Finite Group Databasebeta

← #14763580

Subgroups — #14763580

Order 2816.

1598 conjugacy classes of subgroups.

The subgroup lattice has 822 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623322C211yesmaximal, characteristic
2#13070999C211yesmaximal, characteristic, complemented
3#13069600C212yesmaximal, complemented
4#13069451C212yesmaximal, complemented
5#13069069C214yesmaximal, complemented
6#13068601C214yesmaximal, complemented
7C2×C11×#380C211yesmaximal, characteristic, complemented
8C24×C4×C11C2211yescharacteristic
9C22×#4339C411yescharacteristic, complemented
10C22×C11×C4⋊C4—21no—
11C22×C11×C22⋊C4C2212yes—
12C2×#67006C2212yes—
13#10623322—21no—
14#10623322—21no—
15#10623322—21no—
16#10623322—21no—
17#10623322—21no—
18#10623322—21no—
19#10623322—21no—
20#10623322—21no—
21C2×#66983C411yescharacteristic, complemented
22C2×#66983C2211yescharacteristic
23C2×#66982C412yescomplemented
24C2×C4×C22⋊D11C412yescomplemented
25C2×C4×C22⋊D11C2212yes—
26C2×#66979—21no—
27C2×#66979C411yescharacteristic, complemented
28C2×#66977C411yescharacteristic, complemented
29C2×#66977C2211yescharacteristic
30C11×#380—21no—
31C11×#380—21no—
32C11×#380C2212yes—
33C11×#380C2212yes—
34C2×C11×#95—21no—
35#10622860C2212yes—
36#10622825—21no—
37#10622825C2212yes—
38#10622824—21no—
39C4×C22⋊Dic11—21no—
40C4×C22⋊Dic11C2212yes—
41C2×#66870C2218yes—
42#10622165C2218yes—
43C25×C11C2311yescharacteristic
44C23×C4×C11—22no—
45C23×C4×C11—44no—
46C23×C4×C11C2×C411yescharacteristic
47C23×C4×C11C2×C411yescharacteristic
48C23×C4×C11C2×C411yescharacteristic
49C23×C4×C11C2×C411yescharacteristic
50C23×C4×C11D411yescharacteristic
51C23×C4×C11D411yescharacteristic
52C23×C4×C11D411yescharacteristic
53C23×C4×C11D411yescharacteristic
54C23×C4×C11D411yescharacteristic
55C23×C4×C11D411yescharacteristic
56C23×C4×C11D411yescharacteristic
57C23×C4×C11D411yescharacteristic
58C23×C4×C11C2311yescharacteristic
59C23×C4×C11C2311yescharacteristic
60C22×C22⋊D11C2×C412yes—
61C22×C22⋊D11C2×C412yes—
62C22×C22⋊D11C2312yes—
63C2×#4339—21no—
64C2×#4339—21no—
65C2×#4339—21no—
66C2×#4339—21no—
67C2×#4339—44no—
68C22×D44C2×C411yescharacteristic, complemented
69C22×C4×D11C2×C412yescomplemented
70C22×Dic22C2×C411yescharacteristic, complemented
71C2×C11×C4⋊C4—22no—
72C2×C11×C4⋊C4—22no—
73C2×C11×C4⋊C4—44no—
74C2×C11×C22⋊C4—22no—
75C2×C11×C22⋊C4—44no—
76C2×C11×C22⋊C4C2314yes—
77#67006—22no—
78#67006—22no—
79#67006—22no—
80#67006—22no—
81C2×C22⋊Dic11—22no—
82C2×C22⋊Dic11—22no—
83C2×C22⋊Dic11C2×C412yes—
84C2×C22⋊Dic11C2×C412yes—
85C2×C22⋊Dic11C2314yes—
86C2×C22⋊Dic11C2312yes—
87#66983—21no—
88#66983—21no—
89#66983—21no—
90#66983—21no—
91#66983—21no—
92#66983—21no—
93#66983—21no—
94#66983—21no—
95#66982—22no—
96#66982—22no—
97#66982—22no—
98#66982—22no—
99C4×C22⋊D11—22no—
100C4×C22⋊D11—22no—
101C4×C22⋊D11—22no—
102C4×C22⋊D11—22no—
103C4×C22⋊D11—22no—
104C4×C22⋊D11—22no—
105C4×C22⋊D11—22no—
106C4×C22⋊D11—22no—
107C2×(C2×D11)⋊C4C2×C412yescomplemented
108C2×(C2×D11)⋊C4C2×C412yescomplemented
109#66979—21no—
110#66979—21no—
111#66979—21no—
112#66979—21no—
113#66979—44no—
114C2×C4⋊Dic11—22no—
115C2×C4⋊Dic11C2×C411yescharacteristic, complemented
116C2×C4⋊Dic11C2×C411yescharacteristic, complemented
117#66977—21no—
118#66977—21no—
119#66977—21no—
120#66977—21no—
121#66977—21no—
122#66977—21no—
123#66977—21no—
124#66977—21no—
125C2×Dic11⋊C4C2×C412yescomplemented
126C2×Dic11⋊C4C2×C412yescomplemented
127C2×C4×Dic11—22no—
128C2×C4×Dic11C2×C412yescomplemented
129C11×#95—22no—
130C11×#95—22no—
131C11⋊#95—22no—
132C11⋊#95—22no—
133#66870—48no—
134#21874—111nomaximal, Sylow
135C24×C11—22no—
136C24×C11—22no—
137C24×C11—42no—
138C24×C11—42no—
139C24×C11C22×C411yescharacteristic
140C24×C11C22×C411yescharacteristic
141C24×C11C2×D411yescharacteristic
142C24×C11C2×D411yescharacteristic
143C24×C11C2×D411yescharacteristic
144C24×C11C2×D411yescharacteristic
145C24×C11C2411yescharacteristic
146C23×D11C22×C412yes—
147C22×C4×C11—24no—
148C22×C4×C11—24no—
149C22×C4×C11—24no—
150C22×C4×C11—24no—
151C22×C4×C11—42no—
152C22×C4×C11—42no—
153C22×C4×C11—42no—
154C22×C4×C11—42no—
155C22×C4×C11—42no—
156C22×C4×C11—42no—
157C22×C4×C11—42no—
158C22×C4×C11—42no—
159C22×C4×C11—42no—
160C22×C4×C11—42no—
161C22×C4×C11—42no—
162C22×C4×C11—44no—
163C22×C4×C11—44no—
164C22×C4×C11—44no—
165C22×C4×C11C22⋊C411yescharacteristic
166C22×C4×C11C22⋊C411yescharacteristic
167C22×C4×C11C22⋊C411yescharacteristic
168C22×C4×C11C22⋊C411yescharacteristic
169C22×C4×C11C22⋊C411yescharacteristic
170C22×C4×C11C22⋊C411yescharacteristic
171C22×C4×C11C22⋊C411yescharacteristic
172C22×C4×C11C22⋊C411yescharacteristic
173C22×C4×C11C22⋊C411yescharacteristic
174C22×C4×C11C22⋊C411yescharacteristic
175C22×C4×C11C22⋊C411yescharacteristic
176C22×C4×C11C22⋊C411yescharacteristic
177C22×C4×C11C22⋊C411yescharacteristic
178C22×C4×C11C22⋊C411yescharacteristic
179C22×C4×C11C22⋊C411yescharacteristic
180C22×C4×C11C22⋊C411yescharacteristic
181C22×C4×C11C22×C411yescharacteristic
182C22×C4×C11C22×C411yescharacteristic
183C22×C4×C11C22×C411yescharacteristic
184C22×C4×C11C22×C411yescharacteristic
185C22×C4×C11C2×D411yescharacteristic
186C22×C4×C11C2×D411yescharacteristic
187C22×C4×C11C2×D411yescharacteristic
188C22×C4×C11C2×D411yescharacteristic
189C22×C4×C11C2×D411yescharacteristic
190C22×C4×C11C2×D411yescharacteristic
191C22×C4×C11C2×D411yescharacteristic
192C22×C4×C11C2×D411yescharacteristic
193C2×C22⋊D11—22no—
194C2×C22⋊D11—22no—
195C2×C22⋊D11—22no—
196C2×C22⋊D11—22no—
197C2×C22⋊D11—22no—
198C2×C22⋊D11—22no—
199C2×C22⋊D11—24no—
200C2×C22⋊D11—24no—
201C2×C22⋊D11—44no—
202C2×C22⋊D11—44no—
203C22×Dic11—24no—
204C22×Dic11C22×C412yes—
205C22×Dic11C22×C412yes—
206C22×Dic11C22×C412yes—
207#4339—44no—
208#4339—44no—
209#4339—44no—
210#4339—44no—
211C2×D44—21no—
212C2×D44—21no—
213C2×D44—42no—
214C2×C4×D11—22no—
215C2×C4×D11—22no—
216C2×C4×D11—44no—
217C2×Dic22—21no—
218C2×Dic22—21no—
219C2×Dic22—42no—
220C11×C4⋊C4—44no—
221C11×C4⋊C4—44no—
222C11×C22⋊C4—28no—
223C11×C22⋊C4—44no—
224C22⋊Dic11—22no—
225C22⋊Dic11—22no—
226C22⋊Dic11—22no—
227C22⋊Dic11—22no—
228C22⋊Dic11—22no—
229C22⋊Dic11—22no—
230C22⋊Dic11—24no—
231C22⋊Dic11—24no—
232C22⋊Dic11—44no—
233C22⋊Dic11—44no—
234(C2×D11)⋊C4—22no—
235(C2×D11)⋊C4—22no—
236(C2×D11)⋊C4—22no—
237(C2×D11)⋊C4—22no—
238C4⋊Dic11—21no—
239C4⋊Dic11—21no—
240C4⋊Dic11—21no—
241C4⋊Dic11—21no—
242C4⋊Dic11—44no—
243Dic11⋊C4—22no—
244Dic11⋊C4—22no—
245Dic11⋊C4—22no—
246Dic11⋊C4—22no—
247C4×Dic11—22no—
248C4×Dic11—22no—
249C4×Dic11—44no—
250C2×#525—111no—
251#2280—111no—
252C2×#380D1111yescharacteristic, complemented
253#1996—112no—
254#1964—112no—
255#1898—114no—
256#1799—114no—
257C23×C11—21no—
258C23×C11—21no—
259C23×C11—22no—
260C23×C11—22no—
261C23×C11—22no—
262C23×C11—22no—
263C23×C11—21no—
264C23×C11—21no—
265C23×C11—22no—
266C23×C11—22no—
267C23×C11—22no—
268C23×C11—22no—
269C23×C11—22no—
270C23×C11—22no—
271C23×C11—41no—
272C23×C11—41no—
273C23×C11—41no—
274C23×C11—41no—
275C23×C11—41no—
276C23×C11—41no—
277C23×C11—41no—
278C23×C11—41no—
279C23×C11—48no—
280C23×C11—48no—
281C23×C11C2×C22⋊C411yescharacteristic
282C23×C11C2×C22⋊C411yescharacteristic
283C23×C11C2×C22⋊C411yescharacteristic
284C23×C11C2×C22⋊C411yescharacteristic
285C23×C11C23×C411yescharacteristic
286C23×C11C22×D411yescharacteristic
287C23×C11C22×D411yescharacteristic
288C23×C11H(5,𝔽2)12yes—
289C23×C112−1+412yes—
290C22×D11—22no—
291C22×D11—24no—
292C22×D11—42no—
293C22×D11—42no—
294C2×C4×C11—22no—
295C2×C4×C11—22no—
296C2×C4×C11—22no—
297C2×C4×C11—22no—
298C2×C4×C11—22no—
299C2×C4×C11—22no—
300C2×C4×C11—22no—
301C2×C4×C11—22no—
302C2×C4×C11—22no—
303C2×C4×C11—22no—
304C2×C4×C11—22no—
305C2×C4×C11—22no—
306C2×C4×C11—22no—
307C2×C4×C11—22no—
308C2×C4×C11—22no—
309C2×C4×C11—41no—
310C2×C4×C11—41no—
311C2×C4×C11—41no—
312C2×C4×C11—41no—
313C2×C4×C11—41no—
314C2×C4×C11—41no—
315C2×C4×C11—41no—
316C2×C4×C11—41no—
317C2×C4×C11—41no—
318C2×C4×C11—41no—
319C2×C4×C11—41no—
320C2×C4×C11—41no—
321C2×C4×C11—44no—
322C2×C4×C11—44no—
323C2×C4×C11—44no—
324C2×C4×C11—88no—
325C2×C4×C11#9914yescomplemented
326C2×C4×C11C2×C22⋊C411yescharacteristic
327C2×C4×C11C2×C22⋊C411yescharacteristic
328C2×C4×C11C2×C22⋊C411yescharacteristic
329C2×C4×C11C2×C22⋊C411yescharacteristic
330C2×C4×C11C2×C22⋊C411yescharacteristic
331C2×C4×C11C2×C22⋊C411yescharacteristic
332C2×C4×C11C2×C22⋊C411yescharacteristic
333C2×C4×C11C2×C22⋊C411yescharacteristic
334C22⋊D11—44no—
335C22⋊D11—44no—
336C22⋊D11—42no—
337C22⋊D11—42no—
338C22⋊D11—44no—
339C22⋊D11—44no—
340C22⋊D11—44no—
341C2×Dic11—22no—
342C2×Dic11—22no—
343C2×Dic11—22no—
344C2×Dic11—24no—
345C2×Dic11—42no—
346C2×Dic11—42no—
347C2×Dic11—44no—
348C2×Dic11—44no—
349C2×Dic11—44no—
350D44—42no—
351D44—42no—
352C4×D11—44no—
353C4×D11—44no—
354Dic22—42no—
355Dic22—42no—
356C22×#41—111no—
357C24×C4C2×D1111yescharacteristic
358#525—221no—
359#525—221no—
360#525—221no—
361#525—221no—
362#525—221no—
363#525—221no—
364#525—221no—
365#525—221no—
366C2×#123—112no—
367C2×C22⋊Q8—111no—
368C2×C22⋊Q8—111no—
369C2×#121—111no—
370C2×#121—111no—
371C2×#120—112no—
372C2×C4×D4—112no—
373C2×C4×D4—112no—
374C2×#117—111no—
375C2×#117—221no—
376C22×C4⋊C4—21no—
377C22×C22⋊C4C2×D1112yes—
378C2×#99—118no—
379#381—221no—
380#380—21no—
381#380—21no—
382#380—112no—
383#380—221no—
384#380C2×D1112yes—
385#380C2×D1112yes—
386#379—112no—
387C4×C22⋊C4—112no—
388C4×C22⋊C4—221no—
389C2×#95—21no—
390#342—118no—
391C22×C11—24no—
392C22×C11—24no—
393C22×C11—21no—
394C22×C11—21no—
395C22×C11—21no—
396C22×C11—21no—
397C22×C11—21no—
398C22×C11—21no—
399C22×C11—21no—
400C22×C11—21no—
401C22×C11—21no—
402C22×C11—21no—
403C22×C11—21no—
404C22×C11—21no—
405C22×C11—21no—
406C22×C11—21no—
407C22×C11—21no—
408C22×C11—21no—
409C22×C11—42no—
410C22×C11—42no—
411C22×C11—44no—
412C22×C11—44no—
413C22×C11—44no—
414C22×C11—44no—
415C22×C11—42no—
416C22×C11—42no—
417C22×C11C2×#9912yes—
418C22×C11#41012yes—
419C22×C11C22×C22⋊C411yescharacteristic
420C22×C11#52012yes—
421C22×C11#53511yescharacteristic
422C22×C11#53611yescharacteristic
423C22×C11#53712yes—
424C2×D11—42no—
425C2×D11—42no—
426C2×D11—42no—
427C2×D11—84no—
428C4×C11—21no—
429C4×C11—21no—
430C4×C11—21no—
431C4×C11—21no—
432C4×C11—21no—
433C4×C11—21no—
434C4×C11—84no—
435C4×C11C2×#9912yes—
436C4×C11C2×#9912yes—
437Dic11—42no—
438Dic11—42no—
439Dic11—42no—
440Dic11—84no—
441C25C22×D1111yescharacteristic
442C2×#41—221no—
443C2×#41—221no—
444C2×#41—221no—
445C2×#41—221no—
446C2×#41—444no—
447C22×Q8—111no—
448C22×D4—112no—
449C22×D4—112no—
450C22×D4—112no—
451C22×D4—111no—
452C23×C4—22no—
453C23×C4—44no—
454C23×C4—112no—
455C23×C4C4×D1111yescharacteristic
456C23×C4C4×D1111yescharacteristic
457C23×C4C4×D1111yescharacteristic
458C23×C4C4×D1111yescharacteristic
459C23×C4D4411yescharacteristic
460C23×C4D4411yescharacteristic
461C23×C4D4411yescharacteristic
462C23×C4D4411yescharacteristic
463C23×C4C22⋊D1111yescharacteristic
464C23×C4C22⋊D1111yescharacteristic
465C23×C4C22⋊D1111yescharacteristic
466C23×C4C22⋊D1111yescharacteristic
467C23×C4C22×D1111yescharacteristic
468C23×C4C22×D1111yescharacteristic
469#123—222no—
470#123—222no—
471#123—222no—
472#123—222no—
473C22⋊Q8—221no—
474C22⋊Q8—221no—
475C22⋊Q8—221no—
476C22⋊Q8—221no—
477C22⋊Q8—221no—
478C22⋊Q8—221no—
479C22⋊Q8—221no—
480C22⋊Q8—221no—
481#121—221no—
482#121—221no—
483#121—221no—
484#121—221no—
485#121—221no—
486#121—221no—
487#121—221no—
488#121—221no—
489#120—222no—
490#120—222no—
491#120—222no—
492#120—222no—
493C4×D4—222no—
494C4×D4—222no—
495C4×D4—222no—
496C4×D4—222no—
497C4×D4—222no—
498C4×D4—222no—
499C4×D4—222no—
500C4×D4—222no—
501#117—221no—
502#117—221no—
503#117—221no—
504#117—221no—
505#117—444no—
506C2×C4⋊C4—22no—
507C2×C4⋊C4—22no—
508C2×C4⋊C4—44no—
509C2×C4⋊C4—111no—
510C2×C4⋊C4—111no—
511C2×C4⋊C4—112no—
512C2×C4⋊C4—112no—
513C2×C4⋊C4—222no—
514C2×C22⋊C4—22no—
515C2×C22⋊C4—44no—
516C2×C22⋊C4—112no—
517C2×C22⋊C4—112no—
518C2×C22⋊C4—112no—
519C2×C22⋊C4—112no—
520C2×C22⋊C4—112no—
521C2×C22⋊C4—114no—
522C2×C22⋊C4—222no—
523C2×C22⋊C4—222no—
524C2×C22⋊C4C22×D1114yes—
525C2×C42—112no—
526C2×C42—222no—
527#99—448no—
528#95—22no—
529#95—22no—
530#95—222no—
531#95—222no—
532C2×C11—22no—
533C2×C11—21no—
534C2×C11—22no—
535C2×C11—21no—
536C2×C11—22no—
537C2×C11—22no—
538C2×C11—41no—
539C2×C11—41no—
540C2×C11#231111yescharacteristic
541C2×C11C22×#9911yescharacteristic
542C2×C11C2×#41011yescharacteristic
543D11—82no—
544C24—22no—
545C24—22no—
546C24—42no—
547C24—42no—
548C24—112no—
549C24C2×C4×D1111yescharacteristic
550C24C2×C4×D1111yescharacteristic
551C24C2×D4411yescharacteristic
552C24C2×D4411yescharacteristic
553C24C2×C22⋊D1111yescharacteristic
554C24C2×C22⋊D1111yescharacteristic
555C24C23×D1111yescharacteristic
556#41—444no—
557#41—444no—
558#41—444no—
559#41—444no—
560C2×Q8—221no—
561C2×Q8—221no—
562C2×Q8—442no—
563C2×D4—222no—
564C2×D4—222no—
565C2×D4—222no—
566C2×D4—222no—
567C2×D4—222no—
568C2×D4—224no—
569C2×D4—224no—
570C2×D4—222no—
571C2×D4—221no—
572C2×D4—221no—
573C2×D4—442no—
574C2×D4—444no—
575C2×D4—444no—
576C22×C4—24no—
577C22×C4—24no—
578C22×C4—24no—
579C22×C4—24no—
580C22×C4—42no—
581C22×C4—42no—
582C22×C4—42no—
583C22×C4—42no—
584C22×C4—42no—
585C22×C4—42no—
586C22×C4—42no—
587C22×C4—42no—
588C22×C4—42no—
589C22×C4—42no—
590C22×C4—42no—
591C22×C4—44no—
592C22×C4—44no—
593C22×C4—44no—
594C22×C4—112no—
595C22×C4—112no—
596C22×C4—112no—
597C22×C4—222no—
598C22×C4—222no—
599C22×C4—224no—
600C22×C4—444no—
601C22×C4(C2×D11)⋊C411yescharacteristic
602C22×C4(C2×D11)⋊C411yescharacteristic
603C22×C4(C2×D11)⋊C411yescharacteristic
604C22×C4(C2×D11)⋊C411yescharacteristic
605C22×C4(C2×D11)⋊C411yescharacteristic
606C22×C4(C2×D11)⋊C411yescharacteristic
607C22×C4(C2×D11)⋊C411yescharacteristic
608C22×C4(C2×D11)⋊C411yescharacteristic
609C22×C4(C2×D11)⋊C411yescharacteristic
610C22×C4(C2×D11)⋊C411yescharacteristic
611C22×C4(C2×D11)⋊C411yescharacteristic
612C22×C4(C2×D11)⋊C411yescharacteristic
613C22×C4(C2×D11)⋊C411yescharacteristic
614C22×C4(C2×D11)⋊C411yescharacteristic
615C22×C4(C2×D11)⋊C411yescharacteristic
616C22×C4(C2×D11)⋊C411yescharacteristic
617C22×C4C2×C4×D1111yescharacteristic
618C22×C4C2×C4×D1111yescharacteristic
619C22×C4C2×C4×D1111yescharacteristic
620C22×C4C2×C4×D1111yescharacteristic
621C22×C4C2×D4411yescharacteristic
622C22×C4C2×D4411yescharacteristic
623C22×C4C2×D4411yescharacteristic
624C22×C4C2×D4411yescharacteristic
625C22×C4C2×C22⋊D1111yescharacteristic
626C22×C4C2×C22⋊D1111yescharacteristic
627C22×C4C2×C22⋊D1111yescharacteristic
628C22×C4C2×C22⋊D1111yescharacteristic
629C4⋊C4—44no—
630C4⋊C4—44no—
631C4⋊C4—221no—
632C4⋊C4—221no—
633C4⋊C4—221no—
634C4⋊C4—221no—
635C4⋊C4—222no—
636C4⋊C4—222no—
637C4⋊C4—222no—
638C4⋊C4—222no—
639C4⋊C4—444no—
640C22⋊C4—28no—
641C22⋊C4—44no—
642C22⋊C4—222no—
643C22⋊C4—222no—
644C22⋊C4—222no—
645C22⋊C4—222no—
646C22⋊C4—222no—
647C22⋊C4—222no—
648C22⋊C4—222no—
649C22⋊C4—222no—
650C22⋊C4—222no—
651C22⋊C4—222no—
652C22⋊C4—224no—
653C22⋊C4—224no—
654C22⋊C4—444no—
655C22⋊C4—444no—
656C42—222no—
657C42—222no—
658C42—444no—
659C11#2187411yescharacteristic, complemented, Sylow
660C23—22no—
661C23—21no—
662C23—21no—
663C23—22no—
664C23—22no—
665C23—22no—
666C23—22no—
667C23—22no—
668C23—22no—
669C23—22no—
670C23—21no—
671C23—21no—
672C23—22no—
673C23—22no—
674C23—41no—
675C23—41no—
676C23—41no—
677C23—41no—
678C23—41no—
679C23—41no—
680C23—41no—
681C23—41no—
682C23—48no—
683C23—48no—
684C23—222no—
685C23—224no—
686C23—442no—
687C23—442no—
688C23C2×(C2×D11)⋊C411yescharacteristic
689C23C2×(C2×D11)⋊C411yescharacteristic
690C23C2×(C2×D11)⋊C411yescharacteristic
691C23C2×(C2×D11)⋊C411yescharacteristic
692C23C22×C4×D1111yescharacteristic
693C23C22×D4411yescharacteristic
694C23#6703712yes—
695C23#6704012yes—
696C23C22×C22⋊D1111yescharacteristic
697Q8—442no—
698Q8—442no—
699D4—442no—
700D4—444no—
701D4—444no—
702D4—444no—
703D4—444no—
704D4—442no—
705D4—442no—
706D4—444no—
707D4—442no—
708C2×C4—22no—
709C2×C4—22no—
710C2×C4—22no—
711C2×C4—22no—
712C2×C4—22no—
713C2×C4—22no—
714C2×C4—22no—
715C2×C4—22no—
716C2×C4—22no—
717C2×C4—22no—
718C2×C4—22no—
719C2×C4—22no—
720C2×C4—22no—
721C2×C4—22no—
722C2×C4—22no—
723C2×C4—41no—
724C2×C4—41no—
725C2×C4—41no—
726C2×C4—41no—
727C2×C4—41no—
728C2×C4—41no—
729C2×C4—41no—
730C2×C4—41no—
731C2×C4—41no—
732C2×C4—41no—
733C2×C4—41no—
734C2×C4—41no—
735C2×C4—44no—
736C2×C4—44no—
737C2×C4—44no—
738C2×C4—88no—
739C2×C4—224no—
740C2×C4—222no—
741C2×C4—222no—
742C2×C4—222no—
743C2×C4—444no—
744C2×C4—444no—
745C2×C4—442no—
746C2×C4—442no—
747C2×C4—444no—
748C2×C4—444no—
749C2×C4—444no—
750C2×C4#6687014yescomplemented
751C2×C4C2×(C2×D11)⋊C411yescharacteristic
752C2×C4C2×(C2×D11)⋊C411yescharacteristic
753C2×C4C2×(C2×D11)⋊C411yescharacteristic
754C2×C4C2×(C2×D11)⋊C411yescharacteristic
755C2×C4C2×(C2×D11)⋊C411yescharacteristic
756C2×C4C2×(C2×D11)⋊C411yescharacteristic
757C2×C4C2×(C2×D11)⋊C411yescharacteristic
758C2×C4C2×(C2×D11)⋊C411yescharacteristic
759C22—24no—
760C22—24no—
761C22—21no—
762C22—21no—
763C22—21no—
764C22—21no—
765C22—21no—
766C22—21no—
767C22—21no—
768C22—21no—
769C22—21no—
770C22—21no—
771C22—21no—
772C22—21no—
773C22—21no—
774C22—21no—
775C22—21no—
776C22—21no—
777C22—42no—
778C22—42no—
779C22—44no—
780C22—44no—
781C22—44no—
782C22—44no—
783C22—42no—
784C22—42no—
785C22—442no—
786C22—442no—
787C22—442no—
788C22—884no—
789C22C2×#6687012yes—
790C22#1062261912yes—
791C22#1062303512yes—
792C22#1062304112yes—
793C22C22×(C2×D11)⋊C411yescharacteristic
794C22#1062333611yescharacteristic
795C22#1062334711yescharacteristic
796C4—21no—
797C4—21no—
798C4—21no—
799C4—21no—
800C4—21no—
801C4—21no—
802C4—84no—
803C4—442no—
804C4—442no—
805C4—442no—
806C4—884no—
807C4C2×#6687012yes—
808C4C2×#6687012yes—
809C2—21no—
810C2—22no—
811C2—22no—
812C2—21no—
813C2—22no—
814C2—22no—
815C2—41no—
816C2—41no—
817C2—882no—
818C2#1307120911yescharacteristic
819C2C22×#6687011yescharacteristic
820C2C2×#1062261911yescharacteristic
subgroupG/H
centerC22C22×(C2×D11)⋊C4
commutatorC23×C11C23×C4
FrattiniC24C23×D11
FittingC2×C11×#380C2
socleC22×C11C22×C22⋊C4
prime radicalC2×#10623322C2
cosocleC24×C11C24
hypercenterC2×#380D11
hypocenterC11#21874
LCSG ▷ C23×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C24×C4 ◁ C2×#380

Complements

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

NH ≅ G/Ntype
2. #13070999C2semidirect
3. #13069600C2semidirect
4. #13069451C2semidirect
5. #13069069C2semidirect
6. #13068601C2semidirect
7. C2×C11×#380C2semidirect
9. C22×#4339C4semidirect
21. C2×#66983C4semidirect
23. C2×#66982C4semidirect
24. C2×C4×C22⋊D11C4semidirect
27. C2×#66979C4semidirect
28. C2×#66977C4semidirect
68. C22×D44C2×C4semidirect
69. C22×C4×D11C2×C4semidirect
70. C22×Dic22C2×C4semidirect
107. C2×(C2×D11)⋊C4C2×C4semidirect
108. C2×(C2×D11)⋊C4C2×C4semidirect
115. C2×C4⋊Dic11C2×C4semidirect
116. C2×C4⋊Dic11C2×C4semidirect
125. C2×Dic11⋊C4C2×C4semidirect
126. C2×Dic11⋊C4C2×C4semidirect
128. C2×C4×Dic11C2×C4semidirect
252. C2×#380D11semidirect
325. C2×C4×C11#99semidirect
659. C11#21874semidirect
750. C2×C4#66870semidirect

Maximal subgroups

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

subgroupindex
C2×#106233222
#130709992
#130696002
#130694512
#130690692
#130686012
C2×C11×#3802
#2187411