Finite Group Databasebeta

← #14677132

Subgroups — #14677132

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×(C22⋊D11)⋊C4C211yesmaximal, characteristic
2C23×C4⋊Dic11C211yesmaximal, characteristic, complemented
3C2×#10622826C211yesmaximal, characteristic
4C2×#10622571C211yesmaximal, characteristic
5C2×#10622281C212yesmaximal, complemented
6C2×#10622559C211yesmaximal, characteristic, complemented
7#13066880C212yesmaximal, complemented
8#13066862C212yesmaximal, complemented
9#13066850C212yesmaximal, complemented
10#13066838C211yesmaximal, characteristic, complemented
11C11×C22⋊#95C211yesmaximal, characteristic, complemented
12C24×C4×C11C2211yescharacteristic
13C23×C22⋊D11C2211yescharacteristic
14C24×Dic11C2211yescharacteristic
15C24×Dic11C2211yescharacteristic
16C23×C4×D11C2211yescharacteristic
17C22×C11×C22⋊C4C2211yescharacteristic
18C22×C11×C22⋊C4C2211yescharacteristic
19C22×C22⋊Dic11C2211yescharacteristic
20C22×(C2×D11)⋊C4C2211yescharacteristic
21C22×(C2×D11)⋊C4C2212yes—
22C22×(C2×D11)⋊C4C2212yes—
23C22×C4⋊Dic11—24no—
24C22×C4⋊Dic11—28no—
25C22×C4⋊Dic11C2212yes—
26C22×C4⋊Dic11C2212yes—
27C22×Dic11⋊C4C2211yescharacteristic
28C22×Dic11⋊C4C2212yes—
29C22×C4×Dic11C2211yescharacteristic
30C2×(C22⋊D11)⋊C4—24no—
31C2×(C22⋊D11)⋊C4—24no—
32C2×(C22⋊D11)⋊C4—24no—
33C2×C11×#95C2212yes—
34C2×C11×#95C2212yes—
35#10622826C418yescomplemented
36C2×C11⋊#95C2212yes—
37C2×C11⋊#95C2212yes—
38C2×C11⋊#95C2212yes—
39C2×C11⋊#95C2212yes—
40C2×C11⋊#95C2212yes—
41#10622571—24no—
42#10622559—24no—
43#10622281—28no—
44C25×C11C2311yescharacteristic
45C24×D11C2311yescharacteristic
46C23×C4×C11—22no—
47C23×C4×C11—22no—
48C23×C4×C11—24no—
49C23×C4×C11—24no—
50C23×C4×C11C2×C414yescomplemented
51C23×C4×C11C2312yes—
52C23×C4×C11C2311yescharacteristic
53C23×C4×C11C2311yescharacteristic
54C23×C4×C11C2312yes—
55C22×C22⋊D11—22no—
56C22×C22⋊D11—22no—
57C22×C22⋊D11—22no—
58C22×C22⋊D11—22no—
59C22×C22⋊D11C2×C414yes—
60C22×C22⋊D11D414yes—
61C22×C22⋊D11Q814yes—
62C23×Dic11—22no—
63C23×Dic11—22no—
64C23×Dic11—22no—
65C23×Dic11—24no—
66C23×Dic11—24no—
67C23×Dic11—22no—
68C23×Dic11—22no—
69C23×Dic11—42no—
70C23×Dic11—42no—
71C23×Dic11D414yes—
72C23×Dic11C2312yes—
73C23×Dic11C2312yes—
74C23×Dic11C2311yescharacteristic
75C23×Dic11C2311yescharacteristic
76C23×Dic11C2311yescharacteristic
77C22×C4×D11—22no—
78C22×C4×D11—22no—
79C22×C4×D11—22no—
80C22×C4×D11—24no—
81C22×C4×D11—42no—
82C2×C11×C22⋊C4—22no—
83C2×C11×C22⋊C4—22no—
84C2×C11×C22⋊C4—22no—
85C2×C11×C22⋊C4—22no—
86C2×C11×C22⋊C4—22no—
87C2×C11×C22⋊C4D414yes—
88C2×C22⋊Dic11—22no—
89C2×C22⋊Dic11—22no—
90C2×C22⋊Dic11C2×C414yescomplemented
91C2×(C2×D11)⋊C4—22no—
92C2×(C2×D11)⋊C4—22no—
93C2×(C2×D11)⋊C4—24no—
94C2×(C2×D11)⋊C4—24no—
95C2×(C2×D11)⋊C4—22no—
96C2×(C2×D11)⋊C4—24no—
97C2×(C2×D11)⋊C4—24no—
98C2×(C2×D11)⋊C4—42no—
99C2×(C2×D11)⋊C4C2×C418yescomplemented
100C2×C4⋊Dic11—232no—
101C2×C4⋊Dic11—24no—
102C2×C4⋊Dic11—24no—
103C2×C4⋊Dic11—24no—
104C2×C4⋊Dic11—24no—
105C2×C4⋊Dic11—24no—
106C2×C4⋊Dic11D418yescomplemented
107C2×Dic11⋊C4—22no—
108C2×Dic11⋊C4—22no—
109C2×Dic11⋊C4—22no—
110C2×Dic11⋊C4—24no—
111C2×Dic11⋊C4—24no—
112C2×Dic11⋊C4—42no—
113C2×C4×Dic11—22no—
114C2×C4×Dic11—22no—
115C2×C4×Dic11—22no—
116(C22⋊D11)⋊C4—232no—
117C11×#95—24no—
118C11×#95—24no—
119C11⋊#95—24no—
120C11⋊#95—24no—
121C11⋊#95—24no—
122C11⋊#95—42no—
123C11⋊#95C2×C418yescomplemented
124#14015—111nomaximal, Sylow
125C24×C11—22no—
126C24×C11—22no—
127C24×C11—22no—
128C24×C11—22no—
129C24×C11C22×C412yes—
130C24×C11C2×D412yes—
131C24×C11C2×D412yes—
132C24×C11C2×D412yes—
133C24×C11C2×Q812yes—
134C24×C11#4112yes—
135C24×C11#4112yes—
136C24×C11C2411yescharacteristic
137C23×D11—22no—
138C23×D11—21no—
139C23×D11—21no—
140C23×D11—22no—
141C23×D11—21no—
142C23×D11—21no—
143C23×D11—22no—
144C23×D11—22no—
145C23×D11C22×C412yes—
146C23×D11C2×D412yes—
147C23×D11C2×Q812yes—
148C22×C4×C11—28no—
149C22×C4×C11—216no—
150C22×C4×C11—28no—
151C22×C4×C11—28no—
152C22×C4×C11—22no—
153C22×C4×C11—22no—
154C22×C4×C11—22no—
155C22×C4×C11—22no—
156C22×C4×C11—216no—
157C22×C4×C11—22no—
158C22×C4×C11—21no—
159C22×C4×C11—21no—
160C22×C4×C11—21no—
161C22×C4×C11—21no—
162C22×C4×C11—22no—
163C22×C4×C11—22no—
164C22×C4×C11—22no—
165C22×C4×C11—22no—
166C22×C4×C11—22no—
167C22×C4×C11—22no—
168C22×C4×C11—22no—
169C22×C4×C11—22no—
170C22×C4×C11—22no—
171C22×C4×C11—22no—
172C22×C4×C11C22×C414yes—
173C22×C4×C11C2×D412yes—
174C22×C4×C11C2×D412yes—
175C22×C4×C11C2×D414yes—
176C22×C4×C11#4114yes—
177C2×C22⋊D11—28no—
178C2×C22⋊D11—28no—
179C2×C22⋊D11—28no—
180C2×C22⋊D11—28no—
181C2×C22⋊D11—28no—
182C2×C22⋊D11—28no—
183C2×C22⋊D11C4⋊C4116yescomplemented
184C22×Dic11—28no—
185C22×Dic11—28no—
186C22×Dic11—28no—
187C22×Dic11—21no—
188C22×Dic11—21no—
189C22×Dic11—21no—
190C22×Dic11—21no—
191C22×Dic11—22no—
192C22×Dic11—22no—
193C22×Dic11—22no—
194C22×Dic11—22no—
195C22×Dic11—21no—
196C22×Dic11—21no—
197C22×Dic11—22no—
198C22×Dic11—22no—
199C22×Dic11—22no—
200C22×Dic11—21no—
201C22×Dic11—21no—
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—44no—
211C22×Dic11—48no—
212C22×Dic11—48no—
213C22×Dic11—48no—
214C22×Dic11—48no—
215C22×Dic11—44no—
216C22×Dic11—44no—
217C22×Dic11C22×C414yes—
218C22×Dic11C22×C412yes—
219C22×Dic11C2×D412yes—
220C22×Dic11C2×D414yes—
221C22×Dic11C2×D412yes—
222C22×Dic11C2×D414yes—
223C22×Dic11C2×D412yes—
224C22×Dic11C2×Q812yes—
225C2×C4×D11—28no—
226C2×C4×D11—48no—
227C2×C4×D11—48no—
228C2×C4×D11—44no—
229C2×C4×D11—44no—
230C11×C22⋊C4—28no—
231C11×C22⋊C4—44no—
232C22⋊Dic11—28no—
233(C2×D11)⋊C4—28no—
234(C2×D11)⋊C4—216no—
235(C2×D11)⋊C4—48no—
236C4⋊Dic11—216no—
237C4⋊Dic11—216no—
238Dic11⋊C4—28no—
239Dic11⋊C4—48no—
240C4×Dic11—28no—
241C22×C4×D4—111no—
242C23×C4⋊C4—111no—
243C2×#386—111no—
244C2×#386—111no—
245C2×#385—112no—
246C2×#385—111no—
247#1444—112no—
248#1439—112no—
249#1436—112no—
250C22⋊#95—111no—
251C22⋊#95D1111yescharacteristic, complemented
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×C11C2×C4⋊C414yes—
269C23×C11C4×D414yes—
270C23×C11C4×D414yes—
271C23×C11#12014yes—
272C23×C11C22⋊Q814yes—
273C23×C11C22⋊Q814yes—
274C23×C11#12314yes—
275C23×C11C23×C411yescharacteristic
276C23×C11C22×D411yescharacteristic
277C23×C11C22×D411yescharacteristic
278C23×C11C22×D411yescharacteristic
279C23×C11C22×D412yes—
280C23×C11C22×Q811yescharacteristic
281C23×C11C2×#4111yescharacteristic
282C23×C11C2×#4111yescharacteristic
283C23×C11C2×#4112yes—
284C23×C11H(5,𝔽2)12yes—
285C23×C112−1+412yes—
286C22×D11—24no—
287C22×D11—22no—
288C22×D11—22no—
289C22×D11—24no—
290C22×D11—22no—
291C22×D11—22no—
292C22×D11—22no—
293C22×D11—22no—
294C22×D11—24no—
295C22×D11—24no—
296C22×D11—24no—
297C22×D11—24no—
298C22×D11—41no—
299C22×D11—41no—
300C22×D11—42no—
301C22×D11—41no—
302C22×D11—41no—
303C22×D11—42no—
304C22×D11—42no—
305C22×D11—42no—
306C22×D11—42no—
307C22×D11—42no—
308C22×D11C2×C4⋊C414yescomplemented
309C2×C4×C11—232no—
310C2×C4×C11—24no—
311C2×C4×C11—24no—
312C2×C4×C11—24no—
313C2×C4×C11—24no—
314C2×C4×C11—24no—
315C2×C4×C11—24no—
316C2×C4×C11—22no—
317C2×C4×C11—22no—
318C2×C4×C11—24no—
319C2×C4×C11—24no—
320C2×C4×C11—41no—
321C2×C4×C11—41no—
322C2×C4×C11—41no—
323C2×C4×C11—41no—
324C2×C4×C11—42no—
325C2×C4×C11—42no—
326C2×C4×C11—42no—
327C2×C4×C11—42no—
328C2×C4×C11—42no—
329C2×C4×C11—42no—
330C2×C4×C11—42no—
331C2×C4×C11—42no—
332C2×C4×C11—42no—
333C2×C4×C11C4×D418yescomplemented
334C22⋊D11—232no—
335C2×Dic11—22no—
336C2×Dic11—22no—
337C2×Dic11—22no—
338C2×Dic11—22no—
339C2×Dic11—22no—
340C2×Dic11—22no—
341C2×Dic11—22no—
342C2×Dic11—22no—
343C2×Dic11—24no—
344C2×Dic11—24no—
345C2×Dic11—24no—
346C2×Dic11—24no—
347C2×Dic11—24no—
348C2×Dic11—22no—
349C2×Dic11—22no—
350C2×Dic11—24no—
351C2×Dic11—22no—
352C2×Dic11—24no—
353C2×Dic11—24no—
354C2×Dic11—416no—
355C2×Dic11—416no—
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×Dic11C2×C4⋊C414yescomplemented
367C2×Dic11#12014yes—
368C4×D11—416no—
369C23×D4—111no—
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—111no—
379C22×C4⋊C4—112no—
380C22×C4⋊C4—112no—
381C22×C4⋊C4—228no—
382C22×C4⋊C4—224no—
383C22×C22⋊C4—111no—
384C22×C22⋊C4—112no—
385C22×C22⋊C4—111no—
386C22×C22⋊C4—112no—
387C22×C22⋊C4C2×D1111yescharacteristic
388C22×C22⋊C4C2×D1111yescharacteristic
389C22×C42—111no—
390#386—118no—
391#386—224no—
392#385—228no—
393#385—224no—
394C2×#95—112no—
395C2×#95—112no—
396C2×#95—112no—
397C2×#95—112no—
398C2×#95—112no—
399C2×#95C2×D1112yes—
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#38518yescomplemented
412C22×C11C22×C4⋊C411yescharacteristic
413C22×C11C2×C4×D411yescharacteristic
414C22×C11C2×C4×D411yescharacteristic
415C22×C11C2×C4×D412yes—
416C22×C11#52012yes—
417C22×C11C2×#12011yescharacteristic
418C22×C11C2×#12011yescharacteristic
419C22×C11C2×C22⋊Q811yescharacteristic
420C22×C11C2×C22⋊Q811yescharacteristic
421C22×C11C2×#12311yescharacteristic
422C22×C11#52511yescharacteristic
423C22×C11#52512yes—
424C22×C11#53411yescharacteristic
425C22×C11#53611yescharacteristic
426C22×C11#53912yes—
427C22×C11D4212yes—
428C22×C11D4212yes—
429C22×C11#54712yes—
430C22×C11#54712yes—
431C22×C11#54812yes—
432C22×C11D4×Q812yes—
433C22×C11#55312yes—
434C22×C11#55412yes—
435C2×D11—28no—
436C2×D11—24no—
437C2×D11—42no—
438C2×D11—42no—
439C2×D11—44no—
440C2×D11—42no—
441C2×D11—42no—
442C2×D11—42no—
443C2×D11—44no—
444C2×D11—44no—
445C2×D11—42no—
446C4×C11—28no—
447C4×C11—42no—
448C4×C11—42no—
449C4×C11—82no—
450Dic11—24no—
451Dic11—24no—
452Dic11—44no—
453Dic11—42no—
454Dic11—44no—
455C25—111no—
456C25C22×D1111yescharacteristic
457C22×D4—114no—
458C22×D4—114no—
459C22×D4—114no—
460C22×D4—222no—
461C22×D4—222no—
462C22×D4—222no—
463C22×D4—222no—
464C23×C4—22no—
465C23×C4—22no—
466C23×C4—24no—
467C23×C4—24no—
468C23×C4—111no—
469C23×C4—111no—
470C23×C4—112no—
471C23×C4—112no—
472C23×C4—111no—
473C23×C4—114no—
474C23×C4—222no—
475C23×C4—224no—
476C23×C4—222no—
477C23×C4—224no—
478C23×C4—224no—
479C23×C4—222no—
480C23×C4—222no—
481C23×C4—222no—
482C23×C4—222no—
483C23×C4—222no—
484C23×C4—222no—
485C23×C4—442no—
486C23×C4—442no—
487C23×C4—442no—
488C23×C4C4×D1114yescomplemented
489C23×C4C22×D1112yes—
490C23×C4C22×D1111yescharacteristic
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—22no—
510C2×C22⋊C4—22no—
511C2×C22⋊C4—22no—
512C2×C22⋊C4—114no—
513C2×C22⋊C4—118no—
514C2×C22⋊C4—222no—
515C2×C22⋊C4—222no—
516C2×C22⋊C4—222no—
517C2×C22⋊C4—222no—
518C2×C22⋊C4—222no—
519C2×C22⋊C4—224no—
520C2×C22⋊C4—224no—
521C2×C22⋊C4—224no—
522C2×C22⋊C4—224no—
523C2×C22⋊C4—442no—
524C2×C22⋊C4D4414yes—
525C2×C42—222no—
526C2×C42—222no—
527C2×C42—222no—
528#95—24no—
529#95—24no—
530#95—118no—
531#95—224no—
532#95—224no—
533#95—224no—
534#95—442no—
535C2×C11—28no—
536C2×C11C2×#38511yescharacteristic
537C2×C11C4×#12011yescharacteristic
538C2×C11#232211yescharacteristic
539C2×C11D4×C4⋊C412yes—
540C2×C11#236112yes—
541C2×C11#240311yescharacteristic
542C2×C11#240611yescharacteristic
543C2×C11#240911yescharacteristic
544C2×C11#244312yes—
545C2×C11#244912yes—
546C2×C11#257911yescharacteristic
547D11—44no—
548C24—22no—
549C24—22no—
550C24—22no—
551C24—22no—
552C24—112no—
553C24—112no—
554C24—112no—
555C24—221no—
556C24—221no—
557C24—222no—
558C24—221no—
559C24—222no—
560C24—221no—
561C24—222no—
562C24—222no—
563C24C2×C4×D1112yes—
564C24C2×D4412yes—
565C24#433912yes—
566C24D4×D1112yes—
567C24D4×D1112yes—
568C24#434112yes—
569C24Q8×D1112yes—
570C24C23×D1111yescharacteristic
571C2×D4—1116no—
572C2×D4—228no—
573C2×D4—228no—
574C2×D4—228no—
575C2×D4—228no—
576C2×D4—228no—
577C2×D4—228no—
578C22×C4—28no—
579C22×C4—216no—
580C22×C4—28no—
581C22×C4—28no—
582C22×C4—22no—
583C22×C4—22no—
584C22×C4—22no—
585C22×C4—22no—
586C22×C4—216no—
587C22×C4—22no—
588C22×C4—21no—
589C22×C4—21no—
590C22×C4—21no—
591C22×C4—21no—
592C22×C4—22no—
593C22×C4—22no—
594C22×C4—22no—
595C22×C4—22no—
596C22×C4—22no—
597C22×C4—22no—
598C22×C4—22no—
599C22×C4—22no—
600C22×C4—22no—
601C22×C4—22no—
602C22×C4—112no—
603C22×C4—112no—
604C22×C4—114no—
605C22×C4—112no—
606C22×C4—112no—
607C22×C4—114no—
608C22×C4—114no—
609C22×C4—112no—
610C22×C4—228no—
611C22×C4—228no—
612C22×C4—221no—
613C22×C4—221no—
614C22×C4—221no—
615C22×C4—221no—
616C22×C4—221no—
617C22×C4—221no—
618C22×C4—222no—
619C22×C4—228no—
620C22×C4—228no—
621C22×C4—222no—
622C22×C4—222no—
623C22×C4—221no—
624C22×C4—222no—
625C22×C4—222no—
626C22×C4—222no—
627C22×C4—221no—
628C22×C4—222no—
629C22×C4—222no—
630C22×C4—222no—
631C22×C4—222no—
632C22×C4—222no—
633C22×C4—222no—
634C22×C4—222no—
635C22×C4—222no—
636C22×C4—222no—
637C22×C4—448no—
638C22×C4—444no—
639C22×C4—448no—
640C22×C4—444no—
641C22×C4—444no—
642C22×C4—448no—
643C22×C4—448no—
644C22×C4—448no—
645C22×C4—448no—
646C22×C4—444no—
647C22×C4—444no—
648C22×C4C2×C4×D1114yes—
649C22×C4C2×D4412yes—
650C22×C4C2×D4412yes—
651C22×C4D4×D1114yes—
652C22×C4#434114yes—
653C4⋊C4—2216no—
654C4⋊C4—2216no—
655C4⋊C4—228no—
656C4⋊C4—448no—
657C22⋊C4—28no—
658C22⋊C4—44no—
659C22⋊C4—228no—
660C22⋊C4—228no—
661C22⋊C4—2216no—
662C22⋊C4—448no—
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—114no—
682C23—222no—
683C23—224no—
684C23—222no—
685C23—222no—
686C23—222no—
687C23—222no—
688C23—222no—
689C23—224no—
690C23—224no—
691C23—224no—
692C23—224no—
693C23—224no—
694C23—442no—
695C23—442no—
696C23—442no—
697C23—442no—
698C23—442no—
699C23—441no—
700C23—441no—
701C23—441no—
702C23—441no—
703C23—442no—
704C23C4×D4414yes—
705C23(C22⋊D11)⋊C414yes—
706C23#6693514yes—
707C23#6693614yes—
708C23C4⋊C4×D1114yes—
709C23#6694914yes—
710C23#6695014yes—
711C23C22×C4×D1111yescharacteristic
712C23C22×D4411yescharacteristic
713C23C2×#433911yescharacteristic
714C23C2×D4×D1111yescharacteristic
715C23C2×D4×D1112yes—
716C23C2×D4×D1111yescharacteristic
717C23C2×#434111yescharacteristic
718C23C2×#434112yes—
719C23C2×Q8×D1111yescharacteristic
720C23#6704212yes—
721C23#6704312yes—
722D4—2232no—
723C2×C4—232no—
724C2×C4—24no—
725C2×C4—24no—
726C2×C4—24no—
727C2×C4—24no—
728C2×C4—24no—
729C2×C4—24no—
730C2×C4—22no—
731C2×C4—22no—
732C2×C4—24no—
733C2×C4—24no—
734C2×C4—41no—
735C2×C4—41no—
736C2×C4—42no—
737C2×C4—42no—
738C2×C4—41no—
739C2×C4—41no—
740C2×C4—42no—
741C2×C4—42no—
742C2×C4—42no—
743C2×C4—42no—
744C2×C4—42no—
745C2×C4—42no—
746C2×C4—42no—
747C2×C4—114no—
748C2×C4—114no—
749C2×C4—222no—
750C2×C4—222no—
751C2×C4—222no—
752C2×C4—222no—
753C2×C4—222no—
754C2×C4—222no—
755C2×C4—222no—
756C2×C4—224no—
757C2×C4—224no—
758C2×C4—222no—
759C2×C4—224no—
760C2×C4—224no—
761C2×C4—222no—
762C2×C4—224no—
763C2×C4—224no—
764C2×C4—224no—
765C2×C4—222no—
766C2×C4—224no—
767C2×C4—222no—
768C2×C4—4416no—
769C2×C4—4416no—
770C2×C4—4416no—
771C2×C4—442no—
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×C4—442no—
781C2×C4(C22⋊D11)⋊C418yescomplemented
782C22—24no—
783C22—28no—
784C22—28no—
785C22—24no—
786C22—24no—
787C22—24no—
788C22—24no—
789C22—28no—
790C22—24no—
791C22—28no—
792C22—228no—
793C22—224no—
794C22—442no—
795C22—444no—
796C22—444no—
797C22—442no—
798C22—442no—
799C22—442no—
800C22—442no—
801C22—442no—
802C22—444no—
803C22#1062228118yescomplemented
804C22C2×C4×D4411yescharacteristic
805C22C2×(C22⋊D11)⋊C412yes—
806C22C2×(C22⋊D11)⋊C411yescharacteristic
807C22C2×#6693511yescharacteristic
808C22C2×#6693611yescharacteristic
809C22C2×C4⋊C4×D1111yescharacteristic
810C22C2×#6694911yescharacteristic
811C22C2×#6695011yescharacteristic
812C22#1062305412yes—
813C22D4×D4412yes—
814C22#1062308312yes—
815C22#1062308612yes—
816C22#1062309612yes—
817C22#1062311712yes—
818C22#1062311711yescharacteristic
819C22D11×#12011yescharacteristic
820C22#1062314012yes—
821C22#1062314212yes—
822C22#1062316312yes—
823C22#1062316612yes—
824C22#1062317911yescharacteristic
825C22#1062318411yescharacteristic
826C22#1062319612yes—
827C4—28no—
828C4—42no—
829C4—42no—
830C4—82no—
831C4—224no—
832C4—224no—
833C4—444no—
834C4—442no—
835C4—444no—
836C2—28no—
837C2—444no—
838C2C2×#1062228111yescharacteristic
839C2#1307111511yescharacteristic
840C2#1307128211yescharacteristic
841C2#1307151212yes—
842C2#1307163012yes—
843C2#1307192811yescharacteristic
844C2#1307195011yescharacteristic
845C2#1307198011yescharacteristic
846C2#1307235712yes—
847C2#1307242312yes—
848C2#1307396611yescharacteristic
subgroupG/H
center, FrattiniC24C23×D11
commutatorC23×C11C23×C4
FittingC11×C22⋊#95C2
socle, cosocleC24×C11C24
prime radicalC23×C22⋊D11C22
hypercenterC22⋊#95D11
hypocenterC11#14015
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ C22⋊#95

Complements

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

NH ≅ G/Ntype
2. C23×C4⋊Dic11C2semidirect
5. C2×#10622281C2semidirect
6. C2×#10622559C2semidirect
7. #13066880C2semidirect
8. #13066862C2semidirect
9. #13066850C2semidirect
10. #13066838C2semidirect
11. C11×C22⋊#95C2semidirect
35. #10622826C4semidirect
50. C23×C4×C11C2×C4semidirect
90. C2×C22⋊Dic11C2×C4semidirect
99. C2×(C2×D11)⋊C4C2×C4semidirect
106. C2×C4⋊Dic11D4semidirect
123. C11⋊#95C2×C4semidirect
183. C2×C22⋊D11C4⋊C4semidirect
251. C22⋊#95D11semidirect
308. C22×D11C2×C4⋊C4semidirect
333. C2×C4×C11C4×D4semidirect
366. C2×Dic11C2×C4⋊C4semidirect
411. C22×C11#385semidirect
488. C23×C4C4×D11semidirect
664. C11#14015semidirect
781. C2×C4(C22⋊D11)⋊C4semidirect
803. C22#10622281semidirect

Maximal subgroups

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

subgroupindex
C22×(C22⋊D11)⋊C42
C23×C4⋊Dic112
C2×#106228262
C2×#106225712
C2×#106222812
C2×#106225592
#130668802
#130668622
#130668502
#130668382
C11×C22⋊#952
#1401511