Finite Group Databasebeta

← #14675558

Subgroups — #14675558

Order 2816.

3502 conjugacy classes of subgroups.

The subgroup lattice has 860 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#66946C211yesmaximal, characteristic, complemented
2C22×(C22⋊D11)⋊C4C212yesmaximal, complemented
3C2×#10622573C211yesmaximal, characteristic
4C2×C22⋊C4×Dic11C211yesmaximal, characteristic, complemented
5C2×#10622279C212yesmaximal, complemented
6#13066879C211yesmaximal, characteristic, complemented
7#13066860C212yesmaximal, complemented
8#13066856C211yesmaximal, characteristic, complemented
9#13066855C212yesmaximal, complemented
10#95×Dic11C211yesmaximal, characteristic, complemented
11C11×#1439C211yesmaximal, characteristic, complemented
12C23×C22⋊D11C2212yes—
13C24×Dic11C2211yescharacteristic
14C23×D44C2211yescharacteristic
15C23×C4×D11C2212yes—
16C22×C11×C4⋊C4C2211yescharacteristic
17C22×C11×C22⋊C4C2212yes—
18C22×C11×C22⋊C4C2211yescharacteristic
19C22×C22⋊Dic11C2211yescharacteristic
20C22×(C2×D11)⋊C4C2212yes—
21C22×(C2×D11)⋊C4C2212yes—
22C22×(C2×D11)⋊C4C2212yes—
23C22×(C2×D11)⋊C4C2212yes—
24C22×Dic11⋊C4C2212yes—
25C22×C4×Dic11C2211yescharacteristic
26C22×C4×Dic11C2212yes—
27C22×C4×Dic11C2211yescharacteristic
28C2×#66946—28no—
29C2×#66946—24no—
30C2×(C22⋊D11)⋊C4—28no—
31C2×(C22⋊D11)⋊C4—28no—
32C2×(C22⋊D11)⋊C4—28no—
33C2×C11×#95C2211yescharacteristic
34C2×C11×#95C2212yes—
35C2×C11⋊#95C2212yes—
36C2×C11⋊#95C2212yes—
37C2×C11⋊#95C2211yescharacteristic
38C2×C11⋊#95C2211yescharacteristic
39C2×C11⋊#95C2211yescharacteristic
40#10622573C418yescomplemented
41C22⋊C4×Dic11—24no—
42#10622279—28no—
43C25×C11C2311yescharacteristic
44C24×D11C2312yes—
45C23×C4×C11C2311yescharacteristic
46C23×C4×C11C2312yes—
47C23×C4×C11C2312yes—
48C23×C4×C11C2311yescharacteristic
49C22×C22⋊D11—24no—
50C22×C22⋊D11—24no—
51C22×C22⋊D11—24no—
52C22×C22⋊D11—24no—
53C22×C22⋊D11—24no—
54C22×C22⋊D11—24no—
55C22×C22⋊D11C2×C418yescomplemented
56C23×Dic11—24no—
57C23×Dic11—24no—
58C23×Dic11—22no—
59C23×Dic11—22no—
60C23×Dic11D414yescomplemented
61C23×Dic11C2311yescharacteristic
62C23×Dic11C2311yescharacteristic
63C23×Dic11C2311yescharacteristic
64C23×Dic11C2312yes—
65C23×Dic11C2311yescharacteristic
66C22×D44—24no—
67C22×D44—24no—
68C22×D44—22no—
69C22×D44—22no—
70C22×D44C2×C414yescomplemented
71C22×C4×D11—24no—
72C22×C4×D11—24no—
73C22×C4×D11—24no—
74C22×C4×D11—24no—
75C22×C4×D11—24no—
76C22×C4×D11—24no—
77C22×C4×D11D418yescomplemented
78C2×C11×C4⋊C4—24no—
79C2×C11×C4⋊C4—22no—
80C2×C11×C22⋊C4—24no—
81C2×C11×C22⋊C4—24no—
82C2×C11×C22⋊C4—24no—
83C2×C11×C22⋊C4—22no—
84C2×C11×C22⋊C4—22no—
85C2×C11×C22⋊C4C2×C414yescomplemented
86C2×C22⋊Dic11—22no—
87C2×C22⋊Dic11—22no—
88C2×C22⋊Dic11—22no—
89C2×(C2×D11)⋊C4—24no—
90C2×(C2×D11)⋊C4—24no—
91C2×(C2×D11)⋊C4—24no—
92C2×(C2×D11)⋊C4—24no—
93C2×(C2×D11)⋊C4—24no—
94C2×(C2×D11)⋊C4—24no—
95C2×(C2×D11)⋊C4—24no—
96C2×(C2×D11)⋊C4—24no—
97C2×(C2×D11)⋊C4—24no—
98C2×(C2×D11)⋊C4—24no—
99C2×(C2×D11)⋊C4—24no—
100C2×(C2×D11)⋊C4C2×C418yescomplemented
101C2×Dic11⋊C4—24no—
102C2×Dic11⋊C4—24no—
103C2×Dic11⋊C4—24no—
104C2×C4×Dic11—24no—
105C2×C4×Dic11—24no—
106C2×C4×Dic11—24no—
107C2×C4×Dic11—24no—
108C2×C4×Dic11—22no—
109C2×C4×Dic11D418yescomplemented
110C2×C4×Dic11D414yescomplemented
111#66946—232no—
112(C22⋊D11)⋊C4—264no—
113C11×#95—24no—
114C11×#95—22no—
115C11⋊#95—22no—
116C11⋊#95—24no—
117C11⋊#95—22no—
118C11⋊#95—24no—
119C11⋊#95C2×C414yescomplemented
120C4×#392—111nomaximal, Sylow
121C24×C11—21no—
122C24×C11—22no—
123C24×C11—22no—
124C24×C11—21no—
125C24×C11—21no—
126C24×C11—21no—
127C24×C11—22no—
128C24×C11—22no—
129C24×C11C22×C412yes—
130C24×C11C2×D412yes—
131C24×C11#4112yes—
132C24×C11C2411yescharacteristic
133C23×D11—22no—
134C23×D11—22no—
135C23×D11—22no—
136C23×D11—22no—
137C23×D11—22no—
138C23×D11—22no—
139C23×D11—22no—
140C23×D11—22no—
141C23×D11—22no—
142C23×D11—22no—
143C23×D11—22no—
144C23×D11—22no—
145C23×D11C22×C414yes—
146C23×D11C2×D414yes—
147C23×D11#4114yes—
148C22×C4×C11—22no—
149C22×C4×C11—22no—
150C22×C4×C11—22no—
151C22×C4×C11—21no—
152C22×C4×C11—22no—
153C22×C4×C11—22no—
154C22×C4×C11—22no—
155C22×C4×C11—22no—
156C22×C4×C11—22no—
157C22×C4×C11—22no—
158C22×C4×C11—22no—
159C22×C4×C11—22no—
160C22×C4×C11—22no—
161C22×C4×C11—22no—
162C22×C4×C11—22no—
163C22×C4×C11—22no—
164C22×C4×C11—21no—
165C22×C4×C11—22no—
166C22×C4×C11C22×C412yes—
167C22×C4×C11C22×C412yes—
168C22×C4×C11C2×D414yes—
169C22×C4×C11C2×D414yes—
170C22×C4×C11C2×D412yes—
171C22×C4×C11#4112yes—
172C2×C22⋊D11—216no—
173C2×C22⋊D11—216no—
174C2×C22⋊D11—216no—
175C2×C22⋊D11—216no—
176C2×C22⋊D11—216no—
177C2×C22⋊D11—216no—
178C2×C22⋊D11—216no—
179C22×Dic11—216no—
180C22×Dic11—28no—
181C22×Dic11—22no—
182C22×Dic11—22no—
183C22×Dic11—21no—
184C22×Dic11—22no—
185C22×Dic11—21no—
186C22×Dic11—22no—
187C22×Dic11—22no—
188C22×Dic11—22no—
189C22×Dic11—22no—
190C22×Dic11—22no—
191C22×Dic11—22no—
192C22×Dic11—22no—
193C22×Dic11—21no—
194C22×Dic11—21no—
195C22×Dic11—21no—
196C22×Dic11—21no—
197C22×Dic11—44no—
198C22×Dic11—48no—
199C22×Dic11—44no—
200C22×Dic11C22×C414yes—
201C22×Dic11C2×D412yes—
202C22×Dic11C2×D412yes—
203C22×Dic11C2×D414yes—
204C22×Dic11C2×D412yes—
205C22×Dic11C2×D414yes—
206C22×Dic11C2×D412yes—
207C22×Dic11C2×D414yes—
208C22×Dic11#4112yes—
209C22×Dic11#4114yes—
210C22×Dic11#4112yes—
211C2×D44—28no—
212C2×D44—28no—
213C2×D44—216no—
214C2×D44—216no—
215C2×D44—28no—
216C2×C4×D11—216no—
217C2×C4×D11—216no—
218C2×C4×D11—216no—
219C2×C4×D11—48no—
220C2×C4×D11—48no—
221C2×C4×D11—48no—
222C2×C4×D11—48no—
223C11×C4⋊C4—28no—
224C11×C22⋊C4—216no—
225C11×C22⋊C4—28no—
226C22⋊Dic11—28no—
227(C2×D11)⋊C4—216no—
228(C2×D11)⋊C4—216no—
229(C2×D11)⋊C4—216no—
230(C2×D11)⋊C4—216no—
231Dic11⋊C4—216no—
232C4×Dic11—216no—
233C4×Dic11—28no—
234C4×Dic11—44no—
235C22×C4×D4—111no—
236C22×C4×D4—112no—
237C2×#392—111no—
238C2×C4×C22⋊C4—112no—
239C2×C4×C22⋊C4—111no—
240#1444—111no—
241#1439—112no—
242#1439D1111yescharacteristic, complemented
243#1438—111no—
244#1438—112no—
245C4×#95—111no—
246C23×C11—22no—
247C23×C11—24no—
248C23×C11—24no—
249C23×C11—22no—
250C23×C11—24no—
251C23×C11—22no—
252C23×C11—22no—
253C23×C11—24no—
254C23×C11—24no—
255C23×C11—24no—
256C23×C11—22no—
257C23×C11—22no—
258C23×C11—41no—
259C23×C11—42no—
260C23×C11—42no—
261C23×C11—42no—
262C23×C11—41no—
263C23×C11—42no—
264C23×C11—41no—
265C23×C11—42no—
266C23×C11—41no—
267C23×C11—42no—
268C23×C11C4×D414yescomplemented
269C23×C11C23×C411yescharacteristic
270C23×C11C22×D412yes—
271C23×C11C22×D411yescharacteristic
272C23×C11C22×D411yescharacteristic
273C23×C11C22×D412yes—
274C23×C11C2×#4111yescharacteristic
275C23×C11C2×#4111yescharacteristic
276C23×C11C2×#4112yes—
277C23×C11C2×#4112yes—
278C23×C11C2×#4111yescharacteristic
279C23×C11C2×#4111yescharacteristic
280C22×D11—24no—
281C22×D11—24no—
282C22×D11—24no—
283C22×D11—24no—
284C22×D11—24no—
285C22×D11—24no—
286C22×D11—24no—
287C22×D11—24no—
288C22×D11—24no—
289C22×D11—24no—
290C22×D11—24no—
291C22×D11—24no—
292C22×D11—24no—
293C22×D11—24no—
294C22×D11—24no—
295C22×D11—24no—
296C22×D11—24no—
297C22×D11—24no—
298C22×D11—42no—
299C22×D11—42no—
300C22×D11—42no—
301C22×D11—42no—
302C22×D11—42no—
303C22×D11—42no—
304C22×D11—42no—
305C22×D11—42no—
306C22×D11—42no—
307C22×D11—42no—
308C22×D11—42no—
309C22×D11—42no—
310C22×D11—42no—
311C22×D11—42no—
312C22×D11—42no—
313C22×D11—42no—
314C22×D11C4×D418yescomplemented
315C2×C4×C11—24no—
316C2×C4×C11—22no—
317C2×C4×C11—22no—
318C2×C4×C11—24no—
319C2×C4×C11—24no—
320C2×C4×C11—22no—
321C2×C4×C11—24no—
322C2×C4×C11—24no—
323C2×C4×C11—24no—
324C2×C4×C11—24no—
325C2×C4×C11—24no—
326C2×C4×C11—24no—
327C2×C4×C11—42no—
328C2×C4×C11—42no—
329C2×C4×C11—42no—
330C2×C4×C11—42no—
331C2×C4×C11—42no—
332C2×C4×C11—41no—
333C2×C4×C11—42no—
334C2×C4×C11—42no—
335C2×C4×C11—42no—
336C2×C4×C11—41no—
337C2×C4×C11—42no—
338C2×C4×C11C4×D414yescomplemented
339C22⋊D11—264no—
340C2×Dic11—24no—
341C2×Dic11—24no—
342C2×Dic11—24no—
343C2×Dic11—24no—
344C2×Dic11—24no—
345C2×Dic11—24no—
346C2×Dic11—22no—
347C2×Dic11—24no—
348C2×Dic11—22no—
349C2×Dic11—24no—
350C2×Dic11—22no—
351C2×Dic11—22no—
352C2×Dic11—22no—
353C2×Dic11—41no—
354C2×Dic11—42no—
355C2×Dic11—42no—
356C2×Dic11—42no—
357C2×Dic11—41no—
358C2×Dic11—41no—
359C2×Dic11—41no—
360C2×Dic11—42no—
361C2×Dic11—416no—
362C2×Dic11C4×D418yescomplemented
363C2×Dic11#12014yes—
364C2×Dic11#12018yes—
365C2×Dic11#12118yes—
366C2×Dic11#12114yes—
367C2×Dic11#12714yes—
368D44—232no—
369C4×D11—432no—
370C23×D4—112no—
371C23×D4—111no—
372C24×C4—111no—
373C24×C4—112no—
374C2×C4×D4—228no—
375C2×C4×D4—224no—
376C2×C4×D4—228no—
377C2×C4×D4—228no—
378C2×C4×D4—228no—
379C22×C4⋊C4—112no—
380C22×C4⋊C4C2×D1111yescharacteristic
381C22×C22⋊C4—112no—
382C22×C22⋊C4—111no—
383C22×C22⋊C4—112no—
384C22×C22⋊C4—112no—
385C22×C22⋊C4—112no—
386C22×C22⋊C4C2×D1112yes—
387C22×C22⋊C4C2×D1111yescharacteristic
388C22×C42—112no—
389C22×C42—111no—
390C22×C42—111no—
391#392—118no—
392C4×C22⋊C4—228no—
393C4×C22⋊C4—224no—
394C2×#95—111no—
395C2×#95—112no—
396C2×#95—112no—
397C2×#95—111no—
398C2×#95—111no—
399C2×#95C2×D1111yescharacteristic
400C2×#95C2×D1112yes—
401C22×C11—28no—
402C22×C11—24no—
403C22×C11—42no—
404C22×C11—42no—
405C22×C11—44no—
406C22×C11—42no—
407C22×C11—42no—
408C22×C11—44no—
409C22×C11—42no—
410C22×C11—42no—
411C22×C11—44no—
412C22×C11C2×C4×D411yescharacteristic
413C22×C11C2×C4×D411yescharacteristic
414C22×C11C2×C4×D412yes—
415C22×C11C2×C4×D412yes—
416C22×C11C4×#4111yescharacteristic
417C22×C11C2×#12011yescharacteristic
418C22×C11C2×#12012yes—
419C22×C11C2×#12112yes—
420C22×C11C2×#12111yescharacteristic
421C22×C11#52512yes—
422C22×C11#52512yes—
423C22×C11#52511yescharacteristic
424C22×C11#52512yes—
425C22×C11#52512yes—
426C22×C11#52512yes—
427C22×C11#52511yescharacteristic
428C22×C11#52912yes—
429C22×C11#52911yescharacteristic
430C22×C11C2×#12711yescharacteristic
431C22×C11#53212yes—
432C22×C11#53211yescharacteristic
433C22×C11#53211yescharacteristic
434C22×C11#53212yes—
435C2×D11—28no—
436C2×D11—28no—
437C2×D11—28no—
438C2×D11—44no—
439C2×D11—44no—
440C2×D11—44no—
441C2×D11—44no—
442C2×D11—44no—
443C2×D11—44no—
444C2×D11—44no—
445C2×D11—44no—
446C2×D11—44no—
447C2×D11—44no—
448C2×D11—44no—
449C2×D11—44no—
450C4×C11—24no—
451C4×C11—42no—
452C4×C11—44no—
453C4×C11—44no—
454Dic11—28no—
455Dic11—42no—
456Dic11—42no—
457Dic11—42no—
458Dic11#39218yescomplemented
459C25—112no—
460C25C22×D1111yescharacteristic
461C22×D4—118no—
462C22×D4—114no—
463C22×D4—224no—
464C22×D4—224no—
465C22×D4—224no—
466C22×D4—224no—
467C22×D4—224no—
468C22×D4—224no—
469C22×D4—224no—
470C22×D4—224no—
471C22×D4—222no—
472C22×D4—222no—
473C23×C4—111no—
474C23×C4—112no—
475C23×C4—114no—
476C23×C4—111no—
477C23×C4—111no—
478C23×C4—111no—
479C23×C4—118no—
480C23×C4—224no—
481C23×C4—224no—
482C23×C4—224no—
483C23×C4—224no—
484C23×C4—224no—
485C23×C4—224no—
486C23×C4—224no—
487C23×C4—224no—
488C23×C4—222no—
489C23×C4—222no—
490C23×C4C22×D1111yescharacteristic
491C23×C4C22×D1112yes—
492C23×C4C22×D1112yes—
493C23×C4C22×D1111yescharacteristic
494C4×D4—2264no—
495C4×D4—2232no—
496C2×C4⋊C4—24no—
497C2×C4⋊C4—22no—
498C2×C4⋊C4—224no—
499C2×C4⋊C4—224no—
500C2×C4⋊C4—224no—
501C2×C22⋊C4—24no—
502C2×C22⋊C4—24no—
503C2×C22⋊C4—24no—
504C2×C22⋊C4—22no—
505C2×C22⋊C4—22no—
506C2×C22⋊C4—118no—
507C2×C22⋊C4—224no—
508C2×C22⋊C4—224no—
509C2×C22⋊C4—224no—
510C2×C22⋊C4—224no—
511C2×C22⋊C4—224no—
512C2×C22⋊C4—224no—
513C2×C22⋊C4—224no—
514C2×C22⋊C4—224no—
515C2×C22⋊C4—222no—
516C2×C22⋊C4—222no—
517C2×C22⋊C4—222no—
518C2×C22⋊C4—224no—
519C2×C22⋊C4—224no—
520C2×C22⋊C4—224no—
521C2×C22⋊C4C4×D1114yescomplemented
522C2×C42—118no—
523C2×C42—114no—
524C2×C42—224no—
525C2×C42—224no—
526C2×C42—224no—
527C2×C42—224no—
528C2×C42—222no—
529#95—24no—
530#95—22no—
531#95—114no—
532#95—224no—
533#95—224no—
534#95—222no—
535#95—222no—
536C2×C11—44no—
537C2×C11C4×#12012yes—
538C2×C11C4×#12011yescharacteristic
539C2×C11C4×#12111yescharacteristic
540C2×C11C4×#12112yes—
541C2×C11C4×#12711yescharacteristic
542C2×C11C2×#39211yescharacteristic
543C2×C11#238812yes—
544C2×C11#238811yescharacteristic
545C2×C11#239211yescharacteristic
546C2×C11#239212yes—
547C2×C11#239711yescharacteristic
548D11—48no—
549C24—21no—
550C24—22no—
551C24—22no—
552C24—21no—
553C24—21no—
554C24—21no—
555C24—22no—
556C24—22no—
557C24—114no—
558C24—114no—
559C24—114no—
560C24—222no—
561C24—222no—
562C24—222no—
563C24—222no—
564C24—222no—
565C24—222no—
566C24—222no—
567C24—222no—
568C24—222no—
569C24—222no—
570C24—222no—
571C24—222no—
572C24C2×C4×D1112yes—
573C24D4×D1112yes—
574C24#434312yes—
575C24C23×D1111yescharacteristic
576C2×D4—2216no—
577C2×D4—228no—
578C2×D4—2216no—
579C2×D4—228no—
580C2×D4—2216no—
581C2×D4—2216no—
582C2×D4—2216no—
583C2×D4—2216no—
584C2×D4—2216no—
585C2×D4—2216no—
586C2×D4—2216no—
587C2×D4—228no—
588C22×C4—22no—
589C22×C4—22no—
590C22×C4—22no—
591C22×C4—22no—
592C22×C4—21no—
593C22×C4—22no—
594C22×C4—22no—
595C22×C4—22no—
596C22×C4—22no—
597C22×C4—22no—
598C22×C4—22no—
599C22×C4—22no—
600C22×C4—21no—
601C22×C4—22no—
602C22×C4—22no—
603C22×C4—22no—
604C22×C4—22no—
605C22×C4—22no—
606C22×C4—112no—
607C22×C4—114no—
608C22×C4—112no—
609C22×C4—114no—
610C22×C4—112no—
611C22×C4—114no—
612C22×C4—114no—
613C22×C4—114no—
614C22×C4—112no—
615C22×C4—112no—
616C22×C4—112no—
617C22×C4—2216no—
618C22×C4—2216no—
619C22×C4—2216no—
620C22×C4—2216no—
621C22×C4—228no—
622C22×C4—222no—
623C22×C4—222no—
624C22×C4—222no—
625C22×C4—222no—
626C22×C4—221no—
627C22×C4—221no—
628C22×C4—222no—
629C22×C4—222no—
630C22×C4—222no—
631C22×C4—222no—
632C22×C4—221no—
633C22×C4—221no—
634C22×C4—222no—
635C22×C4—221no—
636C22×C4—222no—
637C22×C4—221no—
638C22×C4—448no—
639C22×C4—448no—
640C22×C4—448no—
641C22×C4—448no—
642C22×C4—444no—
643C22×C4—444no—
644C22×C4—448no—
645C22×C4C2×C4×D1112yes—
646C22×C4C2×C4×D1112yes—
647C22×C4D4×D1114yes—
648C22×C4D4×D1114yes—
649C22×C4D4×D1112yes—
650C22×C4#434112yes—
651C4⋊C4—28no—
652C4⋊C4—2216no—
653C22⋊C4—216no—
654C22⋊C4—28no—
655C22⋊C4—2216no—
656C22⋊C4—2216no—
657C22⋊C4—2216no—
658C22⋊C4—2216no—
659C22⋊C4—228no—
660C42—228no—
661C42—2216no—
662C42—444no—
663C11C4×#39211yescharacteristic, complemented, Sylow
664C23—22no—
665C23—22no—
666C23—24no—
667C23—24no—
668C23—24no—
669C23—22no—
670C23—22no—
671C23—22no—
672C23—22no—
673C23—24no—
674C23—24no—
675C23—24no—
676C23—42no—
677C23—41no—
678C23—41no—
679C23—42no—
680C23—42no—
681C23—42no—
682C23—41no—
683C23—42no—
684C23—42no—
685C23—41no—
686C23—118no—
687C23—224no—
688C23—224no—
689C23—224no—
690C23—224no—
691C23—224no—
692C23—224no—
693C23—224no—
694C23—224no—
695C23—224no—
696C23—224no—
697C23—224no—
698C23—224no—
699C23—224no—
700C23—224no—
701C23—224no—
702C23—224no—
703C23—224no—
704C23—224no—
705C23—442no—
706C23—442no—
707C23—442no—
708C23—442no—
709C23—442no—
710C23—442no—
711C23—442no—
712C23—442no—
713C23—442no—
714C23—442no—
715C23—442no—
716C23—442no—
717C23—442no—
718C23—442no—
719C23—442no—
720C23—442no—
721C23#6694614yescomplemented
722C23C22×C4×D1111yescharacteristic
723C23C2×D4×D1111yescharacteristic
724C23C2×D4×D1112yes—
725C23C2×D4×D1111yescharacteristic
726C23C2×D4×D1112yes—
727C23C2×#434111yescharacteristic
728C23C2×#434311yescharacteristic
729C23#41×D1111yescharacteristic
730C23#41×D1112yes—
731C23#41×D1112yes—
732C23#41×D1111yescharacteristic
733D4—2232no—
734D4—2264no—
735C2×C4—24no—
736C2×C4—22no—
737C2×C4—24no—
738C2×C4—22no—
739C2×C4—22no—
740C2×C4—24no—
741C2×C4—24no—
742C2×C4—24no—
743C2×C4—24no—
744C2×C4—24no—
745C2×C4—24no—
746C2×C4—24no—
747C2×C4—41no—
748C2×C4—42no—
749C2×C4—42no—
750C2×C4—42no—
751C2×C4—42no—
752C2×C4—42no—
753C2×C4—42no—
754C2×C4—42no—
755C2×C4—42no—
756C2×C4—41no—
757C2×C4—42no—
758C2×C4—114no—
759C2×C4—118no—
760C2×C4—114no—
761C2×C4—114no—
762C2×C4—118no—
763C2×C4—118no—
764C2×C4—224no—
765C2×C4—224no—
766C2×C4—224no—
767C2×C4—224no—
768C2×C4—224no—
769C2×C4—224no—
770C2×C4—222no—
771C2×C4—224no—
772C2×C4—222no—
773C2×C4—222no—
774C2×C4—222no—
775C2×C4—224no—
776C2×C4—222no—
777C2×C4—4432no—
778C2×C4—4416no—
779C2×C4—441no—
780C2×C4—441no—
781C2×C4—441no—
782C2×C4—442no—
783C2×C4—442no—
784C2×C4—442no—
785C2×C4—441no—
786C2×C4—442no—
787C2×C4(C22⋊D11)⋊C414yescomplemented
788C22—28no—
789C22—24no—
790C22—42no—
791C22—44no—
792C22—42no—
793C22—42no—
794C22—42no—
795C22—44no—
796C22—42no—
797C22—42no—
798C22—44no—
799C22—228no—
800C22—228no—
801C22—228no—
802C22—444no—
803C22—444no—
804C22—444no—
805C22—444no—
806C22—444no—
807C22—444no—
808C22—444no—
809C22—444no—
810C22—444no—
811C22—444no—
812C22—444no—
813C22—444no—
814C22C2×(C22⋊D11)⋊C411yescharacteristic
815C22C2×#6694611yescharacteristic
816C22#1062305311yescharacteristic
817C22C4×D4×D1112yes—
818C22C4×D4×D1112yes—
819C22D11×#12012yes—
820C22D11×#12011yescharacteristic
821C22#1062312711yescharacteristic
822C22#1062312712yes—
823C22D11×#12111yescharacteristic
824C22D11×#12112yes—
825C22#1062313712yes—
826C22#1062315511yescharacteristic
827C22#1062315812yes—
828C22#1062315812yes—
829C22#1062315811yescharacteristic
830C22#1062318712yes—
831C22#1062318711yescharacteristic
832C22#1062318712yes—
833C22#1062319912yes—
834C22#1062319911yescharacteristic
835C22#1062323712yes—
836C22D11×#12711yescharacteristic
837C4—24no—
838C4—42no—
839C4—44no—
840C4—44no—
841C4—118no—
842C4—228no—
843C4—442no—
844C4—442no—
845C4—442no—
846C2—44no—
847C2—448no—
848C2#1307111712yes—
849C2#1307112111yescharacteristic
850C2#1307112211yescharacteristic
851C2#1307112812yes—
852C2#1307118011yescharacteristic
853C2D11×#39211yescharacteristic
854C2#1307183012yes—
855C2#1307183311yescharacteristic
856C2#1307185311yescharacteristic
857C2#1307186112yes—
858C2#1307189611yescharacteristic
subgroupG/H
center, FrattiniC24C23×D11
commutatorC23×C11C23×C4
FittingC11×#1439C2
socle, cosocleC24×C11C24
prime radicalC2×#10622573C2
hypercenter#1439D11
hypocenterC11C4×#392
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ #1439

Complements

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

NH ≅ G/Ntype
1. C22×#66946C2semidirect
2. C22×(C22⋊D11)⋊C4C2semidirect
4. C2×C22⋊C4×Dic11C2semidirect
5. C2×#10622279C2semidirect
6. #13066879C2semidirect
7. #13066860C2semidirect
8. #13066856C2semidirect
9. #13066855C2semidirect
10. #95×Dic11C2semidirect
11. C11×#1439C2semidirect
40. #10622573C4semidirect
55. C22×C22⋊D11C2×C4semidirect
60. C23×Dic11D4semidirect
70. C22×D44C2×C4semidirect
77. C22×C4×D11D4semidirect
85. C2×C11×C22⋊C4C2×C4semidirect
100. C2×(C2×D11)⋊C4C2×C4semidirect
109. C2×C4×Dic11D4semidirect
110. C2×C4×Dic11D4semidirect
119. C11⋊#95C2×C4semidirect
242. #1439D11semidirect
268. C23×C11C4×D4semidirect
314. C22×D11C4×D4semidirect
338. C2×C4×C11C4×D4semidirect
362. C2×Dic11C4×D4semidirect
458. Dic11#392semidirect
521. C2×C22⋊C4C4×D11semidirect
663. C11C4×#392semidirect
721. C23#66946semidirect
787. C2×C4(C22⋊D11)⋊C4semidirect

Maximal subgroups

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

subgroupindex
C22×#669462
C22×(C22⋊D11)⋊C42
C2×#106225732
C2×C22⋊C4×Dic112
C2×#106222792
#130668792
#130668602
#130668562
#130668552
#95×Dic112
C11×#14392
C4×#39211