Finite Group Databasebeta

← D11×#2820 #14960294

Subgroups — D11×#2820 #14960294

Order 2816.

2566 conjugacy classes of subgroups.

The subgroup lattice has 766 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D11×#125C211yesmaximal, characteristic, complemented
2C2×D11×#124C211yesmaximal, characteristic
3#13076672C212yesmaximal, complemented
4#13076671C212yesmaximal, complemented
5#13076670C212yesmaximal, complemented
6#13076669C212yesmaximal, complemented
7#13076668C211yesmaximal, characteristic, complemented
8#13076667C211yesmaximal, characteristic, complemented
9#13076666C211yesmaximal, characteristic, complemented
10#13076665C214yesmaximal, complemented
11D11×#399C212yesmaximal, complemented
12D11×#397C212yesmaximal, complemented
13D11×#396C214yesmaximal, complemented
14D11×#395C212yesmaximal, complemented
15D11×#394C212yesmaximal
16D11×#382C211yesmaximal, characteristic, complemented
17C11×#2820C211yesmaximal, characteristic, complemented
18C22×Q8×D11C2211yescharacteristic
19C22×D4×D11C2211yescharacteristic
20C2×C11×#125C2211yescharacteristic, complemented
21C2×C11×#124C2211yescharacteristic
22C2×#67000C2211yescharacteristic
23C2×#66989C2211yescharacteristic
24D11×#125—28no—
25D11×#124—28no—
26C2×C4⋊C4×D11C2212yes—
27C2×C4⋊C4×D11C2212yes—
28C2×C4⋊C4×D11C2211yescharacteristic
29C2×C4⋊C4×D11C2211yescharacteristic
30C2×C4⋊C4×D11C2212yes—
31C2×C4⋊C4×D11C2214yes—
32C2×#66943C2211yescharacteristic, complemented
33C2×#66943C2211yescharacteristic, complemented
34C2×#66942C2212yescomplemented
35C2×#66942C2212yescomplemented
36C2×#66938C2212yes—
37C2×#66938C2212yes—
38C2×C22⋊C4×D11C2212yes—
39C2×C22⋊C4×D11C2212yes—
40C2×C22⋊C4×D11C2214yes—
41C2×C22⋊C4×D11C2214yes—
42C2×#66928C2211yescharacteristic
43C2×C42×D11C2211yescharacteristic
44C2×#66923C2211yescharacteristic, complemented
45C11×#399C2212yescomplemented
46C11×#397C2212yescomplemented
47C11×#396C2214yescomplemented
48C11×#395C2212yescomplemented
49C11×#394C2212yes—
50C11×#382C2211yescharacteristic, complemented
51#10622842C2212yescomplemented
52#10622835C2212yes—
53#10622607C2214yescomplemented
54#10622607C2214yescomplemented
55#10622607C2214yescomplemented
56#10622606C2212yescomplemented
57#10622605C2214yescomplemented
58#10622605C2212yescomplemented
59#10622604C2212yes—
60#10622592C2214yescomplemented
61#10622592C2212yescomplemented
62#10622590C2212yescomplemented
63#10622574C2214yes—
64#10622572C2214yes—
65#10622566C2212yescomplemented
66#10622565C2214yescomplemented
67#10622562C2214yescomplemented
68#10622562C2212yescomplemented
69#10622561C2214yescomplemented
70#10622561C2214yescomplemented
71#10622561C2214yescomplemented
72#10622549C2211yescharacteristic, complemented
73#10622290C2212yescomplemented
74#10622289C2214yescomplemented
75#10622288C2214yescomplemented
76#10622287C2212yescomplemented
77#10622285C2212yes—
78D11×#95C2212yes—
79D11×#95C2212yes—
80D11×#95C2214yes—
81#10622269C2214yescomplemented
82#10622269C2212yescomplemented
83#10622263C2212yescomplemented
84#10622263C2212yescomplemented
85C24×D11C2312yes—
86C22×Q8×C11C2311yescharacteristic
87C22×D4×C11C2311yescharacteristic
88C22×C22⋊D11C2312yes—
89C2×Q8×D11—24no—
90C2×Q8×D11—44no—
91C2×D4×D11—24no—
92C2×D4×D11—44no—
93C22×D44C2311yescharacteristic
94C22×C4×D11C2312yes—
95C22×C4×D11C2312yes—
96C22×C4×D11C2314yes—
97C22×C4×D11C2312yes—
98C22×C4×D11C2311yescharacteristic
99C22×C4×D11C2311yescharacteristic
100C22×C4×D11C2311yescharacteristic
101C22×Dic22C2311yescharacteristic
102C22×Dic22C2312yes—
103C11×#125—24no—
104C11×#124—24no—
105C2×C11×C4⋊C4C2312yes—
106C2×C11×C4⋊C4C2312yes—
107C2×C11×C4⋊C4C2311yescharacteristic
108C2×C11×C4⋊C4C2311yescharacteristic
109C2×C11×C4⋊C4C2312yes—
110C2×C11×C4⋊C4C2314yes—
111C2×C11×C22⋊C4C2312yes—
112C2×C11×C22⋊C4C2312yes—
113C2×C11×C22⋊C4C2314yes—
114C2×C11×C22⋊C4C2314yes—
115C2×C42×C11C2311yescharacteristic
116C2×C22⋊Dic11C2312yes—
117C2×C22⋊Dic11C2312yes—
118C2×C22⋊Dic11C2314yes—
119C2×C22⋊Dic11C2314yes—
120#67000—24no—
121#66989—24no—
122C2×(C2×D11)⋊C4C2312yes—
123C2×(C2×D11)⋊C4C2312yes—
124C2×(C2×D11)⋊C4C2312yes—
125C2×(C2×D11)⋊C4C2312yes—
126C2×(C2×D11)⋊C4C2314yes—
127C2×(C2×D11)⋊C4C2314yes—
128C2×(C2×D11)⋊C4C2314yes—
129C2×(C2×D11)⋊C4C2314yes—
130C2×C4⋊Dic11C2311yescharacteristic
131C2×C4⋊Dic11C2311yescharacteristic
132C2×C4⋊Dic11C2312yes—
133C2×C4⋊Dic11C2312yes—
134C2×C4⋊Dic11C2314yes—
135C2×C4⋊Dic11C2312yes—
136C2×Dic11⋊C4C2312yes—
137C2×Dic11⋊C4C2312yes—
138C2×Dic11⋊C4C2312yes—
139C2×Dic11⋊C4C2312yes—
140C2×Dic11⋊C4C2312yes—
141C2×Dic11⋊C4C2312yes—
142C2×Dic11⋊C4C2314yes—
143C2×Dic11⋊C4C2314yes—
144C2×Dic11⋊C4C2314yes—
145C2×C4×Dic11C2311yescharacteristic
146C2×C4×Dic11C2311yescharacteristic
147C2×C4×Dic11C2311yescharacteristic
148C4⋊C4×D11—24no—
149C4⋊C4×D11—24no—
150C4⋊C4×D11—28no—
151C4⋊C4×D11—28no—
152C4⋊C4×D11—44no—
153C4⋊C4×D11—48no—
154#66943—24no—
155#66943—24no—
156#66942—28no—
157#66942—28no—
158#66938—28no—
159#66938—28no—
160C22⋊C4×D11—28no—
161C22⋊C4×D11—28no—
162C22⋊C4×D11—48no—
163C22⋊C4×D11—48no—
164#66928—24no—
165C42×D11D418yes—
166#66923—24no—
167C11×#95C2312yes—
168C11×#95C2312yes—
169C11×#95C2314yes—
170C11⋊#95C2314yes—
171C11⋊#95C2314yes—
172C11⋊#95C2312yes—
173C11⋊#95C2312yes—
174C11⋊#95C2314yes—
175C11⋊#95C2314yes—
176C11⋊#95C2314yes—
177C2×#2820—111nomaximal, Sylow
178C24×C11C2412yes—
179C23×D11—24no—
180C23×D11—24no—
181C23×D11—28no—
182C23×D11—28no—
183C23×D11—24no—
184C23×D11C2412yes—
185C23×D11C2411yescharacteristic
186C2×Q8×C11—22no—
187C2×Q8×C11—42no—
188C2×D4×C11—22no—
189C2×D4×C11—42no—
190C22×C4×C11C2414yes—
191C22×C4×C11C2412yes—
192C22×C4×C11C2412yes—
193C22×C4×C11C2412yes—
194C22×C4×C11C2411yescharacteristic
195C22×C4×C11C2411yescharacteristic
196C22×C4×C11C2411yescharacteristic
197C2×C22⋊D11—24no—
198C2×C22⋊D11—44no—
199C22×Dic11C2414yes—
200C22×Dic11C2412yes—
201C22×Dic11C2412yes—
202C22×Dic11C2412yes—
203C22×Dic11C2411yescharacteristic
204C22×Dic11C2411yescharacteristic
205C22×Dic11C2411yescharacteristic
206Q8×D11—416no—
207D4×D11—416no—
208C2×D44—22no—
209C2×D44—42no—
210C2×C4×D11—24no—
211C2×C4×D11—24no—
212C2×C4×D11—24no—
213C2×C4×D11—22no—
214C2×C4×D11—24no—
215C2×C4×D11—24no—
216C2×C4×D11—28no—
217C2×C4×D11—28no—
218C2×C4×D11—28no—
219C2×C4×D11—28no—
220C2×C4×D11—24no—
221C2×C4×D11—22no—
222C2×C4×D11—28no—
223C2×C4×D11—24no—
224C2×C4×D11C2×D414yes—
225C2×C4×D11C2×D414yes—
226C2×C4×D11C2×D414yes—
227C2×Dic22—24no—
228C2×Dic22—22no—
229C2×Dic22—42no—
230C2×Dic22—44no—
231C11×C4⋊C4—24no—
232C11×C4⋊C4—24no—
233C11×C4⋊C4—22no—
234C11×C4⋊C4—22no—
235C11×C4⋊C4—42no—
236C11×C4⋊C4—44no—
237C11×C22⋊C4—24no—
238C11×C22⋊C4—24no—
239C11×C22⋊C4—44no—
240C11×C22⋊C4—44no—
241C42×C11C2×D414yes—
242C22⋊Dic11—24no—
243C22⋊Dic11—24no—
244C22⋊Dic11—44no—
245C22⋊Dic11—44no—
246(C2×D11)⋊C4—24no—
247(C2×D11)⋊C4—24no—
248(C2×D11)⋊C4—24no—
249(C2×D11)⋊C4—24no—
250(C2×D11)⋊C4—44no—
251(C2×D11)⋊C4—44no—
252(C2×D11)⋊C4—44no—
253(C2×D11)⋊C4—44no—
254C4⋊Dic11—24no—
255C4⋊Dic11—24no—
256C4⋊Dic11—22no—
257C4⋊Dic11—22no—
258C4⋊Dic11—42no—
259C4⋊Dic11—44no—
260Dic11⋊C4—24no—
261Dic11⋊C4—24no—
262Dic11⋊C4—24no—
263Dic11⋊C4—24no—
264Dic11⋊C4—24no—
265Dic11⋊C4—24no—
266Dic11⋊C4—44no—
267Dic11⋊C4—44no—
268Dic11⋊C4—44no—
269C4×Dic11C2×D414yes—
270C4×Dic11C2×D414yes—
271C4×Dic11C2×D414yes—
272C22×#125—111no—
273C22×#124—111no—
274#2820—112no—
275#2820—112no—
276#2820—114no—
277#2820—112no—
278#2820—112no—
279#2820—111no—
280#2820—111no—
281#2820—111no—
282#2820D1111yescharacteristic, direct product factor
283C2×#399—112no—
284C2×#397—112no—
285C2×#396—114no—
286C2×#395—112no—
287C2×#394—112no—
288C2×#382—111no—
289C23×C11—22no—
290C23×C11—22no—
291C23×C11—24no—
292C23×C11—24no—
293C23×C11—22no—
294C23×C11C2511yescharacteristic
295C22×D11—22no—
296C22×D11—22no—
297C22×D11—24no—
298C22×D11—24no—
299C22×D11—22no—
300C22×D11—48no—
301C22×D11—48no—
302C22×D11—48no—
303C22×D11—416no—
304C22×D11—416no—
305C22×D11C22×D412yes—
306C22×D11H(5,𝔽2)14yes—
307C22×D11H(5,𝔽2)12yes—
308C22×D112−1+414yes—
309C22×D112−1+412yes—
310Q8×C11—44no—
311D4×C11—44no—
312C2×C4×C11—21no—
313C2×C4×C11—22no—
314C2×C4×C11—22no—
315C2×C4×C11—21no—
316C2×C4×C11—22no—
317C2×C4×C11—22no—
318C2×C4×C11—22no—
319C2×C4×C11—24no—
320C2×C4×C11—24no—
321C2×C4×C11—24no—
322C2×C4×C11—24no—
323C2×C4×C11—22no—
324C2×C4×C11—22no—
325C2×C4×C11—24no—
326C2×C4×C11C22×D412yes—
327C2×C4×C11C22×D412yes—
328C2×C4×C11C22×D412yes—
329C22⋊D11—48no—
330C2×Dic11—21no—
331C2×Dic11—22no—
332C2×Dic11—22no—
333C2×Dic11—21no—
334C2×Dic11—22no—
335C2×Dic11—22no—
336C2×Dic11—22no—
337C2×Dic11—24no—
338C2×Dic11—24no—
339C2×Dic11—24no—
340C2×Dic11—24no—
341C2×Dic11—22no—
342C2×Dic11—22no—
343C2×Dic11—24no—
344C2×Dic11C22×D412yes—
345C2×Dic11C22×D412yes—
346C2×Dic11C22×D412yes—
347D44—44no—
348C4×D11—28no—
349C4×D11—28no—
350C4×D11—28no—
351C4×D11—48no—
352C4×D11—48no—
353C4×D11—48no—
354C4×D11—416no—
355Dic22—48no—
356Dic22—44no—
357C23×Q8—111no—
358C23×D4—111no—
359C2×#125—112no—
360C2×#125—112no—
361C2×#125—111no—
362C2×#125—111no—
363C2×#125—111no—
364C2×#125—228no—
365C2×#125C2×D1111yescharacteristic, complemented
366C2×#124—111no—
367C2×#124—111no—
368C2×#124—112no—
369C2×#124—112no—
370C2×#124—111no—
371C2×#124—228no—
372C2×#124C2×D1111yescharacteristic
373C22×C4⋊C4—112no—
374C22×C4⋊C4—112no—
375C22×C4⋊C4—111no—
376C22×C4⋊C4—111no—
377C22×C4⋊C4—114no—
378C22×C4⋊C4—112no—
379C22×C22⋊C4—112no—
380C22×C22⋊C4—112no—
381C22×C22⋊C4—114no—
382C22×C22⋊C4—114no—
383C22×C42—111no—
384#399—114no—
385#399—112no—
386#399—114no—
387#399—112no—
388#399—112no—
389#399C2×D1112yescomplemented
390#397—112no—
391#397—114no—
392#397—112no—
393#397—112no—
394#397—114no—
395#397C2×D1112yescomplemented
396#396—114no—
397#396—114no—
398#396—114no—
399#396—114no—
400#396—114no—
401#396—114no—
402#396—114no—
403#396C2×D1114yescomplemented
404#395—112no—
405#395—114no—
406#395—112no—
407#395—114no—
408#395—112no—
409#395C2×D1112yescomplemented
410#394—112no—
411#394—112no—
412#394—114no—
413#394—114no—
414#394—112no—
415#394C2×D1112yes—
416#382—112no—
417#382—111no—
418#382—112no—
419#382—112no—
420#382C2×D1111yescharacteristic, complemented
421C2×#95—112no—
422C2×#95—114no—
423C2×#95—112no—
424C22×C11—42no—
425C22×C11—42no—
426C22×C11—42no—
427C22×C11—44no—
428C22×C11—44no—
429C22×C11C23×D411yescharacteristic
430C22×C11C2×H(5,𝔽2)12yes—
431C22×C11C2×H(5,𝔽2)11yescharacteristic
432C22×C11C2×2−1+412yes—
433C22×C11C2×2−1+411yescharacteristic
434C2×D11—42no—
435C2×D11—42no—
436C2×D11—42no—
437C2×D11—44no—
438C2×D11—44no—
439C2×D11—816no—
440C2×D11#53514yes—
441C2×D11#53614yes—
442C2×D11#53714yes—
443C2×D11#56218yes—
444C2×D11#56318yes—
445C4×C11—22no—
446C4×C11—22no—
447C4×C11—22no—
448C4×C11—42no—
449C4×C11—42no—
450C4×C11—42no—
451C4×C11—44no—
452Dic11—22no—
453Dic11—22no—
454Dic11—22no—
455Dic11—42no—
456Dic11—42no—
457Dic11—42no—
458Dic11—44no—
459C25—112no—
460C22×Q8—112no—
461C22×Q8—111no—
462C22×Q8—224no—
463C22×Q8—444no—
464C22×Q8C22×D1111yescharacteristic
465C22×D4—112no—
466C22×D4—111no—
467C22×D4—224no—
468C22×D4—444no—
469C22×D4C22×D1111yescharacteristic
470C23×C4—111no—
471C23×C4—111no—
472C23×C4—111no—
473C23×C4—112no—
474C23×C4—112no—
475C23×C4—112no—
476C23×C4—114no—
477#125—24no—
478#125—228no—
479#125—228no—
480#125—224no—
481#125—224no—
482#125—224no—
483#124—24no—
484#124—228no—
485#124—228no—
486#124—224no—
487#124—224no—
488#124—224no—
489C2×C4⋊C4—112no—
490C2×C4⋊C4—112no—
491C2×C4⋊C4—112no—
492C2×C4⋊C4—112no—
493C2×C4⋊C4—112no—
494C2×C4⋊C4—112no—
495C2×C4⋊C4—112no—
496C2×C4⋊C4—111no—
497C2×C4⋊C4—112no—
498C2×C4⋊C4—111no—
499C2×C4⋊C4—114no—
500C2×C4⋊C4—112no—
501C2×C4⋊C4—114no—
502C2×C4⋊C4—114no—
503C2×C4⋊C4—114no—
504C2×C4⋊C4—224no—
505C2×C4⋊C4—224no—
506C2×C4⋊C4—228no—
507C2×C4⋊C4—228no—
508C2×C4⋊C4—444no—
509C2×C4⋊C4—448no—
510C2×C4⋊C4C22×D1112yes—
511C2×C4⋊C4C22×D1112yes—
512C2×C4⋊C4C22×D1111yescharacteristic
513C2×C4⋊C4C22×D1111yescharacteristic
514C2×C4⋊C4C22×D1112yes—
515C2×C4⋊C4C22×D1114yes—
516C2×C22⋊C4—112no—
517C2×C22⋊C4—112no—
518C2×C22⋊C4—112no—
519C2×C22⋊C4—112no—
520C2×C22⋊C4—112no—
521C2×C22⋊C4—112no—
522C2×C22⋊C4—114no—
523C2×C22⋊C4—114no—
524C2×C22⋊C4—114no—
525C2×C22⋊C4—114no—
526C2×C22⋊C4—114no—
527C2×C22⋊C4—114no—
528C2×C22⋊C4—228no—
529C2×C22⋊C4—228no—
530C2×C22⋊C4—448no—
531C2×C22⋊C4—448no—
532C2×C22⋊C4C22×D1112yes—
533C2×C22⋊C4C22×D1112yes—
534C2×C22⋊C4C22×D1114yes—
535C2×C22⋊C4C22×D1114yes—
536C2×C42—111no—
537C2×C42—111no—
538C2×C42—111no—
539C2×C42—118no—
540C2×C42C22×D1111yescharacteristic
541#95—114no—
542#95—112no—
543#95—114no—
544#95—112no—
545#95—114no—
546#95—114no—
547#95—114no—
548#95C22×D1112yes—
549#95C22×D1112yes—
550#95C22×D1114yes—
551C2×C11—82no—
552C2×C11C2×#53511yescharacteristic
553C2×C11C2×#53611yescharacteristic
554C2×C11C2×#53711yescharacteristic
555C2×C11C2×#56212yes—
556C2×C11C2×#56312yes—
557D11—82no—
558D11#282018yesdirect product factor
559C24—111no—
560C24—112no—
561C24—224no—
562C24—224no—
563C24—228no—
564C24—228no—
565C24—224no—
566C24C23×D1112yes—
567C2×Q8—22no—
568C2×Q8—42no—
569C2×Q8—224no—
570C2×Q8—222no—
571C2×Q8—442no—
572C2×Q8—444no—
573C2×Q8—4416no—
574C2×D4—22no—
575C2×D4—42no—
576C2×D4—224no—
577C2×D4—222no—
578C2×D4—442no—
579C2×D4—4416no—
580C2×D4—444no—
581C22×C4—111no—
582C22×C4—111no—
583C22×C4—111no—
584C22×C4—114no—
585C22×C4—114no—
586C22×C4—114no—
587C22×C4—114no—
588C22×C4—112no—
589C22×C4—112no—
590C22×C4—112no—
591C22×C4—222no—
592C22×C4—224no—
593C22×C4—222no—
594C22×C4—224no—
595C22×C4—224no—
596C22×C4—224no—
597C22×C4—228no—
598C22×C4—228no—
599C22×C4—228no—
600C22×C4—224no—
601C22×C4—224no—
602C22×C4—228no—
603C22×C4—224no—
604C22×C4—228no—
605C22×C4C23×D1114yes—
606C22×C4C23×D1112yes—
607C22×C4C23×D1112yes—
608C22×C4C23×D1112yes—
609C22×C4C23×D1111yescharacteristic
610C22×C4C23×D1111yescharacteristic
611C22×C4C23×D1111yescharacteristic
612C4⋊C4—24no—
613C4⋊C4—22no—
614C4⋊C4—22no—
615C4⋊C4—24no—
616C4⋊C4—42no—
617C4⋊C4—44no—
618C4⋊C4—224no—
619C4⋊C4—224no—
620C4⋊C4—224no—
621C4⋊C4—224no—
622C4⋊C4—224no—
623C4⋊C4—224no—
624C4⋊C4—224no—
625C4⋊C4—224no—
626C4⋊C4—222no—
627C4⋊C4—222no—
628C4⋊C4—444no—
629C4⋊C4—444no—
630C4⋊C4—444no—
631C4⋊C4—442no—
632C4⋊C4—444no—
633C22⋊C4—24no—
634C22⋊C4—24no—
635C22⋊C4—44no—
636C22⋊C4—44no—
637C22⋊C4—224no—
638C22⋊C4—224no—
639C22⋊C4—224no—
640C22⋊C4—224no—
641C22⋊C4—224no—
642C22⋊C4—224no—
643C22⋊C4—444no—
644C22⋊C4—444no—
645C22⋊C4—444no—
646C22⋊C4—444no—
647C22⋊C4—444no—
648C22⋊C4—444no—
649C42—114no—
650C42—114no—
651C42—114no—
652C42D4×D1114yes—
653C11C2×#282011yescharacteristic, complemented, Sylow
654C23—22no—
655C23—22no—
656C23—24no—
657C23—24no—
658C23—22no—
659C23—112no—
660C23—114no—
661C23—112no—
662C23—114no—
663C23—112no—
664C23—222no—
665C23—222no—
666C23—224no—
667C23—224no—
668C23—222no—
669C23—448no—
670C23—448no—
671C23—448no—
672C23—4416no—
673C23—4416no—
674C23C24×D1111yescharacteristic
675Q8—44no—
676Q8—444no—
677Q8—448no—
678D4—44no—
679D4—444no—
680D4—448no—
681C2×C4—21no—
682C2×C4—22no—
683C2×C4—22no—
684C2×C4—21no—
685C2×C4—22no—
686C2×C4—22no—
687C2×C4—22no—
688C2×C4—22no—
689C2×C4—24no—
690C2×C4—24no—
691C2×C4—24no—
692C2×C4—24no—
693C2×C4—22no—
694C2×C4—24no—
695C2×C4—112no—
696C2×C4—112no—
697C2×C4—112no—
698C2×C4—228no—
699C2×C4—228no—
700C2×C4—228no—
701C2×C4—221no—
702C2×C4—222no—
703C2×C4—222no—
704C2×C4—221no—
705C2×C4—222no—
706C2×C4—222no—
707C2×C4—222no—
708C2×C4—222no—
709C2×C4—224no—
710C2×C4—224no—
711C2×C4—224no—
712C2×C4—224no—
713C2×C4—222no—
714C2×C4—224no—
715C2×C4—448no—
716C2×C4—448no—
717C2×C4—448no—
718C2×C4—4416no—
719C2×C4C2×D4×D1112yes—
720C2×C4C2×D4×D1112yes—
721C2×C4C2×D4×D1112yes—
722C22—42no—
723C22—42no—
724C22—42no—
725C22—44no—
726C22—44no—
727C22—114no—
728C22—114no—
729C22—114no—
730C22—118no—
731C22—118no—
732C22—442no—
733C22—442no—
734C22—442no—
735C22—444no—
736C22—444no—
737C22—8816no—
738C22C22×D4×D1111yescharacteristic
739C22D11×H(5,𝔽2)12yes—
740C22D11×H(5,𝔽2)11yescharacteristic
741C22D11×2−1+412yes—
742C22D11×2−1+411yescharacteristic
743C4—22no—
744C4—22no—
745C4—22no—
746C4—42no—
747C4—42no—
748C4—42no—
749C4—44no—
750C4—222no—
751C4—222no—
752C4—222no—
753C4—442no—
754C4—442no—
755C4—442no—
756C4—444no—
757C2—82no—
758C2—118no—
759C2—882no—
760C2D11×#53511yescharacteristic
761C2D11×#53611yescharacteristic
762C2D11×#53711yescharacteristic
763C2D11×#56212yes—
764C2D11×#56312yes—
subgroupG/H
center, FrattiniC23C24×D11
commutator, socle, cosocleC23×C11C25
FittingC11×#2820C2
prime radicalC22×D4×D11C22
hypercenter#2820D11
hypocenterC11C2×#2820
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C23 ◁ #2820

Complements

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

NH ≅ G/Ntype
1. C2×D11×#125C2semidirect
3. #13076672C2semidirect
4. #13076671C2semidirect
5. #13076670C2semidirect
6. #13076669C2semidirect
7. #13076668C2semidirect
8. #13076667C2semidirect
9. #13076666C2semidirect
10. #13076665C2semidirect
11. D11×#399C2semidirect
12. D11×#397C2semidirect
13. D11×#396C2semidirect
14. D11×#395C2semidirect
16. D11×#382C2semidirect
17. C11×#2820C2semidirect
20. C2×C11×#125C22semidirect
32. C2×#66943C22semidirect
33. C2×#66943C22semidirect
34. C2×#66942C22semidirect
35. C2×#66942C22semidirect
44. C2×#66923C22semidirect
45. C11×#399C22semidirect
46. C11×#397C22semidirect
47. C11×#396C22semidirect
48. C11×#395C22semidirect
50. C11×#382C22semidirect
51. #10622842C22semidirect
53. #10622607C22semidirect
54. #10622607C22semidirect
55. #10622607C22semidirect
56. #10622606C22semidirect
57. #10622605C22semidirect
58. #10622605C22semidirect
60. #10622592C22semidirect
61. #10622592C22semidirect
62. #10622590C22semidirect
65. #10622566C22semidirect
66. #10622565C22semidirect
67. #10622562C22semidirect
68. #10622562C22semidirect
69. #10622561C22semidirect
70. #10622561C22semidirect
71. #10622561C22semidirect
72. #10622549C22semidirect
73. #10622290C22semidirect
74. #10622289C22semidirect
75. #10622288C22semidirect
76. #10622287C22semidirect
81. #10622269C22semidirect
82. #10622269C22semidirect
83. #10622263C22semidirect
84. #10622263C22semidirect
282. #2820D11direct (N × H)
365. C2×#125C2×D11semidirect
389. #399C2×D11semidirect
395. #397C2×D11semidirect
403. #396C2×D11semidirect
409. #395C2×D11semidirect
420. #382C2×D11semidirect
558. D11#2820direct (N × H)
653. C11C2×#2820semidirect

Maximal subgroups

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

subgroupindex
C2×D11×#1252
C2×D11×#1242
#130766722
#130766712
#130766702
#130766692
#130766682
#130766672
#130766662
#130766652
D11×#3992
D11×#3972
D11×#3962
D11×#3952
D11×#3942
D11×#3822
C11×#28202
C2×#282011