Finite Group Databasebeta

← #14788318

Subgroups — #14788318

Order 2816.

1086 conjugacy classes of subgroups.

The subgroup lattice has 742 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623065C211yesmaximal, characteristic
2C2×#10622634C211yesmaximal, characteristic, complemented
3C2×#10622641C211yesmaximal, characteristic, complemented
4#13069819C211yesmaximal, characteristic, complemented
5#13069798C211yesmaximal, characteristic
6#13069624C211yesmaximal, characteristic, complemented
7#13069617C211yesmaximal, characteristic
8#13069568C211yesmaximal, characteristic, complemented
9#13069548C211yesmaximal, characteristic, complemented
10#13068960C211yesmaximal, characteristic, complemented
11#13068953C211yesmaximal, characteristic, complemented
12#13068869C211yesmaximal, characteristic, complemented
13#13068862C211yesmaximal, characteristic, complemented
14#13068600C211yesmaximal, characteristic, complemented
15C11×#2323C211yesmaximal, characteristic, complemented
16C2×C11×C22⋊Q8C2211yescharacteristic
17C2×C4×Q8×C11C2211yescharacteristic
18C2×C11×#117C2211yescharacteristic
19C22×#4326C2211yescharacteristic
20C22×#4325C2211yescharacteristic
21C2×#66983C2211yescharacteristic
22C2×#66977C2211yescharacteristic
23#10623065—24no—
24#10623065—24no—
25C2×#66951—21no—
26C2×#66949—21no—
27C2×#66938—21no—
28C2×#66936—21no—
29C2×#66928C2211yescharacteristic
30C2×C4×D44C2211yescharacteristic
31C2×#66922C2211yescharacteristic
32C2×C4×Dic22C2211yescharacteristic
33C11×#391C2211yescharacteristic
34C11×#389—21no—
35C11×#389C2211yescharacteristic
36C11×#388—21no—
37C11×#388—21no—
38C11×#387—21no—
39C11×#380C2211yescharacteristic
40C4×C11×C4⋊C4C2211yescharacteristic
41C2×#66899C2211yescharacteristic
42C2×#66899C2211yescharacteristic
43C2×C22⋊(C11⋊C8)C2211yescharacteristic
44C2×C22⋊(C11⋊C8)C2211yescharacteristic
45#10622641—24no—
46#10622634—24no—
47C2×#66874C2211yescharacteristic
48C2×#66874C2211yescharacteristic
49C2×#66874C2211yescharacteristic
50C2×#66873C2211yescharacteristic
51C2×#66873C2211yescharacteristic
52C2×#66873C2211yescharacteristic
53C2×#66871C2211yescharacteristic
54C2×#66871C2211yescharacteristic
55C2×C4⋊(C11⋊C8)C2211yescharacteristic
56C2×C4⋊(C11⋊C8)C2211yescharacteristic
57#10622167C2211yescharacteristic
58#10622167C2211yescharacteristic
59#10622167C2211yescharacteristic
60#10622167C2211yescharacteristic
61#10622162C2211yescharacteristic
62#10622162C2211yescharacteristic
63C22×Q8×C11C2311yescharacteristic
64C23×C4×C11C2311yescharacteristic
65C22×C22⋊D11—21no—
66C22×D44C2311yescharacteristic
67C22×C4×D11—21no—
68C22×Dic22—21no—
69C22×Dic22C2311yescharacteristic
70C11×C22⋊Q8—22no—
71C11×C22⋊Q8—22no—
72C4×Q8×C11—22no—
73C4×Q8×C11—22no—
74C11×#117—22no—
75C11×#117—22no—
76C2×C11×C4⋊C4—21no—
77C2×C11×C4⋊C4—21no—
78C2×C11×C4⋊C4—21no—
79C2×C11×C4⋊C4D411yescharacteristic
80C2×C11×C4⋊C4D411yescharacteristic
81C2×C11×C4⋊C4C2311yescharacteristic
82C2×C11×C4⋊C4C2311yescharacteristic
83C2×C11×C4⋊C4C2311yescharacteristic
84C2×C11×C22⋊C4—21no—
85C2×C11×C22⋊C4—21no—
86C2×C11×C22⋊C4D411yescharacteristic
87C2×C11×C22⋊C4D411yescharacteristic
88C2×C42×C11—21no—
89C2×C42×C11—21no—
90C2×C42×C11C2311yescharacteristic
91C2×C42×C11C2311yescharacteristic
92C2×C22⋊Dic11—21no—
93C2×#4326—22no—
94C2×#4326—22no—
95C2×#4326—41no—
96C2×#4325—22no—
97C2×#4325—22no—
98C2×#4325—41no—
99#66983—22no—
100#66983—22no—
101C2×(C2×D11)⋊C4—21no—
102C2×(C2×D11)⋊C4—21no—
103C2×(C2×D11)⋊C4—21no—
104C2×(C2×D11)⋊C4—21no—
105C2×C4⋊Dic11—21no—
106C2×C4⋊Dic11C2311yescharacteristic
107C2×C4⋊Dic11C2311yescharacteristic
108#66977—22no—
109#66977—22no—
110C2×Dic11⋊C4—21no—
111C2×Dic11⋊C4—21no—
112C2×C4×Dic11—21no—
113C22×C11⋊C8C2311yescharacteristic
114C22×C11⋊C8C2311yescharacteristic
115C22×C11⋊C8C2311yescharacteristic
116C22×C11⋊C8C2311yescharacteristic
117#66951—28no—
118#66949—28no—
119#66938—28no—
120#66936—28no—
121#66928—22no—
122#66928D414yes—
123C4×D44—22no—
124C4×D44—22no—
125#66922—22no—
126#66922D414yes—
127C4×Dic22—22no—
128C4×Dic22—22no—
129C11×#95—21no—
130C11×#95—21no—
131C11×#95—21no—
132C11×#95—21no—
133C11×#95—21no—
134#66899—22no—
135#66899—22no—
136C22⋊(C11⋊C8)—41no—
137C22⋊(C11⋊C8)—41no—
138#66874—22no—
139#66874—22no—
140#66874—41no—
141#66873—22no—
142#66873—22no—
143#66873—41no—
144#66871—22no—
145#66871—22no—
146C4⋊(C11⋊C8)—22no—
147C4⋊(C11⋊C8)—22no—
148#24168—111nomaximal, Sylow
149C24×C11C2×D411yescharacteristic
150C23×D11—21no—
151C2×Q8×C11—21no—
152C2×Q8×C11—21no—
153C2×Q8×C11—21no—
154C2×Q8×C11—21no—
155C2×Q8×C11—21no—
156C2×Q8×C11#4112yes—
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—21no—
164C22×C4×C11—21no—
165C22×C4×C11—21no—
166C22×C4×C11—21no—
167C22×C4×C11C2×D411yescharacteristic
168C22×C4×C11C2×D411yescharacteristic
169C22×C4×C11C2×D411yescharacteristic
170C22×C4×C11C2×D411yescharacteristic
171C22×C4×C11C2×D411yescharacteristic
172C22×C4×C11C2411yescharacteristic
173C2×C22⋊D11—24no—
174C2×C22⋊D11—81no—
175C2×C22⋊D11—81no—
176C22×Dic11—21no—
177C22×Dic11—21no—
178C22×Dic11—21no—
179C2×D44—21no—
180C2×D44—21no—
181C2×D44—21no—
182C2×D44—21no—
183C2×D44—21no—
184C2×D44C2×D412yes—
185C2×C4×D11—24no—
186C2×C4×D11—81no—
187C2×C4×D11—81no—
188C2×Dic22—24no—
189C2×Dic22—21no—
190C2×Dic22—21no—
191C2×Dic22—21no—
192C2×Dic22—21no—
193C2×Dic22—21no—
194C2×Dic22—81no—
195C2×Dic22—81no—
196C2×Dic22C2×D412yes—
197C11×C4⋊C4—24no—
198C11×C4⋊C4—22no—
199C11×C4⋊C4—22no—
200C11×C4⋊C4—21no—
201C11×C4⋊C4—21no—
202C11×C4⋊C4—21no—
203C11×C4⋊C4—21no—
204C11×C4⋊C4—21no—
205C11×C4⋊C4—42no—
206C11×C4⋊C4—81no—
207C11×C4⋊C4#4112yes—
208C11×C22⋊C4—24no—
209C11×C22⋊C4—22no—
210C11×C22⋊C4—22no—
211C11×C22⋊C4—81no—
212C42×C11—21no—
213C42×C11—21no—
214C42×C11—42no—
215C42×C11—81no—
216C42×C11C2×D412yes—
217C42×C11C2×D412yes—
218C22⋊Dic11—24no—
219#4326—44no—
220#4325—44no—
221(C2×D11)⋊C4—24no—
222(C2×D11)⋊C4—24no—
223(C2×D11)⋊C4—24no—
224(C2×D11)⋊C4—24no—
225C4⋊Dic11—24no—
226C4⋊Dic11—21no—
227C4⋊Dic11—21no—
228C4⋊Dic11C2×D412yes—
229C4⋊Dic11C2×D412yes—
230Dic11⋊C4—24no—
231Dic11⋊C4—24no—
232C4×Dic11—24no—
233C2×C11⋊C8—21no—
234C2×C11⋊C8—21no—
235C2×C11⋊C8—21no—
236C2×C11⋊C8—21no—
237C2×C11⋊C8—21no—
238C2×C11⋊C8—21no—
239C2×C11⋊C8—21no—
240C2×C11⋊C8—21no—
241C2×C11⋊C8—21no—
242C2×C11⋊C8—21no—
243C2×C11⋊C8—21no—
244C2×C11⋊C8—21no—
245C2×#542—111no—
246C2×#477—111no—
247C2×#464—111no—
248#2323D1111yescharacteristic, complemented
249#2036—111no—
250#2033—111no—
251#2001—111no—
252#2000—111no—
253#1988—111no—
254#1983—111no—
255#1878—111no—
256#1877—111no—
257#1863—111no—
258#1862—111no—
259#1798—111no—
260C23×C11—21no—
261C23×C11—21no—
262C23×C11—21no—
263C23×C11—21no—
264C23×C11—21no—
265C23×C11—21no—
266C23×C11—21no—
267C23×C11C22×D411yescharacteristic
268C22×D11—22no—
269C22×D11—41no—
270C22×D11—41no—
271C22×D11—41no—
272C22×D11—41no—
273C22×D11—41no—
274C22×D11—41no—
275Q8×C11—22no—
276Q8×C11—22no—
277Q8×C11—41no—
278Q8×C11—41no—
279C2×C4×C11—21no—
280C2×C4×C11—21no—
281C2×C4×C11—21no—
282C2×C4×C11—21no—
283C2×C4×C11—21no—
284C2×C4×C11—21no—
285C2×C4×C11—21no—
286C2×C4×C11—22no—
287C2×C4×C11—22no—
288C2×C4×C11—21no—
289C2×C4×C11—21no—
290C2×C4×C11—21no—
291C2×C4×C11—21no—
292C2×C4×C11—21no—
293C2×C4×C11—21no—
294C2×C4×C11—41no—
295C2×C4×C11—41no—
296C2×C4×C11—41no—
297C2×C4×C11—41no—
298C2×C4×C11—41no—
299C2×C4×C11—41no—
300C2×C4×C11—41no—
301C2×C4×C11—41no—
302C2×C4×C11—41no—
303C2×C4×C11—41no—
304C2×C4×C11—41no—
305C2×C4×C11—41no—
306C2×C4×C11—41no—
307C2×C4×C11—41no—
308C2×C4×C11#12012yes—
309C2×C4×C11#12012yes—
310C2×C4×C11C22×D411yescharacteristic
311C2×C4×C11C22×D411yescharacteristic
312C2×C4×C11C2×#4111yescharacteristic
313C2×C4×C11C2×#4111yescharacteristic
314C2×C4×C11H(5,𝔽2)11yescharacteristic
315C2×C4×C112−1+411yescharacteristic
316C22⋊D11—84no—
317C2×Dic11—22no—
318C2×Dic11—22no—
319C2×Dic11—22no—
320C2×Dic11—41no—
321C2×Dic11—41no—
322C2×Dic11—41no—
323C2×Dic11—41no—
324C2×Dic11—41no—
325C2×Dic11—41no—
326D44—22no—
327D44—22no—
328D44—41no—
329D44—41no—
330C4×D11—84no—
331Dic22—22no—
332Dic22—22no—
333Dic22—41no—
334Dic22—41no—
335Dic22—84no—
336C11⋊C8—41no—
337C11⋊C8—41no—
338C11⋊C8—41no—
339C11⋊C8—41no—
340C22×Q16—111no—
341C22×SD16—111no—
342#542—224no—
343#542—224no—
344C2×C4⋊Q8—111no—
345C2×#126—221no—
346C2×#124—111no—
347C2×#124—221no—
348C2×#123—221no—
349C2×C22⋊Q8—111no—
350C2×C22⋊Q8—221no—
351C2×C22⋊Q8C2×D1111yescharacteristic
352C2×#121—111no—
353C2×C4×Q8—111no—
354C2×C4×Q8C2×D1111yescharacteristic
355C2×C4×D4—111no—
356C2×#117C2×D1111yescharacteristic
357#477—224no—
358#464—224no—
359C2×#107—111no—
360C2×#107—111no—
361C2×C4⋊C8—111no—
362C2×C4⋊C8—111no—
363C2×#103—111no—
364C2×#103—111no—
365C2×#103—111no—
366C2×#103—111no—
367C2×#103—111no—
368C2×#102—111no—
369C2×#102—111no—
370C2×#102—111no—
371C2×C22⋊C8—111no—
372C2×C22⋊C8—111no—
373#391C2×D1111yescharacteristic
374#389—21no—
375#389C2×D1111yescharacteristic
376#388—21no—
377#388—21no—
378#387—21no—
379#380C2×D1111yescharacteristic
380C4×C4⋊C4C2×D1111yescharacteristic
381#340—111no—
382#340—111no—
383#340—111no—
384#340—111no—
385#336—111no—
386#336—111no—
387C22×C11—41no—
388C22×C11—41no—
389C22×C11—41no—
390C22×C11—41no—
391C22×C11—41no—
392C22×C11—41no—
393C22×C11—41no—
394C22×C11C2×#12011yescharacteristic
395C22×C11#52511yescharacteristic
396C22×C11#53711yescharacteristic
397C22×C11#57611yescharacteristic
398C22×C11#57711yescharacteristic
399C22×C11#57811yescharacteristic
400C22×C11#57811yescharacteristic
401C2×D11—42no—
402C2×D11—42no—
403C2×D11—42no—
404C2×D11—81no—
405C2×D11—81no—
406C2×D11—81no—
407C2×D11—81no—
408C4×C11—22no—
409C4×C11—22no—
410C4×C11—42no—
411C4×C11—41no—
412C4×C11—42no—
413C4×C11—41no—
414C4×C11—41no—
415C4×C11—81no—
416C4×C11—81no—
417C4×C11#54611yescharacteristic
418C4×C11#54711yescharacteristic
419C4×C11#54811yescharacteristic
420C4×C11#55011yescharacteristic
421Dic11—42no—
422Dic11—42no—
423Dic11—42no—
424C22×Q8—111no—
425C22×Q8—221no—
426C22×Q8C22×D1111yescharacteristic
427C22×D4—111no—
428C22×D4—221no—
429C23×C4—221no—
430C23×C4C22×D1111yescharacteristic
431C2×Q16—222no—
432C2×Q16—222no—
433C2×Q16—441no—
434C2×SD16—222no—
435C2×SD16—222no—
436C2×SD16—441no—
437C22×C8—111no—
438C22×C8—111no—
439C22×C8—111no—
440C22×C8—111no—
441C4⋊Q8—114no—
442C4⋊Q8—222no—
443#126—228no—
444#124—114no—
445#124—228no—
446#124—222no—
447#123—228no—
448C22⋊Q8—22no—
449C22⋊Q8—22no—
450C22⋊Q8—228no—
451C22⋊Q8—222no—
452C22⋊Q8—222no—
453#121—222no—
454#121—222no—
455C4×Q8—22no—
456C4×Q8—22no—
457C4×Q8—222no—
458C4×Q8—222no—
459C4×D4—222no—
460C4×D4—222no—
461#117—22no—
462#117—22no—
463C2×C4⋊C4—21no—
464C2×C4⋊C4—21no—
465C2×C4⋊C4—21no—
466C2×C4⋊C4—111no—
467C2×C4⋊C4—111no—
468C2×C4⋊C4—221no—
469C2×C4⋊C4—221no—
470C2×C4⋊C4—221no—
471C2×C4⋊C4C22⋊D1111yescharacteristic
472C2×C4⋊C4C22⋊D1111yescharacteristic
473C2×C4⋊C4C22×D1111yescharacteristic
474C2×C4⋊C4C22×D1111yescharacteristic
475C2×C4⋊C4C22×D1111yescharacteristic
476C2×C22⋊C4—21no—
477C2×C22⋊C4—21no—
478C2×C22⋊C4—221no—
479C2×C22⋊C4—221no—
480C2×C22⋊C4—221no—
481C2×C22⋊C4—221no—
482C2×C22⋊C4—221no—
483C2×C22⋊C4C22⋊D1111yescharacteristic
484C2×C22⋊C4C22⋊D1111yescharacteristic
485C2×C42—21no—
486C2×C42—21no—
487C2×C42—221no—
488C2×C42C22×D1111yescharacteristic
489C2×C42C22×D1111yescharacteristic
490#107—222no—
491#107—222no—
492C4⋊C8—222no—
493C4⋊C8—222no—
494#103—222no—
495#103—222no—
496#103—222no—
497#103—222no—
498#103—441no—
499#102—222no—
500#102—222no—
501#102—441no—
502C22⋊C8—441no—
503C22⋊C8—441no—
504#95—21no—
505#95—21no—
506#95—21no—
507#95—21no—
508#95—21no—
509C2×C11—81no—
510C2×C11#240711yescharacteristic
511C2×C11#301111yescharacteristic
512C2×C11#301211yescharacteristic
513C2×C11#312111yescharacteristic
514C2×C11#312411yescharacteristic
515C2×C11#325811yescharacteristic
516C2×C11#326211yescharacteristic
517D11—82no—
518C24—221no—
519C24C2×C22⋊D1111yescharacteristic
520C2×Q8—21no—
521C2×Q8—21no—
522C2×Q8—21no—
523C2×Q8—21no—
524C2×Q8—21no—
525C2×Q8—112no—
526C2×Q8—224no—
527C2×Q8—221no—
528C2×Q8—221no—
529C2×Q8—221no—
530C2×Q8—221no—
531C2×Q8—221no—
532C2×Q8—881no—
533C2×Q8—881no—
534C2×Q8#433912yes—
535C2×D4—112no—
536C2×D4—224no—
537C2×D4—221no—
538C2×D4—221no—
539C2×D4—221no—
540C2×D4—221no—
541C2×D4—221no—
542C2×D4—881no—
543C2×D4—881no—
544C22×C4—21no—
545C22×C4—21no—
546C22×C4—21no—
547C22×C4—21no—
548C22×C4—21no—
549C22×C4—21no—
550C22×C4—21no—
551C22×C4—21no—
552C22×C4—21no—
553C22×C4—21no—
554C22×C4—224no—
555C22×C4—221no—
556C22×C4—221no—
557C22×C4—221no—
558C22×C4—881no—
559C22×C4—881no—
560C22×C4C2×C22⋊D1111yescharacteristic
561C22×C4C2×C22⋊D1111yescharacteristic
562C22×C4C2×C22⋊D1111yescharacteristic
563C22×C4C2×C22⋊D1111yescharacteristic
564C22×C4C2×C22⋊D1111yescharacteristic
565C22×C4C23×D1111yescharacteristic
566Q16—444no—
567SD16—444no—
568C2×C8—221no—
569C2×C8—221no—
570C2×C8—221no—
571C2×C8—221no—
572C2×C8—221no—
573C2×C8—221no—
574C2×C8—221no—
575C2×C8—221no—
576C2×C8—221no—
577C2×C8—221no—
578C2×C8—221no—
579C2×C8—221no—
580C4⋊C4—24no—
581C4⋊C4—22no—
582C4⋊C4—22no—
583C4⋊C4—21no—
584C4⋊C4—21no—
585C4⋊C4—21no—
586C4⋊C4—21no—
587C4⋊C4—21no—
588C4⋊C4—42no—
589C4⋊C4—81no—
590C4⋊C4—112no—
591C4⋊C4—112no—
592C4⋊C4—224no—
593C4⋊C4—224no—
594C4⋊C4—224no—
595C4⋊C4—221no—
596C4⋊C4—221no—
597C4⋊C4#433912yes—
598C22⋊C4—24no—
599C22⋊C4—22no—
600C22⋊C4—22no—
601C22⋊C4—81no—
602C22⋊C4—224no—
603C22⋊C4—224no—
604C22⋊C4—224no—
605C22⋊C4—224no—
606C22⋊C4—224no—
607C42—21no—
608C42—21no—
609C42—42no—
610C42—81no—
611C42—224no—
612C42D4×D1112yes—
613C42D4×D1112yes—
614C11#2416811yescharacteristic, complemented, Sylow
615C23—21no—
616C23—21no—
617C23—21no—
618C23—21no—
619C23—21no—
620C23—21no—
621C23—21no—
622C23—222no—
623C23—441no—
624C23—441no—
625C23—441no—
626C23—441no—
627C23—441no—
628C23—441no—
629C23C22×C22⋊D1111yescharacteristic
630Q8—22no—
631Q8—22no—
632Q8—41no—
633Q8—41no—
634Q8—222no—
635Q8—222no—
636Q8—441no—
637Q8—441no—
638Q8—884no—
639D4—222no—
640D4—222no—
641D4—441no—
642D4—441no—
643D4—884no—
644C2×C4—21no—
645C2×C4—21no—
646C2×C4—21no—
647C2×C4—21no—
648C2×C4—22no—
649C2×C4—22no—
650C2×C4—21no—
651C2×C4—21no—
652C2×C4—21no—
653C2×C4—21no—
654C2×C4—21no—
655C2×C4—21no—
656C2×C4—21no—
657C2×C4—21no—
658C2×C4—21no—
659C2×C4—41no—
660C2×C4—41no—
661C2×C4—41no—
662C2×C4—41no—
663C2×C4—41no—
664C2×C4—41no—
665C2×C4—41no—
666C2×C4—41no—
667C2×C4—41no—
668C2×C4—41no—
669C2×C4—41no—
670C2×C4—41no—
671C2×C4—41no—
672C2×C4—41no—
673C2×C4—222no—
674C2×C4—222no—
675C2×C4—222no—
676C2×C4—441no—
677C2×C4—441no—
678C2×C4—441no—
679C2×C4—441no—
680C2×C4—441no—
681C2×C4—441no—
682C2×C4—884no—
683C2×C4#6699012yes—
684C2×C4#6699012yes—
685C2×C4C2×#433911yescharacteristic
686C2×C4C2×#433911yescharacteristic
687C2×C4C2×D4×D1111yescharacteristic
688C2×C4C2×D4×D1111yescharacteristic
689C2×C4#6704211yescharacteristic
690C2×C4#6704311yescharacteristic
691C8—441no—
692C8—441no—
693C8—441no—
694C8—441no—
695C22—41no—
696C22—41no—
697C22—41no—
698C22—41no—
699C22—41no—
700C22—41no—
701C22—41no—
702C22—442no—
703C22—442no—
704C22—442no—
705C22—881no—
706C22—881no—
707C22—881no—
708C22—881no—
709C22#1062332211yescharacteristic
710C22C2×#6699011yescharacteristic
711C22#1062336411yescharacteristic
712C22#1062336611yescharacteristic
713C22#1062336811yescharacteristic
714C22#1062336911yescharacteristic
715C22#1062336911yescharacteristic
716C4—22no—
717C4—22no—
718C4—41no—
719C4—42no—
720C4—42no—
721C4—41no—
722C4—41no—
723C4—81no—
724C4—81no—
725C4—442no—
726C4—442no—
727C4—442no—
728C4#1062308111yescharacteristic
729C4#1062308211yescharacteristic
730C4#1062308311yescharacteristic
731C4#1062308411yescharacteristic
732C2—81no—
733C2—882no—
734C2#1307196111yescharacteristic
735C2#1307790911yescharacteristic
736C2#1307791711yescharacteristic
737C2#1307884511yescharacteristic
738C2#1307887811yescharacteristic
739C2#1308003611yescharacteristic
740C2#1308007211yescharacteristic
subgroupG/H
centerC23C22×C22⋊D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#2323C2
socleC23×C11C22×D4
prime radicalC2×#66983C22
hypercenter#2323D11
hypocenterC11#24168
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×#117 ◁ #2323

Complements

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

NH ≅ G/Ntype
2. C2×#10622634C2semidirect
3. C2×#10622641C2semidirect
4. #13069819C2semidirect
6. #13069624C2semidirect
8. #13069568C2semidirect
9. #13069548C2semidirect
10. #13068960C2semidirect
11. #13068953C2semidirect
12. #13068869C2semidirect
13. #13068862C2semidirect
14. #13068600C2semidirect
15. C11×#2323C2semidirect
248. #2323D11semidirect
614. C11#24168semidirect

Maximal subgroups

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

subgroupindex
C2×#106230652
C2×#106226342
C2×#106226412
#130698192
#130697982
#130696242
#130696172
#130695682
#130695482
#130689602
#130689532
#130688692
#130688622
#130686002
C11×#23232
#2416811