Finite Group Databasebeta

← #14660579

Subgroups — #14660579

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×#4324C211yesmaximal, characteristic
2C22×#66880C211yesmaximal, characteristic, complemented
3C2×#10622587C211yesmaximal, characteristic, complemented
4C2×#10622834C211yesmaximal, characteristic
5C2×#10622167C211yesmaximal, characteristic, complemented
6C2×#10622188C211yesmaximal, characteristic, complemented
7C22×C11×#102C211yesmaximal, characteristic
8C23×D4×C11C2211yescharacteristic
9C23×Dic22C2211yescharacteristic
10C23×C8×C11C2211yescharacteristic
11C22×C11×C4⋊C4C2211yescharacteristic
12C22×C22⋊Dic11—22no—
13C22×#4324—22no—
14C22×#4324—22no—
15C22×#4324—22no—
16C22×#4324—22no—
17C22×#4324—22no—
18C22×#4324—22no—
19C22×#4324C414yescomplemented
20C22×C4⋊Dic11C2211yescharacteristic
21C22×C4×Dic11C2211yescharacteristic
22C23×C11⋊C8C2211yescharacteristic
23C2×C11×#102—22no—
24C2×C11×#102—22no—
25C2×C11×#102—22no—
26#10622834—22no—
27#10622834—22no—
28C2×C11⋊#95—22no—
29C2×#66880—22no—
30C2×#66880—22no—
31C2×#66880—22no—
32#10622587—22no—
33#10622587—22no—
34#10622188—22no—
35#10622167—22no—
36C25×C11—21no—
37C22×D4×C11—21no—
38C22×D4×C11—21no—
39C22×D4×C11—21no—
40C22×D4×C11—21no—
41C22×D4×C11—21no—
42C22×D4×C11—21no—
43C22×D4×C11—21no—
44C22×D4×C11—21no—
45C22×D4×C11—21no—
46C22×D4×C11—21no—
47C22×D4×C11—21no—
48C22×D4×C11C2×C412yes—
49C22×D4×C11D412yes—
50C22×D4×C11D412yes—
51C23×C4×C11—21no—
52C23×C4×C11C2311yescharacteristic
53C23×Dic11—21no—
54C23×Dic11—21no—
55C23×Dic11D412yes—
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×C11D412yes—
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×C22⋊Dic11—28no—
84C2×C22⋊Dic11—44no—
85C2×C22⋊Dic11—44no—
86C2×#4324—28no—
87C2×#4324—28no—
88C2×#4324—28no—
89C2×#4324—28no—
90C2×#4324—28no—
91C2×#4324—28no—
92C2×#4324—28no—
93C2×C4⋊Dic11—21no—
94C2×C4⋊Dic11—21no—
95C2×C4⋊Dic11—21no—
96C2×C4⋊Dic11—21no—
97C2×C4⋊Dic11—21no—
98C2×C4⋊Dic11D412yes—
99C2×C4×Dic11—21no—
100C2×C4×Dic11—21no—
101C2×C4×Dic11—21no—
102C2×C4×Dic11—21no—
103C2×C4×Dic11—21no—
104C2×C4×Dic11—21no—
105C22×C11⋊C8—21no—
106C22×C11⋊C8—21no—
107C22×C11⋊C8—21no—
108C22×C11⋊C8—21no—
109C22×C11⋊C8C2×C412yes—
110C22×C11⋊C8D412yes—
111C22×C11⋊C8D412yes—
112C11×#102—28no—
113C11⋊#95—28no—
114#66880—28no—
115#11023—111nomaximal, Sylow
116C24×C11—22no—
117C24×C11—22no—
118C24×C11—22no—
119C24×C11—41no—
120C24×C11—41no—
121C24×C11—41no—
122C24×C11—41no—
123C24×C11—42no—
124C24×C11—42no—
125C24×C11—42no—
126C24×C11—42no—
127C24×C11C2×D411yescharacteristic
128C2×D4×C11—22no—
129C2×D4×C11—22no—
130C2×D4×C11—22no—
131C2×D4×C11—22no—
132C2×D4×C11—22no—
133C2×D4×C11—22no—
134C2×D4×C11—22no—
135C2×D4×C11—22no—
136C2×D4×C11—22no—
137C2×D4×C11—22no—
138C2×D4×C11—22no—
139C2×D4×C11—22no—
140C2×D4×C11—22no—
141C2×D4×C11—22no—
142C2×D4×C11—22no—
143C2×D4×C11—41no—
144C2×D4×C11—41no—
145C2×D4×C11—41no—
146C2×D4×C11—41no—
147C2×D4×C11—41no—
148C2×D4×C11—41no—
149C2×D4×C11—41no—
150C2×D4×C11—41no—
151C2×D4×C11—41no—
152C2×D4×C11—41no—
153C2×D4×C11—41no—
154C2×D4×C11—41no—
155C2×D4×C11C22⋊C414yes—
156C22×C4×C11—22no—
157C22×C4×C11—41no—
158C22×C4×C11—41no—
159C22×C4×C11—42no—
160C22×C4×C11—42no—
161C22×C4×C11C22×C411yescharacteristic
162C22×C4×C11C2×D411yescharacteristic
163C22×C4×C11C2×D411yescharacteristic
164C22×C4×C11C2×D411yescharacteristic
165C22×C4×C11C2×D411yescharacteristic
166C22×C4×C11C2×D411yescharacteristic
167C22×C4×C11C2×D411yescharacteristic
168C22×C4×C11C2×D411yescharacteristic
169C22×C4×C11C2×D411yescharacteristic
170C22×C4×C11C2×D411yescharacteristic
171C22×C4×C11#4111yescharacteristic
172C22×C4×C11#4111yescharacteristic
173C22×C4×C11#4111yescharacteristic
174C22×C4×C11#4111yescharacteristic
175C22×Dic11—22no—
176C22×Dic11—22no—
177C22×Dic11—22no—
178C22×Dic11—22no—
179C22×Dic11—22no—
180C22×Dic11—22no—
181C22×Dic11—22no—
182C22×Dic11—22no—
183C22×Dic11—22no—
184C22×Dic11—22no—
185C22×Dic11—41no—
186C22×Dic11—41no—
187C22×Dic11—41no—
188C22×Dic11—41no—
189C22×Dic11—41no—
190C22×Dic11—41no—
191C22×Dic11—42no—
192C22×Dic11—42no—
193C22×Dic11SD1614yescomplemented
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—41no—
226C2×C8×C11—41no—
227C2×C8×C11—41no—
228C2×C8×C11—41no—
229C11×C4⋊C4—22no—
230C11×C4⋊C4—22no—
231C11×C4⋊C4—41no—
232C11×C4⋊C4—41no—
233C22⋊Dic11—416no—
234#4324—232no—
235C4⋊Dic11—22no—
236C4⋊Dic11—22no—
237C4⋊Dic11—41no—
238C4⋊Dic11—41no—
239C4×Dic11—41no—
240C4×Dic11—41no—
241C4×Dic11—41no—
242C4×Dic11—41no—
243C2×C11⋊C8—22no—
244C2×C11⋊C8—22no—
245C2×C11⋊C8—22no—
246C2×C11⋊C8—22no—
247C2×C11⋊C8—22no—
248C2×C11⋊C8—22no—
249C2×C11⋊C8C22⋊C414yescomplemented
250C23×SD16—111no—
251C22×#103—111no—
252C22×#102D1111yescharacteristic
253C2×#391—111no—
254C2×#390—111no—
255C2×#340—111no—
256C2×#336—111no—
257C23×C11—24no—
258C23×C11—42no—
259C23×C11—42no—
260C23×C11—42no—
261C23×C11—42no—
262C23×C11—42no—
263C23×C11—42no—
264C23×C11—44no—
265C23×C11—44no—
266C23×C11—44no—
267C23×C11—44no—
268C23×C11—44no—
269C23×C11—44no—
270C23×C11—82no—
271C23×C11—82no—
272C23×C11—82no—
273C23×C11—82no—
274C23×C11—82no—
275C23×C11—82no—
276C23×C11—81no—
277C23×C11—81no—
278C23×C11—81no—
279C23×C11—81no—
280C23×C11C4×D411yescharacteristic
281C23×C11#12011yescharacteristic
282C23×C11#12011yescharacteristic
283C23×C11#12111yescharacteristic
284C23×C11#12111yescharacteristic
285C23×C11#12111yescharacteristic
286C23×C11#12711yescharacteristic
287C23×C11C2×SD1612yes—
288C23×C11#13512yes—
289C23×C11AGL(1,ℤ/8)12yes—
290C23×C11#13712yes—
291D4×C11—24no—
292D4×C11—24no—
293D4×C11—42no—
294D4×C11—42no—
295D4×C11—42no—
296D4×C11—42no—
297D4×C11—42no—
298D4×C11—42no—
299C2×C4×C11—42no—
300C2×C4×C11—44no—
301C2×C4×C11—82no—
302C2×C4×C11—81no—
303C2×C4×C11—81no—
304C2×C4×C11C2×C22⋊C411yescharacteristic
305C2×C4×C11C2×C22⋊C411yescharacteristic
306C2×C4×C11C2×C22⋊C411yescharacteristic
307C2×C4×C11C4×D411yescharacteristic
308C2×C4×C11C4×D411yescharacteristic
309C2×C4×C11C4×D411yescharacteristic
310C2×C4×C11#12011yescharacteristic
311C2×C4×C11#12011yescharacteristic
312C2×C4×C11#12011yescharacteristic
313C2×C4×C11#12011yescharacteristic
314C2×C4×C11#12011yescharacteristic
315C2×C4×C11#12011yescharacteristic
316C2×C4×C11#12111yescharacteristic
317C2×C4×C11#12111yescharacteristic
318C2×C4×C11#12111yescharacteristic
319C2×C4×C11#12111yescharacteristic
320C2×C4×C11#12111yescharacteristic
321C2×C4×C11#12111yescharacteristic
322C2×C4×C11#12111yescharacteristic
323C2×C4×C11#12111yescharacteristic
324C2×C4×C11#12111yescharacteristic
325C2×C4×C11#12311yescharacteristic
326C2×C4×C11#12311yescharacteristic
327C2×C4×C11#12311yescharacteristic
328C2×C4×C11#12311yescharacteristic
329C2×C4×C11#12411yescharacteristic
330C2×C4×C11#12411yescharacteristic
331C2×C4×C11#12711yescharacteristic
332C2×Dic11—24no—
333C2×Dic11—24no—
334C2×Dic11—24no—
335C2×Dic11—24no—
336C2×Dic11—42no—
337C2×Dic11—42no—
338C2×Dic11—42no—
339C2×Dic11—42no—
340C2×Dic11—42no—
341C2×Dic11—42no—
342C2×Dic11—42no—
343C2×Dic11—42no—
344C2×Dic11—42no—
345C2×Dic11—42no—
346C2×Dic11—42no—
347C2×Dic11—44no—
348C2×Dic11—82no—
349C2×Dic11—81no—
350C2×Dic11—81no—
351Dic22—24no—
352Dic22—24no—
353Dic22—42no—
354Dic22—42no—
355Dic22—42no—
356Dic22—42no—
357Dic22—42no—
358Dic22—42no—
359C8×C11—42no—
360C11⋊C8—24no—
361C23×Q8—111no—
362C23×D4C2×D1111yescharacteristic
363C22×SD16—114no—
364C22×SD16—222no—
365C22×SD16—222no—
366C22×SD16—222no—
367C22×SD16—222no—
368C22×SD16—222no—
369C22×SD16—222no—
370C23×C8—111no—
371C23×C8C2×D1111yescharacteristic
372C22×C4⋊C4—111no—
373C22×C4⋊C4C2×D1111yescharacteristic
374C22×C22⋊C4—222no—
375C22×C42—111no—
376C2×#103—222no—
377C2×#103—222no—
378C2×#103—222no—
379C2×#102—22no—
380C2×#102—22no—
381C2×#102—22no—
382#391—222no—
383#391—222no—
384#390—222no—
385#390—222no—
386C2×#95—222no—
387#340—222no—
388#336—222no—
389C22×C11—48no—
390C22×C11—44no—
391C22×C11—84no—
392C22×C11—84no—
393C22×C11—82no—
394C22×C11—82no—
395C22×C11—84no—
396C22×C11—82no—
397C22×C11—82no—
398C22×C11—82no—
399C22×C11—82no—
400C22×C11#38611yescharacteristic
401C22×C11#38611yescharacteristic
402C22×C11#39011yescharacteristic
403C22×C11#39211yescharacteristic
404C22×C11#39211yescharacteristic
405C22×C11#39211yescharacteristic
406C22×C11#39411yescharacteristic
407C22×C11C4×SD1612yes—
408C22×C11#44012yes—
409C22×C11#44812yes—
410C22×C11#44912yes—
411C22×C11#45012yes—
412C22×C11#45212yes—
413C22×C11#46012yes—
414C22×C11#46112yes—
415C22×C11#46312yes—
416C22×C11#46412yes—
417C22×C11#46512yes—
418C22×C11#46812yes—
419C22×C11#49211yescharacteristic
420C22×C11#49511yescharacteristic
421C22×C11#49611yescharacteristic
422C22×C11#49711yescharacteristic
423C4×C11—82no—
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—44no—
434Dic11—82no—
435C25—21no—
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—21no—
451C22×D4—21no—
452C22×D4—21no—
453C22×D4—21no—
454C22×D4—21no—
455C22×D4—21no—
456C22×D4—21no—
457C22×D4—21no—
458C22×D4—21no—
459C22×D4—21no—
460C22×D4—21no—
461C22×D4C4×D1112yes—
462C22×D4D4412yes—
463C22×D4C22⋊D1112yes—
464C23×C4—21no—
465C23×C4—112no—
466C23×C4—221no—
467C23×C4—221no—
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—112no—
483C22×C8—112no—
484C22×C8—112no—
485C22×C8—221no—
486C22×C8—221no—
487C22×C8—221no—
488C22×C8—221no—
489C22×C8C22⋊D1112yes—
490C2×C4⋊C4—21no—
491C2×C4⋊C4—21no—
492C2×C4⋊C4—21no—
493C2×C4⋊C4—21no—
494C2×C4⋊C4—21no—
495C2×C4⋊C4—112no—
496C2×C4⋊C4—221no—
497C2×C4⋊C4—221no—
498C2×C4⋊C4—221no—
499C2×C4⋊C4—221no—
500C2×C4⋊C4—221no—
501C2×C4⋊C4C22⋊D1112yes—
502C2×C22⋊C4—228no—
503C2×C22⋊C4—444no—
504C2×C22⋊C4—444no—
505C2×C42—221no—
506C2×C42—221no—
507C2×C42—221no—
508C2×C42—221no—
509C2×C42—221no—
510C2×C42—221no—
511#103—228no—
512#102—28no—
513#95—228no—
514C2×C11—84no—
515C2×C11#143811yescharacteristic
516C2×C11#187712yes—
517C2×C11#188012yes—
518C2×C11#196811yescharacteristic
519C2×C11#197311yescharacteristic
520C2×C11#200012yes—
521C2×C11#201211yescharacteristic
522C2×C11#201311yescharacteristic
523C2×C11#201411yescharacteristic
524C2×C11#201511yescharacteristic
525C2×C11#205512yes—
526C24—22no—
527C24—22no—
528C24—22no—
529C24—41no—
530C24—41no—
531C24—42no—
532C24—42no—
533C24—42no—
534C24—42no—
535C24—41no—
536C24—41no—
537C24D4×D1111yescharacteristic
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—22no—
567C2×D4—22no—
568C2×D4—22no—
569C2×D4—22no—
570C2×D4—22no—
571C2×D4—22no—
572C2×D4—22no—
573C2×D4—22no—
574C2×D4—22no—
575C2×D4—22no—
576C2×D4—22no—
577C2×D4—22no—
578C2×D4—22no—
579C2×D4—22no—
580C2×D4—22no—
581C2×D4—41no—
582C2×D4—41no—
583C2×D4—41no—
584C2×D4—41no—
585C2×D4—41no—
586C2×D4—41no—
587C2×D4—41no—
588C2×D4—41no—
589C2×D4—41no—
590C2×D4—41no—
591C2×D4—41no—
592C2×D4—41no—
593C2×D4(C2×D11)⋊C414yes—
594C22×C4—22no—
595C22×C4—42no—
596C22×C4—42no—
597C22×C4—41no—
598C22×C4—41no—
599C22×C4—114no—
600C22×C4—222no—
601C22×C4—222no—
602C22×C4—222no—
603C22×C4—222no—
604C22×C4—222no—
605C22×C4—222no—
606C22×C4—222no—
607C22×C4—222no—
608C22×C4—222no—
609C22×C4—222no—
610C22×C4—441no—
611C22×C4—441no—
612C22×C4—441no—
613C22×C4—441no—
614C22×C4—441no—
615C22×C4—442no—
616C22×C4—442no—
617C22×C4—441no—
618C22×C4C2×C4×D1111yescharacteristic
619C22×C4C2×D4411yescharacteristic
620C22×C4#433911yescharacteristic
621C22×C4#433911yescharacteristic
622C22×C4D4×D1111yescharacteristic
623C22×C4D4×D1111yescharacteristic
624C22×C4D4×D1111yescharacteristic
625C22×C4D4×D1111yescharacteristic
626C22×C4D4×D1111yescharacteristic
627C22×C4#434111yescharacteristic
628C22×C4#434111yescharacteristic
629C22×C4C2×C22⋊D1111yescharacteristic
630C22×C4C2×C22⋊D1111yescharacteristic
631C22×C4C2×C22⋊D1111yescharacteristic
632SD16—2232no—
633C2×C8—22no—
634C2×C8—22no—
635C2×C8—22no—
636C2×C8—41no—
637C2×C8—41no—
638C2×C8—41no—
639C2×C8—41no—
640C2×C8—114no—
641C2×C8—222no—
642C2×C8—222no—
643C2×C8—222no—
644C2×C8—222no—
645C2×C8—222no—
646C2×C8—222no—
647C4⋊C4—22no—
648C4⋊C4—22no—
649C4⋊C4—41no—
650C4⋊C4—41no—
651C4⋊C4—222no—
652C4⋊C4—222no—
653C4⋊C4—441no—
654C4⋊C4—441no—
655C22⋊C4—4416no—
656C42—441no—
657C42—441no—
658C42—441no—
659C42—441no—
660C11#1102311yescharacteristic, complemented, Sylow
661C23—24no—
662C23—44no—
663C23—44no—
664C23—42no—
665C23—42no—
666C23—42no—
667C23—42no—
668C23—42no—
669C23—42no—
670C23—44no—
671C23—44no—
672C23—44no—
673C23—44no—
674C23—81no—
675C23—81no—
676C23—82no—
677C23—81no—
678C23—82no—
679C23—81no—
680C23—82no—
681C23—82no—
682C23—82no—
683C23—82no—
684C23(C22⋊D11)⋊C411yescharacteristic
685C23#6693511yescharacteristic
686C23#6693711yescharacteristic
687C23#6693711yescharacteristic
688C23#6696412yes—
689C23#6696512yes—
690C23SD16×D1112yes—
691C23#6696812yes—
692C23#6699011yescharacteristic
693C23#6699211yescharacteristic
694C23#6699311yescharacteristic
695Q8—224no—
696Q8—224no—
697Q8—442no—
698Q8—442no—
699Q8—442no—
700Q8—442no—
701Q8—442no—
702Q8—442no—
703D4—24no—
704D4—24no—
705D4—42no—
706D4—42no—
707D4—42no—
708D4—42no—
709D4—42no—
710D4—42no—
711C2×C4—44no—
712C2×C4—42no—
713C2×C4—82no—
714C2×C4—81no—
715C2×C4—81no—
716C2×C4—224no—
717C2×C4—224no—
718C2×C4—224no—
719C2×C4—224no—
720C2×C4—442no—
721C2×C4—442no—
722C2×C4—442no—
723C2×C4—442no—
724C2×C4—442no—
725C2×C4—442no—
726C2×C4—442no—
727C2×C4—442no—
728C2×C4—442no—
729C2×C4—442no—
730C2×C4—442no—
731C2×C4—444no—
732C2×C4—881no—
733C2×C4—881no—
734C2×C4—882no—
735C2×C4C22⋊C4×D1111yescharacteristic
736C2×C4C22⋊C4×D1111yescharacteristic
737C2×C4(C22⋊D11)⋊C411yescharacteristic
738C2×C4#6693511yescharacteristic
739C2×C4#6693511yescharacteristic
740C2×C4#6693611yescharacteristic
741C2×C4#6693611yescharacteristic
742C2×C4#6693711yescharacteristic
743C2×C4#6693711yescharacteristic
744C2×C4#6693811yescharacteristic
745C2×C4#6693811yescharacteristic
746C2×C4#6693911yescharacteristic
747C2×C4C2×(C2×D11)⋊C411yescharacteristic
748C2×C4C4×C22⋊D1111yescharacteristic
749C2×C4C4×C22⋊D1111yescharacteristic
750C2×C4#6698211yescharacteristic
751C2×C4#6698311yescharacteristic
752C2×C4#6698311yescharacteristic
753C2×C4#6699011yescharacteristic
754C2×C4#6699011yescharacteristic
755C2×C4#6699011yescharacteristic
756C2×C4#6699111yescharacteristic
757C2×C4#6699111yescharacteristic
758C2×C4#6699211yescharacteristic
759C2×C4#6699211yescharacteristic
760C2×C4#6699211yescharacteristic
761C2×C4#6699311yescharacteristic
762C2×C4#6700611yescharacteristic
763C8—42no—
764C8—224no—
765C22—44no—
766C22—48no—
767C22—84no—
768C22—84no—
769C22—82no—
770C22—82no—
771C22—82no—
772C22—82no—
773C22—82no—
774C22—84no—
775C22—82no—
776C22#1062237012yes—
777C22#1062237112yes—
778C22#1062237512yes—
779C22#1062238012yes—
780C22#1062238912yes—
781C22#1062239112yes—
782C22#1062239312yes—
783C22#1062239612yes—
784C22#1062256911yescharacteristic
785C22#1062257011yescharacteristic
786C22#1062257111yescharacteristic
787C22#1062257211yescharacteristic
788C22#1062257311yescharacteristic
789C22#1062257311yescharacteristic
790C22#1062276612yes—
791C22#1062276711yescharacteristic
792C22#1062276811yescharacteristic
793C22#1062277112yes—
794C22#1062277512yes—
795C22#1062278011yescharacteristic
796C22#1062278312yes—
797C22#1062278811yescharacteristic
798C22#1062283611yescharacteristic
799C4—82no—
800C4—444no—
801C4—444no—
802C4—882no—
803C4#1062256811yescharacteristic
804C4#1062256911yescharacteristic
805C4#1062257011yescharacteristic
806C4#1062257211yescharacteristic
807C4#1062257411yescharacteristic
808C4#1062257411yescharacteristic
809C4#1062282611yescharacteristic
810C4#1062283611yescharacteristic
811C2—84no—
812C2#1306685511yescharacteristic
813C2#1306894812yes—
814C2#1306896812yes—
815C2#1306947111yescharacteristic
816C2#1306949811yescharacteristic
817C2#1306962012yes—
818C2#1306969111yescharacteristic
819C2#1306969711yescharacteristic
820C2#1306970511yescharacteristic
821C2#1306971211yescharacteristic
822C2#1306993212yes—
subgroupG/H
centerC24D4×D11
commutatorC22×C4×C11C22×C4
FrattiniC23×C4C22×D11
FittingC22×C11×#102C2
socleC24×C11C2×D4
prime radicalC23×D4×C11C22
cosocleC23×C4×C11C23
hypercenterC22×#102D11
hypocenterC11#11023
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C24 ◁ C23×C4 ◁ C22×#102

Complements

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

NH ≅ G/Ntype
2. C22×#66880C2semidirect
3. C2×#10622587C2semidirect
5. C2×#10622167C2semidirect
6. C2×#10622188C2semidirect
19. C22×#4324C4semidirect
193. C22×Dic11SD16semidirect
221. C2×Dic22C22⋊C4semidirect
249. C2×C11⋊C8C22⋊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×#43242
C22×#668802
C2×#106225872
C2×#106228342
C2×#106221672
C2×#106221882
C22×C11×#1022
#1102311