Finite Group Databasebeta

← #14774170

Subgroups — #14774170

Order 2816.

1190 conjugacy classes of subgroups.

The subgroup lattice has 778 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622347C211yesmaximal, characteristic
2C2×#10622323C211yesmaximal, characteristic, complemented
3C2×#10622746C211yesmaximal, characteristic, complemented
4#13071630C211yesmaximal, characteristic, complemented
5#13071456C211yesmaximal, characteristic, complemented
6#13069482C211yesmaximal, characteristic, complemented
7#13069313C211yesmaximal, characteristic, complemented
8#13069237C211yesmaximal, characteristic, complemented
9#13069054C211yesmaximal, characteristic, complemented
10#13068970C211yesmaximal, characteristic, complemented
11#13068963C211yesmaximal, characteristic, complemented
12#13068873C211yesmaximal, characteristic, complemented
13#13068806C211yesmaximal, characteristic, complemented
14C4×#66880C211yesmaximal, characteristic, complemented
15C11×#1753C211yesmaximal, characteristic, complemented
16C22×#4339C2211yescharacteristic
17C22×C11×M16C2211yescharacteristic
18C2×#66983C2211yescharacteristic
19C22×C4⋊Dic11C2211yescharacteristic
20C22×D88C2211yescharacteristic
21C22×#4314C2211yescharacteristic
22C2×(C22⋊D11)⋊C4—21no—
23C2×C4×D44C2211yescharacteristic
24C2×C4×Dic22C2211yescharacteristic
25C2×C4×Dic22C2211yescharacteristic
26C2×C11×C22⋊C8C2211yescharacteristic
27C2×C11×#97C2211yescharacteristic
28C2×C4×C8×C11C2211yescharacteristic
29C4×C11×C22⋊C4C2211yescharacteristic
30#10622825C2211yescharacteristic
31#10622746—24no—
32C2×#66885C2211yescharacteristic
33C2×#66885C2211yescharacteristic
34C2×#66885C2211yescharacteristic
35C2×#66885C2211yescharacteristic
36C2×#66885C2211yescharacteristic
37C2×#66882C2211yescharacteristic
38C2×#66882C2211yescharacteristic
39C2×#66880C2211yescharacteristic
40C2×#66880C2211yescharacteristic
41C2×#66880C2211yescharacteristic
42#10622571—21no—
43#10622570—21no—
44#10622570—21no—
45#10622552C2211yescharacteristic
46#10622552C2211yescharacteristic
47#10622552C2211yescharacteristic
48C4×C4⋊Dic11C2211yescharacteristic
49#10622541C2211yescharacteristic
50#10622347C418yescomplemented
51#10622323—24no—
52#10622283—21no—
53#10622281—21no—
54#10622280—21no—
55#10622279—21no—
56C11×#336C2211yescharacteristic
57C11×#336C2211yescharacteristic
58#10622189C2211yescharacteristic
59#10622189C2211yescharacteristic
60#10622189C2211yescharacteristic
61#10622189C2211yescharacteristic
62C23×C4×C11C2311yescharacteristic
63C22×C22⋊D11—21no—
64C22×C22⋊D11—21no—
65C23×Dic11—21no—
66C2×#4339—22no—
67C2×#4339—22no—
68C2×#4339—22no—
69C2×#4339—41no—
70C2×#4339—41no—
71C2×#4339C2×C414yescomplemented
72C22×D44C2311yescharacteristic
73C22×D44C2311yescharacteristic
74C22×C4×D11—21no—
75C22×C4×D11—21no—
76C22×Dic22C2311yescharacteristic
77C2×C11×M16—22no—
78C2×C11×M16—22no—
79C2×C11×M16—41no—
80C22×C8×C11C2311yescharacteristic
81C22×C8×C11C2311yescharacteristic
82C22×C8×C11C2311yescharacteristic
83C22×C8×C11C2311yescharacteristic
84C2×C11×C22⋊C4D411yescharacteristic
85C2×C11×C22⋊C4D411yescharacteristic
86C2×C42×C11C2311yescharacteristic
87C2×C42×C11C2311yescharacteristic
88C2×C22⋊Dic11—21no—
89#66983—22no—
90#66983C2×C414yes—
91C2×(C2×D11)⋊C4—21no—
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×C4⋊Dic11—22no—
100C2×C4⋊Dic11—21no—
101C2×C4⋊Dic11—41no—
102C2×C4⋊Dic11C2311yescharacteristic
103C2×C4⋊Dic11C2311yescharacteristic
104C2×C4⋊Dic11C2311yescharacteristic
105C2×C4⋊Dic11C2311yescharacteristic
106C2×C4⋊Dic11C2311yescharacteristic
107C2×Dic11⋊C4—21no—
108C2×Dic11⋊C4—21no—
109C2×Dic11⋊C4—21no—
110C2×C4×Dic11—21no—
111C2×C4×Dic11—21no—
112C2×C4×Dic11—21no—
113C2×D88—41no—
114C2×D88—41no—
115C2×D88C2×C414yescomplemented
116C2×#4314—22no—
117C2×#4314—22no—
118C2×#4314C2×C414yescomplemented
119(C22⋊D11)⋊C4—44no—
120C4×D44—22no—
121C4×D44—41no—
122C4×Dic22—22no—
123C4×Dic22—22no—
124C4×Dic22—41no—
125C4×Dic22—41no—
126C11×C22⋊C8C2×C414yescomplemented
127C11×#97—22no—
128C4×C8×C11—41no—
129C11×#95D411yescharacteristic
130C11×#95D411yescharacteristic
131C11⋊#95—21no—
132C11⋊#95—21no—
133C11⋊#95—21no—
134#66885—22no—
135#66885—22no—
136#66885—22no—
137#66885—41no—
138#66885C2×C414yescomplemented
139#66882—22no—
140#66882—41no—
141#66880—22no—
142#66880C2×C414yescomplemented
143#66880D414yescomplemented
144#22863—111nomaximal, Sylow
145C24×C11C2×D411yescharacteristic
146C23×D11—21no—
147C23×D11—21no—
148C22×C4×C11—21no—
149C22×C4×C11—21no—
150C22×C4×C11—21no—
151C22×C4×C11—21no—
152C22×C4×C11C22×C412yes—
153C22×C4×C11C2×D411yescharacteristic
154C22×C4×C11C2×D411yescharacteristic
155C22×C4×C11C2×D411yescharacteristic
156C22×C4×C11C2×D411yescharacteristic
157C22×C4×C11C2×D411yescharacteristic
158C22×C4×C11#4112yes—
159C22×C4×C11C2411yescharacteristic
160C2×C22⋊D11—24no—
161C2×C22⋊D11—24no—
162C2×C22⋊D11—42no—
163C2×C22⋊D11—42no—
164C2×C22⋊D11—42no—
165C2×C22⋊D11—42no—
166C22×Dic11—21no—
167C22×Dic11—21no—
168C22×Dic11—21no—
169C22×Dic11—21no—
170C22×Dic11—21no—
171C22×Dic11—21no—
172C22×Dic11—42no—
173C22×Dic11—42no—
174C22×Dic11—81no—
175#4339—28no—
176#4339—44no—
177#4339—44no—
178#4339—44no—
179C2×D44—21no—
180C2×D44—21no—
181C2×D44—21no—
182C2×D44—21no—
183C2×D44—21no—
184C2×D44—21no—
185C2×D44—21no—
186C2×D44—21no—
187C2×D44—21no—
188C2×D44—21no—
189C2×D44C22×C412yes—
190C2×D44C22×C412yes—
191C2×C4×D11—24no—
192C2×C4×D11—42no—
193C2×C4×D11—42no—
194C2×C4×D11—42no—
195C2×C4×D11—42no—
196C2×C4×D11—81no—
197C2×Dic22—21no—
198C2×Dic22—21no—
199C2×Dic22—21no—
200C2×Dic22C22×C412yes—
201C2×Dic22C2×D412yes—
202C2×Dic22#4112yes—
203C11×M16—44no—
204C2×C8×C11—21no—
205C2×C8×C11—21no—
206C2×C8×C11—21no—
207C2×C8×C11—21no—
208C2×C8×C11—21no—
209C2×C8×C11—21no—
210C2×C8×C11—21no—
211C2×C8×C11—21no—
212C2×C8×C11—21no—
213C2×C8×C11C22×C412yes—
214C2×C8×C11C22×C412yes—
215C2×C8×C11C2×D412yes—
216C11×C22⋊C4—22no—
217C11×C22⋊C4—41no—
218C42×C11—21no—
219C42×C11—21no—
220C42×C11—21no—
221C42×C11—21no—
222C22⋊Dic11—81no—
223(C2×D11)⋊C4—24no—
224(C2×D11)⋊C4—42no—
225(C2×D11)⋊C4—42no—
226(C2×D11)⋊C4—42no—
227(C2×D11)⋊C4—42no—
228(C2×D11)⋊C4—81no—
229(C2×D11)⋊C4—81no—
230(C2×D11)⋊C4—81no—
231C4⋊Dic11—21no—
232C4⋊Dic11—21no—
233C4⋊Dic11—21no—
234C4⋊Dic11—21no—
235C4⋊Dic11—21no—
236C4⋊Dic11—21no—
237C4⋊Dic11—21no—
238C4⋊Dic11—21no—
239C4⋊Dic11—42no—
240C4⋊Dic11C22×C412yes—
241C4⋊Dic11C2×D412yes—
242Dic11⋊C4—42no—
243Dic11⋊C4—42no—
244Dic11⋊C4—42no—
245C4×Dic11—42no—
246C4×Dic11—42no—
247C4×Dic11—42no—
248D88—44no—
249#4314—28no—
250C2×#449—111no—
251C2×#440—111no—
252C2×#417—111no—
253#2361—111no—
254#2341—111no—
255#1970—111no—
256#1936—111no—
257#1925—111no—
258#1895—111no—
259#1880—111no—
260#1879—111no—
261#1863—111no—
262#1852—111no—
263C4×#103—111no—
264#1753D1111yescharacteristic, complemented
265C23×C11—21no—
266C23×C11—21no—
267C23×C11—21no—
268C23×C11—21no—
269C23×C11—21no—
270C23×C11—21no—
271C23×C11C4×D412yes—
272C23×C11C22×D411yescharacteristic
273C22×D11—22no—
274C22×D11—22no—
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×D11—41no—
284C22×D11—41no—
285C22×D11—41no—
286C22×D11—41no—
287C2×C4×C11—21no—
288C2×C4×C11—21no—
289C2×C4×C11—21no—
290C2×C4×C11—21no—
291C2×C4×C11—22no—
292C2×C4×C11—22no—
293C2×C4×C11—22no—
294C2×C4×C11—22no—
295C2×C4×C11—21no—
296C2×C4×C11—21no—
297C2×C4×C11—21no—
298C2×C4×C11—21no—
299C2×C4×C11—21no—
300C2×C4×C11—21no—
301C2×C4×C11—21no—
302C2×C4×C11—21no—
303C2×C4×C11—21no—
304C2×C4×C11C4×D412yes—
305C2×C4×C11AGL(1,ℤ/8)12yes—
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
312C22⋊D11—48no—
313C22⋊D11—48no—
314C2×Dic11—22no—
315C2×Dic11—22no—
316C2×Dic11—22no—
317C2×Dic11—22no—
318C2×Dic11—22no—
319C2×Dic11—41no—
320C2×Dic11—41no—
321C2×Dic11—41no—
322C2×Dic11—41no—
323C2×Dic11—41no—
324C2×Dic11—41no—
325C2×Dic11—41no—
326C2×Dic11—41no—
327C2×Dic11—41no—
328C2×Dic11—41no—
329C2×Dic11—41no—
330C2×Dic11—41no—
331C2×Dic11—41no—
332C2×Dic11—84no—
333D44—22no—
334D44—22no—
335D44—22no—
336D44—22no—
337D44—41no—
338D44—41no—
339D44—41no—
340D44—41no—
341C4×D11—48no—
342C4×D11—84no—
343Dic22—22no—
344Dic22—22no—
345Dic22—22no—
346Dic22C4×D414yescomplemented
347C8×C11—22no—
348C8×C11—22no—
349C8×C11—22no—
350C8×C11—41no—
351C22×#41—111no—
352C22×SD16—111no—
353C22×D8—111no—
354C22×M16C2×D1111yescharacteristic
355C2×#121—111no—
356C2×C4×Q8—111no—
357C2×C4×Q8—111no—
358C2×C4×D4—111no—
359C2×C4×D4—221no—
360C22×C4⋊C4—111no—
361#449—118no—
362#440—224no—
363C2×#107—111no—
364C2×#107—111no—
365#417—224no—
366C2×#103—111no—
367C2×#103—111no—
368C2×#103—111no—
369C2×#102—111no—
370C2×#102—111no—
371C2×#102—111no—
372C2×#102—111no—
373C2×#102—111no—
374C2×C22⋊C8C2×D1111yescharacteristic
375C2×#97C2×D1111yescharacteristic
376C2×C4×C8C2×D1111yescharacteristic
377#390—111no—
378#390—111no—
379#390—111no—
380#390—221no—
381#390—221no—
382#389—111no—
383#388—221no—
384#386—221no—
385#385—221no—
386#380—111no—
387#380—221no—
388C4×C4⋊C4—111no—
389C4×C22⋊C4—221no—
390C4×C22⋊C4C2×D1111yescharacteristic
391#340—111no—
392#340—111no—
393#340—111no—
394#340—111no—
395#336C2×D1111yescharacteristic
396#336C2×D1111yescharacteristic
397C22×C11—22no—
398C22×C11—22no—
399C22×C11—22no—
400C22×C11—41no—
401C22×C11—41no—
402C22×C11—41no—
403C22×C11—41no—
404C22×C11C2×C4×D411yescharacteristic
405C22×C11D4211yescharacteristic
406C22×C11#54611yescharacteristic
407C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
408C22×C11#57511yescharacteristic
409C22×C11#57611yescharacteristic
410C22×C11#57811yescharacteristic
411C2×D11—42no—
412C2×D11—42no—
413C2×D11—42no—
414C2×D11—42no—
415C2×D11—42no—
416C2×D11—42no—
417C2×D11—81no—
418C2×D11—81no—
419C2×D11—81no—
420C2×D11—81no—
421C2×D11—81no—
422C2×D11—81no—
423C2×D11—81no—
424C2×D11—81no—
425C4×C11—22no—
426C4×C11—22no—
427C4×C11—41no—
428C4×C11—41no—
429C4×C11—41no—
430C4×C11C2×C4×D411yescharacteristic
431C4×C11#51811yescharacteristic
432C4×C11#54611yescharacteristic
433C4×C11#55111yescharacteristic
434Dic11—24no—
435Dic11—42no—
436Dic11—42no—
437Dic11—81no—
438Dic11—81no—
439Dic11—81no—
440C2×#41—114no—
441C2×#41—222no—
442C2×#41—222no—
443C2×#41—222no—
444C2×#41—441no—
445C2×#41—441no—
446C22×Q8—111no—
447C22×D4—111no—
448C22×D4—111no—
449C22×D4—221no—
450C22×D4—221no—
451C23×C4—221no—
452C23×C4—221no—
453C23×C4—221no—
454C23×C4C22×D1111yescharacteristic
455C2×SD16—114no—
456C2×SD16—222no—
457C2×SD16—222no—
458C2×D8—114no—
459C2×D8—441no—
460C2×D8—441no—
461C2×M16—22no—
462C2×M16—22no—
463C2×M16—41no—
464C22×C8C22×D1111yescharacteristic
465C22×C8C22×D1111yescharacteristic
466C22×C8C22×D1111yescharacteristic
467C22×C8C22×D1111yescharacteristic
468#121—114no—
469#121—222no—
470C4×Q8—222no—
471C4×Q8—222no—
472C4×Q8—441no—
473C4×Q8—441no—
474C4×D4—222no—
475C4×D4—441no—
476C4×D4—444no—
477C2×C4⋊C4—111no—
478C2×C4⋊C4—111no—
479C2×C4⋊C4—111no—
480C2×C4⋊C4—111no—
481C2×C4⋊C4—111no—
482C2×C4⋊C4—222no—
483C2×C4⋊C4—221no—
484C2×C4⋊C4—221no—
485C2×C4⋊C4—221no—
486C2×C4⋊C4—221no—
487C2×C4⋊C4—441no—
488C2×C22⋊C4—221no—
489C2×C22⋊C4—221no—
490C2×C22⋊C4—221no—
491C2×C22⋊C4—221no—
492C2×C22⋊C4—221no—
493C2×C22⋊C4—221no—
494C2×C22⋊C4—221no—
495C2×C22⋊C4—221no—
496C2×C22⋊C4—221no—
497C2×C22⋊C4D4411yescharacteristic
498C2×C22⋊C4D4411yescharacteristic
499C2×C42—221no—
500C2×C42—221no—
501C2×C42—221no—
502C2×C42C22×D1111yescharacteristic
503C2×C42C22×D1111yescharacteristic
504#107—222no—
505#107—441no—
506#103—114no—
507#103—114no—
508#103—222no—
509#102—114no—
510#102—222no—
511#102—222no—
512#102—222no—
513#102—441no—
514C22⋊C8C4×D1114yescomplemented
515#97—22no—
516C4×C8—41no—
517#95—221no—
518#95—221no—
519#95—221no—
520#95D4411yescharacteristic
521#95D4411yescharacteristic
522C2×C11—42no—
523C2×C11#235811yescharacteristic
524C2×C11C4×AGL(1,ℤ/8)11yescharacteristic
525C2×C11#295111yescharacteristic
526C2×C11#327411yescharacteristic
527C2×C11#327711yescharacteristic
528C2×C11#330811yescharacteristic
529C2×C11#330911yescharacteristic
530D11—82no—
531D11—82no—
532C24—221no—
533C24—221no—
534C24C2×D4411yescharacteristic
535#41—228no—
536#41—444no—
537#41—444no—
538#41—444no—
539C2×Q8—112no—
540C2×Q8—112no—
541C2×Q8—112no—
542C2×Q8—221no—
543C2×Q8—221no—
544C2×Q8—221no—
545C2×D4—112no—
546C2×D4—112no—
547C2×D4—224no—
548C2×D4—224no—
549C2×D4—221no—
550C2×D4—221no—
551C2×D4—221no—
552C2×D4—221no—
553C2×D4—221no—
554C2×D4—221no—
555C2×D4—221no—
556C2×D4—221no—
557C2×D4—221no—
558C2×D4—221no—
559C2×D4—442no—
560C2×D4—442no—
561C2×D4—442no—
562C2×D4—442no—
563C22×C4—21no—
564C22×C4—21no—
565C22×C4—21no—
566C22×C4—21no—
567C22×C4—221no—
568C22×C4—221no—
569C22×C4—221no—
570C22×C4—224no—
571C22×C4—221no—
572C22×C4—221no—
573C22×C4—221no—
574C22×C4—442no—
575C22×C4—442no—
576C22×C4—442no—
577C22×C4—442no—
578C22×C4—442no—
579C22×C4—442no—
580C22×C4—881no—
581C22×C4—881no—
582C22×C4C2×C4×D1112yes—
583C22×C4C2×D4411yescharacteristic
584C22×C4C2×D4411yescharacteristic
585C22×C4C2×D4411yescharacteristic
586C22×C4C2×D4411yescharacteristic
587C22×C4C2×D4411yescharacteristic
588C22×C4#433912yes—
589C22×C4C23×D1111yescharacteristic
590SD16—228no—
591D8—444no—
592M16—44no—
593C2×C8—21no—
594C2×C8—21no—
595C2×C8—21no—
596C2×C8—21no—
597C2×C8—21no—
598C2×C8—21no—
599C2×C8—21no—
600C2×C8—21no—
601C2×C8—21no—
602C2×C8C2×C4×D1112yes—
603C2×C8C2×C4×D1112yes—
604C2×C8D4×D1112yes—
605C4⋊C4—112no—
606C4⋊C4—112no—
607C4⋊C4—221no—
608C4⋊C4—221no—
609C4⋊C4—221no—
610C4⋊C4—221no—
611C4⋊C4—221no—
612C4⋊C4—221no—
613C4⋊C4—221no—
614C4⋊C4—221no—
615C4⋊C4—442no—
616C4⋊C4—442no—
617C4⋊C4—442no—
618C4⋊C4—442no—
619C22⋊C4—22no—
620C22⋊C4—41no—
621C22⋊C4—224no—
622C22⋊C4—442no—
623C22⋊C4—442no—
624C22⋊C4—442no—
625C22⋊C4—442no—
626C22⋊C4—881no—
627C22⋊C4—881no—
628C22⋊C4—881no—
629C22⋊C4—881no—
630C42—21no—
631C42—21no—
632C42—21no—
633C42—21no—
634C42—442no—
635C42—442no—
636C42—442no—
637C11#2286311yescharacteristic, complemented, Sylow
638C23—21no—
639C23—21no—
640C23—21no—
641C23—21no—
642C23—21no—
643C23—21no—
644C23—222no—
645C23—222no—
646C23—441no—
647C23—441no—
648C23—441no—
649C23—441no—
650C23—441no—
651C23—441no—
652C23—441no—
653C23—441no—
654C23—441no—
655C23—441no—
656C23—441no—
657C23—441no—
658C23C4×D4412yes—
659C23C22×D4411yescharacteristic
660Q8—114no—
661Q8—222no—
662Q8—222no—
663Q8—222no—
664D4—222no—
665D4—222no—
666D4—222no—
667D4—222no—
668D4—448no—
669D4—448no—
670D4—441no—
671D4—441no—
672D4—441no—
673D4—441no—
674C2×C4—21no—
675C2×C4—21no—
676C2×C4—21no—
677C2×C4—21no—
678C2×C4—22no—
679C2×C4—22no—
680C2×C4—22no—
681C2×C4—22no—
682C2×C4—21no—
683C2×C4—21no—
684C2×C4—21no—
685C2×C4—21no—
686C2×C4—21no—
687C2×C4—21no—
688C2×C4—21no—
689C2×C4—21no—
690C2×C4—21no—
691C2×C4—222no—
692C2×C4—222no—
693C2×C4—222no—
694C2×C4—222no—
695C2×C4—222no—
696C2×C4—448no—
697C2×C4—441no—
698C2×C4—441no—
699C2×C4—441no—
700C2×C4—441no—
701C2×C4—441no—
702C2×C4—441no—
703C2×C4—441no—
704C2×C4—441no—
705C2×C4—441no—
706C2×C4—441no—
707C2×C4—441no—
708C2×C4—441no—
709C2×C4—441no—
710C2×C4—884no—
711C2×C4—884no—
712C2×C4C4×D4412yes—
713C2×C4#6696112yes—
714C2×C4C22×C4×D1111yescharacteristic
715C2×C4C2×#433911yescharacteristic
716C2×C4C2×D4×D1111yescharacteristic
717C2×C4#6703711yescharacteristic
718C2×C4#41×D1111yescharacteristic
719C2×C4#6704211yescharacteristic
720C8—22no—
721C8—22no—
722C8—22no—
723C8—41no—
724C22—22no—
725C22—22no—
726C22—22no—
727C22—41no—
728C22—41no—
729C22—41no—
730C22—41no—
731C22—442no—
732C22—442no—
733C22—442no—
734C22—442no—
735C22—442no—
736C22—442no—
737C22—881no—
738C22—881no—
739C22—881no—
740C22—881no—
741C22—881no—
742C22—881no—
743C22—881no—
744C22—881no—
745C22C2×C4×D4411yescharacteristic
746C22D4×D4411yescharacteristic
747C22#1062308511yescharacteristic
748C22C2×#6696111yescharacteristic
749C22#1062327911yescharacteristic
750C22#1062328311yescharacteristic
751C22#1062328411yescharacteristic
752C4—22no—
753C4—22no—
754C4—41no—
755C4—41no—
756C4—41no—
757C4—224no—
758C4—442no—
759C4—442no—
760C4—881no—
761C4—881no—
762C4—881no—
763C4#1062302111yescharacteristic
764C4#1062305811yescharacteristic
765C4C4×D4×D1111yescharacteristic
766C4#1062307611yescharacteristic
767C2—42no—
768C2—882no—
769C2—882no—
770C2#1307159811yescharacteristic
771C2C4×#6696111yescharacteristic
772C2#1307749311yescharacteristic
773C2#1308023811yescharacteristic
774C2#1308027411yescharacteristic
775C2#1308060911yescharacteristic
776C2#1308062411yescharacteristic
subgroupG/H
centerC23C22×D44
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#1753C2
socleC23×C11C22×D4
prime radicalC2×#10622347C2
cosocleC22×C4×C11C24
hypercenter#1753D11
hypocenterC11#22863
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C4×C22⋊C4 ◁ #1753

Complements

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

NH ≅ G/Ntype
2. C2×#10622323C2semidirect
3. C2×#10622746C2semidirect
4. #13071630C2semidirect
5. #13071456C2semidirect
6. #13069482C2semidirect
7. #13069313C2semidirect
8. #13069237C2semidirect
9. #13069054C2semidirect
10. #13068970C2semidirect
11. #13068963C2semidirect
12. #13068873C2semidirect
13. #13068806C2semidirect
14. C4×#66880C2semidirect
15. C11×#1753C2semidirect
50. #10622347C4semidirect
71. C2×#4339C2×C4semidirect
115. C2×D88C2×C4semidirect
118. C2×#4314C2×C4semidirect
126. C11×C22⋊C8C2×C4semidirect
138. #66885C2×C4semidirect
142. #66880C2×C4semidirect
143. #66880D4semidirect
264. #1753D11semidirect
346. Dic22C4×D4semidirect
514. C22⋊C8C4×D11semidirect
637. C11#22863semidirect

Maximal subgroups

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

subgroupindex
C2×#106223472
C2×#106223232
C2×#106227462
#130716302
#130714562
#130694822
#130693132
#130692372
#130690542
#130689702
#130689632
#130688732
#130688062
C4×#668802
C11×#17532
#2286311