Finite Group Databasebeta

← #14797506

Subgroups — #14797506

Order 2816.

1232 conjugacy classes of subgroups.

The subgroup lattice has 818 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622649C211yesmaximal, characteristic
2C2×#10622369C211yesmaximal, characteristic, complemented
3#13072126C211yesmaximal, characteristic, complemented
4#13071436C211yesmaximal, characteristic, complemented
5#13070141C211yesmaximal, characteristic, complemented
6#13070042C211yesmaximal, characteristic, complemented
7#13069925C211yesmaximal, characteristic, complemented
8#13069297C211yesmaximal, characteristic, complemented
9#13069225C211yesmaximal, characteristic, complemented
10#13068962C211yesmaximal, characteristic, complemented
11#13068961C211yesmaximal, characteristic, complemented
12#13068860C211yesmaximal, characteristic, complemented
13#13068615C211yesmaximal, characteristic, complemented
14#13068548C211yesmaximal, characteristic, complemented
15C11×#2033C211yesmaximal, characteristic, complemented
16C23×D44C2211yescharacteristic
17C2×C11×#121C2211yescharacteristic
18C2×#66988—21no—
19C2×D4×Dic11C2211yescharacteristic, complemented
20C22×#4323C2211yescharacteristic
21C22×#4323C2211yescharacteristic
22C2×#66946C2211yescharacteristic
23C2×#66946C2211yescharacteristic
24C2×C22⋊C4×D11—21no—
25C2×C11×#107C2211yescharacteristic, complemented
26C2×C11×#102C2211yescharacteristic, complemented
27C2×C11×#102C2211yescharacteristic, complemented
28C2×C11×C22⋊C8C2211yescharacteristic
29C11×#380C2211yescharacteristic
30#10622835—21no—
31#10622834C2211yescharacteristic, complemented
32#10622825C2211yescharacteristic
33C4×C22⋊Dic11C2211yescharacteristic
34C2×C22⋊(C11⋊C8)C2211yescharacteristic
35C2×#66885C2211yescharacteristic
36C2×#66885C2211yescharacteristic
37C2×#66885C2211yescharacteristic
38C2×#66885C2211yescharacteristic
39C2×Dic11⋊C8C2211yescharacteristic, complemented
40C2×C8×Dic11C2211yescharacteristic, complemented
41#10622649—24no—
42#10622601C2211yescharacteristic
43#10622601C2211yescharacteristic
44#10622589C2211yescharacteristic, complemented
45#10622586C2211yescharacteristic, complemented
46C2×#66873C2211yescharacteristic
47C2×#66873C2211yescharacteristic
48C2×#66871C2211yescharacteristic, complemented
49#10622568—21no—
50#10622565—21no—
51#10622559—21no—
52#10622369—24no—
53#10622278—21no—
54#10622278—21no—
55C11×#340C2211yescharacteristic, complemented
56#10622188C2211yescharacteristic, complemented
57#10622188C2211yescharacteristic, complemented
58#10622167C2211yescharacteristic, complemented
59#10622167C2211yescharacteristic, complemented
60#10622167C2211yescharacteristic, complemented
61C24×D11—21no—
62C22×D4×C11—21no—
63C22×D4×C11C2311yescharacteristic
64C23×C4×C11C2311yescharacteristic
65C23×Dic11—21no—
66C22×D44—21no—
67C22×D44—22no—
68C22×D44—22no—
69C22×D44—22no—
70C22×D44—22no—
71C22×D44—41no—
72C22×D44—41no—
73C22×D44C2311yescharacteristic
74C22×D44C2311yescharacteristic
75C22×C4×D11—21no—
76C22×C4×D11—21no—
77C22×C8×C11C2311yescharacteristic
78C22×C8×C11C2311yescharacteristic
79C11×#121—22no—
80C11×#121—41no—
81C2×C11×C4⋊C4C2311yescharacteristic
82C2×C11×C4⋊C4C2311yescharacteristic
83C2×C11×C4⋊C4C2311yescharacteristic
84C2×C11×C22⋊C4—21no—
85C2×C11×C22⋊C4—21no—
86C2×C22⋊Dic11—21no—
87C2×C22⋊Dic11—21no—
88C2×C22⋊Dic11—21no—
89C2×C22⋊Dic11—21no—
90C2×C22⋊Dic11D411yescharacteristic
91C2×C22⋊Dic11D411yescharacteristic
92#66988—44no—
93D4×Dic11—22no—
94D4×Dic11—41no—
95C2×#4323—22no—
96C2×#4323—22no—
97C2×#4323—22no—
98C2×#4323—22no—
99C2×#4323—41no—
100C2×#4323D414yes—
101C2×(C2×D11)⋊C4—21no—
102C2×(C2×D11)⋊C4—21no—
103C2×(C2×D11)⋊C4—21no—
104C2×(C2×D11)⋊C4—21no—
105C2×(C2×D11)⋊C4—21no—
106C2×(C2×D11)⋊C4—21no—
107C2×C4⋊Dic11C2311yescharacteristic
108C2×C4⋊Dic11C2311yescharacteristic
109C2×Dic11⋊C4—21no—
110C2×Dic11⋊C4—21no—
111C2×Dic11⋊C4—21no—
112C2×C4×Dic11C2311yescharacteristic
113C2×C4×Dic11C2311yescharacteristic
114C22×C11⋊C8C2311yescharacteristic
115C22×C11⋊C8C2311yescharacteristic
116#66946—22no—
117#66946—22no—
118#66946—41no—
119#66946—41no—
120C22⋊C4×D11—44no—
121C11×#107—41no—
122C11×#102—22no—
123C11×#102—41no—
124C11×C22⋊C8—41no—
125C11×#95—21no—
126C11⋊#95—21no—
127C11⋊#95—21no—
128C11⋊#95D411yescharacteristic
129C11⋊#95D411yescharacteristic
130C22⋊(C11⋊C8)—22no—
131#66885—22no—
132#66885—22no—
133#66885—22no—
134#66885—41no—
135Dic11⋊C8—41no—
136C8×Dic11—22no—
137#66873—22no—
138#66873—22no—
139#66871—22no—
140#24893—111nomaximal, Sylow
141C24×C11—21no—
142C24×C11C2×D411yescharacteristic
143C23×D11—21no—
144C23×D11—21no—
145C23×D11—24no—
146C23×D11—42no—
147C23×D11—42no—
148C23×D11—42no—
149C23×D11—42no—
150C23×D11—81no—
151C23×D11—81no—
152C2×D4×C11—21no—
153C2×D4×C11—21no—
154C2×D4×C11—21no—
155C2×D4×C11—21no—
156C2×D4×C11—21no—
157C2×D4×C11—42no—
158C2×D4×C11—42no—
159C2×D4×C11—81no—
160C2×D4×C11C2×D412yes—
161C22×C4×C11—21no—
162C22×C4×C11—21no—
163C22×C4×C11—21no—
164C22×C4×C11—21no—
165C22×C4×C11—21no—
166C22×C4×C11—21no—
167C22×C4×C11—21no—
168C22×C4×C11—21no—
169C22×C4×C11—21no—
170C22×C4×C11C2×D411yescharacteristic
171C22×C4×C11C2411yescharacteristic
172C22×Dic11—21no—
173C22×Dic11—21no—
174C22×Dic11—42no—
175C22×Dic11—42no—
176C22×Dic11—81no—
177C22×Dic11C2×D411yescharacteristic
178C22×Dic11C2×D411yescharacteristic
179C22×Dic11C2×D411yescharacteristic
180C22×Dic11C2×D411yescharacteristic
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—42no—
191C2×D44—42no—
192C2×D44—44no—
193C2×D44—44no—
194C2×D44—44no—
195C2×D44—44no—
196C2×D44C2×D412yes—
197C2×D44#4112yes—
198C2×D44#4112yes—
199C2×D44#4112yes—
200C2×C4×D11—42no—
201C2×C4×D11—42no—
202C2×C4×D11—42no—
203C2×C4×D11—42no—
204C2×C4×D11—81no—
205C2×C4×D11—81no—
206C2×C8×C11—21no—
207C2×C8×C11—21no—
208C2×C8×C11—21no—
209C2×C8×C11—21no—
210C2×C8×C11—21no—
211C2×C8×C11—21no—
212C11×C4⋊C4—21no—
213C11×C4⋊C4—21no—
214C11×C4⋊C4—21no—
215C11×C4⋊C4—21no—
216C11×C4⋊C4—21no—
217C11×C4⋊C4—21no—
218C11×C22⋊C4—42no—
219C11×C22⋊C4—42no—
220C22⋊Dic11—41no—
221C22⋊Dic11—42no—
222C22⋊Dic11—42no—
223C22⋊Dic11—42no—
224C22⋊Dic11—42no—
225C22⋊Dic11D814yescomplemented
226#4323—28no—
227#4323—44no—
228(C2×D11)⋊C4—42no—
229(C2×D11)⋊C4—42no—
230(C2×D11)⋊C4—42no—
231(C2×D11)⋊C4—42no—
232(C2×D11)⋊C4—81no—
233(C2×D11)⋊C4—81no—
234C4⋊Dic11—21no—
235C4⋊Dic11—21no—
236C4⋊Dic11—21no—
237C4⋊Dic11—21no—
238Dic11⋊C4—42no—
239Dic11⋊C4—42no—
240Dic11⋊C4—81no—
241C4×Dic11—21no—
242C4×Dic11—21no—
243C4×Dic11—21no—
244C4×Dic11—21no—
245C2×C11⋊C8—21no—
246C2×C11⋊C8—21no—
247C2×C11⋊C8—21no—
248C2×C11⋊C8—21no—
249C2×C11⋊C8—21no—
250C2×C11⋊C8C2×D412yes—
251C2×#447—111no—
252C2×C4×D8—111no—
253#2422—111no—
254D4×C22⋊C4—111no—
255#2093—111no—
256#2075—111no—
257#2054—111no—
258#2033D1111yescharacteristic, complemented
259#1934—111no—
260#1923—111no—
261#1879—111no—
262#1879—111no—
263#1862—111no—
264#1802—111no—
265#1786—111no—
266C23×C11—21no—
267C23×C11—21no—
268C23×C11—21no—
269C23×C11—21no—
270C23×C11—21no—
271C23×C11—21no—
272C23×C11—22no—
273C23×C11—41no—
274C23×C11—41no—
275C23×C11—41no—
276C23×C11—41no—
277C23×C11—41no—
278C23×C11—41no—
279C23×C11C2×D812yes—
280C23×C11C22×D411yescharacteristic
281C22×D11—22no—
282C22×D11—22no—
283C22×D11—22no—
284C22×D11—22no—
285C22×D11—48no—
286C22×D11—41no—
287C22×D11—41no—
288C22×D11—41no—
289C22×D11—41no—
290C22×D11—48no—
291C22×D11—41no—
292C22×D11—41no—
293C22×D11—41no—
294C22×D11—41no—
295C22×D11—41no—
296C22×D11—41no—
297C22×D11—84no—
298C22×D11—84no—
299C22×D11—84no—
300C22×D11—84no—
301C22×D11—84no—
302D4×C11—22no—
303D4×C11—22no—
304D4×C11—41no—
305D4×C11—41no—
306D4×C11—84no—
307C2×C4×C11—21no—
308C2×C4×C11—21no—
309C2×C4×C11—21no—
310C2×C4×C11—41no—
311C2×C4×C11—41no—
312C2×C4×C11—41no—
313C2×C4×C11—41no—
314C2×C4×C11—41no—
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×C11C22×D411yescharacteristic
324C2×C4×C11C2×#4111yescharacteristic
325C2×C4×C11C2×#4111yescharacteristic
326C2×C4×C11C2×#4111yescharacteristic
327C2×C4×C11H(5,𝔽2)11yescharacteristic
328C2×C4×C11H(5,𝔽2)11yescharacteristic
329C2×Dic11—21no—
330C2×Dic11—21no—
331C2×Dic11—21no—
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×Dic11—84no—
346C2×Dic11C2×D812yes—
347C2×Dic11C2×D812yes—
348D44—22no—
349D44—22no—
350D44—22no—
351D44—22no—
352D44—22no—
353D44—48no—
354D44—41no—
355D44—41no—
356D44#12314yescomplemented
357C4×D11—84no—
358C4×D11—84no—
359C8×C11—41no—
360C8×C11—41no—
361C11⋊C8—22no—
362C11⋊C8—41no—
363C23×D4—111no—
364C22×D8—111no—
365C22×D8—111no—
366C2×#123—221no—
367C2×#121C2×D1111yescharacteristic
368C2×C4×D4—111no—
369C2×C4×D4—111no—
370C2×C4×D4—111no—
371C22×C22⋊C4—221no—
372#447—224no—
373C4×D8—224no—
374C2×#107—111no—
375C2×#107C2×D1111yescharacteristic, complemented
376C2×C4⋊C8—111no—
377C2×#102—111no—
378C2×#102—111no—
379C2×#102—111no—
380C2×#102—111no—
381C2×#102—111no—
382C2×#102—111no—
383C2×#102C2×D1111yescharacteristic, complemented
384C2×#102C2×D1111yescharacteristic, complemented
385C2×C22⋊C8—111no—
386C2×C22⋊C8C2×D1111yescharacteristic
387C2×C4×C8—111no—
388#397—221no—
389#394—221no—
390#390—111no—
391#390—111no—
392#390—111no—
393#389—111no—
394#386—221no—
395#386—221no—
396#385—221no—
397#384—111no—
398#380—111no—
399#380C2×D1111yescharacteristic
400#379—221no—
401C4×C22⋊C4—111no—
402#340—111no—
403#340—111no—
404#340—111no—
405#340C2×D1111yescharacteristic, complemented
406#336—111no—
407#336—111no—
408C22×C11—22no—
409C22×C11—22no—
410C22×C11—22no—
411C22×C11—41no—
412C22×C11—41no—
413C22×C11—41no—
414C22×C11—41no—
415C22×C11—42no—
416C22×C11—42no—
417C22×C11—42no—
418C22×C11—81no—
419C22×C11—81no—
420C22×C11—81no—
421C22×C11—81no—
422C22×C11#52511yescharacteristic
423C22×C11D4211yescharacteristic
424C22×C11#54611yescharacteristic
425C22×C11C22×D811yescharacteristic
426C22×C11#57511yescharacteristic
427C22×C11#57611yescharacteristic
428C22×C11#57711yescharacteristic
429C2×D11—24no—
430C2×D11—42no—
431C2×D11—42no—
432C2×D11—42no—
433C2×D11—42no—
434C2×D11—42no—
435C2×D11—42no—
436C2×D11—42no—
437C2×D11—42no—
438C2×D11—42no—
439C2×D11—816no—
440C2×D11—81no—
441C2×D11—81no—
442C2×D11—81no—
443C2×D11—81no—
444C4×C11—41no—
445C4×C11—81no—
446C4×C11—81no—
447C4×C11—81no—
448C4×C11C2×#12311yescharacteristic
449C4×C11#53811yescharacteristic
450C4×C11#54611yescharacteristic
451C4×C11#55111yescharacteristic
452Dic11—22no—
453Dic11—22no—
454Dic11—41no—
455Dic11—41no—
456Dic11—81no—
457Dic11—81no—
458C25—221no—
459C22×D4—21no—
460C22×D4—111no—
461C22×D4—111no—
462C22×D4—222no—
463C22×D4—222no—
464C22×D4—222no—
465C22×D4—222no—
466C22×D4—221no—
467C22×D4—441no—
468C22×D4—441no—
469C22×D4C22×D1111yescharacteristic
470C23×C4—221no—
471C23×C4—221no—
472C23×C4—221no—
473C23×C4C22×D1111yescharacteristic
474C2×D8—114no—
475C2×D8—222no—
476C2×D8—222no—
477C2×D8—222no—
478C2×D8—222no—
479C2×D8—441no—
480C22×C8—111no—
481C22×C8—111no—
482C22×C8C22×D1111yescharacteristic
483C22×C8C22×D1111yescharacteristic
484#123—444no—
485#121—22no—
486#121—41no—
487C4×D4—222no—
488C4×D4—222no—
489C4×D4—222no—
490C4×D4—441no—
491C4×D4—441no—
492C4×D4—441no—
493C2×C4⋊C4—111no—
494C2×C4⋊C4—111no—
495C2×C4⋊C4—221no—
496C2×C4⋊C4—221no—
497C2×C4⋊C4—221no—
498C2×C4⋊C4C22×D1111yescharacteristic
499C2×C4⋊C4C22×D1111yescharacteristic
500C2×C4⋊C4C22×D1111yescharacteristic
501C2×C22⋊C4—21no—
502C2×C22⋊C4—21no—
503C2×C22⋊C4—111no—
504C2×C22⋊C4—111no—
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—444no—
516C2×C42—111no—
517C2×C42—111no—
518#107—41no—
519#107—222no—
520C4⋊C8—441no—
521#102—22no—
522#102—41no—
523#102—222no—
524#102—222no—
525#102—222no—
526#102—222no—
527#102—222no—
528#102—441no—
529C22⋊C8—41no—
530C22⋊C8—222no—
531C4×C8—222no—
532#95—21no—
533#95—111no—
534#95—111no—
535#95—221no—
536#95—221no—
537C2×C11—42no—
538C2×C11—82no—
539C2×C11#241811yescharacteristic
540C2×C11#310011yescharacteristic
541C2×C11#311811yescharacteristic
542C2×C11#326711yescharacteristic
543C2×C11D4×D811yescharacteristic
544C2×C11#329411yescharacteristic
545C2×C11#332211yescharacteristic
546D11—44no—
547D11—82no—
548C24—21no—
549C24—224no—
550C24—221no—
551C24—221no—
552C24—442no—
553C24—442no—
554C24—442no—
555C24—442no—
556C24—881no—
557C24—881no—
558C24D4×D1111yescharacteristic
559C2×D4—21no—
560C2×D4—21no—
561C2×D4—21no—
562C2×D4—21no—
563C2×D4—21no—
564C2×D4—42no—
565C2×D4—42no—
566C2×D4—81no—
567C2×D4—112no—
568C2×D4—112no—
569C2×D4—112no—
570C2×D4—112no—
571C2×D4—224no—
572C2×D4—221no—
573C2×D4—221no—
574C2×D4—221no—
575C2×D4—221no—
576C2×D4—221no—
577C2×D4—221no—
578C2×D4—221no—
579C2×D4—221no—
580C2×D4—442no—
581C2×D4—442no—
582C2×D4—444no—
583C2×D4—444no—
584C2×D4—444no—
585C2×D4—444no—
586C2×D4D4×D1112yes—
587C22×C4—21no—
588C22×C4—21no—
589C22×C4—21no—
590C22×C4—21no—
591C22×C4—21no—
592C22×C4—21no—
593C22×C4—21no—
594C22×C4—21no—
595C22×C4—21no—
596C22×C4—111no—
597C22×C4—111no—
598C22×C4—111no—
599C22×C4—111no—
600C22×C4—221no—
601C22×C4—221no—
602C22×C4—442no—
603C22×C4—442no—
604C22×C4—442no—
605C22×C4—442no—
606C22×C4—442no—
607C22×C4—442no—
608C22×C4—881no—
609C22×C4—881no—
610C22×C4—881no—
611C22×C4D4×D1111yescharacteristic
612C22×C4C23×D1111yescharacteristic
613D8—228no—
614D8—444no—
615C2×C8—21no—
616C2×C8—21no—
617C2×C8—21no—
618C2×C8—21no—
619C2×C8—21no—
620C2×C8—21no—
621C2×C8—112no—
622C2×C8—221no—
623C2×C8—221no—
624C2×C8—221no—
625C2×C8—221no—
626C2×C8—221no—
627C4⋊C4—21no—
628C4⋊C4—21no—
629C4⋊C4—21no—
630C4⋊C4—21no—
631C4⋊C4—21no—
632C4⋊C4—21no—
633C4⋊C4—221no—
634C4⋊C4—221no—
635C4⋊C4—221no—
636C4⋊C4—221no—
637C4⋊C4—442no—
638C4⋊C4—442no—
639C4⋊C4—881no—
640C22⋊C4—42no—
641C22⋊C4—42no—
642C22⋊C4—114no—
643C22⋊C4—442no—
644C22⋊C4—442no—
645C22⋊C4—442no—
646C22⋊C4—442no—
647C22⋊C4—442no—
648C22⋊C4—441no—
649C22⋊C4—442no—
650C22⋊C4—442no—
651C22⋊C4—442no—
652C22⋊C4—881no—
653C22⋊C4—881no—
654C42—221no—
655C42—221no—
656C42—221no—
657C42—221no—
658C11#2489311yescharacteristic, complemented, Sylow
659C23—21no—
660C23—21no—
661C23—21no—
662C23—21no—
663C23—21no—
664C23—21no—
665C23—22no—
666C23—41no—
667C23—41no—
668C23—41no—
669C23—41no—
670C23—41no—
671C23—41no—
672C23—222no—
673C23—222no—
674C23—222no—
675C23—222no—
676C23—448no—
677C23—448no—
678C23—441no—
679C23—441no—
680C23—441no—
681C23—441no—
682C23—441no—
683C23—441no—
684C23—441no—
685C23—441no—
686C23—441no—
687C23—441no—
688C23—884no—
689C23—884no—
690C23—884no—
691C23—884no—
692C23—884no—
693C23D8×D1112yes—
694C23C2×D4×D1111yescharacteristic
695D4—22no—
696D4—22no—
697D4—41no—
698D4—41no—
699D4—84no—
700D4—114no—
701D4—222no—
702D4—222no—
703D4—222no—
704D4—222no—
705D4—222no—
706D4—448no—
707D4—441no—
708D4—441no—
709C2×C4—21no—
710C2×C4—21no—
711C2×C4—21no—
712C2×C4—41no—
713C2×C4—41no—
714C2×C4—41no—
715C2×C4—41no—
716C2×C4—41no—
717C2×C4—41no—
718C2×C4—41no—
719C2×C4—41no—
720C2×C4—41no—
721C2×C4—41no—
722C2×C4—41no—
723C2×C4—41no—
724C2×C4—41no—
725C2×C4—112no—
726C2×C4—112no—
727C2×C4—221no—
728C2×C4—221no—
729C2×C4—221no—
730C2×C4—221no—
731C2×C4—221no—
732C2×C4—221no—
733C2×C4—221no—
734C2×C4—221no—
735C2×C4—221no—
736C2×C4—221no—
737C2×C4—441no—
738C2×C4—441no—
739C2×C4—441no—
740C2×C4—441no—
741C2×C4—441no—
742C2×C4—441no—
743C2×C4—884no—
744C2×C4—884no—
745C2×C4—884no—
746C2×C4C2×D4×D1111yescharacteristic
747C2×C4#6703711yescharacteristic
748C2×C4#6703711yescharacteristic
749C2×C4#41×D1111yescharacteristic
750C2×C4#41×D1111yescharacteristic
751C2×C4#41×D1111yescharacteristic
752C8—41no—
753C8—41no—
754C8—222no—
755C8—441no—
756C22—22no—
757C22—22no—
758C22—22no—
759C22—41no—
760C22—41no—
761C22—41no—
762C22—41no—
763C22—42no—
764C22—42no—
765C22—42no—
766C22—81no—
767C22—81no—
768C22—81no—
769C22—81no—
770C22—224no—
771C22—442no—
772C22—442no—
773C22—442no—
774C22—442no—
775C22—442no—
776C22—442no—
777C22—442no—
778C22—442no—
779C22—442no—
780C22—8816no—
781C22—881no—
782C22—881no—
783C22—881no—
784C22—881no—
785C22#1062312111yescharacteristic
786C22#1062314111yescharacteristic
787C22#1062318711yescharacteristic
788C22C2×D8×D1111yescharacteristic
789C22#1062330111yescharacteristic
790C22#1062330511yescharacteristic
791C22#1062330811yescharacteristic
792C4—41no—
793C4—81no—
794C4—81no—
795C4—81no—
796C4—222no—
797C4—222no—
798C4—441no—
799C4—441no—
800C4—881no—
801C4—881no—
802C4#1062314111yescharacteristic
803C4#1062314411yescharacteristic
804C4D11×#12311yescharacteristic
805C4#1062321011yescharacteristic
806C2—42no—
807C2—82no—
808C2—444no—
809C2—882no—
810C2#1307207111yescharacteristic
811C2#1307861311yescharacteristic
812C2#1307879511yescharacteristic
813C2#1308014411yescharacteristic
814C2#1308028611yescharacteristic
815C2#1308042411yescharacteristic
816C2#1308082311yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#2033C2
socleC23×C11C22×D4
prime radicalC2×#10622649C2
hypercenter#2033D11
hypocenterC11#24893
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ #2033

Complements

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

NH ≅ G/Ntype
2. C2×#10622369C2semidirect
3. #13072126C2semidirect
4. #13071436C2semidirect
5. #13070141C2semidirect
6. #13070042C2semidirect
7. #13069925C2semidirect
8. #13069297C2semidirect
9. #13069225C2semidirect
10. #13068962C2semidirect
11. #13068961C2semidirect
12. #13068860C2semidirect
13. #13068615C2semidirect
14. #13068548C2semidirect
15. C11×#2033C2semidirect
19. C2×D4×Dic11C22semidirect
25. C2×C11×#107C22semidirect
26. C2×C11×#102C22semidirect
27. C2×C11×#102C22semidirect
31. #10622834C22semidirect
39. C2×Dic11⋊C8C22semidirect
40. C2×C8×Dic11C22semidirect
44. #10622589C22semidirect
45. #10622586C22semidirect
48. C2×#66871C22semidirect
55. C11×#340C22semidirect
56. #10622188C22semidirect
57. #10622188C22semidirect
58. #10622167C22semidirect
59. #10622167C22semidirect
60. #10622167C22semidirect
225. C22⋊Dic11D8semidirect
258. #2033D11semidirect
356. D44#123semidirect
375. C2×#107C2×D11semidirect
383. C2×#102C2×D11semidirect
384. C2×#102C2×D11semidirect
405. #340C2×D11semidirect
658. C11#24893semidirect

Maximal subgroups

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

subgroupindex
C2×#106226492
C2×#106223692
#130721262
#130714362
#130701412
#130700422
#130699252
#130692972
#130692252
#130689622
#130689612
#130688602
#130686152
#130685482
C11×#20332
#2489311