Finite Group Databasebeta

← #14797567

Subgroups — #14797567

Order 2816.

1204 conjugacy classes of subgroups.

The subgroup lattice has 812 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622769C211yesmaximal, characteristic
2#13072102C211yesmaximal, characteristic, complemented
3D4×(C2×D11)⋊C4C211yesmaximal, characteristic, complemented
4#13070134C211yesmaximal, characteristic, complemented
5#13070045C211yesmaximal, characteristic, complemented
6#13069925C211yesmaximal, characteristic, complemented
7#13069803C211yesmaximal, characteristic, complemented
8#13069299C211yesmaximal, characteristic, complemented
9#13069222C211yesmaximal, characteristic, complemented
10#13068966C211yesmaximal, characteristic, complemented
11#13068964C211yesmaximal, characteristic, complemented
12#13068877C211yesmaximal, characteristic, complemented
13#13068624C211yesmaximal, 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
23C22×(C2×D11)⋊C4—21no—
24C4×C11×D8—24no—
25C2×C11×#107C2211yescharacteristic, complemented
26C2×C11×#102C2211yescharacteristic
27C2×C11×#102C2211yescharacteristic, complemented
28C2×C4×C8×C11C2211yescharacteristic, complemented
29#10622834C2211yescharacteristic, complemented
30C2×#66896C2211yescharacteristic
31C2×#66896C2211yescharacteristic
32C2×#66896C2211yescharacteristic, complemented
33#10622826—21no—
34#10622826—21no—
35#10622824—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#10622590C2211yescharacteristic, complemented
46C2×#66873C2211yescharacteristic
47C2×#66872C2211yescharacteristic, 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—
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×(C2×D11)⋊C4—21no—
108C2×(C2×D11)⋊C4—44no—
109C2×(C2×D11)⋊C4D411yescharacteristic
110C2×(C2×D11)⋊C4D411yescharacteristic
111C2×C4⋊Dic11C2311yescharacteristic
112C2×C4⋊Dic11C2311yescharacteristic
113C2×C4⋊Dic11C2311yescharacteristic
114C2×Dic11⋊C4—21no—
115C2×C4×Dic11C2311yescharacteristic
116C22×C11⋊C8C2311yescharacteristic
117C22×C11⋊C8C2311yescharacteristic
118C11×#107—22no—
119C11×#102—22no—
120C11×#102—22no—
121C4×C8×C11—22no—
122#66896—22no—
123#66896—22no—
124#66896—41no—
125C11⋊#95—21no—
126C11⋊#95—21no—
127C11⋊#95—21no—
128C11⋊#95—21no—
129C11⋊#95—21no—
130C11⋊#95D411yescharacteristic
131C11⋊#95D411yescharacteristic
132#66885—22no—
133#66885—22no—
134(C2×D11)⋊C8—22no—
135(C2×D11)⋊C8—41no—
136Dic11⋊C8—41no—
137#66873—41no—
138#66872—41no—
139#24897—111nomaximal, Sylow
140C24×C11—21no—
141C24×C11—21no—
142C23×D11—21no—
143C23×D11—24no—
144C23×D11—42no—
145C23×D11—42no—
146C23×D11—42no—
147C23×D11—42no—
148C23×D11—81no—
149C23×D11—81no—
150C23×D11C2×D411yescharacteristic
151C2×D4×C11—21no—
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×C11C2×D412yes—
160C2×D4×C11C2×D412yes—
161C2×D4×C11#4112yes—
162C2×D4×C11#4112yes—
163C22×C4×C11—21no—
164C22×C4×C11—21no—
165C22×C4×C11—42no—
166C22×C4×C11—42no—
167C22×C4×C11—42no—
168C22×C4×C11—42no—
169C22×C4×C11—81no—
170C22×C4×C11—81no—
171C22×C4×C11C2×D411yescharacteristic
172C22×C4×C11C2×D411yescharacteristic
173C22×C4×C11C2411yescharacteristic
174C2×C22⋊D11—24no—
175C2×C22⋊D11—42no—
176C2×C22⋊D11—42no—
177C2×C22⋊D11—42no—
178C2×C22⋊D11—42no—
179C2×C22⋊D11—81no—
180C22×Dic11—21no—
181C22×Dic11—21no—
182C22×Dic11—21no—
183C22×Dic11—42no—
184C22×Dic11—42no—
185C22×Dic11—81no—
186C22×Dic11C2×D411yescharacteristic
187C22×Dic11C2×D411yescharacteristic
188C22×Dic11C2×D411yescharacteristic
189D4×D11—44no—
190D4×D11—44no—
191D4×D11—44no—
192D4×D11—44no—
193C2×D44—21no—
194C2×D44—21no—
195C2×D44—21no—
196C2×D44—21no—
197C2×D44—21no—
198C2×D44#4112yes—
199C2×C4×D11—21no—
200C2×C4×D11—21no—
201C2×C4×D11—21no—
202C2×C4×D11—21no—
203C2×C4×D11—21no—
204C2×C4×D11—21no—
205C11×D8—28no—
206C2×C8×C11—21no—
207C2×C8×C11—21no—
208C2×C8×C11—21no—
209C2×C8×C11—21no—
210C2×C8×C11—21no—
211C2×C8×C11C2×D412yes—
212C11×C4⋊C4—21no—
213C11×C4⋊C4—21no—
214C11×C4⋊C4—21no—
215C11×C4⋊C4—21no—
216C11×C22⋊C4—42no—
217C11×C22⋊C4—42no—
218C42×C11—21no—
219C42×C11—21no—
220C22⋊Dic11—42no—
221C22⋊Dic11—42no—
222C22⋊Dic11—81no—
223C22⋊Dic11—81no—
224#4323—44no—
225(C2×D11)⋊C4—22no—
226(C2×D11)⋊C4—22no—
227(C2×D11)⋊C4—42no—
228(C2×D11)⋊C4—42no—
229(C2×D11)⋊C4—42no—
230(C2×D11)⋊C4—81no—
231(C2×D11)⋊C4—81no—
232(C2×D11)⋊C4—81no—
233C4⋊Dic11—21no—
234C4⋊Dic11—21no—
235C4⋊Dic11—21no—
236C4⋊Dic11—21no—
237C4⋊Dic11—21no—
238C4⋊Dic11—21no—
239Dic11⋊C4—81no—
240C4×Dic11—21no—
241C4×Dic11—21no—
242C2×C11⋊C8—21no—
243C2×C11⋊C8—21no—
244C2×C11⋊C8—21no—
245C2×C11⋊C8—21no—
246C2×C11⋊C8—21no—
247C2×C11⋊C8—21no—
248C2×#447—111no—
249C2×C4×D8D1111yescharacteristic, complemented
250#2420—111no—
251D4×C22⋊C4—111no—
252#2092—111no—
253#2076—111no—
254#2054—111no—
255#2034—111no—
256#1934—111no—
257#1923—111no—
258#1879—111no—
259#1879—111no—
260#1864—111no—
261#1804—111no—
262#1786—111no—
263C23×C11—22no—
264C23×C11—22no—
265C23×C11—22no—
266C23×C11—22no—
267C23×C11—41no—
268C23×C11—41no—
269C23×C11—41no—
270C23×C11—41no—
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—21no—
283C22×D11—21no—
284C22×D11—22no—
285C22×D11—48no—
286C22×D11—48no—
287C22×D11—41no—
288C22×D11—41no—
289C22×D11—41no—
290C22×D11—41no—
291C22×D11—41no—
292C22×D11—41no—
293C22×D11—84no—
294C22×D11—84no—
295C22×D11—84no—
296C22×D11—84no—
297C22×D11—84no—
298C22×D11#13512yes—
299D4×C11—22no—
300D4×C11—22no—
301D4×C11—22no—
302D4×C11—22no—
303D4×C11—22no—
304D4×C11—41no—
305D4×C11—41no—
306D4×C11#12314yes—
307C2×C4×C11—21no—
308C2×C4×C11—21no—
309C2×C4×C11—21no—
310C2×C4×C11—21no—
311C2×C4×C11—21no—
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—84no—
319C2×C4×C11—84no—
320C2×C4×C11AGL(1,ℤ/8)12yes—
321C2×C4×C11C22×D411yescharacteristic
322C2×C4×C11C2×#4111yescharacteristic
323C2×C4×C11C2×#4111yescharacteristic
324C2×C4×C11C2×#4111yescharacteristic
325C2×C4×C11H(5,𝔽2)11yescharacteristic
326C2×C4×C11H(5,𝔽2)11yescharacteristic
327C22⋊D11—48no—
328C22⋊D11—84no—
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—41no—
339C2×Dic11—41no—
340C2×Dic11—41no—
341C2×Dic11—41no—
342C2×Dic11—41no—
343C2×Dic11—41no—
344C2×Dic11—41no—
345C2×Dic11—41no—
346C2×Dic11—41no—
347C2×Dic11—84no—
348D44—22no—
349D44—22no—
350D44—41no—
351D44—41no—
352C4×D11—41no—
353C4×D11—41no—
354C4×D11—41no—
355C4×D11—41no—
356C8×C11—22no—
357C8×C11—41no—
358C11⋊C8—41no—
359C11⋊C8—41no—
360C23×D4—111no—
361C22×D8—111no—
362C22×D8C2×D1111yescharacteristic
363C2×#121—111no—
364C2×C4×D4—111no—
365C2×C4×D4C2×D1111yescharacteristic
366C2×C4×D4C2×D1111yescharacteristic, complemented
367C22×C22⋊C4—221no—
368#447—224no—
369C4×D8—24no—
370C2×#107C2×D1111yescharacteristic, complemented
371C2×#106—111no—
372C2×C4⋊C8—111no—
373C2×#102—111no—
374C2×#102—111no—
375C2×#102—111no—
376C2×#102—111no—
377C2×#102—111no—
378C2×#102—111no—
379C2×#102C2×D1111yescharacteristic
380C2×#102C2×D1111yescharacteristic, complemented
381C2×C22⋊C8—111no—
382C2×C22⋊C8—111no—
383C2×C4×C8C2×D1111yescharacteristic, complemented
384#397—221no—
385#394—221no—
386#390—111no—
387#390—111no—
388#390—111no—
389#389—111no—
390#386—221no—
391#386—221no—
392#386—221no—
393#382—111no—
394#381—221no—
395#380—111no—
396#380—111no—
397#379—221no—
398C4×C22⋊C4—111no—
399#340—111no—
400#340—111no—
401#340—111no—
402#340—111no—
403#336—111no—
404#336—111no—
405C22×C11—24no—
406C22×C11—42no—
407C22×C11—42no—
408C22×C11—42no—
409C22×C11—42no—
410C22×C11—42no—
411C22×C11—42no—
412C22×C11—42no—
413C22×C11—42no—
414C22×C11—42no—
415C22×C11—81no—
416C22×C11—81no—
417C22×C11—81no—
418C22×C11—81no—
419C22×C11#52511yescharacteristic
420C22×C11D4211yescharacteristic
421C22×C11#54611yescharacteristic
422C22×C11C2×#13511yescharacteristic
423C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
424C22×C11#57611yescharacteristic
425C22×C11#57611yescharacteristic
426C2×D11—22no—
427C2×D11—22no—
428C2×D11—22no—
429C2×D11—41no—
430C2×D11—41no—
431C2×D11—41no—
432C2×D11—41no—
433C2×D11—42no—
434C2×D11—42no—
435C2×D11—42no—
436C2×D11—816no—
437C2×D11—81no—
438C2×D11—81no—
439C2×D11—81no—
440C2×D11—81no—
441C4×C11—22no—
442C4×C11—41no—
443C4×C11—81no—
444C4×C11—81no—
445C4×C11C2×#12311yescharacteristic
446C4×C11#53811yescharacteristic
447C4×C11#54611yescharacteristic
448C4×C11#55111yescharacteristic
449Dic11—41no—
450Dic11—41no—
451Dic11—41no—
452Dic11—81no—
453Dic11—81no—
454Dic11—81no—
455C25—221no—
456C22×D4—111no—
457C22×D4—221no—
458C22×D4—222no—
459C22×D4—222no—
460C22×D4—222no—
461C22×D4—222no—
462C22×D4—221no—
463C22×D4—441no—
464C22×D4—441no—
465C22×D4C22×D1111yescharacteristic
466C22×D4C22×D1111yescharacteristic
467C23×C4—21no—
468C23×C4—21no—
469C23×C4—111no—
470C23×C4—221no—
471C2×D8—22no—
472C2×D8—22no—
473C2×D8—222no—
474C2×D8—222no—
475C2×D8—441no—
476C2×D8C22⋊D1114yes—
477C22×C8—111no—
478C22×C8—111no—
479C22×C8C22×D1111yescharacteristic
480C22×C8C22×D1111yescharacteristic
481#121—222no—
482#121—441no—
483C4×D4—22no—
484C4×D4—22no—
485C4×D4—41no—
486C4×D4—41no—
487C4×D4—222no—
488C4×D4—441no—
489C2×C4⋊C4—111no—
490C2×C4⋊C4—111no—
491C2×C4⋊C4—111no—
492C2×C4⋊C4—221no—
493C2×C4⋊C4C22×D1111yescharacteristic
494C2×C4⋊C4C22×D1111yescharacteristic
495C2×C22⋊C4—21no—
496C2×C22⋊C4—21no—
497C2×C22⋊C4—111no—
498C2×C22⋊C4—111no—
499C2×C22⋊C4—221no—
500C2×C22⋊C4—221no—
501C2×C22⋊C4—221no—
502C2×C22⋊C4—221no—
503C2×C22⋊C4—221no—
504C2×C22⋊C4—221no—
505C2×C22⋊C4—221no—
506C2×C22⋊C4—221no—
507C2×C22⋊C4—221no—
508C2×C22⋊C4—221no—
509C2×C22⋊C4—444no—
510C2×C42—111no—
511C2×C42C22×D1111yescharacteristic
512#107—22no—
513#106—441no—
514C4⋊C8—441no—
515#102—22no—
516#102—22no—
517#102—222no—
518#102—222no—
519#102—222no—
520#102—222no—
521#102—441no—
522#102—441no—
523C22⋊C8—222no—
524C22⋊C8—441no—
525C4×C8—22no—
526#95—111no—
527#95—111no—
528#95—221no—
529#95—221no—
530#95—221no—
531#95—221no—
532#95—221no—
533C2×C11—44no—
534C2×C11—82no—
535C2×C11#241811yescharacteristic
536C2×C11#310511yescharacteristic
537C2×C11#312211yescharacteristic
538C2×C11#326411yescharacteristic
539C2×C11#328011yescharacteristic
540C2×C11#329711yescharacteristic
541C2×C11#332511yescharacteristic
542D11—42no—
543D11—82no—
544C24—21no—
545C24—21no—
546C24—111no—
547C24—224no—
548C24—221no—
549C24—442no—
550C24—442no—
551C24—442no—
552C24—442no—
553C24—881no—
554C24—881no—
555C2×D4—21no—
556C2×D4—21no—
557C2×D4—21no—
558C2×D4—21no—
559C2×D4—21no—
560C2×D4—21no—
561C2×D4—21no—
562C2×D4—21no—
563C2×D4—112no—
564C2×D4—224no—
565C2×D4—221no—
566C2×D4—221no—
567C2×D4—221no—
568C2×D4—221no—
569C2×D4—221no—
570C2×D4—442no—
571C2×D4—442no—
572C2×D4—444no—
573C2×D4—444no—
574C2×D4—444no—
575C2×D4—444no—
576C2×D4—442no—
577C2×D4—442no—
578C2×D4—881no—
579C2×D4#433912yes—
580C2×D4#433912yes—
581C2×D4C2×C22⋊D1112yes—
582C2×D4C2×C22⋊D1112yes—
583C22×C4—21no—
584C22×C4—21no—
585C22×C4—42no—
586C22×C4—42no—
587C22×C4—42no—
588C22×C4—42no—
589C22×C4—81no—
590C22×C4—81no—
591C22×C4—111no—
592C22×C4—111no—
593C22×C4—111no—
594C22×C4—221no—
595C22×C4—221no—
596C22×C4—221no—
597C22×C4—221no—
598C22×C4—221no—
599C22×C4—221no—
600C22×C4—221no—
601C22×C4—221no—
602C22×C4—221no—
603C22×C4—442no—
604C22×C4—442no—
605C22×C4—881no—
606C22×C4D4×D1111yescharacteristic
607C22×C4D4×D1111yescharacteristic
608C22×C4C23×D1111yescharacteristic
609D8—28no—
610D8—444no—
611C2×C8—21no—
612C2×C8—21no—
613C2×C8—21no—
614C2×C8—21no—
615C2×C8—21no—
616C2×C8—221no—
617C2×C8—221no—
618C2×C8—221no—
619C2×C8—221no—
620C2×C8—221no—
621C2×C8—221no—
622C2×C8C2×C22⋊D1112yes—
623C4⋊C4—21no—
624C4⋊C4—21no—
625C4⋊C4—21no—
626C4⋊C4—21no—
627C4⋊C4—221no—
628C4⋊C4—221no—
629C4⋊C4—221no—
630C4⋊C4—221no—
631C4⋊C4—221no—
632C4⋊C4—221no—
633C4⋊C4—881no—
634C22⋊C4—42no—
635C22⋊C4—42no—
636C22⋊C4—222no—
637C22⋊C4—222no—
638C22⋊C4—442no—
639C22⋊C4—442no—
640C22⋊C4—442no—
641C22⋊C4—442no—
642C22⋊C4—442no—
643C22⋊C4—881no—
644C22⋊C4—881no—
645C22⋊C4—881no—
646C22⋊C4—881no—
647C22⋊C4—881no—
648C42—21no—
649C42—21no—
650C42—221no—
651C42—221no—
652C11#2489711yescharacteristic, complemented, Sylow
653C23—22no—
654C23—22no—
655C23—22no—
656C23—22no—
657C23—41no—
658C23—41no—
659C23—41no—
660C23—41no—
661C23—41no—
662C23—41no—
663C23—41no—
664C23—41no—
665C23—41no—
666C23—41no—
667C23—112no—
668C23—221no—
669C23—221no—
670C23—221no—
671C23—221no—
672C23—221no—
673C23—221no—
674C23—222no—
675C23—448no—
676C23—448no—
677C23—441no—
678C23—441no—
679C23—441no—
680C23—441no—
681C23—441no—
682C23—441no—
683C23—884no—
684C23—884no—
685C23—884no—
686C23—884no—
687C23—884no—
688C23C2×D4×D1111yescharacteristic
689D4—22no—
690D4—22no—
691D4—22no—
692D4—22no—
693D4—22no—
694D4—41no—
695D4—41no—
696D4—222no—
697D4—222no—
698D4—448no—
699D4—441no—
700D4—441no—
701D4—884no—
702D4#6698214yes—
703C2×C4—21no—
704C2×C4—21no—
705C2×C4—21no—
706C2×C4—21no—
707C2×C4—21no—
708C2×C4—41no—
709C2×C4—41no—
710C2×C4—41no—
711C2×C4—41no—
712C2×C4—41no—
713C2×C4—41no—
714C2×C4—84no—
715C2×C4—84no—
716C2×C4—221no—
717C2×C4—221no—
718C2×C4—221no—
719C2×C4—221no—
720C2×C4—221no—
721C2×C4—221no—
722C2×C4—221no—
723C2×C4—221no—
724C2×C4—221no—
725C2×C4—441no—
726C2×C4—441no—
727C2×C4—441no—
728C2×C4—441no—
729C2×C4—441no—
730C2×C4—441no—
731C2×C4—441no—
732C2×C4—441no—
733C2×C4—441no—
734C2×C4—441no—
735C2×C4—441no—
736C2×C4—441no—
737C2×C4—441no—
738C2×C4—884no—
739C2×C4#6696412yes—
740C2×C4C2×#433911yescharacteristic
741C2×C4C2×#433911yescharacteristic
742C2×C4#6703711yescharacteristic
743C2×C4#41×D1111yescharacteristic
744C2×C4#6704211yescharacteristic
745C2×C4C22×C22⋊D1111yescharacteristic
746C8—22no—
747C8—41no—
748C8—441no—
749C8—441no—
750C22—24no—
751C22—42no—
752C22—42no—
753C22—42no—
754C22—42no—
755C22—42no—
756C22—42no—
757C22—42no—
758C22—42no—
759C22—42no—
760C22—81no—
761C22—81no—
762C22—81no—
763C22—81no—
764C22—222no—
765C22—222no—
766C22—222no—
767C22—441no—
768C22—441no—
769C22—441no—
770C22—441no—
771C22—442no—
772C22—442no—
773C22—442no—
774C22—8816no—
775C22—881no—
776C22—881no—
777C22—881no—
778C22—881no—
779C22#1062307811yescharacteristic
780C22#1062308111yescharacteristic
781C22C2×#6696411yescharacteristic
782C22#1062328811yescharacteristic
783C22D11×#13511yescharacteristic
784C22#1062330011yescharacteristic
785C22D4×C22⋊D1111yescharacteristic
786C4—22no—
787C4—41no—
788C4—81no—
789C4—81no—
790C4—441no—
791C4—441no—
792C4—441no—
793C4—881no—
794C4—881no—
795C4—881no—
796C4#1062308711yescharacteristic
797C4#1062309111yescharacteristic
798C4C2×#6698211yescharacteristic
799C4#1062336011yescharacteristic
800C2—44no—
801C2—82no—
802C2—442no—
803C2—882no—
804C2#1307207211yescharacteristic
805C2#1307866111yescharacteristic
806C2#1307885611yescharacteristic
807C2#1308009611yescharacteristic
808C2#1308029511yescharacteristic
809C2#1308047111yescharacteristic
810C2#1308086011yescharacteristic
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#24897
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. #13072102C2semidirect
3. D4×(C2×D11)⋊C4C2semidirect
4. #13070134C2semidirect
5. #13070045C2semidirect
6. #13069925C2semidirect
7. #13069803C2semidirect
8. #13069299C2semidirect
9. #13069222C2semidirect
10. #13068966C2semidirect
11. #13068964C2semidirect
12. #13068877C2semidirect
13. #13068624C2semidirect
14. #13068545C2semidirect
15. C2×C4×C11×D8C2semidirect
19. C2×C4×D4×C11C22semidirect
25. C2×C11×#107C22semidirect
27. C2×C11×#102C22semidirect
28. C2×C4×C8×C11C22semidirect
29. #10622834C22semidirect
32. C2×#66896C22semidirect
41. C2×Dic11⋊C8C22semidirect
45. #10622590C22semidirect
47. C2×#66872C22semidirect
54. #10622541C22semidirect
55. #10622189C22semidirect
56. #10622189C22semidirect
57. #10622188C22semidirect
58. #10622167C22semidirect
59. #10622167C22semidirect
60. #10622162C22semidirect
249. C2×C4×D8D11semidirect
366. C2×C4×D4C2×D11semidirect
370. C2×#107C2×D11semidirect
380. C2×#102C2×D11semidirect
383. C2×C4×C8C2×D11semidirect
652. C11#24897semidirect

Maximal subgroups

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

subgroupindex
C2×#106227692
#130721022
D4×(C2×D11)⋊C42
#130701342
#130700452
#130699252
#130698032
#130692992
#130692222
#130689662
#130689642
#130688772
#130686242
#130685452
C2×C4×C11×D82
#2489711