Finite Group Databasebeta

← #14660416

Subgroups — #14660416

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
1C22×#66901C211yesmaximal, characteristic, complemented
2C2×#10622845C211yesmaximal, characteristic, complemented
3C22×#66897C211yesmaximal, characteristic, complemented
4C2×#10622834C211yesmaximal, characteristic, complemented
5#13068337C211yesmaximal, characteristic, complemented
6C2×#10622170C211yesmaximal, characteristic, complemented
7C2×C11×#535C211yesmaximal, characteristic
8C22×C11×#41C2211yescharacteristic
9C23×D4×C11C2211yescharacteristic
10C11×#535—22no—
11C11×#535—22no—
12C11×#535—22no—
13C11×#535C414yescomplemented
14C2×C11×#127—21no—
15C2×C11×#124—21no—
16C2×C11×#121—22no—
17C2×C11×#120—22no—
18C2×C11×#117C2211yescharacteristic
19C22×C22⋊Dic11—22no—
20C22×C4⋊Dic11C2211yescharacteristic
21C22×C4×Dic11C2211yescharacteristic
22C22×#4318C2211yescharacteristic
23C22×#4318C2211yescharacteristic
24C2×#66901—22no—
25C2×#66901—22no—
26C2×#66901—22no—
27#10622845—22no—
28#10622845—22no—
29C2×#66899—21no—
30#10622834—22no—
31#10622834—22no—
32C2×#66897—22no—
33C2×#66897—22no—
34C2×#66897—22no—
35C2×#66896—21no—
36#10622170—22no—
37#10622167—22no—
38C25×C11D412yes—
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×C11—24no—
54C22×D4×C11—21no—
55C22×D4×C11—21no—
56C22×D4×C11—21no—
57C22×D4×C11—21no—
58C22×D4×C11—21no—
59C22×D4×C11—21no—
60C22×D4×C11—21no—
61C22×D4×C11—21no—
62C22×D4×C11—21no—
63C22×D4×C11—21no—
64C22×D4×C11—21no—
65C22×D4×C11—21no—
66C22×D4×C11C2×C412yes—
67C22×D4×C11D412yes—
68C22×D4×C11D411yescharacteristic
69C23×C4×C11—21no—
70C23×C4×C11C2311yescharacteristic
71C23×Dic11—21no—
72C23×Dic11—21no—
73C11×#127—24no—
74C11×#127—24no—
75C11×#124—24no—
76C11×#124—24no—
77C11×#121—28no—
78C11×#121—28no—
79C11×#120—28no—
80C11×#120—28no—
81C11×#117—21no—
82C11×#117—21no—
83C11×#117C2×C412yes—
84C11×#117D412yes—
85C2×C11×C4⋊C4D412yes—
86C2×C11×C22⋊C4—24no—
87C2×C11×C22⋊C4—21no—
88C2×C42×C11—21no—
89C2×C22⋊Dic11—28no—
90C2×C22⋊Dic11—48no—
91C2×C4⋊Dic11—21no—
92C2×C4⋊Dic11—21no—
93C2×C4⋊Dic11—21no—
94C2×C4⋊Dic11—21no—
95C2×C4⋊Dic11—21no—
96C2×C4⋊Dic11D412yescomplemented
97C2×C4×Dic11—21no—
98C2×C4×Dic11—21no—
99C2×C4×Dic11—21no—
100C2×C4×Dic11—21no—
101C2×C4×Dic11—21no—
102C2×C4×Dic11D412yescomplemented
103C2×#4318—21no—
104C2×#4318—21no—
105C2×#4318—21no—
106C2×#4318—21no—
107C2×#4318—21no—
108C2×#4318—21no—
109C2×#4318—21no—
110C2×#4318—21no—
111C2×#4318—21no—
112C2×#4318—21no—
113C2×#4318D412yescomplemented
114C2×#4318D412yescomplemented
115C22×C11⋊C8—21no—
116C22×C11⋊C8—21no—
117#66901—28no—
118#66899—24no—
119#66897—28no—
120#66896—24no—
121#10997—111nomaximal, Sylow
122C24×C11—22no—
123C24×C11—22no—
124C24×C11—21no—
125C24×C11—22no—
126C24×C11—22no—
127C24×C11—22no—
128C24×C11—22no—
129C24×C11—44no—
130C24×C11—44no—
131C24×C11C22⋊C414yes—
132C24×C11C2×D411yescharacteristic
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—216no—
158C2×D4×C11—22no—
159C2×D4×C11—22no—
160C2×D4×C11—22no—
161C2×D4×C11—22no—
162C2×D4×C11—22no—
163C2×D4×C11—22no—
164C2×D4×C11—21no—
165C2×D4×C11—22no—
166C2×D4×C11—22no—
167C2×D4×C11—22no—
168C2×D4×C11—21no—
169C2×D4×C11—21no—
170C2×D4×C11—21no—
171C2×D4×C11—22no—
172C2×D4×C11—22no—
173C2×D4×C11—21no—
174C2×D4×C11—22no—
175C2×D4×C11—41no—
176C2×D4×C11—41no—
177C2×D4×C11—41no—
178C2×D4×C11—41no—
179C2×D4×C11—41no—
180C2×D4×C11—41no—
181C2×D4×C11—41no—
182C2×D4×C11—41no—
183C2×D4×C11—41no—
184C2×D4×C11—41no—
185C2×D4×C11—41no—
186C2×D4×C11—41no—
187C2×D4×C11—41no—
188C2×D4×C11—41no—
189C2×D4×C11—41no—
190C2×D4×C11—41no—
191C2×D4×C11—41no—
192C2×D4×C11—41no—
193C2×D4×C11—41no—
194C2×D4×C11—41no—
195C2×D4×C11—84no—
196C2×D4×C11—84no—
197C2×D4×C11C22⋊C412yescomplemented
198C22×C4×C11—22no—
199C22×C4×C11—21no—
200C22×C4×C11—22no—
201C22×C4×C11—22no—
202C22×C4×C11—41no—
203C22×C4×C11—41no—
204C22×C4×C11—41no—
205C22×C4×C11—41no—
206C22×C4×C11C22×C411yescharacteristic
207C22×C4×C11C2×D411yescharacteristic
208C22×C4×C11C2×D411yescharacteristic
209C22×C4×C11C2×D411yescharacteristic
210C22×C4×C11C2×D411yescharacteristic
211C22×C4×C11C2×D411yescharacteristic
212C22×C4×C11C2×D411yescharacteristic
213C22×C4×C11C2×D411yescharacteristic
214C22×C4×C11C2×D411yescharacteristic
215C22×C4×C11C2×D411yescharacteristic
216C22×C4×C11#4111yescharacteristic
217C22×C4×C11#4111yescharacteristic
218C22×C4×C11#4111yescharacteristic
219C22×C4×C11#4111yescharacteristic
220C22×Dic11—24no—
221C22×Dic11—22no—
222C22×Dic11—22no—
223C22×Dic11—42no—
224C22×Dic11—44no—
225C22×Dic11—41no—
226C22×Dic11—41no—
227C22×Dic11—41no—
228C22×Dic11—41no—
229C11×C4⋊C4—22no—
230C11×C4⋊C4C22⋊C414yescomplemented
231C11×C22⋊C4—216no—
232C11×C22⋊C4—22no—
233C11×C22⋊C4—22no—
234C42×C11—22no—
235C42×C11—22no—
236C22⋊Dic11—416no—
237C4⋊Dic11—22no—
238C4⋊Dic11—22no—
239C4⋊Dic11—41no—
240C4⋊Dic11—41no—
241C4×Dic11—22no—
242C4×Dic11—22no—
243C4×Dic11—41no—
244C4×Dic11—41no—
245#4318—22no—
246#4318—22no—
247#4318—22no—
248#4318—22no—
249#4318—41no—
250#4318—41no—
251#4318—41no—
252#4318—41no—
253C2×C11⋊C8—22no—
254C2×C11⋊C8—22no—
255C2×C11⋊C8—41no—
256C2×C11⋊C8—41no—
257C2×C11⋊C8—41no—
258C2×C11⋊C8—41no—
259C2×#535D1111yescharacteristic
260C22×#104—111no—
261C2×#417—111no—
262C22×#100—111no—
263C2×#390—111no—
264#1736—111no—
265C2×#339—111no—
266C23×C11—22no—
267C23×C11—22no—
268C23×C11—24no—
269C23×C11—22no—
270C23×C11—24no—
271C23×C11—24no—
272C23×C11—48no—
273C23×C11—44no—
274C23×C11—44no—
275C23×C11—48no—
276C23×C11—41no—
277C23×C11—42no—
278C23×C11—42no—
279C23×C11—41no—
280C23×C11—42no—
281C23×C11—42no—
282C23×C11—42no—
283C23×C11—44no—
284C23×C11—42no—
285C23×C11—44no—
286C23×C11—84no—
287C23×C11—82no—
288C23×C11—82no—
289C23×C11—84no—
290C23×C11C2×C22⋊C411yescharacteristic
291C23×C11#12011yescharacteristic
292C23×C11#12011yescharacteristic
293C23×C11#12011yescharacteristic
294C23×C11#12111yescharacteristic
295C23×C11#12111yescharacteristic
296C23×C11#12311yescharacteristic
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—42no—
308D4×C11—42no—
309D4×C11—42no—
310D4×C11—42no—
311D4×C11—42no—
312D4×C11—42no—
313D4×C11—41no—
314D4×C11—42no—
315D4×C11—42no—
316D4×C11—41no—
317D4×C11—816no—
318C2×C4×C11—24no—
319C2×C4×C11—22no—
320C2×C4×C11—41no—
321C2×C4×C11—41no—
322C2×C4×C11—42no—
323C2×C4×C11—42no—
324C2×C4×C11—42no—
325C2×C4×C11—42no—
326C2×C4×C11—42no—
327C2×C4×C11—42no—
328C2×C4×C11C2×C22⋊C411yescharacteristic
329C2×C4×C11C2×C22⋊C411yescharacteristic
330C2×C4×C11C4×D411yescharacteristic
331C2×C4×C11C4×D411yescharacteristic
332C2×C4×C11C4×D411yescharacteristic
333C2×C4×C11C4×D411yescharacteristic
334C2×C4×C11#12011yescharacteristic
335C2×C4×C11#12011yescharacteristic
336C2×C4×C11#12011yescharacteristic
337C2×C4×C11#12011yescharacteristic
338C2×C4×C11#12011yescharacteristic
339C2×C4×C11#12111yescharacteristic
340C2×C4×C11#12111yescharacteristic
341C2×C4×C11#12111yescharacteristic
342C2×C4×C11#12111yescharacteristic
343C2×C4×C11#12111yescharacteristic
344C2×C4×C11#12111yescharacteristic
345C2×C4×C11#12111yescharacteristic
346C2×C4×C11#12111yescharacteristic
347C2×C4×C11#12111yescharacteristic
348C2×C4×C11#12111yescharacteristic
349C2×C4×C11#12311yescharacteristic
350C2×C4×C11#12311yescharacteristic
351C2×C4×C11#12311yescharacteristic
352C2×C4×C11#12411yescharacteristic
353C2×C4×C11#12411yescharacteristic
354C2×C4×C11#12711yescharacteristic
355C2×C4×C11#12711yescharacteristic
356C2×Dic11—24no—
357C2×Dic11—44no—
358C2×Dic11—42no—
359C2×Dic11—44no—
360C2×Dic11—42no—
361C2×Dic11—44no—
362C2×Dic11—42no—
363C2×Dic11—82no—
364C2×Dic11—82no—
365C11⋊C8—42no—
366C11⋊C8—42no—
367C22×#41C2×D1111yescharacteristic
368C23×D4C2×D1111yescharacteristic
369C22×M16—111no—
370C22×M16—111no—
371#535—22no—
372#535—22no—
373#535—22no—
374#535Dic1114yescomplemented
375C2×#127—21no—
376C2×#124—21no—
377C2×#121—22no—
378C2×#120—22no—
379C2×#117C2×D1111yescharacteristic
380C22×C4⋊C4—111no—
381C22×C22⋊C4—222no—
382C22×C42—111no—
383C2×#104—222no—
384C2×#104—222no—
385C2×#104—222no—
386#417—222no—
387#417—222no—
388C2×#103—221no—
389C2×#102—221no—
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—48no—
406C22×C11—44no—
407C22×C11—48no—
408C22×C11—42no—
409C22×C11—44no—
410C22×C11—84no—
411C22×C11—84no—
412C22×C11—84no—
413C22×C11—81no—
414C22×C11—82no—
415C22×C11—81no—
416C22×C11—82no—
417C22×C11—82no—
418C22×C11—84no—
419C22×C11#37911yescharacteristic
420C22×C11#38611yescharacteristic
421C22×C11#38611yescharacteristic
422C22×C11#39211yescharacteristic
423C22×C11#39211yescharacteristic
424C22×C11#39411yescharacteristic
425C22×C11#39411yescharacteristic
426C22×C11#45312yes—
427C22×C11#45512yes—
428C4×C11—44no—
429C4×C11—42no—
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—82no—
440C25C22⋊D1112yes—
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×#41C2×Dic1112yes—
452C2×#41C22⋊D1112yes—
453C22×Q8C22⋊D1111yescharacteristic
454C22×D4—21no—
455C22×D4—24no—
456C22×D4—21no—
457C22×D4—21no—
458C22×D4—21no—
459C22×D4—21no—
460C22×D4—21no—
461C22×D4—21no—
462C22×D4—21no—
463C22×D4—21no—
464C22×D4—21no—
465C22×D4—21no—
466C22×D4—21no—
467C22×D4—21no—
468C22×D4C2×Dic1112yes—
469C22×D4C22⋊D1112yes—
470C22×D4C22⋊D1111yescharacteristic
471C23×C4—21no—
472C23×C4—221no—
473C23×C4—221no—
474C23×C4C22×D1111yescharacteristic
475C2×M16—112no—
476C2×M16—112no—
477C2×M16—221no—
478C2×M16—221no—
479C2×M16—221no—
480C2×M16—221no—
481C2×M16—221no—
482C2×M16—221no—
483C2×M16—221no—
484C2×M16—221no—
485C2×M16—221no—
486C2×M16—221no—
487C22×C8—221no—
488C22×C8—221no—
489#127—24no—
490#127—24no—
491#124—24no—
492#124—24no—
493#121—28no—
494#121—28no—
495#120—28no—
496#120—28no—
497#117—21no—
498#117—21no—
499#117C2×Dic1112yes—
500#117C22⋊D1112yes—
501C2×C4⋊C4—112no—
502C2×C4⋊C4—221no—
503C2×C4⋊C4—221no—
504C2×C4⋊C4—221no—
505C2×C4⋊C4—221no—
506C2×C4⋊C4—221no—
507C2×C4⋊C4C22⋊D1112yes—
508C2×C22⋊C4—24no—
509C2×C22⋊C4—21no—
510C2×C22⋊C4—228no—
511C2×C22⋊C4—448no—
512C2×C42—21no—
513C2×C42—112no—
514C2×C42—221no—
515C2×C42—221no—
516C2×C42—221no—
517C2×C42—221no—
518C2×C42—221no—
519#104—228no—
520#103—224no—
521#102—224no—
522#100—228no—
523C2×C11—21no—
524C2×C11—21no—
525C2×C11—21no—
526C2×C11—21no—
527C2×C11—84no—
528C2×C11—82no—
529C2×C11#143811yescharacteristic
530C2×C11#179212yes—
531C2×C11#200211yescharacteristic
532C2×C11#200411yescharacteristic
533C2×C11#203712yes—
534C24—22no—
535C24—22no—
536C24—22no—
537C24—21no—
538C24—22no—
539C24—22no—
540C24—22no—
541C24—44no—
542C24—44no—
543C24C22⋊Dic1114yes—
544C24C2×C22⋊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×Q8C22⋊Dic1112yescomplemented
567C2×D4—22no—
568C2×D4—22no—
569C2×D4—216no—
570C2×D4—22no—
571C2×D4—22no—
572C2×D4—22no—
573C2×D4—22no—
574C2×D4—21no—
575C2×D4—22no—
576C2×D4—21no—
577C2×D4—22no—
578C2×D4—21no—
579C2×D4—21no—
580C2×D4—22no—
581C2×D4—22no—
582C2×D4—22no—
583C2×D4—22no—
584C2×D4—22no—
585C2×D4—22no—
586C2×D4—21no—
587C2×D4—41no—
588C2×D4—41no—
589C2×D4—41no—
590C2×D4—41no—
591C2×D4—41no—
592C2×D4—41no—
593C2×D4—41no—
594C2×D4—41no—
595C2×D4—41no—
596C2×D4—41no—
597C2×D4—41no—
598C2×D4—41no—
599C2×D4—41no—
600C2×D4—41no—
601C2×D4—41no—
602C2×D4—41no—
603C2×D4—41no—
604C2×D4—41no—
605C2×D4—41no—
606C2×D4—41no—
607C2×D4—84no—
608C2×D4—84no—
609C2×D4C22⋊Dic1112yescomplemented
610C22×C4—22no—
611C22×C4—21no—
612C22×C4—22no—
613C22×C4—22no—
614C22×C4—41no—
615C22×C4—41no—
616C22×C4—41no—
617C22×C4—41no—
618C22×C4—224no—
619C22×C4—222no—
620C22×C4—222no—
621C22×C4—442no—
622C22×C4—441no—
623C22×C4—441no—
624C22×C4—444no—
625C22×C4—441no—
626C22×C4—441no—
627C22×C4D4×D1111yescharacteristic
628C22×C4D4×D1111yescharacteristic
629C22×C4D4×D1111yescharacteristic
630C22×C4D4×D1111yescharacteristic
631C22×C4#434111yescharacteristic
632C22×C4#434111yescharacteristic
633C22×C4#434111yescharacteristic
634C22×C4#434111yescharacteristic
635C22×C4C22×Dic1111yescharacteristic
636C22×C4C2×C22⋊D1111yescharacteristic
637C22×C4C2×C22⋊D1111yescharacteristic
638C22×C4C2×C22⋊D1111yescharacteristic
639C22×C4C2×C22⋊D1111yescharacteristic
640C22×C4C2×C22⋊D1111yescharacteristic
641M16—222no—
642M16—222no—
643M16—222no—
644M16—222no—
645M16—441no—
646M16—441no—
647M16—441no—
648M16—441no—
649C2×C8—222no—
650C2×C8—222no—
651C2×C8—441no—
652C2×C8—441no—
653C2×C8—441no—
654C2×C8—441no—
655C4⋊C4—22no—
656C4⋊C4—222no—
657C4⋊C4—222no—
658C4⋊C4—441no—
659C4⋊C4—441no—
660C4⋊C4C22⋊Dic1114yescomplemented
661C22⋊C4—216no—
662C22⋊C4—22no—
663C22⋊C4—22no—
664C22⋊C4—4416no—
665C42—22no—
666C42—22no—
667C42—222no—
668C42—222no—
669C42—441no—
670C42—441no—
671C11#1099711yescharacteristic, complemented, Sylow
672C23—22no—
673C23—22no—
674C23—24no—
675C23—24no—
676C23—22no—
677C23—24no—
678C23—48no—
679C23—44no—
680C23—44no—
681C23—48no—
682C23—41no—
683C23—42no—
684C23—42no—
685C23—41no—
686C23—42no—
687C23—42no—
688C23—42no—
689C23—44no—
690C23—42no—
691C23—44no—
692C23—84no—
693C23—82no—
694C23—82no—
695C23—84no—
696C23#6698811yescharacteristic
697C23#6699011yescharacteristic
698C23#6699211yescharacteristic
699C23#6699211yescharacteristic
700C23C2×C22⋊Dic1111yescharacteristic
701C23#6700611yescharacteristic
702C23#6700611yescharacteristic
703Q8—22no—
704Q8—22no—
705Q8—41no—
706Q8—41no—
707D4—22no—
708D4—22no—
709D4—42no—
710D4—42no—
711D4—42no—
712D4—42no—
713D4—42no—
714D4—42no—
715D4—42no—
716D4—42no—
717D4—42no—
718D4—42no—
719D4—41no—
720D4—42no—
721D4—42no—
722D4—41no—
723D4—816no—
724C2×C4—24no—
725C2×C4—22no—
726C2×C4—41no—
727C2×C4—41no—
728C2×C4—42no—
729C2×C4—42no—
730C2×C4—42no—
731C2×C4—42no—
732C2×C4—42no—
733C2×C4—42no—
734C2×C4—224no—
735C2×C4—444no—
736C2×C4—442no—
737C2×C4—444no—
738C2×C4—442no—
739C2×C4—444no—
740C2×C4—442no—
741C2×C4—882no—
742C2×C4—882no—
743C2×C4D4×Dic1111yescharacteristic
744C2×C4D4×Dic1111yescharacteristic
745C2×C4D4×Dic1111yescharacteristic
746C2×C4D4×Dic1111yescharacteristic
747C2×C4#6698811yescharacteristic
748C2×C4#6698811yescharacteristic
749C2×C4#6698811yescharacteristic
750C2×C4#6698911yescharacteristic
751C2×C4#6698911yescharacteristic
752C2×C4#6699011yescharacteristic
753C2×C4#6699011yescharacteristic
754C2×C4#6699011yescharacteristic
755C2×C4#6699111yescharacteristic
756C2×C4#6699111yescharacteristic
757C2×C4#6699111yescharacteristic
758C2×C4#6699111yescharacteristic
759C2×C4#6699211yescharacteristic
760C2×C4#6699211yescharacteristic
761C2×C4#6699211yescharacteristic
762C2×C4#6699211yescharacteristic
763C2×C4#6699211yescharacteristic
764C2×C4#6699211yescharacteristic
765C2×C4#6699311yescharacteristic
766C2×C4#6699311yescharacteristic
767C2×C4C2×C22⋊Dic1111yescharacteristic
768C2×C4C2×C22⋊Dic1111yescharacteristic
769C2×C4#6700611yescharacteristic
770C2×C4#6700611yescharacteristic
771C8—442no—
772C8—442no—
773C22—22no—
774C22—22no—
775C22—21no—
776C22—21no—
777C22—21no—
778C22—21no—
779C22—22no—
780C22—22no—
781C22—48no—
782C22—44no—
783C22—48no—
784C22—42no—
785C22—44no—
786C22—84no—
787C22—84no—
788C22—84no—
789C22—82no—
790C22—81no—
791C22—82no—
792C22—81no—
793C22—84no—
794C22—82no—
795C22#1062283311yescharacteristic
796C22#1062283311yescharacteristic
797C22#1062283511yescharacteristic
798C22#1062283511yescharacteristic
799C22#1062283611yescharacteristic
800C22#1062283611yescharacteristic
801C22#1062285412yes—
802C22#1062285512yes—
803C22#1062286011yescharacteristic
804C4—44no—
805C4—42no—
806C4—444no—
807C4—882no—
808C4#1062283311yescharacteristic
809C4#1062283311yescharacteristic
810C4#1062283411yescharacteristic
811C4#1062283411yescharacteristic
812C4#1062283511yescharacteristic
813C4#1062283511yescharacteristic
814C4#1062283611yescharacteristic
815C4#1062283611yescharacteristic
816C2—21no—
817C2—21no—
818C2—21no—
819C2—21no—
820C2—84no—
821C2—82no—
822C2#1306685711yescharacteristic
823C2#1306857012yes—
824C2#1306962911yescharacteristic
825C2#1306964311yescharacteristic
826C2#1306982312yes—
subgroupG/H
centerC23#67006
commutatorC22×C4×C11C22×C4
FrattiniC23×C4C22×D11
Fitting, prime radicalC2×C11×#535C2
socleC23×C11#120
cosocleC23×C4×C11C23
hypercenterC2×#535D11
hypocenterC11#10997
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#535

Complements

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

NH ≅ G/Ntype
1. C22×#66901C2semidirect
2. C2×#10622845C2semidirect
3. C22×#66897C2semidirect
4. C2×#10622834C2semidirect
5. #13068337C2semidirect
6. C2×#10622170C2semidirect
13. C11×#535C4semidirect
96. C2×C4⋊Dic11D4semidirect
102. C2×C4×Dic11D4semidirect
113. C2×#4318D4semidirect
114. C2×#4318D4semidirect
154. C2×Q8×C11C22⋊C4semidirect
197. C2×D4×C11C22⋊C4semidirect
230. C11×C4⋊C4C22⋊C4semidirect
374. #535Dic11semidirect
566. C2×Q8C22⋊Dic11semidirect
609. C2×D4C22⋊Dic11semidirect
660. C4⋊C4C22⋊Dic11semidirect
671. C11#10997semidirect

Maximal subgroups

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

subgroupindex
C22×#669012
C2×#106228452
C22×#668972
C2×#106228342
#130683372
C2×#106221702
C2×C11×#5352
#1099711