Finite Group Databasebeta

← #14757323

Subgroups — #14757323

Order 2816.

874 conjugacy classes of subgroups.

The subgroup lattice has 506 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D11×#108C211yesmaximal, characteristic
2#13077203C212yesmaximal
3C2×#10622493C211yesmaximal, characteristic
4D11×#405C211yesmaximal, characteristic
5#13069402C211yesmaximal, characteristic, complemented
6#13069401C211yesmaximal, characteristic, complemented
7#13069399C211yesmaximal, characteristic, complemented
8#13069395C212yesmaximal, complemented
9#13069393C212yesmaximal, complemented
10#13068353C212yesmaximal
11C11×#1952C211yesmaximal, characteristic, complemented
12C2×M16×D11C2212yes—
13C2×M16×D11C2211yescharacteristic
14C22×C8×D11C2211yescharacteristic
15D11×#117C2211yescharacteristic
16C2×#66945C2212yes—
17C2×C11×#108C2211yescharacteristic
18C11×#428C2212yes—
19C2×C11×#107C2211yescharacteristic
20C11×#405C2211yescharacteristic
21C2×#66886C2212yes—
22#10622735C2211yescharacteristic
23#10622734C2212yes—
24C2×#66883C2211yescharacteristic
25C2×#66882C2211yescharacteristic
26#10622714C2211yescharacteristic
27#10622610C2211yescharacteristic
28#10622608C2212yes—
29#10622577C2212yes—
30C2×#66872C2212yes—
31D11×#108C418yescomplemented
32#10622494—22no—
33#10622493—21no—
34#10622493—21no—
35#10622493—21no—
36#10622493—21no—
37#10622493—22no—
38#10622474—22no—
39#10622473—22no—
40#10622321—21no—
41D11×#97—21no—
42#10622302—21no—
43C4×C8×D11—21no—
44C11×#343C2212yes—
45#10622192C2212yes—
46#10622192C2212yes—
47#10622168C2212yes—
48C22×C4×D11C2311yescharacteristic
49C2×C11×M16C2312yes—
50C2×C11×M16C2311yescharacteristic
51C22×C8×C11C2311yescharacteristic
52C11×#117C2311yescharacteristic
53C2×C11×C4⋊C4C2312yes—
54C2×(C2×D11)⋊C4—22no—
55#66979C2311yescharacteristic
56C2×C4⋊Dic11C2312yes—
57C2×C4×Dic11—22no—
58C2×#4318C2312yes—
59C2×#4318C2311yescharacteristic
60C22×C11⋊C8C2311yescharacteristic
61M16×D11—24no—
62M16×D11—22no—
63M16×D11C2×C418yes—
64M16×D11Q814yes—
65C2×#4313—22no—
66C2×#4313—21no—
67C2×C8×D11—22no—
68C2×C8×D11—21no—
69C2×C8×D11C2×C414yes—
70C2×C8×D11D411yescharacteristic
71C2×C8×D11D411yescharacteristic
72C2×C8×D11D411yescharacteristic
73C2×C8×D11D411yescharacteristic
74C2×C8×D11Q814yes—
75#66945—22no—
76#66945—22no—
77#66945—22no—
78#66945—22no—
79#66945D411yescharacteristic
80#66945D411yescharacteristic
81C4⋊C4×D11D411yescharacteristic
82C4⋊C4×D11D411yescharacteristic
83C22⋊C4×D11—21no—
84#66930—21no—
85#66925—21no—
86C42×D11—21no—
87C11×#108C2×C414yescomplemented
88C11×#107—21no—
89C11×#107—21no—
90C11×#107—22no—
91C11×#106—22no—
92C11×#97—21no—
93C4×C8×C11—21no—
94#66886C2×C418yescomplemented
95#66883C2×C414yescomplemented
96#66882—21no—
97#66882—21no—
98#66882—22no—
99#66881—22no—
100#66879—21no—
101#66879—21no—
102C8×Dic11—21no—
103C8×Dic11—21no—
104#66872—22no—
105#66872—22no—
106#66872—22no—
107#66872—22no—
108#66871—22no—
109#66871—22no—
110#66867—21no—
111C4×C11⋊C8—21no—
112#21181—111nomaximal, Sylow
113C23×D11#4111yescharacteristic
114C22×C4×C11—22no—
115C22×C4×C11C2411yescharacteristic
116C22×Dic11—22no—
117C22×Dic11#4111yescharacteristic
118C2×C4×D11—21no—
119C2×C4×D11—21no—
120C2×C4×D11C22×C412yes—
121C2×C4×D11C2×D411yescharacteristic
122C2×C4×D11C2×D411yescharacteristic
123C2×C4×D11C2×D411yescharacteristic
124C2×C4×D11C2×D411yescharacteristic
125C2×C4×D11C2×Q812yes—
126C2×C4×D11C2×Q812yes—
127C2×C4×D11#4112yes—
128C11×M16—22no—
129C11×M16—21no—
130C11×M16C22×C414yes—
131C11×M16C2×Q812yes—
132C2×C8×C11—21no—
133C2×C8×C11—22no—
134C2×C8×C11C22×C412yes—
135C2×C8×C11C2×D411yescharacteristic
136C2×C8×C11C2×D411yescharacteristic
137C2×C8×C11C2×Q812yes—
138C11×C4⋊C4—22no—
139C11×C4⋊C4—22no—
140C11×C4⋊C4C2×D411yescharacteristic
141C11×C4⋊C4C2×D411yescharacteristic
142C11×C22⋊C4—21no—
143C42×C11—21no—
144C22⋊Dic11—21no—
145(C2×D11)⋊C4—21no—
146(C2×D11)⋊C4—21no—
147(C2×D11)⋊C4—42no—
148(C2×D11)⋊C4—42no—
149C4⋊Dic11—22no—
150C4⋊Dic11—22no—
151C4⋊Dic11C2×D411yescharacteristic
152C4⋊Dic11C2×D411yescharacteristic
153Dic11⋊C4—21no—
154Dic11⋊C4—21no—
155C4×Dic11—21no—
156C4×Dic11—21no—
157C4×Dic11—21no—
158C4×Dic11—42no—
159C4×Dic11—42no—
160#4318—22no—
161#4318—21no—
162#4318C22×C414yes—
163#4318C2×Q812yes—
164C2×C11⋊C8—21no—
165C2×C11⋊C8—22no—
166C2×C11⋊C8C22×C412yes—
167C2×C11⋊C8C2×D411yescharacteristic
168C2×C11⋊C8C2×D411yescharacteristic
169C2×C11⋊C8C2×Q812yes—
170#4313—28no—
171#4313—24no—
172C8×D11—28no—
173C8×D11—24no—
174C8×D11C4⋊C414yes—
175C8×D11C4⋊C414yes—
176C8×D11C4⋊C414yes—
177C8×D11C4⋊C414yes—
178C22×#108—111no—
179#2911—112no—
180C2×#427—111no—
181C2×#405—111no—
182#1952—111no—
183#1952—111no—
184#1952—111no—
185#1952D1111yescharacteristic, complemented
186#1951—112no—
187#1951—112no—
188#1742—112no—
189C23×C11C2×#4111yescharacteristic
190C22×D11—41no—
191C22×D11—41no—
192C22×D11C4×Q812yes—
193C22×D11#12111yescharacteristic
194C22×D11#12111yescharacteristic
195C22×D11#12512yes—
196C2×C4×C11—21no—
197C2×C4×C11—21no—
198C2×C4×C11—42no—
199C2×C4×C11—82no—
200C2×C4×C11C23×C411yescharacteristic
201C2×C4×C11C22×D411yescharacteristic
202C2×C4×C11C22×D411yescharacteristic
203C2×C4×C11C22×Q811yescharacteristic
204C2×C4×C11C22×Q811yescharacteristic
205C2×C4×C11C2×#4111yescharacteristic
206C2×Dic11—21no—
207C2×Dic11—21no—
208C2×Dic11—42no—
209C2×Dic11—82no—
210C2×Dic11C4×Q812yes—
211C2×Dic11#12111yescharacteristic
212C2×Dic11#12111yescharacteristic
213C2×Dic11#12512yes—
214C4×D11—42no—
215C4×D11—42no—
216C4×D11C2×C4⋊C412yes—
217C4×D11C2×C4⋊C412yes—
218C4×D11C4×D412yes—
219C4×D11C4×D412yes—
220C4×D11C22⋊Q812yes—
221C4×D11C22⋊Q812yes—
222C4×D11C4⋊Q812yes—
223C4×D11C4⋊Q812yes—
224C8×C11—24no—
225C8×C11—22no—
226C8×C11C2×C4⋊C412yes—
227C8×C11C2×C4⋊C412yes—
228C11⋊C8—24no—
229C11⋊C8—22no—
230C11⋊C8C2×C4⋊C412yes—
231C11⋊C8C2×C4⋊C412yes—
232C22×M16—111no—
233C22×M16—112no—
234C23×C8—111no—
235C2×#117—111no—
236C2×#117—112no—
237C2×#108—112no—
238C2×#108—111no—
239C2×#108—118no—
240C2×#108C2×D1111yescharacteristic
241#428—112no—
242#428—112no—
243#428—112no—
244#428—222no—
245#428—222no—
246#428C2×D1112yes—
247#427—222no—
248#427—222no—
249#427—221no—
250#427—221no—
251#427—221no—
252#427—221no—
253C2×#107—111no—
254C2×#107C2×D1111yescharacteristic
255C2×#106—112no—
256#405—111no—
257#405—111no—
258#405—111no—
259#405—221no—
260#405—221no—
261#405C2×D1111yescharacteristic
262C2×#97—221no—
263C2×C4×C8—221no—
264#343—112no—
265#343—112no—
266#343—112no—
267#343C2×D1112yes—
268C22×C11—21no—
269C22×C11—21no—
270C22×C11C2×C4×Q811yescharacteristic
271C22×C11C2×#12111yescharacteristic
272C22×C11C2×#12511yescharacteristic
273C2×D11—21no—
274C2×D11—21no—
275C2×D11—21no—
276C2×D11—21no—
277C2×D11—42no—
278C2×D11—42no—
279C2×D11#38912yes—
280C2×D11#38912yes—
281C4×C11—41no—
282C4×C11—41no—
283C4×C11—82no—
284C4×C11C22×C4⋊C411yescharacteristic
285C4×C11C2×C4×D411yescharacteristic
286C4×C11C2×C22⋊Q811yescharacteristic
287C4×C11C2×C4⋊Q811yescharacteristic
288Dic11—41no—
289Dic11—41no—
290Dic11—82no—
291Dic11#38912yes—
292Dic11#38912yes—
293C23×C4—111no—
294C2×M16—111no—
295C2×M16—112no—
296C2×M16—118no—
297C2×M16—114no—
298C2×M16—221no—
299C2×M16—222no—
300C2×M16—222no—
301C2×M16—224no—
302C2×M16C22×D1112yes—
303C2×M16C22×D1111yescharacteristic
304C22×C8—111no—
305C22×C8—114no—
306C22×C8—111no—
307C22×C8—111no—
308C22×C8—111no—
309C22×C8—111no—
310C22×C8—114no—
311C22×C8—221no—
312C22×C8—222no—
313C22×C8C22×D1111yescharacteristic
314#117—111no—
315#117—111no—
316#117—111no—
317#117—221no—
318#117—221no—
319#117—222no—
320#117—222no—
321#117—222no—
322#117—222no—
323#117C22×D1111yescharacteristic
324C2×C4⋊C4—111no—
325C2×C4⋊C4—111no—
326C2×C4⋊C4—112no—
327C2×C4⋊C4C22×D1112yes—
328C2×C22⋊C4—221no—
329C2×C22⋊C4—222no—
330C2×C42—221no—
331C2×C42—222no—
332#108—118no—
333#108—114no—
334#108C4×D1114yescomplemented
335#107—21no—
336#107—21no—
337#107—22no—
338#107—222no—
339#107—222no—
340#107—221no—
341#107—221no—
342#107—222no—
343#106—22no—
344#106—222no—
345#106—222no—
346#106—222no—
347#106—222no—
348#106—222no—
349#97—21no—
350#97—221no—
351#97—221no—
352#97—221no—
353C4×C8—21no—
354C4×C8—221no—
355C4×C8—221no—
356C4×C8—221no—
357C2×C11—21no—
358C2×C11—21no—
359C2×C11C2×#38911yescharacteristic
360C2×C11#306711yescharacteristic
361C2×C11#306711yescharacteristic
362D11—22no—
363D11—22no—
364C24—111no—
365C22×C4—22no—
366C22×C4—111no—
367C22×C4—112no—
368C22×C4—111no—
369C22×C4—111no—
370C22×C4—111no—
371C22×C4—111no—
372C22×C4—112no—
373C22×C4—112no—
374C22×C4—112no—
375C22×C4—221no—
376C22×C4—221no—
377C22×C4—222no—
378C22×C4C23×D1111yescharacteristic
379M16—22no—
380M16—21no—
381M16—114no—
382M16—112no—
383M16—228no—
384M16—224no—
385M16—222no—
386M16—221no—
387M16C2×C4×D1114yes—
388M16Q8×D1112yes—
389C2×C8—21no—
390C2×C8—22no—
391C2×C8—112no—
392C2×C8—111no—
393C2×C8—111no—
394C2×C8—112no—
395C2×C8—114no—
396C2×C8—114no—
397C2×C8—114no—
398C2×C8—114no—
399C2×C8—228no—
400C2×C8—224no—
401C2×C8—221no—
402C2×C8—222no—
403C2×C8C2×C4×D1112yes—
404C2×C8D4×D1111yescharacteristic
405C2×C8D4×D1111yescharacteristic
406C2×C8Q8×D1112yes—
407C4⋊C4—22no—
408C4⋊C4—22no—
409C4⋊C4—111no—
410C4⋊C4—111no—
411C4⋊C4—221no—
412C4⋊C4—221no—
413C4⋊C4—222no—
414C4⋊C4—222no—
415C4⋊C4D4×D1111yescharacteristic
416C4⋊C4D4×D1111yescharacteristic
417C22⋊C4—21no—
418C22⋊C4—221no—
419C22⋊C4—221no—
420C22⋊C4—221no—
421C22⋊C4—442no—
422C22⋊C4—442no—
423C42—21no—
424C42—221no—
425C42—221no—
426C42—221no—
427C42—442no—
428C42—442no—
429C11#2118111yescharacteristic, complemented, Sylow
430C23—111no—
431C23—111no—
432C23—112no—
433C23—112no—
434C23—441no—
435C23—441no—
436C23#41×D1111yescharacteristic
437C2×C4—21no—
438C2×C4—21no—
439C2×C4—42no—
440C2×C4—82no—
441C2×C4—112no—
442C2×C4—111no—
443C2×C4—111no—
444C2×C4—112no—
445C2×C4—112no—
446C2×C4—112no—
447C2×C4—112no—
448C2×C4—112no—
449C2×C4—112no—
450C2×C4—112no—
451C2×C4—112no—
452C2×C4—112no—
453C2×C4—221no—
454C2×C4—221no—
455C2×C4—442no—
456C2×C4—442no—
457C2×C4—442no—
458C2×C4—882no—
459C2×C4C22×C4×D1111yescharacteristic
460C2×C4C2×D4×D1111yescharacteristic
461C2×C4C2×D4×D1111yescharacteristic
462C2×C4C2×Q8×D1111yescharacteristic
463C2×C4C2×Q8×D1111yescharacteristic
464C2×C4#41×D1111yescharacteristic
465C8—24no—
466C8—22no—
467C8—112no—
468C8—112no—
469C8—224no—
470C8—222no—
471C8C4⋊C4×D1112yes—
472C8C4⋊C4×D1112yes—
473C22—21no—
474C22—21no—
475C22—112no—
476C22—112no—
477C22—221no—
478C22—221no—
479C22—221no—
480C22—221no—
481C22—442no—
482C22—442no—
483C22C4×Q8×D1111yescharacteristic
484C22D11×#12111yescharacteristic
485C22D11×#12511yescharacteristic
486C4—41no—
487C4—41no—
488C4—82no—
489C4—112no—
490C4—112no—
491C4—441no—
492C4—441no—
493C4—882no—
494C4C2×C4⋊C4×D1111yescharacteristic
495C4C4×D4×D1111yescharacteristic
496C4D11×C22⋊Q811yescharacteristic
497C4D11×C4⋊Q811yescharacteristic
498C2—21no—
499C2—21no—
500C2—222no—
501C2—222no—
502C2D11×#38911yescharacteristic
503C2#1307833411yescharacteristic
504C2#1307833811yescharacteristic
subgroupG/H
centerC22D11×#121
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#1952C2
socleC22×C11C2×#121
prime radicalC23×D11#41
cosocleC22×C4×C11C24
hypercenter#1952D11
hypocenterC11#21181
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ #1952

Complements

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

NH ≅ G/Ntype
5. #13069402C2semidirect
6. #13069401C2semidirect
7. #13069399C2semidirect
8. #13069395C2semidirect
9. #13069393C2semidirect
11. C11×#1952C2semidirect
31. D11×#108C4semidirect
87. C11×#108C2×C4semidirect
94. #66886C2×C4semidirect
95. #66883C2×C4semidirect
185. #1952D11semidirect
334. #108C4×D11semidirect
429. C11#21181semidirect

Maximal subgroups

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

subgroupindex
C2×D11×#1082
#130772032
C2×#106224932
D11×#4052
#130694022
#130694012
#130693992
#130693952
#130693932
#130683532
C11×#19522
#2118111