Finite Group Databasebeta

← #14810949

Subgroups — #14810949

Order 2816.

1206 conjugacy classes of subgroups.

The subgroup lattice has 772 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622483C211yesmaximal, characteristic, complemented
2C22×#66873C211yesmaximal, characteristic
3#13072312C211yesmaximal, characteristic, complemented
4#13071436C211yesmaximal, characteristic
5#13070146C211yesmaximal, characteristic, complemented
6#13069991C211yesmaximal, characteristic, complemented
7#13069985C211yesmaximal, characteristic, complemented
8#13069751C211yesmaximal, characteristic, complemented
9#13068878C211yesmaximal, characteristic, complemented
10#13068874C211yesmaximal, characteristic, complemented
11#13068793C211yesmaximal, characteristic, complemented
12#13068639C211yesmaximal, characteristic, complemented
13#13068615C211yesmaximal, characteristic, complemented
14#13068548C211yesmaximal, characteristic
15C11×#1853C211yesmaximal, characteristic, complemented
16C23×D44C2211yescharacteristic
17C22×C11×C4⋊C4C2211yescharacteristic
18C2×#66977—21no—
19C23×C11⋊C8C2211yescharacteristic
20C2×#66946C2211yescharacteristic
21C2×#66946C2211yescharacteristic
22C2×#66941C2211yescharacteristic, complemented
23C2×C22⋊C4×D11—21no—
24C2×C11×#106C2211yescharacteristic, complemented
25C2×C11×#106C2211yescharacteristic, complemented
26C2×C11×C22⋊C8C2211yescharacteristic
27C11×#380C2211yescharacteristic
28#10622825C2211yescharacteristic
29#10622823—21no—
30C4×C22⋊Dic11C2211yescharacteristic
31C2×#66885C2211yescharacteristic
32C2×#66885C2211yescharacteristic
33C2×#66885C2211yescharacteristic
34C2×#66885C2211yescharacteristic
35C2×Dic11⋊C8C2211yescharacteristic, complemented
36C2×Dic11⋊C8C2211yescharacteristic, complemented
37#10622601C2211yescharacteristic
38#10622601C2211yescharacteristic
39#10622598C2211yescharacteristic, complemented
40#10622597—21no—
41#10622592—21no—
42#10622589C2211yescharacteristic, complemented
43#10622586C2211yescharacteristic, complemented
44C2×#66873—24no—
45C2×#66873C2211yescharacteristic
46C2×#66873C2211yescharacteristic
47C2×#66873C2211yescharacteristic
48C2×#66873C2211yescharacteristic
49C2×#66872C2211yescharacteristic, complemented
50C2×#66872C2211yescharacteristic, complemented
51#10622568—21no—
52#10622483—24no—
53#10622278—21no—
54#10622278—21no—
55C11×#340C2211yescharacteristic, complemented
56C11×#340C2211yescharacteristic, complemented
57#10622188C2211yescharacteristic, complemented
58#10622188C2211yescharacteristic, complemented
59#10622167C2211yescharacteristic, complemented
60#10622167C2211yescharacteristic, complemented
61C24×D11—21no—
62C23×C4×C11—21no—
63C23×C4×C11C2311yescharacteristic
64C22×D44—22no—
65C22×D44—22no—
66C22×D44—21no—
67C22×D44—22no—
68C22×D44—41no—
69C22×D44—41no—
70C22×D44Q814yescomplemented
71C22×D44C2311yescharacteristic
72C22×D44C2311yescharacteristic
73C22×C4×D11—21no—
74C22×C4×D11—21no—
75C22×Dic22—21no—
76C22×C8×C11C2311yescharacteristic
77C22×C8×C11C2311yescharacteristic
78C2×C11×C4⋊C4—22no—
79C2×C11×C4⋊C4—21no—
80C2×C11×C4⋊C4—41no—
81C2×C11×C4⋊C4C2311yescharacteristic
82C2×C11×C4⋊C4C2311yescharacteristic
83C2×C11×C4⋊C4C2311yescharacteristic
84C2×C11×C4⋊C4C2311yescharacteristic
85C2×C11×C22⋊C4—21no—
86C2×C22⋊Dic11—21no—
87C2×C22⋊Dic11D411yescharacteristic
88C2×C22⋊Dic11D411yescharacteristic
89C2×(C2×D11)⋊C4—21no—
90C2×(C2×D11)⋊C4—21no—
91C2×(C2×D11)⋊C4—21no—
92C2×(C2×D11)⋊C4—21no—
93C2×(C2×D11)⋊C4—21no—
94C2×(C2×D11)⋊C4—21no—
95C2×C4⋊Dic11—21no—
96C2×C4⋊Dic11C2311yescharacteristic
97C2×C4⋊Dic11C2311yescharacteristic
98#66977—44no—
99C2×Dic11⋊C4—21no—
100C2×Dic11⋊C4—21no—
101C2×Dic11⋊C4—21no—
102C2×Dic11⋊C4—21no—
103C2×C4×Dic11C2311yescharacteristic
104C2×C4×Dic11C2311yescharacteristic
105C22×C11⋊C8—22no—
106C22×C11⋊C8—22no—
107C22×C11⋊C8—41no—
108C22×C11⋊C8C2311yescharacteristic
109C22×C11⋊C8C2311yescharacteristic
110#66946—22no—
111#66946—22no—
112#66946—41no—
113#66946—41no—
114#66941—22no—
115#66941—41no—
116C22⋊C4×D11—44no—
117C11×#106—22no—
118C11×#106—41no—
119C11×C22⋊C8—22no—
120C11×#95—21no—
121C11⋊#95—21no—
122C11⋊#95—21no—
123C11⋊#95—21no—
124C11⋊#95D411yescharacteristic
125C11⋊#95D411yescharacteristic
126#66885—22no—
127#66885—22no—
128#66885—41no—
129#66885—41no—
130Dic11⋊C8—22no—
131Dic11⋊C8—41no—
132#66873—22no—
133#66873—22no—
134#66873—22no—
135#66873D414yes—
136#66872—22no—
137#66872—41no—
138#25958—111nomaximal, Sylow
139C24×C11C2×D411yescharacteristic
140C23×D11—21no—
141C23×D11—21no—
142C23×D11—24no—
143C23×D11—42no—
144C23×D11—42no—
145C23×D11—42no—
146C23×D11—42no—
147C23×D11—81no—
148C23×D11—81no—
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—21no—
157C22×C4×C11—42no—
158C22×C4×C11—42no—
159C22×C4×C11—81no—
160C22×C4×C11C2×D411yescharacteristic
161C22×C4×C11C2×Q812yes—
162C22×C4×C11#4112yes—
163C22×C4×C11C2411yescharacteristic
164C22×Dic11—21no—
165C22×Dic11—21no—
166C22×Dic11C2×D411yescharacteristic
167C22×Dic11C2×D411yescharacteristic
168C22×Dic11C2×D411yescharacteristic
169C22×Dic11C2×D411yescharacteristic
170C2×D44—28no—
171C2×D44—24no—
172C2×D44—21no—
173C2×D44—21no—
174C2×D44—21no—
175C2×D44—21no—
176C2×D44—21no—
177C2×D44—21no—
178C2×D44—21no—
179C2×D44—21no—
180C2×D44—42no—
181C2×D44—42no—
182C2×D44—44no—
183C2×D44—44no—
184C2×D44—44no—
185C2×D44C2×D412yes—
186C2×D44C2×Q812yes—
187C2×D44C2×Q812yes—
188C2×D44#4112yes—
189C2×C4×D11—42no—
190C2×C4×D11—42no—
191C2×C4×D11—42no—
192C2×C4×D11—42no—
193C2×C4×D11—81no—
194C2×C4×D11—81no—
195C2×Dic22—42no—
196C2×Dic22—42no—
197C2×Dic22—81no—
198C2×C8×C11—21no—
199C2×C8×C11—21no—
200C2×C8×C11—21no—
201C2×C8×C11—21no—
202C2×C8×C11—21no—
203C2×C8×C11—21no—
204C11×C4⋊C4—21no—
205C11×C4⋊C4—21no—
206C11×C4⋊C4—21no—
207C11×C4⋊C4—21no—
208C11×C4⋊C4—21no—
209C11×C4⋊C4—21no—
210C11×C4⋊C4—21no—
211C11×C4⋊C4—42no—
212C11×C4⋊C4C2×D412yes—
213C11×C22⋊C4—42no—
214C22⋊Dic11—22no—
215C22⋊Dic11—42no—
216C22⋊Dic11SD1614yes—
217(C2×D11)⋊C4—42no—
218(C2×D11)⋊C4—42no—
219(C2×D11)⋊C4—42no—
220(C2×D11)⋊C4—42no—
221(C2×D11)⋊C4—81no—
222(C2×D11)⋊C4—81no—
223C4⋊Dic11—21no—
224C4⋊Dic11—21no—
225C4⋊Dic11—21no—
226C4⋊Dic11—21no—
227C4⋊Dic11—42no—
228Dic11⋊C4—42no—
229Dic11⋊C4—42no—
230Dic11⋊C4—42no—
231Dic11⋊C4—81no—
232C4×Dic11—21no—
233C4×Dic11—21no—
234C4×Dic11—21no—
235C4×Dic11—21no—
236C2×C11⋊C8—21no—
237C2×C11⋊C8—21no—
238C2×C11⋊C8—21no—
239C2×C11⋊C8—21no—
240C2×C11⋊C8—21no—
241C2×C11⋊C8—44no—
242C2×C11⋊C8C2×D412yes—
243C2×#476—111no—
244C22×#102—111no—
245#2440—111no—
246D4×C22⋊C4—111no—
247#2094—111no—
248#2065—111no—
249#2065—111no—
250#2023—111no—
251#1864—111no—
252#1864—111no—
253#1853D1111yescharacteristic, complemented
254#1850—111no—
255#1807—111no—
256#1802—111no—
257#1786—111no—
258C23×C11—21no—
259C23×C11—21no—
260C23×C11—21no—
261C23×C11—21no—
262C23×C11C22⋊Q812yes—
263C23×C11C2×SD1612yes—
264C23×C11AGL(1,ℤ/8)12yes—
265C23×C11C22×D411yescharacteristic
266C22×D11—22no—
267C22×D11—22no—
268C22×D11—22no—
269C22×D11—22no—
270C22×D11—48no—
271C22×D11—41no—
272C22×D11—41no—
273C22×D11—41no—
274C22×D11—41no—
275C22×D11—41no—
276C22×D11—41no—
277C22×D11—41no—
278C22×D11—41no—
279C22×D11—41no—
280C22×D11—41no—
281C22×D11—48no—
282C22×D11—84no—
283C22×D11—84no—
284C22×D11—84no—
285C22×D11—84no—
286C22×D11—84no—
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×C11C22⋊Q812yes—
307C2×C4×C11C22×D411yescharacteristic
308C2×C4×C11C22×Q811yescharacteristic
309C2×C4×C11C2×#4111yescharacteristic
310C2×C4×C11C2×#4111yescharacteristic
311C2×C4×C11H(5,𝔽2)11yescharacteristic
312C2×C4×C11H(5,𝔽2)11yescharacteristic
313C2×Dic11—21no—
314C2×Dic11—21no—
315C2×Dic11—21no—
316C2×Dic11—21no—
317C2×Dic11—21no—
318C2×Dic11—21no—
319C2×Dic11—21no—
320C2×Dic11—21no—
321C2×Dic11—21no—
322C2×Dic11—21no—
323C2×Dic11—41no—
324C2×Dic11—41no—
325C2×Dic11—41no—
326C2×Dic11—41no—
327C2×Dic11—41no—
328C2×Dic11—41no—
329C2×Dic11C2×SD1612yes—
330C2×Dic11C2×SD1612yes—
331D44—22no—
332D44—22no—
333D44—22no—
334D44—22no—
335D44—22no—
336D44—48no—
337D44—41no—
338D44—41no—
339D44C22⋊Q814yescomplemented
340C4×D11—84no—
341C4×D11—84no—
342Dic22—84no—
343C8×C11—41no—
344C8×C11—41no—
345C11⋊C8—22no—
346C11⋊C8—41no—
347C23×D4—111no—
348C23×C8—111no—
349C2×C4⋊Q8—111no—
350C2×C22⋊Q8—221no—
351C2×C4×D4—111no—
352C2×C4×D4—111no—
353C22×C4⋊C4C2×D1111yescharacteristic
354C22×C22⋊C4—221no—
355#476—224no—
356C2×#106—111no—
357C2×#106—111no—
358C2×#106C2×D1111yescharacteristic, complemented
359C2×#106C2×D1111yescharacteristic, complemented
360C2×C4⋊C8—111no—
361C2×C4⋊C8—111no—
362C2×#102—111no—
363C2×#102—111no—
364C2×#102—111no—
365C2×#102—111no—
366C2×#102—111no—
367C2×#102—111no—
368C2×#102—111no—
369C2×#102—111no—
370C2×#102—224no—
371C2×C22⋊C8C2×D1111yescharacteristic
372#398—221no—
373#395—221no—
374#390—111no—
375#390—111no—
376#389—111no—
377#389—111no—
378#386—221no—
379#386—221no—
380#385—221no—
381#384—111no—
382#380—111no—
383#380C2×D1111yescharacteristic
384#379—221no—
385C4×C22⋊C4—111no—
386#340—111no—
387#340—111no—
388#340C2×D1111yescharacteristic, complemented
389#340C2×D1111yescharacteristic, complemented
390#336—111no—
391#336—111no—
392C22×C11—22no—
393C22×C11—22no—
394C22×C11—22no—
395C22×C11—22no—
396C22×C11—22no—
397C22×C11—22no—
398C22×C11#47614yescomplemented
399C22×C11C2×C22⋊Q811yescharacteristic
400C22×C11D4211yescharacteristic
401C22×C11#54611yescharacteristic
402C22×C11C22×SD1611yescharacteristic
403C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
404C22×C11#57611yescharacteristic
405C22×C11#57711yescharacteristic
406C2×D11—24no—
407C2×D11—42no—
408C2×D11—42no—
409C2×D11—42no—
410C2×D11—42no—
411C2×D11—42no—
412C2×D11—42no—
413C2×D11—42no—
414C2×D11—42no—
415C2×D11—42no—
416C2×D11—816no—
417C2×D11—81no—
418C2×D11—81no—
419C2×D11—81no—
420C2×D11—81no—
421C4×C11—22no—
422C4×C11—42no—
423C4×C11—81no—
424C4×C11—81no—
425C4×C11—81no—
426C4×C11C2×C22⋊Q811yescharacteristic
427C4×C11#54311yescharacteristic
428C4×C11#54611yescharacteristic
429C4×C11#55111yescharacteristic
430Dic11—22no—
431Dic11—22no—
432Dic11—41no—
433Dic11—41no—
434Dic11—81no—
435Dic11—81no—
436C25—221no—
437C22×Q8—221no—
438C22×D4—114no—
439C22×D4—111no—
440C22×D4—111no—
441C22×D4—222no—
442C22×D4—222no—
443C22×D4—222no—
444C22×D4—221no—
445C22×D4—441no—
446C22×D4—441no—
447C23×C4—21no—
448C23×C4—221no—
449C23×C4—221no—
450C23×C4C22×D1111yescharacteristic
451C22×C8—111no—
452C22×C8—111no—
453C22×C8—222no—
454C22×C8—222no—
455C22×C8—441no—
456C22×C8C22×D1111yescharacteristic
457C22×C8C22×D1111yescharacteristic
458C4⋊Q8—222no—
459C4⋊Q8—441no—
460C22⋊Q8—444no—
461C4×D4—222no—
462C4×D4—222no—
463C4×D4—441no—
464C4×D4—441no—
465C2×C4⋊C4—22no—
466C2×C4⋊C4—21no—
467C2×C4⋊C4—41no—
468C2×C4⋊C4—111no—
469C2×C4⋊C4—111no—
470C2×C4⋊C4—221no—
471C2×C4⋊C4—221no—
472C2×C4⋊C4—221no—
473C2×C4⋊C4—221no—
474C2×C4⋊C4—221no—
475C2×C4⋊C4C22×D1111yescharacteristic
476C2×C4⋊C4C22×D1111yescharacteristic
477C2×C4⋊C4C22×D1111yescharacteristic
478C2×C4⋊C4C22×D1111yescharacteristic
479C2×C22⋊C4—21no—
480C2×C22⋊C4—111no—
481C2×C22⋊C4—111no—
482C2×C22⋊C4—221no—
483C2×C22⋊C4—221no—
484C2×C22⋊C4—221no—
485C2×C22⋊C4—221no—
486C2×C22⋊C4—221no—
487C2×C22⋊C4—221no—
488C2×C22⋊C4—221no—
489C2×C22⋊C4—444no—
490C2×C42—111no—
491C2×C42—111no—
492#106—22no—
493#106—41no—
494#106—222no—
495#106—441no—
496C4⋊C8—222no—
497C4⋊C8—441no—
498#102—114no—
499#102—222no—
500#102—222no—
501#102—222no—
502#102—222no—
503#102—222no—
504#102—441no—
505#102—441no—
506C22⋊C8—22no—
507#95—21no—
508#95—111no—
509#95—111no—
510#95—221no—
511#95—221no—
512#95—221no—
513C2×C11—24no—
514C2×C11#243711yescharacteristic
515C2×C11C2×#47611yescharacteristic
516C2×C11#308111yescharacteristic
517C2×C11#326411yescharacteristic
518C2×C11D4×SD1611yescharacteristic
519C2×C11#329511yescharacteristic
520C2×C11#330611yescharacteristic
521D11—44no—
522D11—82no—
523C24—221no—
524C24—221no—
525C24—224no—
526C24—442no—
527C24—442no—
528C24—442no—
529C24—442no—
530C24—881no—
531C24—881no—
532C24D4×D1111yescharacteristic
533C2×Q8—442no—
534C2×Q8—442no—
535C2×Q8—881no—
536C2×D4—112no—
537C2×D4—112no—
538C2×D4—112no—
539C2×D4—112no—
540C2×D4—228no—
541C2×D4—224no—
542C2×D4—221no—
543C2×D4—221no—
544C2×D4—221no—
545C2×D4—221no—
546C2×D4—221no—
547C2×D4—221no—
548C2×D4—221no—
549C2×D4—221no—
550C2×D4—444no—
551C2×D4—444no—
552C2×D4—444no—
553C2×D4—442no—
554C2×D4—442no—
555C22×C4—21no—
556C22×C4—21no—
557C22×C4—21no—
558C22×C4—21no—
559C22×C4—21no—
560C22×C4—21no—
561C22×C4—21no—
562C22×C4—21no—
563C22×C4—42no—
564C22×C4—42no—
565C22×C4—81no—
566C22×C4—111no—
567C22×C4—111no—
568C22×C4—111no—
569C22×C4—111no—
570C22×C4—221no—
571C22×C4—221no—
572C22×C4—442no—
573C22×C4—442no—
574C22×C4—442no—
575C22×C4—442no—
576C22×C4—881no—
577C22×C4—881no—
578C22×C4#433912yes—
579C22×C4D4×D1111yescharacteristic
580C22×C4Q8×D1112yes—
581C22×C4C23×D1111yescharacteristic
582C2×C8—21no—
583C2×C8—21no—
584C2×C8—21no—
585C2×C8—21no—
586C2×C8—21no—
587C2×C8—21no—
588C2×C8—112no—
589C2×C8—221no—
590C2×C8—221no—
591C2×C8—221no—
592C2×C8—221no—
593C2×C8—221no—
594C2×C8—444no—
595C4⋊C4—21no—
596C4⋊C4—21no—
597C4⋊C4—21no—
598C4⋊C4—21no—
599C4⋊C4—21no—
600C4⋊C4—21no—
601C4⋊C4—21no—
602C4⋊C4—42no—
603C4⋊C4—221no—
604C4⋊C4—221no—
605C4⋊C4—221no—
606C4⋊C4—221no—
607C4⋊C4—442no—
608C4⋊C4—442no—
609C4⋊C4—442no—
610C4⋊C4—442no—
611C4⋊C4—881no—
612C4⋊C4D4×D1112yes—
613C22⋊C4—42no—
614C22⋊C4—114no—
615C22⋊C4—222no—
616C22⋊C4—442no—
617C22⋊C4—442no—
618C22⋊C4—442no—
619C22⋊C4—442no—
620C22⋊C4—442no—
621C22⋊C4—881no—
622C22⋊C4—881no—
623C42—221no—
624C42—221no—
625C42—221no—
626C42—221no—
627C11#2595811yescharacteristic, complemented, Sylow
628C23—21no—
629C23—21no—
630C23—21no—
631C23—21no—
632C23—222no—
633C23—222no—
634C23—222no—
635C23—222no—
636C23—448no—
637C23—441no—
638C23—441no—
639C23—441no—
640C23—441no—
641C23—448no—
642C23—441no—
643C23—441no—
644C23—441no—
645C23—441no—
646C23—441no—
647C23—441no—
648C23—884no—
649C23—884no—
650C23—884no—
651C23—884no—
652C23—884no—
653C23#6694912yes—
654C23SD16×D1112yes—
655C23#6696712yes—
656C23C2×D4×D1111yescharacteristic
657Q8—884no—
658D4—114no—
659D4—222no—
660D4—222no—
661D4—222no—
662D4—222no—
663D4—222no—
664D4—448no—
665D4—441no—
666D4—441no—
667C2×C4—21no—
668C2×C4—21no—
669C2×C4—22no—
670C2×C4—22no—
671C2×C4—22no—
672C2×C4—22no—
673C2×C4—22no—
674C2×C4—41no—
675C2×C4—41no—
676C2×C4—41no—
677C2×C4—41no—
678C2×C4—41no—
679C2×C4—41no—
680C2×C4—41no—
681C2×C4—41no—
682C2×C4—41no—
683C2×C4—41no—
684C2×C4—41no—
685C2×C4—84no—
686C2×C4—112no—
687C2×C4—112no—
688C2×C4—221no—
689C2×C4—221no—
690C2×C4—221no—
691C2×C4—221no—
692C2×C4—221no—
693C2×C4—221no—
694C2×C4—221no—
695C2×C4—221no—
696C2×C4—221no—
697C2×C4—221no—
698C2×C4—441no—
699C2×C4—441no—
700C2×C4—441no—
701C2×C4—441no—
702C2×C4—441no—
703C2×C4—441no—
704C2×C4—884no—
705C2×C4—884no—
706C2×C4#6694912yes—
707C2×C4C2×#433911yescharacteristic
708C2×C4C2×D4×D1111yescharacteristic
709C2×C4#6703711yescharacteristic
710C2×C4C2×Q8×D1111yescharacteristic
711C2×C4#41×D1111yescharacteristic
712C2×C4#6704211yescharacteristic
713C8—41no—
714C8—41no—
715C8—222no—
716C8—441no—
717C22—22no—
718C22—22no—
719C22—22no—
720C22—22no—
721C22—22no—
722C22—22no—
723C22—224no—
724C22—442no—
725C22—442no—
726C22—442no—
727C22—442no—
728C22—442no—
729C22—442no—
730C22—442no—
731C22—442no—
732C22—442no—
733C22—8816no—
734C22—881no—
735C22—881no—
736C22—881no—
737C22—881no—
738C22#1062248314yescomplemented
739C22C2×#6694911yescharacteristic
740C22#1062312111yescharacteristic
741C22#1062318511yescharacteristic
742C22C2×SD16×D1111yescharacteristic
743C22C2×#6696711yescharacteristic
744C22#1062330511yescharacteristic
745C22#1062330911yescharacteristic
746C4—22no—
747C4—42no—
748C4—81no—
749C4—81no—
750C4—81no—
751C4—222no—
752C4—222no—
753C4—441no—
754C4—441no—
755C4—881no—
756C4—881no—
757C4#1062308111yescharacteristic
758C4#1062308711yescharacteristic
759C4D11×C22⋊Q811yescharacteristic
760C4#1062316511yescharacteristic
761C2—24no—
762C2—444no—
763C2—882no—
764C2#1307228111yescharacteristic
765C2C2×#1062248311yescharacteristic
766C2#1307844511yescharacteristic
767C2#1308010011yescharacteristic
768C2#1308030511yescharacteristic
769C2#1308043811yescharacteristic
770C2#1308057511yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#1853C2
socleC23×C11C22×D4
prime radicalC23×D44C22
hypercenter#1853D11
hypocenterC11#25958
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1853

Complements

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

NH ≅ G/Ntype
1. C2×#10622483C2semidirect
3. #13072312C2semidirect
5. #13070146C2semidirect
6. #13069991C2semidirect
7. #13069985C2semidirect
8. #13069751C2semidirect
9. #13068878C2semidirect
10. #13068874C2semidirect
11. #13068793C2semidirect
12. #13068639C2semidirect
13. #13068615C2semidirect
15. C11×#1853C2semidirect
22. C2×#66941C22semidirect
24. C2×C11×#106C22semidirect
25. C2×C11×#106C22semidirect
35. C2×Dic11⋊C8C22semidirect
36. C2×Dic11⋊C8C22semidirect
39. #10622598C22semidirect
42. #10622589C22semidirect
43. #10622586C22semidirect
49. C2×#66872C22semidirect
50. C2×#66872C22semidirect
55. C11×#340C22semidirect
56. C11×#340C22semidirect
57. #10622188C22semidirect
58. #10622188C22semidirect
59. #10622167C22semidirect
60. #10622167C22semidirect
70. C22×D44Q8semidirect
253. #1853D11semidirect
339. D44C22⋊Q8semidirect
358. C2×#106C2×D11semidirect
359. C2×#106C2×D11semidirect
388. #340C2×D11semidirect
389. #340C2×D11semidirect
398. C22×C11#476semidirect
627. C11#25958semidirect
738. C22#10622483semidirect

Maximal subgroups

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

subgroupindex
C2×#106224832
C22×#668732
#130723122
#130714362
#130701462
#130699912
#130699852
#130697512
#130688782
#130688742
#130687932
#130686392
#130686152
#130685482
C11×#18532
#2595811