Finite Group Databasebeta

← #14774087

Subgroups — #14774087

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×#10622649C211yesmaximal, characteristic
2C2×#10622398C211yesmaximal, characteristic, complemented
3C22×#66885C211yesmaximal, characteristic, complemented
4#13071636C211yesmaximal, characteristic, complemented
5#13071436C211yesmaximal, characteristic, complemented
6#13069489C211yesmaximal, characteristic, complemented
7#13069314C211yesmaximal, characteristic, complemented
8#13069241C211yesmaximal, characteristic, complemented
9#13068962C211yesmaximal, characteristic, complemented
10#13068961C211yesmaximal, characteristic, complemented
11#13068878C211yesmaximal, characteristic, complemented
12#13068808C211yesmaximal, characteristic, complemented
13#13068440C211yesmaximal, characteristic, complemented
14#13068392C211yesmaximal, characteristic, complemented
15C11×#1893C211yesmaximal, characteristic, complemented
16C23×D44C2211yescharacteristic
17C23×C8×C11C2211yescharacteristic
18C2×C11×#121C2211yescharacteristic
19C2×D4×Dic11—21no—
20C2×D4×Dic11C2211yescharacteristic, complemented
21C22×#4323C2211yescharacteristic
22C22×#4323C2211yescharacteristic
23C22×C4⋊Dic11C2211yescharacteristic
24C2×#66946C2211yescharacteristic
25C2×#66946C2211yescharacteristic
26C2×C22⋊C4×D11—21no—
27C2×C11×#102C2211yescharacteristic, complemented
28C2×C11×#102C2211yescharacteristic, complemented
29C11×#380C2211yescharacteristic
30#10622834C2211yescharacteristic, complemented
31#10622833—21no—
32C4×C22⋊Dic11C2211yescharacteristic
33C2×C22⋊(C11⋊C8)C2211yescharacteristic
34C2×#66885—24no—
35C2×#66885C2211yescharacteristic
36C2×#66885C2211yescharacteristic
37C2×#66885C2211yescharacteristic
38C2×#66885C2211yescharacteristic
39C2×#66879C2211yescharacteristic, complemented
40C2×#66879C2211yescharacteristic, complemented
41#10622649C418yescomplemented
42#10622601C2211yescharacteristic
43#10622601C2211yescharacteristic
44#10622598C2211yescharacteristic, complemented
45C4⋊C4×Dic11C2211yescharacteristic, complemented
46C2×#66873C2211yescharacteristic
47C2×#66873C2211yescharacteristic
48C2×#66872C2211yescharacteristic, complemented
49C2×#66872C2211yescharacteristic, complemented
50#10622568—21no—
51#10622564—21no—
52#10622563—21no—
53#10622398—24no—
54#10622278—21no—
55#10622278—21no—
56C11×#340C2211yescharacteristic, complemented
57C11×#340C2211yescharacteristic, complemented
58#10622188C2211yescharacteristic, complemented
59#10622188C2211yescharacteristic, complemented
60#10622167C2211yescharacteristic, complemented
61#10622167C2211yescharacteristic, complemented
62C24×D11—21no—
63C22×D4×C11—21no—
64C22×D4×C11C2311yescharacteristic
65C23×C4×C11C2311yescharacteristic
66C23×Dic11—21no—
67C23×Dic11—21no—
68C22×D44—22no—
69C22×D44—22no—
70C22×D44—21no—
71C22×D44—22no—
72C22×D44—41no—
73C22×D44—41no—
74C22×D44C2×C414yescomplemented
75C22×D44C2311yescharacteristic
76C22×D44C2311yescharacteristic
77C22×C4×D11—21no—
78C22×C4×D11—21no—
79C22×C8×C11—22no—
80C22×C8×C11—22no—
81C22×C8×C11—41no—
82C22×C8×C11C2311yescharacteristic
83C22×C8×C11C2311yescharacteristic
84C11×#121—22no—
85C11×#121C2×C414yescomplemented
86C2×C11×C4⋊C4C2311yescharacteristic
87C2×C11×C4⋊C4C2311yescharacteristic
88C2×C11×C4⋊C4C2311yescharacteristic
89C2×C11×C22⋊C4—21no—
90C2×C11×C22⋊C4—21no—
91C2×C22⋊Dic11—21no—
92C2×C22⋊Dic11—21no—
93C2×C22⋊Dic11—21no—
94C2×C22⋊Dic11D411yescharacteristic
95C2×C22⋊Dic11D411yescharacteristic
96D4×Dic11—22no—
97D4×Dic11—41no—
98D4×Dic11—44no—
99C2×#4323—22no—
100C2×#4323—22no—
101C2×#4323—41no—
102C2×#4323—41no—
103C2×#4323C2×C414yescomplemented
104C2×#4323C2×C414yescomplemented
105C2×(C2×D11)⋊C4—21no—
106C2×(C2×D11)⋊C4—21no—
107C2×(C2×D11)⋊C4—21no—
108C2×(C2×D11)⋊C4—21no—
109C2×(C2×D11)⋊C4—21no—
110C2×(C2×D11)⋊C4—21no—
111C2×C4⋊Dic11—22no—
112C2×C4⋊Dic11—21no—
113C2×C4⋊Dic11—21no—
114C2×C4⋊Dic11—41no—
115C2×C4⋊Dic11C2311yescharacteristic
116C2×C4⋊Dic11C2311yescharacteristic
117C2×C4×Dic11—21no—
118C2×C4×Dic11C2311yescharacteristic
119C2×C4×Dic11C2311yescharacteristic
120C22×C11⋊C8C2311yescharacteristic
121C22×C11⋊C8C2311yescharacteristic
122#66946—22no—
123#66946—22no—
124#66946—41no—
125#66946—41no—
126C22⋊C4×D11—44no—
127C11×#102—22no—
128C11×#102—41no—
129C11×#95—21no—
130C11⋊#95—21no—
131C11⋊#95—21no—
132C11⋊#95D411yescharacteristic
133C11⋊#95D411yescharacteristic
134C22⋊(C11⋊C8)C2×C414yescomplemented
135#66885—22no—
136#66885—22no—
137#66885—22no—
138#66885D414yescomplemented
139#66879—22no—
140#66879—41no—
141#66873C2×C414yescomplemented
142#66873C2×C414yescomplemented
143#66872—22no—
144#66872—41no—
145#22858—111nomaximal, Sylow
146C24×C11—21no—
147C24×C11C2×D411yescharacteristic
148C23×D11—21no—
149C23×D11—21no—
150C23×D11—24no—
151C23×D11—42no—
152C23×D11—42no—
153C23×D11—42no—
154C23×D11—42no—
155C23×D11—81no—
156C23×D11—81no—
157C2×D4×C11—24no—
158C2×D4×C11—21no—
159C2×D4×C11—21no—
160C2×D4×C11—21no—
161C2×D4×C11—21no—
162C2×D4×C11—21no—
163C2×D4×C11—42no—
164C2×D4×C11—42no—
165C2×D4×C11C22×C412yes—
166C22×C4×C11—21no—
167C22×C4×C11—21no—
168C22×C4×C11—21no—
169C22×C4×C11—21no—
170C22×C4×C11—21no—
171C22×C4×C11—21no—
172C22×C4×C11—21no—
173C22×C4×C11C22×C412yes—
174C22×C4×C11C2×D411yescharacteristic
175C22×C4×C11#4112yes—
176C22×C4×C11C2411yescharacteristic
177C22×Dic11—21no—
178C22×Dic11—21no—
179C22×Dic11—42no—
180C22×Dic11—42no—
181C22×Dic11—42no—
182C22×Dic11—42no—
183C22×Dic11—81no—
184C22×Dic11—81no—
185C22×Dic11C2×D411yescharacteristic
186C22×Dic11C2×D411yescharacteristic
187C22×Dic11C2×D411yescharacteristic
188C22×Dic11C2×D411yescharacteristic
189C2×D44—28no—
190C2×D44—24no—
191C2×D44—21no—
192C2×D44—21no—
193C2×D44—21no—
194C2×D44—21no—
195C2×D44—21no—
196C2×D44—21no—
197C2×D44—21no—
198C2×D44—21no—
199C2×D44—42no—
200C2×D44—42no—
201C2×D44—44no—
202C2×D44—44no—
203C2×D44—44no—
204C2×D44C22×C412yes—
205C2×D44C22×C412yes—
206C2×D44C2×D412yes—
207C2×D44#4112yes—
208C2×C4×D11—42no—
209C2×C4×D11—42no—
210C2×C4×D11—42no—
211C2×C4×D11—42no—
212C2×C4×D11—81no—
213C2×C4×D11—81no—
214C2×C8×C11—21no—
215C2×C8×C11—21no—
216C2×C8×C11—21no—
217C2×C8×C11—21no—
218C2×C8×C11—21no—
219C2×C8×C11—44no—
220C2×C8×C11C2×D412yes—
221C11×C4⋊C4—21no—
222C11×C4⋊C4—21no—
223C11×C4⋊C4—21no—
224C11×C4⋊C4—21no—
225C11×C4⋊C4—21no—
226C11×C4⋊C4C22×C412yes—
227C11×C22⋊C4—24no—
228C11×C22⋊C4—42no—
229C22⋊Dic11—22no—
230C22⋊Dic11—22no—
231C22⋊Dic11—42no—
232C22⋊Dic11—42no—
233C22⋊Dic11—81no—
234#4323—28no—
235#4323—44no—
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—
242C4⋊Dic11—21no—
243C4⋊Dic11—21no—
244C4⋊Dic11—21no—
245C4⋊Dic11—42no—
246C4⋊Dic11—42no—
247C4⋊Dic11C2×D412yes—
248C4×Dic11—21no—
249C4×Dic11—21no—
250C4×Dic11—21no—
251C4×Dic11—21no—
252C4×Dic11—42no—
253C2×C11⋊C8—21no—
254C2×C11⋊C8—21no—
255C2×C11⋊C8—21no—
256C2×C11⋊C8—21no—
257C2×C11⋊C8C22×C412yes—
258C2×C11⋊C8C22×C412yes—
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#1893D1111yescharacteristic, complemented
268#1879—111no—
269#1879—111no—
270#1864—111no—
271#1853—111no—
272#1762—111no—
273#1752—111no—
274C23×C11—21no—
275C23×C11—21no—
276C23×C11—21no—
277C23×C11—21no—
278C23×C11—22no—
279C23×C11—41no—
280C23×C11—41no—
281C23×C11—41no—
282C23×C11—41no—
283C23×C11—41no—
284C23×C11—41no—
285C23×C11C4×D412yes—
286C23×C11AGL(1,ℤ/8)12yes—
287C23×C11AGL(1,ℤ/8)12yes—
288C23×C11C22×D411yescharacteristic
289C22×D11—22no—
290C22×D11—22no—
291C22×D11—22no—
292C22×D11—22no—
293C22×D11—48no—
294C22×D11—41no—
295C22×D11—41no—
296C22×D11—41no—
297C22×D11—41no—
298C22×D11—41no—
299C22×D11—41no—
300C22×D11—41no—
301C22×D11—41no—
302C22×D11—41no—
303C22×D11—41no—
304C22×D11—48no—
305C22×D11—84no—
306C22×D11—84no—
307C22×D11—84no—
308C22×D11—84no—
309C22×D11—84no—
310D4×C11—22no—
311D4×C11—22no—
312D4×C11—48no—
313D4×C11—41no—
314D4×C11—41no—
315C2×C4×C11—21no—
316C2×C4×C11—21no—
317C2×C4×C11—22no—
318C2×C4×C11—22no—
319C2×C4×C11—22no—
320C2×C4×C11—22no—
321C2×C4×C11—22no—
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—41no—
330C2×C4×C11C4×D412yes—
331C2×C4×C11C23×C411yescharacteristic
332C2×C4×C11C22×D411yescharacteristic
333C2×C4×C11C2×#4111yescharacteristic
334C2×C4×C11C2×#4111yescharacteristic
335C2×C4×C11H(5,𝔽2)11yescharacteristic
336C2×C4×C11H(5,𝔽2)11yescharacteristic
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—21no—
347C2×Dic11—21no—
348C2×Dic11—21no—
349C2×Dic11—21no—
350C2×Dic11—41no—
351C2×Dic11—41no—
352C2×Dic11—41no—
353C2×Dic11—41no—
354C2×Dic11—41no—
355C2×Dic11—84no—
356C2×Dic11—84no—
357D44—22no—
358D44—22no—
359D44—22no—
360D44—22no—
361D44—22no—
362D44—48no—
363D44—41no—
364D44—41no—
365D44C4×D414yescomplemented
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×C8C2×D1111yescharacteristic
376C2×#121C2×D1111yescharacteristic
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×#106—111no—
387C2×#102—111no—
388C2×#102—111no—
389C2×#102—111no—
390C2×#102—111no—
391C2×#102—111no—
392C2×#102—111no—
393C2×#102—224no—
394C2×#102C2×D1111yescharacteristic, complemented
395C2×#102C2×D1111yescharacteristic, complemented
396C2×C22⋊C8—111no—
397C2×#97—111no—
398C2×#97—111no—
399#390—111no—
400#390—111no—
401#390—111no—
402#389—111no—
403#388—221no—
404#386—221no—
405#386—221no—
406#386—221no—
407#385—221no—
408#380C2×D1111yescharacteristic
409#379—221no—
410C4×C4⋊C4—111no—
411C4×C22⋊C4—111no—
412#340—111no—
413#340—111no—
414#340C2×D1111yescharacteristic, complemented
415#340C2×D1111yescharacteristic, complemented
416#336—111no—
417#336—111no—
418C22×C11—22no—
419C22×C11—22no—
420C22×C11—22no—
421C22×C11—22no—
422C22×C11—22no—
423C22×C11—22no—
424C22×C11—42no—
425C22×C11—42no—
426C22×C11—42no—
427C22×C11—81no—
428C22×C11—81no—
429C22×C11—81no—
430C22×C11—81no—
431C22×C11#44214yescomplemented
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—24no—
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—42no—
449C2×D11—816no—
450C2×D11—81no—
451C2×D11—81no—
452C2×D11—81no—
453C2×D11—81no—
454C4×C11—22no—
455C4×C11—42no—
456C4×C11—81no—
457C4×C11—81no—
458C4×C11C2×C4×D411yescharacteristic
459C4×C11#51811yescharacteristic
460C4×C11#54611yescharacteristic
461C4×C11#55111yescharacteristic
462Dic11—41no—
463Dic11—42no—
464Dic11—41no—
465Dic11—41no—
466Dic11—41no—
467Dic11—81no—
468C25—221no—
469C22×D4—21no—
470C22×D4—114no—
471C22×D4—111no—
472C22×D4—111no—
473C22×D4—222no—
474C22×D4—222no—
475C22×D4—221no—
476C22×D4—222no—
477C22×D4—441no—
478C22×D4—441no—
479C22×D4C22×D1111yescharacteristic
480C23×C4—221no—
481C23×C4—221no—
482C23×C4—221no—
483C23×C4—221no—
484C23×C4C22×D1111yescharacteristic
485C2×D8—114no—
486C2×D8—114no—
487C2×D8—222no—
488C2×D8—222no—
489C2×D8—441no—
490C2×D8—441no—
491C22×C8—22no—
492C22×C8—22no—
493C22×C8—41no—
494C22×C8—111no—
495C22×C8—111no—
496C22×C8C22×D1111yescharacteristic
497C22×C8C22×D1111yescharacteristic
498#121—22no—
499#121C4×D1114yescomplemented
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—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—111no—
531C2×C42—111no—
532C2×C42—221no—
533#106—222no—
534#106—441no—
535#102—22no—
536#102—41no—
537#102—114no—
538#102—114no—
539#102—114no—
540#102—222no—
541#102—222no—
542#102—222no—
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—24no—
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—44no—
561D11—82no—
562C24—21no—
563C24—221no—
564C24—221no—
565C24—224no—
566C24—442no—
567C24—442no—
568C24—442no—
569C24—442no—
570C24—881no—
571C24—881no—
572C24D4×D1111yescharacteristic
573C2×D4—24no—
574C2×D4—21no—
575C2×D4—21no—
576C2×D4—21no—
577C2×D4—21no—
578C2×D4—21no—
579C2×D4—42no—
580C2×D4—42no—
581C2×D4—112no—
582C2×D4—112no—
583C2×D4—112no—
584C2×D4—112no—
585C2×D4—228no—
586C2×D4—224no—
587C2×D4—221no—
588C2×D4—221no—
589C2×D4—221no—
590C2×D4—221no—
591C2×D4—221no—
592C2×D4—221no—
593C2×D4—221no—
594C2×D4—221no—
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—21no—
605C22×C4—21no—
606C22×C4—21no—
607C22×C4—21no—
608C22×C4—111no—
609C22×C4—111no—
610C22×C4—111no—
611C22×C4—111no—
612C22×C4—221no—
613C22×C4—221no—
614C22×C4—442no—
615C22×C4—442no—
616C22×C4—442no—
617C22×C4—442no—
618C22×C4—442no—
619C22×C4—442no—
620C22×C4—442no—
621C22×C4—442no—
622C22×C4—881no—
623C22×C4—881no—
624C22×C4—881no—
625C22×C4—881no—
626C22×C4C2×C4×D1112yes—
627C22×C4D4×D1111yescharacteristic
628C22×C4#434112yes—
629C22×C4C23×D1111yescharacteristic
630D8—228no—
631D8—444no—
632C2×C8—21no—
633C2×C8—21no—
634C2×C8—21no—
635C2×C8—21no—
636C2×C8—21no—
637C2×C8—44no—
638C2×C8—112no—
639C2×C8—112no—
640C2×C8—221no—
641C2×C8—221no—
642C2×C8—221no—
643C2×C8—221no—
644C2×C8D4×D1112yes—
645C4⋊C4—21no—
646C4⋊C4—21no—
647C4⋊C4—21no—
648C4⋊C4—21no—
649C4⋊C4—21no—
650C4⋊C4—112no—
651C4⋊C4—221no—
652C4⋊C4—221no—
653C4⋊C4—221no—
654C4⋊C4—442no—
655C4⋊C4—442no—
656C4⋊C4C2×C4×D1112yes—
657C22⋊C4—24no—
658C22⋊C4—42no—
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—221no—
671C42—221no—
672C42—221no—
673C42—221no—
674C42—442no—
675C11#2285811yescharacteristic, complemented, Sylow
676C23—21no—
677C23—21no—
678C23—21no—
679C23—21no—
680C23—22no—
681C23—41no—
682C23—41no—
683C23—41no—
684C23—41no—
685C23—41no—
686C23—41no—
687C23—222no—
688C23—222no—
689C23—222no—
690C23—222no—
691C23—448no—
692C23—441no—
693C23—441no—
694C23—441no—
695C23—441no—
696C23—441no—
697C23—441no—
698C23—441no—
699C23—441no—
700C23—441no—
701C23—441no—
702C23—448no—
703C23—884no—
704C23—884no—
705C23—884no—
706C23—884no—
707C23—884no—
708C23(C22⋊D11)⋊C412yes—
709C23#6696412yes—
710C23#6696712yes—
711C23C2×D4×D1111yescharacteristic
712D4—22no—
713D4—22no—
714D4—48no—
715D4—41no—
716D4—41no—
717D4—114no—
718D4—222no—
719D4—222no—
720D4—222no—
721D4—222no—
722D4—222no—
723D4—448no—
724D4—441no—
725D4—441no—
726C2×C4—21no—
727C2×C4—21no—
728C2×C4—22no—
729C2×C4—22no—
730C2×C4—22no—
731C2×C4—22no—
732C2×C4—22no—
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—221no—
742C2×C4—221no—
743C2×C4—221no—
744C2×C4—221no—
745C2×C4—221no—
746C2×C4—221no—
747C2×C4—221no—
748C2×C4—221no—
749C2×C4—221no—
750C2×C4—221no—
751C2×C4—222no—
752C2×C4—221no—
753C2×C4—221no—
754C2×C4—441no—
755C2×C4—441no—
756C2×C4—441no—
757C2×C4—441no—
758C2×C4—441no—
759C2×C4—884no—
760C2×C4—884no—
761C2×C4—884no—
762C2×C4—884no—
763C2×C4(C22⋊D11)⋊C412yes—
764C2×C4C22×C4×D1111yescharacteristic
765C2×C4C2×D4×D1111yescharacteristic
766C2×C4C2×#434111yescharacteristic
767C2×C4#6703711yescharacteristic
768C2×C4#41×D1111yescharacteristic
769C2×C4#6704211yescharacteristic
770C8—22no—
771C8—41no—
772C8—222no—
773C8—222no—
774C22—22no—
775C22—22no—
776C22—22no—
777C22—22no—
778C22—22no—
779C22—22no—
780C22—42no—
781C22—42no—
782C22—42no—
783C22—81no—
784C22—81no—
785C22—81no—
786C22—81no—
787C22—224no—
788C22—442no—
789C22—442no—
790C22—442no—
791C22—442no—
792C22—442no—
793C22—442no—
794C22—442no—
795C22—442no—
796C22—442no—
797C22—8816no—
798C22—881no—
799C22—881no—
800C22—881no—
801C22—881no—
802C22#1062239814yescomplemented
803C22C2×(C22⋊D11)⋊C411yescharacteristic
804C22#1062314011yescharacteristic
805C22#1062314111yescharacteristic
806C22C2×#6696411yescharacteristic
807C22C2×#6696711yescharacteristic
808C22#1062330011yescharacteristic
809C22#1062330111yescharacteristic
810C4—22no—
811C4—42no—
812C4—81no—
813C4—81no—
814C4—441no—
815C4—441no—
816C4—442no—
817C4—441no—
818C4—441no—
819C4—881no—
820C4C4×D4×D1111yescharacteristic
821C4#1062307611yescharacteristic
822C4#1062312211yescharacteristic
823C4#1062318911yescharacteristic
824C2—24no—
825C2—82no—
826C2—444no—
827C2—882no—
828C2#1307159611yescharacteristic
829C2C2×#1062239811yescharacteristic
830C2#1307745111yescharacteristic
831C2#1308009311yescharacteristic
832C2#1308010811yescharacteristic
833C2#1308058311yescharacteristic
834C2#1308076311yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#1893C2
socleC23×C11C22×D4
prime radicalC2×#10622649C2
cosocleC22×C4×C11C24
hypercenter#1893D11
hypocenterC11#22858
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1893

Complements

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

NH ≅ G/Ntype
2. C2×#10622398C2semidirect
3. C22×#66885C2semidirect
4. #13071636C2semidirect
5. #13071436C2semidirect
6. #13069489C2semidirect
7. #13069314C2semidirect
8. #13069241C2semidirect
9. #13068962C2semidirect
10. #13068961C2semidirect
11. #13068878C2semidirect
12. #13068808C2semidirect
13. #13068440C2semidirect
14. #13068392C2semidirect
15. C11×#1893C2semidirect
20. C2×D4×Dic11C22semidirect
27. C2×C11×#102C22semidirect
28. C2×C11×#102C22semidirect
30. #10622834C22semidirect
39. C2×#66879C22semidirect
40. C2×#66879C22semidirect
41. #10622649C4semidirect
44. #10622598C22semidirect
45. C4⋊C4×Dic11C22semidirect
48. C2×#66872C22semidirect
49. C2×#66872C22semidirect
56. C11×#340C22semidirect
57. C11×#340C22semidirect
58. #10622188C22semidirect
59. #10622188C22semidirect
60. #10622167C22semidirect
61. #10622167C22semidirect
74. C22×D44C2×C4semidirect
85. C11×#121C2×C4semidirect
103. C2×#4323C2×C4semidirect
104. C2×#4323C2×C4semidirect
134. C22⋊(C11⋊C8)C2×C4semidirect
138. #66885D4semidirect
141. #66873C2×C4semidirect
142. #66873C2×C4semidirect
267. #1893D11semidirect
365. D44C4×D4semidirect
394. C2×#102C2×D11semidirect
395. C2×#102C2×D11semidirect
414. #340C2×D11semidirect
415. #340C2×D11semidirect
431. C22×C11#442semidirect
499. #121C4×D11semidirect
675. C11#22858semidirect
802. C22#10622398semidirect

Maximal subgroups

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

subgroupindex
C2×#106226492
C2×#106223982
C22×#668852
#130716362
#130714362
#130694892
#130693142
#130692412
#130689622
#130689612
#130688782
#130688082
#130684402
#130683922
C11×#18932
#2285811