Finite Group Databasebeta

← #14764899

Subgroups — #14764899

Order 2816.

1308 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
2#13071124C211yesmaximal, characteristic, complemented
3D11×#390C211yesmaximal, characteristic, complemented
4#13069482C211yesmaximal, characteristic, complemented
5#13069481C211yesmaximal, characteristic, complemented
6#13069298C211yesmaximal, characteristic, complemented
7#13069238C211yesmaximal, characteristic, complemented
8#13069234C211yesmaximal, characteristic, complemented
9#13068965C211yesmaximal, characteristic, complemented
10#13068961C211yesmaximal, characteristic, complemented
11#13068932C211yesmaximal, characteristic, complemented
12#13068805C211yesmaximal, characteristic, complemented
13#13068545C211yesmaximal, characteristic, complemented
14C4×(C2×D11)⋊C8C211yesmaximal, characteristic, complemented
15C11×#1934C211yesmaximal, characteristic, complemented
16C22×D4×D11C2211yescharacteristic
17C22×#4323C2211yescharacteristic
18C22×D88C2211yescharacteristic
19C2×#66948C2211yescharacteristic
20C2×#66946—21no—
21C2×#66946C2211yescharacteristic, complemented
22C2×C4⋊C4×D11C2211yescharacteristic
23C2×C22⋊C4×D11—21no—
24C2×C22⋊C4×D11—21no—
25C2×C42×D11C2211yescharacteristic
26C2×C11×#102C2211yescharacteristic
27C2×C11×#102C2211yescharacteristic
28C2×C4×C8×C11C2211yescharacteristic, complemented
29C11×#390C2211yescharacteristic
30C11×#389C2211yescharacteristic, complemented
31#10622834C2211yescharacteristic
32C2×#66896C2211yescharacteristic
33C2×#66885C2211yescharacteristic
34C2×#66885C2211yescharacteristic, complemented
35C2×(C2×D11)⋊C8C2211yescharacteristic
36C2×(C2×D11)⋊C8C2211yescharacteristic
37C2×#66882C2211yescharacteristic, complemented
38#10622603—21no—
39#10622601C2211yescharacteristic
40#10622600C2211yescharacteristic
41C4⋊C4×Dic11C2211yescharacteristic, complemented
42C2×#66873C2211yescharacteristic
43C2×#66873C2211yescharacteristic
44C2×#66873C2211yescharacteristic, complemented
45C2×#66871C2211yescharacteristic, complemented
46#10622570—21no—
47#10622570—21no—
48#10622552C2211yescharacteristic
49#10622552C2211yescharacteristic, complemented
50C2×C4×C11⋊C8C2211yescharacteristic, complemented
51#10622386C418yescomplemented
52#10622279—21no—
53#10622278—21no—
54C11×#340C2211yescharacteristic, complemented
55C11×#340C2211yescharacteristic, complemented
56#10622188C2211yescharacteristic, complemented
57#10622188C2211yescharacteristic, complemented
58#10622167C2211yescharacteristic, complemented
59#10622167C2211yescharacteristic, 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⋊C4—21no—
80C2×C11×C4⋊C4C2311yescharacteristic
81C2×C11×C4⋊C4C2311yescharacteristic
82C2×C11×C4⋊C4C2311yescharacteristic
83C2×C11×C22⋊C4—21no—
84C2×C11×C22⋊C4—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⋊Dic11C2311yescharacteristic
101C2×C4⋊Dic11C2311yescharacteristic
102C2×Dic11⋊C4—21no—
103C2×C4×Dic11—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—
114#66946—41no—
115#66946—41no—
116#66946—44no—
117C4⋊C4×D11—41no—
118C4⋊C4×D11—41no—
119C22⋊C4×D11—44no—
120C22⋊C4×D11—44no—
121C42×D11—41no—
122C42×D11—41no—
123C11×#102—41no—
124C11×#102C2×C414yescomplemented
125C4×C8×C11—41no—
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#66882—41no—
135#66873—41no—
136#66873—41no—
137#66873C2×C414yescomplemented
138#66871—41no—
139C4×C11⋊C8—41no—
140#22040—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—21no—
194C2×C4×D11—21no—
195C2×C4×D11—21no—
196C2×C4×D11—21no—
197C2×C4×D11—41no—
198C2×C4×D11—41no—
199C2×C4×D11—41no—
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×D11D814yescomplemented
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⋊C4—42no—
221C11×C4⋊C4C22×C412yes—
222C11×C22⋊C4—42no—
223C11×C22⋊C4—42no—
224C42×C11—21no—
225C42×C11—21no—
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—
242Dic11⋊C4—42no—
243C4×Dic11—21no—
244C4×Dic11—21no—
245C4×Dic11—41no—
246C4×Dic11—41no—
247C4×Dic11—42no—
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#1970—111no—
259#1970—111no—
260#1934—111no—
261#1934D1111yescharacteristic, complemented
262#1925—111no—
263#1925—111no—
264#1879—111no—
265#1879—111no—
266#1874—111no—
267#1852—111no—
268#1786—111no—
269C4×C22⋊C8—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×D11C2×D812yes—
305C22×D11#13512yes—
306D4×C11—22no—
307D4×C11—22no—
308D4×C11—41no—
309D4×C11—41no—
310C2×C4×C11—21no—
311C2×C4×C11—21no—
312C2×C4×C11—21no—
313C2×C4×C11—21no—
314C2×C4×C11—22no—
315C2×C4×C11—41no—
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×C11C2×D812yes—
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—41no—
340C2×Dic11—41no—
341C2×Dic11—41no—
342C2×Dic11—41no—
343C2×Dic11—41no—
344C2×Dic11—41no—
345C2×Dic11C4×D412yes—
346C2×Dic11C2×D812yes—
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×#107—111no—
380C2×#107—111no—
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×C4×C8—111no—
392C2×C4×C8C2×D1111yescharacteristic, complemented
393#390—111no—
394#390—111no—
395#390—111no—
396#390—111no—
397#390—221no—
398#390—221no—
399#390C2×D1111yescharacteristic
400#389C2×D1111yescharacteristic, complemented
401#388—221no—
402#386—221no—
403#380—111no—
404C4×C4⋊C4—111no—
405C4×C22⋊C4—221no—
406#340—111no—
407#340—111no—
408#340C2×D1111yescharacteristic, complemented
409#340C2×D1111yescharacteristic, complemented
410#336—111no—
411#336—111no—
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×C11C22×D811yescharacteristic
423C22×C11C2×#13511yescharacteristic
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×D11C4×D814yes—
448C4×C11—22no—
449C4×C11—22no—
450C4×C11—42no—
451C4×C11—81no—
452C4×C11—81no—
453C4×C11#51811yescharacteristic
454C4×C11#51811yescharacteristic
455C4×C11#53811yescharacteristic
456C4×C11#53811yescharacteristic
457Dic11—22no—
458Dic11—22no—
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—21no—
495C2×C4⋊C4—111no—
496C2×C4⋊C4—111no—
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—111no—
519C2×C42—111no—
520C2×C42—111no—
521C2×C42—221no—
522C2×C42—441no—
523C2×C42—441no—
524C2×C42C22×D1111yescharacteristic
525#107—441no—
526#107—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—
537C4×C8—41no—
538C4×C8—441no—
539#95—21no—
540#95—221no—
541#95—221no—
542C2×C11—82no—
543C2×C11#232111yescharacteristic
544C2×C11C2×C4×D811yescharacteristic
545C2×C11C4×AGL(1,ℤ/8)11yescharacteristic
546C2×C11#318611yescharacteristic
547C2×C11#318811yescharacteristic
548C2×C11#320511yescharacteristic
549C2×C11#321111yescharacteristic
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—111no—
597C22×C4—112no—
598C22×C4—112no—
599C22×C4—114no—
600C22×C4—111no—
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—42no—
641C4⋊C4—221no—
642C4⋊C4—221no—
643C4⋊C4—221no—
644C4⋊C4—221no—
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—221no—
663C42—221no—
664C42—441no—
665C42—441no—
666C42—442no—
667C11#2204011yescharacteristic, 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—41no—
724C2×C4—41no—
725C2×C4—41no—
726C2×C4—41no—
727C2×C4—41no—
728C2×C4—41no—
729C2×C4—41no—
730C2×C4—41no—
731C2×C4—112no—
732C2×C4—112no—
733C2×C4—221no—
734C2×C4—221no—
735C2×C4—221no—
736C2×C4—221no—
737C2×C4—222no—
738C2×C4—222no—
739C2×C4—222no—
740C2×C4—222no—
741C2×C4—221no—
742C2×C4—221no—
743C2×C4—221no—
744C2×C4—444no—
745C2×C4—444no—
746C2×C4—441no—
747C2×C4—441no—
748C2×C4—441no—
749C2×C4—441no—
750C2×C4—441no—
751C2×C4—441no—
752C2×C4—884no—
753C2×C4—884no—
754C2×C4D8×D1112yes—
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#1062313611yescharacteristic
797C22#1062320511yescharacteristic
798C22C2×D8×D1111yescharacteristic
799C22C2×#6696711yescharacteristic
800C22D11×#13511yescharacteristic
801C22#1062329911yescharacteristic
802C4—22no—
803C4—22no—
804C4—42no—
805C4—81no—
806C4—81no—
807C4—222no—
808C4—222no—
809C4—441no—
810C4—881no—
811C4—881no—
812C4#1062305211yescharacteristic
813C4#1062307611yescharacteristic
814C4#1062318811yescharacteristic
815C4#1062323511yescharacteristic
816C2—82no—
817C2—224no—
818C2—882no—
819C2—882no—
820C2#1307126911yescharacteristic
821C2C4×D8×D1111yescharacteristic
822C2C4×#6696711yescharacteristic
823C2#1307936311yescharacteristic
824C2#1307938211yescharacteristic
825C2#1307953511yescharacteristic
826C2#1307958211yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#1934C2
socleC23×C11C22×D4
prime radicalC2×#10622386C2
cosocleC22×C4×C11C24
hypercenter#1934D11
hypocenterC11#22040
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1934

Complements

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

NH ≅ G/Ntype
2. #13071124C2semidirect
3. D11×#390C2semidirect
4. #13069482C2semidirect
5. #13069481C2semidirect
6. #13069298C2semidirect
7. #13069238C2semidirect
8. #13069234C2semidirect
9. #13068965C2semidirect
10. #13068961C2semidirect
11. #13068932C2semidirect
12. #13068805C2semidirect
13. #13068545C2semidirect
14. C4×(C2×D11)⋊C8C2semidirect
15. C11×#1934C2semidirect
21. C2×#66946C22semidirect
28. C2×C4×C8×C11C22semidirect
30. C11×#389C22semidirect
34. C2×#66885C22semidirect
37. C2×#66882C22semidirect
41. C4⋊C4×Dic11C22semidirect
44. C2×#66873C22semidirect
45. C2×#66871C22semidirect
49. #10622552C22semidirect
50. C2×C4×C11⋊C8C22semidirect
51. #10622386C4semidirect
54. C11×#340C22semidirect
55. C11×#340C22semidirect
56. #10622188C22semidirect
57. #10622188C22semidirect
58. #10622167C22semidirect
59. #10622167C22semidirect
68. C2×D4×D11C2×C4semidirect
90. C2×#4323C2×C4semidirect
111. C2×D88C2×C4semidirect
124. C11×#102C2×C4semidirect
133. (C2×D11)⋊C8C2×C4semidirect
137. #66873C2×C4semidirect
206. C2×C4×D11D8semidirect
261. #1934D11semidirect
392. C2×C4×C8C2×D11semidirect
400. #389C2×D11semidirect
408. #340C2×D11semidirect
409. #340C2×D11semidirect
534. #102C4×D11semidirect
667. C11#22040semidirect

Maximal subgroups

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

subgroupindex
C2×#106223862
#130711242
D11×#3902
#130694822
#130694812
#130692982
#130692382
#130692342
#130689652
#130689612
#130689322
#130688052
#130685452
C4×(C2×D11)⋊C82
C11×#19342
#2204011