Finite Group Databasebeta

← #14764982

Subgroups — #14764982

Order 2816.

1296 conjugacy classes of subgroups.

The subgroup lattice has 828 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622386C211yesmaximal, characteristic
2C4×#66948C211yesmaximal, characteristic, complemented
3D11×#390C211yesmaximal, characteristic, complemented
4#13069490C211yesmaximal, characteristic, complemented
5#13069489C211yesmaximal, characteristic, complemented
6#13069315C211yesmaximal, characteristic, complemented
7#13069314C211yesmaximal, characteristic, complemented
8#13069243C211yesmaximal, characteristic, complemented
9#13068967C211yesmaximal, characteristic, complemented
10#13068963C211yesmaximal, characteristic, complemented
11#13068932C211yesmaximal, characteristic, complemented
12#13068807C211yesmaximal, characteristic, complemented
13#13068545C211yesmaximal, characteristic, complemented
14#13068377C211yesmaximal, characteristic, complemented
15C11×#1926C211yesmaximal, characteristic, complemented
16C22×D4×D11C2211yescharacteristic
17C22×#4323C2211yescharacteristic
18C22×D88C2211yescharacteristic
19C2×#66948C2211yescharacteristic
20C2×C4⋊C4×D11C2211yescharacteristic
21C2×C22⋊C4×D11—21no—
22C2×C22⋊C4×D11—21no—
23C2×C4×D44—21no—
24C2×C4×D44C2211yescharacteristic, complemented
25C2×C42×D11C2211yescharacteristic
26C2×C11×#106C2211yescharacteristic, complemented
27C2×C11×#102C2211yescharacteristic
28C2×C11×#102C2211yescharacteristic
29C11×#390C2211yescharacteristic
30C4×C11×C4⋊C4C2211yescharacteristic, complemented
31#10622834C2211yescharacteristic
32C2×#66896C2211yescharacteristic
33C2×#66885C2211yescharacteristic
34C2×#66885C2211yescharacteristic, complemented
35C2×(C2×D11)⋊C8C2211yescharacteristic
36C2×(C2×D11)⋊C8C2211yescharacteristic
37C2×#66879C2211yescharacteristic, complemented
38C2×#66879C2211yescharacteristic, complemented
39#10622601C2211yescharacteristic
40#10622601C2211yescharacteristic, complemented
41#10622600C2211yescharacteristic
42#10622598C2211yescharacteristic, complemented
43C2×#66873C2211yescharacteristic
44C2×#66873C2211yescharacteristic
45C2×#66873C2211yescharacteristic, complemented
46C2×#66872C2211yescharacteristic, complemented
47#10622570—21no—
48#10622570—21no—
49#10622552C2211yescharacteristic
50C4×(C2×D11)⋊C4—21no—
51#10622386C418yescomplemented
52#10622283—21no—
53#10622278—21no—
54C11×#340C2211yescharacteristic, complemented
55C11×#336C2211yescharacteristic, complemented
56#10622189C2211yescharacteristic, complemented
57#10622167C2211yescharacteristic, complemented
58#10622167C2211yescharacteristic, complemented
59#10622162C2211yescharacteristic, complemented
60C24×D11—21no—
61C22×D4×C11C2311yescharacteristic
62C22×C22⋊D11—21no—
63C2×D4×D11—22no—
64C2×D4×D11—41no—
65C2×D4×D11—41no—
66C2×D4×D11—41no—
67C2×D4×D11—41no—
68C2×D4×D11C2×C414yescomplemented
69C22×D44—21no—
70C22×D44C2311yescharacteristic
71C22×D44C2311yescharacteristic
72C22×C4×D11—21no—
73C22×C4×D11—21no—
74C22×C4×D11D411yescharacteristic
75C22×C4×D11D411yescharacteristic
76C22×C4×D11C2311yescharacteristic
77C22×C8×C11C2311yescharacteristic
78C22×C8×C11C2311yescharacteristic
79C2×C11×C4⋊C4C2311yescharacteristic
80C2×C11×C4⋊C4C2311yescharacteristic
81C2×C11×C4⋊C4C2311yescharacteristic
82C2×C11×C22⋊C4—21no—
83C2×C11×C22⋊C4—21no—
84C2×C42×C11—21no—
85C2×C42×C11C2311yescharacteristic
86C2×C22⋊Dic11—21no—
87C2×C22⋊Dic11—21no—
88C2×#4323—41no—
89C2×#4323—41no—
90C2×#4323C2×C414yescomplemented
91C2×(C2×D11)⋊C4—21no—
92C2×(C2×D11)⋊C4—21no—
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×C4⋊Dic11—21no—
101C2×C4⋊Dic11C2311yescharacteristic
102C2×C4⋊Dic11C2311yescharacteristic
103C2×Dic11⋊C4—21no—
104C2×C4×Dic11D411yescharacteristic
105C2×C4×Dic11D411yescharacteristic
106C2×C4×Dic11C2311yescharacteristic
107C22×C11⋊C8C2311yescharacteristic
108C22×C11⋊C8C2311yescharacteristic
109C2×D88—41no—
110C2×D88—41no—
111C2×D88C2×C414yescomplemented
112#66948—22no—
113#66948C2×C414yes—
114C4⋊C4×D11—41no—
115C4⋊C4×D11—41no—
116C22⋊C4×D11—44no—
117C22⋊C4×D11—44no—
118C4×D44—41no—
119C4×D44—41no—
120C4×D44—44no—
121C42×D11—41no—
122C42×D11—41no—
123C11×#106—41no—
124C11×#102—41no—
125C11×#102C2×C414yescomplemented
126C11×#95—21no—
127#66896—41no—
128C11⋊#95—21no—
129C11⋊#95—21no—
130#66885—41no—
131#66885—41no—
132(C2×D11)⋊C8—22no—
133(C2×D11)⋊C8C2×C414yescomplemented
134#66879—41no—
135#66879—41no—
136#66873—41no—
137#66873—41no—
138#66873C2×C414yescomplemented
139#66872—41no—
140#22046—111nomaximal, Sylow
141C24×C11—21no—
142C23×D11—21no—
143C23×D11—21no—
144C23×D11—24no—
145C23×D11—42no—
146C23×D11—42no—
147C23×D11—42no—
148C23×D11—42no—
149C23×D11—42no—
150C23×D11—42no—
151C23×D11C2×D411yescharacteristic
152C2×D4×C11—21no—
153C2×D4×C11—21no—
154C2×D4×C11—21no—
155C2×D4×C11—21no—
156C2×D4×C11—21no—
157C2×D4×C11C22×C412yes—
158C22×C4×C11—21no—
159C22×C4×C11—21no—
160C22×C4×C11—21no—
161C22×C4×C11C2×D411yescharacteristic
162C22×C4×C11C2×D411yescharacteristic
163C22×C4×C11C2411yescharacteristic
164C2×C22⋊D11—24no—
165C2×C22⋊D11—42no—
166C2×C22⋊D11—42no—
167C22×Dic11—21no—
168C22×Dic11—21no—
169C22×Dic11C2×D411yescharacteristic
170C22×Dic11C2×D411yescharacteristic
171C22×Dic11C2×D411yescharacteristic
172D4×D11—44no—
173D4×D11—44no—
174D4×D11—44no—
175D4×D11—44no—
176C2×D44—24no—
177C2×D44—21no—
178C2×D44—21no—
179C2×D44—21no—
180C2×D44—21no—
181C2×D44—21no—
182C2×D44—21no—
183C2×D44—21no—
184C2×D44—21no—
185C2×D44—21no—
186C2×D44—21no—
187C2×D44—42no—
188C2×D44—42no—
189C2×D44C22×C412yes—
190C2×D44C22×C412yes—
191C2×C4×D11—22no—
192C2×C4×D11—22no—
193C2×C4×D11—22no—
194C2×C4×D11—21no—
195C2×C4×D11—21no—
196C2×C4×D11—21no—
197C2×C4×D11—21no—
198C2×C4×D11—41no—
199C2×C4×D11—41no—
200C2×C4×D11—41no—
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×D11C22×C412yes—
208C2×C4×D11#4112yes—
209C2×C8×C11—21no—
210C2×C8×C11—21no—
211C2×C8×C11—21no—
212C2×C8×C11—21no—
213C2×C8×C11—21no—
214C2×C8×C11C22×C412yes—
215C11×C4⋊C4—21no—
216C11×C4⋊C4—21no—
217C11×C4⋊C4—21no—
218C11×C4⋊C4—21no—
219C11×C4⋊C4—21no—
220C11×C4⋊C4C22×C412yes—
221C11×C22⋊C4—42no—
222C11×C22⋊C4—42no—
223C42×C11—21no—
224C42×C11—21no—
225C42×C11—42no—
226C22⋊Dic11—42no—
227C22⋊Dic11—42no—
228#4323—44no—
229(C2×D11)⋊C4—24no—
230(C2×D11)⋊C4—42no—
231(C2×D11)⋊C4—42no—
232(C2×D11)⋊C4—42no—
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—
238C4⋊Dic11—21no—
239C4⋊Dic11—21no—
240C4⋊Dic11—21no—
241C4⋊Dic11—21no—
242C4⋊Dic11—42no—
243Dic11⋊C4—42no—
244C4×Dic11—21no—
245C4×Dic11—21no—
246C4×Dic11—41no—
247C4×Dic11—41no—
248C2×C11⋊C8—21no—
249C2×C11⋊C8—21no—
250C2×C11⋊C8—21no—
251C2×C11⋊C8—21no—
252C2×C11⋊C8—21no—
253C2×C11⋊C8C22×C412yes—
254D88—44no—
255C2×#447—111no—
256C4×#121—111no—
257C2×#390—111no—
258#1972—111no—
259#1972—111no—
260#1936—111no—
261#1936—111no—
262#1926—111no—
263#1926D1111yescharacteristic, complemented
264#1879—111no—
265#1879—111no—
266#1874—111no—
267#1853—111no—
268#1786—111no—
269#1749—111no—
270C23×C11—22no—
271C23×C11—41no—
272C23×C11—41no—
273C23×C11—41no—
274C23×C11—41no—
275C23×C11—41no—
276C23×C11—41no—
277C23×C11C22×D411yescharacteristic
278C22×D11—21no—
279C22×D11—21no—
280C22×D11—21no—
281C22×D11—21no—
282C22×D11—22no—
283C22×D11—22no—
284C22×D11—48no—
285C22×D11—48no—
286C22×D11—41no—
287C22×D11—41no—
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—48no—
299C22×D11—84no—
300C22×D11—84no—
301C22×D11—84no—
302C22×D11—84no—
303C22×D11C4×D412yes—
304C22×D11AGL(1,ℤ/8)12yes—
305C22×D11AGL(1,ℤ/8)12yes—
306D4×C11—22no—
307D4×C11—22no—
308D4×C11—41no—
309D4×C11—41no—
310C2×C4×C11—21no—
311C2×C4×C11—21no—
312C2×C4×C11—22no—
313C2×C4×C11—21no—
314C2×C4×C11—21no—
315C2×C4×C11—21no—
316C2×C4×C11—41no—
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×C11AGL(1,ℤ/8)12yes—
325C2×C4×C11C23×C411yescharacteristic
326C2×C4×C11C2×#4111yescharacteristic
327C2×C4×C11H(5,𝔽2)11yescharacteristic
328C2×C4×C11H(5,𝔽2)11yescharacteristic
329C2×C4×C11H(5,𝔽2)11yescharacteristic
330C2×C4×C11H(5,𝔽2)11yescharacteristic
331C22⋊D11—48no—
332C2×Dic11—21no—
333C2×Dic11—21no—
334C2×Dic11—21no—
335C2×Dic11—21no—
336C2×Dic11—21no—
337C2×Dic11—21no—
338C2×Dic11—21no—
339C2×Dic11—21no—
340C2×Dic11—41no—
341C2×Dic11—41no—
342C2×Dic11—41no—
343C2×Dic11—41no—
344C2×Dic11—41no—
345C2×Dic11—41no—
346C2×Dic11C4×D412yes—
347D44—22no—
348D44—22no—
349D44—22no—
350D44—22no—
351D44—48no—
352D44—41no—
353D44—41no—
354D44—41no—
355D44—41no—
356C4×D11—22no—
357C4×D11—22no—
358C4×D11—22no—
359C4×D11—22no—
360C4×D11—44no—
361C4×D11—44no—
362C4×D11—84no—
363C4×D11—84no—
364C8×C11—22no—
365C8×C11—41no—
366C11⋊C8—22no—
367C11⋊C8—41no—
368C23×D4—111no—
369C22×D8—111no—
370C22×D8—111no—
371C2×#121—111no—
372C2×C4×D4—111no—
373C2×C4×D4—221no—
374C22×C4⋊C4—111no—
375C22×C22⋊C4—221no—
376C22×C22⋊C4—221no—
377C22×C42—111no—
378#447—118no—
379C2×#106—111no—
380C2×#106C2×D1111yescharacteristic, complemented
381C2×#102—111no—
382C2×#102—111no—
383C2×#102—111no—
384C2×#102—111no—
385C2×#102—111no—
386C2×#102—111no—
387C2×#102C2×D1111yescharacteristic
388C2×#102C2×D1111yescharacteristic
389C2×C22⋊C8—111no—
390C2×C22⋊C8—111no—
391C2×#97—111no—
392C2×#97—111no—
393#390—111no—
394#390—111no—
395#390—111no—
396#390—111no—
397#390—221no—
398#390—221no—
399#390C2×D1111yescharacteristic
400#389—111no—
401#388—221no—
402#386—221no—
403#380—111no—
404C4×C4⋊C4C2×D1111yescharacteristic, complemented
405C4×C22⋊C4—221no—
406#340—111no—
407#340—111no—
408#340—111no—
409#340C2×D1111yescharacteristic, complemented
410#336—111no—
411#336C2×D1111yescharacteristic, complemented
412C22×C11—42no—
413C22×C11—42no—
414C22×C11—42no—
415C22×C11—81no—
416C22×C11—81no—
417C22×C11—81no—
418C22×C11—81no—
419C22×C11C2×C4×D411yescharacteristic
420C22×C11#53411yescharacteristic
421C22×C11#53511yescharacteristic
422C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
423C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
424C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
425C22×C11#57511yescharacteristic
426C2×D11—22no—
427C2×D11—22no—
428C2×D11—22no—
429C2×D11—22no—
430C2×D11—22no—
431C2×D11—22no—
432C2×D11—42no—
433C2×D11—42no—
434C2×D11—42no—
435C2×D11—42no—
436C2×D11—42no—
437C2×D11—42no—
438C2×D11—816no—
439C2×D11—81no—
440C2×D11—81no—
441C2×D11—81no—
442C2×D11—81no—
443C2×D11—81no—
444C2×D11—81no—
445C2×D11—81no—
446C2×D11—81no—
447C2×D11#44214yes—
448C4×C11—22no—
449C4×C11—41no—
450C4×C11—42no—
451C4×C11—81no—
452C4×C11—81no—
453C4×C11#51811yescharacteristic
454C4×C11#51811yescharacteristic
455C4×C11#53811yescharacteristic
456C4×C11#53811yescharacteristic
457Dic11—22no—
458Dic11—41no—
459Dic11—41no—
460Dic11—81no—
461Dic11—81no—
462C25—221no—
463C22×D4—114no—
464C22×D4—111no—
465C22×D4—111no—
466C22×D4—221no—
467C22×D4—222no—
468C22×D4—221no—
469C22×D4—441no—
470C22×D4—441no—
471C22×D4—441no—
472C22×D4—441no—
473C22×D4C22×D1111yescharacteristic
474C23×C4—111no—
475C23×C4—111no—
476C23×C4—111no—
477C23×C4—221no—
478C23×C4—221no—
479C2×D8—114no—
480C2×D8—114no—
481C2×D8—441no—
482C2×D8—441no—
483C2×D8—441no—
484C2×D8—441no—
485C22×C8—111no—
486C22×C8—111no—
487C22×C8C22×D1111yescharacteristic
488C22×C8C22×D1111yescharacteristic
489#121—114no—
490#121—222no—
491C4×D4—441no—
492C4×D4—441no—
493C4×D4—444no—
494C2×C4⋊C4—111no—
495C2×C4⋊C4—111no—
496C2×C4⋊C4—221no—
497C2×C4⋊C4—221no—
498C2×C4⋊C4—441no—
499C2×C4⋊C4—441no—
500C2×C4⋊C4C22×D1111yescharacteristic
501C2×C4⋊C4C22×D1111yescharacteristic
502C2×C4⋊C4C22×D1111yescharacteristic
503C2×C22⋊C4—21no—
504C2×C22⋊C4—21no—
505C2×C22⋊C4—221no—
506C2×C22⋊C4—221no—
507C2×C22⋊C4—221no—
508C2×C22⋊C4—221no—
509C2×C22⋊C4—221no—
510C2×C22⋊C4—221no—
511C2×C22⋊C4—221no—
512C2×C22⋊C4—221no—
513C2×C22⋊C4—221no—
514C2×C22⋊C4—221no—
515C2×C22⋊C4—221no—
516C2×C22⋊C4—444no—
517C2×C22⋊C4—444no—
518C2×C42—21no—
519C2×C42—111no—
520C2×C42—111no—
521C2×C42—111no—
522C2×C42—441no—
523C2×C42—441no—
524C2×C42C22×D1111yescharacteristic
525#106—41no—
526#106—441no—
527#102—41no—
528#102—114no—
529#102—441no—
530#102—441no—
531#102—441no—
532#102—441no—
533#102—441no—
534#102C4×D1114yescomplemented
535C22⋊C8—114no—
536C22⋊C8—222no—
537#97—441no—
538#97—441no—
539#95—21no—
540#95—221no—
541#95—221no—
542C2×C11—82no—
543C2×C11#232111yescharacteristic
544C2×C11C2×#44211yescharacteristic
545C2×C11C4×AGL(1,ℤ/8)11yescharacteristic
546C2×C11#319211yescharacteristic
547C2×C11#319411yescharacteristic
548C2×C11#321311yescharacteristic
549C2×C11#321711yescharacteristic
550D11—24no—
551D11—82no—
552D11—82no—
553C24—21no—
554C24—111no—
555C24—224no—
556C24—221no—
557C24—221no—
558C24—442no—
559C24—442no—
560C24—442no—
561C24—442no—
562C24—442no—
563C24—442no—
564C2×D4—21no—
565C2×D4—21no—
566C2×D4—21no—
567C2×D4—21no—
568C2×D4—21no—
569C2×D4—112no—
570C2×D4—112no—
571C2×D4—224no—
572C2×D4—224no—
573C2×D4—221no—
574C2×D4—221no—
575C2×D4—221no—
576C2×D4—221no—
577C2×D4—221no—
578C2×D4—221no—
579C2×D4—221no—
580C2×D4—221no—
581C2×D4—221no—
582C2×D4—221no—
583C2×D4—442no—
584C2×D4—442no—
585C2×D4—444no—
586C2×D4—444no—
587C2×D4—444no—
588C2×D4—444no—
589C2×D4—442no—
590C2×D4—442no—
591C2×D4C2×C4×D1112yes—
592C22×C4—21no—
593C22×C4—21no—
594C22×C4—21no—
595C22×C4—111no—
596C22×C4—112no—
597C22×C4—112no—
598C22×C4—111no—
599C22×C4—111no—
600C22×C4—222no—
601C22×C4—222no—
602C22×C4—221no—
603C22×C4—221no—
604C22×C4—221no—
605C22×C4—221no—
606C22×C4—222no—
607C22×C4—221no—
608C22×C4—221no—
609C22×C4—441no—
610C22×C4—441no—
611C22×C4—441no—
612C22×C4—442no—
613C22×C4—442no—
614C22×C4—442no—
615C22×C4—442no—
616C22×C4—442no—
617C22×C4—442no—
618C22×C4D4×D1111yescharacteristic
619C22×C4D4×D1111yescharacteristic
620C22×C4C23×D1111yescharacteristic
621D8—444no—
622D8—444no—
623C2×C8—21no—
624C2×C8—21no—
625C2×C8—21no—
626C2×C8—21no—
627C2×C8—21no—
628C2×C8—112no—
629C2×C8—221no—
630C2×C8—221no—
631C2×C8—221no—
632C2×C8—221no—
633C2×C8—221no—
634C2×C8C2×C4×D1112yes—
635C4⋊C4—21no—
636C4⋊C4—21no—
637C4⋊C4—21no—
638C4⋊C4—21no—
639C4⋊C4—21no—
640C4⋊C4—221no—
641C4⋊C4—221no—
642C4⋊C4—221no—
643C4⋊C4—221no—
644C4⋊C4—442no—
645C4⋊C4—442no—
646C4⋊C4C2×C4×D1112yes—
647C22⋊C4—42no—
648C22⋊C4—42no—
649C22⋊C4—224no—
650C22⋊C4—442no—
651C22⋊C4—442no—
652C22⋊C4—442no—
653C22⋊C4—442no—
654C22⋊C4—442no—
655C22⋊C4—442no—
656C22⋊C4—442no—
657C22⋊C4—442no—
658C22⋊C4—442no—
659C22⋊C4—442no—
660C42—21no—
661C42—21no—
662C42—42no—
663C42—221no—
664C42—221no—
665C42—441no—
666C42—441no—
667C11#2204611yescharacteristic, complemented, Sylow
668C23—22no—
669C23—41no—
670C23—41no—
671C23—41no—
672C23—41no—
673C23—41no—
674C23—41no—
675C23—112no—
676C23—112no—
677C23—112no—
678C23—221no—
679C23—221no—
680C23—221no—
681C23—221no—
682C23—222no—
683C23—222no—
684C23—448no—
685C23—448no—
686C23—448no—
687C23—441no—
688C23—441no—
689C23—441no—
690C23—441no—
691C23—441no—
692C23—441no—
693C23—441no—
694C23—441no—
695C23—441no—
696C23—441no—
697C23—441no—
698C23—441no—
699C23—884no—
700C23—884no—
701C23—884no—
702C23—884no—
703C23C2×D4×D1111yescharacteristic
704D4—22no—
705D4—22no—
706D4—41no—
707D4—41no—
708D4—222no—
709D4—222no—
710D4—222no—
711D4—222no—
712D4—448no—
713D4—448no—
714D4—441no—
715D4—441no—
716D4—441no—
717D4—441no—
718C2×C4—21no—
719C2×C4—21no—
720C2×C4—21no—
721C2×C4—21no—
722C2×C4—22no—
723C2×C4—21no—
724C2×C4—41no—
725C2×C4—41no—
726C2×C4—41no—
727C2×C4—41no—
728C2×C4—41no—
729C2×C4—41no—
730C2×C4—41no—
731C2×C4—41no—
732C2×C4—112no—
733C2×C4—221no—
734C2×C4—221no—
735C2×C4—222no—
736C2×C4—222no—
737C2×C4—222no—
738C2×C4—222no—
739C2×C4—221no—
740C2×C4—221no—
741C2×C4—221no—
742C2×C4—221no—
743C2×C4—221no—
744C2×C4—221no—
745C2×C4—444no—
746C2×C4—444no—
747C2×C4—441no—
748C2×C4—441no—
749C2×C4—441no—
750C2×C4—441no—
751C2×C4—441no—
752C2×C4—441no—
753C2×C4—884no—
754C2×C4—884no—
755C2×C4#6696712yes—
756C2×C4C22×C4×D1111yescharacteristic
757C2×C4#6703711yescharacteristic
758C2×C4#41×D1111yescharacteristic
759C2×C4#6704211yescharacteristic
760C2×C4#6704211yescharacteristic
761C2×C4#6704211yescharacteristic
762C8—22no—
763C8—41no—
764C8—222no—
765C8—441no—
766C22—42no—
767C22—42no—
768C22—42no—
769C22—81no—
770C22—81no—
771C22—81no—
772C22—81no—
773C22—114no—
774C22—222no—
775C22—222no—
776C22—222no—
777C22—222no—
778C22—222no—
779C22—222no—
780C22—442no—
781C22—442no—
782C22—442no—
783C22—442no—
784C22—442no—
785C22—442no—
786C22—8816no—
787C22—881no—
788C22—881no—
789C22—881no—
790C22—881no—
791C22—881no—
792C22—881no—
793C22—881no—
794C22—881no—
795C22C4×D4×D1111yescharacteristic
796C22#1062313811yescharacteristic
797C22#1062318411yescharacteristic
798C22C2×#6696711yescharacteristic
799C22#1062329911yescharacteristic
800C22D11×AGL(1,ℤ/8)11yescharacteristic
801C22D11×AGL(1,ℤ/8)11yescharacteristic
802C4—22no—
803C4—41no—
804C4—42no—
805C4—81no—
806C4—81no—
807C4—222no—
808C4—441no—
809C4—441no—
810C4—881no—
811C4—881no—
812C4#1062305211yescharacteristic
813C4#1062307611yescharacteristic
814C4#1062320911yescharacteristic
815C4#1062323511yescharacteristic
816C2—82no—
817C2—224no—
818C2—882no—
819C2—882no—
820C2#1307127811yescharacteristic
821C2D11×#44211yescharacteristic
822C2C4×#6696711yescharacteristic
823C2#1307941511yescharacteristic
824C2#1307943411yescharacteristic
825C2#1307960111yescharacteristic
826C2#1307963811yescharacteristic
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#22046
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. C4×#66948C2semidirect
3. D11×#390C2semidirect
4. #13069490C2semidirect
5. #13069489C2semidirect
6. #13069315C2semidirect
7. #13069314C2semidirect
8. #13069243C2semidirect
9. #13068967C2semidirect
10. #13068963C2semidirect
11. #13068932C2semidirect
12. #13068807C2semidirect
13. #13068545C2semidirect
14. #13068377C2semidirect
15. C11×#1926C2semidirect
24. C2×C4×D44C22semidirect
26. C2×C11×#106C22semidirect
30. C4×C11×C4⋊C4C22semidirect
34. C2×#66885C22semidirect
37. C2×#66879C22semidirect
38. C2×#66879C22semidirect
40. #10622601C22semidirect
42. #10622598C22semidirect
45. C2×#66873C22semidirect
46. C2×#66872C22semidirect
51. #10622386C4semidirect
54. C11×#340C22semidirect
55. C11×#336C22semidirect
56. #10622189C22semidirect
57. #10622167C22semidirect
58. #10622167C22semidirect
59. #10622162C22semidirect
68. C2×D4×D11C2×C4semidirect
90. C2×#4323C2×C4semidirect
111. C2×D88C2×C4semidirect
125. C11×#102C2×C4semidirect
133. (C2×D11)⋊C8C2×C4semidirect
138. #66873C2×C4semidirect
263. #1926D11semidirect
380. C2×#106C2×D11semidirect
404. C4×C4⋊C4C2×D11semidirect
409. #340C2×D11semidirect
411. #336C2×D11semidirect
534. #102C4×D11semidirect
667. C11#22046semidirect

Maximal subgroups

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

subgroupindex
C2×#106223862
C4×#669482
D11×#3902
#130694902
#130694892
#130693152
#130693142
#130692432
#130689672
#130689632
#130689322
#130688072
#130685452
#130683772
C11×#19262
#2204611