Finite Group Databasebeta

← #14774176

Subgroups — #14774176

Order 2816.

1274 conjugacy classes of subgroups.

The subgroup lattice has 790 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622831C211yesmaximal, characteristic
2C2×#10622631C211yesmaximal, characteristic, complemented
3C2×#10622828C211yesmaximal, characteristic
4#13071641C211yesmaximal, characteristic, complemented
5#13069469C211yesmaximal, characteristic, complemented
6#13069316C211yesmaximal, characteristic, complemented
7#13069233C211yesmaximal, characteristic, complemented
8#13069047C211yesmaximal, characteristic, complemented
9#13068974C211yesmaximal, characteristic, complemented
10#13068950C211yesmaximal, characteristic, complemented
11#13068877C211yesmaximal, characteristic, complemented
12#13068813C211yesmaximal, characteristic, complemented
13C4×#66896C211yesmaximal, characteristic, complemented
14#13068400C211yesmaximal, characteristic, complemented
15D4×C11×C22⋊C4C211yesmaximal, characteristic
16C23×D4×C11C2211yescharacteristic
17C2×C4×D4×C11C2211yescharacteristic
18C2×C4×D4×C11C2211yescharacteristic
19C22×C11×C22⋊C4—21no—
20C22×#4324C2211yescharacteristic
21C22×#4324C2211yescharacteristic
22C2×#66979C2211yescharacteristic
23C2×#66977C2211yescharacteristic
24C22×#4318C2211yescharacteristic
25C2×C4×Dic22C2211yescharacteristic, complemented
26C11×#390C2211yescharacteristic
27C11×#390C2211yescharacteristic
28C11×#386—21no—
29C11×#386—21no—
30C11×#380C2211yescharacteristic
31C11×#379—21no—
32C4×C11×C22⋊C4C2211yescharacteristic
33#10622831C418yescomplemented
34#10622828—24no—
35C2×#66896C2211yescharacteristic
36C2×#66896C2211yescharacteristic
37C2×#66896C2211yescharacteristic
38C2×#66896C2211yescharacteristic
39C2×#66896C2211yescharacteristic
40C2×#66896C2211yescharacteristic
41C2×C22⋊(C11⋊C8)C2211yescharacteristic
42#10622631—24no—
43C2×#66874C2211yescharacteristic, complemented
44C2×#66874C2211yescharacteristic, complemented
45C2×#66872C2211yescharacteristic, complemented
46C2×#66871C2211yescharacteristic, complemented
47#10622558—21no—
48#10622557—21no—
49C4×C4⋊Dic11C2211yescharacteristic, complemented
50#10622542C2211yescharacteristic, complemented
51#10622541C2211yescharacteristic, complemented
52C2×#66867C2211yescharacteristic, complemented
53C2×C4×C11⋊C8C2211yescharacteristic, complemented
54#10622265—21no—
55#10622262—21no—
56#10622167C2211yescharacteristic, complemented
57#10622167C2211yescharacteristic, complemented
58#10622167C2211yescharacteristic, complemented
59#10622167C2211yescharacteristic, complemented
60#10622162C2211yescharacteristic, complemented
61#10622162C2211yescharacteristic, complemented
62C25×C11—21no—
63C22×D4×C11—22no—
64C22×D4×C11—22no—
65C22×D4×C11—21no—
66C22×D4×C11—22no—
67C22×D4×C11—41no—
68C22×D4×C11—41no—
69C22×D4×C11C2×C414yes—
70C22×D4×C11C2311yescharacteristic
71C22×D4×C11C2311yescharacteristic
72C23×C4×C11—21no—
73C23×C4×C11—21no—
74C23×C4×C11C2311yescharacteristic
75C22×Dic22C2311yescharacteristic
76C4×D4×C11—22no—
77C4×D4×C11—22no—
78C4×D4×C11—41no—
79C4×D4×C11—41no—
80C2×C11×C4⋊C4C2311yescharacteristic
81C2×C11×C4⋊C4C2311yescharacteristic
82C2×C11×C22⋊C4—21no—
83C2×C11×C22⋊C4—21no—
84C2×C11×C22⋊C4—21no—
85C2×C11×C22⋊C4—21no—
86C2×C11×C22⋊C4—21no—
87C2×C11×C22⋊C4—21no—
88C2×C11×C22⋊C4—21no—
89C2×C11×C22⋊C4—44no—
90C2×C11×C22⋊C4D411yescharacteristic
91C2×C11×C22⋊C4D411yescharacteristic
92C2×C42×C11C2311yescharacteristic
93C2×C42×C11C2311yescharacteristic
94C2×C22⋊Dic11—21no—
95C2×C22⋊Dic11—21no—
96C2×#4324—22no—
97C2×#4324—22no—
98C2×#4324—41no—
99C2×#4324—41no—
100C2×#4324C2×C414yes—
101C2×#4324C2×C414yescomplemented
102#66979—22no—
103#66979—41no—
104C2×C4⋊Dic11C2311yescharacteristic
105C2×C4⋊Dic11C2311yescharacteristic
106C2×C4⋊Dic11C2311yescharacteristic
107#66977—22no—
108#66977C2×C414yescomplemented
109C2×Dic11⋊C4—21no—
110C2×Dic11⋊C4—21no—
111C2×Dic11⋊C4—21no—
112C2×C4×Dic11—21no—
113C2×C4×Dic11—21no—
114C2×C4×Dic11—21no—
115C2×#4318—22no—
116C2×#4318—22no—
117C2×#4318—41no—
118C22×C11⋊C8C2311yescharacteristic
119C22×C11⋊C8C2311yescharacteristic
120C22×C11⋊C8C2311yescharacteristic
121C22×C11⋊C8C2311yescharacteristic
122C4×Dic22—22no—
123C4×Dic22—41no—
124C11×#95—21no—
125C11×#95D411yescharacteristic
126C11×#95D411yescharacteristic
127#66896—22no—
128#66896—22no—
129#66896—22no—
130#66896C2×C414yes—
131#66896C2×C414yescomplemented
132#66896D414yes—
133C11⋊#95—21no—
134C11⋊#95—21no—
135C11⋊#95—21no—
136C11⋊#95—21no—
137C22⋊(C11⋊C8)C2×C414yescomplemented
138#66874—22no—
139#66874—41no—
140#66872—41no—
141#66871—22no—
142#66867—22no—
143C4×C11⋊C8—41no—
144#22864—111nomaximal, Sylow
145C24×C11—21no—
146C24×C11—21no—
147C24×C11—24no—
148C24×C11—42no—
149C24×C11—42no—
150C24×C11—42no—
151C24×C11—42no—
152C24×C11—81no—
153C24×C11—81no—
154C24×C11C2×D411yescharacteristic
155C2×D4×C11—28no—
156C2×D4×C11—24no—
157C2×D4×C11—21no—
158C2×D4×C11—21no—
159C2×D4×C11—21no—
160C2×D4×C11—21no—
161C2×D4×C11—21no—
162C2×D4×C11—21no—
163C2×D4×C11—21no—
164C2×D4×C11—21no—
165C2×D4×C11—44no—
166C2×D4×C11—44no—
167C2×D4×C11—44no—
168C2×D4×C11—42no—
169C2×D4×C11—42no—
170C2×D4×C11C22×C412yes—
171C2×D4×C11C22×C412yes—
172C2×D4×C11C2×D412yes—
173C2×D4×C11#4112yes—
174C22×C4×C11—21no—
175C22×C4×C11—21no—
176C22×C4×C11—21no—
177C22×C4×C11—21no—
178C22×C4×C11—21no—
179C22×C4×C11—21no—
180C22×C4×C11—42no—
181C22×C4×C11—42no—
182C22×C4×C11—42no—
183C22×C4×C11—42no—
184C22×C4×C11—81no—
185C22×C4×C11—81no—
186C22×C4×C11C22×C412yes—
187C22×C4×C11C2×D411yescharacteristic
188C22×C4×C11C2×D411yescharacteristic
189C22×C4×C11C2×D411yescharacteristic
190C22×C4×C11C2×D411yescharacteristic
191C22×C4×C11C2×D411yescharacteristic
192C22×C4×C11#4112yes—
193C22×C4×C11C2411yescharacteristic
194C22×Dic11—21no—
195C22×Dic11—21no—
196C22×Dic11—21no—
197C22×Dic11—21no—
198C2×Dic22—21no—
199C2×Dic22—21no—
200C2×Dic22—21no—
201C2×Dic22—21no—
202C2×Dic22—21no—
203C2×Dic22C22×C412yes—
204C11×C4⋊C4—21no—
205C11×C4⋊C4—21no—
206C11×C4⋊C4—21no—
207C11×C4⋊C4—21no—
208C11×C22⋊C4—22no—
209C11×C22⋊C4—41no—
210C11×C22⋊C4—42no—
211C11×C22⋊C4—42no—
212C11×C22⋊C4—42no—
213C11×C22⋊C4—42no—
214C11×C22⋊C4—42no—
215C11×C22⋊C4—81no—
216C11×C22⋊C4—81no—
217C42×C11—21no—
218C42×C11—21no—
219C42×C11—21no—
220C42×C11—21no—
221C22⋊Dic11—24no—
222C22⋊Dic11—42no—
223#4324—28no—
224#4324—44no—
225C4⋊Dic11—21no—
226C4⋊Dic11—21no—
227C4⋊Dic11—21no—
228C4⋊Dic11—21no—
229C4⋊Dic11C22×C412yes—
230C4⋊Dic11C2×D412yes—
231Dic11⋊C4—24no—
232Dic11⋊C4—42no—
233Dic11⋊C4—42no—
234C4×Dic11—42no—
235C4×Dic11—42no—
236C4×Dic11—42no—
237#4318—44no—
238C2×C11⋊C8—21no—
239C2×C11⋊C8—21no—
240C2×C11⋊C8—21no—
241C2×C11⋊C8—21no—
242C2×C11⋊C8—21no—
243C2×C11⋊C8—21no—
244C2×C11⋊C8—21no—
245C2×C11⋊C8—21no—
246C2×C11⋊C8—21no—
247C2×C11⋊C8C22×C412yes—
248C2×C11⋊C8C22×C412yes—
249C2×C11⋊C8C2×D412yes—
250C2×#450—111no—
251C2×#440—111no—
252C2×#418—111no—
253#2362—111no—
254D4×C22⋊C4D1111yescharacteristic
255#1968—111no—
256#1936—111no—
257#1925—111no—
258#1894—111no—
259#1880—111no—
260#1877—111no—
261#1864—111no—
262#1854—111no—
263C4×#102—111no—
264#1753—111no—
265C23×C11—22no—
266C23×C11—21no—
267C23×C11—22no—
268C23×C11—22no—
269C23×C11—21no—
270C23×C11—21no—
271C23×C11—21no—
272C23×C11—21no—
273C23×C11—21no—
274C23×C11—22no—
275C23×C11—48no—
276C23×C11—48no—
277C23×C11—41no—
278C23×C11—41no—
279C23×C11—41no—
280C23×C11—41no—
281C23×C11—41no—
282C23×C11—41no—
283C23×C11—41no—
284C23×C11—41no—
285C23×C11—41no—
286C23×C11—41no—
287C23×C11—84no—
288C23×C11—84no—
289C23×C11—84no—
290C23×C11—84no—
291C23×C11—84no—
292C23×C11C4×D412yes—
293C23×C11C22×D411yescharacteristic
294D4×C11—22no—
295D4×C11—22no—
296D4×C11—22no—
297D4×C11—22no—
298D4×C11—22no—
299D4×C11—48no—
300D4×C11—41no—
301D4×C11—41no—
302D4×C11C4×D414yes—
303C2×C4×C11—21no—
304C2×C4×C11—21no—
305C2×C4×C11—21no—
306C2×C4×C11—21no—
307C2×C4×C11—22no—
308C2×C4×C11—22no—
309C2×C4×C11—22no—
310C2×C4×C11—22no—
311C2×C4×C11—21no—
312C2×C4×C11—21no—
313C2×C4×C11—21no—
314C2×C4×C11—21no—
315C2×C4×C11—21no—
316C2×C4×C11—21no—
317C2×C4×C11—21no—
318C2×C4×C11—21no—
319C2×C4×C11—21no—
320C2×C4×C11—41no—
321C2×C4×C11—41no—
322C2×C4×C11—41no—
323C2×C4×C11—41no—
324C2×C4×C11—41no—
325C2×C4×C11—41no—
326C2×C4×C11—84no—
327C2×C4×C11—84no—
328C2×C4×C11C4×D412yes—
329C2×C4×C11AGL(1,ℤ/8)12yes—
330C2×C4×C11C23×C411yescharacteristic
331C2×C4×C11C22×D411yescharacteristic
332C2×C4×C11C2×#4111yescharacteristic
333C2×C4×C11C2×#4111yescharacteristic
334C2×C4×C11H(5,𝔽2)11yescharacteristic
335C2×C4×C11H(5,𝔽2)11yescharacteristic
336C2×Dic11—22no—
337C2×Dic11—22no—
338C2×Dic11—22no—
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—41no—
348Dic22—22no—
349Dic22—22no—
350Dic22—41no—
351Dic22—41no—
352C11⋊C8—22no—
353C11⋊C8—22no—
354C11⋊C8—22no—
355C11⋊C8—41no—
356C23×D4C2×D1111yescharacteristic
357C22×SD16—111no—
358C22×SD16—111no—
359C22×M16—111no—
360C2×C22⋊Q8—111no—
361C2×C4×Q8—111no—
362C2×C4×D4C2×D1111yescharacteristic
363C2×C4×D4C2×D1111yescharacteristic
364C2×#117—111no—
365C22×C22⋊C4—21no—
366#450—118no—
367#440—224no—
368C2×#107—111no—
369C2×#106—111no—
370#418—224no—
371C2×#103—111no—
372C2×#103—111no—
373C2×#102—111no—
374C2×#102—111no—
375C2×#102—111no—
376C2×#102—111no—
377C2×#102—111no—
378C2×#102—111no—
379C2×C22⋊C8—111no—
380C2×#97—111no—
381C2×C4×C8—111no—
382#391—111no—
383#390C2×D1111yescharacteristic
384#390C2×D1111yescharacteristic
385#389—111no—
386#388—221no—
387#388—221no—
388#387—221no—
389#386—21no—
390#386—21no—
391#380C2×D1111yescharacteristic
392#379—21no—
393C4×C4⋊C4—111no—
394C4×C4⋊C4—221no—
395C4×C22⋊C4C2×D1111yescharacteristic
396#340—111no—
397#340—111no—
398#340—111no—
399#340—111no—
400#336—111no—
401#336—111no—
402C22×C11—22no—
403C22×C11—24no—
404C22×C11—22no—
405C22×C11—22no—
406C22×C11—42no—
407C22×C11—42no—
408C22×C11—42no—
409C22×C11—41no—
410C22×C11—41no—
411C22×C11—42no—
412C22×C11—42no—
413C22×C11—41no—
414C22×C11—41no—
415C22×C11—42no—
416C22×C11—42no—
417C22×C11—42no—
418C22×C11—42no—
419C22×C11—816no—
420C22×C11—81no—
421C22×C11—81no—
422C22×C11—81no—
423C22×C11—81no—
424C22×C11C2×C4×D411yescharacteristic
425C22×C11D4211yescharacteristic
426C22×C11#54611yescharacteristic
427C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
428C22×C11#57511yescharacteristic
429C22×C11#57711yescharacteristic
430C22×C11#57711yescharacteristic
431C4×C11—22no—
432C4×C11—22no—
433C4×C11—41no—
434C4×C11—41no—
435C4×C11—41no—
436C4×C11—81no—
437C4×C11—81no—
438C4×C11C2×C4×D411yescharacteristic
439C4×C11#51811yescharacteristic
440C4×C11#54611yescharacteristic
441C4×C11#55111yescharacteristic
442Dic11—42no—
443Dic11—42no—
444Dic11—42no—
445Dic11—81no—
446C25—21no—
447C22×Q8—111no—
448C22×D4—22no—
449C22×D4—22no—
450C22×D4—22no—
451C22×D4—21no—
452C22×D4—41no—
453C22×D4—41no—
454C22×D4C4×D1114yes—
455C22×D4C22×D1111yescharacteristic
456C22×D4C22×D1111yescharacteristic
457C23×C4—21no—
458C23×C4—21no—
459C23×C4C22×D1111yescharacteristic
460C2×SD16—114no—
461C2×SD16—114no—
462C2×SD16—222no—
463C2×SD16—222no—
464C2×SD16—441no—
465C2×SD16—441no—
466C2×M16—222no—
467C2×M16—222no—
468C2×M16—441no—
469C22×C8—111no—
470C22×C8—111no—
471C22×C8—111no—
472C22×C8—111no—
473C22⋊Q8—114no—
474C22⋊Q8—222no—
475C4×Q8—222no—
476C4×Q8—441no—
477C4×D4—22no—
478C4×D4—22no—
479C4×D4—41no—
480C4×D4—41no—
481#117—222no—
482#117—441no—
483C2×C4⋊C4—111no—
484C2×C4⋊C4—111no—
485C2×C4⋊C4—111no—
486C2×C4⋊C4—221no—
487C2×C4⋊C4—221no—
488C2×C4⋊C4—221no—
489C2×C4⋊C4C22×D1111yescharacteristic
490C2×C4⋊C4C22×D1111yescharacteristic
491C2×C22⋊C4—21no—
492C2×C22⋊C4—21no—
493C2×C22⋊C4—21no—
494C2×C22⋊C4—21no—
495C2×C22⋊C4—21no—
496C2×C22⋊C4—21no—
497C2×C22⋊C4—21no—
498C2×C22⋊C4—44no—
499C2×C22⋊C4—221no—
500C2×C22⋊C4—221no—
501C2×C22⋊C4C22⋊D1111yescharacteristic
502C2×C22⋊C4C22⋊D1111yescharacteristic
503C2×C42—221no—
504C2×C42—221no—
505C2×C42—221no—
506C2×C42C22×D1111yescharacteristic
507C2×C42C22×D1111yescharacteristic
508#107—222no—
509#106—441no—
510#103—222no—
511#103—441no—
512#102—114no—
513#102—114no—
514#102—114no—
515#102—222no—
516#102—222no—
517#102—222no—
518C22⋊C8—114no—
519#97—222no—
520C4×C8—441no—
521#95—21no—
522#95—221no—
523#95—221no—
524#95—221no—
525#95—221no—
526#95C22⋊D1111yescharacteristic
527#95C22⋊D1111yescharacteristic
528C2×C11—42no—
529C2×C11—44no—
530C2×C11—82no—
531C2×C11#235811yescharacteristic
532C2×C11C4×AGL(1,ℤ/8)11yescharacteristic
533C2×C11#294911yescharacteristic
534C2×C11#327211yescharacteristic
535C2×C11#327511yescharacteristic
536C2×C11#331011yescharacteristic
537C2×C11#331111yescharacteristic
538C24—21no—
539C24—21no—
540C24—24no—
541C24—42no—
542C24—42no—
543C24—42no—
544C24—42no—
545C24—81no—
546C24—81no—
547C24C2×C22⋊D1111yescharacteristic
548C2×Q8—112no—
549C2×Q8—221no—
550C2×Q8—221no—
551C2×Q8—221no—
552C2×Q8—221no—
553C2×Q8—221no—
554C2×D4—28no—
555C2×D4—24no—
556C2×D4—21no—
557C2×D4—21no—
558C2×D4—21no—
559C2×D4—21no—
560C2×D4—21no—
561C2×D4—21no—
562C2×D4—21no—
563C2×D4—21no—
564C2×D4—44no—
565C2×D4—44no—
566C2×D4—44no—
567C2×D4—42no—
568C2×D4—42no—
569C2×D4C2×C4×D1112yes—
570C2×D4C2×C4×D1112yes—
571C2×D4D4×D1112yes—
572C2×D4#434112yes—
573C22×C4—21no—
574C22×C4—21no—
575C22×C4—21no—
576C22×C4—21no—
577C22×C4—21no—
578C22×C4—21no—
579C22×C4—42no—
580C22×C4—42no—
581C22×C4—42no—
582C22×C4—42no—
583C22×C4—81no—
584C22×C4—81no—
585C22×C4—221no—
586C22×C4—221no—
587C22×C4—221no—
588C22×C4—221no—
589C22×C4C2×C4×D1112yes—
590C22×C4#433912yes—
591C22×C4C2×C22⋊D1111yescharacteristic
592C22×C4C2×C22⋊D1111yescharacteristic
593C22×C4C2×C22⋊D1111yescharacteristic
594C22×C4C2×C22⋊D1111yescharacteristic
595C22×C4C2×C22⋊D1111yescharacteristic
596C22×C4C23×D1111yescharacteristic
597SD16—228no—
598SD16—444no—
599M16—444no—
600C2×C8—112no—
601C2×C8—112no—
602C2×C8—112no—
603C2×C8—221no—
604C2×C8—221no—
605C2×C8—221no—
606C2×C8—221no—
607C2×C8—221no—
608C2×C8—221no—
609C2×C8—221no—
610C2×C8—221no—
611C2×C8—221no—
612C4⋊C4—21no—
613C4⋊C4—21no—
614C4⋊C4—21no—
615C4⋊C4—21no—
616C4⋊C4—112no—
617C4⋊C4—112no—
618C4⋊C4—224no—
619C4⋊C4—221no—
620C4⋊C4—221no—
621C4⋊C4—221no—
622C4⋊C4—221no—
623C4⋊C4—442no—
624C4⋊C4—442no—
625C22⋊C4—22no—
626C22⋊C4—41no—
627C22⋊C4—42no—
628C22⋊C4—42no—
629C22⋊C4—42no—
630C22⋊C4—42no—
631C22⋊C4—42no—
632C22⋊C4—81no—
633C22⋊C4—81no—
634C22⋊C4—224no—
635C22⋊C4—442no—
636C42—21no—
637C42—21no—
638C42—21no—
639C42—21no—
640C42—442no—
641C42—442no—
642C42—442no—
643C11#2286411yescharacteristic, complemented, Sylow
644C23—22no—
645C23—21no—
646C23—22no—
647C23—21no—
648C23—22no—
649C23—21no—
650C23—21no—
651C23—21no—
652C23—21no—
653C23—22no—
654C23—48no—
655C23—48no—
656C23—41no—
657C23—41no—
658C23—41no—
659C23—41no—
660C23—41no—
661C23—41no—
662C23—41no—
663C23—41no—
664C23—41no—
665C23—41no—
666C23—84no—
667C23—84no—
668C23—84no—
669C23—84no—
670C23—84no—
671C23C4×C22⋊D1112yes—
672C23C22×C22⋊D1111yescharacteristic
673Q8—222no—
674Q8—222no—
675Q8—441no—
676Q8—441no—
677D4—22no—
678D4—22no—
679D4—22no—
680D4—22no—
681D4—22no—
682D4—48no—
683D4—41no—
684D4—41no—
685D4(C22⋊D11)⋊C414yes—
686C2×C4—21no—
687C2×C4—21no—
688C2×C4—21no—
689C2×C4—21no—
690C2×C4—22no—
691C2×C4—22no—
692C2×C4—22no—
693C2×C4—22no—
694C2×C4—21no—
695C2×C4—21no—
696C2×C4—21no—
697C2×C4—21no—
698C2×C4—21no—
699C2×C4—21no—
700C2×C4—21no—
701C2×C4—21no—
702C2×C4—21no—
703C2×C4—41no—
704C2×C4—41no—
705C2×C4—41no—
706C2×C4—41no—
707C2×C4—41no—
708C2×C4—41no—
709C2×C4—84no—
710C2×C4—84no—
711C2×C4—222no—
712C2×C4—222no—
713C2×C4—222no—
714C2×C4—441no—
715C2×C4—441no—
716C2×C4—441no—
717C2×C4—441no—
718C2×C4—441no—
719C2×C4—441no—
720C2×C4—441no—
721C2×C4—441no—
722C2×C4—441no—
723C2×C4C4×C22⋊D1112yes—
724C2×C4#6698512yes—
725C2×C4C22×C4×D1111yescharacteristic
726C2×C4C2×#433911yescharacteristic
727C2×C4C2×D4×D1111yescharacteristic
728C2×C4C2×#434111yescharacteristic
729C2×C4#6703711yescharacteristic
730C2×C4#6703711yescharacteristic
731C8—222no—
732C8—222no—
733C8—222no—
734C8—441no—
735C22—22no—
736C22—22no—
737C22—22no—
738C22—24no—
739C22—42no—
740C22—41no—
741C22—41no—
742C22—42no—
743C22—42no—
744C22—41no—
745C22—42no—
746C22—41no—
747C22—42no—
748C22—42no—
749C22—42no—
750C22—42no—
751C22—42no—
752C22—816no—
753C22—81no—
754C22—81no—
755C22—81no—
756C22—81no—
757C22C2×C4×C22⋊D1111yescharacteristic
758C22C2×#6698511yescharacteristic
759C22D4×C22⋊D1111yescharacteristic
760C22#1062333711yescharacteristic
761C22#1062335311yescharacteristic
762C22#1062336711yescharacteristic
763C22#1062336711yescharacteristic
764C4—22no—
765C4—22no—
766C4—41no—
767C4—41no—
768C4—41no—
769C4—81no—
770C4—81no—
771C4—442no—
772C4—442no—
773C4—442no—
774C4—881no—
775C4C2×(C22⋊D11)⋊C411yescharacteristic
776C4#1062301711yescharacteristic
777C4#1062302111yescharacteristic
778C4#1062302611yescharacteristic
779C2—42no—
780C2—44no—
781C2—82no—
782C2#1307159511yescharacteristic
783C2C4×#6698511yescharacteristic
784C2#1307747311yescharacteristic
785C2#1308021211yescharacteristic
786C2#1308024311yescharacteristic
787C2#1308063711yescharacteristic
788C2#1308065211yescharacteristic
subgroupG/H
centerC23C22×C22⋊D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingD4×C11×C22⋊C4C2
socleC23×C11C22×D4
prime radicalC23×D4×C11C22
cosocleC22×C4×C11C24
hypercenterD4×C22⋊C4D11
hypocenterC11#22864
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C4×C22⋊C4 ◁ D4×C22⋊C4

Complements

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

NH ≅ G/Ntype
2. C2×#10622631C2semidirect
4. #13071641C2semidirect
5. #13069469C2semidirect
6. #13069316C2semidirect
7. #13069233C2semidirect
8. #13069047C2semidirect
9. #13068974C2semidirect
10. #13068950C2semidirect
11. #13068877C2semidirect
12. #13068813C2semidirect
13. C4×#66896C2semidirect
14. #13068400C2semidirect
25. C2×C4×Dic22C22semidirect
33. #10622831C4semidirect
43. C2×#66874C22semidirect
44. C2×#66874C22semidirect
45. C2×#66872C22semidirect
46. C2×#66871C22semidirect
49. C4×C4⋊Dic11C22semidirect
50. #10622542C22semidirect
51. #10622541C22semidirect
52. C2×#66867C22semidirect
53. C2×C4×C11⋊C8C22semidirect
56. #10622167C22semidirect
57. #10622167C22semidirect
58. #10622167C22semidirect
59. #10622167C22semidirect
60. #10622162C22semidirect
61. #10622162C22semidirect
101. C2×#4324C2×C4semidirect
108. #66977C2×C4semidirect
131. #66896C2×C4semidirect
137. C22⋊(C11⋊C8)C2×C4semidirect
643. C11#22864semidirect

Maximal subgroups

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

subgroupindex
C2×#106228312
C2×#106226312
C2×#106228282
#130716412
#130694692
#130693162
#130692332
#130690472
#130689742
#130689502
#130688772
#130688132
C4×#668962
#130684002
D4×C11×C22⋊C42
#2286411