Finite Group Databasebeta

← #14660528

Subgroups — #14660528

Order 2816.

1574 conjugacy classes of subgroups.

The subgroup lattice has 824 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#67002C211yesmaximal, characteristic
2C22×#66901C211yesmaximal, characteristic, complemented
3C2×#10622614C211yesmaximal, characteristic, complemented
4C2×#10622601C211yesmaximal, characteristic, complemented
5C2×#10622168C211yesmaximal, characteristic, complemented
6C2×#10622170C211yesmaximal, characteristic, complemented
7C11×#2311C211yesmaximal, characteristic, complemented
8C22×C11×#41C2211yescharacteristic
9C23×D44C2211yescharacteristic
10C2×C11×#117C2211yescharacteristic
11C22×C11×C4⋊C4C2211yescharacteristic
12C2×#67002—22no—
13C2×#67002—22no—
14C2×#67002—22no—
15C2×#67002—22no—
16C2×#67002—22no—
17C2×#67002C414yescomplemented
18C22×#4325—21no—
19C22×#4323—21no—
20C22×(C2×D11)⋊C4—22no—
21C22×C4×Dic11C2211yescharacteristic
22C22×#4318C2211yescharacteristic
23C22×#4318C2211yescharacteristic
24C11×#391—21no—
25C11×#390—21no—
26C11×#386—22no—
27C11×#380—22no—
28C2×#66901—22no—
29C2×#66901—22no—
30C2×#66901—22no—
31#10622614—22no—
32#10622614—22no—
33#10622601—22no—
34#10622601—22no—
35C2×#66873—22no—
36#10622170—22no—
37#10622168—22no—
38C24×D11—21no—
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×C11D412yes—
56C23×C4×C11C2311yescharacteristic
57C23×Dic11—21no—
58C22×D44—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×D44C2×C412yes—
70C22×D44D412yes—
71C22×D44D412yes—
72C11×#117—21no—
73C11×#117—21no—
74C11×#117—21no—
75C11×#117—21no—
76C2×C11×C4⋊C4—21no—
77C2×C11×C4⋊C4—21no—
78C2×C11×C4⋊C4—21no—
79C2×C11×C4⋊C4—21no—
80C2×C11×C4⋊C4—21no—
81C2×C11×C4⋊C4—21no—
82C2×C11×C4⋊C4D412yes—
83C2×C11×C22⋊C4—21no—
84C2×C11×C22⋊C4—24no—
85C2×C42×C11—21no—
86#67002—28no—
87#67002—28no—
88#67002—28no—
89#67002—28no—
90C2×#4325—24no—
91C2×#4325—24no—
92C2×#4325—24no—
93C2×#4323—24no—
94C2×#4323—24no—
95C2×#4323—24no—
96C2×(C2×D11)⋊C4—28no—
97C2×(C2×D11)⋊C4—48no—
98C2×C4×Dic11—21no—
99C2×C4×Dic11—21no—
100C2×C4×Dic11—21no—
101C2×C4×Dic11—21no—
102C2×C4×Dic11—21no—
103C2×C4×Dic11D412yes—
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×#4318C2×C412yes—
113C2×#4318D412yes—
114C2×#4318D412yes—
115C2×#4318D412yes—
116C22×C11⋊C8—21no—
117C22×C11⋊C8—21no—
118C11×#95—24no—
119#66901—28no—
120#66873—28no—
121#11016—111nomaximal, Sylow
122C24×C11—21no—
123C24×C11C2×D411yescharacteristic
124C23×D11—22no—
125C23×D11—22no—
126C23×D11—22no—
127C23×D11—44no—
128C23×D11—44no—
129C23×D11—41no—
130C23×D11—41no—
131C23×D11—41no—
132C23×D11—41no—
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—22no—
172C22×C4×C11—22no—
173C22×C4×C11—22no—
174C22×C4×C11—41no—
175C22×C4×C11—41no—
176C22×C4×C11—41no—
177C22×C4×C11—41no—
178C22×C4×C11—44no—
179C22×C4×C11C22×C411yescharacteristic
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×C11C2×D411yescharacteristic
189C22×C4×C11#4111yescharacteristic
190C22×C4×C11#4111yescharacteristic
191C22×C4×C11#4111yescharacteristic
192C22×C4×C11#4111yescharacteristic
193C22×Dic11—24no—
194C22×Dic11—22no—
195C22×Dic11—42no—
196C22×Dic11—41no—
197C22×Dic11—41no—
198C2×D44—22no—
199C2×D44—22no—
200C2×D44—22no—
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×D44C22⋊C414yescomplemented
226C11×C4⋊C4—22no—
227C11×C4⋊C4—22no—
228C11×C4⋊C4—41no—
229C11×C4⋊C4—41no—
230C11×C4⋊C4—41no—
231C11×C4⋊C4—41no—
232C11×C22⋊C4—41no—
233C11×C22⋊C4—41no—
234C11×C22⋊C4—84no—
235C42×C11—41no—
236C42×C11—41no—
237#4325—216no—
238#4323—216no—
239(C2×D11)⋊C4—416no—
240C4×Dic11—22no—
241C4×Dic11—22no—
242C4×Dic11—41no—
243C4×Dic11—41no—
244#4318—22no—
245#4318—22no—
246#4318—22no—
247#4318—22no—
248#4318—22no—
249#4318—41no—
250#4318—41no—
251#4318C22⋊C414yescomplemented
252C2×C11⋊C8—22no—
253C2×C11⋊C8—22no—
254C2×C11⋊C8—22no—
255C2×C11⋊C8—22no—
256C2×C11⋊C8—41no—
257C2×C11⋊C8—41no—
258C22×AGL(1,ℤ/8)—111no—
259C22×#104—111no—
260C2×#418—111no—
261#2311D1111yescharacteristic, complemented
262C2×#390—111no—
263C2×#343—111no—
264C2×#339—111no—
265C23×C11—22no—
266C23×C11—22no—
267C23×C11—22no—
268C23×C11—41no—
269C23×C11—41no—
270C23×C11—42no—
271C23×C11—42no—
272C23×C11C4×D411yescharacteristic
273C23×C11#12011yescharacteristic
274C23×C11#12011yescharacteristic
275C23×C11#12111yescharacteristic
276C23×C11#12111yescharacteristic
277C23×C11#12111yescharacteristic
278C23×C11#12711yescharacteristic
279C22×D11—24no—
280C22×D11—44no—
281C22×D11—48no—
282C22×D11—44no—
283C22×D11—48no—
284C22×D11—42no—
285C22×D11—42no—
286C22×D11—42no—
287C22×D11—42no—
288C22×D11—42no—
289C22×D11—42no—
290C22×D11—84no—
291C22×D11—82no—
292C22×D11—82no—
293C22×D11—84no—
294C22×D11—82no—
295C22×D11—82no—
296Q8×C11—22no—
297Q8×C11—22no—
298Q8×C11—41no—
299Q8×C11—41no—
300D4×C11—22no—
301D4×C11—22no—
302D4×C11—42no—
303D4×C11—42no—
304D4×C11—42no—
305D4×C11—42no—
306D4×C11—41no—
307D4×C11—41no—
308C2×C4×C11—22no—
309C2×C4×C11—41no—
310C2×C4×C11—41no—
311C2×C4×C11—42no—
312C2×C4×C11—42no—
313C2×C4×C11—42no—
314C2×C4×C11—42no—
315C2×C4×C11—44no—
316C2×C4×C11—42no—
317C2×C4×C11—42no—
318C2×C4×C11—42no—
319C2×C4×C11—44no—
320C2×C4×C11—42no—
321C2×C4×C11—82no—
322C2×C4×C11C2×C22⋊C411yescharacteristic
323C2×C4×C11C2×C22⋊C411yescharacteristic
324C2×C4×C11C2×C22⋊C411yescharacteristic
325C2×C4×C11C4×D411yescharacteristic
326C2×C4×C11C4×D411yescharacteristic
327C2×C4×C11C4×D411yescharacteristic
328C2×C4×C11#12011yescharacteristic
329C2×C4×C11#12011yescharacteristic
330C2×C4×C11#12011yescharacteristic
331C2×C4×C11#12011yescharacteristic
332C2×C4×C11#12011yescharacteristic
333C2×C4×C11#12011yescharacteristic
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#12111yescharacteristic
342C2×C4×C11#12111yescharacteristic
343C2×C4×C11#12311yescharacteristic
344C2×C4×C11#12311yescharacteristic
345C2×C4×C11#12311yescharacteristic
346C2×C4×C11#12311yescharacteristic
347C2×C4×C11#12411yescharacteristic
348C2×C4×C11#12411yescharacteristic
349C2×C4×C11#12711yescharacteristic
350C2×Dic11—24no—
351C2×Dic11—44no—
352C2×Dic11—42no—
353C2×Dic11—44no—
354C2×Dic11—42no—
355D44—24no—
356D44—24no—
357D44—42no—
358D44—42no—
359D44—42no—
360D44—42no—
361D44—42no—
362D44—42no—
363C11⋊C8—24no—
364C11⋊C8—42no—
365C22×#41C2×D1111yescharacteristic
366C23×D4—111no—
367C2×AGL(1,ℤ/8)—114no—
368C2×AGL(1,ℤ/8)—222no—
369C2×AGL(1,ℤ/8)—222no—
370C2×AGL(1,ℤ/8)—222no—
371C2×AGL(1,ℤ/8)—222no—
372C2×AGL(1,ℤ/8)—222no—
373C22×SD16—221no—
374C22×D8—221no—
375C22×M16—111no—
376C22×M16—111no—
377C2×#117C2×D1111yescharacteristic
378C22×C4⋊C4C2×D1111yescharacteristic
379C22×C22⋊C4—222no—
380C22×C42—111no—
381C2×#104—222no—
382C2×#104—222no—
383C2×#104—222no—
384#418—222no—
385#418—222no—
386C2×#102—222no—
387#391—21no—
388#390—21no—
389#390—222no—
390#390—222no—
391#386—22no—
392#380—22no—
393#343—222no—
394#339—222no—
395C22×C11—22no—
396C22×C11—22no—
397C22×C11—21no—
398C22×C11—21no—
399C22×C11—21no—
400C22×C11—21no—
401C22×C11—22no—
402C22×C11—22no—
403C22×C11—44no—
404C22×C11—42no—
405C22×C11—81no—
406C22×C11—81no—
407C22×C11—82no—
408C22×C11#38611yescharacteristic
409C22×C11#38611yescharacteristic
410C22×C11#39011yescharacteristic
411C22×C11#39211yescharacteristic
412C22×C11#39211yescharacteristic
413C22×C11#39211yescharacteristic
414C22×C11#39411yescharacteristic
415C22×C11#45312yes—
416C22×C11#45412yes—
417C2×D11—48no—
418C2×D11—44no—
419C2×D11—84no—
420C2×D11—84no—
421C2×D11—84no—
422C2×D11—84no—
423C2×D11—82no—
424C2×D11—82no—
425C2×D11—84no—
426C4×C11—42no—
427C4×C11—82no—
428C4×C11—82no—
429C4×C11#37911yescharacteristic
430C4×C11#38611yescharacteristic
431C4×C11#38611yescharacteristic
432C4×C11#39011yescharacteristic
433C4×C11#39211yescharacteristic
434C4×C11#39411yescharacteristic
435C4×C11#39411yescharacteristic
436C4×C11#39411yescharacteristic
437Dic11—44no—
438C25—221no—
439C2×#41—21no—
440C2×#41—21no—
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×#41C4×D1112yes—
450C2×#41D4412yes—
451C22×Q8C22⋊D1111yescharacteristic
452C22×D4—21no—
453C22×D4—112no—
454C22×D4—112no—
455C22×D4—112no—
456C22×D4—221no—
457C22×D4—221no—
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×D4C22⋊D1111yescharacteristic
468C23×C4—21no—
469C23×C4—221no—
470C23×C4C22⋊D1112yes—
471C23×C4C22×D1111yescharacteristic
472AGL(1,ℤ/8)—228no—
473AGL(1,ℤ/8)—228no—
474AGL(1,ℤ/8)—228no—
475AGL(1,ℤ/8)—228no—
476C2×SD16—224no—
477C2×SD16—224no—
478C2×SD16—224no—
479C2×D8—224no—
480C2×D8—224no—
481C2×D8—224no—
482C2×M16—112no—
483C2×M16—112no—
484C2×M16—112no—
485C2×M16—112no—
486C2×M16—221no—
487C2×M16—221no—
488C2×M16—221no—
489C2×M16—221no—
490C2×M16—221no—
491C2×M16—221no—
492C2×M16—221no—
493C2×M16—221no—
494C22×C8—221no—
495C22×C8—221no—
496#117—21no—
497#117—21no—
498#117—21no—
499#117—21no—
500C2×C4⋊C4—21no—
501C2×C4⋊C4—21no—
502C2×C4⋊C4—21no—
503C2×C4⋊C4—21no—
504C2×C4⋊C4—21no—
505C2×C4⋊C4—21no—
506C2×C4⋊C4C22⋊D1112yes—
507C2×C22⋊C4—21no—
508C2×C22⋊C4—24no—
509C2×C22⋊C4—228no—
510C2×C22⋊C4—448no—
511C2×C42—21no—
512C2×C42—112no—
513C2×C42—221no—
514C2×C42—221no—
515C2×C42—221no—
516C2×C42—221no—
517C2×C42—221no—
518#104—228no—
519#102—228no—
520#95—24no—
521C2×C11—21no—
522C2×C11—21no—
523C2×C11—21no—
524C2×C11—21no—
525C2×C11—82no—
526C2×C11#143811yescharacteristic
527C2×C11#188312yes—
528C2×C11#200211yescharacteristic
529C2×C11#200311yescharacteristic
530C2×C11#200612yes—
531D11—84no—
532C24—21no—
533C24—222no—
534C24—222no—
535C24—222no—
536C24—444no—
537C24—444no—
538C24—441no—
539C24—441no—
540C24—441no—
541C24—441no—
542C24C2×C22⋊D1111yescharacteristic
543#41—22no—
544#41—22no—
545#41—22no—
546#41—22no—
547#41—22no—
548#41—22no—
549#41—22no—
550#41—22no—
551#41—41no—
552#41—41no—
553#41—41no—
554#41—41no—
555#41—41no—
556#41—41no—
557#41—41no—
558#41—41no—
559C2×Q8—21no—
560C2×Q8—21no—
561C2×Q8—21no—
562C2×Q8—21no—
563C2×Q8—21no—
564C2×Q8(C2×D11)⋊C412yescomplemented
565C2×D4—22no—
566C2×D4—22no—
567C2×D4—21no—
568C2×D4—21no—
569C2×D4—21no—
570C2×D4—21no—
571C2×D4—21no—
572C2×D4—41no—
573C2×D4—41no—
574C2×D4—41no—
575C2×D4—41no—
576C2×D4—114no—
577C2×D4—222no—
578C2×D4—222no—
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—222no—
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(C2×D11)⋊C412yescomplemented
605C22×C4—21no—
606C22×C4—22no—
607C22×C4—22no—
608C22×C4—22no—
609C22×C4—22no—
610C22×C4—22no—
611C22×C4—22no—
612C22×C4—41no—
613C22×C4—41no—
614C22×C4—41no—
615C22×C4—41no—
616C22×C4—44no—
617C22×C4—224no—
618C22×C4—222no—
619C22×C4—442no—
620C22×C4—441no—
621C22×C4—441no—
622C22×C4C2×C4×D1111yescharacteristic
623C22×C4C2×D4411yescharacteristic
624C22×C4#433911yescharacteristic
625C22×C4#433911yescharacteristic
626C22×C4D4×D1111yescharacteristic
627C22×C4D4×D1111yescharacteristic
628C22×C4D4×D1111yescharacteristic
629C22×C4D4×D1111yescharacteristic
630C22×C4D4×D1111yescharacteristic
631C22×C4D4×D1111yescharacteristic
632C22×C4#434111yescharacteristic
633C22×C4#434111yescharacteristic
634C22×C4C2×C22⋊D1111yescharacteristic
635C22×C4C2×C22⋊D1111yescharacteristic
636SD16—2216no—
637D8—2216no—
638M16—114no—
639M16—222no—
640M16—222no—
641M16—222no—
642M16—222no—
643M16—222no—
644M16—441no—
645M16—441no—
646C2×C8—222no—
647C2×C8—222no—
648C2×C8—222no—
649C2×C8—222no—
650C2×C8—441no—
651C2×C8—441no—
652C4⋊C4—22no—
653C4⋊C4—22no—
654C4⋊C4—41no—
655C4⋊C4—41no—
656C4⋊C4—41no—
657C4⋊C4—41no—
658C22⋊C4—41no—
659C22⋊C4—41no—
660C22⋊C4—84no—
661C22⋊C4—4416no—
662C42—41no—
663C42—41no—
664C42—222no—
665C42—222no—
666C42—441no—
667C42—441no—
668C11#1101611yescharacteristic, complemented, Sylow
669C23—22no—
670C23—22no—
671C23—22no—
672C23—41no—
673C23—41no—
674C23—42no—
675C23—42no—
676C23—224no—
677C23—444no—
678C23—444no—
679C23—448no—
680C23—448no—
681C23—442no—
682C23—442no—
683C23—442no—
684C23—442no—
685C23—442no—
686C23—442no—
687C23—882no—
688C23—882no—
689C23—884no—
690C23—884no—
691C23—882no—
692C23—882no—
693C23C4×C22⋊D1111yescharacteristic
694C23#6698311yescharacteristic
695C23#6699011yescharacteristic
696C23#6699111yescharacteristic
697C23#6699211yescharacteristic
698C23#6699311yescharacteristic
699C23#6700611yescharacteristic
700Q8—22no—
701Q8—22no—
702Q8—41no—
703Q8—41no—
704D4—22no—
705D4—22no—
706D4—42no—
707D4—42no—
708D4—42no—
709D4—42no—
710D4—41no—
711D4—41no—
712D4—224no—
713D4—224no—
714D4—442no—
715D4—442no—
716D4—442no—
717D4—442no—
718D4—442no—
719D4—442no—
720C2×C4—22no—
721C2×C4—41no—
722C2×C4—41no—
723C2×C4—42no—
724C2×C4—42no—
725C2×C4—42no—
726C2×C4—42no—
727C2×C4—44no—
728C2×C4—42no—
729C2×C4—42no—
730C2×C4—42no—
731C2×C4—44no—
732C2×C4—42no—
733C2×C4—82no—
734C2×C4—224no—
735C2×C4—442no—
736C2×C4—444no—
737C2×C4—444no—
738C2×C4—442no—
739C2×C4C22⋊C4×D1111yescharacteristic
740C2×C4C22⋊C4×D1111yescharacteristic
741C2×C4(C22⋊D11)⋊C411yescharacteristic
742C2×C4(C22⋊D11)⋊C411yescharacteristic
743C2×C4#6693511yescharacteristic
744C2×C4#6693511yescharacteristic
745C2×C4#6693511yescharacteristic
746C2×C4#6693611yescharacteristic
747C2×C4#6693611yescharacteristic
748C2×C4#6693711yescharacteristic
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×C4#6698211yescharacteristic
758C2×C4#6698311yescharacteristic
759C2×C4#6699011yescharacteristic
760C2×C4#6699011yescharacteristic
761C2×C4#6699011yescharacteristic
762C2×C4#6699111yescharacteristic
763C2×C4#6699211yescharacteristic
764C2×C4#6699211yescharacteristic
765C2×C4#6699211yescharacteristic
766C2×C4#6699311yescharacteristic
767C8—224no—
768C8—442no—
769C22—21no—
770C22—21no—
771C22—21no—
772C22—21no—
773C22—22no—
774C22—22no—
775C22—22no—
776C22—22no—
777C22—42no—
778C22—44no—
779C22—81no—
780C22—81no—
781C22—82no—
782C22—448no—
783C22—444no—
784C22—884no—
785C22—884no—
786C22—884no—
787C22—882no—
788C22—882no—
789C22—884no—
790C22—884no—
791C22#1062256911yescharacteristic
792C22#1062257011yescharacteristic
793C22#1062257311yescharacteristic
794C22#1062257411yescharacteristic
795C22#1062282611yescharacteristic
796C22#1062283611yescharacteristic
797C22#1062283611yescharacteristic
798C22#1062285412yes—
799C22#1062285812yes—
800C4—42no—
801C4—82no—
802C4—82no—
803C4—444no—
804C4#1062256811yescharacteristic
805C4#1062256911yescharacteristic
806C4#1062257011yescharacteristic
807C4#1062257111yescharacteristic
808C4#1062257211yescharacteristic
809C4#1062257211yescharacteristic
810C4#1062257311yescharacteristic
811C4#1062257411yescharacteristic
812C2—21no—
813C2—21no—
814C2—21no—
815C2—21no—
816C2—82no—
817C2—884no—
818C2#1306685511yescharacteristic
819C2#1306899212yes—
820C2#1306962911yescharacteristic
821C2#1306963611yescharacteristic
822C2#1306965812yes—
subgroupG/H
centerC23#67006
commutatorC22×C4×C11C22×C4
FrattiniC23×C4C22×D11
FittingC11×#2311C2
socleC23×C11#120
prime radicalC22×#67002C2
cosocleC23×C4×C11C23
hypercenter#2311D11
hypocenterC11#11016
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ #2311

Complements

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

NH ≅ G/Ntype
2. C22×#66901C2semidirect
3. C2×#10622614C2semidirect
4. C2×#10622601C2semidirect
5. C2×#10622168C2semidirect
6. C2×#10622170C2semidirect
7. C11×#2311C2semidirect
17. C2×#67002C4semidirect
154. C2×Q8×C11C22⋊C4semidirect
166. C2×D4×C11C22⋊C4semidirect
225. C2×D44C22⋊C4semidirect
251. #4318C22⋊C4semidirect
261. #2311D11semidirect
564. C2×Q8(C2×D11)⋊C4semidirect
604. C2×D4(C2×D11)⋊C4semidirect
668. C11#11016semidirect

Maximal subgroups

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

subgroupindex
C22×#670022
C22×#669012
C2×#106226142
C2×#106226012
C2×#106221682
C2×#106221702
C11×#23112
#1101611