Finite Group Databasebeta

← #14676899

Subgroups — #14676899

Order 2816.

2474 conjugacy classes of subgroups.

The subgroup lattice has 826 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#66939C211yesmaximal, characteristic
2C2×#10622826C211yesmaximal, characteristic
3C2×#10622571C211yesmaximal, characteristic
4C2×#10622556C211yesmaximal, characteristic, complemented
5C2×C22⋊C4×Dic11C211yesmaximal, characteristic, complemented
6C22×C11⋊#95C211yesmaximal, characteristic, complemented
7#13066885C212yesmaximal, complemented
8#13066858C212yesmaximal, complemented
9#13066852C212yesmaximal, complemented
10#13066845C212yesmaximal, complemented
11C2×C11×#385C211yesmaximal, characteristic, complemented
12C24×C4×C11C2211yescharacteristic
13C23×C22⋊D11C2211yescharacteristic
14C24×Dic11C2211yescharacteristic
15C24×Dic11C2211yescharacteristic
16C22×C11×C4⋊C4C2212yes—
17C22×C11×C22⋊C4C2211yescharacteristic
18C22×C11×C22⋊C4C2211yescharacteristic
19C22×C22⋊Dic11C2211yescharacteristic
20C22×(C2×D11)⋊C4C2211yescharacteristic
21C22×(C2×D11)⋊C4C2212yes—
22C22×(C2×D11)⋊C4C2212yes—
23C22×(C2×D11)⋊C4C2211yescharacteristic
24C22×C4⋊Dic11C2212yes—
25C22×C4×Dic11C2212yes—
26C2×#66939—24no—
27C2×#66939—24no—
28C2×#66939C418yescomplemented
29C11×#385—24no—
30C2×C11×#95C2212yes—
31#10622826—24no—
32C2×C11⋊#95—24no—
33C2×C11⋊#95C2212yes—
34C2×C11⋊#95C2212yes—
35C2×C11⋊#95C2211yescharacteristic
36C2×C11⋊#95C2212yes—
37C2×C11⋊#95C2212yes—
38C2×C11⋊#95C2212yes—
39C2×C11⋊#95C2212yes—
40C2×C11⋊#95C2211yescharacteristic
41#10622571—24no—
42#10622556—24no—
43C22⋊C4×Dic11—24no—
44C25×C11C2311yescharacteristic
45C24×D11C2311yescharacteristic
46C23×C4×C11—22no—
47C23×C4×C11—24no—
48C23×C4×C11—22no—
49C23×C4×C11—22no—
50C23×C4×C11—42no—
51C23×C4×C11C2311yescharacteristic
52C23×C4×C11C2311yescharacteristic
53C23×C4×C11C2312yes—
54C23×C4×C11C2312yes—
55C22×C22⋊D11—22no—
56C22×C22⋊D11—22no—
57C22×C22⋊D11—22no—
58C22×C22⋊D11—22no—
59C22×C22⋊D11—22no—
60C22×C22⋊D11—22no—
61C22×C22⋊D11C2×C414yes—
62C23×Dic11—22no—
63C23×Dic11—22no—
64C23×Dic11—22no—
65C23×Dic11—22no—
66C23×Dic11—22no—
67C23×Dic11—22no—
68C23×Dic11—22no—
69C23×Dic11—22no—
70C23×Dic11—24no—
71C23×Dic11—42no—
72C23×Dic11C2×C414yes—
73C23×Dic11D414yes—
74C23×Dic11C2311yescharacteristic
75C23×Dic11C2312yes—
76C23×Dic11C2312yes—
77C23×Dic11C2311yescharacteristic
78C23×Dic11C2311yescharacteristic
79C2×C11×C4⋊C4—24no—
80C2×C11×C4⋊C4—24no—
81C2×C11×C4⋊C4—42no—
82C2×C11×C22⋊C4—22no—
83C2×C11×C22⋊C4—22no—
84C2×C11×C22⋊C4—22no—
85C2×C11×C22⋊C4C2×C414yes—
86C2×C11×C22⋊C4D414yes—
87C2×C11×C22⋊C4D414yes—
88C2×C22⋊Dic11—22no—
89C2×C22⋊Dic11—22no—
90C2×C22⋊Dic11D414yes—
91C2×(C2×D11)⋊C4—24no—
92C2×(C2×D11)⋊C4—24no—
93C2×(C2×D11)⋊C4—24no—
94C2×(C2×D11)⋊C4—24no—
95C2×(C2×D11)⋊C4—22no—
96C2×(C2×D11)⋊C4—22no—
97C2×(C2×D11)⋊C4—24no—
98C2×(C2×D11)⋊C4—42no—
99C2×(C2×D11)⋊C4—42no—
100C2×(C2×D11)⋊C4C2×C418yescomplemented
101C2×C4⋊Dic11—24no—
102C2×C4⋊Dic11—24no—
103C2×C4⋊Dic11C2×C418yescomplemented
104C2×C4×Dic11—24no—
105C2×C4×Dic11—24no—
106C2×C4×Dic11—42no—
107#66939—232no—
108C11×#95—24no—
109C11⋊#95—24no—
110C11⋊#95—24no—
111C11⋊#95—24no—
112C11⋊#95—24no—
113C11⋊#95—24no—
114C11⋊#95—24no—
115C11⋊#95—22no—
116C11⋊#95—22no—
117#13996—111nomaximal, Sylow
118C24×C11—22no—
119C24×C11—22no—
120C24×C11—22no—
121C24×C11—22no—
122C24×C11C22×C412yes—
123C24×C11C2×D412yes—
124C24×C11C2×D412yes—
125C24×C11C2×D412yes—
126C24×C11C2×D412yes—
127C24×C11#4112yes—
128C24×C11#4112yes—
129C24×C11C2411yescharacteristic
130C23×D11—21no—
131C23×D11—21no—
132C23×D11—21no—
133C23×D11—21no—
134C23×D11—22no—
135C23×D11—22no—
136C23×D11—21no—
137C23×D11—21no—
138C23×D11—22no—
139C23×D11—22no—
140C23×D11C22×C412yes—
141C22×C4×C11—22no—
142C22×C4×C11—22no—
143C22×C4×C11—22no—
144C22×C4×C11—22no—
145C22×C4×C11—28no—
146C22×C4×C11—22no—
147C22×C4×C11—22no—
148C22×C4×C11—22no—
149C22×C4×C11—22no—
150C22×C4×C11—22no—
151C22×C4×C11—22no—
152C22×C4×C11—21no—
153C22×C4×C11—21no—
154C22×C4×C11—21no—
155C22×C4×C11—21no—
156C22×C4×C11—21no—
157C22×C4×C11—21no—
158C22×C4×C11—22no—
159C22×C4×C11—22no—
160C22×C4×C11—22no—
161C22×C4×C11—22no—
162C22×C4×C11—48no—
163C22×C4×C11—48no—
164C22×C4×C11—44no—
165C22×C4×C11—44no—
166C22×C4×C11C22×C414yes—
167C22×C4×C11C2×D414yes—
168C22×C4×C11C2×D414yes—
169C22×C4×C11#4114yes—
170C2×C22⋊D11—28no—
171C2×C22⋊D11—28no—
172C2×C22⋊D11—28no—
173C2×C22⋊D11—44no—
174C2×C22⋊D11—44no—
175C2×C22⋊D11—44no—
176C2×C22⋊D11—44no—
177C22×Dic11—28no—
178C22×Dic11—28no—
179C22×Dic11—28no—
180C22×Dic11—28no—
181C22×Dic11—28no—
182C22×Dic11—21no—
183C22×Dic11—21no—
184C22×Dic11—22no—
185C22×Dic11—22no—
186C22×Dic11—21no—
187C22×Dic11—21no—
188C22×Dic11—22no—
189C22×Dic11—21no—
190C22×Dic11—21no—
191C22×Dic11—22no—
192C22×Dic11—22no—
193C22×Dic11—21no—
194C22×Dic11—22no—
195C22×Dic11—22no—
196C22×Dic11—22no—
197C22×Dic11—22no—
198C22×Dic11—22no—
199C22×Dic11—21no—
200C22×Dic11—22no—
201C22×Dic11—21no—
202C22×Dic11—21no—
203C22×Dic11—22no—
204C22×Dic11—22no—
205C22×Dic11—22no—
206C22×Dic11—22no—
207C22×Dic11—44no—
208C22×Dic11—48no—
209C22×Dic11—48no—
210C22×Dic11—44no—
211C22×Dic11—44no—
212C22×Dic11—44no—
213C22×Dic11—44no—
214C22×Dic11C22×C412yes—
215C22×Dic11C22×C414yes—
216C22×Dic11C2×D414yes—
217C22×Dic11C2×D412yes—
218C22×Dic11C2×D412yes—
219C22×Dic11#4114yes—
220C11×C4⋊C4—48no—
221C11×C22⋊C4—44no—
222C11×C22⋊C4C22⋊C4116yescomplemented
223C22⋊Dic11—28no—
224(C2×D11)⋊C4—216no—
225(C2×D11)⋊C4—48no—
226(C2×D11)⋊C4—44no—
227(C2×D11)⋊C4—44no—
228C4⋊Dic11—216no—
229C4×Dic11—48no—
230C22×#123—111no—
231C2×#386—111no—
232C2×#386—111no—
233C2×#385D1111yescharacteristic, complemented
234C2×#381—111no—
235C2×C4×C22⋊C4—111no—
236C22×#95—111no—
237#1445—112no—
238#1439—112no—
239#1437—112no—
240C4⋊#95—112no—
241C23×C11—24no—
242C23×C11—24no—
243C23×C11—22no—
244C23×C11—22no—
245C23×C11—24no—
246C23×C11—22no—
247C23×C11—22no—
248C23×C11—24no—
249C23×C11—24no—
250C23×C11—24no—
251C23×C11—24no—
252C23×C11—24no—
253C23×C11—24no—
254C23×C11—24no—
255C23×C11—24no—
256C23×C11—24no—
257C23×C11C2×C22⋊C414yes—
258C23×C11C4×D414yes—
259C23×C11C4×D414yes—
260C23×C11#12114yes—
261C23×C11#12114yes—
262C23×C11#12414yes—
263C23×C11#12714yes—
264C23×C11C23×C411yescharacteristic
265C23×C11C22×D411yescharacteristic
266C23×C11C22×D411yescharacteristic
267C23×C11C22×D411yescharacteristic
268C23×C11C22×D411yescharacteristic
269C23×C11C2×#4112yes—
270C23×C11C2×#4111yescharacteristic
271C23×C11C2×#4111yescharacteristic
272C23×C11C2×#4112yes—
273C23×C11H(5,𝔽2)12yes—
274C23×C112−1+412yes—
275C22×D11—22no—
276C22×D11—22no—
277C22×D11—22no—
278C22×D11—24no—
279C22×D11—24no—
280C22×D11—41no—
281C22×D11—41no—
282C22×D11—41no—
283C22×D11—41no—
284C22×D11—41no—
285C22×D11—42no—
286C22×D11—41no—
287C22×D11—41no—
288C22×D11—41no—
289C22×D11—42no—
290C22×D11—42no—
291C22×D11—42no—
292C22×D11—42no—
293C22×D11—42no—
294C22×D11—42no—
295C22×D11—42no—
296C22×D11—42no—
297C22×D11—42no—
298C2×C4×C11—24no—
299C2×C4×C11—24no—
300C2×C4×C11—24no—
301C2×C4×C11—24no—
302C2×C4×C11—24no—
303C2×C4×C11—24no—
304C2×C4×C11—24no—
305C2×C4×C11—24no—
306C2×C4×C11—24no—
307C2×C4×C11—416no—
308C2×C4×C11—42no—
309C2×C4×C11—42no—
310C2×C4×C11—42no—
311C2×C4×C11—42no—
312C2×C4×C11—41no—
313C2×C4×C11—41no—
314C2×C4×C11—41no—
315C2×C4×C11—41no—
316C2×C4×C11—41no—
317C2×C4×C11—41no—
318C2×C4×C11—42no—
319C2×C4×C11—42no—
320C2×C4×C11—42no—
321C2×C4×C11—42no—
322C2×C4×C11C2×C22⋊C418yes—
323C22⋊D11—416no—
324C2×Dic11—22no—
325C2×Dic11—22no—
326C2×Dic11—24no—
327C2×Dic11—24no—
328C2×Dic11—22no—
329C2×Dic11—24no—
330C2×Dic11—24no—
331C2×Dic11—24no—
332C2×Dic11—22no—
333C2×Dic11—22no—
334C2×Dic11—24no—
335C2×Dic11—22no—
336C2×Dic11—22no—
337C2×Dic11—22no—
338C2×Dic11—24no—
339C2×Dic11—24no—
340C2×Dic11—416no—
341C2×Dic11—42no—
342C2×Dic11—42no—
343C2×Dic11—41no—
344C2×Dic11—41no—
345C2×Dic11—42no—
346C2×Dic11—41no—
347C2×Dic11—42no—
348C2×Dic11—42no—
349C2×Dic11—41no—
350C2×Dic11—42no—
351C2×Dic11—42no—
352C2×Dic11—42no—
353C2×Dic11—42no—
354C2×Dic11—42no—
355C2×Dic11—416no—
356C2×Dic11#12314yescomplemented
357C23×D4—111no—
358C24×C4—111no—
359C24×C4—111no—
360C24×C4C2×D1111yescharacteristic
361C2×#123—118no—
362C2×#123—224no—
363C2×#123—224no—
364C22×C4⋊C4—112no—
365C22×C4⋊C4C2×D1112yes—
366C22×C22⋊C4—111no—
367C22×C22⋊C4—112no—
368C22×C22⋊C4—111no—
369C22×C22⋊C4—112no—
370C22×C22⋊C4—111no—
371C22×C22⋊C4C2×D1111yescharacteristic
372C22×C22⋊C4C2×D1111yescharacteristic
373C22×C42—112no—
374#386—224no—
375#386—224no—
376#385—24no—
377#381—224no—
378C4×C22⋊C4—224no—
379C2×#95—111no—
380C2×#95—112no—
381C2×#95—112no—
382C2×#95—112no—
383C2×#95—112no—
384C2×#95—112no—
385C2×#95—112no—
386C2×#95—111no—
387C2×#95—224no—
388C2×#95C2×D1112yes—
389C22×C11—24no—
390C22×C11—28no—
391C22×C11—28no—
392C22×C11—24no—
393C22×C11—24no—
394C22×C11—28no—
395C22×C11—28no—
396C22×C11—24no—
397C22×C11—24no—
398C22×C11—24no—
399C22×C11#39018yes—
400C22×C11C22×C22⋊C411yescharacteristic
401C22×C11C2×C4×D411yescharacteristic
402C22×C11C2×C4×D411yescharacteristic
403C22×C11C4×#4112yes—
404C22×C11#52012yes—
405C22×C11C2×#12111yescharacteristic
406C22×C11C2×#12111yescharacteristic
407C22×C11C2×#12311yescharacteristic
408C22×C11#52511yescharacteristic
409C22×C11C2×#12411yescharacteristic
410C22×C11#52912yes—
411C22×C11C2×#12711yescharacteristic
412C22×C11#53411yescharacteristic
413C22×C11#53611yescharacteristic
414C22×C11#53912yes—
415C22×C11#54612yes—
416C22×C11#54612yes—
417C22×C11#54612yes—
418C22×C11#54712yes—
419C22×C11#54712yes—
420C22×C11#54712yes—
421C22×C11#55112yes—
422C22×C11#55212yes—
423C2×D11—42no—
424C2×D11—44no—
425C2×D11—44no—
426C2×D11—42no—
427C2×D11—42no—
428C2×D11—81no—
429C2×D11—81no—
430C2×D11—82no—
431C2×D11—82no—
432C2×D11—81no—
433C2×D11—81no—
434C4×C11—28no—
435C4×C11—44no—
436C4×C11—81no—
437C4×C11—81no—
438Dic11—24no—
439Dic11—42no—
440Dic11—44no—
441Dic11—44no—
442Dic11—42no—
443C25—111no—
444C25C22×D1111yescharacteristic
445C22×D4—114no—
446C22×D4—222no—
447C22×D4—222no—
448C22×D4—222no—
449C22×D4—222no—
450C22×D4—222no—
451C22×D4—222no—
452C23×C4—22no—
453C23×C4—24no—
454C23×C4—22no—
455C23×C4—22no—
456C23×C4—42no—
457C23×C4—111no—
458C23×C4—114no—
459C23×C4—112no—
460C23×C4—112no—
461C23×C4—111no—
462C23×C4—111no—
463C23×C4—114no—
464C23×C4—224no—
465C23×C4—222no—
466C23×C4—222no—
467C23×C4—222no—
468C23×C4—222no—
469C23×C4—222no—
470C23×C4—222no—
471C23×C4—222no—
472C23×C4—222no—
473C23×C4—442no—
474C23×C4C22×D1111yescharacteristic
475C23×C4C22×D1111yescharacteristic
476C23×C4C22×D1112yes—
477C23×C4C22×D1112yes—
478#123—2232no—
479C2×C4⋊C4—24no—
480C2×C4⋊C4—24no—
481C2×C4⋊C4—42no—
482C2×C4⋊C4—118no—
483C2×C4⋊C4—224no—
484C2×C4⋊C4—224no—
485C2×C22⋊C4—22no—
486C2×C22⋊C4—22no—
487C2×C22⋊C4—22no—
488C2×C22⋊C4—114no—
489C2×C22⋊C4—118no—
490C2×C22⋊C4—222no—
491C2×C22⋊C4—222no—
492C2×C22⋊C4—224no—
493C2×C22⋊C4—224no—
494C2×C22⋊C4—224no—
495C2×C22⋊C4—222no—
496C2×C22⋊C4—222no—
497C2×C22⋊C4—224no—
498C2×C22⋊C4—224no—
499C2×C22⋊C4—442no—
500C2×C22⋊C4—442no—
501C2×C22⋊C4C4×D1114yes—
502C2×C22⋊C4D4414yes—
503C2×C22⋊C4C22⋊D1114yes—
504C2×C42—224no—
505C2×C42—224no—
506C2×C42—442no—
507#95—24no—
508#95—224no—
509#95—224no—
510#95—224no—
511#95—224no—
512#95—224no—
513#95—222no—
514#95—222no—
515#95—224no—
516C2×C11—28no—
517C2×C11C2×#39011yescharacteristic
518C2×C11C4×#12311yescharacteristic
519C2×C11#232211yescharacteristic
520C2×C11#233912yes—
521C2×C11#235912yes—
522C2×C11#241211yescharacteristic
523C2×C11#241311yescharacteristic
524C2×C11#242512yes—
525C2×C11#248812yes—
526C2×C11#250111yescharacteristic
527C2×C11#253911yescharacteristic
528D11—82no—
529C24—22no—
530C24—22no—
531C24—22no—
532C24—22no—
533C24—112no—
534C24—221no—
535C24—221no—
536C24—221no—
537C24—222no—
538C24—222no—
539C24—221no—
540C24—221no—
541C24—222no—
542C24—222no—
543C24—221no—
544C24C2×C4×D1112yes—
545C24C2×D4412yes—
546C24D4×D1112yes—
547C24D4×D1112yes—
548C24#434312yes—
549C24#434312yes—
550C24C2×C22⋊D1112yes—
551C24C23×D1111yescharacteristic
552C2×D4—228no—
553C2×D4—228no—
554C2×D4—228no—
555C2×D4—444no—
556C2×D4—444no—
557C2×D4—444no—
558C2×D4—444no—
559C22×C4—22no—
560C22×C4—22no—
561C22×C4—22no—
562C22×C4—22no—
563C22×C4—28no—
564C22×C4—22no—
565C22×C4—22no—
566C22×C4—22no—
567C22×C4—22no—
568C22×C4—22no—
569C22×C4—22no—
570C22×C4—21no—
571C22×C4—21no—
572C22×C4—21no—
573C22×C4—21no—
574C22×C4—22no—
575C22×C4—22no—
576C22×C4—22no—
577C22×C4—22no—
578C22×C4—21no—
579C22×C4—21no—
580C22×C4—48no—
581C22×C4—48no—
582C22×C4—44no—
583C22×C4—44no—
584C22×C4—112no—
585C22×C4—114no—
586C22×C4—114no—
587C22×C4—112no—
588C22×C4—114no—
589C22×C4—112no—
590C22×C4—228no—
591C22×C4—221no—
592C22×C4—222no—
593C22×C4—221no—
594C22×C4—228no—
595C22×C4—228no—
596C22×C4—228no—
597C22×C4—228no—
598C22×C4—221no—
599C22×C4—222no—
600C22×C4—222no—
601C22×C4—221no—
602C22×C4—222no—
603C22×C4—222no—
604C22×C4—221no—
605C22×C4—221no—
606C22×C4—222no—
607C22×C4—222no—
608C22×C4—222no—
609C22×C4—222no—
610C22×C4—222no—
611C22×C4—222no—
612C22×C4—221no—
613C22×C4—221no—
614C22×C4—221no—
615C22×C4—222no—
616C22×C4—222no—
617C22×C4—222no—
618C22×C4—222no—
619C22×C4—221no—
620C22×C4—444no—
621C22×C4—448no—
622C22×C4—448no—
623C22×C4—444no—
624C22×C4—444no—
625C22×C4—444no—
626C22×C4—444no—
627C22×C4C2×C4×D1114yes—
628C22×C4C2×D4414yes—
629C22×C4#434114yes—
630C22×C4C2×C22⋊D1114yes—
631C4⋊C4—48no—
632C4⋊C4—2216no—
633C22⋊C4—44no—
634C22⋊C4—228no—
635C22⋊C4—2216no—
636C22⋊C4—448no—
637C22⋊C4—444no—
638C22⋊C4—444no—
639C22⋊C4(C2×D11)⋊C4116yescomplemented
640C42—448no—
641C11#1399611yescharacteristic, complemented, Sylow
642C23—24no—
643C23—24no—
644C23—24no—
645C23—24no—
646C23—24no—
647C23—24no—
648C23—22no—
649C23—22no—
650C23—24no—
651C23—24no—
652C23—24no—
653C23—24no—
654C23—24no—
655C23—22no—
656C23—22no—
657C23—24no—
658C23—222no—
659C23—222no—
660C23—222no—
661C23—224no—
662C23—224no—
663C23—441no—
664C23—441no—
665C23—441no—
666C23—442no—
667C23—442no—
668C23—442no—
669C23—441no—
670C23—442no—
671C23—441no—
672C23—441no—
673C23—442no—
674C23—442no—
675C23—442no—
676C23—442no—
677C23—442no—
678C23—441no—
679C23—441no—
680C23—442no—
681C23#6694614yes—
682C23#6694614yes—
683C23#6694814yes—
684C23#6694814yes—
685C23C2×(C2×D11)⋊C414yes—
686C23#6699314yes—
687C23#6700014yes—
688C23C22×C4×D1111yescharacteristic
689C23C22×D4411yescharacteristic
690C23C2×D4×D1111yescharacteristic
691C23C2×D4×D1111yescharacteristic
692C23C2×#434112yes—
693C23#6703712yes—
694C23C2×#434311yescharacteristic
695C23C2×#434311yescharacteristic
696C23#41×D1112yes—
697C23#6704312yes—
698C23C22×C22⋊D1111yescharacteristic
699D4—4416no—
700C2×C4—24no—
701C2×C4—24no—
702C2×C4—24no—
703C2×C4—24no—
704C2×C4—24no—
705C2×C4—24no—
706C2×C4—24no—
707C2×C4—24no—
708C2×C4—24no—
709C2×C4—416no—
710C2×C4—42no—
711C2×C4—42no—
712C2×C4—42no—
713C2×C4—42no—
714C2×C4—41no—
715C2×C4—41no—
716C2×C4—42no—
717C2×C4—42no—
718C2×C4—41no—
719C2×C4—41no—
720C2×C4—42no—
721C2×C4—41no—
722C2×C4—41no—
723C2×C4—42no—
724C2×C4—114no—
725C2×C4—222no—
726C2×C4—224no—
727C2×C4—222no—
728C2×C4—224no—
729C2×C4—224no—
730C2×C4—224no—
731C2×C4—222no—
732C2×C4—222no—
733C2×C4—224no—
734C2×C4—222no—
735C2×C4—224no—
736C2×C4—222no—
737C2×C4—222no—
738C2×C4—224no—
739C2×C4—222no—
740C2×C4—224no—
741C2×C4—4416no—
742C2×C4—442no—
743C2×C4—442no—
744C2×C4—441no—
745C2×C4—441no—
746C2×C4—442no—
747C2×C4—441no—
748C2×C4—442no—
749C2×C4—442no—
750C2×C4—442no—
751C2×C4—442no—
752C2×C4—441no—
753C2×C4—4416no—
754C2×C4—442no—
755C2×C4—442no—
756C2×C4—442no—
757C2×C4C2×(C2×D11)⋊C418yes—
758C22—24no—
759C22—28no—
760C22—28no—
761C22—28no—
762C22—24no—
763C22—24no—
764C22—24no—
765C22—24no—
766C22—24no—
767C22—28no—
768C22—442no—
769C22—444no—
770C22—442no—
771C22—442no—
772C22—444no—
773C22—882no—
774C22—882no—
775C22—881no—
776C22—881no—
777C22—881no—
778C22—881no—
779C22#1062260118yes—
780C22C2×#6694611yescharacteristic
781C22C2×#6694611yescharacteristic
782C22C2×#6694811yescharacteristic
783C22C2×#6694811yescharacteristic
784C22C4×#434112yes—
785C22#1062307712yes—
786C22#1062308512yes—
787C22#1062308612yes—
788C22#1062311711yescharacteristic
789C22#1062312011yescharacteristic
790C22#1062312212yes—
791C22#1062315512yes—
792C22#1062316812yes—
793C22#1062317312yes—
794C22#1062317612yes—
795C22#1062317911yescharacteristic
796C22D11×#12311yescharacteristic
797C22#1062318612yes—
798C22C22×(C2×D11)⋊C411yescharacteristic
799C22C2×#6699311yescharacteristic
800C22#1062333712yes—
801C22C2×#6700011yescharacteristic
802C22#1062335512yes—
803C4—28no—
804C4—44no—
805C4—81no—
806C4—81no—
807C4—224no—
808C4—444no—
809C4—442no—
810C4—444no—
811C4—442no—
812C2—28no—
813C2—882no—
814C2C2×#1062260111yescharacteristic
815C2#1307113511yescharacteristic
816C2#1307128411yescharacteristic
817C2#1307144112yes—
818C2#1307160612yes—
819C2#1307201011yescharacteristic
820C2#1307202111yescharacteristic
821C2#1307216512yes—
822C2#1307294812yes—
823C2#1307308511yescharacteristic
824C2#1307354411yescharacteristic
subgroupG/H
center, FrattiniC24C23×D11
commutatorC23×C11C23×C4
FittingC2×C11×#385C2
socle, cosocleC24×C11C24
prime radicalC23×C22⋊D11C22
hypercenterC2×#385D11
hypocenterC11#13996
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ C2×#385

Complements

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

NH ≅ G/Ntype
4. C2×#10622556C2semidirect
5. C2×C22⋊C4×Dic11C2semidirect
6. C22×C11⋊#95C2semidirect
7. #13066885C2semidirect
8. #13066858C2semidirect
9. #13066852C2semidirect
10. #13066845C2semidirect
11. C2×C11×#385C2semidirect
28. C2×#66939C4semidirect
100. C2×(C2×D11)⋊C4C2×C4semidirect
103. C2×C4⋊Dic11C2×C4semidirect
222. C11×C22⋊C4C22⋊C4semidirect
233. C2×#385D11semidirect
356. C2×Dic11#123semidirect
639. C22⋊C4(C2×D11)⋊C4semidirect
641. C11#13996semidirect

Maximal subgroups

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

subgroupindex
C22×#669392
C2×#106228262
C2×#106225712
C2×#106225562
C2×C22⋊C4×Dic112
C22×C11⋊#952
#130668852
#130668582
#130668522
#130668452
C2×C11×#3852
#1399611