Finite Group Databasebeta

← #14681912

Subgroups — #14681912

Order 2816.

2602 conjugacy classes of subgroups.

The subgroup lattice has 786 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622833C212yesmaximal, complemented
2C2×#10622833C212yesmaximal, complemented
3#13066884C212yesmaximal, complemented
4#13066865C212yesmaximal, complemented
5#13066857C212yesmaximal, complemented
6#13066839C211yesmaximal, characteristic, complemented
7#13066839C211yesmaximal, characteristic, complemented
8#13066838C212yesmaximal, complemented
9C22×C11×#121C211yesmaximal, characteristic
10C23×D4×C11C2212yes—
11C23×D4×C11C2211yescharacteristic
12C24×C4×C11C2211yescharacteristic
13C24×Dic11C2212yes—
14C2×C11×#121—28no—
15C2×C11×#121C418yescomplemented
16C22×C11×C4⋊C4C2211yescharacteristic
17C22×C11×C22⋊C4C2212yes—
18C22×C22⋊Dic11C2212yes—
19C22×C22⋊Dic11C2212yes—
20C22×C22⋊Dic11C2212yes—
21C22×C22⋊Dic11C2211yescharacteristic
22C22×C22⋊Dic11C2212yes—
23C22×C22⋊Dic11C2211yescharacteristic
24#10622833—28no—
25#10622833—28no—
26C2×C11⋊#95C2212yes—
27C2×C11⋊#95C2212yes—
28C2×C11⋊#95C2212yes—
29C2×C11⋊#95C2212yes—
30C2×C11⋊#95C2211yescharacteristic
31C2×C11⋊#95C2212yes—
32C2×C11⋊#95C2212yes—
33C2×C11⋊#95C2211yescharacteristic
34C2×C11⋊#95C2212yes—
35C25×C11C2312yes—
36C25×C11C2311yescharacteristic
37C22×D4×C11—24no—
38C22×D4×C11—24no—
39C22×D4×C11—24no—
40C22×D4×C11—24no—
41C22×D4×C11—41no—
42C22×D4×C11—42no—
43C22×D4×C11—41no—
44C22×D4×C11—42no—
45C22×D4×C11—42no—
46C22×D4×C11C2×C414yes—
47C22×D4×C11C2×C418yescomplemented
48C22×D4×C11D418yes—
49C23×C4×C11—24no—
50C23×C4×C11—41no—
51C23×C4×C11—41no—
52C23×C4×C11—42no—
53C23×C4×C11C2×C414yescomplemented
54C23×C4×C11C2311yescharacteristic
55C23×C4×C11C2312yes—
56C23×C4×C11C2311yescharacteristic
57C23×Dic11—24no—
58C23×Dic11—24no—
59C23×Dic11—24no—
60C23×Dic11—42no—
61C23×Dic11—42no—
62C23×Dic11—42no—
63C23×Dic11—42no—
64C23×Dic11C2312yes—
65C23×Dic11C2312yes—
66C23×Dic11C2312yes—
67C23×Dic11C2312yes—
68C11×#121—232no—
69C2×C11×C4⋊C4—24no—
70C2×C11×C4⋊C4C2×C414yescomplemented
71C2×C11×C22⋊C4—24no—
72C2×C11×C22⋊C4—24no—
73C2×C11×C22⋊C4C2×C418yescomplemented
74C2×C22⋊Dic11—24no—
75C2×C22⋊Dic11—24no—
76C2×C22⋊Dic11—24no—
77C2×C22⋊Dic11—24no—
78C2×C22⋊Dic11—22no—
79C2×C22⋊Dic11—24no—
80C2×C22⋊Dic11—24no—
81C2×C22⋊Dic11—24no—
82C2×C22⋊Dic11—41no—
83C2×C22⋊Dic11—41no—
84C2×C22⋊Dic11—42no—
85C2×C22⋊Dic11—42no—
86C2×C22⋊Dic11—42no—
87C2×C22⋊Dic11—42no—
88C2×C22⋊Dic11—42no—
89C2×C22⋊Dic11—41no—
90C2×C22⋊Dic11—41no—
91C2×C22⋊Dic11D414yescomplemented
92C11⋊#95—24no—
93C11⋊#95—24no—
94C11⋊#95—24no—
95C11⋊#95—24no—
96C11⋊#95—41no—
97C11⋊#95—42no—
98C11⋊#95—42no—
99C11⋊#95—42no—
100C11⋊#95—41no—
101#14417—111nomaximal, Sylow
102C24×C11—22no—
103C24×C11—22no—
104C24×C11—22no—
105C24×C11—22no—
106C24×C11—22no—
107C24×C11—22no—
108C24×C11—21no—
109C24×C11—22no—
110C24×C11—21no—
111C24×C11—21no—
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—21no—
121C24×C11—22no—
122C24×C11C22×C414yes—
123C24×C11C22×C412yes—
124C24×C11C2×D414yes—
125C24×C11C2×D414yes—
126C24×C11C2×D412yes—
127C24×C11#4112yes—
128C24×C11C2411yescharacteristic
129C2×D4×C11—216no—
130C2×D4×C11—216no—
131C2×D4×C11—44no—
132C2×D4×C11—44no—
133C2×D4×C11—48no—
134C2×D4×C11—48no—
135C2×D4×C11—48no—
136C2×D4×C11—48no—
137C2×D4×C11—48no—
138C2×D4×C11—48no—
139C2×D4×C11—48no—
140C2×D4×C11C22⋊C4116yescomplemented
141C22×C4×C11—21no—
142C22×C4×C11—21no—
143C22×C4×C11—22no—
144C22×C4×C11—22no—
145C22×C4×C11—22no—
146C22×C4×C11—22no—
147C22×C4×C11—22no—
148C22×C4×C11—22no—
149C22×C4×C11—21no—
150C22×C4×C11—21no—
151C22×C4×C11—22no—
152C22×C4×C11—22no—
153C22×C4×C11—22no—
154C22×C4×C11—28no—
155C22×C4×C11—44no—
156C22×C4×C11—44no—
157C22×C4×C11—48no—
158C22×C4×C11—48no—
159C22×C4×C11C22×C412yes—
160C22×C4×C11C22×C414yes—
161C22×C4×C11C22×C412yes—
162C22×C4×C11C2×D414yes—
163C22×Dic11—22no—
164C22×Dic11—22no—
165C22×Dic11—22no—
166C22×Dic11—22no—
167C22×Dic11—22no—
168C22×Dic11—22no—
169C22×Dic11—22no—
170C22×Dic11—22no—
171C22×Dic11—22no—
172C22×Dic11—22no—
173C22×Dic11—22no—
174C22×Dic11—22no—
175C22×Dic11—22no—
176C22×Dic11—22no—
177C22×Dic11—22no—
178C22×Dic11—22no—
179C22×Dic11—22no—
180C22×Dic11—22no—
181C22×Dic11—22no—
182C22×Dic11—22no—
183C22×Dic11—22no—
184C22×Dic11—22no—
185C22×Dic11—22no—
186C22×Dic11—22no—
187C22×Dic11—22no—
188C22×Dic11—22no—
189C22×Dic11—48no—
190C22×Dic11—48no—
191C22×Dic11—48no—
192C22×Dic11—48no—
193C22×Dic11—48no—
194C22×Dic11—48no—
195C22×Dic11—48no—
196C22×Dic11C2×D414yes—
197C22×Dic11#4114yes—
198C11×C4⋊C4—28no—
199C11×C22⋊C4—216no—
200C22⋊Dic11—44no—
201C22⋊Dic11—48no—
202C22⋊Dic11—48no—
203C22⋊Dic11—48no—
204C22⋊Dic11—48no—
205C22⋊Dic11—44no—
206C22×#121D1111yescharacteristic
207C2×#386—112no—
208C2×#386—112no—
209#1445—112no—
210#1440—112no—
211#1438—112no—
212C22⋊#95—111no—
213C22⋊#95—111no—
214C22⋊#95—112no—
215C23×C11—22no—
216C23×C11—24no—
217C23×C11—24no—
218C23×C11—22no—
219C23×C11—22no—
220C23×C11—22no—
221C23×C11—22no—
222C23×C11—24no—
223C23×C11—24no—
224C23×C11—24no—
225C23×C11—22no—
226C23×C11—24no—
227C23×C11—24no—
228C23×C11—22no—
229C23×C11—24no—
230C23×C11—24no—
231C23×C11—24no—
232C23×C11—22no—
233C23×C11—22no—
234C23×C11—22no—
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—24no—
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×C11—42no—
263C23×C11—42no—
264C23×C11—42no—
265C23×C11—42no—
266C23×C11—42no—
267C23×C11—42no—
268C23×C11—42no—
269C23×C11—42no—
270C23×C11—42no—
271C23×C11C2×C22⋊C418yes—
272C23×C11C4×D414yes—
273C23×C11C23×C411yescharacteristic
274C23×C11C22×D411yescharacteristic
275C23×C11C22×D412yes—
276C23×C11C2×#4111yescharacteristic
277C23×C11C2×#4112yes—
278C23×C11H(5,𝔽2)11yescharacteristic
279C23×C11H(5,𝔽2)11yescharacteristic
280C23×C11H(5,𝔽2)12yes—
281C23×C11H(5,𝔽2)12yes—
282C23×C11H(5,𝔽2)11yescharacteristic
283C23×C112−1+411yescharacteristic
284D4×C11—416no—
285D4×C11—432no—
286C2×C4×C11—22no—
287C2×C4×C11—22no—
288C2×C4×C11—24no—
289C2×C4×C11—24no—
290C2×C4×C11—22no—
291C2×C4×C11—24no—
292C2×C4×C11—24no—
293C2×C4×C11—22no—
294C2×C4×C11—22no—
295C2×C4×C11—24no—
296C2×C4×C11—416no—
297C2×C4×C11—42no—
298C2×C4×C11—42no—
299C2×C4×C11—42no—
300C2×C4×C11—42no—
301C2×C4×C11—42no—
302C2×C4×C11—42no—
303C2×C4×C11C2×C22⋊C414yes—
304C2×Dic11—24no—
305C2×Dic11—24no—
306C2×Dic11—24no—
307C2×Dic11—24no—
308C2×Dic11—24no—
309C2×Dic11—24no—
310C2×Dic11—432no—
311C2×Dic11—42no—
312C2×Dic11—42no—
313C2×Dic11—42no—
314C2×Dic11—42no—
315C2×Dic11—42no—
316C2×Dic11—42no—
317C2×Dic11—42no—
318C2×Dic11—42no—
319C2×Dic11—42no—
320C2×Dic11—42no—
321C2×Dic11—42no—
322C2×Dic11—42no—
323C2×Dic11—42no—
324C2×Dic11—42no—
325C2×Dic11—42no—
326C2×Dic11—42no—
327C2×Dic11—42no—
328C2×Dic11—42no—
329C2×Dic11—42no—
330C2×Dic11—42no—
331C2×Dic11—42no—
332C2×Dic11—42no—
333C23×D4C2×D1112yes—
334C23×D4C2×D1111yescharacteristic
335C24×C4—112no—
336C24×C4C2×D1111yescharacteristic
337C2×#121—28no—
338C2×#121Dic1118yescomplemented
339C22×C4⋊C4C2×D1111yescharacteristic
340C22×C22⋊C4—111no—
341C22×C22⋊C4—112no—
342C22×C22⋊C4—112no—
343C22×C22⋊C4—112no—
344C22×C22⋊C4—111no—
345C22×C22⋊C4—112no—
346C22×C22⋊C4C2×D1112yes—
347#386—228no—
348#386—228no—
349C2×#95—112no—
350C2×#95—112no—
351C2×#95—112no—
352C2×#95—112no—
353C2×#95—111no—
354C2×#95—112no—
355C2×#95—112no—
356C2×#95—111no—
357C2×#95—112no—
358C22×C11—28no—
359C22×C11—24no—
360C22×C11—24no—
361C22×C11—28no—
362C22×C11—28no—
363C22×C11—24no—
364C22×C11—42no—
365C22×C11—44no—
366C22×C11—42no—
367C22×C11—44no—
368C22×C11—42no—
369C22×C11—44no—
370C22×C11—42no—
371C22×C11—44no—
372C22×C11—44no—
373C22×C11—44no—
374C22×C11—44no—
375C22×C11—44no—
376C22×C11—44no—
377C22×C11—44no—
378C22×C11—44no—
379C22×C11—44no—
380C22×C11—44no—
381C22×C11—44no—
382C22×C11—44no—
383C22×C11—44no—
384C22×C11C22×C22⋊C411yescharacteristic
385C22×C11C2×C4×D411yescharacteristic
386C22×C11C4×#4111yescharacteristic
387C22×C11#51811yescharacteristic
388C22×C11#51811yescharacteristic
389C22×C11#51811yescharacteristic
390C22×C11#52011yescharacteristic
391C22×C11#53412yes—
392C22×C11#53412yes—
393C22×C11#53411yescharacteristic
394C22×C11#53711yescharacteristic
395C22×C11#53812yes—
396C22×C11#53811yescharacteristic
397C22×C11#53911yescharacteristic
398C22×C11#54012yes—
399C22×C11D4212yes—
400C22×C11#54612yes—
401C22×C11#54612yes—
402C22×C11#54612yes—
403C22×C11#54712yes—
404C22×C11#55312yes—
405C22×C11#56012yes—
406C22×C11#56212yes—
407C4×C11—24no—
408C4×C11—42no—
409C4×C11—44no—
410Dic11—44no—
411Dic11—44no—
412Dic11—82no—
413Dic11—82no—
414C25C22×D1111yescharacteristic
415C25C22×D1112yes—
416C22×D4—24no—
417C22×D4—24no—
418C22×D4—24no—
419C22×D4—24no—
420C22×D4—41no—
421C22×D4—42no—
422C22×D4—41no—
423C22×D4—42no—
424C22×D4—42no—
425C22×D4C2×Dic1114yes—
426C22×D4C2×Dic1118yescomplemented
427C22×D4C22⋊D1118yes—
428C23×C4—24no—
429C23×C4—41no—
430C23×C4—42no—
431C23×C4—41no—
432C23×C4—112no—
433C23×C4—112no—
434C23×C4—112no—
435C23×C4—112no—
436C23×C4—224no—
437C23×C4—224no—
438C23×C4—224no—
439C23×C4—442no—
440C23×C4—442no—
441C23×C4—442no—
442C23×C4—442no—
443C23×C4C2×Dic1114yescomplemented
444C23×C4C22×D1111yescharacteristic
445C23×C4C22×D1112yes—
446C23×C4C22×D1111yescharacteristic
447#121—232no—
448C2×C4⋊C4—24no—
449C2×C4⋊C4C2×Dic1114yescomplemented
450C2×C22⋊C4—24no—
451C2×C22⋊C4—24no—
452C2×C22⋊C4—114no—
453C2×C22⋊C4—224no—
454C2×C22⋊C4—224no—
455C2×C22⋊C4—224no—
456C2×C22⋊C4—224no—
457C2×C22⋊C4—222no—
458C2×C22⋊C4—224no—
459C2×C22⋊C4—224no—
460C2×C22⋊C4—224no—
461C2×C22⋊C4—441no—
462C2×C22⋊C4—441no—
463C2×C22⋊C4—442no—
464C2×C22⋊C4—442no—
465C2×C22⋊C4—442no—
466C2×C22⋊C4—442no—
467C2×C22⋊C4—442no—
468C2×C22⋊C4—441no—
469C2×C22⋊C4—441no—
470C2×C22⋊C4C2×Dic1118yescomplemented
471#95—224no—
472#95—224no—
473#95—224no—
474#95—224no—
475#95—441no—
476#95—442no—
477#95—441no—
478#95—442no—
479#95—442no—
480C2×C11—48no—
481C2×C11—44no—
482C2×C11#230811yescharacteristic
483C2×C11#232511yescharacteristic
484C2×C11#233311yescharacteristic
485C2×C11D4×C22⋊C411yescharacteristic
486C2×C11#233911yescharacteristic
487C2×C11#236411yescharacteristic
488C2×C11#237711yescharacteristic
489C2×C11#266812yes—
490C2×C11#267112yes—
491C2×C11#268812yes—
492C2×C11#270812yes—
493C24—22no—
494C24—22no—
495C24—21no—
496C24—22no—
497C24—21no—
498C24—22no—
499C24—22no—
500C24—22no—
501C24—22no—
502C24—22no—
503C24—22no—
504C24—22no—
505C24—22no—
506C24—22no—
507C24—22no—
508C24—21no—
509C24—22no—
510C24—22no—
511C24—21no—
512C24—22no—
513C24D4×D1112yes—
514C24#434112yes—
515C24C22×Dic1112yes—
516C24C22×Dic1114yes—
517C24C2×C22⋊D1114yes—
518C24C2×C22⋊D1114yes—
519C24C23×D1111yescharacteristic
520C2×D4—216no—
521C2×D4—216no—
522C2×D4—44no—
523C2×D4—44no—
524C2×D4—48no—
525C2×D4—48no—
526C2×D4—48no—
527C2×D4—48no—
528C2×D4—48no—
529C2×D4—48no—
530C2×D4—48no—
531C2×D4C22⋊Dic11116yescomplemented
532C22×C4—21no—
533C22×C4—22no—
534C22×C4—21no—
535C22×C4—22no—
536C22×C4—22no—
537C22×C4—21no—
538C22×C4—22no—
539C22×C4—21no—
540C22×C4—22no—
541C22×C4—22no—
542C22×C4—22no—
543C22×C4—22no—
544C22×C4—22no—
545C22×C4—28no—
546C22×C4—44no—
547C22×C4—44no—
548C22×C4—48no—
549C22×C4—48no—
550C22×C4—114no—
551C22×C4—114no—
552C22×C4—222no—
553C22×C4—222no—
554C22×C4—222no—
555C22×C4—222no—
556C22×C4—222no—
557C22×C4—222no—
558C22×C4—222no—
559C22×C4—222no—
560C22×C4—222no—
561C22×C4—222no—
562C22×C4—222no—
563C22×C4—222no—
564C22×C4—222no—
565C22×C4—222no—
566C22×C4—222no—
567C22×C4—222no—
568C22×C4—222no—
569C22×C4—222no—
570C22×C4—222no—
571C22×C4—222no—
572C22×C4—222no—
573C22×C4—222no—
574C22×C4—222no—
575C22×C4—222no—
576C22×C4—222no—
577C22×C4—222no—
578C22×C4—448no—
579C22×C4—448no—
580C22×C4—448no—
581C22×C4—448no—
582C22×C4—448no—
583C22×C4—448no—
584C22×C4—448no—
585C22×C4C22×Dic1112yes—
586C22×C4C22×Dic1114yes—
587C22×C4C22×Dic1112yes—
588C22×C4C2×C22⋊D1114yes—
589C4⋊C4—28no—
590C22⋊C4—216no—
591C22⋊C4—444no—
592C22⋊C4—448no—
593C22⋊C4—448no—
594C22⋊C4—448no—
595C22⋊C4—448no—
596C22⋊C4—444no—
597C11#1441711yescharacteristic, complemented, Sylow
598C23—24no—
599C23—22no—
600C23—22no—
601C23—22no—
602C23—24no—
603C23—24no—
604C23—24no—
605C23—24no—
606C23—24no—
607C23—24no—
608C23—24no—
609C23—24no—
610C23—24no—
611C23—24no—
612C23—24no—
613C23—24no—
614C23—24no—
615C23—24no—
616C23—24no—
617C23—22no—
618C23—24no—
619C23—24no—
620C23—22no—
621C23—24no—
622C23—24no—
623C23—22no—
624C23—22no—
625C23—24no—
626C23—22no—
627C23—22no—
628C23—24no—
629C23—22no—
630C23—42no—
631C23—42no—
632C23—42no—
633C23—42no—
634C23—42no—
635C23—42no—
636C23—42no—
637C23—42no—
638C23—42no—
639C23—42no—
640C23—42no—
641C23—42no—
642C23—42no—
643C23—42no—
644C23—42no—
645C23—42no—
646C23—42no—
647C23—42no—
648C23—42no—
649C23—42no—
650C23—42no—
651C23—42no—
652C23—42no—
653C23—42no—
654C23D4×Dic1114yes—
655C23C2×C22⋊Dic1118yes—
656C23C2×D4×D1111yescharacteristic
657C23C2×#434111yescharacteristic
658C23#6703712yes—
659C23#6703711yescharacteristic
660C23#6703712yes—
661C23#6703711yescharacteristic
662C23#41×D1112yes—
663C23#6704211yescharacteristic
664C23#6704311yescharacteristic
665C23C23×Dic1111yescharacteristic
666C23C22×C22⋊D1112yes—
667D4—416no—
668D4—432no—
669C2×C4—22no—
670C2×C4—22no—
671C2×C4—24no—
672C2×C4—24no—
673C2×C4—24no—
674C2×C4—22no—
675C2×C4—22no—
676C2×C4—24no—
677C2×C4—22no—
678C2×C4—24no—
679C2×C4—416no—
680C2×C4—42no—
681C2×C4—42no—
682C2×C4—42no—
683C2×C4—42no—
684C2×C4—42no—
685C2×C4—42no—
686C2×C4—224no—
687C2×C4—224no—
688C2×C4—224no—
689C2×C4—224no—
690C2×C4—224no—
691C2×C4—224no—
692C2×C4—4432no—
693C2×C4—442no—
694C2×C4—442no—
695C2×C4—442no—
696C2×C4—442no—
697C2×C4—442no—
698C2×C4—442no—
699C2×C4—442no—
700C2×C4—442no—
701C2×C4—442no—
702C2×C4—442no—
703C2×C4—442no—
704C2×C4—442no—
705C2×C4—442no—
706C2×C4—442no—
707C2×C4—442no—
708C2×C4—442no—
709C2×C4—442no—
710C2×C4—442no—
711C2×C4—442no—
712C2×C4—442no—
713C2×C4—442no—
714C2×C4—442no—
715C2×C4C2×C22⋊Dic1114yes—
716C22—24no—
717C22—24no—
718C22—28no—
719C22—28no—
720C22—28no—
721C22—24no—
722C22—42no—
723C22—44no—
724C22—44no—
725C22—42no—
726C22—42no—
727C22—44no—
728C22—44no—
729C22—44no—
730C22—44no—
731C22—44no—
732C22—44no—
733C22—44no—
734C22—44no—
735C22—44no—
736C22—42no—
737C22—44no—
738C22—44no—
739C22—44no—
740C22—44no—
741C22—44no—
742C22#1062312811yescharacteristic
743C22#1062313212yes—
744C22#1062313311yescharacteristic
745C22#1062313611yescharacteristic
746C22#1062314112yes—
747C22#1062314412yes—
748C22#1062314612yes—
749C22#1062314811yescharacteristic
750C22#1062315112yes—
751C22#1062315212yes—
752C22C2×D4×Dic1111yescharacteristic
753C22#1062332911yescharacteristic
754C22#1062332911yescharacteristic
755C22#1062332911yescharacteristic
756C22D4×C22⋊D1112yes—
757C22#1062333512yes—
758C22#1062333512yes—
759C22#1062333712yes—
760C22#1062335512yes—
761C22#41×Dic1111yescharacteristic
762C22#1062335811yescharacteristic
763C22#1062336012yes—
764C22C22×C22⋊Dic1111yescharacteristic
765C4—24no—
766C4—44no—
767C4—42no—
768C4—444no—
769C4—444no—
770C4—882no—
771C4—882no—
772C2—44no—
773C2—48no—
774C2#1307119411yescharacteristic
775C2#1307132111yescharacteristic
776C2#1307138311yescharacteristic
777C2D4×C22⋊Dic1111yescharacteristic
778C2#1307144611yescharacteristic
779C2#1307166811yescharacteristic
780C2#1307177311yescharacteristic
781C2#1307481912yes—
782C2#1307484612yes—
783C2#1307504612yes—
784C2#1307532812yes—
subgroupG/H
center, FrattiniC24C23×D11
commutatorC23×C11C23×C4
Fitting, prime radicalC22×C11×#121C2
socle, cosocleC24×C11C24
hypercenterC22×#121D11
hypocenterC11#14417
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ C22×#121

Complements

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

NH ≅ G/Ntype
1. C2×#10622833C2semidirect
2. C2×#10622833C2semidirect
3. #13066884C2semidirect
4. #13066865C2semidirect
5. #13066857C2semidirect
6. #13066839C2semidirect
7. #13066839C2semidirect
8. #13066838C2semidirect
15. C2×C11×#121C4semidirect
47. C22×D4×C11C2×C4semidirect
53. C23×C4×C11C2×C4semidirect
70. C2×C11×C4⋊C4C2×C4semidirect
73. C2×C11×C22⋊C4C2×C4semidirect
91. C2×C22⋊Dic11D4semidirect
140. C2×D4×C11C22⋊C4semidirect
338. C2×#121Dic11semidirect
426. C22×D4C2×Dic11semidirect
443. C23×C4C2×Dic11semidirect
449. C2×C4⋊C4C2×Dic11semidirect
470. C2×C22⋊C4C2×Dic11semidirect
531. C2×D4C22⋊Dic11semidirect
597. C11#14417semidirect

Maximal subgroups

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

subgroupindex
C2×#106228332
#130668842
#130668652
#130668572
#130668392
#130668382
C22×C11×#1212
#1441711