Finite Group Databasebeta

← #14774050

Subgroups — #14774050

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×#10622351C211yesmaximal, characteristic
2C2×#10622323C211yesmaximal, characteristic, complemented
3C22×#66880C211yesmaximal, characteristic, complemented
4#13071630C211yesmaximal, characteristic
5C22⋊C4×Dic22C211yesmaximal, characteristic, complemented
6#13069497C211yesmaximal, characteristic, complemented
7#13069306C211yesmaximal, characteristic, complemented
8#13069258C211yesmaximal, characteristic, complemented
9#13069044C211yesmaximal, characteristic
10#13068970C211yesmaximal, characteristic, complemented
11#13068949C211yesmaximal, characteristic, complemented
12#13068873C211yesmaximal, characteristic, complemented
13#13068806C211yesmaximal, characteristic, complemented
14#13068447C211yesmaximal, characteristic, complemented
15C11×#1752C211yesmaximal, characteristic, complemented
16C23×Dic22C2211yescharacteristic
17C23×C8×C11C2211yescharacteristic
18C2×#66983C2211yescharacteristic
19C22×C4⋊Dic11C2211yescharacteristic
20C22×#4314C2211yescharacteristic
21C22×#4314C2211yescharacteristic
22C2×(C22⋊D11)⋊C4—21no—
23C2×C4×D44C2211yescharacteristic
24C2×C4×Dic22C2211yescharacteristic
25C2×C4×Dic22C2211yescharacteristic
26C2×C11×C22⋊C8C2211yescharacteristic
27C2×C11×#97C2211yescharacteristic
28C2×C11×#97C2211yescharacteristic
29C4×C11×C22⋊C4C2211yescharacteristic
30#10622825C2211yescharacteristic
31C2×#66885C2211yescharacteristic
32C2×#66885C2211yescharacteristic
33C2×#66882C2211yescharacteristic
34C2×#66882C2211yescharacteristic
35C2×#66880—24no—
36C2×#66880C2211yescharacteristic
37C2×#66880C2211yescharacteristic
38C2×#66880C2211yescharacteristic
39C2×#66880C2211yescharacteristic
40C2×#66880C2211yescharacteristic
41C2×#66880C2211yescharacteristic
42#10622571—21no—
43#10622555—21no—
44C22⋊C4×Dic11—21no—
45#10622552C2211yescharacteristic
46C4×C4⋊Dic11C2211yescharacteristic
47#10622542C2211yescharacteristic
48#10622542C2211yescharacteristic
49#10622541C2211yescharacteristic
50#10622351C418yescomplemented
51#10622323—24no—
52#10622283—21no—
53#10622281—21no—
54#10622259—21no—
55#10622259—21no—
56C11×#336C2211yescharacteristic
57C11×#336C2211yescharacteristic
58#10622189C2211yescharacteristic
59#10622189C2211yescharacteristic
60#10622189C2211yescharacteristic
61#10622189C2211yescharacteristic
62C23×C4×C11C2311yescharacteristic
63C22×C22⋊D11—21no—
64C23×Dic11—21no—
65C23×Dic11—21no—
66C22×D44C2311yescharacteristic
67C22×C4×D11—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
82C22×C8×C11C2311yescharacteristic
83C22×C8×C11C2311yescharacteristic
84C2×C11×C22⋊C4D411yescharacteristic
85C2×C11×C22⋊C4D411yescharacteristic
86C2×C42×C11C2311yescharacteristic
87C2×C42×C11C2311yescharacteristic
88C2×C22⋊Dic11—21no—
89#66983—22no—
90#66983C2×C414yes—
91C2×(C2×D11)⋊C4—21no—
92C2×(C2×D11)⋊C4—21no—
93C2×(C2×D11)⋊C4—21no—
94C2×(C2×D11)⋊C4—21no—
95C2×C4⋊Dic11—22no—
96C2×C4⋊Dic11—21no—
97C2×C4⋊Dic11—41no—
98C2×C4⋊Dic11C2311yescharacteristic
99C2×C4⋊Dic11C2311yescharacteristic
100C2×C4⋊Dic11C2311yescharacteristic
101C2×C4⋊Dic11C2311yescharacteristic
102C2×C4⋊Dic11C2311yescharacteristic
103C2×Dic11⋊C4—21no—
104C2×Dic11⋊C4—21no—
105C2×Dic11⋊C4—21no—
106C2×C4×Dic11—21no—
107C2×C4×Dic11—21no—
108C2×C4×Dic11—21no—
109C2×#4314—22no—
110C2×#4314—22no—
111C2×#4314—41no—
112C2×#4314—41no—
113C2×#4314C2×C414yescomplemented
114C2×#4314C2×C414yescomplemented
115(C22⋊D11)⋊C4—44no—
116C4×D44—22no—
117C4×D44—41no—
118C4×Dic22—22no—
119C4×Dic22—22no—
120C4×Dic22—41no—
121C4×Dic22—41no—
122C11×C22⋊C8C2×C414yescomplemented
123C11×#97—22no—
124C11×#97—41no—
125C11×#95D411yescharacteristic
126C11×#95D411yescharacteristic
127C11⋊#95—21no—
128C11⋊#95—21no—
129C11⋊#95—21no—
130C11⋊#95—21no—
131C11⋊#95—21no—
132C11⋊#95—21no—
133C11⋊#95—21no—
134#66885—22no—
135#66885—41no—
136#66882—22no—
137#66882—41no—
138#66880—22no—
139#66880—22no—
140#66880—22no—
141#66880C2×C414yescomplemented
142#66880C2×C414yescomplemented
143#66880D414yescomplemented
144#22855—111nomaximal, Sylow
145C24×C11C2×D411yescharacteristic
146C23×D11—21no—
147C22×C4×C11—21no—
148C22×C4×C11—21no—
149C22×C4×C11—21no—
150C22×C4×C11—21no—
151C22×C4×C11C22×C412yes—
152C22×C4×C11C2×D411yescharacteristic
153C22×C4×C11C2×D411yescharacteristic
154C22×C4×C11C2×D411yescharacteristic
155C22×C4×C11C2×D411yescharacteristic
156C22×C4×C11C2×D411yescharacteristic
157C22×C4×C11#4112yes—
158C22×C4×C11C2411yescharacteristic
159C2×C22⋊D11—24no—
160C2×C22⋊D11—42no—
161C2×C22⋊D11—42no—
162C22×Dic11—24no—
163C22×Dic11—21no—
164C22×Dic11—21no—
165C22×Dic11—21no—
166C22×Dic11—21no—
167C22×Dic11—21no—
168C22×Dic11—21no—
169C22×Dic11—21no—
170C22×Dic11—42no—
171C22×Dic11—42no—
172C22×Dic11—42no—
173C22×Dic11—42no—
174C22×Dic11—81no—
175C2×D44—21no—
176C2×D44—21no—
177C2×D44—21no—
178C2×D44—21no—
179C2×D44—21no—
180C2×D44C22×C412yes—
181C2×C4×D11—42no—
182C2×C4×D11—42no—
183C2×C4×D11—81no—
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—21no—
209C2×C8×C11—21no—
210C2×C8×C11—21no—
211C2×C8×C11—21no—
212C2×C8×C11—44no—
213C2×C8×C11C22×C412yes—
214C2×C8×C11C22×C412yes—
215C2×C8×C11C2×D412yes—
216C11×C22⋊C4—22no—
217C11×C22⋊C4—22no—
218C42×C11—21no—
219C42×C11—21no—
220C42×C11—21no—
221C42×C11—21no—
222C22⋊Dic11—42no—
223(C2×D11)⋊C4—24no—
224(C2×D11)⋊C4—42no—
225(C2×D11)⋊C4—42no—
226(C2×D11)⋊C4—81no—
227C4⋊Dic11—21no—
228C4⋊Dic11—21no—
229C4⋊Dic11—21no—
230C4⋊Dic11—21no—
231C4⋊Dic11—21no—
232C4⋊Dic11—21no—
233C4⋊Dic11—21no—
234C4⋊Dic11—21no—
235C4⋊Dic11—42no—
236C4⋊Dic11C22×C412yes—
237C4⋊Dic11C2×D412yes—
238Dic11⋊C4—42no—
239Dic11⋊C4—42no—
240Dic11⋊C4—42no—
241C4×Dic11—42no—
242C4×Dic11—42no—
243C4×Dic11—42no—
244#4314—28no—
245#4314—44no—
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#1893—111no—
255#1880—111no—
256#1877—111no—
257#1863—111no—
258#1852—111no—
259#1763—111no—
260#1752D1111yescharacteristic, complemented
261C23×C11—21no—
262C23×C11—21no—
263C23×C11—21no—
264C23×C11—21no—
265C23×C11C4×D412yes—
266C23×C11AGL(1,ℤ/8)12yes—
267C23×C11#13712yes—
268C23×C11C22×D411yescharacteristic
269C22×D11—22no—
270C22×D11—41no—
271C22×D11—41no—
272C22×D11—41no—
273C22×D11—41no—
274C22×D11—41no—
275C22×D11—41no—
276C2×C4×C11—21no—
277C2×C4×C11—21no—
278C2×C4×C11—22no—
279C2×C4×C11—22no—
280C2×C4×C11—22no—
281C2×C4×C11—22no—
282C2×C4×C11—21no—
283C2×C4×C11—21no—
284C2×C4×C11—21no—
285C2×C4×C11—21no—
286C2×C4×C11—21no—
287C2×C4×C11—21no—
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×C11C4×D412yes—
295C2×C4×C11C23×C411yescharacteristic
296C2×C4×C11C22×D411yescharacteristic
297C2×C4×C11C2×#4111yescharacteristic
298C2×C4×C11C2×#4111yescharacteristic
299C2×C4×C11H(5,𝔽2)11yescharacteristic
300C2×C4×C11H(5,𝔽2)11yescharacteristic
301C22⋊D11—48no—
302C2×Dic11—22no—
303C2×Dic11—22no—
304C2×Dic11—22no—
305C2×Dic11—22no—
306C2×Dic11—22no—
307C2×Dic11—22no—
308C2×Dic11—48no—
309C2×Dic11—41no—
310C2×Dic11—41no—
311C2×Dic11—41no—
312C2×Dic11—41no—
313C2×Dic11—41no—
314C2×Dic11—41no—
315C2×Dic11—41no—
316C2×Dic11—41no—
317C2×Dic11—41no—
318C2×Dic11—41no—
319C2×Dic11—41no—
320C2×Dic11—41no—
321C2×Dic11—41no—
322C2×Dic11—41no—
323C2×Dic11—41no—
324C2×Dic11—84no—
325D44—22no—
326D44—22no—
327D44—41no—
328D44—41no—
329C4×D11—84no—
330Dic22—22no—
331Dic22—22no—
332Dic22—22no—
333Dic22—22no—
334Dic22—22no—
335Dic22—48no—
336Dic22—41no—
337Dic22—41no—
338Dic22C4×D414yescomplemented
339C8×C11—22no—
340C8×C11—22no—
341C8×C11—22no—
342C8×C11—41no—
343C23×Q8—111no—
344C22×SD16—111no—
345C22×SD16—111no—
346C23×C8C2×D1111yescharacteristic
347C2×#121—111no—
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×#102—111no—
365C2×#102—111no—
366C2×C22⋊C8C2×D1111yescharacteristic
367C2×#97C2×D1111yescharacteristic
368C2×#97C2×D1111yescharacteristic
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—111no—
379#380—221no—
380C4×C4⋊C4—111no—
381C4×C22⋊C4—221no—
382C4×C22⋊C4C2×D1111yescharacteristic
383#340—111no—
384#340—111no—
385#340—111no—
386#340—111no—
387#336C2×D1111yescharacteristic
388#336C2×D1111yescharacteristic
389C22×C11—22no—
390C22×C11—22no—
391C22×C11—22no—
392C22×C11—22no—
393C22×C11—22no—
394C22×C11—22no—
395C22×C11#44014yescomplemented
396C22×C11C2×C4×D411yescharacteristic
397C22×C11D4211yescharacteristic
398C22×C11#54611yescharacteristic
399C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
400C22×C11C2×#13711yescharacteristic
401C22×C11#57711yescharacteristic
402C22×C11#57811yescharacteristic
403C2×D11—42no—
404C2×D11—42no—
405C2×D11—42no—
406C2×D11—81no—
407C2×D11—81no—
408C2×D11—81no—
409C2×D11—81no—
410C4×C11—22no—
411C4×C11—41no—
412C4×C11—41no—
413C4×C11—41no—
414C4×C11—41no—
415C4×C11C2×C4×D411yescharacteristic
416C4×C11#51811yescharacteristic
417C4×C11#54611yescharacteristic
418C4×C11#55111yescharacteristic
419Dic11—24no—
420Dic11—42no—
421Dic11—42no—
422Dic11—42no—
423Dic11—81no—
424Dic11—81no—
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—111no—
436C22×D4—221no—
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×C8C22×D1111yescharacteristic
451C22×C8C22×D1111yescharacteristic
452C22×C8C22×D1111yescharacteristic
453C22×C8C22×D1111yescharacteristic
454#121—114no—
455#121—222no—
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—111no—
466C2×C4⋊C4—111no—
467C2×C4⋊C4—111no—
468C2×C4⋊C4—222no—
469C2×C4⋊C4—221no—
470C2×C4⋊C4—221no—
471C2×C4⋊C4—221no—
472C2×C4⋊C4—221no—
473C2×C4⋊C4—441no—
474C2×C22⋊C4—221no—
475C2×C22⋊C4—221no—
476C2×C22⋊C4—221no—
477C2×C22⋊C4—221no—
478C2×C22⋊C4—221no—
479C2×C22⋊C4D4411yescharacteristic
480C2×C22⋊C4D4411yescharacteristic
481C2×C42—221no—
482C2×C42—221no—
483C2×C42—221no—
484C2×C42C22×D1111yescharacteristic
485C2×C42C22×D1111yescharacteristic
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—222no—
495#102—441no—
496C22⋊C8C4×D1114yescomplemented
497#97—22no—
498#97—41no—
499#95—221no—
500#95—221no—
501#95—221no—
502#95—221no—
503#95—221no—
504#95—221no—
505#95—221no—
506#95D4411yescharacteristic
507#95D4411yescharacteristic
508C2×C11—24no—
509C2×C11#235811yescharacteristic
510C2×C11C2×#44011yescharacteristic
511C2×C11#294711yescharacteristic
512C2×C11#326511yescharacteristic
513C2×C11#327011yescharacteristic
514C2×C11#330811yescharacteristic
515C2×C11#332011yescharacteristic
516D11—82no—
517C24—221no—
518C24C2×D4411yescharacteristic
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—112no—
539C2×D4—224no—
540C2×D4—221no—
541C2×D4—221no—
542C2×D4—221no—
543C2×D4—221no—
544C2×D4—221no—
545C2×D4—442no—
546C2×D4—442no—
547C22×C4—21no—
548C22×C4—21no—
549C22×C4—21no—
550C22×C4—21no—
551C22×C4—221no—
552C22×C4—224no—
553C22×C4—221no—
554C22×C4—221no—
555C22×C4—221no—
556C22×C4—221no—
557C22×C4—221no—
558C22×C4—221no—
559C22×C4—442no—
560C22×C4—442no—
561C22×C4—442no—
562C22×C4—442no—
563C22×C4—442no—
564C22×C4—442no—
565C22×C4—881no—
566C22×C4—881no—
567C22×C4C2×C4×D1112yes—
568C22×C4C2×D4411yescharacteristic
569C22×C4C2×D4411yescharacteristic
570C22×C4C2×D4411yescharacteristic
571C22×C4C2×D4411yescharacteristic
572C22×C4C2×D4411yescharacteristic
573C22×C4#433912yes—
574C22×C4C23×D1111yescharacteristic
575SD16—228no—
576SD16—444no—
577C2×C8—21no—
578C2×C8—21no—
579C2×C8—21no—
580C2×C8—21no—
581C2×C8—21no—
582C2×C8—21no—
583C2×C8—21no—
584C2×C8—21no—
585C2×C8—21no—
586C2×C8—44no—
587C2×C8C2×C4×D1112yes—
588C2×C8C2×C4×D1112yes—
589C2×C8D4×D1112yes—
590C4⋊C4—112no—
591C4⋊C4—112no—
592C4⋊C4—221no—
593C4⋊C4—221no—
594C4⋊C4—221no—
595C4⋊C4—221no—
596C4⋊C4—221no—
597C4⋊C4—221no—
598C4⋊C4—221no—
599C4⋊C4—221no—
600C4⋊C4—442no—
601C4⋊C4—442no—
602C4⋊C4—442no—
603C4⋊C4—442no—
604C22⋊C4—22no—
605C22⋊C4—22no—
606C22⋊C4—224no—
607C22⋊C4—442no—
608C22⋊C4—442no—
609C22⋊C4—442no—
610C22⋊C4—881no—
611C42—21no—
612C42—21no—
613C42—21no—
614C42—21no—
615C42—442no—
616C42—442no—
617C42—442no—
618C11#2285511yescharacteristic, complemented, Sylow
619C23—21no—
620C23—21no—
621C23—21no—
622C23—21no—
623C23—222no—
624C23—441no—
625C23—441no—
626C23—441no—
627C23—441no—
628C23—441no—
629C23—441no—
630C23C4×D4412yes—
631C23#6696112yes—
632C23#6696212yes—
633C23C22×D4411yescharacteristic
634Q8—114no—
635Q8—222no—
636Q8—222no—
637Q8—222no—
638Q8—222no—
639Q8—222no—
640Q8—448no—
641Q8—441no—
642Q8—441no—
643D4—222no—
644D4—222no—
645D4—448no—
646D4—441no—
647D4—441no—
648C2×C4—21no—
649C2×C4—21no—
650C2×C4—22no—
651C2×C4—22no—
652C2×C4—22no—
653C2×C4—22no—
654C2×C4—21no—
655C2×C4—21no—
656C2×C4—21no—
657C2×C4—21no—
658C2×C4—21no—
659C2×C4—21no—
660C2×C4—21no—
661C2×C4—21no—
662C2×C4—21no—
663C2×C4—21no—
664C2×C4—21no—
665C2×C4—21no—
666C2×C4—222no—
667C2×C4—222no—
668C2×C4—222no—
669C2×C4—222no—
670C2×C4—222no—
671C2×C4—222no—
672C2×C4—448no—
673C2×C4—441no—
674C2×C4—441no—
675C2×C4—441no—
676C2×C4—441no—
677C2×C4—441no—
678C2×C4—441no—
679C2×C4—441no—
680C2×C4—441no—
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×C4C4×D4412yes—
691C2×C4C22×C4×D1111yescharacteristic
692C2×C4C2×#433911yescharacteristic
693C2×C4C2×D4×D1111yescharacteristic
694C2×C4#6703711yescharacteristic
695C2×C4#41×D1111yescharacteristic
696C2×C4#6704211yescharacteristic
697C8—22no—
698C8—22no—
699C8—22no—
700C8—41no—
701C22—22no—
702C22—22no—
703C22—22no—
704C22—22no—
705C22—22no—
706C22—22no—
707C22—442no—
708C22—442no—
709C22—442no—
710C22—881no—
711C22—881no—
712C22—881no—
713C22—881no—
714C22#1062232314yescomplemented
715C22C2×C4×D4411yescharacteristic
716C22D4×D4411yescharacteristic
717C22#1062308511yescharacteristic
718C22C2×#6696111yescharacteristic
719C22C2×#6696211yescharacteristic
720C22#1062328211yescharacteristic
721C22#1062328411yescharacteristic
722C4—22no—
723C4—41no—
724C4—41no—
725C4—41no—
726C4—41no—
727C4—224no—
728C4—442no—
729C4—442no—
730C4—442no—
731C4—881no—
732C4—881no—
733C4—881no—
734C4#1062302111yescharacteristic
735C4#1062305811yescharacteristic
736C4C4×D4×D1111yescharacteristic
737C4#1062307611yescharacteristic
738C2—24no—
739C2—882no—
740C2#1307159811yescharacteristic
741C2C2×#1062232311yescharacteristic
742C2#1307746111yescharacteristic
743C2#1308011611yescharacteristic
744C2#1308019111yescharacteristic
745C2#1308060911yescharacteristic
746C2#1308078911yescharacteristic
subgroupG/H
centerC23C22×D44
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#1752C2
socleC23×C11C22×D4
prime radicalC2×#66983C22
cosocleC22×C4×C11C24
hypercenter#1752D11
hypocenterC11#22855
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C4×C22⋊C4 ◁ #1752

Complements

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

NH ≅ G/Ntype
2. C2×#10622323C2semidirect
3. C22×#66880C2semidirect
5. C22⋊C4×Dic22C2semidirect
6. #13069497C2semidirect
7. #13069306C2semidirect
8. #13069258C2semidirect
10. #13068970C2semidirect
11. #13068949C2semidirect
12. #13068873C2semidirect
13. #13068806C2semidirect
14. #13068447C2semidirect
15. C11×#1752C2semidirect
50. #10622351C4semidirect
74. C22×Dic22C2×C4semidirect
113. C2×#4314C2×C4semidirect
114. C2×#4314C2×C4semidirect
122. C11×C22⋊C8C2×C4semidirect
141. #66880C2×C4semidirect
142. #66880C2×C4semidirect
143. #66880D4semidirect
260. #1752D11semidirect
338. Dic22C4×D4semidirect
395. C22×C11#440semidirect
496. C22⋊C8C4×D11semidirect
618. C11#22855semidirect
714. C22#10622323semidirect

Maximal subgroups

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

subgroupindex
C2×#106223512
C2×#106223232
C22×#668802
#130716302
C22⋊C4×Dic222
#130694972
#130693062
#130692582
#130690442
#130689702
#130689492
#130688732
#130688062
#130684472
C11×#17522
#2285511