Finite Group Databasebeta

← #14656743

Subgroups — #14656743

Order 2816.

900 conjugacy classes of subgroups; only the 115 normal subgroups are shown.

normal subgroups only

This group has 900 conjugacy classes of subgroups — too many to draw. Only its 115 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#13074730C211yesmaximal, characteristic, complemented
2#13068547C212yesmaximal
3#13066495C212yesmaximal, complemented
4#13066459C211yesmaximal, characteristic, complemented
5C11×#1438C211yesmaximal, characteristic
6C23×D4×C11C2211yescharacteristic
7C22×C11×C22⋊C4—21no—
8C22×C11×C22⋊C4—21no—
9C2×#66977—21no—
10C2×C11×#95C2211yescharacteristic
11C2×C11×#95C2211yescharacteristic
12C2×#66896—22no—
13C2×#66896—22no—
14#10622825—21no—
15#10622825C2212yes—
16C2×C22⋊(C11⋊C8)C2212yes—
17#10622274—22no—
18#10622269—22no—
19C25×C11—21no—
20C22×D4×C11—22no—
21C22×D4×C11—22no—
22C22×D4×C11—21no—
23C22×D4×C11—42no—
24C22×D4×C11—42no—
25C22×D4×C11Q812yescomplemented
26C23×C4×C11—21no—
27C23×C4×C11D411yescharacteristic
28C23×C4×C11D411yescharacteristic
29C23×C4×C11C2311yescharacteristic
30C22×Dic22—21no—
31C2×C11×C22⋊C4—42no—
32C2×C11×C22⋊C4—42no—
33C2×C11×C22⋊C4—42no—
34C2×C11×C22⋊C4—42no—
35C2×C11×C22⋊C4—42no—
36C2×C11×C22⋊C4—42no—
37C2×C22⋊Dic11—22no—
38C2×C4⋊Dic11—21no—
39C2×C4⋊Dic11—21no—
40C2×C4⋊Dic11—21no—
41C2×C4⋊Dic11D412yes—
42C2×C4⋊Dic11D412yes—
43#66977—42no—
44#66977—42no—
45C2×Dic11⋊C4—22no—
46C22×C11⋊C8—22no—
47C11×#95—22no—
48C11×#95—22no—
49#66896—44no—
50#66896—44no—
51C11⋊#95—22no—
52C11⋊#95—22no—
53C22⋊(C11⋊C8)—22no—
54C22⋊(C11⋊C8)—22no—
55#10340—111nomaximal, Sylow
56C24×C11—22no—
57C24×C11—22no—
58C24×C11—22no—
59C24×C11—41no—
60C24×C11—41no—
61C24×C11—41no—
62C24×C11—41no—
63C24×C11—41no—
64C24×C11—41no—
65C24×C11—41no—
66C24×C11—41no—
67C24×C11—41no—
68C24×C11—41no—
69C24×C11—41no—
70C24×C11—41no—
71C24×C11C2×D411yescharacteristic
72C2×D4×C11—24no—
73C2×D4×C11—24no—
74C2×D4×C11—24no—
75C2×D4×C11—42no—
76C2×D4×C11—42no—
77C2×D4×C11—44no—
78C2×D4×C11—48no—
79C2×D4×C11—44no—
80C2×D4×C11—42no—
81C22×C4×C11—21no—
82C22×C4×C11—21no—
83C22×C4×C11—21no—
84C22×C4×C11—21no—
85C22×C4×C11—22no—
86C22×C4×C11—41no—
87C22×C4×C11—41no—
88C22×C4×C11—41no—
89C22×C4×C11—41no—
90C22×C4×C11—41no—
91C22×C4×C11—41no—
92C22×C4×C11—41no—
93C22×C4×C11—41no—
94C22×C4×C11—41no—
95C22×C4×C11—41no—
96C22×C4×C11—41no—
97C22×C4×C11—41no—
98C22×C4×C11D812yes—
99C22×C4×C11SD1612yes—
100C22×C4×C11C2×D412yes—
101C22×C4×C11C2×Q811yescharacteristic
102C22×C4×C11#4112yes—
103C22×C4×C11#4111yescharacteristic
104C22×Dic11—22no—
105C22×Dic11—22no—
106C2×Dic22—42no—
107C2×Dic22—81no—
108C2×Dic22—81no—
109C11×C22⋊C4—48no—
110C11×C22⋊C4—48no—
111C22⋊Dic11—42no—
112C22⋊Dic11—42no—
113C4⋊Dic11—42no—
114C4⋊Dic11—42no—
115C4⋊Dic11—42no—
116C4⋊Dic11—81no—
117C4⋊Dic11—81no—
118Dic11⋊C4—44no—
119C2×C11⋊C8—42no—
120C2×C11⋊C8—42no—
121C2×C11⋊C8—42no—
122#2659—111no—
123#1786—112no—
124#1438D1111yescharacteristic
125#1294—112no—
126#1280—111no—
127C23×C11—21no—
128C23×C11—21no—
129C23×C11—21no—
130C23×C11—21no—
131C23×C11—24no—
132C23×C11—42no—
133C23×C11—42no—
134C23×C11—42no—
135C23×C11—42no—
136C23×C11—42no—
137C23×C11—42no—
138C23×C11—42no—
139C23×C11—42no—
140C23×C11—42no—
141C23×C11—42no—
142C23×C11—42no—
143C23×C11—42no—
144C23×C11—42no—
145C23×C11—42no—
146C23×C11—42no—
147C23×C11—42no—
148C23×C11—42no—
149C23×C11—42no—
150C23×C11—81no—
151C23×C11—81no—
152C23×C11—81no—
153C23×C11—81no—
154C23×C11—81no—
155C23×C11—81no—
156C23×C11—81no—
157C23×C11—81no—
158C23×C11—81no—
159C23×C11—81no—
160C23×C11—81no—
161C23×C11—81no—
162C23×C11—81no—
163C23×C11—81no—
164C23×C11—81no—
165C23×C11—81no—
166C23×C11#12011yescharacteristic
167C23×C11C22⋊Q811yescharacteristic
168C23×C11#12411yescharacteristic
169C23×C11C2×D811yescharacteristic
170C23×C11C2×SD1611yescharacteristic
171C23×C11AGL(1,ℤ/8)11yescharacteristic
172C23×C11#13711yescharacteristic
173D4×C11—28no—
174D4×C11—44no—
175D4×C11—44no—
176D4×C11—44no—
177C2×C4×C11—22no—
178C2×C4×C11—22no—
179C2×C4×C11—22no—
180C2×C4×C11—22no—
181C2×C4×C11—41no—
182C2×C4×C11—41no—
183C2×C4×C11—42no—
184C2×C4×C11—41no—
185C2×C4×C11—41no—
186C2×C4×C11—41no—
187C2×C4×C11—41no—
188C2×C4×C11—42no—
189C2×C4×C11—42no—
190C2×C4×C11—42no—
191C2×C4×C11—42no—
192C2×C4×C11—42no—
193C2×C4×C11—81no—
194C2×C4×C11—81no—
195C2×C4×C11—81no—
196C2×C4×C11—81no—
197C2×C4×C11—81no—
198C2×C4×C11—81no—
199C2×C4×C11C22⋊Q812yes—
200C2×C4×C11#12412yes—
201C2×Dic11—42no—
202C2×Dic11—42no—
203C2×Dic11—42no—
204C2×Dic11—42no—
205C2×Dic11—42no—
206C2×Dic11—42no—
207Dic22—84no—
208C11⋊C8—82no—
209C23×D4C2×D1111yescharacteristic
210C2×C22⋊Q8—221no—
211C22×C22⋊C4—21no—
212C22×C22⋊C4—21no—
213C2×#102—222no—
214C2×#102—222no—
215C2×C22⋊C8—112no—
216#398—222no—
217#395—222no—
218#380—112no—
219#380—221no—
220C2×#95C2×D1111yescharacteristic
221C2×#95C2×D1111yescharacteristic
222C22×C11—21no—
223C22×C11—21no—
224C22×C11—21no—
225C22×C11—21no—
226C22×C11—21no—
227C22×C11—21no—
228C22×C11—21no—
229C22×C11—21no—
230C22×C11—21no—
231C22×C11—21no—
232C22×C11—21no—
233C22×C11—21no—
234C22×C11—44no—
235C22×C11—44no—
236C22×C11—44no—
237C22×C11—82no—
238C22×C11—82no—
239C22×C11—82no—
240C22×C11—82no—
241C22×C11—82no—
242C22×C11—82no—
243C22×C11—82no—
244C22×C11—82no—
245C22×C11—82no—
246C22×C11—82no—
247C22×C11—82no—
248C22×C11—82no—
249C22×C11#39311yescharacteristic
250C22×C11#44711yescharacteristic
251C22×C11#44811yescharacteristic
252C22×C11#45311yescharacteristic
253C22×C11#45411yescharacteristic
254C22×C11B(4,𝔽2)11yescharacteristic
255C22×C11B(4,𝔽2)11yescharacteristic
256C22×C11#47411yescharacteristic
257C22×C11#47611yescharacteristic
258C22×C11#48611yescharacteristic
259C22×C11#48911yescharacteristic
260C4×C11—22no—
261C4×C11—22no—
262C4×C11—42no—
263C4×C11—42no—
264C4×C11—82no—
265Dic11—82no—
266Dic11—82no—
267C25—21no—
268C22×Q8—221no—
269C22×D4—21no—
270C22×D4—22no—
271C22×D4—22no—
272C22×D4—42no—
273C22×D4—42no—
274C22×D4Dic2212yescomplemented
275C23×C4—21no—
276C23×C4C22⋊D1111yescharacteristic
277C23×C4C22⋊D1111yescharacteristic
278C23×C4C22×D1111yescharacteristic
279C22×C8—222no—
280C22⋊Q8—442no—
281C22⋊Q8—442no—
282C2×C4⋊C4—112no—
283C2×C4⋊C4—112no—
284C2×C4⋊C4—222no—
285C2×C4⋊C4—221no—
286C2×C4⋊C4—221no—
287C2×C4⋊C4—221no—
288C2×C22⋊C4—42no—
289C2×C22⋊C4—42no—
290C2×C22⋊C4—42no—
291C2×C22⋊C4—42no—
292C2×C22⋊C4—42no—
293C2×C22⋊C4—42no—
294C2×C22⋊C4—222no—
295#102—444no—
296#102—444no—
297C22⋊C8—222no—
298C22⋊C8—222no—
299#95—22no—
300#95—22no—
301#95—222no—
302#95—222no—
303C2×C11—21no—
304C2×C11—21no—
305C2×C11—21no—
306C2×C11—21no—
307C2×C11—84no—
308C2×C11#159511yescharacteristic
309C2×C11#159611yescharacteristic
310C2×C11#159811yescharacteristic
311C2×C11#159911yescharacteristic
312C2×C11#202311yescharacteristic
313C2×C11#202711yescharacteristic
314C2×C11#202911yescharacteristic
315C24—22no—
316C24—22no—
317C24—22no—
318C24—41no—
319C24—41no—
320C24—41no—
321C24—41no—
322C24—41no—
323C24—41no—
324C24—41no—
325C24—41no—
326C24—41no—
327C24—41no—
328C24—41no—
329C24—41no—
330C24C2×C22⋊D1111yescharacteristic
331C2×Q8—442no—
332C2×Q8—881no—
333C2×Q8—881no—
334C2×D4—24no—
335C2×D4—24no—
336C2×D4—24no—
337C2×D4—42no—
338C2×D4—42no—
339C2×D4—44no—
340C2×D4—48no—
341C2×D4—44no—
342C2×D4—42no—
343C22×C4—21no—
344C22×C4—21no—
345C22×C4—21no—
346C22×C4—21no—
347C22×C4—22no—
348C22×C4—41no—
349C22×C4—41no—
350C22×C4—41no—
351C22×C4—41no—
352C22×C4—41no—
353C22×C4—41no—
354C22×C4—41no—
355C22×C4—41no—
356C22×C4—41no—
357C22×C4—41no—
358C22×C4—41no—
359C22×C4—41no—
360C22×C4—222no—
361C22×C4—222no—
362C22×C4#432312yes—
363C22×C4#432412yes—
364C22×C4C2×Dic2211yescharacteristic
365C22×C4#433911yescharacteristic
366C22×C4D4×D1112yes—
367C22×C4#434112yes—
368C2×C8—442no—
369C2×C8—442no—
370C2×C8—442no—
371C4⋊C4—442no—
372C4⋊C4—442no—
373C4⋊C4—444no—
374C4⋊C4—442no—
375C4⋊C4—881no—
376C4⋊C4—881no—
377C22⋊C4—48no—
378C22⋊C4—48no—
379C22⋊C4—442no—
380C22⋊C4—442no—
381C11#1034011yescharacteristic, complemented, Sylow
382C23—21no—
383C23—21no—
384C23—21no—
385C23—21no—
386C23—24no—
387C23—42no—
388C23—42no—
389C23—42no—
390C23—42no—
391C23—42no—
392C23—42no—
393C23—42no—
394C23—42no—
395C23—42no—
396C23—42no—
397C23—42no—
398C23—42no—
399C23—42no—
400C23—42no—
401C23—42no—
402C23—42no—
403C23—42no—
404C23—42no—
405C23—81no—
406C23—81no—
407C23—81no—
408C23—81no—
409C23—81no—
410C23—81no—
411C23—81no—
412C23—81no—
413C23—81no—
414C23—81no—
415C23—81no—
416C23—81no—
417C23—81no—
418C23—81no—
419C23—81no—
420C23—81no—
421C23#6697711yescharacteristic
422C23C2×#432311yescharacteristic
423C23C2×#432411yescharacteristic
424C23#6698911yescharacteristic
425C23#6699011yescharacteristic
426C23#6700211yescharacteristic
427C23#6700411yescharacteristic
428Q8—884no—
429D4—28no—
430D4—44no—
431D4—44no—
432D4—44no—
433C2×C4—22no—
434C2×C4—22no—
435C2×C4—22no—
436C2×C4—22no—
437C2×C4—41no—
438C2×C4—41no—
439C2×C4—42no—
440C2×C4—41no—
441C2×C4—41no—
442C2×C4—41no—
443C2×C4—41no—
444C2×C4—42no—
445C2×C4—42no—
446C2×C4—42no—
447C2×C4—42no—
448C2×C4—42no—
449C2×C4—81no—
450C2×C4—81no—
451C2×C4—81no—
452C2×C4—81no—
453C2×C4—81no—
454C2×C4—81no—
455C2×C4—442no—
456C2×C4—442no—
457C2×C4—442no—
458C2×C4—442no—
459C2×C4—442no—
460C2×C4—442no—
461C2×C4#6693112yes—
462C2×C4#6693812yes—
463C8—882no—
464C22—21no—
465C22—21no—
466C22—21no—
467C22—21no—
468C22—21no—
469C22—21no—
470C22—21no—
471C22—21no—
472C22—21no—
473C22—21no—
474C22—21no—
475C22—21no—
476C22—44no—
477C22—44no—
478C22—44no—
479C22—82no—
480C22—82no—
481C22—82no—
482C22—82no—
483C22—82no—
484C22—82no—
485C22—82no—
486C22—82no—
487C22—82no—
488C22—82no—
489C22—82no—
490C22—82no—
491C22#1062256011yescharacteristic
492C22#1062262011yescharacteristic
493C22#1062262111yescharacteristic
494C22#1062264511yescharacteristic
495C22#1062264511yescharacteristic
496C22#1062264911yescharacteristic
497C22#1062265311yescharacteristic
498C22#1062266811yescharacteristic
499C22#1062267511yescharacteristic
500C22#1062268311yescharacteristic
501C22#1062269011yescharacteristic
502C4—22no—
503C4—22no—
504C4—42no—
505C4—42no—
506C4—82no—
507C4—882no—
508C4—882no—
509C2—21no—
510C2—21no—
511C2—21no—
512C2—21no—
513C2—84no—
514C2#1306753311yescharacteristic
515C2#1306753811yescharacteristic
516C2#1306755011yescharacteristic
517C2#1306755511yescharacteristic
518C2#1306975211yescharacteristic
519C2#1306977211yescharacteristic
520C2#1306978011yescharacteristic
subgroupG/H
centerC23#66990
commutator, cosocleC23×C4×C11C23
FrattiniC23×C4C22×D11
FittingC11×#1438C2
socleC23×C11#120
prime radicalC23×D4×C11C22
hypercenter#1438D11
hypocenterC11#10340
LCSG ▷ C23×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1438

Complements

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

NH ≅ G/Ntype
1. #13074730C2semidirect
3. #13066495C2semidirect
4. #13066459C2semidirect
25. C22×D4×C11Q8semidirect
274. C22×D4Dic22semidirect
381. C11#10340semidirect

Maximal subgroups

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

subgroupindex
#130747302
#130685472
#130664952
#130664592
C11×#14382
#1034011