Finite Group Databasebeta

← #14676550

Subgroups — #14676550

Order 2816.

2742 conjugacy classes of subgroups.

The subgroup lattice has 846 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#66988C211yesmaximal, characteristic
2C2×#10622833C211yesmaximal, characteristic
3C2×#10622556C211yesmaximal, characteristic, complemented
4C22×C11⋊#95C211yesmaximal, characteristic, complemented
5#13066866C212yesmaximal, complemented
6#13066863C212yesmaximal, complemented
7#13066849C212yesmaximal, complemented
8#13066839C211yesmaximal, characteristic, complemented
9#13066839C212yesmaximal, complemented
10#13066838C211yesmaximal, characteristic, complemented
11C22×C4×D4×C11C211yesmaximal, characteristic
12C23×D4×C11C2211yescharacteristic
13C24×C4×C11C2211yescharacteristic
14C24×C4×C11C2211yescharacteristic
15C24×Dic11C2211yescharacteristic
16C24×Dic11C2211yescharacteristic
17C2×C4×D4×C11—24no—
18C2×C4×D4×C11—24no—
19C2×C4×D4×C11—24no—
20C22×C11×C4⋊C4C2211yescharacteristic
21C22×C11×C22⋊C4C2211yescharacteristic
22C22×C11×C22⋊C4C2211yescharacteristic
23C22×C42×C11C2211yescharacteristic
24C22×C22⋊Dic11C2211yescharacteristic
25C22×C22⋊Dic11C2212yes—
26C22×C22⋊Dic11C2211yescharacteristic
27C22×C22⋊Dic11C2212yes—
28C2×#66988—24no—
29C2×#66988—24no—
30C2×#66988C418yescomplemented
31C22×Dic11⋊C4C2212yes—
32#10622833—24no—
33C2×C11⋊#95—24no—
34C2×C11⋊#95C2212yes—
35C2×C11⋊#95C2212yes—
36C2×C11⋊#95C2212yes—
37C2×C11⋊#95C2212yes—
38C2×C11⋊#95C2212yes—
39C2×C11⋊#95C2212yes—
40C2×C11⋊#95C2212yes—
41C2×C11⋊#95C2212yes—
42C2×C11⋊#95C2212yes—
43#10622556—24no—
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×C11D414yes—
53C23×C4×C11—22no—
54C23×C4×C11—22no—
55C23×C4×C11—22no—
56C23×C4×C11—22no—
57C23×C4×C11—22no—
58C23×C4×C11—24no—
59C23×C4×C11—24no—
60C23×C4×C11—42no—
61C23×C4×C11—42no—
62C23×C4×C11D414yes—
63C23×C4×C11C2311yescharacteristic
64C23×C4×C11C2311yescharacteristic
65C23×C4×C11C2311yescharacteristic
66C23×C4×C11C2311yescharacteristic
67C23×C4×C11C2311yescharacteristic
68C23×Dic11—22no—
69C23×Dic11—22no—
70C23×Dic11—22no—
71C23×Dic11—22no—
72C23×Dic11—22no—
73C23×Dic11—22no—
74C23×Dic11—22no—
75C23×Dic11—24no—
76C23×Dic11—22no—
77C23×Dic11—22no—
78C23×Dic11—42no—
79C23×Dic11C2×C414yescomplemented
80C23×Dic11C2312yes—
81C23×Dic11C2312yes—
82C23×Dic11C2312yes—
83C23×Dic11C2312yes—
84C4×D4×C11—232no—
85C2×C11×C4⋊C4—22no—
86C2×C11×C4⋊C4—22no—
87C2×C11×C4⋊C4—22no—
88C2×C11×C22⋊C4—22no—
89C2×C11×C22⋊C4—22no—
90C2×C11×C22⋊C4—22no—
91C2×C11×C22⋊C4—22no—
92C2×C11×C22⋊C4—22no—
93C2×C11×C22⋊C4D414yes—
94C2×C42×C11—22no—
95C2×C42×C11—22no—
96C2×C42×C11—22no—
97C2×C22⋊Dic11—22no—
98C2×C22⋊Dic11—24no—
99C2×C22⋊Dic11—22no—
100C2×C22⋊Dic11—24no—
101C2×C22⋊Dic11—22no—
102C2×C22⋊Dic11—24no—
103C2×C22⋊Dic11—22no—
104C2×C22⋊Dic11—22no—
105C2×C22⋊Dic11—24no—
106C2×C22⋊Dic11—42no—
107C2×C22⋊Dic11C2×C414yescomplemented
108C2×C22⋊Dic11C2×C418yescomplemented
109#66988—232no—
110C2×Dic11⋊C4—24no—
111C2×Dic11⋊C4—24no—
112C2×Dic11⋊C4C2×C418yescomplemented
113C11⋊#95—24no—
114C11⋊#95—24no—
115C11⋊#95—24no—
116C11⋊#95—24no—
117C11⋊#95—24no—
118C11⋊#95—24no—
119C11⋊#95—24no—
120C11⋊#95—42no—
121C11⋊#95—42no—
122#13968—111nomaximal, Sylow
123C24×C11—22no—
124C24×C11—22no—
125C24×C11—22no—
126C24×C11—22no—
127C24×C11—21no—
128C24×C11—21no—
129C24×C11—22no—
130C24×C11—22no—
131C24×C11—21no—
132C24×C11—21no—
133C24×C11—22no—
134C24×C11—22no—
135C24×C11C22×C412yes—
136C24×C11C22×C412yes—
137C24×C11C2×D412yes—
138C24×C11C2×D412yes—
139C24×C11C2×D412yes—
140C24×C11C2×D412yes—
141C24×C11C2×D412yes—
142C24×C11C2×D412yes—
143C24×C11#4112yes—
144C24×C11#4112yes—
145C24×C11C2411yescharacteristic
146C2×D4×C11—28no—
147C2×D4×C11—28no—
148C2×D4×C11—28no—
149C2×D4×C11—28no—
150C2×D4×C11—28no—
151C2×D4×C11—28no—
152C2×D4×C11C22⋊C4116yes—
153C22×C4×C11—21no—
154C22×C4×C11—21no—
155C22×C4×C11—21no—
156C22×C4×C11—21no—
157C22×C4×C11—21no—
158C22×C4×C11—21no—
159C22×C4×C11—22no—
160C22×C4×C11—28no—
161C22×C4×C11—28no—
162C22×C4×C11—21no—
163C22×C4×C11—21no—
164C22×C4×C11—21no—
165C22×C4×C11—21no—
166C22×C4×C11—21no—
167C22×C4×C11—21no—
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×C11—28no—
175C22×C4×C11—44no—
176C22×C4×C11—48no—
177C22×C4×C11—48no—
178C22×C4×C11—48no—
179C22×C4×C11—48no—
180C22×C4×C11—44no—
181C22×C4×C11—44no—
182C22×C4×C11C22×C412yes—
183C22×C4×C11C2×D412yes—
184C22×C4×C11C2×D412yes—
185C22×C4×C11C2×D412yes—
186C22×C4×C11C2×D412yes—
187C22×C4×C11C2×D412yes—
188C22×C4×C11C2×D412yes—
189C22×C4×C11#4114yes—
190C22×Dic11—28no—
191C22×Dic11—28no—
192C22×Dic11—28no—
193C22×Dic11—28no—
194C22×Dic11—22no—
195C22×Dic11—22no—
196C22×Dic11—22no—
197C22×Dic11—22no—
198C22×Dic11—22no—
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—22no—
214C22×Dic11—22no—
215C22×Dic11—22no—
216C22×Dic11—22no—
217C22×Dic11—22no—
218C22×Dic11—22no—
219C22×Dic11—48no—
220C22×Dic11—48no—
221C22×Dic11—44no—
222C22×Dic11—44no—
223C22×Dic11—44no—
224C22×Dic11—44no—
225C22×Dic11—44no—
226C22×Dic11—44no—
227C22×Dic11C22×C414yes—
228C22×Dic11C22×C414yes—
229C22×Dic11#4114yes—
230C11×C4⋊C4—28no—
231C11×C22⋊C4—28no—
232C11×C22⋊C4—28no—
233C42×C11—28no—
234C22⋊Dic11—216no—
235C22⋊Dic11—28no—
236C22⋊Dic11—48no—
237C22⋊Dic11—44no—
238Dic11⋊C4—216no—
239C22×#123—111no—
240C22×C4×D4D1111yescharacteristic
241C2×#386—111no—
242C2×#381—111no—
243C22×#95—111no—
244#1441—112no—
245#1440—112no—
246#1436—112no—
247C22⋊#95—111no—
248C22⋊#95—112no—
249C22⋊#95—111no—
250C23×C11—24no—
251C23×C11—24no—
252C23×C11—22no—
253C23×C11—22no—
254C23×C11—24no—
255C23×C11—22no—
256C23×C11—22no—
257C23×C11—24no—
258C23×C11—24no—
259C23×C11—24no—
260C23×C11—24no—
261C23×C11—24no—
262C23×C11—24no—
263C23×C11—24no—
264C23×C11—24no—
265C23×C11—24no—
266C23×C11—22no—
267C23×C11—22no—
268C23×C11—24no—
269C23×C11—24no—
270C23×C11—22no—
271C23×C11—22no—
272C23×C11—22no—
273C23×C11—22no—
274C23×C11—24no—
275C23×C11—24no—
276C23×C11—24no—
277C23×C11—24no—
278C23×C11—41no—
279C23×C11—41no—
280C23×C11—42no—
281C23×C11—41no—
282C23×C11—41no—
283C23×C11—42no—
284C23×C11—42no—
285C23×C11—42no—
286C23×C11—42no—
287C23×C11—42no—
288C23×C11C2×C22⋊C414yes—
289C23×C11C2×C22⋊C414yes—
290C23×C11C4×D414yes—
291C23×C11C4×D414yes—
292C23×C11#12014yes—
293C23×C11#12114yes—
294C23×C11#12114yes—
295C23×C11#12314yes—
296C23×C11C23×C411yescharacteristic
297C23×C11C22×D411yescharacteristic
298C23×C11C22×D411yescharacteristic
299C23×C11C22×D411yescharacteristic
300C23×C11C22×D411yescharacteristic
301C23×C11C2×#4111yescharacteristic
302C23×C11C2×#4111yescharacteristic
303C23×C11C2×#4112yes—
304C23×C11C2×#4112yes—
305C23×C11H(5,𝔽2)12yes—
306C23×C112−1+412yes—
307D4×C11—232no—
308C2×C4×C11—22no—
309C2×C4×C11—22no—
310C2×C4×C11—22no—
311C2×C4×C11—22no—
312C2×C4×C11—22no—
313C2×C4×C11—22no—
314C2×C4×C11—22no—
315C2×C4×C11—22no—
316C2×C4×C11—24no—
317C2×C4×C11—24no—
318C2×C4×C11—22no—
319C2×C4×C11—22no—
320C2×C4×C11—22no—
321C2×C4×C11—22no—
322C2×C4×C11—22no—
323C2×C4×C11—24no—
324C2×C4×C11—24no—
325C2×C4×C11—416no—
326C2×C4×C11—416no—
327C2×C4×C11—41no—
328C2×C4×C11—41no—
329C2×C4×C11—41no—
330C2×C4×C11—41no—
331C2×C4×C11—42no—
332C2×C4×C11—42no—
333C2×C4×C11—42no—
334C2×C4×C11—42no—
335C2×C4×C11C2×C22⋊C414yes—
336C2×C4×C11#12314yescomplemented
337C2×Dic11—24no—
338C2×Dic11—24no—
339C2×Dic11—24no—
340C2×Dic11—24no—
341C2×Dic11—24no—
342C2×Dic11—24no—
343C2×Dic11—24no—
344C2×Dic11—24no—
345C2×Dic11—24no—
346C2×Dic11—416no—
347C2×Dic11—42no—
348C2×Dic11—42no—
349C2×Dic11—42no—
350C2×Dic11—42no—
351C2×Dic11—42no—
352C2×Dic11—42no—
353C2×Dic11—42no—
354C2×Dic11—42no—
355C2×Dic11—42no—
356C2×Dic11—42no—
357C2×Dic11—42no—
358C2×Dic11—42no—
359C2×Dic11—416no—
360C2×Dic11—42no—
361C2×Dic11—42no—
362C2×Dic11—42no—
363C2×Dic11—42no—
364C2×Dic11—42no—
365C2×Dic11—42no—
366C2×Dic11—42no—
367C23×D4C2×D1111yescharacteristic
368C24×C4—111no—
369C24×C4—111no—
370C24×C4C2×D1111yescharacteristic
371C24×C4C2×D1111yescharacteristic
372C2×#123—118no—
373C2×#123—224no—
374C2×#123—224no—
375C2×C4×D4—24no—
376C2×C4×D4—24no—
377C2×C4×D4—24no—
378C22×C4⋊C4—112no—
379C22×C4⋊C4C2×D1111yescharacteristic
380C22×C22⋊C4—111no—
381C22×C22⋊C4—112no—
382C22×C22⋊C4—111no—
383C22×C22⋊C4—112no—
384C22×C22⋊C4C2×D1111yescharacteristic
385C22×C22⋊C4C2×D1111yescharacteristic
386C22×C42C2×D1111yescharacteristic
387#386—224no—
388#381—224no—
389C2×#95—112no—
390C2×#95—112no—
391C2×#95—112no—
392C2×#95—112no—
393C2×#95—112no—
394C2×#95—112no—
395C2×#95—112no—
396C2×#95—112no—
397C2×#95—112no—
398C2×#95—224no—
399C22×C11—24no—
400C22×C11—28no—
401C22×C11—28no—
402C22×C11—24no—
403C22×C11—24no—
404C22×C11—28no—
405C22×C11—28no—
406C22×C11—24no—
407C22×C11—24no—
408C22×C11—24no—
409C22×C11—28no—
410C22×C11—24no—
411C22×C11—42no—
412C22×C11—44no—
413C22×C11—42no—
414C22×C11—42no—
415C22×C11—44no—
416C22×C11—44no—
417C22×C11—42no—
418C22×C11—42no—
419C22×C11—42no—
420C22×C11#38618yes—
421C22×C11C22×C22⋊C411yescharacteristic
422C22×C11C2×C4×D411yescharacteristic
423C22×C11C2×C4×D411yescharacteristic
424C22×C11C4×#4112yes—
425C22×C11#52012yes—
426C22×C11C2×#12011yescharacteristic
427C22×C11C2×#12111yescharacteristic
428C22×C11C2×#12111yescharacteristic
429C22×C11C2×#12311yescharacteristic
430C22×C11C2×#12311yescharacteristic
431C22×C11#52511yescharacteristic
432C22×C11#52912yes—
433C22×C11#53411yescharacteristic
434C22×C11#53611yescharacteristic
435C22×C11#53912yes—
436C22×C11#54612yes—
437C22×C11#54612yes—
438C22×C11#54612yes—
439C22×C11#54712yes—
440C22×C11#54712yes—
441C22×C11#54712yes—
442C22×C11#55112yes—
443C22×C11#55212yes—
444C4×C11—24no—
445C4×C11—24no—
446C4×C11—42no—
447C4×C11—42no—
448C4×C11—42no—
449Dic11—44no—
450Dic11—44no—
451Dic11—44no—
452Dic11—82no—
453C25C22×D1111yescharacteristic
454C25C22×D1111yescharacteristic
455C22×D4—22no—
456C22×D4—22no—
457C22×D4—22no—
458C22×D4—22no—
459C22×D4C4×D1114yes—
460C22×D4D4414yes—
461C22×D4C22⋊D1114yes—
462C23×C4—22no—
463C23×C4—22no—
464C23×C4—22no—
465C23×C4—24no—
466C23×C4—22no—
467C23×C4—22no—
468C23×C4—24no—
469C23×C4—42no—
470C23×C4—42no—
471C23×C4—114no—
472C23×C4—112no—
473C23×C4—112no—
474C23×C4—112no—
475C23×C4—112no—
476C23×C4—224no—
477C23×C4—222no—
478C23×C4—222no—
479C23×C4—222no—
480C23×C4—222no—
481C23×C4—222no—
482C23×C4—222no—
483C23×C4—222no—
484C23×C4—222no—
485C23×C4—222no—
486C23×C4—442no—
487C23×C4C22⋊D1114yes—
488C23×C4C22×D1111yescharacteristic
489C23×C4C22×D1111yescharacteristic
490C23×C4C22×D1111yescharacteristic
491C23×C4C22×D1111yescharacteristic
492C23×C4C22×D1111yescharacteristic
493#123—2232no—
494C4×D4—232no—
495C2×C4⋊C4—22no—
496C2×C4⋊C4—22no—
497C2×C4⋊C4—22no—
498C2×C4⋊C4—118no—
499C2×C4⋊C4—224no—
500C2×C4⋊C4—224no—
501C2×C22⋊C4—22no—
502C2×C22⋊C4—22no—
503C2×C22⋊C4—22no—
504C2×C22⋊C4—22no—
505C2×C22⋊C4—22no—
506C2×C22⋊C4—114no—
507C2×C22⋊C4—118no—
508C2×C22⋊C4—222no—
509C2×C22⋊C4—224no—
510C2×C22⋊C4—222no—
511C2×C22⋊C4—224no—
512C2×C22⋊C4—224no—
513C2×C22⋊C4—224no—
514C2×C22⋊C4—222no—
515C2×C22⋊C4—222no—
516C2×C22⋊C4—222no—
517C2×C22⋊C4—442no—
518C2×C22⋊C4C22⋊D1114yes—
519C2×C42—22no—
520C2×C42—22no—
521C2×C42—22no—
522#95—224no—
523#95—224no—
524#95—224no—
525#95—224no—
526#95—224no—
527#95—224no—
528#95—224no—
529#95—442no—
530#95—442no—
531C2×C11—28no—
532C2×C11—44no—
533C2×C11C2×#38611yescharacteristic
534C2×C11C4×#12311yescharacteristic
535C2×C11#232211yescharacteristic
536C2×C11#233912yes—
537C2×C11#235912yes—
538C2×C11#240511yescharacteristic
539C2×C11#240611yescharacteristic
540C2×C11#241912yes—
541C2×C11#242512yes—
542C2×C11#248611yescharacteristic
543C2×C11#253411yescharacteristic
544C24—22no—
545C24—22no—
546C24—22no—
547C24—22no—
548C24—21no—
549C24—21no—
550C24—22no—
551C24—22no—
552C24—22no—
553C24—22no—
554C24—21no—
555C24—21no—
556C24C2×C4×D1112yes—
557C24C2×C4×D1112yes—
558C24C2×D4412yes—
559C24C2×D4412yes—
560C24#433912yes—
561C24#433912yes—
562C24C2×C22⋊D1112yes—
563C24C2×C22⋊D1112yes—
564C24C2×C22⋊D1112yes—
565C24C2×C22⋊D1112yes—
566C24C23×D1111yescharacteristic
567C2×D4—28no—
568C2×D4—28no—
569C2×D4—28no—
570C2×D4—28no—
571C2×D4—28no—
572C2×D4—28no—
573C2×D4(C2×D11)⋊C4116yes—
574C22×C4—21no—
575C22×C4—21no—
576C22×C4—22no—
577C22×C4—21no—
578C22×C4—21no—
579C22×C4—21no—
580C22×C4—21no—
581C22×C4—28no—
582C22×C4—28no—
583C22×C4—22no—
584C22×C4—22no—
585C22×C4—22no—
586C22×C4—22no—
587C22×C4—22no—
588C22×C4—22no—
589C22×C4—21no—
590C22×C4—21no—
591C22×C4—21no—
592C22×C4—21no—
593C22×C4—21no—
594C22×C4—21no—
595C22×C4—28no—
596C22×C4—44no—
597C22×C4—48no—
598C22×C4—48no—
599C22×C4—48no—
600C22×C4—48no—
601C22×C4—44no—
602C22×C4—44no—
603C22×C4—114no—
604C22×C4—114no—
605C22×C4—114no—
606C22×C4—228no—
607C22×C4—228no—
608C22×C4—228no—
609C22×C4—228no—
610C22×C4—222no—
611C22×C4—222no—
612C22×C4—222no—
613C22×C4—222no—
614C22×C4—222no—
615C22×C4—222no—
616C22×C4—222no—
617C22×C4—222no—
618C22×C4—222no—
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—448no—
636C22×C4—448no—
637C22×C4—444no—
638C22×C4—444no—
639C22×C4—444no—
640C22×C4—444no—
641C22×C4—444no—
642C22×C4—444no—
643C22×C4C2×C4×D1112yes—
644C22×C4C2×D4412yes—
645C22×C4#434114yes—
646C22×C4C2×C22⋊D1112yes—
647C22×C4C2×C22⋊D1112yes—
648C22×C4C2×C22⋊D1112yes—
649C22×C4C2×C22⋊D1112yes—
650C22×C4C2×C22⋊D1112yes—
651C4⋊C4—28no—
652C4⋊C4—2216no—
653C22⋊C4—28no—
654C22⋊C4—28no—
655C22⋊C4—228no—
656C22⋊C4—2216no—
657C22⋊C4—448no—
658C22⋊C4—444no—
659C42—28no—
660C11#1396811yescharacteristic, complemented, Sylow
661C23—24no—
662C23—24no—
663C23—22no—
664C23—24no—
665C23—24no—
666C23—22no—
667C23—24no—
668C23—24no—
669C23—24no—
670C23—24no—
671C23—24no—
672C23—24no—
673C23—24no—
674C23—24no—
675C23—22no—
676C23—22no—
677C23—22no—
678C23—22no—
679C23—22no—
680C23—22no—
681C23—22no—
682C23—24no—
683C23—24no—
684C23—24no—
685C23—24no—
686C23—24no—
687C23—24no—
688C23—22no—
689C23—42no—
690C23—41no—
691C23—42no—
692C23—41no—
693C23—42no—
694C23—42no—
695C23—42no—
696C23—42no—
697C23—41no—
698C23—41no—
699C23C2×(C2×D11)⋊C414yes—
700C23C2×(C2×D11)⋊C414yes—
701C23C4×C22⋊D1114yes—
702C23C4×C22⋊D1114yes—
703C23#6698214yes—
704C23#6698314yes—
705C23#6698314yes—
706C23#6700614yes—
707C23C22×C4×D1111yescharacteristic
708C23C22×D4411yescharacteristic
709C23C2×#433911yescharacteristic
710C23C2×#433911yescharacteristic
711C23C2×#434112yes—
712C23#6703712yes—
713C23#41×D1112yes—
714C23#6704312yes—
715C23C22×C22⋊D1111yescharacteristic
716C23C22×C22⋊D1111yescharacteristic
717C23C22×C22⋊D1111yescharacteristic
718D4—232no—
719C2×C4—22no—
720C2×C4—22no—
721C2×C4—22no—
722C2×C4—22no—
723C2×C4—22no—
724C2×C4—22no—
725C2×C4—24no—
726C2×C4—24no—
727C2×C4—22no—
728C2×C4—22no—
729C2×C4—22no—
730C2×C4—22no—
731C2×C4—24no—
732C2×C4—24no—
733C2×C4—22no—
734C2×C4—22no—
735C2×C4—22no—
736C2×C4—416no—
737C2×C4—416no—
738C2×C4—41no—
739C2×C4—41no—
740C2×C4—42no—
741C2×C4—42no—
742C2×C4—42no—
743C2×C4—42no—
744C2×C4—41no—
745C2×C4—41no—
746C2×C4—224no—
747C2×C4—224no—
748C2×C4—224no—
749C2×C4—224no—
750C2×C4—224no—
751C2×C4—224no—
752C2×C4—224no—
753C2×C4—224no—
754C2×C4—224no—
755C2×C4—4416no—
756C2×C4—442no—
757C2×C4—442no—
758C2×C4—442no—
759C2×C4—442no—
760C2×C4—442no—
761C2×C4—442no—
762C2×C4—4416no—
763C2×C4—442no—
764C2×C4—442no—
765C2×C4—442no—
766C2×C4—442no—
767C2×C4—442no—
768C2×C4—442no—
769C2×C4—442no—
770C2×C4—442no—
771C2×C4—442no—
772C2×C4—442no—
773C2×C4—442no—
774C2×C4—442no—
775C2×C4—442no—
776C2×C4C2×(C2×D11)⋊C414yes—
777C2×C4#6698814yescomplemented
778C22—24no—
779C22—24no—
780C22—28no—
781C22—24no—
782C22—24no—
783C22—28no—
784C22—24no—
785C22—24no—
786C22—28no—
787C22—28no—
788C22—28no—
789C22—24no—
790C22—42no—
791C22—42no—
792C22—44no—
793C22—42no—
794C22—42no—
795C22—42no—
796C22—42no—
797C22—44no—
798C22—44no—
799C22#1062282618yes—
800C22C4×#434112yes—
801C22#1062306912yes—
802C22#1062307212yes—
803C22#1062307712yes—
804C22#1062308512yes—
805C22#1062308612yes—
806C22#1062308712yes—
807C22#1062309512yes—
808C22C22×(C2×D11)⋊C411yescharacteristic
809C22C2×C4×C22⋊D1111yescharacteristic
810C22C2×C4×C22⋊D1111yescharacteristic
811C22C2×#6698211yescharacteristic
812C22C2×#6698311yescharacteristic
813C22C2×#6698311yescharacteristic
814C22C2×#6698811yescharacteristic
815C22#1062333511yescharacteristic
816C22#1062333712yes—
817C22#1062333712yes—
818C22#1062335512yes—
819C22#1062335512yes—
820C22#1062335611yescharacteristic
821C22#1062335911yescharacteristic
822C22C2×#6700611yescharacteristic
823C4—24no—
824C4—24no—
825C4—42no—
826C4—42no—
827C4—42no—
828C4—444no—
829C4—444no—
830C4—444no—
831C4—882no—
832C2—28no—
833C2—44no—
834C2C2×#1062282611yescharacteristic
835C2C4×#6698811yescharacteristic
836C2#1307128111yescharacteristic
837C2#1307144112yes—
838C2#1307160212yes—
839C2#1307193911yescharacteristic
840C2#1307194711yescharacteristic
841C2#1307208712yes—
842C2#1307216112yes—
843C2#1307292411yescharacteristic
844C2#1307350211yescharacteristic
subgroupG/H
center, FrattiniC24C23×D11
commutatorC23×C11C23×C4
FittingC22×C4×D4×C11C2
socle, cosocleC24×C11C24
prime radicalC23×D4×C11C22
hypercenterC22×C4×D4D11
hypocenterC11#13968
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ C22×C4×D4

Complements

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

NH ≅ G/Ntype
3. C2×#10622556C2semidirect
4. C22×C11⋊#95C2semidirect
5. #13066866C2semidirect
6. #13066863C2semidirect
7. #13066849C2semidirect
8. #13066839C2semidirect
9. #13066839C2semidirect
10. #13066838C2semidirect
30. C2×#66988C4semidirect
79. C23×Dic11C2×C4semidirect
107. C2×C22⋊Dic11C2×C4semidirect
108. C2×C22⋊Dic11C2×C4semidirect
112. C2×Dic11⋊C4C2×C4semidirect
336. C2×C4×C11#123semidirect
660. C11#13968semidirect
777. C2×C4#66988semidirect

Maximal subgroups

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

subgroupindex
C22×#669882
C2×#106228332
C2×#106225562
C22×C11⋊#952
#130668662
#130668632
#130668492
#130668392
#130668382
C22×C4×D4×C112
#1396811