Finite Group Databasebeta

← #14664895

Subgroups — #14664895

Order 2816.

580 conjugacy classes of subgroups; only the 79 normal subgroups are shown.

normal subgroups only

This group has 580 conjugacy classes of subgroups — too many to draw. Only its 79 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#13071974C211yesmaximal, characteristic
2#13068603C211yesmaximal, characteristic
3#13066935C211yesmaximal, characteristic
4#13066638C211yesmaximal, characteristic, complemented
5#13066637C211yesmaximal, characteristic, complemented
6#13066636C211yesmaximal, characteristic, complemented
7C11×#1351C211yesmaximal, characteristic, complemented
8C22×Q8×D11C411yescharacteristic, complemented
9C2×(C22⋊D11)⋊C4C2211yescharacteristic
10C2×#66931—21no—
11C11×#393C2211yescharacteristic
12#10622842C411yescharacteristic, complemented
13#10622569—21no—
14C2×#66870—21no—
15#10622560C2211yescharacteristic
16#10622555—21no—
17#10622331—21no—
18#10622281—21no—
19#10622280C411yescharacteristic, complemented
20#10622269C411yescharacteristic, complemented
21#10622259—21no—
22C11×#342C2211yescharacteristic
23C11×#323C2211yescharacteristic
24#10622164C2211yescharacteristic
25#10622163C2211yescharacteristic
26#10622106—21no—
27C22×Q8×C11C2×C411yescharacteristic
28C22×C22⋊D11D411yescharacteristic
29C23×Dic11D411yescharacteristic
30C2×Q8×D11—44no—
31C2×Q8×D11—41no—
32C2×Q8×D11—41no—
33C22×C4×D11—21no—
34C22×C4×D11C2×C411yescharacteristic
35C22×Dic22—21no—
36C22×Dic22C2×C411yescharacteristic
37C2×C11×C22⋊C4—21no—
38C2×C11×C22⋊C4—21no—
39C2×C11×C22⋊C4C2311yescharacteristic
40C2×C22⋊Dic11—21no—
41C2×C22⋊Dic11—21no—
42C2×(C2×D11)⋊C4—21no—
43C2×(C2×D11)⋊C4D411yescharacteristic
44C2×C4⋊Dic11—21no—
45C2×Dic11⋊C4—21no—
46C2×Dic11⋊C4—21no—
47C2×Dic11⋊C4—41no—
48C2×Dic11⋊C4C2×C411yescharacteristic
49C2×C4×Dic11D411yescharacteristic
50(C22⋊D11)⋊C4—41no—
51(C22⋊D11)⋊C4—41no—
52#66931—44no—
53C11×C22⋊C8—21no—
54C11×#95—21no—
55C11×#95C2×C411yescharacteristic
56C11⋊#95—21no—
57C11⋊#95—21no—
58C11⋊#95—21no—
59C11⋊#95—41no—
60C11⋊#95C2×C411yescharacteristic
61C22⋊(C11⋊C8)—21no—
62Dic11⋊C8—41no—
63C8×Dic11—41no—
64#66870—42no—
65#11898—111nomaximal, Sylow
66C24×C11C2×D411yescharacteristic
67C23×D11C22⋊C411yescharacteristic
68C2×Q8×C11—42no—
69C2×Q8×C11—41no—
70C22×C4×C11—21no—
71C22×C4×C11—21no—
72C22×C4×C11—41no—
73C22×C4×C11C22×C411yescharacteristic
74C22×C4×C11C2×D411yescharacteristic
75C2×C22⋊D11—41no—
76C2×C22⋊D11—41no—
77C2×C22⋊D11SD1612yes—
78C2×C22⋊D11Q1612yes—
79C22×Dic11—21no—
80C22×Dic11—21no—
81C22×Dic11—21no—
82C22×Dic11—21no—
83C22×Dic11—41no—
84C22×Dic11—42no—
85C22×Dic11C22⋊C411yescharacteristic
86C22×Dic11C22⋊C411yescharacteristic
87C22×Dic11C22⋊C411yescharacteristic
88Q8×D11—44no—
89Q8×D11—44no—
90Q8×D11—44no—
91Q8×D11—44no—
92C2×C4×D11—21no—
93C2×C4×D11—21no—
94C2×C4×D11—42no—
95C2×C4×D11—42no—
96C2×C4×D11—42no—
97C2×C4×D11—42no—
98C2×Dic22—24no—
99C2×Dic22—41no—
100C2×Dic22—42no—
101C2×Dic22—41no—
102C2×Dic22—41no—
103C2×Dic22—42no—
104C2×C8×C11—41no—
105C11×C22⋊C4—41no—
106C11×C22⋊C4—42no—
107C11×C22⋊C4—41no—
108C11×C22⋊C4—41no—
109C22⋊Dic11—41no—
110C22⋊Dic11—42no—
111C22⋊Dic11—41no—
112(C2×D11)⋊C4—41no—
113(C2×D11)⋊C4—42no—
114C4⋊Dic11—42no—
115Dic11⋊C4—41no—
116Dic11⋊C4—42no—
117Dic11⋊C4—42no—
118Dic11⋊C4—82no—
119C4×Dic11—21no—
120C4×Dic11—21no—
121C2×C11⋊C8—41no—
122#2409—111no—
123#1799—111no—
124#1460—111no—
125#1351—111no—
126#1351—111no—
127#1351—111no—
128#1351D1111yescharacteristic, complemented
129C23×C11—21no—
130C23×C11—21no—
131C23×C11—41no—
132C23×C11—41no—
133C23×C11C2×C22⋊C411yescharacteristic
134C23×C11C2×SD1611yescharacteristic
135C23×C11C2×Q1611yescharacteristic
136C22×D11—21no—
137C22×D11—21no—
138C22×D11—41no—
139C22×D11—41no—
140C22×D11#10312yes—
141Q8×C11—42no—
142Q8×C11—42no—
143C2×C4×C11—22no—
144C2×C4×C11—21no—
145C2×C4×C11—21no—
146C2×C4×C11—41no—
147C2×C4×C11—41no—
148C2×C4×C11—41no—
149C2×C4×C11—41no—
150C2×C4×C11—41no—
151C2×C4×C11—41no—
152C2×C4×C11—41no—
153C2×C4×C11—81no—
154C2×C4×C11—81no—
155C2×C4×C11—81no—
156C22⋊D11—42no—
157C22⋊D11—42no—
158C2×Dic11—21no—
159C2×Dic11—21no—
160C2×Dic11—22no—
161C2×Dic11—22no—
162C2×Dic11—21no—
163C2×Dic11—41no—
164C2×Dic11—41no—
165C2×Dic11—42no—
166C2×Dic11—41no—
167C2×Dic11—41no—
168C2×Dic11—41no—
169C2×Dic11—41no—
170C2×Dic11—81no—
171C2×Dic11—81no—
172C2×Dic11—81no—
173C2×Dic11—81no—
174C2×Dic11#9911yescharacteristic
175C2×Dic11#9911yescharacteristic
176C2×Dic11#10312yes—
177C4×D11—42no—
178C4×D11—48no—
179C4×D11—42no—
180Dic22—44no—
181Dic22—42no—
182Dic22—44no—
183Dic22—42no—
184C8×C11—81no—
185C11⋊C8—81no—
186C23×Q8—111no—
187C2×C22⋊Q8—221no—
188C2×C4×D4—111no—
189#431—221no—
190C2×#99—221no—
191#395—111no—
192#395—111no—
193#393—111no—
194#393C2×D1111yescharacteristic
195#391—221no—
196#386—221no—
197#385—221no—
198#380—111no—
199#380—221no—
200#342—111no—
201#342C2×D1111yescharacteristic
202#323—111no—
203#323—221no—
204#323C2×D1111yescharacteristic
205C22×C11—21no—
206C22×C11—21no—
207C22×C11—21no—
208C22×C11—21no—
209C22×C11—41no—
210C22×C11—41no—
211C22×C11—41no—
212C22×C11—41no—
213C22×C11—81no—
214C22×C11C2×#9911yescharacteristic
215C22×C11C2×#10311yescharacteristic
216C22×C11#42111yescharacteristic
217C2×D11—22no—
218C2×D11—42no—
219C2×D11—41no—
220C2×D11—41no—
221C2×D11—42no—
222C4×C11—42no—
223C4×C11—41no—
224C4×C11—41no—
225C4×C11—81no—
226C4×C11—161no—
227Dic11—21no—
228Dic11—22no—
229Dic11—42no—
230Dic11—41no—
231Dic11—81no—
232Dic11—161no—
233Dic11AΣL(1,𝔽16)12yes—
234C22×Q8—111no—
235C22×Q8—221no—
236C22×Q8—441no—
237C22×Q8—441no—
238C22×Q8—444no—
239C22×Q8C4×D1111yescharacteristic
240C22×D4—111no—
241C23×C4—111no—
242C23×C4—111no—
243C23×C4—221no—
244C22⋊Q8—444no—
245C4×D4—441no—
246C4×D4—441no—
247C2×C4⋊C4—111no—
248C2×C4⋊C4—221no—
249C2×C4⋊C4—221no—
250C2×C4⋊C4—221no—
251C2×C4⋊C4—441no—
252C2×C22⋊C4—21no—
253C2×C22⋊C4—21no—
254C2×C22⋊C4—111no—
255C2×C22⋊C4—221no—
256C2×C22⋊C4—221no—
257C2×C22⋊C4—221no—
258C2×C22⋊C4C22×D1111yescharacteristic
259C2×C42—111no—
260C4⋊C8—441no—
261#99—442no—
262C22⋊C8—21no—
263C22⋊C8—221no—
264C4×C8—441no—
265#95—21no—
266#95—111no—
267#95—221no—
268#95—221no—
269#95—221no—
270#95—441no—
271#95C4×D1111yescharacteristic
272C2×C11—21no—
273C2×C11—21no—
274C2×C11—41no—
275C2×C11—41no—
276C2×C11#152011yescharacteristic
277C2×C11C2×AΣL(1,𝔽16)11yescharacteristic
278C2×C11#212911yescharacteristic
279D11—42no—
280C24—111no—
281C24D4×D1111yescharacteristic
282C2×Q8—42no—
283C2×Q8—41no—
284C2×Q8—224no—
285C2×Q8—441no—
286C2×Q8—441no—
287C2×Q8—441no—
288C2×Q8—442no—
289C2×Q8—442no—
290C2×Q8—444no—
291C2×Q8—444no—
292C2×Q8—444no—
293C2×Q8—444no—
294C2×D4—112no—
295C2×D4—112no—
296C2×D4—441no—
297C2×D4—441no—
298C22×C4—21no—
299C22×C4—21no—
300C22×C4—41no—
301C22×C4—111no—
302C22×C4—111no—
303C22×C4—111no—
304C22×C4—221no—
305C22×C4—221no—
306C22×C4—221no—
307C22×C4—221no—
308C22×C4—221no—
309C22×C4—221no—
310C22×C4—442no—
311C22×C4—442no—
312C22×C4—442no—
313C22×C4—442no—
314C22×C4—442no—
315C22×C4—441no—
316C22×C4C2×C4×D1111yescharacteristic
317C22×C4D4×D1111yescharacteristic
318C2×C8—41no—
319C2×C8—441no—
320C4⋊C4—441no—
321C4⋊C4—442no—
322C4⋊C4—442no—
323C4⋊C4—442no—
324C4⋊C4—882no—
325C22⋊C4—41no—
326C22⋊C4—42no—
327C22⋊C4—41no—
328C22⋊C4—41no—
329C22⋊C4—441no—
330C22⋊C4—442no—
331C22⋊C4—442no—
332C22⋊C4—441no—
333C22⋊C4—441no—
334C42—221no—
335C42—221no—
336C11#1189811yescharacteristic, complemented, Sylow
337C23—21no—
338C23—21no—
339C23—41no—
340C23—41no—
341C23—112no—
342C23—221no—
343C23—221no—
344C23—441no—
345C23—441no—
346C23C22⋊C4×D1111yescharacteristic
347C23SD16×D1111yescharacteristic
348C23Q16×D1111yescharacteristic
349Q8—42no—
350Q8—42no—
351Q8—444no—
352Q8—444no—
353Q8—442no—
354Q8—442no—
355D4—442no—
356D4—442no—
357C2×C4—22no—
358C2×C4—21no—
359C2×C4—21no—
360C2×C4—41no—
361C2×C4—41no—
362C2×C4—41no—
363C2×C4—41no—
364C2×C4—41no—
365C2×C4—41no—
366C2×C4—41no—
367C2×C4—81no—
368C2×C4—81no—
369C2×C4—81no—
370C2×C4—111no—
371C2×C4—111no—
372C2×C4—112no—
373C2×C4—222no—
374C2×C4—221no—
375C2×C4—221no—
376C2×C4—222no—
377C2×C4—221no—
378C2×C4—442no—
379C2×C4—442no—
380C2×C4—448no—
381C2×C4—442no—
382C2×C4—441no—
383C2×C4—441no—
384C2×C4—441no—
385C2×C4—441no—
386C2×C4—441no—
387C2×C4—441no—
388C2×C4—881no—
389C2×C4—881no—
390C2×C4—881no—
391C2×C4—881no—
392C8—81no—
393C8—881no—
394C22—21no—
395C22—21no—
396C22—21no—
397C22—21no—
398C22—41no—
399C22—41no—
400C22—41no—
401C22—41no—
402C22—81no—
403C22—222no—
404C22—442no—
405C22—442no—
406C22—441no—
407C22—441no—
408C22D11×#9911yescharacteristic
409C22D11×#10311yescharacteristic
410C22#1062243411yescharacteristic
411C4—42no—
412C4—41no—
413C4—41no—
414C4—81no—
415C4—112no—
416C4—161no—
417C4—221no—
418C4—222no—
419C4—442no—
420C4—441no—
421C4—881no—
422C4—1761no—
423C2—21no—
424C2—21no—
425C2—41no—
426C2—41no—
427C2—442no—
428C2#1306718611yescharacteristic
429C2D11×AΣL(1,𝔽16)11yescharacteristic
430C2#1307028911yescharacteristic
subgroupG/H
centerC22D11×#99
commutatorC22×C4×C11C22×C4
FrattiniC2×C22⋊C4C22×D11
FittingC11×#1351C2
socleC22×C11C2×#99
prime radicalC22×C22⋊D11D4
cosocleC2×C11×C22⋊C4C23
hypercenter#1351D11
hypocenterC11#11898
LCSG ▷ C22×C4×C11 ▷ C23×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23 ◁ C2×C22⋊C4 ◁ #1351

Complements

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

NH ≅ G/Ntype
4. #13066638C2semidirect
5. #13066637C2semidirect
6. #13066636C2semidirect
7. C11×#1351C2semidirect
8. C22×Q8×D11C4semidirect
12. #10622842C4semidirect
19. #10622280C4semidirect
20. #10622269C4semidirect
128. #1351D11semidirect
336. C11#11898semidirect

Maximal subgroups

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

subgroupindex
#130719742
#130686032
#130669352
#130666382
#130666372
#130666362
C11×#13512
#1189811