Finite Group Databasebeta

← #14675722

Subgroups — #14675722

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×#10622283C212yesmaximal
2C2×#10622548C211yesmaximal, characteristic, complemented
3C2×#10622600C211yesmaximal, characteristic
4C2×#10622600C211yesmaximal, characteristic
5C2×C4⋊C4×Dic11C211yesmaximal, characteristic, complemented
6C2×C4×(C2×D11)⋊C4C211yesmaximal, characteristic
7#13066872C212yesmaximal, complemented
8#13066862C212yesmaximal
9#13066850C212yesmaximal, complemented
10#13066845C211yesmaximal, characteristic, complemented
11C11×C4⋊#95C211yesmaximal, characteristic, complemented
12C23×C4×D11C2211yescharacteristic
13C22×C11×C4⋊C4C2211yescharacteristic
14C22×C11×C4⋊C4C2211yescharacteristic
15C22×C42×C11C2211yescharacteristic
16C22×(C2×D11)⋊C4C2212yes—
17C22×(C2×D11)⋊C4C2212yes—
18C22×(C2×D11)⋊C4C2211yescharacteristic
19C22×(C2×D11)⋊C4C2211yescharacteristic
20C22×C4⋊Dic11C2211yescharacteristic
21C22×C4⋊Dic11C2212yes—
22C22×C4⋊Dic11C2212yes—
23C22×C4⋊Dic11C2211yescharacteristic
24C22×C4×Dic11C2212yes—
25C22×C4×Dic11C2211yescharacteristic
26C2×C11×#95C2212yes—
27C2×C11×#95C2212yes—
28C2×C11⋊#95C2212yes—
29C2×C11⋊#95C2212yes—
30C2×C11⋊#95C2212yes—
31C2×C11⋊#95C2212yes—
32C2×C11⋊#95C2212yes—
33C2×C11⋊#95C2211yescharacteristic
34C2×C11⋊#95C2211yescharacteristic
35#10622600—24no—
36#10622600—24no—
37C4⋊C4×Dic11—24no—
38C4×(C2×D11)⋊C4C418yescomplemented
39#10622548—24no—
40#10622283—28no—
41C24×D11C2311yescharacteristic
42C23×C4×C11C2312yes—
43C23×C4×C11C2312yes—
44C23×C4×C11C2311yescharacteristic
45C23×C4×C11C2311yescharacteristic
46C23×C4×C11C2311yescharacteristic
47C23×Dic11C2312yes—
48C23×Dic11C2311yescharacteristic
49C23×Dic11C2311yescharacteristic
50C23×Dic11C2312yes—
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⋊C4—22no—
64C2×C11×C4⋊C4D414yes—
65C2×C42×C11—22no—
66C2×C42×C11—22no—
67C2×C42×C11C2×C414yes—
68C2×(C2×D11)⋊C4—22no—
69C2×(C2×D11)⋊C4—22no—
70C2×(C2×D11)⋊C4—24no—
71C2×(C2×D11)⋊C4—24no—
72C2×(C2×D11)⋊C4—24no—
73C2×(C2×D11)⋊C4—24no—
74C2×(C2×D11)⋊C4—42no—
75C2×(C2×D11)⋊C4—42no—
76C2×(C2×D11)⋊C4C2×C414yes—
77C2×(C2×D11)⋊C4C2×C414yes—
78C2×(C2×D11)⋊C4D414yes—
79C2×(C2×D11)⋊C4Q814yes—
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—24no—
88C2×C4⋊Dic11—24no—
89C2×C4⋊Dic11—42no—
90C2×C4⋊Dic11—42no—
91C2×C4⋊Dic11D414yes—
92C2×C4×Dic11—22no—
93C2×C4×Dic11—22no—
94C2×C4×Dic11—24no—
95C2×C4×Dic11—24no—
96C2×C4×Dic11—42no—
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—21no—
129C22×C4×C11—21no—
130C22×C4×C11—21no—
131C22×C4×C11—21no—
132C22×C4×C11—22no—
133C22×C4×C11—22no—
134C22×C4×C11—22no—
135C22×C4×C11—22no—
136C22×C4×C11—22no—
137C22×C4×C11—22no—
138C22×C4×C11—22no—
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×C11C22×C412yes—
146C22×C4×C11C22×C412yes—
147C22×C4×C11C22×C412yes—
148C22×C4×C11C2×D414yes—
149C22×C4×C11C2×D412yes—
150C22×C4×C11C2×D412yes—
151C22×C4×C11C2×D412yes—
152C22×C4×C11C2×Q812yes—
153C22×C4×C11#4112yes—
154C22×C4×C11#4112yes—
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—22no—
171C22×Dic11—22no—
172C22×Dic11—21no—
173C22×Dic11—21no—
174C22×Dic11—21no—
175C22×Dic11—21no—
176C22×Dic11—21no—
177C22×Dic11—21no—
178C22×Dic11—22no—
179C22×Dic11—22no—
180C22×Dic11—21no—
181C22×Dic11—21no—
182C22×Dic11—22no—
183C22×Dic11—22no—
184C22×Dic11—22no—
185C22×Dic11—22no—
186C22×Dic11—21no—
187C22×Dic11—21no—
188C22×Dic11C22×C412yes—
189C22×Dic11C22×C412yes—
190C22×Dic11C22×C412yes—
191C22×Dic11C2×D414yes—
192C22×Dic11C2×D412yes—
193C22×Dic11C2×Q812yes—
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—44no—
203C42×C11—28no—
204(C2×D11)⋊C4—28no—
205(C2×D11)⋊C4—48no—
206(C2×D11)⋊C4—48no—
207(C2×D11)⋊C4C4⋊C4116yescomplemented
208C4⋊Dic11—28no—
209C4⋊Dic11—48no—
210C4⋊Dic11—48no—
211C4⋊Dic11—44no—
212C4×Dic11—28no—
213C4×Dic11—48no—
214C2×#388—112no—
215C2×#384—111no—
216C2×#380—111no—
217C2×#380—111no—
218C2×C4×C4⋊C4—111no—
219C2×C4×C22⋊C4—111no—
220#1442—112no—
221#1439—112no—
222#1436—112no—
223C4⋊#95—111no—
224C4⋊#95D1111yescharacteristic, complemented
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—22no—
285C2×C4×C11—22no—
286C2×C4×C11—22no—
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—42no—
297C2×C4×C11—42no—
298C2×C4×C11—42no—
299C2×C4×C11—42no—
300C2×C4×C11—42no—
301C2×C4×C11C2×C4⋊C414yes—
302C2×C4×C11#11714yes—
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—24no—
323C2×Dic11—24no—
324C2×Dic11—24no—
325C2×Dic11—41no—
326C2×Dic11—41no—
327C2×Dic11—41no—
328C2×Dic11—41no—
329C2×Dic11—42no—
330C2×Dic11—42no—
331C2×Dic11—42no—
332C2×Dic11—41no—
333C2×Dic11—41no—
334C2×Dic11—42no—
335C2×Dic11—41no—
336C2×Dic11—41no—
337C2×Dic11—42no—
338C2×Dic11—42no—
339C2×Dic11—42no—
340C2×Dic11—42no—
341C2×Dic11—42no—
342C2×Dic11—42no—
343C2×Dic11—42no—
344C2×Dic11C2×C4⋊C414yes—
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×C42—112no—
359C22×C42C2×D1111yescharacteristic
360#388—228no—
361#384—224no—
362#380—224no—
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×#95C2×D1112yes—
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—24no—
427C4×C11—44no—
428C4×C11—82no—
429C4×C11#38818yescomplemented
430Dic11—24no—
431Dic11—42no—
432Dic11—44no—
433Dic11—42no—
434Dic11—82no—
435C25—111no—
436C23×C4—111no—
437C23×C4—112no—
438C23×C4—111no—
439C23×C4—111no—
440C23×C4—114no—
441C23×C4—112no—
442C23×C4—222no—
443C23×C4—222no—
444C23×C4—222no—
445C23×C4—222no—
446C23×C4—222no—
447C23×C4—222no—
448C23×C4C22×D1112yes—
449C23×C4C22×D1112yes—
450C23×C4C22×D1111yescharacteristic
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—22no—
458C2×C4⋊C4—114no—
459C2×C4⋊C4—222no—
460C2×C4⋊C4—222no—
461C2×C4⋊C4—224no—
462C2×C4⋊C4—224no—
463C2×C4⋊C4—222no—
464C2×C4⋊C4—222no—
465C2×C4⋊C4—224no—
466C2×C4⋊C4—224no—
467C2×C4⋊C4—222no—
468C2×C4⋊C4—442no—
469C2×C4⋊C4—442no—
470C2×C4⋊C4D4414yes—
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—114no—
486C2×C42—222no—
487C2×C42—222no—
488C2×C42—224no—
489C2×C42—224no—
490C2×C42—442no—
491C2×C42C4×D1114yes—
492#95—24no—
493#95—24no—
494#95—114no—
495#95—114no—
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—21no—
539C22×C4—21no—
540C22×C4—21no—
541C22×C4—22no—
542C22×C4—22no—
543C22×C4—22no—
544C22×C4—22no—
545C22×C4—22no—
546C22×C4—22no—
547C22×C4—22no—
548C22×C4—22no—
549C22×C4—22no—
550C22×C4—22no—
551C22×C4—22no—
552C22×C4—22no—
553C22×C4—22no—
554C22×C4—112no—
555C22×C4—112no—
556C22×C4—112no—
557C22×C4—112no—
558C22×C4—112no—
559C22×C4—114no—
560C22×C4—221no—
561C22×C4—221no—
562C22×C4—221no—
563C22×C4—221no—
564C22×C4—221no—
565C22×C4—221no—
566C22×C4—222no—
567C22×C4—221no—
568C22×C4—221no—
569C22×C4—221no—
570C22×C4—222no—
571C22×C4—221no—
572C22×C4—221no—
573C22×C4—221no—
574C22×C4—221no—
575C22×C4—222no—
576C22×C4—222no—
577C22×C4—221no—
578C22×C4—221no—
579C22×C4—222no—
580C22×C4—222no—
581C22×C4—221no—
582C22×C4—228no—
583C22×C4—228no—
584C22×C4—228no—
585C22×C4—222no—
586C22×C4—222no—
587C22×C4—222no—
588C22×C4—222no—
589C22×C4—222no—
590C22×C4—222no—
591C22×C4—222no—
592C22×C4—444no—
593C22×C4—444no—
594C22×C4—444no—
595C22×C4—444no—
596C22×C4C2×C4×D1112yes—
597C22×C4C2×C4×D1112yes—
598C22×C4C2×C4×D1112yes—
599C22×C4C2×D4414yes—
600C22×C4C2×D4412yes—
601C22×C4#433912yes—
602C22×C4D4×D1112yes—
603C22×C4D4×D1112yes—
604C22×C4#434112yes—
605C22×C4#434112yes—
606C22×C4#434112yes—
607C22×C4Q8×D1112yes—
608C22×C4#434312yes—
609C22×C4#434312yes—
610C4⋊C4—28no—
611C4⋊C4—44no—
612C4⋊C4—228no—
613C4⋊C4—448no—
614C4⋊C4—448no—
615C4⋊C4—444no—
616C22⋊C4—1116no—
617C22⋊C4—228no—
618C22⋊C4—448no—
619C22⋊C4—448no—
620C42—28no—
621C42—228no—
622C42—448no—
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×D4×D1111yescharacteristic
663C23C2×D4×D1111yescharacteristic
664C23C2×#434111yescharacteristic
665C23C2×#434111yescharacteristic
666C23C2×#434111yescharacteristic
667C23C2×Q8×D1111yescharacteristic
668C23C2×#434311yescharacteristic
669C23C2×#434311yescharacteristic
670C23#6704211yescharacteristic
671C23#6704211yescharacteristic
672C23#6704311yescharacteristic
673C23#6704311yescharacteristic
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—24no—
687C2×C4—24no—
688C2×C4—24no—
689C2×C4—42no—
690C2×C4—42no—
691C2×C4—42no—
692C2×C4—42no—
693C2×C4—42no—
694C2×C4—42no—
695C2×C4—42no—
696C2×C4—42no—
697C2×C4—42no—
698C2×C4—42no—
699C2×C4—42no—
700C2×C4—114no—
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—224no—
713C2×C4—222no—
714C2×C4—224no—
715C2×C4—224no—
716C2×C4—442no—
717C2×C4—441no—
718C2×C4—441no—
719C2×C4—441no—
720C2×C4—441no—
721C2×C4—442no—
722C2×C4—441no—
723C2×C4—441no—
724C2×C4—442no—
725C2×C4—441no—
726C2×C4—441no—
727C2×C4—442no—
728C2×C4—4416no—
729C2×C4—442no—
730C2×C4—442no—
731C2×C4—442no—
732C2×C4—442no—
733C2×C4—442no—
734C2×C4—442no—
735C2×C4—442no—
736C2×C4C4×D4414yes—
737C2×C4(C22⋊D11)⋊C414yes—
738C2×C4#6693814yes—
739C2×C4#6693914yes—
740C2×C4C4⋊C4×D1114yes—
741C2×C4#6694514yes—
742C2×C4#6694514yes—
743C2×C4#6694814yes—
744C2×C4#6695114yes—
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×C4×D4411yescharacteristic
761C22C2×(C22⋊D11)⋊C411yescharacteristic
762C22C2×#6693811yescharacteristic
763C22C2×#6693911yescharacteristic
764C22C2×C4⋊C4×D1111yescharacteristic
765C22C2×#6694511yescharacteristic
766C22C2×#6694511yescharacteristic
767C22C2×#6694811yescharacteristic
768C22C2×#6695111yescharacteristic
769C22#1062305411yescharacteristic
770C22#1062305411yescharacteristic
771C22D4×D4411yescharacteristic
772C22#1062308211yescharacteristic
773C22#1062308611yescharacteristic
774C22#1062309411yescharacteristic
775C22Q8×D4411yescharacteristic
776C22#1062310811yescharacteristic
777C22#1062311011yescharacteristic
778C22#1062311511yescharacteristic
779C22#1062312911yescharacteristic
780C22#1062314011yescharacteristic
781C22#1062314211yescharacteristic
782C22#1062314911yescharacteristic
783C22#1062316111yescharacteristic
784C22#1062316311yescharacteristic
785C22#1062316611yescharacteristic
786C22#1062317311yescharacteristic
787C22#1062321311yescharacteristic
788C22#1062321311yescharacteristic
789C22#1062322811yescharacteristic
790C22#1062322911yescharacteristic
791C22#1062324711yescharacteristic
792C22#1062325611yescharacteristic
793C22#1062325911yescharacteristic
794C22#1062325911yescharacteristic
795C4—24no—
796C4—24no—
797C4—44no—
798C4—82no—
799C4—224no—
800C4—444no—
801C4—442no—
802C4—442no—
803C4—882no—
804C4#1062228318yescomplemented
805C2—444no—
806C2#1307102111yescharacteristic
807C2C2×#1062228311yescharacteristic
808C2#1307122611yescharacteristic
809C2#1307151211yescharacteristic
810C2C4⋊C4×D4411yescharacteristic
811C2#1307154711yescharacteristic
812C2#1307156311yescharacteristic
813C2#1307212811yescharacteristic
814C2#1307213911yescharacteristic
815C2#1307220211yescharacteristic
816C2#1307221311yescharacteristic
817C2#1307297711yescharacteristic
818C2#1307298811yescharacteristic
819C2#1307303611yescharacteristic
820C2#1307304711yescharacteristic
subgroupG/H
center, FrattiniC24C23×D11
commutatorC23×C11C23×C4
FittingC11×C4⋊#95C2
socle, cosocleC24×C11C24
prime radicalC24×D11C23
hypercenterC4⋊#95D11
hypocenterC11#13876
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ C4⋊#95

Complements

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

NH ≅ G/Ntype
2. C2×#10622548C2semidirect
5. C2×C4⋊C4×Dic11C2semidirect
7. #13066872C2semidirect
9. #13066850C2semidirect
10. #13066845C2semidirect
11. C11×C4⋊#95C2semidirect
38. C4×(C2×D11)⋊C4C4semidirect
207. (C2×D11)⋊C4C4⋊C4semidirect
224. C4⋊#95D11semidirect
429. C4×C11#388semidirect
623. C11#13876semidirect
804. C4#10622283semidirect

Maximal subgroups

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

subgroupindex
C2×#106222832
C2×#106225482
C2×#106226002
C2×C4⋊C4×Dic112
C2×C4×(C2×D11)⋊C42
#130668722
#130668622
#130668502
#130668452
C11×C4⋊#952
#1387611