Finite Group Databasebeta

← #14759116

Subgroups — #14759116

Order 2816.

1678 conjugacy classes of subgroups.

The subgroup lattice has 798 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623322C211yesmaximal, characteristic
2#13070999C211yesmaximal, characteristic, complemented
3#13069601C212yesmaximal, complemented
4#13069452C212yesmaximal, complemented
5#13069069C214yesmaximal, complemented
6C4×#66870C214yesmaximal, complemented
7C2×C4×C11×C22⋊C4C211yesmaximal, characteristic, complemented
8C24×C4×C11C2211yescharacteristic
9C22×#4339C411yescharacteristic, complemented
10C22×C11×C22⋊C4C2212yes—
11C22×C42×C11—21no—
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
30C4×C11×C22⋊C4—21no—
31C4×C11×C22⋊C4—21no—
32C4×C11×C22⋊C4C2212yes—
33C4×C11×C22⋊C4C2212yes—
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×C22⋊C4—22no—
72C2×C11×C22⋊C4—28no—
73C2×C11×C22⋊C4C2314yes—
74C2×C42×C11—22no—
75C2×C42×C11—22no—
76C2×C42×C11—44no—
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—216no—
134#21420—111nomaximal, Sylow
135C24×C11—24no—
136C24×C11—42no—
137C24×C11—42no—
138C24×C11C22×C411yescharacteristic
139C24×C11C22×C411yescharacteristic
140C24×C11C2×D411yescharacteristic
141C24×C11C2×D411yescharacteristic
142C24×C11C2×D411yescharacteristic
143C24×C11C2×D411yescharacteristic
144C24×C11C2411yescharacteristic
145C23×D11C22×C412yes—
146C22×C4×C11—24no—
147C22×C4×C11—24no—
148C22×C4×C11—24no—
149C22×C4×C11—28no—
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×C11C22⋊C411yescharacteristic
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×C11C2×D411yescharacteristic
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
192C2×C22⋊D11—22no—
193C2×C22⋊D11—22no—
194C2×C22⋊D11—22no—
195C2×C22⋊D11—22no—
196C2×C22⋊D11—22no—
197C2×C22⋊D11—22no—
198C2×C22⋊D11—28no—
199C2×C22⋊D11—44no—
200C2×C22⋊D11—44no—
201C22×Dic11—24no—
202C22×Dic11C22×C412yes—
203C22×Dic11C22×C412yes—
204C22×Dic11C22×C412yes—
205#4339—44no—
206#4339—44no—
207#4339—44no—
208#4339—44no—
209C2×D44—21no—
210C2×D44—21no—
211C2×D44—42no—
212C2×C4×D11—22no—
213C2×C4×D11—22no—
214C2×C4×D11—44no—
215C2×Dic22—21no—
216C2×Dic22—21no—
217C2×Dic22—42no—
218C11×C22⋊C4—28no—
219C11×C22⋊C4—24no—
220C11×C22⋊C4#4118yescomplemented
221C42×C11—44no—
222C42×C11—44no—
223C22⋊Dic11—22no—
224C22⋊Dic11—22no—
225C22⋊Dic11—22no—
226C22⋊Dic11—22no—
227C22⋊Dic11—22no—
228C22⋊Dic11—22no—
229C22⋊Dic11—28no—
230C22⋊Dic11—44no—
231C22⋊Dic11—44no—
232(C2×D11)⋊C4—22no—
233(C2×D11)⋊C4—22no—
234(C2×D11)⋊C4—22no—
235(C2×D11)⋊C4—22no—
236C4⋊Dic11—21no—
237C4⋊Dic11—21no—
238C4⋊Dic11—21no—
239C4⋊Dic11—21no—
240C4⋊Dic11—44no—
241Dic11⋊C4—22no—
242Dic11⋊C4—22no—
243Dic11⋊C4—22no—
244Dic11⋊C4—22no—
245C4×Dic11—22no—
246C4×Dic11—22no—
247C4×Dic11—44no—
248C2×#525—111no—
249#2280—111no—
250C2×C4×C22⋊C4D1111yescharacteristic, complemented
251#1996—112no—
252#1964—112no—
253#1898—114no—
254C4×#99—114no—
255C23×C11—22no—
256C23×C11—22no—
257C23×C11—22no—
258C23×C11—22no—
259C23×C11—22no—
260C23×C11—22no—
261C23×C11—22no—
262C23×C11—22no—
263C23×C11—22no—
264C23×C11—22no—
265C23×C11—22no—
266C23×C11—22no—
267C23×C11—41no—
268C23×C11—41no—
269C23×C11—41no—
270C23×C11—41no—
271C23×C11—41no—
272C23×C11—41no—
273C23×C11—41no—
274C23×C11—41no—
275C23×C11—416no—
276C23×C11C2×C22⋊C411yescharacteristic
277C23×C11C2×C22⋊C411yescharacteristic
278C23×C11C2×C22⋊C411yescharacteristic
279C23×C11C2×C22⋊C411yescharacteristic
280C23×C11C23×C411yescharacteristic
281C23×C11C22×D411yescharacteristic
282C23×C11C22×D411yescharacteristic
283C23×C11C2×#4114yes—
284C22×D11—22no—
285C22×D11—24no—
286C22×D11—42no—
287C22×D11—42no—
288C2×C4×C11—22no—
289C2×C4×C11—22no—
290C2×C4×C11—22no—
291C2×C4×C11—22no—
292C2×C4×C11—22no—
293C2×C4×C11—22no—
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—28no—
304C2×C4×C11—41no—
305C2×C4×C11—41no—
306C2×C4×C11—41no—
307C2×C4×C11—41no—
308C2×C4×C11—41no—
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—44no—
317C2×C4×C11—416no—
318C2×C4×C11—44no—
319C2×C4×C11#9914yescomplemented
320C2×C4×C11C2×C22⋊C411yescharacteristic
321C2×C4×C11C2×C22⋊C411yescharacteristic
322C2×C4×C11C2×C22⋊C411yescharacteristic
323C2×C4×C11C2×C22⋊C411yescharacteristic
324C2×C4×C11C2×C22⋊C411yescharacteristic
325C2×C4×C11C2×C22⋊C411yescharacteristic
326C2×C4×C11C2×C22⋊C411yescharacteristic
327C2×C4×C11C2×C22⋊C411yescharacteristic
328C22⋊D11—44no—
329C22⋊D11—44no—
330C22⋊D11—44no—
331C22⋊D11—44no—
332C22⋊D11—44no—
333C22⋊D11—44no—
334C2×Dic11—22no—
335C2×Dic11—22no—
336C2×Dic11—22no—
337C2×Dic11—24no—
338C2×Dic11—42no—
339C2×Dic11—42no—
340C2×Dic11—44no—
341C2×Dic11—44no—
342C2×Dic11—44no—
343D44—42no—
344D44—42no—
345C4×D11—44no—
346C4×D11—44no—
347Dic22—42no—
348Dic22—42no—
349C22×#41—111no—
350C24×C4C2×D1111yescharacteristic
351#525—221no—
352#525—221no—
353#525—221no—
354#525—221no—
355#525—221no—
356#525—221no—
357#525—221no—
358#525—221no—
359C2×#123—112no—
360C2×C22⋊Q8—111no—
361C2×C22⋊Q8—111no—
362C2×#121—111no—
363C2×#121—111no—
364C2×#120—112no—
365C2×C4×D4—112no—
366C2×C4×D4—112no—
367C2×#117—111no—
368C2×#117—221no—
369C22×C22⋊C4C2×D1112yes—
370C22×C42—21no—
371C2×#99—118no—
372#381—221no—
373#380—112no—
374#380—221no—
375#379—112no—
376C4×C22⋊C4—21no—
377C4×C22⋊C4—21no—
378C4×C22⋊C4—112no—
379C4×C22⋊C4—221no—
380C4×C22⋊C4C2×D1112yes—
381C4×C22⋊C4C2×D1112yes—
382C2×#95—21no—
383#342—118no—
384C22×C11—28no—
385C22×C11—21no—
386C22×C11—21no—
387C22×C11—21no—
388C22×C11—21no—
389C22×C11—21no—
390C22×C11—21no—
391C22×C11—21no—
392C22×C11—21no—
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—44no—
402C22×C11—44no—
403C22×C11—44no—
404C22×C11—44no—
405C22×C11—44no—
406C22×C11—44no—
407C22×C11C2×#9912yes—
408C22×C11#41012yes—
409C22×C11C22×C22⋊C411yescharacteristic
410C22×C11C4×#4112yes—
411C22×C11#52512yes—
412C22×C11#53212yes—
413C2×D11—42no—
414C2×D11—42no—
415C2×D11—42no—
416C2×D11—84no—
417C4×C11—21no—
418C4×C11—21no—
419C4×C11—21no—
420C4×C11—21no—
421C4×C11—21no—
422C4×C11—21no—
423C4×C11—48no—
424C4×C11C2×#9912yes—
425C4×C11C2×#9912yes—
426Dic11—42no—
427Dic11—42no—
428Dic11—42no—
429Dic11—84no—
430C25C22×D1111yescharacteristic
431C2×#41—221no—
432C2×#41—221no—
433C2×#41—221no—
434C2×#41—221no—
435C2×#41—444no—
436C22×Q8—111no—
437C22×D4—112no—
438C22×D4—112no—
439C22×D4—112no—
440C22×D4—111no—
441C23×C4—22no—
442C23×C4—44no—
443C23×C4—112no—
444C23×C4C4×D1111yescharacteristic
445C23×C4C4×D1111yescharacteristic
446C23×C4C4×D1111yescharacteristic
447C23×C4C4×D1111yescharacteristic
448C23×C4D4411yescharacteristic
449C23×C4D4411yescharacteristic
450C23×C4D4411yescharacteristic
451C23×C4D4411yescharacteristic
452C23×C4C22⋊D1111yescharacteristic
453C23×C4C22⋊D1111yescharacteristic
454C23×C4C22⋊D1111yescharacteristic
455C23×C4C22⋊D1111yescharacteristic
456C23×C4C22×D1111yescharacteristic
457C23×C4C22×D1111yescharacteristic
458#123—222no—
459#123—222no—
460#123—222no—
461#123—222no—
462C22⋊Q8—221no—
463C22⋊Q8—221no—
464C22⋊Q8—221no—
465C22⋊Q8—221no—
466C22⋊Q8—221no—
467C22⋊Q8—221no—
468C22⋊Q8—221no—
469C22⋊Q8—221no—
470#121—221no—
471#121—221no—
472#121—221no—
473#121—221no—
474#121—221no—
475#121—221no—
476#121—221no—
477#121—221no—
478#120—222no—
479#120—222no—
480#120—222no—
481#120—222no—
482C4×D4—222no—
483C4×D4—222no—
484C4×D4—222no—
485C4×D4—222no—
486C4×D4—222no—
487C4×D4—222no—
488C4×D4—222no—
489C4×D4—222no—
490#117—221no—
491#117—221no—
492#117—221no—
493#117—221no—
494#117—444no—
495C2×C4⋊C4—111no—
496C2×C4⋊C4—111no—
497C2×C4⋊C4—112no—
498C2×C4⋊C4—112no—
499C2×C4⋊C4—222no—
500C2×C22⋊C4—22no—
501C2×C22⋊C4—28no—
502C2×C22⋊C4—112no—
503C2×C22⋊C4—112no—
504C2×C22⋊C4—112no—
505C2×C22⋊C4—112no—
506C2×C22⋊C4—112no—
507C2×C22⋊C4—114no—
508C2×C22⋊C4—222no—
509C2×C22⋊C4—222no—
510C2×C22⋊C4C22×D1114yes—
511C2×C42—22no—
512C2×C42—22no—
513C2×C42—44no—
514C2×C42—112no—
515C2×C42—222no—
516#99—2216no—
517#95—22no—
518#95—22no—
519#95—222no—
520#95—222no—
521C2×C11—22no—
522C2×C11—22no—
523C2×C11—22no—
524C2×C11—22no—
525C2×C11—22no—
526C2×C11—41no—
527C2×C11—41no—
528C2×C11#229711yescharacteristic
529C2×C11C22×#9911yescharacteristic
530C2×C11C2×#41011yescharacteristic
531D11—82no—
532C24—24no—
533C24—42no—
534C24—42no—
535C24—112no—
536C24C2×C4×D1111yescharacteristic
537C24C2×C4×D1111yescharacteristic
538C24C2×D4411yescharacteristic
539C24C2×D4411yescharacteristic
540C24C2×C22⋊D1111yescharacteristic
541C24C2×C22⋊D1111yescharacteristic
542C24C23×D1111yescharacteristic
543#41—444no—
544#41—444no—
545#41—444no—
546#41—444no—
547C2×Q8—221no—
548C2×Q8—221no—
549C2×Q8—442no—
550C2×D4—222no—
551C2×D4—222no—
552C2×D4—222no—
553C2×D4—222no—
554C2×D4—222no—
555C2×D4—228no—
556C2×D4—222no—
557C2×D4—221no—
558C2×D4—221no—
559C2×D4—442no—
560C2×D4—444no—
561C2×D4—444no—
562C22×C4—24no—
563C22×C4—24no—
564C22×C4—24no—
565C22×C4—28no—
566C22×C4—24no—
567C22×C4—42no—
568C22×C4—42no—
569C22×C4—42no—
570C22×C4—42no—
571C22×C4—42no—
572C22×C4—42no—
573C22×C4—42no—
574C22×C4—42no—
575C22×C4—42no—
576C22×C4—42no—
577C22×C4—42no—
578C22×C4—44no—
579C22×C4—44no—
580C22×C4—112no—
581C22×C4—112no—
582C22×C4—112no—
583C22×C4—222no—
584C22×C4—222no—
585C22×C4—224no—
586C22×C4—444no—
587C22×C4(C2×D11)⋊C411yescharacteristic
588C22×C4(C2×D11)⋊C411yescharacteristic
589C22×C4(C2×D11)⋊C411yescharacteristic
590C22×C4(C2×D11)⋊C411yescharacteristic
591C22×C4(C2×D11)⋊C411yescharacteristic
592C22×C4(C2×D11)⋊C411yescharacteristic
593C22×C4(C2×D11)⋊C411yescharacteristic
594C22×C4(C2×D11)⋊C411yescharacteristic
595C22×C4(C2×D11)⋊C411yescharacteristic
596C22×C4(C2×D11)⋊C411yescharacteristic
597C22×C4(C2×D11)⋊C411yescharacteristic
598C22×C4(C2×D11)⋊C411yescharacteristic
599C22×C4(C2×D11)⋊C411yescharacteristic
600C22×C4(C2×D11)⋊C411yescharacteristic
601C22×C4(C2×D11)⋊C411yescharacteristic
602C22×C4(C2×D11)⋊C411yescharacteristic
603C22×C4C2×C4×D1111yescharacteristic
604C22×C4C2×C4×D1111yescharacteristic
605C22×C4C2×C4×D1111yescharacteristic
606C22×C4C2×C4×D1111yescharacteristic
607C22×C4C2×D4411yescharacteristic
608C22×C4C2×D4411yescharacteristic
609C22×C4C2×D4411yescharacteristic
610C22×C4C2×D4411yescharacteristic
611C22×C4C2×C22⋊D1111yescharacteristic
612C22×C4C2×C22⋊D1111yescharacteristic
613C22×C4C2×C22⋊D1111yescharacteristic
614C22×C4C2×C22⋊D1111yescharacteristic
615C4⋊C4—221no—
616C4⋊C4—221no—
617C4⋊C4—221no—
618C4⋊C4—221no—
619C4⋊C4—222no—
620C4⋊C4—222no—
621C4⋊C4—222no—
622C4⋊C4—222no—
623C4⋊C4—444no—
624C22⋊C4—28no—
625C22⋊C4—24no—
626C22⋊C4—222no—
627C22⋊C4—222no—
628C22⋊C4—222no—
629C22⋊C4—222no—
630C22⋊C4—222no—
631C22⋊C4—222no—
632C22⋊C4—222no—
633C22⋊C4—222no—
634C22⋊C4—222no—
635C22⋊C4—222no—
636C22⋊C4—228no—
637C22⋊C4—444no—
638C22⋊C4—444no—
639C22⋊C4#433918yescomplemented
640C42—44no—
641C42—44no—
642C42—222no—
643C42—222no—
644C42—444no—
645C11#2142011yescharacteristic, complemented, Sylow
646C23—22no—
647C23—22no—
648C23—22no—
649C23—22no—
650C23—22no—
651C23—22no—
652C23—22no—
653C23—22no—
654C23—22no—
655C23—22no—
656C23—22no—
657C23—22no—
658C23—41no—
659C23—41no—
660C23—41no—
661C23—41no—
662C23—41no—
663C23—41no—
664C23—41no—
665C23—41no—
666C23—416no—
667C23—222no—
668C23—224no—
669C23—442no—
670C23—442no—
671C23C2×(C2×D11)⋊C411yescharacteristic
672C23C2×(C2×D11)⋊C411yescharacteristic
673C23C2×(C2×D11)⋊C411yescharacteristic
674C23C2×(C2×D11)⋊C411yescharacteristic
675C23C22×C4×D1111yescharacteristic
676C23C22×D4411yescharacteristic
677C23C2×#433914yes—
678C23C22×C22⋊D1111yescharacteristic
679Q8—442no—
680Q8—442no—
681D4—442no—
682D4—444no—
683D4—444no—
684D4—444no—
685D4—444no—
686D4—444no—
687D4—444no—
688D4—442no—
689C2×C4—22no—
690C2×C4—22no—
691C2×C4—22no—
692C2×C4—22no—
693C2×C4—22no—
694C2×C4—22no—
695C2×C4—22no—
696C2×C4—22no—
697C2×C4—22no—
698C2×C4—22no—
699C2×C4—22no—
700C2×C4—22no—
701C2×C4—22no—
702C2×C4—22no—
703C2×C4—22no—
704C2×C4—28no—
705C2×C4—41no—
706C2×C4—41no—
707C2×C4—41no—
708C2×C4—41no—
709C2×C4—41no—
710C2×C4—41no—
711C2×C4—41no—
712C2×C4—41no—
713C2×C4—41no—
714C2×C4—41no—
715C2×C4—41no—
716C2×C4—41no—
717C2×C4—44no—
718C2×C4—416no—
719C2×C4—44no—
720C2×C4—224no—
721C2×C4—222no—
722C2×C4—222no—
723C2×C4—222no—
724C2×C4—444no—
725C2×C4—444no—
726C2×C4—442no—
727C2×C4—442no—
728C2×C4—444no—
729C2×C4—444no—
730C2×C4—444no—
731C2×C4#6687014yescomplemented
732C2×C4C2×(C2×D11)⋊C411yescharacteristic
733C2×C4C2×(C2×D11)⋊C411yescharacteristic
734C2×C4C2×(C2×D11)⋊C411yescharacteristic
735C2×C4C2×(C2×D11)⋊C411yescharacteristic
736C2×C4C2×(C2×D11)⋊C411yescharacteristic
737C2×C4C2×(C2×D11)⋊C411yescharacteristic
738C2×C4C2×(C2×D11)⋊C411yescharacteristic
739C2×C4C2×(C2×D11)⋊C411yescharacteristic
740C22—28no—
741C22—21no—
742C22—21no—
743C22—21no—
744C22—21no—
745C22—21no—
746C22—21no—
747C22—21no—
748C22—21no—
749C22—21no—
750C22—21no—
751C22—21no—
752C22—21no—
753C22—21no—
754C22—21no—
755C22—21no—
756C22—21no—
757C22—44no—
758C22—44no—
759C22—44no—
760C22—44no—
761C22—44no—
762C22—44no—
763C22—442no—
764C22—442no—
765C22—442no—
766C22—884no—
767C22C2×#6687012yes—
768C22#1062261912yes—
769C22C4×#433912yes—
770C22#1062300812yes—
771C22C22×(C2×D11)⋊C411yescharacteristic
772C22#1062332212yes—
773C4—21no—
774C4—21no—
775C4—21no—
776C4—21no—
777C4—21no—
778C4—21no—
779C4—48no—
780C4—442no—
781C4—442no—
782C4—442no—
783C4—884no—
784C4C2×#6687012yes—
785C4C2×#6687012yes—
786C2—22no—
787C2—22no—
788C2—22no—
789C2—22no—
790C2—22no—
791C2—41no—
792C2—41no—
793C2—882no—
794C2#1307110611yescharacteristic
795C2C22×#6687011yescharacteristic
796C2C2×#1062261911yescharacteristic
subgroupG/H
centerC2×C4C2×(C2×D11)⋊C4
commutatorC23×C11C23×C4
FrattiniC24C23×D11
FittingC2×C4×C11×C22⋊C4C2
socleC22×C11C22×C22⋊C4
prime radicalC2×#10623322C2
cosocleC24×C11C24
hypercenterC2×C4×C22⋊C4D11
hypocenterC11#21420
LCSG ▷ C23×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C24×C4 ◁ C2×C4×C22⋊C4

Complements

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

NH ≅ G/Ntype
2. #13070999C2semidirect
3. #13069601C2semidirect
4. #13069452C2semidirect
5. #13069069C2semidirect
6. C4×#66870C2semidirect
7. C2×C4×C11×C22⋊C4C2semidirect
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
220. C11×C22⋊C4#41semidirect
250. C2×C4×C22⋊C4D11semidirect
319. C2×C4×C11#99semidirect
639. C22⋊C4#4339semidirect
645. C11#21420semidirect
731. 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
#130696012
#130694522
#130690692
C4×#668702
C2×C4×C11×C22⋊C42
#2142011