Finite Group Databasebeta

← #14915029

Subgroups — #14915029

Order 2816.

3578 conjugacy classes of subgroups.

The subgroup lattice has 782 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623335C211yesmaximal, characteristic
2C2×#10623329C211yesmaximal, characteristic, complemented
3C2×#10623017C211yesmaximal, characteristic, complemented
4#13071614C214yesmaximal, complemented
5#13071604C214yesmaximal, complemented
6#13071596C214yesmaximal, complemented
7#13071595C214yesmaximal, complemented
8#13071317C214yesmaximal, complemented
9#13071228C211yesmaximal, characteristic, complemented
10#13071126C214yesmaximal, complemented
11C2×#10622826C211yesmaximal, characteristic, complemented
12C2×C4×C22⋊Dic11C211yesmaximal, characteristic, complemented
13C2×C11×#386C211yesmaximal, characteristic, complemented
14C23×D4×C11C2211yescharacteristic
15C24×C4×C11C2211yescharacteristic
16C23×C22⋊D11C2211yescharacteristic
17C22×C11×C22⋊C4C2211yescharacteristic
18C22×C11×C22⋊C4C2212yescomplemented
19C2×#67006C2212yes—
20C22×C22⋊Dic11C2211yescharacteristic
21C22×C22⋊Dic11C2211yescharacteristic
22C22×C22⋊Dic11C2211yescharacteristic
23C22×C22⋊Dic11C2212yescomplemented
24#10623335C4116yescomplemented
25C2×#66992C2214yes—
26C2×#66990C2212yes—
27#10623329—28no—
28C2×#66988C2212yes—
29C2×D4×Dic11C2214yes—
30C2×D4×Dic11C2214yescomplemented
31C2×#66982C2212yes—
32C2×C4×C22⋊D11C2214yes—
33C22×(C2×D11)⋊C4C2212yescomplemented
34C2×#66979C2212yescomplemented
35C22×C4×Dic11C2212yescomplemented
36#10623017—28no—
37C2×(C22⋊D11)⋊C4C2214yescomplemented
38C2×(C22⋊D11)⋊C4C2214yescomplemented
39C2×C22⋊C4×D11C2212yescomplemented
40C2×#66930C2212yescomplemented
41C11×#386C2214yes—
42C11×#386C2212yescomplemented
43C11×#386C2212yescomplemented
44C2×C11×#95C2212yescomplemented
45#10622826C2214yes—
46#10622826C2212yescomplemented
47#10622826C2212yescomplemented
48#10622823C2214yescomplemented
49C4×C22⋊Dic11C2214yescomplemented
50C4×C22⋊Dic11C2214yescomplemented
51C2×C11⋊#95C2212yescomplemented
52C2×C11⋊#95C2212yescomplemented
53#10622571C2214yescomplemented
54#10622570C2214yescomplemented
55#10622569C2214yescomplemented
56#10622559C2214yescomplemented
57#10622559C2214yescomplemented
58#10622558C2214yescomplemented
59#10622557C2214yescomplemented
60#10622555C2214yescomplemented
61C22⋊C4×Dic11C2214yescomplemented
62#10622283C2214yescomplemented
63#10622282C2214yescomplemented
64#10622281C2214yescomplemented
65#10622279C2214yescomplemented
66#10622268C2214yescomplemented
67#10622265C2214yescomplemented
68#10622262C2214yescomplemented
69#10622260C2214yescomplemented
70C25×C11C2311yescharacteristic
71C25×C11C2311yescharacteristic
72C24×D11C2311yescharacteristic
73C22×D4×C11—24no—
74C22×D4×C11—24no—
75C22×D4×C11C2×C418yescomplemented
76C22×D4×C11C2312yes—
77C22×D4×C11C2312yes—
78C23×C4×C11—24no—
79C23×C4×C11—44no—
80C23×C4×C11C2311yescharacteristic
81C23×C4×C11C2312yes—
82C23×C4×C11C2312yes—
83C23×C4×C11C2311yescharacteristic
84C23×C4×C11C2312yes—
85C23×C4×C11C2311yescharacteristic
86C22×C22⋊D11—24no—
87C22×C22⋊D11—24no—
88C22×C22⋊D11C2×C418yescomplemented
89C22×C22⋊D11C2312yes—
90C22×C22⋊D11C2312yes—
91C22×C22⋊D11C2314yes—
92C23×Dic11C2311yescharacteristic
93C23×Dic11C2314yes—
94C23×Dic11C2312yes—
95C23×Dic11C2312yes—
96C23×Dic11C2312yes—
97C22×C4×D11C2314yes—
98C2×C11×C22⋊C4—24no—
99C2×C11×C22⋊C4—44no—
100C2×C11×C22⋊C4C2312yes—
101C2×C11×C22⋊C4C2312yes—
102C2×C11×C22⋊C4C2314yes—
103C2×C11×C22⋊C4C2314yes—
104#67006C2×C4116yescomplemented
105C2×C22⋊Dic11—24no—
106C2×C22⋊Dic11—28no—
107C2×C22⋊Dic11C2×C418yescomplemented
108C2×C22⋊Dic11D418yescomplemented
109C2×C22⋊Dic11C2312yes—
110C2×C22⋊Dic11C2312yes—
111C2×C22⋊Dic11C2314yes—
112C2×C22⋊Dic11C2312yes—
113C2×C22⋊Dic11C2312yes—
114C2×C22⋊Dic11C2314yes—
115C2×C22⋊Dic11C2312yes—
116C2×C22⋊Dic11C2312yes—
117#66992C2×C4132yescomplemented
118#66990C2×C4116yescomplemented
119#66988C2×C4116yescomplemented
120D4×Dic11—216no—
121D4×Dic11—216no—
122#66982C2×C4116yescomplemented
123C4×C22⋊D11—216no—
124C2×(C2×D11)⋊C4—44no—
125C2×(C2×D11)⋊C4C2314yes—
126C2×(C2×D11)⋊C4C2314yes—
127C2×(C2×D11)⋊C4C2314yes—
128C2×(C2×D11)⋊C4C2314yes—
129#66979—28no—
130C2×C4⋊Dic11C2314yes—
131C2×Dic11⋊C4C2314yes—
132C2×Dic11⋊C4C2314yes—
133C2×Dic11⋊C4C2314yes—
134C2×Dic11⋊C4C2314yes—
135C2×C4×Dic11—44no—
136C2×C4×Dic11C2314yes—
137C2×C4×Dic11C2314yes—
138C2×C4×Dic11C2314yes—
139C2×C4×Dic11C2314yes—
140(C22⋊D11)⋊C4—216no—
141(C22⋊D11)⋊C4—48no—
142C22⋊C4×D11—28no—
143#66930—28no—
144C11×#95C2314yes—
145C11×#95C2314yes—
146C11⋊#95C2314yes—
147C11⋊#95C2314yes—
148C11⋊#95C2314yes—
149C11⋊#95C2314yes—
150C11⋊#95C2314yes—
151C11⋊#95C2314yes—
152#34273—111nomaximal, Sylow
153C24×C11—22no—
154C24×C11—22no—
155C24×C11—42no—
156C24×C11—42no—
157C24×C11—42no—
158C24×C11—42no—
159C24×C11C22×C414yes—
160C24×C11C22×C414yes—
161C24×C11C2×D414yes—
162C24×C11#4114yes—
163C24×C11C2412yes—
164C24×C11C2411yescharacteristic
165C24×C11C2411yescharacteristic
166C24×C11C2411yescharacteristic
167C23×D11—22no—
168C23×D11—22no—
169C23×D11—42no—
170C23×D11—42no—
171C23×D11C22×C414yes—
172C23×D11C2412yes—
173C2×D4×C11—232no—
174C2×D4×C11—24no—
175C2×D4×C11—24no—
176C2×D4×C11—24no—
177C2×D4×C11—24no—
178C2×D4×C11C22×C418yes—
179C2×D4×C11C22×C418yes—
180C22×C4×C11—22no—
181C22×C4×C11—22no—
182C22×C4×C11—22no—
183C22×C4×C11—24no—
184C22×C4×C11—24no—
185C22×C4×C11—24no—
186C22×C4×C11—22no—
187C22×C4×C11—24no—
188C22×C4×C11—24no—
189C22×C4×C11—24no—
190C22×C4×C11—42no—
191C22×C4×C11—42no—
192C22×C4×C11—42no—
193C22×C4×C11—42no—
194C22×C4×C11—42no—
195C22×C4×C11—416no—
196C22×C4×C11C22×C414yes—
197C22×C4×C11C2412yes—
198C22×C4×C11C2414yes—
199C22×C4×C11C2412yes—
200C22×C4×C11C2412yes—
201C2×C22⋊D11—232no—
202C2×C22⋊D11—24no—
203C2×C22⋊D11—24no—
204C2×C22⋊D11—24no—
205C2×C22⋊D11—24no—
206C2×C22⋊D11—44no—
207C2×C22⋊D11—44no—
208C2×C22⋊D11C22×C418yes—
209C2×C22⋊D11C22×C418yes—
210C2×C22⋊D11C22×C4116yescomplemented
211C22×Dic11—28no—
212C22×Dic11—22no—
213C22×Dic11—24no—
214C22×Dic11—22no—
215C22×Dic11—42no—
216C22×Dic11—42no—
217C22×Dic11—42no—
218C22×Dic11—42no—
219C22×Dic11—44no—
220C22×Dic11—42no—
221C22×Dic11—42no—
222C22×Dic11—44no—
223C22×Dic11C22×C414yes—
224C22×Dic11C22×C418yes—
225C22×Dic11C2×D418yes—
226C22×Dic11C2414yes—
227C22×Dic11C2412yes—
228C22×Dic11C2414yes—
229C22×Dic11C2414yes—
230C2×C4×D11—28no—
231C2×C4×D11—44no—
232C2×C4×D11—44no—
233C11×C22⋊C4—24no—
234C11×C22⋊C4—24no—
235C11×C22⋊C4—28no—
236C11×C22⋊C4—44no—
237C22⋊Dic11—28no—
238C22⋊Dic11—24no—
239C22⋊Dic11—24no—
240C22⋊Dic11C22×C418yes—
241C22⋊Dic11C22×C418yes—
242C22⋊Dic11C22×C4116yescomplemented
243C22⋊Dic11C2×D418yes—
244C22⋊Dic11C2×D418yes—
245(C2×D11)⋊C4—28no—
246(C2×D11)⋊C4—28no—
247(C2×D11)⋊C4—44no—
248(C2×D11)⋊C4C22×C4116yescomplemented
249C4⋊Dic11—28no—
250Dic11⋊C4—28no—
251Dic11⋊C4—44no—
252Dic11⋊C4—44no—
253Dic11⋊C4C22×C4116yescomplemented
254C4×Dic11—28no—
255C4×Dic11—28no—
256C4×Dic11—28no—
257C4×Dic11—44no—
258C2×#534—111no—
259C2×#518—111no—
260C2×#518—111no—
261#2359—114no—
262#2359—114no—
263#2358—114no—
264#2358—114no—
265#2325—114no—
266#2315—111no—
267C4×#121—114no—
268C2×#386—111no—
269C2×#386D1111yescharacteristic, complemented
270C2×C4×C22⋊C4—111no—
271C23×C11—22no—
272C23×C11—22no—
273C23×C11—22no—
274C23×C11—22no—
275C23×C11—22no—
276C23×C11—22no—
277C23×C11—22no—
278C23×C11—22no—
279C23×C11—24no—
280C23×C11—24no—
281C23×C11—28no—
282C23×C11—44no—
283C23×C11—48no—
284C23×C11—48no—
285C23×C11—44no—
286C23×C11—48no—
287C23×C11—82no—
288C23×C11—82no—
289C23×C11—84no—
290C23×C11C4×D4116yescomplemented
291C23×C11C23×C414yes—
292C23×C11C23×C412yes—
293C23×C11C23×C412yes—
294C23×C11C23×C412yes—
295C23×C11C22×D412yes—
296C23×C11C22×D412yes—
297C23×C11C22×D412yes—
298C23×C11C2×#4112yes—
299C23×C11C2×#4112yes—
300C23×C11C2×#4112yes—
301C23×C11C2511yescharacteristic
302C22×D11—22no—
303C22×D11—22no—
304C22×D11—24no—
305C22×D11—24no—
306C22×D11—28no—
307C22×D11—48no—
308C22×D11—82no—
309C22×D11—82no—
310C22×D11—84no—
311C22×D11C23×C414yes—
312D4×C11—216no—
313D4×C11—216no—
314C2×C4×C11—28no—
315C2×C4×C11—28no—
316C2×C4×C11—22no—
317C2×C4×C11—22no—
318C2×C4×C11—22no—
319C2×C4×C11—22no—
320C2×C4×C11—24no—
321C2×C4×C11—22no—
322C2×C4×C11—24no—
323C2×C4×C11—22no—
324C2×C4×C11—22no—
325C2×C4×C11—24no—
326C2×C4×C11—48no—
327C2×C4×C11—48no—
328C2×C4×C11—44no—
329C2×C4×C11—84no—
330C2×C4×C11C23×C414yes—
331C2×C4×C11H(5,𝔽2)14yes—
332C22⋊D11—216no—
333C22⋊D11—216no—
334C22⋊D11—416no—
335C2×Dic11—28no—
336C2×Dic11—22no—
337C2×Dic11—22no—
338C2×Dic11—24no—
339C2×Dic11—24no—
340C2×Dic11—24no—
341C2×Dic11—24no—
342C2×Dic11—24no—
343C2×Dic11—24no—
344C2×Dic11—24no—
345C2×Dic11—48no—
346C2×Dic11—48no—
347C2×Dic11—88no—
348C2×Dic11—84no—
349C2×Dic11C23×C414yes—
350C2×Dic11C23×C418yes—
351C2×Dic11C22×D418yes—
352C4×D11—88no—
353C23×D4—111no—
354C23×D4C2×D1111yescharacteristic
355C24×C4C2×D1111yescharacteristic
356#534—1116no—
357C2×#123—112no—
358C2×#123—112no—
359C2×#121—114no—
360C2×#120—112no—
361C2×#120—112no—
362#518—228no—
363#518—228no—
364C2×C4×D4—114no—
365C2×C4×D4—114no—
366C2×C4×D4—114no—
367C2×C4×D4—114no—
368C2×C4×D4—114no—
369C2×#117—112no—
370C2×#117—112no—
371C22×C22⋊C4—111no—
372C22×C22⋊C4—111no—
373C22×C22⋊C4—111no—
374C22×C22⋊C4—112no—
375C22×C22⋊C4—112no—
376C22×C22⋊C4—112no—
377C22×C22⋊C4C2×D1111yescharacteristic
378C22×C22⋊C4C2×D1112yescomplemented
379C22×C42—112no—
380#390—114no—
381#389—114no—
382#388—114no—
383#388—114no—
384#388—114no—
385#388—114no—
386#387—114no—
387#387—114no—
388#386—112no—
389#386—114no—
390#386—112no—
391#386—114no—
392#386—114no—
393#386C2×D1114yes—
394#386C2×D1112yescomplemented
395#386C2×D1112yescomplemented
396#385—114no—
397#385—114no—
398#385—114no—
399#385—114no—
400#380—114no—
401C4×C4⋊C4—114no—
402C4×C22⋊C4—114no—
403C4×C22⋊C4—114no—
404C4×C22⋊C4—114no—
405C4×C22⋊C4—114no—
406C2×#95—112no—
407C2×#95—112no—
408C2×#95C2×D1112yescomplemented
409C22×C11—24no—
410C22×C11—24no—
411C22×C11—24no—
412C22×C11—22no—
413C22×C11—22no—
414C22×C11—22no—
415C22×C11—22no—
416C22×C11—22no—
417C22×C11—22no—
418C22×C11—24no—
419C22×C11—24no—
420C22×C11—24no—
421C22×C11—24no—
422C22×C11—28no—
423C22×C11—416no—
424C22×C11—42no—
425C22×C11—42no—
426C22×C11—44no—
427C22×C11—88no—
428C22×C11C2×C4×D414yes—
429C22×C11C2×C4×D414yes—
430C22×C11C2×C4×D414yes—
431C22×C11C24×C411yescharacteristic
432C22×C11C23×D411yescharacteristic
433C22×C11C22×#4111yescharacteristic
434C22×C11C2×H(5,𝔽2)12yes—
435C22×C11#58512yes—
436C2×D11—24no—
437C2×D11—28no—
438C2×D11—42no—
439C2×D11—42no—
440C2×D11—44no—
441C2×D11—88no—
442C4×C11—24no—
443C4×C11—24no—
444C4×C11—42no—
445C4×C11—44no—
446Dic11—24no—
447Dic11—28no—
448Dic11—28no—
449Dic11—44no—
450C25—111no—
451C25C22×D1111yescharacteristic
452C25C22×D1111yescharacteristic
453C22×D4—24no—
454C22×D4—24no—
455C22×D4—118no—
456C22×D4—112no—
457C22×D4—112no—
458C22×D4—114no—
459C22×D4—224no—
460C22×D4—224no—
461C22×D4C4×D1118yescomplemented
462C22×D4C22×D1112yes—
463C22×D4C22×D1112yes—
464C23×C4—24no—
465C23×C4—44no—
466C23×C4—111no—
467C23×C4—112no—
468C23×C4—112no—
469C23×C4—112no—
470C23×C4—114no—
471C23×C4—114no—
472C23×C4C22×D1111yescharacteristic
473C23×C4C22×D1112yes—
474C23×C4C22×D1112yes—
475C23×C4C22×D1111yescharacteristic
476C23×C4C22×D1112yes—
477C23×C4C22×D1111yescharacteristic
478#123—1116no—
479#123—1116no—
480#121—1132no—
481#120—1116no—
482#120—1116no—
483C4×D4—2216no—
484C4×D4—2216no—
485C4×D4—2216no—
486C4×D4—2216no—
487C4×D4—448no—
488#117—228no—
489#117—228no—
490C2×C4⋊C4—114no—
491C2×C4⋊C4—114no—
492C2×C4⋊C4—114no—
493C2×C4⋊C4—114no—
494C2×C4⋊C4—114no—
495C2×C22⋊C4—24no—
496C2×C22⋊C4—44no—
497C2×C22⋊C4—118no—
498C2×C22⋊C4—118no—
499C2×C22⋊C4—112no—
500C2×C22⋊C4—112no—
501C2×C22⋊C4—112no—
502C2×C22⋊C4—112no—
503C2×C22⋊C4—114no—
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—228no—
512C2×C22⋊C4—228no—
513C2×C22⋊C4—224no—
514C2×C22⋊C4—444no—
515C2×C22⋊C4C22×D1112yes—
516C2×C22⋊C4C22×D1112yes—
517C2×C22⋊C4C22×D1114yes—
518C2×C22⋊C4C22×D1114yes—
519C2×C42—114no—
520C2×C42—114no—
521C2×C42—114no—
522C2×C42—114no—
523C2×C42—444no—
524#95—114no—
525#95—114no—
526#95—114no—
527#95—114no—
528#95—114no—
529#95—114no—
530#95C22×D1114yes—
531#95C22×D1114yes—
532C2×C11—24no—
533C2×C11—24no—
534C2×C11—24no—
535C2×C11—44no—
536C2×C11C22×C4×D411yescharacteristic
537C2×C11C4×H(5,𝔽2)12yes—
538C2×C11#349011yescharacteristic
539C2×C11#349111yescharacteristic
540C2×C11#349612yes—
541D11—44no—
542C24—22no—
543C24—22no—
544C24—42no—
545C24—42no—
546C24—42no—
547C24—42no—
548C24—112no—
549C24—114no—
550C24—222no—
551C24—222no—
552C24—442no—
553C24—442no—
554C24C2×C4×D1114yes—
555C24C2×C4×D1114yes—
556C24D4×D1114yes—
557C24#434114yes—
558C24C23×D1112yes—
559C24C23×D1111yescharacteristic
560C24C23×D1111yescharacteristic
561C24C23×D1111yescharacteristic
562C2×D4—232no—
563C2×D4—24no—
564C2×D4—24no—
565C2×D4—24no—
566C2×D4—24no—
567C2×D4—118no—
568C2×D4—118no—
569C2×D4—1116no—
570C2×D4—2232no—
571C2×D4—224no—
572C2×D4—224no—
573C2×D4—224no—
574C2×D4—224no—
575C2×D4—444no—
576C2×D4—444no—
577C2×D4C2×C4×D1118yes—
578C2×D4C2×C4×D1118yes—
579C22×C4—22no—
580C22×C4—22no—
581C22×C4—22no—
582C22×C4—24no—
583C22×C4—24no—
584C22×C4—24no—
585C22×C4—22no—
586C22×C4—24no—
587C22×C4—24no—
588C22×C4—24no—
589C22×C4—42no—
590C22×C4—42no—
591C22×C4—42no—
592C22×C4—42no—
593C22×C4—42no—
594C22×C4—416no—
595C22×C4—114no—
596C22×C4—114no—
597C22×C4—112no—
598C22×C4—114no—
599C22×C4—118no—
600C22×C4—118no—
601C22×C4—114no—
602C22×C4—228no—
603C22×C4—228no—
604C22×C4—222no—
605C22×C4—222no—
606C22×C4—224no—
607C22×C4—444no—
608C22×C4—444no—
609C22×C4—442no—
610C22×C4—442no—
611C22×C4—442no—
612C22×C4—442no—
613C22×C4—442no—
614C22×C4—444no—
615C22×C4—444no—
616C22×C4—442no—
617C22×C4C2×C4×D1114yes—
618C22×C4C23×D1112yes—
619C22×C4C23×D1114yes—
620C22×C4C23×D1112yes—
621C22×C4C23×D1112yes—
622C4⋊C4—1116no—
623C4⋊C4—228no—
624C4⋊C4—228no—
625C4⋊C4—444no—
626C4⋊C4—444no—
627C22⋊C4—24no—
628C22⋊C4—24no—
629C22⋊C4—28no—
630C22⋊C4—44no—
631C22⋊C4—118no—
632C22⋊C4—118no—
633C22⋊C4—1116no—
634C22⋊C4—118no—
635C22⋊C4—118no—
636C22⋊C4—1116no—
637C22⋊C4—228no—
638C22⋊C4—228no—
639C22⋊C4—224no—
640C22⋊C4—224no—
641C22⋊C4—228no—
642C22⋊C4—444no—
643C42—228no—
644C42—228no—
645C42—228no—
646C42—444no—
647C11#3427311yescharacteristic, complemented, Sylow
648C23—22no—
649C23—22no—
650C23—22no—
651C23—22no—
652C23—22no—
653C23—22no—
654C23—22no—
655C23—22no—
656C23—24no—
657C23—24no—
658C23—28no—
659C23—44no—
660C23—48no—
661C23—48no—
662C23—44no—
663C23—48no—
664C23—84no—
665C23—82no—
666C23—82no—
667C23—114no—
668C23—222no—
669C23—222no—
670C23—224no—
671C23—224no—
672C23—228no—
673C23—448no—
674C23—884no—
675C23—882no—
676C23—882no—
677C23(C22⋊D11)⋊C4116yescomplemented
678C23C22×C4×D1114yes—
679C23C22×C4×D1112yes—
680C23C22×C4×D1112yes—
681C23C22×C4×D1112yes—
682C23C2×D4×D1112yes—
683C23C2×D4×D1112yes—
684C23C2×D4×D1112yes—
685C23C2×#434112yes—
686C23C2×#434112yes—
687C23C2×#434112yes—
688C23C24×D1111yescharacteristic
689D4—216no—
690D4—216no—
691D4—2216no—
692D4—2216no—
693D4—4416no—
694C2×C4—28no—
695C2×C4—28no—
696C2×C4—22no—
697C2×C4—22no—
698C2×C4—22no—
699C2×C4—22no—
700C2×C4—24no—
701C2×C4—22no—
702C2×C4—24no—
703C2×C4—22no—
704C2×C4—22no—
705C2×C4—24no—
706C2×C4—48no—
707C2×C4—48no—
708C2×C4—44no—
709C2×C4—84no—
710C2×C4—118no—
711C2×C4—114no—
712C2×C4—118no—
713C2×C4—228no—
714C2×C4—222no—
715C2×C4—222no—
716C2×C4—224no—
717C2×C4—224no—
718C2×C4—224no—
719C2×C4—224no—
720C2×C4—224no—
721C2×C4—224no—
722C2×C4—224no—
723C2×C4—448no—
724C2×C4—448no—
725C2×C4—888no—
726C2×C4—888no—
727C2×C4—884no—
728C2×C4C22×C4×D1114yes—
729C2×C4#6703714yes—
730C22—24no—
731C22—24no—
732C22—24no—
733C22—22no—
734C22—22no—
735C22—22no—
736C22—22no—
737C22—22no—
738C22—22no—
739C22—24no—
740C22—24no—
741C22—24no—
742C22—24no—
743C22—28no—
744C22—416no—
745C22—44no—
746C22—42no—
747C22—42no—
748C22—88no—
749C22—224no—
750C22—228no—
751C22—444no—
752C22—442no—
753C22—442no—
754C22—888no—
755C22C2×(C22⋊D11)⋊C414yes—
756C22C2×(C22⋊D11)⋊C414yes—
757C22C2×(C22⋊D11)⋊C414yes—
758C22C23×C4×D1111yescharacteristic
759C22C22×D4×D1111yescharacteristic
760C22C22×#434111yescharacteristic
761C22C2×#6703712yes—
762C22#1062345312yes—
763C4—24no—
764C4—24no—
765C4—44no—
766C4—42no—
767C4—228no—
768C4—224no—
769C4—228no—
770C4—444no—
771C2—24no—
772C2—24no—
773C2—24no—
774C2—44no—
775C2—444no—
776C2C22×(C22⋊D11)⋊C411yescharacteristic
777C2C4×#6703712yes—
778C2#1308230311yescharacteristic
779C2#1308231211yescharacteristic
780C2#1308237312yes—
subgroupG/H
center, FrattiniC23C24×D11
commutatorC22×C11C24×C4
FittingC2×C11×#386C2
socle, cosocleC23×C11C25
prime radicalC2×#10623335C2
hypercenterC2×#386D11
hypocenterC11#34273
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×#386

Complements

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

NH ≅ G/Ntype
2. C2×#10623329C2semidirect
3. C2×#10623017C2semidirect
4. #13071614C2semidirect
5. #13071604C2semidirect
6. #13071596C2semidirect
7. #13071595C2semidirect
8. #13071317C2semidirect
9. #13071228C2semidirect
10. #13071126C2semidirect
11. C2×#10622826C2semidirect
12. C2×C4×C22⋊Dic11C2semidirect
13. C2×C11×#386C2semidirect
18. C22×C11×C22⋊C4C22semidirect
23. C22×C22⋊Dic11C22semidirect
24. #10623335C4semidirect
30. C2×D4×Dic11C22semidirect
33. C22×(C2×D11)⋊C4C22semidirect
34. C2×#66979C22semidirect
35. C22×C4×Dic11C22semidirect
37. C2×(C22⋊D11)⋊C4C22semidirect
38. C2×(C22⋊D11)⋊C4C22semidirect
39. C2×C22⋊C4×D11C22semidirect
40. C2×#66930C22semidirect
42. C11×#386C22semidirect
43. C11×#386C22semidirect
44. C2×C11×#95C22semidirect
46. #10622826C22semidirect
47. #10622826C22semidirect
48. #10622823C22semidirect
49. C4×C22⋊Dic11C22semidirect
50. C4×C22⋊Dic11C22semidirect
51. C2×C11⋊#95C22semidirect
52. C2×C11⋊#95C22semidirect
53. #10622571C22semidirect
54. #10622570C22semidirect
55. #10622569C22semidirect
56. #10622559C22semidirect
57. #10622559C22semidirect
58. #10622558C22semidirect
59. #10622557C22semidirect
60. #10622555C22semidirect
61. C22⋊C4×Dic11C22semidirect
62. #10622283C22semidirect
63. #10622282C22semidirect
64. #10622281C22semidirect
65. #10622279C22semidirect
66. #10622268C22semidirect
67. #10622265C22semidirect
68. #10622262C22semidirect
69. #10622260C22semidirect
75. C22×D4×C11C2×C4semidirect
88. C22×C22⋊D11C2×C4semidirect
104. #67006C2×C4semidirect
107. C2×C22⋊Dic11C2×C4semidirect
108. C2×C22⋊Dic11D4semidirect
117. #66992C2×C4semidirect
118. #66990C2×C4semidirect
119. #66988C2×C4semidirect
122. #66982C2×C4semidirect
210. C2×C22⋊D11C22×C4semidirect
242. C22⋊Dic11C22×C4semidirect
248. (C2×D11)⋊C4C22×C4semidirect
253. Dic11⋊C4C22×C4semidirect
269. C2×#386D11semidirect
290. C23×C11C4×D4semidirect
378. C22×C22⋊C4C2×D11semidirect
394. #386C2×D11semidirect
395. #386C2×D11semidirect
408. C2×#95C2×D11semidirect
461. C22×D4C4×D11semidirect
647. C11#34273semidirect
677. C23(C22⋊D11)⋊C4semidirect

Maximal subgroups

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

subgroupindex
C2×#106233352
C2×#106233292
C2×#106230172
#130716142
#130716042
#130715962
#130715952
#130713172
#130712282
#130711262
C2×#106228262
C2×C4×C22⋊Dic112
C2×C11×#3862
#3427311