Finite Group Databasebeta

← #14720144

Subgroups — #14720144

Order 2816.

1314 conjugacy classes of subgroups.

The subgroup lattice has 874 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C4×#41×D11C211yesmaximal, characteristic
2C2×#10622298C211yesmaximal, characteristic, complemented
3D11×#431C211yesmaximal, characteristic, complemented
4#13067009C212yesmaximal, complemented
5#13067005C212yesmaximal, complemented
6#13067002C212yesmaximal, complemented
7#13067000C212yesmaximal, complemented
8#13066999C211yesmaximal, characteristic, complemented
9#13066998C211yesmaximal, characteristic, complemented
10#13066996C211yesmaximal, characteristic, complemented
11C11×#1476C211yesmaximal, 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×C4×C8×C11C2211yescharacteristic, complemented
37C2×(C2×D11)⋊C8—21no—
38C2×Dic11⋊C8—21no—
39#10622538C2211yescharacteristic, complemented
40C2×C4×C11⋊C8C2211yescharacteristic, complemented
41#10622446C2212yes—
42D11×C4⋊C8C2212yescomplemented
43D11×C22⋊C8—21no—
44#10622331—21no—
45#10622298—21no—
46#10622298—21no—
47#10622298—21no—
48#10622298C2212yes—
49#10622298C2212yescomplemented
50C4×C8×D11—21no—
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⋊C8C2312yes—
164C11×C22⋊C8—21no—
165C4×C8×C11—21no—
166C4×C8×C11—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—
173Dic11⋊C8—22no—
174Dic11⋊C8—22no—
175C8×Dic11—22no—
176C4⋊(C11⋊C8)C2312yes—
177C4×C11⋊C8—21no—
178C4×C11⋊C8—21no—
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—42no—
229C2×C4×D11—42no—
230C2×C4×D11—44no—
231C2×C4×D11—44no—
232C2×C4×D11C22⋊C411yescharacteristic
233C2×C4×D11C22⋊C411yescharacteristic
234C2×C4×D11C22⋊C411yescharacteristic
235C2×C4×D11C22⋊C411yescharacteristic
236C2×C4×D11C22⋊C411yescharacteristic
237C2×C4×D11C22⋊C411yescharacteristic
238C2×C4×D11C2×C814yes—
239C2×C4×D11M1614yes—
240C2×C4×D11C22×C411yescharacteristic
241C2×C4×D11C22×C411yescharacteristic
242C2×C4×D11C2×D411yescharacteristic
243C2×C4×D11C2×D411yescharacteristic
244C2×C4×D11C2×D411yescharacteristic
245C2×C4×D11C2×D411yescharacteristic
246C2×Dic22—21no—
247C2×Dic22C22×C411yescharacteristic
248C2×C8×C11—22no—
249C2×C8×C11—22no—
250C2×C8×C11—42no—
251C11×C4⋊C4—21no—
252C11×C4⋊C4—21no—
253C11×C4⋊C4C22×C411yescharacteristic
254C11×C4⋊C4C22×C411yescharacteristic
255C11×C22⋊C4—21no—
256C11×C22⋊C4—21no—
257C11×C22⋊C4—21no—
258C42×C11—21no—
259C42×C11—21no—
260C42×C11—21no—
261C42×C11C22×C411yescharacteristic
262C42×C11C2×D411yescharacteristic
263C42×C11C2×D411yescharacteristic
264C42×C11C2411yescharacteristic
265C22⋊Dic11—21no—
266C22⋊Dic11—21no—
267C22⋊Dic11—21no—
268(C2×D11)⋊C4—21no—
269(C2×D11)⋊C4—21no—
270(C2×D11)⋊C4—21no—
271(C2×D11)⋊C4—21no—
272(C2×D11)⋊C4—21no—
273(C2×D11)⋊C4—21no—
274C4⋊Dic11—21no—
275C4⋊Dic11—21no—
276C4⋊Dic11C22×C411yescharacteristic
277C4⋊Dic11C22×C411yescharacteristic
278Dic11⋊C4—21no—
279Dic11⋊C4—21no—
280Dic11⋊C4—21no—
281Dic11⋊C4—21no—
282Dic11⋊C4—21no—
283Dic11⋊C4—21no—
284C4×Dic11—21no—
285C4×Dic11—21no—
286C4×Dic11—21no—
287C4×Dic11—21no—
288C4×Dic11—21no—
289C4×Dic11—21no—
290C4×Dic11—21no—
291C4×Dic11—21no—
292C4×Dic11—21no—
293C4×Dic11C22⋊C411yescharacteristic
294C4×Dic11C22⋊C411yescharacteristic
295C4×Dic11C22⋊C411yescharacteristic
296C4×Dic11C22⋊C411yescharacteristic
297C4×Dic11C22⋊C411yescharacteristic
298C4×Dic11C22⋊C411yescharacteristic
299C4×Dic11C22×C411yescharacteristic
300C4×Dic11C22×C411yescharacteristic
301C4×Dic11C2×D411yescharacteristic
302C4×Dic11C2×D411yescharacteristic
303C4×Dic11C2×D411yescharacteristic
304C4×Dic11C2×D411yescharacteristic
305C2×C11⋊C8—22no—
306C2×C11⋊C8—22no—
307C2×C11⋊C8—42no—
308C8×D11—44no—
309C2×C4×#41—111no—
310C2×#431—111no—
311C2×#431—111no—
312#1479—112no—
313#1478—112no—
314#1477—112no—
315#1477—112no—
316#1476—111no—
317#1476—111no—
318#1476—111no—
319#1476D1111yescharacteristic, complemented
320C23×C11—21no—
321C23×C11C2×C22⋊C411yescharacteristic
322C22×D11—21no—
323C22×D11—24no—
324C22×D11—41no—
325C22×D11—41no—
326C22×D11—42no—
327C22×D11—42no—
328C22×D11C22⋊C814yes—
329C22×D11C2×C22⋊C411yescharacteristic
330C22×D11C2×C22⋊C411yescharacteristic
331Q8×C11—21no—
332Q8×C11C22×C812yes—
333D4×C11—24no—
334D4×C11—21no—
335D4×C11C22×C812yes—
336C2×C4×C11—21no—
337C2×C4×C11—22no—
338C2×C4×C11—24no—
339C2×C4×C11—22no—
340C2×C4×C11—21no—
341C2×C4×C11—21no—
342C2×C4×C11—42no—
343C2×C4×C11—42no—
344C2×C4×C11C2×C22⋊C411yescharacteristic
345C2×C4×C11C2×C22⋊C411yescharacteristic
346C2×C4×C11C2×C22⋊C411yescharacteristic
347C2×C4×C11C22×C812yes—
348C2×C4×C11C2×M1612yes—
349C2×C4×C11C23×C411yescharacteristic
350C2×C4×C11C22×D411yescharacteristic
351C2×C4×C11C22×D411yescharacteristic
352C22⋊D11—24no—
353C22⋊D11—24no—
354C22⋊D11—24no—
355C2×Dic11—21no—
356C2×Dic11—24no—
357C2×Dic11—21no—
358C2×Dic11—21no—
359C2×Dic11—41no—
360C2×Dic11—41no—
361C2×Dic11—42no—
362C2×Dic11—42no—
363C2×Dic11C22⋊C814yes—
364C2×Dic11C2×C22⋊C411yescharacteristic
365C2×Dic11C2×C22⋊C411yescharacteristic
366C2×Dic11C2×C22⋊C411yescharacteristic
367C2×Dic11C2×C22⋊C411yescharacteristic
368C2×Dic11C2×C22⋊C411yescharacteristic
369C2×Dic11C2×C22⋊C411yescharacteristic
370D44—24no—
371D44—21no—
372D44C22×C812yes—
373C4×D11—24no—
374C4×D11—22no—
375C4×D11—22no—
376C4×D11—24no—
377C4×D11—22no—
378C4×D11—22no—
379C4×D11—24no—
380C4×D11—41no—
381C4×D11—41no—
382C4×D11—41no—
383C4×D11—41no—
384C4×D11—42no—
385C4×D11—42no—
386C4×D11—42no—
387C4×D11—42no—
388C4×D11—42no—
389C4×D11—42no—
390C4×D11C22⋊C814yes—
391C4×D11C22⋊C814yes—
392C4×D11C22×C812yes—
393C4×D11C22×C812yes—
394C4×D11C2×M1612yes—
395C4×D11C2×M1612yes—
396Dic22—21no—
397Dic22—24no—
398Dic22C22×C812yes—
399C8×C11—42no—
400C8×C11—42no—
401C11⋊C8—42no—
402C11⋊C8—42no—
403C22×#41—111no—
404C4×#41—111no—
405C4×#41—111no—
406C4×#41—111no—
407C4×#41—111no—
408C4×#41—111no—
409C4×#41—111no—
410C4×#41—111no—
411C4×#41—221no—
412C4×#41—221no—
413C4×#41—221no—
414C4×#41—221no—
415C4×#41C2×D1111yescharacteristic
416C2×C4×Q8—111no—
417C2×C4×Q8—111no—
418C2×C4×D4—111no—
419C2×C4×D4—111no—
420C2×C4×D4—221no—
421C2×C4×D4—221no—
422C2×#117—111no—
423C2×#117—221no—
424C22×C42—111no—
425C22×C42—221no—
426#431—112no—
427#431—112no—
428#431—111no—
429#431—112no—
430#431—221no—
431#431—221no—
432#431—221no—
433#431—221no—
434#431C2×D1111yescharacteristic, complemented
435C2×C4⋊C8—112no—
436C2×C4⋊C8—221no—
437C2×C22⋊C8—221no—
438C2×C22⋊C8—221no—
439C2×C4×C8—111no—
440C2×C4×C8—221no—
441C2×C4×C8C2×D1111yescharacteristic, complemented
442Q8⋊C8—112no—
443Q8⋊C8—112no—
444Q8⋊C8—112no—
445Q8⋊C8C2×D1112yescomplemented
446D4⋊C8—112no—
447D4⋊C8—112no—
448D4⋊C8—112no—
449D4⋊C8C2×D1112yescomplemented
450C22×C11—21no—
451C22×C11—21no—
452C22×C11—22no—
453C22×C11—41no—
454C22×C11—41no—
455C22×C11C2×C22⋊C812yes—
456C22×C11C22×C22⋊C411yescharacteristic
457C2×D11—21no—
458C2×D11—21no—
459C2×D11—21no—
460C2×D11—21no—
461C2×D11—22no—
462C2×D11—44no—
463C2×D11—48no—
464C2×D11—41no—
465C2×D11—41no—
466C2×D11C2×C22⋊C812yes—
467C2×D11C2×C22⋊C812yes—
468C4×C11—22no—
469C4×C11—21no—
470C4×C11—21no—
471C4×C11—41no—
472C4×C11—41no—
473C4×C11C2×C22⋊C812yes—
474C4×C11#42112yes—
475C4×C11C23×C811yescharacteristic
476C4×C11C22×M1611yescharacteristic
477C4×C11#57512yes—
478Dic11—22no—
479Dic11—21no—
480Dic11—21no—
481Dic11—21no—
482Dic11—21no—
483Dic11—41no—
484Dic11—41no—
485Dic11C2×C22⋊C812yes—
486Dic11C2×C22⋊C812yes—
487C2×#41—118no—
488C2×#41—111no—
489C2×#41—111no—
490C2×#41—111no—
491C2×#41—221no—
492C2×#41—221no—
493C2×#41—224no—
494C2×#41C4×D1111yescharacteristic
495C22×Q8—111no—
496C22×D4—111no—
497C22×D4—221no—
498C23×C4—111no—
499C23×C4—111no—
500C23×C4—111no—
501C23×C4—221no—
502C23×C4—221no—
503C23×C4—221no—
504C22×C8—21no—
505C22×C8—222no—
506C22×C8—221no—
507C4×Q8—111no—
508C4×Q8—111no—
509C4×Q8—111no—
510C4×Q8—111no—
511C4×Q8—111no—
512C4×Q8—111no—
513C4×Q8—221no—
514C4×Q8—221no—
515C4×Q8—221no—
516C4×Q8—221no—
517C4×Q8C4×D1111yescharacteristic
518C4×Q8C22×D1111yescharacteristic
519C4×D4—21no—
520C4×D4—21no—
521C4×D4—111no—
522C4×D4—111no—
523C4×D4—111no—
524C4×D4—111no—
525C4×D4—111no—
526C4×D4—111no—
527C4×D4—221no—
528C4×D4—221no—
529C4×D4—221no—
530C4×D4—221no—
531C4×D4—221no—
532C4×D4—221no—
533C4×D4—221no—
534C4×D4—221no—
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×D4C4×D1111yescharacteristic
546C4×D4C22×D1111yescharacteristic
547#117—21no—
548#117—111no—
549#117—111no—
550#117—111no—
551#117—221no—
552#117—221no—
553#117—221no—
554#117—221no—
555#117—221no—
556#117—221no—
557#117—221no—
558#117—221no—
559#117—221no—
560#117C4×D1111yescharacteristic
561C2×C4⋊C4—111no—
562C2×C4⋊C4—111no—
563C2×C4⋊C4—221no—
564C2×C4⋊C4—221no—
565C2×C22⋊C4—221no—
566C2×C22⋊C4—221no—
567C2×C22⋊C4—221no—
568C2×C42—21no—
569C2×C42—111no—
570C2×C42—111no—
571C2×C42—111no—
572C2×C42—111no—
573C2×C42—111no—
574C2×C42—111no—
575C2×C42—111no—
576C2×C42—111no—
577C2×C42—111no—
578C2×C42—111no—
579C2×C42—111no—
580C2×C42—221no—
581C2×C42—221no—
582C2×C42—221no—
583C2×C42—221no—
584C2×C42—221no—
585C2×C42—221no—
586C2×C42—221no—
587C2×C42—221no—
588C2×C42—221no—
589C2×C42—221no—
590C2×C42C22×D1111yescharacteristic
591C4⋊C8—112no—
592C4⋊C8—222no—
593C4⋊C8—222no—
594C4⋊C8—222no—
595C4⋊C8C22×D1112yes—
596C22⋊C8—21no—
597C22⋊C8—222no—
598C22⋊C8—222no—
599C22⋊C8—222no—
600C22⋊C8—221no—
601C4×C8—21no—
602C4×C8—21no—
603C4×C8—112no—
604C4×C8—222no—
605C4×C8—221no—
606C4×C8—221no—
607C4×C8C22×D1112yes—
608C2×C11—22no—
609C2×C11—42no—
610C2×C11C22×C22⋊C811yescharacteristic
611C2×C11#289611yescharacteristic
612C2×C11C2×#42111yescharacteristic
613D11—22no—
614D11—22no—
615D11—42no—
616C24—111no—
617C24—221no—
618#41—22no—
619#41—114no—
620#41—114no—
621#41—114no—
622#41—228no—
623#41—228no—
624#41—222no—
625#41—222no—
626#41—222no—
627#41C8×D1114yescomplemented
628C2×Q8—114no—
629C2×Q8—111no—
630C2×Q8—221no—
631C2×Q8—222no—
632C2×Q8C2×C4×D1111yescharacteristic
633C2×D4—21no—
634C2×D4—114no—
635C2×D4—111no—
636C2×D4—221no—
637C2×D4—222no—
638C2×D4—221no—
639C2×D4—228no—
640C2×D4—221no—
641C2×D4—221no—
642C2×D4C2×C4×D1111yescharacteristic
643C22×C4—21no—
644C22×C4—21no—
645C22×C4—21no—
646C22×C4—111no—
647C22×C4—111no—
648C22×C4—111no—
649C22×C4—114no—
650C22×C4—114no—
651C22×C4—111no—
652C22×C4—111no—
653C22×C4—111no—
654C22×C4—111no—
655C22×C4—111no—
656C22×C4—111no—
657C22×C4—111no—
658C22×C4—111no—
659C22×C4—111no—
660C22×C4—111no—
661C22×C4—111no—
662C22×C4—111no—
663C22×C4—221no—
664C22×C4—228no—
665C22×C4—221no—
666C22×C4—221no—
667C22×C4—221no—
668C22×C4—221no—
669C22×C4—221no—
670C22×C4—221no—
671C22×C4—221no—
672C22×C4—221no—
673C22×C4—221no—
674C22×C4—221no—
675C22×C4—221no—
676C22×C4—442no—
677C22×C4—442no—
678C22×C4—444no—
679C22×C4—444no—
680C22×C4C2×C4×D1111yescharacteristic
681C22×C4D4×D1111yescharacteristic
682C22×C4D4×D1111yescharacteristic
683C2×C8—22no—
684C2×C8—22no—
685C2×C8—42no—
686C2×C8—222no—
687C2×C8—222no—
688C2×C8—444no—
689C2×C8—442no—
690C4⋊C4—21no—
691C4⋊C4—21no—
692C4⋊C4—111no—
693C4⋊C4—111no—
694C4⋊C4—221no—
695C4⋊C4—221no—
696C4⋊C4—221no—
697C4⋊C4—221no—
698C4⋊C4—221no—
699C4⋊C4—221no—
700C4⋊C4—221no—
701C4⋊C4—221no—
702C4⋊C4C2×C4×D1111yescharacteristic
703C4⋊C4C2×C4×D1111yescharacteristic
704C22⋊C4—21no—
705C22⋊C4—21no—
706C22⋊C4—21no—
707C22⋊C4—221no—
708C22⋊C4—221no—
709C22⋊C4—221no—
710C22⋊C4—221no—
711C22⋊C4—221no—
712C22⋊C4—221no—
713C22⋊C4—221no—
714C22⋊C4—221no—
715C22⋊C4—221no—
716C42—21no—
717C42—21no—
718C42—21no—
719C42—111no—
720C42—111no—
721C42—111no—
722C42—111no—
723C42—111no—
724C42—111no—
725C42—111no—
726C42—111no—
727C42—111no—
728C42—111no—
729C42—111no—
730C42—111no—
731C42—221no—
732C42—221no—
733C42—221no—
734C42—221no—
735C42—221no—
736C42—221no—
737C42—221no—
738C42—221no—
739C42—221no—
740C42C2×C4×D1111yescharacteristic
741C42D4×D1111yescharacteristic
742C42D4×D1111yescharacteristic
743C42C23×D1111yescharacteristic
744C11#1743711yescharacteristic, complemented, Sylow
745C23—21no—
746C23—111no—
747C23—111no—
748C23—114no—
749C23—224no—
750C23—221no—
751C23—441no—
752C23—441no—
753C23—442no—
754C23—442no—
755C23C22⋊C4×D1111yescharacteristic
756Q8—21no—
757Q8—112no—
758Q8—224no—
759Q8—221no—
760Q8C2×C8×D1112yes—
761D4—24no—
762D4—21no—
763D4—112no—
764D4—224no—
765D4—224no—
766D4—224no—
767D4—224no—
768D4—221no—
769D4C2×C8×D1112yes—
770C2×C4—21no—
771C2×C4—22no—
772C2×C4—24no—
773C2×C4—22no—
774C2×C4—21no—
775C2×C4—21no—
776C2×C4—42no—
777C2×C4—42no—
778C2×C4—111no—
779C2×C4—111no—
780C2×C4—114no—
781C2×C4—112no—
782C2×C4—112no—
783C2×C4—112no—
784C2×C4—112no—
785C2×C4—114no—
786C2×C4—114no—
787C2×C4—111no—
788C2×C4—111no—
789C2×C4—111no—
790C2×C4—111no—
791C2×C4—224no—
792C2×C4—224no—
793C2×C4—224no—
794C2×C4—221no—
795C2×C4—222no—
796C2×C4—222no—
797C2×C4—224no—
798C2×C4—222no—
799C2×C4—222no—
800C2×C4—221no—
801C2×C4—221no—
802C2×C4—441no—
803C2×C4—441no—
804C2×C4—441no—
805C2×C4—441no—
806C2×C4—442no—
807C2×C4—442no—
808C2×C4—442no—
809C2×C4—442no—
810C2×C4—441no—
811C2×C4—441no—
812C2×C4—442no—
813C2×C4—442no—
814C2×C4—442no—
815C2×C4—442no—
816C2×C4C22⋊C4×D1111yescharacteristic
817C2×C4C22⋊C4×D1111yescharacteristic
818C2×C4C22⋊C4×D1111yescharacteristic
819C2×C4C2×C8×D1112yes—
820C2×C4M16×D1112yes—
821C2×C4C22×C4×D1111yescharacteristic
822C2×C4C2×D4×D1111yescharacteristic
823C2×C4C2×D4×D1111yescharacteristic
824C8—42no—
825C8—42no—
826C8—442no—
827C8—442no—
828C22—21no—
829C22—21no—
830C22—22no—
831C22—41no—
832C22—41no—
833C22—112no—
834C22—112no—
835C22—221no—
836C22—221no—
837C22—221no—
838C22—221no—
839C22—222no—
840C22—444no—
841C22—448no—
842C22—441no—
843C22—441no—
844C22D11×C22⋊C812yes—
845C22C2×C22⋊C4×D1111yescharacteristic
846C4—22no—
847C4—21no—
848C4—21no—
849C4—41no—
850C4—41no—
851C4—112no—
852C4—112no—
853C4—222no—
854C4—221no—
855C4—221no—
856C4—221no—
857C4—221no—
858C4—441no—
859C4—441no—
860C4D11×C22⋊C812yes—
861C4#1062243412yes—
862C4C22×C8×D1111yescharacteristic
863C4C2×M16×D1111yescharacteristic
864C4#1062329912yes—
865C2—22no—
866C2—42no—
867C2—222no—
868C2—222no—
869C2—442no—
870C2C2×D11×C22⋊C811yescharacteristic
871C2#1307713111yescharacteristic
872C2C2×#1062243411yescharacteristic
subgroupG/H
centerC42D4×D11
commutatorC4×C11C23×C8
FrattiniC42C23×D11
FittingC11×#1476C2
socleC22×C11C22×C22⋊C4
prime radicalC2×#41×D11C4
cosocleC42×C11C24
hypercenter#1476D11
hypocenterC11#17437
LCSG ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C42 ◁ C2×C42 ◁ #1476

Complements

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

NH ≅ G/Ntype
2. C2×#10622298C2semidirect
3. D11×#431C2semidirect
4. #13067009C2semidirect
5. #13067005C2semidirect
6. #13067002C2semidirect
7. #13067000C2semidirect
8. #13066999C2semidirect
9. #13066998C2semidirect
10. #13066996C2semidirect
11. C11×#1476C2semidirect
35. C11×#431C22semidirect
36. C2×C4×C8×C11C22semidirect
39. #10622538C22semidirect
40. C2×C4×C11⋊C8C22semidirect
42. D11×C4⋊C8C22semidirect
49. #10622298C22semidirect
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. #1476D11semidirect
434. #431C2×D11semidirect
441. C2×C4×C8C2×D11semidirect
445. Q8⋊C8C2×D11semidirect
449. D4⋊C8C2×D11semidirect
627. #41C8×D11semidirect
744. 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×#106222982
D11×#4312
#130670092
#130670052
#130670022
#130670002
#130669992
#130669982
#130669962
C11×#14762
#1743711