Finite Group Databasebeta

← #14915027

Subgroups — #14915027

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×#10623017C211yesmaximal, characteristic, complemented
3#13071608C214yesmaximal, complemented
4#13071602C214yesmaximal, complemented
5#13071595C214yesmaximal, complemented
6#13071593C214yesmaximal, complemented
7#13071314C214yesmaximal, complemented
8#13071228C211yesmaximal, characteristic, complemented
9C4×#66992C214yesmaximal, complemented
10C2×#10622833C211yesmaximal, characteristic, complemented
11C2×#10622571C211yesmaximal, characteristic, complemented
12C2×C22⋊C4×Dic11C211yesmaximal, characteristic, complemented
13C2×C11×#518C211yesmaximal, characteristic, complemented
14C23×D4×C11C2211yescharacteristic
15C23×C22⋊D11C2211yescharacteristic
16C24×Dic11C2211yescharacteristic
17C11×#518—28no—
18C2×C4×D4×C11C2214yes—
19C2×C4×D4×C11C2214yescomplemented
20C2×C11×#117C2212yescomplemented
21C22×C11×C22⋊C4C2211yescharacteristic
22C22×C11×C22⋊C4C2211yescharacteristic
23C22×C11×C22⋊C4C2212yescomplemented
24C2×#67006C2212yes—
25C22×C22⋊Dic11C2211yescharacteristic
26C22×C22⋊Dic11C2211yescharacteristic
27C22×C22⋊Dic11C2212yescomplemented
28#10623335C4116yescomplemented
29C2×#66992C2214yes—
30C2×#66990C2212yes—
31C2×#66988C2212yes—
32C2×#66982C2212yes—
33C2×C4×C22⋊D11C2214yescomplemented
34C2×C4×C22⋊D11C2214yescomplemented
35C22×(C2×D11)⋊C4C2212yescomplemented
36C22×C4×Dic11C2212yescomplemented
37#10623017—28no—
38C2×(C22⋊D11)⋊C4C2214yes—
39C2×C22⋊C4×D11C2212yescomplemented
40C2×#66930C2212yescomplemented
41#10622833C2214yes—
42#10622833C2212yescomplemented
43#10622833C2212yescomplemented
44#10622826C2214yescomplemented
45#10622823C2214yescomplemented
46#10622823C2214yescomplemented
47C4×C22⋊Dic11C2214yescomplemented
48C2×C11⋊#95C2212yescomplemented
49C2×C11⋊#95C2212yescomplemented
50C2×C11⋊#95C2212yescomplemented
51#10622603C2214yescomplemented
52#10622602C2214yescomplemented
53#10622591C2214yescomplemented
54#10622585C2214yescomplemented
55#10622571C2214yes—
56#10622571C2212yescomplemented
57#10622571C2212yescomplemented
58#10622570C2214yescomplemented
59#10622569C2214yescomplemented
60#10622559C2214yescomplemented
61#10622558C2214yescomplemented
62#10622557C2214yescomplemented
63#10622555C2214yescomplemented
64C22⋊C4×Dic11C2214yescomplemented
65C22⋊C4×Dic11C2214yescomplemented
66#10622553C2214yescomplemented
67C4×(C2×D11)⋊C4C2214yescomplemented
68#10622546C2214yescomplemented
69C4×Dic11⋊C4C2214yescomplemented
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×C11C2311yescharacteristic
79C23×C4×C11C2312yes—
80C23×C4×C11C2314yes—
81C23×C4×C11C2312yes—
82C22×C22⋊D11—24no—
83C22×C22⋊D11—24no—
84C22×C22⋊D11C2×C418yescomplemented
85C22×C22⋊D11C2312yes—
86C22×C22⋊D11C2312yes—
87C22×C22⋊D11C2314yes—
88C23×Dic11—24no—
89C23×Dic11—44no—
90C23×Dic11C2311yescharacteristic
91C23×Dic11C2312yes—
92C23×Dic11C2312yes—
93C23×Dic11C2311yescharacteristic
94C23×Dic11C2312yes—
95C23×Dic11C2311yescharacteristic
96C23×Dic11C2312yes—
97C22×C4×D11C2314yes—
98C4×D4×C11—216no—
99C4×D4×C11—216no—
100C11×#117—28no—
101C2×C11×C4⋊C4C2314yes—
102C2×C11×C22⋊C4—24no—
103C2×C11×C22⋊C4—28no—
104C2×C11×C22⋊C4D418yescomplemented
105C2×C11×C22⋊C4C2312yes—
106C2×C11×C22⋊C4C2314yes—
107C2×C11×C22⋊C4C2312yes—
108C2×C11×C22⋊C4C2312yes—
109C2×C11×C22⋊C4C2312yes—
110C2×C42×C11C2314yes—
111#67006C2×C4116yescomplemented
112C2×C22⋊Dic11—24no—
113C2×C22⋊Dic11—44no—
114C2×C22⋊Dic11C2×C418yescomplemented
115C2×C22⋊Dic11C2312yes—
116C2×C22⋊Dic11C2312yes—
117C2×C22⋊Dic11C2314yes—
118C2×C22⋊Dic11C2314yes—
119C2×C22⋊Dic11C2312yes—
120C2×C22⋊Dic11C2312yes—
121C2×C22⋊Dic11C2314yes—
122#66992C2×C4132yescomplemented
123#66990C2×C4116yescomplemented
124#66988C2×C4116yescomplemented
125#66982C2×C4116yescomplemented
126C4×C22⋊D11—216no—
127C4×C22⋊D11—48no—
128C2×(C2×D11)⋊C4—44no—
129C2×(C2×D11)⋊C4C2314yes—
130C2×(C2×D11)⋊C4C2314yes—
131C2×(C2×D11)⋊C4C2314yes—
132C2×(C2×D11)⋊C4C2314yes—
133C2×Dic11⋊C4C2314yes—
134C2×Dic11⋊C4C2314yes—
135C2×Dic11⋊C4C2314yes—
136C2×Dic11⋊C4C2314yes—
137C2×C4×Dic11—44no—
138C2×C4×Dic11C2314yes—
139C2×C4×Dic11C2314yes—
140C2×C4×Dic11C2314yes—
141(C22⋊D11)⋊C4—216no—
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—24no—
183C22×C4×C11—28no—
184C22×C4×C11—42no—
185C22×C4×C11—42no—
186C22×C4×C11—42no—
187C22×C4×C11—44no—
188C22×C4×C11—44no—
189C22×C4×C11—42no—
190C22×C4×C11C22×C414yes—
191C22×C4×C11C2×D418yes—
192C22×C4×C11C2414yes—
193C22×C4×C11C2412yes—
194C22×C4×C11C2414yes—
195C2×C22⋊D11—232no—
196C2×C22⋊D11—24no—
197C2×C22⋊D11—24no—
198C2×C22⋊D11—24no—
199C2×C22⋊D11—24no—
200C2×C22⋊D11—44no—
201C2×C22⋊D11—44no—
202C2×C22⋊D11C22×C418yes—
203C2×C22⋊D11C22×C418yes—
204C2×C22⋊D11C22×C4116yescomplemented
205C22×Dic11—24no—
206C22×Dic11—24no—
207C22×Dic11—24no—
208C22×Dic11—22no—
209C22×Dic11—24no—
210C22×Dic11—22no—
211C22×Dic11—22no—
212C22×Dic11—24no—
213C22×Dic11—24no—
214C22×Dic11—22no—
215C22×Dic11—42no—
216C22×Dic11—42no—
217C22×Dic11—42no—
218C22×Dic11—42no—
219C22×Dic11—42no—
220C22×Dic11—42no—
221C22×Dic11—42no—
222C22×Dic11—416no—
223C22×Dic11C22×C414yes—
224C22×Dic11C22×C418yes—
225C22×Dic11C2412yes—
226C22×Dic11C2414yes—
227C22×Dic11C2412yes—
228C22×Dic11C2414yes—
229C22×Dic11C2412yes—
230C2×C4×D11—28no—
231C2×C4×D11—44no—
232C2×C4×D11—44no—
233C11×C4⋊C4—28no—
234C11×C22⋊C4—24no—
235C11×C22⋊C4—24no—
236C11×C22⋊C4—28no—
237C11×C22⋊C4C2×D418yes—
238C11×C22⋊C4C2×D418yes—
239C42×C11—28no—
240C22⋊Dic11—28no—
241C22⋊Dic11—24no—
242C22⋊Dic11—24no—
243C22⋊Dic11—44no—
244C22⋊Dic11C22×C418yes—
245C22⋊Dic11C22×C418yes—
246C22⋊Dic11C22×C4116yescomplemented
247(C2×D11)⋊C4—28no—
248(C2×D11)⋊C4—28no—
249(C2×D11)⋊C4—44no—
250(C2×D11)⋊C4C22×C4116yescomplemented
251Dic11⋊C4—28no—
252Dic11⋊C4—44no—
253Dic11⋊C4—44no—
254Dic11⋊C4C22×C4116yescomplemented
255C4×Dic11—28no—
256C4×Dic11—28no—
257C4×Dic11—44no—
258C2×#534—111no—
259C2×#518—111no—
260C2×#518D1111yescharacteristic, complemented
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×#386—111no—
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—22no—
316C2×C4×C11—22no—
317C2×C4×C11—24no—
318C2×C4×C11—24no—
319C2×C4×C11—24no—
320C2×C4×C11—24no—
321C2×C4×C11—24no—
322C2×C4×C11—48no—
323C2×C4×C11—88no—
324C2×C4×C11—84no—
325C2×C4×C11C23×C414yes—
326C2×C4×C11C22×D418yes—
327C22⋊D11—216no—
328C22⋊D11—216no—
329C22⋊D11—416no—
330C2×Dic11—28no—
331C2×Dic11—28no—
332C2×Dic11—22no—
333C2×Dic11—22no—
334C2×Dic11—22no—
335C2×Dic11—24no—
336C2×Dic11—22no—
337C2×Dic11—24no—
338C2×Dic11—24no—
339C2×Dic11—22no—
340C2×Dic11—24no—
341C2×Dic11—22no—
342C2×Dic11—22no—
343C2×Dic11—24no—
344C2×Dic11—48no—
345C2×Dic11—48no—
346C2×Dic11—48no—
347C2×Dic11—44no—
348C2×Dic11—84no—
349C2×Dic11C23×C414yes—
350C2×Dic11C23×C418yes—
351C2×Dic11H(5,𝔽2)14yes—
352C4×D11—88no—
353C23×D4—111no—
354C23×D4C2×D1111yescharacteristic
355C24×C4—111no—
356#534—1116no—
357C2×#123—112no—
358C2×#123—112no—
359C2×#121—114no—
360C2×#120—112no—
361C2×#120—112no—
362#518—28no—
363#518—228no—
364C2×C4×D4—114no—
365C2×C4×D4—114no—
366C2×C4×D4—114no—
367C2×C4×D4C2×D1114yes—
368C2×C4×D4C2×D1114yescomplemented
369C2×#117—112no—
370C2×#117C2×D1112yescomplemented
371C22×C22⋊C4—111no—
372C22×C22⋊C4—111no—
373C22×C22⋊C4—112no—
374C22×C22⋊C4—112no—
375C22×C22⋊C4—112no—
376C22×C22⋊C4C2×D1111yescharacteristic
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—112no—
393#386—114no—
394#386—114no—
395#386—112no—
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×#95—112no—
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—28no—
444C4×C11—44no—
445Dic11—24no—
446Dic11—28no—
447Dic11—24no—
448Dic11—42no—
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—111no—
465C23×C4—112no—
466C23×C4—111no—
467C23×C4—112no—
468C23×C4—112no—
469C23×C4—112no—
470C23×C4—111no—
471C23×C4—114no—
472C23×C4—224no—
473C23×C4—444no—
474C23×C4C22×D1111yescharacteristic
475C23×C4C22×D1112yes—
476C23×C4C22×D1114yes—
477C23×C4C22×D1112yes—
478#123—1116no—
479#123—1116no—
480#121—1132no—
481#120—1116no—
482#120—1116no—
483C4×D4—216no—
484C4×D4—216no—
485C4×D4—2216no—
486C4×D4—2216no—
487C4×D4—448no—
488#117—28no—
489#117—228no—
490C2×C4⋊C4—114no—
491C2×C4⋊C4—114no—
492C2×C4⋊C4—114no—
493C2×C4⋊C4—114no—
494C2×C4⋊C4C22×D1114yes—
495C2×C22⋊C4—24no—
496C2×C22⋊C4—28no—
497C2×C22⋊C4—118no—
498C2×C22⋊C4—112no—
499C2×C22⋊C4—112no—
500C2×C22⋊C4—114no—
501C2×C22⋊C4—114no—
502C2×C22⋊C4—112no—
503C2×C22⋊C4—112no—
504C2×C22⋊C4—114no—
505C2×C22⋊C4—114no—
506C2×C22⋊C4—114no—
507C2×C22⋊C4—114no—
508C2×C22⋊C4—114no—
509C2×C22⋊C4—224no—
510C2×C22⋊C4—228no—
511C2×C22⋊C4—444no—
512C2×C22⋊C4—444no—
513C2×C22⋊C4C22⋊D1118yescomplemented
514C2×C22⋊C4C22×D1112yes—
515C2×C22⋊C4C22×D1112yes—
516C2×C22⋊C4C22×D1114yes—
517C2×C22⋊C4C22×D1112yes—
518C2×C22⋊C4C22×D1112yes—
519C2×C42—114no—
520C2×C42—114no—
521C2×C42—114no—
522C2×C42—444no—
523C2×C42C22×D1114yes—
524#95—114no—
525#95—114no—
526#95—114no—
527#95—114no—
528#95—114no—
529#95—114no—
530#95—114no—
531#95—114no—
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—
556C24#433914yes—
557C24C2×C22⋊D1114yes—
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—24no—
582C22×C4—28no—
583C22×C4—42no—
584C22×C4—42no—
585C22×C4—42no—
586C22×C4—44no—
587C22×C4—44no—
588C22×C4—42no—
589C22×C4—114no—
590C22×C4—112no—
591C22×C4—114no—
592C22×C4—112no—
593C22×C4—118no—
594C22×C4—112no—
595C22×C4—114no—
596C22×C4—224no—
597C22×C4—224no—
598C22×C4—224no—
599C22×C4—222no—
600C22×C4—222no—
601C22×C4—222no—
602C22×C4—224no—
603C22×C4—224no—
604C22×C4—222no—
605C22×C4—224no—
606C22×C4—228no—
607C22×C4—444no—
608C22×C4—444no—
609C22×C4—442no—
610C22×C4—442no—
611C22×C4—442no—
612C22×C4—442no—
613C22×C4—442no—
614C22×C4—442no—
615C22×C4—442no—
616C22×C4—4416no—
617C22×C4C2×C4×D1114yes—
618C22×C4C2×C22⋊D1118yes—
619C22×C4C23×D1114yes—
620C22×C4C23×D1112yes—
621C22×C4C23×D1114yes—
622C4⋊C4—28no—
623C4⋊C4—1116no—
624C4⋊C4—228no—
625C4⋊C4—444no—
626C4⋊C4—444no—
627C22⋊C4—24no—
628C22⋊C4—24no—
629C22⋊C4—28no—
630C22⋊C4—118no—
631C22⋊C4—118no—
632C22⋊C4—1116no—
633C22⋊C4—1116no—
634C22⋊C4—228no—
635C22⋊C4—228no—
636C22⋊C4—224no—
637C22⋊C4—224no—
638C22⋊C4—228no—
639C22⋊C4—444no—
640C22⋊C4—444no—
641C22⋊C4C2×C22⋊D1118yes—
642C22⋊C4C2×C22⋊D1118yes—
643C42—28no—
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—24no—
656C23—24no—
657C23—22no—
658C23—28no—
659C23—44no—
660C23—48no—
661C23—44no—
662C23—48no—
663C23—48no—
664C23—84no—
665C23—82no—
666C23—82no—
667C23—114no—
668C23—222no—
669C23—224no—
670C23—224no—
671C23—222no—
672C23—228no—
673C23—448no—
674C23—884no—
675C23—882no—
676C23—882no—
677C23C4×C22⋊D11116yescomplemented
678C23C22×C4×D1114yes—
679C23C22×C4×D1112yes—
680C23C22×C4×D1112yes—
681C23C22×C4×D1112yes—
682C23C2×#433912yes—
683C23C2×#433912yes—
684C23C2×#433912yes—
685C23C22×C22⋊D1112yes—
686C23C22×C22⋊D1112yes—
687C23C22×C22⋊D1112yes—
688C23C24×D1111yescharacteristic
689D4—216no—
690D4—216no—
691D4—2216no—
692D4—2216no—
693D4—4416no—
694C2×C4—28no—
695C2×C4—22no—
696C2×C4—24no—
697C2×C4—24no—
698C2×C4—22no—
699C2×C4—24no—
700C2×C4—24no—
701C2×C4—24no—
702C2×C4—48no—
703C2×C4—88no—
704C2×C4—84no—
705C2×C4—118no—
706C2×C4—114no—
707C2×C4—114no—
708C2×C4—228no—
709C2×C4—228no—
710C2×C4—222no—
711C2×C4—222no—
712C2×C4—224no—
713C2×C4—222no—
714C2×C4—224no—
715C2×C4—222no—
716C2×C4—222no—
717C2×C4—224no—
718C2×C4—222no—
719C2×C4—222no—
720C2×C4—224no—
721C2×C4—224no—
722C2×C4—448no—
723C2×C4—448no—
724C2×C4—448no—
725C2×C4—444no—
726C2×C4—888no—
727C2×C4—884no—
728C2×C4C22×C4×D1114yes—
729C2×C4C22×C22⋊D1118yes—
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×C4×C22⋊D1114yes—
756C22C2×C4×C22⋊D1114yes—
757C22C2×C4×C22⋊D1114yes—
758C22C23×C4×D1111yescharacteristic
759C22C22×#433911yescharacteristic
760C22D11×H(5,𝔽2)12yes—
761C22#1062345512yes—
762C22C23×C22⋊D1111yescharacteristic
763C4—28no—
764C4—24no—
765C4—44no—
766C4—224no—
767C4—224no—
768C4—228no—
769C4—444no—
770C4—442no—
771C2—24no—
772C2—24no—
773C2—24no—
774C2—44no—
775C2—444no—
776C2C22×C4×C22⋊D1111yescharacteristic
777C2#1308182012yes—
778C2#1308230111yescharacteristic
779C2#1308230911yescharacteristic
780C2#1308237512yes—
subgroupG/H
center, FrattiniC23C24×D11
commutatorC22×C11C24×C4
FittingC2×C11×#518C2
socle, cosocleC23×C11C25
prime radicalC2×#10623335C2
hypercenterC2×#518D11
hypocenterC11#34273
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×#518

Complements

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

NH ≅ G/Ntype
2. C2×#10623017C2semidirect
3. #13071608C2semidirect
4. #13071602C2semidirect
5. #13071595C2semidirect
6. #13071593C2semidirect
7. #13071314C2semidirect
8. #13071228C2semidirect
9. C4×#66992C2semidirect
10. C2×#10622833C2semidirect
11. C2×#10622571C2semidirect
12. C2×C22⋊C4×Dic11C2semidirect
13. C2×C11×#518C2semidirect
19. C2×C4×D4×C11C22semidirect
20. C2×C11×#117C22semidirect
23. C22×C11×C22⋊C4C22semidirect
27. C22×C22⋊Dic11C22semidirect
28. #10623335C4semidirect
33. C2×C4×C22⋊D11C22semidirect
34. C2×C4×C22⋊D11C22semidirect
35. C22×(C2×D11)⋊C4C22semidirect
36. C22×C4×Dic11C22semidirect
39. C2×C22⋊C4×D11C22semidirect
40. C2×#66930C22semidirect
42. #10622833C22semidirect
43. #10622833C22semidirect
44. #10622826C22semidirect
45. #10622823C22semidirect
46. #10622823C22semidirect
47. C4×C22⋊Dic11C22semidirect
48. C2×C11⋊#95C22semidirect
49. C2×C11⋊#95C22semidirect
50. C2×C11⋊#95C22semidirect
51. #10622603C22semidirect
52. #10622602C22semidirect
53. #10622591C22semidirect
54. #10622585C22semidirect
56. #10622571C22semidirect
57. #10622571C22semidirect
58. #10622570C22semidirect
59. #10622569C22semidirect
60. #10622559C22semidirect
61. #10622558C22semidirect
62. #10622557C22semidirect
63. #10622555C22semidirect
64. C22⋊C4×Dic11C22semidirect
65. C22⋊C4×Dic11C22semidirect
66. #10622553C22semidirect
67. C4×(C2×D11)⋊C4C22semidirect
68. #10622546C22semidirect
69. C4×Dic11⋊C4C22semidirect
75. C22×D4×C11C2×C4semidirect
84. C22×C22⋊D11C2×C4semidirect
104. C2×C11×C22⋊C4D4semidirect
111. #67006C2×C4semidirect
114. C2×C22⋊Dic11C2×C4semidirect
122. #66992C2×C4semidirect
123. #66990C2×C4semidirect
124. #66988C2×C4semidirect
125. #66982C2×C4semidirect
204. C2×C22⋊D11C22×C4semidirect
246. C22⋊Dic11C22×C4semidirect
250. (C2×D11)⋊C4C22×C4semidirect
254. Dic11⋊C4C22×C4semidirect
260. C2×#518D11semidirect
290. C23×C11C4×D4semidirect
368. C2×C4×D4C2×D11semidirect
370. C2×#117C2×D11semidirect
378. C22×C22⋊C4C2×D11semidirect
461. C22×D4C4×D11semidirect
513. C2×C22⋊C4C22⋊D11semidirect
647. C11#34273semidirect
677. C23C4×C22⋊D11semidirect

Maximal subgroups

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

subgroupindex
C2×#106233352
C2×#106230172
#130716082
#130716022
#130715952
#130715932
#130713142
#130712282
C4×#669922
C2×#106228332
C2×#106225712
C2×C22⋊C4×Dic112
C2×C11×#5182
#3427311