Finite Group Databasebeta

← #14774088

Subgroups — #14774088

Order 2816.

1386 conjugacy classes of subgroups.

The subgroup lattice has 836 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622386C211yesmaximal, characteristic
2C2×#10622627C211yesmaximal, characteristic, complemented
3C2×D11×#102C211yesmaximal, characteristic, complemented
4#13071631C211yesmaximal, characteristic, complemented
5D4×(C2×D11)⋊C4C211yesmaximal, characteristic, complemented
6#13069490C211yesmaximal, characteristic, complemented
7#13069312C211yesmaximal, characteristic, complemented
8#13069241C211yesmaximal, characteristic, complemented
9#13069043C211yesmaximal, characteristic, complemented
10#13068963C211yesmaximal, characteristic, complemented
11#13068962C211yesmaximal, characteristic, complemented
12#13068807C211yesmaximal, characteristic, complemented
13#13068443C211yesmaximal, characteristic, complemented
14#13068391C211yesmaximal, characteristic, complemented
15C11×#1864C211yesmaximal, characteristic, complemented
16C22×D4×D11C2211yescharacteristic
17C2×C4×D4×C11C2211yescharacteristic
18C2×D4×Dic11C2211yescharacteristic
19C22×#4323C2211yescharacteristic
20C22×(C2×D11)⋊C4—21no—
21C22×D88C2211yescharacteristic
22C22×C8×D11C2211yescharacteristic
23C2×#66948C2211yescharacteristic
24C2×#66946—21no—
25C2×C4⋊C4×D11C2211yescharacteristic
26C2×C4×D44C2211yescharacteristic, complemented
27C2×C11×#106C2211yescharacteristic, complemented
28C2×C11×#102C2211yescharacteristic
29C2×C11×#102C2211yescharacteristic
30C11×#389C2211yescharacteristic, complemented
31C2×#66896C2211yescharacteristic
32#10622826—21no—
33C2×#66885C2211yescharacteristic
34C2×#66885C2211yescharacteristic, complemented
35C2×(C2×D11)⋊C8C2211yescharacteristic
36C2×#66879C2211yescharacteristic, complemented
37#10622627—24no—
38#10622602—21no—
39#10622601C2211yescharacteristic
40#10622601C2211yescharacteristic, complemented
41#10622600C2211yescharacteristic
42C4⋊C4×Dic11C2211yescharacteristic, complemented
43C2×#66873C2211yescharacteristic
44C2×#66873C2211yescharacteristic
45C2×#66873C2211yescharacteristic, complemented
46C2×#66872C2211yescharacteristic, complemented
47#10622571—21no—
48#10622568—21no—
49#10622552C2211yescharacteristic
50C4×(C2×D11)⋊C4C2211yescharacteristic
51C2×#66867C2211yescharacteristic, complemented
52#10622386C418yescomplemented
53D11×#102—24no—
54#10622282—21no—
55#10622278—21no—
56C11×#340C2211yescharacteristic, complemented
57C11×#336C2211yescharacteristic, complemented
58#10622189C2211yescharacteristic, complemented
59#10622188C2211yescharacteristic, complemented
60#10622167C2211yescharacteristic, complemented
61#10622167C2211yescharacteristic, complemented
62C24×D11—21no—
63C22×D4×C11C2311yescharacteristic
64C23×C4×C11—21no—
65C22×C22⋊D11—21no—
66C23×Dic11—21no—
67C2×D4×D11—22no—
68C2×D4×D11—22no—
69C2×D4×D11—22no—
70C2×D4×D11—41no—
71C2×D4×D11—41no—
72C2×D4×D11C2×C414yescomplemented
73C22×D44—21no—
74C22×D44C2311yescharacteristic
75C22×D44C2311yescharacteristic
76C22×C4×D11—21no—
77C22×C4×D11—21no—
78C22×C4×D11C2311yescharacteristic
79C22×C8×C11C2311yescharacteristic
80C22×C8×C11C2311yescharacteristic
81C4×D4×C11—22no—
82C4×D4×C11—41no—
83C2×C11×C4⋊C4—21no—
84C2×C11×C4⋊C4C2311yescharacteristic
85C2×C11×C4⋊C4C2311yescharacteristic
86C2×C11×C4⋊C4C2311yescharacteristic
87C2×C11×C22⋊C4—21no—
88C2×C42×C11C2311yescharacteristic
89C2×C22⋊Dic11—21no—
90D4×Dic11—22no—
91D4×Dic11—41no—
92C2×#4323—22no—
93C2×#4323—22no—
94C2×#4323C2×C414yescomplemented
95C2×(C2×D11)⋊C4—21no—
96C2×(C2×D11)⋊C4—21no—
97C2×(C2×D11)⋊C4—21no—
98C2×(C2×D11)⋊C4—21no—
99C2×(C2×D11)⋊C4—21no—
100C2×(C2×D11)⋊C4—21no—
101C2×(C2×D11)⋊C4—21no—
102C2×(C2×D11)⋊C4—21no—
103C2×(C2×D11)⋊C4—21no—
104C2×(C2×D11)⋊C4—44no—
105C2×(C2×D11)⋊C4D411yescharacteristic
106C2×(C2×D11)⋊C4D411yescharacteristic
107C2×C4⋊Dic11C2311yescharacteristic
108C2×C4⋊Dic11C2311yescharacteristic
109C2×Dic11⋊C4—21no—
110C2×C4×Dic11—21no—
111C2×C4×Dic11C2311yescharacteristic
112C22×C11⋊C8C2311yescharacteristic
113C22×C11⋊C8C2311yescharacteristic
114C2×D88—41no—
115C2×D88—41no—
116C2×D88C2×C414yescomplemented
117C2×C8×D11—22no—
118C2×C8×D11—22no—
119C2×C8×D11—41no—
120#66948—22no—
121#66948C2×C414yescomplemented
122#66946—44no—
123C4⋊C4×D11—22no—
124C4⋊C4×D11—41no—
125C4×D44—22no—
126C4×D44—41no—
127C11×#106—41no—
128C11×#102—22no—
129C11×#102C2×C414yescomplemented
130C11×#95—21no—
131#66896D414yescomplemented
132C11⋊#95—21no—
133C11⋊#95—21no—
134C11⋊#95D411yescharacteristic
135C11⋊#95D411yescharacteristic
136#66885—22no—
137#66885—41no—
138(C2×D11)⋊C8C2×C414yescomplemented
139#66879—41no—
140#66873—22no—
141#66873—22no—
142#66873C2×C414yescomplemented
143#66872—22no—
144#66867—22no—
145#22858—111nomaximal, Sylow
146C24×C11—21no—
147C23×D11—21no—
148C23×D11—21no—
149C23×D11—24no—
150C23×D11—42no—
151C23×D11—42no—
152C23×D11—42no—
153C23×D11—42no—
154C23×D11—81no—
155C23×D11—81no—
156C23×D11C2×D411yescharacteristic
157C2×D4×C11—21no—
158C2×D4×C11—21no—
159C2×D4×C11—21no—
160C2×D4×C11C22×C412yes—
161C2×D4×C11C2×D412yes—
162C2×D4×C11#4112yes—
163C22×C4×C11—21no—
164C22×C4×C11—21no—
165C22×C4×C11—21no—
166C22×C4×C11—42no—
167C22×C4×C11—42no—
168C22×C4×C11—81no—
169C22×C4×C11C2×D411yescharacteristic
170C22×C4×C11C2×D411yescharacteristic
171C22×C4×C11C2411yescharacteristic
172C2×C22⋊D11—24no—
173C2×C22⋊D11—42no—
174C2×C22⋊D11—42no—
175C22×Dic11—21no—
176C22×Dic11—21no—
177C22×Dic11—42no—
178C22×Dic11—42no—
179C22×Dic11—81no—
180C22×Dic11C2×D411yescharacteristic
181C22×Dic11C2×D411yescharacteristic
182C22×Dic11C2×D411yescharacteristic
183D4×D11—28no—
184D4×D11—44no—
185D4×D11—44no—
186D4×D11—44no—
187C2×D44—24no—
188C2×D44—21no—
189C2×D44—21no—
190C2×D44—21no—
191C2×D44—21no—
192C2×D44—21no—
193C2×D44—21no—
194C2×D44—21no—
195C2×D44—21no—
196C2×D44—21no—
197C2×D44—21no—
198C2×D44—42no—
199C2×D44—42no—
200C2×D44C22×C412yes—
201C2×D44C22×C412yes—
202C2×C4×D11—21no—
203C2×C4×D11—21no—
204C2×C4×D11—21no—
205C2×C4×D11—21no—
206C2×C4×D11—42no—
207C2×C4×D11—42no—
208C2×C4×D11—42no—
209C2×C4×D11—42no—
210C2×C4×D11—81no—
211C2×C4×D11—81no—
212C2×C4×D11C22×C412yes—
213C2×C4×D11#4112yes—
214C2×C8×C11—21no—
215C2×C8×C11—21no—
216C2×C8×C11—21no—
217C2×C8×C11—21no—
218C2×C8×C11—21no—
219C2×C8×C11C22×C412yes—
220C11×C4⋊C4—21no—
221C11×C4⋊C4—21no—
222C11×C4⋊C4—21no—
223C11×C4⋊C4—21no—
224C11×C4⋊C4—21no—
225C11×C4⋊C4—42no—
226C11×C4⋊C4C22×C412yes—
227C11×C22⋊C4—42no—
228C42×C11—21no—
229C42×C11—21no—
230C22⋊Dic11—42no—
231#4323—28no—
232(C2×D11)⋊C4—24no—
233(C2×D11)⋊C4—22no—
234(C2×D11)⋊C4—22no—
235(C2×D11)⋊C4—42no—
236(C2×D11)⋊C4—42no—
237(C2×D11)⋊C4—42no—
238(C2×D11)⋊C4—42no—
239(C2×D11)⋊C4—42no—
240(C2×D11)⋊C4—81no—
241(C2×D11)⋊C4—81no—
242(C2×D11)⋊C4—81no—
243C4⋊Dic11—21no—
244C4⋊Dic11—21no—
245C4⋊Dic11—21no—
246C4⋊Dic11C2×D412yes—
247Dic11⋊C4—42no—
248C4×Dic11—21no—
249C4×Dic11—21no—
250C4×Dic11—42no—
251C2×C11⋊C8—21no—
252C2×C11⋊C8—21no—
253C2×C11⋊C8—21no—
254C2×C11⋊C8—21no—
255C2×C11⋊C8C22×C412yes—
256C2×C11⋊C8C2×D412yes—
257D88—44no—
258C8×D11—44no—
259C2×#447—111no—
260C2×#442—111no—
261C22×#102—111no—
262#2361—111no—
263D4×C22⋊C4—111no—
264#1972—111no—
265#1936—111no—
266#1926—111no—
267#1893—111no—
268#1879—111no—
269#1879—111no—
270#1864D1111yescharacteristic, complemented
271#1853—111no—
272#1762—111no—
273#1752—111no—
274C23×C11—22no—
275C23×C11—22no—
276C23×C11—22no—
277C23×C11—41no—
278C23×C11—41no—
279C23×C11—41no—
280C23×C11—41no—
281C23×C11C22×D411yescharacteristic
282C22×D11—21no—
283C22×D11—21no—
284C22×D11—21no—
285C22×D11—21no—
286C22×D11—22no—
287C22×D11—22no—
288C22×D11—48no—
289C22×D11—41no—
290C22×D11—41no—
291C22×D11—41no—
292C22×D11—41no—
293C22×D11—41no—
294C22×D11—41no—
295C22×D11—41no—
296C22×D11—41no—
297C22×D11—41no—
298C22×D11—41no—
299C22×D11—41no—
300C22×D11—41no—
301C22×D11—48no—
302C22×D11—84no—
303C22×D11—84no—
304C22×D11—84no—
305C22×D11—84no—
306C22×D11—84no—
307C22×D11C4×D412yes—
308C22×D11AGL(1,ℤ/8)12yes—
309C22×D11AGL(1,ℤ/8)12yes—
310D4×C11—22no—
311D4×C11—22no—
312D4×C11—22no—
313D4×C11C4×D414yescomplemented
314C2×C4×C11—22no—
315C2×C4×C11—21no—
316C2×C4×C11—21no—
317C2×C4×C11—21no—
318C2×C4×C11—21no—
319C2×C4×C11—21no—
320C2×C4×C11—21no—
321C2×C4×C11—41no—
322C2×C4×C11—41no—
323C2×C4×C11—41no—
324C2×C4×C11—41no—
325C2×C4×C11—41no—
326C2×C4×C11—41no—
327C2×C4×C11—41no—
328C2×C4×C11—41no—
329C2×C4×C11—84no—
330C2×C4×C11C23×C411yescharacteristic
331C2×C4×C11C22×D411yescharacteristic
332C2×C4×C11C2×#4111yescharacteristic
333C2×C4×C11C2×#4111yescharacteristic
334C2×C4×C11H(5,𝔽2)11yescharacteristic
335C2×C4×C11H(5,𝔽2)11yescharacteristic
336C22⋊D11—48no—
337C2×Dic11—21no—
338C2×Dic11—21no—
339C2×Dic11—22no—
340C2×Dic11—21no—
341C2×Dic11—21no—
342C2×Dic11—21no—
343C2×Dic11—21no—
344C2×Dic11—21no—
345C2×Dic11—21no—
346C2×Dic11—41no—
347C2×Dic11—41no—
348C2×Dic11—41no—
349C2×Dic11—41no—
350C2×Dic11—41no—
351C2×Dic11—84no—
352C2×Dic11C4×D412yes—
353D44—22no—
354D44—22no—
355D44—22no—
356D44—22no—
357D44—48no—
358D44—41no—
359D44—41no—
360D44—41no—
361D44—41no—
362C4×D11—22no—
363C4×D11—22no—
364C4×D11—22no—
365C4×D11—22no—
366C4×D11—84no—
367C4×D11—84no—
368C8×C11—22no—
369C8×C11—41no—
370C11⋊C8—22no—
371C11⋊C8—22no—
372C23×D4—111no—
373C22×D8—111no—
374C22×D8—111no—
375C23×C8—111no—
376C2×#121—111no—
377C2×C4×D4—111no—
378C2×C4×D4—111no—
379C2×C4×D4—221no—
380C2×C4×D4C2×D1111yescharacteristic
381C22×C4⋊C4—111no—
382C22×C22⋊C4—221no—
383#447—118no—
384#442—224no—
385C2×#106—111no—
386C2×#106C2×D1111yescharacteristic, complemented
387C2×#102—111no—
388C2×#102—111no—
389C2×#102—111no—
390C2×#102—111no—
391C2×#102—111no—
392C2×#102—111no—
393C2×#102—224no—
394C2×#102C2×D1111yescharacteristic
395C2×#102C2×D1111yescharacteristic
396C2×C22⋊C8—111no—
397C2×#97—111no—
398C2×#97—111no—
399#390—111no—
400#390—111no—
401#390—111no—
402#389C2×D1111yescharacteristic, complemented
403#388—221no—
404#386—221no—
405#386—221no—
406#386—221no—
407#385—221no—
408#380—111no—
409#379—221no—
410C4×C4⋊C4—111no—
411C4×C22⋊C4—111no—
412#340—111no—
413#340—111no—
414#340—111no—
415#340C2×D1111yescharacteristic, complemented
416#336—111no—
417#336C2×D1111yescharacteristic, complemented
418C22×C11—24no—
419C22×C11—42no—
420C22×C11—42no—
421C22×C11—42no—
422C22×C11—42no—
423C22×C11—42no—
424C22×C11—42no—
425C22×C11C2×C4×D411yescharacteristic
426C22×C11D4211yescharacteristic
427C22×C11#54611yescharacteristic
428C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
429C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
430C22×C11#57611yescharacteristic
431C22×C11#57711yescharacteristic
432C2×D11—22no—
433C2×D11—22no—
434C2×D11—22no—
435C2×D11—22no—
436C2×D11—22no—
437C2×D11—22no—
438C2×D11—42no—
439C2×D11—42no—
440C2×D11—42no—
441C2×D11—42no—
442C2×D11—42no—
443C2×D11—42no—
444C2×D11—816no—
445C2×D11—81no—
446C2×D11—81no—
447C2×D11—81no—
448C2×D11—81no—
449C2×D11—81no—
450C2×D11—81no—
451C2×D11—81no—
452C2×D11—81no—
453C2×D11#44214yescomplemented
454C4×C11—42no—
455C4×C11—41no—
456C4×C11—41no—
457C4×C11—81no—
458C4×C11—81no—
459C4×C11C2×C4×D411yescharacteristic
460C4×C11#51811yescharacteristic
461C4×C11#54611yescharacteristic
462C4×C11#55111yescharacteristic
463Dic11—22no—
464Dic11—42no—
465Dic11—41no—
466Dic11—41no—
467Dic11—81no—
468C25—221no—
469C22×D4—114no—
470C22×D4—111no—
471C22×D4—111no—
472C22×D4—221no—
473C22×D4—222no—
474C22×D4—221no—
475C22×D4—222no—
476C22×D4—222no—
477C22×D4—441no—
478C22×D4—441no—
479C22×D4C22×D1111yescharacteristic
480C23×C4—21no—
481C23×C4—111no—
482C23×C4—221no—
483C23×C4—221no—
484C23×C4—221no—
485C2×D8—114no—
486C2×D8—114no—
487C2×D8—222no—
488C2×D8—222no—
489C2×D8—441no—
490C2×D8—441no—
491C22×C8—111no—
492C22×C8—111no—
493C22×C8—222no—
494C22×C8—222no—
495C22×C8—441no—
496C22×C8C22×D1111yescharacteristic
497C22×C8C22×D1111yescharacteristic
498#121—114no—
499#121—222no—
500C4×D4—22no—
501C4×D4—41no—
502C4×D4—222no—
503C4×D4—222no—
504C4×D4—441no—
505C4×D4—441no—
506C4×D4—444no—
507C2×C4⋊C4—21no—
508C2×C4⋊C4—111no—
509C2×C4⋊C4—111no—
510C2×C4⋊C4—222no—
511C2×C4⋊C4—221no—
512C2×C4⋊C4—441no—
513C2×C4⋊C4C22×D1111yescharacteristic
514C2×C4⋊C4C22×D1111yescharacteristic
515C2×C4⋊C4C22×D1111yescharacteristic
516C2×C22⋊C4—21no—
517C2×C22⋊C4—111no—
518C2×C22⋊C4—111no—
519C2×C22⋊C4—221no—
520C2×C22⋊C4—221no—
521C2×C22⋊C4—221no—
522C2×C22⋊C4—221no—
523C2×C22⋊C4—221no—
524C2×C22⋊C4—221no—
525C2×C22⋊C4—221no—
526C2×C22⋊C4—221no—
527C2×C22⋊C4—221no—
528C2×C22⋊C4—221no—
529C2×C22⋊C4—444no—
530C2×C42—111no—
531C2×C42—221no—
532C2×C42C22×D1111yescharacteristic
533#106—41no—
534#106—222no—
535#102—22no—
536#102—114no—
537#102—114no—
538#102—222no—
539#102—222no—
540#102—222no—
541#102—441no—
542#102C4×D1114yescomplemented
543C22⋊C8—114no—
544#97—222no—
545#97—441no—
546#95—21no—
547#95—111no—
548#95—111no—
549#95—221no—
550#95—221no—
551C2×C11—44no—
552C2×C11#235811yescharacteristic
553C2×C11C2×#44211yescharacteristic
554C2×C11#294611yescharacteristic
555C2×C11#326411yescharacteristic
556C2×C11#326511yescharacteristic
557C2×C11#330611yescharacteristic
558C2×C11#331811yescharacteristic
559D11—24no—
560D11—82no—
561D11—82no—
562C24—21no—
563C24—111no—
564C24—224no—
565C24—221no—
566C24—221no—
567C24—442no—
568C24—442no—
569C24—442no—
570C24—442no—
571C24—881no—
572C24—881no—
573C2×D4—21no—
574C2×D4—21no—
575C2×D4—21no—
576C2×D4—112no—
577C2×D4—112no—
578C2×D4—224no—
579C2×D4—224no—
580C2×D4—228no—
581C2×D4—221no—
582C2×D4—221no—
583C2×D4—221no—
584C2×D4—221no—
585C2×D4—221no—
586C2×D4—221no—
587C2×D4—221no—
588C2×D4—221no—
589C2×D4—221no—
590C2×D4—221no—
591C2×D4—442no—
592C2×D4—442no—
593C2×D4—444no—
594C2×D4—444no—
595C2×D4—444no—
596C2×D4—442no—
597C2×D4—442no—
598C2×D4C2×C4×D1112yes—
599C2×D4D4×D1112yes—
600C2×D4#434312yes—
601C22×C4—21no—
602C22×C4—21no—
603C22×C4—21no—
604C22×C4—42no—
605C22×C4—42no—
606C22×C4—81no—
607C22×C4—111no—
608C22×C4—112no—
609C22×C4—112no—
610C22×C4—111no—
611C22×C4—111no—
612C22×C4—221no—
613C22×C4—221no—
614C22×C4—221no—
615C22×C4—221no—
616C22×C4—221no—
617C22×C4—221no—
618C22×C4—442no—
619C22×C4—442no—
620C22×C4—442no—
621C22×C4—442no—
622C22×C4—442no—
623C22×C4—442no—
624C22×C4—881no—
625C22×C4—881no—
626C22×C4—881no—
627C22×C4D4×D1111yescharacteristic
628C22×C4D4×D1111yescharacteristic
629C22×C4C23×D1111yescharacteristic
630D8—228no—
631D8—444no—
632C2×C8—21no—
633C2×C8—21no—
634C2×C8—21no—
635C2×C8—21no—
636C2×C8—21no—
637C2×C8—112no—
638C2×C8—112no—
639C2×C8—221no—
640C2×C8—221no—
641C2×C8—221no—
642C2×C8—221no—
643C2×C8—444no—
644C2×C8C2×C4×D1112yes—
645C4⋊C4—21no—
646C4⋊C4—21no—
647C4⋊C4—21no—
648C4⋊C4—21no—
649C4⋊C4—21no—
650C4⋊C4—42no—
651C4⋊C4—112no—
652C4⋊C4—221no—
653C4⋊C4—221no—
654C4⋊C4—221no—
655C4⋊C4—442no—
656C4⋊C4C2×C4×D1112yes—
657C22⋊C4—42no—
658C22⋊C4—224no—
659C22⋊C4—222no—
660C22⋊C4—222no—
661C22⋊C4—442no—
662C22⋊C4—442no—
663C22⋊C4—442no—
664C22⋊C4—442no—
665C22⋊C4—442no—
666C22⋊C4—442no—
667C22⋊C4—881no—
668C22⋊C4—881no—
669C22⋊C4—881no—
670C42—21no—
671C42—21no—
672C42—221no—
673C42—221no—
674C42—442no—
675C11#2285811yescharacteristic, complemented, Sylow
676C23—22no—
677C23—22no—
678C23—22no—
679C23—41no—
680C23—41no—
681C23—41no—
682C23—41no—
683C23—112no—
684C23—112no—
685C23—112no—
686C23—221no—
687C23—221no—
688C23—221no—
689C23—221no—
690C23—222no—
691C23—222no—
692C23—448no—
693C23—448no—
694C23—441no—
695C23—441no—
696C23—441no—
697C23—441no—
698C23—441no—
699C23—441no—
700C23—441no—
701C23—441no—
702C23—441no—
703C23—441no—
704C23—441no—
705C23—441no—
706C23—884no—
707C23—884no—
708C23—884no—
709C23—884no—
710C23—884no—
711C23C2×D4×D1111yescharacteristic
712D4—22no—
713D4—22no—
714D4—22no—
715D4—222no—
716D4—222no—
717D4—222no—
718D4—222no—
719D4—448no—
720D4—448no—
721D4—441no—
722D4—441no—
723D4—441no—
724D4—441no—
725D4#6694614yescomplemented
726C2×C4—21no—
727C2×C4—21no—
728C2×C4—21no—
729C2×C4—21no—
730C2×C4—22no—
731C2×C4—21no—
732C2×C4—21no—
733C2×C4—41no—
734C2×C4—41no—
735C2×C4—41no—
736C2×C4—41no—
737C2×C4—41no—
738C2×C4—41no—
739C2×C4—41no—
740C2×C4—41no—
741C2×C4—84no—
742C2×C4—112no—
743C2×C4—221no—
744C2×C4—221no—
745C2×C4—222no—
746C2×C4—222no—
747C2×C4—222no—
748C2×C4—222no—
749C2×C4—221no—
750C2×C4—221no—
751C2×C4—221no—
752C2×C4—221no—
753C2×C4—222no—
754C2×C4—221no—
755C2×C4—221no—
756C2×C4—441no—
757C2×C4—441no—
758C2×C4—441no—
759C2×C4—441no—
760C2×C4—441no—
761C2×C4—884no—
762C2×C4—884no—
763C2×C4—884no—
764C2×C4C22×C4×D1111yescharacteristic
765C2×C4C2×D4×D1111yescharacteristic
766C2×C4#6703711yescharacteristic
767C2×C4C2×#434311yescharacteristic
768C2×C4#41×D1111yescharacteristic
769C2×C4#6704211yescharacteristic
770C8—22no—
771C8—41no—
772C8—222no—
773C8—222no—
774C22—24no—
775C22—42no—
776C22—42no—
777C22—42no—
778C22—42no—
779C22—42no—
780C22—42no—
781C22—114no—
782C22—222no—
783C22—222no—
784C22—222no—
785C22—222no—
786C22—222no—
787C22—222no—
788C22—442no—
789C22—442no—
790C22—442no—
791C22—442no—
792C22—442no—
793C22—442no—
794C22—8816no—
795C22—881no—
796C22—881no—
797C22—881no—
798C22—881no—
799C22—881no—
800C22—881no—
801C22—881no—
802C22—881no—
803C22C4×D4×D1111yescharacteristic
804C22#1062312111yescharacteristic
805C22#1062316111yescharacteristic
806C22#1062329311yescharacteristic
807C22#1062330011yescharacteristic
808C22D11×AGL(1,ℤ/8)11yescharacteristic
809C22D11×AGL(1,ℤ/8)11yescharacteristic
810C4—41no—
811C4—41no—
812C4—42no—
813C4—81no—
814C4—81no—
815C4—222no—
816C4—442no—
817C4—441no—
818C4—441no—
819C4—881no—
820C4C2×#6694611yescharacteristic
821C4#1062307611yescharacteristic
822C4#1062316811yescharacteristic
823C4#1062318511yescharacteristic
824C2—44no—
825C2—224no—
826C2—882no—
827C2—882no—
828C2#1307159211yescharacteristic
829C2D11×#44211yescharacteristic
830C2#1307744311yescharacteristic
831C2#1308009911yescharacteristic
832C2#1308010911yescharacteristic
833C2#1308057411yescharacteristic
834C2#1308075411yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#1864C2
socleC23×C11C22×D4
prime radicalC2×#10622386C2
cosocleC22×C4×C11C24
hypercenter#1864D11
hypocenterC11#22858
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1864

Complements

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

NH ≅ G/Ntype
2. C2×#10622627C2semidirect
3. C2×D11×#102C2semidirect
4. #13071631C2semidirect
5. D4×(C2×D11)⋊C4C2semidirect
6. #13069490C2semidirect
7. #13069312C2semidirect
8. #13069241C2semidirect
9. #13069043C2semidirect
10. #13068963C2semidirect
11. #13068962C2semidirect
12. #13068807C2semidirect
13. #13068443C2semidirect
14. #13068391C2semidirect
15. C11×#1864C2semidirect
26. C2×C4×D44C22semidirect
27. C2×C11×#106C22semidirect
30. C11×#389C22semidirect
34. C2×#66885C22semidirect
36. C2×#66879C22semidirect
40. #10622601C22semidirect
42. C4⋊C4×Dic11C22semidirect
45. C2×#66873C22semidirect
46. C2×#66872C22semidirect
51. C2×#66867C22semidirect
52. #10622386C4semidirect
56. C11×#340C22semidirect
57. C11×#336C22semidirect
58. #10622189C22semidirect
59. #10622188C22semidirect
60. #10622167C22semidirect
61. #10622167C22semidirect
72. C2×D4×D11C2×C4semidirect
94. C2×#4323C2×C4semidirect
116. C2×D88C2×C4semidirect
121. #66948C2×C4semidirect
129. C11×#102C2×C4semidirect
131. #66896D4semidirect
138. (C2×D11)⋊C8C2×C4semidirect
142. #66873C2×C4semidirect
270. #1864D11semidirect
313. D4×C11C4×D4semidirect
386. C2×#106C2×D11semidirect
402. #389C2×D11semidirect
415. #340C2×D11semidirect
417. #336C2×D11semidirect
453. C2×D11#442semidirect
542. #102C4×D11semidirect
675. C11#22858semidirect
725. D4#66946semidirect

Maximal subgroups

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

subgroupindex
C2×#106223862
C2×#106226272
C2×D11×#1022
#130716312
D4×(C2×D11)⋊C42
#130694902
#130693122
#130692412
#130690432
#130689632
#130689622
#130688072
#130684432
#130683912
C11×#18642
#2285811