Finite Group Databasebeta

← #14792575

Subgroups — #14792575

Order 2816.

986 conjugacy classes of subgroups.

The subgroup lattice has 754 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622650C211yesmaximal, characteristic
2C2×#10622613C211yesmaximal, characteristic, complemented
3#13071204C211yesmaximal, characteristic, complemented
4#13070008C211yesmaximal, characteristic, complemented
5#13070001C211yesmaximal, characteristic, complemented
6#13069933C211yesmaximal, characteristic, complemented
7#13069926C211yesmaximal, characteristic, complemented
8#13069496C211yesmaximal, characteristic, complemented
9#13069481C211yesmaximal, characteristic, complemented
10#13069312C211yesmaximal, characteristic, complemented
11#13069291C211yesmaximal, characteristic, complemented
12#13068934C211yesmaximal, characteristic, complemented
13#13068803C211yesmaximal, characteristic, complemented
14#13068554C211yesmaximal, characteristic, complemented
15C11×#2624C211yesmaximal, characteristic, complemented
16C22×#4339C2211yescharacteristic
17C2×C11×#121C2211yescharacteristic
18C2×C11×#117C2211yescharacteristic
19C22×#4324C2211yescharacteristic
20C22×#4323C2211yescharacteristic
21C22×C4⋊Dic11C2211yescharacteristic
22C11×#399—21no—
23C11×#397—21no—
24C11×#394—21no—
25C11×#394—21no—
26C11×#390C2211yescharacteristic
27C11×#390C2211yescharacteristic
28C11×#389C2211yescharacteristic
29C11×#389C2211yescharacteristic
30C11×#380C2211yescharacteristic
31C2×#66896C2211yescharacteristic
32C2×#66896C2211yescharacteristic
33C2×C22⋊(C11⋊C8)C2211yescharacteristic
34C2×C22⋊(C11⋊C8)C2211yescharacteristic
35#10622650—24no—
36#10622613—24no—
37#10622600—21no—
38#10622600—21no—
39C2×#66874C2211yescharacteristic
40C2×#66874C2211yescharacteristic
41C2×#66874C2211yescharacteristic
42C2×#66873C2211yescharacteristic
43C2×#66873C2211yescharacteristic
44C2×#66873C2211yescharacteristic
45C2×#66871C2211yescharacteristic
46C2×#66871C2211yescharacteristic
47#10622571—21no—
48#10622571—21no—
49#10622552C2211yescharacteristic
50#10622552C2211yescharacteristic
51#10622542C2211yescharacteristic
52#10622542C2211yescharacteristic
53C2×C4⋊(C11⋊C8)C2211yescharacteristic
54C2×C4⋊(C11⋊C8)C2211yescharacteristic
55C2×#66867C2211yescharacteristic
56C2×C4×C11⋊C8C2211yescharacteristic
57#10622167C2211yescharacteristic
58#10622167C2211yescharacteristic
59#10622167C2211yescharacteristic
60#10622167C2211yescharacteristic
61C22×D4×C11—21no—
62C22×D4×C11C2311yescharacteristic
63C23×C4×C11C2311yescharacteristic
64C22×C22⋊D11—21no—
65C23×Dic11—21no—
66C2×#4339—22no—
67C2×#4339—22no—
68C2×#4339—22no—
69C2×#4339—22no—
70C2×#4339—41no—
71C2×#4339—41no—
72C22×D44C2311yescharacteristic
73C22×C4×D11—21no—
74C22×Dic22C2311yescharacteristic
75C11×#121—22no—
76C11×#121—22no—
77C11×#117—22no—
78C11×#117—22no—
79C2×C11×C4⋊C4—21no—
80C2×C11×C4⋊C4—21no—
81C2×C11×C4⋊C4D411yescharacteristic
82C2×C11×C4⋊C4D411yescharacteristic
83C2×C11×C4⋊C4C2311yescharacteristic
84C2×C11×C4⋊C4C2311yescharacteristic
85C2×C11×C4⋊C4C2311yescharacteristic
86C2×C11×C22⋊C4—21no—
87C2×C11×C22⋊C4—21no—
88C2×C11×C22⋊C4—21no—
89C2×C11×C22⋊C4—21no—
90C2×C11×C22⋊C4—21no—
91C2×C11×C22⋊C4—21no—
92C2×C11×C22⋊C4D411yescharacteristic
93C2×C11×C22⋊C4D411yescharacteristic
94C2×C42×C11C2311yescharacteristic
95C2×C42×C11C2311yescharacteristic
96C2×#4324—22no—
97C2×#4324—22no—
98C2×#4324—41no—
99C2×#4323—22no—
100C2×#4323—22no—
101C2×#4323—41no—
102C2×(C2×D11)⋊C4—21no—
103C2×(C2×D11)⋊C4—21no—
104C2×(C2×D11)⋊C4—21no—
105C2×(C2×D11)⋊C4—21no—
106C2×C4⋊Dic11—21no—
107C2×C4⋊Dic11—41no—
108C2×C4⋊Dic11—41no—
109C2×C4⋊Dic11C2311yescharacteristic
110C2×C4⋊Dic11C2311yescharacteristic
111C22×C11⋊C8C2311yescharacteristic
112C22×C11⋊C8C2311yescharacteristic
113C22×C11⋊C8C2311yescharacteristic
114C22×C11⋊C8C2311yescharacteristic
115C11×#95—21no—
116C11×#95—21no—
117C11×#95—21no—
118#66896—41no—
119#66896—41no—
120C11⋊#95—21no—
121C11⋊#95—21no—
122C11⋊#95—21no—
123C11⋊#95—21no—
124C22⋊(C11⋊C8)—22no—
125C22⋊(C11⋊C8)D414yes—
126#66874—22no—
127#66874—22no—
128#66874—41no—
129#66873—22no—
130#66873—22no—
131#66873—41no—
132#66871—41no—
133#66871—41no—
134C4⋊(C11⋊C8)—22no—
135C4⋊(C11⋊C8)—22no—
136#66867—22no—
137C4×C11⋊C8—22no—
138#24513—111nomaximal, Sylow
139C24×C11—21no—
140C24×C11C2×D411yescharacteristic
141C23×D11—21no—
142C2×D4×C11—21no—
143C2×D4×C11—21no—
144C2×D4×C11—21no—
145C2×D4×C11—21no—
146C2×D4×C11—21no—
147C2×D4×C11—21no—
148C2×D4×C11—42no—
149C2×D4×C11—81no—
150C2×D4×C11—81no—
151C22×C4×C11—21no—
152C22×C4×C11—21no—
153C22×C4×C11—21no—
154C22×C4×C11—21no—
155C22×C4×C11—21no—
156C22×C4×C11—21no—
157C22×C4×C11—21no—
158C22×C4×C11C2×D411yescharacteristic
159C22×C4×C11C2×D411yescharacteristic
160C22×C4×C11C2×D411yescharacteristic
161C22×C4×C11C2×D411yescharacteristic
162C22×C4×C11C2×D411yescharacteristic
163C22×C4×C11C2×D412yes—
164C22×C4×C11#4112yes—
165C22×C4×C11C2411yescharacteristic
166C2×C22⋊D11—24no—
167C2×C22⋊D11—42no—
168C2×C22⋊D11—42no—
169C22×Dic11—21no—
170C22×Dic11—21no—
171C22×Dic11—21no—
172C22×Dic11—42no—
173C22×Dic11—81no—
174C22×Dic11—81no—
175#4339—44no—
176#4339—44no—
177#4339—44no—
178#4339—44no—
179C2×D44—21no—
180C2×D44—21no—
181C2×D44—21no—
182C2×D44—21no—
183C2×D44—21no—
184C2×D44#4112yes—
185C2×C4×D11—24no—
186C2×C4×D11—42no—
187C2×C4×D11—42no—
188C2×Dic22—21no—
189C2×Dic22—21no—
190C2×Dic22—21no—
191C2×Dic22—21no—
192C2×Dic22—21no—
193C2×Dic22#4112yes—
194C11×C4⋊C4—22no—
195C11×C4⋊C4—22no—
196C11×C4⋊C4—21no—
197C11×C4⋊C4—21no—
198C11×C4⋊C4—21no—
199C11×C4⋊C4—21no—
200C11×C4⋊C4—21no—
201C11×C4⋊C4—21no—
202C11×C4⋊C4—81no—
203C11×C4⋊C4—81no—
204C11×C22⋊C4—22no—
205C11×C22⋊C4—22no—
206C11×C22⋊C4—42no—
207C11×C22⋊C4—81no—
208C11×C22⋊C4—81no—
209C11×C22⋊C4—81no—
210C11×C22⋊C4—81no—
211C11×C22⋊C4—81no—
212C42×C11—21no—
213C42×C11—21no—
214C42×C11—21no—
215C42×C11—21no—
216#4324—44no—
217#4323—44no—
218(C2×D11)⋊C4—81no—
219(C2×D11)⋊C4—81no—
220(C2×D11)⋊C4—81no—
221(C2×D11)⋊C4—81no—
222C4⋊Dic11—21no—
223C4⋊Dic11—21no—
224C4⋊Dic11—21no—
225C4⋊Dic11—21no—
226C4⋊Dic11—42no—
227C2×C11⋊C8—21no—
228C2×C11⋊C8—21no—
229C2×C11⋊C8—21no—
230C2×C11⋊C8—21no—
231C2×C11⋊C8—21no—
232C2×C11⋊C8—21no—
233C2×C11⋊C8—21no—
234C2×C11⋊C8—21no—
235C2×C11⋊C8—21no—
236C2×C11⋊C8—21no—
237C2×C11⋊C8C2×D412yes—
238C2×C11⋊C8C2×D412yes—
239C2×#449—111no—
240C2×#433—111no—
241#2624D1111yescharacteristic, complemented
242#2311—111no—
243#2068—111no—
244#2067—111no—
245#2055—111no—
246#2054—111no—
247#1973—111no—
248#1970—111no—
249#1936—111no—
250#1933—111no—
251#1874—111no—
252#1852—111no—
253#1788—111no—
254C23×C11—21no—
255C23×C11—21no—
256C23×C11—21no—
257C23×C11—21no—
258C23×C11—21no—
259C23×C11—21no—
260C23×C11—41no—
261C23×C11—41no—
262C23×C11—41no—
263C23×C11—41no—
264C23×C11—41no—
265C23×C11—41no—
266C23×C11—41no—
267C23×C11#12112yes—
268C23×C11C22×D411yescharacteristic
269C22×D11—22no—
270C22×D11—41no—
271C22×D11—41no—
272C22×D11—41no—
273C22×D11—41no—
274C22×D11—41no—
275C22×D11—41no—
276D4×C11—41no—
277D4×C11—41no—
278D4×C11—41no—
279D4×C11—41no—
280D4×C11—84no—
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—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×C11—21no—
295C2×C4×C11—21no—
296C2×C4×C11—21no—
297C2×C4×C11—21no—
298C2×C4×C11—21no—
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#12112yes—
309C2×C4×C11C22×D411yescharacteristic
310C2×C4×C11C2×#4111yescharacteristic
311C2×C4×C11C2×#4111yescharacteristic
312C2×C4×C11C2×#4111yescharacteristic
313C2×C4×C11H(5,𝔽2)11yescharacteristic
314C2×C4×C11H(5,𝔽2)11yescharacteristic
315C22⋊D11—48no—
316C2×Dic11—22no—
317C2×Dic11—41no—
318C2×Dic11—41no—
319C2×Dic11—41no—
320C2×Dic11—41no—
321C2×Dic11—41no—
322C2×Dic11—41no—
323C2×Dic11—41no—
324C2×Dic11—41no—
325C2×Dic11—84no—
326D44—22no—
327D44—22no—
328D44—41no—
329D44—41no—
330C4×D11—48no—
331Dic22—22no—
332Dic22—22no—
333Dic22—41no—
334Dic22—41no—
335C11⋊C8—22no—
336C11⋊C8—22no—
337C11⋊C8—41no—
338C11⋊C8—41no—
339C22×#41—111no—
340C22×SD16—111no—
341C22×D8—111no—
342C2×#121C2×D1111yescharacteristic
343C2×#117C2×D1111yescharacteristic
344C22×C4⋊C4—111no—
345#449—224no—
346#433—224no—
347C2×#107—111no—
348C2×#107—111no—
349C2×C4⋊C8—111no—
350C2×C4⋊C8—111no—
351C2×#103—111no—
352C2×#103—111no—
353C2×#103—111no—
354C2×#102—111no—
355C2×#102—111no—
356C2×#102—111no—
357C2×#102—111no—
358C2×#102—111no—
359C2×C22⋊C8—111no—
360C2×C22⋊C8—111no—
361C2×#97—111no—
362C2×C4×C8—111no—
363#399—21no—
364#397—21no—
365#394—21no—
366#394—21no—
367#391—111no—
368#391—111no—
369#390—111no—
370#390—111no—
371#390C2×D1111yescharacteristic
372#390C2×D1111yescharacteristic
373#389C2×D1111yescharacteristic
374#389C2×D1111yescharacteristic
375#386—221no—
376#386—221no—
377#380—221no—
378#380—221no—
379#380C2×D1111yescharacteristic
380#340—111no—
381#340—111no—
382#340—111no—
383#340—111no—
384C22×C11—22no—
385C22×C11—22no—
386C22×C11—22no—
387C22×C11—41no—
388C22×C11—41no—
389C22×C11—41no—
390C22×C11—41no—
391C22×C11—81no—
392C22×C11—81no—
393C22×C11—81no—
394C22×C11—81no—
395C22×C11—81no—
396C22×C11—81no—
397C22×C11—81no—
398C22×C11C2×#12111yescharacteristic
399C22×C11#52511yescharacteristic
400C22×C11#53511yescharacteristic
401C22×C11#57611yescharacteristic
402C22×C11#57611yescharacteristic
403C22×C11#57711yescharacteristic
404C22×C11#57811yescharacteristic
405C2×D11—42no—
406C2×D11—42no—
407C2×D11—42no—
408C2×D11—81no—
409C2×D11—81no—
410C2×D11—81no—
411C2×D11—81no—
412C4×C11—22no—
413C4×C11—41no—
414C4×C11—41no—
415C4×C11—41no—
416C4×C11—41no—
417C4×C11—81no—
418C4×C11—81no—
419C4×C11—81no—
420C4×C11#54611yescharacteristic
421C4×C11#54611yescharacteristic
422C4×C11#55111yescharacteristic
423C4×C11#55111yescharacteristic
424Dic11—42no—
425Dic11—81no—
426Dic11—81no—
427C2×#41—222no—
428C2×#41—222no—
429C2×#41—222no—
430C2×#41—222no—
431C2×#41—441no—
432C2×#41—441no—
433C22×Q8—111no—
434C22×D4—21no—
435C22×D4—111no—
436C22×D4—221no—
437C22×D4C22×D1111yescharacteristic
438C23×C4—221no—
439C23×C4—221no—
440C23×C4C22×D1111yescharacteristic
441C2×SD16—222no—
442C2×SD16—222no—
443C2×SD16—441no—
444C2×D8—222no—
445C2×D8—222no—
446C2×D8—441no—
447C22×C8—111no—
448C22×C8—111no—
449C22×C8—111no—
450C22×C8—111no—
451#121—22no—
452#121—22no—
453#117—22no—
454#117—22no—
455C2×C4⋊C4—21no—
456C2×C4⋊C4—21no—
457C2×C4⋊C4—111no—
458C2×C4⋊C4—111no—
459C2×C4⋊C4—221no—
460C2×C4⋊C4—441no—
461C2×C4⋊C4—441no—
462C2×C4⋊C4C22⋊D1111yescharacteristic
463C2×C4⋊C4C22⋊D1111yescharacteristic
464C2×C4⋊C4C22×D1111yescharacteristic
465C2×C4⋊C4C22×D1111yescharacteristic
466C2×C4⋊C4C22×D1111yescharacteristic
467C2×C22⋊C4—21no—
468C2×C22⋊C4—21no—
469C2×C22⋊C4—21no—
470C2×C22⋊C4—21no—
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⋊C4C22⋊D1111yescharacteristic
478C2×C22⋊C4C22⋊D1111yescharacteristic
479C2×C42C22×D1111yescharacteristic
480C2×C42C22×D1111yescharacteristic
481#107—441no—
482#107—441no—
483C4⋊C8—222no—
484C4⋊C8—222no—
485#103—222no—
486#103—222no—
487#103—441no—
488#102—222no—
489#102—222no—
490#102—441no—
491#102—441no—
492#102—441no—
493C22⋊C8—114no—
494C22⋊C8—222no—
495#97—222no—
496C4×C8—222no—
497#95—21no—
498#95—21no—
499#95—21no—
500#95—221no—
501#95—221no—
502#95—221no—
503#95—221no—
504C2×C11—42no—
505C2×C11—161no—
506C2×C11#241111yescharacteristic
507C2×C11#306111yescharacteristic
508C2×C11#306211yescharacteristic
509C2×C11#311911yescharacteristic
510C2×C11#312411yescharacteristic
511C2×C11#322011yescharacteristic
512C2×C11#322511yescharacteristic
513D11—82no—
514C24—21no—
515C24—221no—
516C24C2×C22⋊D1111yescharacteristic
517#41—444no—
518#41—444no—
519#41—444no—
520#41—444no—
521C2×Q8—112no—
522C2×Q8—221no—
523C2×Q8—221no—
524C2×Q8—221no—
525C2×Q8—221no—
526C2×Q8—221no—
527C2×D4—21no—
528C2×D4—21no—
529C2×D4—21no—
530C2×D4—21no—
531C2×D4—21no—
532C2×D4—21no—
533C2×D4—42no—
534C2×D4—81no—
535C2×D4—81no—
536C2×D4—112no—
537C2×D4—224no—
538C2×D4—221no—
539C2×D4—221no—
540C2×D4—221no—
541C2×D4—221no—
542C2×D4—221no—
543C2×D4—442no—
544C2×D4—442no—
545C22×C4—21no—
546C22×C4—21no—
547C22×C4—21no—
548C22×C4—21no—
549C22×C4—21no—
550C22×C4—21no—
551C22×C4—21no—
552C22×C4—224no—
553C22×C4—221no—
554C22×C4—221no—
555C22×C4—221no—
556C22×C4—442no—
557C22×C4—442no—
558C22×C4—442no—
559C22×C4—881no—
560C22×C4—881no—
561C22×C4D4×D1112yes—
562C22×C4#434112yes—
563C22×C4C2×C22⋊D1111yescharacteristic
564C22×C4C2×C22⋊D1111yescharacteristic
565C22×C4C2×C22⋊D1111yescharacteristic
566C22×C4C2×C22⋊D1111yescharacteristic
567C22×C4C2×C22⋊D1111yescharacteristic
568C22×C4C23×D1111yescharacteristic
569SD16—444no—
570D8—444no—
571C2×C8—112no—
572C2×C8—112no—
573C2×C8—221no—
574C2×C8—221no—
575C2×C8—221no—
576C2×C8—221no—
577C2×C8—221no—
578C2×C8—221no—
579C2×C8—221no—
580C2×C8—221no—
581C2×C8—221no—
582C2×C8—221no—
583C4⋊C4—22no—
584C4⋊C4—22no—
585C4⋊C4—21no—
586C4⋊C4—21no—
587C4⋊C4—21no—
588C4⋊C4—21no—
589C4⋊C4—21no—
590C4⋊C4—21no—
591C4⋊C4—81no—
592C4⋊C4—81no—
593C4⋊C4—221no—
594C4⋊C4—221no—
595C4⋊C4—221no—
596C4⋊C4—221no—
597C4⋊C4—442no—
598C22⋊C4—22no—
599C22⋊C4—22no—
600C22⋊C4—42no—
601C22⋊C4—81no—
602C22⋊C4—81no—
603C22⋊C4—81no—
604C22⋊C4—81no—
605C22⋊C4—81no—
606C22⋊C4—881no—
607C22⋊C4—881no—
608C22⋊C4—881no—
609C22⋊C4—881no—
610C42—21no—
611C42—21no—
612C42—21no—
613C42—21no—
614C11#2451311yescharacteristic, complemented, Sylow
615C23—21no—
616C23—21no—
617C23—21no—
618C23—21no—
619C23—21no—
620C23—21no—
621C23—41no—
622C23—41no—
623C23—41no—
624C23—41no—
625C23—41no—
626C23—41no—
627C23—41no—
628C23—222no—
629C23—441no—
630C23—441no—
631C23—441no—
632C23—441no—
633C23—441no—
634C23—441no—
635C23#6699212yes—
636C23C22×C22⋊D1111yescharacteristic
637Q8—222no—
638Q8—222no—
639Q8—441no—
640Q8—441no—
641D4—41no—
642D4—41no—
643D4—41no—
644D4—41no—
645D4—84no—
646D4—222no—
647D4—222no—
648D4—448no—
649D4—441no—
650D4—441no—
651C2×C4—21no—
652C2×C4—21no—
653C2×C4—22no—
654C2×C4—22no—
655C2×C4—22no—
656C2×C4—22no—
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—21no—
667C2×C4—21no—
668C2×C4—21no—
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—222no—
679C2×C4—448no—
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#6699212yes—
690C2×C4C2×D4×D1111yescharacteristic
691C2×C4C2×#434111yescharacteristic
692C2×C4#41×D1111yescharacteristic
693C2×C4#41×D1111yescharacteristic
694C2×C4#6704211yescharacteristic
695C2×C4#6704211yescharacteristic
696C8—222no—
697C8—222no—
698C8—441no—
699C8—441no—
700C22—22no—
701C22—22no—
702C22—22no—
703C22—41no—
704C22—41no—
705C22—41no—
706C22—41no—
707C22—81no—
708C22—81no—
709C22—81no—
710C22—81no—
711C22—81no—
712C22—81no—
713C22—81no—
714C22—442no—
715C22—442no—
716C22—442no—
717C22—881no—
718C22—881no—
719C22—881no—
720C22—881no—
721C22C2×#6699211yescharacteristic
722C22#1062335911yescharacteristic
723C22#1062336111yescharacteristic
724C22#1062336611yescharacteristic
725C22#1062336611yescharacteristic
726C22#1062336711yescharacteristic
727C22#1062336911yescharacteristic
728C4—22no—
729C4—41no—
730C4—41no—
731C4—41no—
732C4—41no—
733C4—81no—
734C4—81no—
735C4—81no—
736C4—442no—
737C4—881no—
738C4—881no—
739C4#1062318511yescharacteristic
740C4#1062318511yescharacteristic
741C4#1062318911yescharacteristic
742C4#1062318911yescharacteristic
743C2—42no—
744C2—161no—
745C2—882no—
746C2#1307200211yescharacteristic
747C2#1307828311yescharacteristic
748C2#1307829211yescharacteristic
749C2#1307880911yescharacteristic
750C2#1307887211yescharacteristic
751C2#1307966011yescharacteristic
752C2#1307971911yescharacteristic
subgroupG/H
centerC23C22×C22⋊D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#2624C2
socleC23×C11C22×D4
prime radicalC2×#10622650C2
hypercenter#2624D11
hypocenterC11#24513
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×#117 ◁ #2624

Complements

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

NH ≅ G/Ntype
2. C2×#10622613C2semidirect
3. #13071204C2semidirect
4. #13070008C2semidirect
5. #13070001C2semidirect
6. #13069933C2semidirect
7. #13069926C2semidirect
8. #13069496C2semidirect
9. #13069481C2semidirect
10. #13069312C2semidirect
11. #13069291C2semidirect
12. #13068934C2semidirect
13. #13068803C2semidirect
14. #13068554C2semidirect
15. C11×#2624C2semidirect
241. #2624D11semidirect
614. C11#24513semidirect

Maximal subgroups

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

subgroupindex
C2×#106226502
C2×#106226132
#130712042
#130700082
#130700012
#130699332
#130699262
#130694962
#130694812
#130693122
#130692912
#130689342
#130688032
#130685542
C11×#26242
#2451311