Finite Group Databasebeta

← #14676492

Subgroups — #14676492

Order 2816.

2590 conjugacy classes of subgroups.

The subgroup lattice has 812 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C4×D44C211yesmaximal, characteristic
2C2×#10622278C212yesmaximal
3C2×#10622280C211yesmaximal, characteristic, complemented
4C2×D11×#95C211yesmaximal, characteristic, complemented
5#13066868C212yesmaximal, complemented
6#13066860C212yesmaximal, complemented
7#13066843C211yesmaximal, characteristic, complemented
8(C2×D11)⋊#95C212yesmaximal, complemented
9(C2×D11)⋊#95C211yesmaximal, characteristic, complemented
10(C2×D11)⋊#95C211yesmaximal, characteristic, complemented
11C11×#1434C211yesmaximal, characteristic, complemented
12C23×D44C2211yescharacteristic
13C23×C4×D11C2212yes—
14C23×C4×D11C2211yescharacteristic
15C23×C4×D11C2211yescharacteristic
16C22×C42×C11C2211yescharacteristic
17C22×(C2×D11)⋊C4C2212yes—
18C22×(C2×D11)⋊C4C2212yes—
19C22×(C2×D11)⋊C4C2212yes—
20C22×(C2×D11)⋊C4C2211yescharacteristic
21C22×(C2×D11)⋊C4C2211yescharacteristic
22C22×C4⋊Dic11C2211yescharacteristic
23C22×Dic11⋊C4C2212yes—
24C2×C4×D44—24no—
25C2×C4×D44—24no—
26C2×C4×D44C418yescomplemented
27C2×C11×#95C2211yescharacteristic
28C2×C11×#95C2212yes—
29C2×C11×#95C2211yescharacteristic
30C2×C11×#95C2212yes—
31C2×C11⋊#95C2211yescharacteristic
32C2×C11⋊#95C2212yes—
33C2×C11⋊#95C2211yescharacteristic
34C2×C11⋊#95C2212yes—
35C2×C11⋊#95C2212yes—
36C2×C11⋊#95C2212yes—
37C2×C11⋊#95C2212yes—
38#10622280—24no—
39#10622278—28no—
40D11×#95—24no—
41C24×D11C2311yescharacteristic
42C24×D11C2311yescharacteristic
43C23×C4×C11C2312yes—
44C23×C4×C11C2311yescharacteristic
45C23×C4×C11C2312yes—
46C23×C4×C11C2311yescharacteristic
47C23×C4×C11C2311yescharacteristic
48C23×Dic11C2312yes—
49C23×Dic11C2311yescharacteristic
50C23×Dic11C2312yes—
51C23×Dic11C2311yescharacteristic
52C22×D44—22no—
53C22×D44—22no—
54C22×D44—22no—
55C22×D44—22no—
56C22×D44C2×C414yes—
57C22×D44D414yes—
58C22×D44Q814yes—
59C22×C4×D11—24no—
60C22×C4×D11—22no—
61C22×C4×D11—22no—
62C22×C4×D11—24no—
63C22×C4×D11—24no—
64C22×C4×D11—24no—
65C22×C4×D11—24no—
66C22×C4×D11—42no—
67C22×C4×D11—42no—
68C22×C4×D11—42no—
69C22×C4×D11—42no—
70C22×C4×D11—42no—
71C22×C4×D11—42no—
72C22×C4×D11C2×C414yes—
73C22×C4×D11C2×C414yescomplemented
74C22×C4×D11D414yes—
75C22×C4×D11D414yes—
76C2×C42×C11—22no—
77C2×C42×C11—22no—
78C2×C42×C11C2×C414yescomplemented
79C2×(C2×D11)⋊C4—22no—
80C2×(C2×D11)⋊C4—22no—
81C2×(C2×D11)⋊C4—22no—
82C2×(C2×D11)⋊C4—22no—
83C2×(C2×D11)⋊C4—24no—
84C2×(C2×D11)⋊C4—24no—
85C2×(C2×D11)⋊C4—24no—
86C2×(C2×D11)⋊C4—24no—
87C2×(C2×D11)⋊C4—24no—
88C2×(C2×D11)⋊C4—24no—
89C2×(C2×D11)⋊C4—24no—
90C2×(C2×D11)⋊C4—42no—
91C2×(C2×D11)⋊C4—42no—
92C2×(C2×D11)⋊C4C2×C414yes—
93C2×(C2×D11)⋊C4C2×C414yescomplemented
94C2×C4⋊Dic11—22no—
95C2×C4⋊Dic11—22no—
96C2×C4⋊Dic11C2×C414yescomplemented
97C2×Dic11⋊C4—24no—
98C2×Dic11⋊C4—42no—
99C2×Dic11⋊C4—42no—
100C4×D44—232no—
101C11×#95—22no—
102C11×#95—24no—
103C11×#95—22no—
104C11×#95—24no—
105C11⋊#95—22no—
106C11⋊#95—24no—
107C11⋊#95—22no—
108C11⋊#95—24no—
109C11⋊#95—24no—
110C11⋊#95—42no—
111C11⋊#95—42no—
112#13960—111nomaximal, Sylow
113C24×C11C2411yescharacteristic
114C23×D11—22no—
115C23×D11—22no—
116C23×D11—22no—
117C23×D11—22no—
118C23×D11—21no—
119C23×D11—21no—
120C23×D11—22no—
121C23×D11—22no—
122C23×D11—21no—
123C23×D11—21no—
124C23×D11—22no—
125C23×D11—22no—
126C23×D11C22×C412yes—
127C23×D11C22×C412yes—
128C23×D11C2×D412yes—
129C23×D11C2×D412yes—
130C23×D11C2×D412yes—
131C23×D11C2×D412yes—
132C23×D11C2×Q812yes—
133C23×D11C2×Q812yes—
134C23×D11#4112yes—
135C23×D11#4112yes—
136C22×C4×C11—21no—
137C22×C4×C11—21no—
138C22×C4×C11—21no—
139C22×C4×C11—21no—
140C22×C4×C11—22no—
141C22×C4×C11—22no—
142C22×C4×C11—22no—
143C22×C4×C11—22no—
144C22×C4×C11—21no—
145C22×C4×C11—21no—
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—22no—
153C22×C4×C11—22no—
154C22×C4×C11—22no—
155C22×C4×C11—22no—
156C22×C4×C11—22no—
157C22×C4×C11—22no—
158C22×C4×C11—22no—
159C22×C4×C11C22×C412yes—
160C22×C4×C11C22×C412yes—
161C22×C4×C11C22×C412yes—
162C22×C4×C11C2×D412yes—
163C22×C4×C11C2×D412yes—
164C22×C4×C11C2×D412yes—
165C22×C4×C11C2×Q812yes—
166C22×C4×C11#4114yes—
167C22×Dic11—22no—
168C22×Dic11—22no—
169C22×Dic11—21no—
170C22×Dic11—21no—
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×Dic11C22×C412yes—
187C22×Dic11C22×C412yes—
188C22×Dic11C2×D412yes—
189C22×Dic11C2×D412yes—
190C22×Dic11#4114yes—
191C2×D44—28no—
192C2×D44—28no—
193C2×D44—28no—
194C2×D44—28no—
195C2×D44—28no—
196C2×D44—28no—
197C2×D44C4⋊C4116yescomplemented
198C2×C4×D11—216no—
199C2×C4×D11—28no—
200C2×C4×D11—44no—
201C2×C4×D11—44no—
202C2×C4×D11—44no—
203C2×C4×D11—44no—
204C2×C4×D11—48no—
205C2×C4×D11—48no—
206C2×C4×D11—48no—
207C2×C4×D11—48no—
208C2×C4×D11—48no—
209C2×C4×D11—48no—
210C2×C4×D11—48no—
211C2×C4×D11—48no—
212C2×C4×D11—48no—
213C2×C4×D11—48no—
214C2×C4×D11C22⋊C4116yescomplemented
215C42×C11—28no—
216(C2×D11)⋊C4—28no—
217(C2×D11)⋊C4—28no—
218(C2×D11)⋊C4—48no—
219(C2×D11)⋊C4—48no—
220(C2×D11)⋊C4—48no—
221C4⋊Dic11—28no—
222Dic11⋊C4—48no—
223C22×C4×D4—111no—
224C2×#386—112no—
225C2×#380—111no—
226C22×#95—111no—
227#1441—112no—
228#1439—112no—
229#1434—111no—
230#1434D1111yescharacteristic, complemented
231C22⋊#95—112no—
232C22⋊#95—111no—
233C22⋊#95—111no—
234C23×C11C23×C411yescharacteristic
235C23×C11C22×D411yescharacteristic
236C23×C11C22×D411yescharacteristic
237C23×C11C22×D411yescharacteristic
238C23×C11C22×Q811yescharacteristic
239C23×C11C2×#4112yes—
240C23×C11C2×#4111yescharacteristic
241C23×C11C2×#4111yescharacteristic
242C23×C11C2×#4112yes—
243C23×C11H(5,𝔽2)12yes—
244C23×C11H(5,𝔽2)12yes—
245C22×D11—22no—
246C22×D11—22no—
247C22×D11—22no—
248C22×D11—22no—
249C22×D11—24no—
250C22×D11—24no—
251C22×D11—24no—
252C22×D11—24no—
253C22×D11—24no—
254C22×D11—24no—
255C22×D11—24no—
256C22×D11—24no—
257C22×D11—24no—
258C22×D11—24no—
259C22×D11—24no—
260C22×D11—24no—
261C22×D11—22no—
262C22×D11—22no—
263C22×D11—22no—
264C22×D11—22no—
265C22×D11—22no—
266C22×D11—22no—
267C22×D11—22no—
268C22×D11—22no—
269C22×D11—22no—
270C22×D11—22no—
271C22×D11—24no—
272C22×D11—24no—
273C22×D11—24no—
274C22×D11—24no—
275C22×D11—42no—
276C22×D11—42no—
277C22×D11—42no—
278C22×D11—42no—
279C22×D11—42no—
280C22×D11—42no—
281C22×D11—42no—
282C22×D11—42no—
283C22×D11C2×C22⋊C414yes—
284C22×D11C2×C4⋊C414yes—
285C22×D11C2×C4⋊C414yes—
286C22×D11#11714yes—
287C22×D11#12114yes—
288C22×D11#12114yes—
289C22×D11C22⋊Q814yes—
290C22×D11C22⋊Q814yes—
291C2×C4×C11—22no—
292C2×C4×C11—22no—
293C2×C4×C11—22no—
294C2×C4×C11—22no—
295C2×C4×C11—22no—
296C2×C4×C11—22no—
297C2×C4×C11—22no—
298C2×C4×C11—22no—
299C2×C4×C11—24no—
300C2×C4×C11—24no—
301C2×C4×C11—22no—
302C2×C4×C11—22no—
303C2×C4×C11—22no—
304C2×C4×C11—24no—
305C2×C4×C11—24no—
306C2×C4×C11—24no—
307C2×C4×C11—42no—
308C2×C4×C11—42no—
309C2×C4×C11—42no—
310C2×C4×C11—42no—
311C2×C4×C11—42no—
312C2×C4×C11—42no—
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×C11—42no—
320C2×C4×C11C2×C22⋊C414yes—
321C2×C4×C11C2×C4⋊C414yes—
322C2×Dic11—22no—
323C2×Dic11—22no—
324C2×Dic11—24no—
325C2×Dic11—24no—
326C2×Dic11—22no—
327C2×Dic11—22no—
328C2×Dic11—22no—
329C2×Dic11—24no—
330C2×Dic11—24no—
331C2×Dic11—24no—
332C2×Dic11—42no—
333C2×Dic11—42no—
334C2×Dic11—42no—
335C2×Dic11—42no—
336C2×Dic11—42no—
337C2×Dic11—42no—
338C2×Dic11—42no—
339C2×Dic11—42no—
340C2×Dic11—42no—
341C2×Dic11—42no—
342C2×Dic11—42no—
343C2×Dic11—42no—
344C2×Dic11—42no—
345C2×Dic11C2×C22⋊C414yes—
346D44—232no—
347C4×D11—416no—
348C4×D11—416no—
349C4×D11—432no—
350C23×D4—111no—
351C24×C4—111no—
352C24×C4—111no—
353C24×C4—112no—
354C2×C4×D4—118no—
355C2×C4×D4—224no—
356C2×C4×D4—224no—
357C22×C4⋊C4—111no—
358C22×C4⋊C4—112no—
359C22×C22⋊C4—111no—
360C22×C22⋊C4—111no—
361C22×C22⋊C4—112no—
362C22×C22⋊C4—112no—
363C22×C22⋊C4—112no—
364C22×C42C2×D1111yescharacteristic
365#386—228no—
366#380—224no—
367C2×#95—112no—
368C2×#95—111no—
369C2×#95—111no—
370C2×#95—112no—
371C2×#95—112no—
372C2×#95—112no—
373C2×#95—112no—
374C2×#95—224no—
375C2×#95C2×D1112yes—
376C2×#95C2×D1111yescharacteristic
377C2×#95C2×D1111yescharacteristic
378C2×#95C2×D1112yes—
379C22×C11C22×C22⋊C411yescharacteristic
380C22×C11C22×C4⋊C411yescharacteristic
381C22×C11C2×#11711yescharacteristic
382C22×C11C4×#4111yescharacteristic
383C22×C11C4×#4111yescharacteristic
384C22×C11#51811yescharacteristic
385C22×C11#51811yescharacteristic
386C22×C11C2×#12111yescharacteristic
387C22×C11C2×#12111yescharacteristic
388C22×C11C2×C22⋊Q811yescharacteristic
389C22×C11C2×C22⋊Q811yescharacteristic
390C22×C11#52512yes—
391C22×C11#53212yes—
392C22×C11#53412yes—
393C22×C11#53412yes—
394C22×C11#54612yes—
395C22×C11#54612yes—
396C22×C11#55112yes—
397C22×C11#55112yes—
398C22×C11#55312yes—
399C22×C11#55312yes—
400C22×C11#55412yes—
401C22×C11#55412yes—
402C2×D11—24no—
403C2×D11—28no—
404C2×D11—28no—
405C2×D11—24no—
406C2×D11—24no—
407C2×D11—24no—
408C2×D11—24no—
409C2×D11—28no—
410C2×D11—28no—
411C2×D11—24no—
412C2×D11—24no—
413C2×D11—24no—
414C2×D11—24no—
415C2×D11—42no—
416C2×D11—44no—
417C2×D11—44no—
418C2×D11—42no—
419C2×D11—42no—
420C2×D11—44no—
421C2×D11—44no—
422C2×D11—42no—
423C2×D11#38018yes—
424C4×C11—24no—
425C4×C11—24no—
426C4×C11—44no—
427C4×C11—42no—
428C4×C11—82no—
429Dic11—24no—
430Dic11—42no—
431Dic11—44no—
432Dic11—82no—
433C25—111no—
434C25—111no—
435C22×D4—114no—
436C22×D4—114no—
437C22×D4—114no—
438C22×D4—222no—
439C22×D4—222no—
440C22×D4—222no—
441C22×D4—222no—
442C23×C4—111no—
443C23×C4—114no—
444C23×C4—114no—
445C23×C4—114no—
446C23×C4—111no—
447C23×C4—112no—
448C23×C4—114no—
449C23×C4—112no—
450C23×C4—224no—
451C23×C4—224no—
452C23×C4—224no—
453C23×C4—224no—
454C23×C4—224no—
455C23×C4—222no—
456C23×C4—222no—
457C23×C4—442no—
458C23×C4—442no—
459C23×C4—442no—
460C23×C4—442no—
461C23×C4—442no—
462C23×C4—442no—
463C23×C4C22×D1112yes—
464C23×C4C22×D1111yescharacteristic
465C23×C4C22×D1112yes—
466C23×C4C22×D1111yescharacteristic
467C23×C4C22×D1111yescharacteristic
468C4×D4—2232no—
469C2×C4⋊C4—114no—
470C2×C4⋊C4—222no—
471C2×C4⋊C4—222no—
472C2×C4⋊C4—224no—
473C2×C4⋊C4—442no—
474C2×C4⋊C4—442no—
475C2×C22⋊C4—114no—
476C2×C22⋊C4—114no—
477C2×C22⋊C4—222no—
478C2×C22⋊C4—222no—
479C2×C22⋊C4—222no—
480C2×C22⋊C4—222no—
481C2×C22⋊C4—224no—
482C2×C22⋊C4—224no—
483C2×C22⋊C4—224no—
484C2×C22⋊C4—224no—
485C2×C22⋊C4—224no—
486C2×C22⋊C4—224no—
487C2×C22⋊C4—224no—
488C2×C22⋊C4—442no—
489C2×C22⋊C4—442no—
490C2×C42—22no—
491C2×C42—22no—
492C2×C42C4×D1114yescomplemented
493#95—24no—
494#95—22no—
495#95—22no—
496#95—24no—
497#95—224no—
498#95—224no—
499#95—222no—
500#95—222no—
501#95—224no—
502#95—442no—
503#95—442no—
504C2×C11C2×#38011yescharacteristic
505C2×C11#229711yescharacteristic
506C2×C11#230811yescharacteristic
507C2×C11#234911yescharacteristic
508C2×C11#234911yescharacteristic
509C2×C11#235311yescharacteristic
510C2×C11#235311yescharacteristic
511C2×C11#253412yes—
512C2×C11#254312yes—
513C2×C11#256412yes—
514C2×C11#257912yes—
515D11—28no—
516D11—44no—
517C24—112no—
518C24—112no—
519C24—112no—
520C24—112no—
521C24—112no—
522C24—112no—
523C24—112no—
524C24—112no—
525C24—112no—
526C24—112no—
527C24—222no—
528C24—222no—
529C24—222no—
530C24—222no—
531C24—222no—
532C24—221no—
533C24—221no—
534C24—222no—
535C24—221no—
536C24—221no—
537C24—222no—
538C24—222no—
539C24C23×D1111yescharacteristic
540C2×D4—1116no—
541C2×D4—228no—
542C2×D4—228no—
543C2×D4—228no—
544C2×D4—228no—
545C2×D4—228no—
546C2×D4—228no—
547C22×C4—21no—
548C22×C4—21no—
549C22×C4—21no—
550C22×C4—21no—
551C22×C4—22no—
552C22×C4—22no—
553C22×C4—22no—
554C22×C4—22no—
555C22×C4—22no—
556C22×C4—21no—
557C22×C4—21no—
558C22×C4—22no—
559C22×C4—22no—
560C22×C4—22no—
561C22×C4—22no—
562C22×C4—22no—
563C22×C4—22no—
564C22×C4—22no—
565C22×C4—22no—
566C22×C4—22no—
567C22×C4—22no—
568C22×C4—22no—
569C22×C4—22no—
570C22×C4—112no—
571C22×C4—112no—
572C22×C4—112no—
573C22×C4—1116no—
574C22×C4—112no—
575C22×C4—114no—
576C22×C4—2216no—
577C22×C4—222no—
578C22×C4—222no—
579C22×C4—222no—
580C22×C4—222no—
581C22×C4—222no—
582C22×C4—221no—
583C22×C4—221no—
584C22×C4—222no—
585C22×C4—222no—
586C22×C4—222no—
587C22×C4—222no—
588C22×C4—222no—
589C22×C4—228no—
590C22×C4—222no—
591C22×C4—222no—
592C22×C4—222no—
593C22×C4—222no—
594C22×C4—222no—
595C22×C4—222no—
596C22×C4—222no—
597C22×C4—444no—
598C22×C4—444no—
599C22×C4—444no—
600C22×C4—444no—
601C22×C4—448no—
602C22×C4—448no—
603C22×C4—448no—
604C22×C4—448no—
605C22×C4—448no—
606C22×C4—448no—
607C22×C4—448no—
608C22×C4—448no—
609C22×C4—448no—
610C22×C4—448no—
611C22×C4C2×C4×D1112yes—
612C22×C4C2×C4×D1112yes—
613C22×C4C2×C4×D1112yes—
614C22×C4#433914yes—
615C22×C4D4×D1112yes—
616C22×C4D4×D1112yes—
617C22×C4D4×D1112yes—
618C22×C4Q8×D1112yes—
619C4⋊C4—228no—
620C4⋊C4—448no—
621C22⋊C4—228no—
622C22⋊C4—228no—
623C22⋊C4—448no—
624C22⋊C4—448no—
625C22⋊C4—448no—
626C42—28no—
627C11#1396011yescharacteristic, complemented, Sylow
628C23—114no—
629C23—114no—
630C23—114no—
631C23—114no—
632C23—114no—
633C23—114no—
634C23—114no—
635C23—114no—
636C23—224no—
637C23—224no—
638C23—222no—
639C23—222no—
640C23—222no—
641C23—222no—
642C23—224no—
643C23—224no—
644C23—224no—
645C23—224no—
646C23—224no—
647C23—224no—
648C23—224no—
649C23—224no—
650C23—224no—
651C23—224no—
652C23—222no—
653C23—222no—
654C23—222no—
655C23—222no—
656C23—222no—
657C23—222no—
658C23—224no—
659C23—224no—
660C23—222no—
661C23—222no—
662C23—222no—
663C23—222no—
664C23—224no—
665C23—224no—
666C23—442no—
667C23—442no—
668C23—442no—
669C23—442no—
670C23—442no—
671C23—442no—
672C23—442no—
673C23—442no—
674C23C22×C4×D1111yescharacteristic
675C23C2×#433912yes—
676C23C2×D4×D1111yescharacteristic
677C23C2×D4×D1111yescharacteristic
678C23C2×D4×D1111yescharacteristic
679C23C2×Q8×D1111yescharacteristic
680C23#41×D1111yescharacteristic
681C23#41×D1112yes—
682C23#41×D1111yescharacteristic
683C23#6704212yes—
684C23#6704212yes—
685D4—2232no—
686C2×C4—22no—
687C2×C4—22no—
688C2×C4—22no—
689C2×C4—22no—
690C2×C4—22no—
691C2×C4—22no—
692C2×C4—22no—
693C2×C4—22no—
694C2×C4—24no—
695C2×C4—24no—
696C2×C4—22no—
697C2×C4—22no—
698C2×C4—22no—
699C2×C4—24no—
700C2×C4—24no—
701C2×C4—24no—
702C2×C4—42no—
703C2×C4—42no—
704C2×C4—42no—
705C2×C4—42no—
706C2×C4—42no—
707C2×C4—42no—
708C2×C4—42no—
709C2×C4—42no—
710C2×C4—42no—
711C2×C4—42no—
712C2×C4—42no—
713C2×C4—42no—
714C2×C4—42no—
715C2×C4—114no—
716C2×C4—222no—
717C2×C4—222no—
718C2×C4—224no—
719C2×C4—224no—
720C2×C4—224no—
721C2×C4—222no—
722C2×C4—222no—
723C2×C4—222no—
724C2×C4—224no—
725C2×C4—224no—
726C2×C4—4416no—
727C2×C4—4416no—
728C2×C4—4432no—
729C2×C4—442no—
730C2×C4—442no—
731C2×C4—442no—
732C2×C4—442no—
733C2×C4—442no—
734C2×C4—442no—
735C2×C4—442no—
736C2×C4—442no—
737C2×C4—442no—
738C2×C4—442no—
739C2×C4—442no—
740C2×C4—442no—
741C2×C4—442no—
742C2×C4C22⋊C4×D1114yes—
743C2×C4C4⋊C4×D1114yes—
744C22—118no—
745C22—228no—
746C22—224no—
747C22—228no—
748C22—228no—
749C22—224no—
750C22—224no—
751C22—228no—
752C22—224no—
753C22—224no—
754C22—224no—
755C22—224no—
756C22—224no—
757C22—224no—
758C22—444no—
759C22—442no—
760C22—444no—
761C22—444no—
762C22—444no—
763C22—442no—
764C22—442no—
765C22—442no—
766C22C4×#433911yescharacteristic
767C22C2×C22⋊C4×D1111yescharacteristic
768C22C2×C4⋊C4×D1111yescharacteristic
769C22D11×#11711yescharacteristic
770C22#1062305211yescharacteristic
771C22#1062305211yescharacteristic
772C22#1062305311yescharacteristic
773C22#1062305812yes—
774C22#1062306112yes—
775C22#1062307812yes—
776C22#1062307912yes—
777C22#1062308112yes—
778C22#1062311012yes—
779C22D11×#12111yescharacteristic
780C22D11×#12111yescharacteristic
781C22D11×C22⋊Q811yescharacteristic
782C22D11×C22⋊Q811yescharacteristic
783C22#1062318412yes—
784C22#1062318412yes—
785C22#1062320712yes—
786C22#1062322112yes—
787C22#1062323612yes—
788C22#1062324012yes—
789C4—24no—
790C4—24no—
791C4—44no—
792C4—42no—
793C4—82no—
794C4—224no—
795C4—442no—
796C4—444no—
797C4—882no—
798C2—228no—
799C2—444no—
800C2D11×#38011yescharacteristic
801C2#1307110211yescharacteristic
802C2#1307119311yescharacteristic
803C2#1307152411yescharacteristic
804C2#1307152711yescharacteristic
805C2#1307154911yescharacteristic
806C2#1307155711yescharacteristic
807C2#1307351012yes—
808C2#1307358112yes—
809C2#1307379512yes—
810C2#1307396712yes—
subgroupG/H
center, FrattiniC24C23×D11
commutatorC23×C11C23×C4
FittingC11×#1434C2
socle, cosocleC24×C11C24
prime radicalC23×D44C22
hypercenter#1434D11
hypocenterC11#13960
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ #1434

Complements

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

NH ≅ G/Ntype
3. C2×#10622280C2semidirect
4. C2×D11×#95C2semidirect
5. #13066868C2semidirect
6. #13066860C2semidirect
7. #13066843C2semidirect
8. (C2×D11)⋊#95C2semidirect
9. (C2×D11)⋊#95C2semidirect
10. (C2×D11)⋊#95C2semidirect
11. C11×#1434C2semidirect
26. C2×C4×D44C4semidirect
73. C22×C4×D11C2×C4semidirect
78. C2×C42×C11C2×C4semidirect
93. C2×(C2×D11)⋊C4C2×C4semidirect
96. C2×C4⋊Dic11C2×C4semidirect
197. C2×D44C4⋊C4semidirect
214. C2×C4×D11C22⋊C4semidirect
230. #1434D11semidirect
492. C2×C42C4×D11semidirect
627. C11#13960semidirect

Maximal subgroups

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

subgroupindex
C22×C4×D442
C2×#106222782
C2×#106222802
C2×D11×#952
#130668682
#130668602
#130668432
(C2×D11)⋊#952
C11×#14342
#1396011