Finite Group Databasebeta

← #14660413

Subgroups — #14660413

Order 2816.

1630 conjugacy classes of subgroups.

The subgroup lattice has 828 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623361C211yesmaximal, characteristic
2C22×#66901C211yesmaximal, characteristic, complemented
3C22×#66887C211yesmaximal, characteristic, complemented
4C2×#10622601C211yesmaximal, characteristic, complemented
5#13068335C211yesmaximal, characteristic, complemented
6C2×#10622193C211yesmaximal, characteristic, complemented
7C2×C11×#417C211yesmaximal, characteristic, complemented
8C22×C11×#41C2211yescharacteristic
9C23×D44C2211yescharacteristic
10C22×C11×M16C2211yescharacteristic
11C22×C11×C4⋊C4C2211yescharacteristic
12#10623361—22no—
13#10623361—22no—
14#10623361—22no—
15#10623361C414yescomplemented
16C2×#67000—21no—
17C2×#66993—21no—
18C2×#66990—22no—
19C2×#66983—22no—
20C22×(C2×D11)⋊C4—22no—
21C2×#66979C2211yescharacteristic
22C22×C4×Dic11C2211yescharacteristic
23C22×#4318C2211yescharacteristic
24C11×#417—22no—
25C11×#417—22no—
26C2×C11×#103—21no—
27C2×C11×#102—21no—
28C2×#66901—22no—
29C2×#66901—22no—
30C2×#66901—22no—
31C2×#66887—22no—
32C2×#66887—22no—
33C2×#66887—22no—
34#10622601—22no—
35#10622601—22no—
36#10622193—22no—
37#10622167—22no—
38C24×D11D412yes—
39C2×C11×#41—21no—
40C2×C11×#41—21no—
41C2×C11×#41—21no—
42C2×C11×#41—21no—
43C2×C11×#41—21no—
44C2×C11×#41—21no—
45C2×C11×#41—21no—
46C2×C11×#41—21no—
47C2×C11×#41—21no—
48C2×C11×#41—21no—
49C2×C11×#41C2×C412yes—
50C2×C11×#41D412yes—
51C22×Q8×C11D411yescharacteristic
52C22×D4×C11—21no—
53C22×D4×C11D411yescharacteristic
54C23×C4×C11—21no—
55C23×C4×C11—21no—
56C23×C4×C11C2311yescharacteristic
57C22×C22⋊D11—24no—
58C23×Dic11—21no—
59C22×D44—21no—
60C22×D44—21no—
61C22×D44—21no—
62C22×D44—21no—
63C22×D44—21no—
64C22×D44—21no—
65C22×D44—21no—
66C22×D44—21no—
67C22×D44—21no—
68C22×D44—21no—
69C22×D44—21no—
70C22×D44—21no—
71C22×D44C2×C412yes—
72C22×D44D412yes—
73C2×C11×M16—21no—
74C2×C11×M16—21no—
75C2×C11×M16—21no—
76C2×C11×M16—21no—
77C2×C11×M16—21no—
78C2×C11×M16D412yescomplemented
79C22×C8×C11—21no—
80C2×C11×C4⋊C4—21no—
81C2×C11×C4⋊C4—21no—
82C2×C11×C4⋊C4—21no—
83C2×C11×C4⋊C4—21no—
84C2×C11×C4⋊C4—21no—
85C2×C11×C4⋊C4D412yescomplemented
86C2×C22⋊Dic11—21no—
87#67000—24no—
88#67000—24no—
89#66993—24no—
90#66993—24no—
91#66990—28no—
92#66990—28no—
93#66983—28no—
94#66983—28no—
95C2×(C2×D11)⋊C4—24no—
96C2×(C2×D11)⋊C4—28no—
97C2×(C2×D11)⋊C4—48no—
98#66979—21no—
99#66979—21no—
100#66979C2×C412yes—
101#66979D412yes—
102C2×C4⋊Dic11D412yes—
103C2×C4×Dic11—21no—
104C2×C4×Dic11—21no—
105C2×C4×Dic11—21no—
106C2×C4×Dic11—21no—
107C2×C4×Dic11—21no—
108C2×C4×Dic11—21no—
109C2×C4×Dic11D412yescomplemented
110C2×#4318—21no—
111C2×#4318—21no—
112C2×#4318—21no—
113C2×#4318—21no—
114C2×#4318—21no—
115C2×#4318D412yescomplemented
116C22×C11⋊C8—21no—
117C11×#103—24no—
118C11×#102—24no—
119#66901—28no—
120#66887—28no—
121#10997—111nomaximal, Sylow
122C24×C11—21no—
123C24×C11C2×D411yescharacteristic
124C23×D11—22no—
125C23×D11—22no—
126C23×D11—22no—
127C23×D11—22no—
128C23×D11—22no—
129C23×D11—22no—
130C23×D11—44no—
131C23×D11—44no—
132C23×D11C22⋊C414yes—
133C11×#41—22no—
134C11×#41—22no—
135C11×#41—22no—
136C11×#41—22no—
137C11×#41—22no—
138C11×#41—22no—
139C11×#41—22no—
140C11×#41—22no—
141C11×#41—41no—
142C11×#41—41no—
143C11×#41—41no—
144C11×#41—41no—
145C11×#41—41no—
146C11×#41—41no—
147C11×#41—41no—
148C11×#41—41no—
149C2×Q8×C11—21no—
150C2×Q8×C11—21no—
151C2×Q8×C11—21no—
152C2×Q8×C11—21no—
153C2×Q8×C11—21no—
154C2×Q8×C11C22⋊C412yescomplemented
155C2×D4×C11—22no—
156C2×D4×C11—22no—
157C2×D4×C11—21no—
158C2×D4×C11—21no—
159C2×D4×C11—21no—
160C2×D4×C11—21no—
161C2×D4×C11—21no—
162C2×D4×C11—41no—
163C2×D4×C11—41no—
164C2×D4×C11—41no—
165C2×D4×C11—41no—
166C2×D4×C11C22⋊C412yescomplemented
167C22×C4×C11—21no—
168C22×C4×C11—22no—
169C22×C4×C11—22no—
170C22×C4×C11—22no—
171C22×C4×C11—41no—
172C22×C4×C11—41no—
173C22×C4×C11—41no—
174C22×C4×C11—41no—
175C22×C4×C11—44no—
176C22×C4×C11—41no—
177C22×C4×C11—41no—
178C22×C4×C11C22×C411yescharacteristic
179C22×C4×C11C2×D411yescharacteristic
180C22×C4×C11C2×D411yescharacteristic
181C22×C4×C11C2×D411yescharacteristic
182C22×C4×C11C2×D411yescharacteristic
183C22×C4×C11C2×D411yescharacteristic
184C22×C4×C11C2×D411yescharacteristic
185C22×C4×C11C2×D411yescharacteristic
186C22×C4×C11C2×D411yescharacteristic
187C22×C4×C11C2×D411yescharacteristic
188C22×C4×C11#4111yescharacteristic
189C22×C4×C11#4111yescharacteristic
190C22×C4×C11#4111yescharacteristic
191C22×C4×C11#4111yescharacteristic
192C2×C22⋊D11—216no—
193C2×C22⋊D11—84no—
194C2×C22⋊D11—84no—
195C22×Dic11—24no—
196C22×Dic11—22no—
197C22×Dic11—22no—
198C22×Dic11—42no—
199C22×Dic11—41no—
200C22×Dic11—41no—
201C2×D44—22no—
202C2×D44—22no—
203C2×D44—22no—
204C2×D44—22no—
205C2×D44—22no—
206C2×D44—22no—
207C2×D44—22no—
208C2×D44—22no—
209C2×D44—22no—
210C2×D44—22no—
211C2×D44—22no—
212C2×D44—22no—
213C2×D44—41no—
214C2×D44—41no—
215C2×D44—41no—
216C2×D44—41no—
217C2×D44—41no—
218C2×D44—41no—
219C2×D44—41no—
220C2×D44—41no—
221C2×D44—41no—
222C2×D44—41no—
223C2×D44—41no—
224C2×D44—41no—
225C2×D44—41no—
226C2×D44—41no—
227C2×D44—41no—
228C2×D44—41no—
229C11×M16—22no—
230C11×M16—22no—
231C11×M16—41no—
232C11×M16—41no—
233C2×C8×C11—22no—
234C2×C8×C11—41no—
235C2×C8×C11—41no—
236C11×C4⋊C4—22no—
237C11×C4⋊C4—22no—
238C11×C4⋊C4—41no—
239C11×C4⋊C4—41no—
240C22⋊Dic11—22no—
241C22⋊Dic11—22no—
242(C2×D11)⋊C4—216no—
243(C2×D11)⋊C4—416no—
244C4⋊Dic11—22no—
245C4⋊Dic11C22⋊C414yescomplemented
246C4×Dic11—22no—
247C4×Dic11—22no—
248C4×Dic11—22no—
249C4×Dic11—22no—
250C4×Dic11—41no—
251C4×Dic11—41no—
252#4318—22no—
253#4318—22no—
254#4318—41no—
255#4318—41no—
256C2×C11⋊C8—22no—
257C2×C11⋊C8—41no—
258C2×C11⋊C8—41no—
259C2×#535—111no—
260C22×#104—111no—
261C2×#417D1111yescharacteristic, complemented
262C22×#100—111no—
263C2×#390—111no—
264#1736—111no—
265C2×#339—111no—
266C23×C11—22no—
267C23×C11—22no—
268C23×C11—22no—
269C23×C11—41no—
270C23×C11—41no—
271C23×C11—42no—
272C23×C11—42no—
273C23×C11C2×C22⋊C411yescharacteristic
274C23×C11#12011yescharacteristic
275C23×C11#12011yescharacteristic
276C23×C11#12011yescharacteristic
277C23×C11#12111yescharacteristic
278C23×C11#12111yescharacteristic
279C23×C11#12311yescharacteristic
280C22×D11—24no—
281C22×D11—24no—
282C22×D11—24no—
283C22×D11—48no—
284C22×D11—44no—
285C22×D11—44no—
286C22×D11—48no—
287C22×D11—42no—
288C22×D11—42no—
289C22×D11—42no—
290C22×D11—42no—
291C22×D11—44no—
292C22×D11—44no—
293C22×D11—84no—
294C22×D11—82no—
295C22×D11—82no—
296C22×D11—84no—
297Q8×C11—22no—
298Q8×C11—22no—
299Q8×C11—41no—
300Q8×C11—41no—
301D4×C11—22no—
302D4×C11—22no—
303D4×C11—42no—
304D4×C11—42no—
305D4×C11—42no—
306D4×C11—42no—
307D4×C11—41no—
308D4×C11—41no—
309C2×C4×C11—22no—
310C2×C4×C11—41no—
311C2×C4×C11—41no—
312C2×C4×C11—42no—
313C2×C4×C11—42no—
314C2×C4×C11—42no—
315C2×C4×C11—42no—
316C2×C4×C11—44no—
317C2×C4×C11—42no—
318C2×C4×C11—82no—
319C2×C4×C11—82no—
320C2×C4×C11C2×C22⋊C411yescharacteristic
321C2×C4×C11C2×C22⋊C411yescharacteristic
322C2×C4×C11C4×D411yescharacteristic
323C2×C4×C11C4×D411yescharacteristic
324C2×C4×C11C4×D411yescharacteristic
325C2×C4×C11C4×D411yescharacteristic
326C2×C4×C11#12011yescharacteristic
327C2×C4×C11#12011yescharacteristic
328C2×C4×C11#12011yescharacteristic
329C2×C4×C11#12011yescharacteristic
330C2×C4×C11#12011yescharacteristic
331C2×C4×C11#12111yescharacteristic
332C2×C4×C11#12111yescharacteristic
333C2×C4×C11#12111yescharacteristic
334C2×C4×C11#12111yescharacteristic
335C2×C4×C11#12111yescharacteristic
336C2×C4×C11#12111yescharacteristic
337C2×C4×C11#12111yescharacteristic
338C2×C4×C11#12111yescharacteristic
339C2×C4×C11#12111yescharacteristic
340C2×C4×C11#12111yescharacteristic
341C2×C4×C11#12311yescharacteristic
342C2×C4×C11#12311yescharacteristic
343C2×C4×C11#12311yescharacteristic
344C2×C4×C11#12411yescharacteristic
345C2×C4×C11#12411yescharacteristic
346C2×C4×C11#12711yescharacteristic
347C2×C4×C11#12711yescharacteristic
348C22⋊D11—816no—
349C2×Dic11—24no—
350C2×Dic11—24no—
351C2×Dic11—44no—
352C2×Dic11—42no—
353C2×Dic11—44no—
354C2×Dic11—42no—
355C2×Dic11—42no—
356C2×Dic11—42no—
357D44—42no—
358D44—42no—
359D44—42no—
360D44—42no—
361D44—42no—
362D44—42no—
363D44—42no—
364D44—42no—
365C8×C11—42no—
366C11⋊C8—42no—
367C22×#41C2×D1111yescharacteristic
368C23×D4—111no—
369C22×M16—111no—
370C22×M16C2×D1111yescharacteristic
371#535—114no—
372#535—222no—
373#535—222no—
374#535—222no—
375C2×#127—221no—
376C2×#124—221no—
377C2×#121—222no—
378C2×#120—222no—
379C2×#117—111no—
380C22×C4⋊C4C2×D1111yescharacteristic
381C22×C22⋊C4—222no—
382C22×C42—111no—
383C2×#104—222no—
384C2×#104—222no—
385C2×#104—222no—
386#417—22no—
387#417—22no—
388C2×#103—21no—
389C2×#102—21no—
390C2×#100—222no—
391C2×#100—222no—
392C2×#100—222no—
393#390—222no—
394#390—222no—
395#340—222no—
396#339—222no—
397C22×C11—22no—
398C22×C11—22no—
399C22×C11—21no—
400C22×C11—21no—
401C22×C11—21no—
402C22×C11—21no—
403C22×C11—22no—
404C22×C11—22no—
405C22×C11—44no—
406C22×C11—42no—
407C22×C11—81no—
408C22×C11—81no—
409C22×C11—82no—
410C22×C11#37911yescharacteristic
411C22×C11#38611yescharacteristic
412C22×C11#38611yescharacteristic
413C22×C11#39211yescharacteristic
414C22×C11#39211yescharacteristic
415C22×C11#39411yescharacteristic
416C22×C11#39411yescharacteristic
417C22×C11#45312yes—
418C22×C11#45512yes—
419C2×D11—48no—
420C2×D11—48no—
421C2×D11—44no—
422C2×D11—84no—
423C2×D11—84no—
424C2×D11—82no—
425C2×D11—82no—
426C2×D11—84no—
427C2×D11—84no—
428C4×C11—42no—
429C4×C11—82no—
430C4×C11#38611yescharacteristic
431C4×C11#38611yescharacteristic
432C4×C11#39011yescharacteristic
433C4×C11#39011yescharacteristic
434C4×C11#39211yescharacteristic
435C4×C11#39211yescharacteristic
436C4×C11#39411yescharacteristic
437C4×C11#39411yescharacteristic
438Dic11—44no—
439Dic11—44no—
440C25—112no—
441C2×#41—21no—
442C2×#41—21no—
443C2×#41—21no—
444C2×#41—21no—
445C2×#41—21no—
446C2×#41—21no—
447C2×#41—21no—
448C2×#41—21no—
449C2×#41—21no—
450C2×#41—21no—
451C2×#41C4×D1112yes—
452C2×#41D4412yes—
453C22×Q8C22⋊D1111yescharacteristic
454C22×D4—21no—
455C22×D4—112no—
456C22×D4—112no—
457C22×D4—224no—
458C22×D4—221no—
459C22×D4—221no—
460C22×D4—221no—
461C22×D4—221no—
462C22×D4—221no—
463C22×D4—221no—
464C22×D4—221no—
465C22×D4—221no—
466C22×D4—221no—
467C22×D4—221no—
468C22×D4—221no—
469C22×D4—221no—
470C22×D4C22⋊D1111yescharacteristic
471C23×C4—21no—
472C23×C4—21no—
473C23×C4—221no—
474C23×C4C22×D1111yescharacteristic
475C2×M16—21no—
476C2×M16—21no—
477C2×M16—21no—
478C2×M16—21no—
479C2×M16—21no—
480C2×M16—112no—
481C2×M16—221no—
482C2×M16—221no—
483C2×M16—221no—
484C2×M16—221no—
485C2×M16—221no—
486C2×M16C22⋊D1112yescomplemented
487C22×C8—21no—
488C22×C8—221no—
489#127—224no—
490#127—224no—
491#124—224no—
492#124—224no—
493#121—228no—
494#121—228no—
495#120—228no—
496#120—228no—
497#117—112no—
498#117—112no—
499#117—221no—
500#117—221no—
501C2×C4⋊C4—21no—
502C2×C4⋊C4—21no—
503C2×C4⋊C4—21no—
504C2×C4⋊C4—21no—
505C2×C4⋊C4—21no—
506C2×C4⋊C4—112no—
507C2×C4⋊C4C22⋊D1112yescomplemented
508C2×C22⋊C4—224no—
509C2×C22⋊C4—221no—
510C2×C22⋊C4—228no—
511C2×C22⋊C4—448no—
512C2×C42—112no—
513C2×C42—221no—
514C2×C42—221no—
515C2×C42—221no—
516C2×C42—221no—
517C2×C42—221no—
518C2×C42—221no—
519#104—228no—
520#103—24no—
521#102—24no—
522#100—228no—
523C2×C11—21no—
524C2×C11—21no—
525C2×C11—21no—
526C2×C11—21no—
527C2×C11—82no—
528C2×C11#143811yescharacteristic
529C2×C11#179212yes—
530C2×C11#200211yescharacteristic
531C2×C11#200411yescharacteristic
532C2×C11#203712yes—
533D11—84no—
534C24—21no—
535C24—114no—
536C24—222no—
537C24—222no—
538C24—222no—
539C24—222no—
540C24—222no—
541C24—222no—
542C24—444no—
543C24—444no—
544C24D4×D1111yescharacteristic
545#41—22no—
546#41—22no—
547#41—22no—
548#41—22no—
549#41—22no—
550#41—22no—
551#41—22no—
552#41—22no—
553#41—41no—
554#41—41no—
555#41—41no—
556#41—41no—
557#41—41no—
558#41—41no—
559#41—41no—
560#41—41no—
561C2×Q8—21no—
562C2×Q8—21no—
563C2×Q8—21no—
564C2×Q8—21no—
565C2×Q8—21no—
566C2×Q8(C2×D11)⋊C412yescomplemented
567C2×D4—22no—
568C2×D4—22no—
569C2×D4—21no—
570C2×D4—21no—
571C2×D4—21no—
572C2×D4—21no—
573C2×D4—21no—
574C2×D4—41no—
575C2×D4—41no—
576C2×D4—41no—
577C2×D4—41no—
578C2×D4—2216no—
579C2×D4—222no—
580C2×D4—222no—
581C2×D4—222no—
582C2×D4—222no—
583C2×D4—222no—
584C2×D4—222no—
585C2×D4—222no—
586C2×D4—222no—
587C2×D4—222no—
588C2×D4—222no—
589C2×D4—222no—
590C2×D4—222no—
591C2×D4—441no—
592C2×D4—441no—
593C2×D4—441no—
594C2×D4—441no—
595C2×D4—441no—
596C2×D4—441no—
597C2×D4—441no—
598C2×D4—441no—
599C2×D4—441no—
600C2×D4—441no—
601C2×D4—441no—
602C2×D4—441no—
603C2×D4—441no—
604C2×D4—441no—
605C2×D4—441no—
606C2×D4—441no—
607C2×D4—884no—
608C2×D4—884no—
609C2×D4(C2×D11)⋊C412yescomplemented
610C22×C4—21no—
611C22×C4—22no—
612C22×C4—22no—
613C22×C4—22no—
614C22×C4—41no—
615C22×C4—41no—
616C22×C4—41no—
617C22×C4—41no—
618C22×C4—44no—
619C22×C4—41no—
620C22×C4—41no—
621C22×C4—224no—
622C22×C4—222no—
623C22×C4—222no—
624C22×C4—442no—
625C22×C4—441no—
626C22×C4—441no—
627C22×C4C2×C4×D1111yescharacteristic
628C22×C4C2×D4411yescharacteristic
629C22×C4#433911yescharacteristic
630C22×C4#433911yescharacteristic
631C22×C4D4×D1111yescharacteristic
632C22×C4D4×D1111yescharacteristic
633C22×C4D4×D1111yescharacteristic
634C22×C4D4×D1111yescharacteristic
635C22×C4D4×D1111yescharacteristic
636C22×C4#434111yescharacteristic
637C22×C4#434111yescharacteristic
638C22×C4C2×C22⋊D1111yescharacteristic
639C22×C4C2×C22⋊D1111yescharacteristic
640C22×C4C2×C22⋊D1111yescharacteristic
641M16—22no—
642M16—22no—
643M16—41no—
644M16—41no—
645M16—222no—
646M16—222no—
647M16—441no—
648M16—441no—
649C2×C8—22no—
650C2×C8—41no—
651C2×C8—41no—
652C2×C8—222no—
653C2×C8—441no—
654C2×C8—441no—
655C4⋊C4—22no—
656C4⋊C4—22no—
657C4⋊C4—41no—
658C4⋊C4—41no—
659C4⋊C4—114no—
660C4⋊C4—222no—
661C22⋊C4—2216no—
662C22⋊C4—222no—
663C22⋊C4—222no—
664C22⋊C4—4416no—
665C42—222no—
666C42—222no—
667C42—222no—
668C42—222no—
669C42—441no—
670C42—441no—
671C11#1099711yescharacteristic, complemented, Sylow
672C23—22no—
673C23—22no—
674C23—22no—
675C23—42no—
676C23—42no—
677C23—41no—
678C23—41no—
679C23—224no—
680C23—224no—
681C23—224no—
682C23—448no—
683C23—444no—
684C23—448no—
685C23—444no—
686C23—444no—
687C23—444no—
688C23—442no—
689C23—442no—
690C23—442no—
691C23—442no—
692C23—884no—
693C23—884no—
694C23—882no—
695C23—882no—
696C23C22⋊C4×D1111yescharacteristic
697C23#6693511yescharacteristic
698C23#6693611yescharacteristic
699C23#6693711yescharacteristic
700C23#6699011yescharacteristic
701C23#6699011yescharacteristic
702C23#6699111yescharacteristic
703Q8—22no—
704Q8—22no—
705Q8—41no—
706Q8—41no—
707D4—22no—
708D4—22no—
709D4—42no—
710D4—42no—
711D4—42no—
712D4—42no—
713D4—41no—
714D4—41no—
715D4—442no—
716D4—442no—
717D4—442no—
718D4—442no—
719D4—442no—
720D4—442no—
721D4—442no—
722D4—442no—
723D4—8816no—
724C2×C4—22no—
725C2×C4—41no—
726C2×C4—41no—
727C2×C4—42no—
728C2×C4—42no—
729C2×C4—42no—
730C2×C4—42no—
731C2×C4—44no—
732C2×C4—42no—
733C2×C4—82no—
734C2×C4—82no—
735C2×C4—224no—
736C2×C4—224no—
737C2×C4—444no—
738C2×C4—444no—
739C2×C4—442no—
740C2×C4—442no—
741C2×C4—442no—
742C2×C4—442no—
743C2×C4C22⋊C4×D1111yescharacteristic
744C2×C4(C22⋊D11)⋊C411yescharacteristic
745C2×C4(C22⋊D11)⋊C411yescharacteristic
746C2×C4#6693511yescharacteristic
747C2×C4#6693511yescharacteristic
748C2×C4#6693611yescharacteristic
749C2×C4#6693711yescharacteristic
750C2×C4#6693711yescharacteristic
751C2×C4#6693711yescharacteristic
752C2×C4#6693811yescharacteristic
753C2×C4#6693811yescharacteristic
754C2×C4#6693911yescharacteristic
755C2×C4C2×(C2×D11)⋊C411yescharacteristic
756C2×C4C4×C22⋊D1111yescharacteristic
757C2×C4C4×C22⋊D1111yescharacteristic
758C2×C4#6698211yescharacteristic
759C2×C4#6698311yescharacteristic
760C2×C4#6698311yescharacteristic
761C2×C4#6699011yescharacteristic
762C2×C4#6699011yescharacteristic
763C2×C4#6699111yescharacteristic
764C2×C4#6699211yescharacteristic
765C2×C4#6699211yescharacteristic
766C2×C4#6699211yescharacteristic
767C2×C4#6699211yescharacteristic
768C2×C4#6699311yescharacteristic
769C2×C4#6699311yescharacteristic
770C2×C4#6700611yescharacteristic
771C8—42no—
772C8—442no—
773C22—22no—
774C22—22no—
775C22—22no—
776C22—22no—
777C22—21no—
778C22—21no—
779C22—21no—
780C22—21no—
781C22—44no—
782C22—42no—
783C22—82no—
784C22—81no—
785C22—81no—
786C22—448no—
787C22—448no—
788C22—444no—
789C22—884no—
790C22—884no—
791C22—884no—
792C22—884no—
793C22—882no—
794C22—882no—
795C22#1062256811yescharacteristic
796C22#1062256911yescharacteristic
797C22#1062256911yescharacteristic
798C22#1062257211yescharacteristic
799C22#1062257311yescharacteristic
800C22#1062257411yescharacteristic
801C22#1062281112yes—
802C22#1062281512yes—
803C22#1062283611yescharacteristic
804C4—42no—
805C4—82no—
806C4—444no—
807C4—444no—
808C4#1062257011yescharacteristic
809C4#1062257011yescharacteristic
810C4#1062257111yescharacteristic
811C4#1062257211yescharacteristic
812C4#1062257311yescharacteristic
813C4#1062257411yescharacteristic
814C4#1062282611yescharacteristic
815C4#1062283611yescharacteristic
816C2—21no—
817C2—21no—
818C2—21no—
819C2—21no—
820C2—82no—
821C2—884no—
822C2#1306685511yescharacteristic
823C2#1306856812yes—
824C2#1306962811yescharacteristic
825C2#1306964211yescharacteristic
826C2#1306982412yes—
subgroupG/H
centerC23#66990
commutatorC22×C4×C11C22×C4
FrattiniC23×C4C22×D11
FittingC2×C11×#417C2
socleC23×C11#120
prime radicalC2×#10623361C2
cosocleC23×C4×C11C23
hypercenterC2×#417D11
hypocenterC11#10997
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#417

Complements

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

NH ≅ G/Ntype
2. C22×#66901C2semidirect
3. C22×#66887C2semidirect
4. C2×#10622601C2semidirect
5. #13068335C2semidirect
6. C2×#10622193C2semidirect
7. C2×C11×#417C2semidirect
15. #10623361C4semidirect
78. C2×C11×M16D4semidirect
85. C2×C11×C4⋊C4D4semidirect
109. C2×C4×Dic11D4semidirect
115. C2×#4318D4semidirect
154. C2×Q8×C11C22⋊C4semidirect
166. C2×D4×C11C22⋊C4semidirect
245. C4⋊Dic11C22⋊C4semidirect
261. C2×#417D11semidirect
486. C2×M16C22⋊D11semidirect
507. C2×C4⋊C4C22⋊D11semidirect
566. C2×Q8(C2×D11)⋊C4semidirect
609. C2×D4(C2×D11)⋊C4semidirect
671. C11#10997semidirect

Maximal subgroups

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

subgroupindex
C2×#106233612
C22×#669012
C22×#668872
C2×#106226012
#130683352
C2×#106221932
C2×C11×#4172
#1099711