Finite Group Databasebeta

← #14756276

Subgroups — #14756276

Order 2816.

1026 conjugacy classes of subgroups.

The subgroup lattice has 812 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622506C211yesmaximal, characteristic, complemented
2C2×#10622434C211yesmaximal, characteristic
3#13077131C211yesmaximal, characteristic
4D11×#408C211yesmaximal, characteristic
5D11×#405C211yesmaximal, characteristic, complemented
6#13069267C211yesmaximal, characteristic, complemented
7#13069266C211yesmaximal, characteristic, complemented
8#13069265C211yesmaximal, characteristic, complemented
9#13069264C211yesmaximal, characteristic, complemented
10#13069263C211yesmaximal, characteristic, complemented
11#13069262C211yesmaximal, characteristic, complemented
12#13069261C211yesmaximal, characteristic, complemented
13#13068324C211yesmaximal, characteristic, complemented
14#13068311C211yesmaximal, characteristic, complemented
15C11×#1929C211yesmaximal, characteristic, complemented
16C2×#41×D11C2211yescharacteristic
17C2×M16×D11C2211yescharacteristic
18C2×M16×D11C2211yescharacteristic
19C22×#4313C2211yescharacteristic
20C22×C8×D11C2211yescharacteristic
21D11×#117C2211yescharacteristic
22C2×#66925C2211yescharacteristic
23C2×C11×#108C2211yescharacteristic, complemented
24C2×C11×#104C2211yescharacteristic
25C11×#416C2211yescharacteristic
26C11×#408C2211yescharacteristic
27C11×#405C2211yescharacteristic, complemented
28C2×#66901C2211yescharacteristic
29#10622847C2211yescharacteristic
30#10622846C2211yescharacteristic
31C2×#66889C2211yescharacteristic
32#10622742C2211yescharacteristic
33C2×#66886C2211yescharacteristic, complemented
34C2×#66886C2211yescharacteristic, complemented
35#10622735C2211yescharacteristic, complemented
36#10622726C2211yescharacteristic
37#10622723C2211yescharacteristic
38C2×#66883C2211yescharacteristic, complemented
39#10622714C2211yescharacteristic, complemented
40#10622615C2211yescharacteristic
41#10622610C2211yescharacteristic, complemented
42C2×#66869C2211yescharacteristic
43#10622506—24no—
44#10622434—24no—
45#10622416C411yescharacteristic, complemented
46#10622416C411yescharacteristic, complemented
47#10622415C411yescharacteristic, complemented
48#10622415C411yescharacteristic, complemented
49#10622384C411yescharacteristic, complemented
50#10622384C411yescharacteristic, complemented
51#10622383C411yescharacteristic, complemented
52#10622383C411yescharacteristic, complemented
53#10622340—21no—
54#10622340—21no—
55D11×C22⋊C8—21no—
56D11×C22⋊C8—21no—
57#10622321—21no—
58D11×#97—21no—
59#10622302—21no—
60C4×C8×D11—21no—
61C11×#339C2211yescharacteristic, complemented
62C11×#336C2211yescharacteristic, complemented
63#10622193C2211yescharacteristic, complemented
64#10622188C2211yescharacteristic, complemented
65#10622188C2211yescharacteristic, complemented
66#10622170C2211yescharacteristic, complemented
67#10622162C2211yescharacteristic, complemented
68#10622161C2211yescharacteristic, complemented
69C2×C11×#41C2311yescharacteristic
70#41×D11—22no—
71#41×D11—22no—
72#41×D11—22no—
73#41×D11—22no—
74C2×#4343C2×C411yescharacteristic
75C2×Q8×D11C2×C411yescharacteristic
76C2×#4341—21no—
77C2×#4341C2×C411yescharacteristic
78C2×D4×D11—21no—
79C2×D4×D11C2×C411yescharacteristic
80C2×#4339—21no—
81C2×#4339C2311yescharacteristic
82C22×C4×D11—21no—
83C22×C4×D11C2311yescharacteristic
84C2×C11×M16C2311yescharacteristic
85C2×C11×M16C2311yescharacteristic
86C22×C8×C11C2311yescharacteristic
87C22×C8×C11C2311yescharacteristic
88C11×#117C2311yescharacteristic
89C2×C42×C11C2311yescharacteristic
90C2×(C2×D11)⋊C4—21no—
91#66979C2311yescharacteristic
92C2×Dic11⋊C4—21no—
93C2×C4×Dic11C2311yescharacteristic
94C2×#4318C2311yescharacteristic
95C2×#4318C2311yescharacteristic
96C22×C11⋊C8C2311yescharacteristic
97C22×C11⋊C8C2311yescharacteristic
98M16×D11—22no—
99M16×D11—22no—
100M16×D11—22no—
101M16×D11D414yes—
102C2×#4313—22no—
103C2×#4313—21no—
104C2×#4313—22no—
105C2×#4313—21no—
106C2×#4313C2×C411yescharacteristic
107C2×#4313C2×C411yescharacteristic
108C2×#4313C2×C411yescharacteristic
109C2×#4313C2×C411yescharacteristic
110C2×C8×D11—21no—
111C2×C8×D11—22no—
112C2×C8×D11—22no—
113C2×C8×D11—21no—
114C2×C8×D11D411yescharacteristic
115C2×C8×D11D411yescharacteristic
116C2×C8×D11D411yescharacteristic
117C2×C8×D11D411yescharacteristic
118#66945C2×C411yescharacteristic
119#66945C2×C411yescharacteristic
120C4⋊C4×D11C2×C411yescharacteristic
121C4⋊C4×D11C2×C411yescharacteristic
122C22⋊C4×D11—21no—
123#66930—21no—
124#66925—21no—
125#66925—22no—
126#66925—22no—
127C42×D11—21no—
128C11×#108—22no—
129C11×#104—22no—
130C11×#103C2×C411yescharacteristic
131C11×#103C2×C411yescharacteristic
132C11×#102C2×C411yescharacteristic
133C11×#102C2×C411yescharacteristic
134C11×C22⋊C8—21no—
135C11×C22⋊C8—21no—
136C11×#97—21no—
137C4×C8×C11—21no—
138#66901—22no—
139#66899C2×C411yescharacteristic
140#66899C2×C411yescharacteristic
141#66896C2×C411yescharacteristic
142#66896C2×C411yescharacteristic
143C22⋊(C11⋊C8)—21no—
144C22⋊(C11⋊C8)—21no—
145#66889—22no—
146#66886—22no—
147#66886—22no—
148#66885C2×C411yescharacteristic
149#66885C2×C411yescharacteristic
150(C2×D11)⋊C8—21no—
151(C2×D11)⋊C8—21no—
152(C2×D11)⋊C8—21no—
153(C2×D11)⋊C8—21no—
154#66883—22no—
155#66880C2×C411yescharacteristic
156#66880C2×C411yescharacteristic
157#66879—21no—
158#66879—21no—
159C8×Dic11—21no—
160C8×Dic11—21no—
161#66874C2×C411yescharacteristic
162#66874C2×C411yescharacteristic
163#66873C2×C411yescharacteristic
164#66873C2×C411yescharacteristic
165#66869—22no—
166#66867—21no—
167C4×C11⋊C8—21no—
168#21070—111nomaximal, Sylow
169C23×D11—21no—
170C23×D11#4111yescharacteristic
171C11×#41—21no—
172C11×#41—21no—
173C11×#41—21no—
174C11×#41—21no—
175C2×Q8×C11C22×C411yescharacteristic
176C2×D4×C11—21no—
177C2×D4×C11C22×C411yescharacteristic
178C22×C4×C11—21no—
179C22×C4×C11—21no—
180C22×C4×C11C2411yescharacteristic
181C2×C22⋊D11—21no—
182C2×C22⋊D11—21no—
183C2×C22⋊D11—21no—
184C22×Dic11—21no—
185C22×Dic11—21no—
186C22×Dic11#4111yescharacteristic
187#4343—22no—
188#4343—22no—
189Q8×D11—22no—
190Q8×D11—22no—
191#4341—22no—
192#4341—22no—
193#4341—42no—
194#4341—42no—
195D4×D11—22no—
196D4×D11—22no—
197D4×D11—42no—
198D4×D11—42no—
199#4339—21no—
200#4339—21no—
201#4339—21no—
202#4339—21no—
203#4339—42no—
204#4339—42no—
205C2×D44—21no—
206C2×D44C22×C411yescharacteristic
207C2×C4×D11—21no—
208C2×C4×D11—21no—
209C2×C4×D11—21no—
210C2×C4×D11—21no—
211C2×C4×D11—21no—
212C2×C4×D11—42no—
213C2×C4×D11—42no—
214C2×C4×D11C22×C411yescharacteristic
215C2×C4×D11C22×C411yescharacteristic
216C2×C4×D11C2×D411yescharacteristic
217C2×C4×D11C2×D411yescharacteristic
218C2×C4×D11C2×D412yes—
219C2×C4×D11#4112yes—
220C2×C4×D11#4112yes—
221C2×C4×D11#4112yes—
222C2×Dic22—21no—
223C2×Dic22C22×C411yescharacteristic
224C11×M16—21no—
225C11×M16—21no—
226C11×M16—21no—
227C11×M16C2×D412yes—
228C2×C8×C11—21no—
229C2×C8×C11—21no—
230C2×C8×C11—21no—
231C2×C8×C11—21no—
232C2×C8×C11—21no—
233C2×C8×C11—21no—
234C2×C8×C11C22×C411yescharacteristic
235C2×C8×C11C22×C411yescharacteristic
236C2×C8×C11C2×D411yescharacteristic
237C2×C8×C11C2×D411yescharacteristic
238C11×C4⋊C4C22×C411yescharacteristic
239C11×C4⋊C4C22×C411yescharacteristic
240C11×C22⋊C4—21no—
241C42×C11—21no—
242C42×C11—21no—
243C42×C11—21no—
244C22⋊Dic11—21no—
245(C2×D11)⋊C4—21no—
246(C2×D11)⋊C4—21no—
247(C2×D11)⋊C4—42no—
248C4⋊Dic11C22×C411yescharacteristic
249C4⋊Dic11C22×C411yescharacteristic
250Dic11⋊C4—21no—
251Dic11⋊C4—21no—
252Dic11⋊C4—42no—
253C4×Dic11—21no—
254C4×Dic11—21no—
255C4×Dic11—21no—
256C4×Dic11—21no—
257C4×Dic11—21no—
258#4318—21no—
259#4318—21no—
260#4318—21no—
261#4318C2×D412yes—
262C2×C11⋊C8—21no—
263C2×C11⋊C8—21no—
264C2×C11⋊C8—21no—
265C2×C11⋊C8—21no—
266C2×C11⋊C8—21no—
267C2×C11⋊C8—21no—
268C2×C11⋊C8C22×C411yescharacteristic
269C2×C11⋊C8C22×C411yescharacteristic
270C2×C11⋊C8C2×D411yescharacteristic
271C2×C11⋊C8C2×D411yescharacteristic
272#4313—22no—
273#4313—22no—
274#4313—22no—
275#4313—22no—
276#4313—24no—
277#4313—42no—
278C8×D11—24no—
279C8×D11—22no—
280C8×D11—22no—
281C8×D11—22no—
282C8×D11—22no—
283C8×D11—42no—
284C2×#430—111no—
285C2×#421—111no—
286#2896—111no—
287C2×#408—111no—
288C2×#405—111no—
289#1929—111no—
290#1929—111no—
291#1929—111no—
292#1929—111no—
293#1929—111no—
294#1929—111no—
295#1929—111no—
296#1929D1111yescharacteristic, complemented
297#1733—111no—
298#1729—111no—
299C23×C11—21no—
300C23×C11C2×#4111yescharacteristic
301C22×D11—21no—
302C22×D11—41no—
303C22×D11—41no—
304C22×D11—42no—
305C22×D11—42no—
306C22×D11—42no—
307C22×D11C4×D411yescharacteristic
308C22×D11C4×D411yescharacteristic
309C22×D11#12412yes—
310C22×D11#12612yes—
311Q8×C11—21no—
312Q8×C11—21no—
313D4×C11—21no—
314D4×C11—21no—
315D4×C11—41no—
316D4×C11—41no—
317C2×C4×C11—21no—
318C2×C4×C11—21no—
319C2×C4×C11—21no—
320C2×C4×C11—41no—
321C2×C4×C11—41no—
322C2×C4×C11—41no—
323C2×C4×C11—41no—
324C2×C4×C11—41no—
325C2×C4×C11C23×C411yescharacteristic
326C2×C4×C11C22×D411yescharacteristic
327C2×C4×C11C22×D411yescharacteristic
328C2×C4×C11C2×#4111yescharacteristic
329C2×C4×C11C2×#4111yescharacteristic
330C2×C4×C11C2×#4111yescharacteristic
331C22⋊D11—41no—
332C22⋊D11—41no—
333C22⋊D11—42no—
334C22⋊D11—42no—
335C2×Dic11—21no—
336C2×Dic11—21no—
337C2×Dic11—21no—
338C2×Dic11—42no—
339C2×Dic11—41no—
340C2×Dic11—41no—
341C2×Dic11—41no—
342C2×Dic11C4×D411yescharacteristic
343C2×Dic11C4×D411yescharacteristic
344C2×Dic11#12412yes—
345C2×Dic11#12612yes—
346D44—21no—
347D44—21no—
348D44—42no—
349C4×D11—42no—
350C4×D11—42no—
351C4×D11—42no—
352C4×D11—41no—
353C4×D11—41no—
354C4×D11—42no—
355C4×D11#11712yes—
356C4×D11#11712yes—
357C4×D11C4×D412yes—
358C4×D11C4×D412yes—
359C4×D11#12112yes—
360C4×D11#12112yes—
361C4×D11#12312yes—
362C4×D11#12312yes—
363Dic22—21no—
364Dic22—21no—
365Dic22—42no—
366C8×C11—21no—
367C8×C11—21no—
368C8×C11—22no—
369C8×C11—21no—
370C8×C11—21no—
371C8×C11—41no—
372C11⋊C8—21no—
373C11⋊C8—21no—
374C11⋊C8—22no—
375C11⋊C8—21no—
376C11⋊C8—21no—
377C11⋊C8—41no—
378C22×#41—111no—
379C22×M16—111no—
380C22×M16—111no—
381C22×M16—111no—
382C23×C8—111no—
383C2×#117—111no—
384C2×#117—111no—
385#430—224no—
386C2×#108—111no—
387C2×#108—111no—
388C2×#108—111no—
389C2×#108C2×D1111yescharacteristic, complemented
390#421—224no—
391C2×#104—111no—
392C2×#104—111no—
393C2×#104—111no—
394C2×#104C2×D1111yescharacteristic
395#419—111no—
396#419—111no—
397#418—111no—
398#418—111no—
399#417—111no—
400#417—111no—
401#417—111no—
402#417—111no—
403#416—111no—
404#416—111no—
405#416—111no—
406#416C2×D1111yescharacteristic
407#408—111no—
408#408—111no—
409#408—111no—
410#408—221no—
411#408—221no—
412#408C2×D1111yescharacteristic
413C2×C22⋊C8—221no—
414C2×C22⋊C8—221no—
415#405—111no—
416#405—111no—
417#405—111no—
418#405—221no—
419#405—221no—
420#405C2×D1111yescharacteristic, complemented
421C2×#97—221no—
422C2×C4×C8—221no—
423#339—111no—
424#339—111no—
425#339—111no—
426#339C2×D1111yescharacteristic, complemented
427#336—111no—
428#336—111no—
429#336—111no—
430#336C2×D1111yescharacteristic, complemented
431C22×C11—21no—
432C22×C11—21no—
433C22×C11—41no—
434C22×C11—41no—
435C22×C11—41no—
436C22×C11C2×C4×D411yescharacteristic
437C22×C11C2×#12411yescharacteristic
438C22×C11C2×#12611yescharacteristic
439C2×D11—21no—
440C2×D11—21no—
441C2×D11—21no—
442C2×D11—21no—
443C2×D11—42no—
444C2×D11—42no—
445C2×D11—41no—
446C2×D11—41no—
447C2×D11—41no—
448C2×D11—84no—
449C2×D11#38812yes—
450C2×D11#38812yes—
451C4×C11—41no—
452C4×C11—41no—
453C4×C11—41no—
454C4×C11—81no—
455C4×C11C2×#11711yescharacteristic
456C4×C11C2×C4×D411yescharacteristic
457C4×C11C2×#12111yescharacteristic
458C4×C11C2×#12311yescharacteristic
459Dic11—41no—
460Dic11—41no—
461Dic11—41no—
462Dic11—81no—
463Dic11#38812yes—
464Dic11#38812yes—
465C2×#41—111no—
466C2×#41—111no—
467C2×#41—111no—
468C2×#41—221no—
469C2×#41—221no—
470C2×#41—222no—
471C2×#41—222no—
472C2×#41—222no—
473C2×#41—222no—
474C2×#41C22×D1111yescharacteristic
475C22×Q8—111no—
476C22×D4—111no—
477C22×D4—221no—
478C23×C4—111no—
479C23×C4—221no—
480C2×M16—111no—
481C2×M16—111no—
482C2×M16—111no—
483C2×M16—111no—
484C2×M16—111no—
485C2×M16—114no—
486C2×M16—111no—
487C2×M16—222no—
488C2×M16—221no—
489C2×M16—222no—
490C2×M16—221no—
491C2×M16—222no—
492C2×M16—222no—
493C2×M16—222no—
494C2×M16C22×D1111yescharacteristic
495C2×M16C22×D1111yescharacteristic
496C22×C8—111no—
497C22×C8—111no—
498C22×C8—111no—
499C22×C8—111no—
500C22×C8—111no—
501C22×C8—111no—
502C22×C8—222no—
503C22×C8—222no—
504C22×C8—221no—
505C22×C8—221no—
506C22×C8C22×D1111yescharacteristic
507C22×C8C22×D1111yescharacteristic
508#117—111no—
509#117—111no—
510#117—111no—
511#117—221no—
512#117—222no—
513#117—222no—
514#117—221no—
515#117C22×D1111yescharacteristic
516C2×C4⋊C4—111no—
517C2×C4⋊C4—111no—
518C2×C4⋊C4—221no—
519C2×C22⋊C4—221no—
520C2×C22⋊C4—221no—
521C2×C42—111no—
522C2×C42—221no—
523C2×C42C22×D1111yescharacteristic
524#108—22no—
525#108—222no—
526#108—222no—
527#108—222no—
528#104—22no—
529#104—222no—
530#104—222no—
531#104—222no—
532#103—111no—
533#103—111no—
534#103—111no—
535#103—111no—
536#103—111no—
537#103—111no—
538#103C4×D1111yescharacteristic
539#103C4×D1111yescharacteristic
540#102—111no—
541#102—111no—
542#102—111no—
543#102—111no—
544#102—111no—
545#102—111no—
546#102C4×D1111yescharacteristic
547#102C4×D1111yescharacteristic
548C22⋊C8—21no—
549C22⋊C8—21no—
550C22⋊C8—221no—
551C22⋊C8—221no—
552C22⋊C8—221no—
553C22⋊C8—221no—
554C22⋊C8—221no—
555C22⋊C8—221no—
556#97—21no—
557#97—221no—
558#97—221no—
559#97—221no—
560C4×C8—21no—
561C4×C8—221no—
562C4×C8—221no—
563C4×C8—221no—
564C2×C11—21no—
565C2×C11—21no—
566C2×C11—81no—
567C2×C11C2×#38811yescharacteristic
568C2×C11#295511yescharacteristic
569C2×C11#295511yescharacteristic
570D11—22no—
571D11—22no—
572D11—81no—
573C24—111no—
574C24—221no—
575#41—21no—
576#41—21no—
577#41—21no—
578#41—21no—
579#41—222no—
580#41—222no—
581#41—222no—
582#41—222no—
583#41—221no—
584#41—221no—
585#41—221no—
586#41—221no—
587#41—442no—
588#41—442no—
589#41—442no—
590#41—442no—
591C2×Q8—111no—
592C2×Q8—221no—
593C2×Q8—222no—
594C2×Q8—222no—
595C2×Q8C2×C4×D1111yescharacteristic
596C2×D4—21no—
597C2×D4—111no—
598C2×D4—221no—
599C2×D4—222no—
600C2×D4—222no—
601C2×D4—221no—
602C2×D4—221no—
603C2×D4—221no—
604C2×D4—442no—
605C2×D4—442no—
606C2×D4C2×C4×D1111yescharacteristic
607C22×C4—21no—
608C22×C4—21no—
609C22×C4—111no—
610C22×C4—111no—
611C22×C4—111no—
612C22×C4—112no—
613C22×C4—111no—
614C22×C4—111no—
615C22×C4—112no—
616C22×C4—112no—
617C22×C4—112no—
618C22×C4—221no—
619C22×C4—221no—
620C22×C4—221no—
621C22×C4—221no—
622C22×C4—221no—
623C22×C4—221no—
624C22×C4—221no—
625C22×C4—442no—
626C22×C4—442no—
627C22×C4C23×D1111yescharacteristic
628M16—21no—
629M16—21no—
630M16—21no—
631M16—112no—
632M16—222no—
633M16—222no—
634M16—222no—
635M16—222no—
636M16—224no—
637M16—221no—
638M16—221no—
639M16—221no—
640M16—442no—
641M16D4×D1112yes—
642C2×C8—21no—
643C2×C8—21no—
644C2×C8—21no—
645C2×C8—21no—
646C2×C8—21no—
647C2×C8—21no—
648C2×C8—111no—
649C2×C8—111no—
650C2×C8—111no—
651C2×C8—111no—
652C2×C8—222no—
653C2×C8—222no—
654C2×C8—222no—
655C2×C8—222no—
656C2×C8—224no—
657C2×C8—221no—
658C2×C8—221no—
659C2×C8—221no—
660C2×C8—221no—
661C2×C8—221no—
662C2×C8—221no—
663C2×C8—442no—
664C2×C8C2×C4×D1111yescharacteristic
665C2×C8C2×C4×D1111yescharacteristic
666C2×C8D4×D1111yescharacteristic
667C2×C8D4×D1111yescharacteristic
668C4⋊C4—111no—
669C4⋊C4—111no—
670C4⋊C4—221no—
671C4⋊C4—221no—
672C4⋊C4—442no—
673C4⋊C4C2×C4×D1111yescharacteristic
674C4⋊C4C2×C4×D1111yescharacteristic
675C22⋊C4—21no—
676C22⋊C4—221no—
677C22⋊C4—221no—
678C22⋊C4—221no—
679C22⋊C4—442no—
680C42—21no—
681C42—21no—
682C42—21no—
683C42—221no—
684C42—221no—
685C42—221no—
686C42—221no—
687C42—221no—
688C11#2107011yescharacteristic, complemented, Sylow
689C23—21no—
690C23—111no—
691C23—111no—
692C23—112no—
693C23—112no—
694C23—221no—
695C23—441no—
696C23—441no—
697C23—442no—
698C23—442no—
699C23—442no—
700C23#41×D1111yescharacteristic
701Q8—21no—
702Q8—21no—
703Q8—221no—
704Q8—221no—
705Q8—442no—
706D4—21no—
707D4—21no—
708D4—41no—
709D4—41no—
710D4—221no—
711D4—221no—
712D4—442no—
713D4—442no—
714D4—442no—
715D4—441no—
716D4—441no—
717C2×C4—21no—
718C2×C4—21no—
719C2×C4—21no—
720C2×C4—41no—
721C2×C4—41no—
722C2×C4—41no—
723C2×C4—41no—
724C2×C4—41no—
725C2×C4—112no—
726C2×C4—111no—
727C2×C4—111no—
728C2×C4—112no—
729C2×C4—112no—
730C2×C4—112no—
731C2×C4—112no—
732C2×C4—112no—
733C2×C4—112no—
734C2×C4—112no—
735C2×C4—112no—
736C2×C4—112no—
737C2×C4—221no—
738C2×C4—221no—
739C2×C4—221no—
740C2×C4—442no—
741C2×C4—442no—
742C2×C4—442no—
743C2×C4—442no—
744C2×C4—442no—
745C2×C4—441no—
746C2×C4—441no—
747C2×C4—441no—
748C2×C4—441no—
749C2×C4—441no—
750C2×C4C22×C4×D1111yescharacteristic
751C2×C4C2×D4×D1111yescharacteristic
752C2×C4C2×D4×D1111yescharacteristic
753C2×C4#41×D1111yescharacteristic
754C2×C4#41×D1111yescharacteristic
755C2×C4#41×D1111yescharacteristic
756C8—21no—
757C8—21no—
758C8—22no—
759C8—21no—
760C8—21no—
761C8—41no—
762C8—221no—
763C8—221no—
764C8—222no—
765C8—221no—
766C8—221no—
767C8—441no—
768C22—21no—
769C22—21no—
770C22—41no—
771C22—41no—
772C22—41no—
773C22—112no—
774C22—112no—
775C22—221no—
776C22—221no—
777C22—221no—
778C22—221no—
779C22—442no—
780C22—442no—
781C22—441no—
782C22—441no—
783C22—441no—
784C22—884no—
785C22C4×D4×D1111yescharacteristic
786C22D11×#12411yescharacteristic
787C22D11×#12611yescharacteristic
788C4—41no—
789C4—41no—
790C4—41no—
791C4—81no—
792C4—112no—
793C4—112no—
794C4—441no—
795C4—441no—
796C4—441no—
797C4—881no—
798C4D11×#11711yescharacteristic
799C4C4×D4×D1111yescharacteristic
800C4D11×#12111yescharacteristic
801C4D11×#12311yescharacteristic
802C2—21no—
803C2—21no—
804C2—81no—
805C2—222no—
806C2—222no—
807C2—881no—
808C2D11×#38811yescharacteristic
809C2#1307751411yescharacteristic
810C2#1307751611yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#1929C2
socleC22×C11C2×C4×D4
prime radicalC2×#41×D11C22
cosocleC22×C4×C11C24
hypercenter#1929D11
hypocenterC11#21070
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C22×C8 ◁ #1929

Complements

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

NH ≅ G/Ntype
1. C2×#10622506C2semidirect
5. D11×#405C2semidirect
6. #13069267C2semidirect
7. #13069266C2semidirect
8. #13069265C2semidirect
9. #13069264C2semidirect
10. #13069263C2semidirect
11. #13069262C2semidirect
12. #13069261C2semidirect
13. #13068324C2semidirect
14. #13068311C2semidirect
15. C11×#1929C2semidirect
23. C2×C11×#108C22semidirect
27. C11×#405C22semidirect
33. C2×#66886C22semidirect
34. C2×#66886C22semidirect
35. #10622735C22semidirect
38. C2×#66883C22semidirect
39. #10622714C22semidirect
41. #10622610C22semidirect
45. #10622416C4semidirect
46. #10622416C4semidirect
47. #10622415C4semidirect
48. #10622415C4semidirect
49. #10622384C4semidirect
50. #10622384C4semidirect
51. #10622383C4semidirect
52. #10622383C4semidirect
61. C11×#339C22semidirect
62. C11×#336C22semidirect
63. #10622193C22semidirect
64. #10622188C22semidirect
65. #10622188C22semidirect
66. #10622170C22semidirect
67. #10622162C22semidirect
68. #10622161C22semidirect
296. #1929D11semidirect
389. C2×#108C2×D11semidirect
420. #405C2×D11semidirect
426. #339C2×D11semidirect
430. #336C2×D11semidirect
688. C11#21070semidirect

Maximal subgroups

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

subgroupindex
C2×#106225062
C2×#106224342
#130771312
D11×#4082
D11×#4052
#130692672
#130692662
#130692652
#130692642
#130692632
#130692622
#130692612
#130683242
#130683112
C11×#19292
#2107011