Finite Group Databasebeta

← #14765093

Subgroups — #14765093

Order 2816.

1024 conjugacy classes of subgroups.

The subgroup lattice has 758 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622650C211yesmaximal, characteristic
2#13071204C211yesmaximal, characteristic, complemented
3#13069496C211yesmaximal, characteristic, complemented
4#13069481C211yesmaximal, characteristic, complemented
5#13069312C211yesmaximal, characteristic, complemented
6#13069291C211yesmaximal, characteristic, complemented
7#13069257C211yesmaximal, characteristic, complemented
8#13069236C211yesmaximal, characteristic, complemented
9#13068964C211yesmaximal, characteristic, complemented
10#13068950C211yesmaximal, characteristic, complemented
11#13068934C211yesmaximal, characteristic, complemented
12#13068803C211yesmaximal, characteristic, complemented
13#13068554C211yesmaximal, characteristic, complemented
14#13068382C211yesmaximal, characteristic, complemented
15C11×#2324C211yesmaximal, characteristic, complemented
16C22×#4339C2211yescharacteristic
17C2×C11×#121C2211yescharacteristic
18C2×C4×D4×C11C2211yescharacteristic
19C2×C11×#117C2211yescharacteristic
20C22×#4324C2211yescharacteristic
21C22×#4323C2211yescharacteristic
22C22×C4⋊Dic11C2211yescharacteristic
23C11×#390—21no—
24C11×#390C2211yescharacteristic
25C11×#389C2211yescharacteristic
26C11×#388—21no—
27C11×#386—21no—
28C11×#385—21no—
29C11×#380C2211yescharacteristic
30C4×C11×C4⋊C4C2211yescharacteristic
31C2×#66896C2211yescharacteristic
32C2×#66896C2211yescharacteristic
33C2×C22⋊(C11⋊C8)C2211yescharacteristic
34C2×C22⋊(C11⋊C8)C2211yescharacteristic
35#10622650C418yescomplemented
36#10622600—21no—
37#10622600—21no—
38C2×#66874C2211yescharacteristic
39C2×#66874C2211yescharacteristic
40C2×#66874C2211yescharacteristic
41C2×#66873C2211yescharacteristic
42C2×#66873C2211yescharacteristic
43C2×#66873C2211yescharacteristic
44C2×#66871C2211yescharacteristic
45C2×#66871C2211yescharacteristic
46#10622571—21no—
47#10622571—21no—
48#10622552C2211yescharacteristic
49#10622552C2211yescharacteristic
50#10622542C2211yescharacteristic
51#10622542C2211yescharacteristic
52C2×#66867C2211yescharacteristic
53C2×C4×C11⋊C8C2211yescharacteristic
54#10622167C2211yescharacteristic
55#10622167C2211yescharacteristic
56#10622167C2211yescharacteristic
57#10622167C2211yescharacteristic
58#10622162C2211yescharacteristic
59#10622162C2211yescharacteristic
60C22×D4×C11—21no—
61C22×D4×C11C2311yescharacteristic
62C23×C4×C11—21no—
63C23×C4×C11C2311yescharacteristic
64C22×C22⋊D11—21no—
65C23×Dic11—21no—
66C2×#4339—22no—
67C2×#4339—41no—
68C2×#4339—41no—
69C2×#4339—41no—
70C2×#4339—41no—
71C2×#4339C2×C414yescomplemented
72C22×D44C2311yescharacteristic
73C22×C4×D11—21no—
74C22×Dic22C2311yescharacteristic
75C11×#121—22no—
76C11×#121C2×C414yes—
77C4×D4×C11—41no—
78C4×D4×C11—41no—
79C11×#117—41no—
80C11×#117—41no—
81C2×C11×C4⋊C4—21no—
82C2×C11×C4⋊C4D411yescharacteristic
83C2×C11×C4⋊C4D411yescharacteristic
84C2×C11×C4⋊C4C2311yescharacteristic
85C2×C11×C4⋊C4C2311yescharacteristic
86C2×C11×C4⋊C4C2311yescharacteristic
87C2×C11×C22⋊C4—21no—
88C2×C11×C22⋊C4—21no—
89C2×C11×C22⋊C4—21no—
90C2×C11×C22⋊C4—21no—
91C2×C11×C22⋊C4—21no—
92C2×C11×C22⋊C4D411yescharacteristic
93C2×C11×C22⋊C4D411yescharacteristic
94C2×C42×C11—21no—
95C2×C42×C11C2311yescharacteristic
96C2×C42×C11C2311yescharacteristic
97C2×#4324—41no—
98C2×#4324—41no—
99C2×#4324C2×C414yescomplemented
100C2×#4323—41no—
101C2×#4323—41no—
102C2×#4323C2×C414yescomplemented
103C2×(C2×D11)⋊C4—21no—
104C2×(C2×D11)⋊C4—21no—
105C2×(C2×D11)⋊C4—21no—
106C2×(C2×D11)⋊C4—21no—
107C2×C4⋊Dic11—21no—
108C2×C4⋊Dic11—41no—
109C2×C4⋊Dic11—41no—
110C2×C4⋊Dic11C2311yescharacteristic
111C2×C4⋊Dic11C2311yescharacteristic
112C22×C11⋊C8C2311yescharacteristic
113C22×C11⋊C8C2311yescharacteristic
114C22×C11⋊C8C2311yescharacteristic
115C22×C11⋊C8C2311yescharacteristic
116C11×#95—21no—
117C11×#95—21no—
118C11×#95—21no—
119#66896—41no—
120#66896—41no—
121C11⋊#95—21no—
122C11⋊#95—21no—
123C11⋊#95—21no—
124C11⋊#95—21no—
125C22⋊(C11⋊C8)—22no—
126C22⋊(C11⋊C8)C2×C414yescomplemented
127#66874—41no—
128#66874—41no—
129#66874C2×C414yescomplemented
130#66873—41no—
131#66873—41no—
132#66873C2×C414yescomplemented
133#66871—41no—
134#66871—41no—
135#66867—41no—
136C4×C11⋊C8—41no—
137#22055—111nomaximal, Sylow
138C24×C11—21no—
139C24×C11C2×D411yescharacteristic
140C23×D11—21no—
141C2×D4×C11—24no—
142C2×D4×C11—21no—
143C2×D4×C11—21no—
144C2×D4×C11—21no—
145C2×D4×C11—21no—
146C2×D4×C11—21no—
147C2×D4×C11—81no—
148C2×D4×C11—81no—
149C2×D4×C11C22×C412yes—
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—81no—
159C22×C4×C11—81no—
160C22×C4×C11C22×C412yes—
161C22×C4×C11C2×D411yescharacteristic
162C22×C4×C11C2×D411yescharacteristic
163C22×C4×C11C2×D411yescharacteristic
164C22×C4×C11C2×D411yescharacteristic
165C22×C4×C11C2×D411yescharacteristic
166C22×C4×C11#4112yes—
167C22×C4×C11C2411yescharacteristic
168C2×C22⋊D11—24no—
169C2×C22⋊D11—42no—
170C2×C22⋊D11—42no—
171C22×Dic11—21no—
172C22×Dic11—21no—
173C22×Dic11—21no—
174C22×Dic11—42no—
175C22×Dic11—81no—
176C22×Dic11—81no—
177#4339—44no—
178#4339—44no—
179#4339—44no—
180#4339—44no—
181C2×D44—21no—
182C2×D44—21no—
183C2×D44—21no—
184C2×D44—21no—
185C2×D44—21no—
186C2×D44C22×C412yes—
187C2×C4×D11—24no—
188C2×C4×D11—42no—
189C2×C4×D11—42no—
190C2×Dic22—21no—
191C2×Dic22—21no—
192C2×Dic22—21no—
193C2×Dic22—21no—
194C2×Dic22—21no—
195C2×Dic22C22×C412yes—
196C11×C4⋊C4—21no—
197C11×C4⋊C4—21no—
198C11×C4⋊C4—21no—
199C11×C4⋊C4—21no—
200C11×C4⋊C4—21no—
201C11×C4⋊C4—41no—
202C11×C4⋊C4—41no—
203C11×C4⋊C4—81no—
204C11×C4⋊C4C22×C412yes—
205C11×C22⋊C4—24no—
206C11×C22⋊C4—41no—
207C11×C22⋊C4—41no—
208C11×C22⋊C4—42no—
209C11×C22⋊C4—81no—
210C11×C22⋊C4—81no—
211C11×C22⋊C4—81no—
212C42×C11—21no—
213C42×C11—21no—
214C42×C11—21no—
215C42×C11—21no—
216C42×C11—81no—
217#4324—44no—
218#4323—44no—
219(C2×D11)⋊C4—81no—
220(C2×D11)⋊C4—81no—
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—
228C2×C11⋊C8—21no—
229C2×C11⋊C8—21no—
230C2×C11⋊C8—21no—
231C2×C11⋊C8—21no—
232C2×C11⋊C8—21no—
233C2×C11⋊C8—21no—
234C2×C11⋊C8—21no—
235C2×C11⋊C8—21no—
236C2×C11⋊C8—21no—
237C2×C11⋊C8—21no—
238C2×C11⋊C8C22×C412yes—
239C2×C11⋊C8C22×C412yes—
240C2×#449—111no—
241#2324D1111yescharacteristic, complemented
242#2311—111no—
243#1973—111no—
244#1970—111no—
245#1936—111no—
246#1933—111no—
247#1928—111no—
248#1925—111no—
249#1879—111no—
250#1877—111no—
251#1874—111no—
252#1852—111no—
253#1788—111no—
254#1750—111no—
255C23×C11—21no—
256C23×C11—21no—
257C23×C11—21no—
258C23×C11—21no—
259C23×C11—21no—
260C23×C11—21no—
261C23×C11—22no—
262C23×C11—41no—
263C23×C11—41no—
264C23×C11—41no—
265C23×C11—41no—
266C23×C11—41no—
267C23×C11—41no—
268C23×C11C4×D412yes—
269C23×C11C22×D411yescharacteristic
270C22×D11—22no—
271C22×D11—41no—
272C22×D11—41no—
273C22×D11—41no—
274C22×D11—41no—
275C22×D11—41no—
276C22×D11—41no—
277D4×C11—22no—
278D4×C11—22no—
279D4×C11—41no—
280D4×C11—41no—
281D4×C11—84no—
282C2×C4×C11—21no—
283C2×C4×C11—21no—
284C2×C4×C11—22no—
285C2×C4×C11—22no—
286C2×C4×C11—22no—
287C2×C4×C11—22no—
288C2×C4×C11—22no—
289C2×C4×C11—21no—
290C2×C4×C11—21no—
291C2×C4×C11—21no—
292C2×C4×C11—21no—
293C2×C4×C11—21no—
294C2×C4×C11—21no—
295C2×C4×C11—21no—
296C2×C4×C11—21no—
297C2×C4×C11—21no—
298C2×C4×C11—21no—
299C2×C4×C11—21no—
300C2×C4×C11—21no—
301C2×C4×C11—41no—
302C2×C4×C11—41no—
303C2×C4×C11—41no—
304C2×C4×C11—41no—
305C2×C4×C11—41no—
306C2×C4×C11—41no—
307C2×C4×C11—41no—
308C2×C4×C11—41no—
309C2×C4×C11—84no—
310C2×C4×C11C4×D412yes—
311C2×C4×C11C23×C411yescharacteristic
312C2×C4×C11C2×#4111yescharacteristic
313C2×C4×C11H(5,𝔽2)11yescharacteristic
314C2×C4×C11H(5,𝔽2)11yescharacteristic
315C2×C4×C11H(5,𝔽2)11yescharacteristic
316C2×C4×C11H(5,𝔽2)11yescharacteristic
317C22⋊D11—48no—
318C2×Dic11—22no—
319C2×Dic11—41no—
320C2×Dic11—41no—
321C2×Dic11—41no—
322C2×Dic11—41no—
323C2×Dic11—41no—
324C2×Dic11—41no—
325C2×Dic11—41no—
326C2×Dic11—41no—
327C2×Dic11—84no—
328D44—22no—
329D44—22no—
330D44—41no—
331D44—41no—
332C4×D11—48no—
333Dic22—22no—
334Dic22—22no—
335Dic22—41no—
336Dic22—41no—
337C11⋊C8—22no—
338C11⋊C8—22no—
339C11⋊C8—41no—
340C11⋊C8—41no—
341C22×#41—111no—
342C22×SD16—111no—
343C22×D8—111no—
344C2×#121C2×D1111yescharacteristic
345C2×C4×D4C2×D1111yescharacteristic
346C2×#117C2×D1111yescharacteristic
347C22×C4⋊C4—111no—
348#449—118no—
349C2×#107—111no—
350C2×#107—111no—
351C2×#103—111no—
352C2×#103—111no—
353C2×#103—111no—
354C2×#102—111no—
355C2×#102—111no—
356C2×#102—111no—
357C2×#102—111no—
358C2×#102—111no—
359C2×C22⋊C8—111no—
360C2×C22⋊C8—111no—
361C2×#97—111no—
362C2×C4×C8—111no—
363#391—111no—
364#391—111no—
365#390—21no—
366#390—111no—
367#390—111no—
368#390C2×D1111yescharacteristic
369#389C2×D1111yescharacteristic
370#388—21no—
371#386—21no—
372#386—221no—
373#386—221no—
374#385—21no—
375#380—221no—
376#380—221no—
377#380C2×D1111yescharacteristic
378C4×C4⋊C4C2×D1111yescharacteristic
379#340—111no—
380#340—111no—
381#340—111no—
382#340—111no—
383#336—111no—
384#336—111no—
385C22×C11—22no—
386C22×C11—22no—
387C22×C11—22no—
388C22×C11—41no—
389C22×C11—41no—
390C22×C11—41no—
391C22×C11—41no—
392C22×C11—42no—
393C22×C11—42no—
394C22×C11—42no—
395C22×C11—81no—
396C22×C11—81no—
397C22×C11—81no—
398C22×C11—81no—
399C22×C11C2×C4×D411yescharacteristic
400C22×C11#53411yescharacteristic
401C22×C11#53511yescharacteristic
402C22×C11#57611yescharacteristic
403C22×C11#57611yescharacteristic
404C22×C11#57711yescharacteristic
405C22×C11#57811yescharacteristic
406C2×D11—42no—
407C2×D11—42no—
408C2×D11—42no—
409C2×D11—81no—
410C2×D11—81no—
411C2×D11—81no—
412C2×D11—81no—
413C4×C11—22no—
414C4×C11—41no—
415C4×C11—41no—
416C4×C11—42no—
417C4×C11—41no—
418C4×C11—41no—
419C4×C11—81no—
420C4×C11—81no—
421C4×C11#51811yescharacteristic
422C4×C11#51811yescharacteristic
423C4×C11#53811yescharacteristic
424C4×C11#53811yescharacteristic
425Dic11—42no—
426Dic11—81no—
427Dic11—81no—
428C2×#41—114no—
429C2×#41—222no—
430C2×#41—441no—
431C2×#41—441no—
432C2×#41—441no—
433C2×#41—441no—
434C22×Q8—111no—
435C22×D4—21no—
436C22×D4—111no—
437C22×D4—221no—
438C22×D4C22×D1111yescharacteristic
439C23×C4—21no—
440C23×C4—221no—
441C23×C4—221no—
442C23×C4C22×D1111yescharacteristic
443C2×SD16—114no—
444C2×SD16—441no—
445C2×SD16—441no—
446C2×D8—114no—
447C2×D8—441no—
448C2×D8—441no—
449C22×C8—111no—
450C22×C8—111no—
451C22×C8—111no—
452C22×C8—111no—
453#121—22no—
454#121C4×D1114yes—
455C4×D4—41no—
456C4×D4—41no—
457#117—41no—
458#117—41no—
459C2×C4⋊C4—21no—
460C2×C4⋊C4—111no—
461C2×C4⋊C4—111no—
462C2×C4⋊C4—221no—
463C2×C4⋊C4—441no—
464C2×C4⋊C4—441no—
465C2×C4⋊C4C22⋊D1111yescharacteristic
466C2×C4⋊C4C22⋊D1111yescharacteristic
467C2×C4⋊C4C22×D1111yescharacteristic
468C2×C4⋊C4C22×D1111yescharacteristic
469C2×C4⋊C4C22×D1111yescharacteristic
470C2×C22⋊C4—21no—
471C2×C22⋊C4—21no—
472C2×C22⋊C4—21no—
473C2×C22⋊C4—21no—
474C2×C22⋊C4—21no—
475C2×C22⋊C4—221no—
476C2×C22⋊C4—221no—
477C2×C22⋊C4—221no—
478C2×C22⋊C4—221no—
479C2×C22⋊C4C22⋊D1111yescharacteristic
480C2×C22⋊C4C22⋊D1111yescharacteristic
481C2×C42—21no—
482C2×C42C22×D1111yescharacteristic
483C2×C42C22×D1111yescharacteristic
484#107—441no—
485#107—441no—
486#103—114no—
487#103—441no—
488#103—441no—
489#102—114no—
490#102—441no—
491#102—441no—
492#102—441no—
493#102—441no—
494C22⋊C8—114no—
495C22⋊C8—222no—
496#97—441no—
497C4×C8—441no—
498#95—21no—
499#95—21no—
500#95—21no—
501#95—221no—
502#95—221no—
503#95—221no—
504#95—221no—
505C2×C11—42no—
506C2×C11—82no—
507C2×C11#232111yescharacteristic
508C2×C11#294611yescharacteristic
509C2×C11#295111yescharacteristic
510C2×C11#319811yescharacteristic
511C2×C11#320311yescharacteristic
512C2×C11#322011yescharacteristic
513C2×C11#322511yescharacteristic
514D11—82no—
515C24—21no—
516C24—221no—
517C24C2×C22⋊D1111yescharacteristic
518#41—444no—
519#41—444no—
520#41—444no—
521#41—444no—
522C2×Q8—112no—
523C2×Q8—221no—
524C2×Q8—221no—
525C2×Q8—221no—
526C2×Q8—221no—
527C2×Q8—221no—
528C2×D4—24no—
529C2×D4—21no—
530C2×D4—21no—
531C2×D4—21no—
532C2×D4—21no—
533C2×D4—21no—
534C2×D4—81no—
535C2×D4—81no—
536C2×D4—112no—
537C2×D4—224no—
538C2×D4—221no—
539C2×D4—221no—
540C2×D4—221no—
541C2×D4—221no—
542C2×D4—221no—
543C2×D4—442no—
544C2×D4—442no—
545C2×D4C2×C4×D1112yes—
546C22×C4—21no—
547C22×C4—21no—
548C22×C4—21no—
549C22×C4—21no—
550C22×C4—21no—
551C22×C4—21no—
552C22×C4—21no—
553C22×C4—42no—
554C22×C4—81no—
555C22×C4—81no—
556C22×C4—221no—
557C22×C4—224no—
558C22×C4—221no—
559C22×C4—221no—
560C22×C4—442no—
561C22×C4—442no—
562C22×C4—442no—
563C22×C4—881no—
564C22×C4—881no—
565C22×C4C2×C4×D1112yes—
566C22×C4#433912yes—
567C22×C4C2×C22⋊D1111yescharacteristic
568C22×C4C2×C22⋊D1111yescharacteristic
569C22×C4C2×C22⋊D1111yescharacteristic
570C22×C4C2×C22⋊D1111yescharacteristic
571C22×C4C2×C22⋊D1111yescharacteristic
572C22×C4C23×D1111yescharacteristic
573SD16—444no—
574D8—444no—
575C2×C8—112no—
576C2×C8—112no—
577C2×C8—221no—
578C2×C8—221no—
579C2×C8—221no—
580C2×C8—221no—
581C2×C8—221no—
582C2×C8—221no—
583C2×C8—221no—
584C2×C8—221no—
585C2×C8—221no—
586C2×C8—221no—
587C4⋊C4—21no—
588C4⋊C4—21no—
589C4⋊C4—21no—
590C4⋊C4—21no—
591C4⋊C4—21no—
592C4⋊C4—41no—
593C4⋊C4—41no—
594C4⋊C4—81no—
595C4⋊C4—221no—
596C4⋊C4—221no—
597C4⋊C4—221no—
598C4⋊C4—221no—
599C4⋊C4—442no—
600C4⋊C4C2×C4×D1112yes—
601C22⋊C4—24no—
602C22⋊C4—41no—
603C22⋊C4—41no—
604C22⋊C4—42no—
605C22⋊C4—81no—
606C22⋊C4—81no—
607C22⋊C4—81no—
608C22⋊C4—881no—
609C22⋊C4—881no—
610C22⋊C4—881no—
611C22⋊C4—881no—
612C42—21no—
613C42—21no—
614C42—21no—
615C42—21no—
616C42—81no—
617C11#2205511yescharacteristic, complemented, Sylow
618C23—21no—
619C23—21no—
620C23—21no—
621C23—21no—
622C23—21no—
623C23—21no—
624C23—22no—
625C23—41no—
626C23—41no—
627C23—41no—
628C23—41no—
629C23—41no—
630C23—41no—
631C23—222no—
632C23—441no—
633C23—441no—
634C23—441no—
635C23—441no—
636C23—441no—
637C23—441no—
638C23C4×C22⋊D1112yes—
639C23C22×C22⋊D1111yescharacteristic
640Q8—222no—
641Q8—222no—
642Q8—441no—
643Q8—441no—
644D4—22no—
645D4—22no—
646D4—41no—
647D4—41no—
648D4—84no—
649D4—222no—
650D4—222no—
651D4—448no—
652D4—441no—
653D4—441no—
654C2×C4—21no—
655C2×C4—21no—
656C2×C4—22no—
657C2×C4—22no—
658C2×C4—22no—
659C2×C4—22no—
660C2×C4—22no—
661C2×C4—21no—
662C2×C4—21no—
663C2×C4—21no—
664C2×C4—21no—
665C2×C4—21no—
666C2×C4—21no—
667C2×C4—21no—
668C2×C4—21no—
669C2×C4—21no—
670C2×C4—21no—
671C2×C4—21no—
672C2×C4—21no—
673C2×C4—41no—
674C2×C4—41no—
675C2×C4—41no—
676C2×C4—41no—
677C2×C4—41no—
678C2×C4—41no—
679C2×C4—41no—
680C2×C4—41no—
681C2×C4—84no—
682C2×C4—222no—
683C2×C4—448no—
684C2×C4—441no—
685C2×C4—441no—
686C2×C4—441no—
687C2×C4—441no—
688C2×C4—441no—
689C2×C4—441no—
690C2×C4—441no—
691C2×C4—441no—
692C2×C4—884no—
693C2×C4C4×C22⋊D1112yes—
694C2×C4C22×C4×D1111yescharacteristic
695C2×C4C2×#433911yescharacteristic
696C2×C4#6703711yescharacteristic
697C2×C4#6703711yescharacteristic
698C2×C4#6704211yescharacteristic
699C2×C4#6704211yescharacteristic
700C8—222no—
701C8—222no—
702C8—441no—
703C8—441no—
704C22—22no—
705C22—22no—
706C22—22no—
707C22—41no—
708C22—41no—
709C22—41no—
710C22—41no—
711C22—42no—
712C22—42no—
713C22—42no—
714C22—81no—
715C22—81no—
716C22—81no—
717C22—81no—
718C22—442no—
719C22—442no—
720C22—442no—
721C22—881no—
722C22—881no—
723C22—881no—
724C22—881no—
725C22C2×C4×C22⋊D1111yescharacteristic
726C22#1062333511yescharacteristic
727C22#1062336111yescharacteristic
728C22#1062336611yescharacteristic
729C22#1062336611yescharacteristic
730C22#1062336711yescharacteristic
731C22#1062336911yescharacteristic
732C4—22no—
733C4—41no—
734C4—41no—
735C4—42no—
736C4—41no—
737C4—41no—
738C4—81no—
739C4—81no—
740C4—442no—
741C4—881no—
742C4—881no—
743C4#1062307611yescharacteristic
744C4#1062307611yescharacteristic
745C4#1062309111yescharacteristic
746C4#1062309111yescharacteristic
747C2—42no—
748C2—82no—
749C2—882no—
750C2#1307127011yescharacteristic
751C2#1307744811yescharacteristic
752C2#1307748911yescharacteristic
753C2#1307946811yescharacteristic
754C2#1307951311yescharacteristic
755C2#1307966011yescharacteristic
756C2#1307971911yescharacteristic
subgroupG/H
centerC23C22×C22⋊D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#2324C2
socleC23×C11C22×D4
prime radicalC2×#10622650C2
cosocleC22×C4×C11C24
hypercenter#2324D11
hypocenterC11#22055
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×#117 ◁ #2324

Complements

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

NH ≅ G/Ntype
2. #13071204C2semidirect
3. #13069496C2semidirect
4. #13069481C2semidirect
5. #13069312C2semidirect
6. #13069291C2semidirect
7. #13069257C2semidirect
8. #13069236C2semidirect
9. #13068964C2semidirect
10. #13068950C2semidirect
11. #13068934C2semidirect
12. #13068803C2semidirect
13. #13068554C2semidirect
14. #13068382C2semidirect
15. C11×#2324C2semidirect
35. #10622650C4semidirect
71. C2×#4339C2×C4semidirect
99. C2×#4324C2×C4semidirect
102. C2×#4323C2×C4semidirect
126. C22⋊(C11⋊C8)C2×C4semidirect
129. #66874C2×C4semidirect
132. #66873C2×C4semidirect
241. #2324D11semidirect
617. C11#22055semidirect

Maximal subgroups

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

subgroupindex
C2×#106226502
#130712042
#130694962
#130694812
#130693122
#130692912
#130692572
#130692362
#130689642
#130689502
#130689342
#130688032
#130685542
#130683822
C11×#23242
#2205511