Finite Group Databasebeta

← #14774077

Subgroups — #14774077

Order 2816.

1146 conjugacy classes of subgroups.

The subgroup lattice has 770 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622424C211yesmaximal, characteristic
2C2×#10622430C211yesmaximal, characteristic, complemented
3C2×#10622417C211yesmaximal, characteristic, complemented
4#13071656C211yesmaximal, characteristic, complemented
5#13071454C211yesmaximal, characteristic, complemented
6#13069492C211yesmaximal, characteristic, complemented
7#13069314C211yesmaximal, characteristic, complemented
8#13069236C211yesmaximal, characteristic, complemented
9#13069043C211yesmaximal, characteristic, complemented
10#13068971C211yesmaximal, characteristic, complemented
11#13068965C211yesmaximal, characteristic, complemented
12#13068886C211yesmaximal, characteristic, complemented
13#13068816C211yesmaximal, characteristic, complemented
14#13068393C211yesmaximal, characteristic, complemented
15C11×#1763C211yesmaximal, characteristic, complemented
16C22×#4343C2211yescharacteristic
17C2×C4×Q8×C11C2211yescharacteristic
18C2×Q8×Dic11C2211yescharacteristic
19C22×#4325C2211yescharacteristic
20C22×D88C2211yescharacteristic
21C22×C8×D11C2211yescharacteristic
22C2×#66948C2211yescharacteristic
23C2×#66946C2211yescharacteristic
24C2×#66945C2211yescharacteristic
25C2×C11×#103C2211yescharacteristic
26C2×C11×#103C2211yescharacteristic
27C2×C11×#97C2211yescharacteristic
28C4×C11×C4⋊C4C2211yescharacteristic
29C2×#66899C2211yescharacteristic
30C2×#66885C2211yescharacteristic
31C2×#66885C2211yescharacteristic
32C2×(C2×D11)⋊C8C2211yescharacteristic
33C2×#66881C2211yescharacteristic
34C2×#66879C2211yescharacteristic
35#10622601—21no—
36#10622601C2211yescharacteristic
37#10622600—21no—
38#10622600C2211yescharacteristic
39#10622598C2211yescharacteristic
40C2×#66873C2211yescharacteristic
41C2×#66873C2211yescharacteristic
42C2×#66873C2211yescharacteristic
43C2×#66871C2211yescharacteristic
44#10622552—21no—
45#10622552—21no—
46#10622552C2211yescharacteristic
47#10622552C2211yescharacteristic
48C4×(C2×D11)⋊C4—21no—
49C4×(C2×D11)⋊C4—21no—
50C4×(C2×D11)⋊C4C2211yescharacteristic
51#10622430—24no—
52#10622424C418yescomplemented
53#10622417—24no—
54#10622283—21no—
55#10622278—21no—
56C11×#340C2211yescharacteristic
57C11×#340C2211yescharacteristic
58#10622188C2211yescharacteristic
59#10622167C2211yescharacteristic
60#10622167C2211yescharacteristic
61#10622162C2211yescharacteristic
62C22×Q8×C11C2311yescharacteristic
63C2×#4343—22no—
64C2×#4343—22no—
65C2×#4343—22no—
66C2×#4343—41no—
67C2×#4343—41no—
68C2×#4343C2×C414yescomplemented
69C22×D44—21no—
70C22×D44—21no—
71C22×D44C2311yescharacteristic
72C22×D44C2311yescharacteristic
73C22×C4×D11—21no—
74C22×C4×D11—21no—
75C22×C4×D11C2311yescharacteristic
76C22×C8×C11C2311yescharacteristic
77C22×C8×C11C2311yescharacteristic
78C4×Q8×C11—22no—
79C4×Q8×C11—41no—
80C2×C11×C4⋊C4—21no—
81C2×C11×C4⋊C4C2311yescharacteristic
82C2×C11×C4⋊C4C2311yescharacteristic
83C2×C11×C4⋊C4C2311yescharacteristic
84C2×C42×C11—21no—
85C2×C42×C11—21no—
86C2×C42×C11C2311yescharacteristic
87Q8×Dic11—22no—
88Q8×Dic11—41no—
89C2×#4325—22no—
90C2×#4325—22no—
91C2×#4325C2×C414yes—
92C2×(C2×D11)⋊C4—21no—
93C2×(C2×D11)⋊C4—21no—
94C2×(C2×D11)⋊C4—21no—
95C2×(C2×D11)⋊C4—21no—
96C2×(C2×D11)⋊C4—21no—
97C2×(C2×D11)⋊C4—21no—
98C2×(C2×D11)⋊C4—21no—
99C2×(C2×D11)⋊C4—21no—
100C2×(C2×D11)⋊C4—21no—
101C2×(C2×D11)⋊C4—21no—
102C2×(C2×D11)⋊C4D411yescharacteristic
103C2×(C2×D11)⋊C4D411yescharacteristic
104C2×C4⋊Dic11—21no—
105C2×C4⋊Dic11—21no—
106C2×C4⋊Dic11C2311yescharacteristic
107C2×C4⋊Dic11C2311yescharacteristic
108C2×C4×Dic11—21no—
109C2×C4×Dic11—21no—
110C2×C4×Dic11C2311yescharacteristic
111C22×C11⋊C8C2311yescharacteristic
112C22×C11⋊C8C2311yescharacteristic
113C2×D88—41no—
114C2×D88—41no—
115C2×D88C2×C414yes—
116C2×C8×D11—22no—
117C2×C8×D11—22no—
118C2×C8×D11—41no—
119#66948—22no—
120#66948C2×C414yes—
121#66946—22no—
122#66946—41no—
123#66945—22no—
124#66945—41no—
125C11×#103C2×C414yescomplemented
126C11×#103D414yescomplemented
127C11×#97—41no—
128C11×#95—21no—
129#66899—22no—
130C11⋊#95—21no—
131C11⋊#95—21no—
132C11⋊#95D411yescharacteristic
133C11⋊#95D411yescharacteristic
134#66885—22no—
135#66885—22no—
136(C2×D11)⋊C8C2×C414yescomplemented
137#66881—41no—
138#66879—22no—
139#66873—22no—
140#66873—41no—
141#66873C2×C414yescomplemented
142#66871—22no—
143#22857—111nomaximal, Sylow
144C23×D11—21no—
145C23×D11—21no—
146C23×D11C2×D411yescharacteristic
147C2×Q8×C11—21no—
148C2×Q8×C11—21no—
149C2×Q8×C11—21no—
150C2×Q8×C11C22×C412yes—
151C2×Q8×C11C2×D412yes—
152C2×Q8×C11#4112yes—
153C22×C4×C11—21no—
154C22×C4×C11—21no—
155C22×C4×C11—21no—
156C22×C4×C11—21no—
157C22×C4×C11C2×D411yescharacteristic
158C22×C4×C11C2×D411yescharacteristic
159C22×C4×C11C2411yescharacteristic
160C22×Dic11—21no—
161C22×Dic11—21no—
162C22×Dic11C2×D411yescharacteristic
163C22×Dic11C2×D411yescharacteristic
164C22×Dic11C2×D411yescharacteristic
165#4343—28no—
166#4343—44no—
167#4343—44no—
168#4343—44no—
169C2×D44—24no—
170C2×D44—24no—
171C2×D44—21no—
172C2×D44—21no—
173C2×D44—21no—
174C2×D44—21no—
175C2×D44—21no—
176C2×D44—21no—
177C2×D44—21no—
178C2×D44—21no—
179C2×D44—21no—
180C2×D44—21no—
181C2×D44—42no—
182C2×D44—42no—
183C2×D44—81no—
184C2×D44—81no—
185C2×D44C22×C412yes—
186C2×D44C22×C412yes—
187C2×C4×D11—24no—
188C2×C4×D11—21no—
189C2×C4×D11—21no—
190C2×C4×D11—21no—
191C2×C4×D11—21no—
192C2×C4×D11—42no—
193C2×C4×D11—42no—
194C2×C4×D11—42no—
195C2×C4×D11—42no—
196C2×C4×D11—81no—
197C2×C4×D11C22×C412yes—
198C2×C4×D11#4112yes—
199C2×C8×C11—21no—
200C2×C8×C11—21no—
201C2×C8×C11—21no—
202C2×C8×C11—21no—
203C2×C8×C11C22×C412yes—
204C2×C8×C11C2×D412yes—
205C11×C4⋊C4—21no—
206C11×C4⋊C4—21no—
207C11×C4⋊C4—21no—
208C11×C4⋊C4—21no—
209C11×C4⋊C4—42no—
210C11×C4⋊C4C22×C412yes—
211C11×C4⋊C4C2×D412yes—
212C42×C11—21no—
213C42×C11—21no—
214C42×C11—42no—
215C42×C11—81no—
216#4325—28no—
217(C2×D11)⋊C4—24no—
218(C2×D11)⋊C4—41no—
219(C2×D11)⋊C4—41no—
220(C2×D11)⋊C4—42no—
221(C2×D11)⋊C4—42no—
222(C2×D11)⋊C4—42no—
223(C2×D11)⋊C4—42no—
224(C2×D11)⋊C4—42no—
225(C2×D11)⋊C4—81no—
226(C2×D11)⋊C4—81no—
227(C2×D11)⋊C4—81no—
228(C2×D11)⋊C4—81no—
229C4⋊Dic11—21no—
230C4⋊Dic11—21no—
231C4⋊Dic11—21no—
232C4⋊Dic11—21no—
233C4⋊Dic11—42no—
234C4⋊Dic11—81no—
235C4×Dic11—21no—
236C4×Dic11—21no—
237C4×Dic11—42no—
238C4×Dic11—42no—
239C2×C11⋊C8—21no—
240C2×C11⋊C8—21no—
241C2×C11⋊C8—21no—
242C2×C11⋊C8—21no—
243C2×C11⋊C8—21no—
244C2×C11⋊C8C22×C412yes—
245D88—44no—
246C8×D11—44no—
247C2×#449—111no—
248C2×#440—111no—
249C2×#416—111no—
250#2363—111no—
251#2341—111no—
252#1972—111no—
253#1936—111no—
254#1925—111no—
255#1893—111no—
256#1880—111no—
257#1879—111no—
258#1865—111no—
259#1854—111no—
260#1763D1111yescharacteristic, complemented
261#1752—111no—
262C23×C11C22×D411yescharacteristic
263C22×D11—21no—
264C22×D11—21no—
265C22×D11—21no—
266C22×D11—21no—
267C22×D11—21no—
268C22×D11—21no—
269C22×D11—22no—
270C22×D11—22no—
271C22×D11—41no—
272C22×D11—41no—
273C22×D11—41no—
274C22×D11—41no—
275C22×D11—41no—
276C22×D11—41no—
277C22×D11—41no—
278C22×D11—41no—
279C22×D11—41no—
280C22×D11—41no—
281C22×D11—41no—
282C22×D11—41no—
283C22×D11C4×D412yes—
284Q8×C11—22no—
285Q8×C11—22no—
286Q8×C11—22no—
287Q8×C11C4×D414yes—
288C2×C4×C11—22no—
289C2×C4×C11—22no—
290C2×C4×C11—22no—
291C2×C4×C11—22no—
292C2×C4×C11—22no—
293C2×C4×C11—21no—
294C2×C4×C11—21no—
295C2×C4×C11—21no—
296C2×C4×C11—21no—
297C2×C4×C11—21no—
298C2×C4×C11—21no—
299C2×C4×C11—41no—
300C2×C4×C11—41no—
301C2×C4×C11—41no—
302C2×C4×C11—41no—
303C2×C4×C11—41no—
304C2×C4×C11—41no—
305C2×C4×C11—41no—
306C2×C4×C11C23×C411yescharacteristic
307C2×C4×C11C22×D411yescharacteristic
308C2×C4×C11C2×#4111yescharacteristic
309C2×C4×C11C2×#4111yescharacteristic
310C2×C4×C11H(5,𝔽2)11yescharacteristic
311C2×C4×C11H(5,𝔽2)11yescharacteristic
312C2×Dic11—21no—
313C2×Dic11—21no—
314C2×Dic11—21no—
315C2×Dic11—21no—
316C2×Dic11—21no—
317C2×Dic11—21no—
318C2×Dic11—21no—
319C2×Dic11—21no—
320C2×Dic11—41no—
321C2×Dic11—41no—
322C2×Dic11—41no—
323C2×Dic11—41no—
324C2×Dic11—41no—
325C2×Dic11—41no—
326C2×Dic11C4×D412yes—
327D44—22no—
328D44—22no—
329D44—22no—
330D44—22no—
331D44—48no—
332D44—41no—
333D44—41no—
334D44—41no—
335D44—41no—
336D44—84no—
337C4×D11—22no—
338C4×D11—22no—
339C4×D11—22no—
340C4×D11—22no—
341C4×D11—48no—
342C4×D11—84no—
343C8×C11—22no—
344C8×C11—22no—
345C11⋊C8—22no—
346C11⋊C8—41no—
347C22×#41—111no—
348C22×SD16—111no—
349C22×D8—111no—
350C23×C8—111no—
351C2×#121—111no—
352C2×C4×Q8—111no—
353C2×C4×Q8C2×D1111yescharacteristic
354C2×C4×D4—111no—
355C2×#117—111no—
356#449—118no—
357#440—224no—
358C2×#107—111no—
359C2×#106—111no—
360#416—224no—
361C2×#103—111no—
362C2×#103C2×D1111yescharacteristic
363C2×#103C2×D1111yescharacteristic
364C2×#102—111no—
365C2×#102—111no—
366C2×#102—111no—
367C2×#102—111no—
368C2×#102—111no—
369C2×C22⋊C8—111no—
370C2×#97—111no—
371C2×#97C2×D1111yescharacteristic
372#390—111no—
373#390—111no—
374#390—111no—
375#390—221no—
376#390—221no—
377#390—221no—
378#389—111no—
379#388—221no—
380#386—221no—
381#380—111no—
382#380—221no—
383C4×C4⋊C4C2×D1111yescharacteristic
384C4×C22⋊C4—111no—
385C4×C22⋊C4—221no—
386C4×C22⋊C4—221no—
387#340—111no—
388#340—111no—
389#340C2×D1111yescharacteristic
390#340C2×D1111yescharacteristic
391#336—111no—
392#336—111no—
393C22×C11C2×C4×D411yescharacteristic
394C22×C11D4211yescharacteristic
395C22×C11#54611yescharacteristic
396C22×C11#57511yescharacteristic
397C22×C11#57511yescharacteristic
398C22×C11#57611yescharacteristic
399C22×C11#57711yescharacteristic
400C2×D11—22no—
401C2×D11—22no—
402C2×D11—22no—
403C2×D11—41no—
404C2×D11—41no—
405C2×D11—41no—
406C2×D11—41no—
407C2×D11—42no—
408C2×D11—42no—
409C2×D11—42no—
410C2×D11—42no—
411C2×D11—42no—
412C2×D11—42no—
413C2×D11—81no—
414C2×D11—81no—
415C2×D11—81no—
416C2×D11—81no—
417C2×D11—81no—
418C2×D11—81no—
419C2×D11—81no—
420C2×D11—81no—
421C4×C11—24no—
422C4×C11—42no—
423C4×C11—42no—
424C4×C11—41no—
425C4×C11—41no—
426C4×C11—81no—
427C4×C11C2×C4×D411yescharacteristic
428C4×C11#51811yescharacteristic
429C4×C11#54611yescharacteristic
430C4×C11#55111yescharacteristic
431Dic11—22no—
432Dic11—41no—
433Dic11—41no—
434Dic11—81no—
435Dic11—81no—
436C2×#41—114no—
437C2×#41—222no—
438C2×#41—222no—
439C2×#41—222no—
440C2×#41—441no—
441C2×#41—441no—
442C22×Q8C22×D1111yescharacteristic
443C22×D4—111no—
444C22×D4—111no—
445C22×D4—221no—
446C22×D4—221no—
447C23×C4—111no—
448C23×C4—221no—
449C23×C4—221no—
450C2×SD16—114no—
451C2×SD16—222no—
452C2×SD16—222no—
453C2×D8—114no—
454C2×D8—441no—
455C2×D8—441no—
456C22×C8—111no—
457C22×C8—111no—
458C22×C8—222no—
459C22×C8—222no—
460C22×C8—441no—
461C22×C8C22×D1111yescharacteristic
462C22×C8C22×D1111yescharacteristic
463#121—114no—
464#121—222no—
465C4×Q8—22no—
466C4×Q8—41no—
467C4×Q8—222no—
468C4×Q8—441no—
469C4×D4—222no—
470C4×D4—441no—
471#117—222no—
472#117—441no—
473C2×C4⋊C4—21no—
474C2×C4⋊C4—111no—
475C2×C4⋊C4—111no—
476C2×C4⋊C4—221no—
477C2×C4⋊C4—221no—
478C2×C4⋊C4C22×D1111yescharacteristic
479C2×C4⋊C4C22×D1111yescharacteristic
480C2×C4⋊C4C22×D1111yescharacteristic
481C2×C22⋊C4—111no—
482C2×C22⋊C4—111no—
483C2×C22⋊C4—221no—
484C2×C22⋊C4—221no—
485C2×C22⋊C4—221no—
486C2×C22⋊C4—221no—
487C2×C22⋊C4—221no—
488C2×C22⋊C4—221no—
489C2×C22⋊C4—221no—
490C2×C22⋊C4—221no—
491C2×C22⋊C4—221no—
492C2×C22⋊C4—221no—
493C2×C42—21no—
494C2×C42—21no—
495C2×C42—111no—
496C2×C42—221no—
497C2×C42—221no—
498C2×C42C22×D1111yescharacteristic
499#107—222no—
500#106—441no—
501#103—222no—
502#103C4×D1114yescomplemented
503#103D4414yescomplemented
504#102—114no—
505#102—222no—
506#102—222no—
507#102—222no—
508#102—441no—
509C22⋊C8—114no—
510#97—41no—
511#97—222no—
512#95—21no—
513#95—111no—
514#95—111no—
515#95—221no—
516#95—221no—
517C2×C11#235811yescharacteristic
518C2×C11#294311yescharacteristic
519C2×C11#294611yescharacteristic
520C2×C11#326811yescharacteristic
521C2×C11#327111yescharacteristic
522C2×C11#330911yescharacteristic
523C2×C11#332111yescharacteristic
524D11—42no—
525D11—82no—
526D11—82no—
527C24—111no—
528C24—221no—
529C24—221no—
530#41—228no—
531#41—444no—
532#41—444no—
533#41—444no—
534C2×Q8—21no—
535C2×Q8—21no—
536C2×Q8—21no—
537C2×Q8C2×C4×D1112yes—
538C2×Q8C2×D4412yes—
539C2×Q8#433912yes—
540C2×D4—112no—
541C2×D4—112no—
542C2×D4—224no—
543C2×D4—224no—
544C2×D4—221no—
545C2×D4—221no—
546C2×D4—221no—
547C2×D4—221no—
548C2×D4—221no—
549C2×D4—221no—
550C2×D4—221no—
551C2×D4—221no—
552C2×D4—221no—
553C2×D4—221no—
554C2×D4—442no—
555C2×D4—442no—
556C2×D4—881no—
557C2×D4—881no—
558C22×C4—21no—
559C22×C4—21no—
560C22×C4—21no—
561C22×C4—21no—
562C22×C4—111no—
563C22×C4—112no—
564C22×C4—112no—
565C22×C4—111no—
566C22×C4—111no—
567C22×C4—224no—
568C22×C4—221no—
569C22×C4—221no—
570C22×C4—221no—
571C22×C4—221no—
572C22×C4—221no—
573C22×C4—221no—
574C22×C4—442no—
575C22×C4—442no—
576C22×C4—442no—
577C22×C4—442no—
578C22×C4—881no—
579C22×C4D4×D1111yescharacteristic
580C22×C4D4×D1111yescharacteristic
581C22×C4C23×D1111yescharacteristic
582SD16—228no—
583D8—444no—
584C2×C8—21no—
585C2×C8—21no—
586C2×C8—21no—
587C2×C8—21no—
588C2×C8—112no—
589C2×C8—221no—
590C2×C8—221no—
591C2×C8—221no—
592C2×C8—221no—
593C2×C8—221no—
594C2×C8—444no—
595C2×C8C2×C4×D1112yes—
596C2×C8C2×D4412yes—
597C4⋊C4—21no—
598C4⋊C4—21no—
599C4⋊C4—21no—
600C4⋊C4—21no—
601C4⋊C4—42no—
602C4⋊C4—221no—
603C4⋊C4—221no—
604C4⋊C4—221no—
605C4⋊C4—221no—
606C4⋊C4—442no—
607C4⋊C4—881no—
608C4⋊C4C2×C4×D1112yes—
609C4⋊C4C2×D4412yes—
610C22⋊C4—224no—
611C22⋊C4—441no—
612C22⋊C4—441no—
613C22⋊C4—442no—
614C22⋊C4—442no—
615C22⋊C4—442no—
616C22⋊C4—442no—
617C22⋊C4—442no—
618C22⋊C4—881no—
619C22⋊C4—881no—
620C22⋊C4—881no—
621C22⋊C4—881no—
622C42—21no—
623C42—21no—
624C42—42no—
625C42—81no—
626C42—221no—
627C42—221no—
628C42—442no—
629C42—442no—
630C11#2285711yescharacteristic, complemented, Sylow
631C23—112no—
632C23—221no—
633C23—221no—
634C23—221no—
635C23—221no—
636C23—221no—
637C23—221no—
638C23—222no—
639C23—222no—
640C23—441no—
641C23—441no—
642C23—441no—
643C23—441no—
644C23—441no—
645C23—441no—
646C23—441no—
647C23—441no—
648C23—441no—
649C23—441no—
650C23—441no—
651C23—441no—
652C23C2×D4×D1111yescharacteristic
653Q8—22no—
654Q8—22no—
655Q8—22no—
656Q8C4×D4414yes—
657D4—222no—
658D4—222no—
659D4—222no—
660D4—222no—
661D4—448no—
662D4—441no—
663D4—441no—
664D4—441no—
665D4—441no—
666D4—884no—
667C2×C4—22no—
668C2×C4—22no—
669C2×C4—22no—
670C2×C4—21no—
671C2×C4—21no—
672C2×C4—21no—
673C2×C4—21no—
674C2×C4—21no—
675C2×C4—21no—
676C2×C4—22no—
677C2×C4—22no—
678C2×C4—41no—
679C2×C4—41no—
680C2×C4—41no—
681C2×C4—41no—
682C2×C4—41no—
683C2×C4—41no—
684C2×C4—41no—
685C2×C4—112no—
686C2×C4—221no—
687C2×C4—221no—
688C2×C4—222no—
689C2×C4—222no—
690C2×C4—222no—
691C2×C4—222no—
692C2×C4—221no—
693C2×C4—221no—
694C2×C4—221no—
695C2×C4—221no—
696C2×C4—221no—
697C2×C4—221no—
698C2×C4—448no—
699C2×C4—441no—
700C2×C4—441no—
701C2×C4—441no—
702C2×C4—441no—
703C2×C4—441no—
704C2×C4—441no—
705C2×C4—884no—
706C2×C4C22×C4×D1111yescharacteristic
707C2×C4C22×D4411yescharacteristic
708C2×C4C2×#433911yescharacteristic
709C2×C4#6703711yescharacteristic
710C2×C4#41×D1111yescharacteristic
711C2×C4#6704211yescharacteristic
712C8—22no—
713C8—22no—
714C8—222no—
715C8—441no—
716C22—222no—
717C22—222no—
718C22—222no—
719C22—441no—
720C22—441no—
721C22—441no—
722C22—441no—
723C22—442no—
724C22—442no—
725C22—442no—
726C22—442no—
727C22—442no—
728C22—442no—
729C22—881no—
730C22—881no—
731C22—881no—
732C22—881no—
733C22—881no—
734C22—881no—
735C22—881no—
736C22—881no—
737C22#1062302111yescharacteristic
738C22C4×D4×D1111yescharacteristic
739C22D4×D4411yescharacteristic
740C22#1062330511yescharacteristic
741C22#1062330811yescharacteristic
742C22#1062330811yescharacteristic
743C22#1062330911yescharacteristic
744C4—24no—
745C4—41no—
746C4—42no—
747C4—42no—
748C4—41no—
749C4—81no—
750C4—222no—
751C4—441no—
752C4—441no—
753C4—881no—
754C4—881no—
755C4C2×C4×D4411yescharacteristic
756C4#1062305811yescharacteristic
757C4#1062307611yescharacteristic
758C4#1062308511yescharacteristic
759C2—442no—
760C2—882no—
761C2—882no—
762C2#1307159811yescharacteristic
763C2#1307741511yescharacteristic
764C2#1307744711yescharacteristic
765C2#1308015811yescharacteristic
766C2#1308020311yescharacteristic
767C2#1308062311yescharacteristic
768C2#1308080311yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#1763C2
socleC23×C11C22×D4
prime radicalC2×#10622424C2
cosocleC22×C4×C11C24
hypercenter#1763D11
hypocenterC11#22857
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1763

Complements

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

NH ≅ G/Ntype
2. C2×#10622430C2semidirect
3. C2×#10622417C2semidirect
4. #13071656C2semidirect
5. #13071454C2semidirect
6. #13069492C2semidirect
7. #13069314C2semidirect
8. #13069236C2semidirect
9. #13069043C2semidirect
10. #13068971C2semidirect
11. #13068965C2semidirect
12. #13068886C2semidirect
13. #13068816C2semidirect
14. #13068393C2semidirect
15. C11×#1763C2semidirect
52. #10622424C4semidirect
68. C2×#4343C2×C4semidirect
125. C11×#103C2×C4semidirect
126. C11×#103D4semidirect
136. (C2×D11)⋊C8C2×C4semidirect
141. #66873C2×C4semidirect
260. #1763D11semidirect
502. #103C4×D11semidirect
503. #103D44semidirect
630. C11#22857semidirect

Maximal subgroups

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

subgroupindex
C2×#106224242
C2×#106224302
C2×#106224172
#130716562
#130714542
#130694922
#130693142
#130692362
#130690432
#130689712
#130689652
#130688862
#130688162
#130683932
C11×#17632
#2285711