Finite Group Databasebeta

← #14660486

Subgroups — #14660486

Order 2816.

1558 conjugacy classes of subgroups.

The subgroup lattice has 820 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#67000C211yesmaximal, characteristic
2C22×#66899C211yesmaximal, characteristic, complemented
3C22×#66885C211yesmaximal, characteristic
4C22×#66873C211yesmaximal, characteristic
5C2×#10622188C211yesmaximal, characteristic, complemented
6#13066845C211yesmaximal, characteristic, complemented
7C22×C11×#103C211yesmaximal, characteristic, complemented
8C23×Q8×C11C2211yescharacteristic
9C23×D44C2211yescharacteristic
10C23×C8×C11C2211yescharacteristic
11C22×C11×C4⋊C4C2211yescharacteristic
12C2×#67000—22no—
13C2×#67000—22no—
14C2×#67000—22no—
15C2×#67000—22no—
16C2×#67000—22no—
17C2×#67000C414yescomplemented
18C22×(C2×D11)⋊C4—22no—
19C22×C4⋊Dic11C2211yescharacteristic
20C22×C4×Dic11C2211yescharacteristic
21C23×C11⋊C8C2211yescharacteristic
22C2×C11×#103—22no—
23C2×C11×#103—22no—
24C2×C11×#103—22no—
25C2×#66899—22no—
26C2×#66899—22no—
27C2×#66899—22no—
28C2×C11⋊#95—22no—
29C2×#66885—22no—
30C2×#66885—22no—
31C2×#66885—22no—
32C2×#66873—22no—
33C2×#66873—22no—
34C2×#66873—22no—
35#10622188—22no—
36C24×D11—21no—
37C22×Q8×C11—21no—
38C22×Q8×C11—21no—
39C22×Q8×C11—21no—
40C22×Q8×C11—21no—
41C22×Q8×C11—21no—
42C22×Q8×C11—21no—
43C22×Q8×C11—21no—
44C22×Q8×C11—21no—
45C22×Q8×C11—21no—
46C22×Q8×C11—21no—
47C22×Q8×C11—21no—
48C22×Q8×C11C2×C412yes—
49C22×Q8×C11D412yes—
50C22×Q8×C11D412yes—
51C23×C4×C11—21no—
52C23×C4×C11—21no—
53C23×C4×C11C2311yescharacteristic
54C23×Dic11—21no—
55C23×Dic11D412yes—
56C22×D44—21no—
57C22×D44—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×D44C2×C412yes—
68C22×D44D412yes—
69C22×D44D412yes—
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—
83#67000—28no—
84#67000—28no—
85#67000—28no—
86#67000—28no—
87C2×(C2×D11)⋊C4—28no—
88C2×(C2×D11)⋊C4—28no—
89C2×(C2×D11)⋊C4—28no—
90C2×C4⋊Dic11—21no—
91C2×C4⋊Dic11—21no—
92C2×C4⋊Dic11—21no—
93C2×C4⋊Dic11—21no—
94C2×C4⋊Dic11—21no—
95C2×C4⋊Dic11D412yes—
96C2×C4×Dic11—21no—
97C2×C4×Dic11—21no—
98C2×C4×Dic11—21no—
99C2×C4×Dic11—21no—
100C2×C4×Dic11C2×C412yes—
101C2×C4×Dic11D412yes—
102C22×C11⋊C8—21no—
103C22×C11⋊C8—21no—
104C22×C11⋊C8—21no—
105C22×C11⋊C8—21no—
106C22×C11⋊C8—21no—
107C22×C11⋊C8—21no—
108C22×C11⋊C8D412yes—
109C11×#103—28no—
110#66899—28no—
111C11⋊#95—44no—
112#66885—28no—
113#66873—28no—
114#11009—111nomaximal, Sylow
115C24×C11C2×D411yescharacteristic
116C23×D11—22no—
117C23×D11—22no—
118C23×D11—22no—
119C23×D11—41no—
120C23×D11—41no—
121C23×D11—41no—
122C23×D11—41no—
123C23×D11—42no—
124C23×D11—42no—
125C23×D11—42no—
126C23×D11—42no—
127C2×Q8×C11—22no—
128C2×Q8×C11—22no—
129C2×Q8×C11—22no—
130C2×Q8×C11—22no—
131C2×Q8×C11—22no—
132C2×Q8×C11—22no—
133C2×Q8×C11—22no—
134C2×Q8×C11—22no—
135C2×Q8×C11—22no—
136C2×Q8×C11—22no—
137C2×Q8×C11—22no—
138C2×Q8×C11—22no—
139C2×Q8×C11—22no—
140C2×Q8×C11—22no—
141C2×Q8×C11—22no—
142C2×Q8×C11—41no—
143C2×Q8×C11—41no—
144C2×Q8×C11—41no—
145C2×Q8×C11—41no—
146C2×Q8×C11—41no—
147C2×Q8×C11—41no—
148C2×Q8×C11—41no—
149C2×Q8×C11—41no—
150C2×Q8×C11—41no—
151C2×Q8×C11—41no—
152C2×Q8×C11—41no—
153C2×Q8×C11—41no—
154C2×Q8×C11C22⋊C414yes—
155C22×C4×C11—22no—
156C22×C4×C11—22no—
157C22×C4×C11—22no—
158C22×C4×C11—22no—
159C22×C4×C11—41no—
160C22×C4×C11—41no—
161C22×C4×C11—41no—
162C22×C4×C11—41no—
163C22×C4×C11—41no—
164C22×C4×C11—41no—
165C22×C4×C11—42no—
166C22×C4×C11—42no—
167C22×C4×C11C22×C411yescharacteristic
168C22×C4×C11C2×D411yescharacteristic
169C22×C4×C11C2×D411yescharacteristic
170C22×C4×C11C2×D411yescharacteristic
171C22×C4×C11C2×D411yescharacteristic
172C22×C4×C11C2×D411yescharacteristic
173C22×C4×C11C2×D411yescharacteristic
174C22×C4×C11C2×D411yescharacteristic
175C22×C4×C11C2×D411yescharacteristic
176C22×C4×C11C2×D411yescharacteristic
177C22×C4×C11#4111yescharacteristic
178C22×C4×C11#4111yescharacteristic
179C22×C4×C11#4111yescharacteristic
180C22×C4×C11#4111yescharacteristic
181C22×Dic11—22no—
182C22×Dic11—22no—
183C22×Dic11—22no—
184C22×Dic11—22no—
185C22×Dic11—22no—
186C22×Dic11—22no—
187C22×Dic11—22no—
188C22×Dic11—41no—
189C22×Dic11—41no—
190C22×Dic11—42no—
191C22×Dic11—42no—
192C22×Dic11C22⋊C414yes—
193C2×D44—22no—
194C2×D44—22no—
195C2×D44—22no—
196C2×D44—22no—
197C2×D44—22no—
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—41no—
209C2×D44—41no—
210C2×D44—41no—
211C2×D44—41no—
212C2×D44—41no—
213C2×D44—41no—
214C2×D44—41no—
215C2×D44—41no—
216C2×D44—41no—
217C2×D44—41no—
218C2×D44—41no—
219C2×D44—41no—
220C2×D44C22⋊C414yes—
221C2×C8×C11—22no—
222C2×C8×C11—22no—
223C2×C8×C11—22no—
224C2×C8×C11—41no—
225C2×C8×C11—41no—
226C2×C8×C11—41no—
227C2×C8×C11—41no—
228C11×C4⋊C4—22no—
229C11×C4⋊C4—22no—
230C11×C4⋊C4—41no—
231C11×C4⋊C4—41no—
232(C2×D11)⋊C4—232no—
233C4⋊Dic11—22no—
234C4⋊Dic11—22no—
235C4⋊Dic11—41no—
236C4⋊Dic11—41no—
237C4×Dic11—22no—
238C4×Dic11—22no—
239C4×Dic11—22no—
240C4×Dic11—22no—
241C2×C11⋊C8—22no—
242C2×C11⋊C8—22no—
243C2×C11⋊C8—22no—
244C2×C11⋊C8—41no—
245C2×C11⋊C8—41no—
246C2×C11⋊C8—41no—
247C2×C11⋊C8—41no—
248C22×#124—111no—
249C22×#103—111no—
250C22×#103D1111yescharacteristic, complemented
251C22×#102—111no—
252C22×#102—111no—
253C2×#336—111no—
254C4⋊#95—111no—
255C23×C11C2×C22⋊C411yescharacteristic
256C23×C11#12011yescharacteristic
257C23×C11#12011yescharacteristic
258C23×C11#12111yescharacteristic
259C23×C11#12111yescharacteristic
260C23×C11#12411yescharacteristic
261C23×C11#12711yescharacteristic
262C23×C11#13512yes—
263C23×C11#13512yes—
264C23×C11AGL(1,ℤ/8)12yes—
265C23×C11#13712yes—
266C22×D11—24no—
267C22×D11—42no—
268C22×D11—42no—
269C22×D11—42no—
270C22×D11—42no—
271C22×D11—42no—
272C22×D11—42no—
273C22×D11—44no—
274C22×D11—44no—
275C22×D11—44no—
276C22×D11—44no—
277C22×D11—44no—
278C22×D11—44no—
279C22×D11—82no—
280C22×D11—82no—
281C22×D11—82no—
282C22×D11—82no—
283C22×D11—82no—
284C22×D11—82no—
285C22×D11—81no—
286C22×D11—81no—
287C22×D11—81no—
288C22×D11—81no—
289Q8×C11—24no—
290Q8×C11—24no—
291Q8×C11—42no—
292Q8×C11—42no—
293Q8×C11—42no—
294Q8×C11—42no—
295Q8×C11—42no—
296Q8×C11—42no—
297C2×C4×C11—24no—
298C2×C4×C11—42no—
299C2×C4×C11—42no—
300C2×C4×C11—42no—
301C2×C4×C11—42no—
302C2×C4×C11—42no—
303C2×C4×C11—42no—
304C2×C4×C11—42no—
305C2×C4×C11—44no—
306C2×C4×C11—82no—
307C2×C4×C11—81no—
308C2×C4×C11—81no—
309C2×C4×C11C2×C22⋊C411yescharacteristic
310C2×C4×C11C2×C22⋊C411yescharacteristic
311C2×C4×C11C4×D411yescharacteristic
312C2×C4×C11C4×D411yescharacteristic
313C2×C4×C11C4×D411yescharacteristic
314C2×C4×C11C4×D411yescharacteristic
315C2×C4×C11#12011yescharacteristic
316C2×C4×C11#12011yescharacteristic
317C2×C4×C11#12011yescharacteristic
318C2×C4×C11#12011yescharacteristic
319C2×C4×C11#12011yescharacteristic
320C2×C4×C11#12011yescharacteristic
321C2×C4×C11#12111yescharacteristic
322C2×C4×C11#12111yescharacteristic
323C2×C4×C11#12111yescharacteristic
324C2×C4×C11#12111yescharacteristic
325C2×C4×C11#12111yescharacteristic
326C2×C4×C11#12111yescharacteristic
327C2×C4×C11#12111yescharacteristic
328C2×C4×C11#12111yescharacteristic
329C2×C4×C11#12111yescharacteristic
330C2×C4×C11#12111yescharacteristic
331C2×C4×C11#12311yescharacteristic
332C2×C4×C11#12311yescharacteristic
333C2×C4×C11#12311yescharacteristic
334C2×C4×C11#12311yescharacteristic
335C2×C4×C11#12411yescharacteristic
336C2×C4×C11#12711yescharacteristic
337C2×Dic11—24no—
338C2×Dic11—24no—
339C2×Dic11—24no—
340C2×Dic11—42no—
341C2×Dic11—42no—
342C2×Dic11—42no—
343C2×Dic11—42no—
344C2×Dic11—42no—
345C2×Dic11—44no—
346C2×Dic11—82no—
347C2×Dic11—81no—
348C2×Dic11—81no—
349D44—24no—
350D44—24no—
351D44—42no—
352D44—42no—
353D44—42no—
354D44—42no—
355D44—42no—
356D44—42no—
357C8×C11—42no—
358C11⋊C8—42no—
359C23×Q8C2×D1111yescharacteristic
360C23×D4—111no—
361C23×C8—111no—
362C23×C8C2×D1111yescharacteristic
363C2×#124—114no—
364C2×#124—222no—
365C2×#124—222no—
366C2×#124—222no—
367C2×#124—222no—
368C2×#124—222no—
369C22×C4⋊C4—111no—
370C22×C4⋊C4C2×D1111yescharacteristic
371C22×C22⋊C4—222no—
372C22×C42—111no—
373C2×#103—22no—
374C2×#103—22no—
375C2×#103—22no—
376C2×#103—222no—
377C2×#103—222no—
378C2×#103—222no—
379C2×#102—222no—
380C2×#102—222no—
381C2×#102—222no—
382C2×#102—222no—
383C2×#102—222no—
384C2×#102—222no—
385C2×#95—222no—
386#336—222no—
387C22×C11#37911yescharacteristic
388C22×C11#39011yescharacteristic
389C22×C11#39011yescharacteristic
390C22×C11#39211yescharacteristic
391C22×C11#39211yescharacteristic
392C22×C11#39411yescharacteristic
393C22×C11#39411yescharacteristic
394C22×C11#41612yes—
395C22×C11#41712yes—
396C22×C11#44912yes—
397C22×C11#44912yes—
398C22×C11#45212yes—
399C22×C11#45212yes—
400C22×C11#46312yes—
401C22×C11#46312yes—
402C22×C11#46412yes—
403C22×C11#46412yes—
404C22×C11#48812yes—
405C22×C11#48912yes—
406C22×C11#49511yescharacteristic
407C22×C11#49511yescharacteristic
408C22×C11#49611yescharacteristic
409C22×C11#49711yescharacteristic
410C2×D11—44no—
411C2×D11—48no—
412C2×D11—82no—
413C2×D11—82no—
414C2×D11—84no—
415C2×D11—82no—
416C2×D11—82no—
417C2×D11—82no—
418C2×D11—82no—
419C2×D11—84no—
420C2×D11—84no—
421C4×C11—44no—
422C4×C11—82no—
423C4×C11#38611yescharacteristic
424C4×C11#38611yescharacteristic
425C4×C11#38611yescharacteristic
426C4×C11#38611yescharacteristic
427C4×C11#39211yescharacteristic
428C4×C11#39211yescharacteristic
429C4×C11#39411yescharacteristic
430C4×C11#39411yescharacteristic
431Dic11—44no—
432Dic11—82no—
433C25—221no—
434C22×Q8—21no—
435C22×Q8—21no—
436C22×Q8—21no—
437C22×Q8—21no—
438C22×Q8—21no—
439C22×Q8—21no—
440C22×Q8—21no—
441C22×Q8—21no—
442C22×Q8—21no—
443C22×Q8—21no—
444C22×Q8—21no—
445C22×Q8C4×D1112yes—
446C22×Q8D4412yes—
447C22×Q8C22⋊D1112yes—
448C22×D4—112no—
449C22×D4—112no—
450C22×D4—112no—
451C22×D4—221no—
452C22×D4—221no—
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—
462C23×C4—21no—
463C23×C4—21no—
464C23×C4—112no—
465C23×C4—221no—
466C23×C4C22×D1111yescharacteristic
467C22×C8—21no—
468C22×C8—21no—
469C22×C8—21no—
470C22×C8—21no—
471C22×C8—21no—
472C22×C8—21no—
473C22×C8—112no—
474C22×C8—221no—
475C22×C8—221no—
476C22×C8—221no—
477C22×C8—221no—
478C22×C8—221no—
479C22×C8—221no—
480C22×C8C22⋊D1112yes—
481#124—228no—
482#124—228no—
483#124—228no—
484#124—228no—
485C2×C4⋊C4—21no—
486C2×C4⋊C4—21no—
487C2×C4⋊C4—21no—
488C2×C4⋊C4—21no—
489C2×C4⋊C4—21no—
490C2×C4⋊C4—112no—
491C2×C4⋊C4—221no—
492C2×C4⋊C4—221no—
493C2×C4⋊C4—221no—
494C2×C4⋊C4—221no—
495C2×C4⋊C4—221no—
496C2×C4⋊C4C22⋊D1112yes—
497C2×C22⋊C4—228no—
498C2×C22⋊C4—228no—
499C2×C22⋊C4—228no—
500C2×C42—112no—
501C2×C42—112no—
502C2×C42—221no—
503C2×C42—221no—
504C2×C42—221no—
505C2×C42—221no—
506#103—28no—
507#103—228no—
508#102—228no—
509#102—228no—
510#95—444no—
511C2×C11#143811yescharacteristic
512C2×C11#178812yes—
513C2×C11#195811yescharacteristic
514C2×C11#195911yescharacteristic
515C2×C11#198312yes—
516C2×C11#201211yescharacteristic
517C2×C11#201211yescharacteristic
518C2×C11#201511yescharacteristic
519C2×C11#201511yescharacteristic
520C2×C11#204212yes—
521C2×C11#204212yes—
522D11—84no—
523C24—222no—
524C24—222no—
525C24—222no—
526C24—441no—
527C24—441no—
528C24—442no—
529C24—442no—
530C24—442no—
531C24—442no—
532C24—441no—
533C24—441no—
534C24D4×D1111yescharacteristic
535C2×Q8—22no—
536C2×Q8—22no—
537C2×Q8—22no—
538C2×Q8—22no—
539C2×Q8—22no—
540C2×Q8—22no—
541C2×Q8—22no—
542C2×Q8—22no—
543C2×Q8—22no—
544C2×Q8—22no—
545C2×Q8—22no—
546C2×Q8—22no—
547C2×Q8—22no—
548C2×Q8—22no—
549C2×Q8—22no—
550C2×Q8—41no—
551C2×Q8—41no—
552C2×Q8—41no—
553C2×Q8—41no—
554C2×Q8—41no—
555C2×Q8—41no—
556C2×Q8—41no—
557C2×Q8—41no—
558C2×Q8—41no—
559C2×Q8—41no—
560C2×Q8—41no—
561C2×Q8—41no—
562C2×Q8(C2×D11)⋊C414yes—
563C2×D4—114no—
564C2×D4—222no—
565C2×D4—222no—
566C2×D4—222no—
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—441no—
580C2×D4—441no—
581C2×D4—441no—
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—
591C22×C4—22no—
592C22×C4—22no—
593C22×C4—22no—
594C22×C4—22no—
595C22×C4—41no—
596C22×C4—41no—
597C22×C4—41no—
598C22×C4—41no—
599C22×C4—42no—
600C22×C4—42no—
601C22×C4—41no—
602C22×C4—41no—
603C22×C4—114no—
604C22×C4—222no—
605C22×C4—222no—
606C22×C4—222no—
607C22×C4—222no—
608C22×C4—222no—
609C22×C4—222no—
610C22×C4—222no—
611C22×C4—441no—
612C22×C4—442no—
613C22×C4—442no—
614C22×C4—441no—
615C22×C4C2×C4×D1111yescharacteristic
616C22×C4C2×D4411yescharacteristic
617C22×C4#433911yescharacteristic
618C22×C4#433911yescharacteristic
619C22×C4D4×D1111yescharacteristic
620C22×C4D4×D1111yescharacteristic
621C22×C4D4×D1111yescharacteristic
622C22×C4D4×D1111yescharacteristic
623C22×C4D4×D1111yescharacteristic
624C22×C4#434111yescharacteristic
625C22×C4#434111yescharacteristic
626C22×C4C2×C22⋊D1111yescharacteristic
627C22×C4C2×C22⋊D1111yescharacteristic
628C22×C4C2×C22⋊D1111yescharacteristic
629C2×C8—22no—
630C2×C8—22no—
631C2×C8—22no—
632C2×C8—41no—
633C2×C8—41no—
634C2×C8—41no—
635C2×C8—41no—
636C2×C8—222no—
637C2×C8—222no—
638C2×C8—222no—
639C2×C8—441no—
640C2×C8—441no—
641C2×C8—441no—
642C2×C8—441no—
643C4⋊C4—22no—
644C4⋊C4—22no—
645C4⋊C4—41no—
646C4⋊C4—41no—
647C4⋊C4—222no—
648C4⋊C4—222no—
649C4⋊C4—441no—
650C4⋊C4—441no—
651C22⋊C4—2232no—
652C42—222no—
653C42—222no—
654C42—222no—
655C42—222no—
656C11#1100911yescharacteristic, complemented, Sylow
657C23—224no—
658C23—444no—
659C23—444no—
660C23—442no—
661C23—442no—
662C23—442no—
663C23—442no—
664C23—442no—
665C23—442no—
666C23—444no—
667C23—444no—
668C23—444no—
669C23—444no—
670C23—882no—
671C23—881no—
672C23—881no—
673C23—882no—
674C23—881no—
675C23—881no—
676C23—882no—
677C23—882no—
678C23—882no—
679C23—882no—
680C23C22⋊C4×D1111yescharacteristic
681C23#6693511yescharacteristic
682C23#6693711yescharacteristic
683C23#6693811yescharacteristic
684C23#6696712yes—
685C23#6696912yes—
686C23#6697112yes—
687C23#6697212yes—
688C23#6699011yescharacteristic
689C23#6699211yescharacteristic
690C23#6699311yescharacteristic
691Q8—24no—
692Q8—24no—
693Q8—42no—
694Q8—42no—
695Q8—42no—
696Q8—42no—
697Q8—42no—
698Q8—42no—
699D4—224no—
700D4—224no—
701D4—442no—
702D4—442no—
703D4—442no—
704D4—442no—
705D4—442no—
706D4—442no—
707C2×C4—24no—
708C2×C4—42no—
709C2×C4—42no—
710C2×C4—42no—
711C2×C4—42no—
712C2×C4—42no—
713C2×C4—42no—
714C2×C4—44no—
715C2×C4—42no—
716C2×C4—81no—
717C2×C4—82no—
718C2×C4—81no—
719C2×C4—224no—
720C2×C4—224no—
721C2×C4—224no—
722C2×C4—442no—
723C2×C4—442no—
724C2×C4—442no—
725C2×C4—442no—
726C2×C4—442no—
727C2×C4—444no—
728C2×C4—881no—
729C2×C4—881no—
730C2×C4—882no—
731C2×C4C22⋊C4×D1111yescharacteristic
732C2×C4(C22⋊D11)⋊C411yescharacteristic
733C2×C4(C22⋊D11)⋊C411yescharacteristic
734C2×C4#6693511yescharacteristic
735C2×C4#6693511yescharacteristic
736C2×C4#6693611yescharacteristic
737C2×C4#6693611yescharacteristic
738C2×C4#6693711yescharacteristic
739C2×C4#6693711yescharacteristic
740C2×C4#6693711yescharacteristic
741C2×C4#6693811yescharacteristic
742C2×C4#6693911yescharacteristic
743C2×C4C2×(C2×D11)⋊C411yescharacteristic
744C2×C4C4×C22⋊D1111yescharacteristic
745C2×C4C4×C22⋊D1111yescharacteristic
746C2×C4#6698211yescharacteristic
747C2×C4#6698311yescharacteristic
748C2×C4#6698311yescharacteristic
749C2×C4#6699011yescharacteristic
750C2×C4#6699011yescharacteristic
751C2×C4#6699011yescharacteristic
752C2×C4#6699111yescharacteristic
753C2×C4#6699111yescharacteristic
754C2×C4#6699211yescharacteristic
755C2×C4#6699211yescharacteristic
756C2×C4#6699211yescharacteristic
757C2×C4#6699311yescharacteristic
758C2×C4#6700611yescharacteristic
759C8—42no—
760C8—442no—
761C22—448no—
762C22—444no—
763C22—884no—
764C22—884no—
765C22—882no—
766C22—882no—
767C22—882no—
768C22—882no—
769C22—882no—
770C22—882no—
771C22—884no—
772C22#1062240812yes—
773C22#1062241112yes—
774C22#1062241312yes—
775C22#1062241612yes—
776C22#1062241712yes—
777C22#1062242312yes—
778C22#1062242412yes—
779C22#1062243212yes—
780C22#1062256811yescharacteristic
781C22#1062257011yescharacteristic
782C22#1062257011yescharacteristic
783C22#1062257211yescharacteristic
784C22#1062257311yescharacteristic
785C22#1062257411yescharacteristic
786C22#1062277812yes—
787C22#1062278111yescharacteristic
788C22#1062278512yes—
789C22#1062278911yescharacteristic
790C22#1062279812yes—
791C22#1062280012yes—
792C22#1062280311yescharacteristic
793C22#1062280411yescharacteristic
794C22#1062283611yescharacteristic
795C4—44no—
796C4—82no—
797C4—444no—
798C4—882no—
799C4#1062256911yescharacteristic
800C4#1062256911yescharacteristic
801C4#1062257111yescharacteristic
802C4#1062257211yescharacteristic
803C4#1062257311yescharacteristic
804C4#1062257411yescharacteristic
805C4#1062282611yescharacteristic
806C4#1062283611yescharacteristic
807C2—884no—
808C2#1306685511yescharacteristic
809C2#1306855512yes—
810C2#1306942411yescharacteristic
811C2#1306942911yescharacteristic
812C2#1306954512yes—
813C2#1306969011yescharacteristic
814C2#1306969411yescharacteristic
815C2#1306970711yescharacteristic
816C2#1306971111yescharacteristic
817C2#1306985312yes—
818C2#1306985412yes—
subgroupG/H
centerC24D4×D11
commutatorC22×C4×C11C22×C4
FrattiniC23×C4C22×D11
FittingC22×C11×#103C2
socleC24×C11C2×D4
prime radicalC23×D44C22
cosocleC23×C4×C11C23
hypercenterC22×#103D11
hypocenterC11#11009
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C24 ◁ C23×C4 ◁ C22×#103

Complements

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

NH ≅ G/Ntype
2. C22×#66899C2semidirect
5. C2×#10622188C2semidirect
6. #13066845C2semidirect
7. C22×C11×#103C2semidirect
17. C2×#67000C4semidirect
250. C22×#103D11semidirect
656. C11#11009semidirect

Maximal subgroups

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

subgroupindex
C22×#670002
C22×#668992
C22×#668852
C22×#668732
C2×#106221882
#130668452
C22×C11×#1032
#1100911