Finite Group Databasebeta

← #14764963

Subgroups — #14764963

Order 2816.

1096 conjugacy classes of subgroups.

The subgroup lattice has 766 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622347C211yesmaximal, characteristic
2#13071122C211yesmaximal, characteristic, complemented
3#13071104C211yesmaximal, characteristic, complemented
4#13069480C211yesmaximal, characteristic, complemented
5#13069468C211yesmaximal, characteristic, complemented
6#13069297C211yesmaximal, characteristic, complemented
7#13069290C211yesmaximal, characteristic, complemented
8#13069256C211yesmaximal, characteristic, complemented
9#13069242C211yesmaximal, characteristic, complemented
10#13068965C211yesmaximal, characteristic, complemented
11#13068951C211yesmaximal, characteristic, complemented
12#13068938C211yesmaximal, characteristic, complemented
13#13068554C211yesmaximal, characteristic, complemented
14C22⋊C8×Dic11C211yesmaximal, characteristic, complemented
15C11×#1854C211yesmaximal, characteristic, complemented
16C22×#4339C2211yescharacteristic
17C2×C11×#117C2211yescharacteristic
18C2×#66983C2211yescharacteristic
19C22×C4×Dic11C2211yescharacteristic
20C22×D88C2211yescharacteristic
21C22×#4314C2211yescharacteristic
22C2×#66946C2211yescharacteristic
23C2×(C22⋊D11)⋊C4—21no—
24C2×C11×#107C2211yescharacteristic
25C2×C11×#106C2211yescharacteristic
26C2×C11×C22⋊C8C2211yescharacteristic
27C11×#380C2211yescharacteristic
28C2×C22⋊(C11⋊C8)C2211yescharacteristic
29C2×#66885C2211yescharacteristic
30C2×#66880C2211yescharacteristic
31C2×C8×Dic11C2211yescharacteristic
32C2×C8×Dic11C2211yescharacteristic
33#10622601C2211yescharacteristic
34#10622601C2211yescharacteristic
35#10622601C2211yescharacteristic
36C4⋊C4×Dic11C2211yescharacteristic
37#10622587C2211yescharacteristic
38#10622587C2211yescharacteristic
39#10622586C2211yescharacteristic
40C2×#66874C2211yescharacteristic
41C2×#66874C2211yescharacteristic
42C2×#66873C2211yescharacteristic
43C2×#66873C2211yescharacteristic
44C2×#66873C2211yescharacteristic
45C2×#66873C2211yescharacteristic
46#10622571—21no—
47#10622571—21no—
48#10622571—21no—
49C4×(C2×D11)⋊C4—21no—
50C4×(C2×D11)⋊C4—21no—
51#10622347C418yescomplemented
52#10622282—21no—
53#10622279—21no—
54C11×#340C2211yescharacteristic
55C11×#340C2211yescharacteristic
56#10622188C2211yescharacteristic
57#10622188C2211yescharacteristic
58#10622167C2211yescharacteristic
59#10622167C2211yescharacteristic
60C23×C4×C11C2311yescharacteristic
61C22×C22⋊D11—21no—
62C22×C22⋊D11—21no—
63C23×Dic11D411yescharacteristic
64C23×Dic11D411yescharacteristic
65C2×#4339—22no—
66C2×#4339—41no—
67C2×#4339—41no—
68C2×#4339—41no—
69C2×#4339—41no—
70C2×#4339C2×C414yescomplemented
71C22×D44C2311yescharacteristic
72C22×D44C2311yescharacteristic
73C22×C4×D11—21no—
74C22×C4×D11—21no—
75C22×Dic22C2311yescharacteristic
76C22×C8×C11C2311yescharacteristic
77C22×C8×C11C2311yescharacteristic
78C11×#117—41no—
79C11×#117—41no—
80C2×C11×C4⋊C4C2311yescharacteristic
81C2×C11×C4⋊C4C2311yescharacteristic
82C2×C11×C4⋊C4C2311yescharacteristic
83C2×C11×C4⋊C4C2311yescharacteristic
84C2×C11×C22⋊C4—21no—
85C2×C11×C22⋊C4—21no—
86C2×C42×C11—21no—
87#66983—22no—
88#66983C2×C414yes—
89C2×(C2×D11)⋊C4—21no—
90C2×(C2×D11)⋊C4—21no—
91C2×(C2×D11)⋊C4—21no—
92C2×(C2×D11)⋊C4—21no—
93C2×(C2×D11)⋊C4—21no—
94C2×(C2×D11)⋊C4—21no—
95C2×(C2×D11)⋊C4—21no—
96C2×(C2×D11)⋊C4—21no—
97C2×C4⋊Dic11C2311yescharacteristic
98C2×Dic11⋊C4—21no—
99C2×C4×Dic11—21no—
100C2×C4×Dic11—41no—
101C2×C4×Dic11—41no—
102C2×C4×Dic11D411yescharacteristic
103C2×C4×Dic11D411yescharacteristic
104C2×C4×Dic11C2311yescharacteristic
105C2×C4×Dic11C2311yescharacteristic
106C22×C11⋊C8C2311yescharacteristic
107C22×C11⋊C8C2311yescharacteristic
108C2×D88—41no—
109C2×D88—41no—
110C2×D88C2×C414yescomplemented
111C2×#4314—41no—
112C2×#4314—41no—
113C2×#4314C2×C414yescomplemented
114#66946—41no—
115#66946—41no—
116(C22⋊D11)⋊C4—44no—
117C11×#107—41no—
118C11×#106—41no—
119C11×C22⋊C8C2×C414yescomplemented
120C11×#95—21no—
121C11⋊#95—21no—
122C11⋊#95—21no—
123C11⋊#95—21no—
124C11⋊#95—21no—
125C11⋊#95—21no—
126C11⋊#95—21no—
127C22⋊(C11⋊C8)—22no—
128#66885C2×C414yescomplemented
129#66880C2×C414yescomplemented
130C8×Dic11—41no—
131C8×Dic11—41no—
132#66874—41no—
133#66874—41no—
134#66873—41no—
135#66873—41no—
136#66873—41no—
137#66873—41no—
138#22045—111nomaximal, Sylow
139C24×C11C2×D411yescharacteristic
140C23×D11—21no—
141C23×D11—21no—
142C22×C4×C11—21no—
143C22×C4×C11—21no—
144C22×C4×C11—21no—
145C22×C4×C11—21no—
146C22×C4×C11—21no—
147C22×C4×C11—21no—
148C22×C4×C11—21no—
149C22×C4×C11—21no—
150C22×C4×C11C22×C412yes—
151C22×C4×C11C2×D411yescharacteristic
152C22×C4×C11#4112yes—
153C22×C4×C11C2411yescharacteristic
154C2×C22⋊D11—24no—
155C2×C22⋊D11—24no—
156C2×C22⋊D11—42no—
157C2×C22⋊D11—42no—
158C2×C22⋊D11—42no—
159C2×C22⋊D11—42no—
160C22×Dic11—22no—
161C22×Dic11—22no—
162C22×Dic11—22no—
163C22×Dic11—21no—
164C22×Dic11—21no—
165C22×Dic11—41no—
166C22×Dic11—41no—
167C22×Dic11—41no—
168C22×Dic11C2×D411yescharacteristic
169C22×Dic11C2×D411yescharacteristic
170C22×Dic11C2×D411yescharacteristic
171C22×Dic11C2×D411yescharacteristic
172#4339—44no—
173#4339—44no—
174#4339—44no—
175#4339—44no—
176C2×D44—21no—
177C2×D44—21no—
178C2×D44—21no—
179C2×D44—21no—
180C2×D44—21no—
181C2×D44—21no—
182C2×D44—21no—
183C2×D44—21no—
184C2×D44—21no—
185C2×D44—21no—
186C2×D44C22×C412yes—
187C2×D44C22×C412yes—
188C2×C4×D11—24no—
189C2×C4×D11—42no—
190C2×C4×D11—42no—
191C2×C4×D11—42no—
192C2×C4×D11—42no—
193C2×C4×D11—42no—
194C2×Dic22—21no—
195C2×Dic22—21no—
196C2×Dic22—21no—
197C2×Dic22—21no—
198C2×Dic22—21no—
199C2×Dic22C22×C412yes—
200C2×C8×C11—21no—
201C2×C8×C11—21no—
202C2×C8×C11—21no—
203C2×C8×C11—21no—
204C2×C8×C11C22×C412yes—
205C2×C8×C11C22×C412yes—
206C11×C4⋊C4—21no—
207C11×C4⋊C4—21no—
208C11×C4⋊C4—21no—
209C11×C4⋊C4—21no—
210C11×C4⋊C4—21no—
211C11×C4⋊C4—21no—
212C11×C4⋊C4—21no—
213C11×C4⋊C4—21no—
214C11×C22⋊C4—42no—
215C11×C22⋊C4—42no—
216C42×C11—42no—
217(C2×D11)⋊C4—24no—
218(C2×D11)⋊C4—42no—
219(C2×D11)⋊C4—42no—
220(C2×D11)⋊C4—42no—
221(C2×D11)⋊C4—42no—
222(C2×D11)⋊C4—42no—
223(C2×D11)⋊C4—42no—
224(C2×D11)⋊C4—42no—
225C4⋊Dic11—21no—
226C4⋊Dic11C22×C412yes—
227Dic11⋊C4—42no—
228C4×Dic11—21no—
229C4×Dic11—21no—
230C4×Dic11—21no—
231C4×Dic11—21no—
232C4×Dic11—41no—
233C4×Dic11—41no—
234C4×Dic11—42no—
235C2×C11⋊C8—21no—
236C2×C11⋊C8—21no—
237C2×C11⋊C8—21no—
238C2×C11⋊C8—21no—
239C2×C11⋊C8—21no—
240C2×C11⋊C8—21no—
241D88—44no—
242#4314—44no—
243C2×#449—111no—
244C4×#121—111no—
245#2297—111no—
246#1970—111no—
247#1968—111no—
248#1934—111no—
249#1933—111no—
250#1928—111no—
251#1926—111no—
252#1879—111no—
253#1877—111no—
254#1875—111no—
255#1854D1111yescharacteristic, complemented
256#1788—111no—
257C4×C22⋊C8—111no—
258C23×C11—21no—
259C23×C11—21no—
260C23×C11—21no—
261C23×C11—21no—
262C23×C11—21no—
263C23×C11—21no—
264C23×C11C4×D412yes—
265C23×C11C22×D411yescharacteristic
266C22×D11—22no—
267C22×D11—22no—
268C22×D11—41no—
269C22×D11—41no—
270C22×D11—41no—
271C22×D11—41no—
272C22×D11—41no—
273C22×D11—41no—
274C22×D11—41no—
275C22×D11—41no—
276C22×D11—41no—
277C22×D11—41no—
278C22×D11—41no—
279C22×D11—41no—
280C2×C4×C11—21no—
281C2×C4×C11—21no—
282C2×C4×C11—22no—
283C2×C4×C11—22no—
284C2×C4×C11—22no—
285C2×C4×C11—22no—
286C2×C4×C11—41no—
287C2×C4×C11—41no—
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×C11—41no—
297C2×C4×C11—41no—
298C2×C4×C11C4×D412yes—
299C2×C4×C11C23×C411yescharacteristic
300C2×C4×C11C2×#4111yescharacteristic
301C2×C4×C11H(5,𝔽2)11yescharacteristic
302C2×C4×C11H(5,𝔽2)11yescharacteristic
303C2×C4×C11H(5,𝔽2)11yescharacteristic
304C2×C4×C11H(5,𝔽2)11yescharacteristic
305C22⋊D11—48no—
306C22⋊D11—48no—
307C2×Dic11—21no—
308C2×Dic11—21no—
309C2×Dic11—21no—
310C2×Dic11—21no—
311C2×Dic11—21no—
312C2×Dic11—21no—
313C2×Dic11—22no—
314C2×Dic11—22no—
315C2×Dic11—21no—
316C2×Dic11—21no—
317C2×Dic11—21no—
318C2×Dic11—44no—
319C2×Dic11—44no—
320C2×Dic11—41no—
321C2×Dic11—41no—
322C2×Dic11—41no—
323C2×Dic11—41no—
324C2×Dic11#13512yes—
325C2×Dic11#13512yes—
326C2×Dic11AGL(1,ℤ/8)12yes—
327D44—22no—
328D44—22no—
329D44—22no—
330D44—22no—
331D44—41no—
332D44—41no—
333D44—41no—
334D44—41no—
335C4×D11—48no—
336C4×D11—84no—
337Dic22—22no—
338Dic22—22no—
339Dic22—41no—
340Dic22—41no—
341C8×C11—22no—
342C8×C11—22no—
343C11⋊C8—41no—
344C11⋊C8—41no—
345C22×#41—111no—
346C22×SD16—111no—
347C22×D8—111no—
348C2×#121—111no—
349C2×C4×D4—111no—
350C2×C4×D4—221no—
351C2×#117C2×D1111yescharacteristic
352C22×C42—111no—
353#449—118no—
354C2×#107C2×D1111yescharacteristic
355C2×#106C2×D1111yescharacteristic
356C2×#103—111no—
357C2×#103—111no—
358C2×#103—111no—
359C2×#102—111no—
360C2×#102—111no—
361C2×#102—111no—
362C2×#102—111no—
363C2×#102—111no—
364C2×C22⋊C8—111no—
365C2×C22⋊C8C2×D1111yescharacteristic
366C2×C4×C8—111no—
367C2×C4×C8—111no—
368#391—111no—
369#391—111no—
370#390—111no—
371#390—111no—
372#390—111no—
373#389—111no—
374#388—221no—
375#386—221no—
376#386—221no—
377#386—221no—
378#380C2×D1111yescharacteristic
379C4×C4⋊C4—111no—
380C4×C22⋊C4—221no—
381C4×C22⋊C4—221no—
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—41no—
393C22×C11—41no—
394C22×C11—41no—
395C22×C11—41no—
396C22×C11C2×C4×D411yescharacteristic
397C22×C11#53411yescharacteristic
398C22×C11#53511yescharacteristic
399C22×C11C2×#13511yescharacteristic
400C22×C11C2×#13511yescharacteristic
401C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
402C22×C11#57511yescharacteristic
403C2×D11—42no—
404C2×D11—42no—
405C2×D11—42no—
406C2×D11—42no—
407C2×D11—42no—
408C2×D11—42no—
409C2×D11—81no—
410C2×D11—81no—
411C2×D11—81no—
412C2×D11—81no—
413C2×D11—81no—
414C2×D11—81no—
415C2×D11—81no—
416C2×D11—81no—
417C4×C11—22no—
418C4×C11—81no—
419C4×C11—81no—
420C4×C11—81no—
421C4×C11—81no—
422C4×C11#51811yescharacteristic
423C4×C11#51811yescharacteristic
424C4×C11#53811yescharacteristic
425C4×C11#53811yescharacteristic
426Dic11—22no—
427Dic11—22no—
428Dic11—22no—
429Dic11—42no—
430Dic11—41no—
431Dic11—42no—
432C2×#41—114no—
433C2×#41—222no—
434C2×#41—441no—
435C2×#41—441no—
436C2×#41—441no—
437C2×#41—441no—
438C22×Q8—111no—
439C22×D4—111no—
440C22×D4—111no—
441C22×D4—221no—
442C22×D4—221no—
443C23×C4—111no—
444C23×C4—111no—
445C23×C4—221no—
446C23×C4—221no—
447C23×C4C22×D1111yescharacteristic
448C2×SD16—114no—
449C2×SD16—441no—
450C2×SD16—441no—
451C2×D8—114no—
452C2×D8—441no—
453C2×D8—441no—
454C22×C8—111no—
455C22×C8—111no—
456C22×C8C22×D1111yescharacteristic
457C22×C8C22×D1111yescharacteristic
458#121—114no—
459#121—222no—
460C4×D4—441no—
461C4×D4—441no—
462C4×D4—444no—
463#117—41no—
464#117—41no—
465C2×C4⋊C4—111no—
466C2×C4⋊C4—221no—
467C2×C4⋊C4C22×D1111yescharacteristic
468C2×C4⋊C4C22×D1111yescharacteristic
469C2×C4⋊C4C22×D1111yescharacteristic
470C2×C4⋊C4C22×D1111yescharacteristic
471C2×C22⋊C4—21no—
472C2×C22⋊C4—21no—
473C2×C22⋊C4—221no—
474C2×C22⋊C4—221no—
475C2×C22⋊C4—221no—
476C2×C22⋊C4—221no—
477C2×C22⋊C4—221no—
478C2×C22⋊C4—221no—
479C2×C22⋊C4—221no—
480C2×C22⋊C4—221no—
481C2×C42—21no—
482C2×C42—111no—
483C2×C42—111no—
484C2×C42—111no—
485C2×C42—111no—
486C2×C42—221no—
487C2×C42—441no—
488C2×C42—441no—
489#107—41no—
490#106—41no—
491#103—114no—
492#103—441no—
493#103—441no—
494#102—114no—
495#102—441no—
496#102—441no—
497#102—441no—
498#102—441no—
499C22⋊C8—222no—
500C22⋊C8C4×D1114yescomplemented
501C4×C8—441no—
502C4×C8—441no—
503#95—21no—
504#95—221no—
505#95—221no—
506#95—221no—
507#95—221no—
508#95—221no—
509#95—221no—
510C2×C11—42no—
511C2×C11#232111yescharacteristic
512C2×C11C4×#13511yescharacteristic
513C2×C11C4×AGL(1,ℤ/8)11yescharacteristic
514C2×C11#318811yescharacteristic
515C2×C11#319111yescharacteristic
516C2×C11#320711yescharacteristic
517C2×C11#321211yescharacteristic
518D11—82no—
519D11—82no—
520C24—221no—
521C24—221no—
522C24D4×D1111yescharacteristic
523#41—444no—
524#41—444no—
525#41—444no—
526#41—444no—
527C2×Q8—112no—
528C2×Q8—221no—
529C2×Q8—221no—
530C2×Q8—221no—
531C2×Q8—221no—
532C2×Q8—221no—
533C2×D4—112no—
534C2×D4—112no—
535C2×D4—224no—
536C2×D4—224no—
537C2×D4—221no—
538C2×D4—221no—
539C2×D4—221no—
540C2×D4—221no—
541C2×D4—221no—
542C2×D4—221no—
543C2×D4—221no—
544C2×D4—221no—
545C2×D4—221no—
546C2×D4—221no—
547C2×D4—442no—
548C2×D4—442no—
549C2×D4—442no—
550C2×D4—442no—
551C22×C4—21no—
552C22×C4—21no—
553C22×C4—21no—
554C22×C4—21no—
555C22×C4—21no—
556C22×C4—21no—
557C22×C4—21no—
558C22×C4—21no—
559C22×C4—111no—
560C22×C4—111no—
561C22×C4—111no—
562C22×C4—111no—
563C22×C4—222no—
564C22×C4—222no—
565C22×C4—222no—
566C22×C4—221no—
567C22×C4—221no—
568C22×C4—224no—
569C22×C4—442no—
570C22×C4—442no—
571C22×C4—442no—
572C22×C4—442no—
573C22×C4—442no—
574C22×C4—441no—
575C22×C4—441no—
576C22×C4—441no—
577C22×C4C2×C4×D1112yes—
578C22×C4D4×D1111yescharacteristic
579C22×C4#434312yes—
580C22×C4C23×D1111yescharacteristic
581SD16—444no—
582D8—444no—
583C2×C8—21no—
584C2×C8—21no—
585C2×C8—21no—
586C2×C8—21no—
587C2×C8—221no—
588C2×C8—221no—
589C2×C8—221no—
590C2×C8—221no—
591C2×C8—221no—
592C2×C8—221no—
593C2×C8C2×C4×D1112yes—
594C2×C8C2×C4×D1112yes—
595C4⋊C4—21no—
596C4⋊C4—21no—
597C4⋊C4—21no—
598C4⋊C4—21no—
599C4⋊C4—21no—
600C4⋊C4—21no—
601C4⋊C4—21no—
602C4⋊C4—21no—
603C4⋊C4—112no—
604C4⋊C4—221no—
605C4⋊C4—442no—
606C22⋊C4—42no—
607C22⋊C4—42no—
608C22⋊C4—224no—
609C22⋊C4—442no—
610C22⋊C4—442no—
611C22⋊C4—442no—
612C22⋊C4—442no—
613C22⋊C4—442no—
614C22⋊C4—442no—
615C22⋊C4—442no—
616C42—42no—
617C42—221no—
618C42—221no—
619C42—221no—
620C42—221no—
621C42—441no—
622C42—441no—
623C42—442no—
624C11#2204511yescharacteristic, complemented, Sylow
625C23—21no—
626C23—21no—
627C23—21no—
628C23—21no—
629C23—21no—
630C23—21no—
631C23—222no—
632C23—222no—
633C23—441no—
634C23—441no—
635C23—441no—
636C23—441no—
637C23—441no—
638C23—441no—
639C23—441no—
640C23—441no—
641C23—441no—
642C23—441no—
643C23—441no—
644C23—441no—
645C23#6694612yes—
646C23C2×D4×D1111yescharacteristic
647Q8—222no—
648Q8—222no—
649Q8—441no—
650Q8—441no—
651D4—222no—
652D4—222no—
653D4—222no—
654D4—222no—
655D4—448no—
656D4—448no—
657D4—441no—
658D4—441no—
659D4—441no—
660D4—441no—
661C2×C4—21no—
662C2×C4—21no—
663C2×C4—22no—
664C2×C4—22no—
665C2×C4—22no—
666C2×C4—22no—
667C2×C4—41no—
668C2×C4—41no—
669C2×C4—41no—
670C2×C4—41no—
671C2×C4—41no—
672C2×C4—41no—
673C2×C4—41no—
674C2×C4—41no—
675C2×C4—41no—
676C2×C4—41no—
677C2×C4—41no—
678C2×C4—41no—
679C2×C4—112no—
680C2×C4—112no—
681C2×C4—112no—
682C2×C4—221no—
683C2×C4—221no—
684C2×C4—221no—
685C2×C4—221no—
686C2×C4—221no—
687C2×C4—221no—
688C2×C4—222no—
689C2×C4—222no—
690C2×C4—221no—
691C2×C4—221no—
692C2×C4—221no—
693C2×C4—448no—
694C2×C4—444no—
695C2×C4—444no—
696C2×C4—441no—
697C2×C4—441no—
698C2×C4—441no—
699C2×C4—441no—
700C2×C4—884no—
701C2×C4#6694612yes—
702C2×C4C22×C4×D1111yescharacteristic
703C2×C4#6703711yescharacteristic
704C2×C4#6703711yescharacteristic
705C2×C4C2×#434311yescharacteristic
706C2×C4#6704211yescharacteristic
707C2×C4#6704211yescharacteristic
708C8—22no—
709C8—22no—
710C8—441no—
711C8—441no—
712C22—22no—
713C22—22no—
714C22—22no—
715C22—41no—
716C22—41no—
717C22—41no—
718C22—41no—
719C22—442no—
720C22—442no—
721C22—442no—
722C22—442no—
723C22—442no—
724C22—442no—
725C22—881no—
726C22—881no—
727C22—881no—
728C22—881no—
729C22—881no—
730C22—881no—
731C22—881no—
732C22—881no—
733C22C2×#6694611yescharacteristic
734C22#1062312311yescharacteristic
735C22#1062318411yescharacteristic
736C22D11×#13511yescharacteristic
737C22D11×#13511yescharacteristic
738C22D11×AGL(1,ℤ/8)11yescharacteristic
739C22#1062330811yescharacteristic
740C4—22no—
741C4—81no—
742C4—81no—
743C4—81no—
744C4—81no—
745C4—222no—
746C4—222no—
747C4—222no—
748C4—441no—
749C4—442no—
750C4—442no—
751C4#1062307611yescharacteristic
752C4#1062307611yescharacteristic
753C4#1062317511yescharacteristic
754C4#1062317511yescharacteristic
755C2—42no—
756C2—882no—
757C2—882no—
758C2#1307127311yescharacteristic
759C2#1307738711yescharacteristic
760C2#1307742311yescharacteristic
761C2#1307938511yescharacteristic
762C2#1307941111yescharacteristic
763C2#1307954711yescharacteristic
764C2#1307959511yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#1854C2
socleC23×C11C22×D4
prime radicalC2×#10622347C2
cosocleC22×C4×C11C24
hypercenter#1854D11
hypocenterC11#22045
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1854

Complements

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

NH ≅ G/Ntype
2. #13071122C2semidirect
3. #13071104C2semidirect
4. #13069480C2semidirect
5. #13069468C2semidirect
6. #13069297C2semidirect
7. #13069290C2semidirect
8. #13069256C2semidirect
9. #13069242C2semidirect
10. #13068965C2semidirect
11. #13068951C2semidirect
12. #13068938C2semidirect
13. #13068554C2semidirect
14. C22⋊C8×Dic11C2semidirect
15. C11×#1854C2semidirect
51. #10622347C4semidirect
70. C2×#4339C2×C4semidirect
110. C2×D88C2×C4semidirect
113. C2×#4314C2×C4semidirect
119. C11×C22⋊C8C2×C4semidirect
128. #66885C2×C4semidirect
129. #66880C2×C4semidirect
255. #1854D11semidirect
500. C22⋊C8C4×D11semidirect
624. C11#22045semidirect

Maximal subgroups

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

subgroupindex
C2×#106223472
#130711222
#130711042
#130694802
#130694682
#130692972
#130692902
#130692562
#130692422
#130689652
#130689512
#130689382
#130685542
C22⋊C8×Dic112
C11×#18542
#2204511