Finite Group Databasebeta

← #14680526

Subgroups — #14680526

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
1C22×D4×Dic11C211yesmaximal, characteristic, complemented
2C2×#10622836C211yesmaximal, characteristic
3C2×#10622282C211yesmaximal, characteristic, complemented
4C2×#10622571C212yesmaximal, complemented
5#13066872C211yesmaximal, characteristic, complemented
6#13066862C211yesmaximal, characteristic, complemented
7#13066859C212yesmaximal, complemented
8#13066855C212yesmaximal, complemented
9#13066841C211yesmaximal, characteristic, complemented
10#13066838C212yesmaximal, complemented
11C11×#1438C211yesmaximal, characteristic, complemented
12C23×D4×C11C2211yescharacteristic
13C23×C22⋊D11C2212yes—
14C24×Dic11C2212yes—
15C22×C11×C22⋊C4C2212yes—
16C22×C11×C22⋊C4C2212yes—
17C22×C22⋊Dic11C2212yes—
18C22×C22⋊Dic11C2212yes—
19C2×D4×Dic11—28no—
20C2×D4×Dic11—24no—
21C22×(C2×D11)⋊C4C2211yescharacteristic
22C22×(C2×D11)⋊C4C2211yescharacteristic
23C22×(C2×D11)⋊C4C2211yescharacteristic
24C22×(C2×D11)⋊C4C2212yes—
25C22×C4⋊Dic11C2211yescharacteristic
26C22×Dic11⋊C4C2211yescharacteristic
27C22×C4×Dic11C2211yescharacteristic
28C2×C11×#95C2211yescharacteristic
29C2×C11×#95C2211yescharacteristic
30#10622836C418yescomplemented
31C2×C11⋊#95C2211yescharacteristic
32C2×C11⋊#95C2212yes—
33C2×C11⋊#95C2212yes—
34C2×C11⋊#95C2212yes—
35C2×C11⋊#95C2212yes—
36C2×C11⋊#95C2212yes—
37C2×C11⋊#95C2211yescharacteristic
38#10622571—28no—
39#10622282—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×C11C2311yescharacteristic
48C23×C4×C11C2311yescharacteristic
49C23×C4×C11C2312yes—
50C23×C4×C11C2311yescharacteristic
51C22×C22⋊D11—24no—
52C22×C22⋊D11—24no—
53C22×C22⋊D11—42no—
54C22×C22⋊D11—42no—
55C22×C22⋊D11—42no—
56C22×C22⋊D11—42no—
57C22×C22⋊D11C2×C418yescomplemented
58C23×Dic11—24no—
59C23×Dic11—24no—
60C23×Dic11—42no—
61C23×Dic11—42no—
62C23×Dic11—42no—
63C23×Dic11—42no—
64C23×Dic11D418yescomplemented
65C23×Dic11C2311yescharacteristic
66C23×Dic11C2312yes—
67C23×Dic11C2311yescharacteristic
68C23×Dic11C2312yes—
69C23×Dic11C2311yescharacteristic
70C2×C11×C22⋊C4—24no—
71C2×C11×C22⋊C4—24no—
72C2×C11×C22⋊C4—42no—
73C2×C11×C22⋊C4—42no—
74C2×C11×C22⋊C4—42no—
75C2×C11×C22⋊C4—42no—
76C2×C22⋊Dic11—24no—
77C2×C22⋊Dic11—24no—
78C2×C22⋊Dic11—24no—
79C2×C22⋊Dic11—42no—
80C2×C22⋊Dic11—42no—
81C2×C22⋊Dic11C2×C418yescomplemented
82D4×Dic11—232no—
83C2×(C2×D11)⋊C4—22no—
84C2×(C2×D11)⋊C4—22no—
85C2×(C2×D11)⋊C4—22no—
86C2×(C2×D11)⋊C4—22no—
87C2×(C2×D11)⋊C4—24no—
88C2×(C2×D11)⋊C4—24no—
89C2×(C2×D11)⋊C4—42no—
90C2×(C2×D11)⋊C4—42no—
91C2×(C2×D11)⋊C4—42no—
92C2×(C2×D11)⋊C4C2×C414yescomplemented
93C2×C4⋊Dic11—22no—
94C2×C4⋊Dic11—24no—
95C2×Dic11⋊C4—22no—
96C2×Dic11⋊C4—42no—
97C2×C4×Dic11—24no—
98C2×C4×Dic11D414yescomplemented
99C11×#95—22no—
100C11×#95—22no—
101C11⋊#95—22no—
102C11⋊#95—24no—
103C11⋊#95—24no—
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—22no—
146C22×C4×C11—21no—
147C22×C4×C11—22no—
148C22×C4×C11—22no—
149C22×C4×C11—22no—
150C22×C4×C11—21no—
151C22×C4×C11—22no—
152C22×C4×C11—22no—
153C22×C4×C11—22no—
154C22×C4×C11—22no—
155C22×C4×C11—22no—
156C22×C4×C11—21no—
157C22×C4×C11—22no—
158C22×C4×C11—21no—
159C22×C4×C11—21no—
160C22×C4×C11C22×C412yes—
161C22×C4×C11C2×D412yes—
162C22×C4×C11#4112yes—
163C2×C22⋊D11—216no—
164C2×C22⋊D11—48no—
165C2×C22⋊D11—48no—
166C2×C22⋊D11—48no—
167C2×C22⋊D11—48no—
168C2×C22⋊D11—48no—
169C2×C22⋊D11—48no—
170C22×Dic11—216no—
171C22×Dic11—22no—
172C22×Dic11—21no—
173C22×Dic11—22no—
174C22×Dic11—22no—
175C22×Dic11—22no—
176C22×Dic11—21no—
177C22×Dic11—22no—
178C22×Dic11—21no—
179C22×Dic11—21no—
180C22×Dic11—22no—
181C22×Dic11—21no—
182C22×Dic11—22no—
183C22×Dic11—22no—
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—21no—
194C22×Dic11—48no—
195C22×Dic11—48no—
196C22×Dic11—48no—
197C22×Dic11—48no—
198C22×Dic11—48no—
199C22×Dic11—48no—
200C22×Dic11C22×C414yes—
201C22×Dic11C22×C412yes—
202C22×Dic11C2×D414yes—
203C22×Dic11C2×D412yes—
204C22×Dic11C2×D414yes—
205C22×Dic11C2×D412yes—
206C11×C22⋊C4—48no—
207C11×C22⋊C4—48no—
208C22⋊Dic11—216no—
209C22⋊Dic11—48no—
210(C2×D11)⋊C4—28no—
211(C2×D11)⋊C4—48no—
212(C2×D11)⋊C4—44no—
213(C2×D11)⋊C4—44no—
214C4⋊Dic11—28no—
215Dic11⋊C4—44no—
216C4×Dic11—28no—
217C22×C4×D4—111no—
218C2×#392—111no—
219C2×#388—111no—
220C2×#386—112no—
221#1442—111no—
222#1439—111no—
223#1439—112no—
224#1438—112no—
225#1438D1111yescharacteristic, complemented
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)12yes—
269C23×C11H(5,𝔽2)11yescharacteristic
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—42no—
289C22×D11—41no—
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—41no—
303C2×C4×C11—41no—
304C2×C4×C11—42no—
305C2×C4×C11—42no—
306C2×C4×C11—41no—
307C2×C4×C11—41no—
308C2×C4×C11—42no—
309C2×C4×C11—42no—
310C2×C4×C11—41no—
311C2×C4×C11—42no—
312C2×C4×C11—41no—
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—
320C22⋊D11—432no—
321C2×Dic11—24no—
322C2×Dic11—24no—
323C2×Dic11—22no—
324C2×Dic11—22no—
325C2×Dic11—22no—
326C2×Dic11—24no—
327C2×Dic11—24no—
328C2×Dic11—24no—
329C2×Dic11—24no—
330C2×Dic11—22no—
331C2×Dic11—24no—
332C2×Dic11—24no—
333C2×Dic11—24no—
334C2×Dic11—22no—
335C2×Dic11—22no—
336C2×Dic11—432no—
337C2×Dic11—42no—
338C2×Dic11—42no—
339C2×Dic11—42no—
340C2×Dic11—41no—
341C2×Dic11—42no—
342C2×Dic11—41no—
343C2×Dic11—42no—
344C2×Dic11—42no—
345C2×Dic11—42no—
346C2×Dic11—42no—
347C2×Dic11—42no—
348C2×Dic11—42no—
349C2×Dic11—42no—
350C2×Dic11#12014yes—
351C23×D4—112no—
352C23×D4C2×D1111yescharacteristic
353C24×C4—112no—
354C2×C4×D4—224no—
355C2×C4×D4—228no—
356C22×C4⋊C4—111no—
357C22×C4⋊C4—111no—
358C22×C22⋊C4—111no—
359C22×C22⋊C4—112no—
360C22×C22⋊C4—112no—
361C22×C22⋊C4—111no—
362C22×C22⋊C4—111no—
363C22×C22⋊C4—112no—
364C22×C22⋊C4C2×D1112yes—
365C22×C22⋊C4C2×D1112yes—
366C22×C42—111no—
367#392—118no—
368#388—224no—
369#386—228no—
370C2×#95—111no—
371C2×#95—111no—
372C2×#95—112no—
373C2×#95—112no—
374C2×#95—112no—
375C2×#95—112no—
376C2×#95—112no—
377C2×#95C2×D1111yescharacteristic
378C2×#95C2×D1111yescharacteristic
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#53512yes—
406C22×C11#53511yescharacteristic
407C22×C11#53511yescharacteristic
408C22×C11#53712yes—
409C22×C11#53711yescharacteristic
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—81no—
430C4×C11—81no—
431C4×C11—82no—
432Dic11—24no—
433Dic11—44no—
434Dic11—42no—
435Dic11—44no—
436Dic11—42no—
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—111no—
452C23×C4—111no—
453C23×C4—111no—
454C23×C4—112no—
455C23×C4—112no—
456C23×C4—118no—
457C23×C4—224no—
458C23×C4—224no—
459C23×C4—442no—
460C23×C4—442no—
461C23×C4—442no—
462C23×C4—442no—
463C23×C4C22×D1111yescharacteristic
464C23×C4C22×D1111yescharacteristic
465C23×C4C22×D1112yes—
466C23×C4C22×D1111yescharacteristic
467C4×D4—2232no—
468C2×C4⋊C4—224no—
469C2×C4⋊C4—222no—
470C2×C4⋊C4—222no—
471C2×C4⋊C4—442no—
472C2×C22⋊C4—24no—
473C2×C22⋊C4—24no—
474C2×C22⋊C4—42no—
475C2×C22⋊C4—42no—
476C2×C22⋊C4—42no—
477C2×C22⋊C4—42no—
478C2×C22⋊C4—114no—
479C2×C22⋊C4—118no—
480C2×C22⋊C4—224no—
481C2×C22⋊C4—224no—
482C2×C22⋊C4—224no—
483C2×C22⋊C4—222no—
484C2×C22⋊C4—222no—
485C2×C22⋊C4—224no—
486C2×C22⋊C4—224no—
487C2×C22⋊C4—222no—
488C2×C22⋊C4—222no—
489C2×C22⋊C4—442no—
490C2×C22⋊C4—442no—
491C2×C22⋊C4—442no—
492C2×C22⋊C4—442no—
493C2×C22⋊C4—442no—
494C2×C42—114no—
495C2×C42—224no—
496#95—22no—
497#95—22no—
498#95—114no—
499#95—224no—
500#95—224no—
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—222no—
539C24—221no—
540C24—221no—
541C24C2×C4×D1114yes—
542C24D4×D1114yes—
543C24#434114yes—
544C24C23×D1111yescharacteristic
545C2×D4—28no—
546C2×D4—28no—
547C2×D4—216no—
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—22no—
559C22×C4—21no—
560C22×C4—21no—
561C22×C4—22no—
562C22×C4—22no—
563C22×C4—22no—
564C22×C4—22no—
565C22×C4—22no—
566C22×C4—22no—
567C22×C4—21no—
568C22×C4—22no—
569C22×C4—21no—
570C22×C4—22no—
571C22×C4—22no—
572C22×C4—22no—
573C22×C4—21no—
574C22×C4—22no—
575C22×C4—21no—
576C22×C4—112no—
577C22×C4—114no—
578C22×C4—114no—
579C22×C4—112no—
580C22×C4—114no—
581C22×C4—112no—
582C22×C4—2216no—
583C22×C4—221no—
584C22×C4—222no—
585C22×C4—221no—
586C22×C4—222no—
587C22×C4—221no—
588C22×C4—222no—
589C22×C4—222no—
590C22×C4—222no—
591C22×C4—221no—
592C22×C4—222no—
593C22×C4—221no—
594C22×C4—222no—
595C22×C4—222no—
596C22×C4—222no—
597C22×C4—222no—
598C22×C4—222no—
599C22×C4—222no—
600C22×C4—222no—
601C22×C4—222no—
602C22×C4—222no—
603C22×C4—222no—
604C22×C4—222no—
605C22×C4—221no—
606C22×C4—448no—
607C22×C4—448no—
608C22×C4—448no—
609C22×C4—448no—
610C22×C4—448no—
611C22×C4—448no—
612C22×C4C2×C4×D1112yes—
613C22×C4D4×D1112yes—
614C22×C4#434112yes—
615C4⋊C4—228no—
616C4⋊C4—444no—
617C22⋊C4—48no—
618C22⋊C4—48no—
619C22⋊C4—2216no—
620C22⋊C4—228no—
621C22⋊C4—444no—
622C22⋊C4—444no—
623C22⋊C4—448no—
624C22⋊C4—448no—
625C42—228no—
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—441no—
667C23—441no—
668C23—442no—
669C23—441no—
670C23—441no—
671C23—442no—
672C23—442no—
673C23—442no—
674C23—442no—
675C23—441no—
676C23—441no—
677C23—442no—
678C23—442no—
679C23—442no—
680C23—442no—
681C23—442no—
682C23—441no—
683C23—441no—
684C23(C22⋊D11)⋊C418yes—
685C23C22×C4×D1111yescharacteristic
686C23C2×D4×D1111yescharacteristic
687C23C2×D4×D1112yes—
688C23C2×#434111yescharacteristic
689C23C2×#434112yes—
690C23#6703712yes—
691C23#6703711yescharacteristic
692C23#6703711yescharacteristic
693C23#6704212yes—
694C23#6704211yescharacteristic
695C23#6704311yescharacteristic
696D4—232no—
697D4—4432no—
698C2×C4—24no—
699C2×C4—22no—
700C2×C4—24no—
701C2×C4—22no—
702C2×C4—41no—
703C2×C4—41no—
704C2×C4—42no—
705C2×C4—41no—
706C2×C4—42no—
707C2×C4—41no—
708C2×C4—42no—
709C2×C4—42no—
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—42no—
719C2×C4—114no—
720C2×C4—224no—
721C2×C4—222no—
722C2×C4—224no—
723C2×C4—222no—
724C2×C4—222no—
725C2×C4—222no—
726C2×C4—224no—
727C2×C4—224no—
728C2×C4—224no—
729C2×C4—224no—
730C2×C4—222no—
731C2×C4—224no—
732C2×C4—224no—
733C2×C4—222no—
734C2×C4—224no—
735C2×C4—4432no—
736C2×C4—441no—
737C2×C4—442no—
738C2×C4—442no—
739C2×C4—442no—
740C2×C4—442no—
741C2×C4—442no—
742C2×C4—442no—
743C2×C4—442no—
744C2×C4—442no—
745C2×C4—442no—
746C2×C4—442no—
747C2×C4—442no—
748C2×C4—441no—
749C2×C4(C22⋊D11)⋊C414yes—
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—
776C22C2×(C22⋊D11)⋊C412yes—
777C22C2×(C22⋊D11)⋊C411yescharacteristic
778C22#1062307611yescharacteristic
779C22#1062307612yes—
780C22#1062307711yescharacteristic
781C22#1062311712yes—
782C22#1062311711yescharacteristic
783C22D11×#12011yescharacteristic
784C22#1062312312yes—
785C22#1062312412yes—
786C22#1062312812yes—
787C22#1062313612yes—
788C22#1062313811yescharacteristic
789C22#1062313911yescharacteristic
790C22#1062314812yes—
791C22#1062314812yes—
792C22#1062315012yes—
793C22#1062318412yes—
794C22#1062319612yes—
795C22#1062320511yescharacteristic
796C22#1062321311yescharacteristic
797C22#1062324611yescharacteristic
798C22#1062325011yescharacteristic
799C4—24no—
800C4—81no—
801C4—82no—
802C4—81no—
803C4—224no—
804C4—444no—
805C4—442no—
806C4—444no—
807C4—442no—
808C2—48no—
809C2—882no—
810C2#1307111511yescharacteristic
811C2#1307127912yes—
812C2#1307131211yescharacteristic
813C2#1307131712yes—
814C2#1307134011yescharacteristic
815C2#1307432911yescharacteristic
816C2#1307433911yescharacteristic
817C2#1307445412yes—
818C2#1307446711yescharacteristic
819C2#1307449912yes—
820C2#1307451211yescharacteristic
subgroupG/H
center, FrattiniC24C23×D11
commutatorC23×C11C23×C4
FittingC11×#1438C2
socle, cosocleC24×C11C24
prime radicalC2×#10622836C2
hypercenter#1438D11
hypocenterC11#14299
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ #1438

Complements

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

NH ≅ G/Ntype
1. C22×D4×Dic11C2semidirect
3. C2×#10622282C2semidirect
4. C2×#10622571C2semidirect
5. #13066872C2semidirect
6. #13066862C2semidirect
7. #13066859C2semidirect
8. #13066855C2semidirect
9. #13066841C2semidirect
10. #13066838C2semidirect
11. C11×#1438C2semidirect
30. #10622836C4semidirect
57. C22×C22⋊D11C2×C4semidirect
64. C23×Dic11D4semidirect
81. C2×C22⋊Dic11C2×C4semidirect
92. C2×(C2×D11)⋊C4C2×C4semidirect
98. C2×C4×Dic11D4semidirect
107. C11⋊#95C2×C4semidirect
225. #1438D11semidirect
626. C11#14299semidirect

Maximal subgroups

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

subgroupindex
C22×D4×Dic112
C2×#106228362
C2×#106222822
C2×#106225712
#130668722
#130668622
#130668592
#130668552
#130668412
#130668382
C11×#14382
#1429911