Finite Group Databasebeta

← #14800792

Subgroups — #14800792

Order 2816.

1362 conjugacy classes of subgroups.

The subgroup lattice has 900 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622652C211yesmaximal, characteristic, complemented
2C2×#10622649C211yesmaximal, characteristic, complemented
3C2×#10622624C211yesmaximal, characteristic, complemented
4C22×#66873C211yesmaximal, characteristic, complemented
5#13071972C211yesmaximal, characteristic, complemented
6#13069987C211yesmaximal, characteristic, complemented
7#13069926C211yesmaximal, characteristic, complemented
8#13069805C211yesmaximal, characteristic, complemented
9#13069612C211yesmaximal, characteristic, complemented
10#13069491C211yesmaximal, characteristic, complemented
11#13069312C211yesmaximal, characteristic, complemented
12#13069052C211yesmaximal, characteristic, complemented
13#13069045C211yesmaximal, characteristic, complemented
14#13068809C211yesmaximal, characteristic, complemented
15C11×#2416C211yesmaximal, characteristic, complemented
16C23×D44C2211yescharacteristic
17C2×C11×#121—21no—
18C2×C11×#121C2211yescharacteristic
19C2×C11×#121C2211yescharacteristic, complemented
20C2×C4×D4×C11C2211yescharacteristic
21C22×C11×C4⋊C4C2211yescharacteristic
22C2×#66990—21no—
23C22×#4323C2211yescharacteristic
24C22×#4323C2211yescharacteristic
25C2×#66983C2211yescharacteristic
26C2×#66983C2211yescharacteristic
27C22×#4318C2211yescharacteristic, complemented
28C23×C11⋊C8C2211yescharacteristic
29C11×#396—21no—
30C11×#394—21no—
31C11×#390C2211yescharacteristic, complemented
32C11×#389C2211yescharacteristic, complemented
33C11×#386—21no—
34C11×#380C2211yescharacteristic, complemented
35C2×#66896C2211yescharacteristic, complemented
36C2×#66896C2211yescharacteristic, complemented
37#10622825C2211yescharacteristic
38C2×C22⋊(C11⋊C8)C2211yescharacteristic
39C2×C22⋊(C11⋊C8)C2211yescharacteristic, complemented
40#10622652—24no—
41#10622649—24no—
42#10622624—24no—
43#10622604—21no—
44C2×#66873—24no—
45C2×#66873C2211yescharacteristic
46C2×#66873C2211yescharacteristic
47C2×#66873C2211yescharacteristic
48C2×#66873C2211yescharacteristic
49C2×#66873C2211yescharacteristic
50C2×#66873C2211yescharacteristic
51C2×#66872C2211yescharacteristic, complemented
52C2×#66872C2211yescharacteristic, complemented
53#10622573—21no—
54#10622568—21no—
55#10622552C2211yescharacteristic
56#10622552C2211yescharacteristic
57C2×C4⋊(C11⋊C8)C2211yescharacteristic, complemented
58C2×#66867C2211yescharacteristic, complemented
59#10622167C2211yescharacteristic, complemented
60#10622167C2211yescharacteristic, complemented
61#10622167C2211yescharacteristic, complemented
62#10622167C2211yescharacteristic, complemented
63C24×D11—21no—
64C22×D4×C11—21no—
65C22×D4×C11—21no—
66C22×D4×C11D411yescharacteristic
67C22×D4×C11C2311yescharacteristic
68C23×C4×C11—21no—
69C23×C4×C11C2311yescharacteristic
70C23×C4×C11C2311yescharacteristic
71C22×C22⋊D11—21no—
72C22×C22⋊D11—21no—
73C22×D44—22no—
74C22×D44—22no—
75C22×D44—22no—
76C22×D44—22no—
77C22×D44—21no—
78C22×D44—41no—
79C22×D44—41no—
80C22×D44C2311yescharacteristic
81C22×D44C2311yescharacteristic
82C11×#121—22no—
83C11×#121—22no—
84C11×#121—22no—
85C11×#121—41no—
86C11×#121—44no—
87C4×D4×C11—22no—
88C4×D4×C11—22no—
89C2×C11×C4⋊C4—22no—
90C2×C11×C4⋊C4—21no—
91C2×C11×C4⋊C4—21no—
92C2×C11×C4⋊C4—41no—
93C2×C11×C4⋊C4D411yescharacteristic
94C2×C11×C4⋊C4C2311yescharacteristic
95C2×C11×C4⋊C4C2311yescharacteristic
96C2×C11×C4⋊C4C2311yescharacteristic
97C2×C11×C22⋊C4—21no—
98C2×C11×C22⋊C4—21no—
99C2×C11×C22⋊C4—21no—
100C2×C11×C22⋊C4—21no—
101C2×C11×C22⋊C4—21no—
102C2×C11×C22⋊C4D411yescharacteristic
103C2×C11×C22⋊C4D411yescharacteristic
104C2×C42×C11C2311yescharacteristic
105C2×C22⋊Dic11—21no—
106#66990—44no—
107C2×#4323—22no—
108C2×#4323—22no—
109C2×#4323—22no—
110C2×#4323—22no—
111C2×#4323—41no—
112C2×#4323—41no—
113#66983—22no—
114#66983—22no—
115#66983—41no—
116#66983—41no—
117C2×(C2×D11)⋊C4—21no—
118C2×(C2×D11)⋊C4—21no—
119C2×(C2×D11)⋊C4—21no—
120C2×(C2×D11)⋊C4—21no—
121C2×(C2×D11)⋊C4—21no—
122C2×(C2×D11)⋊C4—21no—
123C2×C4⋊Dic11C2311yescharacteristic
124C2×C4⋊Dic11C2311yescharacteristic
125C2×#4318—22no—
126C2×#4318—22no—
127C2×#4318—41no—
128C22×C11⋊C8—22no—
129C22×C11⋊C8—22no—
130C22×C11⋊C8—41no—
131C22×C11⋊C8C2311yescharacteristic
132C22×C11⋊C8C2311yescharacteristic
133C22×C11⋊C8C2311yescharacteristic
134C22×C11⋊C8C2311yescharacteristic
135C11×#95—21no—
136C11×#95—21no—
137#66896—22no—
138#66896—41no—
139C11⋊#95—21no—
140C22⋊(C11⋊C8)—22no—
141C22⋊(C11⋊C8)D414yescomplemented
142#66873—22no—
143#66873—22no—
144#66873—22no—
145#66873—22no—
146#66873—22no—
147#66873D414yescomplemented
148#66872—22no—
149#66872—41no—
150C4⋊(C11⋊C8)—22no—
151#66867—22no—
152#25124—111nomaximal, Sylow
153C24×C11—21no—
154C24×C11C2×D411yescharacteristic
155C24×C11C2×D411yescharacteristic
156C23×D11—21no—
157C23×D11—21no—
158C23×D11—42no—
159C23×D11—42no—
160C23×D11—42no—
161C23×D11—42no—
162C23×D11—42no—
163C23×D11—81no—
164C23×D11—81no—
165C2×D4×C11—22no—
166C2×D4×C11—22no—
167C2×D4×C11—22no—
168C2×D4×C11—21no—
169C2×D4×C11—21no—
170C2×D4×C11—21no—
171C2×D4×C11—21no—
172C2×D4×C11—21no—
173C2×D4×C11—21no—
174C2×D4×C11—42no—
175C2×D4×C11—42no—
176C2×D4×C11—42no—
177C2×D4×C11—42no—
178C2×D4×C11—42no—
179C2×D4×C11—81no—
180C22×C4×C11—21no—
181C22×C4×C11—21no—
182C22×C4×C11—21no—
183C22×C4×C11—21no—
184C22×C4×C11—21no—
185C22×C4×C11—21no—
186C22×C4×C11—21no—
187C22×C4×C11—21no—
188C22×C4×C11—21no—
189C22×C4×C11—21no—
190C22×C4×C11—21no—
191C22×C4×C11—21no—
192C22×C4×C11—21no—
193C22×C4×C11—42no—
194C22×C4×C11—42no—
195C22×C4×C11—81no—
196C22×C4×C11C2×D411yescharacteristic
197C22×C4×C11C2×D411yescharacteristic
198C22×C4×C11C2×D411yescharacteristic
199C22×C4×C11C2×D411yescharacteristic
200C22×C4×C11C2×D412yes—
201C22×C4×C11#4112yes—
202C22×C4×C11C2411yescharacteristic
203C2×C22⋊D11—42no—
204C2×C22⋊D11—42no—
205C2×C22⋊D11—42no—
206C2×C22⋊D11—42no—
207C2×C22⋊D11—81no—
208C2×C22⋊D11—81no—
209C22×Dic11—21no—
210C22×Dic11—21no—
211C2×D44—28no—
212C2×D44—21no—
213C2×D44—21no—
214C2×D44—21no—
215C2×D44—21no—
216C2×D44—21no—
217C2×D44—21no—
218C2×D44—21no—
219C2×D44—21no—
220C2×D44—21no—
221C2×D44—21no—
222C2×D44—42no—
223C2×D44—42no—
224C2×D44—44no—
225C2×D44—44no—
226C2×D44—44no—
227C2×D44—42no—
228C2×D44C2×D412yes—
229C2×D44#4112yes—
230C11×C4⋊C4—22no—
231C11×C4⋊C4—21no—
232C11×C4⋊C4—21no—
233C11×C4⋊C4—21no—
234C11×C4⋊C4—21no—
235C11×C4⋊C4—21no—
236C11×C4⋊C4—42no—
237C11×C4⋊C4—42no—
238C11×C4⋊C4C2×D412yes—
239C11×C22⋊C4—22no—
240C11×C22⋊C4—22no—
241C11×C22⋊C4—42no—
242C11×C22⋊C4—42no—
243C11×C22⋊C4—42no—
244C11×C22⋊C4—42no—
245C11×C22⋊C4—81no—
246C42×C11—21no—
247C42×C11—21no—
248C22⋊Dic11—42no—
249#4323—44no—
250#4323—44no—
251(C2×D11)⋊C4—42no—
252(C2×D11)⋊C4—42no—
253(C2×D11)⋊C4—42no—
254(C2×D11)⋊C4—42no—
255(C2×D11)⋊C4—81no—
256(C2×D11)⋊C4—81no—
257C4⋊Dic11—21no—
258C4⋊Dic11—21no—
259C4⋊Dic11—21no—
260C4⋊Dic11—21no—
261#4318—44no—
262C2×C11⋊C8—21no—
263C2×C11⋊C8—21no—
264C2×C11⋊C8—21no—
265C2×C11⋊C8—21no—
266C2×C11⋊C8—21no—
267C2×C11⋊C8—21no—
268C2×C11⋊C8—21no—
269C2×C11⋊C8—21no—
270C2×C11⋊C8—21no—
271C2×C11⋊C8—44no—
272C2×C11⋊C8C2×D412yes—
273C2×C11⋊C8C2×D412yes—
274C2×C11⋊C8C2×D412yes—
275C2×#469—111no—
276C2×#447—111no—
277C2×#435—111no—
278C22×#102—111no—
279#2416D1111yescharacteristic, complemented
280#2408—111no—
281#2065—111no—
282#2054—111no—
283#2034—111no—
284#1999—111no—
285#1972—111no—
286#1936—111no—
287#1895—111no—
288#1893—111no—
289#1853—111no—
290C23×C11—21no—
291C23×C11—21no—
292C23×C11—21no—
293C23×C11—21no—
294C23×C11—21no—
295C23×C11—21no—
296C23×C11—21no—
297C23×C11—21no—
298C23×C11—21no—
299C23×C11—21no—
300C23×C11—21no—
301C23×C11—41no—
302C23×C11—41no—
303C23×C11—41no—
304C23×C11—41no—
305C23×C11—41no—
306C23×C11—41no—
307C23×C11—41no—
308C23×C11#12112yes—
309C23×C11AGL(1,ℤ/8)12yes—
310C23×C11AGL(1,ℤ/8)12yes—
311C23×C11C22×D411yescharacteristic
312C22×D11—22no—
313C22×D11—22no—
314C22×D11—48no—
315C22×D11—41no—
316C22×D11—41no—
317C22×D11—41no—
318C22×D11—41no—
319C22×D11—41no—
320C22×D11—41no—
321C22×D11—41no—
322C22×D11—41no—
323C22×D11—41no—
324C22×D11—41no—
325C22×D11—41no—
326C22×D11—41no—
327C22×D11—84no—
328C22×D11—84no—
329C22×D11—84no—
330C22×D11—84no—
331C22×D11—84no—
332C22×D11—84no—
333D4×C11—44no—
334D4×C11—41no—
335D4×C11—41no—
336D4×C11—41no—
337D4×C11—41no—
338D4×C11—84no—
339D4×C11—84no—
340C2×C4×C11—21no—
341C2×C4×C11—21no—
342C2×C4×C11—22no—
343C2×C4×C11—22no—
344C2×C4×C11—22no—
345C2×C4×C11—22no—
346C2×C4×C11—21no—
347C2×C4×C11—21no—
348C2×C4×C11—21no—
349C2×C4×C11—21no—
350C2×C4×C11—22no—
351C2×C4×C11—21no—
352C2×C4×C11—21no—
353C2×C4×C11—21no—
354C2×C4×C11—21no—
355C2×C4×C11—21no—
356C2×C4×C11—41no—
357C2×C4×C11—41no—
358C2×C4×C11—41no—
359C2×C4×C11—41no—
360C2×C4×C11—41no—
361C2×C4×C11—41no—
362C2×C4×C11—41no—
363C2×C4×C11—41no—
364C2×C4×C11—41no—
365C2×C4×C11—41no—
366C2×C4×C11—41no—
367C2×C4×C11—41no—
368C2×C4×C11—84no—
369C2×C4×C11#12112yes—
370C2×C4×C11C22×D411yescharacteristic
371C2×C4×C11C22×D411yescharacteristic
372C2×C4×C11C2×#4111yescharacteristic
373C2×C4×C11C2×#4111yescharacteristic
374C2×C4×C11H(5,𝔽2)11yescharacteristic
375C2×C4×C11H(5,𝔽2)11yescharacteristic
376C22⋊D11—84no—
377C22⋊D11—84no—
378C2×Dic11—41no—
379C2×Dic11—41no—
380C2×Dic11—41no—
381C2×Dic11—41no—
382C2×Dic11—41no—
383C2×Dic11—41no—
384D44—22no—
385D44—22no—
386D44—22no—
387D44—22no—
388D44—48no—
389D44—41no—
390D44—41no—
391D44—41no—
392D44—41no—
393C11⋊C8—22no—
394C11⋊C8—22no—
395C11⋊C8—22no—
396C11⋊C8—41no—
397C23×D4—111no—
398C22×D8—111no—
399C22×D8—111no—
400C22×M16—111no—
401C23×C8—111no—
402C2×#121—21no—
403C2×#121—111no—
404C2×#121—111no—
405C2×#121C2×D1111yescharacteristic
406C2×#121C2×D1111yescharacteristic, complemented
407C2×#120—221no—
408C2×C4×D4C2×D1111yescharacteristic
409C22×C4⋊C4C2×D1111yescharacteristic
410#469—224no—
411#447—224no—
412#435—224no—
413C2×#106—111no—
414C2×#106—111no—
415C2×C4⋊C8—111no—
416C2×#102—111no—
417C2×#102—111no—
418C2×#102—111no—
419C2×#102—111no—
420C2×#102—111no—
421C2×#102—111no—
422C2×#102—111no—
423C2×#102—111no—
424C2×#102—224no—
425C2×C22⋊C8—111no—
426C2×C22⋊C8—111no—
427C2×#97—111no—
428#396—21no—
429#394—21no—
430#394—221no—
431#392—221no—
432#390—111no—
433#390—111no—
434#390C2×D1111yescharacteristic, complemented
435#389C2×D1111yescharacteristic, complemented
436#386—21no—
437#380—111no—
438#380C2×D1111yescharacteristic, complemented
439#379—221no—
440#340—111no—
441#340—111no—
442#340—111no—
443#340—111no—
444C22×C11—22no—
445C22×C11—22no—
446C22×C11—22no—
447C22×C11—22no—
448C22×C11—22no—
449C22×C11—22no—
450C22×C11—41no—
451C22×C11—41no—
452C22×C11—41no—
453C22×C11—41no—
454C22×C11—41no—
455C22×C11—41no—
456C22×C11—41no—
457C22×C11—81no—
458C22×C11—81no—
459C22×C11—81no—
460C22×C11—81no—
461C22×C11—81no—
462C22×C11—81no—
463C22×C11—81no—
464C22×C11#46914yescomplemented
465C22×C11C2×#12111yescharacteristic
466C22×C11D4211yescharacteristic
467C22×C11#54611yescharacteristic
468C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
469C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
470C22×C11#57611yescharacteristic
471C22×C11#57711yescharacteristic
472C2×D11—42no—
473C2×D11—42no—
474C2×D11—42no—
475C2×D11—42no—
476C2×D11—42no—
477C2×D11—42no—
478C2×D11—816no—
479C2×D11—81no—
480C2×D11—81no—
481C2×D11—81no—
482C2×D11—81no—
483C2×D11—81no—
484C2×D11—81no—
485C2×D11—81no—
486C2×D11—81no—
487C4×C11—22no—
488C4×C11—41no—
489C4×C11—42no—
490C4×C11—41no—
491C4×C11—41no—
492C4×C11—81no—
493C4×C11—81no—
494C4×C11#52511yescharacteristic
495C4×C11#53811yescharacteristic
496C4×C11D4211yescharacteristic
497C4×C11#54611yescharacteristic
498Dic11—81no—
499Dic11—81no—
500C25—221no—
501C22×D4—21no—
502C22×D4—21no—
503C22×D4—111no—
504C22×D4—111no—
505C22×D4—222no—
506C22×D4—222no—
507C22×D4—221no—
508C22×D4—221no—
509C22×D4—222no—
510C22×D4—222no—
511C22×D4—221no—
512C22×D4—441no—
513C22×D4—441no—
514C22×D4C22⋊D1111yescharacteristic
515C22×D4C22×D1111yescharacteristic
516C23×C4—21no—
517C23×C4C22×D1111yescharacteristic
518C23×C4C22×D1111yescharacteristic
519C2×D8—222no—
520C2×D8—222no—
521C2×D8—222no—
522C2×D8—222no—
523C2×D8—441no—
524C2×D8—441no—
525C2×M16—222no—
526C2×M16—222no—
527C2×M16—441no—
528C22×C8—111no—
529C22×C8—111no—
530C22×C8—111no—
531C22×C8—111no—
532C22×C8—222no—
533C22×C8—222no—
534C22×C8—441no—
535#121—22no—
536#121—22no—
537#121—22no—
538#121—41no—
539#121—44no—
540#121—222no—
541#121—222no—
542#121—441no—
543#121—441no—
544#120—444no—
545C4×D4—22no—
546C4×D4—22no—
547C2×C4⋊C4—22no—
548C2×C4⋊C4—21no—
549C2×C4⋊C4—21no—
550C2×C4⋊C4—41no—
551C2×C4⋊C4—111no—
552C2×C4⋊C4—111no—
553C2×C4⋊C4C22⋊D1111yescharacteristic
554C2×C4⋊C4C22×D1111yescharacteristic
555C2×C4⋊C4C22×D1111yescharacteristic
556C2×C4⋊C4C22×D1111yescharacteristic
557C2×C22⋊C4—21no—
558C2×C22⋊C4—21no—
559C2×C22⋊C4—21no—
560C2×C22⋊C4—21no—
561C2×C22⋊C4—21no—
562C2×C22⋊C4—221no—
563C2×C22⋊C4—221no—
564C2×C22⋊C4—221no—
565C2×C22⋊C4—221no—
566C2×C22⋊C4—221no—
567C2×C22⋊C4—221no—
568C2×C22⋊C4—221no—
569C2×C22⋊C4C22⋊D1111yescharacteristic
570C2×C22⋊C4C22⋊D1111yescharacteristic
571C2×C42C22×D1111yescharacteristic
572#106—222no—
573#106—441no—
574C4⋊C8—222no—
575#102—114no—
576#102—222no—
577#102—222no—
578#102—222no—
579#102—222no—
580#102—222no—
581#102—222no—
582#102—441no—
583C22⋊C8—114no—
584C22⋊C8—222no—
585#97—222no—
586#95—21no—
587#95—21no—
588#95—221no—
589C2×C11—24no—
590C2×C11—81no—
591C2×C11—161no—
592C2×C11#242411yescharacteristic
593C2×C11C2×#46911yescharacteristic
594C2×C11#306211yescharacteristic
595C2×C11#326411yescharacteristic
596C2×C11#326511yescharacteristic
597C2×C11#330611yescharacteristic
598C2×C11#331811yescharacteristic
599D11—82no—
600D11—82no—
601C24—21no—
602C24—221no—
603C24—221no—
604C24—442no—
605C24—442no—
606C24—442no—
607C24—442no—
608C24—442no—
609C24—881no—
610C24—881no—
611C24C2×C22⋊D1111yescharacteristic
612C24C2×C22⋊D1111yescharacteristic
613C2×D4—22no—
614C2×D4—22no—
615C2×D4—22no—
616C2×D4—21no—
617C2×D4—21no—
618C2×D4—21no—
619C2×D4—21no—
620C2×D4—21no—
621C2×D4—21no—
622C2×D4—42no—
623C2×D4—42no—
624C2×D4—42no—
625C2×D4—42no—
626C2×D4—42no—
627C2×D4—81no—
628C2×D4—112no—
629C2×D4—112no—
630C2×D4—228no—
631C2×D4—221no—
632C2×D4—221no—
633C2×D4—221no—
634C2×D4—221no—
635C2×D4—221no—
636C2×D4—221no—
637C2×D4—221no—
638C2×D4—221no—
639C2×D4—221no—
640C2×D4—221no—
641C2×D4—444no—
642C2×D4—444no—
643C2×D4—442no—
644C2×D4—442no—
645C2×D4—444no—
646C2×D4—442no—
647C2×D4—442no—
648C2×D4—442no—
649C2×D4—442no—
650C2×D4—442no—
651C2×D4—881no—
652C2×D4—881no—
653C22×C4—21no—
654C22×C4—21no—
655C22×C4—21no—
656C22×C4—21no—
657C22×C4—21no—
658C22×C4—21no—
659C22×C4—21no—
660C22×C4—21no—
661C22×C4—21no—
662C22×C4—21no—
663C22×C4—21no—
664C22×C4—21no—
665C22×C4—21no—
666C22×C4—42no—
667C22×C4—42no—
668C22×C4—81no—
669C22×C4—221no—
670C22×C4—221no—
671C22×C4D4×D1112yes—
672C22×C4#434112yes—
673C22×C4C2×C22⋊D1111yescharacteristic
674C22×C4C2×C22⋊D1111yescharacteristic
675C22×C4C2×C22⋊D1111yescharacteristic
676C22×C4C2×C22⋊D1111yescharacteristic
677C22×C4C23×D1111yescharacteristic
678D8—444no—
679D8—444no—
680M16—444no—
681C2×C8—112no—
682C2×C8—112no—
683C2×C8—112no—
684C2×C8—221no—
685C2×C8—221no—
686C2×C8—221no—
687C2×C8—221no—
688C2×C8—221no—
689C2×C8—221no—
690C2×C8—221no—
691C2×C8—221no—
692C2×C8—221no—
693C2×C8—444no—
694C4⋊C4—22no—
695C4⋊C4—21no—
696C4⋊C4—21no—
697C4⋊C4—21no—
698C4⋊C4—21no—
699C4⋊C4—21no—
700C4⋊C4—42no—
701C4⋊C4—42no—
702C4⋊C4—221no—
703C4⋊C4—221no—
704C4⋊C4—221no—
705C4⋊C4—221no—
706C4⋊C4D4×D1112yes—
707C22⋊C4—22no—
708C22⋊C4—22no—
709C22⋊C4—42no—
710C22⋊C4—42no—
711C22⋊C4—42no—
712C22⋊C4—42no—
713C22⋊C4—81no—
714C22⋊C4—442no—
715C22⋊C4—442no—
716C22⋊C4—442no—
717C22⋊C4—442no—
718C22⋊C4—442no—
719C22⋊C4—881no—
720C22⋊C4—881no—
721C42—21no—
722C42—21no—
723C11#2512411yescharacteristic, complemented, Sylow
724C23—21no—
725C23—21no—
726C23—21no—
727C23—21no—
728C23—21no—
729C23—21no—
730C23—21no—
731C23—21no—
732C23—21no—
733C23—21no—
734C23—21no—
735C23—41no—
736C23—41no—
737C23—41no—
738C23—41no—
739C23—41no—
740C23—41no—
741C23—41no—
742C23—222no—
743C23—222no—
744C23—448no—
745C23—441no—
746C23—441no—
747C23—441no—
748C23—441no—
749C23—441no—
750C23—441no—
751C23—441no—
752C23—441no—
753C23—441no—
754C23—441no—
755C23—441no—
756C23—441no—
757C23—884no—
758C23—884no—
759C23—884no—
760C23—884no—
761C23—884no—
762C23—884no—
763C23#6698512yes—
764C23#6699212yes—
765C23#6700212yes—
766C23C22×C22⋊D1111yescharacteristic
767D4—44no—
768D4—41no—
769D4—41no—
770D4—41no—
771D4—41no—
772D4—84no—
773D4—84no—
774D4—222no—
775D4—222no—
776D4—222no—
777D4—222no—
778D4—448no—
779D4—441no—
780D4—441no—
781D4—441no—
782D4—441no—
783D4—884no—
784D4—884no—
785C2×C4—21no—
786C2×C4—21no—
787C2×C4—22no—
788C2×C4—22no—
789C2×C4—22no—
790C2×C4—22no—
791C2×C4—21no—
792C2×C4—21no—
793C2×C4—22no—
794C2×C4—21no—
795C2×C4—21no—
796C2×C4—21no—
797C2×C4—21no—
798C2×C4—21no—
799C2×C4—21no—
800C2×C4—21no—
801C2×C4—41no—
802C2×C4—41no—
803C2×C4—41no—
804C2×C4—41no—
805C2×C4—41no—
806C2×C4—41no—
807C2×C4—41no—
808C2×C4—41no—
809C2×C4—41no—
810C2×C4—41no—
811C2×C4—41no—
812C2×C4—41no—
813C2×C4—84no—
814C2×C4—441no—
815C2×C4—441no—
816C2×C4—441no—
817C2×C4—441no—
818C2×C4—441no—
819C2×C4—441no—
820C2×C4#6699212yes—
821C2×C4C2×D4×D1111yescharacteristic
822C2×C4C2×D4×D1111yescharacteristic
823C2×C4C2×#434111yescharacteristic
824C2×C4#6703711yescharacteristic
825C2×C4#41×D1111yescharacteristic
826C2×C4#6704211yescharacteristic
827C8—222no—
828C8—222no—
829C8—222no—
830C8—441no—
831C22—22no—
832C22—22no—
833C22—22no—
834C22—22no—
835C22—22no—
836C22—22no—
837C22—41no—
838C22—41no—
839C22—41no—
840C22—41no—
841C22—41no—
842C22—41no—
843C22—41no—
844C22—81no—
845C22—81no—
846C22—81no—
847C22—81no—
848C22—81no—
849C22—81no—
850C22—81no—
851C22—442no—
852C22—442no—
853C22—442no—
854C22—442no—
855C22—442no—
856C22—442no—
857C22—8816no—
858C22—881no—
859C22—881no—
860C22—881no—
861C22—881no—
862C22—881no—
863C22—881no—
864C22—881no—
865C22—881no—
866C22#1062265214yescomplemented
867C22C2×#6698511yescharacteristic
868C22D4×C22⋊D1111yescharacteristic
869C22C2×#6699211yescharacteristic
870C22C2×#6700211yescharacteristic
871C22#1062336011yescharacteristic
872C22#1062336611yescharacteristic
873C22#1062336811yescharacteristic
874C4—22no—
875C4—41no—
876C4—42no—
877C4—41no—
878C4—41no—
879C4—81no—
880C4—81no—
881C4—881no—
882C4—881no—
883C4#1062313711yescharacteristic
884C4#1062314011yescharacteristic
885C4#1062314111yescharacteristic
886C4#1062314811yescharacteristic
887C2—24no—
888C2—81no—
889C2—161no—
890C2—882no—
891C2—882no—
892C2#1307215811yescharacteristic
893C2C2×#1062265211yescharacteristic
894C2#1307829811yescharacteristic
895C2#1308009211yescharacteristic
896C2#1308011211yescharacteristic
897C2#1308057111yescharacteristic
898C2#1308075111yescharacteristic
subgroupG/H
centerC23C22×C22⋊D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#2416C2
socleC23×C11C22×D4
hypercenter#2416D11
hypocenterC11#25124
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ #2416

Complements

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

NH ≅ G/Ntype
1. C2×#10622652C2semidirect
2. C2×#10622649C2semidirect
3. C2×#10622624C2semidirect
4. C22×#66873C2semidirect
5. #13071972C2semidirect
6. #13069987C2semidirect
7. #13069926C2semidirect
8. #13069805C2semidirect
9. #13069612C2semidirect
10. #13069491C2semidirect
11. #13069312C2semidirect
12. #13069052C2semidirect
13. #13069045C2semidirect
14. #13068809C2semidirect
15. C11×#2416C2semidirect
19. C2×C11×#121C22semidirect
27. C22×#4318C22semidirect
31. C11×#390C22semidirect
32. C11×#389C22semidirect
34. C11×#380C22semidirect
35. C2×#66896C22semidirect
36. C2×#66896C22semidirect
39. C2×C22⋊(C11⋊C8)C22semidirect
51. C2×#66872C22semidirect
52. C2×#66872C22semidirect
57. C2×C4⋊(C11⋊C8)C22semidirect
58. C2×#66867C22semidirect
59. #10622167C22semidirect
60. #10622167C22semidirect
61. #10622167C22semidirect
62. #10622167C22semidirect
141. C22⋊(C11⋊C8)D4semidirect
147. #66873D4semidirect
279. #2416D11semidirect
406. C2×#121C2×D11semidirect
434. #390C2×D11semidirect
435. #389C2×D11semidirect
438. #380C2×D11semidirect
464. C22×C11#469semidirect
723. C11#25124semidirect
866. C22#10622652semidirect

Maximal subgroups

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

subgroupindex
C2×#106226522
C2×#106226492
C2×#106226242
C22×#668732
#130719722
#130699872
#130699262
#130698052
#130696122
#130694912
#130693122
#130690522
#130690452
#130688092
C11×#24162
#2512411