Finite Group Databasebeta

← #14677142

Subgroups — #14677142

Order 2816.

2590 conjugacy classes of subgroups.

The subgroup lattice has 832 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622833C211yesmaximal, characteristic
2C2×#10622833C211yesmaximal, characteristic
3C2×#10622559C211yesmaximal, characteristic, complemented
4C22×C11⋊#95C211yesmaximal, characteristic, complemented
5#13066875C212yesmaximal, complemented
6#13066859C212yesmaximal, 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—
28C22×Dic11⋊C4C2212yes—
29#10622833—24no—
30#10622833C418yescomplemented
31C2×C11⋊#95—24no—
32C2×C11⋊#95C2212yes—
33C2×C11⋊#95C2212yes—
34C2×C11⋊#95C2212yes—
35C2×C11⋊#95C2212yes—
36C2×C11⋊#95C2212yes—
37C2×C11⋊#95C2212yes—
38C2×C11⋊#95C2212yes—
39C2×C11⋊#95C2212yes—
40C2×C11⋊#95C2212yes—
41#10622559—24no—
42C25×C11C2311yescharacteristic
43C25×C11C2311yescharacteristic
44C22×D4×C11—22no—
45C22×D4×C11—22no—
46C22×D4×C11—22no—
47C22×D4×C11—22no—
48C22×D4×C11C2×C414yes—
49C22×D4×C11D414yes—
50C22×D4×C11Q814yes—
51C23×C4×C11—22no—
52C23×C4×C11—22no—
53C23×C4×C11—22no—
54C23×C4×C11—22no—
55C23×C4×C11—22no—
56C23×C4×C11—24no—
57C23×C4×C11—24no—
58C23×C4×C11—42no—
59C23×C4×C11—42no—
60C23×C4×C11D414yes—
61C23×C4×C11C2311yescharacteristic
62C23×C4×C11C2311yescharacteristic
63C23×C4×C11C2311yescharacteristic
64C23×C4×C11C2311yescharacteristic
65C23×C4×C11C2311yescharacteristic
66C23×Dic11—22no—
67C23×Dic11—22no—
68C23×Dic11—22no—
69C23×Dic11—24no—
70C23×Dic11—22no—
71C23×Dic11—22no—
72C23×Dic11—42no—
73C23×Dic11—42no—
74C23×Dic11—42no—
75C23×Dic11C2×C414yescomplemented
76C23×Dic11C2312yes—
77C23×Dic11C2312yes—
78C23×Dic11C2312yes—
79C23×Dic11C2312yes—
80C4×D4×C11—232no—
81C2×C11×C4⋊C4—22no—
82C2×C11×C4⋊C4—22no—
83C2×C11×C4⋊C4—22no—
84C2×C11×C22⋊C4—22no—
85C2×C11×C22⋊C4—22no—
86C2×C11×C22⋊C4—22no—
87C2×C11×C22⋊C4—22no—
88C2×C11×C22⋊C4—22no—
89C2×C11×C22⋊C4D414yes—
90C2×C42×C11—22no—
91C2×C42×C11—22no—
92C2×C42×C11—22no—
93C2×C22⋊Dic11—22no—
94C2×C22⋊Dic11—22no—
95C2×C22⋊Dic11—24no—
96C2×C22⋊Dic11—22no—
97C2×C22⋊Dic11—22no—
98C2×C22⋊Dic11—22no—
99C2×C22⋊Dic11—24no—
100C2×C22⋊Dic11—42no—
101C2×C22⋊Dic11—42no—
102C2×C22⋊Dic11—42no—
103C2×C22⋊Dic11C2×C414yescomplemented
104C2×C22⋊Dic11C2×C418yescomplemented
105C2×Dic11⋊C4—24no—
106C2×Dic11⋊C4—24no—
107C2×Dic11⋊C4—42no—
108C11⋊#95—24no—
109C11⋊#95—24no—
110C11⋊#95—24no—
111C11⋊#95—24no—
112C11⋊#95—24no—
113C11⋊#95—42no—
114C11⋊#95—42no—
115C11⋊#95—42no—
116C11⋊#95C2×C418yescomplemented
117#14016—111nomaximal, Sylow
118C24×C11—22no—
119C24×C11—22no—
120C24×C11—22no—
121C24×C11—22no—
122C24×C11—21no—
123C24×C11—21no—
124C24×C11—22no—
125C24×C11—22no—
126C24×C11—21no—
127C24×C11—21no—
128C24×C11—22no—
129C24×C11—22no—
130C24×C11C22×C412yes—
131C24×C11C22×C412yes—
132C24×C11C2×D412yes—
133C24×C11C2×D412yes—
134C24×C11C2×D412yes—
135C24×C11C2×D412yes—
136C24×C11C2×Q812yes—
137C24×C11C2×Q812yes—
138C24×C11#4112yes—
139C24×C11#4112yes—
140C24×C11C2411yescharacteristic
141C2×D4×C11—28no—
142C2×D4×C11—28no—
143C2×D4×C11—28no—
144C2×D4×C11—28no—
145C2×D4×C11—28no—
146C2×D4×C11—28no—
147C2×D4×C11C4⋊C4116yescomplemented
148C22×C4×C11—21no—
149C22×C4×C11—21no—
150C22×C4×C11—21no—
151C22×C4×C11—21no—
152C22×C4×C11—21no—
153C22×C4×C11—21no—
154C22×C4×C11—22no—
155C22×C4×C11—28no—
156C22×C4×C11—28no—
157C22×C4×C11—21no—
158C22×C4×C11—21no—
159C22×C4×C11—21no—
160C22×C4×C11—21no—
161C22×C4×C11—21no—
162C22×C4×C11—21no—
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—28no—
170C22×C4×C11—44no—
171C22×C4×C11—48no—
172C22×C4×C11—48no—
173C22×C4×C11—48no—
174C22×C4×C11—48no—
175C22×C4×C11—44no—
176C22×C4×C11—44no—
177C22×C4×C11C22×C412yes—
178C22×C4×C11C2×D412yes—
179C22×C4×C11C2×D412yes—
180C22×C4×C11C2×D412yes—
181C22×C4×C11C2×D412yes—
182C22×C4×C11C2×D412yes—
183C22×C4×C11C2×Q812yes—
184C22×C4×C11#4114yes—
185C22×Dic11—28no—
186C22×Dic11—28no—
187C22×Dic11—22no—
188C22×Dic11—22no—
189C22×Dic11—22no—
190C22×Dic11—22no—
191C22×Dic11—22no—
192C22×Dic11—22no—
193C22×Dic11—22no—
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—48no—
213C22×Dic11—48no—
214C22×Dic11—48no—
215C22×Dic11—44no—
216C22×Dic11—44no—
217C22×Dic11—44no—
218C22×Dic11—48no—
219C22×Dic11—44no—
220C22×Dic11C22×C414yes—
221C22×Dic11C22×C414yes—
222C22×Dic11#4114yes—
223C11×C4⋊C4—28no—
224C11×C22⋊C4—28no—
225C11×C22⋊C4—28no—
226C42×C11—28no—
227C22⋊Dic11—28no—
228C22⋊Dic11—48no—
229C22⋊Dic11—48no—
230C22⋊Dic11—44no—
231Dic11⋊C4—48no—
232C22×C4×D4D1111yescharacteristic
233C2×#386—111no—
234C2×#386—111no—
235C2×#385—111no—
236C22×#95—111no—
237#1442—112no—
238#1439—112no—
239#1436—112no—
240C22⋊#95—111no—
241C22⋊#95—112no—
242C22⋊#95—111no—
243C23×C11—24no—
244C23×C11—24no—
245C23×C11—22no—
246C23×C11—22no—
247C23×C11—24no—
248C23×C11—22no—
249C23×C11—22no—
250C23×C11—24no—
251C23×C11—24no—
252C23×C11—24no—
253C23×C11—24no—
254C23×C11—24no—
255C23×C11—24no—
256C23×C11—24no—
257C23×C11—24no—
258C23×C11—24no—
259C23×C11—22no—
260C23×C11—22no—
261C23×C11—24no—
262C23×C11—24no—
263C23×C11—22no—
264C23×C11—22no—
265C23×C11—22no—
266C23×C11—22no—
267C23×C11—24no—
268C23×C11—24no—
269C23×C11—24no—
270C23×C11—24no—
271C23×C11—41no—
272C23×C11—41no—
273C23×C11—42no—
274C23×C11—41no—
275C23×C11—41no—
276C23×C11—42no—
277C23×C11—42no—
278C23×C11—42no—
279C23×C11—42no—
280C23×C11—42no—
281C23×C11C2×C4⋊C414yes—
282C23×C11C2×C4⋊C414yes—
283C23×C11C4×D414yes—
284C23×C11C4×D414yes—
285C23×C11#12014yes—
286C23×C11C22⋊Q814yes—
287C23×C11C22⋊Q814yes—
288C23×C11#12314yes—
289C23×C11C23×C411yescharacteristic
290C23×C11C22×D411yescharacteristic
291C23×C11C22×D411yescharacteristic
292C23×C11C22×D411yescharacteristic
293C23×C11C22×Q811yescharacteristic
294C23×C11C2×#4111yescharacteristic
295C23×C11C2×#4111yescharacteristic
296C23×C11C2×#4112yes—
297C23×C11C2×#4112yes—
298C23×C11H(5,𝔽2)12yes—
299C23×C11H(5,𝔽2)12yes—
300D4×C11—232no—
301C2×C4×C11—22no—
302C2×C4×C11—22no—
303C2×C4×C11—22no—
304C2×C4×C11—22no—
305C2×C4×C11—22no—
306C2×C4×C11—22no—
307C2×C4×C11—22no—
308C2×C4×C11—22no—
309C2×C4×C11—24no—
310C2×C4×C11—24no—
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—416no—
319C2×C4×C11—416no—
320C2×C4×C11—41no—
321C2×C4×C11—41no—
322C2×C4×C11—41no—
323C2×C4×C11—41no—
324C2×C4×C11—42no—
325C2×C4×C11—42no—
326C2×C4×C11—42no—
327C2×C4×C11—42no—
328C2×C4×C11C2×C4⋊C414yes—
329C2×C4×C11#12314yes—
330C2×Dic11—24no—
331C2×Dic11—24no—
332C2×Dic11—24no—
333C2×Dic11—24no—
334C2×Dic11—24no—
335C2×Dic11—24no—
336C2×Dic11—24no—
337C2×Dic11—24no—
338C2×Dic11—24no—
339C2×Dic11—416no—
340C2×Dic11—416no—
341C2×Dic11—42no—
342C2×Dic11—42no—
343C2×Dic11—42no—
344C2×Dic11—42no—
345C2×Dic11—42no—
346C2×Dic11—42no—
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—42no—
360C23×D4C2×D1111yescharacteristic
361C24×C4—111no—
362C24×C4—111no—
363C24×C4C2×D1111yescharacteristic
364C24×C4C2×D1111yescharacteristic
365C2×C4×D4—24no—
366C2×C4×D4—24no—
367C2×C4×D4—24no—
368C22×C4⋊C4—112no—
369C22×C4⋊C4C2×D1111yescharacteristic
370C22×C22⋊C4—111no—
371C22×C22⋊C4—112no—
372C22×C22⋊C4—111no—
373C22×C22⋊C4—112no—
374C22×C22⋊C4C2×D1111yescharacteristic
375C22×C22⋊C4C2×D1111yescharacteristic
376C22×C42C2×D1111yescharacteristic
377#386—118no—
378#386—224no—
379#385—224no—
380C2×#95—112no—
381C2×#95—112no—
382C2×#95—112no—
383C2×#95—112no—
384C2×#95—112no—
385C2×#95—112no—
386C2×#95—112no—
387C2×#95—112no—
388C2×#95—112no—
389C2×#95—224no—
390C22×C11—24no—
391C22×C11—24no—
392C22×C11—28no—
393C22×C11—28no—
394C22×C11—24no—
395C22×C11—24no—
396C22×C11—28no—
397C22×C11—28no—
398C22×C11—24no—
399C22×C11—24no—
400C22×C11—28no—
401C22×C11—24no—
402C22×C11—42no—
403C22×C11—42no—
404C22×C11—44no—
405C22×C11—42no—
406C22×C11—42no—
407C22×C11—44no—
408C22×C11—44no—
409C22×C11—42no—
410C22×C11—42no—
411C22×C11#38518yes—
412C22×C11C22×C4⋊C411yescharacteristic
413C22×C11C2×C4×D411yescharacteristic
414C22×C11C2×C4×D411yescharacteristic
415C22×C11C4×#4112yes—
416C22×C11#51812yes—
417C22×C11C2×#12011yescharacteristic
418C22×C11C2×C22⋊Q811yescharacteristic
419C22×C11C2×C22⋊Q811yescharacteristic
420C22×C11C2×#12311yescharacteristic
421C22×C11C2×#12311yescharacteristic
422C22×C11#52511yescharacteristic
423C22×C11#52912yes—
424C22×C11#53411yescharacteristic
425C22×C11#53511yescharacteristic
426C22×C11#53812yes—
427C22×C11#54612yes—
428C22×C11#54612yes—
429C22×C11#54612yes—
430C22×C11#54612yes—
431C22×C11#55312yes—
432C22×C11#55312yes—
433C22×C11#55412yes—
434C22×C11#55412yes—
435C4×C11—24no—
436C4×C11—24no—
437C4×C11—42no—
438C4×C11—42no—
439C4×C11—42no—
440Dic11—44no—
441Dic11—44no—
442Dic11—44no—
443Dic11—82no—
444C25C22×D1111yescharacteristic
445C25C22×D1111yescharacteristic
446C22×D4—22no—
447C22×D4—22no—
448C22×D4—22no—
449C22×D4—22no—
450C22×D4Dic2214yes—
451C22×D4C4×D1114yes—
452C22×D4C22⋊D1114yes—
453C23×C4—22no—
454C23×C4—22no—
455C23×C4—22no—
456C23×C4—24no—
457C23×C4—22no—
458C23×C4—22no—
459C23×C4—24no—
460C23×C4—42no—
461C23×C4—42no—
462C23×C4—112no—
463C23×C4—112no—
464C23×C4—112no—
465C23×C4—114no—
466C23×C4—112no—
467C23×C4—224no—
468C23×C4—222no—
469C23×C4—222no—
470C23×C4—222no—
471C23×C4—222no—
472C23×C4—222no—
473C23×C4—442no—
474C23×C4—442no—
475C23×C4—442no—
476C23×C4C22⋊D1114yes—
477C23×C4C22×D1111yescharacteristic
478C23×C4C22×D1111yescharacteristic
479C23×C4C22×D1111yescharacteristic
480C23×C4C22×D1111yescharacteristic
481C23×C4C22×D1111yescharacteristic
482C4×D4—232no—
483C2×C4⋊C4—22no—
484C2×C4⋊C4—22no—
485C2×C4⋊C4—22no—
486C2×C4⋊C4—224no—
487C2×C4⋊C4—224no—
488C2×C4⋊C4—442no—
489C2×C22⋊C4—22no—
490C2×C22⋊C4—22no—
491C2×C22⋊C4—22no—
492C2×C22⋊C4—22no—
493C2×C22⋊C4—22no—
494C2×C22⋊C4—114no—
495C2×C22⋊C4—118no—
496C2×C22⋊C4—222no—
497C2×C22⋊C4—222no—
498C2×C22⋊C4—224no—
499C2×C22⋊C4—222no—
500C2×C22⋊C4—222no—
501C2×C22⋊C4—224no—
502C2×C22⋊C4—222no—
503C2×C22⋊C4—442no—
504C2×C22⋊C4—442no—
505C2×C22⋊C4—442no—
506C2×C22⋊C4C22⋊D1114yes—
507C2×C42—22no—
508C2×C42—22no—
509C2×C42—22no—
510#95—118no—
511#95—224no—
512#95—224no—
513#95—224no—
514#95—224no—
515#95—224no—
516#95—442no—
517#95—442no—
518#95—442no—
519C2×C11—28no—
520C2×C11—44no—
521C2×C11C2×#38511yescharacteristic
522C2×C11C4×#12311yescharacteristic
523C2×C11#232111yescharacteristic
524C2×C11#234912yes—
525C2×C11#236412yes—
526C2×C11#240411yescharacteristic
527C2×C11#240511yescharacteristic
528C2×C11#244412yes—
529C2×C11#245012yes—
530C2×C11#248711yescharacteristic
531C2×C11#257911yescharacteristic
532C24—22no—
533C24—22no—
534C24—22no—
535C24—22no—
536C24—21no—
537C24—21no—
538C24—22no—
539C24—22no—
540C24—22no—
541C24—22no—
542C24—21no—
543C24—21no—
544C24C2×Dic2212yes—
545C24C2×Dic2212yes—
546C24C2×C4×D1112yes—
547C24C2×C4×D1112yes—
548C24#433912yes—
549C24#433912yes—
550C24C2×C22⋊D1112yes—
551C24C2×C22⋊D1112yes—
552C24C2×C22⋊D1112yes—
553C24C2×C22⋊D1112yes—
554C24C23×D1111yescharacteristic
555C2×D4—28no—
556C2×D4—28no—
557C2×D4—28no—
558C2×D4—28no—
559C2×D4—28no—
560C2×D4—28no—
561C2×D4Dic11⋊C4116yescomplemented
562C22×C4—21no—
563C22×C4—21no—
564C22×C4—22no—
565C22×C4—21no—
566C22×C4—21no—
567C22×C4—21no—
568C22×C4—21no—
569C22×C4—28no—
570C22×C4—28no—
571C22×C4—22no—
572C22×C4—22no—
573C22×C4—22no—
574C22×C4—22no—
575C22×C4—22no—
576C22×C4—22no—
577C22×C4—21no—
578C22×C4—21no—
579C22×C4—21no—
580C22×C4—21no—
581C22×C4—21no—
582C22×C4—21no—
583C22×C4—28no—
584C22×C4—44no—
585C22×C4—48no—
586C22×C4—48no—
587C22×C4—48no—
588C22×C4—48no—
589C22×C4—44no—
590C22×C4—44no—
591C22×C4—114no—
592C22×C4—114no—
593C22×C4—114no—
594C22×C4—228no—
595C22×C4—228no—
596C22×C4—222no—
597C22×C4—222no—
598C22×C4—222no—
599C22×C4—222no—
600C22×C4—222no—
601C22×C4—222no—
602C22×C4—222no—
603C22×C4—222no—
604C22×C4—222no—
605C22×C4—222no—
606C22×C4—222no—
607C22×C4—222no—
608C22×C4—222no—
609C22×C4—222no—
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—448no—
622C22×C4—448no—
623C22×C4—448no—
624C22×C4—444no—
625C22×C4—448no—
626C22×C4—444no—
627C22×C4—444no—
628C22×C4—444no—
629C22×C4C2×Dic2212yes—
630C22×C4C2×C4×D1112yes—
631C22×C4#434114yes—
632C22×C4C2×C22⋊D1112yes—
633C22×C4C2×C22⋊D1112yes—
634C22×C4C2×C22⋊D1112yes—
635C22×C4C2×C22⋊D1112yes—
636C22×C4C2×C22⋊D1112yes—
637C4⋊C4—28no—
638C4⋊C4—448no—
639C22⋊C4—28no—
640C22⋊C4—28no—
641C22⋊C4—228no—
642C22⋊C4—448no—
643C22⋊C4—448no—
644C22⋊C4—444no—
645C42—28no—
646C11#1401611yescharacteristic, complemented, Sylow
647C23—24no—
648C23—24no—
649C23—24no—
650C23—24no—
651C23—22no—
652C23—24no—
653C23—24no—
654C23—22no—
655C23—24no—
656C23—24no—
657C23—24no—
658C23—24no—
659C23—22no—
660C23—24no—
661C23—24no—
662C23—22no—
663C23—22no—
664C23—22no—
665C23—22no—
666C23—22no—
667C23—22no—
668C23—24no—
669C23—24no—
670C23—24no—
671C23—24no—
672C23—24no—
673C23—24no—
674C23—22no—
675C23—42no—
676C23—42no—
677C23—41no—
678C23—41no—
679C23—42no—
680C23—42no—
681C23—42no—
682C23—41no—
683C23—42no—
684C23—41no—
685C23C2×Dic11⋊C414yes—
686C23C2×Dic11⋊C414yes—
687C23#6697714yes—
688C23#6697714yes—
689C23C4×C22⋊D1114yes—
690C23C4×C22⋊D1114yes—
691C23#6698214yes—
692C23#6700614yes—
693C23C22×Dic2211yescharacteristic
694C23C22×C4×D1111yescharacteristic
695C23C2×#433911yescharacteristic
696C23C2×#433911yescharacteristic
697C23C2×#434112yes—
698C23#6703712yes—
699C23#41×D1112yes—
700C23#6704212yes—
701C23C22×C22⋊D1111yescharacteristic
702C23C22×C22⋊D1111yescharacteristic
703C23C22×C22⋊D1111yescharacteristic
704D4—232no—
705C2×C4—22no—
706C2×C4—22no—
707C2×C4—22no—
708C2×C4—22no—
709C2×C4—22no—
710C2×C4—22no—
711C2×C4—24no—
712C2×C4—24no—
713C2×C4—22no—
714C2×C4—22no—
715C2×C4—22no—
716C2×C4—22no—
717C2×C4—24no—
718C2×C4—24no—
719C2×C4—22no—
720C2×C4—22no—
721C2×C4—22no—
722C2×C4—416no—
723C2×C4—416no—
724C2×C4—41no—
725C2×C4—41no—
726C2×C4—42no—
727C2×C4—42no—
728C2×C4—42no—
729C2×C4—41no—
730C2×C4—42no—
731C2×C4—41no—
732C2×C4—224no—
733C2×C4—224no—
734C2×C4—224no—
735C2×C4—224no—
736C2×C4—224no—
737C2×C4—224no—
738C2×C4—224no—
739C2×C4—224no—
740C2×C4—224no—
741C2×C4—4416no—
742C2×C4—4416no—
743C2×C4—442no—
744C2×C4—442no—
745C2×C4—442no—
746C2×C4—442no—
747C2×C4—442no—
748C2×C4—442no—
749C2×C4—442no—
750C2×C4—442no—
751C2×C4—442no—
752C2×C4—442no—
753C2×C4—442no—
754C2×C4—442no—
755C2×C4—442no—
756C2×C4—442no—
757C2×C4—442no—
758C2×C4—442no—
759C2×C4—442no—
760C2×C4—442no—
761C2×C4—442no—
762C2×C4C2×Dic11⋊C414yes—
763C2×C4#6698814yes—
764C22—24no—
765C22—24no—
766C22—24no—
767C22—28no—
768C22—28no—
769C22—24no—
770C22—24no—
771C22—28no—
772C22—24no—
773C22—28no—
774C22—28no—
775C22—24no—
776C22—42no—
777C22—42no—
778C22—42no—
779C22—44no—
780C22—44no—
781C22—42no—
782C22—42no—
783C22—42no—
784C22—44no—
785C22#1062282318yes—
786C22C4×#434112yes—
787C22#1062306912yes—
788C22#1062307012yes—
789C22#1062307112yes—
790C22#1062307412yes—
791C22#1062307612yes—
792C22#1062309112yes—
793C22#1062309612yes—
794C22C22×Dic11⋊C411yescharacteristic
795C22C2×#6697711yescharacteristic
796C22C2×#6697711yescharacteristic
797C22C2×C4×C22⋊D1111yescharacteristic
798C22C2×C4×C22⋊D1111yescharacteristic
799C22C2×#6698211yescharacteristic
800C22C2×#6698811yescharacteristic
801C22#1062333511yescharacteristic
802C22#1062333712yes—
803C22#1062333712yes—
804C22#1062335911yescharacteristic
805C22#1062336012yes—
806C22#1062336012yes—
807C22#1062336111yescharacteristic
808C22C2×#6700611yescharacteristic
809C4—24no—
810C4—24no—
811C4—42no—
812C4—42no—
813C4—42no—
814C4—444no—
815C4—444no—
816C4—444no—
817C4—882no—
818C2—28no—
819C2—44no—
820C2C2×#1062282311yescharacteristic
821C2C4×#6698811yescharacteristic
822C2#1307127011yescharacteristic
823C2#1307152112yes—
824C2#1307166112yes—
825C2#1307193111yescharacteristic
826C2#1307193911yescharacteristic
827C2#1307236012yes—
828C2#1307243412yes—
829C2#1307293311yescharacteristic
830C2#1307395911yescharacteristic
subgroupG/H
center, FrattiniC24C23×D11
commutatorC23×C11C23×C4
FittingC22×C4×D4×C11C2
socle, cosocleC24×C11C24
prime radicalC23×D4×C11C22
hypercenterC22×C4×D4D11
hypocenterC11#14016
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×#10622559C2semidirect
4. C22×C11⋊#95C2semidirect
5. #13066875C2semidirect
6. #13066859C2semidirect
7. #13066849C2semidirect
8. #13066839C2semidirect
9. #13066839C2semidirect
10. #13066838C2semidirect
30. #10622833C4semidirect
75. C23×Dic11C2×C4semidirect
103. C2×C22⋊Dic11C2×C4semidirect
104. C2×C22⋊Dic11C2×C4semidirect
116. C11⋊#95C2×C4semidirect
147. C2×D4×C11C4⋊C4semidirect
561. C2×D4Dic11⋊C4semidirect
646. C11#14016semidirect

Maximal subgroups

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

subgroupindex
C2×#106228332
C2×#106225592
C22×C11⋊#952
#130668752
#130668592
#130668492
#130668392
#130668382
C22×C4×D4×C112
#1401611