Finite Group Databasebeta

← #14804443

Subgroups — #14804443

Order 2816.

1012 conjugacy classes of subgroups.

The subgroup lattice has 756 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622673C211yesmaximal, characteristic, complemented
2C2×#10622641C211yesmaximal, characteristic, complemented
3C2×#10622629C211yesmaximal, characteristic
4C2×#10622670C211yesmaximal, characteristic
5#13073611C211yesmaximal, characteristic, complemented
6#13069938C211yesmaximal, characteristic, complemented
7#13069933C211yesmaximal, characteristic, complemented
8#13069709C211yesmaximal, characteristic, complemented
9#13069692C211yesmaximal, characteristic
10#13069539C211yesmaximal, characteristic, complemented
11#13069340C211yesmaximal, characteristic, complemented
12#13068957C211yesmaximal, characteristic, complemented
13#13068950C211yesmaximal, characteristic, complemented
14#13068444C211yesmaximal, characteristic, complemented
15C11×#2367C211yesmaximal, characteristic, complemented
16C2×C11×#124C2211yescharacteristic
17C2×C4×Q8×C11C2211yescharacteristic
18C2×C4×D4×C11C2211yescharacteristic
19C22×#4326C2211yescharacteristic
20C22×#4326C2211yescharacteristic
21C22×#4325C2211yescharacteristic
22C22×#4324C2211yescharacteristic
23C22×#4324C2211yescharacteristic
24C22×#4323C2211yescharacteristic
25C2×#66928C2211yescharacteristic
26C2×#66928C2211yescharacteristic
27C2×C4×D44C2211yescharacteristic
28C2×#66922C2211yescharacteristic
29C11×#391C2211yescharacteristic
30C11×#390C2211yescharacteristic
31C11×#388—21no—
32C11×#388—21no—
33C11×#385—21no—
34C4×C11×C4⋊C4C2211yescharacteristic
35C4×C11×C4⋊C4C2211yescharacteristic
36C4×C11×C22⋊C4—21no—
37C2×#66899C2211yescharacteristic
38C2×#66896C2211yescharacteristic
39#10622673—24no—
40#10622670—24no—
41#10622641—24no—
42#10622629—24no—
43#10622600—21no—
44#10622600—21no—
45C2×#66874C2211yescharacteristic
46C2×#66874C2211yescharacteristic
47C2×#66874C2211yescharacteristic
48C2×#66874C2211yescharacteristic
49C2×#66873C2211yescharacteristic
50C2×#66873C2211yescharacteristic
51#10622542C2211yescharacteristic
52#10622542C2211yescharacteristic
53C2×C4⋊(C11⋊C8)C2211yescharacteristic
54C2×C4⋊(C11⋊C8)C2211yescharacteristic
55C2×C4⋊(C11⋊C8)C2211yescharacteristic
56C2×#66867C2211yescharacteristic
57#10622287—21no—
58#10622287—21no—
59#10622167C2211yescharacteristic
60#10622167C2211yescharacteristic
61#10622162C2211yescharacteristic
62#10622162C2211yescharacteristic
63C22×Q8×C11C2311yescharacteristic
64C22×D4×C11C2311yescharacteristic
65C23×C4×C11—21no—
66C22×D44C2311yescharacteristic
67C22×C4×D11—21no—
68C22×Dic22C2311yescharacteristic
69C22×Dic22C2311yescharacteristic
70C11×#124—22no—
71C11×#124D414yes—
72C4×Q8×C11—22no—
73C4×Q8×C11—41no—
74C4×D4×C11—22no—
75C4×D4×C11—41no—
76C2×C11×C4⋊C4—21no—
77C2×C11×C4⋊C4D411yescharacteristic
78C2×C11×C4⋊C4D411yescharacteristic
79C2×C11×C4⋊C4C2311yescharacteristic
80C2×C11×C4⋊C4C2311yescharacteristic
81C2×C11×C22⋊C4—21no—
82C2×C11×C22⋊C4—21no—
83C2×C11×C22⋊C4—21no—
84C2×C11×C22⋊C4—21no—
85C2×C11×C22⋊C4—21no—
86C2×C42×C11—21no—
87C2×C42×C11—21no—
88C2×C42×C11C2311yescharacteristic
89C2×C42×C11C2311yescharacteristic
90C2×C42×C11C2311yescharacteristic
91C2×#4326—22no—
92C2×#4326—22no—
93C2×#4326—22no—
94C2×#4326—22no—
95C2×#4326—41no—
96C2×#4326—41no—
97C2×#4325—22no—
98C2×#4325—22no—
99C2×#4325—41no—
100C2×#4324—22no—
101C2×#4324—22no—
102C2×#4324—22no—
103C2×#4324—22no—
104C2×#4324—41no—
105C2×#4324—41no—
106C2×#4323—22no—
107C2×#4323—22no—
108C2×#4323—41no—
109C2×(C2×D11)⋊C4—21no—
110C2×(C2×D11)⋊C4—21no—
111C2×(C2×D11)⋊C4—21no—
112C2×(C2×D11)⋊C4—21no—
113C2×(C2×D11)⋊C4—21no—
114C2×C4⋊Dic11—21no—
115C2×C4⋊Dic11—21no—
116C2×C4⋊Dic11C2311yescharacteristic
117C22×C11⋊C8C2311yescharacteristic
118C22×C11⋊C8C2311yescharacteristic
119C22×C11⋊C8C2311yescharacteristic
120C22×C11⋊C8C2311yescharacteristic
121#66928—22no—
122#66928—22no—
123#66928—41no—
124#66928—41no—
125C4×D44—22no—
126C4×D44—22no—
127#66922—22no—
128#66922—22no—
129C11×#95—21no—
130C11×#95—21no—
131C11×#95—21no—
132C11×#95D411yescharacteristic
133C11×#95D411yescharacteristic
134#66899—22no—
135#66896—22no—
136C11⋊#95—21no—
137C11⋊#95—21no—
138C11⋊#95—21no—
139C11⋊#95—21no—
140#66874—22no—
141#66874—22no—
142#66874—41no—
143#66874—41no—
144#66873—22no—
145#66873D414yes—
146C4⋊(C11⋊C8)—22no—
147C4⋊(C11⋊C8)—22no—
148C4⋊(C11⋊C8)—22no—
149#66867—22no—
150#25381—111nomaximal, Sylow
151C24×C11—21no—
152C23×D11—21no—
153C2×Q8×C11—21no—
154C2×Q8×C11—21no—
155C2×Q8×C11—21no—
156C2×Q8×C11—21no—
157C2×Q8×C11—21no—
158C2×Q8×C11C2×D412yes—
159C2×D4×C11—21no—
160C2×D4×C11—21no—
161C2×D4×C11—21no—
162C2×D4×C11—21no—
163C2×D4×C11—21no—
164C2×D4×C11C2×D412yes—
165C22×C4×C11—21no—
166C22×C4×C11—21no—
167C22×C4×C11—21no—
168C22×C4×C11—42no—
169C22×C4×C11—42no—
170C22×C4×C11—81no—
171C22×C4×C11C2×D411yescharacteristic
172C22×C4×C11C2×D411yescharacteristic
173C22×C4×C11C2×D411yescharacteristic
174C22×C4×C11C2×D411yescharacteristic
175C22×C4×C11C2×D411yescharacteristic
176C22×C4×C11C2×D411yescharacteristic
177C22×C4×C11C2411yescharacteristic
178C22×Dic11—21no—
179C22×Dic11—21no—
180C22×Dic11—21no—
181C2×D44—21no—
182C2×D44—21no—
183C2×D44—21no—
184C2×D44—21no—
185C2×D44—21no—
186C2×D44C2×D412yes—
187C2×C4×D11—42no—
188C2×C4×D11—42no—
189C2×C4×D11—42no—
190C2×Dic22—21no—
191C2×Dic22—21no—
192C2×Dic22—21no—
193C2×Dic22—21no—
194C2×Dic22—21no—
195C2×Dic22—21no—
196C2×Dic22—21no—
197C2×Dic22—21no—
198C2×Dic22—21no—
199C2×Dic22—21no—
200C2×Dic22—21no—
201C2×Dic22—21no—
202C11×C4⋊C4—21no—
203C11×C4⋊C4—21no—
204C11×C4⋊C4—21no—
205C11×C4⋊C4—41no—
206C11×C4⋊C4—41no—
207C11×C4⋊C4—42no—
208C11×C4⋊C4C2×D412yes—
209C11×C22⋊C4—24no—
210C11×C22⋊C4—24no—
211C11×C22⋊C4—42no—
212C11×C22⋊C4—42no—
213C11×C22⋊C4—81no—
214C42×C11—21no—
215C42×C11—21no—
216C42×C11—21no—
217C42×C11—21no—
218C42×C11—42no—
219C42×C11—81no—
220C42×C11C2×D412yes—
221C42×C11#4112yes—
222#4326—44no—
223#4326—44no—
224#4325—44no—
225#4324—44no—
226#4324—44no—
227#4323—44no—
228(C2×D11)⋊C4—42no—
229(C2×D11)⋊C4—42no—
230(C2×D11)⋊C4—42no—
231(C2×D11)⋊C4—42no—
232(C2×D11)⋊C4—42no—
233C4⋊Dic11—21no—
234C4⋊Dic11—21no—
235C4⋊Dic11—42no—
236C4⋊Dic11—42no—
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×C11⋊C8—21no—
246C2×C11⋊C8—21no—
247C2×C11⋊C8C2×D412yes—
248C2×C11⋊C8#4112yes—
249C2×#497—111no—
250C2×#464—111no—
251C2×#463—111no—
252C2×#463—111no—
253#2547—111no—
254#2367D1111yescharacteristic, complemented
255#2056—111no—
256#2055—111no—
257#2015—111no—
258#2012—111no—
259#1981—111no—
260#1940—111no—
261#1878—111no—
262#1877—111no—
263#1762—111no—
264C23×C11—22no—
265C23×C11—41no—
266C23×C11—41no—
267C23×C11—41no—
268C23×C11—41no—
269C23×C11—41no—
270C23×C11—41no—
271C23×C11C22×D411yescharacteristic
272C22×D11—22no—
273C22×D11—41no—
274C22×D11—41no—
275C22×D11—41no—
276C22×D11—41no—
277C22×D11—41no—
278C22×D11—41no—
279Q8×C11—22no—
280Q8×C11—22no—
281Q8×C11—41no—
282Q8×C11—41no—
283D4×C11—22no—
284D4×C11—22no—
285D4×C11—41no—
286D4×C11—41no—
287C2×C4×C11—21no—
288C2×C4×C11—21no—
289C2×C4×C11—21no—
290C2×C4×C11—21no—
291C2×C4×C11—22no—
292C2×C4×C11—21no—
293C2×C4×C11—21no—
294C2×C4×C11—21no—
295C2×C4×C11—21no—
296C2×C4×C11—22no—
297C2×C4×C11—21no—
298C2×C4×C11—21no—
299C2×C4×C11—21no—
300C2×C4×C11—21no—
301C2×C4×C11—21no—
302C2×C4×C11—21no—
303C2×C4×C11—21no—
304C2×C4×C11—21no—
305C2×C4×C11—41no—
306C2×C4×C11—41no—
307C2×C4×C11—41no—
308C2×C4×C11—41no—
309C2×C4×C11—41no—
310C2×C4×C11—41no—
311C2×C4×C11—41no—
312C2×C4×C11—84no—
313C2×C4×C11#12112yes—
314C2×C4×C11#12112yes—
315C2×C4×C11C22×D411yescharacteristic
316C2×C4×C11C22×D411yescharacteristic
317C2×C4×C11C2×#4111yescharacteristic
318C2×C4×C11C2×#4111yescharacteristic
319C2×C4×C11H(5,𝔽2)11yescharacteristic
320C2×C4×C11H(5,𝔽2)11yescharacteristic
321C2×Dic11—41no—
322C2×Dic11—41no—
323C2×Dic11—41no—
324C2×Dic11—41no—
325C2×Dic11—41no—
326C2×Dic11—41no—
327C2×Dic11—41no—
328C2×Dic11—41no—
329C2×Dic11—41no—
330D44—22no—
331D44—22no—
332D44—41no—
333D44—41no—
334C4×D11—84no—
335Dic22—41no—
336Dic22—41no—
337Dic22—41no—
338Dic22—41no—
339Dic22—41no—
340Dic22—41no—
341Dic22—41no—
342Dic22—41no—
343C11⋊C8—22no—
344C11⋊C8—22no—
345C11⋊C8—41no—
346C11⋊C8—41no—
347C22×Q16—111no—
348C22×Q16—111no—
349C22×SD16—111no—
350C22×SD16—111no—
351C22×SD16—111no—
352C22×D8—111no—
353C2×C4⋊Q8—111no—
354C2×#124—111no—
355C2×#124—111no—
356C2×#124C2×D1111yescharacteristic
357C2×C4×Q8C2×D1111yescharacteristic
358C2×C4×D4—111no—
359C2×C4×D4C2×D1111yescharacteristic
360#497—224no—
361#464—224no—
362#463—224no—
363#463—224no—
364C2×C4⋊C8—111no—
365C2×C4⋊C8—111no—
366C2×C4⋊C8—111no—
367C2×#103—111no—
368C2×#103—111no—
369C2×#103—111no—
370C2×#103—111no—
371C2×#103—111no—
372C2×#102—111no—
373C2×#102—111no—
374C2×#102—111no—
375C2×#97—111no—
376#397—221no—
377#397—221no—
378#391—111no—
379#391—111no—
380#391C2×D1111yescharacteristic
381#390C2×D1111yescharacteristic
382#388—21no—
383#388—21no—
384#385—21no—
385#380—221no—
386#380—221no—
387C4×C4⋊C4C2×D1111yescharacteristic
388C4×C4⋊C4C2×D1111yescharacteristic
389C4×C22⋊C4—21no—
390#340—111no—
391#340—111no—
392#336—111no—
393#336—111no—
394C22×C11—42no—
395C22×C11—42no—
396C22×C11—42no—
397C22×C11—81no—
398C22×C11—81no—
399C22×C11—81no—
400C22×C11—81no—
401C22×C11C2×#12111yescharacteristic
402C22×C11D4211yescharacteristic
403C22×C11#55011yescharacteristic
404C22×C11#57511yescharacteristic
405C22×C11#57511yescharacteristic
406C22×C11#57711yescharacteristic
407C22×C11#57811yescharacteristic
408C2×D11—42no—
409C2×D11—42no—
410C2×D11—42no—
411C2×D11—81no—
412C2×D11—81no—
413C2×D11—81no—
414C2×D11—81no—
415C4×C11—22no—
416C4×C11—22no—
417C4×C11—42no—
418C4×C11—41no—
419C4×C11—41no—
420C4×C11—42no—
421C4×C11—41no—
422C4×C11—41no—
423C4×C11—81no—
424C4×C11#53211yescharacteristic
425C4×C11#54011yescharacteristic
426C4×C11D4211yescharacteristic
427C4×C11#54611yescharacteristic
428Dic11—81no—
429Dic11—81no—
430Dic11—81no—
431C22×Q8—111no—
432C22×Q8—111no—
433C22×Q8C22×D1111yescharacteristic
434C22×D4—111no—
435C22×D4C22×D1111yescharacteristic
436C23×C4—21no—
437C23×C4—221no—
438C2×Q16—222no—
439C2×Q16—222no—
440C2×Q16—222no—
441C2×Q16—222no—
442C2×Q16—441no—
443C2×Q16—441no—
444C2×SD16—222no—
445C2×SD16—222no—
446C2×SD16—222no—
447C2×SD16—222no—
448C2×SD16—222no—
449C2×SD16—222no—
450C2×SD16—441no—
451C2×SD16—441no—
452C2×SD16—441no—
453C2×D8—222no—
454C2×D8—222no—
455C2×D8—441no—
456C22×C8—111no—
457C22×C8—111no—
458C22×C8—111no—
459C22×C8—111no—
460C4⋊Q8—222no—
461C4⋊Q8—222no—
462#124—22no—
463#124—222no—
464#124—222no—
465#124—441no—
466#124—441no—
467#124D4414yes—
468C4×Q8—22no—
469C4×Q8—41no—
470C4×D4—22no—
471C4×D4—41no—
472C4×D4—222no—
473C4×D4—222no—
474C2×C4⋊C4—21no—
475C2×C4⋊C4—111no—
476C2×C4⋊C4—221no—
477C2×C4⋊C4—221no—
478C2×C4⋊C4C22⋊D1111yescharacteristic
479C2×C4⋊C4C22⋊D1111yescharacteristic
480C2×C4⋊C4C22×D1111yescharacteristic
481C2×C4⋊C4C22×D1111yescharacteristic
482C2×C22⋊C4—21no—
483C2×C22⋊C4—21no—
484C2×C22⋊C4—21no—
485C2×C22⋊C4—21no—
486C2×C22⋊C4—21no—
487C2×C22⋊C4—221no—
488C2×C22⋊C4—221no—
489C2×C22⋊C4—221no—
490C2×C22⋊C4—221no—
491C2×C22⋊C4—221no—
492C2×C42—21no—
493C2×C42—21no—
494C2×C42C22×D1111yescharacteristic
495C2×C42C22×D1111yescharacteristic
496C2×C42C22×D1111yescharacteristic
497C4⋊C8—222no—
498C4⋊C8—222no—
499C4⋊C8—222no—
500#103—222no—
501#103—222no—
502#103—222no—
503#103—441no—
504#103—441no—
505#102—114no—
506#102—222no—
507#102—222no—
508#97—222no—
509#95—21no—
510#95—21no—
511#95—21no—
512#95—221no—
513#95—221no—
514#95—221no—
515#95—221no—
516#95C22⋊D1111yescharacteristic
517#95C22⋊D1111yescharacteristic
518C2×C11—82no—
519C2×C11#242811yescharacteristic
520C2×C11#304011yescharacteristic
521C2×C11#304611yescharacteristic
522C2×C11#326711yescharacteristic
523C2×C11#326911yescharacteristic
524C2×C11#340111yescharacteristic
525C2×C11#340211yescharacteristic
526D11—82no—
527C24—21no—
528C24—221no—
529C2×Q8—21no—
530C2×Q8—21no—
531C2×Q8—21no—
532C2×Q8—21no—
533C2×Q8—21no—
534C2×Q8—221no—
535C2×Q8—221no—
536C2×Q8—221no—
537C2×Q8—221no—
538C2×Q8—221no—
539C2×Q8—221no—
540C2×Q8—221no—
541C2×Q8—221no—
542C2×Q8—221no—
543C2×Q8—221no—
544C2×Q8—221no—
545C2×Q8—221no—
546C2×Q8C2×D4412yes—
547C2×D4—21no—
548C2×D4—21no—
549C2×D4—21no—
550C2×D4—21no—
551C2×D4—21no—
552C2×D4—112no—
553C2×D4—221no—
554C2×D4—221no—
555C2×D4—221no—
556C2×D4—221no—
557C2×D4—221no—
558C2×D4C2×D4412yes—
559C22×C4—21no—
560C22×C4—21no—
561C22×C4—21no—
562C22×C4—42no—
563C22×C4—42no—
564C22×C4—81no—
565C22×C4—221no—
566C22×C4—221no—
567C22×C4—221no—
568C22×C4—442no—
569C22×C4—442no—
570C22×C4—442no—
571C22×C4C2×C22⋊D1111yescharacteristic
572C22×C4C2×C22⋊D1111yescharacteristic
573C22×C4C2×C22⋊D1111yescharacteristic
574C22×C4C2×C22⋊D1111yescharacteristic
575C22×C4C2×C22⋊D1111yescharacteristic
576C22×C4C2×C22⋊D1111yescharacteristic
577C22×C4C23×D1111yescharacteristic
578Q16—444no—
579Q16—444no—
580SD16—444no—
581SD16—444no—
582SD16—444no—
583D8—444no—
584C2×C8—112no—
585C2×C8—112no—
586C2×C8—221no—
587C2×C8—221no—
588C2×C8—221no—
589C2×C8—221no—
590C2×C8—221no—
591C2×C8—221no—
592C2×C8—221no—
593C2×C8—221no—
594C2×C8—221no—
595C2×C8—221no—
596C4⋊C4—21no—
597C4⋊C4—21no—
598C4⋊C4—21no—
599C4⋊C4—41no—
600C4⋊C4—41no—
601C4⋊C4—42no—
602C4⋊C4—221no—
603C4⋊C4—221no—
604C4⋊C4—442no—
605C4⋊C4—442no—
606C4⋊C4D4×D1112yes—
607C22⋊C4—24no—
608C22⋊C4—24no—
609C22⋊C4—42no—
610C22⋊C4—42no—
611C22⋊C4—81no—
612C22⋊C4—442no—
613C22⋊C4—442no—
614C22⋊C4—442no—
615C22⋊C4—442no—
616C22⋊C4—442no—
617C42—21no—
618C42—21no—
619C42—21no—
620C42—21no—
621C42—42no—
622C42—81no—
623C42C2×D4412yes—
624C42#433912yes—
625C11#2538111yescharacteristic, complemented, Sylow
626C23—22no—
627C23—41no—
628C23—41no—
629C23—41no—
630C23—41no—
631C23—41no—
632C23—41no—
633C23—222no—
634C23—441no—
635C23—441no—
636C23—441no—
637C23—441no—
638C23—441no—
639C23—441no—
640C23C22×C22⋊D1111yescharacteristic
641Q8—22no—
642Q8—22no—
643Q8—41no—
644Q8—41no—
645Q8—441no—
646Q8—441no—
647Q8—441no—
648Q8—441no—
649Q8—441no—
650Q8—441no—
651Q8—441no—
652Q8—441no—
653D4—22no—
654D4—22no—
655D4—41no—
656D4—41no—
657D4—222no—
658D4—222no—
659D4—441no—
660D4—441no—
661C2×C4—21no—
662C2×C4—21no—
663C2×C4—21no—
664C2×C4—21no—
665C2×C4—22no—
666C2×C4—21no—
667C2×C4—21no—
668C2×C4—21no—
669C2×C4—21no—
670C2×C4—22no—
671C2×C4—21no—
672C2×C4—21no—
673C2×C4—21no—
674C2×C4—21no—
675C2×C4—21no—
676C2×C4—21no—
677C2×C4—21no—
678C2×C4—21no—
679C2×C4—41no—
680C2×C4—41no—
681C2×C4—41no—
682C2×C4—41no—
683C2×C4—41no—
684C2×C4—41no—
685C2×C4—41no—
686C2×C4—84no—
687C2×C4—441no—
688C2×C4—441no—
689C2×C4—441no—
690C2×C4—441no—
691C2×C4—441no—
692C2×C4—441no—
693C2×C4—441no—
694C2×C4—441no—
695C2×C4—441no—
696C2×C4—884no—
697C2×C4#6698312yes—
698C2×C4#6698312yes—
699C2×C4C22×D4411yescharacteristic
700C2×C4C2×#433911yescharacteristic
701C2×C4C2×D4×D1111yescharacteristic
702C2×C4#6703711yescharacteristic
703C2×C4#41×D1111yescharacteristic
704C2×C4#6704211yescharacteristic
705C8—222no—
706C8—222no—
707C8—441no—
708C8—441no—
709C22—42no—
710C22—42no—
711C22—42no—
712C22—81no—
713C22—81no—
714C22—81no—
715C22—81no—
716C22—442no—
717C22—442no—
718C22—442no—
719C22—881no—
720C22—881no—
721C22—881no—
722C22—881no—
723C22C2×#6698311yescharacteristic
724C22D4×C22⋊D1111yescharacteristic
725C22#1062335311yescharacteristic
726C22#1062335311yescharacteristic
727C22#1062336511yescharacteristic
728C22#1062336711yescharacteristic
729C22#1062336911yescharacteristic
730C4—22no—
731C4—22no—
732C4—42no—
733C4—41no—
734C4—41no—
735C4—42no—
736C4—41no—
737C4—41no—
738C4—81no—
739C4—881no—
740C4—881no—
741C4—881no—
742C4#1062307911yescharacteristic
743C4D4×D4411yescharacteristic
744C4#1062308511yescharacteristic
745C4#1062309311yescharacteristic
746C2—82no—
747C2—882no—
748C2#1307219811yescharacteristic
749C2#1307811011yescharacteristic
750C2#1307816611yescharacteristic
751C2#1308013711yescharacteristic
752C2#1308017211yescharacteristic
753C2#1308167611yescharacteristic
754C2#1308169111yescharacteristic
subgroupG/H
centerC23C22×C22⋊D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#2367C2
socleC23×C11C22×D4
prime radicalC22×#4323C22
hypercenter#2367D11
hypocenterC11#25381
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C4×C4⋊C4 ◁ #2367

Complements

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

NH ≅ G/Ntype
1. C2×#10622673C2semidirect
2. C2×#10622641C2semidirect
5. #13073611C2semidirect
6. #13069938C2semidirect
7. #13069933C2semidirect
8. #13069709C2semidirect
10. #13069539C2semidirect
11. #13069340C2semidirect
12. #13068957C2semidirect
13. #13068950C2semidirect
14. #13068444C2semidirect
15. C11×#2367C2semidirect
254. #2367D11semidirect
625. C11#25381semidirect

Maximal subgroups

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

subgroupindex
C2×#106226732
C2×#106226412
C2×#106226292
C2×#106226702
#130736112
#130699382
#130699332
#130697092
#130696922
#130695392
#130693402
#130689572
#130689502
#130684442
C11×#23672
#2538111