Finite Group Databasebeta

← #14797507

Subgroups — #14797507

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×#10622769C211yesmaximal, characteristic
2#13072124C211yesmaximal, characteristic, complemented
3D4×(C2×D11)⋊C4C211yesmaximal, characteristic, complemented
4#13070141C211yesmaximal, characteristic, complemented
5#13070040C211yesmaximal, characteristic, complemented
6#13069925C211yesmaximal, characteristic, complemented
7#13069796C211yesmaximal, characteristic, complemented
8#13069299C211yesmaximal, characteristic, complemented
9#13069222C211yesmaximal, characteristic, complemented
10#13068966C211yesmaximal, characteristic, complemented
11#13068964C211yesmaximal, characteristic, complemented
12#13068863C211yesmaximal, characteristic, complemented
13#13068614C211yesmaximal, characteristic, complemented
14#13068545C211yesmaximal, characteristic, complemented
15C2×C4×C11×D8C211yesmaximal, 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×#66982—21no—
24C22×(C2×D11)⋊C4—21no—
25C4×C11×D8—24no—
26C2×C11×#107C2211yescharacteristic, complemented
27C2×C11×#102C2211yescharacteristic
28C2×C11×#102C2211yescharacteristic, complemented
29C2×C4×C8×C11C2211yescharacteristic, complemented
30#10622834C2211yescharacteristic, complemented
31C2×#66896C2211yescharacteristic
32C2×#66896C2211yescharacteristic
33C2×#66896C2211yescharacteristic, complemented
34#10622826—21no—
35#10622823—21no—
36#10622769—24no—
37C2×#66885C2211yescharacteristic
38C2×#66885C2211yescharacteristic
39C2×(C2×D11)⋊C8C2211yescharacteristic
40C2×(C2×D11)⋊C8C2211yescharacteristic
41C2×Dic11⋊C8C2211yescharacteristic, complemented
42#10622601C2211yescharacteristic
43#10622600C2211yescharacteristic
44#10622600C2211yescharacteristic
45#10622589C2211yescharacteristic, complemented
46C2×#66873C2211yescharacteristic
47C2×#66871C2211yescharacteristic, complemented
48#10622572—21no—
49#10622571—21no—
50#10622568—21no—
51#10622565—21no—
52#10622552C2211yescharacteristic
53C4×(C2×D11)⋊C4C2211yescharacteristic
54#10622541C2211yescharacteristic, complemented
55#10622189C2211yescharacteristic, complemented
56#10622189C2211yescharacteristic, complemented
57#10622188C2211yescharacteristic, complemented
58#10622167C2211yescharacteristic, complemented
59#10622167C2211yescharacteristic, complemented
60#10622162C2211yescharacteristic, complemented
61C24×D11—21no—
62C22×D4×C11C2311yescharacteristic
63C22×D4×C11C2311yescharacteristic
64C23×C4×C11—21no—
65C23×C4×C11—21no—
66C22×C22⋊D11—21no—
67C22×C22⋊D11—21no—
68C23×Dic11—21no—
69C2×D4×D11—22no—
70C2×D4×D11—22no—
71C2×D4×D11—22no—
72C2×D4×D11—22no—
73C2×D4×D11—41no—
74C2×D4×D11—41no—
75C22×D44C2311yescharacteristic
76C22×C4×D11C2311yescharacteristic
77C2×C11×D8—22no—
78C2×C11×D8—22no—
79C2×C11×D8D414yes—
80C22×C8×C11C2311yescharacteristic
81C22×C8×C11C2311yescharacteristic
82C4×D4×C11—22no—
83C4×D4×C11—22no—
84C4×D4×C11—41no—
85C4×D4×C11—41no—
86C2×C11×C4⋊C4C2311yescharacteristic
87C2×C11×C4⋊C4C2311yescharacteristic
88C2×C11×C22⋊C4—21no—
89C2×C11×C22⋊C4—21no—
90C2×C42×C11C2311yescharacteristic
91C2×C22⋊Dic11—21no—
92C2×C22⋊Dic11—21no—
93C2×C22⋊Dic11—21no—
94C2×C22⋊Dic11—21no—
95#66991—22no—
96#66991—41no—
97D4×Dic11—22no—
98D4×Dic11—41no—
99C2×#4323—22no—
100C2×#4323—22no—
101C2×#4323—41no—
102#66982—44no—
103C2×(C2×D11)⋊C4—21no—
104C2×(C2×D11)⋊C4—21no—
105C2×(C2×D11)⋊C4—21no—
106C2×(C2×D11)⋊C4—21no—
107C2×(C2×D11)⋊C4—21no—
108C2×(C2×D11)⋊C4—21no—
109C2×(C2×D11)⋊C4—44no—
110C2×(C2×D11)⋊C4D411yescharacteristic
111C2×(C2×D11)⋊C4D411yescharacteristic
112C2×C4⋊Dic11C2311yescharacteristic
113C2×C4⋊Dic11C2311yescharacteristic
114C2×C4⋊Dic11C2311yescharacteristic
115C2×Dic11⋊C4—21no—
116C2×Dic11⋊C4—21no—
117C2×Dic11⋊C4—21no—
118C2×C4×Dic11C2311yescharacteristic
119C22×C11⋊C8C2311yescharacteristic
120C22×C11⋊C8C2311yescharacteristic
121C11×#107—22no—
122C11×#102—22no—
123C11×#102—22no—
124C4×C8×C11—22no—
125#66896—22no—
126#66896—22no—
127#66896—41no—
128C11⋊#95—21no—
129C11⋊#95—21no—
130C11⋊#95—21no—
131C11⋊#95D411yescharacteristic
132C11⋊#95D411yescharacteristic
133#66885—22no—
134#66885—22no—
135(C2×D11)⋊C8—22no—
136(C2×D11)⋊C8—41no—
137Dic11⋊C8—41no—
138#66873—41no—
139#66871—41no—
140#24893—111nomaximal, Sylow
141C24×C11—21no—
142C24×C11—21no—
143C23×D11—21no—
144C23×D11—24no—
145C23×D11—42no—
146C23×D11—42no—
147C23×D11—42no—
148C23×D11—42no—
149C23×D11—81no—
150C23×D11—81no—
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×C11—21no—
158C2×D4×C11—21no—
159C2×D4×C11—21no—
160C2×D4×C11C2×D412yes—
161C2×D4×C11C2×D412yes—
162C2×D4×C11#4112yes—
163C2×D4×C11#4112yes—
164C22×C4×C11—21no—
165C22×C4×C11—21no—
166C22×C4×C11—42no—
167C22×C4×C11—42no—
168C22×C4×C11—42no—
169C22×C4×C11—42no—
170C22×C4×C11—81no—
171C22×C4×C11—81no—
172C22×C4×C11C2×D411yescharacteristic
173C22×C4×C11C2×D411yescharacteristic
174C22×C4×C11C2411yescharacteristic
175C2×C22⋊D11—24no—
176C2×C22⋊D11—42no—
177C2×C22⋊D11—42no—
178C2×C22⋊D11—42no—
179C2×C22⋊D11—42no—
180C2×C22⋊D11—81no—
181C22×Dic11—21no—
182C22×Dic11—21no—
183C22×Dic11—21no—
184C22×Dic11—42no—
185C22×Dic11—42no—
186C22×Dic11—81no—
187C22×Dic11C2×D411yescharacteristic
188C22×Dic11C2×D411yescharacteristic
189C22×Dic11C2×D411yescharacteristic
190D4×D11—44no—
191D4×D11—44no—
192D4×D11—44no—
193D4×D11—44no—
194C2×D44—21no—
195C2×D44—21no—
196C2×D44—21no—
197C2×D44—21no—
198C2×D44—21no—
199C2×D44#4112yes—
200C2×C4×D11—21no—
201C2×C4×D11—21no—
202C2×C4×D11—21no—
203C2×C4×D11—21no—
204C2×C4×D11—21no—
205C2×C4×D11—21no—
206C11×D8—28no—
207C2×C8×C11—21no—
208C2×C8×C11—21no—
209C2×C8×C11—21no—
210C2×C8×C11—21no—
211C2×C8×C11—21no—
212C2×C8×C11C2×D412yes—
213C11×C4⋊C4—21no—
214C11×C4⋊C4—21no—
215C11×C4⋊C4—21no—
216C11×C4⋊C4—21no—
217C11×C22⋊C4—42no—
218C11×C22⋊C4—42no—
219C42×C11—21no—
220C42×C11—21no—
221C22⋊Dic11—42no—
222C22⋊Dic11—42no—
223C22⋊Dic11—42no—
224C22⋊Dic11—42no—
225#4323—44no—
226(C2×D11)⋊C4—41no—
227(C2×D11)⋊C4—42no—
228(C2×D11)⋊C4—42no—
229(C2×D11)⋊C4—42no—
230(C2×D11)⋊C4—42no—
231(C2×D11)⋊C4—81no—
232(C2×D11)⋊C4—81no—
233(C2×D11)⋊C4D814yescomplemented
234C4⋊Dic11—21no—
235C4⋊Dic11—21no—
236C4⋊Dic11—21no—
237C4⋊Dic11—21no—
238C4⋊Dic11—21no—
239C4⋊Dic11—21no—
240Dic11⋊C4—42no—
241Dic11⋊C4—42no—
242Dic11⋊C4—81no—
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⋊C8—21no—
251C2×#447—111no—
252C2×C4×D8D1111yescharacteristic, complemented
253#2422—111no—
254D4×C22⋊C4—111no—
255#2093—111no—
256#2075—111no—
257#2054—111no—
258#2033—111no—
259#1934—111no—
260#1923—111no—
261#1879—111no—
262#1879—111no—
263#1862—111no—
264#1802—111no—
265#1786—111no—
266C23×C11—22no—
267C23×C11—22no—
268C23×C11—22no—
269C23×C11—22no—
270C23×C11—41no—
271C23×C11—41no—
272C23×C11—41no—
273C23×C11—41no—
274C23×C11—41no—
275C23×C11—41no—
276C23×C11—41no—
277C23×C11—41no—
278C23×C11—41no—
279C23×C11—41no—
280C23×C11C22×D411yescharacteristic
281C22×D11—21no—
282C22×D11—21no—
283C22×D11—21no—
284C22×D11—21no—
285C22×D11—21no—
286C22×D11—21no—
287C22×D11—22no—
288C22×D11—48no—
289C22×D11—48no—
290C22×D11—41no—
291C22×D11—41no—
292C22×D11—41no—
293C22×D11—41no—
294C22×D11—41no—
295C22×D11—41no—
296C22×D11—84no—
297C22×D11—84no—
298C22×D11—84no—
299C22×D11—84no—
300C22×D11—84no—
301C22×D11C2×D812yes—
302D4×C11—22no—
303D4×C11—22no—
304D4×C11—22no—
305D4×C11—22no—
306D4×C11—22no—
307D4×C11—41no—
308D4×C11—41no—
309D4×C11#12314yescomplemented
310C2×C4×C11—21no—
311C2×C4×C11—21no—
312C2×C4×C11—21no—
313C2×C4×C11—21no—
314C2×C4×C11—21no—
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—84no—
322C2×C4×C11—84no—
323C2×C4×C11C2×D812yes—
324C2×C4×C11C22×D411yescharacteristic
325C2×C4×C11C2×#4111yescharacteristic
326C2×C4×C11C2×#4111yescharacteristic
327C2×C4×C11C2×#4111yescharacteristic
328C2×C4×C11H(5,𝔽2)11yescharacteristic
329C2×C4×C11H(5,𝔽2)11yescharacteristic
330C22⋊D11—48no—
331C22⋊D11—84no—
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×Dic11—41no—
347C2×Dic11—41no—
348C2×Dic11—41no—
349C2×Dic11—84no—
350C2×Dic11C2×D812yes—
351D44—22no—
352D44—22no—
353D44—41no—
354D44—41no—
355C4×D11—41no—
356C4×D11—41no—
357C4×D11—41no—
358C4×D11—41no—
359C8×C11—22no—
360C8×C11—41no—
361C11⋊C8—41no—
362C11⋊C8—41no—
363C23×D4—111no—
364C22×D8—111no—
365C22×D8C2×D1111yescharacteristic
366C2×#123—221no—
367C2×#121—111no—
368C2×C4×D4—111no—
369C2×C4×D4C2×D1111yescharacteristic
370C2×C4×D4C2×D1111yescharacteristic, complemented
371C22×C22⋊C4—221no—
372#447—224no—
373C4×D8—24no—
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
384C2×#102C2×D1111yescharacteristic, complemented
385C2×C22⋊C8—111no—
386C2×C22⋊C8—111no—
387C2×C4×C8C2×D1111yescharacteristic, complemented
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#380—111no—
400#379—221no—
401C4×C22⋊C4—111no—
402#340—111no—
403#340—111no—
404#340—111no—
405#340—111no—
406#336—111no—
407#336—111no—
408C22×C11—24no—
409C22×C11—42no—
410C22×C11—42no—
411C22×C11—42no—
412C22×C11—42no—
413C22×C11—42no—
414C22×C11—42no—
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—22no—
430C2×D11—22no—
431C2×D11—22no—
432C2×D11—41no—
433C2×D11—41no—
434C2×D11—41no—
435C2×D11—41no—
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—22no—
445C4×C11—41no—
446C4×C11—81no—
447C4×C11—81no—
448C4×C11C2×#12311yescharacteristic
449C4×C11#53811yescharacteristic
450C4×C11#54611yescharacteristic
451C4×C11#55111yescharacteristic
452Dic11—22no—
453Dic11—41no—
454Dic11—41no—
455Dic11—81no—
456Dic11—81no—
457Dic11—81no—
458C25—221no—
459C22×D4—111no—
460C22×D4—221no—
461C22×D4—222no—
462C22×D4—222no—
463C22×D4—222no—
464C22×D4—222no—
465C22×D4—221no—
466C22×D4—441no—
467C22×D4—441no—
468C22×D4C22×D1111yescharacteristic
469C22×D4C22×D1111yescharacteristic
470C23×C4—21no—
471C23×C4—21no—
472C23×C4—111no—
473C23×C4—221no—
474C2×D8—22no—
475C2×D8—22no—
476C2×D8—222no—
477C2×D8—222no—
478C2×D8—441no—
479C2×D8C22⋊D1114yes—
480C22×C8—111no—
481C22×C8—111no—
482C22×C8C22×D1111yescharacteristic
483C22×C8C22×D1111yescharacteristic
484#123—444no—
485#121—222no—
486#121—441no—
487C4×D4—22no—
488C4×D4—22no—
489C4×D4—41no—
490C4×D4—41no—
491C4×D4—222no—
492C4×D4—441no—
493C2×C4⋊C4—111no—
494C2×C4⋊C4—111no—
495C2×C4⋊C4—111no—
496C2×C4⋊C4—221no—
497C2×C4⋊C4—221no—
498C2×C4⋊C4—221no—
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×C42C22×D1111yescharacteristic
518#107—22no—
519#107—441no—
520C4⋊C8—441no—
521#102—22no—
522#102—22no—
523#102—222no—
524#102—222no—
525#102—222no—
526#102—222no—
527#102—441no—
528#102—441no—
529C22⋊C8—222no—
530C22⋊C8—441no—
531C4×C8—22no—
532#95—111no—
533#95—111no—
534#95—221no—
535#95—221no—
536#95—221no—
537C2×C11—44no—
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—42no—
547D11—82no—
548C24—21no—
549C24—21no—
550C24—111no—
551C24—224no—
552C24—221no—
553C24—442no—
554C24—442no—
555C24—442no—
556C24—442no—
557C24—881no—
558C24—881no—
559C2×D4—21no—
560C2×D4—21no—
561C2×D4—21no—
562C2×D4—21no—
563C2×D4—21no—
564C2×D4—21no—
565C2×D4—21no—
566C2×D4—21no—
567C2×D4—112no—
568C2×D4—224no—
569C2×D4—221no—
570C2×D4—221no—
571C2×D4—221no—
572C2×D4—221no—
573C2×D4—221no—
574C2×D4—442no—
575C2×D4—442no—
576C2×D4—444no—
577C2×D4—444no—
578C2×D4—444no—
579C2×D4—444no—
580C2×D4—442no—
581C2×D4—442no—
582C2×D4—881no—
583C2×D4#433912yes—
584C2×D4#433912yes—
585C2×D4C2×C22⋊D1112yes—
586C2×D4C2×C22⋊D1112yes—
587C22×C4—21no—
588C22×C4—21no—
589C22×C4—42no—
590C22×C4—42no—
591C22×C4—42no—
592C22×C4—42no—
593C22×C4—81no—
594C22×C4—81no—
595C22×C4—111no—
596C22×C4—111no—
597C22×C4—111no—
598C22×C4—221no—
599C22×C4—221no—
600C22×C4—221no—
601C22×C4—221no—
602C22×C4—221no—
603C22×C4—221no—
604C22×C4—221no—
605C22×C4—221no—
606C22×C4—221no—
607C22×C4—442no—
608C22×C4—442no—
609C22×C4—881no—
610C22×C4D4×D1111yescharacteristic
611C22×C4D4×D1111yescharacteristic
612C22×C4C23×D1111yescharacteristic
613D8—28no—
614D8—444no—
615C2×C8—21no—
616C2×C8—21no—
617C2×C8—21no—
618C2×C8—21no—
619C2×C8—21no—
620C2×C8—221no—
621C2×C8—221no—
622C2×C8—221no—
623C2×C8—221no—
624C2×C8—221no—
625C2×C8—221no—
626C2×C8C2×C22⋊D1112yes—
627C4⋊C4—21no—
628C4⋊C4—21no—
629C4⋊C4—21no—
630C4⋊C4—21no—
631C4⋊C4—221no—
632C4⋊C4—221no—
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—441no—
644C22⋊C4—442no—
645C22⋊C4—442no—
646C22⋊C4—442no—
647C22⋊C4—442no—
648C22⋊C4—442no—
649C22⋊C4—442no—
650C22⋊C4—442no—
651C22⋊C4—442no—
652C22⋊C4—881no—
653C22⋊C4—881no—
654C42—21no—
655C42—21no—
656C42—221no—
657C42—221no—
658C11#2489311yescharacteristic, complemented, Sylow
659C23—22no—
660C23—22no—
661C23—22no—
662C23—22no—
663C23—41no—
664C23—41no—
665C23—41no—
666C23—41no—
667C23—41no—
668C23—41no—
669C23—41no—
670C23—41no—
671C23—41no—
672C23—41no—
673C23—112no—
674C23—221no—
675C23—221no—
676C23—221no—
677C23—221no—
678C23—221no—
679C23—221no—
680C23—222no—
681C23—448no—
682C23—448no—
683C23—441no—
684C23—441no—
685C23—441no—
686C23—441no—
687C23—441no—
688C23—441no—
689C23—884no—
690C23—884no—
691C23—884no—
692C23—884no—
693C23—884no—
694C23C2×D4×D1111yescharacteristic
695D4—22no—
696D4—22no—
697D4—22no—
698D4—22no—
699D4—22no—
700D4—41no—
701D4—41no—
702D4—222no—
703D4—222no—
704D4—448no—
705D4—441no—
706D4—441no—
707D4—884no—
708D4#6698214yescomplemented
709C2×C4—21no—
710C2×C4—21no—
711C2×C4—21no—
712C2×C4—21no—
713C2×C4—21no—
714C2×C4—41no—
715C2×C4—41no—
716C2×C4—41no—
717C2×C4—41no—
718C2×C4—41no—
719C2×C4—41no—
720C2×C4—84no—
721C2×C4—84no—
722C2×C4—112no—
723C2×C4—221no—
724C2×C4—221no—
725C2×C4—221no—
726C2×C4—221no—
727C2×C4—221no—
728C2×C4—221no—
729C2×C4—221no—
730C2×C4—221no—
731C2×C4—441no—
732C2×C4—441no—
733C2×C4—441no—
734C2×C4—441no—
735C2×C4—441no—
736C2×C4—441no—
737C2×C4—441no—
738C2×C4—441no—
739C2×C4—441no—
740C2×C4—441no—
741C2×C4—441no—
742C2×C4—441no—
743C2×C4—441no—
744C2×C4—884no—
745C2×C4D8×D1112yes—
746C2×C4C2×#433911yescharacteristic
747C2×C4C2×#433911yescharacteristic
748C2×C4#6703711yescharacteristic
749C2×C4#41×D1111yescharacteristic
750C2×C4#6704211yescharacteristic
751C2×C4C22×C22⋊D1111yescharacteristic
752C8—22no—
753C8—41no—
754C8—441no—
755C8—441no—
756C22—24no—
757C22—42no—
758C22—42no—
759C22—42no—
760C22—42no—
761C22—42no—
762C22—42no—
763C22—42no—
764C22—42no—
765C22—42no—
766C22—81no—
767C22—81no—
768C22—81no—
769C22—81no—
770C22—222no—
771C22—222no—
772C22—222no—
773C22—441no—
774C22—441no—
775C22—441no—
776C22—441no—
777C22—442no—
778C22—442no—
779C22—442no—
780C22—8816no—
781C22—881no—
782C22—881no—
783C22—881no—
784C22—881no—
785C22#1062307811yescharacteristic
786C22#1062308111yescharacteristic
787C22C2×D8×D1111yescharacteristic
788C22#1062328811yescharacteristic
789C22#1062329911yescharacteristic
790C22#1062330111yescharacteristic
791C22D4×C22⋊D1111yescharacteristic
792C4—22no—
793C4—41no—
794C4—81no—
795C4—81no—
796C4—222no—
797C4—441no—
798C4—441no—
799C4—881no—
800C4—881no—
801C4—881no—
802C4#1062308711yescharacteristic
803C4#1062309111yescharacteristic
804C4C2×#6698211yescharacteristic
805C4#1062336011yescharacteristic
806C2—44no—
807C2—82no—
808C2—442no—
809C2—882no—
810C2#1307207211yescharacteristic
811C2#1307861411yescharacteristic
812C2#1307879611yescharacteristic
813C2#1308014111yescharacteristic
814C2D8×C22⋊D1111yescharacteristic
815C2#1308043111yescharacteristic
816C2#1308082211yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC2×C4×C11×D8C2
socleC23×C11C22×D4
prime radicalC2×#10622769C2
hypercenterC2×C4×D8D11
hypocenterC11#24893
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×C4×D8

Complements

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

NH ≅ G/Ntype
2. #13072124C2semidirect
3. D4×(C2×D11)⋊C4C2semidirect
4. #13070141C2semidirect
5. #13070040C2semidirect
6. #13069925C2semidirect
7. #13069796C2semidirect
8. #13069299C2semidirect
9. #13069222C2semidirect
10. #13068966C2semidirect
11. #13068964C2semidirect
12. #13068863C2semidirect
13. #13068614C2semidirect
14. #13068545C2semidirect
15. C2×C4×C11×D8C2semidirect
19. C2×C4×D4×C11C22semidirect
26. C2×C11×#107C22semidirect
28. C2×C11×#102C22semidirect
29. C2×C4×C8×C11C22semidirect
30. #10622834C22semidirect
33. C2×#66896C22semidirect
41. C2×Dic11⋊C8C22semidirect
45. #10622589C22semidirect
47. C2×#66871C22semidirect
54. #10622541C22semidirect
55. #10622189C22semidirect
56. #10622189C22semidirect
57. #10622188C22semidirect
58. #10622167C22semidirect
59. #10622167C22semidirect
60. #10622162C22semidirect
233. (C2×D11)⋊C4D8semidirect
252. C2×C4×D8D11semidirect
309. D4×C11#123semidirect
370. C2×C4×D4C2×D11semidirect
375. C2×#107C2×D11semidirect
384. C2×#102C2×D11semidirect
387. C2×C4×C8C2×D11semidirect
658. C11#24893semidirect
708. D4#66982semidirect

Maximal subgroups

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

subgroupindex
C2×#106227692
#130721242
D4×(C2×D11)⋊C42
#130701412
#130700402
#130699252
#130697962
#130692992
#130692222
#130689662
#130689642
#130688632
#130686142
#130685452
C2×C4×C11×D82
#2489311