Finite Group Databasebeta

← #14774083

Subgroups — #14774083

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×#10622345C211yesmaximal, characteristic
2C2×#10622482C211yesmaximal, characteristic, complemented
3C22×#66873C211yesmaximal, characteristic, complemented
4#13071632C211yesmaximal, characteristic, complemented
5#13071436C211yesmaximal, characteristic, complemented
6#13069490C211yesmaximal, characteristic, complemented
7#13069311C211yesmaximal, characteristic, complemented
8#13069242C211yesmaximal, characteristic, complemented
9#13069042C211yesmaximal, characteristic, complemented
10#13068965C211yesmaximal, characteristic, complemented
11#13068965C211yesmaximal, characteristic, complemented
12#13068874C211yesmaximal, characteristic, complemented
13#13068440C211yesmaximal, characteristic, complemented
14#13068395C211yesmaximal, characteristic, complemented
15C11×#1853C211yesmaximal, characteristic, complemented
16C23×D44C2211yescharacteristic
17C22×C11×C4⋊C4C2211yescharacteristic
18C2×#66983C2211yescharacteristic
19C2×C4×C22⋊D11—21no—
20C23×C11⋊C8C2211yescharacteristic
21C22×D88C2211yescharacteristic
22C22×D88C2211yescharacteristic
23C2×#66946C2211yescharacteristic
24C2×#66946C2211yescharacteristic
25C2×#66946C2211yescharacteristic, complemented
26C2×C22⋊C4×D11—21no—
27C2×C11×#106C2211yescharacteristic, complemented
28C2×C11×#106C2211yescharacteristic, complemented
29C2×C11×C22⋊C8C2211yescharacteristic
30C11×#380C2211yescharacteristic
31#10622826—21no—
32C4×C22⋊Dic11C2211yescharacteristic
33C2×#66885C2211yescharacteristic
34C2×#66885C2211yescharacteristic
35C2×#66879C2211yescharacteristic, complemented
36C2×#66879C2211yescharacteristic, complemented
37#10622603—21no—
38#10622602—21no—
39#10622601C2211yescharacteristic
40#10622601C2211yescharacteristic
41#10622601C2211yescharacteristic, complemented
42C4⋊C4×Dic11C2211yescharacteristic, complemented
43#10622586C2211yescharacteristic, complemented
44C2×#66873—24no—
45C2×#66873C2211yescharacteristic
46C2×#66873C2211yescharacteristic
47C2×#66873C2211yescharacteristic
48C2×#66873C2211yescharacteristic
49C2×#66873C2211yescharacteristic, complemented
50C2×#66873C2211yescharacteristic, complemented
51#10622568—21no—
52#10622482—24no—
53#10622345C418yescomplemented
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—
63C23×C4×C11—21no—
64C23×C4×C11C2311yescharacteristic
65C22×C22⋊D11—21no—
66C22×D44—22no—
67C22×D44—22no—
68C22×D44—21no—
69C22×D44—22no—
70C22×D44—41no—
71C22×D44—41no—
72C22×D44C2×C414yescomplemented
73C22×D44C2311yescharacteristic
74C22×D44C2311yescharacteristic
75C22×D44C2311yescharacteristic
76C22×C4×D11—21no—
77C22×C4×D11—21no—
78C22×C4×D11—21no—
79C22×C8×C11C2311yescharacteristic
80C22×C8×C11C2311yescharacteristic
81C2×C11×C4⋊C4—22no—
82C2×C11×C4⋊C4—21no—
83C2×C11×C4⋊C4—41no—
84C2×C11×C4⋊C4C2311yescharacteristic
85C2×C11×C4⋊C4C2311yescharacteristic
86C2×C11×C4⋊C4C2311yescharacteristic
87C2×C11×C4⋊C4C2311yescharacteristic
88C2×C11×C22⋊C4—21no—
89C2×C22⋊Dic11D411yescharacteristic
90C2×C22⋊Dic11D411yescharacteristic
91#66983—22no—
92#66983C2×C414yescomplemented
93C4×C22⋊D11—44no—
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)⋊C4—21no—
101C2×(C2×D11)⋊C4—21no—
102C2×(C2×D11)⋊C4—21no—
103C2×(C2×D11)⋊C4—21no—
104C2×C4⋊Dic11C2311yescharacteristic
105C2×Dic11⋊C4—21no—
106C2×C4×Dic11—21no—
107C2×C4×Dic11C2311yescharacteristic
108C2×C4×Dic11C2311yescharacteristic
109C22×C11⋊C8—22no—
110C22×C11⋊C8—22no—
111C22×C11⋊C8—41no—
112C22×C11⋊C8C2311yescharacteristic
113C22×C11⋊C8C2311yescharacteristic
114C2×D88—22no—
115C2×D88—22no—
116C2×D88—41no—
117C2×D88—41no—
118C2×D88C2×C414yescomplemented
119C2×D88C2×C414yescomplemented
120#66946—22no—
121#66946—22no—
122#66946—22no—
123#66946—41no—
124#66946—41no—
125#66946—41no—
126C22⋊C4×D11—44no—
127C11×#106—22no—
128C11×#106—41no—
129C11×C22⋊C8C2×C414yescomplemented
130C11×#95—21no—
131C11⋊#95—21no—
132C11⋊#95—21no—
133C11⋊#95D411yescharacteristic
134C11⋊#95D411yescharacteristic
135#66885C2×C414yescomplemented
136#66885C2×C414yescomplemented
137#66879—22no—
138#66879—41no—
139#66873—22no—
140#66873—22no—
141#66873—22no—
142#66873—22no—
143#66873—41no—
144#66873D414yescomplemented
145#22858—111nomaximal, Sylow
146C24×C11C2×D411yescharacteristic
147C23×D11—21no—
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—
157C22×C4×C11—21no—
158C22×C4×C11—21no—
159C22×C4×C11—21no—
160C22×C4×C11—21no—
161C22×C4×C11—21no—
162C22×C4×C11—21no—
163C22×C4×C11—21no—
164C22×C4×C11—21no—
165C22×C4×C11—42no—
166C22×C4×C11—42no—
167C22×C4×C11—81no—
168C22×C4×C11C22×C412yes—
169C22×C4×C11C2×D411yescharacteristic
170C22×C4×C11#4112yes—
171C22×C4×C11C2411yescharacteristic
172C2×C22⋊D11—24no—
173C2×C22⋊D11—42no—
174C2×C22⋊D11—42no—
175C22×Dic11—21no—
176C22×Dic11C2×D411yescharacteristic
177C22×Dic11C2×D411yescharacteristic
178C22×Dic11C2×D411yescharacteristic
179C22×Dic11C2×D411yescharacteristic
180C2×D44—28no—
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—21no—
191C2×D44—21no—
192C2×D44—21no—
193C2×D44—21no—
194C2×D44—21no—
195C2×D44—42no—
196C2×D44—42no—
197C2×D44—44no—
198C2×D44—44no—
199C2×D44—44no—
200C2×D44C22×C412yes—
201C2×D44C22×C412yes—
202C2×D44C22×C412yes—
203C2×D44C2×D412yes—
204C2×D44#4112yes—
205C2×C4×D11—42no—
206C2×C4×D11—42no—
207C2×C4×D11—42no—
208C2×C4×D11—42no—
209C2×C4×D11—42no—
210C2×C4×D11—42no—
211C2×C4×D11—81no—
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×C11C22×C412yes—
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—21no—
226C11×C4⋊C4—21no—
227C11×C4⋊C4—42no—
228C11×C4⋊C4C2×D412yes—
229C11×C22⋊C4—42no—
230C22⋊Dic11—22no—
231C22⋊Dic11—22no—
232(C2×D11)⋊C4—24no—
233(C2×D11)⋊C4—42no—
234(C2×D11)⋊C4—42no—
235(C2×D11)⋊C4—42no—
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—
241(C2×D11)⋊C4—81no—
242C4⋊Dic11—21no—
243C4⋊Dic11C22×C412yes—
244Dic11⋊C4—42no—
245C4×Dic11—21no—
246C4×Dic11—21no—
247C4×Dic11—21no—
248C4×Dic11—21no—
249C4×Dic11—42no—
250C2×C11⋊C8—21no—
251C2×C11⋊C8—21no—
252C2×C11⋊C8—21no—
253C2×C11⋊C8—21no—
254C2×C11⋊C8—21no—
255C2×C11⋊C8—44no—
256C2×C11⋊C8C2×D412yes—
257D88—28no—
258D88—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#1864—111no—
271#1853D1111yescharacteristic, complemented
272#1762—111no—
273#1752—111no—
274C23×C11—21no—
275C23×C11—21no—
276C23×C11—21no—
277C23×C11—21no—
278C23×C11C4×D412yes—
279C23×C11AGL(1,ℤ/8)12yes—
280C23×C11AGL(1,ℤ/8)12yes—
281C23×C11C22×D411yescharacteristic
282C22×D11—22no—
283C22×D11—22no—
284C22×D11—22no—
285C22×D11—22no—
286C22×D11—22no—
287C22×D11—48no—
288C22×D11—41no—
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—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—
310C2×C4×C11—21no—
311C2×C4×C11—21no—
312C2×C4×C11—22no—
313C2×C4×C11—22no—
314C2×C4×C11—22no—
315C2×C4×C11—22no—
316C2×C4×C11—22no—
317C2×C4×C11—41no—
318C2×C4×C11—41no—
319C2×C4×C11—41no—
320C2×C4×C11—41no—
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—84no—
329C2×C4×C11C4×D412yes—
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—22no—
338C2×Dic11—21no—
339C2×Dic11—21no—
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—
352D44—22no—
353D44—22no—
354D44—22no—
355D44—22no—
356D44—22no—
357D44—22no—
358D44—22no—
359D44—48no—
360D44—41no—
361D44—41no—
362D44—41no—
363D44—41no—
364D44C4×D414yescomplemented
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×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⋊C4C2×D1111yescharacteristic
382C22×C22⋊C4—221no—
383#447—118no—
384#442—224no—
385C2×#106C2×D1111yescharacteristic, complemented
386C2×#106C2×D1111yescharacteristic, complemented
387C2×#102—111no—
388C2×#102—111no—
389C2×#102—111no—
390C2×#102—111no—
391C2×#102—111no—
392C2×#102—111no—
393C2×#102—111no—
394C2×#102—111no—
395C2×#102—224no—
396C2×C22⋊C8C2×D1111yescharacteristic
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#44214yescomplemented
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—24no—
433C2×D11—42no—
434C2×D11—42no—
435C2×D11—42no—
436C2×D11—42no—
437C2×D11—42no—
438C2×D11—42no—
439C2×D11—42no—
440C2×D11—42no—
441C2×D11—42no—
442C2×D11—42no—
443C2×D11—42no—
444C2×D11—42no—
445C2×D11—816no—
446C2×D11—81no—
447C2×D11—81no—
448C2×D11—81no—
449C2×D11—81no—
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×C11—81no—
459C4×C11C2×C4×D411yescharacteristic
460C4×C11#51811yescharacteristic
461C4×C11#54611yescharacteristic
462C4×C11#55111yescharacteristic
463Dic11—42no—
464Dic11—41no—
465Dic11—41no—
466Dic11—41no—
467Dic11—41no—
468C25—221no—
469C22×D4—114no—
470C22×D4—111no—
471C22×D4—111no—
472C22×D4—111no—
473C22×D4—222no—
474C22×D4—222no—
475C22×D4—221no—
476C22×D4—221no—
477C22×D4—222no—
478C22×D4—441no—
479C22×D4—441no—
480C23×C4—21no—
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—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—22no—
508C2×C4⋊C4—21no—
509C2×C4⋊C4—41no—
510C2×C4⋊C4—111no—
511C2×C4⋊C4—221no—
512C2×C4⋊C4C22×D1111yescharacteristic
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—111no—
532C2×C42—221no—
533#106—22no—
534#106—41no—
535#102—114no—
536#102—114no—
537#102—114no—
538#102—222no—
539#102—222no—
540#102—222no—
541#102—222no—
542#102—441no—
543C22⋊C8C4×D1114yescomplemented
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#235811yescharacteristic
553C2×C11C2×#44211yescharacteristic
554C2×C11#294611yescharacteristic
555C2×C11#326411yescharacteristic
556C2×C11#326511yescharacteristic
557C2×C11#330611yescharacteristic
558C2×C11#331811yescharacteristic
559D11—44no—
560D11—82no—
561D11—82no—
562C24—221no—
563C24—221no—
564C24—221no—
565C24—224no—
566C24—442no—
567C24—442no—
568C24—442no—
569C24—442no—
570C24—881no—
571C24—881no—
572C24D4×D1111yescharacteristic
573C2×D4—112no—
574C2×D4—112no—
575C2×D4—112no—
576C2×D4—112no—
577C2×D4—112no—
578C2×D4—228no—
579C2×D4—224no—
580C2×D4—224no—
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—221no—
592C2×D4—221no—
593C2×D4—221no—
594C2×D4—444no—
595C2×D4—444no—
596C2×D4—444no—
597C2×D4—442no—
598C2×D4—442no—
599C2×D4—442no—
600C2×D4—442no—
601C22×C4—21no—
602C22×C4—21no—
603C22×C4—21no—
604C22×C4—21no—
605C22×C4—21no—
606C22×C4—21no—
607C22×C4—21no—
608C22×C4—21no—
609C22×C4—42no—
610C22×C4—42no—
611C22×C4—81no—
612C22×C4—111no—
613C22×C4—111no—
614C22×C4—111no—
615C22×C4—111no—
616C22×C4—221no—
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×C4C2×C4×D1112yes—
627C22×C4D4×D1111yescharacteristic
628C22×C4#434312yes—
629C22×C4C23×D1111yescharacteristic
630D8—228no—
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×C4×D1112yes—
645C4⋊C4—21no—
646C4⋊C4—21no—
647C4⋊C4—21no—
648C4⋊C4—21no—
649C4⋊C4—21no—
650C4⋊C4—21no—
651C4⋊C4—21no—
652C4⋊C4—42no—
653C4⋊C4—112no—
654C4⋊C4—221no—
655C4⋊C4—442no—
656C4⋊C4D4×D1112yes—
657C22⋊C4—42no—
658C22⋊C4—222no—
659C22⋊C4—222no—
660C22⋊C4—224no—
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—222no—
681C23—222no—
682C23—222no—
683C23—222no—
684C23—222no—
685C23—448no—
686C23—441no—
687C23—441no—
688C23—441no—
689C23—441no—
690C23—448no—
691C23—441no—
692C23—441no—
693C23—441no—
694C23—441no—
695C23—441no—
696C23—441no—
697C23—441no—
698C23—441no—
699C23—441no—
700C23—441no—
701C23—441no—
702C23—441no—
703C23—884no—
704C23—884no—
705C23—884no—
706C23—884no—
707C23—884no—
708C23#6694612yes—
709C23#6696712yes—
710C23#6696712yes—
711C23C2×D4×D1111yescharacteristic
712D4—114no—
713D4—222no—
714D4—222no—
715D4—222no—
716D4—222no—
717D4—222no—
718D4—222no—
719D4—222no—
720D4—448no—
721D4—448no—
722D4—441no—
723D4—441no—
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—41no—
742C2×C4—41no—
743C2×C4—41no—
744C2×C4—84no—
745C2×C4—222no—
746C2×C4—221no—
747C2×C4—221no—
748C2×C4—221no—
749C2×C4—221no—
750C2×C4—221no—
751C2×C4—221no—
752C2×C4—221no—
753C2×C4—221no—
754C2×C4—221no—
755C2×C4—221no—
756C2×C4—221no—
757C2×C4—221no—
758C2×C4—441no—
759C2×C4—441no—
760C2×C4—884no—
761C2×C4—884no—
762C2×C4—884no—
763C2×C4#6694612yes—
764C2×C4C22×C4×D1111yescharacteristic
765C2×C4C2×D4×D1111yescharacteristic
766C2×C4#6703711yescharacteristic
767C2×C4C2×#434311yescharacteristic
768C2×C4#41×D1111yescharacteristic
769C2×C4#6704211yescharacteristic
770C8—22no—
771C8—22no—
772C8—222no—
773C8—441no—
774C22—22no—
775C22—22no—
776C22—22no—
777C22—22no—
778C22—22no—
779C22—22no—
780C22—224no—
781C22—442no—
782C22—442no—
783C22—442no—
784C22—442no—
785C22—442no—
786C22—442no—
787C22—442no—
788C22—442no—
789C22—442no—
790C22—442no—
791C22—442no—
792C22—442no—
793C22—8816no—
794C22—881no—
795C22—881no—
796C22—881no—
797C22—881no—
798C22—881no—
799C22—881no—
800C22—881no—
801C22—881no—
802C22#1062248214yescomplemented
803C22C2×#6694611yescharacteristic
804C22#1062312111yescharacteristic
805C22#1062318511yescharacteristic
806C22C2×#6696711yescharacteristic
807C22C2×#6696711yescharacteristic
808C22#1062330511yescharacteristic
809C22#1062330911yescharacteristic
810C4—22no—
811C4—42no—
812C4—81no—
813C4—81no—
814C4—81no—
815C4—441no—
816C4—441no—
817C4—442no—
818C4—441no—
819C4—441no—
820C4C4×D4×D1111yescharacteristic
821C4#1062307611yescharacteristic
822C4#1062316111yescharacteristic
823C4#1062316811yescharacteristic
824C2—24no—
825C2—444no—
826C2—882no—
827C2—882no—
828C2#1307159211yescharacteristic
829C2C2×#1062248211yescharacteristic
830C2#1307744611yescharacteristic
831C2#1308010011yescharacteristic
832C2#1308010411yescharacteristic
833C2#1308057511yescharacteristic
834C2#1308075511yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#1853C2
socleC23×C11C22×D4
prime radicalC2×#10622345C2
cosocleC22×C4×C11C24
hypercenter#1853D11
hypocenterC11#22858
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1853

Complements

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

NH ≅ G/Ntype
2. C2×#10622482C2semidirect
3. C22×#66873C2semidirect
4. #13071632C2semidirect
5. #13071436C2semidirect
6. #13069490C2semidirect
7. #13069311C2semidirect
8. #13069242C2semidirect
9. #13069042C2semidirect
10. #13068965C2semidirect
11. #13068965C2semidirect
12. #13068874C2semidirect
13. #13068440C2semidirect
14. #13068395C2semidirect
15. C11×#1853C2semidirect
25. C2×#66946C22semidirect
27. C2×C11×#106C22semidirect
28. C2×C11×#106C22semidirect
35. C2×#66879C22semidirect
36. C2×#66879C22semidirect
41. #10622601C22semidirect
42. C4⋊C4×Dic11C22semidirect
43. #10622586C22semidirect
49. C2×#66873C22semidirect
50. C2×#66873C22semidirect
53. #10622345C4semidirect
56. C11×#340C22semidirect
57. C11×#340C22semidirect
58. #10622188C22semidirect
59. #10622188C22semidirect
60. #10622167C22semidirect
61. #10622167C22semidirect
72. C22×D44C2×C4semidirect
92. #66983C2×C4semidirect
118. C2×D88C2×C4semidirect
119. C2×D88C2×C4semidirect
129. C11×C22⋊C8C2×C4semidirect
135. #66885C2×C4semidirect
136. #66885C2×C4semidirect
144. #66873D4semidirect
271. #1853D11semidirect
364. D44C4×D4semidirect
385. C2×#106C2×D11semidirect
386. C2×#106C2×D11semidirect
414. #340C2×D11semidirect
415. #340C2×D11semidirect
424. C22×C11#442semidirect
543. C22⋊C8C4×D11semidirect
675. C11#22858semidirect
802. C22#10622482semidirect

Maximal subgroups

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

subgroupindex
C2×#106223452
C2×#106224822
C22×#668732
#130716322
#130714362
#130694902
#130693112
#130692422
#130690422
#130689652
#130688742
#130684402
#130683952
C11×#18532
#2285811