Finite Group Databasebeta

← #14680290

Subgroups — #14680290

Order 2816.

2718 conjugacy classes of subgroups.

The subgroup lattice has 896 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#66937C211yesmaximal, characteristic
2C2×#10622278C212yesmaximal, complemented
3C2×#10622569C212yesmaximal, complemented
4C2×#10622600C211yesmaximal, characteristic, complemented
5C2×D11×#95C211yesmaximal, characteristic, complemented
6#13066882C212yesmaximal, complemented
7#13066862C211yesmaximal, characteristic, complemented
8#13066861C211yesmaximal, characteristic, complemented
9#13066858C211yesmaximal, characteristic, complemented
10#13066855C212yesmaximal, complemented
11C11×#1439C211yesmaximal, characteristic, complemented
12C23×C22⋊D11C2211yescharacteristic
13C23×C22⋊D11C2211yescharacteristic
14C23×D44C2211yescharacteristic
15C23×C4×D11C2212yes—
16C23×C4×D11C2211yescharacteristic
17C22×C11×C4⋊C4C2211yescharacteristic
18C22×C11×C22⋊C4C2211yescharacteristic
19C22×C11×C22⋊C4C2212yes—
20C22×C22⋊Dic11C2212yes—
21C22×(C2×D11)⋊C4C2212yes—
22C22×(C2×D11)⋊C4C2211yescharacteristic
23C22×(C2×D11)⋊C4C2212yes—
24C22×(C2×D11)⋊C4C2212yes—
25C22×C4⋊Dic11C2211yescharacteristic
26C22×Dic11⋊C4C2211yescharacteristic
27C2×#66937—24no—
28C2×#66937—24no—
29C2×#66937C418yescomplemented
30C2×C11×#95C2211yescharacteristic
31C2×C11×#95C2212yes—
32C2×C11⋊#95C2212yes—
33C2×C11⋊#95C2211yescharacteristic
34C2×C11⋊#95C2212yes—
35C2×C11⋊#95C2212yes—
36C2×C11⋊#95C2212yes—
37C2×C11⋊#95C2212yes—
38#10622600—24no—
39#10622569—28no—
40#10622278—28no—
41D11×#95—24no—
42C25×C11C2311yescharacteristic
43C24×D11C2311yescharacteristic
44C24×D11C2311yescharacteristic
45C23×C4×C11C2312yes—
46C23×C4×C11C2311yescharacteristic
47C23×C4×C11C2312yes—
48C23×C4×C11C2311yescharacteristic
49C22×C22⋊D11—22no—
50C22×C22⋊D11—22no—
51C22×C22⋊D11—24no—
52C22×C22⋊D11—24no—
53C22×C22⋊D11—22no—
54C22×C22⋊D11—22no—
55C22×C22⋊D11—42no—
56C22×C22⋊D11—42no—
57C22×C22⋊D11C2×C414yes—
58C22×C22⋊D11C2×C414yescomplemented
59C23×Dic11C2312yes—
60C23×Dic11C2311yescharacteristic
61C23×Dic11C2312yes—
62C23×Dic11C2311yescharacteristic
63C22×D44—22no—
64C22×D44—22no—
65C22×D44—24no—
66C22×D44—24no—
67C22×D44C2×C414yes—
68C22×C4×D11—24no—
69C22×C4×D11—24no—
70C22×C4×D11—42no—
71C22×C4×D11—42no—
72C22×C4×D11—42no—
73C22×C4×D11—42no—
74C22×C4×D11—42no—
75C22×C4×D11—42no—
76C22×C4×D11C2×C414yes—
77C22×C4×D11D414yes—
78C22×C4×D11D414yes—
79C22×C4×D11D418yescomplemented
80C2×C11×C4⋊C4—22no—
81C2×C11×C4⋊C4—42no—
82C2×C11×C22⋊C4—22no—
83C2×C11×C22⋊C4—22no—
84C2×C11×C22⋊C4—24no—
85C2×C11×C22⋊C4—42no—
86C2×C11×C22⋊C4—42no—
87C2×C11×C22⋊C4C2×C414yescomplemented
88C2×C22⋊Dic11—24no—
89C2×C22⋊Dic11—42no—
90C2×C22⋊Dic11—42no—
91C2×(C2×D11)⋊C4—22no—
92C2×(C2×D11)⋊C4—22no—
93C2×(C2×D11)⋊C4—24no—
94C2×(C2×D11)⋊C4—24no—
95C2×(C2×D11)⋊C4—24no—
96C2×(C2×D11)⋊C4—24no—
97C2×(C2×D11)⋊C4—24no—
98C2×(C2×D11)⋊C4—42no—
99C2×(C2×D11)⋊C4—42no—
100C2×(C2×D11)⋊C4—42no—
101C2×(C2×D11)⋊C4—42no—
102C2×(C2×D11)⋊C4C2×C414yescomplemented
103C2×C4⋊Dic11—22no—
104C2×C4⋊Dic11—42no—
105C2×Dic11⋊C4—22no—
106C2×Dic11⋊C4—22no—
107C2×Dic11⋊C4C2×C414yescomplemented
108#66937—232no—
109C11×#95—22no—
110C11×#95—24no—
111C11⋊#95—22no—
112C11⋊#95—24no—
113C11⋊#95—24no—
114C11⋊#95—24no—
115C11⋊#95—24no—
116C11⋊#95—24no—
117#14271—111nomaximal, Sylow
118C24×C11—22no—
119C24×C11—21no—
120C24×C11—21no—
121C24×C11—22no—
122C24×C11—21no—
123C24×C11—22no—
124C24×C11—21no—
125C24×C11—22no—
126C24×C11—21no—
127C24×C11—21no—
128C24×C11C22×C412yes—
129C24×C11C2411yescharacteristic
130C23×D11—22no—
131C23×D11—22no—
132C23×D11—21no—
133C23×D11—21no—
134C23×D11—21no—
135C23×D11—21no—
136C23×D11—22no—
137C23×D11—21no—
138C23×D11—21no—
139C23×D11—22no—
140C23×D11—21no—
141C23×D11—21no—
142C23×D11—22no—
143C23×D11—22no—
144C23×D11—21no—
145C23×D11—21no—
146C23×D11C22×C412yes—
147C23×D11C22×C412yes—
148C23×D11C2×D412yes—
149C23×D11C2×D412yes—
150C23×D11C2×D414yes—
151C23×D11#4114yes—
152C22×C4×C11—22no—
153C22×C4×C11—22no—
154C22×C4×C11—22no—
155C22×C4×C11—22no—
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—22no—
163C22×C4×C11—22no—
164C22×C4×C11—22no—
165C22×C4×C11—22no—
166C22×C4×C11—22no—
167C22×C4×C11—22no—
168C22×C4×C11—22no—
169C22×C4×C11—22no—
170C22×C4×C11—22no—
171C22×C4×C11C22×C412yes—
172C22×C4×C11C22×C412yes—
173C22×C4×C11C2×D414yes—
174C22×C4×C11C2×D412yes—
175C22×C4×C11C2×D412yes—
176C2×C22⋊D11—28no—
177C2×C22⋊D11—28no—
178C2×C22⋊D11—216no—
179C2×C22⋊D11—48no—
180C2×C22⋊D11—44no—
181C2×C22⋊D11—48no—
182C2×C22⋊D11—44no—
183C2×C22⋊D11—48no—
184C2×C22⋊D11—44no—
185C2×C22⋊D11—44no—
186C22×Dic11—22no—
187C22×Dic11—22no—
188C22×Dic11—21no—
189C22×Dic11—21no—
190C22×Dic11—22no—
191C22×Dic11—22no—
192C22×Dic11—22no—
193C22×Dic11—22no—
194C22×Dic11—22no—
195C22×Dic11—22no—
196C22×Dic11—22no—
197C22×Dic11—22no—
198C22×Dic11—22no—
199C22×Dic11—22no—
200C22×Dic11—22no—
201C22×Dic11—22no—
202C22×Dic11—22no—
203C22×Dic11—22no—
204C22×Dic11—22no—
205C22×Dic11C22×C412yes—
206C22×Dic11C22×C412yes—
207C22×Dic11C2×D414yes—
208C22×Dic11C2×D412yes—
209C22×Dic11C2×D412yes—
210C2×D44—28no—
211C2×D44—216no—
212C2×D44—48no—
213C2×D44—44no—
214C2×D44—44no—
215C2×C4×D11—216no—
216C2×C4×D11—48no—
217C2×C4×D11—44no—
218C2×C4×D11—44no—
219C2×C4×D11—48no—
220C2×C4×D11—48no—
221C2×C4×D11—48no—
222C2×C4×D11—48no—
223C2×C4×D11—48no—
224C2×C4×D11—48no—
225C2×C4×D11—48no—
226C2×C4×D11C22⋊C4116yescomplemented
227C11×C4⋊C4—44no—
228C11×C22⋊C4—28no—
229C11×C22⋊C4—48no—
230C22⋊Dic11—48no—
231(C2×D11)⋊C4—28no—
232(C2×D11)⋊C4—48no—
233(C2×D11)⋊C4—48no—
234(C2×D11)⋊C4—48no—
235C4⋊Dic11—44no—
236Dic11⋊C4—28no—
237C22×#121—111no—
238C2×#386—112no—
239C2×#386—112no—
240C2×#380—111no—
241C22×#95—111no—
242#1445—112no—
243#1439—111no—
244#1439—111no—
245#1439—111no—
246#1439D1111yescharacteristic, complemented
247#1438—112no—
248C23×C11—22no—
249C23×C11—24no—
250C23×C11—24no—
251C23×C11—22no—
252C23×C11—22no—
253C23×C11—42no—
254C23×C11—41no—
255C23×C11—41no—
256C23×C11—42no—
257C23×C11—42no—
258C23×C11—41no—
259C23×C11—42no—
260C23×C11—41no—
261C23×C11—41no—
262C23×C11—41no—
263C23×C11—41no—
264C23×C11—42no—
265C23×C11—41no—
266C23×C11—42no—
267C23×C11—42no—
268C23×C11—42no—
269C23×C11—42no—
270C23×C11—42no—
271C23×C11C23×C411yescharacteristic
272C23×C11C22×D411yescharacteristic
273C23×C11C22×D411yescharacteristic
274C23×C11C22×D412yes—
275C23×C11C2×#4112yes—
276C23×C11H(5,𝔽2)12yes—
277C23×C11H(5,𝔽2)11yescharacteristic
278C23×C11H(5,𝔽2)12yes—
279C23×C11H(5,𝔽2)11yescharacteristic
280C23×C112−1+411yescharacteristic
281C23×C112−1+411yescharacteristic
282C22×D11—24no—
283C22×D11—22no—
284C22×D11—22no—
285C22×D11—24no—
286C22×D11—22no—
287C22×D11—24no—
288C22×D11—22no—
289C22×D11—24no—
290C22×D11—22no—
291C22×D11—22no—
292C22×D11—22no—
293C22×D11—24no—
294C22×D11—22no—
295C22×D11—24no—
296C22×D11—24no—
297C22×D11—24no—
298C22×D11—24no—
299C22×D11—24no—
300C22×D11—22no—
301C22×D11—24no—
302C22×D11—24no—
303C22×D11—22no—
304C22×D11—22no—
305C22×D11—42no—
306C22×D11—41no—
307C22×D11—41no—
308C22×D11—42no—
309C22×D11—42no—
310C22×D11—41no—
311C22×D11—42no—
312C22×D11—41no—
313C22×D11—41no—
314C22×D11—41no—
315C22×D11—41no—
316C22×D11—42no—
317C22×D11—41no—
318C22×D11—42no—
319C22×D11—42no—
320C22×D11—42no—
321C22×D11—42no—
322C22×D11—42no—
323C22×D11C2×C22⋊C414yes—
324C22×D11C4×D418yes—
325C22×D11#12118yes—
326C22×D11#12414yes—
327C22×D11#12714yes—
328C2×C4×C11—24no—
329C2×C4×C11—22no—
330C2×C4×C11—22no—
331C2×C4×C11—24no—
332C2×C4×C11—22no—
333C2×C4×C11—24no—
334C2×C4×C11—24no—
335C2×C4×C11—24no—
336C2×C4×C11—24no—
337C2×C4×C11—42no—
338C2×C4×C11—41no—
339C2×C4×C11—41no—
340C2×C4×C11—42no—
341C2×C4×C11—42no—
342C2×C4×C11—42no—
343C2×C4×C11—42no—
344C2×C4×C11—42no—
345C2×C4×C11—42no—
346C2×C4×C11—42no—
347C2×C4×C11—42no—
348C2×C4×C11—42no—
349C2×C4×C11—42no—
350C2×C4×C11—42no—
351C2×C4×C11C2×C22⋊C414yes—
352C22⋊D11—416no—
353C22⋊D11—416no—
354C2×Dic11—24no—
355C2×Dic11—22no—
356C2×Dic11—24no—
357C2×Dic11—22no—
358C2×Dic11—22no—
359C2×Dic11—24no—
360C2×Dic11—24no—
361C2×Dic11—24no—
362C2×Dic11—24no—
363C2×Dic11—42no—
364C2×Dic11—41no—
365C2×Dic11—41no—
366C2×Dic11—42no—
367C2×Dic11—42no—
368C2×Dic11—42no—
369C2×Dic11—42no—
370C2×Dic11—42no—
371C2×Dic11—42no—
372C2×Dic11—42no—
373C2×Dic11—42no—
374C2×Dic11—42no—
375C2×Dic11—42no—
376C2×Dic11—42no—
377C2×Dic11C2×C22⋊C414yes—
378D44—416no—
379C4×D11—416no—
380C4×D11—432no—
381C23×D4—111no—
382C23×D4—111no—
383C23×D4—111no—
384C24×C4—111no—
385C24×C4—112no—
386C2×#121—118no—
387C2×#121—224no—
388C2×#121—224no—
389C22×C4⋊C4—111no—
390C22×C4⋊C4—111no—
391C22×C4⋊C4C2×D1111yescharacteristic
392C22×C22⋊C4—111no—
393C22×C22⋊C4—112no—
394C22×C22⋊C4—112no—
395C22×C22⋊C4—112no—
396C22×C22⋊C4—112no—
397C22×C22⋊C4C2×D1111yescharacteristic
398C22×C22⋊C4C2×D1112yes—
399#386—228no—
400#386—228no—
401#380—224no—
402C2×#95—112no—
403C2×#95—112no—
404C2×#95—111no—
405C2×#95—112no—
406C2×#95—112no—
407C2×#95—112no—
408C2×#95—224no—
409C2×#95C2×D1111yescharacteristic
410C2×#95C2×D1112yes—
411C22×C11—42no—
412C22×C11—42no—
413C22×C11—44no—
414C22×C11—44no—
415C22×C11—42no—
416C22×C11—82no—
417C22×C11—82no—
418C22×C11—81no—
419C22×C11—81no—
420C22×C11—81no—
421C22×C11—81no—
422C22×C11C22×C22⋊C411yescharacteristic
423C22×C11C2×C4×D412yes—
424C22×C11#51812yes—
425C22×C11#52011yescharacteristic
426C22×C11#52011yescharacteristic
427C22×C11C2×#12112yes—
428C22×C11C2×#12411yescharacteristic
429C22×C11C2×#12711yescharacteristic
430C22×C11#53411yescharacteristic
431C22×C11#53412yes—
432C22×C11#53412yes—
433C22×C11#53411yescharacteristic
434C22×C11#53412yes—
435C22×C11#53511yescharacteristic
436C22×C11#53611yescharacteristic
437C22×C11#53711yescharacteristic
438C22×C11#53712yes—
439C22×C11#53711yescharacteristic
440C22×C11#53712yes—
441C22×C11#53812yes—
442C22×C11#53812yes—
443C22×C11#53912yes—
444C22×C11#53912yes—
445C2×D11—24no—
446C2×D11—24no—
447C2×D11—28no—
448C2×D11—28no—
449C2×D11—28no—
450C2×D11—28no—
451C2×D11—24no—
452C2×D11—24no—
453C2×D11—24no—
454C2×D11—24no—
455C2×D11—42no—
456C2×D11—42no—
457C2×D11—44no—
458C2×D11—44no—
459C2×D11—42no—
460C2×D11—82no—
461C2×D11—82no—
462C2×D11—81no—
463C2×D11—81no—
464C2×D11—81no—
465C2×D11—81no—
466C2×D11#39018yes—
467C4×C11—24no—
468C4×C11—44no—
469C4×C11—42no—
470C4×C11—82no—
471Dic11—24no—
472Dic11—44no—
473Dic11—42no—
474Dic11—82no—
475C25—111no—
476C25—111no—
477C25C22×D1111yescharacteristic
478C22×D4—114no—
479C22×D4—114no—
480C22×D4—114no—
481C22×D4—222no—
482C22×D4—222no—
483C22×D4—224no—
484C22×D4—224no—
485C22×D4—222no—
486C22×D4—222no—
487C22×D4—222no—
488C22×D4—222no—
489C22×D4—224no—
490C22×D4—224no—
491C22×D4—442no—
492C22×D4—442no—
493C23×C4—111no—
494C23×C4—114no—
495C23×C4—114no—
496C23×C4—114no—
497C23×C4—112no—
498C23×C4—111no—
499C23×C4—118no—
500C23×C4—112no—
501C23×C4—224no—
502C23×C4—224no—
503C23×C4—442no—
504C23×C4—442no—
505C23×C4—442no—
506C23×C4—442no—
507C23×C4—442no—
508C23×C4—442no—
509C23×C4C22×D1112yes—
510C23×C4C22×D1111yescharacteristic
511C23×C4C22×D1112yes—
512C23×C4C22×D1111yescharacteristic
513#121—2232no—
514C2×C4⋊C4—22no—
515C2×C4⋊C4—42no—
516C2×C4⋊C4—114no—
517C2×C4⋊C4—222no—
518C2×C4⋊C4—222no—
519C2×C4⋊C4—222no—
520C2×C4⋊C4—442no—
521C2×C22⋊C4—22no—
522C2×C22⋊C4—22no—
523C2×C22⋊C4—24no—
524C2×C22⋊C4—42no—
525C2×C22⋊C4—42no—
526C2×C22⋊C4—114no—
527C2×C22⋊C4—222no—
528C2×C22⋊C4—222no—
529C2×C22⋊C4—224no—
530C2×C22⋊C4—224no—
531C2×C22⋊C4—224no—
532C2×C22⋊C4—224no—
533C2×C22⋊C4—224no—
534C2×C22⋊C4—224no—
535C2×C22⋊C4—442no—
536C2×C22⋊C4—442no—
537C2×C22⋊C4—442no—
538C2×C22⋊C4—442no—
539C2×C22⋊C4—442no—
540C2×C22⋊C4—442no—
541C2×C22⋊C4C4×D1114yescomplemented
542#95—22no—
543#95—24no—
544#95—224no—
545#95—224no—
546#95—224no—
547#95—224no—
548#95—222no—
549#95—224no—
550C2×C11—82no—
551C2×C11C2×#39011yescharacteristic
552C2×C11#230811yescharacteristic
553C2×C11#231111yescharacteristic
554C2×C11#232512yes—
555C2×C11#232512yes—
556C2×C11#261712yes—
557C2×C11#261812yes—
558C2×C11#263911yescharacteristic
559C2×C11#263911yescharacteristic
560C2×C11#265611yescharacteristic
561C2×C11#265611yescharacteristic
562D11—28no—
563D11—82no—
564C24—22no—
565C24—21no—
566C24—21no—
567C24—21no—
568C24—22no—
569C24—21no—
570C24—22no—
571C24—21no—
572C24—22no—
573C24—21no—
574C24—112no—
575C24—112no—
576C24—114no—
577C24—112no—
578C24—114no—
579C24—112no—
580C24—221no—
581C24—222no—
582C24—221no—
583C24—222no—
584C24—221no—
585C24—221no—
586C24—222no—
587C24—221no—
588C24—221no—
589C24—221no—
590C24—222no—
591C24—221no—
592C24—222no—
593C24—221no—
594C24—222no—
595C24—221no—
596C24C2×C4×D1112yes—
597C24C23×D1111yescharacteristic
598C2×D4—228no—
599C2×D4—2216no—
600C2×D4—228no—
601C2×D4—228no—
602C2×D4—2216no—
603C2×D4—444no—
604C2×D4—448no—
605C2×D4—444no—
606C2×D4—448no—
607C2×D4—444no—
608C2×D4—448no—
609C2×D4—444no—
610C2×D4—444no—
611C2×D4—448no—
612C2×D4—444no—
613C22×C4—22no—
614C22×C4—22no—
615C22×C4—22no—
616C22×C4—22no—
617C22×C4—21no—
618C22×C4—21no—
619C22×C4—22no—
620C22×C4—22no—
621C22×C4—22no—
622C22×C4—22no—
623C22×C4—22no—
624C22×C4—22no—
625C22×C4—22no—
626C22×C4—22no—
627C22×C4—22no—
628C22×C4—22no—
629C22×C4—22no—
630C22×C4—22no—
631C22×C4—22no—
632C22×C4—112no—
633C22×C4—112no—
634C22×C4—112no—
635C22×C4—1116no—
636C22×C4—112no—
637C22×C4—114no—
638C22×C4—2216no—
639C22×C4—222no—
640C22×C4—222no—
641C22×C4—222no—
642C22×C4—222no—
643C22×C4—221no—
644C22×C4—221no—
645C22×C4—222no—
646C22×C4—222no—
647C22×C4—222no—
648C22×C4—222no—
649C22×C4—222no—
650C22×C4—222no—
651C22×C4—222no—
652C22×C4—222no—
653C22×C4—222no—
654C22×C4—222no—
655C22×C4—222no—
656C22×C4—222no—
657C22×C4—222no—
658C22×C4—448no—
659C22×C4—444no—
660C22×C4—448no—
661C22×C4—444no—
662C22×C4—448no—
663C22×C4—448no—
664C22×C4—448no—
665C22×C4—448no—
666C22×C4—448no—
667C22×C4—448no—
668C22×C4C2×C4×D1112yes—
669C22×C4C2×C4×D1112yes—
670C22×C4D4×D1114yes—
671C22×C4D4×D1112yes—
672C22×C4D4×D1112yes—
673C4⋊C4—44no—
674C4⋊C4—228no—
675C4⋊C4—444no—
676C22⋊C4—28no—
677C22⋊C4—48no—
678C22⋊C4—228no—
679C22⋊C4—448no—
680C22⋊C4—448no—
681C22⋊C4—448no—
682C22⋊C4—448no—
683C11#1427111yescharacteristic, complemented, Sylow
684C23—22no—
685C23—22no—
686C23—22no—
687C23—24no—
688C23—24no—
689C23—42no—
690C23—41no—
691C23—42no—
692C23—41no—
693C23—42no—
694C23—42no—
695C23—41no—
696C23—41no—
697C23—42no—
698C23—41no—
699C23—41no—
700C23—42no—
701C23—42no—
702C23—42no—
703C23—41no—
704C23—42no—
705C23—41no—
706C23—42no—
707C23—114no—
708C23—114no—
709C23—118no—
710C23—118no—
711C23—114no—
712C23—224no—
713C23—222no—
714C23—222no—
715C23—224no—
716C23—222no—
717C23—224no—
718C23—224no—
719C23—222no—
720C23—222no—
721C23—224no—
722C23—222no—
723C23—222no—
724C23—224no—
725C23—224no—
726C23—222no—
727C23—224no—
728C23—224no—
729C23—224no—
730C23—222no—
731C23—222no—
732C23—222no—
733C23—224no—
734C23—224no—
735C23—442no—
736C23—441no—
737C23—442no—
738C23—441no—
739C23—442no—
740C23—442no—
741C23—441no—
742C23—441no—
743C23—442no—
744C23—441no—
745C23—441no—
746C23—442no—
747C23—442no—
748C23—442no—
749C23—441no—
750C23—442no—
751C23—441no—
752C23—442no—
753C23C22×C4×D1111yescharacteristic
754C23C2×D4×D1111yescharacteristic
755C23C2×D4×D1112yes—
756C23C2×D4×D1111yescharacteristic
757C23#6703711yescharacteristic
758C23#6703712yes—
759C23#6704011yescharacteristic
760C23#41×D1112yes—
761C23#6704212yes—
762C23#6704211yescharacteristic
763C23#6704311yescharacteristic
764D4—4416no—
765D4—4416no—
766D4—4416no—
767C2×C4—24no—
768C2×C4—22no—
769C2×C4—24no—
770C2×C4—22no—
771C2×C4—22no—
772C2×C4—24no—
773C2×C4—24no—
774C2×C4—24no—
775C2×C4—24no—
776C2×C4—41no—
777C2×C4—42no—
778C2×C4—42no—
779C2×C4—42no—
780C2×C4—42no—
781C2×C4—41no—
782C2×C4—42no—
783C2×C4—42no—
784C2×C4—42no—
785C2×C4—42no—
786C2×C4—42no—
787C2×C4—42no—
788C2×C4—42no—
789C2×C4—42no—
790C2×C4—114no—
791C2×C4—224no—
792C2×C4—222no—
793C2×C4—224no—
794C2×C4—222no—
795C2×C4—222no—
796C2×C4—224no—
797C2×C4—224no—
798C2×C4—224no—
799C2×C4—224no—
800C2×C4—4416no—
801C2×C4—4432no—
802C2×C4—441no—
803C2×C4—442no—
804C2×C4—442no—
805C2×C4—442no—
806C2×C4—442no—
807C2×C4—441no—
808C2×C4—442no—
809C2×C4—442no—
810C2×C4—442no—
811C2×C4—442no—
812C2×C4—442no—
813C2×C4—442no—
814C2×C4—442no—
815C2×C4—442no—
816C2×C4C22⋊C4×D1114yes—
817C22—42no—
818C22—42no—
819C22—44no—
820C22—44no—
821C22—42no—
822C22—81no—
823C22—81no—
824C22—81no—
825C22—81no—
826C22—82no—
827C22—82no—
828C22—118no—
829C22—224no—
830C22—224no—
831C22—224no—
832C22—224no—
833C22—224no—
834C22—224no—
835C22—228no—
836C22—228no—
837C22—228no—
838C22—228no—
839C22—442no—
840C22—442no—
841C22—444no—
842C22—444no—
843C22—442no—
844C22—881no—
845C22—881no—
846C22—881no—
847C22—881no—
848C22—882no—
849C22—882no—
850C22C2×C22⋊C4×D1111yescharacteristic
851C22#1062303511yescharacteristic
852C22#1062305411yescharacteristic
853C22C4×D4×D1112yes—
854C22#1062307612yes—
855C22#1062312011yescharacteristic
856C22#1062312012yes—
857C22D11×#12112yes—
858C22#1062313612yes—
859C22#1062313811yescharacteristic
860C22#1062313911yescharacteristic
861C22#1062313912yes—
862C22#1062315911yescharacteristic
863C22#1062316011yescharacteristic
864C22#1062316012yes—
865C22#1062316912yes—
866C22#1062318411yescharacteristic
867C22#1062318412yes—
868C22#1062318812yes—
869C22D11×#12411yescharacteristic
870C22#1062320912yes—
871C22#1062323812yes—
872C22D11×#12711yescharacteristic
873C4—24no—
874C4—44no—
875C4—42no—
876C4—82no—
877C4—224no—
878C4—444no—
879C4—442no—
880C4—882no—
881C2—82no—
882C2—228no—
883C2—882no—
884C2D11×#39011yescharacteristic
885C2#1307119011yescharacteristic
886C2#1307120511yescharacteristic
887C2#1307131312yes—
888C2#1307132012yes—
889C2#1307435512yes—
890C2#1307436312yes—
891C2#1307454311yescharacteristic
892C2#1307454511yescharacteristic
893C2#1307471711yescharacteristic
894C2#1307471911yescharacteristic
subgroupG/H
center, FrattiniC24C23×D11
commutatorC23×C11C23×C4
FittingC11×#1439C2
socle, cosocleC24×C11C24
prime radicalC22×#66937C2
hypercenter#1439D11
hypocenterC11#14271
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ #1439

Complements

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

NH ≅ G/Ntype
2. C2×#10622278C2semidirect
3. C2×#10622569C2semidirect
4. C2×#10622600C2semidirect
5. C2×D11×#95C2semidirect
6. #13066882C2semidirect
7. #13066862C2semidirect
8. #13066861C2semidirect
9. #13066858C2semidirect
10. #13066855C2semidirect
11. C11×#1439C2semidirect
29. C2×#66937C4semidirect
58. C22×C22⋊D11C2×C4semidirect
79. C22×C4×D11D4semidirect
87. C2×C11×C22⋊C4C2×C4semidirect
102. C2×(C2×D11)⋊C4C2×C4semidirect
107. C2×Dic11⋊C4C2×C4semidirect
226. C2×C4×D11C22⋊C4semidirect
246. #1439D11semidirect
541. C2×C22⋊C4C4×D11semidirect
683. C11#14271semidirect

Maximal subgroups

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

subgroupindex
C22×#669372
C2×#106222782
C2×#106225692
C2×#106226002
C2×D11×#952
#130668822
#130668622
#130668612
#130668582
#130668552
C11×#14392
#1427111