
155C2×Dic11—22no—
156C2×Dic11—21no—
157C2×Dic11—21no—
158C2×Dic11—21no—
159C2×Dic11—21no—
160C2×Dic11—21no—
161C2×Dic11—41no—
162C2×Dic11—41no—
163C2×Dic11—41no—
164C2×Dic11—41no—
165C2×Dic11—41no—
166C2×Dic11#9912yes—
167C4×D11—42no—
168C4×D11—42no—
169C4×D11—42no—
170C4×D11—42no—
171C4×D11—42no—
172C4×D11—42no—
173C8×C11—42no—
174C8×C11—81no—
175C11⋊C8—42no—
176C11⋊C8—81no—
177C2×C22⋊Q8—111no—
178C2×C4×Q8—111no—
179C22×C42—111no—
180C2×C22⋊C8—221no—
181C2×C22⋊C8—221no—
182C2×#97—221no—
183#391C2×D1111yescharacteristic
184#389—111no—
185#387—221no—
186#385—221no—
187#380—111no—
188C4×C4⋊C4—111no—
189C4×C4⋊C4—221no—
190C4×C22⋊C4—221no—
191#336—111no—
192#336—111no—
193#336—221no—
194#336C2×D1111yescharacteristic
195#336C2×D1111yescharacteristic
196C22×C11#40711yescharacteristic
197C22×C11C2×#9911yescharacteristic
198C22×C11#41311yescharacteristic
199C22×C11#41611yescharacteristic
200C22×C11#41911yescharacteristic
201C22×C11C2×#10411yescharacteristic
202C22×C11#42111yescharacteristic
203C2×D11—22no—
204C2×D11—22no—
205C2×D11—22no—
206C2×D11—41no—
207C2×D11—41no—
208C2×D11—41no—
209C2×D11—41no—
210C4×C11—21no—
211C4×C11—21no—
212C4×C11—21no—
213C4×C11—21no—
214C4×C11—21no—
215C4×C11—21no—
216C4×C11—42no—
217C4×C11—81no—
218Dic11—22no—
219Dic11—41no—
220Dic11—42no—
221Dic11—41no—
222Dic11—81no—
223C22×Q8C4×D1111yescharacteristic
224C23×C4—111no—
225C23×C4—111no—
226C23×C4—111no—
227C22×C8—21no—
228C22×C8—21no—
229C22×C8—221no—
230C22×C8—221no—
231C22⋊Q8—222no—
232C22⋊Q8—222no—
233C4×Q8—442no—
234C2×C4⋊C4—111no—
235C2×C4⋊C4—111no—
236C2×C4⋊C4—221no—
237C2×C4⋊C4—221no—
238C2×C4⋊C4—221no—
239C2×C4⋊C4C4×D1111yescharacteristic
240C2×C22⋊C4—221no—
241C2×C22⋊C4—221no—
242C2×C42—111no—
243C2×C42—111no—
244C2×C42—111no—
245C2×C42—221no—
246C2×C42—221no—
247C2×C42—442no—
248C2×C42C22×D1111yescharacteristic
249C22⋊C8—224no—
250C22⋊C8—442no—
251#97—442no—
252#95—21no—
253#95—21no—
254#95—221no—
255#95—221no—
256#95—221no—
257C2×C11#146511yescharacteristic
258C2×C11#148811yescharacteristic
259C2×C11#149111yescharacteristic
260C2×C11#150111yescharacteristic
261C2×C11#151111yescharacteristic
262C2×C11#153211yescharacteristic
263C2×C11#155411yescharacteristic
264D11—42no—
265C24—111no—
266C2×Q8—21no—
267C2×Q8—41no—
268C2×Q8—41no—
269C2×Q8#431312yes—
270C22×C4—21no—
271C22×C4—21no—
272C22×C4—111no—
273C22×C4—111no—
274C22×C4—111no—
275C22×C4—222no—
276C22×C4—222no—
277C22×C4—221no—
278C22×C4—221no—
279C22×C4—221no—
280C22×C4—221no—
281C22×C4—221no—
282C22×C4—221no—
283C22×C4—221no—
284C22×C4—221no—
285C22×C4—441no—
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—41no—
305C4⋊C4—112no—
306C4⋊C4—224no—
307C4⋊C4—221no—
308C4⋊C4—441no—
309C4⋊C4—442no—
310C4⋊C4—441no—
311C4⋊C4—441no—
312C22⋊C4—224no—
313C22⋊C4—442no—
314C42—41no—
315C42—222no—
316C42—222no—
317C42—441no—
318C42—442no—
319C42—442no—
320C11#762311yescharacteristic, complemented, Sylow
321C23—112no—
322C23—221no—
323C23—221no—
324C23—221no—
325C23—221no—
326C23—221no—
327C23—221no—
328C23C22⋊C4×D1111yescharacteristic
329Q8—42no—
330Q8—42no—
331C2×C4—21no—
332C2×C4—21no—
333C2×C4—21no—
334C2×C4—21no—
335C2×C4—21no—
336C2×C4—21no—
337C2×C4—22no—
338C2×C4—41no—
339C2×C4—41no—
340C2×C4—41no—
341C2×C4—41no—
342C2×C4—41no—
343C2×C4—112no—
344C2×C4—221no—
345C2×C4—221no—
346C2×C4—222no—
347C2×C4—221no—
348C2×C4—221no—
349C2×C4—221no—
350C2×C4—221no—
351C2×C4—221no—
352C2×C4—221no—
353C2×C4—442no—
354C2×C4—442no—
355C2×C4—442no—
356C2×C4—442no—
357C2×C4—442no—
358C2×C4—442no—
359C2×C4—441no—
360C2×C4—441no—
361C2×C4—441no—
362C2×C4—441no—
363C2×C4—441no—
364C2×C4C2×#431311yescharacteristic
365C2×C4M16×D1111yescharacteristic
366C2×C4#6696811yescharacteristic
367C2×C4#6696911yescharacteristic
368C2×C4#6697111yescharacteristic
369C2×C4#6697211yescharacteristic
370C8—42no—
371C8—81no—
372C8—442no—
373C8—881no—
374C22—222no—
375C22—222no—
376C22—222no—
377C22—441no—
378C22—441no—
379C22—441no—
380C22—441no—
381C22#1062233911yescharacteristic
382C22D11×#9911yescharacteristic
383C22#1062235811yescharacteristic
384C22#1062241511yescharacteristic
385C22#1062241711yescharacteristic
386C22D11×#10411yescharacteristic
387C22#1062243411yescharacteristic
388C4—21no—
389C4—21no—
390C4—21no—
391C4—21no—
392C4—21no—
393C4—21no—
394C4—42no—
395C4—81no—
396C4—222no—
397C4—442no—
398C4—441no—
399C4—441no—
400C4—881no—
401C2—442no—
402C2#1306695111yescharacteristic
403C2#1306704911yescharacteristic
404C2#1306706111yescharacteristic
405C2#1306710611yescharacteristic
406C2#1306714711yescharacteristic
407C2#1306723311yescharacteristic
408C2#1306732511yescharacteristic
subgroupG/H
centerC23C22⋊C4×D11
commutatorC22×C4×C11C22×C4
FrattiniC2×C42C22×D11
FittingC11×#1272C2
socleC23×C11C2×C22⋊C4
prime radicalC23×D11C22⋊C4
cosocleC2×C42×C11C23
hypercenter#1272D11
hypocenterC11#7623
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1272

Complements

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

NH ≅ G/Ntype
4. #13066442C2semidirect
5. #13066440C2semidirect
6. #13066438C2semidirect
7. C11×#1272C2semidirect
121. #1272D11semidirect
320. C11#7623semidirect

Maximal subgroups

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

subgroupindex
#130711542
#130686832
#130683772
#130664422
#130664402
#130664382
C11×#12722
#762311