Finite Group Databasebeta

← #14720145

Subgroups — #14720145

Order 2816.

1314 conjugacy classes of subgroups.

The subgroup lattice has 890 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C4×#41×D11C211yesmaximal, characteristic
2C2×#10622446C211yesmaximal, characteristic, complemented
3D11×#431C211yesmaximal, characteristic, complemented
4#13067009C212yesmaximal, complemented
5#13067005C212yesmaximal, complemented
6#13067004C211yesmaximal, characteristic, complemented
7#13067003C211yesmaximal, characteristic, complemented
8#13067001C211yesmaximal, characteristic, complemented
9#13066997C212yesmaximal, complemented
10#13066995C212yesmaximal, complemented
11C11×#1477C211yesmaximal, characteristic, complemented
12C2×#41×D11C411yescharacteristic
13C4×C11×#41C2211yescharacteristic
14#41×Dic11C411yescharacteristic
15C4×#4343C411yescharacteristic
16C4×#4343C2211yescharacteristic
17C4×Q8×D11C411yescharacteristic
18C4×Q8×D11C2211yescharacteristic
19C4×D4×D11—21no—
20C4×D4×D11—21no—
21C4×D4×D11C411yescharacteristic
22C4×D4×D11C2211yescharacteristic
23C4×#4341—21no—
24C4×#4341—21no—
25C4×#4341C411yescharacteristic
26C4×#4341C2211yescharacteristic
27#10623053—21no—
28#10623053C411yescharacteristic
29D11×#117—21no—
30D11×#117C411yescharacteristic
31C4×#4339—21no—
32C4×#4339C2211yescharacteristic
33C2×C42×D11—21no—
34C2×C42×D11C2211yescharacteristic
35C11×#431C2211yescharacteristic, complemented
36C2×C11×C4⋊C8C2211yescharacteristic, complemented
37C2×(C2×D11)⋊C8—21no—
38C2×C8×Dic11—21no—
39#10622538C2211yescharacteristic, complemented
40C2×C4⋊(C11⋊C8)C2211yescharacteristic, complemented
41#10622446—21no—
42#10622446—21no—
43#10622446—21no—
44#10622446C2212yes—
45#10622446C2212yescomplemented
46D11×C4⋊C8—21no—
47D11×C22⋊C8—21no—
48#10622331—21no—
49#10622298C2212yes—
50C4×C8×D11C2212yescomplemented
51C11×Q8⋊C8C2212yescomplemented
52C11×D4⋊C8C2212yescomplemented
53Q8⋊(C11⋊C8)C2212yescomplemented
54D4⋊(C11⋊C8)C2212yescomplemented
55#10622122C2212yescomplemented
56#10622121C2212yescomplemented
57#10622097C2212yescomplemented
58#10622094C2212yescomplemented
59C2×C11×#41C2×C411yescharacteristic
60#41×D11—24no—
61#41×D11C818yescomplemented
62C2×#4343C2×C411yescharacteristic
63C2×Q8×D11C2×C411yescharacteristic
64C2×#4341—21no—
65C2×#4341C2×C411yescharacteristic
66C2×D4×D11—21no—
67C2×D4×D11C2×C411yescharacteristic
68C2×#4339—21no—
69C2×#4339C2×C411yescharacteristic
70C22×C4×D11—21no—
71C22×C4×D11—21no—
72C22×C4×D11—21no—
73C22×C4×D11C2×C411yescharacteristic
74C22×C4×D11D411yescharacteristic
75C22×C4×D11D411yescharacteristic
76C22×C8×C11—21no—
77C4×Q8×C11C2×C411yescharacteristic
78C4×Q8×C11C2311yescharacteristic
79C4×D4×C11—21no—
80C4×D4×C11—21no—
81C4×D4×C11C2×C411yescharacteristic
82C4×D4×C11C2311yescharacteristic
83C11×#117—21no—
84C11×#117C2×C411yescharacteristic
85C2×C42×C11—21no—
86C2×C42×C11C2311yescharacteristic
87Q8×Dic11C2×C411yescharacteristic
88Q8×Dic11C2×C411yescharacteristic
89D4×Dic11—21no—
90D4×Dic11—21no—
91D4×Dic11C2×C411yescharacteristic
92D4×Dic11C2×C411yescharacteristic
93C4×C22⋊D11—21no—
94C4×C22⋊D11—21no—
95C4×C22⋊D11—21no—
96C4×C22⋊D11—21no—
97C4×C22⋊D11—21no—
98C4×C22⋊D11—21no—
99#66979—21no—
100#66979C2×C411yescharacteristic
101C2×C4×Dic11—21no—
102C2×C4×Dic11—21no—
103C2×C4×Dic11—21no—
104C2×C4×Dic11C2×C411yescharacteristic
105C2×C4×Dic11D411yescharacteristic
106C2×C4×Dic11D411yescharacteristic
107C22×C11⋊C8—21no—
108C2×C8×D11—22no—
109#66946—21no—
110#66946—21no—
111#66946C2×C411yescharacteristic
112#66946C2×C411yescharacteristic
113#66945—21no—
114#66945—21no—
115#66945C2×C411yescharacteristic
116#66945C2×C411yescharacteristic
117C4⋊C4×D11—21no—
118C4⋊C4×D11—21no—
119C4⋊C4×D11C2×C411yescharacteristic
120C4⋊C4×D11C2×C411yescharacteristic
121#66940—21no—
122#66940—21no—
123#66940C2×C411yescharacteristic
124#66940C2×C411yescharacteristic
125(C22⋊D11)⋊C4—21no—
126(C22⋊D11)⋊C4—21no—
127(C22⋊D11)⋊C4—21no—
128(C22⋊D11)⋊C4—21no—
129(C22⋊D11)⋊C4—21no—
130(C22⋊D11)⋊C4—21no—
131C22⋊C4×D11—21no—
132C22⋊C4×D11—21no—
133C22⋊C4×D11—21no—
134#66930—21no—
135#66930—21no—
136#66930—21no—
137C4×D44—21no—
138C4×D44—21no—
139C4×D44C2×C411yescharacteristic
140C4×D44C2311yescharacteristic
141#66925—21no—
142#66925—21no—
143#66925—21no—
144C42×D11—21no—
145C42×D11—21no—
146C42×D11—21no—
147C42×D11—21no—
148C42×D11—21no—
149C42×D11—21no—
150C42×D11—21no—
151C42×D11C2×C411yescharacteristic
152C42×D11C2×C411yescharacteristic
153C42×D11D411yescharacteristic
154C42×D11D411yescharacteristic
155C42×D11D411yescharacteristic
156C42×D11D411yescharacteristic
157C42×D11C2311yescharacteristic
158C42×D11C2311yescharacteristic
159C4×Dic22—21no—
160C4×Dic22—21no—
161C4×Dic22C2×C411yescharacteristic
162C4×Dic22C2311yescharacteristic
163C11×C4⋊C8—21no—
164C11×C4⋊C8—21no—
165C11×C4⋊C8C2312yes—
166C11×C22⋊C8—21no—
167C4×C8×C11C2312yes—
168C22⋊(C11⋊C8)—21no—
169(C2×D11)⋊C8—22no—
170(C2×D11)⋊C8—22no—
171(C2×D11)⋊C8—22no—
172Dic11⋊C8—22no—
173C8×Dic11—22no—
174C8×Dic11—22no—
175C8×Dic11—22no—
176C4⋊(C11⋊C8)—21no—
177C4⋊(C11⋊C8)—21no—
178C4⋊(C11⋊C8)C2312yes—
179C4×C11⋊C8C2312yes—
180#17437—111nomaximal, Sylow
181C23×D11—21no—
182C23×D11C22⋊C411yescharacteristic
183C11×#41—22no—
184C11×#41C2×C814yescomplemented
185C2×Q8×C11C22×C411yescharacteristic
186C2×D4×C11—21no—
187C2×D4×C11C22×C411yescharacteristic
188C22×C4×C11—21no—
189C22×C4×C11—21no—
190C22×C4×C11—21no—
191C22×C4×C11C22×C411yescharacteristic
192C22×C4×C11C2×D411yescharacteristic
193C22×C4×C11C2×D411yescharacteristic
194C2×C22⋊D11—21no—
195C2×C22⋊D11—21no—
196C2×C22⋊D11—21no—
197C22×Dic11—21no—
198C22×Dic11—21no—
199C22×Dic11—21no—
200C22×Dic11C22⋊C411yescharacteristic
201C22×Dic11C22⋊C411yescharacteristic
202C22×Dic11C22⋊C411yescharacteristic
203#4343—22no—
204#4343C2×C814yescomplemented
205Q8×D11—22no—
206Q8×D11C2×C814yescomplemented
207#4341—28no—
208#4341—22no—
209#4341C2×C814yescomplemented
210D4×D11—22no—
211D4×D11—28no—
212D4×D11C2×C814yescomplemented
213#4339—28no—
214#4339—22no—
215#4339C2×C814yescomplemented
216C2×D44—21no—
217C2×D44C22×C411yescharacteristic
218C2×C4×D11—21no—
219C2×C4×D11—28no—
220C2×C4×D11—21no—
221C2×C4×D11—21no—
222C2×C4×D11—21no—
223C2×C4×D11—21no—
224C2×C4×D11—21no—
225C2×C4×D11—21no—
226C2×C4×D11—21no—
227C2×C4×D11—21no—
228C2×C4×D11—41no—
229C2×C4×D11—41no—
230C2×C4×D11—42no—
231C2×C4×D11—44no—
232C2×C4×D11—42no—
233C2×C4×D11—42no—
234C2×C4×D11C22⋊C411yescharacteristic
235C2×C4×D11C22⋊C411yescharacteristic
236C2×C4×D11C22⋊C411yescharacteristic
237C2×C4×D11C22⋊C411yescharacteristic
238C2×C4×D11C22⋊C411yescharacteristic
239C2×C4×D11C22⋊C411yescharacteristic
240C2×C4×D11C2×C814yes—
241C2×C4×D11M1614yes—
242C2×C4×D11C22×C411yescharacteristic
243C2×C4×D11C22×C411yescharacteristic
244C2×C4×D11C2×D411yescharacteristic
245C2×C4×D11C2×D411yescharacteristic
246C2×C4×D11C2×D411yescharacteristic
247C2×C4×D11C2×D411yescharacteristic
248C2×Dic22—21no—
249C2×Dic22C22×C411yescharacteristic
250C2×C8×C11—22no—
251C2×C8×C11—22no—
252C2×C8×C11—42no—
253C11×C4⋊C4—21no—
254C11×C4⋊C4—21no—
255C11×C4⋊C4C22×C411yescharacteristic
256C11×C4⋊C4C22×C411yescharacteristic
257C11×C22⋊C4—21no—
258C11×C22⋊C4—21no—
259C11×C22⋊C4—21no—
260C42×C11—21no—
261C42×C11—21no—
262C42×C11—21no—
263C42×C11C22×C411yescharacteristic
264C42×C11C2×D411yescharacteristic
265C42×C11C2×D411yescharacteristic
266C42×C11C2411yescharacteristic
267C22⋊Dic11—21no—
268C22⋊Dic11—21no—
269C22⋊Dic11—21no—
270(C2×D11)⋊C4—21no—
271(C2×D11)⋊C4—21no—
272(C2×D11)⋊C4—21no—
273(C2×D11)⋊C4—21no—
274(C2×D11)⋊C4—21no—
275(C2×D11)⋊C4—21no—
276C4⋊Dic11—21no—
277C4⋊Dic11—21no—
278C4⋊Dic11C22×C411yescharacteristic
279C4⋊Dic11C22×C411yescharacteristic
280Dic11⋊C4—21no—
281Dic11⋊C4—21no—
282Dic11⋊C4—21no—
283Dic11⋊C4—21no—
284Dic11⋊C4—21no—
285Dic11⋊C4—21no—
286C4×Dic11—21no—
287C4×Dic11—21no—
288C4×Dic11—21no—
289C4×Dic11—21no—
290C4×Dic11—21no—
291C4×Dic11—21no—
292C4×Dic11—21no—
293C4×Dic11—21no—
294C4×Dic11—21no—
295C4×Dic11C22⋊C411yescharacteristic
296C4×Dic11C22⋊C411yescharacteristic
297C4×Dic11C22⋊C411yescharacteristic
298C4×Dic11C22⋊C411yescharacteristic
299C4×Dic11C22⋊C411yescharacteristic
300C4×Dic11C22⋊C411yescharacteristic
301C4×Dic11C22×C411yescharacteristic
302C4×Dic11C22×C411yescharacteristic
303C4×Dic11C2×D411yescharacteristic
304C4×Dic11C2×D411yescharacteristic
305C4×Dic11C2×D411yescharacteristic
306C4×Dic11C2×D411yescharacteristic
307C2×C11⋊C8—22no—
308C2×C11⋊C8—22no—
309C2×C11⋊C8—42no—
310C8×D11—44no—
311C2×C4×#41—111no—
312C2×#431—111no—
313C2×#431—111no—
314#1479—112no—
315#1478—112no—
316#1477—111no—
317#1477—111no—
318#1477—111no—
319#1477D1111yescharacteristic, complemented
320#1476—112no—
321#1476—112no—
322C23×C11—21no—
323C23×C11C2×C22⋊C411yescharacteristic
324C22×D11—21no—
325C22×D11—24no—
326C22×D11—41no—
327C22×D11—41no—
328C22×D11—42no—
329C22×D11—42no—
330C22×D11C22⋊C814yes—
331C22×D11C2×C22⋊C411yescharacteristic
332C22×D11C2×C22⋊C411yescharacteristic
333Q8×C11—21no—
334Q8×C11C22×C812yes—
335D4×C11—24no—
336D4×C11—21no—
337D4×C11C22×C812yes—
338C2×C4×C11—21no—
339C2×C4×C11—21no—
340C2×C4×C11—21no—
341C2×C4×C11—24no—
342C2×C4×C11—21no—
343C2×C4×C11—21no—
344C2×C4×C11—41no—
345C2×C4×C11—42no—
346C2×C4×C11—41no—
347C2×C4×C11—41no—
348C2×C4×C11C2×C22⋊C411yescharacteristic
349C2×C4×C11C2×C22⋊C411yescharacteristic
350C2×C4×C11C2×C22⋊C411yescharacteristic
351C2×C4×C11C22×C812yes—
352C2×C4×C11C2×M1612yes—
353C2×C4×C11C23×C411yescharacteristic
354C2×C4×C11C22×D411yescharacteristic
355C2×C4×C11C22×D411yescharacteristic
356C22⋊D11—24no—
357C22⋊D11—24no—
358C22⋊D11—24no—
359C2×Dic11—21no—
360C2×Dic11—24no—
361C2×Dic11—22no—
362C2×Dic11—21no—
363C2×Dic11—21no—
364C2×Dic11—41no—
365C2×Dic11—42no—
366C2×Dic11—42no—
367C2×Dic11C22⋊C814yes—
368C2×Dic11C2×C22⋊C411yescharacteristic
369C2×Dic11C2×C22⋊C411yescharacteristic
370C2×Dic11C2×C22⋊C411yescharacteristic
371C2×Dic11C2×C22⋊C411yescharacteristic
372C2×Dic11C2×C22⋊C411yescharacteristic
373C2×Dic11C2×C22⋊C411yescharacteristic
374D44—24no—
375D44—21no—
376D44C22×C812yes—
377C4×D11—24no—
378C4×D11—21no—
379C4×D11—21no—
380C4×D11—21no—
381C4×D11—21no—
382C4×D11—24no—
383C4×D11—24no—
384C4×D11—22no—
385C4×D11—22no—
386C4×D11—41no—
387C4×D11—41no—
388C4×D11—41no—
389C4×D11—41no—
390C4×D11—42no—
391C4×D11—42no—
392C4×D11—42no—
393C4×D11—42no—
394C4×D11—41no—
395C4×D11—41no—
396C4×D11—42no—
397C4×D11C22⋊C814yes—
398C4×D11C22⋊C814yes—
399C4×D11C22×C812yes—
400C4×D11C22×C812yes—
401C4×D11C2×M1612yes—
402C4×D11C2×M1612yes—
403Dic22—21no—
404Dic22—24no—
405Dic22C22×C812yes—
406C8×C11—42no—
407C8×C11—42no—
408C11⋊C8—42no—
409C11⋊C8—42no—
410C22×#41—111no—
411C4×#41—111no—
412C4×#41—111no—
413C4×#41—111no—
414C4×#41—111no—
415C4×#41—111no—
416C4×#41—111no—
417C4×#41—111no—
418C4×#41—221no—
419C4×#41—221no—
420C4×#41—221no—
421C4×#41—221no—
422C4×#41C2×D1111yescharacteristic
423C2×C4×Q8—111no—
424C2×C4×Q8—111no—
425C2×C4×D4—111no—
426C2×C4×D4—111no—
427C2×C4×D4—221no—
428C2×C4×D4—221no—
429C2×#117—111no—
430C2×#117—221no—
431C22×C42—111no—
432C22×C42—221no—
433#431—111no—
434#431—112no—
435#431—112no—
436#431—112no—
437#431—221no—
438#431—221no—
439#431—221no—
440#431—221no—
441#431C2×D1111yescharacteristic, complemented
442C2×C4⋊C8—111no—
443C2×C4⋊C8—221no—
444C2×C4⋊C8C2×D1111yescharacteristic, complemented
445C2×C22⋊C8—221no—
446C2×C22⋊C8—221no—
447C2×C4×C8—112no—
448C2×C4×C8—221no—
449Q8⋊C8—112no—
450Q8⋊C8—112no—
451Q8⋊C8—112no—
452Q8⋊C8C2×D1112yescomplemented
453D4⋊C8—112no—
454D4⋊C8—112no—
455D4⋊C8—112no—
456D4⋊C8C2×D1112yescomplemented
457C22×C11—21no—
458C22×C11—21no—
459C22×C11—22no—
460C22×C11—41no—
461C22×C11—41no—
462C22×C11C2×C22⋊C812yes—
463C22×C11C22×C22⋊C411yescharacteristic
464C2×D11—21no—
465C2×D11—21no—
466C2×D11—21no—
467C2×D11—21no—
468C2×D11—22no—
469C2×D11—44no—
470C2×D11—48no—
471C2×D11—41no—
472C2×D11—41no—
473C2×D11C2×C22⋊C812yes—
474C2×D11C2×C22⋊C812yes—
475C4×C11—22no—
476C4×C11—21no—
477C4×C11—21no—
478C4×C11—21no—
479C4×C11—41no—
480C4×C11—41no—
481C4×C11C2×C22⋊C812yes—
482C4×C11C23×C811yescharacteristic
483C4×C11C22×M1611yescharacteristic
484C4×C11#57511yescharacteristic
485C4×C11#57511yescharacteristic
486Dic11—22no—
487Dic11—21no—
488Dic11—21no—
489Dic11—21no—
490Dic11—41no—
491Dic11—41no—
492Dic11C2×C22⋊C812yes—
493Dic11C2×C22⋊C812yes—
494Dic11#42112yes—
495C2×#41—118no—
496C2×#41—111no—
497C2×#41—111no—
498C2×#41—111no—
499C2×#41—221no—
500C2×#41—221no—
501C2×#41—224no—
502C2×#41C4×D1111yescharacteristic
503C22×Q8—111no—
504C22×D4—111no—
505C22×D4—221no—
506C23×C4—111no—
507C23×C4—111no—
508C23×C4—111no—
509C23×C4—221no—
510C23×C4—221no—
511C23×C4—221no—
512C22×C8—21no—
513C22×C8—222no—
514C22×C8—221no—
515C4×Q8—111no—
516C4×Q8—111no—
517C4×Q8—111no—
518C4×Q8—111no—
519C4×Q8—111no—
520C4×Q8—111no—
521C4×Q8—221no—
522C4×Q8—221no—
523C4×Q8—221no—
524C4×Q8—221no—
525C4×Q8C4×D1111yescharacteristic
526C4×Q8C22×D1111yescharacteristic
527C4×D4—21no—
528C4×D4—21no—
529C4×D4—111no—
530C4×D4—111no—
531C4×D4—111no—
532C4×D4—111no—
533C4×D4—111no—
534C4×D4—111no—
535C4×D4—221no—
536C4×D4—221no—
537C4×D4—221no—
538C4×D4—221no—
539C4×D4—221no—
540C4×D4—221no—
541C4×D4—221no—
542C4×D4—221no—
543C4×D4—221no—
544C4×D4—221no—
545C4×D4—221no—
546C4×D4—221no—
547C4×D4—221no—
548C4×D4—221no—
549C4×D4—221no—
550C4×D4—221no—
551C4×D4—221no—
552C4×D4—221no—
553C4×D4C4×D1111yescharacteristic
554C4×D4C22×D1111yescharacteristic
555#117—21no—
556#117—111no—
557#117—111no—
558#117—111no—
559#117—221no—
560#117—221no—
561#117—221no—
562#117—221no—
563#117—221no—
564#117—221no—
565#117—221no—
566#117—221no—
567#117—221no—
568#117C4×D1111yescharacteristic
569C2×C4⋊C4—111no—
570C2×C4⋊C4—111no—
571C2×C4⋊C4—221no—
572C2×C4⋊C4—221no—
573C2×C22⋊C4—221no—
574C2×C22⋊C4—221no—
575C2×C22⋊C4—221no—
576C2×C42—21no—
577C2×C42—111no—
578C2×C42—111no—
579C2×C42—111no—
580C2×C42—111no—
581C2×C42—111no—
582C2×C42—111no—
583C2×C42—111no—
584C2×C42—111no—
585C2×C42—111no—
586C2×C42—111no—
587C2×C42—111no—
588C2×C42—221no—
589C2×C42—221no—
590C2×C42—221no—
591C2×C42—221no—
592C2×C42—221no—
593C2×C42—221no—
594C2×C42—221no—
595C2×C42—221no—
596C2×C42—221no—
597C2×C42—221no—
598C2×C42C22×D1111yescharacteristic
599C4⋊C8—21no—
600C4⋊C8—21no—
601C4⋊C8—112no—
602C4⋊C8—222no—
603C4⋊C8—221no—
604C4⋊C8—221no—
605C4⋊C8C22×D1112yes—
606C22⋊C8—21no—
607C22⋊C8—222no—
608C22⋊C8—222no—
609C22⋊C8—222no—
610C22⋊C8—221no—
611C4×C8—112no—
612C4×C8—222no—
613C4×C8—222no—
614C4×C8—222no—
615C4×C8C22×D1112yes—
616C2×C11—22no—
617C2×C11—42no—
618C2×C11C22×C22⋊C811yescharacteristic
619C2×C11#289611yescharacteristic
620C2×C11C2×#42111yescharacteristic
621D11—22no—
622D11—22no—
623D11—42no—
624C24—111no—
625C24—221no—
626#41—22no—
627#41—114no—
628#41—114no—
629#41—114no—
630#41—228no—
631#41—228no—
632#41—222no—
633#41—222no—
634#41—222no—
635#41C8×D1114yescomplemented
636C2×Q8—114no—
637C2×Q8—111no—
638C2×Q8—221no—
639C2×Q8—222no—
640C2×Q8C2×C4×D1111yescharacteristic
641C2×D4—21no—
642C2×D4—114no—
643C2×D4—111no—
644C2×D4—221no—
645C2×D4—222no—
646C2×D4—221no—
647C2×D4—228no—
648C2×D4—221no—
649C2×D4—221no—
650C2×D4C2×C4×D1111yescharacteristic
651C22×C4—21no—
652C22×C4—21no—
653C22×C4—21no—
654C22×C4—111no—
655C22×C4—111no—
656C22×C4—111no—
657C22×C4—114no—
658C22×C4—114no—
659C22×C4—111no—
660C22×C4—111no—
661C22×C4—111no—
662C22×C4—111no—
663C22×C4—111no—
664C22×C4—111no—
665C22×C4—111no—
666C22×C4—111no—
667C22×C4—111no—
668C22×C4—111no—
669C22×C4—111no—
670C22×C4—111no—
671C22×C4—221no—
672C22×C4—228no—
673C22×C4—221no—
674C22×C4—221no—
675C22×C4—221no—
676C22×C4—221no—
677C22×C4—221no—
678C22×C4—221no—
679C22×C4—221no—
680C22×C4—221no—
681C22×C4—221no—
682C22×C4—221no—
683C22×C4—221no—
684C22×C4—441no—
685C22×C4—441no—
686C22×C4—442no—
687C22×C4—444no—
688C22×C4—442no—
689C22×C4—442no—
690C22×C4C2×C4×D1111yescharacteristic
691C22×C4D4×D1111yescharacteristic
692C22×C4D4×D1111yescharacteristic
693C2×C8—22no—
694C2×C8—22no—
695C2×C8—42no—
696C2×C8—222no—
697C2×C8—222no—
698C2×C8—444no—
699C2×C8—442no—
700C4⋊C4—21no—
701C4⋊C4—21no—
702C4⋊C4—111no—
703C4⋊C4—111no—
704C4⋊C4—221no—
705C4⋊C4—221no—
706C4⋊C4—221no—
707C4⋊C4—221no—
708C4⋊C4—221no—
709C4⋊C4—221no—
710C4⋊C4—221no—
711C4⋊C4—221no—
712C4⋊C4C2×C4×D1111yescharacteristic
713C4⋊C4C2×C4×D1111yescharacteristic
714C22⋊C4—21no—
715C22⋊C4—21no—
716C22⋊C4—21no—
717C22⋊C4—221no—
718C22⋊C4—221no—
719C22⋊C4—221no—
720C22⋊C4—221no—
721C22⋊C4—221no—
722C22⋊C4—221no—
723C22⋊C4—221no—
724C22⋊C4—221no—
725C22⋊C4—221no—
726C42—21no—
727C42—21no—
728C42—21no—
729C42—111no—
730C42—111no—
731C42—111no—
732C42—111no—
733C42—111no—
734C42—111no—
735C42—111no—
736C42—111no—
737C42—111no—
738C42—111no—
739C42—111no—
740C42—111no—
741C42—221no—
742C42—221no—
743C42—221no—
744C42—221no—
745C42—221no—
746C42—221no—
747C42—221no—
748C42—221no—
749C42—221no—
750C42C2×C4×D1111yescharacteristic
751C42D4×D1111yescharacteristic
752C42D4×D1111yescharacteristic
753C42C23×D1111yescharacteristic
754C11#1743711yescharacteristic, complemented, Sylow
755C23—21no—
756C23—111no—
757C23—111no—
758C23—114no—
759C23—224no—
760C23—221no—
761C23—441no—
762C23—441no—
763C23—442no—
764C23—442no—
765C23C22⋊C4×D1111yescharacteristic
766Q8—21no—
767Q8—112no—
768Q8—224no—
769Q8—221no—
770Q8C2×C8×D1112yes—
771D4—24no—
772D4—21no—
773D4—112no—
774D4—224no—
775D4—224no—
776D4—224no—
777D4—224no—
778D4—221no—
779D4C2×C8×D1112yes—
780C2×C4—21no—
781C2×C4—21no—
782C2×C4—21no—
783C2×C4—24no—
784C2×C4—21no—
785C2×C4—21no—
786C2×C4—41no—
787C2×C4—42no—
788C2×C4—41no—
789C2×C4—41no—
790C2×C4—111no—
791C2×C4—111no—
792C2×C4—111no—
793C2×C4—114no—
794C2×C4—112no—
795C2×C4—112no—
796C2×C4—112no—
797C2×C4—112no—
798C2×C4—114no—
799C2×C4—114no—
800C2×C4—111no—
801C2×C4—111no—
802C2×C4—111no—
803C2×C4—222no—
804C2×C4—222no—
805C2×C4—224no—
806C2×C4—224no—
807C2×C4—222no—
808C2×C4—224no—
809C2×C4—221no—
810C2×C4—221no—
811C2×C4—221no—
812C2×C4—221no—
813C2×C4—221no—
814C2×C4—224no—
815C2×C4—221no—
816C2×C4—221no—
817C2×C4—441no—
818C2×C4—441no—
819C2×C4—441no—
820C2×C4—441no—
821C2×C4—442no—
822C2×C4—442no—
823C2×C4—442no—
824C2×C4—442no—
825C2×C4—442no—
826C2×C4—442no—
827C2×C4—441no—
828C2×C4—442no—
829C2×C4—441no—
830C2×C4—441no—
831C2×C4C22⋊C4×D1111yescharacteristic
832C2×C4C22⋊C4×D1111yescharacteristic
833C2×C4C22⋊C4×D1111yescharacteristic
834C2×C4C2×C8×D1112yes—
835C2×C4M16×D1112yes—
836C2×C4C22×C4×D1111yescharacteristic
837C2×C4C2×D4×D1111yescharacteristic
838C2×C4C2×D4×D1111yescharacteristic
839C8—42no—
840C8—42no—
841C8—442no—
842C8—442no—
843C22—21no—
844C22—21no—
845C22—22no—
846C22—41no—
847C22—41no—
848C22—112no—
849C22—112no—
850C22—221no—
851C22—221no—
852C22—221no—
853C22—221no—
854C22—222no—
855C22—444no—
856C22—448no—
857C22—441no—
858C22—441no—
859C22D11×C22⋊C812yes—
860C22C2×C22⋊C4×D1111yescharacteristic
861C4—22no—
862C4—21no—
863C4—21no—
864C4—21no—
865C4—41no—
866C4—41no—
867C4—112no—
868C4—112no—
869C4—112no—
870C4—222no—
871C4—221no—
872C4—221no—
873C4—221no—
874C4—441no—
875C4—441no—
876C4D11×C22⋊C812yes—
877C4C22×C8×D1111yescharacteristic
878C4C2×M16×D1111yescharacteristic
879C4#1062330411yescharacteristic
880C4#1062330811yescharacteristic
881C2—22no—
882C2—42no—
883C2—222no—
884C2—222no—
885C2—442no—
886C2C2×D11×C22⋊C811yescharacteristic
887C2#1307713211yescharacteristic
888C2D11×#42111yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D11
commutatorC4×C11C23×C8
FrattiniC42C23×D11
FittingC11×#1477C2
socleC22×C11C22×C22⋊C4
prime radicalC2×#41×D11C4
cosocleC42×C11C24
hypercenter#1477D11
hypocenterC11#17437
LCSG ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1477

Complements

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

NH ≅ G/Ntype
2. C2×#10622446C2semidirect
3. D11×#431C2semidirect
4. #13067009C2semidirect
5. #13067005C2semidirect
6. #13067004C2semidirect
7. #13067003C2semidirect
8. #13067001C2semidirect
9. #13066997C2semidirect
10. #13066995C2semidirect
11. C11×#1477C2semidirect
35. C11×#431C22semidirect
36. C2×C11×C4⋊C8C22semidirect
39. #10622538C22semidirect
40. C2×C4⋊(C11⋊C8)C22semidirect
45. #10622446C22semidirect
50. C4×C8×D11C22semidirect
51. C11×Q8⋊C8C22semidirect
52. C11×D4⋊C8C22semidirect
53. Q8⋊(C11⋊C8)C22semidirect
54. D4⋊(C11⋊C8)C22semidirect
55. #10622122C22semidirect
56. #10622121C22semidirect
57. #10622097C22semidirect
58. #10622094C22semidirect
61. #41×D11C8semidirect
184. C11×#41C2×C8semidirect
204. #4343C2×C8semidirect
206. Q8×D11C2×C8semidirect
209. #4341C2×C8semidirect
212. D4×D11C2×C8semidirect
215. #4339C2×C8semidirect
319. #1477D11semidirect
441. #431C2×D11semidirect
444. C2×C4⋊C8C2×D11semidirect
452. Q8⋊C8C2×D11semidirect
456. D4⋊C8C2×D11semidirect
635. #41C8×D11semidirect
754. C11#17437semidirect

Maximal subgroups

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

subgroupindex
C4×#41×D112
C2×#106224462
D11×#4312
#130670092
#130670052
#130670042
#130670032
#130670012
#130669972
#130669952
C11×#14772
#1743711