Finite Group Databasebeta

← #14664057

Subgroups — #14664057

Order 2816.

592 conjugacy classes of subgroups; only the 83 normal subgroups are shown.

normal subgroups only

This group has 592 conjugacy classes of subgroups — too many to draw. Only its 83 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#13074422C211yesmaximal, characteristic
2D11×#342C211yesmaximal, characteristic
3D11×#323C211yesmaximal, characteristic
4#13066640C211yesmaximal, characteristic, complemented
5#13066638C211yesmaximal, characteristic, complemented
6#13066636C211yesmaximal, characteristic, complemented
7C11×#1352C211yesmaximal, characteristic, complemented
8C2×#66950C411yescharacteristic, complemented
9C2×C22⋊C4×D11—21no—
10C2×C22⋊C4×D11C2211yescharacteristic
11C11×#399C2211yescharacteristic
12#10622607—21no—
13#10622605C411yescharacteristic, complemented
14#10622602—21no—
15#10622568—21no—
16#10622561—21no—
17#10622560C2211yescharacteristic
18D11×C22⋊C8—21no—
19#10622286C411yescharacteristic, complemented
20#10622280C411yescharacteristic, complemented
21C11×#342C2211yescharacteristic
22C11×#323C2211yescharacteristic
23#10622165—21no—
24#10622164C2211yescharacteristic
25#10622163C2211yescharacteristic
26#10622106—21no—
27C24×D11D411yescharacteristic
28C22×C4×D11—41no—
29C22×C4×D11C2×C411yescharacteristic
30C22×C4×D11D411yescharacteristic
31C22×Dic22C2×C411yescharacteristic, complemented
32C2×C11×C4⋊C4—21no—
33C2×C11×C4⋊C4C2×C411yescharacteristic, complemented
34C2×C11×C22⋊C4—21no—
35C2×C11×C22⋊C4—21no—
36C2×C11×C22⋊C4C2311yescharacteristic
37C2×C22⋊Dic11—21no—
38C2×C22⋊Dic11—21no—
39C2×C22⋊Dic11D411yescharacteristic
40C2×(C2×D11)⋊C4—21no—
41C2×(C2×D11)⋊C4—21no—
42C2×(C2×D11)⋊C4—21no—
43C2×(C2×D11)⋊C4—21no—
44C2×(C2×D11)⋊C4—41no—
45C2×(C2×D11)⋊C4C2×C411yescharacteristic
46C2×(C2×D11)⋊C4D411yescharacteristic
47C2×C4⋊Dic11—21no—
48C2×Dic11⋊C4—21no—
49C2×Dic11⋊C4—21no—
50C2×C8×D11—41no—
51#66950—41no—
52#66950—41no—
53C22⋊C4×D11—24no—
54C22⋊C4×D11—41no—
55C22⋊C4×D11—41no—
56C22⋊C4×D11—42no—
57C11×C22⋊C8—21no—
58C11×#95C2×C411yescharacteristic, complemented
59C11⋊#95—21no—
60C11⋊#95—21no—
61C11⋊#95C2×C411yescharacteristic, complemented
62C22⋊(C11⋊C8)—21no—
63(C2×D11)⋊C8—41no—
64#11716—111nomaximal, Sylow
65C24×C11C2×D411yescharacteristic
66C23×D11—21no—
67C23×D11—21no—
68C23×D11—22no—
69C23×D11—81no—
70C23×D11—81no—
71C23×D11C22⋊C411yescharacteristic
72C23×D11C22⋊C411yescharacteristic
73C23×D11SD1612yes—
74C23×D11Q1612yes—
75C22×C4×C11—21no—
76C22×C4×C11—21no—
77C22×C4×C11—41no—
78C22×C4×C11C22×C411yescharacteristic
79C22×C4×C11C2×D411yescharacteristic
80C22×Dic11—21no—
81C22×Dic11—21no—
82C22×Dic11—41no—
83C22×Dic11C22⋊C411yescharacteristic
84C22×Dic11C22⋊C411yescharacteristic
85C2×C4×D11—21no—
86C2×C4×D11—21no—
87C2×C4×D11—21no—
88C2×C4×D11—21no—
89C2×C4×D11—44no—
90C2×C4×D11—81no—
91C2×C4×D11—81no—
92C2×C4×D11—82no—
93C2×C4×D11—82no—
94C2×Dic22—41no—
95C2×Dic22—81no—
96C2×C8×C11—41no—
97C11×C4⋊C4—41no—
98C11×C4⋊C4—81no—
99C11×C22⋊C4—22no—
100C11×C22⋊C4—41no—
101C11×C22⋊C4—41no—
102C11×C22⋊C4—81no—
103C22⋊Dic11—22no—
104C22⋊Dic11—41no—
105C22⋊Dic11—41no—
106C22⋊Dic11—81no—
107(C2×D11)⋊C4—41no—
108(C2×D11)⋊C4—41no—
109(C2×D11)⋊C4—44no—
110(C2×D11)⋊C4—41no—
111(C2×D11)⋊C4—41no—
112(C2×D11)⋊C4—42no—
113(C2×D11)⋊C4—81no—
114(C2×D11)⋊C4—81no—
115C4⋊Dic11—42no—
116Dic11⋊C4—81no—
117Dic11⋊C4—81no—
118C2×C11⋊C8—41no—
119C8×D11—82no—
120#2626—111no—
121C2×#342—111no—
122C2×#323—111no—
123#1352—111no—
124#1352D1111yescharacteristic, complemented
125#1351—111no—
126#1351—111no—
127C23×C11—21no—
128C23×C11—21no—
129C23×C11—41no—
130C23×C11—41no—
131C23×C11C2×C22⋊C411yescharacteristic
132C23×C11C2×SD1611yescharacteristic
133C23×C11C2×Q1611yescharacteristic
134C22×D11—21no—
135C22×D11—21no—
136C22×D11—22no—
137C22×D11—22no—
138C22×D11—22no—
139C22×D11—22no—
140C22×D11—41no—
141C22×D11—41no—
142C22×D11—42no—
143C22×D11—42no—
144C22×D11—41no—
145C22×D11—41no—
146C22×D11—81no—
147C22×D11—81no—
148C22×D11—82no—
149C22×D11—82no—
150C22×D11—84no—
151C22×D11#9911yescharacteristic
152C22×D11#9911yescharacteristic
153C22×D11#10312yes—
154C22×D11#10312yes—
155C22×D11#10412yes—
156C2×C4×C11—21no—
157C2×C4×C11—21no—
158C2×C4×C11—41no—
159C2×C4×C11—41no—
160C2×C4×C11—41no—
161C2×C4×C11—41no—
162C2×C4×C11—42no—
163C2×C4×C11—41no—
164C2×C4×C11—41no—
165C2×C4×C11—41no—
166C2×C4×C11—41no—
167C2×C4×C11—81no—
168C2×C4×C11—81no—
169C2×Dic11—21no—
170C2×Dic11—21no—
171C2×Dic11—41no—
172C2×Dic11—41no—
173C2×Dic11—41no—
174C2×Dic11—41no—
175C2×Dic11—42no—
176C2×Dic11—41no—
177C2×Dic11—41no—
178C2×Dic11—41no—
179C2×Dic11—41no—
180C2×Dic11—81no—
181C2×Dic11—81no—
182C4×D11—42no—
183C4×D11—81no—
184C4×D11—81no—
185C4×D11—81no—
186C4×D11—88no—
187Dic22—82no—
188C8×C11—81no—
189C11⋊C8—81no—
190C2×C22⋊Q8—111no—
191C22×C22⋊C4—111no—
192C22×C22⋊C4—221no—
193C2×C22⋊C8—221no—
194#399—111no—
195#399C2×D1111yescharacteristic
196#396—221no—
197#396—221no—
198#393—111no—
199#393—111no—
200#385—221no—
201#380—111no—
202#379—221no—
203#342—111no—
204#342—221no—
205#342C2×D1111yescharacteristic
206#323—111no—
207#323—221no—
208#323C2×D1111yescharacteristic
209C22×C11—21no—
210C22×C11—21no—
211C22×C11—21no—
212C22×C11—21no—
213C22×C11—41no—
214C22×C11—41no—
215C22×C11—41no—
216C22×C11—41no—
217C22×C11—81no—
218C22×C11C2×#9911yescharacteristic
219C22×C11C2×#10311yescharacteristic
220C22×C11C2×#10411yescharacteristic
221C2×D11—21no—
222C2×D11—21no—
223C2×D11—21no—
224C2×D11—21no—
225C2×D11—22no—
226C2×D11—42no—
227C2×D11—42no—
228C2×D11—44no—
229C2×D11—44no—
230C2×D11—41no—
231C2×D11—41no—
232C2×D11—42no—
233C2×D11—82no—
234C2×D11—82no—
235C2×D11—81no—
236C2×D11#32812yes—
237C2×D11#32812yes—
238C4×C11—41no—
239C4×C11—41no—
240C4×C11—81no—
241C4×C11—82no—
242C4×C11—81no—
243Dic11—41no—
244Dic11—41no—
245Dic11—81no—
246Dic11—82no—
247Dic11—81no—
248C25—111no—
249C22×Q8—111no—
250C23×C4—111no—
251C23×C4—111no—
252C23×C4—441no—
253C22×C8—441no—
254C22⋊Q8—441no—
255C22⋊Q8—441no—
256C2×C4⋊C4—21no—
257C2×C4⋊C4—221no—
258C2×C4⋊C4—221no—
259C2×C4⋊C4—221no—
260C2×C4⋊C4C4×D1111yescharacteristic, complemented
261C2×C22⋊C4—21no—
262C2×C22⋊C4—21no—
263C2×C22⋊C4—111no—
264C2×C22⋊C4—111no—
265C2×C22⋊C4—111no—
266C2×C22⋊C4—224no—
267C2×C22⋊C4—221no—
268C2×C22⋊C4—221no—
269C2×C22⋊C4—221no—
270C2×C22⋊C4—221no—
271C2×C22⋊C4—221no—
272C2×C22⋊C4—221no—
273C2×C22⋊C4—441no—
274C2×C22⋊C4—441no—
275C2×C22⋊C4—442no—
276C2×C22⋊C4—441no—
277C2×C22⋊C4C22×D1111yescharacteristic
278C22⋊C8—21no—
279C22⋊C8—221no—
280C22⋊C8—441no—
281#95—111no—
282#95—221no—
283#95—221no—
284#95C4×D1111yescharacteristic, complemented
285C2×C11—21no—
286C2×C11—21no—
287C2×C11—41no—
288C2×C11—41no—
289C2×C11C2×#32811yescharacteristic
290C2×C11#212111yescharacteristic
291C2×C11#212711yescharacteristic
292D11—22no—
293D11—22no—
294D11—42no—
295C24—111no—
296C24—111no—
297C24—112no—
298C24—112no—
299C24—221no—
300C24—222no—
301C24—221no—
302C24—881no—
303C24—881no—
304C24D4×D1111yescharacteristic
305C2×Q8—441no—
306C2×Q8—881no—
307C22×C4—21no—
308C22×C4—21no—
309C22×C4—41no—
310C22×C4—111no—
311C22×C4—111no—
312C22×C4—221no—
313C22×C4—221no—
314C22×C4—221no—
315C22×C4—221no—
316C22×C4—221no—
317C22×C4—221no—
318C22×C4—444no—
319C22×C4—441no—
320C22×C4—881no—
321C22×C4—881no—
322C22×C4—882no—
323C22×C4—882no—
324C22×C4C2×C4×D1111yescharacteristic
325C22×C4D4×D1111yescharacteristic
326C2×C8—41no—
327C2×C8—441no—
328C2×C8—882no—
329C4⋊C4—41no—
330C4⋊C4—81no—
331C4⋊C4—442no—
332C4⋊C4—881no—
333C4⋊C4—881no—
334C22⋊C4—22no—
335C22⋊C4—41no—
336C22⋊C4—41no—
337C22⋊C4—81no—
338C22⋊C4—222no—
339C22⋊C4—441no—
340C22⋊C4—441no—
341C22⋊C4—441no—
342C22⋊C4—441no—
343C22⋊C4—442no—
344C22⋊C4—444no—
345C22⋊C4—441no—
346C22⋊C4—441no—
347C22⋊C4—881no—
348C22⋊C4—881no—
349C22⋊C4—881no—
350C11#1171611yescharacteristic, complemented, Sylow
351C23—21no—
352C23—21no—
353C23—41no—
354C23—41no—
355C23—111no—
356C23—111no—
357C23—112no—
358C23—112no—
359C23—112no—
360C23—222no—
361C23—222no—
362C23—222no—
363C23—222no—
364C23—221no—
365C23—221no—
366C23—441no—
367C23—441no—
368C23—441no—
369C23—441no—
370C23—442no—
371C23—442no—
372C23—881no—
373C23—881no—
374C23—882no—
375C23—882no—
376C23—884no—
377C23C22⋊C4×D1111yescharacteristic
378C23SD16×D1111yescharacteristic
379C23Q16×D1111yescharacteristic
380Q8—882no—
381C2×C4—21no—
382C2×C4—21no—
383C2×C4—41no—
384C2×C4—41no—
385C2×C4—42no—
386C2×C4—41no—
387C2×C4—41no—
388C2×C4—41no—
389C2×C4—41no—
390C2×C4—41no—
391C2×C4—41no—
392C2×C4—81no—
393C2×C4—81no—
394C2×C4—221no—
395C2×C4—221no—
396C2×C4—442no—
397C2×C4—441no—
398C2×C4—441no—
399C2×C4—442no—
400C2×C4—441no—
401C2×C4—441no—
402C2×C4—441no—
403C2×C4—441no—
404C2×C4—441no—
405C2×C4—441no—
406C2×C4—881no—
407C2×C4—881no—
408C2×C4—881no—
409C2×C4—888no—
410C2×C4—881no—
411C2×C4—881no—
412C8—81no—
413C8—881no—
414C22—21no—
415C22—21no—
416C22—21no—
417C22—21no—
418C22—41no—
419C22—41no—
420C22—41no—
421C22—41no—
422C22—81no—
423C22—112no—
424C22—112no—
425C22—221no—
426C22—221no—
427C22—221no—
428C22—221no—
429C22—222no—
430C22—442no—
431C22—442no—
432C22—442no—
433C22—444no—
434C22—444no—
435C22—441no—
436C22—441no—
437C22—881no—
438C22—882no—
439C22—882no—
440C22D11×#9911yescharacteristic
441C22D11×#10311yescharacteristic
442C22D11×#10411yescharacteristic
443C4—41no—
444C4—41no—
445C4—81no—
446C4—82no—
447C4—81no—
448C4—441no—
449C4—441no—
450C4—881no—
451C4—882no—
452C4—881no—
453C2—21no—
454C2—21no—
455C2—41no—
456C2—41no—
457C2—222no—
458C2—222no—
459C2—442no—
460C2D11×#32811yescharacteristic
461C2#1307026111yescharacteristic
462C2#1307028211yescharacteristic
subgroupG/H
centerC22D11×#99
commutatorC22×C4×C11C22×C4
FrattiniC2×C22⋊C4C22×D11
FittingC11×#1352C2
socleC22×C11C2×#99
prime radicalC24×D11D4
cosocleC2×C11×C22⋊C4C23
hypercenter#1352D11
hypocenterC11#11716
LCSG ▷ C22×C4×C11 ▷ C23×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23 ◁ C2×C22⋊C4 ◁ #1352

Complements

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

NH ≅ G/Ntype
4. #13066640C2semidirect
5. #13066638C2semidirect
6. #13066636C2semidirect
7. C11×#1352C2semidirect
8. C2×#66950C4semidirect
13. #10622605C4semidirect
19. #10622286C4semidirect
20. #10622280C4semidirect
31. C22×Dic22C2×C4semidirect
33. C2×C11×C4⋊C4C2×C4semidirect
58. C11×#95C2×C4semidirect
61. C11⋊#95C2×C4semidirect
124. #1352D11semidirect
260. C2×C4⋊C4C4×D11semidirect
284. #95C4×D11semidirect
350. C11#11716semidirect

Maximal subgroups

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

subgroupindex
#130744222
D11×#3422
D11×#3232
#130666402
#130666382
#130666362
C11×#13522
#1171611