Finite Group Databasebeta

← #14774042

Subgroups — #14774042

Order 2816.

1170 conjugacy classes of subgroups.

The subgroup lattice has 748 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622653C211yesmaximal, characteristic
2C2×#10622370C211yesmaximal, characteristic, complemented
3C22×#66880C211yesmaximal, characteristic, complemented
4#13071636C211yesmaximal, characteristic
5#13071448C211yesmaximal, characteristic, complemented
6#13069498C211yesmaximal, characteristic, complemented
7#13069307C211yesmaximal, characteristic, complemented
8#13069255C211yesmaximal, characteristic, complemented
9#13068968C211yesmaximal, characteristic, complemented
10#13068948C211yesmaximal, characteristic, complemented
11#13068871C211yesmaximal, characteristic, complemented
12#13068803C211yesmaximal, characteristic, complemented
13#13068445C211yesmaximal, characteristic, complemented
14#13068392C211yesmaximal, characteristic, complemented
15C11×#1893C211yesmaximal, characteristic
16C23×Dic22C2211yescharacteristic
17C23×C8×C11C2211yescharacteristic
18C2×C11×#121C2211yescharacteristic
19C2×D4×Dic11—21no—
20C2×D4×Dic11C2211yescharacteristic
21C22×#4324C2211yescharacteristic
22C22×#4324C2211yescharacteristic
23C22×C4⋊Dic11C2211yescharacteristic
24C2×#66940C2211yescharacteristic
25C2×#66940C2211yescharacteristic
26C2×C11×#102C2211yescharacteristic
27C2×C11×#102C2211yescharacteristic
28C11×#380C2211yescharacteristic
29#10622834C2211yescharacteristic
30#10622833—21no—
31C4×C22⋊Dic11C2211yescharacteristic
32C2×C22⋊(C11⋊C8)C2211yescharacteristic
33C2×#66880—24no—
34C2×#66880C2211yescharacteristic
35C2×#66880C2211yescharacteristic
36C2×#66880C2211yescharacteristic
37C2×#66880C2211yescharacteristic
38C2×#66879C2211yescharacteristic
39C2×#66879C2211yescharacteristic
40#10622653C418yescomplemented
41#10622598C2211yescharacteristic
42C4⋊C4×Dic11C2211yescharacteristic
43#10622587C2211yescharacteristic
44#10622587C2211yescharacteristic
45C2×#66874C2211yescharacteristic
46C2×#66874C2211yescharacteristic
47C2×#66871C2211yescharacteristic
48C2×#66871C2211yescharacteristic
49#10622564—21no—
50#10622563—21no—
51#10622555—21no—
52C22⋊C4×Dic11—21no—
53#10622370—24no—
54#10622259—21no—
55#10622259—21no—
56C11×#340C2211yescharacteristic
57C11×#340C2211yescharacteristic
58#10622188C2211yescharacteristic
59#10622188C2211yescharacteristic
60#10622167C2211yescharacteristic
61#10622167C2211yescharacteristic
62C22×D4×C11—21no—
63C22×D4×C11C2311yescharacteristic
64C23×C4×C11C2311yescharacteristic
65C23×Dic11—21no—
66C23×Dic11—21no—
67C23×Dic11—21no—
68C22×Dic22—22no—
69C22×Dic22—22no—
70C22×Dic22—21no—
71C22×Dic22—22no—
72C22×Dic22—41no—
73C22×Dic22—41no—
74C22×Dic22C2×C414yescomplemented
75C22×Dic22C2311yescharacteristic
76C22×Dic22C2311yescharacteristic
77C22×C8×C11—22no—
78C22×C8×C11—22no—
79C22×C8×C11—41no—
80C22×C8×C11C2311yescharacteristic
81C22×C8×C11C2311yescharacteristic
82C11×#121—22no—
83C11×#121C2×C414yes—
84C2×C11×C4⋊C4C2311yescharacteristic
85C2×C11×C4⋊C4C2311yescharacteristic
86C2×C11×C4⋊C4C2311yescharacteristic
87C2×C11×C22⋊C4—21no—
88C2×C11×C22⋊C4—21no—
89C2×C22⋊Dic11—21no—
90C2×C22⋊Dic11—21no—
91C2×C22⋊Dic11—21no—
92C2×C22⋊Dic11D411yescharacteristic
93C2×C22⋊Dic11D411yescharacteristic
94D4×Dic11—22no—
95D4×Dic11—41no—
96D4×Dic11—44no—
97C2×#4324—22no—
98C2×#4324—22no—
99C2×#4324—41no—
100C2×#4324—41no—
101C2×#4324C2×C414yescomplemented
102C2×#4324C2×C414yescomplemented
103C2×C4⋊Dic11—22no—
104C2×C4⋊Dic11—21no—
105C2×C4⋊Dic11—21no—
106C2×C4⋊Dic11—41no—
107C2×C4⋊Dic11C2311yescharacteristic
108C2×C4⋊Dic11C2311yescharacteristic
109C2×Dic11⋊C4—21no—
110C2×Dic11⋊C4—21no—
111C2×C4×Dic11—21no—
112C2×C4×Dic11—21no—
113C2×C4×Dic11—21no—
114C2×C4×Dic11C2311yescharacteristic
115C2×C4×Dic11C2311yescharacteristic
116C22×C11⋊C8C2311yescharacteristic
117C22×C11⋊C8C2311yescharacteristic
118#66940—22no—
119#66940—22no—
120#66940—41no—
121#66940—41no—
122C11×#102—22no—
123C11×#102—41no—
124C11×#95—21no—
125C11⋊#95—21no—
126C11⋊#95—21no—
127C11⋊#95—21no—
128C11⋊#95—21no—
129C11⋊#95—21no—
130C11⋊#95—21no—
131C11⋊#95D411yescharacteristic
132C11⋊#95D411yescharacteristic
133C22⋊(C11⋊C8)C2×C414yescomplemented
134#66880—22no—
135#66880—22no—
136#66880—22no—
137#66880D414yescomplemented
138#66879—22no—
139#66879—41no—
140#66874C2×C414yescomplemented
141#66874C2×C414yescomplemented
142#66871—22no—
143#66871—41no—
144#22855—111nomaximal, Sylow
145C24×C11—21no—
146C24×C11C2×D411yescharacteristic
147C2×D4×C11—24no—
148C2×D4×C11—21no—
149C2×D4×C11—21no—
150C2×D4×C11—21no—
151C2×D4×C11—21no—
152C2×D4×C11—21no—
153C2×D4×C11—42no—
154C2×D4×C11—42no—
155C2×D4×C11C22×C412yes—
156C22×C4×C11—21no—
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×C11C22×C412yes—
164C22×C4×C11C2×D411yescharacteristic
165C22×C4×C11#4112yes—
166C22×C4×C11C2411yescharacteristic
167C22×Dic11—24no—
168C22×Dic11—21no—
169C22×Dic11—21no—
170C22×Dic11—21no—
171C22×Dic11—21no—
172C22×Dic11—42no—
173C22×Dic11—42no—
174C22×Dic11—42no—
175C22×Dic11—42no—
176C22×Dic11—42no—
177C22×Dic11—42no—
178C22×Dic11—81no—
179C22×Dic11—81no—
180C22×Dic11C2×D411yescharacteristic
181C22×Dic11C2×D411yescharacteristic
182C22×Dic11C2×D411yescharacteristic
183C22×Dic11C2×D411yescharacteristic
184C2×Dic22—28no—
185C2×Dic22—24no—
186C2×Dic22—21no—
187C2×Dic22—21no—
188C2×Dic22—21no—
189C2×Dic22—21no—
190C2×Dic22—21no—
191C2×Dic22—21no—
192C2×Dic22—21no—
193C2×Dic22—21no—
194C2×Dic22—44no—
195C2×Dic22—44no—
196C2×Dic22—44no—
197C2×Dic22—42no—
198C2×Dic22—42no—
199C2×Dic22C22×C412yes—
200C2×Dic22C22×C412yes—
201C2×Dic22C2×D412yes—
202C2×Dic22#4112yes—
203C2×C8×C11—21no—
204C2×C8×C11—21no—
205C2×C8×C11—21no—
206C2×C8×C11—21no—
207C2×C8×C11—21no—
208C2×C8×C11—44no—
209C2×C8×C11C2×D412yes—
210C11×C4⋊C4—21no—
211C11×C4⋊C4—21no—
212C11×C4⋊C4—21no—
213C11×C4⋊C4—21no—
214C11×C4⋊C4—21no—
215C11×C4⋊C4C22×C412yes—
216C11×C22⋊C4—24no—
217C11×C22⋊C4—42no—
218C22⋊Dic11—22no—
219C22⋊Dic11—22no—
220C22⋊Dic11—42no—
221C22⋊Dic11—42no—
222C22⋊Dic11—81no—
223#4324—28no—
224#4324—44no—
225C4⋊Dic11—21no—
226C4⋊Dic11—21no—
227C4⋊Dic11—21no—
228C4⋊Dic11—42no—
229C4⋊Dic11—42no—
230C4⋊Dic11C2×D412yes—
231Dic11⋊C4—42no—
232Dic11⋊C4—42no—
233C4×Dic11—21no—
234C4×Dic11—21no—
235C4×Dic11—21no—
236C4×Dic11—21no—
237C4×Dic11—42no—
238C4×Dic11—42no—
239C4×Dic11—42no—
240C2×C11⋊C8—21no—
241C2×C11⋊C8—21no—
242C2×C11⋊C8—21no—
243C2×C11⋊C8—21no—
244C2×C11⋊C8C22×C412yes—
245C2×C11⋊C8C22×C412yes—
246C2×#448—111no—
247C2×#440—111no—
248C22×#103—111no—
249#2361—111no—
250Q8×C22⋊C4—111no—
251#1973—111no—
252#1935—111no—
253#1928—111no—
254#1893D1111yescharacteristic
255#1880—111no—
256#1877—111no—
257#1863—111no—
258#1852—111no—
259#1763—111no—
260#1752—111no—
261C23×C11—21no—
262C23×C11—21no—
263C23×C11—21no—
264C23×C11—21no—
265C23×C11—22no—
266C23×C11—41no—
267C23×C11—41no—
268C23×C11—41no—
269C23×C11—41no—
270C23×C11—41no—
271C23×C11—41no—
272C23×C11C4×D412yes—
273C23×C11AGL(1,ℤ/8)12yes—
274C23×C11#13712yes—
275C23×C11C22×D411yescharacteristic
276D4×C11—22no—
277D4×C11—22no—
278D4×C11—48no—
279D4×C11—41no—
280D4×C11—41no—
281C2×C4×C11—21no—
282C2×C4×C11—21no—
283C2×C4×C11—22no—
284C2×C4×C11—22no—
285C2×C4×C11—22no—
286C2×C4×C11—22no—
287C2×C4×C11—22no—
288C2×C4×C11—41no—
289C2×C4×C11—41no—
290C2×C4×C11—41no—
291C2×C4×C11—41no—
292C2×C4×C11—41no—
293C2×C4×C11—41no—
294C2×C4×C11—41no—
295C2×C4×C11—41no—
296C2×C4×C11C4×D412yes—
297C2×C4×C11C23×C411yescharacteristic
298C2×C4×C11C22×D411yescharacteristic
299C2×C4×C11C2×#4111yescharacteristic
300C2×C4×C11C2×#4111yescharacteristic
301C2×C4×C11H(5,𝔽2)11yescharacteristic
302C2×C4×C11H(5,𝔽2)11yescharacteristic
303C2×Dic11—22no—
304C2×Dic11—22no—
305C2×Dic11—22no—
306C2×Dic11—22no—
307C2×Dic11—21no—
308C2×Dic11—21no—
309C2×Dic11—22no—
310C2×Dic11—21no—
311C2×Dic11—21no—
312C2×Dic11—21no—
313C2×Dic11—21no—
314C2×Dic11—21no—
315C2×Dic11—21no—
316C2×Dic11—21no—
317C2×Dic11—21no—
318C2×Dic11—21no—
319C2×Dic11—21no—
320C2×Dic11—48no—
321C2×Dic11—41no—
322C2×Dic11—41no—
323C2×Dic11—41no—
324C2×Dic11—41no—
325C2×Dic11—41no—
326C2×Dic11—41no—
327C2×Dic11—41no—
328C2×Dic11—84no—
329C2×Dic11—84no—
330Dic22—22no—
331Dic22—22no—
332Dic22—22no—
333Dic22—22no—
334Dic22—22no—
335Dic22—48no—
336Dic22—41no—
337Dic22—41no—
338Dic22C4×D414yescomplemented
339C8×C11—22no—
340C8×C11—41no—
341C11⋊C8—22no—
342C11⋊C8—22no—
343C23×Q8—111no—
344C22×SD16—111no—
345C22×SD16—111no—
346C23×C8C2×D1111yescharacteristic
347C2×#121C2×D1111yescharacteristic
348C2×C4×Q8—111no—
349C2×C4×Q8—111no—
350C2×C4×D4—111no—
351C2×C4×D4—221no—
352C22×C4⋊C4—111no—
353#448—118no—
354#440—224no—
355C2×#107—111no—
356C2×#107—111no—
357C2×#103—111no—
358C2×#103—111no—
359C2×#103—111no—
360C2×#103—111no—
361C2×#103—111no—
362C2×#103—111no—
363C2×#103—224no—
364C2×#102C2×D1111yescharacteristic
365C2×#102C2×D1111yescharacteristic
366C2×C22⋊C8—111no—
367C2×#97—111no—
368C2×#97—111no—
369#391—111no—
370#391—111no—
371#391—221no—
372#391—221no—
373#390—111no—
374#389—111no—
375#388—221no—
376#386—221no—
377#385—221no—
378#380—221no—
379#380C2×D1111yescharacteristic
380C4×C4⋊C4—111no—
381C4×C22⋊C4—111no—
382C4×C22⋊C4—221no—
383#340—111no—
384#340—111no—
385#340C2×D1111yescharacteristic
386#340C2×D1111yescharacteristic
387#336—111no—
388#336—111no—
389C22×C11—22no—
390C22×C11—22no—
391C22×C11—22no—
392C22×C11—22no—
393C22×C11—22no—
394C22×C11—22no—
395C22×C11—42no—
396C22×C11—42no—
397C22×C11—42no—
398C22×C11—81no—
399C22×C11—81no—
400C22×C11—81no—
401C22×C11—81no—
402C22×C11#44014yescomplemented
403C22×C11C2×C4×D411yescharacteristic
404C22×C11D4211yescharacteristic
405C22×C11#54611yescharacteristic
406C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
407C22×C11C2×#13711yescharacteristic
408C22×C11#57711yescharacteristic
409C22×C11#57811yescharacteristic
410C4×C11—22no—
411C4×C11—42no—
412C4×C11—81no—
413C4×C11—81no—
414C4×C11C2×C4×D411yescharacteristic
415C4×C11#51811yescharacteristic
416C4×C11#54611yescharacteristic
417C4×C11#55111yescharacteristic
418Dic11—24no—
419Dic11—42no—
420Dic11—41no—
421Dic11—42no—
422Dic11—41no—
423Dic11—41no—
424Dic11—41no—
425Dic11—81no—
426C22×Q8—114no—
427C22×Q8—111no—
428C22×Q8—111no—
429C22×Q8—222no—
430C22×Q8—222no—
431C22×Q8—221no—
432C22×Q8—222no—
433C22×Q8—441no—
434C22×Q8—441no—
435C22×D4—21no—
436C22×D4C22×D1111yescharacteristic
437C23×C4—221no—
438C23×C4—221no—
439C23×C4—221no—
440C23×C4C22×D1111yescharacteristic
441C2×SD16—114no—
442C2×SD16—114no—
443C2×SD16—222no—
444C2×SD16—222no—
445C2×SD16—441no—
446C2×SD16—441no—
447C22×C8—22no—
448C22×C8—22no—
449C22×C8—41no—
450C22×C8—111no—
451C22×C8—111no—
452C22×C8C22×D1111yescharacteristic
453C22×C8C22×D1111yescharacteristic
454#121—22no—
455#121C4×D1114yes—
456C4×Q8—222no—
457C4×Q8—222no—
458C4×Q8—441no—
459C4×Q8—441no—
460C4×D4—222no—
461C4×D4—441no—
462C4×D4—444no—
463C2×C4⋊C4—111no—
464C2×C4⋊C4—111no—
465C2×C4⋊C4—222no—
466C2×C4⋊C4—221no—
467C2×C4⋊C4—221no—
468C2×C4⋊C4—221no—
469C2×C4⋊C4—221no—
470C2×C4⋊C4—441no—
471C2×C4⋊C4C22×D1111yescharacteristic
472C2×C4⋊C4C22×D1111yescharacteristic
473C2×C4⋊C4C22×D1111yescharacteristic
474C2×C22⋊C4—21no—
475C2×C22⋊C4—21no—
476C2×C22⋊C4—111no—
477C2×C22⋊C4—111no—
478C2×C22⋊C4—221no—
479C2×C22⋊C4—221no—
480C2×C22⋊C4—221no—
481C2×C42—111no—
482C2×C42—111no—
483C2×C42—221no—
484C2×C42—221no—
485C2×C42—221no—
486#107—222no—
487#107—441no—
488#103—114no—
489#103—114no—
490#103—114no—
491#103—222no—
492#103—222no—
493#103—222no—
494#102—22no—
495#102—41no—
496C22⋊C8—114no—
497#97—222no—
498#97—441no—
499#95—21no—
500#95—111no—
501#95—111no—
502#95—221no—
503#95—221no—
504#95—221no—
505#95—221no—
506#95—221no—
507#95—221no—
508C2×C11—24no—
509C2×C11—82no—
510C2×C11#235811yescharacteristic
511C2×C11C2×#44011yescharacteristic
512C2×C11#294711yescharacteristic
513C2×C11#326511yescharacteristic
514C2×C11#327011yescharacteristic
515C2×C11#330811yescharacteristic
516C2×C11#332011yescharacteristic
517C24—21no—
518C24D4×D1111yescharacteristic
519C2×Q8—112no—
520C2×Q8—112no—
521C2×Q8—112no—
522C2×Q8—112no—
523C2×Q8—228no—
524C2×Q8—224no—
525C2×Q8—221no—
526C2×Q8—221no—
527C2×Q8—221no—
528C2×Q8—221no—
529C2×Q8—221no—
530C2×Q8—221no—
531C2×Q8—221no—
532C2×Q8—221no—
533C2×Q8—442no—
534C2×Q8—442no—
535C2×Q8—444no—
536C2×Q8—444no—
537C2×Q8—444no—
538C2×D4—24no—
539C2×D4—21no—
540C2×D4—21no—
541C2×D4—21no—
542C2×D4—21no—
543C2×D4—21no—
544C2×D4—42no—
545C2×D4—42no—
546C2×D4C2×C4×D1112yes—
547C22×C4—21no—
548C22×C4—21no—
549C22×C4—21no—
550C22×C4—21no—
551C22×C4—21no—
552C22×C4—21no—
553C22×C4—21no—
554C22×C4—111no—
555C22×C4—111no—
556C22×C4—111no—
557C22×C4—111no—
558C22×C4—221no—
559C22×C4—224no—
560C22×C4—221no—
561C22×C4—221no—
562C22×C4—221no—
563C22×C4—442no—
564C22×C4—442no—
565C22×C4—442no—
566C22×C4—442no—
567C22×C4—442no—
568C22×C4—442no—
569C22×C4—881no—
570C22×C4—881no—
571C22×C4C2×C4×D1112yes—
572C22×C4D4×D1111yescharacteristic
573C22×C4#434112yes—
574C22×C4C23×D1111yescharacteristic
575SD16—228no—
576SD16—444no—
577C2×C8—21no—
578C2×C8—21no—
579C2×C8—21no—
580C2×C8—21no—
581C2×C8—21no—
582C2×C8—44no—
583C2×C8—112no—
584C2×C8—112no—
585C2×C8—221no—
586C2×C8—221no—
587C2×C8—221no—
588C2×C8—221no—
589C2×C8D4×D1112yes—
590C4⋊C4—21no—
591C4⋊C4—21no—
592C4⋊C4—21no—
593C4⋊C4—21no—
594C4⋊C4—21no—
595C4⋊C4—112no—
596C4⋊C4—221no—
597C4⋊C4—221no—
598C4⋊C4—221no—
599C4⋊C4—442no—
600C4⋊C4—442no—
601C4⋊C4—442no—
602C4⋊C4—442no—
603C4⋊C4C2×C4×D1112yes—
604C22⋊C4—24no—
605C22⋊C4—42no—
606C22⋊C4—222no—
607C22⋊C4—222no—
608C22⋊C4—442no—
609C22⋊C4—442no—
610C22⋊C4—881no—
611C42—221no—
612C42—221no—
613C42—221no—
614C42—221no—
615C42—442no—
616C42—442no—
617C42—442no—
618C11#2285511yescharacteristic, complemented, Sylow
619C23—21no—
620C23—21no—
621C23—21no—
622C23—21no—
623C23—22no—
624C23—41no—
625C23—41no—
626C23—41no—
627C23—41no—
628C23—41no—
629C23—41no—
630C23(C22⋊D11)⋊C412yes—
631C23#6696412yes—
632C23#6696812yes—
633C23C2×D4×D1111yescharacteristic
634Q8—114no—
635Q8—222no—
636Q8—222no—
637Q8—222no—
638Q8—222no—
639Q8—222no—
640Q8—448no—
641Q8—441no—
642Q8—441no—
643D4—22no—
644D4—22no—
645D4—48no—
646D4—41no—
647D4—41no—
648C2×C4—21no—
649C2×C4—21no—
650C2×C4—22no—
651C2×C4—22no—
652C2×C4—22no—
653C2×C4—22no—
654C2×C4—22no—
655C2×C4—41no—
656C2×C4—41no—
657C2×C4—41no—
658C2×C4—41no—
659C2×C4—41no—
660C2×C4—41no—
661C2×C4—41no—
662C2×C4—41no—
663C2×C4—222no—
664C2×C4—222no—
665C2×C4—222no—
666C2×C4—222no—
667C2×C4—221no—
668C2×C4—221no—
669C2×C4—221no—
670C2×C4—221no—
671C2×C4—221no—
672C2×C4—221no—
673C2×C4—221no—
674C2×C4—221no—
675C2×C4—221no—
676C2×C4—221no—
677C2×C4—222no—
678C2×C4—221no—
679C2×C4—221no—
680C2×C4—448no—
681C2×C4—441no—
682C2×C4—441no—
683C2×C4—441no—
684C2×C4—441no—
685C2×C4—441no—
686C2×C4—441no—
687C2×C4—441no—
688C2×C4—884no—
689C2×C4—884no—
690C2×C4(C22⋊D11)⋊C412yes—
691C2×C4C22×C4×D1111yescharacteristic
692C2×C4C2×D4×D1111yescharacteristic
693C2×C4C2×#434111yescharacteristic
694C2×C4#6703711yescharacteristic
695C2×C4#41×D1111yescharacteristic
696C2×C4#6704211yescharacteristic
697C8—22no—
698C8—41no—
699C8—222no—
700C8—222no—
701C22—22no—
702C22—22no—
703C22—22no—
704C22—22no—
705C22—22no—
706C22—22no—
707C22—42no—
708C22—42no—
709C22—42no—
710C22—81no—
711C22—81no—
712C22—81no—
713C22—81no—
714C22#1062237014yescomplemented
715C22C2×(C22⋊D11)⋊C411yescharacteristic
716C22#1062314011yescharacteristic
717C22#1062314111yescharacteristic
718C22C2×#6696411yescharacteristic
719C22C2×#6696811yescharacteristic
720C22#1062330111yescharacteristic
721C22#1062330211yescharacteristic
722C4—22no—
723C4—42no—
724C4—81no—
725C4—81no—
726C4—224no—
727C4—441no—
728C4—441no—
729C4—442no—
730C4—441no—
731C4—441no—
732C4—442no—
733C4—881no—
734C4C4×D4×D1111yescharacteristic
735C4#1062307611yescharacteristic
736C4#1062312211yescharacteristic
737C4#1062318911yescharacteristic
738C2—24no—
739C2—82no—
740C2#1307159611yescharacteristic
741C2C2×#1062237011yescharacteristic
742C2#1307746211yescharacteristic
743C2#1308010811yescharacteristic
744C2#1308018311yescharacteristic
745C2#1308061311yescharacteristic
746C2#1308079311yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#1893C2
socleC23×C11C22×D4
prime radicalC2×C11×#121C22
cosocleC22×C4×C11C24
hypercenter#1893D11
hypocenterC11#22855
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1893

Complements

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

NH ≅ G/Ntype
2. C2×#10622370C2semidirect
3. C22×#66880C2semidirect
5. #13071448C2semidirect
6. #13069498C2semidirect
7. #13069307C2semidirect
8. #13069255C2semidirect
9. #13068968C2semidirect
10. #13068948C2semidirect
11. #13068871C2semidirect
12. #13068803C2semidirect
13. #13068445C2semidirect
14. #13068392C2semidirect
40. #10622653C4semidirect
74. C22×Dic22C2×C4semidirect
101. C2×#4324C2×C4semidirect
102. C2×#4324C2×C4semidirect
133. C22⋊(C11⋊C8)C2×C4semidirect
137. #66880D4semidirect
140. #66874C2×C4semidirect
141. #66874C2×C4semidirect
338. Dic22C4×D4semidirect
402. C22×C11#440semidirect
618. C11#22855semidirect
714. C22#10622370semidirect

Maximal subgroups

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

subgroupindex
C2×#106226532
C2×#106223702
C22×#668802
#130716362
#130714482
#130694982
#130693072
#130692552
#130689682
#130689482
#130688712
#130688032
#130684452
#130683922
C11×#18932
#2285511