Finite Group Databasebeta

← #14774085

Subgroups — #14774085

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×#10622482C211yesmaximal, characteristic, complemented
3C2×D11×#102C211yesmaximal, characteristic, complemented
4#13071634C211yesmaximal, characteristic, complemented
5#13071437C211yesmaximal, characteristic, complemented
6#13069491C211yesmaximal, characteristic, complemented
7#13069315C211yesmaximal, characteristic, complemented
8#13069043C211yesmaximal, characteristic, complemented
9#13068963C211yesmaximal, characteristic, complemented
10#13068961C211yesmaximal, characteristic, complemented
11#13068878C211yesmaximal, characteristic, complemented
12#13068807C211yesmaximal, characteristic, complemented
13#13068444C211yesmaximal, characteristic, complemented
14#13068391C211yesmaximal, characteristic, complemented
15C11×#1926C211yesmaximal, characteristic, complemented
16C22×D4×D11C2211yescharacteristic
17C22×#4323C2211yescharacteristic
18C22×D88C2211yescharacteristic
19C22×C8×D11C2211yescharacteristic
20C2×#66948C2211yescharacteristic
21C2×#66946C2211yescharacteristic
22C2×#66946C2211yescharacteristic, complemented
23C2×C4⋊C4×D11C2211yescharacteristic
24C2×C22⋊C4×D11—21no—
25C2×C4×D44—21no—
26C2×C4×D44C2211yescharacteristic
27C2×C11×#106C2211yescharacteristic, complemented
28C2×C11×#102C2211yescharacteristic
29C2×C11×#102C2211yescharacteristic
30C11×#390C2211yescharacteristic
31C4×C11×C4⋊C4C2211yescharacteristic, complemented
32#10622834C2211yescharacteristic
33C2×#66896C2211yescharacteristic
34C2×#66885C2211yescharacteristic
35C2×#66885C2211yescharacteristic, complemented
36C2×(C2×D11)⋊C8C2211yescharacteristic
37C2×#66879C2211yescharacteristic, complemented
38#10622600C2211yescharacteristic
39#10622598C2211yescharacteristic, complemented
40C2×#66873C2211yescharacteristic
41C2×#66873C2211yescharacteristic
42C2×#66873C2211yescharacteristic, complemented
43C2×#66872C2211yescharacteristic, complemented
44#10622569—21no—
45#10622569—21no—
46#10622568—21no—
47#10622553—21no—
48#10622552C2211yescharacteristic, complemented
49C4×(C2×D11)⋊C4C2211yescharacteristic
50C2×#66867C2211yescharacteristic, complemented
51#10622482—24no—
52#10622386C418yescomplemented
53D11×#102—24no—
54#10622281—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
64C22×C22⋊D11—21no—
65C2×D4×D11—22no—
66C2×D4×D11—22no—
67C2×D4×D11—22no—
68C2×D4×D11—41no—
69C2×D4×D11—41no—
70C2×D4×D11C2×C414yescomplemented
71C22×D44—21no—
72C22×D44C2311yescharacteristic
73C22×D44C2311yescharacteristic
74C22×C4×D11—21no—
75C22×C4×D11—21no—
76C22×C4×D11—21no—
77C22×C4×D11—21no—
78C22×C4×D11C2311yescharacteristic
79C22×C8×C11C2311yescharacteristic
80C22×C8×C11C2311yescharacteristic
81C2×C11×C4⋊C4C2311yescharacteristic
82C2×C11×C4⋊C4C2311yescharacteristic
83C2×C11×C4⋊C4C2311yescharacteristic
84C2×C11×C22⋊C4—21no—
85C2×C11×C22⋊C4—21no—
86C2×C42×C11—21no—
87C2×C42×C11C2311yescharacteristic
88C2×C22⋊Dic11—21no—
89C2×C22⋊Dic11—21no—
90C2×#4323—41no—
91C2×#4323—41no—
92C2×#4323C2×C414yescomplemented
93C2×(C2×D11)⋊C4—21no—
94C2×(C2×D11)⋊C4—21no—
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)⋊C4D411yescharacteristic
101C2×(C2×D11)⋊C4D411yescharacteristic
102C2×C4⋊Dic11—21no—
103C2×C4⋊Dic11C2311yescharacteristic
104C2×C4⋊Dic11C2311yescharacteristic
105C2×Dic11⋊C4—21no—
106C2×C4×Dic11C2311yescharacteristic
107C22×C11⋊C8C2311yescharacteristic
108C22×C11⋊C8C2311yescharacteristic
109C2×D88—22no—
110C2×D88—22no—
111C2×D88C2×C414yescomplemented
112C2×C8×D11—22no—
113C2×C8×D11—22no—
114C2×C8×D11—41no—
115#66948—22no—
116#66948C2×C414yescomplemented
117#66946—22no—
118#66946—22no—
119#66946—41no—
120#66946—41no—
121C4⋊C4×D11—22no—
122C4⋊C4×D11—41no—
123C22⋊C4×D11—44no—
124C4×D44—22no—
125C4×D44—41no—
126C4×D44—44no—
127C11×#106—22no—
128C11×#102—22no—
129C11×#102C2×C414yescomplemented
130C11×#95—21no—
131#66896—22no—
132C11⋊#95—21no—
133C11⋊#95—21no—
134C11⋊#95D411yescharacteristic
135C11⋊#95D411yescharacteristic
136#66885—22no—
137#66885—41no—
138(C2×D11)⋊C8C2×C414yescomplemented
139#66879—22no—
140#66873—22no—
141#66873C2×C414yescomplemented
142#66873D414yescomplemented
143#66872—41no—
144#66867—41no—
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×C11—21no—
161C2×D4×C11—21no—
162C2×D4×C11C22×C412yes—
163C22×C4×C11—21no—
164C22×C4×C11—21no—
165C22×C4×C11—21no—
166C22×C4×C11C2×D411yescharacteristic
167C22×C4×C11C2×D411yescharacteristic
168C22×C4×C11C2411yescharacteristic
169C2×C22⋊D11—24no—
170C2×C22⋊D11—42no—
171C2×C22⋊D11—42no—
172C22×Dic11—21no—
173C22×Dic11—21no—
174C22×Dic11C2×D411yescharacteristic
175C22×Dic11C2×D411yescharacteristic
176C22×Dic11C2×D411yescharacteristic
177D4×D11—28no—
178D4×D11—44no—
179D4×D11—44no—
180D4×D11—44no—
181C2×D44—24no—
182C2×D44—21no—
183C2×D44—21no—
184C2×D44—21no—
185C2×D44—21no—
186C2×D44—21no—
187C2×D44—21no—
188C2×D44—21no—
189C2×D44—21no—
190C2×D44—42no—
191C2×D44—42no—
192C2×D44C22×C412yes—
193C2×D44C22×C412yes—
194C2×D44C2×D412yes—
195C2×D44#4112yes—
196C2×C4×D11—21no—
197C2×C4×D11—21no—
198C2×C4×D11—21no—
199C2×C4×D11—21no—
200C2×C4×D11—42no—
201C2×C4×D11—42no—
202C2×C4×D11—42no—
203C2×C4×D11—42no—
204C2×C4×D11—42no—
205C2×C4×D11—42no—
206C2×C4×D11—42no—
207C2×C4×D11—42no—
208C2×C4×D11—81no—
209C2×C4×D11—81no—
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⋊C4C22×C412yes—
225C11×C4⋊C4C2×D412yes—
226C11×C22⋊C4—42no—
227C11×C22⋊C4—81no—
228C42×C11—21no—
229C42×C11—21no—
230C42×C11—42no—
231C22⋊Dic11—42no—
232C22⋊Dic11—81no—
233#4323—44no—
234(C2×D11)⋊C4—24no—
235(C2×D11)⋊C4—22no—
236(C2×D11)⋊C4—22no—
237(C2×D11)⋊C4—42no—
238(C2×D11)⋊C4—42no—
239(C2×D11)⋊C4—42no—
240(C2×D11)⋊C4—42no—
241(C2×D11)⋊C4—42no—
242(C2×D11)⋊C4—81no—
243C4⋊Dic11—21no—
244C4⋊Dic11—21no—
245C4⋊Dic11—21no—
246C4⋊Dic11—21no—
247C4⋊Dic11—42no—
248Dic11⋊C4—42no—
249C4×Dic11—21no—
250C4×Dic11—21no—
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—28no—
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#1926D1111yescharacteristic, complemented
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—41no—
276C23×C11—41no—
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—22no—
289C22×D11—22no—
290C22×D11—48no—
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—41no—
313D4×C11—41no—
314C2×C4×C11—22no—
315C2×C4×C11—22no—
316C2×C4×C11—21no—
317C2×C4×C11—21no—
318C2×C4×C11—21no—
319C2×C4×C11—21no—
320C2×C4×C11—21no—
321C2×C4×C11—21no—
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×C11C23×C411yescharacteristic
330C2×C4×C11C22×D411yescharacteristic
331C2×C4×C11C2×#4111yescharacteristic
332C2×C4×C11C2×#4111yescharacteristic
333C2×C4×C11H(5,𝔽2)11yescharacteristic
334C2×C4×C11H(5,𝔽2)11yescharacteristic
335C22⋊D11—48no—
336C2×Dic11—21no—
337C2×Dic11—21no—
338C2×Dic11—21no—
339C2×Dic11—21no—
340C2×Dic11—21no—
341C2×Dic11—21no—
342C2×Dic11—21no—
343C2×Dic11—21no—
344C2×Dic11—41no—
345C2×Dic11—41no—
346C2×Dic11—41no—
347C2×Dic11—41no—
348C2×Dic11—41no—
349C2×Dic11—41no—
350C2×Dic11C4×D412yes—
351D44—22no—
352D44—22no—
353D44—22no—
354D44—22no—
355D44—22no—
356D44—48no—
357D44—41no—
358D44—41no—
359D44C4×D414yescomplemented
360C4×D11—22no—
361C4×D11—22no—
362C4×D11—22no—
363C4×D11—22no—
364C4×D11—84no—
365C4×D11—84no—
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—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
396C2×C22⋊C8—111no—
397C2×#97—111no—
398C2×#97—111no—
399#390—111no—
400#390—111no—
401#390C2×D1111yescharacteristic
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⋊C4C2×D1111yescharacteristic, complemented
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—42no—
419C22×C11—42no—
420C22×C11—42no—
421C22×C11—81no—
422C22×C11—81no—
423C22×C11—81no—
424C22×C11—81no—
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—24no—
439C2×D11—42no—
440C2×D11—42no—
441C2×D11—42no—
442C2×D11—42no—
443C2×D11—42no—
444C2×D11—42no—
445C2×D11—42no—
446C2×D11—42no—
447C2×D11—42no—
448C2×D11—816no—
449C2×D11—81no—
450C2×D11—81no—
451C2×D11—81no—
452C2×D11—81no—
453C2×D11#44214yescomplemented
454C4×C11—42no—
455C4×C11—42no—
456C4×C11—41no—
457C4×C11—41no—
458C4×C11—81no—
459C4×C11C2×C4×D411yescharacteristic
460C4×C11#51811yescharacteristic
461C4×C11#54611yescharacteristic
462C4×C11#55111yescharacteristic
463Dic11—22no—
464Dic11—41no—
465Dic11—41no—
466Dic11—81no—
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—111no—
481C23×C4—221no—
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—222no—
501C4×D4—222no—
502C4×D4—222no—
503C4×D4—441no—
504C4×D4—444no—
505C4×D4—441no—
506C4×D4—441no—
507C2×C4⋊C4—111no—
508C2×C4⋊C4—111no—
509C2×C4⋊C4—222no—
510C2×C4⋊C4—221no—
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—21no—
518C2×C22⋊C4—111no—
519C2×C22⋊C4—111no—
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—21no—
531C2×C42—111no—
532C2×C42C22×D1111yescharacteristic
533#106—22no—
534#106—441no—
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—82no—
552C2×C11#235811yescharacteristic
553C2×C11C2×#44211yescharacteristic
554C2×C11#294611yescharacteristic
555C2×C11#326411yescharacteristic
556C2×C11#326511yescharacteristic
557C2×C11#330611yescharacteristic
558C2×C11#331811yescharacteristic
559D11—24no—
560D11—44no—
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—21no—
577C2×D4—21no—
578C2×D4—112no—
579C2×D4—112no—
580C2×D4—112no—
581C2×D4—112no—
582C2×D4—224no—
583C2×D4—224no—
584C2×D4—228no—
585C2×D4—221no—
586C2×D4—221no—
587C2×D4—221no—
588C2×D4—221no—
589C2×D4—221no—
590C2×D4—221no—
591C2×D4—221no—
592C2×D4—221no—
593C2×D4—442no—
594C2×D4—442no—
595C2×D4—444no—
596C2×D4—444no—
597C2×D4—444no—
598C2×D4—442no—
599C2×D4—442no—
600C2×D4C2×C4×D1112yes—
601C22×C4—21no—
602C22×C4—21no—
603C22×C4—21no—
604C22×C4—111no—
605C22×C4—112no—
606C22×C4—112no—
607C22×C4—111no—
608C22×C4—111no—
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—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—221no—
650C4⋊C4—221no—
651C4⋊C4—221no—
652C4⋊C4—221no—
653C4⋊C4—442no—
654C4⋊C4—442no—
655C4⋊C4C2×C4×D1112yes—
656C4⋊C4D4×D1112yes—
657C22⋊C4—42no—
658C22⋊C4—81no—
659C22⋊C4—224no—
660C22⋊C4—222no—
661C22⋊C4—222no—
662C22⋊C4—442no—
663C22⋊C4—442no—
664C22⋊C4—442no—
665C22⋊C4—442no—
666C22⋊C4—442no—
667C22⋊C4—442no—
668C22⋊C4—881no—
669C22⋊C4—881no—
670C42—21no—
671C42—21no—
672C42—42no—
673C42—221no—
674C42—221no—
675C11#2285811yescharacteristic, complemented, Sylow
676C23—22no—
677C23—41no—
678C23—41no—
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—222no—
693C23—222no—
694C23—448no—
695C23—448no—
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—41no—
715D4—41no—
716D4—114no—
717D4—222no—
718D4—222no—
719D4—222no—
720D4—222no—
721D4—222no—
722D4—448no—
723D4—448no—
724D4—441no—
725D4—441no—
726C2×C4—21no—
727C2×C4—21no—
728C2×C4—21no—
729C2×C4—21no—
730C2×C4—22no—
731C2×C4—22no—
732C2×C4—21no—
733C2×C4—21no—
734C2×C4—41no—
735C2×C4—41no—
736C2×C4—41no—
737C2×C4—41no—
738C2×C4—41no—
739C2×C4—41no—
740C2×C4—41no—
741C2×C4—112no—
742C2×C4—221no—
743C2×C4—221no—
744C2×C4—222no—
745C2×C4—222no—
746C2×C4—222no—
747C2×C4—222no—
748C2×C4—221no—
749C2×C4—221no—
750C2×C4—221no—
751C2×C4—221no—
752C2×C4—221no—
753C2×C4—221no—
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#41×D1111yescharacteristic
767C2×C4#41×D1111yescharacteristic
768C2×C4#6704211yescharacteristic
769C2×C4#6704211yescharacteristic
770C8—22no—
771C8—41no—
772C8—222no—
773C8—222no—
774C22—42no—
775C22—42no—
776C22—42no—
777C22—81no—
778C22—81no—
779C22—81no—
780C22—81no—
781C22—114no—
782C22—222no—
783C22—222no—
784C22—222no—
785C22—222no—
786C22—222no—
787C22—222no—
788C22—224no—
789C22—442no—
790C22—442no—
791C22—442no—
792C22—442no—
793C22—442no—
794C22—442no—
795C22—442no—
796C22—442no—
797C22—442no—
798C22—8816no—
799C22—881no—
800C22—881no—
801C22—881no—
802C22—881no—
803C22C4×D4×D1111yescharacteristic
804C22#1062314011yescharacteristic
805C22#1062318511yescharacteristic
806C22#1062329311yescharacteristic
807C22#1062330011yescharacteristic
808C22D11×AGL(1,ℤ/8)11yescharacteristic
809C22D11×AGL(1,ℤ/8)11yescharacteristic
810C4—41no—
811C4—42no—
812C4—42no—
813C4—41no—
814C4—81no—
815C4—222no—
816C4—441no—
817C4—441no—
818C4—881no—
819C4—881no—
820C4#1062305211yescharacteristic
821C4C4×D4×D1111yescharacteristic
822C4#1062320711yescharacteristic
823C4#1062323611yescharacteristic
824C2—82no—
825C2—224no—
826C2—444no—
827C2—882no—
828C2#1307159411yescharacteristic
829C2D11×#44211yescharacteristic
830C2#1307744311yescharacteristic
831C2#1308010211yescharacteristic
832C2#1308010611yescharacteristic
833C2#1308058011yescharacteristic
834C2#1308076011yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#1926C2
socleC23×C11C22×D4
prime radicalC2×#10622386C2
cosocleC22×C4×C11C24
hypercenter#1926D11
hypocenterC11#22858
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1926

Complements

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

NH ≅ G/Ntype
2. C2×#10622482C2semidirect
3. C2×D11×#102C2semidirect
4. #13071634C2semidirect
5. #13071437C2semidirect
6. #13069491C2semidirect
7. #13069315C2semidirect
8. #13069043C2semidirect
9. #13068963C2semidirect
10. #13068961C2semidirect
11. #13068878C2semidirect
12. #13068807C2semidirect
13. #13068444C2semidirect
14. #13068391C2semidirect
15. C11×#1926C2semidirect
22. C2×#66946C22semidirect
27. C2×C11×#106C22semidirect
31. C4×C11×C4⋊C4C22semidirect
35. C2×#66885C22semidirect
37. C2×#66879C22semidirect
39. #10622598C22semidirect
42. C2×#66873C22semidirect
43. C2×#66872C22semidirect
48. #10622552C22semidirect
50. C2×#66867C22semidirect
52. #10622386C4semidirect
56. C11×#340C22semidirect
57. C11×#336C22semidirect
58. #10622189C22semidirect
59. #10622188C22semidirect
60. #10622167C22semidirect
61. #10622167C22semidirect
70. C2×D4×D11C2×C4semidirect
92. C2×#4323C2×C4semidirect
111. C2×D88C2×C4semidirect
116. #66948C2×C4semidirect
129. C11×#102C2×C4semidirect
138. (C2×D11)⋊C8C2×C4semidirect
141. #66873C2×C4semidirect
142. #66873D4semidirect
266. #1926D11semidirect
359. D44C4×D4semidirect
386. C2×#106C2×D11semidirect
410. C4×C4⋊C4C2×D11semidirect
415. #340C2×D11semidirect
417. #336C2×D11semidirect
453. C2×D11#442semidirect
542. #102C4×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×#106223862
C2×#106224822
C2×D11×#1022
#130716342
#130714372
#130694912
#130693152
#130690432
#130689632
#130689612
#130688782
#130688072
#130684442
#130683912
C11×#19262
#2285811