Finite Group Databasebeta

← #14675718

Subgroups — #14675718

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×#10622553C212yesmaximal
2C2×#10622589C211yesmaximal, characteristic, complemented
3C2×#10622600C211yesmaximal, characteristic
4C2×#10622600C211yesmaximal, characteristic
5C2×C4×(C2×D11)⋊C4C211yesmaximal, characteristic
6#13066871C212yesmaximal, complemented
7#13066860C212yesmaximal
8#13066849C212yesmaximal, complemented
9#13066846C211yesmaximal, characteristic, complemented
10#13066845C211yesmaximal, characteristic, complemented
11C2×C4×C11×C4⋊C4C211yesmaximal, characteristic, complemented
12C23×C4×D11C2211yescharacteristic
13C22×C11×C4⋊C4C2211yescharacteristic
14C22×C11×C4⋊C4C2211yescharacteristic
15C22×C42×C11C2212yes—
16C22×C42×C11C2211yescharacteristic
17C22×(C2×D11)⋊C4C2212yes—
18C22×(C2×D11)⋊C4C2212yes—
19C22×(C2×D11)⋊C4C2211yescharacteristic
20C22×(C2×D11)⋊C4C2211yescharacteristic
21C22×C4⋊Dic11C2211yescharacteristic
22C22×C4⋊Dic11C2211yescharacteristic
23C22×Dic11⋊C4C2212yes—
24C22×Dic11⋊C4C2212yes—
25C22×C4×Dic11C2211yescharacteristic
26C4×C11×C4⋊C4—24no—
27C2×C11×#95C2212yes—
28C2×C11⋊#95C2212yes—
29C2×C11⋊#95C2212yes—
30C2×C11⋊#95C2212yes—
31C2×C11⋊#95C2212yes—
32C2×C11⋊#95C2212yes—
33C2×C11⋊#95C2212yes—
34C2×C11⋊#95C2211yescharacteristic
35C2×C11⋊#95C2211yescharacteristic
36#10622600—24no—
37#10622600—24no—
38#10622589—24no—
39#10622553—28no—
40C4×(C2×D11)⋊C4C418yescomplemented
41C24×D11C2311yescharacteristic
42C23×C4×C11C2311yescharacteristic
43C23×C4×C11C2312yes—
44C23×C4×C11C2312yes—
45C23×C4×C11C2311yescharacteristic
46C23×C4×C11C2311yescharacteristic
47C23×Dic11C2312yes—
48C23×Dic11C2312yes—
49C23×Dic11C2311yescharacteristic
50C23×Dic11C2311yescharacteristic
51C23×Dic11C2311yescharacteristic
52C22×C4×D11—22no—
53C22×C4×D11—22no—
54C22×C4×D11—22no—
55C22×C4×D11—22no—
56C22×C4×D11—22no—
57C22×C4×D11—22no—
58C22×C4×D11C2×C414yes—
59C2×C11×C4⋊C4—22no—
60C2×C11×C4⋊C4—22no—
61C2×C11×C4⋊C4—22no—
62C2×C11×C4⋊C4—22no—
63C2×C11×C4⋊C4D414yes—
64C2×C11×C4⋊C4D414yes—
65C2×C42×C11—22no—
66C2×C42×C11—22no—
67C2×C42×C11—24no—
68C2×C42×C11—24no—
69C2×C42×C11—42no—
70C2×C42×C11C2×C414yes—
71C2×(C2×D11)⋊C4—22no—
72C2×(C2×D11)⋊C4—22no—
73C2×(C2×D11)⋊C4—24no—
74C2×(C2×D11)⋊C4—24no—
75C2×(C2×D11)⋊C4—24no—
76C2×(C2×D11)⋊C4—24no—
77C2×(C2×D11)⋊C4—42no—
78C2×(C2×D11)⋊C4—42no—
79C2×(C2×D11)⋊C4C2×C414yes—
80C2×(C2×D11)⋊C4C2×C414yes—
81C2×(C2×D11)⋊C4D414yes—
82C2×(C2×D11)⋊C4Q814yes—
83C2×C4⋊Dic11—22no—
84C2×C4⋊Dic11—22no—
85C2×C4⋊Dic11—22no—
86C2×C4⋊Dic11—22no—
87C2×C4⋊Dic11—22no—
88C2×C4⋊Dic11—22no—
89C2×Dic11⋊C4—24no—
90C2×Dic11⋊C4—24no—
91C2×Dic11⋊C4—24no—
92C2×Dic11⋊C4—24no—
93C2×Dic11⋊C4—42no—
94C2×Dic11⋊C4—42no—
95C2×C4×Dic11—22no—
96C2×C4×Dic11—22no—
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×C11C2411yescharacteristic
109C23×D11—21no—
110C23×D11—21no—
111C23×D11—21no—
112C23×D11—21no—
113C23×D11—21no—
114C23×D11—21no—
115C23×D11—21no—
116C23×D11—21no—
117C23×D11—21no—
118C23×D11—21no—
119C23×D11—21no—
120C23×D11—21no—
121C23×D11C22×C412yes—
122C23×D11C2×D412yes—
123C23×D11C2×Q812yes—
124C22×C4×C11—21no—
125C22×C4×C11—21no—
126C22×C4×C11—21no—
127C22×C4×C11—21no—
128C22×C4×C11—22no—
129C22×C4×C11—21no—
130C22×C4×C11—22no—
131C22×C4×C11—22no—
132C22×C4×C11—22no—
133C22×C4×C11—22no—
134C22×C4×C11—21no—
135C22×C4×C11—21no—
136C22×C4×C11—21no—
137C22×C4×C11—22no—
138C22×C4×C11—22no—
139C22×C4×C11—22no—
140C22×C4×C11—21no—
141C22×C4×C11—22no—
142C22×C4×C11—22no—
143C22×C4×C11—22no—
144C22×C4×C11—21no—
145C22×C4×C11—22no—
146C22×C4×C11C22×C412yes—
147C22×C4×C11C22×C412yes—
148C22×C4×C11C22×C412yes—
149C22×C4×C11C2×D414yes—
150C22×C4×C11C2×D414yes—
151C22×C4×C11C2×D412yes—
152C22×C4×C11C2×D412yes—
153C22×C4×C11C2×D412yes—
154C22×C4×C11C2×Q812yes—
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—22no—
168C22×Dic11—21no—
169C22×Dic11—21no—
170C22×Dic11—21no—
171C22×Dic11—21no—
172C22×Dic11—21no—
173C22×Dic11—21no—
174C22×Dic11—22no—
175C22×Dic11—22no—
176C22×Dic11—22no—
177C22×Dic11—22no—
178C22×Dic11—22no—
179C22×Dic11—21no—
180C22×Dic11—21no—
181C22×Dic11—22no—
182C22×Dic11—22no—
183C22×Dic11—22no—
184C22×Dic11—21no—
185C22×Dic11—21no—
186C22×Dic11—22no—
187C22×Dic11C22×C412yes—
188C22×Dic11C22×C412yes—
189C22×Dic11C22×C412yes—
190C22×Dic11C2×D412yes—
191C22×Dic11C2×Q812yes—
192C22×Dic11#4112yes—
193C22×Dic11#4112yes—
194C2×C4×D11—28no—
195C2×C4×D11—28no—
196C2×C4×D11—28no—
197C2×C4×D11—44no—
198C2×C4×D11—44no—
199C2×C4×D11—44no—
200C2×C4×D11—44no—
201C11×C4⋊C4—28no—
202C11×C4⋊C4—28no—
203C42×C11—28no—
204C42×C11—48no—
205(C2×D11)⋊C4—28no—
206(C2×D11)⋊C4—48no—
207(C2×D11)⋊C4—48no—
208(C2×D11)⋊C4C4⋊C4116yescomplemented
209C4⋊Dic11—44no—
210C4⋊Dic11—44no—
211Dic11⋊C4—48no—
212Dic11⋊C4—48no—
213C4×Dic11—28no—
214C2×#388—112no—
215C2×#384—111no—
216C2×#380—111no—
217C2×#380—111no—
218C2×C4×C4⋊C4D1111yescharacteristic, complemented
219C2×C4×C22⋊C4—111no—
220#1442—112no—
221#1439—112no—
222#1436—112no—
223C4⋊#95—111no—
224C4⋊#95—111no—
225C23×C11C23×C411yescharacteristic
226C23×C11C22×D411yescharacteristic
227C23×C11C22×D411yescharacteristic
228C23×C11C22×D411yescharacteristic
229C23×C11C22×Q811yescharacteristic
230C23×C11C2×#4111yescharacteristic
231C23×C11C2×#4111yescharacteristic
232C23×C11C2×#4111yescharacteristic
233C23×C11C2×#4111yescharacteristic
234C23×C11C2×#4111yescharacteristic
235C23×C11C2×#4111yescharacteristic
236C23×C11H(5,𝔽2)11yescharacteristic
237C23×C11H(5,𝔽2)11yescharacteristic
238C23×C112−1+411yescharacteristic
239C23×C112−1+411yescharacteristic
240C22×D11—22no—
241C22×D11—22no—
242C22×D11—22no—
243C22×D11—22no—
244C22×D11—22no—
245C22×D11—22no—
246C22×D11—22no—
247C22×D11—22no—
248C22×D11—22no—
249C22×D11—22no—
250C22×D11—22no—
251C22×D11—22no—
252C22×D11—22no—
253C22×D11—22no—
254C22×D11—22no—
255C22×D11—22no—
256C22×D11—22no—
257C22×D11—22no—
258C22×D11—41no—
259C22×D11—41no—
260C22×D11—41no—
261C22×D11—41no—
262C22×D11—41no—
263C22×D11—41no—
264C22×D11—41no—
265C22×D11—41no—
266C22×D11—41no—
267C22×D11—41no—
268C22×D11—41no—
269C22×D11—41no—
270C22×D11—41no—
271C22×D11—41no—
272C22×D11—41no—
273C22×D11—41no—
274C22×D11C2×C4⋊C414yes—
275C2×C4×C11—22no—
276C2×C4×C11—22no—
277C2×C4×C11—22no—
278C2×C4×C11—22no—
279C2×C4×C11—22no—
280C2×C4×C11—22no—
281C2×C4×C11—22no—
282C2×C4×C11—22no—
283C2×C4×C11—22no—
284C2×C4×C11—24no—
285C2×C4×C11—24no—
286C2×C4×C11—24no—
287C2×C4×C11—24no—
288C2×C4×C11—24no—
289C2×C4×C11—24no—
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—41no—
297C2×C4×C11—41no—
298C2×C4×C11—42no—
299C2×C4×C11—42no—
300C2×C4×C11—41no—
301C2×C4×C11—41no—
302C2×C4×C11C2×C4⋊C414yes—
303C2×C4×C11#11714yes—
304C2×C4×C11C4×D414yes—
305C2×C4×C11C4×D414yes—
306C2×C4×C11#12114yes—
307C2×C4×C11#12314yes—
308C2×C4×C11#12414yes—
309C2×C4×C11#12614yes—
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—41no—
326C2×Dic11—41no—
327C2×Dic11—41no—
328C2×Dic11—41no—
329C2×Dic11—42no—
330C2×Dic11—42no—
331C2×Dic11—42no—
332C2×Dic11—42no—
333C2×Dic11—42no—
334C2×Dic11—42no—
335C2×Dic11—42no—
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×Dic11#11714yes—
345C4×D11—416no—
346C24×C4—111no—
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⋊C4—112no—
357C22×C42—111no—
358C22×C42C2×D1112yes—
359C22×C42C2×D1111yescharacteristic
360#388—228no—
361#384—224no—
362#380—224no—
363#380—224no—
364C4×C4⋊C4—24no—
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×C11C22×C4⋊C411yescharacteristic
376C22×C11C2×#11711yescharacteristic
377C22×C11C2×#11711yescharacteristic
378C22×C11C2×C4×D411yescharacteristic
379C22×C11C2×C4×D411yescharacteristic
380C22×C11#52011yescharacteristic
381C22×C11#52011yescharacteristic
382C22×C11C2×#12111yescharacteristic
383C22×C11C2×#12311yescharacteristic
384C22×C11C2×#12411yescharacteristic
385C22×C11C2×#12611yescharacteristic
386C22×C11#53211yescharacteristic
387C22×C11#53211yescharacteristic
388C22×C11#53311yescharacteristic
389C22×C11#53311yescharacteristic
390C22×C11#54011yescharacteristic
391C22×C11#54111yescharacteristic
392C22×C11#54211yescharacteristic
393C22×C11#54211yescharacteristic
394C22×C11D4211yescharacteristic
395C22×C11D4211yescharacteristic
396C22×C11#54611yescharacteristic
397C22×C11#54711yescharacteristic
398C22×C11#54711yescharacteristic
399C22×C11#54711yescharacteristic
400C22×C11#54811yescharacteristic
401C22×C11D4×Q811yescharacteristic
402C22×C11D4×Q811yescharacteristic
403C22×C11#55011yescharacteristic
404C22×C11#55211yescharacteristic
405C22×C11#55311yescharacteristic
406C22×C11#55411yescharacteristic
407C22×C11#55411yescharacteristic
408C22×C11#55511yescharacteristic
409C22×C11#55611yescharacteristic
410C2×D11—24no—
411C2×D11—24no—
412C2×D11—24no—
413C2×D11—42no—
414C2×D11—42no—
415C2×D11—42no—
416C2×D11—42no—
417C2×D11—42no—
418C2×D11—42no—
419C2×D11—42no—
420C2×D11—42no—
421C2×D11—42no—
422C2×D11—42no—
423C2×D11—42no—
424C2×D11—42no—
425C4×C11—24no—
426C4×C11—42no—
427C4×C11—44no—
428C4×C11—44no—
429C4×C11#38818yescomplemented
430Dic11—24no—
431Dic11—24no—
432Dic11—42no—
433Dic11—82no—
434Dic11—82no—
435C25—111no—
436C23×C4—111no—
437C23×C4—111no—
438C23×C4—111no—
439C23×C4—114no—
440C23×C4—112no—
441C23×C4—112no—
442C23×C4—222no—
443C23×C4—222no—
444C23×C4—222no—
445C23×C4—222no—
446C23×C4—222no—
447C23×C4—222no—
448C23×C4C22×D1111yescharacteristic
449C23×C4C22×D1112yes—
450C23×C4C22×D1112yes—
451C23×C4C22×D1111yescharacteristic
452C23×C4C22×D1111yescharacteristic
453C2×C4⋊C4—22no—
454C2×C4⋊C4—22no—
455C2×C4⋊C4—22no—
456C2×C4⋊C4—22no—
457C2×C4⋊C4—224no—
458C2×C4⋊C4—224no—
459C2×C4⋊C4—222no—
460C2×C4⋊C4—224no—
461C2×C4⋊C4—224no—
462C2×C4⋊C4—222no—
463C2×C4⋊C4—222no—
464C2×C4⋊C4—222no—
465C2×C4⋊C4—222no—
466C2×C4⋊C4—222no—
467C2×C4⋊C4—442no—
468C2×C4⋊C4—442no—
469C2×C4⋊C4D4414yes—
470C2×C4⋊C4C22⋊D1114yes—
471C2×C22⋊C4—114no—
472C2×C22⋊C4—114no—
473C2×C22⋊C4—114no—
474C2×C22⋊C4—114no—
475C2×C22⋊C4—222no—
476C2×C22⋊C4—222no—
477C2×C22⋊C4—224no—
478C2×C22⋊C4—224no—
479C2×C22⋊C4—224no—
480C2×C22⋊C4—224no—
481C2×C22⋊C4—442no—
482C2×C22⋊C4—442no—
483C2×C42—22no—
484C2×C42—22no—
485C2×C42—24no—
486C2×C42—24no—
487C2×C42—42no—
488C2×C42—114no—
489C2×C42—222no—
490C2×C42—222no—
491C2×C42C4×D1114yes—
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#228511yescharacteristic
502C2×C11C2×#38811yescharacteristic
503C2×C11#231411yescharacteristic
504C2×C11D4×C4⋊C411yescharacteristic
505C2×C11D4×C4⋊C411yescharacteristic
506C2×C11#235211yescharacteristic
507C2×C11#235411yescharacteristic
508C2×C11#242211yescharacteristic
509C2×C11#242311yescharacteristic
510C2×C11#242811yescharacteristic
511C2×C11#242911yescharacteristic
512C2×C11#249111yescharacteristic
513C2×C11#249211yescharacteristic
514C2×C11#249611yescharacteristic
515C2×C11#249711yescharacteristic
516D11—44no—
517C24—112no—
518C24—112no—
519C24—112no—
520C24—221no—
521C24—221no—
522C24—221no—
523C24—221no—
524C24—221no—
525C24—221no—
526C24—221no—
527C24—221no—
528C24—221no—
529C24—221no—
530C24—221no—
531C24—221no—
532C24C23×D1111yescharacteristic
533C22×C4—21no—
534C22×C4—21no—
535C22×C4—21no—
536C22×C4—21no—
537C22×C4—21no—
538C22×C4—22no—
539C22×C4—22no—
540C22×C4—22no—
541C22×C4—22no—
542C22×C4—22no—
543C22×C4—22no—
544C22×C4—22no—
545C22×C4—22no—
546C22×C4—21no—
547C22×C4—21no—
548C22×C4—22no—
549C22×C4—21no—
550C22×C4—22no—
551C22×C4—21no—
552C22×C4—22no—
553C22×C4—21no—
554C22×C4—22no—
555C22×C4—112no—
556C22×C4—112no—
557C22×C4—112no—
558C22×C4—112no—
559C22×C4—112no—
560C22×C4—112no—
561C22×C4—112no—
562C22×C4—221no—
563C22×C4—221no—
564C22×C4—221no—
565C22×C4—221no—
566C22×C4—221no—
567C22×C4—221no—
568C22×C4—221no—
569C22×C4—221no—
570C22×C4—221no—
571C22×C4—221no—
572C22×C4—221no—
573C22×C4—221no—
574C22×C4—221no—
575C22×C4—221no—
576C22×C4—228no—
577C22×C4—228no—
578C22×C4—228no—
579C22×C4—222no—
580C22×C4—222no—
581C22×C4—222no—
582C22×C4—222no—
583C22×C4—222no—
584C22×C4—222no—
585C22×C4—222no—
586C22×C4—222no—
587C22×C4—222no—
588C22×C4—222no—
589C22×C4—222no—
590C22×C4—222no—
591C22×C4—222no—
592C22×C4—222no—
593C22×C4—444no—
594C22×C4—444no—
595C22×C4—444no—
596C22×C4—444no—
597C22×C4C2×C4×D1112yes—
598C22×C4C2×C4×D1112yes—
599C22×C4C2×C4×D1112yes—
600C22×C4C2×D4414yes—
601C22×C4C2×D4412yes—
602C22×C4#433912yes—
603C22×C4#433912yes—
604C22×C4#433912yes—
605C22×C4#433912yes—
606C22×C4D4×D1112yes—
607C22×C4Q8×D1112yes—
608C22×C4C2×C22⋊D1114yes—
609C22×C4C2×C22⋊D1112yes—
610C4⋊C4—28no—
611C4⋊C4—28no—
612C4⋊C4—448no—
613C4⋊C4—448no—
614C4⋊C4—444no—
615C4⋊C4—444no—
616C22⋊C4—1116no—
617C22⋊C4—228no—
618C22⋊C4—448no—
619C22⋊C4—448no—
620C42—28no—
621C42—48no—
622C42—228no—
623C11#1387611yescharacteristic, complemented, Sylow
624C23—114no—
625C23—222no—
626C23—222no—
627C23—222no—
628C23—222no—
629C23—222no—
630C23—222no—
631C23—222no—
632C23—222no—
633C23—222no—
634C23—222no—
635C23—222no—
636C23—222no—
637C23—222no—
638C23—222no—
639C23—222no—
640C23—222no—
641C23—222no—
642C23—222no—
643C23—441no—
644C23—441no—
645C23—441no—
646C23—441no—
647C23—441no—
648C23—441no—
649C23—441no—
650C23—441no—
651C23—441no—
652C23—441no—
653C23—441no—
654C23—441no—
655C23—441no—
656C23—441no—
657C23—441no—
658C23—441no—
659C23C22×C4×D1111yescharacteristic
660C23C22×D4411yescharacteristic
661C23C2×#433911yescharacteristic
662C23C2×#433911yescharacteristic
663C23C2×#433911yescharacteristic
664C23C2×#433911yescharacteristic
665C23C2×D4×D1111yescharacteristic
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—22no—
678C2×C4—22no—
679C2×C4—22no—
680C2×C4—22no—
681C2×C4—22no—
682C2×C4—22no—
683C2×C4—24no—
684C2×C4—24no—
685C2×C4—24no—
686C2×C4—24no—
687C2×C4—24no—
688C2×C4—24no—
689C2×C4—41no—
690C2×C4—41no—
691C2×C4—42no—
692C2×C4—42no—
693C2×C4—42no—
694C2×C4—42no—
695C2×C4—42no—
696C2×C4—42no—
697C2×C4—42no—
698C2×C4—41no—
699C2×C4—42no—
700C2×C4—41no—
701C2×C4—114no—
702C2×C4—114no—
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—441no—
719C2×C4—441no—
720C2×C4—441no—
721C2×C4—441no—
722C2×C4—4416no—
723C2×C4—442no—
724C2×C4—442no—
725C2×C4—442no—
726C2×C4—442no—
727C2×C4—442no—
728C2×C4—442no—
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#6692514yes—
738C2×C4C4×D4414yes—
739C2×C4#6692814yes—
740C2×C4#6692914yes—
741C2×C4C4⋊C4×D1114yes—
742C2×C4C4×C22⋊D1114yes—
743C2×C4#6698214yes—
744C2×C4#6698314yes—
745C22—224no—
746C22—224no—
747C22—224no—
748C22—442no—
749C22—442no—
750C22—442no—
751C22—442no—
752C22—442no—
753C22—442no—
754C22—442no—
755C22—442no—
756C22—442no—
757C22—442no—
758C22—442no—
759C22—442no—
760C22C2×#6692511yescharacteristic
761C22C2×C4×D4411yescharacteristic
762C22C2×#6692811yescharacteristic
763C22C2×#6692911yescharacteristic
764C22C2×C4⋊C4×D1111yescharacteristic
765C22#1062303511yescharacteristic
766C22#1062303811yescharacteristic
767C22#1062304211yescharacteristic
768C22D11×#11711yescharacteristic
769C22#1062305411yescharacteristic
770C22#1062306311yescharacteristic
771C22#1062306411yescharacteristic
772C22#1062307911yescharacteristic
773C22#1062307911yescharacteristic
774C22D4×D4411yescharacteristic
775C22#1062308211yescharacteristic
776C22#1062308511yescharacteristic
777C22#1062308911yescharacteristic
778C22#1062309211yescharacteristic
779C22#1062309311yescharacteristic
780C22Q8×D4411yescharacteristic
781C22#1062310711yescharacteristic
782C22#1062310911yescharacteristic
783C22#1062310911yescharacteristic
784C22#1062311011yescharacteristic
785C22#1062311211yescharacteristic
786C22#1062311311yescharacteristic
787C22#1062311411yescharacteristic
788C22C2×C4×C22⋊D1111yescharacteristic
789C22C2×#6698211yescharacteristic
790C22C2×#6698311yescharacteristic
791C22D4×C22⋊D1111yescharacteristic
792C22Q8×C22⋊D1111yescharacteristic
793C22#1062335511yescharacteristic
794C22#1062336511yescharacteristic
795C4—24no—
796C4—44no—
797C4—42no—
798C4—44no—
799C4—224no—
800C4—224no—
801C4—442no—
802C4—882no—
803C4—882no—
804C4#1062255318yescomplemented
805C2—444no—
806C2#1307102011yescharacteristic
807C2C2×#1062255311yescharacteristic
808C2#1307122111yescharacteristic
809C2C4⋊C4×C22⋊D1111yescharacteristic
810C2C4⋊C4×D4411yescharacteristic
811C2#1307154811yescharacteristic
812C2#1307156611yescharacteristic
813C2#1307212411yescharacteristic
814C2#1307213511yescharacteristic
815C2#1307219811yescharacteristic
816C2#1307220911yescharacteristic
817C2#1307297311yescharacteristic
818C2#1307298411yescharacteristic
819C2#1307303211yescharacteristic
820C2#1307304311yescharacteristic
subgroupG/H
center, FrattiniC24C23×D11
commutatorC23×C11C23×C4
FittingC2×C4×C11×C4⋊C4C2
socle, cosocleC24×C11C24
prime radicalC24×D11C23
hypercenterC2×C4×C4⋊C4D11
hypocenterC11#13876
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ C2×C4×C4⋊C4

Complements

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

NH ≅ G/Ntype
2. C2×#10622589C2semidirect
6. #13066871C2semidirect
8. #13066849C2semidirect
9. #13066846C2semidirect
10. #13066845C2semidirect
11. C2×C4×C11×C4⋊C4C2semidirect
40. C4×(C2×D11)⋊C4C4semidirect
208. (C2×D11)⋊C4C4⋊C4semidirect
218. C2×C4×C4⋊C4D11semidirect
429. C4×C11#388semidirect
623. C11#13876semidirect
804. C4#10622553semidirect

Maximal subgroups

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

subgroupindex
C2×#106225532
C2×#106225892
C2×#106226002
C2×C4×(C2×D11)⋊C42
#130668712
#130668602
#130668492
#130668462
#130668452
C2×C4×C11×C4⋊C42
#1387611