Finite Group Databasebeta

← #14685063

Subgroups — #14685063

Order 2816.

2734 conjugacy classes of subgroups.

The subgroup lattice has 734 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#66931C211yesmaximal, characteristic
2C23×C4×Dic11C211yesmaximal, characteristic
3C2×#10622259C212yesmaximal, complemented
4C2×#10622555C211yesmaximal, characteristic
5#13066850C212yesmaximal, complemented
6#13066847C212yesmaximal, complemented
7Dic11⋊#95C212yesmaximal, complemented
8#13066839C211yesmaximal, characteristic
9#13066838C211yesmaximal, characteristic
10#13066838C211yesmaximal, characteristic
11C11×C22⋊#95C211yesmaximal, characteristic
12C24×C4×C11C2211yescharacteristic
13C24×Dic11C2211yescharacteristic
14C24×Dic11C2211yescharacteristic
15C23×Dic22C2211yescharacteristic
16C22×C11×C22⋊C4C2211yescharacteristic
17C22×C11×C22⋊C4C2211yescharacteristic
18C22×C22⋊Dic11C2211yescharacteristic
19C22×C22⋊Dic11C2211yescharacteristic
20C22×C4⋊Dic11C2211yescharacteristic
21C22×Dic11⋊C4C2212yes—
22C22×Dic11⋊C4C2211yescharacteristic
23C22×Dic11⋊C4C2211yescharacteristic
24C22×C4×Dic11—24no—
25C22×C4×Dic11—28no—
26C22×C4×Dic11C2212yes—
27C22×C4×Dic11C2212yes—
28C2×#66931—24no—
29C2×#66931—24no—
30C2×#66931C418yescomplemented
31C2×C11×#95C2212yes—
32C2×C11×#95C2212yes—
33C2×C11⋊#95C2212yes—
34C2×C11⋊#95C2212yes—
35C2×C11⋊#95C2212yes—
36C2×C11⋊#95C2212yes—
37C2×C11⋊#95C2212yes—
38C2×C11⋊#95C2212yes—
39C2×C11⋊#95C2212yes—
40#10622555—24no—
41#10622259—28no—
42C25×C11C2311yescharacteristic
43C23×C4×C11—22no—
44C23×C4×C11—22no—
45C23×C4×C11—24no—
46C23×C4×C11—24no—
47C23×C4×C11Q814yescomplemented
48C23×C4×C11C2312yes—
49C23×C4×C11C2311yescharacteristic
50C23×C4×C11C2311yescharacteristic
51C23×C4×C11C2312yes—
52C23×Dic11—22no—
53C23×Dic11—22no—
54C23×Dic11—24no—
55C23×Dic11—24no—
56C23×Dic11—24no—
57C23×Dic11—24no—
58C23×Dic11C2×C414yes—
59C23×Dic11D414yes—
60C23×Dic11D414yes—
61C23×Dic11Q814yescomplemented
62C23×Dic11C2312yes—
63C23×Dic11C2311yescharacteristic
64C23×Dic11C2311yescharacteristic
65C23×Dic11C2311yescharacteristic
66C23×Dic11C2312yes—
67C23×Dic11C2311yescharacteristic
68C22×Dic22—22no—
69C22×Dic22—22no—
70C22×Dic22—24no—
71C22×Dic22—24no—
72C22×Dic22C2×C414yescomplemented
73C2×C11×C22⋊C4—22no—
74C2×C11×C22⋊C4—22no—
75C2×C11×C22⋊C4—22no—
76C2×C11×C22⋊C4—22no—
77C2×C11×C22⋊C4—22no—
78C2×C11×C22⋊C4C2×C414yes—
79C2×C22⋊Dic11—22no—
80C2×C22⋊Dic11—22no—
81C2×C22⋊Dic11—22no—
82C2×C22⋊Dic11—22no—
83C2×C22⋊Dic11—22no—
84C2×C22⋊Dic11C2×C414yes—
85C2×C4⋊Dic11—22no—
86C2×C4⋊Dic11—22no—
87C2×C4⋊Dic11C2×C414yescomplemented
88C2×Dic11⋊C4—22no—
89C2×Dic11⋊C4—22no—
90C2×Dic11⋊C4—22no—
91C2×Dic11⋊C4—22no—
92C2×Dic11⋊C4—24no—
93C2×Dic11⋊C4—24no—
94C2×Dic11⋊C4—24no—
95C2×Dic11⋊C4C2×C414yescomplemented
96C2×Dic11⋊C4C2×C414yescomplemented
97C2×C4×Dic11—232no—
98C2×C4×Dic11—24no—
99C2×C4×Dic11—24no—
100C2×C4×Dic11—24no—
101C2×C4×Dic11—24no—
102C2×C4×Dic11—24no—
103C2×C4×Dic11D418yes—
104#66931—232no—
105C11×#95—24no—
106C11×#95—24no—
107C11⋊#95—24no—
108C11⋊#95—24no—
109C11⋊#95—24no—
110C11⋊#95—24no—
111C11⋊#95—24no—
112C11⋊#95—24no—
113C11⋊#95—24no—
114#14702—111nomaximal, Sylow
115C24×C11—22no—
116C24×C11—22no—
117C24×C11—22no—
118C24×C11—22no—
119C24×C11C22×C412yes—
120C24×C11C2×D412yes—
121C24×C11C2×D412yes—
122C24×C11C2×Q812yes—
123C24×C11C2×Q812yes—
124C24×C11#4112yes—
125C24×C11#4112yes—
126C24×C11C2411yescharacteristic
127C22×C4×C11—28no—
128C22×C4×C11—216no—
129C22×C4×C11—28no—
130C22×C4×C11—28no—
131C22×C4×C11—22no—
132C22×C4×C11—22no—
133C22×C4×C11—22no—
134C22×C4×C11—22no—
135C22×C4×C11—216no—
136C22×C4×C11—22no—
137C22×C4×C11—21no—
138C22×C4×C11—21no—
139C22×C4×C11—21no—
140C22×C4×C11—21no—
141C22×C4×C11—22no—
142C22×C4×C11—22no—
143C22×C4×C11—22no—
144C22×C4×C11—22no—
145C22×C4×C11—22no—
146C22×C4×C11—22no—
147C22×C4×C11—22no—
148C22×C4×C11—22no—
149C22×C4×C11—22no—
150C22×C4×C11—22no—
151C22×C4×C11C22×C412yes—
152C22×C4×C11C22×C412yes—
153C22×C4×C11C2×D414yes—
154C22×C4×C11C2×Q814yes—
155C22×C4×C11#4114yes—
156C22×Dic11—28no—
157C22×Dic11—28no—
158C22×Dic11—216no—
159C22×Dic11—216no—
160C22×Dic11—28no—
161C22×Dic11—216no—
162C22×Dic11—216no—
163C22×Dic11—28no—
164C22×Dic11—28no—
165C22×Dic11—22no—
166C22×Dic11—22no—
167C22×Dic11—22no—
168C22×Dic11—22no—
169C22×Dic11—21no—
170C22×Dic11—21no—
171C22×Dic11—21no—
172C22×Dic11—21no—
173C22×Dic11—22no—
174C22×Dic11—22no—
175C22×Dic11—22no—
176C22×Dic11—22no—
177C22×Dic11—22no—
178C22×Dic11—22no—
179C22×Dic11—22no—
180C22×Dic11—22no—
181C22×Dic11—22no—
182C22×Dic11—22no—
183C22×Dic11—22no—
184C22×Dic11—22no—
185C22×Dic11—22no—
186C22×Dic11C22⋊C4116yes—
187C22×Dic11C22×C412yes—
188C22×Dic11C22×C412yes—
189C22×Dic11C22×C412yes—
190C22×Dic11C22×C412yes—
191C22×Dic11C2×D412yes—
192C22×Dic11C2×D412yes—
193C22×Dic11C2×D414yes—
194C22×Dic11C2×D412yes—
195C22×Dic11C2×D412yes—
196C22×Dic11C2×D414yes—
197C22×Dic11C2×Q814yes—
198C22×Dic11#4114yes—
199C22×Dic11#4114yes—
200C2×Dic22—28no—
201C2×Dic22—216no—
202C2×Dic22—44no—
203C2×Dic22—48no—
204C2×Dic22—44no—
205C11×C22⋊C4—28no—
206C11×C22⋊C4—44no—
207C22⋊Dic11—28no—
208C22⋊Dic11—44no—
209C4⋊Dic11—28no—
210Dic11⋊C4—28no—
211Dic11⋊C4—28no—
212Dic11⋊C4—48no—
213C4×Dic11—216no—
214C4×Dic11—216no—
215C22×C22⋊Q8—111no—
216C23×C42—111no—
217C2×#391—112no—
218C2×#380—111no—
219#1436—112no—
220#1436—112no—
221C4⋊#95—112no—
222C22⋊#95—111no—
223C22⋊#95—111no—
224C22⋊#95—111no—
225C22⋊#95D1111yescharacteristic
226C23×C11—24no—
227C23×C11—24no—
228C23×C11—22no—
229C23×C11—24no—
230C23×C11—24no—
231C23×C11—24no—
232C23×C11—22no—
233C23×C11—22no—
234C23×C11—24no—
235C23×C11—22no—
236C23×C11—24no—
237C23×C11—24no—
238C23×C11—24no—
239C23×C11—24no—
240C23×C11—24no—
241C23×C11—24no—
242C23×C11C2×C22⋊C414yes—
243C23×C11C4×Q814yes—
244C23×C11C4×Q814yes—
245C23×C11C22⋊Q814yes—
246C23×C11C22⋊Q814yes—
247C23×C11#12414yes—
248C23×C11C4⋊Q814yes—
249C23×C11C23×C411yescharacteristic
250C23×C11C22×D411yescharacteristic
251C23×C11C22×D411yescharacteristic
252C23×C11C22×D412yes—
253C23×C11C22×Q811yescharacteristic
254C23×C11C22×Q811yescharacteristic
255C23×C11C2×#4111yescharacteristic
256C23×C11C2×#4111yescharacteristic
257C23×C11C2×#4112yes—
258C23×C11C2×#4112yes—
259C23×C11C2×#4112yes—
260C2×C4×C11—232no—
261C2×C4×C11—24no—
262C2×C4×C11—24no—
263C2×C4×C11—24no—
264C2×C4×C11—24no—
265C2×C4×C11—24no—
266C2×C4×C11—24no—
267C2×C4×C11—22no—
268C2×C4×C11—22no—
269C2×C4×C11—24no—
270C2×C4×C11—24no—
271C2×C4×C11—41no—
272C2×C4×C11—42no—
273C2×C4×C11—41no—
274C2×C4×C11—41no—
275C2×C4×C11—41no—
276C2×C4×C11—42no—
277C2×C4×C11—42no—
278C2×C4×C11—42no—
279C2×C4×C11—42no—
280C2×C4×C11—42no—
281C2×C4×C11—42no—
282C2×C4×C11—42no—
283C2×C4×C11—42no—
284C2×C4×C11C22⋊Q818yescomplemented
285C2×Dic11—232no—
286C2×Dic11—24no—
287C2×Dic11—24no—
288C2×Dic11—22no—
289C2×Dic11—24no—
290C2×Dic11—24no—
291C2×Dic11—24no—
292C2×Dic11—22no—
293C2×Dic11—24no—
294C2×Dic11—24no—
295C2×Dic11—24no—
296C2×Dic11—232no—
297C2×Dic11—22no—
298C2×Dic11—22no—
299C2×Dic11—24no—
300C2×Dic11—24no—
301C2×Dic11—41no—
302C2×Dic11—42no—
303C2×Dic11—41no—
304C2×Dic11—41no—
305C2×Dic11—41no—
306C2×Dic11—42no—
307C2×Dic11—42no—
308C2×Dic11—42no—
309C2×Dic11—42no—
310C2×Dic11—42no—
311C2×Dic11—42no—
312C2×Dic11—42no—
313C2×Dic11—42no—
314C2×Dic11C2×C22⋊C414yes—
315C2×Dic11C2×C22⋊C414yes—
316C2×Dic11C4×D418yes—
317C2×Dic11#12014yes—
318C2×Dic11#12118yes—
319C2×Dic11C22⋊Q818yescomplemented
320C2×Dic11#12314yes—
321Dic22—416no—
322C23×Q8—111no—
323C24×C4—111no—
324C24×C4—111no—
325C24×C4C2×D1111yescharacteristic
326C2×C22⋊Q8—118no—
327C2×C22⋊Q8—224no—
328C2×C22⋊Q8—224no—
329C22×C4⋊C4—111no—
330C22×C4⋊C4—111no—
331C22×C4⋊C4—111no—
332C22×C4⋊C4—112no—
333C22×C22⋊C4—111no—
334C22×C22⋊C4—111no—
335C22×C22⋊C4C2×D1111yescharacteristic
336C22×C22⋊C4C2×D1111yescharacteristic
337C22×C42—112no—
338C22×C42—112no—
339C22×C42—228no—
340C22×C42—224no—
341#391—228no—
342#380—224no—
343C2×#95—112no—
344C2×#95—112no—
345C2×#95—112no—
346C2×#95—112no—
347C2×#95—112no—
348C2×#95—112no—
349C2×#95—112no—
350C2×#95C2×D1112yes—
351C2×#95C2×D1112yes—
352C22×C11—24no—
353C22×C11—24no—
354C22×C11—28no—
355C22×C11—24no—
356C22×C11—24no—
357C22×C11—28no—
358C22×C11—24no—
359C22×C11—24no—
360C22×C11—28no—
361C22×C11—28no—
362C22×C11#39118yescomplemented
363C22×C11C22×C22⋊C411yescharacteristic
364C22×C11C2×C4×D412yes—
365C22×C11C2×C4×Q811yescharacteristic
366C22×C11C2×C4×Q811yescharacteristic
367C22×C11C4×#4112yes—
368C22×C11C2×#12011yescharacteristic
369C22×C11C2×#12112yes—
370C22×C11C2×C22⋊Q811yescharacteristic
371C22×C11C2×C22⋊Q812yes—
372C22×C11C2×C22⋊Q811yescharacteristic
373C22×C11C2×C22⋊Q812yes—
374C22×C11C2×#12311yescharacteristic
375C22×C11#52512yes—
376C22×C11#52512yes—
377C22×C11#52511yescharacteristic
378C22×C11#52511yescharacteristic
379C22×C11C2×#12411yescharacteristic
380C22×C11#52912yes—
381C22×C11#52912yes—
382C22×C11C2×C4⋊Q811yescharacteristic
383C22×C11#53212yes—
384C22×C11#53312yes—
385C22×C11#53312yes—
386C4×C11—28no—
387C4×C11—42no—
388C4×C11—42no—
389C4×C11—82no—
390Dic11—28no—
391Dic11—24no—
392Dic11—42no—
393Dic11—42no—
394Dic11—82no—
395Dic11#38618yes—
396C25C22×D1111yescharacteristic
397C22×Q8—114no—
398C22×Q8—222no—
399C22×Q8—222no—
400C22×Q8—224no—
401C22×Q8—224no—
402C23×C4—22no—
403C23×C4—22no—
404C23×C4—24no—
405C23×C4—24no—
406C23×C4—111no—
407C23×C4—114no—
408C23×C4—114no—
409C23×C4—114no—
410C23×C4—111no—
411C23×C4—112no—
412C23×C4—114no—
413C23×C4—111no—
414C23×C4—111no—
415C23×C4—112no—
416C23×C4—224no—
417C23×C4—224no—
418C23×C4—224no—
419C23×C4—224no—
420C23×C4—222no—
421C23×C4—222no—
422C23×C4Dic2214yescomplemented
423C23×C4C22×D1112yes—
424C23×C4C22×D1111yescharacteristic
425C23×C4C22×D1111yescharacteristic
426C23×C4C22×D1112yes—
427C22⋊Q8—2232no—
428C2×C4⋊C4—114no—
429C2×C4⋊C4—114no—
430C2×C4⋊C4—114no—
431C2×C4⋊C4—222no—
432C2×C4⋊C4—222no—
433C2×C4⋊C4—222no—
434C2×C4⋊C4—222no—
435C2×C4⋊C4—222no—
436C2×C4⋊C4—222no—
437C2×C4⋊C4—224no—
438C2×C4⋊C4—224no—
439C2×C4⋊C4—224no—
440C2×C22⋊C4—22no—
441C2×C22⋊C4—22no—
442C2×C22⋊C4—22no—
443C2×C22⋊C4—22no—
444C2×C22⋊C4—22no—
445C2×C22⋊C4—114no—
446C2×C22⋊C4—222no—
447C2×C22⋊C4—222no—
448C2×C22⋊C4—222no—
449C2×C22⋊C4—222no—
450C2×C22⋊C4—222no—
451C2×C22⋊C4C4×D1114yes—
452C2×C42—118no—
453C2×C42—224no—
454C2×C42—224no—
455C2×C42—224no—
456C2×C42—224no—
457C2×C42—2232no—
458C2×C42—224no—
459#95—24no—
460#95—24no—
461#95—224no—
462#95—224no—
463#95—224no—
464#95—224no—
465#95—224no—
466#95—224no—
467#95—224no—
468C2×C11—28no—
469C2×C11C2×#38611yescharacteristic
470C2×C11C2×#39111yescharacteristic
471C2×C11#229711yescharacteristic
472C2×C11C4×C22⋊Q812yes—
473C2×C11C4×C22⋊Q812yes—
474C2×C11#284811yescharacteristic
475C2×C11#284811yescharacteristic
476C2×C11#285012yes—
477C2×C11#285511yescharacteristic
478C2×C11#285511yescharacteristic
479C2×C11#285712yes—
480C24—22no—
481C24—22no—
482C24—22no—
483C24—22no—
484C24C2×Dic2212yes—
485C24C2×C4×D1112yes—
486C24#433912yes—
487C24D4×D1112yes—
488C24D4×D1112yes—
489C24#434112yes—
490C24Q8×D1112yes—
491C24C23×D1111yescharacteristic
492C2×Q8—228no—
493C2×Q8—2216no—
494C2×Q8—444no—
495C2×Q8—448no—
496C2×Q8—444no—
497C22×C4—28no—
498C22×C4—216no—
499C22×C4—28no—
500C22×C4—28no—
501C22×C4—22no—
502C22×C4—22no—
503C22×C4—22no—
504C22×C4—22no—
505C22×C4—216no—
506C22×C4—22no—
507C22×C4—21no—
508C22×C4—21no—
509C22×C4—21no—
510C22×C4—21no—
511C22×C4—22no—
512C22×C4—22no—
513C22×C4—22no—
514C22×C4—22no—
515C22×C4—22no—
516C22×C4—22no—
517C22×C4—22no—
518C22×C4—22no—
519C22×C4—22no—
520C22×C4—22no—
521C22×C4—112no—
522C22×C4—114no—
523C22×C4—112no—
524C22×C4—112no—
525C22×C4—114no—
526C22×C4—1116no—
527C22×C4—112no—
528C22×C4—114no—
529C22×C4—112no—
530C22×C4—112no—
531C22×C4—114no—
532C22×C4—114no—
533C22×C4—112no—
534C22×C4—112no—
535C22×C4—228no—
536C22×C4—2216no—
537C22×C4—2216no—
538C22×C4—228no—
539C22×C4—2216no—
540C22×C4—228no—
541C22×C4—2216no—
542C22×C4—228no—
543C22×C4—228no—
544C22×C4—222no—
545C22×C4—222no—
546C22×C4—222no—
547C22×C4—222no—
548C22×C4—222no—
549C22×C4—222no—
550C22×C4—222no—
551C22×C4—221no—
552C22×C4—221no—
553C22×C4—221no—
554C22×C4—221no—
555C22×C4—222no—
556C22×C4—222no—
557C22×C4—222no—
558C22×C4—222no—
559C22×C4—222no—
560C22×C4—222no—
561C22×C4—222no—
562C22×C4—222no—
563C22×C4—222no—
564C22×C4—222no—
565C22×C4C2×Dic2214yes—
566C22×C4C2×C4×D1112yes—
567C22×C4C2×C4×D1112yes—
568C22×C4D4×D1114yes—
569C22×C4#434114yes—
570C4⋊C4—228no—
571C4⋊C4—228no—
572C4⋊C4—228no—
573C4⋊C4—448no—
574C22⋊C4—28no—
575C22⋊C4—44no—
576C22⋊C4—228no—
577C22⋊C4—444no—
578C42—2216no—
579C42—2216no—
580C11#1470211yescharacteristic, complemented, Sylow
581C23—24no—
582C23—24no—
583C23—24no—
584C23—24no—
585C23—24no—
586C23—24no—
587C23—22no—
588C23—24no—
589C23—22no—
590C23—24no—
591C23—24no—
592C23—24no—
593C23—24no—
594C23—24no—
595C23—22no—
596C23—22no—
597C23C4×Dic2214yes—
598C23#6693114yes—
599C23C22⋊C4×D1114yes—
600C23#6693814yes—
601C23#6694014yes—
602C23#6694114yes—
603C23#6694914yes—
604C23C22×Dic2211yescharacteristic
605C23C22×C4×D1111yescharacteristic
606C23C2×#433911yescharacteristic
607C23C2×D4×D1111yescharacteristic
608C23C2×D4×D1112yes—
609C23C2×D4×D1111yescharacteristic
610C23C2×#434111yescharacteristic
611C23C2×#434112yes—
612C23C2×Q8×D1111yescharacteristic
613C23#41×D1112yes—
614C23#41×D1112yes—
615Q8—4416no—
616C2×C4—232no—
617C2×C4—24no—
618C2×C4—24no—
619C2×C4—24no—
620C2×C4—24no—
621C2×C4—24no—
622C2×C4—24no—
623C2×C4—22no—
624C2×C4—22no—
625C2×C4—24no—
626C2×C4—24no—
627C2×C4—41no—
628C2×C4—41no—
629C2×C4—42no—
630C2×C4—42no—
631C2×C4—41no—
632C2×C4—41no—
633C2×C4—42no—
634C2×C4—42no—
635C2×C4—42no—
636C2×C4—42no—
637C2×C4—42no—
638C2×C4—42no—
639C2×C4—42no—
640C2×C4—114no—
641C2×C4—118no—
642C2×C4—114no—
643C2×C4—118no—
644C2×C4—114no—
645C2×C4—114no—
646C2×C4—118no—
647C2×C4—2232no—
648C2×C4—2232no—
649C2×C4—224no—
650C2×C4—224no—
651C2×C4—224no—
652C2×C4—224no—
653C2×C4—224no—
654C2×C4—222no—
655C2×C4—224no—
656C2×C4—224no—
657C2×C4—222no—
658C2×C4—224no—
659C2×C4—222no—
660C2×C4—222no—
661C2×C4—224no—
662C2×C4—224no—
663C2×C4—441no—
664C2×C4—441no—
665C2×C4—442no—
666C2×C4—442no—
667C2×C4—441no—
668C2×C4—441no—
669C2×C4—442no—
670C2×C4—442no—
671C2×C4—442no—
672C2×C4—442no—
673C2×C4—442no—
674C2×C4—442no—
675C2×C4—442no—
676C2×C4#6693118yescomplemented
677C22—28no—
678C22—28no—
679C22—24no—
680C22—24no—
681C22—28no—
682C22—24no—
683C22—24no—
684C22—24no—
685C22—28no—
686C22—24no—
687C22#1062225918yescomplemented
688C22C2×C4×Dic2211yescharacteristic
689C22C2×#6693112yes—
690C22C2×#6693111yescharacteristic
691C22C2×C22⋊C4×D1111yescharacteristic
692C22C2×#6693811yescharacteristic
693C22C2×#6694011yescharacteristic
694C22C2×#6694111yescharacteristic
695C22C2×#6694911yescharacteristic
696C22#1062304812yes—
697C22C4×#434112yes—
698C22#1062306912yes—
699C22C4×D4×D1112yes—
700C22#1062307812yes—
701C22#1062311712yes—
702C22#1062311711yescharacteristic
703C22D11×#12011yescharacteristic
704C22#1062312712yes—
705C22D11×#12112yes—
706C22#1062315312yes—
707C22D11×C22⋊Q812yes—
708C22#1062318012yes—
709C22D11×#12311yescharacteristic
710C22#1062318711yescharacteristic
711C4—28no—
712C4—42no—
713C4—42no—
714C4—82no—
715C4—118no—
716C4—228no—
717C4—224no—
718C4—442no—
719C4—442no—
720C4—882no—
721C2—28no—
722C2D11×#38611yescharacteristic
723C2C2×#1062225911yescharacteristic
724C2#1307110111yescharacteristic
725C2C4×#6693112yes—
726C2#1307114812yes—
727C2#1307690111yescharacteristic
728C2#1307690211yescharacteristic
729C2#1307691312yes—
730C2#1307695211yescharacteristic
731C2#1307695311yescharacteristic
732C2#1307696612yes—
subgroupG/H
center, FrattiniC24C23×D11
commutatorC23×C11C23×C4
FittingC11×C22⋊#95C2
socle, cosocleC24×C11C24
prime radicalC25×C11C23
hypercenterC22⋊#95D11
hypocenterC11#14702
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ C22⋊#95

Complements

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

NH ≅ G/Ntype
3. C2×#10622259C2semidirect
5. #13066850C2semidirect
6. #13066847C2semidirect
7. Dic11⋊#95C2semidirect
30. C2×#66931C4semidirect
47. C23×C4×C11Q8semidirect
61. C23×Dic11Q8semidirect
72. C22×Dic22C2×C4semidirect
87. C2×C4⋊Dic11C2×C4semidirect
95. C2×Dic11⋊C4C2×C4semidirect
96. C2×Dic11⋊C4C2×C4semidirect
284. C2×C4×C11C22⋊Q8semidirect
319. C2×Dic11C22⋊Q8semidirect
362. C22×C11#391semidirect
422. C23×C4Dic22semidirect
580. C11#14702semidirect
676. C2×C4#66931semidirect
687. C22#10622259semidirect

Maximal subgroups

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

subgroupindex
C22×#669312
C23×C4×Dic112
C2×#106222592
C2×#106225552
#130668502
#130668472
Dic11⋊#952
#130668392
#130668382
C11×C22⋊#952
#1470211