Finite Group Databasebeta

← #14671319

Subgroups — #14671319

Order 2816.

676 conjugacy classes of subgroups; only the 95 normal subgroups are shown.

normal subgroups only

This group has 676 conjugacy classes of subgroups — too many to draw. Only its 95 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
1C2×D11×#101C211yesmaximal, characteristic
2#13072257C211yesmaximal, characteristic
3C2×#10622186C211yesmaximal, characteristic, complemented
4#13068538C211yesmaximal, characteristic
5#13066742C211yesmaximal, characteristic, complemented
6#13066742C211yesmaximal, characteristic, complemented
7C2×C11×#356C211yesmaximal, characteristic, complemented
8C22×Q8×D11C2211yescharacteristic
9C2×C11×C4⋊Q8C2211yescharacteristic
10C2×#66999C411yescharacteristic
11C2×#66997C411yescharacteristic
12C2×M16×D11—21no—
13C2×C11×#101C2211yescharacteristic
14C2×C11×#101C2211yescharacteristic
15#10622843C2211yescharacteristic
16C2×#66900C2211yescharacteristic
17C2×#66900C2211yescharacteristic
18C2×#66888—21no—
19C2×#66888—21no—
20#10622739—21no—
21#10622602—21no—
22#10622602—21no—
23#10622592—21no—
24#10622592—21no—
25C4×(C2×D11)⋊C4C411yescharacteristic
26#10622542C411yescharacteristic
27D11×#101—22no—
28D11×#101—22no—
29C11×#356—22no—
30#10622186—22no—
31C22×Q8×C11C2×C411yescharacteristic
32C22×Q8×C11C2311yescharacteristic
33C2×Q8×D11—21no—
34C2×Q8×D11—21no—
35C2×Q8×D11—21no—
36C2×Q8×D11—21no—
37C2×Q8×D11—42no—
38C2×Q8×D11—41no—
39C2×Q8×D11—41no—
40C22×C4×D11C2×C411yescharacteristic
41C22×C4×D11D411yescharacteristic
42C22×C4×D11D411yescharacteristic
43C22×Dic22C2×C411yescharacteristic
44C22×Dic22D411yescharacteristic
45C22×Dic22D411yescharacteristic
46C2×C11×M16—21no—
47C2×C11×M16—21no—
48C11×C4⋊Q8—21no—
49C11×C4⋊Q8—21no—
50C11×C4⋊Q8—21no—
51C11×C4⋊Q8—21no—
52C2×C11×C4⋊C4—21no—
53C2×C11×C4⋊C4—21no—
54C2×C42×C11C2×C411yescharacteristic
55#66999—41no—
56#66999—41no—
57#66997—42no—
58C2×(C2×D11)⋊C4—21no—
59C2×(C2×D11)⋊C4—21no—
60C2×C4⋊Dic11C2×C411yescharacteristic
61C2×Dic11⋊C4—21no—
62C2×Dic11⋊C4—21no—
63C2×Dic11⋊C4—21no—
64C2×C4×Dic11C2×C411yescharacteristic
65C2×#4318—21no—
66C2×#4318—21no—
67M16×D11—24no—
68M16×D11—42no—
69C2×#4313—41no—
70C2×C8×D11—41no—
71C11×#101—21no—
72C11×#101—21no—
73C11×#101—21no—
74C11×#101D412yes—
75#66900—21no—
76#66900—21no—
77#66900—21no—
78#66900D412yes—
79C11⋊#95—21no—
80C11⋊#95—21no—
81C11⋊#95—21no—
82C11⋊#95—21no—
83C11⋊#95—21no—
84#66888—24no—
85#66888—42no—
86(C2×D11)⋊C8—41no—
87(C2×D11)⋊C8—41no—
88#13094—111nomaximal, Sylow
89C23×D11C22⋊C411yescharacteristic
90C2×Q8×C11—21no—
91C2×Q8×C11—21no—
92C2×Q8×C11—41no—
93C2×Q8×C11—41no—
94C2×Q8×C11—41no—
95C2×Q8×C11—41no—
96C2×Q8×C11C2×D411yescharacteristic
97C2×Q8×C11C2×D411yescharacteristic
98C2×Q8×C11#4111yescharacteristic
99C2×Q8×C11#4111yescharacteristic
100C22×C4×C11—21no—
101C22×C4×C11—21no—
102C22×C4×C11C22×C411yescharacteristic
103C22×C4×C11C2×D411yescharacteristic
104C22×C4×C11C2×D411yescharacteristic
105C22×Dic11—21no—
106C22×Dic11—21no—
107C22×Dic11C22⋊C411yescharacteristic
108C22×Dic11C22⋊C411yescharacteristic
109C22×Dic11C22⋊C411yescharacteristic
110Q8×D11—42no—
111Q8×D11—42no—
112Q8×D11—42no—
113Q8×D11—42no—
114Q8×D11—42no—
115Q8×D11—42no—
116Q8×D11—42no—
117Q8×D11—42no—
118C2×C4×D11—22no—
119C2×C4×D11—21no—
120C2×C4×D11—21no—
121C2×C4×D11—21no—
122C2×C4×D11—21no—
123C2×C4×D11—21no—
124C2×C4×D11—21no—
125C2×C4×D11—21no—
126C2×C4×D11—21no—
127C2×C4×D11—21no—
128C2×C4×D11—21no—
129C2×C4×D11—21no—
130C2×C4×D11—21no—
131C2×C4×D11—41no—
132C2×C4×D11—41no—
133C2×Dic22—22no—
134C2×Dic22—22no—
135C2×Dic22—21no—
136C2×Dic22—21no—
137C2×Dic22—21no—
138C2×Dic22—21no—
139C2×Dic22—21no—
140C2×Dic22—21no—
141C2×Dic22—41no—
142C2×Dic22—41no—
143C2×Dic22—41no—
144C2×Dic22—41no—
145C11×M16—22no—
146C11×M16—41no—
147C11×M16—41no—
148C11×M16—41no—
149C2×C8×C11—41no—
150C2×C8×C11—41no—
151C11×C4⋊C4—41no—
152C11×C4⋊C4—41no—
153C11×C4⋊C4—41no—
154C11×C4⋊C4—41no—
155C42×C11—21no—
156C42×C11—21no—
157(C2×D11)⋊C4—24no—
158(C2×D11)⋊C4—41no—
159(C2×D11)⋊C4—41no—
160C4⋊Dic11—41no—
161Dic11⋊C4—42no—
162Dic11⋊C4—42no—
163Dic11⋊C4—42no—
164C4×Dic11—41no—
165#4318—22no—
166#4318—41no—
167#4318—41no—
168#4318—41no—
169C2×C11⋊C8—41no—
170C2×C11⋊C8—41no—
171#4313—44no—
172C8×D11—44no—
173C22×#101—111no—
174#2434—111no—
175C2×#356—111no—
176C2×#356D1111yescharacteristic, complemented
177#1784—111no—
178#1394—111no—
179#1394—111no—
180C23×C11C2×C22⋊C411yescharacteristic
181C22×D11—21no—
182C22×D11—21no—
183C22×D11—22no—
184C22×D11—41no—
185C22×D11#9911yescharacteristic
186C22×D11#9911yescharacteristic
187Q8×C11—41no—
188Q8×C11—41no—
189Q8×C11—41no—
190Q8×C11—41no—
191Q8×C11—81no—
192Q8×C11—81no—
193C2×C4×C11—21no—
194C2×C4×C11—21no—
195C2×C4×C11—21no—
196C2×C4×C11—21no—
197C2×C4×C11—21no—
198C2×C4×C11—21no—
199C2×C4×C11—22no—
200C2×C4×C11—41no—
201C2×C4×C11—41no—
202C2×C4×C11—41no—
203C2×C4×C11—41no—
204C2×C4×C11—41no—
205C2×C4×C11C4×D411yescharacteristic
206C2×C4×C11C4×D411yescharacteristic
207C2×C4×C11#12011yescharacteristic
208C2×C4×C11#12111yescharacteristic
209C2×C4×C11#12111yescharacteristic
210C2×C4×C11#12311yescharacteristic
211C2×Dic11—21no—
212C2×Dic11—21no—
213C2×Dic11—22no—
214C2×Dic11—21no—
215C2×Dic11—21no—
216C2×Dic11—21no—
217C2×Dic11—21no—
218C2×Dic11—21no—
219C2×Dic11—21no—
220C2×Dic11—41no—
221C2×Dic11—41no—
222C2×Dic11—42no—
223C2×Dic11—41no—
224C2×Dic11#9912yes—
225C4×D11—22no—
226C4×D11—22no—
227C4×D11—22no—
228C4×D11—22no—
229C4×D11—41no—
230C4×D11—41no—
231C4×D11—41no—
232C4×D11—41no—
233C4×D11—41no—
234C4×D11—41no—
235C4×D11—41no—
236C4×D11—41no—
237Dic22—42no—
238Dic22—42no—
239Dic22—42no—
240Dic22—42no—
241Dic22—42no—
242Dic22—42no—
243C8×C11—42no—
244C8×C11—81no—
245C11⋊C8—42no—
246C11⋊C8—81no—
247C23×Q8—111no—
248C22×M16—221no—
249C2×C4⋊Q8—111no—
250C2×C4⋊Q8C2×D1111yescharacteristic
251C2×C22⋊Q8—111no—
252C2×#101—111no—
253C2×#101—111no—
254C2×#101—222no—
255C2×#101—221no—
256C2×#101—222no—
257C2×#101—221no—
258C2×#101C2×D1111yescharacteristic
259C2×#101C2×D1111yescharacteristic
260#407—221no—
261#395—221no—
262#395—221no—
263#391—111no—
264#391—111no—
265#385—221no—
266#385—221no—
267C4×C22⋊C4—111no—
268#356—22no—
269#356—222no—
270C22×C11—21no—
271C22×C11—21no—
272C22×C11#38611yescharacteristic
273C22×C11C2×#9911yescharacteristic
274C22×C11C2×#9911yescharacteristic
275C2×D11—21no—
276C2×D11—21no—
277C2×D11—21no—
278C2×D11—21no—
279C2×D11—21no—
280C2×D11—42no—
281C2×D11—42no—
282C2×D11#35612yescomplemented
283C4×C11—21no—
284C4×C11—21no—
285C4×C11—21no—
286C4×C11—21no—
287C4×C11—21no—
288C4×C11—21no—
289C4×C11—42no—
290C4×C11—81no—
291Dic11—22no—
292Dic11—42no—
293Dic11—41no—
294Dic11—41no—
295Dic11—81no—
296C22×Q8—111no—
297C22×Q8—111no—
298C22×Q8—111no—
299C22×Q8—221no—
300C22×Q8—221no—
301C22×Q8—221no—
302C22×Q8—221no—
303C22×Q8—441no—
304C22×Q8—441no—
305C22×Q8—442no—
306C22×Q8C4×D1111yescharacteristic
307C22×Q8C22×D1111yescharacteristic
308C23×C4—111no—
309C23×C4—111no—
310C23×C4—111no—
311C2×M16—21no—
312C2×M16—21no—
313C2×M16—224no—
314C2×M16—221no—
315C2×M16—221no—
316C2×M16—441no—
317C2×M16—442no—
318C22×C8—441no—
319C4⋊Q8—21no—
320C4⋊Q8—21no—
321C4⋊Q8—21no—
322C4⋊Q8—21no—
323C4⋊Q8—442no—
324C22⋊Q8—441no—
325C22⋊Q8—441no—
326C2×C4⋊C4—21no—
327C2×C4⋊C4—21no—
328C2×C4⋊C4—111no—
329C2×C4⋊C4—221no—
330C2×C4⋊C4—221no—
331C2×C4⋊C4—221no—
332C2×C22⋊C4—221no—
333C2×C22⋊C4—221no—
334C2×C42—111no—
335C2×C42C4×D1111yescharacteristic
336#101—21no—
337#101—21no—
338#101—21no—
339#101—112no—
340#101—224no—
341#101—221no—
342#101—221no—
343#101—221no—
344#101—442no—
345#101C22⋊D1112yes—
346C22⋊C8—441no—
347C22⋊C8—441no—
348#95—221no—
349#95—221no—
350#95—221no—
351#95—221no—
352#95—221no—
353C2×C11—21no—
354C2×C11—21no—
355C2×C11#189811yescharacteristic
356C2×C11C2×#35611yescharacteristic
357C2×C11#213311yescharacteristic
358D11—22no—
359D11—41no—
360C24—111no—
361C2×Q8—21no—
362C2×Q8—21no—
363C2×Q8—41no—
364C2×Q8—41no—
365C2×Q8—41no—
366C2×Q8—41no—
367C2×Q8—222no—
368C2×Q8—222no—
369C2×Q8—221no—
370C2×Q8—221no—
371C2×Q8—221no—
372C2×Q8—221no—
373C2×Q8—221no—
374C2×Q8—221no—
375C2×Q8—441no—
376C2×Q8—441no—
377C2×Q8—441no—
378C2×Q8—441no—
379C2×Q8—442no—
380C2×Q8—442no—
381C2×Q8—442no—
382C2×Q8—442no—
383C2×Q8—442no—
384C2×Q8—442no—
385C2×Q8—442no—
386C2×Q8—442no—
387C2×Q8#433911yescharacteristic
388C2×Q8D4×D1111yescharacteristic
389C2×Q8#434111yescharacteristic
390C2×Q8C2×C22⋊D1111yescharacteristic
391C22×C4—21no—
392C22×C4—21no—
393C22×C4—111no—
394C22×C4—111no—
395C22×C4—111no—
396C22×C4—222no—
397C22×C4—221no—
398C22×C4—221no—
399C22×C4—221no—
400C22×C4—221no—
401C22×C4—221no—
402C22×C4—221no—
403C22×C4—221no—
404C22×C4—221no—
405C22×C4—221no—
406C22×C4—221no—
407C22×C4—221no—
408C22×C4—221no—
409C22×C4—221no—
410C22×C4—221no—
411C22×C4—441no—
412C22×C4—441no—
413C22×C4C2×C4×D1111yescharacteristic
414C22×C4D4×D1111yescharacteristic
415C22×C4D4×D1111yescharacteristic
416M16—22no—
417M16—41no—
418M16—41no—
419M16—41no—
420M16—222no—
421M16—444no—
422M16—441no—
423M16—441no—
424M16—441no—
425C2×C8—41no—
426C2×C8—41no—
427C2×C8—444no—
428C2×C8—441no—
429C2×C8—441no—
430C4⋊C4—41no—
431C4⋊C4—41no—
432C4⋊C4—41no—
433C4⋊C4—41no—
434C4⋊C4—441no—
435C4⋊C4—442no—
436C4⋊C4—442no—
437C4⋊C4—442no—
438C22⋊C4—224no—
439C22⋊C4—441no—
440C22⋊C4—441no—
441C42—21no—
442C42—21no—
443C42—441no—
444C11#1309411yescharacteristic, complemented, Sylow
445C23—111no—
446C23—111no—
447C23—222no—
448C23—221no—
449C23—221no—
450C23—441no—
451C23C22⋊C4×D1111yescharacteristic
452Q8—41no—
453Q8—41no—
454Q8—41no—
455Q8—41no—
456Q8—81no—
457Q8—81no—
458Q8—442no—
459Q8—442no—
460Q8—442no—
461Q8—442no—
462Q8—442no—
463Q8—442no—
464C2×C4—21no—
465C2×C4—21no—
466C2×C4—21no—
467C2×C4—21no—
468C2×C4—21no—
469C2×C4—21no—
470C2×C4—22no—
471C2×C4—41no—
472C2×C4—41no—
473C2×C4—41no—
474C2×C4—41no—
475C2×C4—41no—
476C2×C4—112no—
477C2×C4—222no—
478C2×C4—222no—
479C2×C4—222no—
480C2×C4—222no—
481C2×C4—221no—
482C2×C4—221no—
483C2×C4—222no—
484C2×C4—221no—
485C2×C4—221no—
486C2×C4—221no—
487C2×C4—221no—
488C2×C4—221no—
489C2×C4—221no—
490C2×C4—441no—
491C2×C4—441no—
492C2×C4—441no—
493C2×C4—441no—
494C2×C4—441no—
495C2×C4—441no—
496C2×C4—441no—
497C2×C4—441no—
498C2×C4—441no—
499C2×C4—441no—
500C2×C4—442no—
501C2×C4—441no—
502C2×C4(C22⋊D11)⋊C411yescharacteristic
503C2×C4#6693611yescharacteristic
504C2×C4#6693711yescharacteristic
505C2×C4C4×C22⋊D1111yescharacteristic
506C2×C4#6699011yescharacteristic
507C2×C4#6699111yescharacteristic
508C8—42no—
509C8—81no—
510C8—442no—
511C8—881no—
512C22—21no—
513C22—21no—
514C22—112no—
515C22—221no—
516C22—221no—
517C22—221no—
518C22—221no—
519C22—221no—
520C22—442no—
521C22—442no—
522C22D11×#9911yescharacteristic
523C22D11×#9911yescharacteristic
524C22#1062256911yescharacteristic
525C4—21no—
526C4—21no—
527C4—21no—
528C4—21no—
529C4—21no—
530C4—21no—
531C4—42no—
532C4—81no—
533C4—222no—
534C4—442no—
535C4—441no—
536C4—441no—
537C4—881no—
538C2—21no—
539C2—21no—
540C2—222no—
541C2—441no—
542C2#1306906611yescharacteristic
543C2D11×#35611yescharacteristic
544C2#1307030411yescharacteristic
subgroupG/H
centerC22D11×#99
commutatorC22×C4×C11C22×C4
FrattiniC22×Q8C22×D11
FittingC2×C11×#356C2
socleC22×C11C2×#99
prime radicalC23×D11C22⋊C4
cosocleC22×Q8×C11C23
hypercenterC2×#356D11
hypocenterC11#13094
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23 ◁ C22×Q8 ◁ C2×#356

Complements

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

NH ≅ G/Ntype
3. C2×#10622186C2semidirect
5. #13066742C2semidirect
6. #13066742C2semidirect
7. C2×C11×#356C2semidirect
176. C2×#356D11semidirect
282. C2×D11#356semidirect
444. C11#13094semidirect

Maximal subgroups

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

subgroupindex
C2×D11×#1012
#130722572
C2×#106221862
#130685382
#130667422
C2×C11×#3562
#1309411