Finite Group Databasebeta

← #14676563

Subgroups — #14676563

Order 2816.

2266 conjugacy classes of subgroups.

The subgroup lattice has 854 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#66977C211yesmaximal, characteristic
2C22×#66940C211yesmaximal, characteristic, complemented
3C2×#10622587C211yesmaximal, characteristic, complemented
4C2×C4×C22⋊Dic11C211yesmaximal, characteristic
5#13066867C212yesmaximal, complemented
6#13066859C212yesmaximal
7#13066853C212yesmaximal
8#13066847C212yesmaximal, complemented
9#13066845C211yesmaximal, characteristic, complemented
10#13066845C211yesmaximal, characteristic, complemented
11C2×C11×#380C211yesmaximal, characteristic
12C24×C4×C11C2211yescharacteristic
13C23×Dic22C2211yescharacteristic
14C22×C11×C4⋊C4C2211yescharacteristic
15C22×C11×C4⋊C4C2211yescharacteristic
16C22×C11×C22⋊C4C2212yes—
17C22×C22⋊Dic11C2211yescharacteristic
18C22×C22⋊Dic11C2212yes—
19C22×C22⋊Dic11C2211yescharacteristic
20C22×C4⋊Dic11C2211yescharacteristic
21C2×#66977—24no—
22C2×#66977—24no—
23C2×#66977C418yescomplemented
24C22×Dic11⋊C4C2212yes—
25C22×Dic11⋊C4C2212yes—
26C22×C4×Dic11C2211yescharacteristic
27C22×C4×Dic11C2212yes—
28C22×C4×Dic11C2211yescharacteristic
29C2×#66940—24no—
30C2×#66940—24no—
31C2×#66940—24no—
32C11×#380—24no—
33C2×C11×#95C2212yes—
34C4×C22⋊Dic11—24no—
35C2×C11⋊#95C2212yes—
36C2×C11⋊#95C2212yes—
37C2×C11⋊#95C2211yescharacteristic
38C2×C11⋊#95C2212yes—
39C2×C11⋊#95C2211yescharacteristic
40C2×C11⋊#95C2212yes—
41C2×C11⋊#95C2212yes—
42C2×C11⋊#95C2212yes—
43#10622587—24no—
44C25×C11C2311yescharacteristic
45C23×C4×C11—22no—
46C23×C4×C11—22no—
47C23×C4×C11—22no—
48C23×C4×C11—22no—
49C23×C4×C11—22no—
50C23×C4×C11—22no—
51C23×C4×C11C2×C414yes—
52C23×C4×C11C2312yes—
53C23×C4×C11C2311yescharacteristic
54C23×C4×C11C2312yes—
55C23×C4×C11C2311yescharacteristic
56C23×Dic11C2312yes—
57C23×Dic11C2311yescharacteristic
58C23×Dic11C2311yescharacteristic
59C23×Dic11C2311yescharacteristic
60C23×Dic11C2312yes—
61C23×Dic11C2311yescharacteristic
62C22×Dic22—22no—
63C22×Dic22—22no—
64C22×Dic22—22no—
65C22×Dic22—22no—
66C22×Dic22C2×C414yes—
67C22×Dic22D414yes—
68C22×Dic22D414yes—
69C2×C11×C4⋊C4—22no—
70C2×C11×C4⋊C4—22no—
71C2×C11×C4⋊C4—22no—
72C2×C11×C4⋊C4—22no—
73C2×C11×C4⋊C4—22no—
74C2×C11×C4⋊C4D414yes—
75C2×C11×C22⋊C4—24no—
76C2×C11×C22⋊C4—24no—
77C2×C11×C22⋊C4—42no—
78C2×C22⋊Dic11—22no—
79C2×C22⋊Dic11—24no—
80C2×C22⋊Dic11—24no—
81C2×C22⋊Dic11—22no—
82C2×C22⋊Dic11—22no—
83C2×C22⋊Dic11—22no—
84C2×C22⋊Dic11—22no—
85C2×C22⋊Dic11C2×C418yes—
86C2×C22⋊Dic11Q814yescomplemented
87C2×C4⋊Dic11—22no—
88C2×C4⋊Dic11—22no—
89C2×C4⋊Dic11C2×C414yes—
90#66977—232no—
91C2×Dic11⋊C4—24no—
92C2×Dic11⋊C4—24no—
93C2×Dic11⋊C4—24no—
94C2×Dic11⋊C4—24no—
95C2×Dic11⋊C4—24no—
96C2×Dic11⋊C4C2×C418yes—
97C2×C4×Dic11—22no—
98C2×C4×Dic11—24no—
99C2×C4×Dic11—22no—
100C2×C4×Dic11—24no—
101C2×C4×Dic11—24no—
102C2×C4×Dic11—22no—
103C2×C4×Dic11—22no—
104C2×C4×Dic11—22no—
105C2×C4×Dic11D414yes—
106#66940—232no—
107C11×#95—24no—
108C11⋊#95—22no—
109C11⋊#95—22no—
110C11⋊#95—24no—
111C11⋊#95—24no—
112C11⋊#95—24no—
113C11⋊#95—24no—
114C11⋊#95—42no—
115C11⋊#95—42no—
116#13969—111nomaximal, Sylow
117C24×C11—21no—
118C24×C11—21no—
119C24×C11—21no—
120C24×C11—21no—
121C24×C11—21no—
122C24×C11—21no—
123C24×C11—21no—
124C24×C11—21no—
125C24×C11—21no—
126C24×C11—21no—
127C24×C11—21no—
128C24×C11—21no—
129C24×C11C22×C412yes—
130C24×C11C2×Q812yes—
131C24×C11#4112yes—
132C24×C11C2411yescharacteristic
133C22×C4×C11—21no—
134C22×C4×C11—21no—
135C22×C4×C11—22no—
136C22×C4×C11—22no—
137C22×C4×C11—21no—
138C22×C4×C11—21no—
139C22×C4×C11—22no—
140C22×C4×C11—22no—
141C22×C4×C11—21no—
142C22×C4×C11—21no—
143C22×C4×C11—22no—
144C22×C4×C11—22no—
145C22×C4×C11—28no—
146C22×C4×C11—28no—
147C22×C4×C11—28no—
148C22×C4×C11—22no—
149C22×C4×C11—22no—
150C22×C4×C11—22no—
151C22×C4×C11—22no—
152C22×C4×C11—22no—
153C22×C4×C11—22no—
154C22×C4×C11—22no—
155C22×C4×C11—44no—
156C22×C4×C11—44no—
157C22×C4×C11—44no—
158C22×C4×C11—44no—
159C22×C4×C11C22×C412yes—
160C22×C4×C11C22×C412yes—
161C22×C4×C11C2×D414yes—
162C22×C4×C11C2×D412yes—
163C22×C4×C11C2×D412yes—
164C22×C4×C11C2×D412yes—
165C22×C4×C11C2×D412yes—
166C22×C4×C11#4112yes—
167C22×C4×C11#4112yes—
168C22×Dic11—21no—
169C22×Dic11—21no—
170C22×Dic11—22no—
171C22×Dic11—22no—
172C22×Dic11—21no—
173C22×Dic11—21no—
174C22×Dic11—21no—
175C22×Dic11—21no—
176C22×Dic11—21no—
177C22×Dic11—21no—
178C22×Dic11—22no—
179C22×Dic11—22no—
180C22×Dic11—22no—
181C22×Dic11—22no—
182C22×Dic11—22no—
183C22×Dic11—22no—
184C22×Dic11—21no—
185C22×Dic11—21no—
186C22×Dic11—21no—
187C22×Dic11—21no—
188C22×Dic11—21no—
189C22×Dic11—21no—
190C22×Dic11—22no—
191C22×Dic11—21no—
192C22×Dic11—21no—
193C22×Dic11—21no—
194C22×Dic11—21no—
195C22×Dic11—22no—
196C22×Dic11—21no—
197C22×Dic11—21no—
198C22×Dic11—21no—
199C22×Dic11—21no—
200C22×Dic11C22×C414yes—
201C22×Dic11C22×C414yes—
202C22×Dic11C2×D412yes—
203C22×Dic11C2×D414yes—
204C22×Dic11C2×D414yes—
205C22×Dic11C2×D412yes—
206C22×Dic11C2×Q812yes—
207C22×Dic11C2×Q812yes—
208C22×Dic11#4112yes—
209C22×Dic11#4112yes—
210C2×Dic22—28no—
211C2×Dic22—28no—
212C2×Dic22—28no—
213C2×Dic22—28no—
214C2×Dic22—28no—
215C2×Dic22—28no—
216C2×Dic22C22⋊C4116yescomplemented
217C11×C4⋊C4—28no—
218C11×C4⋊C4—44no—
219C11×C22⋊C4—48no—
220C22⋊Dic11—28no—
221C22⋊Dic11—216no—
222C22⋊Dic11—28no—
223C4⋊Dic11—28no—
224Dic11⋊C4—216no—
225Dic11⋊C4—216no—
226C4×Dic11—216no—
227C4×Dic11—28no—
228C4×Dic11—44no—
229C22×C22⋊Q8—111no—
230C22×C4×Q8—111no—
231C2×#391—111no—
232C2×#380D1111yescharacteristic
233C2×C4×C22⋊C4—111no—
234#1441—112no—
235#1439—112no—
236#1437—112no—
237#1436—112no—
238C4⋊#95—111no—
239C4⋊#95—111no—
240C23×C11—22no—
241C23×C11—22no—
242C23×C11—22no—
243C23×C11—22no—
244C23×C11—22no—
245C23×C11—22no—
246C23×C11—22no—
247C23×C11—22no—
248C23×C11—22no—
249C23×C11—22no—
250C23×C11—22no—
251C23×C11—22no—
252C23×C11—22no—
253C23×C11—22no—
254C23×C11—22no—
255C23×C11—22no—
256C23×C11—22no—
257C23×C11—22no—
258C23×C11—41no—
259C23×C11—41no—
260C23×C11—41no—
261C23×C11—41no—
262C23×C11—41no—
263C23×C11—41no—
264C23×C11—41no—
265C23×C11—41no—
266C23×C11—41no—
267C23×C11—41no—
268C23×C11—41no—
269C23×C11—41no—
270C23×C11—41no—
271C23×C11—41no—
272C23×C11—41no—
273C23×C11—41no—
274C23×C11C4×Q814yescomplemented
275C23×C11C23×C411yescharacteristic
276C23×C11C22×D411yescharacteristic
277C23×C11C22×D411yescharacteristic
278C23×C11C22×D411yescharacteristic
279C23×C11C22×D411yescharacteristic
280C23×C11C22×Q811yescharacteristic
281C23×C11C2×#4111yescharacteristic
282C23×C11C2×#4111yescharacteristic
283C23×C11C2×#4111yescharacteristic
284C23×C11C2×#4111yescharacteristic
285C23×C11C2×#4111yescharacteristic
286C23×C11H(5,𝔽2)11yescharacteristic
287C23×C112−1+411yescharacteristic
288C23×C112−1+411yescharacteristic
289C23×C112−1+411yescharacteristic
290C2×C4×C11—22no—
291C2×C4×C11—22no—
292C2×C4×C11—22no—
293C2×C4×C11—24no—
294C2×C4×C11—24no—
295C2×C4×C11—24no—
296C2×C4×C11—41no—
297C2×C4×C11—41no—
298C2×C4×C11—41no—
299C2×C4×C11—41no—
300C2×C4×C11—42no—
301C2×C4×C11—42no—
302C2×C4×C11—42no—
303C2×C4×C11—42no—
304C2×C4×C11—416no—
305C2×C4×C11—42no—
306C2×C4×C11—42no—
307C2×C4×C11—42no—
308C2×C4×C11—42no—
309C2×C4×C11—42no—
310C2×C4×C11—42no—
311C2×C4×C11—42no—
312C2×C4×C11C2×C22⋊C414yes—
313C2×C4×C11C4×D414yes—
314C2×C4×C11C4×D414yes—
315C2×C4×C11#12014yes—
316C2×C4×C11#12114yes—
317C2×C4×C11#12114yes—
318C2×C4×C11#12314yes—
319C2×Dic11—24no—
320C2×Dic11—24no—
321C2×Dic11—22no—
322C2×Dic11—24no—
323C2×Dic11—24no—
324C2×Dic11—24no—
325C2×Dic11—24no—
326C2×Dic11—22no—
327C2×Dic11—22no—
328C2×Dic11—22no—
329C2×Dic11—22no—
330C2×Dic11—22no—
331C2×Dic11—24no—
332C2×Dic11—24no—
333C2×Dic11—24no—
334C2×Dic11—22no—
335C2×Dic11—22no—
336C2×Dic11—22no—
337C2×Dic11—22no—
338C2×Dic11—22no—
339C2×Dic11—22no—
340C2×Dic11—22no—
341C2×Dic11—22no—
342C2×Dic11—22no—
343C2×Dic11—41no—
344C2×Dic11—41no—
345C2×Dic11—41no—
346C2×Dic11—41no—
347C2×Dic11—41no—
348C2×Dic11—41no—
349C2×Dic11—41no—
350C2×Dic11—41no—
351C2×Dic11—42no—
352C2×Dic11—42no—
353C2×Dic11—42no—
354C2×Dic11—42no—
355C2×Dic11—41no—
356C2×Dic11—41no—
357C2×Dic11—41no—
358C2×Dic11—41no—
359C2×Dic11C2×C22⋊C418yes—
360C2×Dic11C22⋊Q814yescomplemented
361Dic22—232no—
362C23×Q8—111no—
363C24×C4C2×D1111yescharacteristic
364C2×C22⋊Q8—118no—
365C2×C22⋊Q8—224no—
366C2×C22⋊Q8—224no—
367C2×C4×Q8—224no—
368C2×C4×Q8—224no—
369C2×C4×Q8—224no—
370C22×C4⋊C4—112no—
371C22×C4⋊C4—111no—
372C22×C4⋊C4—112no—
373C22×C4⋊C4C2×D1111yescharacteristic
374C22×C4⋊C4C2×D1111yescharacteristic
375C22×C22⋊C4—112no—
376C22×C22⋊C4—111no—
377C22×C22⋊C4—111no—
378C22×C22⋊C4C2×D1112yes—
379C22×C42—111no—
380C22×C42—112no—
381C22×C42—111no—
382#391—224no—
383#380—24no—
384C4×C22⋊C4—224no—
385C2×#95—112no—
386C2×#95—112no—
387C2×#95—111no—
388C2×#95—112no—
389C2×#95—112no—
390C2×#95—111no—
391C2×#95—112no—
392C2×#95—112no—
393C2×#95C2×D1112yes—
394C22×C11—24no—
395C22×C11—24no—
396C22×C11—24no—
397C22×C11—42no—
398C22×C11—42no—
399C22×C11—42no—
400C22×C11—42no—
401C22×C11—42no—
402C22×C11—42no—
403C22×C11—42no—
404C22×C11—42no—
405C22×C11—42no—
406C22×C11—42no—
407C22×C11—42no—
408C22×C11—42no—
409C22×C11C22×C22⋊C411yescharacteristic
410C22×C11C2×C4×D411yescharacteristic
411C22×C11C2×C4×D411yescharacteristic
412C22×C11C2×C4×Q811yescharacteristic
413C22×C11C4×#4111yescharacteristic
414C22×C11#51911yescharacteristic
415C22×C11#52011yescharacteristic
416C22×C11C2×#12011yescharacteristic
417C22×C11C2×#12111yescharacteristic
418C22×C11C2×#12111yescharacteristic
419C22×C11C2×C22⋊Q811yescharacteristic
420C22×C11C2×#12311yescharacteristic
421C22×C11#52511yescharacteristic
422C22×C11#52911yescharacteristic
423C22×C11#53311yescharacteristic
424C22×C11#53611yescharacteristic
425C22×C11#53711yescharacteristic
426C22×C11#54111yescharacteristic
427C22×C11#54211yescharacteristic
428C22×C11#54611yescharacteristic
429C22×C11#54711yescharacteristic
430C22×C11#54811yescharacteristic
431C22×C11#54811yescharacteristic
432C22×C11#54811yescharacteristic
433C22×C11#54811yescharacteristic
434C22×C11#54811yescharacteristic
435C22×C11D4×Q811yescharacteristic
436C22×C11D4×Q811yescharacteristic
437C22×C11D4×Q811yescharacteristic
438C22×C11#55011yescharacteristic
439C22×C11#55011yescharacteristic
440C22×C11#55211yescharacteristic
441C22×C11#55211yescharacteristic
442C22×C11#55411yescharacteristic
443C22×C11#55611yescharacteristic
444C4×C11—44no—
445C4×C11—42no—
446C4×C11—82no—
447C4×C11#38618yes—
448Dic11—24no—
449Dic11—28no—
450Dic11—44no—
451Dic11—42no—
452Dic11—42no—
453Dic11—42no—
454C25C22×D1111yescharacteristic
455C22×Q8—114no—
456C22×Q8—114no—
457C22×Q8—114no—
458C22×Q8—222no—
459C22×Q8—222no—
460C22×Q8—222no—
461C22×Q8—222no—
462C23×C4—22no—
463C23×C4—22no—
464C23×C4—22no—
465C23×C4—22no—
466C23×C4—22no—
467C23×C4—22no—
468C23×C4—112no—
469C23×C4—111no—
470C23×C4—112no—
471C23×C4—111no—
472C23×C4—111no—
473C23×C4—111no—
474C23×C4C4×D1114yes—
475C23×C4C22×D1112yes—
476C23×C4C22×D1111yescharacteristic
477C23×C4C22×D1112yes—
478C23×C4C22×D1111yescharacteristic
479C22⋊Q8—2232no—
480C4×Q8—2232no—
481C2×C4⋊C4—22no—
482C2×C4⋊C4—22no—
483C2×C4⋊C4—22no—
484C2×C4⋊C4—22no—
485C2×C4⋊C4—22no—
486C2×C4⋊C4—118no—
487C2×C4⋊C4—114no—
488C2×C4⋊C4—224no—
489C2×C4⋊C4—224no—
490C2×C4⋊C4—224no—
491C2×C4⋊C4—224no—
492C2×C4⋊C4—222no—
493C2×C4⋊C4—222no—
494C2×C4⋊C4—224no—
495C2×C4⋊C4C22⋊D1114yes—
496C2×C22⋊C4—24no—
497C2×C22⋊C4—24no—
498C2×C22⋊C4—42no—
499C2×C22⋊C4—118no—
500C2×C22⋊C4—114no—
501C2×C22⋊C4—224no—
502C2×C22⋊C4—224no—
503C2×C22⋊C4—222no—
504C2×C22⋊C4—222no—
505C2×C22⋊C4—222no—
506C2×C22⋊C4—222no—
507C2×C22⋊C4—222no—
508C2×C42—114no—
509C2×C42—224no—
510C2×C42—224no—
511C2×C42—222no—
512C2×C42—224no—
513C2×C42—222no—
514C2×C42—222no—
515C2×C42—222no—
516C2×C42—222no—
517#95—24no—
518#95—224no—
519#95—224no—
520#95—222no—
521#95—222no—
522#95—224no—
523#95—224no—
524#95—442no—
525#95—442no—
526C2×C11—44no—
527C2×C11C2×#38611yescharacteristic
528C2×C11C4×C22⋊Q811yescharacteristic
529C2×C11#232311yescharacteristic
530C2×C11Q8×C22⋊C411yescharacteristic
531C2×C11#234111yescharacteristic
532C2×C11#236011yescharacteristic
533C2×C11#236211yescharacteristic
534C2×C11#240711yescharacteristic
535C2×C11#240911yescharacteristic
536C2×C11#242111yescharacteristic
537C2×C11#242311yescharacteristic
538C2×C11#242611yescharacteristic
539C2×C11#242911yescharacteristic
540C2×C11#253611yescharacteristic
541C2×C11#253811yescharacteristic
542C24—21no—
543C24—21no—
544C24—21no—
545C24—21no—
546C24—21no—
547C24—21no—
548C24—21no—
549C24—21no—
550C24—21no—
551C24—21no—
552C24—21no—
553C24—21no—
554C24C2×C4×D1112yes—
555C24#434112yes—
556C24Q8×D1112yes—
557C24C23×D1111yescharacteristic
558C2×Q8—1116no—
559C2×Q8—228no—
560C2×Q8—228no—
561C2×Q8—228no—
562C2×Q8—228no—
563C2×Q8—228no—
564C2×Q8—228no—
565C22×C4—21no—
566C22×C4—21no—
567C22×C4—22no—
568C22×C4—22no—
569C22×C4—21no—
570C22×C4—21no—
571C22×C4—22no—
572C22×C4—21no—
573C22×C4—22no—
574C22×C4—22no—
575C22×C4—22no—
576C22×C4—21no—
577C22×C4—28no—
578C22×C4—28no—
579C22×C4—28no—
580C22×C4—22no—
581C22×C4—22no—
582C22×C4—22no—
583C22×C4—22no—
584C22×C4—22no—
585C22×C4—22no—
586C22×C4—22no—
587C22×C4—44no—
588C22×C4—44no—
589C22×C4—44no—
590C22×C4—44no—
591C22×C4—114no—
592C22×C4—114no—
593C22×C4—112no—
594C22×C4—114no—
595C22×C4—112no—
596C22×C4—112no—
597C22×C4—114no—
598C22×C4—112no—
599C22×C4—112no—
600C22×C4—112no—
601C22×C4—222no—
602C22×C4—221no—
603C22×C4—222no—
604C22×C4—222no—
605C22×C4—221no—
606C22×C4—221no—
607C22×C4—221no—
608C22×C4—222no—
609C22×C4—221no—
610C22×C4—221no—
611C22×C4—221no—
612C22×C4—221no—
613C22×C4—221no—
614C22×C4—221no—
615C22×C4—221no—
616C22×C4—222no—
617C22×C4—222no—
618C22×C4—221no—
619C22×C4—221no—
620C22×C4—222no—
621C22×C4—221no—
622C22×C4—221no—
623C22×C4—222no—
624C22×C4—221no—
625C22×C4—222no—
626C22×C4—222no—
627C22×C4—221no—
628C22×C4—221no—
629C22×C4—221no—
630C22×C4—221no—
631C22×C4—221no—
632C22×C4—221no—
633C22×C4C2×C4×D1112yes—
634C22×C4C2×C4×D1112yes—
635C22×C4#433912yes—
636C22×C4D4×D1112yes—
637C22×C4D4×D1112yes—
638C22×C4D4×D1112yes—
639C22×C4#434112yes—
640C22×C4C2×C22⋊D1114yes—
641C22×C4C2×C22⋊D1112yes—
642C4⋊C4—28no—
643C4⋊C4—44no—
644C4⋊C4—2216no—
645C4⋊C4—2216no—
646C4⋊C4—228no—
647C22⋊C4—48no—
648C22⋊C4—2216no—
649C22⋊C4—228no—
650C22⋊C4—228no—
651C42—2216no—
652C42—228no—
653C42—444no—
654C11#1396911yescharacteristic, complemented, Sylow
655C23—22no—
656C23—22no—
657C23—22no—
658C23—22no—
659C23—22no—
660C23—22no—
661C23—22no—
662C23—22no—
663C23—22no—
664C23—22no—
665C23—22no—
666C23—22no—
667C23—22no—
668C23—22no—
669C23—22no—
670C23—22no—
671C23—22no—
672C23—22no—
673C23—41no—
674C23—41no—
675C23—41no—
676C23—41no—
677C23—41no—
678C23—41no—
679C23—41no—
680C23—41no—
681C23—41no—
682C23—41no—
683C23—41no—
684C23—41no—
685C23—41no—
686C23—41no—
687C23—41no—
688C23—41no—
689C23#6694014yescomplemented
690C23C22×C4×D1111yescharacteristic
691C23C2×#433911yescharacteristic
692C23C2×D4×D1111yescharacteristic
693C23C2×D4×D1111yescharacteristic
694C23C2×D4×D1111yescharacteristic
695C23C2×#434111yescharacteristic
696C23C2×#434111yescharacteristic
697C23#6703711yescharacteristic
698C23C2×Q8×D1111yescharacteristic
699C23#6704011yescharacteristic
700C23#41×D1111yescharacteristic
701C23#41×D1111yescharacteristic
702C23#6704311yescharacteristic
703C23#6704311yescharacteristic
704C23C22×C22⋊D1111yescharacteristic
705Q8—2232no—
706C2×C4—22no—
707C2×C4—22no—
708C2×C4—22no—
709C2×C4—24no—
710C2×C4—24no—
711C2×C4—24no—
712C2×C4—41no—
713C2×C4—41no—
714C2×C4—41no—
715C2×C4—41no—
716C2×C4—42no—
717C2×C4—42no—
718C2×C4—42no—
719C2×C4—42no—
720C2×C4—416no—
721C2×C4—42no—
722C2×C4—42no—
723C2×C4—42no—
724C2×C4—42no—
725C2×C4—42no—
726C2×C4—42no—
727C2×C4—42no—
728C2×C4—118no—
729C2×C4—114no—
730C2×C4—224no—
731C2×C4—224no—
732C2×C4—224no—
733C2×C4—224no—
734C2×C4—222no—
735C2×C4—224no—
736C2×C4—224no—
737C2×C4—222no—
738C2×C4—222no—
739C2×C4—222no—
740C2×C4—222no—
741C2×C4—222no—
742C2×C4—224no—
743C2×C4—224no—
744C2×C4—222no—
745C2×C4—224no—
746C2×C4—222no—
747C2×C4—222no—
748C2×C4—222no—
749C2×C4—222no—
750C2×C4—222no—
751C2×C4—222no—
752C2×C4—222no—
753C2×C4—222no—
754C2×C4—441no—
755C2×C4—441no—
756C2×C4—441no—
757C2×C4—441no—
758C2×C4—441no—
759C2×C4—441no—
760C2×C4—441no—
761C2×C4—441no—
762C2×C4—441no—
763C2×C4—442no—
764C2×C4—442no—
765C2×C4—441no—
766C2×C4—441no—
767C2×C4—441no—
768C2×C4—442no—
769C2×C4—442no—
770C2×C4C22⋊C4×D1114yes—
771C2×C4(C22⋊D11)⋊C414yes—
772C2×C4#6693614yes—
773C2×C4#6693714yes—
774C2×C4C4×C22⋊D1114yes—
775C2×C4#6699014yes—
776C2×C4#6699114yes—
777C22—24no—
778C22—24no—
779C22—24no—
780C22—42no—
781C22—42no—
782C22—42no—
783C22—42no—
784C22—42no—
785C22—42no—
786C22—42no—
787C22—42no—
788C22—42no—
789C22—42no—
790C22—42no—
791C22—42no—
792C22C2×C22⋊C4×D1111yescharacteristic
793C22C2×(C22⋊D11)⋊C411yescharacteristic
794C22C2×#6693611yescharacteristic
795C22C2×#6693711yescharacteristic
796C22C2×#6694011yescharacteristic
797C22#1062303511yescharacteristic
798C22#1062304211yescharacteristic
799C22#1062304411yescharacteristic
800C22#1062304711yescharacteristic
801C22#1062305311yescharacteristic
802C22#1062306011yescharacteristic
803C22#1062306411yescharacteristic
804C22#1062312911yescharacteristic
805C22#1062312911yescharacteristic
806C22#1062313011yescharacteristic
807C22#1062313011yescharacteristic
808C22#1062313111yescharacteristic
809C22#1062313411yescharacteristic
810C22#1062313711yescharacteristic
811C22#1062313911yescharacteristic
812C22#1062315311yescharacteristic
813C22#1062315611yescharacteristic
814C22D11×C22⋊Q811yescharacteristic
815C22#1062315911yescharacteristic
816C22#1062316311yescharacteristic
817C22#1062316311yescharacteristic
818C22#1062316411yescharacteristic
819C22#1062316411yescharacteristic
820C22C2×C4×C22⋊D1111yescharacteristic
821C22C2×#6699011yescharacteristic
822C22C2×#6699111yescharacteristic
823C22#1062333711yescharacteristic
824C22Q8×C22⋊D1111yescharacteristic
825C22#1062335511yescharacteristic
826C22#1062336211yescharacteristic
827C4—44no—
828C4—42no—
829C4—82no—
830C4—224no—
831C4—228no—
832C4—442no—
833C4—444no—
834C4—442no—
835C4—442no—
836C4#1062256918yes—
837C2—44no—
838C2C2×#1062256911yescharacteristic
839C2#1307114411yescharacteristic
840C2#1307129411yescharacteristic
841C2#1307144811yescharacteristic
842C2#1307145311yescharacteristic
843C2#1307162111yescharacteristic
844C2#1307164311yescharacteristic
845C2#1307195711yescharacteristic
846C2#1307197711yescharacteristic
847C2#1307212111yescharacteristic
848C2#1307214311yescharacteristic
849C2#1307217811yescharacteristic
850C2#1307221111yescharacteristic
851C2#1307352711yescharacteristic
852C2#1307354011yescharacteristic
subgroupG/H
center, FrattiniC24C23×D11
commutatorC23×C11C23×C4
FittingC2×C11×#380C2
socle, cosocleC24×C11C24
prime radicalC25×C11C23
hypercenterC2×#380D11
hypocenterC11#13969
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ C2×#380

Complements

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

NH ≅ G/Ntype
2. C22×#66940C2semidirect
3. C2×#10622587C2semidirect
5. #13066867C2semidirect
8. #13066847C2semidirect
9. #13066845C2semidirect
10. #13066845C2semidirect
23. C2×#66977C4semidirect
86. C2×C22⋊Dic11Q8semidirect
216. C2×Dic22C22⋊C4semidirect
274. C23×C11C4×Q8semidirect
360. C2×Dic11C22⋊Q8semidirect
654. C11#13969semidirect
689. C23#66940semidirect

Maximal subgroups

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

subgroupindex
C22×#669772
C22×#669402
C2×#106225872
C2×C4×C22⋊Dic112
#130668672
#130668592
#130668532
#130668472
#130668452
C2×C11×#3802
#1396911