Finite Group Databasebeta

← #14800912

Subgroups — #14800912

Order 2816.

1314 conjugacy classes of subgroups.

The subgroup lattice has 892 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×#10622625C211yesmaximal, characteristic, complemented
4C2×#10622614C211yesmaximal, characteristic, complemented
5#13071972C211yesmaximal, characteristic, complemented
6#13069987C211yesmaximal, characteristic, complemented
7#13069926C211yesmaximal, characteristic, complemented
8#13069798C211yesmaximal, characteristic, complemented
9#13069612C211yesmaximal, characteristic, complemented
10#13069481C211yesmaximal, characteristic, complemented
11#13069298C211yesmaximal, characteristic, complemented
12#13069055C211yesmaximal, characteristic, complemented
13#13069052C211yesmaximal, characteristic, complemented
14#13068815C211yesmaximal, characteristic, complemented
15C11×#2414C211yesmaximal, characteristic, complemented
16C23×D44C2211yescharacteristic
17C2×C11×#121C2211yescharacteristic
18C2×C11×#121C2211yescharacteristic, complemented
19C2×C4×D4×C11C2211yescharacteristic
20C2×C11×#117C2211yescharacteristic
21C2×#66990—21no—
22C22×#4323C2211yescharacteristic
23C22×#4323C2211yescharacteristic
24C2×#66983C2211yescharacteristic
25C2×#66983C2211yescharacteristic
26C22×#4318C2211yescharacteristic
27C22×#4318C2211yescharacteristic, complemented
28C11×#394—21no—
29C11×#392—21no—
30C11×#390—21no—
31C11×#390C2211yescharacteristic, complemented
32C11×#389C2211yescharacteristic, complemented
33C11×#388—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#10622625—24no—
43#10622614—24no—
44#10622604—21no—
45C2×#66873C2211yescharacteristic
46C2×#66873C2211yescharacteristic
47C2×#66873C2211yescharacteristic
48C2×#66873C2211yescharacteristic
49C2×#66873C2211yescharacteristic
50C2×#66873C2211yescharacteristic
51C2×#66872C2211yescharacteristic, complemented
52C2×#66871C2211yescharacteristic, complemented
53#10622573—21no—
54#10622568—21no—
55#10622552C2211yescharacteristic
56#10622552C2211yescharacteristic
57C2×C4⋊(C11⋊C8)C2211yescharacteristic, complemented
58C2×C4×C11⋊C8C2211yescharacteristic, 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×C11C2311yescharacteristic
69C23×C4×C11C2311yescharacteristic
70C22×C22⋊D11—21no—
71C22×C22⋊D11—21no—
72C22×D44—22no—
73C22×D44—22no—
74C22×D44—22no—
75C22×D44—22no—
76C22×D44—21no—
77C22×D44—41no—
78C22×D44—41no—
79C22×D44C2311yescharacteristic
80C22×D44C2311yescharacteristic
81C11×#121—22no—
82C11×#121—22no—
83C11×#121—22no—
84C11×#121—41no—
85C4×D4×C11—22no—
86C4×D4×C11—22no—
87C11×#117—22no—
88C11×#117—41no—
89C2×C11×C4⋊C4—21no—
90C2×C11×C4⋊C4D411yescharacteristic
91C2×C11×C4⋊C4C2311yescharacteristic
92C2×C11×C4⋊C4C2311yescharacteristic
93C2×C11×C4⋊C4C2311yescharacteristic
94C2×C11×C22⋊C4—21no—
95C2×C11×C22⋊C4—21no—
96C2×C11×C22⋊C4—21no—
97C2×C11×C22⋊C4—21no—
98C2×C11×C22⋊C4—21no—
99C2×C11×C22⋊C4—21no—
100C2×C11×C22⋊C4D411yescharacteristic
101C2×C11×C22⋊C4D411yescharacteristic
102C2×C42×C11—21no—
103C2×C42×C11C2311yescharacteristic
104C2×C22⋊Dic11—21no—
105#66990—44no—
106C2×#4323—22no—
107C2×#4323—22no—
108C2×#4323—22no—
109C2×#4323—22no—
110C2×#4323—41no—
111C2×#4323—41no—
112#66983—22no—
113#66983—22no—
114#66983—41no—
115#66983—41no—
116C2×(C2×D11)⋊C4—21no—
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×C4⋊Dic11C2311yescharacteristic
123C2×C4⋊Dic11C2311yescharacteristic
124C2×#4318—22no—
125C2×#4318—22no—
126C2×#4318—22no—
127C2×#4318—22no—
128C2×#4318—41no—
129C2×#4318—41no—
130C22×C11⋊C8C2311yescharacteristic
131C22×C11⋊C8C2311yescharacteristic
132C22×C11⋊C8C2311yescharacteristic
133C22×C11⋊C8C2311yescharacteristic
134C11×#95—21no—
135C11×#95—21no—
136#66896—22no—
137#66896—41no—
138C11⋊#95—21no—
139C22⋊(C11⋊C8)—22no—
140C22⋊(C11⋊C8)D414yescomplemented
141#66873—22no—
142#66873—22no—
143#66873—22no—
144#66873—22no—
145#66873—22no—
146#66873D414yescomplemented
147#66872—22no—
148#66871—41no—
149C4⋊(C11⋊C8)—22no—
150C4×C11⋊C8—22no—
151#25132—111nomaximal, Sylow
152C24×C11—21no—
153C24×C11C2×D411yescharacteristic
154C24×C11C2×D411yescharacteristic
155C23×D11—21no—
156C23×D11—21no—
157C23×D11—42no—
158C23×D11—42no—
159C23×D11—42no—
160C23×D11—42no—
161C23×D11—42no—
162C23×D11—81no—
163C23×D11—81no—
164C2×D4×C11—22no—
165C2×D4×C11—22no—
166C2×D4×C11—21no—
167C2×D4×C11—21no—
168C2×D4×C11—21no—
169C2×D4×C11—21no—
170C2×D4×C11—21no—
171C2×D4×C11—21no—
172C2×D4×C11—41no—
173C2×D4×C11—42no—
174C2×D4×C11—42no—
175C2×D4×C11—42no—
176C2×D4×C11—81no—
177C2×D4×C11—81no—
178C2×D4×C11—81no—
179C22×C4×C11—21no—
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×C11C2×D411yescharacteristic
193C22×C4×C11C2×D411yescharacteristic
194C22×C4×C11C2×D411yescharacteristic
195C22×C4×C11C2×D412yes—
196C22×C4×C11C2×D411yescharacteristic
197C22×C4×C11#4112yes—
198C22×C4×C11C2411yescharacteristic
199C2×C22⋊D11—42no—
200C2×C22⋊D11—42no—
201C2×C22⋊D11—42no—
202C2×C22⋊D11—42no—
203C2×C22⋊D11—81no—
204C2×C22⋊D11—81no—
205C22×Dic11—21no—
206C22×Dic11—21no—
207C2×D44—28no—
208C2×D44—21no—
209C2×D44—21no—
210C2×D44—21no—
211C2×D44—21no—
212C2×D44—21no—
213C2×D44—21no—
214C2×D44—21no—
215C2×D44—21no—
216C2×D44—21no—
217C2×D44—21no—
218C2×D44—42no—
219C2×D44—42no—
220C2×D44—44no—
221C2×D44—44no—
222C2×D44—44no—
223C2×D44—42no—
224C2×D44C2×D412yes—
225C2×D44#4112yes—
226C11×C4⋊C4—22no—
227C11×C4⋊C4—21no—
228C11×C4⋊C4—21no—
229C11×C4⋊C4—21no—
230C11×C4⋊C4—21no—
231C11×C4⋊C4—21no—
232C11×C4⋊C4—81no—
233C11×C4⋊C4C2×D412yes—
234C11×C22⋊C4—22no—
235C11×C22⋊C4—22no—
236C11×C22⋊C4—42no—
237C11×C22⋊C4—42no—
238C11×C22⋊C4—42no—
239C11×C22⋊C4—42no—
240C11×C22⋊C4—81no—
241C11×C22⋊C4—81no—
242C42×C11—21no—
243C42×C11—21no—
244C42×C11—42no—
245C22⋊Dic11—42no—
246#4323—44no—
247#4323—44no—
248(C2×D11)⋊C4—42no—
249(C2×D11)⋊C4—42no—
250(C2×D11)⋊C4—42no—
251(C2×D11)⋊C4—42no—
252(C2×D11)⋊C4—81no—
253(C2×D11)⋊C4—81no—
254C4⋊Dic11—21no—
255C4⋊Dic11—21no—
256C4⋊Dic11—21no—
257C4⋊Dic11—21no—
258#4318—44no—
259#4318—44no—
260C2×C11⋊C8—21no—
261C2×C11⋊C8—21no—
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⋊C8C2×D412yes—
270C2×C11⋊C8C2×D412yes—
271C2×C11⋊C8C2×D412yes—
272C2×#469—111no—
273C2×#447—111no—
274C2×#436—111no—
275C2×#418—111no—
276#2414D1111yescharacteristic, complemented
277#2408—111no—
278#2065—111no—
279#2054—111no—
280#2033—111no—
281#1999—111no—
282#1970—111no—
283#1934—111no—
284#1895—111no—
285#1895—111no—
286#1854—111no—
287C23×C11—21no—
288C23×C11—21no—
289C23×C11—21no—
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—41no—
301C23×C11—41no—
302C23×C11—41no—
303C23×C11—41no—
304C23×C11—41no—
305C23×C11—41no—
306C23×C11—41no—
307C23×C11#12112yes—
308C23×C11C22×D411yescharacteristic
309C22×D11—22no—
310C22×D11—22no—
311C22×D11—48no—
312C22×D11—41no—
313C22×D11—41no—
314C22×D11—41no—
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—84no—
325C22×D11—84no—
326C22×D11—84no—
327C22×D11—84no—
328C22×D11—84no—
329C22×D11—84no—
330D4×C11—44no—
331D4×C11—41no—
332D4×C11—41no—
333D4×C11—41no—
334D4×C11—41no—
335D4×C11—84no—
336D4×C11—84no—
337C2×C4×C11—21no—
338C2×C4×C11—21no—
339C2×C4×C11—21no—
340C2×C4×C11—21no—
341C2×C4×C11—22no—
342C2×C4×C11—22no—
343C2×C4×C11—22no—
344C2×C4×C11—22no—
345C2×C4×C11—21no—
346C2×C4×C11—21no—
347C2×C4×C11—21no—
348C2×C4×C11—22no—
349C2×C4×C11—21no—
350C2×C4×C11—21no—
351C2×C4×C11—21no—
352C2×C4×C11—41no—
353C2×C4×C11—41no—
354C2×C4×C11—41no—
355C2×C4×C11—41no—
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#12112yes—
365C2×C4×C11AGL(1,ℤ/8)12yes—
366C2×C4×C11C22×D411yescharacteristic
367C2×C4×C11C22×D411yescharacteristic
368C2×C4×C11C2×#4111yescharacteristic
369C2×C4×C11C2×#4111yescharacteristic
370C2×C4×C11H(5,𝔽2)11yescharacteristic
371C2×C4×C11H(5,𝔽2)11yescharacteristic
372C22⋊D11—84no—
373C22⋊D11—84no—
374C2×Dic11—41no—
375C2×Dic11—41no—
376C2×Dic11—41no—
377C2×Dic11—41no—
378C2×Dic11—41no—
379C2×Dic11—41no—
380D44—22no—
381D44—22no—
382D44—22no—
383D44—22no—
384D44—48no—
385D44—41no—
386D44—41no—
387D44—41no—
388D44—41no—
389C11⋊C8—22no—
390C11⋊C8—22no—
391C11⋊C8—22no—
392C11⋊C8—41no—
393C23×D4—111no—
394C22×D8—111no—
395C22×D8—111no—
396C22×M16—111no—
397C22×M16—111no—
398C2×#121—111no—
399C2×#121—111no—
400C2×#121C2×D1111yescharacteristic
401C2×#121C2×D1111yescharacteristic, complemented
402C2×#120—221no—
403C2×C4×D4C2×D1111yescharacteristic
404C2×#117C2×D1111yescharacteristic
405#469—224no—
406#447—224no—
407#436—224no—
408C2×#107—111no—
409C2×#106—111no—
410C2×C4⋊C8—111no—
411#418—224no—
412C2×#102—111no—
413C2×#102—111no—
414C2×#102—111no—
415C2×#102—111no—
416C2×#102—111no—
417C2×#102—111no—
418C2×#102—111no—
419C2×#102—111no—
420C2×C22⋊C8—111no—
421C2×C22⋊C8—111no—
422C2×C4×C8—111no—
423#394—21no—
424#394—221no—
425#392—21no—
426#392—221no—
427#390—21no—
428#390—111no—
429#390—111no—
430#390C2×D1111yescharacteristic, complemented
431#389C2×D1111yescharacteristic, complemented
432#388—21no—
433#380—111no—
434#380C2×D1111yescharacteristic, complemented
435#379—221no—
436#340—111no—
437#340—111no—
438#340—111no—
439#340—111no—
440C22×C11—22no—
441C22×C11—22no—
442C22×C11—22no—
443C22×C11—41no—
444C22×C11—41no—
445C22×C11—41no—
446C22×C11—41no—
447C22×C11—41no—
448C22×C11—41no—
449C22×C11—41no—
450C22×C11—41no—
451C22×C11—41no—
452C22×C11—41no—
453C22×C11—41no—
454C22×C11—81no—
455C22×C11—81no—
456C22×C11—81no—
457C22×C11—81no—
458C22×C11—81no—
459C22×C11—81no—
460C22×C11—81no—
461C22×C11C2×#12111yescharacteristic
462C22×C11D4211yescharacteristic
463C22×C11#54611yescharacteristic
464C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
465C22×C11#57511yescharacteristic
466C22×C11#57611yescharacteristic
467C22×C11#57611yescharacteristic
468C2×D11—42no—
469C2×D11—42no—
470C2×D11—42no—
471C2×D11—42no—
472C2×D11—42no—
473C2×D11—42no—
474C2×D11—816no—
475C2×D11—81no—
476C2×D11—81no—
477C2×D11—81no—
478C2×D11—81no—
479C2×D11—81no—
480C2×D11—81no—
481C2×D11—81no—
482C2×D11—81no—
483C4×C11—22no—
484C4×C11—22no—
485C4×C11—41no—
486C4×C11—42no—
487C4×C11—41no—
488C4×C11—81no—
489C4×C11—81no—
490C4×C11#52511yescharacteristic
491C4×C11#53811yescharacteristic
492C4×C11D4211yescharacteristic
493C4×C11#54611yescharacteristic
494Dic11—81no—
495Dic11—81no—
496C25—221no—
497C22×D4—21no—
498C22×D4—21no—
499C22×D4—111no—
500C22×D4—111no—
501C22×D4—222no—
502C22×D4—222no—
503C22×D4—221no—
504C22×D4—221no—
505C22×D4—222no—
506C22×D4—222no—
507C22×D4—221no—
508C22×D4—441no—
509C22×D4—441no—
510C22×D4C22⋊D1111yescharacteristic
511C22×D4C22×D1111yescharacteristic
512C23×C4C22×D1111yescharacteristic
513C23×C4C22×D1111yescharacteristic
514C2×D8—222no—
515C2×D8—222no—
516C2×D8—222no—
517C2×D8—222no—
518C2×D8—441no—
519C2×D8—441no—
520C2×M16—222no—
521C2×M16—222no—
522C2×M16—222no—
523C2×M16—222no—
524C2×M16—441no—
525C2×M16—441no—
526C22×C8—111no—
527C22×C8—111no—
528C22×C8—111no—
529C22×C8—111no—
530#121—22no—
531#121—22no—
532#121—22no—
533#121—41no—
534#121—222no—
535#121—222no—
536#121—441no—
537#121—441no—
538#120—444no—
539C4×D4—22no—
540C4×D4—22no—
541#117—22no—
542#117—41no—
543C2×C4⋊C4—21no—
544C2×C4⋊C4—111no—
545C2×C4⋊C4—111no—
546C2×C4⋊C4C22⋊D1111yescharacteristic
547C2×C4⋊C4C22×D1111yescharacteristic
548C2×C4⋊C4C22×D1111yescharacteristic
549C2×C4⋊C4C22×D1111yescharacteristic
550C2×C22⋊C4—21no—
551C2×C22⋊C4—21no—
552C2×C22⋊C4—21no—
553C2×C22⋊C4—21no—
554C2×C22⋊C4—21no—
555C2×C22⋊C4—21no—
556C2×C22⋊C4—221no—
557C2×C22⋊C4—221no—
558C2×C22⋊C4—221no—
559C2×C22⋊C4—221no—
560C2×C22⋊C4—221no—
561C2×C22⋊C4—221no—
562C2×C22⋊C4—221no—
563C2×C22⋊C4C22⋊D1111yescharacteristic
564C2×C22⋊C4C22⋊D1111yescharacteristic
565C2×C42—21no—
566C2×C42C22×D1111yescharacteristic
567#107—441no—
568#106—222no—
569C4⋊C8—222no—
570#102—114no—
571#102—222no—
572#102—222no—
573#102—222no—
574#102—222no—
575#102—222no—
576#102—222no—
577#102—441no—
578C22⋊C8—114no—
579C22⋊C8—222no—
580C4×C8—222no—
581#95—21no—
582#95—21no—
583#95—221no—
584C2×C11—42no—
585C2×C11—81no—
586C2×C11—161no—
587C2×C11#242411yescharacteristic
588C2×C11#305511yescharacteristic
589C2×C11#305811yescharacteristic
590C2×C11#327311yescharacteristic
591C2×C11#327411yescharacteristic
592C2×C11#332211yescharacteristic
593C2×C11#332511yescharacteristic
594D11—82no—
595D11—82no—
596C24—21no—
597C24—221no—
598C24—221no—
599C24—442no—
600C24—442no—
601C24—442no—
602C24—442no—
603C24—442no—
604C24—881no—
605C24—881no—
606C24C2×C22⋊D1111yescharacteristic
607C24C2×C22⋊D1111yescharacteristic
608C2×D4—22no—
609C2×D4—22no—
610C2×D4—21no—
611C2×D4—21no—
612C2×D4—21no—
613C2×D4—21no—
614C2×D4—21no—
615C2×D4—21no—
616C2×D4—41no—
617C2×D4—42no—
618C2×D4—42no—
619C2×D4—42no—
620C2×D4—81no—
621C2×D4—81no—
622C2×D4—81no—
623C2×D4—112no—
624C2×D4—112no—
625C2×D4—228no—
626C2×D4—221no—
627C2×D4—221no—
628C2×D4—221no—
629C2×D4—221no—
630C2×D4—221no—
631C2×D4—221no—
632C2×D4—221no—
633C2×D4—221no—
634C2×D4—221no—
635C2×D4—221no—
636C2×D4—444no—
637C2×D4—444no—
638C2×D4—442no—
639C2×D4—442no—
640C2×D4—444no—
641C2×D4—442no—
642C2×D4—442no—
643C2×D4—442no—
644C2×D4—442no—
645C2×D4—442no—
646C2×D4—881no—
647C2×D4—881no—
648C22×C4—21no—
649C22×C4—21no—
650C22×C4—21no—
651C22×C4—21no—
652C22×C4—21no—
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—221no—
662C22×C4—221no—
663C22×C4D4×D1112yes—
664C22×C4#434112yes—
665C22×C4C2×C22⋊D1111yescharacteristic
666C22×C4C2×C22⋊D1111yescharacteristic
667C22×C4C2×C22⋊D1111yescharacteristic
668C22×C4C2×C22⋊D1111yescharacteristic
669C22×C4C23×D1111yescharacteristic
670D8—444no—
671D8—444no—
672M16—444no—
673M16—444no—
674C2×C8—112no—
675C2×C8—112no—
676C2×C8—112no—
677C2×C8—221no—
678C2×C8—221no—
679C2×C8—221no—
680C2×C8—221no—
681C2×C8—221no—
682C2×C8—221no—
683C2×C8—221no—
684C2×C8—221no—
685C2×C8—221no—
686C4⋊C4—22no—
687C4⋊C4—21no—
688C4⋊C4—21no—
689C4⋊C4—21no—
690C4⋊C4—21no—
691C4⋊C4—21no—
692C4⋊C4—81no—
693C4⋊C4—221no—
694C4⋊C4—221no—
695C4⋊C4—221no—
696C4⋊C4—221no—
697C4⋊C4D4×D1112yes—
698C22⋊C4—22no—
699C22⋊C4—22no—
700C22⋊C4—42no—
701C22⋊C4—42no—
702C22⋊C4—42no—
703C22⋊C4—42no—
704C22⋊C4—81no—
705C22⋊C4—81no—
706C22⋊C4—442no—
707C22⋊C4—442no—
708C22⋊C4—442no—
709C22⋊C4—442no—
710C22⋊C4—442no—
711C22⋊C4—881no—
712C22⋊C4—881no—
713C42—21no—
714C42—21no—
715C42—42no—
716C11#2513211yescharacteristic, complemented, Sylow
717C23—21no—
718C23—21no—
719C23—21no—
720C23—21no—
721C23—21no—
722C23—21no—
723C23—21no—
724C23—21no—
725C23—21no—
726C23—21no—
727C23—21no—
728C23—21no—
729C23—21no—
730C23—41no—
731C23—41no—
732C23—41no—
733C23—41no—
734C23—41no—
735C23—41no—
736C23—41no—
737C23—222no—
738C23—222no—
739C23—448no—
740C23—441no—
741C23—441no—
742C23—441no—
743C23—441no—
744C23—441no—
745C23—441no—
746C23—441no—
747C23—441no—
748C23—441no—
749C23—441no—
750C23—441no—
751C23—441no—
752C23—884no—
753C23—884no—
754C23—884no—
755C23—884no—
756C23—884no—
757C23—884no—
758C23#6699212yes—
759C23C22×C22⋊D1111yescharacteristic
760D4—44no—
761D4—41no—
762D4—41no—
763D4—41no—
764D4—41no—
765D4—84no—
766D4—84no—
767D4—222no—
768D4—222no—
769D4—222no—
770D4—222no—
771D4—448no—
772D4—441no—
773D4—441no—
774D4—441no—
775D4—441no—
776D4—884no—
777D4—884no—
778C2×C4—21no—
779C2×C4—21no—
780C2×C4—21no—
781C2×C4—21no—
782C2×C4—22no—
783C2×C4—22no—
784C2×C4—22no—
785C2×C4—22no—
786C2×C4—22no—
787C2×C4—21no—
788C2×C4—21no—
789C2×C4—21no—
790C2×C4—21no—
791C2×C4—21no—
792C2×C4—21no—
793C2×C4—41no—
794C2×C4—41no—
795C2×C4—41no—
796C2×C4—41no—
797C2×C4—41no—
798C2×C4—41no—
799C2×C4—41no—
800C2×C4—41no—
801C2×C4—41no—
802C2×C4—41no—
803C2×C4—41no—
804C2×C4—41no—
805C2×C4—441no—
806C2×C4—441no—
807C2×C4—441no—
808C2×C4—441no—
809C2×C4—441no—
810C2×C4—441no—
811C2×C4#6699212yes—
812C2×C4#6700212yes—
813C2×C4C2×D4×D1111yescharacteristic
814C2×C4C2×D4×D1111yescharacteristic
815C2×C4C2×#434111yescharacteristic
816C2×C4#6703711yescharacteristic
817C2×C4#41×D1111yescharacteristic
818C2×C4#6704211yescharacteristic
819C8—222no—
820C8—222no—
821C8—222no—
822C8—441no—
823C22—22no—
824C22—22no—
825C22—22no—
826C22—41no—
827C22—41no—
828C22—41no—
829C22—41no—
830C22—41no—
831C22—41no—
832C22—41no—
833C22—41no—
834C22—41no—
835C22—41no—
836C22—41no—
837C22—81no—
838C22—81no—
839C22—81no—
840C22—81no—
841C22—81no—
842C22—81no—
843C22—81no—
844C22—442no—
845C22—442no—
846C22—442no—
847C22—442no—
848C22—442no—
849C22—442no—
850C22—8816no—
851C22—881no—
852C22—881no—
853C22—881no—
854C22—881no—
855C22—881no—
856C22—881no—
857C22—881no—
858C22—881no—
859C22D4×C22⋊D1111yescharacteristic
860C22C2×#6699211yescharacteristic
861C22C2×#6700211yescharacteristic
862C22#1062335311yescharacteristic
863C22#1062336011yescharacteristic
864C22#1062336611yescharacteristic
865C22#1062336611yescharacteristic
866C4—22no—
867C4—22no—
868C4—41no—
869C4—42no—
870C4—41no—
871C4—81no—
872C4—81no—
873C4—881no—
874C4—881no—
875C4#1062313711yescharacteristic
876C4#1062314011yescharacteristic
877C4#1062314111yescharacteristic
878C4#1062314811yescharacteristic
879C2—42no—
880C2—81no—
881C2—161no—
882C2—882no—
883C2—882no—
884C2#1307215811yescharacteristic
885C2#1307823711yescharacteristic
886C2#1307826111yescharacteristic
887C2#1308022311yescharacteristic
888C2#1308023611yescharacteristic
889C2#1308081111yescharacteristic
890C2#1308085211yescharacteristic
subgroupG/H
centerC23C22×C22⋊D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#2414C2
socleC23×C11C22×D4
hypercenter#2414D11
hypocenterC11#25132
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ #2414

Complements

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

NH ≅ G/Ntype
1. C2×#10622652C2semidirect
2. C2×#10622649C2semidirect
3. C2×#10622625C2semidirect
4. C2×#10622614C2semidirect
5. #13071972C2semidirect
6. #13069987C2semidirect
7. #13069926C2semidirect
8. #13069798C2semidirect
9. #13069612C2semidirect
10. #13069481C2semidirect
11. #13069298C2semidirect
12. #13069055C2semidirect
13. #13069052C2semidirect
14. #13068815C2semidirect
15. C11×#2414C2semidirect
18. 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×#66871C22semidirect
57. C2×C4⋊(C11⋊C8)C22semidirect
58. C2×C4×C11⋊C8C22semidirect
59. #10622167C22semidirect
60. #10622167C22semidirect
61. #10622167C22semidirect
62. #10622167C22semidirect
140. C22⋊(C11⋊C8)D4semidirect
146. #66873D4semidirect
276. #2414D11semidirect
401. C2×#121C2×D11semidirect
430. #390C2×D11semidirect
431. #389C2×D11semidirect
434. #380C2×D11semidirect
716. C11#25132semidirect

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×#106226252
C2×#106226142
#130719722
#130699872
#130699262
#130697982
#130696122
#130694812
#130692982
#130690552
#130690522
#130688152
C11×#24142
#2513211