Finite Group Databasebeta

← #14916576

Subgroups — #14916576

Order 2816.

2954 conjugacy classes of subgroups.

The subgroup lattice has 768 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#66992C211yesmaximal, characteristic
2#13071774C214yesmaximal, complemented
3#13071657C214yesmaximal, complemented
4#13071480C212yesmaximal, complemented
5#13071461C212yesmaximal, complemented
6#13071458C212yesmaximal, complemented
7C22⋊C4×C22⋊D11C212yesmaximal, complemented
8#13071382C214yesmaximal, complemented
9#13071306C214yesmaximal, complemented
10#13071198C211yesmaximal, characteristic, complemented
11#13071197C211yesmaximal, characteristic, complemented
12#13071192C211yesmaximal, characteristic, complemented
13#13070994C211yesmaximal, characteristic, complemented
14#13070994C211yesmaximal, characteristic, complemented
15C11×#2308C211yesmaximal, characteristic, complemented
16C23×D4×C11C2211yescharacteristic
17C23×C22⋊D11C2211yescharacteristic
18C23×C22⋊D11C2211yescharacteristic
19C24×Dic11C2211yescharacteristic
20C22×C11×C22⋊C4C2212yes—
21C22×C22⋊Dic11C2211yescharacteristic
22C2×#66992C4116yescomplemented
23C2×#66992C2212yes—
24C2×#66992C2212yes—
25C2×#66992C2212yes—
26C2×#66992C2212yes—
27C2×C4×C22⋊D11C2214yescomplemented
28C22×(C2×D11)⋊C4C2211yescharacteristic
29C2×#66979C2212yes—
30C22×Dic11⋊C4C2211yescharacteristic
31C2×C22⋊C4×D11C2212yes—
32C2×#66930C2212yes—
33C2×#66930C2212yescomplemented
34C2×#66930C2212yescomplemented
35C11×#386C2214yescomplemented
36C11×#386C2214yescomplemented
37C11×#381C2212yes—
38C11×#379C2211yescharacteristic
39C11×#379C2211yescharacteristic
40#10622860C2212yes—
41#10622860C2211yescharacteristic
42#10622860C2211yescharacteristic
43#10622834C2214yescomplemented
44#10622834C2214yescomplemented
45#10622826C2214yescomplemented
46#10622823C2214yescomplemented
47C4×C22⋊Dic11C2214yescomplemented
48#10622570C2214yescomplemented
49#10622570C2214yescomplemented
50#10622570C2214yescomplemented
51#10622569C2214yescomplemented
52#10622569C2214yescomplemented
53#10622569C2214yescomplemented
54#10622568C2212yes—
55#10622558C2214yescomplemented
56#10622557C2214yescomplemented
57#10622556C2212yes—
58#10622556C2212yescomplemented
59#10622556C2212yescomplemented
60#10622555C2212yes—
61#10622555C2212yes—
62#10622555C2212yescomplemented
63#10622555C2212yescomplemented
64C22⋊C4×Dic11C2212yes—
65C22⋊C4×Dic11C2212yes—
66C22⋊C4×Dic11C2212yescomplemented
67C22⋊C4×Dic11C2212yescomplemented
68#10622283C2214yescomplemented
69#10622282C2214yescomplemented
70#10622281C2214yescomplemented
71#10622279C2214yescomplemented
72#10622268C2214yescomplemented
73#10622265C2214yescomplemented
74#10622262C2214yescomplemented
75#10622260C2214yescomplemented
76C25×C11C2311yescharacteristic
77C25×C11C2311yescharacteristic
78C24×D11C2311yescharacteristic
79C22×D4×C11—44no—
80C22×D4×C11C2×C418yescomplemented
81C22×D4×C11C2312yes—
82C22×D4×C11C2312yes—
83C23×C4×C11C2311yescharacteristic
84C23×C4×C11C2314yes—
85C22×C22⋊D11—44no—
86C22×C22⋊D11—44no—
87C22×C22⋊D11C2×C418yes—
88C22×C22⋊D11C2×C418yescomplemented
89C22×C22⋊D11C2312yes—
90C22×C22⋊D11C2312yes—
91C22×C22⋊D11C2312yes—
92C22×C22⋊D11C2312yes—
93C23×Dic11—44no—
94C23×Dic11C2×C418yescomplemented
95C23×Dic11C2311yescharacteristic
96C23×Dic11C2311yescharacteristic
97C23×Dic11C2311yescharacteristic
98C23×Dic11C2311yescharacteristic
99C23×Dic11C2311yescharacteristic
100C23×Dic11C2311yescharacteristic
101C23×Dic11C2311yescharacteristic
102C22×C4×D11C2314yes—
103C2×C11×C22⋊C4—44no—
104C2×C11×C22⋊C4C2312yes—
105C2×C11×C22⋊C4C2312yes—
106C2×C11×C22⋊C4C2312yes—
107C2×C11×C22⋊C4C2312yes—
108C2×C11×C22⋊C4C2312yes—
109C2×C11×C22⋊C4C2312yes—
110C2×C11×C22⋊C4C2314yes—
111C2×C22⋊Dic11C2×C418yescomplemented
112C2×C22⋊Dic11C2312yes—
113C2×C22⋊Dic11C2312yes—
114C2×C22⋊Dic11C2312yes—
115C2×C22⋊Dic11C2312yes—
116C2×C22⋊Dic11C2314yes—
117C2×C22⋊Dic11C2312yes—
118C2×C22⋊Dic11C2312yes—
119C2×C22⋊Dic11C2314yes—
120C2×C22⋊Dic11C2312yes—
121C2×C22⋊Dic11C2312yes—
122#66992C2×C4116yescomplemented
123#66992C2×C4116yescomplemented
124#66992C2×C4116yescomplemented
125#66992C2×C4116yescomplemented
126C4×C22⋊D11—48no—
127C2×(C2×D11)⋊C4C2×C418yescomplemented
128C2×(C2×D11)⋊C4C2314yes—
129C2×(C2×D11)⋊C4C2314yes—
130C2×(C2×D11)⋊C4C2314yes—
131C2×(C2×D11)⋊C4C2312yes—
132C2×(C2×D11)⋊C4C2312yes—
133#66979—44no—
134C2×C4⋊Dic11C2314yes—
135C2×Dic11⋊C4C2×C418yescomplemented
136C2×Dic11⋊C4C2314yes—
137C2×Dic11⋊C4C2314yes—
138C2×Dic11⋊C4C2314yes—
139C2×Dic11⋊C4C2312yes—
140C2×Dic11⋊C4C2312yes—
141C2×C4×Dic11C2314yes—
142C2×C4×Dic11C2314yes—
143C2×C4×Dic11C2314yes—
144C2×C4×Dic11C2314yes—
145C22⋊C4×D11—44no—
146#66930—44no—
147#66930—44no—
148#66930—44no—
149C11×#95C2314yes—
150C11×#95C2314yes—
151C11⋊#95C2314yes—
152C11⋊#95C2314yes—
153C11⋊#95C2314yes—
154C11⋊#95C2314yes—
155C11⋊#95C2314yes—
156C11⋊#95C2314yes—
157#34363—111nomaximal, Sylow
158C24×C11—24no—
159C24×C11—24no—
160C24×C11—42no—
161C24×C11—42no—
162C24×C11—42no—
163C24×C11—42no—
164C24×C11C22×C414yes—
165C24×C11C22×C414yes—
166C24×C11C2412yes—
167C24×C11C2411yescharacteristic
168C24×C11C2411yescharacteristic
169C24×C11C2411yescharacteristic
170C23×D11—24no—
171C23×D11—42no—
172C23×D11—42no—
173C23×D11C22×C414yes—
174C23×D11C2412yes—
175C2×D4×C11—416no—
176C2×D4×C11—42no—
177C2×D4×C11—42no—
178C2×D4×C11—42no—
179C2×D4×C11—42no—
180C2×D4×C11C22×C418yes—
181C2×D4×C11C22×C418yes—
182C22×C4×C11—24no—
183C22×C4×C11—44no—
184C22×C4×C11—44no—
185C22×C4×C11—44no—
186C22×C4×C11C22×C414yes—
187C22×C4×C11C2414yes—
188C22×C4×C11C2414yes—
189C22×C4×C11C2412yes—
190C2×C22⋊D11—28no—
191C2×C22⋊D11—416no—
192C2×C22⋊D11—42no—
193C2×C22⋊D11—42no—
194C2×C22⋊D11—44no—
195C2×C22⋊D11—42no—
196C2×C22⋊D11—42no—
197C2×C22⋊D11—416no—
198C2×C22⋊D11C22×C418yes—
199C2×C22⋊D11C22×C418yes—
200C2×C22⋊D11C22×C418yes—
201C2×C22⋊D11C22×C418yes—
202C22×Dic11—24no—
203C22×Dic11—24no—
204C22×Dic11—24no—
205C22×Dic11—24no—
206C22×Dic11—42no—
207C22×Dic11—42no—
208C22×Dic11—42no—
209C22×Dic11—416no—
210C22×Dic11C22×C414yes—
211C22×Dic11C22×C414yes—
212C22×Dic11C22×C414yes—
213C22×Dic11C22×C414yes—
214C22×Dic11C22×C414yes—
215C22×Dic11C22×C414yes—
216C22×Dic11C22×C414yes—
217C22×Dic11C2414yes—
218C22×Dic11C2414yes—
219C22×Dic11C2411yescharacteristic
220C22×Dic11C2411yescharacteristic
221C22×Dic11C2412yes—
222C22×Dic11C2411yescharacteristic
223C22×Dic11C2411yescharacteristic
224C2×C4×D11—44no—
225C2×C4×D11—44no—
226C2×C4×D11—44no—
227C11×C22⋊C4—24no—
228C11×C22⋊C4—24no—
229C11×C22⋊C4—42no—
230C11×C22⋊C4—42no—
231C11×C22⋊C4—44no—
232C11×C22⋊C4—42no—
233C11×C22⋊C4—42no—
234C22⋊Dic11—24no—
235C22⋊Dic11—24no—
236C22⋊Dic11—42no—
237C22⋊Dic11—42no—
238C22⋊Dic11—44no—
239C22⋊Dic11—42no—
240C22⋊Dic11—42no—
241C22⋊Dic11—44no—
242C22⋊Dic11C22×C418yes—
243C22⋊Dic11C22×C418yes—
244(C2×D11)⋊C4—44no—
245(C2×D11)⋊C4—44no—
246(C2×D11)⋊C4—44no—
247(C2×D11)⋊C4C22×C418yes—
248(C2×D11)⋊C4C22×C418yes—
249C4⋊Dic11—44no—
250Dic11⋊C4—28no—
251Dic11⋊C4—44no—
252Dic11⋊C4—44no—
253Dic11⋊C4C22×C418yes—
254Dic11⋊C4C22×C418yes—
255C4×Dic11—28no—
256C4×Dic11—44no—
257C4×Dic11—44no—
258C4×Dic11—44no—
259C22×#121—111no—
260#2377—114no—
261#2363—114no—
262#2344—112no—
263#2342—112no—
264#2342—112no—
265D4×C22⋊C4—112no—
266#2333—114no—
267#2324—114no—
268#2309—111no—
269#2309—111no—
270#2308—111no—
271#2308D1111yescharacteristic, complemented
272#2280—111no—
273#2280—111no—
274C23×C11—22no—
275C23×C11—22no—
276C23×C11—28no—
277C23×C11—22no—
278C23×C11—22no—
279C23×C11—24no—
280C23×C11—22no—
281C23×C11—22no—
282C23×C11—22no—
283C23×C11—22no—
284C23×C11—22no—
285C23×C11—22no—
286C23×C11—24no—
287C23×C11—28no—
288C23×C11—44no—
289C23×C11—44no—
290C23×C11—44no—
291C23×C11—44no—
292C23×C11—416no—
293C23×C11—88no—
294C23×C11C23×C414yes—
295C23×C11C23×C412yes—
296C23×C11C23×C412yes—
297C23×C11C23×C412yes—
298C23×C11H(5,𝔽2)14yes—
299C23×C11C2511yescharacteristic
300C22×D11—22no—
301C22×D11—24no—
302C22×D11—22no—
303C22×D11—24no—
304C22×D11—28no—
305C22×D11—44no—
306C22×D11—44no—
307C22×D11—88no—
308C22×D11C23×C414yes—
309D4×C11—48no—
310D4×C11—48no—
311C2×C4×C11—28no—
312C2×C4×C11—22no—
313C2×C4×C11—22no—
314C2×C4×C11—24no—
315C2×C4×C11—24no—
316C2×C4×C11—24no—
317C2×C4×C11—24no—
318C2×C4×C11—24no—
319C2×C4×C11—24no—
320C2×C4×C11—88no—
321C2×C4×C11C23×C414yes—
322C22⋊D11—216no—
323C22⋊D11—48no—
324C22⋊D11—48no—
325C22⋊D11—48no—
326C2×Dic11—28no—
327C2×Dic11—22no—
328C2×Dic11—22no—
329C2×Dic11—22no—
330C2×Dic11—22no—
331C2×Dic11—22no—
332C2×Dic11—28no—
333C2×Dic11—28no—
334C2×Dic11—28no—
335C2×Dic11—24no—
336C2×Dic11—24no—
337C2×Dic11—24no—
338C2×Dic11—24no—
339C2×Dic11—24no—
340C2×Dic11—24no—
341C2×Dic11—44no—
342C2×Dic11—44no—
343C2×Dic11—44no—
344C2×Dic11C23×C414yes—
345C2×Dic11C23×C412yes—
346C2×Dic11C23×C412yes—
347C2×Dic11C23×C412yes—
348C2×Dic11C23×C412yes—
349C2×Dic11H(5,𝔽2)14yes—
350C4×D11—88no—
351C23×D4—111no—
352C23×D4—111no—
353C23×D4C2×D1111yescharacteristic
354C24×C4—111no—
355C2×#121—112no—
356C2×#121—112no—
357C2×#121—112no—
358C2×#121—112no—
359C2×#121—1116no—
360C2×C4×D4—114no—
361C2×#117—112no—
362C2×#117—112no—
363C2×#117—112no—
364C2×#117—112no—
365C22×C4⋊C4—111no—
366C22×C22⋊C4—111no—
367C22×C22⋊C4—111no—
368C22×C22⋊C4—112no—
369C22×C22⋊C4C2×D1112yes—
370#390—114no—
371#390—114no—
372#390—114no—
373#390—114no—
374#390—114no—
375#389—114no—
376#388—114no—
377#388—114no—
378#388—114no—
379#388—114no—
380#387—114no—
381#387—114no—
382#386—114no—
383#386—114no—
384#386—114no—
385#386—114no—
386#386C2×D1114yescomplemented
387#386C2×D1114yescomplemented
388#385—114no—
389#385—114no—
390#381—112no—
391#381—112no—
392#381—112no—
393#381C2×D1112yes—
394#380—112no—
395#380—112no—
396#380—112no—
397#380—112no—
398#379—111no—
399#379—111no—
400#379—112no—
401#379—112no—
402#379C2×D1111yescharacteristic
403#379C2×D1111yescharacteristic
404C4×C4⋊C4—114no—
405C4×C22⋊C4—114no—
406C4×C22⋊C4—112no—
407C4×C22⋊C4—112no—
408C4×C22⋊C4—112no—
409C4×C22⋊C4—112no—
410C4×C22⋊C4—114no—
411C22×C11—22no—
412C22×C11—22no—
413C22×C11—28no—
414C22×C11—24no—
415C22×C11—22no—
416C22×C11—22no—
417C22×C11—22no—
418C22×C11—22no—
419C22×C11—24no—
420C22×C11—22no—
421C22×C11—22no—
422C22×C11—24no—
423C22×C11—416no—
424C22×C11—44no—
425C22×C11—44no—
426C22×C11—44no—
427C22×C11—44no—
428C22×C11—88no—
429C22×C11#51814yes—
430C22×C11C24×C411yescharacteristic
431C22×C11C2×H(5,𝔽2)12yes—
432C22×C11C2×H(5,𝔽2)12yes—
433C22×C11#58512yes—
434C2×D11—24no—
435C2×D11—24no—
436C2×D11—24no—
437C2×D11—44no—
438C2×D11—44no—
439C2×D11—88no—
440C4×C11—24no—
441C4×C11—44no—
442C4×C11—44no—
443Dic11—22no—
444Dic11—22no—
445Dic11—22no—
446Dic11—24no—
447Dic11—44no—
448Dic11—44no—
449Dic11#51814yes—
450C25—111no—
451C25C22×D1111yescharacteristic
452C25C22×D1111yescharacteristic
453C22×D4—44no—
454C22×D4—112no—
455C22×D4—118no—
456C22×D4—118no—
457C22×D4—112no—
458C22×D4—112no—
459C22×D4—112no—
460C22×D4—444no—
461C22×D4—444no—
462C22×D4C4×D1118yescomplemented
463C22×D4C22×D1112yes—
464C22×D4C22×D1112yes—
465C23×C4—111no—
466C23×C4—111no—
467C23×C4—111no—
468C23×C4—111no—
469C23×C4—118no—
470C23×C4—111no—
471C23×C4—111no—
472C23×C4—111no—
473C23×C4—114no—
474C23×C4—444no—
475C23×C4C22×D1111yescharacteristic
476C23×C4C22×D1114yes—
477#121—1116no—
478#121—1116no—
479#121—1116no—
480#121—1116no—
481C4×D4—448no—
482#117—444no—
483#117—444no—
484#117—444no—
485#117—444no—
486C2×C4⋊C4—118no—
487C2×C4⋊C4—112no—
488C2×C4⋊C4—112no—
489C2×C4⋊C4—114no—
490C2×C4⋊C4—114no—
491C2×C4⋊C4—114no—
492C2×C4⋊C4—114no—
493C2×C22⋊C4—44no—
494C2×C22⋊C4—118no—
495C2×C22⋊C4—112no—
496C2×C22⋊C4—112no—
497C2×C22⋊C4—118no—
498C2×C22⋊C4—112no—
499C2×C22⋊C4—112no—
500C2×C22⋊C4—112no—
501C2×C22⋊C4—112no—
502C2×C22⋊C4—112no—
503C2×C22⋊C4—112no—
504C2×C22⋊C4—114no—
505C2×C22⋊C4—112no—
506C2×C22⋊C4—112no—
507C2×C22⋊C4—114no—
508C2×C22⋊C4—114no—
509C2×C22⋊C4—114no—
510C2×C22⋊C4—114no—
511C2×C22⋊C4—444no—
512C2×C22⋊C4C22×D1112yes—
513C2×C22⋊C4C22×D1112yes—
514C2×C22⋊C4C22×D1114yes—
515C2×C22⋊C4C22×D1112yes—
516C2×C22⋊C4C22×D1112yes—
517C2×C22⋊C4C22×D1112yes—
518C2×C22⋊C4C22×D1112yes—
519C2×C42—114no—
520C2×C42—114no—
521C2×C42—114no—
522C2×C42—114no—
523#95—114no—
524#95—114no—
525#95—114no—
526#95—114no—
527#95—114no—
528#95—114no—
529#95C22×D1114yes—
530#95C22×D1114yes—
531C2×C11—24no—
532C2×C11—42no—
533C2×C11—42no—
534C2×C11—44no—
535C2×C11C2×#51811yescharacteristic
536C2×C11C2×#51811yescharacteristic
537C2×C11#342811yescharacteristic
538C2×C11#354214yes—
539D11—44no—
540C24—24no—
541C24—24no—
542C24—42no—
543C24—42no—
544C24—42no—
545C24—42no—
546C24—112no—
547C24—114no—
548C24—224no—
549C24—442no—
550C24—442no—
551C24C2×C4×D1114yes—
552C24C2×C4×D1114yes—
553C24C23×D1112yes—
554C24C23×D1111yescharacteristic
555C24C23×D1111yescharacteristic
556C24C23×D1111yescharacteristic
557C2×D4—42no—
558C2×D4—42no—
559C2×D4—42no—
560C2×D4—42no—
561C2×D4—416no—
562C2×D4—118no—
563C2×D4—118no—
564C2×D4—118no—
565C2×D4—118no—
566C2×D4—228no—
567C2×D4—4416no—
568C2×D4—4416no—
569C2×D4—442no—
570C2×D4—442no—
571C2×D4—442no—
572C2×D4—442no—
573C2×D4—444no—
574C2×D4C2×C4×D1118yes—
575C2×D4C2×C4×D1118yes—
576C22×C4—24no—
577C22×C4—44no—
578C22×C4—44no—
579C22×C4—44no—
580C22×C4—111no—
581C22×C4—114no—
582C22×C4—114no—
583C22×C4—114no—
584C22×C4—114no—
585C22×C4—111no—
586C22×C4—111no—
587C22×C4—112no—
588C22×C4—111no—
589C22×C4—114no—
590C22×C4—114no—
591C22×C4—114no—
592C22×C4—114no—
593C22×C4—114no—
594C22×C4—224no—
595C22×C4—224no—
596C22×C4—224no—
597C22×C4—224no—
598C22×C4—444no—
599C22×C4—444no—
600C22×C4—444no—
601C22×C4—4416no—
602C22×C4—442no—
603C22×C4—442no—
604C22×C4—442no—
605C22×C4C2×C4×D1114yes—
606C22×C4C23×D1114yes—
607C22×C4C23×D1114yes—
608C22×C4C23×D1112yes—
609C4⋊C4—118no—
610C4⋊C4—118no—
611C4⋊C4—228no—
612C4⋊C4—444no—
613C4⋊C4—444no—
614C4⋊C4—444no—
615C22⋊C4—24no—
616C22⋊C4—24no—
617C22⋊C4—44no—
618C22⋊C4—42no—
619C22⋊C4—42no—
620C22⋊C4—42no—
621C22⋊C4—42no—
622C22⋊C4—118no—
623C22⋊C4—118no—
624C22⋊C4—118no—
625C22⋊C4—118no—
626C22⋊C4—224no—
627C22⋊C4—224no—
628C22⋊C4—444no—
629C22⋊C4—444no—
630C22⋊C4—444no—
631C22⋊C4—442no—
632C22⋊C4—442no—
633C22⋊C4—444no—
634C22⋊C4—442no—
635C22⋊C4—444no—
636C22⋊C4—442no—
637C42—228no—
638C42—444no—
639C42—444no—
640C42—444no—
641C11#3436311yescharacteristic, complemented, Sylow
642C23—22no—
643C23—22no—
644C23—28no—
645C23—22no—
646C23—22no—
647C23—22no—
648C23—22no—
649C23—22no—
650C23—22no—
651C23—24no—
652C23—22no—
653C23—22no—
654C23—24no—
655C23—28no—
656C23—44no—
657C23—44no—
658C23—44no—
659C23—44no—
660C23—416no—
661C23—88no—
662C23—114no—
663C23—222no—
664C23—222no—
665C23—224no—
666C23—224no—
667C23—228no—
668C23—444no—
669C23—444no—
670C23—888no—
671C23C22×C4×D1114yes—
672C23C22×C4×D1112yes—
673C23C22×C4×D1112yes—
674C23C22×C4×D1112yes—
675C23#6703714yes—
676C23C24×D1111yescharacteristic
677D4—48no—
678D4—48no—
679D4—2216no—
680D4—448no—
681D4—448no—
682D4—448no—
683C2×C4—28no—
684C2×C4—22no—
685C2×C4—22no—
686C2×C4—24no—
687C2×C4—24no—
688C2×C4—24no—
689C2×C4—24no—
690C2×C4—24no—
691C2×C4—24no—
692C2×C4—88no—
693C2×C4—112no—
694C2×C4—114no—
695C2×C4—112no—
696C2×C4—112no—
697C2×C4—114no—
698C2×C4—112no—
699C2×C4—228no—
700C2×C4—228no—
701C2×C4—228no—
702C2×C4—228no—
703C2×C4—222no—
704C2×C4—222no—
705C2×C4—222no—
706C2×C4—222no—
707C2×C4—222no—
708C2×C4—224no—
709C2×C4—224no—
710C2×C4—224no—
711C2×C4—224no—
712C2×C4—224no—
713C2×C4—224no—
714C2×C4—444no—
715C2×C4—444no—
716C2×C4—444no—
717C2×C4—888no—
718C2×C4C22×C4×D1114yes—
719C22—28no—
720C22—22no—
721C22—22no—
722C22—22no—
723C22—22no—
724C22—24no—
725C22—22no—
726C22—22no—
727C22—24no—
728C22—22no—
729C22—22no—
730C22—24no—
731C22—416no—
732C22—44no—
733C22—44no—
734C22—44no—
735C22—44no—
736C22—88no—
737C22—224no—
738C22—224no—
739C22—224no—
740C22—444no—
741C22—444no—
742C22—888no—
743C22#1062301714yes—
744C22C23×C4×D1111yescharacteristic
745C22C2×#6703712yes—
746C22D11×H(5,𝔽2)12yes—
747C22#1062345512yes—
748C4—24no—
749C4—44no—
750C4—44no—
751C4—114no—
752C4—222no—
753C4—222no—
754C4—222no—
755C4—224no—
756C4—444no—
757C4—444no—
758C2—24no—
759C2—42no—
760C2—42no—
761C2—44no—
762C2—444no—
763C2D11×#51811yescharacteristic
764C2C2×#1062301711yescharacteristic
765C2#1308181411yescharacteristic
766C2#1308292714yes—
subgroupG/H
center, FrattiniC23C24×D11
commutatorC22×C11C24×C4
FittingC11×#2308C2
socle, cosocleC23×C11C25
prime radicalC22×#66992C2
hypercenter#2308D11
hypocenterC11#34363
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ #2308

Complements

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

NH ≅ G/Ntype
2. #13071774C2semidirect
3. #13071657C2semidirect
4. #13071480C2semidirect
5. #13071461C2semidirect
6. #13071458C2semidirect
7. C22⋊C4×C22⋊D11C2semidirect
8. #13071382C2semidirect
9. #13071306C2semidirect
10. #13071198C2semidirect
11. #13071197C2semidirect
12. #13071192C2semidirect
13. #13070994C2semidirect
14. #13070994C2semidirect
15. C11×#2308C2semidirect
22. C2×#66992C4semidirect
27. C2×C4×C22⋊D11C22semidirect
33. C2×#66930C22semidirect
34. C2×#66930C22semidirect
35. C11×#386C22semidirect
36. C11×#386C22semidirect
43. #10622834C22semidirect
44. #10622834C22semidirect
45. #10622826C22semidirect
46. #10622823C22semidirect
47. C4×C22⋊Dic11C22semidirect
48. #10622570C22semidirect
49. #10622570C22semidirect
50. #10622570C22semidirect
51. #10622569C22semidirect
52. #10622569C22semidirect
53. #10622569C22semidirect
55. #10622558C22semidirect
56. #10622557C22semidirect
58. #10622556C22semidirect
59. #10622556C22semidirect
62. #10622555C22semidirect
63. #10622555C22semidirect
66. C22⋊C4×Dic11C22semidirect
67. C22⋊C4×Dic11C22semidirect
68. #10622283C22semidirect
69. #10622282C22semidirect
70. #10622281C22semidirect
71. #10622279C22semidirect
72. #10622268C22semidirect
73. #10622265C22semidirect
74. #10622262C22semidirect
75. #10622260C22semidirect
80. C22×D4×C11C2×C4semidirect
88. C22×C22⋊D11C2×C4semidirect
94. C23×Dic11C2×C4semidirect
111. C2×C22⋊Dic11C2×C4semidirect
122. #66992C2×C4semidirect
123. #66992C2×C4semidirect
124. #66992C2×C4semidirect
125. #66992C2×C4semidirect
127. C2×(C2×D11)⋊C4C2×C4semidirect
135. C2×Dic11⋊C4C2×C4semidirect
271. #2308D11semidirect
386. #386C2×D11semidirect
387. #386C2×D11semidirect
462. C22×D4C4×D11semidirect
641. C11#34363semidirect

Maximal subgroups

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

subgroupindex
C22×#669922
#130717742
#130716572
#130714802
#130714612
#130714582
C22⋊C4×C22⋊D112
#130713822
#130713062
#130711982
#130711972
#130711922
#130709942
C11×#23082
#3436311