Finite Group Databasebeta

← #14677137

Subgroups — #14677137

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×C4×C22⋊D11C211yesmaximal, characteristic
2C23×Dic11⋊C4C211yesmaximal, characteristic, complemented
3C2×#10622571C211yesmaximal, characteristic
4C2×#10622571C211yesmaximal, characteristic
5C2×#10622563C211yesmaximal, characteristic, complemented
6C2×#10622281C212yesmaximal, complemented
7#13066880C212yesmaximal, complemented
8#13066860C212yesmaximal, complemented
9#13066851C212yesmaximal, 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
20C2×C4×C22⋊D11—24no—
21C2×C4×C22⋊D11—24no—
22C2×C4×C22⋊D11—24no—
23C22×(C2×D11)⋊C4C2211yescharacteristic
24C22×(C2×D11)⋊C4C2212yes—
25C22×(C2×D11)⋊C4C2212yes—
26C22×C4⋊Dic11C2212yes—
27C22×Dic11⋊C4—24no—
28C22×Dic11⋊C4—28no—
29C22×Dic11⋊C4C2212yes—
30C22×Dic11⋊C4C2211yescharacteristic
31C22×Dic11⋊C4C2212yes—
32C22×C4×Dic11C2211yescharacteristic
33C2×C11×#95C2212yes—
34C2×C11×#95C2212yes—
35C2×C11⋊#95C2212yes—
36C2×C11⋊#95C2212yes—
37C2×C11⋊#95C2212yes—
38C2×C11⋊#95C2212yes—
39C2×C11⋊#95C2212yes—
40#10622571—24no—
41#10622571C418yescomplemented
42#10622563—24no—
43#10622281—28no—
44C25×C11C2311yescharacteristic
45C24×D11C2311yescharacteristic
46C23×C4×C11—22no—
47C23×C4×C11—22no—
48C23×C4×C11—24no—
49C23×C4×C11—42no—
50C23×C4×C11D414yes—
51C23×C4×C11C2312yes—
52C23×C4×C11C2312yes—
53C23×C4×C11C2311yescharacteristic
54C23×C4×C11C2311yescharacteristic
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—24no—
65C23×Dic11—24no—
66C23×Dic11—22no—
67C23×Dic11—24no—
68C23×Dic11—22no—
69C23×Dic11—22no—
70C23×Dic11—42no—
71C23×Dic11C2×C414yescomplemented
72C23×Dic11C2311yescharacteristic
73C23×Dic11C2312yes—
74C23×Dic11C2311yescharacteristic
75C23×Dic11C2311yescharacteristic
76C23×Dic11C2312yes—
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⋊C4C2×C414yescomplemented
88C2×C22⋊Dic11—22no—
89C2×C22⋊Dic11—22no—
90C2×C22⋊Dic11D414yes—
91C4×C22⋊D11—232no—
92C2×(C2×D11)⋊C4—22no—
93C2×(C2×D11)⋊C4—22no—
94C2×(C2×D11)⋊C4—24no—
95C2×(C2×D11)⋊C4—22no—
96C2×(C2×D11)⋊C4—24no—
97C2×(C2×D11)⋊C4—24no—
98C2×(C2×D11)⋊C4—24no—
99C2×(C2×D11)⋊C4—42no—
100C2×(C2×D11)⋊C4C2×C418yescomplemented
101C2×C4⋊Dic11—24no—
102C2×C4⋊Dic11—24no—
103C2×C4⋊Dic11—42no—
104C2×Dic11⋊C4—232no—
105C2×Dic11⋊C4—24no—
106C2×Dic11⋊C4—24no—
107C2×Dic11⋊C4—24no—
108C2×Dic11⋊C4—22no—
109C2×Dic11⋊C4—24no—
110C2×Dic11⋊C4—24no—
111C2×Dic11⋊C4—22no—
112C2×Dic11⋊C4—22no—
113C2×Dic11⋊C4D418yescomplemented
114C2×C4×Dic11—22no—
115C2×C4×Dic11—22no—
116C2×C4×Dic11—22no—
117C11×#95—24no—
118C11×#95—42no—
119C11⋊#95—24no—
120C11⋊#95—24no—
121C11⋊#95—24no—
122C11⋊#95—24no—
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—21no—
149C22×C4×C11—21no—
150C22×C4×C11—22no—
151C22×C4×C11—28no—
152C22×C4×C11—22no—
153C22×C4×C11—22no—
154C22×C4×C11—22no—
155C22×C4×C11—21no—
156C22×C4×C11—21no—
157C22×C4×C11—22no—
158C22×C4×C11—22no—
159C22×C4×C11—22no—
160C22×C4×C11—22no—
161C22×C4×C11—22no—
162C22×C4×C11—28no—
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—44no—
171C22×C4×C11—48no—
172C22×C4×C11—48no—
173C22×C4×C11C22×C414yes—
174C22×C4×C11C2×D412yes—
175C22×C4×C11C2×D412yes—
176C22×C4×C11C2×D414yes—
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—216no—
187C22×Dic11—216no—
188C22×Dic11—28no—
189C22×Dic11—28no—
190C22×Dic11—21no—
191C22×Dic11—21no—
192C22×Dic11—22no—
193C22×Dic11—22no—
194C22×Dic11—22no—
195C22×Dic11—22no—
196C22×Dic11—22no—
197C22×Dic11—21no—
198C22×Dic11—21no—
199C22×Dic11—22no—
200C22×Dic11—22no—
201C22×Dic11—21no—
202C22×Dic11—21no—
203C22×Dic11—22no—
204C22×Dic11—22no—
205C22×Dic11—21no—
206C22×Dic11—21no—
207C22×Dic11—22no—
208C22×Dic11—22no—
209C22×Dic11—22no—
210C22×Dic11—22no—
211C22×Dic11—22no—
212C22×Dic11—48no—
213C22×Dic11—48no—
214C22×Dic11—44no—
215C22×Dic11—44no—
216C22×Dic11C22×C412yes—
217C22×Dic11C22×C414yes—
218C22×Dic11C2×D412yes—
219C22×Dic11C2×D414yes—
220C22×Dic11C2×D412yes—
221C22×Dic11C2×D412yes—
222C22×Dic11C2×D414yes—
223C22×Dic11C2×Q812yes—
224C22×Dic11#4114yes—
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—48no—
237Dic11⋊C4—216no—
238Dic11⋊C4—28no—
239Dic11⋊C4—216no—
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—22no—
310C2×C4×C11—22no—
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—22no—
319C2×C4×C11—416no—
320C2×C4×C11—42no—
321C2×C4×C11—42no—
322C2×C4×C11—42no—
323C2×C4×C11—42no—
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×C11#12014yes—
334C22⋊D11—232no—
335C2×Dic11—232no—
336C2×Dic11—24no—
337C2×Dic11—24no—
338C2×Dic11—22no—
339C2×Dic11—22no—
340C2×Dic11—22no—
341C2×Dic11—24no—
342C2×Dic11—22no—
343C2×Dic11—22no—
344C2×Dic11—22no—
345C2×Dic11—24no—
346C2×Dic11—24no—
347C2×Dic11—24no—
348C2×Dic11—22no—
349C2×Dic11—24no—
350C2×Dic11—22no—
351C2×Dic11—24no—
352C2×Dic11—24no—
353C2×Dic11—24no—
354C2×Dic11—24no—
355C2×Dic11—416no—
356C2×Dic11—41no—
357C2×Dic11—42no—
358C2×Dic11—41no—
359C2×Dic11—41no—
360C2×Dic11—42no—
361C2×Dic11—41no—
362C2×Dic11—42no—
363C2×Dic11—42no—
364C2×Dic11—42no—
365C2×Dic11—42no—
366C2×Dic11C2×C4⋊C414yescomplemented
367C2×Dic11C4×D418yescomplemented
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—112no—
379C22×C4⋊C4—111no—
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—24no—
447C4×C11—44no—
448C4×C11—42no—
449C4×C11—82no—
450Dic11—24no—
451Dic11—28no—
452Dic11—42no—
453Dic11—44no—
454Dic11—42no—
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—42no—
468C23×C4—112no—
469C23×C4—111no—
470C23×C4—114no—
471C23×C4—111no—
472C23×C4—111no—
473C23×C4—112no—
474C23×C4—222no—
475C23×C4—222no—
476C23×C4—224no—
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—224no—
486C23×C4—442no—
487C23×C4—442no—
488C23×C4D4414yes—
489C23×C4C22×D1112yes—
490C23×C4C22×D1112yes—
491C23×C4C22×D1111yescharacteristic
492C23×C4C22×D1111yescharacteristic
493C4×D4—2232no—
494C2×C4⋊C4—118no—
495C2×C4⋊C4—224no—
496C2×C4⋊C4—224no—
497C2×C4⋊C4—222no—
498C2×C4⋊C4—222no—
499C2×C4⋊C4—2232no—
500C2×C4⋊C4—224no—
501C2×C4⋊C4—224no—
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—224no—
516C2×C22⋊C4—224no—
517C2×C22⋊C4—222no—
518C2×C22⋊C4—222no—
519C2×C22⋊C4—222no—
520C2×C22⋊C4—222no—
521C2×C22⋊C4—224no—
522C2×C22⋊C4—224no—
523C2×C22⋊C4—442no—
524C2×C22⋊C4C4×D1114yescomplemented
525C2×C42—222no—
526C2×C42—222no—
527C2×C42—222no—
528#95—24no—
529#95—42no—
530#95—118no—
531#95—224no—
532#95—224no—
533#95—224no—
534#95—224no—
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—221no—
560C24—222no—
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—21no—
579C22×C4—21no—
580C22×C4—22no—
581C22×C4—28no—
582C22×C4—22no—
583C22×C4—22no—
584C22×C4—21no—
585C22×C4—21no—
586C22×C4—22no—
587C22×C4—22no—
588C22×C4—22no—
589C22×C4—22no—
590C22×C4—22no—
591C22×C4—22no—
592C22×C4—28no—
593C22×C4—22no—
594C22×C4—22no—
595C22×C4—22no—
596C22×C4—22no—
597C22×C4—22no—
598C22×C4—22no—
599C22×C4—22no—
600C22×C4—44no—
601C22×C4—48no—
602C22×C4—48no—
603C22×C4—112no—
604C22×C4—114no—
605C22×C4—112no—
606C22×C4—114no—
607C22×C4—112no—
608C22×C4—114no—
609C22×C4—112no—
610C22×C4—112no—
611C22×C4—114no—
612C22×C4—228no—
613C22×C4—2216no—
614C22×C4—228no—
615C22×C4—228no—
616C22×C4—2216no—
617C22×C4—228no—
618C22×C4—221no—
619C22×C4—222no—
620C22×C4—222no—
621C22×C4—221no—
622C22×C4—221no—
623C22×C4—222no—
624C22×C4—221no—
625C22×C4—222no—
626C22×C4—228no—
627C22×C4—221no—
628C22×C4—221no—
629C22×C4—222no—
630C22×C4—222no—
631C22×C4—222no—
632C22×C4—222no—
633C22×C4—221no—
634C22×C4—221no—
635C22×C4—222no—
636C22×C4—222no—
637C22×C4—222no—
638C22×C4—222no—
639C22×C4—222no—
640C22×C4—222no—
641C22×C4—448no—
642C22×C4—448no—
643C22×C4—444no—
644C22×C4—448no—
645C22×C4—448no—
646C22×C4—444no—
647C22×C4—444no—
648C22×C4—444no—
649C22×C4C2×C4×D1114yes—
650C22×C4C2×D4412yes—
651C22×C4C2×D4412yes—
652C22×C4D4×D1114yes—
653C4⋊C4—2216no—
654C4⋊C4—228no—
655C4⋊C4—2216no—
656C4⋊C4—448no—
657C22⋊C4—28no—
658C22⋊C4—44no—
659C22⋊C4—2216no—
660C22⋊C4—228no—
661C22⋊C4—228no—
662C22⋊C4—448no—
663C42—228no—
664C11#1401511yescharacteristic, complemented, Sylow
665C23—22no—
666C23—22no—
667C23—22no—
668C23—22no—
669C23—24no—
670C23—24no—
671C23—24no—
672C23—24no—
673C23—24no—
674C23—24no—
675C23—24no—
676C23—24no—
677C23—24no—
678C23—24no—
679C23—24no—
680C23—24no—
681C23—114no—
682C23—222no—
683C23—222no—
684C23—222no—
685C23—222no—
686C23—222no—
687C23—222no—
688C23—224no—
689C23—224no—
690C23—224no—
691C23—224no—
692C23—224no—
693C23—224no—
694C23—441no—
695C23—441no—
696C23—441no—
697C23—441no—
698C23—442no—
699C23—442no—
700C23—442no—
701C23—442no—
702C23—442no—
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×D1111yescharacteristic
716C23C2×D4×D1112yes—
717C23C2×#434111yescharacteristic
718C23#6703712yes—
719C23C2×Q8×D1111yescharacteristic
720C23#41×D1112yes—
721C23#6704312yes—
722D4—2232no—
723C2×C4—22no—
724C2×C4—22no—
725C2×C4—24no—
726C2×C4—24no—
727C2×C4—24no—
728C2×C4—22no—
729C2×C4—22no—
730C2×C4—22no—
731C2×C4—24no—
732C2×C4—24no—
733C2×C4—416no—
734C2×C4—42no—
735C2×C4—42no—
736C2×C4—42no—
737C2×C4—42no—
738C2×C4—42no—
739C2×C4—42no—
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—118no—
749C2×C4—2232no—
750C2×C4—224no—
751C2×C4—222no—
752C2×C4—222no—
753C2×C4—222no—
754C2×C4—224no—
755C2×C4—222no—
756C2×C4—222no—
757C2×C4—222no—
758C2×C4—224no—
759C2×C4—224no—
760C2×C4—224no—
761C2×C4—224no—
762C2×C4—222no—
763C2×C4—222no—
764C2×C4—224no—
765C2×C4—224no—
766C2×C4—224no—
767C2×C4—224no—
768C2×C4—224no—
769C2×C4—4416no—
770C2×C4—4416no—
771C2×C4—441no—
772C2×C4—442no—
773C2×C4—441no—
774C2×C4—442no—
775C2×C4—441no—
776C2×C4—441no—
777C2×C4—442no—
778C2×C4—442no—
779C2×C4—442no—
780C2×C4—442no—
781C2×C4#6693514yes—
782C22—28no—
783C22—24no—
784C22—28no—
785C22—24no—
786C22—24no—
787C22—24no—
788C22—24no—
789C22—28no—
790C22—24no—
791C22—28no—
792C22—228no—
793C22—224no—
794C22—444no—
795C22—442no—
796C22—444no—
797C22—442no—
798C22—442no—
799C22—442no—
800C22—442no—
801C22—442no—
802C22—444no—
803C22#1062228118yescomplemented
804C22C2×C4×D4411yescharacteristic
805C22C2×(C22⋊D11)⋊C411yescharacteristic
806C22C2×#6693511yescharacteristic
807C22C2×#6693511yescharacteristic
808C22C2×#6693611yescharacteristic
809C22#1062302411yescharacteristic
810C22C2×C4⋊C4×D1111yescharacteristic
811C22C2×#6694911yescharacteristic
812C22C2×#6695011yescharacteristic
813C22#1062305511yescharacteristic
814C22#1062305711yescharacteristic
815C22C4×D4×D1112yes—
816C22#1062307712yes—
817C22#1062307812yes—
818C22#1062309512yes—
819C22#1062312112yes—
820C22#1062312112yes—
821C22#1062312912yes—
822C22#1062313212yes—
823C22#1062316312yes—
824C22#1062316712yes—
825C22#1062318612yes—
826C22#1062318612yes—
827C4—24no—
828C4—44no—
829C4—42no—
830C4—82no—
831C4—228no—
832C4—224no—
833C4—442no—
834C4—444no—
835C4—442no—
836C2—28no—
837C2—444no—
838C2C2×#1062228111yescharacteristic
839C2C4×#6693511yescharacteristic
840C2#1307128711yescharacteristic
841C2#1307151412yes—
842C2#1307162712yes—
843C2#1307192911yescharacteristic
844C2#1307195311yescharacteristic
845C2#1307198211yescharacteristic
846C2#1307235312yes—
847C2#1307242712yes—
848C2#1307396511yescharacteristic
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×Dic11⋊C4C2semidirect
5. C2×#10622563C2semidirect
6. C2×#10622281C2semidirect
7. #13066880C2semidirect
8. #13066860C2semidirect
9. #13066851C2semidirect
10. #13066838C2semidirect
11. C11×C22⋊#95C2semidirect
41. #10622571C4semidirect
71. C23×Dic11C2×C4semidirect
87. C2×C11×C22⋊C4C2×C4semidirect
100. C2×(C2×D11)⋊C4C2×C4semidirect
113. C2×Dic11⋊C4D4semidirect
123. C11⋊#95C2×C4semidirect
183. C2×C22⋊D11C4⋊C4semidirect
251. C22⋊#95D11semidirect
308. C22×D11C2×C4⋊C4semidirect
366. C2×Dic11C2×C4⋊C4semidirect
367. C2×Dic11C4×D4semidirect
411. C22×C11#385semidirect
524. C2×C22⋊C4C4×D11semidirect
664. C11#14015semidirect
803. C22#10622281semidirect

Maximal subgroups

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

subgroupindex
C22×C4×C22⋊D112
C23×Dic11⋊C42
C2×#106225712
C2×#106225632
C2×#106222812
#130668802
#130668602
#130668512
#130668382
C11×C22⋊#952
#1401511