Finite Group Databasebeta

← #14660580

Subgroups — #14660580

Order 2816.

1606 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
1C23×#4314C211yesmaximal, characteristic
2C22×#66880C211yesmaximal, characteristic, complemented
3C22×#66885C211yesmaximal, characteristic
4C2×#10622542C211yesmaximal, characteristic, complemented
5C2×#10622552C211yesmaximal, characteristic
6C2×#10622189C211yesmaximal, characteristic, complemented
7C2×C11×#336C211yesmaximal, characteristic, complemented
8C23×D44C2211yescharacteristic
9C23×Dic22C2211yescharacteristic
10C23×C8×C11C2211yescharacteristic
11C23×C8×C11C2211yescharacteristic
12C22×C42×C11C2211yescharacteristic
13C22×(C2×D11)⋊C4—22no—
14C22×C4⋊Dic11C2211yescharacteristic
15C22×C4⋊Dic11C2211yescharacteristic
16C22×#4314—22no—
17C22×#4314—22no—
18C22×#4314—22no—
19C22×#4314—22no—
20C22×#4314—22no—
21C22×#4314—22no—
22C22×#4314C414yescomplemented
23C2×C11⋊#95—22no—
24C2×#66885—22no—
25C2×#66885—22no—
26C2×#66885—22no—
27C2×#66880—22no—
28C2×#66880—22no—
29C2×#66880—22no—
30#10622552—22no—
31#10622552—22no—
32#10622542—22no—
33#10622542—22no—
34C11×#336—22no—
35#10622189—22no—
36C24×D11—21no—
37C23×C4×C11D412yes—
38C23×C4×C11C2311yescharacteristic
39C23×Dic11—21no—
40C23×Dic11—21no—
41C23×Dic11—21no—
42C22×D44—21no—
43C22×D44—21no—
44C22×D44—21no—
45C22×D44—21no—
46C22×D44—21no—
47C22×D44—21no—
48C22×D44—21no—
49C22×D44—21no—
50C22×D44—21no—
51C22×D44—21no—
52C22×D44—21no—
53C22×D44C2×C412yes—
54C22×D44D412yes—
55C22×D44D412yes—
56C22×Dic22—21no—
57C22×Dic22—21no—
58C22×Dic22—21no—
59C22×Dic22—21no—
60C22×Dic22—21no—
61C22×Dic22—21no—
62C22×Dic22—21no—
63C22×Dic22—21no—
64C22×Dic22—21no—
65C22×Dic22—21no—
66C22×Dic22—21no—
67C22×Dic22C2×C412yes—
68C22×Dic22D412yes—
69C22×Dic22D412yes—
70C22×C8×C11—21no—
71C22×C8×C11—21no—
72C22×C8×C11—21no—
73C22×C8×C11—21no—
74C22×C8×C11—21no—
75C22×C8×C11—21no—
76C22×C8×C11—21no—
77C22×C8×C11—21no—
78C22×C8×C11—21no—
79C22×C8×C11—21no—
80C22×C8×C11C2×C412yes—
81C22×C8×C11D412yes—
82C22×C8×C11D412yes—
83C22×C8×C11D412yes—
84C2×C42×C11—21no—
85C2×C42×C11—21no—
86C2×C42×C11—21no—
87C2×C42×C11—21no—
88C2×C42×C11—21no—
89C2×C42×C11—21no—
90C2×(C2×D11)⋊C4—28no—
91C2×(C2×D11)⋊C4—44no—
92C2×(C2×D11)⋊C4—44no—
93C2×C4⋊Dic11—21no—
94C2×C4⋊Dic11—21no—
95C2×C4⋊Dic11—21no—
96C2×C4⋊Dic11—21no—
97C2×C4⋊Dic11—21no—
98C2×C4⋊Dic11—21no—
99C2×C4⋊Dic11—21no—
100C2×C4⋊Dic11—21no—
101C2×C4⋊Dic11—21no—
102C2×C4⋊Dic11—21no—
103C2×C4⋊Dic11D412yes—
104C2×C4⋊Dic11D412yes—
105C2×#4314—28no—
106C2×#4314—28no—
107C2×#4314—28no—
108C2×#4314—28no—
109C2×#4314—28no—
110C2×#4314—28no—
111C2×#4314—28no—
112C11⋊#95—28no—
113#66885—28no—
114#66880—28no—
115#11023—111nomaximal, Sylow
116C24×C11C2×D411yescharacteristic
117C23×D11—22no—
118C23×D11—22no—
119C23×D11—22no—
120C23×D11—41no—
121C23×D11—41no—
122C23×D11—41no—
123C23×D11—41no—
124C23×D11—42no—
125C23×D11—42no—
126C23×D11—42no—
127C23×D11—42no—
128C22×C4×C11—22no—
129C22×C4×C11—22no—
130C22×C4×C11—22no—
131C22×C4×C11—22no—
132C22×C4×C11—22no—
133C22×C4×C11—22no—
134C22×C4×C11SD1614yescomplemented
135C22×C4×C11C22×C411yescharacteristic
136C22×C4×C11C2×D411yescharacteristic
137C22×C4×C11C2×D411yescharacteristic
138C22×C4×C11C2×D411yescharacteristic
139C22×C4×C11C2×D411yescharacteristic
140C22×C4×C11C2×D411yescharacteristic
141C22×C4×C11C2×D411yescharacteristic
142C22×C4×C11C2×D411yescharacteristic
143C22×C4×C11C2×D411yescharacteristic
144C22×C4×C11C2×D411yescharacteristic
145C22×C4×C11#4111yescharacteristic
146C22×C4×C11#4111yescharacteristic
147C22×C4×C11#4111yescharacteristic
148C22×C4×C11#4111yescharacteristic
149C22×Dic11—22no—
150C22×Dic11—22no—
151C22×Dic11—22no—
152C22×Dic11—22no—
153C22×Dic11—22no—
154C22×Dic11—41no—
155C22×Dic11—41no—
156C22×Dic11—41no—
157C22×Dic11—41no—
158C22×Dic11—41no—
159C22×Dic11—41no—
160C22×Dic11—41no—
161C22×Dic11—41no—
162C22×Dic11—42no—
163C22×Dic11—42no—
164C22×Dic11—42no—
165C22×Dic11—42no—
166C2×D44—22no—
167C2×D44—22no—
168C2×D44—22no—
169C2×D44—22no—
170C2×D44—22no—
171C2×D44—22no—
172C2×D44—22no—
173C2×D44—22no—
174C2×D44—22no—
175C2×D44—22no—
176C2×D44—22no—
177C2×D44—22no—
178C2×D44—22no—
179C2×D44—22no—
180C2×D44—22no—
181C2×D44—41no—
182C2×D44—41no—
183C2×D44—41no—
184C2×D44—41no—
185C2×D44—41no—
186C2×D44—41no—
187C2×D44—41no—
188C2×D44—41no—
189C2×D44—41no—
190C2×D44—41no—
191C2×D44—41no—
192C2×D44—41no—
193C2×D44C22⋊C414yes—
194C2×Dic22—22no—
195C2×Dic22—22no—
196C2×Dic22—22no—
197C2×Dic22—22no—
198C2×Dic22—22no—
199C2×Dic22—22no—
200C2×Dic22—22no—
201C2×Dic22—22no—
202C2×Dic22—22no—
203C2×Dic22—22no—
204C2×Dic22—22no—
205C2×Dic22—22no—
206C2×Dic22—22no—
207C2×Dic22—22no—
208C2×Dic22—22no—
209C2×Dic22—41no—
210C2×Dic22—41no—
211C2×Dic22—41no—
212C2×Dic22—41no—
213C2×Dic22—41no—
214C2×Dic22—41no—
215C2×Dic22—41no—
216C2×Dic22—41no—
217C2×Dic22—41no—
218C2×Dic22—41no—
219C2×Dic22—41no—
220C2×Dic22—41no—
221C2×Dic22C22⋊C414yescomplemented
222C2×C8×C11—22no—
223C2×C8×C11—22no—
224C2×C8×C11—22no—
225C2×C8×C11—22no—
226C2×C8×C11—22no—
227C2×C8×C11—22no—
228C2×C8×C11—22no—
229C2×C8×C11—22no—
230C2×C8×C11—22no—
231C2×C8×C11—41no—
232C2×C8×C11—41no—
233C2×C8×C11—41no—
234C2×C8×C11—41no—
235C2×C8×C11C22⋊C414yescomplemented
236C42×C11—41no—
237C42×C11—41no—
238C42×C11—41no—
239C42×C11—41no—
240(C2×D11)⋊C4—416no—
241C4⋊Dic11—22no—
242C4⋊Dic11—22no—
243C4⋊Dic11—22no—
244C4⋊Dic11—22no—
245C4⋊Dic11—41no—
246C4⋊Dic11—41no—
247C4⋊Dic11—41no—
248C4⋊Dic11—41no—
249#4314—232no—
250C23×SD16—111no—
251C22×#103—111no—
252C22×#102—111no—
253C2×#391—111no—
254C2×#390—111no—
255C2×#340—111no—
256C2×#336D1111yescharacteristic, complemented
257C23×C11C4×D411yescharacteristic
258C23×C11#12011yescharacteristic
259C23×C11#12011yescharacteristic
260C23×C11#12111yescharacteristic
261C23×C11#12111yescharacteristic
262C23×C11#12111yescharacteristic
263C23×C11#12711yescharacteristic
264C23×C11C2×SD1612yes—
265C23×C11#13512yes—
266C23×C11AGL(1,ℤ/8)12yes—
267C23×C11#13712yes—
268C22×D11—24no—
269C22×D11—42no—
270C22×D11—42no—
271C22×D11—42no—
272C22×D11—42no—
273C22×D11—42no—
274C22×D11—42no—
275C22×D11—44no—
276C22×D11—44no—
277C22×D11—44no—
278C22×D11—44no—
279C22×D11—44no—
280C22×D11—44no—
281C22×D11—82no—
282C22×D11—82no—
283C22×D11—82no—
284C22×D11—82no—
285C22×D11—82no—
286C22×D11—82no—
287C22×D11—81no—
288C22×D11—81no—
289C22×D11—81no—
290C22×D11—81no—
291C2×C4×C11—24no—
292C2×C4×C11—24no—
293C2×C4×C11—24no—
294C2×C4×C11—42no—
295C2×C4×C11—42no—
296C2×C4×C11—42no—
297C2×C4×C11—42no—
298C2×C4×C11C2×C22⋊C411yescharacteristic
299C2×C4×C11C2×C22⋊C411yescharacteristic
300C2×C4×C11C2×C22⋊C411yescharacteristic
301C2×C4×C11C4×D411yescharacteristic
302C2×C4×C11C4×D411yescharacteristic
303C2×C4×C11C4×D411yescharacteristic
304C2×C4×C11#12011yescharacteristic
305C2×C4×C11#12011yescharacteristic
306C2×C4×C11#12011yescharacteristic
307C2×C4×C11#12011yescharacteristic
308C2×C4×C11#12011yescharacteristic
309C2×C4×C11#12011yescharacteristic
310C2×C4×C11#12111yescharacteristic
311C2×C4×C11#12111yescharacteristic
312C2×C4×C11#12111yescharacteristic
313C2×C4×C11#12111yescharacteristic
314C2×C4×C11#12111yescharacteristic
315C2×C4×C11#12111yescharacteristic
316C2×C4×C11#12111yescharacteristic
317C2×C4×C11#12111yescharacteristic
318C2×C4×C11#12111yescharacteristic
319C2×C4×C11#12311yescharacteristic
320C2×C4×C11#12311yescharacteristic
321C2×C4×C11#12311yescharacteristic
322C2×C4×C11#12311yescharacteristic
323C2×C4×C11#12411yescharacteristic
324C2×C4×C11#12411yescharacteristic
325C2×C4×C11#12711yescharacteristic
326C2×Dic11—24no—
327C2×Dic11—42no—
328C2×Dic11—42no—
329C2×Dic11—42no—
330C2×Dic11—42no—
331C2×Dic11—42no—
332C2×Dic11—42no—
333C2×Dic11—42no—
334C2×Dic11—42no—
335C2×Dic11—44no—
336C2×Dic11—44no—
337C2×Dic11—82no—
338C2×Dic11—82no—
339C2×Dic11—81no—
340C2×Dic11—81no—
341C2×Dic11—81no—
342C2×Dic11—81no—
343D44—24no—
344D44—24no—
345D44—42no—
346D44—42no—
347D44—42no—
348D44—42no—
349D44—42no—
350D44—42no—
351Dic22—24no—
352Dic22—24no—
353Dic22—42no—
354Dic22—42no—
355Dic22—42no—
356Dic22—42no—
357Dic22—42no—
358Dic22—42no—
359C8×C11—24no—
360C8×C11—42no—
361C23×Q8—111no—
362C23×D4—111no—
363C22×SD16—114no—
364C22×SD16—222no—
365C22×SD16—222no—
366C22×SD16—222no—
367C22×SD16—222no—
368C22×SD16—222no—
369C22×SD16—222no—
370C23×C8C2×D1111yescharacteristic
371C23×C8C2×D1111yescharacteristic
372C22×C4⋊C4—111no—
373C22×C4⋊C4—111no—
374C22×C22⋊C4—222no—
375C22×C42C2×D1111yescharacteristic
376C2×#103—222no—
377C2×#103—222no—
378C2×#103—222no—
379C2×#102—222no—
380C2×#102—222no—
381C2×#102—222no—
382#391—222no—
383#391—222no—
384#390—222no—
385#390—222no—
386C2×#95—222no—
387#340—222no—
388#336—22no—
389C22×C11#38611yescharacteristic
390C22×C11#38611yescharacteristic
391C22×C11#39011yescharacteristic
392C22×C11#39211yescharacteristic
393C22×C11#39211yescharacteristic
394C22×C11#39211yescharacteristic
395C22×C11#39411yescharacteristic
396C22×C11C4×SD1612yes—
397C22×C11#44012yes—
398C22×C11#44812yes—
399C22×C11#44912yes—
400C22×C11#45012yes—
401C22×C11#45212yes—
402C22×C11#46012yes—
403C22×C11#46112yes—
404C22×C11#46312yes—
405C22×C11#46412yes—
406C22×C11#46512yes—
407C22×C11#46812yes—
408C22×C11#49211yescharacteristic
409C22×C11#49511yescharacteristic
410C22×C11#49611yescharacteristic
411C22×C11#49711yescharacteristic
412C2×D11—48no—
413C2×D11—44no—
414C2×D11—84no—
415C2×D11—84no—
416C2×D11—82no—
417C2×D11—82no—
418C2×D11—84no—
419C2×D11—82no—
420C2×D11—82no—
421C2×D11—82no—
422C2×D11—82no—
423C4×C11—44no—
424C4×C11#37911yescharacteristic
425C4×C11#38611yescharacteristic
426C4×C11#38611yescharacteristic
427C4×C11#39011yescharacteristic
428C4×C11#39211yescharacteristic
429C4×C11#39411yescharacteristic
430C4×C11#39411yescharacteristic
431C4×C11#39411yescharacteristic
432Dic11—44no—
433Dic11—82no—
434Dic11—82no—
435C25—221no—
436C22×Q8—112no—
437C22×Q8—112no—
438C22×Q8—112no—
439C22×Q8—221no—
440C22×Q8—221no—
441C22×Q8—221no—
442C22×Q8—221no—
443C22×Q8—221no—
444C22×Q8—221no—
445C22×Q8—221no—
446C22×Q8—221no—
447C22×Q8—221no—
448C22×Q8—221no—
449C22×Q8—221no—
450C22×D4—112no—
451C22×D4—112no—
452C22×D4—112no—
453C22×D4—221no—
454C22×D4—221no—
455C22×D4—221no—
456C22×D4—221no—
457C22×D4—221no—
458C22×D4—221no—
459C22×D4—221no—
460C22×D4—221no—
461C22×D4—221no—
462C22×D4—221no—
463C22×D4—221no—
464C23×C4—221no—
465C23×C4—221no—
466C23×C4—221no—
467C23×C4D4412yes—
468C23×C4C22×D1111yescharacteristic
469C2×SD16—228no—
470C2×SD16—228no—
471C2×SD16—228no—
472C2×SD16—228no—
473C2×SD16—228no—
474C2×SD16—228no—
475C2×SD16—228no—
476C22×C8—21no—
477C22×C8—21no—
478C22×C8—21no—
479C22×C8—21no—
480C22×C8—21no—
481C22×C8—21no—
482C22×C8—21no—
483C22×C8—21no—
484C22×C8—21no—
485C22×C8—21no—
486C22×C8C4×D1112yes—
487C22×C8D4412yes—
488C22×C8D4412yes—
489C22×C8C22⋊D1112yes—
490C2×C4⋊C4—112no—
491C2×C4⋊C4—112no—
492C2×C4⋊C4—221no—
493C2×C4⋊C4—221no—
494C2×C4⋊C4—221no—
495C2×C4⋊C4—221no—
496C2×C4⋊C4—221no—
497C2×C4⋊C4—221no—
498C2×C4⋊C4—221no—
499C2×C4⋊C4—221no—
500C2×C4⋊C4—221no—
501C2×C4⋊C4—221no—
502C2×C22⋊C4—228no—
503C2×C22⋊C4—444no—
504C2×C22⋊C4—444no—
505C2×C42—21no—
506C2×C42—21no—
507C2×C42—21no—
508C2×C42—21no—
509C2×C42—21no—
510C2×C42—21no—
511#103—228no—
512#102—228no—
513#95—228no—
514C2×C11#143811yescharacteristic
515C2×C11#187712yes—
516C2×C11#188012yes—
517C2×C11#196811yescharacteristic
518C2×C11#197311yescharacteristic
519C2×C11#200012yes—
520C2×C11#201211yescharacteristic
521C2×C11#201311yescharacteristic
522C2×C11#201411yescharacteristic
523C2×C11#201511yescharacteristic
524C2×C11#205512yes—
525D11—84no—
526C24—222no—
527C24—222no—
528C24—222no—
529C24—441no—
530C24—441no—
531C24—441no—
532C24—442no—
533C24—442no—
534C24—442no—
535C24—442no—
536C24—441no—
537C24C2×D4411yescharacteristic
538C2×Q8—114no—
539C2×Q8—222no—
540C2×Q8—222no—
541C2×Q8—222no—
542C2×Q8—222no—
543C2×Q8—222no—
544C2×Q8—222no—
545C2×Q8—222no—
546C2×Q8—222no—
547C2×Q8—222no—
548C2×Q8—222no—
549C2×Q8—222no—
550C2×Q8—222no—
551C2×Q8—222no—
552C2×Q8—222no—
553C2×Q8—222no—
554C2×Q8—441no—
555C2×Q8—441no—
556C2×Q8—441no—
557C2×Q8—441no—
558C2×Q8—441no—
559C2×Q8—441no—
560C2×Q8—441no—
561C2×Q8—441no—
562C2×Q8—441no—
563C2×Q8—441no—
564C2×Q8—441no—
565C2×Q8—441no—
566C2×D4—114no—
567C2×D4—222no—
568C2×D4—222no—
569C2×D4—222no—
570C2×D4—222no—
571C2×D4—222no—
572C2×D4—222no—
573C2×D4—222no—
574C2×D4—222no—
575C2×D4—222no—
576C2×D4—222no—
577C2×D4—222no—
578C2×D4—222no—
579C2×D4—222no—
580C2×D4—222no—
581C2×D4—222no—
582C2×D4—441no—
583C2×D4—441no—
584C2×D4—441no—
585C2×D4—441no—
586C2×D4—441no—
587C2×D4—441no—
588C2×D4—441no—
589C2×D4—441no—
590C2×D4—441no—
591C2×D4—441no—
592C2×D4—441no—
593C2×D4—441no—
594C22×C4—22no—
595C22×C4—22no—
596C22×C4—22no—
597C22×C4—22no—
598C22×C4—22no—
599C22×C4—22no—
600C22×C4—222no—
601C22×C4—222no—
602C22×C4—222no—
603C22×C4—222no—
604C22×C4—222no—
605C22×C4—441no—
606C22×C4—441no—
607C22×C4—441no—
608C22×C4—441no—
609C22×C4—441no—
610C22×C4—441no—
611C22×C4—441no—
612C22×C4—441no—
613C22×C4—442no—
614C22×C4—442no—
615C22×C4—442no—
616C22×C4—442no—
617C22×C4#431414yescomplemented
618C22×C4C2×C4×D1111yescharacteristic
619C22×C4C2×D4411yescharacteristic
620C22×C4C2×D4411yescharacteristic
621C22×C4#433911yescharacteristic
622C22×C4#433911yescharacteristic
623C22×C4D4×D1111yescharacteristic
624C22×C4D4×D1111yescharacteristic
625C22×C4D4×D1111yescharacteristic
626C22×C4D4×D1111yescharacteristic
627C22×C4D4×D1111yescharacteristic
628C22×C4D4×D1111yescharacteristic
629C22×C4#434311yescharacteristic
630C22×C4#434311yescharacteristic
631C22×C4C2×C22⋊D1111yescharacteristic
632SD16—2232no—
633C2×C8—22no—
634C2×C8—22no—
635C2×C8—22no—
636C2×C8—22no—
637C2×C8—22no—
638C2×C8—22no—
639C2×C8—22no—
640C2×C8—22no—
641C2×C8—22no—
642C2×C8—41no—
643C2×C8—41no—
644C2×C8—41no—
645C2×C8—41no—
646C2×C8(C2×D11)⋊C414yescomplemented
647C4⋊C4—222no—
648C4⋊C4—222no—
649C4⋊C4—222no—
650C4⋊C4—222no—
651C4⋊C4—441no—
652C4⋊C4—441no—
653C4⋊C4—441no—
654C4⋊C4—441no—
655C22⋊C4—4416no—
656C42—41no—
657C42—41no—
658C42—41no—
659C42—41no—
660C11#1102311yescharacteristic, complemented, Sylow
661C23—224no—
662C23—442no—
663C23—442no—
664C23—442no—
665C23—442no—
666C23—444no—
667C23—442no—
668C23—444no—
669C23—444no—
670C23—444no—
671C23—442no—
672C23—444no—
673C23—444no—
674C23—882no—
675C23—882no—
676C23—881no—
677C23—881no—
678C23—881no—
679C23—881no—
680C23—882no—
681C23—882no—
682C23—882no—
683C23—882no—
684C23C4×D4411yescharacteristic
685C23#6692711yescharacteristic
686C23#6693511yescharacteristic
687C23#6693511yescharacteristic
688C23#6694811yescharacteristic
689C23#6694811yescharacteristic
690C23C2×#431412yes—
691C23#6695712yes—
692C23#6696112yes—
693C23#6696212yes—
694C23#6698311yescharacteristic
695Q8—224no—
696Q8—224no—
697Q8—442no—
698Q8—442no—
699Q8—442no—
700Q8—442no—
701Q8—442no—
702Q8—442no—
703D4—224no—
704D4—224no—
705D4—442no—
706D4—442no—
707D4—442no—
708D4—442no—
709D4—442no—
710D4—442no—
711C2×C4—24no—
712C2×C4—24no—
713C2×C4—24no—
714C2×C4—42no—
715C2×C4—42no—
716C2×C4—42no—
717C2×C4—42no—
718C2×C4—224no—
719C2×C4—442no—
720C2×C4—442no—
721C2×C4—442no—
722C2×C4—442no—
723C2×C4—442no—
724C2×C4—442no—
725C2×C4—442no—
726C2×C4—442no—
727C2×C4—444no—
728C2×C4—444no—
729C2×C4—881no—
730C2×C4—881no—
731C2×C4—881no—
732C2×C4—881no—
733C2×C4—882no—
734C2×C4—882no—
735C2×C4C4×D4411yescharacteristic
736C2×C4#6692811yescharacteristic
737C2×C4C22⋊C4×D1111yescharacteristic
738C2×C4C22⋊C4×D1111yescharacteristic
739C2×C4#6693511yescharacteristic
740C2×C4#6693511yescharacteristic
741C2×C4#6693511yescharacteristic
742C2×C4#6693511yescharacteristic
743C2×C4#6693711yescharacteristic
744C2×C4#6693711yescharacteristic
745C2×C4#6693711yescharacteristic
746C2×C4#6693711yescharacteristic
747C2×C4#6694611yescharacteristic
748C2×C4#6694611yescharacteristic
749C2×C4#6694711yescharacteristic
750C2×C4#6694711yescharacteristic
751C2×C4#6694711yescharacteristic
752C2×C4#6694711yescharacteristic
753C2×C4#6694811yescharacteristic
754C2×C4#6694811yescharacteristic
755C2×C4#6694811yescharacteristic
756C2×C4#6694811yescharacteristic
757C2×C4C2×(C2×D11)⋊C411yescharacteristic
758C2×C4#6698311yescharacteristic
759C2×C4#6699011yescharacteristic
760C2×C4#6699011yescharacteristic
761C2×C4#6699311yescharacteristic
762C2×C4#6700011yescharacteristic
763C8—24no—
764C8—42no—
765C22—444no—
766C22—448no—
767C22—884no—
768C22—884no—
769C22—882no—
770C22—882no—
771C22—882no—
772C22—882no—
773C22—882no—
774C22—884no—
775C22—882no—
776C22#1062227811yescharacteristic
777C22#1062227811yescharacteristic
778C22#1062228411yescharacteristic
779C22#1062228411yescharacteristic
780C22C4×#431412yes—
781C22#1062230611yescharacteristic
782C22#1062230911yescharacteristic
783C22#1062232312yes—
784C22#1062232511yescharacteristic
785C22#1062232811yescharacteristic
786C22#1062234412yes—
787C22#1062234612yes—
788C22#1062234712yes—
789C22#1062235112yes—
790C22#1062245412yes—
791C22#1062245712yes—
792C22#1062245812yes—
793C22#1062246112yes—
794C22#1062255211yescharacteristic
795C22#1062257311yescharacteristic
796C22#1062260411yescharacteristic
797C22#1062272712yes—
798C22#1062274712yes—
799C4—44no—
800C4—444no—
801C4—882no—
802C4—882no—
803C4#1062227811yescharacteristic
804C4#1062227811yescharacteristic
805C4#1062228511yescharacteristic
806C4#1062228511yescharacteristic
807C4#1062256811yescharacteristic
808C4#1062257311yescharacteristic
809C4#1062260111yescharacteristic
810C4#1062260411yescharacteristic
811C2—884no—
812C2#1306685611yescharacteristic
813C2#1306894912yes—
814C2#1306897012yes—
815C2#1306947011yescharacteristic
816C2#1306949711yescharacteristic
817C2#1306962112yes—
818C2#1306969611yescharacteristic
819C2#1306970111yescharacteristic
820C2#1306970611yescharacteristic
821C2#1306971311yescharacteristic
822C2#1306993412yes—
subgroupG/H
centerC24C2×D44
commutatorC22×C4×C11C22×C4
FrattiniC23×C4C22×D11
FittingC2×C11×#336C2
socleC24×C11C2×D4
prime radicalC23×D44C22
cosocleC23×C4×C11C23
hypercenterC2×#336D11
hypocenterC11#11023
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C24 ◁ C22×C42 ◁ C2×#336

Complements

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

NH ≅ G/Ntype
2. C22×#66880C2semidirect
4. C2×#10622542C2semidirect
6. C2×#10622189C2semidirect
7. C2×C11×#336C2semidirect
22. C22×#4314C4semidirect
134. C22×C4×C11SD16semidirect
221. C2×Dic22C22⋊C4semidirect
235. C2×C8×C11C22⋊C4semidirect
256. C2×#336D11semidirect
617. C22×C4#4314semidirect
646. C2×C8(C2×D11)⋊C4semidirect
660. C11#11023semidirect

Maximal subgroups

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

subgroupindex
C23×#43142
C22×#668802
C22×#668852
C2×#106225422
C2×#106225522
C2×#106221892
C2×C11×#3362
#1102311