Finite Group Databasebeta

← #14680519

Subgroups — #14680519

Order 2816.

2566 conjugacy classes of subgroups.

The subgroup lattice has 822 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622836C211yesmaximal, characteristic
2C2×#10622553C211yesmaximal, characteristic, complemented
3C2×#10622826C212yesmaximal, complemented
4#13066875C211yesmaximal, characteristic, complemented
5#13066859C212yesmaximal, complemented
6#13066858C211yesmaximal, characteristic, complemented
7#13066857C211yesmaximal, characteristic, complemented
8#13066855C212yesmaximal, complemented
9#13066843C211yesmaximal, characteristic, complemented
10#13066839C212yesmaximal, complemented
11C22×C4×D4×C11C211yesmaximal, characteristic, complemented
12C23×D4×C11C2211yescharacteristic
13C24×C4×C11C2212yes—
14C23×C22⋊D11C2212yes—
15C2×C4×D4×C11—28no—
16C2×C4×D4×C11—24no—
17C22×C11×C4⋊C4C2211yescharacteristic
18C22×C11×C22⋊C4C2212yes—
19C22×C42×C11C2211yescharacteristic
20C22×C22⋊Dic11C2212yes—
21C22×C22⋊Dic11C2212yes—
22C22×C22⋊Dic11C2212yes—
23C22×(C2×D11)⋊C4C2211yescharacteristic
24C22×(C2×D11)⋊C4C2211yescharacteristic
25C22×(C2×D11)⋊C4C2211yescharacteristic
26C22×(C2×D11)⋊C4C2212yes—
27C22×Dic11⋊C4C2211yescharacteristic
28#10622836C418yescomplemented
29#10622826—28no—
30C2×C11⋊#95C2211yescharacteristic
31C2×C11⋊#95C2212yes—
32C2×C11⋊#95C2211yescharacteristic
33C2×C11⋊#95C2211yescharacteristic
34C2×C11⋊#95C2212yes—
35C2×C11⋊#95C2212yes—
36C2×C11⋊#95C2212yes—
37C2×C11⋊#95C2212yes—
38C2×C11⋊#95C2211yescharacteristic
39#10622553—24no—
40C25×C11C2312yes—
41C24×D11C2311yescharacteristic
42C22×D4×C11—24no—
43C22×D4×C11—24no—
44C22×D4×C11—22no—
45C22×D4×C11—22no—
46C22×D4×C11C2×C414yes—
47C23×C4×C11—24no—
48C23×C4×C11—24no—
49C23×C4×C11—42no—
50C23×C4×C11—42no—
51C23×C4×C11—42no—
52C23×C4×C11—42no—
53C23×C4×C11D418yescomplemented
54C23×C4×C11C2311yescharacteristic
55C23×C4×C11C2312yes—
56C23×C4×C11C2311yescharacteristic
57C23×C4×C11C2311yescharacteristic
58C22×C22⋊D11—24no—
59C22×C22⋊D11—24no—
60C22×C22⋊D11—42no—
61C22×C22⋊D11—42no—
62C22×C22⋊D11—42no—
63C22×C22⋊D11—42no—
64C22×C22⋊D11C2×C418yescomplemented
65C23×Dic11C2311yescharacteristic
66C23×Dic11C2311yescharacteristic
67C23×Dic11C2312yes—
68C23×Dic11C2311yescharacteristic
69C23×Dic11C2312yes—
70C4×D4×C11—232no—
71C2×C11×C4⋊C4—24no—
72C2×C11×C4⋊C4—22no—
73C2×C11×C22⋊C4—24no—
74C2×C11×C22⋊C4—24no—
75C2×C11×C22⋊C4—24no—
76C2×C42×C11—24no—
77C2×C42×C11D414yescomplemented
78C2×C22⋊Dic11—24no—
79C2×C22⋊Dic11—24no—
80C2×C22⋊Dic11—42no—
81C2×C22⋊Dic11—42no—
82C2×C22⋊Dic11—42no—
83C2×C22⋊Dic11—42no—
84C2×C22⋊Dic11—42no—
85C2×C22⋊Dic11—42no—
86C2×C22⋊Dic11C2×C418yescomplemented
87C2×(C2×D11)⋊C4—22no—
88C2×(C2×D11)⋊C4—22no—
89C2×(C2×D11)⋊C4—22no—
90C2×(C2×D11)⋊C4—22no—
91C2×(C2×D11)⋊C4—24no—
92C2×(C2×D11)⋊C4—24no—
93C2×(C2×D11)⋊C4—42no—
94C2×(C2×D11)⋊C4—42no—
95C2×(C2×D11)⋊C4—42no—
96C2×(C2×D11)⋊C4C2×C414yescomplemented
97C2×Dic11⋊C4—22no—
98C2×Dic11⋊C4—42no—
99C11⋊#95—22no—
100C11⋊#95—22no—
101C11⋊#95—24no—
102C11⋊#95—24no—
103C11⋊#95—22no—
104C11⋊#95—42no—
105C11⋊#95—42no—
106C11⋊#95—42no—
107C11⋊#95C2×C414yescomplemented
108#14299—111nomaximal, Sylow
109C24×C11—22no—
110C24×C11—22no—
111C24×C11—22no—
112C24×C11—22no—
113C24×C11—22no—
114C24×C11—22no—
115C24×C11—22no—
116C24×C11—22no—
117C24×C11—22no—
118C24×C11—22no—
119C24×C11—22no—
120C24×C11—22no—
121C24×C11C22×C414yes—
122C24×C11C2×D414yes—
123C24×C11#4114yes—
124C24×C11C2411yescharacteristic
125C23×D11—21no—
126C23×D11—22no—
127C23×D11—21no—
128C23×D11—22no—
129C23×D11—21no—
130C23×D11—22no—
131C23×D11—22no—
132C23×D11—21no—
133C23×D11—21no—
134C23×D11—21no—
135C23×D11C22×C412yes—
136C2×D4×C11—28no—
137C2×D4×C11—28no—
138C2×D4×C11—216no—
139C2×D4×C11—216no—
140C2×D4×C11—28no—
141C22×C4×C11—22no—
142C22×C4×C11—22no—
143C22×C4×C11—21no—
144C22×C4×C11—22no—
145C22×C4×C11—21no—
146C22×C4×C11—22no—
147C22×C4×C11—22no—
148C22×C4×C11—22no—
149C22×C4×C11—21no—
150C22×C4×C11—22no—
151C22×C4×C11—22no—
152C22×C4×C11—22no—
153C22×C4×C11—22no—
154C22×C4×C11—22no—
155C22×C4×C11—21no—
156C22×C4×C11—216no—
157C22×C4×C11—48no—
158C22×C4×C11—48no—
159C22×C4×C11—48no—
160C22×C4×C11—48no—
161C22×C4×C11—48no—
162C22×C4×C11—48no—
163C22×C4×C11C22×C412yes—
164C22×C4×C11C2×D414yes—
165C22×C4×C11C2×D412yes—
166C22×C4×C11C2×D412yes—
167C22×C4×C11C2×D414yes—
168C22×C4×C11C2×D412yes—
169C22×C4×C11#4112yes—
170C2×C22⋊D11—216no—
171C2×C22⋊D11—48no—
172C2×C22⋊D11—48no—
173C2×C22⋊D11—48no—
174C2×C22⋊D11—48no—
175C2×C22⋊D11—48no—
176C2×C22⋊D11—48no—
177C22×Dic11—22no—
178C22×Dic11—21no—
179C22×Dic11—21no—
180C22×Dic11—21no—
181C22×Dic11—22no—
182C22×Dic11—22no—
183C22×Dic11—21no—
184C22×Dic11—22no—
185C22×Dic11—22no—
186C22×Dic11—22no—
187C22×Dic11—22no—
188C22×Dic11—22no—
189C22×Dic11—22no—
190C22×Dic11—22no—
191C22×Dic11—22no—
192C22×Dic11—22no—
193C22×Dic11—22no—
194C22×Dic11—21no—
195C22×Dic11—22no—
196C22×Dic11—22no—
197C22×Dic11—22no—
198C22×Dic11—22no—
199C22×Dic11—22no—
200C22×Dic11—21no—
201C22×Dic11—21no—
202C22×Dic11—22no—
203C22×Dic11—21no—
204C22×Dic11C22×C414yes—
205C22×Dic11C22×C412yes—
206C11×C4⋊C4—28no—
207C11×C22⋊C4—216no—
208C42×C11—28no—
209C22⋊Dic11—48no—
210C22⋊Dic11—48no—
211C22⋊Dic11—48no—
212(C2×D11)⋊C4—28no—
213(C2×D11)⋊C4—48no—
214(C2×D11)⋊C4—44no—
215(C2×D11)⋊C4—44no—
216Dic11⋊C4—44no—
217C22×C4×D4D1111yescharacteristic, complemented
218C2×#392—111no—
219C2×#388—111no—
220C2×#386—112no—
221#1442—111no—
222#1439—111no—
223#1439—112no—
224#1438—111no—
225#1438—112no—
226#1434—111no—
227C22⋊#95—112no—
228C23×C11—24no—
229C23×C11—24no—
230C23×C11—24no—
231C23×C11—24no—
232C23×C11—24no—
233C23×C11—24no—
234C23×C11—24no—
235C23×C11—24no—
236C23×C11—24no—
237C23×C11—24no—
238C23×C11—24no—
239C23×C11—24no—
240C23×C11—24no—
241C23×C11—24no—
242C23×C11—24no—
243C23×C11—24no—
244C23×C11—24no—
245C23×C11—24no—
246C23×C11—42no—
247C23×C11—42no—
248C23×C11—42no—
249C23×C11—42no—
250C23×C11—42no—
251C23×C11—42no—
252C23×C11—42no—
253C23×C11—42no—
254C23×C11—42no—
255C23×C11—42no—
256C23×C11—42no—
257C23×C11—42no—
258C23×C11—42no—
259C23×C11—42no—
260C23×C11—42no—
261C23×C11—42no—
262C23×C11C4×D418yes—
263C23×C11C23×C411yescharacteristic
264C23×C11C22×D412yes—
265C23×C11C22×D411yescharacteristic
266C23×C11C2×#4112yes—
267C23×C11C2×#4111yescharacteristic
268C23×C11H(5,𝔽2)11yescharacteristic
269C23×C11H(5,𝔽2)12yes—
270C23×C11H(5,𝔽2)11yescharacteristic
271C23×C11H(5,𝔽2)11yescharacteristic
272C23×C11H(5,𝔽2)12yes—
273C23×C112−1+411yescharacteristic
274C22×D11—22no—
275C22×D11—24no—
276C22×D11—22no—
277C22×D11—24no—
278C22×D11—22no—
279C22×D11—41no—
280C22×D11—42no—
281C22×D11—41no—
282C22×D11—42no—
283C22×D11—42no—
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—41no—
295C22×D11—42no—
296C22×D11—41no—
297D4×C11—232no—
298C2×C4×C11—24no—
299C2×C4×C11—22no—
300C2×C4×C11—22no—
301C2×C4×C11—24no—
302C2×C4×C11—24no—
303C2×C4×C11—24no—
304C2×C4×C11—22no—
305C2×C4×C11—22no—
306C2×C4×C11—22no—
307C2×C4×C11—24no—
308C2×C4×C11—24no—
309C2×C4×C11—24no—
310C2×C4×C11—22no—
311C2×C4×C11—22no—
312C2×C4×C11—432no—
313C2×C4×C11—42no—
314C2×C4×C11—42no—
315C2×C4×C11—42no—
316C2×C4×C11—42no—
317C2×C4×C11—42no—
318C2×C4×C11—42no—
319C2×C4×C11C4×D414yes—
320C2×C4×C11#12014yes—
321C22⋊D11—432no—
322C2×Dic11—22no—
323C2×Dic11—24no—
324C2×Dic11—24no—
325C2×Dic11—24no—
326C2×Dic11—24no—
327C2×Dic11—42no—
328C2×Dic11—41no—
329C2×Dic11—41no—
330C2×Dic11—42no—
331C2×Dic11—42no—
332C2×Dic11—42no—
333C2×Dic11—42no—
334C2×Dic11—41no—
335C2×Dic11—41no—
336C2×Dic11—42no—
337C2×Dic11—42no—
338C2×Dic11—41no—
339C2×Dic11—41no—
340C2×Dic11—42no—
341C2×Dic11—42no—
342C2×Dic11—41no—
343C2×Dic11—41no—
344C2×Dic11—42no—
345C2×Dic11—42no—
346C2×Dic11—42no—
347C2×Dic11—42no—
348C2×Dic11—42no—
349C2×Dic11—42no—
350C2×Dic11—42no—
351C23×D4—112no—
352C23×D4C2×D1111yescharacteristic
353C24×C4C2×D1112yes—
354C2×C4×D4—28no—
355C2×C4×D4—24no—
356C22×C4⋊C4—111no—
357C22×C4⋊C4C2×D1111yescharacteristic
358C22×C22⋊C4—111no—
359C22×C22⋊C4—112no—
360C22×C22⋊C4—111no—
361C22×C22⋊C4—112no—
362C22×C22⋊C4—112no—
363C22×C22⋊C4—111no—
364C22×C22⋊C4—112no—
365C22×C22⋊C4C2×D1112yes—
366C22×C42C2×D1111yescharacteristic
367#392—118no—
368#388—224no—
369#386—228no—
370C2×#95—111no—
371C2×#95—111no—
372C2×#95—112no—
373C2×#95—111no—
374C2×#95—111no—
375C2×#95—112no—
376C2×#95—112no—
377C2×#95—112no—
378C2×#95—112no—
379C22×C11—28no—
380C22×C11—28no—
381C22×C11—28no—
382C22×C11—44no—
383C22×C11—44no—
384C22×C11—44no—
385C22×C11—44no—
386C22×C11—44no—
387C22×C11—44no—
388C22×C11—44no—
389C22×C11—44no—
390C22×C11—44no—
391C22×C11—44no—
392C22×C11—44no—
393C22×C11—44no—
394C22×C11C2×C4×D412yes—
395C22×C11C2×C4×D411yescharacteristic
396C22×C11#51811yescharacteristic
397C22×C11#51812yes—
398C22×C11#52011yescharacteristic
399C22×C11C2×#12011yescharacteristic
400C22×C11#52512yes—
401C22×C11#52511yescharacteristic
402C22×C11#53412yes—
403C22×C11#53412yes—
404C22×C11#53511yescharacteristic
405C22×C11#53511yescharacteristic
406C22×C11#53512yes—
407C22×C11#53511yescharacteristic
408C22×C11#53711yescharacteristic
409C22×C11#53712yes—
410C22×C11#53812yes—
411C22×C11#53812yes—
412C22×C11#53812yes—
413C22×C11#53912yes—
414C22×C11#54011yescharacteristic
415C22×C11#54012yes—
416C22×C11#54211yescharacteristic
417C2×D11—44no—
418C2×D11—42no—
419C2×D11—44no—
420C2×D11—42no—
421C2×D11—42no—
422C2×D11—81no—
423C2×D11—81no—
424C2×D11—82no—
425C2×D11—81no—
426C2×D11—82no—
427C2×D11—81no—
428C4×C11—24no—
429C4×C11—24no—
430C4×C11—44no—
431C4×C11—42no—
432Dic11—44no—
433Dic11—42no—
434Dic11—81no—
435Dic11—81no—
436Dic11—82no—
437C25—111no—
438C25C22×D1112yes—
439C22×D4—24no—
440C22×D4—24no—
441C22×D4—22no—
442C22×D4—22no—
443C22×D4—118no—
444C22×D4—224no—
445C22×D4—224no—
446C22×D4—442no—
447C22×D4—442no—
448C22×D4—442no—
449C22×D4—442no—
450C22×D4C4×D1114yes—
451C23×C4—24no—
452C23×C4—24no—
453C23×C4—42no—
454C23×C4—42no—
455C23×C4—42no—
456C23×C4—42no—
457C23×C4—111no—
458C23×C4—112no—
459C23×C4—111no—
460C23×C4—112no—
461C23×C4—111no—
462C23×C4C22⋊D1118yescomplemented
463C23×C4C22×D1111yescharacteristic
464C23×C4C22×D1112yes—
465C23×C4C22×D1111yescharacteristic
466C23×C4C22×D1111yescharacteristic
467C4×D4—232no—
468C2×C4⋊C4—24no—
469C2×C4⋊C4—22no—
470C2×C4⋊C4—222no—
471C2×C4⋊C4—442no—
472C2×C22⋊C4—24no—
473C2×C22⋊C4—24no—
474C2×C22⋊C4—24no—
475C2×C22⋊C4—114no—
476C2×C22⋊C4—118no—
477C2×C22⋊C4—222no—
478C2×C22⋊C4—222no—
479C2×C22⋊C4—224no—
480C2×C22⋊C4—224no—
481C2×C22⋊C4—224no—
482C2×C22⋊C4—224no—
483C2×C22⋊C4—222no—
484C2×C22⋊C4—222no—
485C2×C22⋊C4—442no—
486C2×C22⋊C4—442no—
487C2×C22⋊C4—442no—
488C2×C22⋊C4—442no—
489C2×C22⋊C4—442no—
490C2×C22⋊C4—442no—
491C2×C22⋊C4—442no—
492C2×C22⋊C4—442no—
493C2×C22⋊C4—442no—
494C2×C42—24no—
495C2×C42C22⋊D1114yescomplemented
496#95—114no—
497#95—222no—
498#95—224no—
499#95—224no—
500#95—222no—
501#95—222no—
502#95—442no—
503#95—442no—
504#95—442no—
505C2×C11—48no—
506C2×C11C4×#12011yescharacteristic
507C2×C11#232112yes—
508C2×C11#232411yescharacteristic
509C2×C11#232512yes—
510C2×C11#232811yescharacteristic
511C2×C11#261311yescharacteristic
512C2×C11#261511yescharacteristic
513C2×C11#263012yes—
514C2×C11#263111yescharacteristic
515C2×C11#263512yes—
516C2×C11#263611yescharacteristic
517D11—82no—
518C24—22no—
519C24—22no—
520C24—22no—
521C24—22no—
522C24—22no—
523C24—22no—
524C24—22no—
525C24—22no—
526C24—22no—
527C24—22no—
528C24—22no—
529C24—22no—
530C24—112no—
531C24—221no—
532C24—222no—
533C24—221no—
534C24—222no—
535C24—221no—
536C24—222no—
537C24—221no—
538C24—221no—
539C24—221no—
540C24—222no—
541C24C2×C4×D1114yes—
542C24#433914yes—
543C24C2×C22⋊D1114yes—
544C24C23×D1111yescharacteristic
545C2×D4—28no—
546C2×D4—216no—
547C2×D4—28no—
548C2×D4—216no—
549C2×D4—28no—
550C2×D4—2216no—
551C2×D4—448no—
552C2×D4—448no—
553C2×D4—448no—
554C2×D4—448no—
555C2×D4—448no—
556C2×D4—448no—
557C22×C4—22no—
558C22×C4—21no—
559C22×C4—22no—
560C22×C4—21no—
561C22×C4—22no—
562C22×C4—22no—
563C22×C4—22no—
564C22×C4—22no—
565C22×C4—22no—
566C22×C4—21no—
567C22×C4—22no—
568C22×C4—21no—
569C22×C4—22no—
570C22×C4—22no—
571C22×C4—22no—
572C22×C4—216no—
573C22×C4—48no—
574C22×C4—48no—
575C22×C4—48no—
576C22×C4—48no—
577C22×C4—48no—
578C22×C4—48no—
579C22×C4—114no—
580C22×C4—112no—
581C22×C4—221no—
582C22×C4—222no—
583C22×C4—222no—
584C22×C4—222no—
585C22×C4—222no—
586C22×C4—222no—
587C22×C4—222no—
588C22×C4—222no—
589C22×C4—222no—
590C22×C4—221no—
591C22×C4—222no—
592C22×C4—222no—
593C22×C4—222no—
594C22×C4—221no—
595C22×C4—222no—
596C22×C4—222no—
597C22×C4—221no—
598C22×C4—222no—
599C22×C4—222no—
600C22×C4—222no—
601C22×C4—221no—
602C22×C4—222no—
603C22×C4—221no—
604C22×C4—221no—
605C22×C4—222no—
606C22×C4—222no—
607C22×C4—221no—
608C22×C4C2×C4×D1112yes—
609C22×C4#433912yes—
610C22×C4C2×C22⋊D1114yes—
611C22×C4C2×C22⋊D1112yes—
612C22×C4C2×C22⋊D1112yes—
613C22×C4C2×C22⋊D1114yes—
614C22×C4C2×C22⋊D1112yes—
615C4⋊C4—28no—
616C4⋊C4—444no—
617C22⋊C4—216no—
618C22⋊C4—228no—
619C22⋊C4—448no—
620C22⋊C4—444no—
621C22⋊C4—448no—
622C22⋊C4—448no—
623C22⋊C4—448no—
624C22⋊C4—444no—
625C42—28no—
626C11#1429911yescharacteristic, complemented, Sylow
627C23—24no—
628C23—24no—
629C23—24no—
630C23—24no—
631C23—24no—
632C23—24no—
633C23—24no—
634C23—24no—
635C23—24no—
636C23—24no—
637C23—24no—
638C23—24no—
639C23—24no—
640C23—24no—
641C23—24no—
642C23—24no—
643C23—24no—
644C23—24no—
645C23—42no—
646C23—42no—
647C23—42no—
648C23—42no—
649C23—42no—
650C23—42no—
651C23—42no—
652C23—42no—
653C23—42no—
654C23—42no—
655C23—42no—
656C23—42no—
657C23—42no—
658C23—42no—
659C23—42no—
660C23—42no—
661C23—222no—
662C23—224no—
663C23—222no—
664C23—224no—
665C23—222no—
666C23—442no—
667C23—441no—
668C23—442no—
669C23—442no—
670C23—441no—
671C23—441no—
672C23—442no—
673C23—442no—
674C23—442no—
675C23—441no—
676C23—441no—
677C23—442no—
678C23—442no—
679C23—441no—
680C23—442no—
681C23—441no—
682C23—442no—
683C23—441no—
684C23C4×C22⋊D1118yes—
685C23C22×C4×D1111yescharacteristic
686C23C2×#433912yes—
687C23C2×#433911yescharacteristic
688C23#6703711yescharacteristic
689C23#6703712yes—
690C23#6703711yescharacteristic
691C23#6704211yescharacteristic
692C23#6704212yes—
693C23#6704311yescharacteristic
694C23C22×C22⋊D1112yes—
695C23C22×C22⋊D1111yescharacteristic
696D4—232no—
697D4—4432no—
698C2×C4—24no—
699C2×C4—24no—
700C2×C4—22no—
701C2×C4—24no—
702C2×C4—24no—
703C2×C4—22no—
704C2×C4—22no—
705C2×C4—22no—
706C2×C4—24no—
707C2×C4—24no—
708C2×C4—22no—
709C2×C4—22no—
710C2×C4—22no—
711C2×C4—24no—
712C2×C4—432no—
713C2×C4—42no—
714C2×C4—42no—
715C2×C4—42no—
716C2×C4—42no—
717C2×C4—42no—
718C2×C4—42no—
719C2×C4—222no—
720C2×C4—224no—
721C2×C4—224no—
722C2×C4—224no—
723C2×C4—224no—
724C2×C4—442no—
725C2×C4—441no—
726C2×C4—442no—
727C2×C4—442no—
728C2×C4—442no—
729C2×C4—441no—
730C2×C4—442no—
731C2×C4—441no—
732C2×C4—442no—
733C2×C4—442no—
734C2×C4—441no—
735C2×C4—442no—
736C2×C4—442no—
737C2×C4—442no—
738C2×C4—442no—
739C2×C4—442no—
740C2×C4—442no—
741C2×C4—441no—
742C2×C4—442no—
743C2×C4—442no—
744C2×C4—441no—
745C2×C4—442no—
746C2×C4—441no—
747C2×C4—441no—
748C2×C4C4×C22⋊D1114yes—
749C2×C4#6700614yes—
750C22—28no—
751C22—28no—
752C22—28no—
753C22—44no—
754C22—44no—
755C22—44no—
756C22—44no—
757C22—44no—
758C22—44no—
759C22—44no—
760C22—44no—
761C22—44no—
762C22—44no—
763C22—44no—
764C22—44no—
765C22—442no—
766C22—444no—
767C22—442no—
768C22—444no—
769C22—442no—
770C22—882no—
771C22—881no—
772C22—882no—
773C22—881no—
774C22—881no—
775C22—881no—
776C22#1062307611yescharacteristic
777C22#1062307612yes—
778C22#1062307711yescharacteristic
779C22#1062309112yes—
780C22#1062309112yes—
781C22#1062309112yes—
782C22#1062309211yescharacteristic
783C22#1062309312yes—
784C22#1062309311yescharacteristic
785C22#1062309512yes—
786C22C2×C4×C22⋊D1112yes—
787C22C2×C4×C22⋊D1111yescharacteristic
788C22#1062332212yes—
789C22#1062332211yescharacteristic
790C22#1062333512yes—
791C22#1062333512yes—
792C22#1062333611yescharacteristic
793C22#1062333611yescharacteristic
794C22#1062336111yescharacteristic
795C22#1062336112yes—
796C22#1062336412yes—
797C22#1062336411yescharacteristic
798C22C2×#6700611yescharacteristic
799C4—24no—
800C4—24no—
801C4—44no—
802C4—42no—
803C4—444no—
804C4—442no—
805C4—881no—
806C4—882no—
807C4—881no—
808C2—48no—
809C2—882no—
810C2C4×#6700611yescharacteristic
811C2#1307127012yes—
812C2#1307130311yescharacteristic
813C2#1307131412yes—
814C2#1307133811yescharacteristic
815C2#1307432811yescharacteristic
816C2#1307434011yescharacteristic
817C2#1307445312yes—
818C2#1307446811yescharacteristic
819C2#1307450012yes—
820C2#1307451111yescharacteristic
subgroupG/H
center, FrattiniC24C23×D11
commutatorC23×C11C23×C4
FittingC22×C4×D4×C11C2
socle, cosocleC24×C11C24
prime radicalC2×#10622836C2
hypercenterC22×C4×D4D11
hypocenterC11#14299
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ C22×C4×D4

Complements

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

NH ≅ G/Ntype
2. C2×#10622553C2semidirect
3. C2×#10622826C2semidirect
4. #13066875C2semidirect
5. #13066859C2semidirect
6. #13066858C2semidirect
7. #13066857C2semidirect
8. #13066855C2semidirect
9. #13066843C2semidirect
10. #13066839C2semidirect
11. C22×C4×D4×C11C2semidirect
28. #10622836C4semidirect
53. C23×C4×C11D4semidirect
64. C22×C22⋊D11C2×C4semidirect
77. C2×C42×C11D4semidirect
86. C2×C22⋊Dic11C2×C4semidirect
96. C2×(C2×D11)⋊C4C2×C4semidirect
107. C11⋊#95C2×C4semidirect
217. C22×C4×D4D11semidirect
462. C23×C4C22⋊D11semidirect
495. C2×C42C22⋊D11semidirect
626. C11#14299semidirect

Maximal subgroups

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

subgroupindex
C2×#106228362
C2×#106225532
C2×#106228262
#130668752
#130668592
#130668582
#130668572
#130668552
#130668432
#130668392
C22×C4×D4×C112
#1429911