Finite Group Databasebeta

← #14675724

Subgroups — #14675724

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×#10622564C212yesmaximal
2C2×#10622548C211yesmaximal, characteristic, complemented
3C2×#10622825C211yesmaximal, characteristic
4C2×#10622825C211yesmaximal, characteristic
5C2×C4×C4⋊Dic11C211yesmaximal, characteristic, complemented
6#13066873C212yesmaximal, complemented
7#13066861C212yesmaximal
8#13066850C212yesmaximal, complemented
9#13066846C211yesmaximal, characteristic, complemented
10#13066846C211yesmaximal, characteristic, complemented
11C2×C4×C11×C22⋊C4C211yesmaximal, characteristic
12C24×C4×C11C2211yescharacteristic
13C22×C11×C22⋊C4C2211yescharacteristic
14C22×C11×C22⋊C4C2211yescharacteristic
15C22×C42×C11C2211yescharacteristic
16C22×C42×C11C2211yescharacteristic
17C22×C22⋊Dic11C2212yes—
18C22×C22⋊Dic11C2212yes—
19C22×C4⋊Dic11C2211yescharacteristic
20C22×C4⋊Dic11C2211yescharacteristic
21C22×C4⋊Dic11C2212yes—
22C22×C4⋊Dic11C2212yes—
23C22×C4⋊Dic11C2211yescharacteristic
24C22×C4⋊Dic11C2211yescharacteristic
25C22×C4×Dic11C2212yes—
26C4×C11×C22⋊C4C418yescomplemented
27C2×C11×#95C2211yescharacteristic
28C2×C11×#95C2211yescharacteristic
29#10622825—24no—
30#10622825—24no—
31C2×C11⋊#95C2212yes—
32C2×C11⋊#95C2212yes—
33C2×C11⋊#95C2212yes—
34C2×C11⋊#95C2212yes—
35C2×C11⋊#95C2212yes—
36C2×C11⋊#95C2212yes—
37C2×C11⋊#95C2212yes—
38#10622564—28no—
39#10622548—24no—
40C4×C4⋊Dic11—24no—
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×C11C2311yescharacteristic
50C23×C4×C11C2311yescharacteristic
51C23×C4×C11C2311yescharacteristic
52C23×C4×C11C2311yescharacteristic
53C23×C4×C11C2311yescharacteristic
54C23×C4×C11C2311yescharacteristic
55C23×Dic11C2312yes—
56C23×Dic11C2312yes—
57C23×Dic11C2312yes—
58C23×Dic11C2312yes—
59C2×C11×C22⋊C4—22no—
60C2×C11×C22⋊C4—22no—
61C2×C11×C22⋊C4C2×C414yes—
62C2×C11×C22⋊C4C2×C414yes—
63C2×C11×C22⋊C4D414yes—
64C2×C11×C22⋊C4Q814yes—
65C2×C42×C11—22no—
66C2×C42×C11—22no—
67C2×C42×C11—22no—
68C2×C42×C11—22no—
69C2×C42×C11C2×C414yes—
70C2×C42×C11C2×C414yes—
71C2×C22⋊Dic11—24no—
72C2×C22⋊Dic11—24no—
73C2×C22⋊Dic11—24no—
74C2×C22⋊Dic11—24no—
75C2×C22⋊Dic11—42no—
76C2×C22⋊Dic11—42no—
77C2×C4⋊Dic11—22no—
78C2×C4⋊Dic11—22no—
79C2×C4⋊Dic11—22no—
80C2×C4⋊Dic11—22no—
81C2×C4⋊Dic11—22no—
82C2×C4⋊Dic11—24no—
83C2×C4⋊Dic11—22no—
84C2×C4⋊Dic11—22no—
85C2×C4⋊Dic11—24no—
86C2×C4⋊Dic11—22no—
87C2×C4⋊Dic11—22no—
88C2×C4⋊Dic11—22no—
89C2×C4⋊Dic11—24no—
90C2×C4⋊Dic11—24no—
91C2×C4⋊Dic11—42no—
92C2×C4⋊Dic11—42no—
93C2×C4⋊Dic11D414yes—
94C2×C4⋊Dic11D414yes—
95C2×C4×Dic11—24no—
96C2×C4×Dic11—24no—
97C2×C4×Dic11—42no—
98C11×#95C2×C414yes—
99C11×#95C2×C414yes—
100C11⋊#95—24no—
101C11⋊#95—24no—
102C11⋊#95—24no—
103C11⋊#95—24no—
104C11⋊#95—24no—
105C11⋊#95—24no—
106C11⋊#95—42no—
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—21no—
126C22×C4×C11—21no—
127C22×C4×C11—21no—
128C22×C4×C11—21no—
129C22×C4×C11—21no—
130C22×C4×C11—21no—
131C22×C4×C11—21no—
132C22×C4×C11—21no—
133C22×C4×C11—21no—
134C22×C4×C11—21no—
135C22×C4×C11—21no—
136C22×C4×C11—21no—
137C22×C4×C11—21no—
138C22×C4×C11—21no—
139C22×C4×C11—21no—
140C22×C4×C11—21no—
141C22×C4×C11—21no—
142C22×C4×C11—21no—
143C22×C4×C11—21no—
144C22×C4×C11—21no—
145C22×C4×C11—21no—
146C22×C4×C11—21no—
147C22×C4×C11—21no—
148C22×C4×C11—28no—
149C22×C4×C11—28no—
150C22×C4×C11—28no—
151C22×C4×C11—44no—
152C22×C4×C11—44no—
153C22×C4×C11—44no—
154C22×C4×C11—44no—
155C22×C4×C11C22×C412yes—
156C22×C4×C11C22×C412yes—
157C22×C4×C11C22×C412yes—
158C22×C4×C11C22×C412yes—
159C22×C4×C11C22×C412yes—
160C22×C4×C11C22×C412yes—
161C22×C4×C11C2×D412yes—
162C22×C4×C11C2×D412yes—
163C22×C4×C11C2×D412yes—
164C22×C4×C11C2×D412yes—
165C22×C4×C11C2×Q812yes—
166C22×C4×C11C2×Q812yes—
167C22×C4×C11#4112yes—
168C22×C4×C11#4112yes—
169C22×C4×C11#4112yes—
170C22×C4×C11#4112yes—
171C22×C4×C11#4112yes—
172C22×C4×C11#4112yes—
173C22×Dic11—22no—
174C22×Dic11—22no—
175C22×Dic11—22no—
176C22×Dic11—22no—
177C22×Dic11—22no—
178C22×Dic11—22no—
179C22×Dic11—22no—
180C22×Dic11—22no—
181C22×Dic11—22no—
182C22×Dic11—22no—
183C22×Dic11—22no—
184C22×Dic11—22no—
185C22×Dic11—22no—
186C22×Dic11—22no—
187C22×Dic11—22no—
188C22×Dic11—22no—
189C22×Dic11—22no—
190C22×Dic11—22no—
191C22×Dic11—22no—
192C22×Dic11—22no—
193C22×Dic11—22no—
194C22×Dic11—22no—
195C22×Dic11—22no—
196C22×Dic11—22no—
197C22×Dic11—22no—
198C22×Dic11—22no—
199C22×Dic11C2×D414yes—
200C22×Dic11C2×D414yes—
201C11×C22⋊C4—28no—
202C11×C22⋊C4C4⋊C4116yescomplemented
203C42×C11—28no—
204C42×C11—28no—
205C22⋊Dic11—48no—
206C22⋊Dic11—48no—
207C4⋊Dic11—28no—
208C4⋊Dic11—28no—
209C4⋊Dic11—48no—
210C4⋊Dic11—48no—
211C4⋊Dic11—44no—
212C4⋊Dic11—44no—
213C4×Dic11—48no—
214C2×#388—112no—
215C2×#384—111no—
216C2×#380—111no—
217C2×#380—111no—
218C2×C4×C4⋊C4—111no—
219C2×C4×C22⋊C4D1111yescharacteristic
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—22no—
279C2×C4×C11—22no—
280C2×C4×C11—22no—
281C2×C4×C11—22no—
282C2×C4×C11—22no—
283C2×C4×C11—22no—
284C2×C4×C11—22no—
285C2×C4×C11—22no—
286C2×C4×C11—22no—
287C2×C4×C11—22no—
288C2×C4×C11—22no—
289C2×C4×C11—22no—
290C2×C4×C11—22no—
291C2×C4×C11—22no—
292C2×C4×C11—22no—
293C2×C4×C11—22no—
294C2×C4×C11—22no—
295C2×C4×C11—22no—
296C2×C4×C11—22no—
297C2×C4×C11—22no—
298C2×C4×C11—22no—
299C2×C4×C11—41no—
300C2×C4×C11—41no—
301C2×C4×C11—41no—
302C2×C4×C11—41no—
303C2×C4×C11—41no—
304C2×C4×C11—41no—
305C2×C4×C11—41no—
306C2×C4×C11—41no—
307C2×C4×C11—416no—
308C2×C4×C11C2×C4⋊C414yes—
309C2×C4×C11C2×C4⋊C414yes—
310C2×C4×C11#11714yes—
311C2×C4×C11#11714yes—
312C2×C4×C11C4×D414yes—
313C2×C4×C11C4×D414yes—
314C2×C4×C11#12114yes—
315C2×C4×C11#12314yes—
316C2×C4×C11#12414yes—
317C2×C4×C11#12614yes—
318C2×Dic11—24no—
319C2×Dic11—24no—
320C2×Dic11—24no—
321C2×Dic11—24no—
322C2×Dic11—24no—
323C2×Dic11—24no—
324C2×Dic11—42no—
325C2×Dic11—42no—
326C2×Dic11—42no—
327C2×Dic11—42no—
328C2×Dic11—42no—
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×Dic11—42no—
344C2×Dic11—42no—
345C2×Dic11—42no—
346C24×C4C2×D1111yescharacteristic
347C22×C4⋊C4—111no—
348C22×C4⋊C4—111no—
349C22×C4⋊C4—111no—
350C22×C4⋊C4—111no—
351C22×C4⋊C4—112no—
352C22×C4⋊C4—112no—
353C22×C22⋊C4—112no—
354C22×C22⋊C4—112no—
355C22×C22⋊C4C2×D1111yescharacteristic
356C22×C22⋊C4C2×D1111yescharacteristic
357C22×C42—112no—
358C22×C42C2×D1111yescharacteristic
359C22×C42C2×D1111yescharacteristic
360#388—228no—
361#384—224no—
362#380—224no—
363#380—224no—
364C4×C4⋊C4—224no—
365C4×C22⋊C4Dic1118yescomplemented
366C2×#95—112no—
367C2×#95—112no—
368C2×#95—112no—
369C2×#95—112no—
370C2×#95—112no—
371C2×#95—112no—
372C2×#95—112no—
373C2×#95C2×D1111yescharacteristic
374C2×#95C2×D1111yescharacteristic
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—24no—
426C4×C11—24no—
427C4×C11—24no—
428C4×C11—42no—
429C4×C11—42no—
430C4×C11#38818yescomplemented
431Dic11—44no—
432Dic11—44no—
433Dic11—82no—
434Dic11—82no—
435C25C22×D1111yescharacteristic
436C23×C4—22no—
437C23×C4—22no—
438C23×C4—22no—
439C23×C4—22no—
440C23×C4—22no—
441C23×C4—22no—
442C23×C4—112no—
443C23×C4—112no—
444C23×C4—112no—
445C23×C4—112no—
446C23×C4C2×Dic1114yes—
447C23×C4C22×D1111yescharacteristic
448C23×C4C22×D1111yescharacteristic
449C23×C4C22×D1111yescharacteristic
450C23×C4C22×D1111yescharacteristic
451C23×C4C22×D1111yescharacteristic
452C23×C4C22×D1111yescharacteristic
453C2×C4⋊C4—114no—
454C2×C4⋊C4—114no—
455C2×C4⋊C4—222no—
456C2×C4⋊C4—222no—
457C2×C4⋊C4—222no—
458C2×C4⋊C4—222no—
459C2×C4⋊C4—224no—
460C2×C4⋊C4—224no—
461C2×C4⋊C4—224no—
462C2×C4⋊C4—224no—
463C2×C4⋊C4—222no—
464C2×C4⋊C4—222no—
465C2×C4⋊C4—222no—
466C2×C4⋊C4—222no—
467C2×C4⋊C4—222no—
468C2×C4⋊C4—222no—
469C2×C4⋊C4—442no—
470C2×C4⋊C4—442no—
471C2×C22⋊C4—22no—
472C2×C22⋊C4—22no—
473C2×C22⋊C4—224no—
474C2×C22⋊C4—224no—
475C2×C22⋊C4—224no—
476C2×C22⋊C4—224no—
477C2×C22⋊C4—442no—
478C2×C22⋊C4—442no—
479C2×C22⋊C4Dic2214yes—
480C2×C22⋊C4D4414yes—
481C2×C22⋊C4C2×Dic1114yes—
482C2×C22⋊C4C2×Dic1114yes—
483C2×C42—22no—
484C2×C42—22no—
485C2×C42—22no—
486C2×C42—22no—
487C2×C42—224no—
488C2×C42—224no—
489C2×C42—442no—
490C2×C42C2×Dic1114yes—
491C2×C42C2×Dic1114yes—
492#95—224no—
493#95—224no—
494#95—224no—
495#95—224no—
496#95—224no—
497#95—224no—
498#95—442no—
499#95C2×Dic1114yes—
500#95C2×Dic1114yes—
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×Dic2212yes—
530C24C2×D4412yes—
531C24C22×Dic1112yes—
532C24C23×D1111yescharacteristic
533C22×C4—21no—
534C22×C4—21no—
535C22×C4—21no—
536C22×C4—21no—
537C22×C4—21no—
538C22×C4—21no—
539C22×C4—21no—
540C22×C4—21no—
541C22×C4—21no—
542C22×C4—21no—
543C22×C4—21no—
544C22×C4—21no—
545C22×C4—21no—
546C22×C4—21no—
547C22×C4—21no—
548C22×C4—21no—
549C22×C4—21no—
550C22×C4—21no—
551C22×C4—21no—
552C22×C4—21no—
553C22×C4—21no—
554C22×C4—21no—
555C22×C4—21no—
556C22×C4—21no—
557C22×C4—28no—
558C22×C4—28no—
559C22×C4—28no—
560C22×C4—44no—
561C22×C4—44no—
562C22×C4—44no—
563C22×C4—44no—
564C22×C4—114no—
565C22×C4—114no—
566C22×C4—222no—
567C22×C4—222no—
568C22×C4—222no—
569C22×C4—222no—
570C22×C4—222no—
571C22×C4—222no—
572C22×C4—222no—
573C22×C4—222no—
574C22×C4—222no—
575C22×C4—222no—
576C22×C4—222no—
577C22×C4—222no—
578C22×C4—222no—
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×C4C2×Dic2212yes—
593C22×C4C2×Dic2212yes—
594C22×C4C2×D4412yes—
595C22×C4C2×D4412yes—
596C22×C4#433912yes—
597C22×C4#433912yes—
598C22×C4#433912yes—
599C22×C4#433912yes—
600C22×C4D4×D1112yes—
601C22×C4D4×D1112yes—
602C22×C4#434112yes—
603C22×C4#434112yes—
604C22×C4C22×Dic1112yes—
605C22×C4C22×Dic1112yes—
606C22×C4C22×Dic1112yes—
607C22×C4C22×Dic1112yes—
608C22×C4C22×Dic1112yes—
609C22×C4C22×Dic1112yes—
610C4⋊C4—228no—
611C4⋊C4—228no—
612C4⋊C4—448no—
613C4⋊C4—448no—
614C4⋊C4—444no—
615C4⋊C4—444no—
616C22⋊C4—28no—
617C22⋊C4—448no—
618C22⋊C4—448no—
619C22⋊C4C4⋊Dic11116yescomplemented
620C42—28no—
621C42—28no—
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—
658C23C2×C4⋊Dic1114yes—
659C23C22×Dic2211yescharacteristic
660C23C22×D4411yescharacteristic
661C23C2×#433911yescharacteristic
662C23C2×#433911yescharacteristic
663C23C2×#433911yescharacteristic
664C23C2×#433911yescharacteristic
665C23C2×D4×D1111yescharacteristic
666C23C2×D4×D1111yescharacteristic
667C23C2×#434111yescharacteristic
668C23C2×#434111yescharacteristic
669C23#6704211yescharacteristic
670C23#6704211yescharacteristic
671C23#6704311yescharacteristic
672C23#6704311yescharacteristic
673C23C23×Dic1111yescharacteristic
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—22no—
684C2×C4—22no—
685C2×C4—22no—
686C2×C4—22no—
687C2×C4—22no—
688C2×C4—22no—
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—41no—
699C2×C4—41no—
700C2×C4—41no—
701C2×C4—41no—
702C2×C4—41no—
703C2×C4—41no—
704C2×C4—41no—
705C2×C4—41no—
706C2×C4—416no—
707C2×C4—224no—
708C2×C4—224no—
709C2×C4—224no—
710C2×C4—224no—
711C2×C4—224no—
712C2×C4—224no—
713C2×C4—442no—
714C2×C4—442no—
715C2×C4—442no—
716C2×C4—442no—
717C2×C4—442no—
718C2×C4—442no—
719C2×C4—442no—
720C2×C4—442no—
721C2×C4—442no—
722C2×C4—442no—
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#6693214yes—
736C2×C4#6693614yes—
737C2×C4#6693714yes—
738C2×C4#6693814yes—
739C2×C4C2×C4⋊Dic1114yes—
740C2×C4C2×C4⋊Dic1114yes—
741C2×C4#6697914yes—
742C2×C4#6697914yes—
743C2×C4D4×Dic1114yes—
744C2×C4D4×Dic1114yes—
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—
760C22#1062300111yescharacteristic
761C22#1062300111yescharacteristic
762C22#1062300811yescharacteristic
763C22#1062300811yescharacteristic
764C22C2×#6693211yescharacteristic
765C22C2×#6693611yescharacteristic
766C22C2×#6693711yescharacteristic
767C22C2×#6693811yescharacteristic
768C22#1062304911yescharacteristic
769C22#1062306511yescharacteristic
770C22#1062306511yescharacteristic
771C22#1062306611yescharacteristic
772C22D4×Dic2211yescharacteristic
773C22D4×Dic2211yescharacteristic
774C22#1062307211yescharacteristic
775C22#1062307311yescharacteristic
776C22#1062307411yescharacteristic
777C22#1062307411yescharacteristic
778C22D4×D4411yescharacteristic
779C22D4×D4411yescharacteristic
780C22#1062308111yescharacteristic
781C22#1062308211yescharacteristic
782C22#1062308311yescharacteristic
783C22#1062308411yescharacteristic
784C22#1062308611yescharacteristic
785C22#1062308611yescharacteristic
786C22#1062309411yescharacteristic
787C22#1062309611yescharacteristic
788C22C22×C4⋊Dic1111yescharacteristic
789C22C2×#6697911yescharacteristic
790C22C2×#6697911yescharacteristic
791C22C2×D4×Dic1111yescharacteristic
792C22C2×D4×Dic1111yescharacteristic
793C22#1062335811yescharacteristic
794C22#1062335811yescharacteristic
795C4—24no—
796C4—24no—
797C4—24no—
798C4—42no—
799C4—42no—
800C4—444no—
801C4—444no—
802C4—882no—
803C4—882no—
804C4#1062256418yescomplemented
805C2—44no—
806C2#1307102311yescharacteristic
807C2C2×#1062256411yescharacteristic
808C2#1307122511yescharacteristic
809C2D4×C4⋊Dic1111yescharacteristic
810C2D4×C4⋊Dic1111yescharacteristic
811C2#1307154511yescharacteristic
812C2#1307156511yescharacteristic
813C2#1307213011yescharacteristic
814C2#1307214111yescharacteristic
815C2#1307220411yescharacteristic
816C2#1307221511yescharacteristic
817C2#1307297911yescharacteristic
818C2#1307299011yescharacteristic
819C2#1307303811yescharacteristic
820C2#1307304911yescharacteristic
subgroupG/H
center, FrattiniC24C23×D11
commutatorC23×C11C23×C4
FittingC2×C4×C11×C22⋊C4C2
socle, cosocleC24×C11C24
prime radicalC25×C11C23
hypercenterC2×C4×C22⋊C4D11
hypocenterC11#13876
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ C2×C4×C22⋊C4

Complements

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

NH ≅ G/Ntype
2. C2×#10622548C2semidirect
5. C2×C4×C4⋊Dic11C2semidirect
6. #13066873C2semidirect
8. #13066850C2semidirect
9. #13066846C2semidirect
10. #13066846C2semidirect
26. C4×C11×C22⋊C4C4semidirect
202. C11×C22⋊C4C4⋊C4semidirect
365. C4×C22⋊C4Dic11semidirect
430. C4×C11#388semidirect
619. C22⋊C4C4⋊Dic11semidirect
623. C11#13876semidirect
804. C4#10622564semidirect

Maximal subgroups

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

subgroupindex
C2×#106225642
C2×#106225482
C2×#106228252
C2×C4×C4⋊Dic112
#130668732
#130668612
#130668502
#130668462
C2×C4×C11×C22⋊C42
#1387611