Finite Group Databasebeta

← #14759117

Subgroups — #14759117

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
1#13070999C211yesmaximal, characteristic, complemented
2C2×C4×C22⋊Dic11C211yesmaximal, characteristic, complemented
3#13069602C212yesmaximal, complemented
4#13069453C212yesmaximal, complemented
5#13069070C214yesmaximal, complemented
6C4×#66898C214yesmaximal, complemented
7C2×C11×#525C211yesmaximal, characteristic
8C22×C11×#41C411yescharacteristic, complemented
9C24×C4×C11C2211yescharacteristic
10C11×#525—21no—
11C11×#525—21no—
12C11×#525—21no—
13C11×#525—21no—
14C11×#525—21no—
15C11×#525—21no—
16C11×#525—21no—
17C11×#525—21no—
18C2×C11×#123C412yescomplemented
19C2×C11×C22⋊Q8C411yescharacteristic, complemented
20C2×C11×C22⋊Q8C2211yescharacteristic
21C2×C11×#121C411yescharacteristic, complemented
22C2×C11×#121C2211yescharacteristic
23C2×C11×#120C2212yes—
24C2×C4×D4×C11C412yescomplemented
25C2×C4×D4×C11C2212yes—
26C2×C11×#117C411yescharacteristic, complemented
27C22×C22⋊Dic11C2212yes—
28C2×#66979—21no—
29C22×C4×Dic11—21no—
30#10622860C2212yes—
31C2×#66898C2218yes—
32#10622825—21no—
33#10622825C2212yes—
34#10622824—21no—
35C4×C22⋊Dic11—21no—
36C4×C22⋊Dic11—21no—
37C4×C22⋊Dic11—21no—
38C4×C22⋊Dic11C2212yes—
39C4×C22⋊Dic11C2212yes—
40C4×C22⋊Dic11C2212yes—
41C2×C11⋊#95—21no—
42#10622164C2218yes—
43C25×C11C2311yescharacteristic
44C2×C11×#41—21no—
45C2×C11×#41—21no—
46C2×C11×#41—21no—
47C2×C11×#41—21no—
48C2×C11×#41—44no—
49C22×Q8×C11C2×C411yescharacteristic, complemented
50C22×D4×C11C2×C412yes—
51C22×D4×C11C2×C412yes—
52C22×D4×C11C2×C411yescharacteristic, complemented
53C22×D4×C11C2312yes—
54C23×C4×C11—44no—
55C23×C4×C11C2×C411yescharacteristic
56C23×C4×C11C2×C411yescharacteristic
57C23×C4×C11C2×C411yescharacteristic
58C23×C4×C11C2×C411yescharacteristic
59C23×C4×C11C2×C412yescomplemented
60C23×C4×C11D411yescharacteristic
61C23×C4×C11D411yescharacteristic
62C23×C4×C11D411yescharacteristic
63C23×C4×C11D411yescharacteristic
64C23×C4×C11D411yescharacteristic
65C23×C4×C11D411yescharacteristic
66C23×C4×C11D411yescharacteristic
67C23×C4×C11D411yescharacteristic
68C23×C4×C11C2311yescharacteristic
69C23×C4×C11C2311yescharacteristic
70C23×Dic11—22no—
71C11×#123—22no—
72C11×#123—22no—
73C11×#123—22no—
74C11×#123—22no—
75C11×C22⋊Q8—21no—
76C11×C22⋊Q8—21no—
77C11×C22⋊Q8—21no—
78C11×C22⋊Q8—21no—
79C11×C22⋊Q8—21no—
80C11×C22⋊Q8—21no—
81C11×C22⋊Q8—21no—
82C11×C22⋊Q8—21no—
83C11×#121—21no—
84C11×#121—21no—
85C11×#121—21no—
86C11×#121—21no—
87C11×#121—21no—
88C11×#121—21no—
89C11×#121—21no—
90C11×#121—21no—
91C11×#120—22no—
92C11×#120—22no—
93C11×#120—22no—
94C11×#120—22no—
95C4×D4×C11—22no—
96C4×D4×C11—22no—
97C4×D4×C11—22no—
98C4×D4×C11—22no—
99C4×D4×C11—22no—
100C4×D4×C11—22no—
101C4×D4×C11—22no—
102C4×D4×C11—22no—
103C11×#117—21no—
104C11×#117—21no—
105C11×#117—21no—
106C11×#117—21no—
107C2×C11×C4⋊C4C2×C411yescharacteristic, complemented
108C2×C11×C4⋊C4C2×C411yescharacteristic, complemented
109C2×C11×C4⋊C4C2×C412yescomplemented
110C2×C11×C4⋊C4C2×C412yescomplemented
111C2×C11×C22⋊C4C2×C412yes—
112C2×C11×C22⋊C4C2×C412yes—
113C2×C11×C22⋊C4C2×C412yescomplemented
114C2×C11×C22⋊C4C2×C412yescomplemented
115C2×C11×C22⋊C4C2312yes—
116C2×C42×C11C2×C412yescomplemented
117C2×C22⋊Dic11—22no—
118C2×C22⋊Dic11—28no—
119C2×C22⋊Dic11—22no—
120C2×C22⋊Dic11—22no—
121C2×C22⋊Dic11C2314yes—
122C2×C22⋊Dic11C2314yes—
123#66979—44no—
124C2×C4⋊Dic11—22no—
125C2×C4×Dic11—22no—
126C2×C4×Dic11—22no—
127C2×C4×Dic11—22no—
128C2×C4×Dic11—44no—
129#66898—216no—
130C11⋊#95—22no—
131C11⋊#95—22no—
132C11⋊#95—22no—
133C11⋊#95—22no—
134#21420—111nomaximal, Sylow
135C24×C11—24no—
136C24×C11—42no—
137C24×C11—42no—
138C24×C11C22×C411yescharacteristic
139C24×C11C22×C411yescharacteristic
140C24×C11C22×C412yes—
141C24×C11C2×D411yescharacteristic
142C24×C11C2×D411yescharacteristic
143C24×C11C2×D411yescharacteristic
144C24×C11C2×D411yescharacteristic
145C24×C11C2411yescharacteristic
146C11×#41—44no—
147C11×#41—44no—
148C11×#41—44no—
149C11×#41—44no—
150C2×Q8×C11—21no—
151C2×Q8×C11—21no—
152C2×Q8×C11—42no—
153C2×D4×C11—22no—
154C2×D4×C11—22no—
155C2×D4×C11—22no—
156C2×D4×C11—22no—
157C2×D4×C11—22no—
158C2×D4×C11—22no—
159C2×D4×C11—28no—
160C2×D4×C11—21no—
161C2×D4×C11—21no—
162C2×D4×C11—42no—
163C2×D4×C11—44no—
164C2×D4×C11—44no—
165C22×C4×C11—24no—
166C22×C4×C11—24no—
167C22×C4×C11—24no—
168C22×C4×C11—22no—
169C22×C4×C11—22no—
170C22×C4×C11—42no—
171C22×C4×C11—42no—
172C22×C4×C11—42no—
173C22×C4×C11—42no—
174C22×C4×C11—42no—
175C22×C4×C11—42no—
176C22×C4×C11—42no—
177C22×C4×C11—42no—
178C22×C4×C11—42no—
179C22×C4×C11—42no—
180C22×C4×C11—42no—
181C22×C4×C11—44no—
182C22×C4×C11C22⋊C411yescharacteristic
183C22×C4×C11C22⋊C411yescharacteristic
184C22×C4×C11C22⋊C411yescharacteristic
185C22×C4×C11C22⋊C411yescharacteristic
186C22×C4×C11C22⋊C411yescharacteristic
187C22×C4×C11C22⋊C411yescharacteristic
188C22×C4×C11C22⋊C411yescharacteristic
189C22×C4×C11C22⋊C411yescharacteristic
190C22×C4×C11C22⋊C411yescharacteristic
191C22×C4×C11C22⋊C411yescharacteristic
192C22×C4×C11C22⋊C411yescharacteristic
193C22×C4×C11C22⋊C411yescharacteristic
194C22×C4×C11C22⋊C411yescharacteristic
195C22×C4×C11C22⋊C411yescharacteristic
196C22×C4×C11C22⋊C411yescharacteristic
197C22×C4×C11C22⋊C411yescharacteristic
198C22×C4×C11C22×C412yes—
199C22×C4×C11C22×C411yescharacteristic
200C22×C4×C11C22×C411yescharacteristic
201C22×C4×C11C22×C412yes—
202C22×C4×C11C22×C412yes—
203C22×C4×C11C22×C411yescharacteristic
204C22×C4×C11C22×C411yescharacteristic
205C22×C4×C11C2×D411yescharacteristic
206C22×C4×C11C2×D411yescharacteristic
207C22×C4×C11C2×D411yescharacteristic
208C22×C4×C11C2×D411yescharacteristic
209C22×C4×C11C2×D411yescharacteristic
210C22×C4×C11C2×D411yescharacteristic
211C22×C4×C11C2×D411yescharacteristic
212C22×C4×C11C2×D411yescharacteristic
213C22×Dic11—28no—
214C22×Dic11—24no—
215C22×Dic11—24no—
216C22×Dic11—44no—
217C22×Dic11—44no—
218C11×C4⋊C4—21no—
219C11×C4⋊C4—21no—
220C11×C4⋊C4—21no—
221C11×C4⋊C4—21no—
222C11×C4⋊C4—22no—
223C11×C4⋊C4—22no—
224C11×C4⋊C4—22no—
225C11×C4⋊C4—22no—
226C11×C22⋊C4—22no—
227C11×C22⋊C4—22no—
228C11×C22⋊C4—22no—
229C11×C22⋊C4—22no—
230C11×C22⋊C4—22no—
231C11×C22⋊C4—22no—
232C11×C22⋊C4—22no—
233C11×C22⋊C4—22no—
234C11×C22⋊C4—22no—
235C11×C22⋊C4—22no—
236C42×C11—22no—
237C42×C11—22no—
238C22⋊Dic11—28no—
239C22⋊Dic11—24no—
240C22⋊Dic11—28no—
241C22⋊Dic11—44no—
242C22⋊Dic11—44no—
243C22⋊Dic11#4118yescomplemented
244C4⋊Dic11—44no—
245C4×Dic11—44no—
246C4×Dic11—44no—
247C4×Dic11—44no—
248C2×#525D1111yescharacteristic
249#2280—111no—
250C2×C4×C22⋊C4—111no—
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—22no—
268C23×C11—24no—
269C23×C11—41no—
270C23×C11—41no—
271C23×C11—41no—
272C23×C11—41no—
273C23×C11—41no—
274C23×C11—41no—
275C23×C11—41no—
276C23×C11—41no—
277C23×C11—416no—
278C23×C11—42no—
279C23×C11—42no—
280C23×C11C2×C22⋊C411yescharacteristic
281C23×C11C2×C22⋊C411yescharacteristic
282C23×C11C2×C22⋊C411yescharacteristic
283C23×C11C2×C22⋊C411yescharacteristic
284C23×C11C23×C411yescharacteristic
285C23×C11C22×D411yescharacteristic
286C23×C11C22×D411yescharacteristic
287C23×C11C2×#4114yes—
288Q8×C11—42no—
289Q8×C11—42no—
290D4×C11—42no—
291D4×C11—44no—
292D4×C11—44no—
293D4×C11—44no—
294D4×C11—44no—
295D4×C11—44no—
296D4×C11—44no—
297D4×C11—42no—
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—22no—
310C2×C4×C11—22no—
311C2×C4×C11—22no—
312C2×C4×C11—22no—
313C2×C4×C11—22no—
314C2×C4×C11—22no—
315C2×C4×C11—22no—
316C2×C4×C11—24no—
317C2×C4×C11—41no—
318C2×C4×C11—41no—
319C2×C4×C11—41no—
320C2×C4×C11—41no—
321C2×C4×C11—41no—
322C2×C4×C11—41no—
323C2×C4×C11—41no—
324C2×C4×C11—41no—
325C2×C4×C11—41no—
326C2×C4×C11—41no—
327C2×C4×C11—41no—
328C2×C4×C11—41no—
329C2×C4×C11—44no—
330C2×C4×C11—44no—
331C2×C4×C11—42no—
332C2×C4×C11—42no—
333C2×C4×C11#9914yescomplemented
334C2×C4×C11C2×C22⋊C411yescharacteristic
335C2×C4×C11C2×C22⋊C411yescharacteristic
336C2×C4×C11C2×C22⋊C411yescharacteristic
337C2×C4×C11C2×C22⋊C411yescharacteristic
338C2×C4×C11C2×C22⋊C411yescharacteristic
339C2×C4×C11C2×C22⋊C411yescharacteristic
340C2×C4×C11C2×C22⋊C411yescharacteristic
341C2×C4×C11C2×C22⋊C411yescharacteristic
342C2×Dic11—28no—
343C2×Dic11—44no—
344C2×Dic11—416no—
345C2×Dic11—44no—
346C2×Dic11—44no—
347C2×Dic11—44no—
348C2×Dic11—44no—
349C22×#41Dic1111yescharacteristic, complemented
350C24×C4C2×D1111yescharacteristic
351#525—21no—
352#525—21no—
353#525—21no—
354#525—21no—
355#525—21no—
356#525—21no—
357#525—21no—
358#525—21no—
359C2×#123Dic1112yescomplemented
360C2×C22⋊Q8Dic1111yescharacteristic, complemented
361C2×C22⋊Q8C2×D1111yescharacteristic
362C2×#121Dic1111yescharacteristic, complemented
363C2×#121C2×D1111yescharacteristic
364C2×#120C2×D1112yes—
365C2×C4×D4Dic1112yescomplemented
366C2×C4×D4C2×D1112yes—
367C2×#117—221no—
368C2×#117Dic1111yescharacteristic, complemented
369C22×C22⋊C4—112no—
370C22×C42—221no—
371C2×#99—118no—
372#381—221no—
373#380—112no—
374#380—221no—
375#379—112no—
376C4×C22⋊C4—112no—
377C4×C22⋊C4—112no—
378C4×C22⋊C4—112no—
379C4×C22⋊C4—221no—
380C4×C22⋊C4—221no—
381C4×C22⋊C4—221no—
382C2×#95—221no—
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×C11—42no—
408C22×C11—42no—
409C22×C11—42no—
410C22×C11—84no—
411C22×C11C2×#9912yes—
412C22×C11#41012yes—
413C22×C11C22×C22⋊C411yescharacteristic
414C22×C11C4×#4112yes—
415C22×C11#52512yes—
416C22×C11#53212yes—
417C4×C11—21no—
418C4×C11—21no—
419C4×C11—21no—
420C4×C11—21no—
421C4×C11—21no—
422C4×C11—21no—
423C4×C11—42no—
424C4×C11—42no—
425C4×C11—42no—
426C4×C11C2×#9912yes—
427C4×C11C2×#9912yes—
428Dic11—48no—
429Dic11—84no—
430C25C22×D1111yescharacteristic
431C2×#41—21no—
432C2×#41—21no—
433C2×#41—21no—
434C2×#41—21no—
435C2×#41—44no—
436C22×Q8C2×Dic1111yescharacteristic, complemented
437C22×D4C2×Dic1112yes—
438C22×D4C2×Dic1112yes—
439C22×D4C2×Dic1111yescharacteristic, complemented
440C22×D4C22×D1112yes—
441C23×C4—44no—
442C23×C4—222no—
443C23×C4C2×Dic1111yescharacteristic
444C23×C4C2×Dic1111yescharacteristic
445C23×C4C2×Dic1111yescharacteristic
446C23×C4C2×Dic1111yescharacteristic
447C23×C4C2×Dic1112yescomplemented
448C23×C4C22⋊D1111yescharacteristic
449C23×C4C22⋊D1111yescharacteristic
450C23×C4C22⋊D1111yescharacteristic
451C23×C4C22⋊D1111yescharacteristic
452C23×C4C22⋊D1111yescharacteristic
453C23×C4C22⋊D1111yescharacteristic
454C23×C4C22⋊D1111yescharacteristic
455C23×C4C22⋊D1111yescharacteristic
456C23×C4C22×D1111yescharacteristic
457C23×C4C22×D1111yescharacteristic
458#123—22no—
459#123—22no—
460#123—22no—
461#123—22no—
462C22⋊Q8—21no—
463C22⋊Q8—21no—
464C22⋊Q8—21no—
465C22⋊Q8—21no—
466C22⋊Q8—21no—
467C22⋊Q8—21no—
468C22⋊Q8—21no—
469C22⋊Q8—21no—
470#121—21no—
471#121—21no—
472#121—21no—
473#121—21no—
474#121—21no—
475#121—21no—
476#121—21no—
477#121—21no—
478#120—22no—
479#120—22no—
480#120—22no—
481#120—22no—
482C4×D4—22no—
483C4×D4—22no—
484C4×D4—22no—
485C4×D4—22no—
486C4×D4—22no—
487C4×D4—22no—
488C4×D4—22no—
489C4×D4—22no—
490#117—21no—
491#117—21no—
492#117—21no—
493#117—21no—
494#117—444no—
495C2×C4⋊C4—222no—
496C2×C4⋊C4C2×Dic1111yescharacteristic, complemented
497C2×C4⋊C4C2×Dic1111yescharacteristic, complemented
498C2×C4⋊C4C2×Dic1112yescomplemented
499C2×C4⋊C4C2×Dic1112yescomplemented
500C2×C22⋊C4—114no—
501C2×C22⋊C4—114no—
502C2×C22⋊C4—228no—
503C2×C22⋊C4—222no—
504C2×C22⋊C4—222no—
505C2×C22⋊C4—222no—
506C2×C22⋊C4C2×Dic1112yes—
507C2×C22⋊C4C2×Dic1112yes—
508C2×C22⋊C4C2×Dic1112yescomplemented
509C2×C22⋊C4C2×Dic1112yescomplemented
510C2×C22⋊C4C22×D1112yes—
511C2×C42—222no—
512C2×C42—222no—
513C2×C42—222no—
514C2×C42—444no—
515C2×C42C2×Dic1112yescomplemented
516#99—2216no—
517#95—222no—
518#95—222no—
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—82no—
529C2×C11#229711yescharacteristic
530C2×C11C22×#9911yescharacteristic
531C2×C11C2×#41011yescharacteristic
532C24—24no—
533C24—42no—
534C24—42no—
535C24C22×Dic1111yescharacteristic
536C24C22×Dic1111yescharacteristic
537C24C22×Dic1112yes—
538C24C2×C22⋊D1111yescharacteristic
539C24C2×C22⋊D1111yescharacteristic
540C24C2×C22⋊D1111yescharacteristic
541C24C2×C22⋊D1111yescharacteristic
542C24C23×D1111yescharacteristic
543#41—44no—
544#41—44no—
545#41—44no—
546#41—44no—
547C2×Q8—21no—
548C2×Q8—21no—
549C2×Q8—42no—
550C2×D4—22no—
551C2×D4—22no—
552C2×D4—22no—
553C2×D4—22no—
554C2×D4—28no—
555C2×D4—22no—
556C2×D4—22no—
557C2×D4—21no—
558C2×D4—21no—
559C2×D4—42no—
560C2×D4—44no—
561C2×D4—44no—
562C22×C4—24no—
563C22×C4—24no—
564C22×C4—24no—
565C22×C4—22no—
566C22×C4—22no—
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—228no—
580C22×C4—224no—
581C22×C4—224no—
582C22×C4—444no—
583C22×C4—444no—
584C22×C4C22⋊Dic1111yescharacteristic
585C22×C4C22⋊Dic1111yescharacteristic
586C22×C4C22⋊Dic1111yescharacteristic
587C22×C4C22⋊Dic1111yescharacteristic
588C22×C4C22⋊Dic1111yescharacteristic
589C22×C4C22⋊Dic1111yescharacteristic
590C22×C4C22⋊Dic1111yescharacteristic
591C22×C4C22⋊Dic1111yescharacteristic
592C22×C4C22⋊Dic1111yescharacteristic
593C22×C4C22⋊Dic1111yescharacteristic
594C22×C4C22⋊Dic1111yescharacteristic
595C22×C4C22⋊Dic1111yescharacteristic
596C22×C4C22⋊Dic1111yescharacteristic
597C22×C4C22⋊Dic1111yescharacteristic
598C22×C4C22⋊Dic1111yescharacteristic
599C22×C4C22⋊Dic1111yescharacteristic
600C22×C4C22×Dic1112yes—
601C22×C4C22×Dic1111yescharacteristic
602C22×C4C22×Dic1111yescharacteristic
603C22×C4C22×Dic1112yes—
604C22×C4C22×Dic1112yes—
605C22×C4C22×Dic1111yescharacteristic
606C22×C4C22×Dic1111yescharacteristic
607C22×C4C2×C22⋊D1111yescharacteristic
608C22×C4C2×C22⋊D1111yescharacteristic
609C22×C4C2×C22⋊D1111yescharacteristic
610C22×C4C2×C22⋊D1111yescharacteristic
611C22×C4C2×C22⋊D1111yescharacteristic
612C22×C4C2×C22⋊D1111yescharacteristic
613C22×C4C2×C22⋊D1111yescharacteristic
614C22×C4C2×C22⋊D1111yescharacteristic
615C4⋊C4—21no—
616C4⋊C4—21no—
617C4⋊C4—21no—
618C4⋊C4—21no—
619C4⋊C4—22no—
620C4⋊C4—22no—
621C4⋊C4—22no—
622C4⋊C4—22no—
623C4⋊C4—444no—
624C22⋊C4—22no—
625C22⋊C4—22no—
626C22⋊C4—22no—
627C22⋊C4—22no—
628C22⋊C4—22no—
629C22⋊C4—22no—
630C22⋊C4—22no—
631C22⋊C4—22no—
632C22⋊C4—22no—
633C22⋊C4—22no—
634C22⋊C4—118no—
635C22⋊C4—228no—
636C22⋊C4—224no—
637C22⋊C4—228no—
638C22⋊C4—444no—
639C22⋊C4—444no—
640C42—22no—
641C42—22no—
642C42—444no—
643C42—444no—
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—22no—
659C23—24no—
660C23—41no—
661C23—41no—
662C23—41no—
663C23—41no—
664C23—41no—
665C23—41no—
666C23—41no—
667C23—41no—
668C23—416no—
669C23—42no—
670C23—42no—
671C23C2×C22⋊Dic1111yescharacteristic
672C23C2×C22⋊Dic1111yescharacteristic
673C23C2×C22⋊Dic1111yescharacteristic
674C23C2×C22⋊Dic1111yescharacteristic
675C23#41×D1114yes—
676C23C23×Dic1111yescharacteristic
677C23C22×C22⋊D1111yescharacteristic
678C23C22×C22⋊D1111yescharacteristic
679Q8—42no—
680Q8—42no—
681D4—42no—
682D4—44no—
683D4—44no—
684D4—44no—
685D4—44no—
686D4—44no—
687D4—44no—
688D4—42no—
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—24no—
705C2×C4—22no—
706C2×C4—22no—
707C2×C4—22no—
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—41no—
718C2×C4—41no—
719C2×C4—41no—
720C2×C4—44no—
721C2×C4—44no—
722C2×C4—42no—
723C2×C4—42no—
724C2×C4—228no—
725C2×C4—444no—
726C2×C4—4416no—
727C2×C4—444no—
728C2×C4—444no—
729C2×C4—444no—
730C2×C4—444no—
731C2×C4#6689814yescomplemented
732C2×C4C2×C22⋊Dic1111yescharacteristic
733C2×C4C2×C22⋊Dic1111yescharacteristic
734C2×C4C2×C22⋊Dic1111yescharacteristic
735C2×C4C2×C22⋊Dic1111yescharacteristic
736C2×C4C2×C22⋊Dic1111yescharacteristic
737C2×C4C2×C22⋊Dic1111yescharacteristic
738C2×C4C2×C22⋊Dic1111yescharacteristic
739C2×C4C2×C22⋊Dic1111yescharacteristic
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—42no—
764C22—42no—
765C22—42no—
766C22—84no—
767C22C2×#6689812yes—
768C22#1062285312yes—
769C22#41×Dic1112yes—
770C22#1062335912yes—
771C22#1062336312yes—
772C22C22×C22⋊Dic1111yescharacteristic
773C4—21no—
774C4—21no—
775C4—21no—
776C4—21no—
777C4—21no—
778C4—21no—
779C4—42no—
780C4—42no—
781C4—42no—
782C4—448no—
783C4—884no—
784C4C2×#6689812yes—
785C4C2×#6689812yes—
786C2—22no—
787C2—22no—
788C2—22no—
789C2—22no—
790C2—22no—
791C2—41no—
792C2—41no—
793C2—82no—
794C2#1307110711yescharacteristic
795C2C22×#6689811yescharacteristic
796C2C2×#1062285311yescharacteristic
subgroupG/H
centerC2×C4C2×C22⋊Dic11
commutatorC23×C11C23×C4
FrattiniC24C23×D11
Fitting, prime radicalC2×C11×#525C2
socleC22×C11C22×C22⋊C4
cosocleC24×C11C24
hypercenterC2×#525D11
hypocenterC11#21420
LCSG ▷ C23×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C24×C4 ◁ C2×#525

Complements

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

NH ≅ G/Ntype
1. #13070999C2semidirect
2. C2×C4×C22⋊Dic11C2semidirect
3. #13069602C2semidirect
4. #13069453C2semidirect
5. #13069070C2semidirect
6. C4×#66898C2semidirect
8. C22×C11×#41C4semidirect
18. C2×C11×#123C4semidirect
19. C2×C11×C22⋊Q8C4semidirect
21. C2×C11×#121C4semidirect
24. C2×C4×D4×C11C4semidirect
26. C2×C11×#117C4semidirect
49. C22×Q8×C11C2×C4semidirect
52. C22×D4×C11C2×C4semidirect
59. C23×C4×C11C2×C4semidirect
107. C2×C11×C4⋊C4C2×C4semidirect
108. C2×C11×C4⋊C4C2×C4semidirect
109. C2×C11×C4⋊C4C2×C4semidirect
110. C2×C11×C4⋊C4C2×C4semidirect
113. C2×C11×C22⋊C4C2×C4semidirect
114. C2×C11×C22⋊C4C2×C4semidirect
116. C2×C42×C11C2×C4semidirect
243. C22⋊Dic11#41semidirect
333. C2×C4×C11#99semidirect
349. C22×#41Dic11semidirect
359. C2×#123Dic11semidirect
360. C2×C22⋊Q8Dic11semidirect
362. C2×#121Dic11semidirect
365. C2×C4×D4Dic11semidirect
368. C2×#117Dic11semidirect
436. C22×Q8C2×Dic11semidirect
439. C22×D4C2×Dic11semidirect
447. C23×C4C2×Dic11semidirect
496. C2×C4⋊C4C2×Dic11semidirect
497. C2×C4⋊C4C2×Dic11semidirect
498. C2×C4⋊C4C2×Dic11semidirect
499. C2×C4⋊C4C2×Dic11semidirect
508. C2×C22⋊C4C2×Dic11semidirect
509. C2×C22⋊C4C2×Dic11semidirect
515. C2×C42C2×Dic11semidirect
645. C11#21420semidirect
731. C2×C4#66898semidirect

Maximal subgroups

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

subgroupindex
#130709992
C2×C4×C22⋊Dic112
#130696022
#130694532
#130690702
C4×#668982
C2×C11×#5252
#2142011