Finite Group Databasebeta

← #14677138

Subgroups — #14677138

Order 2816.

2950 conjugacy classes of subgroups.

The subgroup lattice has 850 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×D4×Dic11C211yesmaximal, characteristic
2C23×C4⋊Dic11C211yesmaximal, characteristic, complemented
3C2×#10622833C211yesmaximal, characteristic
4C2×#10622563C211yesmaximal, characteristic, complemented
5C2×#10622563C212yesmaximal, complemented
6#13066881C212yesmaximal, complemented
7#13066861C212yesmaximal, complemented
8#13066850C212yesmaximal, complemented
9#13066839C211yesmaximal, characteristic, complemented
10#13066838C211yesmaximal, characteristic, complemented
11C2×C11×#386C211yesmaximal, characteristic
12C23×D4×C11C2211yescharacteristic
13C24×C4×C11C2211yescharacteristic
14C24×Dic11C2211yescharacteristic
15C24×Dic11C2211yescharacteristic
16C24×Dic11C2211yescharacteristic
17C22×C11×C22⋊C4C2211yescharacteristic
18C22×C11×C22⋊C4C2212yes—
19C22×C22⋊Dic11C2211yescharacteristic
20C22×C22⋊Dic11C2211yescharacteristic
21C22×C22⋊Dic11C2212yes—
22C22×C22⋊Dic11C2211yescharacteristic
23C2×D4×Dic11—24no—
24C2×D4×Dic11—24no—
25C2×D4×Dic11—24no—
26C22×C4⋊Dic11—24no—
27C22×C4⋊Dic11—28no—
28C22×C4⋊Dic11C2212yes—
29C22×C4⋊Dic11C2211yescharacteristic
30C22×C4⋊Dic11C2212yes—
31C22×C4⋊Dic11C2212yes—
32C22×C4×Dic11C2211yescharacteristic
33C11×#386C418yescomplemented
34C2×C11×#95C2212yes—
35#10622833—24no—
36C2×C11⋊#95C2212yes—
37C2×C11⋊#95C2212yes—
38C2×C11⋊#95C2212yes—
39C2×C11⋊#95C2212yes—
40C2×C11⋊#95C2212yes—
41C2×C11⋊#95C2212yes—
42#10622563—24no—
43#10622563—28no—
44C25×C11C2311yescharacteristic
45C25×C11C2311yescharacteristic
46C22×D4×C11—22no—
47C22×D4×C11—22no—
48C22×D4×C11—22no—
49C22×D4×C11—22no—
50C22×D4×C11C2×C414yes—
51C22×D4×C11D414yes—
52C22×D4×C11Q814yes—
53C23×C4×C11—22no—
54C23×C4×C11—22no—
55C23×C4×C11—24no—
56C23×C4×C11—24no—
57C23×C4×C11C2×C414yescomplemented
58C23×C4×C11C2312yes—
59C23×C4×C11C2311yescharacteristic
60C23×C4×C11C2312yes—
61C23×Dic11—22no—
62C23×Dic11—22no—
63C23×Dic11—22no—
64C23×Dic11—22no—
65C23×Dic11—24no—
66C23×Dic11—24no—
67C23×Dic11—22no—
68C23×Dic11—22no—
69C23×Dic11—22no—
70C23×Dic11—22no—
71C23×Dic11—24no—
72C23×Dic11—42no—
73C23×Dic11—42no—
74C23×Dic11—42no—
75C23×Dic11D414yes—
76C23×Dic11C2312yes—
77C23×Dic11C2311yescharacteristic
78C23×Dic11C2311yescharacteristic
79C23×Dic11C2312yes—
80C23×Dic11C2311yescharacteristic
81C23×Dic11C2311yescharacteristic
82C2×C11×C22⋊C4—22no—
83C2×C11×C22⋊C4—22no—
84C2×C11×C22⋊C4—24no—
85C2×C11×C22⋊C4—24no—
86C2×C11×C22⋊C4C2×C414yescomplemented
87C2×C11×C22⋊C4C2×C418yescomplemented
88C2×C22⋊Dic11—22no—
89C2×C22⋊Dic11—22no—
90C2×C22⋊Dic11—22no—
91C2×C22⋊Dic11—22no—
92C2×C22⋊Dic11—22no—
93C2×C22⋊Dic11—24no—
94C2×C22⋊Dic11—22no—
95C2×C22⋊Dic11—22no—
96C2×C22⋊Dic11—22no—
97C2×C22⋊Dic11—24no—
98C2×C22⋊Dic11—42no—
99C2×C22⋊Dic11D414yes—
100D4×Dic11—232no—
101C2×C4⋊Dic11—232no—
102C2×C4⋊Dic11—24no—
103C2×C4⋊Dic11—22no—
104C2×C4⋊Dic11—24no—
105C2×C4⋊Dic11—24no—
106C2×C4⋊Dic11—24no—
107C2×C4⋊Dic11—24no—
108C2×C4⋊Dic11—22no—
109C2×C4⋊Dic11—22no—
110C2×C4⋊Dic11—24no—
111C2×C4⋊Dic11—24no—
112C2×C4⋊Dic11—42no—
113C2×C4⋊Dic11D418yescomplemented
114C2×C4×Dic11—22no—
115C2×C4×Dic11—22no—
116C2×C4×Dic11—22no—
117C11×#95C2×C418yescomplemented
118C11⋊#95—24no—
119C11⋊#95—24no—
120C11⋊#95—24no—
121C11⋊#95—24no—
122C11⋊#95—24no—
123C11⋊#95—42no—
124#14015—111nomaximal, Sylow
125C24×C11—22no—
126C24×C11—22no—
127C24×C11—22no—
128C24×C11—22no—
129C24×C11—22no—
130C24×C11—21no—
131C24×C11—21no—
132C24×C11—22no—
133C24×C11—21no—
134C24×C11—21no—
135C24×C11—22no—
136C24×C11—22no—
137C24×C11C22×C412yes—
138C24×C11C22×C412yes—
139C24×C11C2×D412yes—
140C24×C11C2×D412yes—
141C24×C11C2×D412yes—
142C24×C11C2×D412yes—
143C24×C11C2×Q812yes—
144C24×C11C2×Q812yes—
145C24×C11#4112yes—
146C24×C11#4112yes—
147C24×C11C2411yescharacteristic
148C2×D4×C11—28no—
149C2×D4×C11—28no—
150C2×D4×C11—28no—
151C2×D4×C11—28no—
152C2×D4×C11—28no—
153C2×D4×C11—28no—
154C2×D4×C11C4⋊C4116yescomplemented
155C22×C4×C11—28no—
156C22×C4×C11—216no—
157C22×C4×C11—28no—
158C22×C4×C11—28no—
159C22×C4×C11—21no—
160C22×C4×C11—21no—
161C22×C4×C11—22no—
162C22×C4×C11—22no—
163C22×C4×C11—22no—
164C22×C4×C11—22no—
165C22×C4×C11—21no—
166C22×C4×C11—21no—
167C22×C4×C11—216no—
168C22×C4×C11—22no—
169C22×C4×C11—22no—
170C22×C4×C11—22no—
171C22×C4×C11—22no—
172C22×C4×C11—22no—
173C22×C4×C11—22no—
174C22×C4×C11C22×C414yes—
175C22×C4×C11C22×C412yes—
176C22×C4×C11C22×C414yes—
177C22×C4×C11C2×D412yes—
178C22×C4×C11C2×D414yes—
179C22×C4×C11C2×Q812yes—
180C22×C4×C11#4114yes—
181C22×Dic11—28no—
182C22×Dic11—28no—
183C22×Dic11—28no—
184C22×Dic11—28no—
185C22×Dic11—21no—
186C22×Dic11—21no—
187C22×Dic11—22no—
188C22×Dic11—22no—
189C22×Dic11—22no—
190C22×Dic11—21no—
191C22×Dic11—21no—
192C22×Dic11—22no—
193C22×Dic11—22no—
194C22×Dic11—22no—
195C22×Dic11—21no—
196C22×Dic11—21no—
197C22×Dic11—21no—
198C22×Dic11—21no—
199C22×Dic11—22no—
200C22×Dic11—22no—
201C22×Dic11—22no—
202C22×Dic11—22no—
203C22×Dic11—22no—
204C22×Dic11—22no—
205C22×Dic11—22no—
206C22×Dic11—22no—
207C22×Dic11—22no—
208C22×Dic11—22no—
209C22×Dic11—22no—
210C22×Dic11—22no—
211C22×Dic11—22no—
212C22×Dic11—22no—
213C22×Dic11—44no—
214C22×Dic11—48no—
215C22×Dic11—48no—
216C22×Dic11—48no—
217C22×Dic11—48no—
218C22×Dic11—48no—
219C22×Dic11—44no—
220C22×Dic11—48no—
221C22×Dic11—44no—
222C22×Dic11—44no—
223C22×Dic11—44no—
224C22×Dic11C2×D412yes—
225C22×Dic11C2×D412yes—
226C22×Dic11C2×D412yes—
227C22×Dic11C2×D414yes—
228C22×Dic11C2×D414yes—
229C22×Dic11C2×D412yes—
230C11×C22⋊C4—28no—
231C11×C22⋊C4—216no—
232C22⋊Dic11—28no—
233C22⋊Dic11—28no—
234C22⋊Dic11—48no—
235C22⋊Dic11—44no—
236C4⋊Dic11—216no—
237C4⋊Dic11—28no—
238C4⋊Dic11—216no—
239C4⋊Dic11—48no—
240C4×Dic11—28no—
241C22×C4×D4—111no—
242C23×C4⋊C4—111no—
243C2×#386—111no—
244C2×#386D1111yescharacteristic
245C2×#385—111no—
246C2×#385—112no—
247#1444—112no—
248#1439—112no—
249#1436—112no—
250C22⋊#95—111no—
251C22⋊#95—111no—
252C23×C11—24no—
253C23×C11—24no—
254C23×C11—22no—
255C23×C11—22no—
256C23×C11—24no—
257C23×C11—22no—
258C23×C11—22no—
259C23×C11—24no—
260C23×C11—24no—
261C23×C11—24no—
262C23×C11—24no—
263C23×C11—24no—
264C23×C11—24no—
265C23×C11—24no—
266C23×C11—24no—
267C23×C11—24no—
268C23×C11—24no—
269C23×C11—22no—
270C23×C11—22no—
271C23×C11—24no—
272C23×C11—22no—
273C23×C11—22no—
274C23×C11—22no—
275C23×C11—22no—
276C23×C11—24no—
277C23×C11—24no—
278C23×C11—24no—
279C23×C11—24no—
280C23×C11—41no—
281C23×C11—41no—
282C23×C11—42no—
283C23×C11—41no—
284C23×C11—41no—
285C23×C11—42no—
286C23×C11—42no—
287C23×C11—42no—
288C23×C11—42no—
289C23×C11—42no—
290C23×C11C2×C4⋊C414yes—
291C23×C11C2×C4⋊C414yescomplemented
292C23×C11C4×D414yes—
293C23×C11C4×D414yes—
294C23×C11#12014yes—
295C23×C11C22⋊Q814yes—
296C23×C11C22⋊Q814yes—
297C23×C11#12314yes—
298C23×C11C23×C411yescharacteristic
299C23×C11C22×D411yescharacteristic
300C23×C11C22×D411yescharacteristic
301C23×C11C22×D411yescharacteristic
302C23×C11C22×D412yes—
303C23×C11C22×Q811yescharacteristic
304C23×C11C2×#4111yescharacteristic
305C23×C11C2×#4111yescharacteristic
306C23×C11C2×#4112yes—
307C23×C11H(5,𝔽2)12yes—
308C23×C112−1+412yes—
309D4×C11—232no—
310C2×C4×C11—232no—
311C2×C4×C11—24no—
312C2×C4×C11—24no—
313C2×C4×C11—22no—
314C2×C4×C11—22no—
315C2×C4×C11—22no—
316C2×C4×C11—24no—
317C2×C4×C11—22no—
318C2×C4×C11—22no—
319C2×C4×C11—22no—
320C2×C4×C11—24no—
321C2×C4×C11—24no—
322C2×C4×C11—24no—
323C2×C4×C11—24no—
324C2×C4×C11—24no—
325C2×C4×C11—24no—
326C2×C4×C11—42no—
327C2×C4×C11—42no—
328C2×C4×C11—42no—
329C2×C4×C11—42no—
330C2×C4×C11C2×C4⋊C414yescomplemented
331C2×C4×C11C4×D418yescomplemented
332C2×Dic11—22no—
333C2×Dic11—22no—
334C2×Dic11—24no—
335C2×Dic11—24no—
336C2×Dic11—22no—
337C2×Dic11—22no—
338C2×Dic11—24no—
339C2×Dic11—22no—
340C2×Dic11—22no—
341C2×Dic11—22no—
342C2×Dic11—24no—
343C2×Dic11—24no—
344C2×Dic11—24no—
345C2×Dic11—24no—
346C2×Dic11—416no—
347C2×Dic11—416no—
348C2×Dic11—416no—
349C2×Dic11—42no—
350C2×Dic11—41no—
351C2×Dic11—41no—
352C2×Dic11—42no—
353C2×Dic11—41no—
354C2×Dic11—41no—
355C2×Dic11—42no—
356C2×Dic11—42no—
357C2×Dic11—42no—
358C2×Dic11—42no—
359C2×Dic11—42no—
360C2×Dic11—42no—
361C2×Dic11—42no—
362C2×Dic11—42no—
363C2×Dic11—42no—
364C2×Dic11—42no—
365C2×Dic11—42no—
366C2×Dic11—42no—
367C2×Dic11—42no—
368C2×Dic11#12014yes—
369C23×D4C2×D1111yescharacteristic
370C24×C4—111no—
371C24×C4—111no—
372C24×C4—111no—
373C24×C4C2×D1111yescharacteristic
374C2×C4×D4—224no—
375C2×C4×D4—224no—
376C2×C4×D4—224no—
377C22×C4⋊C4—112no—
378C22×C4⋊C4—112no—
379C22×C4⋊C4—111no—
380C22×C4⋊C4—112no—
381C22×C4⋊C4—228no—
382C22×C4⋊C4—224no—
383C22×C22⋊C4—111no—
384C22×C22⋊C4—111no—
385C22×C22⋊C4—111no—
386C22×C22⋊C4—112no—
387C22×C22⋊C4C2×D1111yescharacteristic
388C22×C22⋊C4C2×D1112yes—
389C22×C42—111no—
390#386—224no—
391#386Dic1118yescomplemented
392#385—224no—
393#385—228no—
394C2×#95—112no—
395C2×#95—112no—
396C2×#95—112no—
397C2×#95—112no—
398C2×#95—112no—
399C2×#95—112no—
400C2×#95C2×D1112yes—
401C22×C11—24no—
402C22×C11—24no—
403C22×C11—28no—
404C22×C11—28no—
405C22×C11—24no—
406C22×C11—24no—
407C22×C11—24no—
408C22×C11—28no—
409C22×C11—28no—
410C22×C11—24no—
411C22×C11—28no—
412C22×C11—24no—
413C22×C11—42no—
414C22×C11—42no—
415C22×C11—44no—
416C22×C11—42no—
417C22×C11—42no—
418C22×C11—42no—
419C22×C11—44no—
420C22×C11—44no—
421C22×C11—42no—
422C22×C11#38518yescomplemented
423C22×C11C22×C4⋊C411yescharacteristic
424C22×C11C2×C4×D411yescharacteristic
425C22×C11C2×C4×D412yes—
426C22×C11C2×C4×D411yescharacteristic
427C22×C11#52012yes—
428C22×C11C2×#12011yescharacteristic
429C22×C11C2×#12011yescharacteristic
430C22×C11C2×C22⋊Q811yescharacteristic
431C22×C11C2×C22⋊Q811yescharacteristic
432C22×C11C2×#12311yescharacteristic
433C22×C11#52511yescharacteristic
434C22×C11#52512yes—
435C22×C11#53411yescharacteristic
436C22×C11#53611yescharacteristic
437C22×C11#53912yes—
438C22×C11D4212yes—
439C22×C11D4212yes—
440C22×C11#54712yes—
441C22×C11#54712yes—
442C22×C11#54812yes—
443C22×C11D4×Q812yes—
444C22×C11#55312yes—
445C22×C11#55412yes—
446C4×C11—24no—
447C4×C11—28no—
448C4×C11—44no—
449Dic11—24no—
450Dic11—42no—
451Dic11—44no—
452Dic11—42no—
453Dic11—42no—
454Dic11—82no—
455C25C22×D1111yescharacteristic
456C25C22×D1111yescharacteristic
457C22×D4—22no—
458C22×D4—22no—
459C22×D4—22no—
460C22×D4—22no—
461C22×D4Dic2214yes—
462C22×D4D4414yes—
463C22×D4C2×Dic1114yes—
464C23×C4—22no—
465C23×C4—22no—
466C23×C4—24no—
467C23×C4—24no—
468C23×C4—111no—
469C23×C4—111no—
470C23×C4—111no—
471C23×C4—112no—
472C23×C4—111no—
473C23×C4—114no—
474C23×C4—112no—
475C23×C4—224no—
476C23×C4—224no—
477C23×C4—222no—
478C23×C4—222no—
479C23×C4—224no—
480C23×C4—222no—
481C23×C4—222no—
482C23×C4—222no—
483C23×C4—222no—
484C23×C4—222no—
485C23×C4—222no—
486C23×C4—442no—
487C23×C4—442no—
488C23×C4—442no—
489C23×C4C2×Dic1114yescomplemented
490C23×C4C22×D1112yes—
491C23×C4C22×D1111yescharacteristic
492C23×C4C22×D1112yes—
493C4×D4—2232no—
494C2×C4⋊C4—118no—
495C2×C4⋊C4—224no—
496C2×C4⋊C4—224no—
497C2×C4⋊C4—224no—
498C2×C4⋊C4—224no—
499C2×C4⋊C4—222no—
500C2×C4⋊C4—222no—
501C2×C4⋊C4—2232no—
502C2×C4⋊C4—222no—
503C2×C4⋊C4—224no—
504C2×C4⋊C4—224no—
505C2×C4⋊C4—224no—
506C2×C4⋊C4—442no—
507C2×C22⋊C4—22no—
508C2×C22⋊C4—22no—
509C2×C22⋊C4—24no—
510C2×C22⋊C4—24no—
511C2×C22⋊C4—114no—
512C2×C22⋊C4—222no—
513C2×C22⋊C4—222no—
514C2×C22⋊C4—222no—
515C2×C22⋊C4—222no—
516C2×C22⋊C4—222no—
517C2×C22⋊C4—224no—
518C2×C22⋊C4—224no—
519C2×C22⋊C4—222no—
520C2×C22⋊C4—222no—
521C2×C22⋊C4—222no—
522C2×C22⋊C4—442no—
523C2×C22⋊C4C2×Dic1114yescomplemented
524C2×C22⋊C4C2×Dic1118yescomplemented
525C2×C42—222no—
526C2×C42—222no—
527C2×C42—222no—
528#95—224no—
529#95—224no—
530#95—224no—
531#95—224no—
532#95—224no—
533#95—442no—
534#95C2×Dic1118yescomplemented
535C2×C11—28no—
536C2×C11—44no—
537C2×C11C2×#38511yescharacteristic
538C2×C11C4×#12011yescharacteristic
539C2×C11#232211yescharacteristic
540C2×C11D4×C4⋊C412yes—
541C2×C11#236112yes—
542C2×C11#240311yescharacteristic
543C2×C11#240611yescharacteristic
544C2×C11#240911yescharacteristic
545C2×C11#244312yes—
546C2×C11#244912yes—
547C2×C11#257911yescharacteristic
548C24—22no—
549C24—22no—
550C24—22no—
551C24—22no—
552C24—22no—
553C24—21no—
554C24—21no—
555C24—22no—
556C24—21no—
557C24—21no—
558C24—22no—
559C24—22no—
560C24C2×Dic2212yes—
561C24C2×Dic2212yes—
562C24C2×D4412yes—
563C24C2×D4412yes—
564C24D4×D1112yes—
565C24D4×D1112yes—
566C24#434112yes—
567C24#434112yes—
568C24C22×Dic1112yes—
569C24C22×Dic1112yes—
570C24C23×D1111yescharacteristic
571C2×D4—28no—
572C2×D4—28no—
573C2×D4—28no—
574C2×D4—28no—
575C2×D4—28no—
576C2×D4—28no—
577C2×D4C4⋊Dic11116yescomplemented
578C22×C4—28no—
579C22×C4—216no—
580C22×C4—28no—
581C22×C4—28no—
582C22×C4—21no—
583C22×C4—21no—
584C22×C4—22no—
585C22×C4—22no—
586C22×C4—22no—
587C22×C4—22no—
588C22×C4—21no—
589C22×C4—21no—
590C22×C4—216no—
591C22×C4—22no—
592C22×C4—22no—
593C22×C4—22no—
594C22×C4—22no—
595C22×C4—22no—
596C22×C4—22no—
597C22×C4—114no—
598C22×C4—112no—
599C22×C4—112no—
600C22×C4—112no—
601C22×C4—114no—
602C22×C4—112no—
603C22×C4—228no—
604C22×C4—221no—
605C22×C4—221no—
606C22×C4—222no—
607C22×C4—228no—
608C22×C4—228no—
609C22×C4—228no—
610C22×C4—222no—
611C22×C4—221no—
612C22×C4—221no—
613C22×C4—221no—
614C22×C4—222no—
615C22×C4—222no—
616C22×C4—221no—
617C22×C4—221no—
618C22×C4—221no—
619C22×C4—222no—
620C22×C4—222no—
621C22×C4—222no—
622C22×C4—222no—
623C22×C4—222no—
624C22×C4—222no—
625C22×C4—222no—
626C22×C4—222no—
627C22×C4—222no—
628C22×C4—222no—
629C22×C4—222no—
630C22×C4—222no—
631C22×C4—222no—
632C22×C4—222no—
633C22×C4—222no—
634C22×C4—222no—
635C22×C4—444no—
636C22×C4—444no—
637C22×C4—448no—
638C22×C4—448no—
639C22×C4—448no—
640C22×C4—448no—
641C22×C4—448no—
642C22×C4—448no—
643C22×C4—444no—
644C22×C4—444no—
645C22×C4—444no—
646C22×C4C2×Dic2212yes—
647C22×C4C2×D4412yes—
648C22×C4D4×D1114yes—
649C22×C4#434114yes—
650C22×C4C22×Dic1114yes—
651C22×C4C22×Dic1112yes—
652C22×C4C22×Dic1114yes—
653C4⋊C4—2216no—
654C4⋊C4—2216no—
655C4⋊C4—228no—
656C4⋊C4—448no—
657C22⋊C4—28no—
658C22⋊C4—216no—
659C22⋊C4—228no—
660C22⋊C4—228no—
661C22⋊C4—448no—
662C22⋊C4—444no—
663C42—228no—
664C11#1401511yescharacteristic, complemented, Sylow
665C23—24no—
666C23—24no—
667C23—24no—
668C23—24no—
669C23—24no—
670C23—24no—
671C23—22no—
672C23—24no—
673C23—22no—
674C23—24no—
675C23—24no—
676C23—24no—
677C23—24no—
678C23—22no—
679C23—22no—
680C23—24no—
681C23—22no—
682C23—22no—
683C23—22no—
684C23—22no—
685C23—24no—
686C23—24no—
687C23—22no—
688C23—22no—
689C23—24no—
690C23—24no—
691C23—24no—
692C23—24no—
693C23—41no—
694C23—42no—
695C23—41no—
696C23—42no—
697C23—42no—
698C23—42no—
699C23—42no—
700C23—41no—
701C23—41no—
702C23—42no—
703C23#6693114yes—
704C23#6693114yes—
705C23#6693514yes—
706C23#6693914yes—
707C23C2×C4⋊Dic1114yes—
708C23C2×C4⋊Dic1114yescomplemented
709C23D4×Dic1114yes—
710C23D4×Dic1114yes—
711C23C22×Dic2211yescharacteristic
712C23C22×D4411yescharacteristic
713C23C2×D4×D1111yescharacteristic
714C23C2×D4×D1111yescharacteristic
715C23C2×D4×D1112yes—
716C23C2×#434111yescharacteristic
717C23C2×#434111yescharacteristic
718C23C2×#434112yes—
719C23#6704212yes—
720C23#6704312yes—
721C23C23×Dic1111yescharacteristic
722D4—232no—
723C2×C4—232no—
724C2×C4—22no—
725C2×C4—22no—
726C2×C4—22no—
727C2×C4—22no—
728C2×C4—24no—
729C2×C4—24no—
730C2×C4—22no—
731C2×C4—22no—
732C2×C4—24no—
733C2×C4—24no—
734C2×C4—24no—
735C2×C4—24no—
736C2×C4—24no—
737C2×C4—24no—
738C2×C4—24no—
739C2×C4—42no—
740C2×C4—42no—
741C2×C4—42no—
742C2×C4—42no—
743C2×C4—114no—
744C2×C4—222no—
745C2×C4—224no—
746C2×C4—224no—
747C2×C4—222no—
748C2×C4—222no—
749C2×C4—222no—
750C2×C4—222no—
751C2×C4—224no—
752C2×C4—224no—
753C2×C4—222no—
754C2×C4—224no—
755C2×C4—224no—
756C2×C4—224no—
757C2×C4—222no—
758C2×C4—4416no—
759C2×C4—4416no—
760C2×C4—4416no—
761C2×C4—442no—
762C2×C4—442no—
763C2×C4—442no—
764C2×C4—442no—
765C2×C4—442no—
766C2×C4—441no—
767C2×C4—441no—
768C2×C4—442no—
769C2×C4—442no—
770C2×C4—441no—
771C2×C4—441no—
772C2×C4—442no—
773C2×C4—442no—
774C2×C4—442no—
775C2×C4—442no—
776C2×C4—442no—
777C2×C4—442no—
778C2×C4—442no—
779C2×C4—442no—
780C2×C4C2×C4⋊Dic1114yescomplemented
781C2×C4D4×Dic1118yescomplemented
782C22—24no—
783C22—28no—
784C22—24no—
785C22—28no—
786C22—24no—
787C22—24no—
788C22—24no—
789C22—28no—
790C22—24no—
791C22—28no—
792C22—28no—
793C22—24no—
794C22—42no—
795C22—44no—
796C22—42no—
797C22—44no—
798C22—42no—
799C22—42no—
800C22—42no—
801C22—42no—
802C22—44no—
803C22#1062256318yescomplemented
804C22C2×#6693111yescharacteristic
805C22C2×#6693111yescharacteristic
806C22C2×#6693511yescharacteristic
807C22C2×#6693911yescharacteristic
808C22D4×Dic2212yes—
809C22#1062307412yes—
810C22D4×D4412yes—
811C22#1062308612yes—
812C22#1062311711yescharacteristic
813C22#1062311712yes—
814C22D11×#12011yescharacteristic
815C22#1062312912yes—
816C22#1062314012yes—
817C22#1062314212yes—
818C22#1062314912yes—
819C22#1062317911yescharacteristic
820C22#1062318411yescharacteristic
821C22#1062319612yes—
822C22C22×C4⋊Dic1111yescharacteristic
823C22C2×D4×Dic1112yes—
824C22C2×D4×Dic1111yescharacteristic
825C22C2×D4×Dic1111yescharacteristic
826C22#1062335812yes—
827C4—28no—
828C4—24no—
829C4—44no—
830C4—224no—
831C4—442no—
832C4—442no—
833C4—444no—
834C4—442no—
835C4—882no—
836C2—28no—
837C2—44no—
838C2C2×#1062256311yescharacteristic
839C2#120×Dic1111yescharacteristic
840C2#1307128811yescharacteristic
841C2D4×C4⋊Dic1112yes—
842C2#1307163612yes—
843C2#1307192811yescharacteristic
844C2#1307195011yescharacteristic
845C2#1307197811yescharacteristic
846C2#1307234912yes—
847C2#1307243112yes—
848C2#1307396011yescharacteristic
subgroupG/H
center, FrattiniC24C23×D11
commutatorC23×C11C23×C4
FittingC2×C11×#386C2
socle, cosocleC24×C11C24
prime radicalC23×D4×C11C22
hypercenterC2×#386D11
hypocenterC11#14015
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ C2×#386

Complements

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

NH ≅ G/Ntype
2. C23×C4⋊Dic11C2semidirect
4. C2×#10622563C2semidirect
5. C2×#10622563C2semidirect
6. #13066881C2semidirect
7. #13066861C2semidirect
8. #13066850C2semidirect
9. #13066839C2semidirect
10. #13066838C2semidirect
33. C11×#386C4semidirect
57. C23×C4×C11C2×C4semidirect
86. C2×C11×C22⋊C4C2×C4semidirect
87. C2×C11×C22⋊C4C2×C4semidirect
113. C2×C4⋊Dic11D4semidirect
117. C11×#95C2×C4semidirect
154. C2×D4×C11C4⋊C4semidirect
291. C23×C11C2×C4⋊C4semidirect
330. C2×C4×C11C2×C4⋊C4semidirect
331. C2×C4×C11C4×D4semidirect
391. #386Dic11semidirect
422. C22×C11#385semidirect
489. C23×C4C2×Dic11semidirect
523. C2×C22⋊C4C2×Dic11semidirect
524. C2×C22⋊C4C2×Dic11semidirect
534. #95C2×Dic11semidirect
577. C2×D4C4⋊Dic11semidirect
664. C11#14015semidirect
708. C23C2×C4⋊Dic11semidirect
780. C2×C4C2×C4⋊Dic11semidirect
781. C2×C4D4×Dic11semidirect
803. C22#10622563semidirect

Maximal subgroups

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

subgroupindex
C22×D4×Dic112
C23×C4⋊Dic112
C2×#106228332
C2×#106225632
#130668812
#130668612
#130668502
#130668392
#130668382
C2×C11×#3862
#1401511