Finite Group Databasebeta

← #14675720

Subgroups — #14675720

Order 2816.

1846 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×#10622557C212yesmaximal
2C2×#10622589C211yesmaximal, characteristic, complemented
3C2×#10622825C211yesmaximal, characteristic
4C2×C4⋊C4×Dic11C211yesmaximal, characteristic, complemented
5C2×C4×C22⋊Dic11C211yesmaximal, characteristic
6#13066871C212yesmaximal, complemented
7#13066859C212yesmaximal
8#13066847C212yesmaximal, complemented
9#13066845C211yesmaximal, characteristic, complemented
10#13066845C211yesmaximal, characteristic, complemented
11C2×C11×#380C211yesmaximal, characteristic
12C24×C4×C11C2211yescharacteristic
13C22×C11×C4⋊C4C2211yescharacteristic
14C22×C11×C4⋊C4C2211yescharacteristic
15C22×C11×C22⋊C4C2212yes—
16C22×C22⋊Dic11C2212yes—
17C22×C22⋊Dic11C2211yescharacteristic
18C22×C22⋊Dic11C2211yescharacteristic
19C22×C4⋊Dic11C2211yescharacteristic
20C22×C4⋊Dic11C2211yescharacteristic
21C22×Dic11⋊C4C2212yes—
22C22×Dic11⋊C4C2212yes—
23C22×C4×Dic11C2212yes—
24C22×C4×Dic11C2211yescharacteristic
25C22×C4×Dic11C2211yescharacteristic
26C11×#380—24no—
27C2×C11×#95C2212yes—
28#10622825—24no—
29C4×C22⋊Dic11C418yescomplemented
30C2×C11⋊#95C2212yes—
31C2×C11⋊#95C2212yes—
32C2×C11⋊#95C2212yes—
33C2×C11⋊#95C2212yes—
34C2×C11⋊#95C2212yes—
35C2×C11⋊#95C2212yes—
36C2×C11⋊#95C2211yescharacteristic
37C2×C11⋊#95C2211yescharacteristic
38#10622589—24no—
39C4⋊C4×Dic11—24no—
40#10622557—28no—
41C25×C11C2311yescharacteristic
42C23×C4×C11—22no—
43C23×C4×C11—22no—
44C23×C4×C11—22no—
45C23×C4×C11—22no—
46C23×C4×C11—22no—
47C23×C4×C11—22no—
48C23×C4×C11C2×C414yes—
49C23×C4×C11C2312yes—
50C23×C4×C11C2311yescharacteristic
51C23×C4×C11C2312yes—
52C23×C4×C11C2311yescharacteristic
53C23×Dic11C2312yes—
54C23×Dic11C2311yescharacteristic
55C23×Dic11C2312yes—
56C23×Dic11C2311yescharacteristic
57C23×Dic11C2311yescharacteristic
58C23×Dic11C2311yescharacteristic
59C2×C11×C4⋊C4—22no—
60C2×C11×C4⋊C4—22no—
61C2×C11×C4⋊C4—22no—
62C2×C11×C4⋊C4—22no—
63C2×C11×C4⋊C4—22no—
64C2×C11×C4⋊C4D414yes—
65C2×C11×C22⋊C4—24no—
66C2×C11×C22⋊C4—24no—
67C2×C11×C22⋊C4—42no—
68C2×C22⋊Dic11—22no—
69C2×C22⋊Dic11—22no—
70C2×C22⋊Dic11—24no—
71C2×C22⋊Dic11—24no—
72C2×C22⋊Dic11—42no—
73C2×C22⋊Dic11C2×C414yes—
74C2×C22⋊Dic11C2×C414yes—
75C2×C22⋊Dic11D414yes—
76C2×C22⋊Dic11Q814yes—
77C2×C4⋊Dic11—22no—
78C2×C4⋊Dic11—22no—
79C2×C4⋊Dic11—22no—
80C2×C4⋊Dic11—22no—
81C2×C4⋊Dic11—22no—
82C2×C4⋊Dic11D414yes—
83C2×Dic11⋊C4—24no—
84C2×Dic11⋊C4—24no—
85C2×Dic11⋊C4—24no—
86C2×Dic11⋊C4—24no—
87C2×Dic11⋊C4—42no—
88C2×Dic11⋊C4—42no—
89C2×C4×Dic11—22no—
90C2×C4×Dic11—22no—
91C2×C4×Dic11—22no—
92C2×C4×Dic11—22no—
93C2×C4×Dic11—24no—
94C2×C4×Dic11—24no—
95C2×C4×Dic11—42no—
96C2×C4×Dic11C2×C414yes—
97C2×C4×Dic11C2×C414yes—
98C11×#95—24no—
99C11⋊#95—24no—
100C11⋊#95—24no—
101C11⋊#95—24no—
102C11⋊#95—24no—
103C11⋊#95—24no—
104C11⋊#95—42no—
105C11⋊#95C2×C414yes—
106C11⋊#95C2×C414yes—
107#13876—111nomaximal, Sylow
108C24×C11—21no—
109C24×C11—21no—
110C24×C11—21no—
111C24×C11—21no—
112C24×C11—21no—
113C24×C11—21no—
114C24×C11—21no—
115C24×C11—21no—
116C24×C11—21no—
117C24×C11—21no—
118C24×C11—21no—
119C24×C11—21no—
120C24×C11C22×C412yes—
121C24×C11C2×D412yes—
122C24×C11C2×Q812yes—
123C24×C11C2411yescharacteristic
124C22×C4×C11—21no—
125C22×C4×C11—22no—
126C22×C4×C11—21no—
127C22×C4×C11—22no—
128C22×C4×C11—22no—
129C22×C4×C11—22no—
130C22×C4×C11—21no—
131C22×C4×C11—21no—
132C22×C4×C11—21no—
133C22×C4×C11—21no—
134C22×C4×C11—22no—
135C22×C4×C11—22no—
136C22×C4×C11—28no—
137C22×C4×C11—28no—
138C22×C4×C11—28no—
139C22×C4×C11—22no—
140C22×C4×C11—22no—
141C22×C4×C11—22no—
142C22×C4×C11—22no—
143C22×C4×C11—22no—
144C22×C4×C11—22no—
145C22×C4×C11—22no—
146C22×C4×C11—44no—
147C22×C4×C11—44no—
148C22×C4×C11—44no—
149C22×C4×C11—44no—
150C22×C4×C11C22×C412yes—
151C22×C4×C11C22×C412yes—
152C22×C4×C11C2×D414yes—
153C22×C4×C11C2×D412yes—
154C22×C4×C11C2×D412yes—
155C22×C4×C11#4112yes—
156C22×C4×C11#4112yes—
157C22×C4×C11#4112yes—
158C22×C4×C11#4112yes—
159C22×Dic11—21no—
160C22×Dic11—21no—
161C22×Dic11—21no—
162C22×Dic11—21no—
163C22×Dic11—22no—
164C22×Dic11—22no—
165C22×Dic11—22no—
166C22×Dic11—22no—
167C22×Dic11—21no—
168C22×Dic11—21no—
169C22×Dic11—21no—
170C22×Dic11—21no—
171C22×Dic11—22no—
172C22×Dic11—22no—
173C22×Dic11—21no—
174C22×Dic11—21no—
175C22×Dic11—22no—
176C22×Dic11—22no—
177C22×Dic11—22no—
178C22×Dic11—21no—
179C22×Dic11—21no—
180C22×Dic11—21no—
181C22×Dic11—21no—
182C22×Dic11—22no—
183C22×Dic11—22no—
184C22×Dic11—22no—
185C22×Dic11—21no—
186C22×Dic11—21no—
187C22×Dic11—21no—
188C22×Dic11—21no—
189C22×Dic11—22no—
190C22×Dic11C22×C412yes—
191C22×Dic11C22×C412yes—
192C22×Dic11C22×C412yes—
193C22×Dic11C22×C412yes—
194C22×Dic11C2×D414yes—
195C22×Dic11C2×D412yes—
196C22×Dic11C2×D412yes—
197C22×Dic11C2×Q812yes—
198C22×Dic11C2×Q812yes—
199C22×Dic11#4112yes—
200C22×Dic11#4112yes—
201C11×C4⋊C4—28no—
202C11×C4⋊C4—44no—
203C11×C22⋊C4—48no—
204C22⋊Dic11—28no—
205C22⋊Dic11—48no—
206C22⋊Dic11C4⋊C4116yescomplemented
207C4⋊Dic11—28no—
208C4⋊Dic11—44no—
209Dic11⋊C4—48no—
210Dic11⋊C4—48no—
211C4×Dic11—28no—
212C4×Dic11—28no—
213C4×Dic11—48no—
214C2×#388—112no—
215C2×#384—111no—
216C2×#380—111no—
217C2×#380D1111yescharacteristic
218C2×C4×C4⋊C4—111no—
219C2×C4×C22⋊C4—111no—
220#1442—112no—
221#1439—112no—
222#1436—112no—
223C4⋊#95—111no—
224C4⋊#95—111no—
225C23×C11—22no—
226C23×C11—22no—
227C23×C11—22no—
228C23×C11—22no—
229C23×C11—22no—
230C23×C11—22no—
231C23×C11—22no—
232C23×C11—22no—
233C23×C11—22no—
234C23×C11—22no—
235C23×C11—22no—
236C23×C11—22no—
237C23×C11—22no—
238C23×C11—22no—
239C23×C11—22no—
240C23×C11—22no—
241C23×C11—22no—
242C23×C11—22no—
243C23×C11—41no—
244C23×C11—41no—
245C23×C11—41no—
246C23×C11—41no—
247C23×C11—41no—
248C23×C11—41no—
249C23×C11—41no—
250C23×C11—41no—
251C23×C11—41no—
252C23×C11—41no—
253C23×C11—41no—
254C23×C11—41no—
255C23×C11—41no—
256C23×C11—41no—
257C23×C11—41no—
258C23×C11—41no—
259C23×C11C2×C4⋊C414yes—
260C23×C11C23×C411yescharacteristic
261C23×C11C22×D411yescharacteristic
262C23×C11C22×D411yescharacteristic
263C23×C11C22×D411yescharacteristic
264C23×C11C22×Q811yescharacteristic
265C23×C11C2×#4111yescharacteristic
266C23×C11C2×#4111yescharacteristic
267C23×C11C2×#4111yescharacteristic
268C23×C11C2×#4111yescharacteristic
269C23×C11C2×#4111yescharacteristic
270C23×C11C2×#4111yescharacteristic
271C23×C11H(5,𝔽2)11yescharacteristic
272C23×C11H(5,𝔽2)11yescharacteristic
273C23×C112−1+411yescharacteristic
274C23×C112−1+411yescharacteristic
275C2×C4×C11—22no—
276C2×C4×C11—22no—
277C2×C4×C11—22no—
278C2×C4×C11—24no—
279C2×C4×C11—24no—
280C2×C4×C11—24no—
281C2×C4×C11—41no—
282C2×C4×C11—41no—
283C2×C4×C11—41no—
284C2×C4×C11—41no—
285C2×C4×C11—42no—
286C2×C4×C11—42no—
287C2×C4×C11—42no—
288C2×C4×C11—42no—
289C2×C4×C11—416no—
290C2×C4×C11—42no—
291C2×C4×C11—42no—
292C2×C4×C11—42no—
293C2×C4×C11—42no—
294C2×C4×C11—42no—
295C2×C4×C11—42no—
296C2×C4×C11—42no—
297C2×C4×C11#11714yes—
298C2×C4×C11C4×D414yes—
299C2×C4×C11C4×D414yes—
300C2×C4×C11#12114yes—
301C2×C4×C11#12314yes—
302C2×C4×C11#12414yes—
303C2×C4×C11#12614yes—
304C2×Dic11—22no—
305C2×Dic11—22no—
306C2×Dic11—22no—
307C2×Dic11—22no—
308C2×Dic11—22no—
309C2×Dic11—22no—
310C2×Dic11—22no—
311C2×Dic11—22no—
312C2×Dic11—22no—
313C2×Dic11—22no—
314C2×Dic11—22no—
315C2×Dic11—22no—
316C2×Dic11—22no—
317C2×Dic11—22no—
318C2×Dic11—22no—
319C2×Dic11—22no—
320C2×Dic11—22no—
321C2×Dic11—22no—
322C2×Dic11—22no—
323C2×Dic11—22no—
324C2×Dic11—22no—
325C2×Dic11—24no—
326C2×Dic11—24no—
327C2×Dic11—24no—
328C2×Dic11—42no—
329C2×Dic11—42no—
330C2×Dic11—42no—
331C2×Dic11—41no—
332C2×Dic11—41no—
333C2×Dic11—42no—
334C2×Dic11—41no—
335C2×Dic11—41no—
336C2×Dic11—42no—
337C2×Dic11—42no—
338C2×Dic11—42no—
339C2×Dic11—42no—
340C2×Dic11—42no—
341C2×Dic11—42no—
342C2×Dic11—42no—
343C2×Dic11C2×C4⋊C414yes—
344C2×Dic11C2×C4⋊C414yes—
345C2×Dic11#11714yes—
346C24×C4C2×D1111yescharacteristic
347C22×C4⋊C4—111no—
348C22×C4⋊C4—111no—
349C22×C4⋊C4—112no—
350C22×C4⋊C4—112no—
351C22×C4⋊C4C2×D1111yescharacteristic
352C22×C4⋊C4C2×D1111yescharacteristic
353C22×C22⋊C4—111no—
354C22×C22⋊C4—111no—
355C22×C22⋊C4—112no—
356C22×C22⋊C4C2×D1112yes—
357C22×C42—111no—
358C22×C42—111no—
359C22×C42—112no—
360#388—228no—
361#384—224no—
362#380—24no—
363#380—224no—
364C4×C4⋊C4—224no—
365C4×C22⋊C4—118no—
366C2×#95—111no—
367C2×#95—111no—
368C2×#95—112no—
369C2×#95—112no—
370C2×#95—112no—
371C2×#95—112no—
372C2×#95—112no—
373C2×#95—112no—
374C2×#95C2×D1112yes—
375C22×C11—24no—
376C22×C11—24no—
377C22×C11—24no—
378C22×C11—42no—
379C22×C11—42no—
380C22×C11—42no—
381C22×C11—42no—
382C22×C11—42no—
383C22×C11—42no—
384C22×C11—42no—
385C22×C11—42no—
386C22×C11—42no—
387C22×C11—42no—
388C22×C11—42no—
389C22×C11—42no—
390C22×C11C22×C4⋊C411yescharacteristic
391C22×C11C2×#11711yescharacteristic
392C22×C11C2×#11711yescharacteristic
393C22×C11C2×C4×D411yescharacteristic
394C22×C11C2×C4×D411yescharacteristic
395C22×C11#52011yescharacteristic
396C22×C11#52011yescharacteristic
397C22×C11C2×#12111yescharacteristic
398C22×C11C2×#12311yescharacteristic
399C22×C11C2×#12411yescharacteristic
400C22×C11C2×#12611yescharacteristic
401C22×C11#53211yescharacteristic
402C22×C11#53211yescharacteristic
403C22×C11#53311yescharacteristic
404C22×C11#53311yescharacteristic
405C22×C11#54011yescharacteristic
406C22×C11#54111yescharacteristic
407C22×C11#54211yescharacteristic
408C22×C11#54211yescharacteristic
409C22×C11D4211yescharacteristic
410C22×C11D4211yescharacteristic
411C22×C11#54611yescharacteristic
412C22×C11#54711yescharacteristic
413C22×C11#54711yescharacteristic
414C22×C11#54711yescharacteristic
415C22×C11#54811yescharacteristic
416C22×C11D4×Q811yescharacteristic
417C22×C11D4×Q811yescharacteristic
418C22×C11#55011yescharacteristic
419C22×C11#55211yescharacteristic
420C22×C11#55311yescharacteristic
421C22×C11#55411yescharacteristic
422C22×C11#55411yescharacteristic
423C22×C11#55511yescharacteristic
424C22×C11#55611yescharacteristic
425C4×C11—44no—
426C4×C11—42no—
427C4×C11—82no—
428C4×C11#38818yescomplemented
429Dic11—24no—
430Dic11—24no—
431Dic11—24no—
432Dic11—42no—
433Dic11—44no—
434Dic11—82no—
435C25C22×D1111yescharacteristic
436C23×C4—22no—
437C23×C4—22no—
438C23×C4—22no—
439C23×C4—22no—
440C23×C4—22no—
441C23×C4—22no—
442C23×C4—111no—
443C23×C4—111no—
444C23×C4—111no—
445C23×C4—112no—
446C23×C4—111no—
447C23×C4—112no—
448C23×C4C4×D1114yes—
449C23×C4C22×D1112yes—
450C23×C4C22×D1111yescharacteristic
451C23×C4C22×D1112yes—
452C23×C4C22×D1111yescharacteristic
453C2×C4⋊C4—22no—
454C2×C4⋊C4—22no—
455C2×C4⋊C4—22no—
456C2×C4⋊C4—22no—
457C2×C4⋊C4—22no—
458C2×C4⋊C4—114no—
459C2×C4⋊C4—222no—
460C2×C4⋊C4—222no—
461C2×C4⋊C4—224no—
462C2×C4⋊C4—224no—
463C2×C4⋊C4—224no—
464C2×C4⋊C4—224no—
465C2×C4⋊C4—222no—
466C2×C4⋊C4—222no—
467C2×C4⋊C4—222no—
468C2×C4⋊C4—442no—
469C2×C4⋊C4—442no—
470C2×C4⋊C4C22⋊D1114yes—
471C2×C22⋊C4—24no—
472C2×C22⋊C4—24no—
473C2×C22⋊C4—42no—
474C2×C22⋊C4—114no—
475C2×C22⋊C4—114no—
476C2×C22⋊C4—114no—
477C2×C22⋊C4—114no—
478C2×C22⋊C4—222no—
479C2×C22⋊C4—222no—
480C2×C22⋊C4—224no—
481C2×C22⋊C4—224no—
482C2×C22⋊C4—442no—
483C2×C42—114no—
484C2×C42—114no—
485C2×C42—222no—
486C2×C42—222no—
487C2×C42—222no—
488C2×C42—222no—
489C2×C42—224no—
490C2×C42—224no—
491C2×C42—442no—
492#95—24no—
493#95—114no—
494#95—114no—
495#95—224no—
496#95—224no—
497#95—224no—
498#95—224no—
499#95—224no—
500#95—442no—
501C2×C11—44no—
502C2×C11#228511yescharacteristic
503C2×C11C2×#38811yescharacteristic
504C2×C11#231411yescharacteristic
505C2×C11D4×C4⋊C411yescharacteristic
506C2×C11D4×C4⋊C411yescharacteristic
507C2×C11#235211yescharacteristic
508C2×C11#235411yescharacteristic
509C2×C11#242211yescharacteristic
510C2×C11#242311yescharacteristic
511C2×C11#242811yescharacteristic
512C2×C11#242911yescharacteristic
513C2×C11#249111yescharacteristic
514C2×C11#249211yescharacteristic
515C2×C11#249611yescharacteristic
516C2×C11#249711yescharacteristic
517C24—21no—
518C24—21no—
519C24—21no—
520C24—21no—
521C24—21no—
522C24—21no—
523C24—21no—
524C24—21no—
525C24—21no—
526C24—21no—
527C24—21no—
528C24—21no—
529C24C2×C4×D1112yes—
530C24D4×D1112yes—
531C24Q8×D1112yes—
532C24C23×D1111yescharacteristic
533C22×C4—21no—
534C22×C4—21no—
535C22×C4—22no—
536C22×C4—22no—
537C22×C4—22no—
538C22×C4—21no—
539C22×C4—21no—
540C22×C4—21no—
541C22×C4—22no—
542C22×C4—22no—
543C22×C4—22no—
544C22×C4—21no—
545C22×C4—28no—
546C22×C4—28no—
547C22×C4—28no—
548C22×C4—22no—
549C22×C4—22no—
550C22×C4—22no—
551C22×C4—22no—
552C22×C4—22no—
553C22×C4—22no—
554C22×C4—22no—
555C22×C4—44no—
556C22×C4—44no—
557C22×C4—44no—
558C22×C4—44no—
559C22×C4—112no—
560C22×C4—112no—
561C22×C4—112no—
562C22×C4—112no—
563C22×C4—112no—
564C22×C4—112no—
565C22×C4—112no—
566C22×C4—112no—
567C22×C4—112no—
568C22×C4—112no—
569C22×C4—114no—
570C22×C4—221no—
571C22×C4—221no—
572C22×C4—221no—
573C22×C4—221no—
574C22×C4—221no—
575C22×C4—221no—
576C22×C4—221no—
577C22×C4—221no—
578C22×C4—221no—
579C22×C4—221no—
580C22×C4—221no—
581C22×C4—221no—
582C22×C4—221no—
583C22×C4—222no—
584C22×C4—222no—
585C22×C4—222no—
586C22×C4—221no—
587C22×C4—221no—
588C22×C4—222no—
589C22×C4—221no—
590C22×C4—222no—
591C22×C4—221no—
592C22×C4—221no—
593C22×C4—222no—
594C22×C4—222no—
595C22×C4—222no—
596C22×C4—222no—
597C22×C4—222no—
598C22×C4—222no—
599C22×C4—222no—
600C22×C4—222no—
601C22×C4C2×C4×D1112yes—
602C22×C4C2×C4×D1112yes—
603C22×C4#433912yes—
604C22×C4D4×D1112yes—
605C22×C4#434112yes—
606C22×C4#434112yes—
607C22×C4#434112yes—
608C22×C4C2×C22⋊D1114yes—
609C22×C4C2×C22⋊D1112yes—
610C4⋊C4—28no—
611C4⋊C4—44no—
612C4⋊C4—228no—
613C4⋊C4—448no—
614C4⋊C4—448no—
615C4⋊C4—444no—
616C22⋊C4—48no—
617C22⋊C4—1116no—
618C22⋊C4—228no—
619C22⋊C4—448no—
620C42—228no—
621C42—228no—
622C42—448no—
623C11#1387611yescharacteristic, complemented, Sylow
624C23—22no—
625C23—22no—
626C23—22no—
627C23—22no—
628C23—22no—
629C23—22no—
630C23—22no—
631C23—22no—
632C23—22no—
633C23—22no—
634C23—22no—
635C23—22no—
636C23—22no—
637C23—22no—
638C23—22no—
639C23—22no—
640C23—22no—
641C23—22no—
642C23—41no—
643C23—41no—
644C23—41no—
645C23—41no—
646C23—41no—
647C23—41no—
648C23—41no—
649C23—41no—
650C23—41no—
651C23—41no—
652C23—41no—
653C23—41no—
654C23—41no—
655C23—41no—
656C23—41no—
657C23—41no—
658C23C4⋊C4×D1114yes—
659C23C22×C4×D1111yescharacteristic
660C23C2×#433911yescharacteristic
661C23C2×D4×D1111yescharacteristic
662C23C2×D4×D1111yescharacteristic
663C23C2×#434111yescharacteristic
664C23C2×#434111yescharacteristic
665C23C2×#434111yescharacteristic
666C23#6703711yescharacteristic
667C23C2×Q8×D1111yescharacteristic
668C23#6704011yescharacteristic
669C23#41×D1111yescharacteristic
670C23#41×D1111yescharacteristic
671C23#6704211yescharacteristic
672C23#6704311yescharacteristic
673C23C22×C22⋊D1111yescharacteristic
674C2×C4—22no—
675C2×C4—22no—
676C2×C4—22no—
677C2×C4—24no—
678C2×C4—24no—
679C2×C4—24no—
680C2×C4—41no—
681C2×C4—41no—
682C2×C4—41no—
683C2×C4—41no—
684C2×C4—42no—
685C2×C4—42no—
686C2×C4—42no—
687C2×C4—42no—
688C2×C4—416no—
689C2×C4—42no—
690C2×C4—42no—
691C2×C4—42no—
692C2×C4—42no—
693C2×C4—42no—
694C2×C4—42no—
695C2×C4—42no—
696C2×C4—114no—
697C2×C4—114no—
698C2×C4—114no—
699C2×C4—222no—
700C2×C4—222no—
701C2×C4—222no—
702C2×C4—222no—
703C2×C4—222no—
704C2×C4—222no—
705C2×C4—222no—
706C2×C4—222no—
707C2×C4—222no—
708C2×C4—222no—
709C2×C4—222no—
710C2×C4—222no—
711C2×C4—222no—
712C2×C4—222no—
713C2×C4—222no—
714C2×C4—222no—
715C2×C4—222no—
716C2×C4—222no—
717C2×C4—222no—
718C2×C4—222no—
719C2×C4—222no—
720C2×C4—224no—
721C2×C4—224no—
722C2×C4—224no—
723C2×C4—441no—
724C2×C4—441no—
725C2×C4—442no—
726C2×C4—441no—
727C2×C4—442no—
728C2×C4—441no—
729C2×C4—442no—
730C2×C4—442no—
731C2×C4—442no—
732C2×C4—442no—
733C2×C4—442no—
734C2×C4—442no—
735C2×C4—442no—
736C2×C4—442no—
737C2×C4—442no—
738C2×C4#6693014yes—
739C2×C4#6693214yes—
740C2×C4(C22⋊D11)⋊C414yes—
741C2×C4#6693814yes—
742C2×C4C4×C22⋊D1114yes—
743C2×C4#6698814yes—
744C2×C4#6699114yes—
745C22—24no—
746C22—24no—
747C22—24no—
748C22—42no—
749C22—42no—
750C22—42no—
751C22—42no—
752C22—42no—
753C22—42no—
754C22—42no—
755C22—42no—
756C22—42no—
757C22—42no—
758C22—42no—
759C22—42no—
760C22C2×#6693011yescharacteristic
761C22C2×#6693211yescharacteristic
762C22C2×(C22⋊D11)⋊C411yescharacteristic
763C22C2×#6693811yescharacteristic
764C22C2×C4⋊C4×D1111yescharacteristic
765C22#1062303511yescharacteristic
766C22#1062303811yescharacteristic
767C22#1062304211yescharacteristic
768C22D11×#11711yescharacteristic
769C22#1062305411yescharacteristic
770C22#1062306311yescharacteristic
771C22#1062306411yescharacteristic
772C22#1062312711yescharacteristic
773C22#1062312711yescharacteristic
774C22#1062313411yescharacteristic
775C22#1062314011yescharacteristic
776C22#1062314211yescharacteristic
777C22#1062314311yescharacteristic
778C22#1062314511yescharacteristic
779C22#1062315011yescharacteristic
780C22#1062315311yescharacteristic
781C22#1062315311yescharacteristic
782C22#1062315611yescharacteristic
783C22#1062316311yescharacteristic
784C22#1062316411yescharacteristic
785C22#1062316611yescharacteristic
786C22#1062317011yescharacteristic
787C22#1062317411yescharacteristic
788C22C2×C4×C22⋊D1111yescharacteristic
789C22C2×#6698811yescharacteristic
790C22C2×#6699111yescharacteristic
791C22D4×C22⋊D1111yescharacteristic
792C22Q8×C22⋊D1111yescharacteristic
793C22#1062335511yescharacteristic
794C22#1062336511yescharacteristic
795C4—42no—
796C4—44no—
797C4—82no—
798C4—224no—
799C4—224no—
800C4—224no—
801C4—444no—
802C4—442no—
803C4—882no—
804C4#1062255718yescomplemented
805C2—44no—
806C2#1307101811yescharacteristic
807C2C2×#1062255711yescharacteristic
808C2#1307122311yescharacteristic
809C2#1307151211yescharacteristic
810C2C4⋊C4×C22⋊D1111yescharacteristic
811C2#1307153811yescharacteristic
812C2#1307156611yescharacteristic
813C2#1307212611yescharacteristic
814C2#1307213711yescharacteristic
815C2#1307220011yescharacteristic
816C2#1307221111yescharacteristic
817C2#1307297511yescharacteristic
818C2#1307298611yescharacteristic
819C2#1307303411yescharacteristic
820C2#1307304511yescharacteristic
subgroupG/H
center, FrattiniC24C23×D11
commutatorC23×C11C23×C4
FittingC2×C11×#380C2
socle, cosocleC24×C11C24
prime radicalC25×C11C23
hypercenterC2×#380D11
hypocenterC11#13876
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ C2×#380

Complements

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

NH ≅ G/Ntype
2. C2×#10622589C2semidirect
4. C2×C4⋊C4×Dic11C2semidirect
6. #13066871C2semidirect
8. #13066847C2semidirect
9. #13066845C2semidirect
10. #13066845C2semidirect
29. C4×C22⋊Dic11C4semidirect
206. C22⋊Dic11C4⋊C4semidirect
428. C4×C11#388semidirect
623. C11#13876semidirect
804. C4#10622557semidirect

Maximal subgroups

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

subgroupindex
C2×#106225572
C2×#106225892
C2×#106228252
C2×C4⋊C4×Dic112
C2×C4×C22⋊Dic112
#130668712
#130668592
#130668472
#130668452
C2×C11×#3802
#1387611