Finite Group Databasebeta

← #14774158

Subgroups — #14774158

Order 2816.

1190 conjugacy classes of subgroups.

The subgroup lattice has 778 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622347C211yesmaximal, characteristic
2C2×#10622502C211yesmaximal, characteristic, complemented
3C2×#10622579C211yesmaximal, characteristic, complemented
4#13071632C211yesmaximal, characteristic, complemented
5#13071453C211yesmaximal, characteristic, complemented
6#13069480C211yesmaximal, characteristic, complemented
7#13069311C211yesmaximal, characteristic, complemented
8#13069235C211yesmaximal, characteristic, complemented
9#13069052C211yesmaximal, characteristic, complemented
10#13068972C211yesmaximal, characteristic, complemented
11#13068965C211yesmaximal, characteristic, complemented
12#13068867C211yesmaximal, characteristic, complemented
13#13068435C211yesmaximal, characteristic, complemented
14#13068402C211yesmaximal, characteristic, complemented
15C11×#1852C211yesmaximal, characteristic, complemented
16C22×#4339C2211yescharacteristic
17C22×C11×C4⋊C4C2211yescharacteristic
18C2×#66983C2211yescharacteristic
19C2×C4×C22⋊D11—21no—
20C22×#4318C2211yescharacteristic
21C22×D88C2211yescharacteristic
22C22×#4314C2211yescharacteristic
23C2×#66946C2211yescharacteristic
24C2×#66940C2211yescharacteristic
25C2×#66940C2211yescharacteristic
26C2×C11×#107C2211yescharacteristic
27C2×C11×#107C2211yescharacteristic
28C2×C11×C22⋊C8C2211yescharacteristic
29C11×#380C2211yescharacteristic
30#10622826—21no—
31C4×C22⋊Dic11C2211yescharacteristic
32C2×#66885C2211yescharacteristic
33C2×#66880C2211yescharacteristic
34C2×#66879C2211yescharacteristic
35C2×C8×Dic11C2211yescharacteristic
36#10622603—21no—
37#10622602—21no—
38#10622601C2211yescharacteristic
39#10622601C2211yescharacteristic
40#10622601C2211yescharacteristic
41C4⋊C4×Dic11C2211yescharacteristic
42#10622586C2211yescharacteristic
43C2×#66874C2211yescharacteristic
44C2×#66874C2211yescharacteristic
45#10622579—24no—
46C2×#66873C2211yescharacteristic
47C2×#66873C2211yescharacteristic
48C2×#66873C2211yescharacteristic
49C2×#66873C2211yescharacteristic
50#10622570—21no—
51#10622570—21no—
52#10622502—24no—
53#10622347C418yescomplemented
54#10622280—21no—
55#10622279—21no—
56C11×#340C2211yescharacteristic
57C11×#340C2211yescharacteristic
58#10622188C2211yescharacteristic
59#10622188C2211yescharacteristic
60#10622167C2211yescharacteristic
61#10622167C2211yescharacteristic
62C23×C4×C11—21no—
63C23×C4×C11C2311yescharacteristic
64C22×C22⋊D11—21no—
65C22×C22⋊D11—21no—
66C2×#4339—22no—
67C2×#4339—22no—
68C2×#4339—22no—
69C2×#4339—41no—
70C2×#4339—41no—
71C2×#4339C2×C414yescomplemented
72C22×D44C2311yescharacteristic
73C22×D44C2311yescharacteristic
74C22×C4×D11—21no—
75C22×C4×D11—21no—
76C22×Dic22C2311yescharacteristic
77C22×C8×C11C2311yescharacteristic
78C22×C8×C11C2311yescharacteristic
79C2×C11×C4⋊C4—22no—
80C2×C11×C4⋊C4—21no—
81C2×C11×C4⋊C4—41no—
82C2×C11×C4⋊C4C2311yescharacteristic
83C2×C11×C4⋊C4C2311yescharacteristic
84C2×C11×C4⋊C4C2311yescharacteristic
85C2×C11×C4⋊C4C2311yescharacteristic
86C2×C11×C22⋊C4—21no—
87C2×C22⋊Dic11D411yescharacteristic
88C2×C22⋊Dic11D411yescharacteristic
89#66983—22no—
90#66983C2×C414yes—
91C4×C22⋊D11—44no—
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×Dic11⋊C4—21no—
102C2×Dic11⋊C4—21no—
103C2×Dic11⋊C4—21no—
104C2×C4×Dic11—21no—
105C2×C4×Dic11—21no—
106C2×C4×Dic11—21no—
107C2×C4×Dic11C2311yescharacteristic
108C2×C4×Dic11C2311yescharacteristic
109C2×#4318—22no—
110C2×#4318—22no—
111C2×#4318—41no—
112C22×C11⋊C8C2311yescharacteristic
113C22×C11⋊C8C2311yescharacteristic
114C2×D88—41no—
115C2×D88—41no—
116C2×D88C2×C414yescomplemented
117C2×#4314—22no—
118C2×#4314—22no—
119C2×#4314C2×C414yescomplemented
120#66946—22no—
121#66946—41no—
122#66940—22no—
123#66940—22no—
124#66940—41no—
125#66940—41no—
126C11×#107—22no—
127C11×#107—41no—
128C11×C22⋊C8C2×C414yescomplemented
129C11×#95—21no—
130C11⋊#95—21no—
131C11⋊#95—21no—
132C11⋊#95D411yescharacteristic
133C11⋊#95D411yescharacteristic
134#66885C2×C414yescomplemented
135#66880C2×C414yescomplemented
136#66879—22no—
137C8×Dic11—41no—
138#66874—22no—
139#66874D414yescomplemented
140#66873—22no—
141#66873—22no—
142#66873—22no—
143#66873—41no—
144#22863—111nomaximal, Sylow
145C24×C11C2×D411yescharacteristic
146C23×D11—21no—
147C23×D11—21no—
148C22×C4×C11—21no—
149C22×C4×C11—21no—
150C22×C4×C11—21no—
151C22×C4×C11—21no—
152C22×C4×C11—21no—
153C22×C4×C11—21no—
154C22×C4×C11—21no—
155C22×C4×C11—21no—
156C22×C4×C11—42no—
157C22×C4×C11—42no—
158C22×C4×C11—81no—
159C22×C4×C11C22×C412yes—
160C22×C4×C11C2×D411yescharacteristic
161C22×C4×C11#4112yes—
162C22×C4×C11C2411yescharacteristic
163C2×C22⋊D11—24no—
164C2×C22⋊D11—24no—
165C2×C22⋊D11—42no—
166C2×C22⋊D11—42no—
167C2×C22⋊D11—42no—
168C2×C22⋊D11—42no—
169C22×Dic11—21no—
170C22×Dic11—21no—
171C22×Dic11C2×D411yescharacteristic
172C22×Dic11C2×D411yescharacteristic
173C22×Dic11C2×D411yescharacteristic
174C22×Dic11C2×D411yescharacteristic
175#4339—28no—
176#4339—44no—
177#4339—44no—
178#4339—44no—
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—21no—
188C2×D44—21no—
189C2×D44C22×C412yes—
190C2×D44C22×C412yes—
191C2×C4×D11—24no—
192C2×C4×D11—42no—
193C2×C4×D11—42no—
194C2×C4×D11—42no—
195C2×C4×D11—42no—
196C2×C4×D11—81no—
197C2×Dic22—21no—
198C2×Dic22—21no—
199C2×Dic22—21no—
200C2×Dic22C22×C412yes—
201C2×Dic22C2×D412yes—
202C2×Dic22#4112yes—
203C2×C8×C11—21no—
204C2×C8×C11—21no—
205C2×C8×C11—21no—
206C2×C8×C11—21no—
207C2×C8×C11C22×C412yes—
208C2×C8×C11C22×C412yes—
209C11×C4⋊C4—21no—
210C11×C4⋊C4—21no—
211C11×C4⋊C4—21no—
212C11×C4⋊C4—21no—
213C11×C4⋊C4—21no—
214C11×C4⋊C4—21no—
215C11×C4⋊C4—21no—
216C11×C4⋊C4—42no—
217C11×C4⋊C4C2×D412yes—
218C11×C22⋊C4—81no—
219C22⋊Dic11—22no—
220C22⋊Dic11—41no—
221(C2×D11)⋊C4—24no—
222(C2×D11)⋊C4—42no—
223(C2×D11)⋊C4—42no—
224(C2×D11)⋊C4—42no—
225(C2×D11)⋊C4—42no—
226(C2×D11)⋊C4—81no—
227(C2×D11)⋊C4—81no—
228(C2×D11)⋊C4—81no—
229C4⋊Dic11—21no—
230C4⋊Dic11C22×C412yes—
231Dic11⋊C4—42no—
232Dic11⋊C4—42no—
233Dic11⋊C4—42no—
234C4×Dic11—21no—
235C4×Dic11—21no—
236C4×Dic11—21no—
237C4×Dic11—21no—
238C4×Dic11—42no—
239C4×Dic11—42no—
240C4×Dic11—42no—
241#4318—44no—
242C2×C11⋊C8—21no—
243C2×C11⋊C8—21no—
244C2×C11⋊C8—21no—
245C2×C11⋊C8—21no—
246C2×C11⋊C8—21no—
247C2×C11⋊C8C2×D412yes—
248D88—44no—
249#4314—28no—
250C2×#449—111no—
251C2×#440—111no—
252C2×#417—111no—
253#2361—111no—
254#2341—111no—
255#1970—111no—
256#1936—111no—
257#1925—111no—
258#1895—111no—
259#1880—111no—
260#1879—111no—
261#1863—111no—
262#1852D1111yescharacteristic, complemented
263C4×#103—111no—
264#1753—111no—
265C23×C11—21no—
266C23×C11—21no—
267C23×C11—21no—
268C23×C11—21no—
269C23×C11—21no—
270C23×C11—21no—
271C23×C11C4×D412yes—
272C23×C11C22×D411yescharacteristic
273C22×D11—22no—
274C22×D11—22no—
275C22×D11—41no—
276C22×D11—41no—
277C22×D11—41no—
278C22×D11—41no—
279C22×D11—41no—
280C22×D11—41no—
281C22×D11—41no—
282C22×D11—41no—
283C22×D11—41no—
284C22×D11—41no—
285C22×D11—41no—
286C22×D11—41no—
287C2×C4×C11—21no—
288C2×C4×C11—21no—
289C2×C4×C11—22no—
290C2×C4×C11—22no—
291C2×C4×C11—22no—
292C2×C4×C11—22no—
293C2×C4×C11—22no—
294C2×C4×C11—41no—
295C2×C4×C11—41no—
296C2×C4×C11—41no—
297C2×C4×C11—41no—
298C2×C4×C11—41no—
299C2×C4×C11—41no—
300C2×C4×C11—41no—
301C2×C4×C11—41no—
302C2×C4×C11—41no—
303C2×C4×C11—41no—
304C2×C4×C11—41no—
305C2×C4×C11—84no—
306C2×C4×C11C4×D412yes—
307C2×C4×C11C23×C411yescharacteristic
308C2×C4×C11C22×D411yescharacteristic
309C2×C4×C11C2×#4111yescharacteristic
310C2×C4×C11C2×#4111yescharacteristic
311C2×C4×C11H(5,𝔽2)11yescharacteristic
312C2×C4×C11H(5,𝔽2)11yescharacteristic
313C22⋊D11—48no—
314C22⋊D11—48no—
315C2×Dic11—22no—
316C2×Dic11—22no—
317C2×Dic11—21no—
318C2×Dic11—22no—
319C2×Dic11—21no—
320C2×Dic11—22no—
321C2×Dic11—21no—
322C2×Dic11—21no—
323C2×Dic11—21no—
324C2×Dic11—21no—
325C2×Dic11—21no—
326C2×Dic11—21no—
327C2×Dic11—21no—
328C2×Dic11—21no—
329C2×Dic11—21no—
330C2×Dic11—41no—
331C2×Dic11—41no—
332C2×Dic11AGL(1,ℤ/8)12yes—
333D44—22no—
334D44—22no—
335D44—22no—
336D44—22no—
337D44—41no—
338D44—41no—
339D44—41no—
340D44—41no—
341C4×D11—48no—
342C4×D11—84no—
343Dic22—22no—
344Dic22—22no—
345Dic22—22no—
346Dic22C4×D414yescomplemented
347C8×C11—22no—
348C8×C11—22no—
349C11⋊C8—22no—
350C11⋊C8—41no—
351C22×#41—111no—
352C22×SD16—111no—
353C22×D8—111no—
354C22×M16—111no—
355C2×#121—111no—
356C2×C4×Q8—111no—
357C2×C4×Q8—111no—
358C2×C4×D4—111no—
359C2×C4×D4—221no—
360C22×C4⋊C4C2×D1111yescharacteristic
361#449—118no—
362#440—224no—
363C2×#107C2×D1111yescharacteristic
364C2×#107C2×D1111yescharacteristic
365#417—224no—
366C2×#103—111no—
367C2×#103—111no—
368C2×#103—111no—
369C2×#102—111no—
370C2×#102—111no—
371C2×#102—111no—
372C2×#102—111no—
373C2×#102—111no—
374C2×C22⋊C8C2×D1111yescharacteristic
375C2×#97—111no—
376C2×C4×C8—111no—
377#390—111no—
378#390—111no—
379#390—111no—
380#390—221no—
381#390—221no—
382#389—111no—
383#388—221no—
384#386—221no—
385#385—221no—
386#380—221no—
387#380C2×D1111yescharacteristic
388C4×C4⋊C4—111no—
389C4×C22⋊C4—111no—
390C4×C22⋊C4—221no—
391#340—111no—
392#340—111no—
393#340C2×D1111yescharacteristic
394#340C2×D1111yescharacteristic
395#336—111no—
396#336—111no—
397C22×C11—22no—
398C22×C11—22no—
399C22×C11—22no—
400C22×C11—41no—
401C22×C11—41no—
402C22×C11—41no—
403C22×C11—41no—
404C22×C11C2×C4×D411yescharacteristic
405C22×C11D4211yescharacteristic
406C22×C11#54611yescharacteristic
407C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
408C22×C11#57511yescharacteristic
409C22×C11#57611yescharacteristic
410C22×C11#57811yescharacteristic
411C2×D11—42no—
412C2×D11—42no—
413C2×D11—42no—
414C2×D11—42no—
415C2×D11—42no—
416C2×D11—42no—
417C2×D11—81no—
418C2×D11—81no—
419C2×D11—81no—
420C2×D11—81no—
421C2×D11—81no—
422C2×D11—81no—
423C2×D11—81no—
424C2×D11—81no—
425C4×C11—22no—
426C4×C11—42no—
427C4×C11—81no—
428C4×C11—81no—
429C4×C11—81no—
430C4×C11C2×C4×D411yescharacteristic
431C4×C11#51811yescharacteristic
432C4×C11#54611yescharacteristic
433C4×C11#55111yescharacteristic
434Dic11—24no—
435Dic11—22no—
436Dic11—42no—
437Dic11—41no—
438Dic11—41no—
439Dic11—41no—
440C2×#41—114no—
441C2×#41—222no—
442C2×#41—222no—
443C2×#41—222no—
444C2×#41—441no—
445C2×#41—441no—
446C22×Q8—111no—
447C22×D4—111no—
448C22×D4—111no—
449C22×D4—221no—
450C22×D4—221no—
451C23×C4—21no—
452C23×C4—221no—
453C23×C4—221no—
454C23×C4C22×D1111yescharacteristic
455C2×SD16—114no—
456C2×SD16—222no—
457C2×SD16—222no—
458C2×D8—114no—
459C2×D8—441no—
460C2×D8—441no—
461C2×M16—222no—
462C2×M16—222no—
463C2×M16—441no—
464C22×C8—111no—
465C22×C8—111no—
466C22×C8C22×D1111yescharacteristic
467C22×C8C22×D1111yescharacteristic
468#121—114no—
469#121—222no—
470C4×Q8—222no—
471C4×Q8—222no—
472C4×Q8—441no—
473C4×Q8—441no—
474C4×D4—222no—
475C4×D4—441no—
476C4×D4—444no—
477C2×C4⋊C4—22no—
478C2×C4⋊C4—21no—
479C2×C4⋊C4—41no—
480C2×C4⋊C4—111no—
481C2×C4⋊C4—221no—
482C2×C4⋊C4—221no—
483C2×C4⋊C4—221no—
484C2×C4⋊C4C22×D1111yescharacteristic
485C2×C4⋊C4C22×D1111yescharacteristic
486C2×C4⋊C4C22×D1111yescharacteristic
487C2×C4⋊C4C22×D1111yescharacteristic
488C2×C22⋊C4—21no—
489C2×C22⋊C4—111no—
490C2×C22⋊C4—111no—
491C2×C22⋊C4—221no—
492C2×C22⋊C4—221no—
493C2×C22⋊C4—221no—
494C2×C22⋊C4—221no—
495C2×C22⋊C4—221no—
496C2×C22⋊C4—221no—
497C2×C22⋊C4—221no—
498C2×C22⋊C4—221no—
499C2×C42—111no—
500C2×C42—111no—
501C2×C42—221no—
502C2×C42—221no—
503C2×C42—221no—
504#107—22no—
505#107—41no—
506#103—114no—
507#103—114no—
508#103—222no—
509#102—114no—
510#102—222no—
511#102—222no—
512#102—222no—
513#102—441no—
514C22⋊C8C4×D1114yescomplemented
515#97—222no—
516C4×C8—441no—
517#95—21no—
518#95—111no—
519#95—111no—
520#95—221no—
521#95—221no—
522C2×C11—42no—
523C2×C11#235811yescharacteristic
524C2×C11C4×AGL(1,ℤ/8)11yescharacteristic
525C2×C11#295111yescharacteristic
526C2×C11#327411yescharacteristic
527C2×C11#327711yescharacteristic
528C2×C11#330811yescharacteristic
529C2×C11#330911yescharacteristic
530D11—82no—
531D11—82no—
532C24—221no—
533C24—221no—
534C24D4×D1111yescharacteristic
535#41—228no—
536#41—444no—
537#41—444no—
538#41—444no—
539C2×Q8—112no—
540C2×Q8—112no—
541C2×Q8—112no—
542C2×Q8—221no—
543C2×Q8—221no—
544C2×Q8—221no—
545C2×D4—112no—
546C2×D4—112no—
547C2×D4—224no—
548C2×D4—224no—
549C2×D4—221no—
550C2×D4—221no—
551C2×D4—221no—
552C2×D4—221no—
553C2×D4—221no—
554C2×D4—221no—
555C2×D4—221no—
556C2×D4—221no—
557C2×D4—221no—
558C2×D4—221no—
559C2×D4—442no—
560C2×D4—442no—
561C2×D4—442no—
562C2×D4—442no—
563C22×C4—21no—
564C22×C4—21no—
565C22×C4—21no—
566C22×C4—21no—
567C22×C4—21no—
568C22×C4—21no—
569C22×C4—21no—
570C22×C4—21no—
571C22×C4—42no—
572C22×C4—42no—
573C22×C4—81no—
574C22×C4—111no—
575C22×C4—111no—
576C22×C4—111no—
577C22×C4—111no—
578C22×C4—221no—
579C22×C4—221no—
580C22×C4—224no—
581C22×C4—442no—
582C22×C4—442no—
583C22×C4—442no—
584C22×C4—442no—
585C22×C4—881no—
586C22×C4C2×C4×D1112yes—
587C22×C4D4×D1111yescharacteristic
588C22×C4#434312yes—
589C22×C4C23×D1111yescharacteristic
590SD16—228no—
591D8—444no—
592M16—444no—
593C2×C8—21no—
594C2×C8—21no—
595C2×C8—21no—
596C2×C8—21no—
597C2×C8—112no—
598C2×C8—221no—
599C2×C8—221no—
600C2×C8—221no—
601C2×C8—221no—
602C2×C8—221no—
603C2×C8C2×C4×D1112yes—
604C2×C8C2×C4×D1112yes—
605C4⋊C4—21no—
606C4⋊C4—21no—
607C4⋊C4—21no—
608C4⋊C4—21no—
609C4⋊C4—21no—
610C4⋊C4—21no—
611C4⋊C4—21no—
612C4⋊C4—42no—
613C4⋊C4—112no—
614C4⋊C4—221no—
615C4⋊C4—442no—
616C4⋊C4—442no—
617C4⋊C4—442no—
618C4⋊C4D4×D1112yes—
619C22⋊C4—81no—
620C22⋊C4—222no—
621C22⋊C4—224no—
622C22⋊C4—442no—
623C22⋊C4—442no—
624C22⋊C4—442no—
625C22⋊C4—442no—
626C22⋊C4—441no—
627C22⋊C4—881no—
628C22⋊C4—881no—
629C22⋊C4—881no—
630C42—221no—
631C42—221no—
632C42—221no—
633C42—221no—
634C42—442no—
635C42—442no—
636C42—442no—
637C11#2286311yescharacteristic, complemented, Sylow
638C23—21no—
639C23—21no—
640C23—21no—
641C23—21no—
642C23—21no—
643C23—21no—
644C23—222no—
645C23—222no—
646C23—441no—
647C23—441no—
648C23—441no—
649C23—441no—
650C23—441no—
651C23—441no—
652C23—441no—
653C23—441no—
654C23—441no—
655C23—441no—
656C23—441no—
657C23—441no—
658C23#6694612yes—
659C23C2×D4×D1111yescharacteristic
660Q8—114no—
661Q8—222no—
662Q8—222no—
663Q8—222no—
664D4—222no—
665D4—222no—
666D4—222no—
667D4—222no—
668D4—448no—
669D4—448no—
670D4—441no—
671D4—441no—
672D4—441no—
673D4—441no—
674C2×C4—21no—
675C2×C4—21no—
676C2×C4—22no—
677C2×C4—22no—
678C2×C4—22no—
679C2×C4—22no—
680C2×C4—22no—
681C2×C4—41no—
682C2×C4—41no—
683C2×C4—41no—
684C2×C4—41no—
685C2×C4—41no—
686C2×C4—41no—
687C2×C4—41no—
688C2×C4—41no—
689C2×C4—41no—
690C2×C4—41no—
691C2×C4—41no—
692C2×C4—84no—
693C2×C4—112no—
694C2×C4—222no—
695C2×C4—221no—
696C2×C4—222no—
697C2×C4—221no—
698C2×C4—222no—
699C2×C4—221no—
700C2×C4—221no—
701C2×C4—222no—
702C2×C4—221no—
703C2×C4—221no—
704C2×C4—221no—
705C2×C4—221no—
706C2×C4—221no—
707C2×C4—221no—
708C2×C4—221no—
709C2×C4—448no—
710C2×C4—441no—
711C2×C4—441no—
712C2×C4—884no—
713C2×C4#6694612yes—
714C2×C4C22×C4×D1111yescharacteristic
715C2×C4C2×D4×D1111yescharacteristic
716C2×C4#6703711yescharacteristic
717C2×C4C2×#434311yescharacteristic
718C2×C4#41×D1111yescharacteristic
719C2×C4#6704211yescharacteristic
720C8—22no—
721C8—22no—
722C8—222no—
723C8—441no—
724C22—22no—
725C22—22no—
726C22—22no—
727C22—41no—
728C22—41no—
729C22—41no—
730C22—41no—
731C22—442no—
732C22—442no—
733C22—442no—
734C22—442no—
735C22—442no—
736C22—442no—
737C22—881no—
738C22—881no—
739C22—881no—
740C22—881no—
741C22—881no—
742C22—881no—
743C22—881no—
744C22—881no—
745C22C2×#6694611yescharacteristic
746C22#1062312111yescharacteristic
747C22#1062318511yescharacteristic
748C22#1062328811yescharacteristic
749C22#1062329711yescharacteristic
750C22D11×AGL(1,ℤ/8)11yescharacteristic
751C22#1062330811yescharacteristic
752C4—22no—
753C4—42no—
754C4—81no—
755C4—81no—
756C4—81no—
757C4—222no—
758C4—224no—
759C4—441no—
760C4—441no—
761C4—442no—
762C4—441no—
763C4C4×D4×D1111yescharacteristic
764C4#1062307611yescharacteristic
765C4#1062316111yescharacteristic
766C4#1062316811yescharacteristic
767C2—42no—
768C2—882no—
769C2—882no—
770C2#1307159211yescharacteristic
771C2#1307742311yescharacteristic
772C2#1307749011yescharacteristic
773C2#1308023411yescharacteristic
774C2#1308027311yescharacteristic
775C2#1308061011yescharacteristic
776C2#1308062511yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#1852C2
socleC23×C11C22×D4
prime radicalC2×#10622347C2
cosocleC22×C4×C11C24
hypercenter#1852D11
hypocenterC11#22863
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1852

Complements

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

NH ≅ G/Ntype
2. C2×#10622502C2semidirect
3. C2×#10622579C2semidirect
4. #13071632C2semidirect
5. #13071453C2semidirect
6. #13069480C2semidirect
7. #13069311C2semidirect
8. #13069235C2semidirect
9. #13069052C2semidirect
10. #13068972C2semidirect
11. #13068965C2semidirect
12. #13068867C2semidirect
13. #13068435C2semidirect
14. #13068402C2semidirect
15. C11×#1852C2semidirect
53. #10622347C4semidirect
71. C2×#4339C2×C4semidirect
116. C2×D88C2×C4semidirect
119. C2×#4314C2×C4semidirect
128. C11×C22⋊C8C2×C4semidirect
134. #66885C2×C4semidirect
135. #66880C2×C4semidirect
139. #66874D4semidirect
262. #1852D11semidirect
346. Dic22C4×D4semidirect
514. C22⋊C8C4×D11semidirect
637. C11#22863semidirect

Maximal subgroups

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

subgroupindex
C2×#106223472
C2×#106225022
C2×#106225792
#130716322
#130714532
#130694802
#130693112
#130692352
#130690522
#130689722
#130689652
#130688672
#130684352
#130684022
C11×#18522
#2286311