Finite Group Databasebeta

← #14774089

Subgroups — #14774089

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×#10622769C211yesmaximal, characteristic
2C2×#10622398C211yesmaximal, characteristic, complemented
3C2×D11×#102C211yesmaximal, characteristic, complemented
4#13071637C211yesmaximal, characteristic, complemented
5#13071437C211yesmaximal, characteristic, complemented
6#13069310C211yesmaximal, characteristic, complemented
7#13069240C211yesmaximal, characteristic, complemented
8#13069041C211yesmaximal, characteristic, complemented
9#13068967C211yesmaximal, characteristic, complemented
10#13068966C211yesmaximal, characteristic, complemented
11#13068874C211yesmaximal, characteristic, complemented
12#13068807C211yesmaximal, characteristic, complemented
13#13068442C211yesmaximal, characteristic, complemented
14#13068393C211yesmaximal, characteristic, complemented
15C11×#1972C211yesmaximal, characteristic, complemented
16C22×D4×D11C2211yescharacteristic
17C22×C11×D8C2211yescharacteristic
18C2×#66991C2211yescharacteristic
19C2×D4×Dic11C2211yescharacteristic, complemented
20C22×#4323C2211yescharacteristic
21C22×C8×D11C2211yescharacteristic
22C2×#66946C2211yescharacteristic
23C2×C4⋊C4×D11C2211yescharacteristic
24C2×(C22⋊D11)⋊C4—21no—
25C2×C22⋊C4×D11—21no—
26C2×C4×D44C2211yescharacteristic
27C2×C11×#106C2211yescharacteristic, complemented
28C2×C11×#102C2211yescharacteristic
29C2×C11×#102C2211yescharacteristic, complemented
30C2×C11×#97C2211yescharacteristic, complemented
31C11×#390C2211yescharacteristic
32C11×#390C2211yescharacteristic, complemented
33#10622834C2211yescharacteristic
34C2×#66896C2211yescharacteristic
35C2×#66896C2211yescharacteristic
36C2×#66896C2211yescharacteristic, complemented
37#10622769C418yescomplemented
38C2×#66885C2211yescharacteristic
39C2×#66885C2211yescharacteristic
40C2×(C2×D11)⋊C8C2211yescharacteristic
41C2×#66879C2211yescharacteristic, complemented
42#10622600C2211yescharacteristic
43#10622586C2211yescharacteristic, complemented
44C2×#66873C2211yescharacteristic
45C2×#66872C2211yescharacteristic, complemented
46#10622569—21no—
47#10622569—21no—
48#10622569—21no—
49#10622568—21no—
50#10622559—21no—
51#10622557—21no—
52C4×(C2×D11)⋊C4C2211yescharacteristic
53C4×C4⋊Dic11C2211yescharacteristic, complemented
54#10622398—24no—
55D11×#102—24no—
56#10622189C2211yescharacteristic, complemented
57#10622189C2211yescharacteristic, complemented
58#10622188C2211yescharacteristic, complemented
59#10622167C2211yescharacteristic, complemented
60#10622167C2211yescharacteristic, complemented
61#10622162C2211yescharacteristic, complemented
62C24×D11—21no—
63C22×D4×C11C2311yescharacteristic
64C22×D4×C11C2311yescharacteristic
65C22×C22⋊D11—21no—
66C22×C22⋊D11—21no—
67C23×Dic11—21no—
68C2×D4×D11—22no—
69C2×D4×D11—22no—
70C2×D4×D11—22no—
71C2×D4×D11—41no—
72C2×D4×D11—41no—
73C2×D4×D11C2×C414yescomplemented
74C22×D44C2311yescharacteristic
75C22×C4×D11—21no—
76C22×C4×D11—21no—
77C22×C4×D11—21no—
78C22×C4×D11C2311yescharacteristic
79C2×C11×D8—41no—
80C2×C11×D8—41no—
81C2×C11×D8C2×C414yescomplemented
82C22×C8×C11C2311yescharacteristic
83C22×C8×C11C2311yescharacteristic
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×C42×C11C2311yescharacteristic
91C2×C22⋊Dic11—21no—
92C2×C22⋊Dic11—21no—
93C2×C22⋊Dic11—21no—
94C2×C22⋊Dic11—21no—
95#66991—22no—
96#66991C2×C414yescomplemented
97D4×Dic11—22no—
98D4×Dic11—41no—
99C2×#4323—22no—
100C2×#4323—22no—
101C2×#4323C2×C414yescomplemented
102C2×(C2×D11)⋊C4—21no—
103C2×(C2×D11)⋊C4—21no—
104C2×(C2×D11)⋊C4—21no—
105C2×(C2×D11)⋊C4D411yescharacteristic
106C2×(C2×D11)⋊C4D411yescharacteristic
107C2×C4⋊Dic11C2311yescharacteristic
108C2×C4⋊Dic11C2311yescharacteristic
109C2×C4⋊Dic11C2311yescharacteristic
110C2×Dic11⋊C4—21no—
111C2×Dic11⋊C4—21no—
112C2×C4×Dic11—21no—
113C2×C4×Dic11C2311yescharacteristic
114C22×C11⋊C8C2311yescharacteristic
115C22×C11⋊C8C2311yescharacteristic
116C2×C8×D11—22no—
117C2×C8×D11—22no—
118C2×C8×D11—41no—
119#66946—22no—
120#66946—41no—
121C4⋊C4×D11—22no—
122C4⋊C4×D11—41no—
123(C22⋊D11)⋊C4—44no—
124C22⋊C4×D11—44no—
125C4×D44—22no—
126C4×D44—41no—
127C11×#106—41no—
128C11×#102—22no—
129C11×#102—22no—
130C11×#97—41no—
131#66896—22no—
132#66896—41no—
133#66896C2×C414yescomplemented
134C11⋊#95—21no—
135C11⋊#95—21no—
136C11⋊#95—21no—
137C11⋊#95D411yescharacteristic
138C11⋊#95D411yescharacteristic
139#66885C2×C414yescomplemented
140#66885D414yescomplemented
141(C2×D11)⋊C8C2×C414yescomplemented
142#66879—22no—
143#66873—22no—
144#66872—22no—
145#22858—111nomaximal, Sylow
146C24×C11—21no—
147C24×C11—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×C11—21no—
161C2×D4×C11—21no—
162C2×D4×C11—21no—
163C2×D4×C11—21no—
164C2×D4×C11—21no—
165C2×D4×C11—21no—
166C2×D4×C11—21no—
167C2×D4×C11C22×C412yes—
168C2×D4×C11C22×C412yes—
169C22×C4×C11—21no—
170C22×C4×C11—21no—
171C22×C4×C11C2×D411yescharacteristic
172C22×C4×C11C2×D411yescharacteristic
173C22×C4×C11C2411yescharacteristic
174C2×C22⋊D11—24no—
175C2×C22⋊D11—24no—
176C2×C22⋊D11—42no—
177C2×C22⋊D11—42no—
178C2×C22⋊D11—42no—
179C2×C22⋊D11—42no—
180C22×Dic11—21no—
181C22×Dic11—21no—
182C22×Dic11—21no—
183C22×Dic11—42no—
184C22×Dic11—42no—
185C22×Dic11—81no—
186C22×Dic11C2×D411yescharacteristic
187C22×Dic11C2×D411yescharacteristic
188C22×Dic11C2×D411yescharacteristic
189D4×D11—28no—
190D4×D11—44no—
191D4×D11—44no—
192D4×D11—44no—
193C2×D44—21no—
194C2×D44—21no—
195C2×D44—21no—
196C2×D44C22×C412yes—
197C2×D44C2×D412yes—
198C2×D44#4112yes—
199C2×C4×D11—21no—
200C2×C4×D11—21no—
201C2×C4×D11—21no—
202C2×C4×D11—21no—
203C2×C4×D11—42no—
204C2×C4×D11—42no—
205C2×C4×D11—42no—
206C2×C4×D11—42no—
207C2×C4×D11—42no—
208C2×C4×D11—42no—
209C2×C4×D11—81no—
210C2×C4×D11—81no—
211C2×C4×D11—81no—
212C2×C4×D11C22×C412yes—
213C2×C4×D11#4112yes—
214C11×D8—44no—
215C2×C8×C11—21no—
216C2×C8×C11—21no—
217C2×C8×C11—21no—
218C2×C8×C11—21no—
219C2×C8×C11C22×C412yes—
220C2×C8×C11C2×D412yes—
221C11×C4⋊C4—21no—
222C11×C4⋊C4—21no—
223C11×C4⋊C4—21no—
224C11×C4⋊C4—21no—
225C11×C22⋊C4—42no—
226C11×C22⋊C4—42no—
227C11×C22⋊C4—81no—
228C11×C22⋊C4—81no—
229C42×C11—21no—
230C42×C11—21no—
231C22⋊Dic11—24no—
232C22⋊Dic11—42no—
233C22⋊Dic11—42no—
234C22⋊Dic11—81no—
235#4323—28no—
236(C2×D11)⋊C4—22no—
237(C2×D11)⋊C4—22no—
238(C2×D11)⋊C4—42no—
239(C2×D11)⋊C4—42no—
240(C2×D11)⋊C4—42no—
241C4⋊Dic11—21no—
242C4⋊Dic11—21no—
243C4⋊Dic11—21no—
244C4⋊Dic11—21no—
245C4⋊Dic11C22×C412yes—
246C4⋊Dic11C2×D412yes—
247Dic11⋊C4—42no—
248Dic11⋊C4—42no—
249C4×Dic11—21no—
250C4×Dic11—21no—
251C4×Dic11—42no—
252C2×C11⋊C8—21no—
253C2×C11⋊C8—21no—
254C2×C11⋊C8—21no—
255C2×C11⋊C8—21no—
256C2×C11⋊C8—21no—
257C2×C11⋊C8C22×C412yes—
258C8×D11—44no—
259C2×#447—111no—
260C2×#442—111no—
261C22×#102—111no—
262#2361—111no—
263D4×C22⋊C4—111no—
264#1972D1111yescharacteristic, complemented
265#1936—111no—
266#1926—111no—
267#1893—111no—
268#1879—111no—
269#1879—111no—
270#1864—111no—
271#1853—111no—
272#1762—111no—
273#1752—111no—
274C23×C11—22no—
275C23×C11—22no—
276C23×C11—41no—
277C23×C11—41no—
278C23×C11—41no—
279C23×C11—41no—
280C23×C11—41no—
281C23×C11—41no—
282C23×C11—41no—
283C23×C11—41no—
284C23×C11—41no—
285C23×C11—41no—
286C23×C11—41no—
287C23×C11—41no—
288C23×C11C22×D411yescharacteristic
289C22×D11—21no—
290C22×D11—21no—
291C22×D11—21no—
292C22×D11—21no—
293C22×D11—22no—
294C22×D11—22no—
295C22×D11—22no—
296C22×D11—48no—
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×C11—22no—
314D4×C11—41no—
315D4×C11—41no—
316D4×C11—41no—
317D4×C11—41no—
318C2×C4×C11—21no—
319C2×C4×C11—21no—
320C2×C4×C11—21no—
321C2×C4×C11—21no—
322C2×C4×C11—21no—
323C2×C4×C11—21no—
324C2×C4×C11—41no—
325C2×C4×C11—41no—
326C2×C4×C11—41no—
327C2×C4×C11—41no—
328C2×C4×C11—41no—
329C2×C4×C11—41no—
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—
337C22⋊D11—48no—
338C2×Dic11—21no—
339C2×Dic11—21no—
340C2×Dic11—22no—
341C2×Dic11—21no—
342C2×Dic11—21no—
343C2×Dic11—22no—
344C2×Dic11—21no—
345C2×Dic11—21no—
346C2×Dic11—21no—
347C2×Dic11—21no—
348C2×Dic11—41no—
349C2×Dic11—41no—
350C2×Dic11—41no—
351C2×Dic11—41no—
352C2×Dic11—41no—
353C2×Dic11—41no—
354C2×Dic11—41no—
355C2×Dic11—84no—
356C2×Dic11C4×D412yes—
357D44—22no—
358D44—22no—
359D44—22no—
360D44C4×D414yescomplemented
361C4×D11—22no—
362C4×D11—22no—
363C4×D11—22no—
364C4×D11—22no—
365C4×D11—84no—
366C4×D11—84no—
367C4×D11—84no—
368C8×C11—22no—
369C8×C11—22no—
370C11⋊C8—22no—
371C11⋊C8—41no—
372C23×D4—111no—
373C22×D8—111no—
374C22×D8C2×D1111yescharacteristic
375C23×C8—111no—
376C2×#121—111no—
377C2×C4×D4—111no—
378C2×C4×D4—111no—
379C2×C4×D4—111no—
380C2×C4×D4—221no—
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, complemented
396C2×C22⋊C8—111no—
397C2×#97—111no—
398C2×#97C2×D1111yescharacteristic, complemented
399#390—111no—
400#390C2×D1111yescharacteristic
401#390C2×D1111yescharacteristic, complemented
402#389—111no—
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#340—111no—
416#336—111no—
417#336—111no—
418C22×C11—42no—
419C22×C11—42no—
420C22×C11—42no—
421C22×C11—42no—
422C22×C11—42no—
423C22×C11—42no—
424C22×C11—81no—
425C22×C11—81no—
426C22×C11—81no—
427C22×C11—81no—
428C22×C11—81no—
429C22×C11—81no—
430C22×C11—81no—
431C22×C11—81no—
432C22×C11C2×C4×D411yescharacteristic
433C22×C11D4211yescharacteristic
434C22×C11#54611yescharacteristic
435C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
436C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
437C22×C11#57611yescharacteristic
438C22×C11#57711yescharacteristic
439C2×D11—22no—
440C2×D11—22no—
441C2×D11—22no—
442C2×D11—22no—
443C2×D11—22no—
444C2×D11—22no—
445C2×D11—24no—
446C2×D11—42no—
447C2×D11—42no—
448C2×D11—42no—
449C2×D11—42no—
450C2×D11—42no—
451C2×D11—42no—
452C2×D11—816no—
453C2×D11#44214yescomplemented
454C4×C11—41no—
455C4×C11—41no—
456C4×C11—81no—
457C4×C11—81no—
458C4×C11C2×C4×D411yescharacteristic
459C4×C11#51811yescharacteristic
460C4×C11#54611yescharacteristic
461C4×C11#55111yescharacteristic
462Dic11—22no—
463Dic11—42no—
464Dic11—42no—
465Dic11—41no—
466Dic11—41no—
467Dic11—81no—
468C25—221no—
469C22×D4—114no—
470C22×D4—111no—
471C22×D4—222no—
472C22×D4—221no—
473C22×D4—222no—
474C22×D4—222no—
475C22×D4—221no—
476C22×D4—441no—
477C22×D4—441no—
478C22×D4C22×D1111yescharacteristic
479C22×D4C22×D1111yescharacteristic
480C23×C4—111no—
481C23×C4—221no—
482C23×C4—221no—
483C23×C4—221no—
484C23×C4—221no—
485C2×D8—41no—
486C2×D8—41no—
487C2×D8—114no—
488C2×D8—222no—
489C2×D8—222no—
490C2×D8C4×D1114yescomplemented
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—222no—
501C4×D4—222no—
502C4×D4—222no—
503C4×D4—441no—
504C4×D4—441no—
505C4×D4—441no—
506C4×D4—444no—
507C2×C4⋊C4—111no—
508C2×C4⋊C4—111no—
509C2×C4⋊C4—111no—
510C2×C4⋊C4—222no—
511C2×C4⋊C4—221no—
512C2×C4⋊C4—221no—
513C2×C4⋊C4—441no—
514C2×C4⋊C4C22×D1111yescharacteristic
515C2×C4⋊C4C22×D1111yescharacteristic
516C2×C22⋊C4—21no—
517C2×C22⋊C4—21no—
518C2×C22⋊C4—21no—
519C2×C22⋊C4—21no—
520C2×C22⋊C4—111no—
521C2×C22⋊C4—111no—
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—22no—
537#102—114no—
538#102—114no—
539#102—114no—
540#102—222no—
541#102—222no—
542#102—441no—
543C22⋊C8—114no—
544#97—41no—
545#97—222no—
546#95—111no—
547#95—111no—
548#95—221no—
549#95—221no—
550#95—221no—
551C2×C11—82no—
552C2×C11—82no—
553C2×C11#235811yescharacteristic
554C2×C11C2×#44211yescharacteristic
555C2×C11#294611yescharacteristic
556C2×C11#326411yescharacteristic
557C2×C11#326511yescharacteristic
558C2×C11#330611yescharacteristic
559C2×C11#331811yescharacteristic
560D11—24no—
561D11—44no—
562C24—21no—
563C24—21no—
564C24—111no—
565C24—224no—
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—21no—
577C2×D4—21no—
578C2×D4—21no—
579C2×D4—21no—
580C2×D4—21no—
581C2×D4—21no—
582C2×D4—21no—
583C2×D4—112no—
584C2×D4—112no—
585C2×D4—112no—
586C2×D4—224no—
587C2×D4—228no—
588C2×D4—224no—
589C2×D4—221no—
590C2×D4—221no—
591C2×D4—221no—
592C2×D4—444no—
593C2×D4—444no—
594C2×D4—444no—
595C2×D4—442no—
596C2×D4—442no—
597C2×D4—442no—
598C2×D4—442no—
599C2×D4C2×C4×D1112yes—
600C2×D4C2×C4×D1112yes—
601C22×C4—21no—
602C22×C4—21no—
603C22×C4—111no—
604C22×C4—112no—
605C22×C4—112no—
606C22×C4—111no—
607C22×C4—111no—
608C22×C4—221no—
609C22×C4—221no—
610C22×C4—221no—
611C22×C4—221no—
612C22×C4—221no—
613C22×C4—221no—
614C22×C4—221no—
615C22×C4—442no—
616C22×C4—442no—
617C22×C4—442no—
618C22×C4—442no—
619C22×C4—442no—
620C22×C4—442no—
621C22×C4—442no—
622C22×C4—442no—
623C22×C4—881no—
624C22×C4—881no—
625C22×C4—881no—
626C22×C4—881no—
627C22×C4D4×D1111yescharacteristic
628C22×C4D4×D1111yescharacteristic
629C22×C4C23×D1111yescharacteristic
630D8—44no—
631D8—228no—
632C2×C8—21no—
633C2×C8—21no—
634C2×C8—21no—
635C2×C8—21no—
636C2×C8—112no—
637C2×C8—221no—
638C2×C8—221no—
639C2×C8—221no—
640C2×C8—221no—
641C2×C8—221no—
642C2×C8—444no—
643C2×C8C2×C4×D1112yes—
644C2×C8D4×D1112yes—
645C4⋊C4—21no—
646C4⋊C4—21no—
647C4⋊C4—21no—
648C4⋊C4—21no—
649C4⋊C4—112no—
650C4⋊C4—112no—
651C4⋊C4—221no—
652C4⋊C4—221no—
653C4⋊C4—221no—
654C4⋊C4—221no—
655C4⋊C4—442no—
656C4⋊C4—442no—
657C22⋊C4—42no—
658C22⋊C4—42no—
659C22⋊C4—81no—
660C22⋊C4—81no—
661C22⋊C4—222no—
662C22⋊C4—222no—
663C22⋊C4—224no—
664C22⋊C4—442no—
665C22⋊C4—442no—
666C22⋊C4—442no—
667C22⋊C4—442no—
668C22⋊C4—442no—
669C22⋊C4—881no—
670C42—21no—
671C42—21no—
672C42—221no—
673C42—221no—
674C42—442no—
675C11#2285811yescharacteristic, complemented, Sylow
676C23—22no—
677C23—22no—
678C23—41no—
679C23—41no—
680C23—41no—
681C23—41no—
682C23—41no—
683C23—41no—
684C23—41no—
685C23—41no—
686C23—41no—
687C23—41no—
688C23—41no—
689C23—41no—
690C23—112no—
691C23—112no—
692C23—112no—
693C23—221no—
694C23—221no—
695C23—221no—
696C23—221no—
697C23—222no—
698C23—222no—
699C23—222no—
700C23—448no—
701C23—448no—
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—22no—
716D4—41no—
717D4—41no—
718D4—41no—
719D4—41no—
720D4—114no—
721D4—222no—
722D4—222no—
723D4—222no—
724D4—448no—
725D4—448no—
726C2×C4—21no—
727C2×C4—21no—
728C2×C4—21no—
729C2×C4—21no—
730C2×C4—21no—
731C2×C4—21no—
732C2×C4—41no—
733C2×C4—41no—
734C2×C4—41no—
735C2×C4—41no—
736C2×C4—41no—
737C2×C4—41no—
738C2×C4—112no—
739C2×C4—221no—
740C2×C4—221no—
741C2×C4—222no—
742C2×C4—222no—
743C2×C4—222no—
744C2×C4—222no—
745C2×C4—221no—
746C2×C4—221no—
747C2×C4—222no—
748C2×C4—221no—
749C2×C4—221no—
750C2×C4—221no—
751C2×C4—221no—
752C2×C4—222no—
753C2×C4—441no—
754C2×C4—441no—
755C2×C4—441no—
756C2×C4—441no—
757C2×C4—441no—
758C2×C4—441no—
759C2×C4—441no—
760C2×C4—884no—
761C2×C4—884no—
762C2×C4—884no—
763C2×C4—884no—
764C2×C4C22×C4×D1111yescharacteristic
765C2×C4C2×D4×D1111yescharacteristic
766C2×C4#6703711yescharacteristic
767C2×C4#6703711yescharacteristic
768C2×C4#41×D1111yescharacteristic
769C2×C4#41×D1111yescharacteristic
770C8—22no—
771C8—22no—
772C8—222no—
773C8—441no—
774C22—42no—
775C22—42no—
776C22—42no—
777C22—42no—
778C22—42no—
779C22—42no—
780C22—81no—
781C22—81no—
782C22—81no—
783C22—81no—
784C22—81no—
785C22—81no—
786C22—81no—
787C22—81no—
788C22—114no—
789C22—222no—
790C22—222no—
791C22—222no—
792C22—222no—
793C22—222no—
794C22—222no—
795C22—224no—
796C22—442no—
797C22—442no—
798C22—442no—
799C22—442no—
800C22—442no—
801C22—442no—
802C22—8816no—
803C22C4×D4×D1111yescharacteristic
804C22#1062314111yescharacteristic
805C22#1062324811yescharacteristic
806C22D11×AGL(1,ℤ/8)11yescharacteristic
807C22D11×AGL(1,ℤ/8)11yescharacteristic
808C22#1062330511yescharacteristic
809C22#1062330611yescharacteristic
810C4—41no—
811C4—41no—
812C4—81no—
813C4—81no—
814C4—222no—
815C4—441no—
816C4—442no—
817C4—441no—
818C4—442no—
819C4—881no—
820C4#1062301711yescharacteristic
821C4C4×D4×D1111yescharacteristic
822C4#1062314111yescharacteristic
823C4#1062321011yescharacteristic
824C2—82no—
825C2—82no—
826C2—224no—
827C2—444no—
828C2#1307159711yescharacteristic
829C2D11×#44211yescharacteristic
830C2#1307744511yescharacteristic
831C2#1308009511yescharacteristic
832C2#1308011011yescharacteristic
833C2#1308057211yescharacteristic
834C2#1308075211yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#1972C2
socleC23×C11C22×D4
prime radicalC2×#10622769C2
cosocleC22×C4×C11C24
hypercenter#1972D11
hypocenterC11#22858
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1972

Complements

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

NH ≅ G/Ntype
2. C2×#10622398C2semidirect
3. C2×D11×#102C2semidirect
4. #13071637C2semidirect
5. #13071437C2semidirect
6. #13069310C2semidirect
7. #13069240C2semidirect
8. #13069041C2semidirect
9. #13068967C2semidirect
10. #13068966C2semidirect
11. #13068874C2semidirect
12. #13068807C2semidirect
13. #13068442C2semidirect
14. #13068393C2semidirect
15. C11×#1972C2semidirect
19. C2×D4×Dic11C22semidirect
27. C2×C11×#106C22semidirect
29. C2×C11×#102C22semidirect
30. C2×C11×#97C22semidirect
32. C11×#390C22semidirect
36. C2×#66896C22semidirect
37. #10622769C4semidirect
41. C2×#66879C22semidirect
43. #10622586C22semidirect
45. C2×#66872C22semidirect
53. C4×C4⋊Dic11C22semidirect
56. #10622189C22semidirect
57. #10622189C22semidirect
58. #10622188C22semidirect
59. #10622167C22semidirect
60. #10622167C22semidirect
61. #10622162C22semidirect
73. C2×D4×D11C2×C4semidirect
81. C2×C11×D8C2×C4semidirect
96. #66991C2×C4semidirect
101. C2×#4323C2×C4semidirect
133. #66896C2×C4semidirect
139. #66885C2×C4semidirect
140. #66885D4semidirect
141. (C2×D11)⋊C8C2×C4semidirect
264. #1972D11semidirect
360. D44C4×D4semidirect
386. C2×#106C2×D11semidirect
395. C2×#102C2×D11semidirect
398. C2×#97C2×D11semidirect
401. #390C2×D11semidirect
453. C2×D11#442semidirect
490. C2×D8C4×D11semidirect
675. C11#22858semidirect

Maximal subgroups

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

subgroupindex
C2×#106227692
C2×#106223982
C2×D11×#1022
#130716372
#130714372
#130693102
#130692402
#130690412
#130689672
#130689662
#130688742
#130688072
#130684422
#130683932
C11×#19722
#2285811