Finite Group Databasebeta

← #14676557

Subgroups — #14676557

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×D4×Dic11C211yesmaximal, characteristic
2C2×#10622833C211yesmaximal, characteristic
3C2×#10622824C211yesmaximal, characteristic, complemented
4C22×C11⋊#95C211yesmaximal, characteristic, complemented
5#13066869C212yesmaximal, complemented
6#13066865C212yesmaximal, complemented
7#13066848C212yesmaximal, complemented
8#13066838C211yesmaximal, characteristic, complemented
9#13066838C212yesmaximal, complemented
10#13066838C211yesmaximal, characteristic, complemented
11C22×C11×#123C211yesmaximal, characteristic
12C23×D4×C11C2211yescharacteristic
13C24×C4×C11C2211yescharacteristic
14C24×Dic11C2211yescharacteristic
15C24×Dic11C2211yescharacteristic
16C24×Dic11C2211yescharacteristic
17C2×C11×#123—24no—
18C2×C11×#123—24no—
19C2×C11×#123C418yescomplemented
20C22×C11×C4⋊C4C2212yes—
21C22×C11×C22⋊C4C2211yescharacteristic
22C22×C11×C22⋊C4C2212yes—
23C22×C22⋊Dic11C2211yescharacteristic
24C22×C22⋊Dic11C2211yescharacteristic
25C22×C22⋊Dic11C2212yes—
26C22×C22⋊Dic11C2211yescharacteristic
27C2×D4×Dic11—24no—
28C2×D4×Dic11—24no—
29C2×D4×Dic11—24no—
30C22×C4⋊Dic11C2211yescharacteristic
31C22×C4×Dic11C2211yescharacteristic
32#10622833—24no—
33#10622824—24no—
34C2×C11⋊#95—24no—
35C2×C11⋊#95C2212yes—
36C2×C11⋊#95C2212yes—
37C2×C11⋊#95C2212yes—
38C2×C11⋊#95C2212yes—
39C2×C11⋊#95C2212yes—
40C2×C11⋊#95C2212yes—
41C2×C11⋊#95C2212yes—
42C2×C11⋊#95C2212yes—
43C2×C11⋊#95C2212yes—
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—22no—
59C23×C4×C11C2×C414yescomplemented
60C23×C4×C11C2312yes—
61C23×C4×C11C2312yes—
62C23×C4×C11C2311yescharacteristic
63C23×Dic11—22no—
64C23×Dic11—22no—
65C23×Dic11—22no—
66C23×Dic11—22no—
67C23×Dic11—22no—
68C23×Dic11—22no—
69C23×Dic11—24no—
70C23×Dic11—24no—
71C23×Dic11—22no—
72C23×Dic11—22no—
73C23×Dic11—24no—
74C23×Dic11—42no—
75C23×Dic11—42no—
76C23×Dic11—42no—
77C23×Dic11D414yes—
78C23×Dic11C2312yes—
79C23×Dic11C2311yescharacteristic
80C23×Dic11C2311yescharacteristic
81C23×Dic11C2311yescharacteristic
82C23×Dic11C2312yes—
83C23×Dic11C2311yescharacteristic
84C11×#123—232no—
85C2×C11×C4⋊C4—24no—
86C2×C11×C4⋊C4—24no—
87C2×C11×C4⋊C4C2×C418yescomplemented
88C2×C11×C22⋊C4—22no—
89C2×C11×C22⋊C4—22no—
90C2×C11×C22⋊C4—24no—
91C2×C11×C22⋊C4—24no—
92C2×C11×C22⋊C4C2×C414yescomplemented
93C2×C11×C22⋊C4C2×C418yescomplemented
94C2×C22⋊Dic11—22no—
95C2×C22⋊Dic11—22no—
96C2×C22⋊Dic11—22no—
97C2×C22⋊Dic11—22no—
98C2×C22⋊Dic11—22no—
99C2×C22⋊Dic11—22no—
100C2×C22⋊Dic11—24no—
101C2×C22⋊Dic11—22no—
102C2×C22⋊Dic11—22no—
103C2×C22⋊Dic11—24no—
104C2×C22⋊Dic11—42no—
105C2×C22⋊Dic11D414yes—
106D4×Dic11—232no—
107C2×C4⋊Dic11—22no—
108C2×C4⋊Dic11—22no—
109C2×C4⋊Dic11—22no—
110C2×C4×Dic11—22no—
111C2×C4×Dic11—22no—
112C2×C4×Dic11—22no—
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—28no—
158C22×C4×C11—28no—
159C22×C4×C11—28no—
160C22×C4×C11—22no—
161C22×C4×C11—22no—
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×C11—44no—
173C22×C4×C11—44no—
174C22×C4×C11—44no—
175C22×C4×C11—44no—
176C22×C4×C11C22×C414yes—
177C22×C4×C11C22×C414yes—
178C22×C4×C11C22×C412yes—
179C22×C4×C11C2×D412yes—
180C22×C4×C11C2×D412yes—
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—21no—
190C22×Dic11—21no—
191C22×Dic11—21no—
192C22×Dic11—21no—
193C22×Dic11—21no—
194C22×Dic11—21no—
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—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×D412yes—
228C22×Dic11#4114yes—
229C22×Dic11#4114yes—
230C11×C4⋊C4—216no—
231C11×C22⋊C4—28no—
232C11×C22⋊C4—216no—
233C22⋊Dic11—28no—
234C22⋊Dic11—28no—
235C22⋊Dic11—48no—
236C22⋊Dic11—44no—
237C4⋊Dic11—28no—
238C4×Dic11—28no—
239C22×#123D1111yescharacteristic
240C22×C4×D4—111no—
241C2×#386—111no—
242C2×#381—111no—
243C22×#95—111no—
244#1441—112no—
245#1440—112no—
246#1436—112no—
247C22⋊#95—111no—
248C22⋊#95—111no—
249C22⋊#95—112no—
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—24no—
315C2×C4×C11—24no—
316C2×C4×C11—24no—
317C2×C4×C11—24no—
318C2×C4×C11—24no—
319C2×C4×C11—24no—
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—416no—
329C2×C4×C11C2×C22⋊C414yes—
330C2×Dic11—22no—
331C2×Dic11—22no—
332C2×Dic11—24no—
333C2×Dic11—24no—
334C2×Dic11—22no—
335C2×Dic11—22no—
336C2×Dic11—22no—
337C2×Dic11—22no—
338C2×Dic11—24no—
339C2×Dic11—22no—
340C2×Dic11—24no—
341C2×Dic11—24no—
342C2×Dic11—24no—
343C2×Dic11—24no—
344C2×Dic11—416no—
345C2×Dic11—416no—
346C2×Dic11—416no—
347C2×Dic11—42no—
348C2×Dic11—41no—
349C2×Dic11—41no—
350C2×Dic11—41no—
351C2×Dic11—42no—
352C2×Dic11—41no—
353C2×Dic11—42no—
354C2×Dic11—42no—
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#12314yescomplemented
367C23×D4C2×D1111yescharacteristic
368C24×C4—111no—
369C24×C4—111no—
370C24×C4—111no—
371C24×C4C2×D1111yescharacteristic
372C2×#123—24no—
373C2×#123—24no—
374C2×#123Dic1118yescomplemented
375C2×C4×D4—224no—
376C2×C4×D4—224no—
377C2×C4×D4—224no—
378C22×C4⋊C4—111no—
379C22×C4⋊C4C2×D1112yes—
380C22×C22⋊C4—111no—
381C22×C22⋊C4—111no—
382C22×C22⋊C4—111no—
383C22×C22⋊C4—112no—
384C22×C22⋊C4C2×D1111yescharacteristic
385C22×C22⋊C4C2×D1112yes—
386C22×C42—111no—
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—44no—
446C4×C11—44no—
447Dic11—24no—
448Dic11—42no—
449Dic11—42no—
450Dic11—42no—
451Dic11—44no—
452Dic11—82no—
453C25C22×D1111yescharacteristic
454C25C22×D1111yescharacteristic
455C22×D4—22no—
456C22×D4—22no—
457C22×D4—22no—
458C22×D4—22no—
459C22×D4C2×Dic1114yes—
460C22×D4C22⋊D1114yes—
461C22×D4C22⋊D1114yes—
462C23×C4—22no—
463C23×C4—22no—
464C23×C4—22no—
465C23×C4—22no—
466C23×C4—22no—
467C23×C4—22no—
468C23×C4—111no—
469C23×C4—111no—
470C23×C4—111no—
471C23×C4—111no—
472C23×C4—112no—
473C23×C4—114no—
474C23×C4—112no—
475C23×C4—222no—
476C23×C4—222no—
477C23×C4—224no—
478C23×C4—224no—
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×D1112yes—
492C23×C4C22×D1111yescharacteristic
493#123—232no—
494C4×D4—2232no—
495C2×C4⋊C4—24no—
496C2×C4⋊C4—24no—
497C2×C4⋊C4—222no—
498C2×C4⋊C4—222no—
499C2×C4⋊C4—222no—
500C2×C4⋊C4C2×Dic1118yescomplemented
501C2×C22⋊C4—22no—
502C2×C22⋊C4—22no—
503C2×C22⋊C4—24no—
504C2×C22⋊C4—24no—
505C2×C22⋊C4—114no—
506C2×C22⋊C4—222no—
507C2×C22⋊C4—222no—
508C2×C22⋊C4—222no—
509C2×C22⋊C4—222no—
510C2×C22⋊C4—222no—
511C2×C22⋊C4—224no—
512C2×C22⋊C4—222no—
513C2×C22⋊C4—222no—
514C2×C22⋊C4—224no—
515C2×C22⋊C4—222no—
516C2×C22⋊C4—442no—
517C2×C22⋊C4C2×Dic1114yescomplemented
518C2×C22⋊C4C2×Dic1118yescomplemented
519C2×C42—222no—
520C2×C42—222no—
521C2×C42—222no—
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—21no—
551C24—21no—
552C24—22no—
553C24—22no—
554C24—22no—
555C24—22no—
556C24D4×D1112yes—
557C24D4×D1112yes—
558C24#434112yes—
559C24#434112yes—
560C24C22×Dic1112yes—
561C24C22×Dic1112yes—
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×D4C22⋊Dic11116yes—
574C22×C4—21no—
575C22×C4—21no—
576C22×C4—21no—
577C22×C4—21no—
578C22×C4—28no—
579C22×C4—28no—
580C22×C4—28no—
581C22×C4—22no—
582C22×C4—22no—
583C22×C4—22no—
584C22×C4—22no—
585C22×C4—22no—
586C22×C4—22no—
587C22×C4—22no—
588C22×C4—22no—
589C22×C4—22no—
590C22×C4—22no—
591C22×C4—22no—
592C22×C4—22no—
593C22×C4—44no—
594C22×C4—44no—
595C22×C4—44no—
596C22×C4—44no—
597C22×C4—112no—
598C22×C4—114no—
599C22×C4—112no—
600C22×C4—112no—
601C22×C4—112no—
602C22×C4—114no—
603C22×C4—228no—
604C22×C4—221no—
605C22×C4—222no—
606C22×C4—221no—
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—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—221no—
626C22×C4—221no—
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—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×C4C22×Dic1114yes—
647C22×C4C22×Dic1114yes—
648C22×C4C22×Dic1112yes—
649C22×C4C2×C22⋊D1112yes—
650C22×C4C2×C22⋊D1112yes—
651C4⋊C4—216no—
652C4⋊C4—228no—
653C22⋊C4—28no—
654C22⋊C4—216no—
655C22⋊C4—228no—
656C22⋊C4—228no—
657C22⋊C4—448no—
658C22⋊C4—444no—
659C42—228no—
660C11#1396811yescharacteristic, complemented, Sylow
661C23—24no—
662C23—24no—
663C23—24no—
664C23—24no—
665C23—24no—
666C23—24no—
667C23—22no—
668C23—24no—
669C23—24no—
670C23—22no—
671C23—22no—
672C23—24no—
673C23—24no—
674C23—22no—
675C23—24no—
676C23—24no—
677C23—22no—
678C23—22no—
679C23—22no—
680C23—22no—
681C23—22no—
682C23—22no—
683C23—24no—
684C23—24no—
685C23—24no—
686C23—24no—
687C23—24no—
688C23—24no—
689C23—41no—
690C23—42no—
691C23—42no—
692C23—41no—
693C23—41no—
694C23—42no—
695C23—42no—
696C23—41no—
697C23—42no—
698C23—42no—
699C23D4×Dic1114yes—
700C23D4×Dic1114yes—
701C23#6698814yes—
702C23#6699014yes—
703C23#6699214yes—
704C23#6699214yes—
705C23C2×C22⋊Dic1114yes—
706C23C2×C22⋊Dic1114yes—
707C23C2×D4×D1111yescharacteristic
708C23C2×D4×D1111yescharacteristic
709C23C2×#434111yescharacteristic
710C23C2×#434111yescharacteristic
711C23#41×D1112yes—
712C23#41×D1112yes—
713C23#6704212yes—
714C23#6704312yes—
715C23C23×Dic1111yescharacteristic
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—24no—
728C2×C4—24no—
729C2×C4—24no—
730C2×C4—24no—
731C2×C4—42no—
732C2×C4—42no—
733C2×C4—42no—
734C2×C4—42no—
735C2×C4—416no—
736C2×C4—42no—
737C2×C4—42no—
738C2×C4—42no—
739C2×C4—42no—
740C2×C4—114no—
741C2×C4—222no—
742C2×C4—224no—
743C2×C4—222no—
744C2×C4—224no—
745C2×C4—222no—
746C2×C4—222no—
747C2×C4—222no—
748C2×C4—224no—
749C2×C4—222no—
750C2×C4—222no—
751C2×C4—224no—
752C2×C4—224no—
753C2×C4—224no—
754C2×C4—224no—
755C2×C4—4416no—
756C2×C4—4416no—
757C2×C4—4416no—
758C2×C4—442no—
759C2×C4—442no—
760C2×C4—442no—
761C2×C4—442no—
762C2×C4—442no—
763C2×C4—441no—
764C2×C4—441no—
765C2×C4—441no—
766C2×C4—442no—
767C2×C4—442no—
768C2×C4—441no—
769C2×C4—442no—
770C2×C4—442no—
771C2×C4—442no—
772C2×C4—442no—
773C2×C4—442no—
774C2×C4—442no—
775C2×C4—442no—
776C2×C4—442no—
777C2×C4C2×C22⋊Dic1114yes—
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#1062283318yes—
800C22#1062317911yescharacteristic
801C22#1062318012yes—
802C22#1062318112yes—
803C22D11×#12311yescharacteristic
804C22#1062318411yescharacteristic
805C22#1062318512yes—
806C22#1062318612yes—
807C22#1062318711yescharacteristic
808C22#1062318912yes—
809C22#1062319612yes—
810C22C2×D4×Dic1111yescharacteristic
811C22C2×D4×Dic1111yescharacteristic
812C22C2×#6698811yescharacteristic
813C22C2×#6699011yescharacteristic
814C22C2×#6699211yescharacteristic
815C22C2×#6699211yescharacteristic
816C22#1062335512yes—
817C22#1062335512yes—
818C22#41×Dic1112yes—
819C22#1062335812yes—
820C22#1062336012yes—
821C22#1062336012yes—
822C22C22×C22⋊Dic1111yescharacteristic
823C4—24no—
824C4—44no—
825C4—44no—
826C4—224no—
827C4—442no—
828C4—442no—
829C4—442no—
830C4—444no—
831C4—882no—
832C2—28no—
833C2—44no—
834C2C2×#1062283311yescharacteristic
835C2#123×Dic1111yescharacteristic
836C2#1307128811yescharacteristic
837C2#1307144612yes—
838C2#1307161212yes—
839C2#1307194011yescharacteristic
840C2#1307194811yescharacteristic
841C2#1307208912yes—
842C2#1307217112yes—
843C2#1307292111yescharacteristic
844C2#1307350511yescharacteristic
subgroupG/H
center, FrattiniC24C23×D11
commutatorC23×C11C23×C4
FittingC22×C11×#123C2
socle, cosocleC24×C11C24
prime radicalC23×D4×C11C22
hypercenterC22×#123D11
hypocenterC11#13968
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ C22×#123

Complements

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

NH ≅ G/Ntype
3. C2×#10622824C2semidirect
4. C22×C11⋊#95C2semidirect
5. #13066869C2semidirect
6. #13066865C2semidirect
7. #13066848C2semidirect
8. #13066838C2semidirect
9. #13066838C2semidirect
10. #13066838C2semidirect
19. C2×C11×#123C4semidirect
59. C23×C4×C11C2×C4semidirect
87. C2×C11×C4⋊C4C2×C4semidirect
92. C2×C11×C22⋊C4C2×C4semidirect
93. C2×C11×C22⋊C4C2×C4semidirect
366. C2×Dic11#123semidirect
374. C2×#123Dic11semidirect
489. C23×C4C2×Dic11semidirect
500. C2×C4⋊C4C2×Dic11semidirect
517. C2×C22⋊C4C2×Dic11semidirect
518. C2×C22⋊C4C2×Dic11semidirect
660. C11#13968semidirect

Maximal subgroups

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

subgroupindex
C22×D4×Dic112
C2×#106228332
C2×#106228242
C22×C11⋊#952
#130668692
#130668652
#130668482
#130668382
C22×C11×#1232
#1396811