Finite Group Databasebeta

← #14774084

Subgroups — #14774084

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×D11×#102C211yesmaximal, characteristic, complemented
3#13071628C211yesmaximal, characteristic, complemented
4D4×(C2×D11)⋊C4C211yesmaximal, characteristic, complemented
5#13069489C211yesmaximal, characteristic, complemented
6#13069313C211yesmaximal, characteristic, complemented
7#13069242C211yesmaximal, characteristic, complemented
8#13069041C211yesmaximal, characteristic, complemented
9#13068966C211yesmaximal, characteristic, complemented
10#13068964C211yesmaximal, characteristic, complemented
11#13068877C211yesmaximal, characteristic, complemented
12#13068807C211yesmaximal, characteristic, complemented
13#13068443C211yesmaximal, characteristic, complemented
14#13068393C211yesmaximal, characteristic, complemented
15C2×C11×#442C211yesmaximal, characteristic, complemented
16C22×D4×D11C2211yescharacteristic
17C22×C11×D8C2211yescharacteristic
18C2×C4×D4×C11C2211yescharacteristic
19C2×C4×D4×C11C2211yescharacteristic, complemented
20C2×#66991C2211yescharacteristic
21C2×D4×Dic11C2211yescharacteristic
22C22×#4323C2211yescharacteristic
23C2×C4×C22⋊D11—21no—
24C22×(C2×D11)⋊C4—21no—
25C22×C8×D11C2211yescharacteristic
26C2×C4⋊C4×D11C2211yescharacteristic
27C11×#442—24no—
28C2×C11×#106C2211yescharacteristic, complemented
29C2×C11×#102C2211yescharacteristic
30C2×C11×#102C2211yescharacteristic, complemented
31C2×C11×#97C2211yescharacteristic, complemented
32#10622834C2211yescharacteristic, complemented
33C2×#66896C2211yescharacteristic
34C2×#66896C2211yescharacteristic
35C2×#66896C2211yescharacteristic, complemented
36#10622826—21no—
37#10622823—21no—
38#10622769C418yescomplemented
39C2×#66885C2211yescharacteristic
40C2×#66885C2211yescharacteristic
41C2×(C2×D11)⋊C8C2211yescharacteristic
42C2×#66879C2211yescharacteristic, complemented
43#10622601C2211yescharacteristic
44#10622600C2211yescharacteristic
45C4⋊C4×Dic11C2211yescharacteristic, complemented
46C2×#66873C2211yescharacteristic
47C2×#66872C2211yescharacteristic, complemented
48#10622571—21no—
49#10622569—21no—
50#10622568—21no—
51#10622558—21no—
52#10622552C2211yescharacteristic
53C4×(C2×D11)⋊C4C2211yescharacteristic
54#10622541C2211yescharacteristic, complemented
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
65C23×C4×C11—21no—
66C23×C4×C11—21no—
67C22×C22⋊D11—21no—
68C22×C22⋊D11—21no—
69C23×Dic11—21no—
70C2×D4×D11—22no—
71C2×D4×D11—22no—
72C2×D4×D11—22no—
73C2×D4×D11—41no—
74C2×D4×D11—41no—
75C2×D4×D11C2×C414yescomplemented
76C22×D44C2311yescharacteristic
77C22×C4×D11—21no—
78C22×C4×D11C2311yescharacteristic
79C2×C11×D8—22no—
80C2×C11×D8—22no—
81C2×C11×D8C2×C414yescomplemented
82C22×C8×C11C2311yescharacteristic
83C22×C8×C11C2311yescharacteristic
84C4×D4×C11—22no—
85C4×D4×C11—22no—
86C4×D4×C11—41no—
87C4×D4×C11—41no—
88C2×C11×C4⋊C4C2311yescharacteristic
89C2×C11×C4⋊C4C2311yescharacteristic
90C2×C11×C22⋊C4—21no—
91C2×C11×C22⋊C4—21no—
92C2×C42×C11C2311yescharacteristic
93C2×C22⋊Dic11—21no—
94C2×C22⋊Dic11—21no—
95C2×C22⋊Dic11—21no—
96C2×C22⋊Dic11—21no—
97#66991—22no—
98#66991C2×C414yescomplemented
99D4×Dic11—22no—
100D4×Dic11—41no—
101C2×#4323—41no—
102C2×#4323—41no—
103C2×#4323C2×C414yescomplemented
104C4×C22⋊D11—44no—
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—44no—
111C2×(C2×D11)⋊C4D411yescharacteristic
112C2×(C2×D11)⋊C4D411yescharacteristic
113C2×C4⋊Dic11C2311yescharacteristic
114C2×C4⋊Dic11C2311yescharacteristic
115C2×C4⋊Dic11C2311yescharacteristic
116C2×Dic11⋊C4—21no—
117C2×Dic11⋊C4—21no—
118C2×C4×Dic11—21no—
119C2×C4×Dic11C2311yescharacteristic
120C22×C11⋊C8C2311yescharacteristic
121C22×C11⋊C8C2311yescharacteristic
122C2×C8×D11—22no—
123C2×C8×D11—22no—
124C2×C8×D11—41no—
125C4⋊C4×D11—22no—
126C4⋊C4×D11—41no—
127C11×#106—22no—
128C11×#102—22no—
129C11×#102D414yescomplemented
130C11×#97—22no—
131#66896—22no—
132#66896—41no—
133#66896C2×C414yescomplemented
134C11⋊#95—21no—
135C11⋊#95—21no—
136C11⋊#95—21no—
137C11⋊#95D411yescharacteristic
138C11⋊#95D411yescharacteristic
139#66885—22no—
140#66885C2×C414yescomplemented
141(C2×D11)⋊C8C2×C414yescomplemented
142#66879—41no—
143#66873—22no—
144#66872—41no—
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×C11C22×C412yes—
166C2×D4×C11C22×C412yes—
167C2×D4×C11C2×D412yes—
168C2×D4×C11#4112yes—
169C22×C4×C11—21no—
170C22×C4×C11—21no—
171C22×C4×C11—42no—
172C22×C4×C11—42no—
173C22×C4×C11—42no—
174C22×C4×C11—42no—
175C22×C4×C11—81no—
176C22×C4×C11—81no—
177C22×C4×C11C2×D411yescharacteristic
178C22×C4×C11C2×D411yescharacteristic
179C22×C4×C11C2411yescharacteristic
180C2×C22⋊D11—24no—
181C2×C22⋊D11—24no—
182C2×C22⋊D11—42no—
183C2×C22⋊D11—42no—
184C2×C22⋊D11—42no—
185C2×C22⋊D11—42no—
186C22×Dic11—21no—
187C22×Dic11—21no—
188C22×Dic11—21no—
189C22×Dic11—42no—
190C22×Dic11—42no—
191C22×Dic11—81no—
192C22×Dic11C2×D411yescharacteristic
193C22×Dic11C2×D411yescharacteristic
194C22×Dic11C2×D411yescharacteristic
195D4×D11—28no—
196D4×D11—44no—
197D4×D11—44no—
198D4×D11—44no—
199C2×D44—21no—
200C2×D44—21no—
201C2×D44—21no—
202C2×D44—21no—
203C2×D44—21no—
204C2×D44C22×C412yes—
205C2×C4×D11—21no—
206C2×C4×D11—21no—
207C2×C4×D11—21no—
208C2×C4×D11—21no—
209C2×C4×D11—42no—
210C2×C4×D11—42no—
211C2×C4×D11—81no—
212C2×C4×D11C22×C412yes—
213C2×C4×D11#4112yes—
214C11×D8—28no—
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⋊C4C2×D412yes—
225C11×C22⋊C4—42no—
226C11×C22⋊C4—42no—
227C42×C11—21no—
228C42×C11—21no—
229C22⋊Dic11—24no—
230C22⋊Dic11—42no—
231C22⋊Dic11—42no—
232C22⋊Dic11—81no—
233#4323—44no—
234(C2×D11)⋊C4—22no—
235(C2×D11)⋊C4—22no—
236(C2×D11)⋊C4—42no—
237(C2×D11)⋊C4—42no—
238(C2×D11)⋊C4—42no—
239(C2×D11)⋊C4—81no—
240(C2×D11)⋊C4—81no—
241C4⋊Dic11—21no—
242C4⋊Dic11—21no—
243C4⋊Dic11—21no—
244C4⋊Dic11—21no—
245C4⋊Dic11—21no—
246C4⋊Dic11C22×C412yes—
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×#442D1111yescharacteristic, complemented
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#1864—111no—
271#1853—111no—
272#1762—111no—
273#1752—111no—
274C23×C11—22no—
275C23×C11—22no—
276C23×C11—22no—
277C23×C11—22no—
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—48no—
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×C11—22no—
314D4×C11—22no—
315D4×C11—41no—
316D4×C11—41no—
317D4×C11C4×D414yescomplemented
318C2×C4×C11—22no—
319C2×C4×C11—21no—
320C2×C4×C11—21no—
321C2×C4×C11—21no—
322C2×C4×C11—21no—
323C2×C4×C11—21no—
324C2×C4×C11—21no—
325C2×C4×C11—41no—
326C2×C4×C11—41no—
327C2×C4×C11—41no—
328C2×C4×C11—41no—
329C2×C4×C11—41no—
330C2×C4×C11—84no—
331C2×C4×C11—84no—
332C2×C4×C11C23×C411yescharacteristic
333C2×C4×C11C22×D411yescharacteristic
334C2×C4×C11C2×#4111yescharacteristic
335C2×C4×C11C2×#4111yescharacteristic
336C2×C4×C11H(5,𝔽2)11yescharacteristic
337C2×C4×C11H(5,𝔽2)11yescharacteristic
338C22⋊D11—48no—
339C22⋊D11—48no—
340C2×Dic11—21no—
341C2×Dic11—21no—
342C2×Dic11—22no—
343C2×Dic11—21no—
344C2×Dic11—21no—
345C2×Dic11—21no—
346C2×Dic11—21no—
347C2×Dic11—21no—
348C2×Dic11—21no—
349C2×Dic11—41no—
350C2×Dic11—41no—
351C2×Dic11—41no—
352C2×Dic11—41no—
353C2×Dic11—41no—
354C2×Dic11—41no—
355C2×Dic11—41no—
356C2×Dic11—41no—
357C2×Dic11—84no—
358C2×Dic11C4×D412yes—
359D44—22no—
360D44—22no—
361D44—41no—
362D44—41no—
363C4×D11—22no—
364C4×D11—22no—
365C4×D11—22no—
366C4×D11—22no—
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—221no—
379C2×C4×D4C2×D1111yescharacteristic
380C2×C4×D4C2×D1111yescharacteristic, complemented
381C22×C4⋊C4—111no—
382C22×C22⋊C4—221no—
383#447—118no—
384#442—24no—
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#390—111no—
401#390—111no—
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—24no—
419C22×C11—42no—
420C22×C11—42no—
421C22×C11—42no—
422C22×C11—42no—
423C22×C11—42no—
424C22×C11—42no—
425C22×C11—42no—
426C22×C11—42no—
427C22×C11—42no—
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—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—41no—
455C4×C11—42no—
456C4×C11—41no—
457C4×C11—81no—
458C4×C11C2×C4×D411yescharacteristic
459C4×C11#51811yescharacteristic
460C4×C11#54611yescharacteristic
461C4×C11#55111yescharacteristic
462Dic11—22no—
463Dic11—42no—
464Dic11—41no—
465Dic11—41no—
466Dic11—81no—
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—21no—
481C23×C4—21no—
482C23×C4—111no—
483C23×C4—221no—
484C23×C4—221no—
485C2×D8—22no—
486C2×D8—22no—
487C2×D8—114no—
488C2×D8—441no—
489C2×D8—441no—
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—22no—
501C4×D4—22no—
502C4×D4—41no—
503C4×D4—41no—
504C4×D4—222no—
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—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—221no—
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#102C22⋊D1114yescomplemented
543C22⋊C8—114no—
544#97—22no—
545#97—441no—
546#95—111no—
547#95—111no—
548#95—221no—
549#95—221no—
550#95—221no—
551C2×C11—44no—
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—82no—
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—112no—
582C2×D4—224no—
583C2×D4—228no—
584C2×D4—224no—
585C2×D4—221no—
586C2×D4—221no—
587C2×D4—221no—
588C2×D4—221no—
589C2×D4—221no—
590C2×D4—444no—
591C2×D4—444no—
592C2×D4—444no—
593C2×D4—442no—
594C2×D4—442no—
595C2×D4—442no—
596C2×D4—442no—
597C2×D4C2×C4×D1112yes—
598C2×D4C2×C4×D1112yes—
599C2×D4#433912yes—
600C2×D4C2×C22⋊D1112yes—
601C22×C4—21no—
602C22×C4—21no—
603C22×C4—42no—
604C22×C4—42no—
605C22×C4—42no—
606C22×C4—42no—
607C22×C4—81no—
608C22×C4—81no—
609C22×C4—111no—
610C22×C4—112no—
611C22×C4—112no—
612C22×C4—111no—
613C22×C4—111no—
614C22×C4—221no—
615C22×C4—221no—
616C22×C4—221no—
617C22×C4—221no—
618C22×C4—221no—
619C22×C4—221no—
620C22×C4—221no—
621C22×C4—442no—
622C22×C4—442no—
623C22×C4—442no—
624C22×C4—442no—
625C22×C4—881no—
626C22×C4—881no—
627C22×C4D4×D1111yescharacteristic
628C22×C4D4×D1111yescharacteristic
629C22×C4C23×D1111yescharacteristic
630D8—28no—
631D8—444no—
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×C8C2×C22⋊D1112yes—
645C4⋊C4—21no—
646C4⋊C4—21no—
647C4⋊C4—21no—
648C4⋊C4—112no—
649C4⋊C4—221no—
650C4⋊C4—221no—
651C4⋊C4—221no—
652C4⋊C4—221no—
653C4⋊C4—221no—
654C4⋊C4—442no—
655C4⋊C4—442no—
656C4⋊C4C2×C22⋊D1112yes—
657C22⋊C4—42no—
658C22⋊C4—42no—
659C22⋊C4—222no—
660C22⋊C4—222no—
661C22⋊C4—224no—
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—22no—
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—448no—
699C23—448no—
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—22no—
716D4—22no—
717D4—41no—
718D4—41no—
719D4—222no—
720D4—222no—
721D4—448no—
722D4—448no—
723D4—441no—
724D4—441no—
725D4C4×C22⋊D1114yescomplemented
726C2×C4—21no—
727C2×C4—21no—
728C2×C4—21no—
729C2×C4—21no—
730C2×C4—21no—
731C2×C4—21no—
732C2×C4—22no—
733C2×C4—41no—
734C2×C4—41no—
735C2×C4—41no—
736C2×C4—41no—
737C2×C4—41no—
738C2×C4—84no—
739C2×C4—84no—
740C2×C4—112no—
741C2×C4—221no—
742C2×C4—221no—
743C2×C4—222no—
744C2×C4—222no—
745C2×C4—222no—
746C2×C4—222no—
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—441no—
760C2×C4—441no—
761C2×C4—441no—
762C2×C4—884no—
763C2×C4—884no—
764C2×C4C22×C4×D1111yescharacteristic
765C2×C4C2×#433911yescharacteristic
766C2×C4#6703711yescharacteristic
767C2×C4#41×D1111yescharacteristic
768C2×C4#6704211yescharacteristic
769C2×C4C22×C22⋊D1111yescharacteristic
770C8—22no—
771C8—22no—
772C8—222no—
773C8—441no—
774C22—24no—
775C22—42no—
776C22—42no—
777C22—42no—
778C22—42no—
779C22—42no—
780C22—42no—
781C22—42no—
782C22—42no—
783C22—42no—
784C22—81no—
785C22—81no—
786C22—81no—
787C22—81no—
788C22—114no—
789C22—222no—
790C22—222no—
791C22—222no—
792C22—222no—
793C22—222no—
794C22—222no—
795C22—442no—
796C22—442no—
797C22—442no—
798C22—8816no—
799C22—881no—
800C22—881no—
801C22—881no—
802C22—881no—
803C22C4×D4×D1111yescharacteristic
804C22#1062308111yescharacteristic
805C22D11×AGL(1,ℤ/8)11yescharacteristic
806C22D11×AGL(1,ℤ/8)11yescharacteristic
807C22#1062330511yescharacteristic
808C22#1062330611yescharacteristic
809C22D4×C22⋊D1111yescharacteristic
810C4—41no—
811C4—42no—
812C4—41no—
813C4—81no—
814C4—222no—
815C4—441no—
816C4—442no—
817C4—441no—
818C4—881no—
819C4—881no—
820C4#1062307611yescharacteristic
821C4#1062308711yescharacteristic
822C4C2×C4×C22⋊D1111yescharacteristic
823C4#1062336011yescharacteristic
824C2—44no—
825C2—82no—
826C2—224no—
827C2—882no—
828C2#1307159311yescharacteristic
829C2D11×#44211yescharacteristic
830C2#1307744511yescharacteristic
831C2#1308009011yescharacteristic
832C2#1308010511yescharacteristic
833C2#1308058211yescharacteristic
834C2#1308076211yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC2×C11×#442C2
socleC23×C11C22×D4
prime radicalC2×#10622769C2
cosocleC22×C4×C11C24
hypercenterC2×#442D11
hypocenterC11#22858
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#442

Complements

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

NH ≅ G/Ntype
2. C2×D11×#102C2semidirect
3. #13071628C2semidirect
4. D4×(C2×D11)⋊C4C2semidirect
5. #13069489C2semidirect
6. #13069313C2semidirect
7. #13069242C2semidirect
8. #13069041C2semidirect
9. #13068966C2semidirect
10. #13068964C2semidirect
11. #13068877C2semidirect
12. #13068807C2semidirect
13. #13068443C2semidirect
14. #13068393C2semidirect
15. C2×C11×#442C2semidirect
19. C2×C4×D4×C11C22semidirect
28. C2×C11×#106C22semidirect
30. C2×C11×#102C22semidirect
31. C2×C11×#97C22semidirect
32. #10622834C22semidirect
35. C2×#66896C22semidirect
38. #10622769C4semidirect
42. C2×#66879C22semidirect
45. C4⋊C4×Dic11C22semidirect
47. C2×#66872C22semidirect
54. #10622541C22semidirect
56. #10622189C22semidirect
57. #10622189C22semidirect
58. #10622188C22semidirect
59. #10622167C22semidirect
60. #10622167C22semidirect
61. #10622162C22semidirect
75. C2×D4×D11C2×C4semidirect
81. C2×C11×D8C2×C4semidirect
98. #66991C2×C4semidirect
103. C2×#4323C2×C4semidirect
129. C11×#102D4semidirect
133. #66896C2×C4semidirect
140. #66885C2×C4semidirect
141. (C2×D11)⋊C8C2×C4semidirect
260. C2×#442D11semidirect
317. D4×C11C4×D4semidirect
380. C2×C4×D4C2×D11semidirect
386. C2×#106C2×D11semidirect
395. C2×#102C2×D11semidirect
398. C2×#97C2×D11semidirect
453. C2×D11#442semidirect
490. C2×D8C4×D11semidirect
542. #102C22⋊D11semidirect
675. C11#22858semidirect
725. D4C4×C22⋊D11semidirect

Maximal subgroups

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

subgroupindex
C2×#106227692
C2×D11×#1022
#130716282
D4×(C2×D11)⋊C42
#130694892
#130693132
#130692422
#130690412
#130689662
#130689642
#130688772
#130688072
#130684432
#130683932
C2×C11×#4422
#2285811