Finite Group Databasebeta

← #14758149

Subgroups — #14758149

Order 2816.

814 conjugacy classes of subgroups.

The subgroup lattice has 610 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622323C211yesmaximal, characteristic
2#13071268C211yesmaximal, characteristic, complemented
3#13071260C211yesmaximal, characteristic
4#13069497C211yesmaximal, characteristic
5#13069470C211yesmaximal, characteristic
6#13069354C211yesmaximal, characteristic, complemented
7#13069349C211yesmaximal, characteristic, complemented
8#13069313C211yesmaximal, characteristic
9#13069306C211yesmaximal, characteristic, complemented
10#13069299C211yesmaximal, characteristic
11#13069292C211yesmaximal, characteristic, complemented
12#13068513C211yesmaximal, characteristic, complemented
13C4×#66880C211yesmaximal, characteristic, complemented
14C4×#66885C211yesmaximal, characteristic
15C11×#1726C211yesmaximal, characteristic, complemented
16C22×#4314C2211yescharacteristic
17C2×C4×D44C2211yescharacteristic
18C2×C4×Dic22C2211yescharacteristic
19C2×C11×#97C2211yescharacteristic
20C2×C11×#97C2211yescharacteristic
21C2×C11×#97C2211yescharacteristic
22C2×C4×C8×C11C2211yescharacteristic
23C2×C4×C8×C11C2211yescharacteristic
24C2×C4×C8×C11C2211yescharacteristic
25C11×#376C2211yescharacteristic
26C2×#66885C2211yescharacteristic
27C2×#66885C2211yescharacteristic
28C2×#66885C2211yescharacteristic
29C2×#66882C2211yescharacteristic
30C2×#66882C2211yescharacteristic
31C2×#66881C2211yescharacteristic
32C2×#66880C2211yescharacteristic
33C2×#66880C2211yescharacteristic
34C2×#66880C2211yescharacteristic
35#10622552C2211yescharacteristic
36#10622552C2211yescharacteristic
37C4×C4⋊Dic11C2211yescharacteristic
38C4×C4⋊Dic11C2211yescharacteristic
39#10622542C2211yescharacteristic
40#10622542C2211yescharacteristic
41#10622541C2211yescharacteristic
42#10622541C2211yescharacteristic
43#10622541C2211yescharacteristic
44#10622541C2211yescharacteristic
45#10622323C418yescomplemented
46#10622282—21no—
47#10622282—21no—
48#10622280—21no—
49#10622277—21no—
50#10622265—21no—
51#10622265—21no—
52#10622264—21no—
53#10622263—21no—
54#10622189C2211yescharacteristic
55#10622189C2211yescharacteristic
56#10622189C2211yescharacteristic
57#10622189C2211yescharacteristic
58#10622189C2211yescharacteristic
59#10622189C2211yescharacteristic
60C22×D44C2311yescharacteristic
61C22×C4×D11—21no—
62C22×Dic22C2311yescharacteristic
63C22×C8×C11C2311yescharacteristic
64C22×C8×C11C2311yescharacteristic
65C22×C8×C11C2311yescharacteristic
66C22×C8×C11C2311yescharacteristic
67C2×C42×C11C2311yescharacteristic
68C2×C42×C11C2311yescharacteristic
69C2×C42×C11C2311yescharacteristic
70C2×(C2×D11)⋊C4—21no—
71C2×(C2×D11)⋊C4—21no—
72C2×(C2×D11)⋊C4—21no—
73C2×(C2×D11)⋊C4—21no—
74C2×(C2×D11)⋊C4—21no—
75C2×C4⋊Dic11C2311yescharacteristic
76C2×C4⋊Dic11C2311yescharacteristic
77C2×C4⋊Dic11C2311yescharacteristic
78C2×C4⋊Dic11C2311yescharacteristic
79C2×C4⋊Dic11C2311yescharacteristic
80C2×C4⋊Dic11C2311yescharacteristic
81C2×Dic11⋊C4—21no—
82C2×Dic11⋊C4—21no—
83C2×Dic11⋊C4—21no—
84C2×Dic11⋊C4—21no—
85C2×Dic11⋊C4—21no—
86C2×C4×Dic11—21no—
87C2×C4×Dic11—21no—
88C2×C4×Dic11—21no—
89C2×#4314—22no—
90C2×#4314—22no—
91C2×#4314C2×C414yes—
92C4×D44—22no—
93C4×D44C2×C414yes—
94C4×Dic22—22no—
95C4×Dic22C2×C414yes—
96C11×#97—22no—
97C11×#97—22no—
98C11×#97C2×C414yes—
99C4×C8×C11—22no—
100C4×C8×C11—22no—
101C4×C8×C11—22no—
102C11×#95D411yescharacteristic
103C11×#95D411yescharacteristic
104C11×#95D411yescharacteristic
105C11×#95D411yescharacteristic
106C11⋊#95—21no—
107C11⋊#95—21no—
108C11⋊#95—21no—
109C11⋊#95—21no—
110C11⋊#95—21no—
111C11⋊#95—21no—
112C11⋊#95—21no—
113C11⋊#95—21no—
114C11⋊#95—21no—
115C11⋊#95—21no—
116#66885—22no—
117#66885—22no—
118#66885C2×C414yes—
119#66882—22no—
120#66882C2×C414yes—
121#66881—22no—
122#66880—22no—
123#66880—22no—
124#66880C2×C414yes—
125#21291—111nomaximal, Sylow
126C23×D11—21no—
127C22×C4×C11C2×D411yescharacteristic
128C22×C4×C11C2×D411yescharacteristic
129C22×C4×C11C2×D411yescharacteristic
130C22×C4×C11C2×D411yescharacteristic
131C22×C4×C11C2×D411yescharacteristic
132C22×C4×C11C2×D411yescharacteristic
133C22×C4×C11C2411yescharacteristic
134C22×Dic11—21no—
135C22×Dic11—21no—
136C22×Dic11—21no—
137C22×Dic11—21no—
138C22×Dic11—21no—
139C22×Dic11—21no—
140C22×Dic11—21no—
141C2×D44—21no—
142C2×D44—21no—
143C2×D44—21no—
144C2×D44—21no—
145C2×D44—21no—
146C2×D44C22×C412yes—
147C2×C4×D11—24no—
148C2×C4×D11—81no—
149C2×C4×D11—81no—
150C2×Dic22—21no—
151C2×Dic22—21no—
152C2×Dic22—21no—
153C2×Dic22—21no—
154C2×Dic22—21no—
155C2×Dic22C22×C412yes—
156C2×C8×C11—21no—
157C2×C8×C11—21no—
158C2×C8×C11—21no—
159C2×C8×C11—21no—
160C2×C8×C11—21no—
161C2×C8×C11—21no—
162C2×C8×C11C22×C412yes—
163C2×C8×C11C22×C412yes—
164C2×C8×C11#4112yes—
165C2×C8×C11#4112yes—
166C2×C8×C11#4112yes—
167C2×C8×C11#4112yes—
168C42×C11—21no—
169C42×C11—21no—
170C42×C11—21no—
171C42×C11—21no—
172C42×C11C22×C412yes—
173C42×C11#4112yes—
174(C2×D11)⋊C4—24no—
175(C2×D11)⋊C4—81no—
176(C2×D11)⋊C4—81no—
177(C2×D11)⋊C4—81no—
178(C2×D11)⋊C4—81no—
179C4⋊Dic11—21no—
180C4⋊Dic11—21no—
181C4⋊Dic11—21no—
182C4⋊Dic11—21no—
183C4⋊Dic11—21no—
184C4⋊Dic11—21no—
185C4⋊Dic11—21no—
186C4⋊Dic11—21no—
187C4⋊Dic11—21no—
188C4⋊Dic11—21no—
189C4⋊Dic11C22×C412yes—
190C4⋊Dic11C22×C412yes—
191Dic11⋊C4—24no—
192Dic11⋊C4—81no—
193Dic11⋊C4—81no—
194Dic11⋊C4—81no—
195Dic11⋊C4—81no—
196C4×Dic11—24no—
197C4×Dic11—81no—
198C4×Dic11—81no—
199#4314—28no—
200C2×#440—111no—
201#2320—111no—
202#2319—111no—
203#1973—111no—
204#1968—111no—
205#1943—111no—
206#1942—111no—
207#1936—111no—
208#1935—111no—
209#1934—111no—
210#1933—111no—
211#1776—111no—
212C4×#103—111no—
213C4×#102—111no—
214#1726D1111yescharacteristic, complemented
215C23×C11C22×D411yescharacteristic
216C22×D11—22no—
217C22×D11—41no—
218C22×D11—41no—
219C22×D11—41no—
220C22×D11—41no—
221C22×D11—41no—
222C22×D11—41no—
223C2×C4×C11—21no—
224C2×C4×C11—21no—
225C2×C4×C11—21no—
226C2×C4×C11—21no—
227C2×C4×C11—21no—
228C2×C4×C11—21no—
229C2×C4×C11—21no—
230C2×C4×C11—21no—
231C2×C4×C11—21no—
232C2×C4×C11—21no—
233C2×C4×C11—21no—
234C2×C4×C11—21no—
235C2×C4×C11—21no—
236C2×C4×C11—21no—
237C2×C4×C11—21no—
238C2×C4×C11—21no—
239C2×C4×C11C4×D412yes—
240C2×C4×C11C4×D412yes—
241C2×C4×C11C23×C411yescharacteristic
242C2×C4×C11C2×#4111yescharacteristic
243C2×C4×C11C2×#4111yescharacteristic
244C2×C4×C11C2×#4111yescharacteristic
245C2×C4×C11C2×#4111yescharacteristic
246C2×C4×C11C2×#4111yescharacteristic
247C2×Dic11—22no—
248C2×Dic11—22no—
249C2×Dic11—22no—
250C2×Dic11—41no—
251C2×Dic11—41no—
252C2×Dic11—41no—
253C2×Dic11—41no—
254C2×Dic11—41no—
255C2×Dic11—41no—
256C2×Dic11—41no—
257C2×Dic11—41no—
258C2×Dic11—41no—
259C2×Dic11—41no—
260C2×Dic11—41no—
261C2×Dic11—41no—
262C2×Dic11—41no—
263C2×Dic11—41no—
264C2×Dic11—41no—
265C2×Dic11—41no—
266C2×Dic11—41no—
267C2×Dic11—41no—
268D44—22no—
269D44—22no—
270D44—41no—
271D44—41no—
272C4×D11—84no—
273Dic22—22no—
274Dic22—22no—
275Dic22—41no—
276Dic22—41no—
277C8×C11—22no—
278C8×C11—22no—
279C8×C11—22no—
280C8×C11#11714yes—
281C22×SD16—111no—
282C2×C4×Q8—111no—
283C2×C4×D4—111no—
284#440—118no—
285C2×#107—111no—
286C2×#107—111no—
287C2×#106—111no—
288C2×#103—111no—
289C2×#103—111no—
290C2×#103—111no—
291C2×#102—111no—
292C2×#102—111no—
293C2×#102—111no—
294C2×#97C2×D1111yescharacteristic
295C2×#97C2×D1111yescharacteristic
296C2×#97C2×D1111yescharacteristic
297C2×C4×C8C2×D1111yescharacteristic
298C2×C4×C8C2×D1111yescharacteristic
299C2×C4×C8C2×D1111yescharacteristic
300#391—111no—
301#391—111no—
302#390—111no—
303#390—111no—
304#389—111no—
305#389—111no—
306#389—111no—
307#389—111no—
308#388—221no—
309#388—221no—
310#387—221no—
311#387—221no—
312#383—221no—
313#382—221no—
314#381—221no—
315#380—221no—
316C4×C4⋊C4—111no—
317C4×C4⋊C4—111no—
318#376C2×D1111yescharacteristic
319#340—111no—
320#340—111no—
321#340—111no—
322#340—111no—
323#340—111no—
324#340—111no—
325C22×C11C2×C4×D411yescharacteristic
326C22×C11#53211yescharacteristic
327C22×C11#53211yescharacteristic
328C22×C11#57611yescharacteristic
329C22×C11#57711yescharacteristic
330C22×C11#57711yescharacteristic
331C22×C11#57811yescharacteristic
332C2×D11—42no—
333C2×D11—42no—
334C2×D11—42no—
335C2×D11—81no—
336C2×D11—81no—
337C2×D11—81no—
338C2×D11—81no—
339C4×C11—22no—
340C4×C11—22no—
341C4×C11—41no—
342C4×C11—41no—
343C4×C11—41no—
344C4×C11—41no—
345C4×C11C2×#11711yescharacteristic
346C4×C11C4×#4111yescharacteristic
347C4×C11#52911yescharacteristic
348C4×C11#52911yescharacteristic
349Dic11—42no—
350Dic11—42no—
351Dic11—42no—
352Dic11—81no—
353Dic11—81no—
354Dic11—81no—
355Dic11—81no—
356C22×Q8—111no—
357C22×D4—111no—
358C23×C4—221no—
359C2×SD16—114no—
360C2×SD16—222no—
361C2×SD16—222no—
362C22×C8C22×D1111yescharacteristic
363C22×C8C22×D1111yescharacteristic
364C22×C8C22×D1111yescharacteristic
365C22×C8C22×D1111yescharacteristic
366C4×Q8—114no—
367C4×Q8—222no—
368C4×D4—114no—
369C4×D4—222no—
370C2×C4⋊C4—111no—
371C2×C4⋊C4—111no—
372C2×C4⋊C4—111no—
373C2×C4⋊C4—111no—
374C2×C4⋊C4—111no—
375C2×C4⋊C4—111no—
376C2×C4⋊C4—221no—
377C2×C4⋊C4—221no—
378C2×C4⋊C4—221no—
379C2×C4⋊C4—221no—
380C2×C4⋊C4—221no—
381C2×C22⋊C4—221no—
382C2×C22⋊C4—221no—
383C2×C22⋊C4—221no—
384C2×C22⋊C4—221no—
385C2×C22⋊C4—221no—
386C2×C42—221no—
387C2×C42—221no—
388C2×C42—221no—
389C2×C42C22×D1111yescharacteristic
390C2×C42C22×D1111yescharacteristic
391C2×C42C22×D1111yescharacteristic
392#107—114no—
393#107—222no—
394#106—222no—
395#103—114no—
396#103—222no—
397#103—222no—
398#102—114no—
399#102—222no—
400#102—222no—
401#97—22no—
402#97—22no—
403#97C4×D1114yes—
404C4×C8—22no—
405C4×C8—22no—
406C4×C8—22no—
407#95—221no—
408#95—221no—
409#95—221no—
410#95—221no—
411#95—221no—
412#95—221no—
413#95—221no—
414#95—221no—
415#95—221no—
416#95—221no—
417#95D4411yescharacteristic
418#95D4411yescharacteristic
419#95D4411yescharacteristic
420#95D4411yescharacteristic
421C2×C11#229311yescharacteristic
422C2×C11#294611yescharacteristic
423C2×C11#294711yescharacteristic
424C2×C11#317411yescharacteristic
425C2×C11#317511yescharacteristic
426C2×C11#317811yescharacteristic
427C2×C11#317911yescharacteristic
428D11—82no—
429C24—221no—
430C2×Q8—112no—
431C2×Q8—221no—
432C2×Q8—221no—
433C2×Q8—221no—
434C2×Q8—221no—
435C2×Q8—221no—
436C2×D4—112no—
437C2×D4—221no—
438C2×D4—221no—
439C2×D4—221no—
440C2×D4—221no—
441C2×D4—221no—
442C22×C4—221no—
443C22×C4—221no—
444C22×C4—221no—
445C22×C4—224no—
446C22×C4—221no—
447C22×C4—221no—
448C22×C4—221no—
449C22×C4—221no—
450C22×C4—881no—
451C22×C4—881no—
452C22×C4C2×D4411yescharacteristic
453C22×C4C2×D4411yescharacteristic
454C22×C4C2×D4411yescharacteristic
455C22×C4C2×D4411yescharacteristic
456C22×C4C2×D4411yescharacteristic
457C22×C4C2×D4411yescharacteristic
458C22×C4C23×D1111yescharacteristic
459SD16—228no—
460C2×C8—21no—
461C2×C8—21no—
462C2×C8—21no—
463C2×C8—21no—
464C2×C8—21no—
465C2×C8—21no—
466C2×C8C2×C4×D1112yes—
467C2×C8C2×C4×D1112yes—
468C2×C8#433912yes—
469C2×C8#433912yes—
470C2×C8#433912yes—
471C2×C8#433912yes—
472C4⋊C4—112no—
473C4⋊C4—112no—
474C4⋊C4—224no—
475C4⋊C4—221no—
476C4⋊C4—221no—
477C4⋊C4—221no—
478C4⋊C4—221no—
479C4⋊C4—221no—
480C4⋊C4—221no—
481C4⋊C4—221no—
482C4⋊C4—221no—
483C4⋊C4—221no—
484C4⋊C4—221no—
485C4⋊C4—881no—
486C4⋊C4—881no—
487C4⋊C4—881no—
488C4⋊C4—881no—
489C22⋊C4—224no—
490C22⋊C4—881no—
491C22⋊C4—881no—
492C22⋊C4—881no—
493C22⋊C4—881no—
494C42—21no—
495C42—21no—
496C42—21no—
497C42—21no—
498C42—224no—
499C42—881no—
500C42—881no—
501C42C2×C4×D1112yes—
502C42#433912yes—
503C11#2129111yescharacteristic, complemented, Sylow
504C23—222no—
505C23—441no—
506C23—441no—
507C23—441no—
508C23—441no—
509C23—441no—
510C23—441no—
511C23C22×D4411yescharacteristic
512Q8—222no—
513Q8—222no—
514Q8—441no—
515Q8—441no—
516D4—222no—
517D4—222no—
518D4—441no—
519D4—441no—
520C2×C4—21no—
521C2×C4—21no—
522C2×C4—21no—
523C2×C4—21no—
524C2×C4—21no—
525C2×C4—21no—
526C2×C4—21no—
527C2×C4—21no—
528C2×C4—21no—
529C2×C4—21no—
530C2×C4—21no—
531C2×C4—21no—
532C2×C4—21no—
533C2×C4—21no—
534C2×C4—21no—
535C2×C4—21no—
536C2×C4—222no—
537C2×C4—222no—
538C2×C4—222no—
539C2×C4—441no—
540C2×C4—441no—
541C2×C4—441no—
542C2×C4—441no—
543C2×C4—441no—
544C2×C4—441no—
545C2×C4—441no—
546C2×C4—441no—
547C2×C4—441no—
548C2×C4—441no—
549C2×C4—441no—
550C2×C4—441no—
551C2×C4—441no—
552C2×C4—441no—
553C2×C4—441no—
554C2×C4—441no—
555C2×C4—441no—
556C2×C4—441no—
557C2×C4—884no—
558C2×C4C4×D4412yes—
559C2×C4C4×D4412yes—
560C2×C4C22×C4×D1111yescharacteristic
561C2×C4C2×#433911yescharacteristic
562C2×C4C2×#433911yescharacteristic
563C2×C4C2×#433911yescharacteristic
564C2×C4C2×#433911yescharacteristic
565C2×C4C2×#433911yescharacteristic
566C8—22no—
567C8—22no—
568C8—22no—
569C8#6692514yes—
570C22—442no—
571C22—442no—
572C22—442no—
573C22—881no—
574C22—881no—
575C22—881no—
576C22—881no—
577C22C2×C4×D4411yescharacteristic
578C22#1062300811yescharacteristic
579C22#1062300811yescharacteristic
580C22#1062328211yescharacteristic
581C22#1062328211yescharacteristic
582C22#1062328311yescharacteristic
583C22#1062328411yescharacteristic
584C4—22no—
585C4—22no—
586C4—41no—
587C4—41no—
588C4—41no—
589C4—41no—
590C4—442no—
591C4—442no—
592C4—442no—
593C4—881no—
594C4—881no—
595C4—881no—
596C4—881no—
597C4C2×#6692511yescharacteristic
598C4C4×#433911yescharacteristic
599C4#1062301011yescharacteristic
600C4#1062301011yescharacteristic
601C2—882no—
602C2#1307108011yescharacteristic
603C2#1307745011yescharacteristic
604C2#1307746111yescharacteristic
605C2#1307924411yescharacteristic
606C2#1307925511yescharacteristic
607C2#1307928411yescharacteristic
608C2#1307929911yescharacteristic
subgroupG/H
centerC23C22×D44
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#1726C2
socleC23×C11C22×D4
prime radicalC22×D44C23
cosocleC22×C4×C11C24
hypercenter#1726D11
hypocenterC11#21291
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ #376 ◁ #1726

Complements

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

NH ≅ G/Ntype
2. #13071268C2semidirect
6. #13069354C2semidirect
7. #13069349C2semidirect
9. #13069306C2semidirect
11. #13069292C2semidirect
12. #13068513C2semidirect
13. C4×#66880C2semidirect
15. C11×#1726C2semidirect
45. #10622323C4semidirect
214. #1726D11semidirect
503. C11#21291semidirect

Maximal subgroups

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

subgroupindex
C2×#106223232
#130712682
#130712602
#130694972
#130694702
#130693542
#130693492
#130693132
#130693062
#130692992
#130692922
#130685132
C4×#668802
C4×#668852
C11×#17262
#2129111