Finite Group Databasebeta

← #14676863

Subgroups — #14676863

Order 2816.

1746 conjugacy classes of subgroups.

The subgroup lattice has 814 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622541C211yesmaximal, characteristic, complemented
2C2×#10622825C211yesmaximal, characteristic
3C2×#10622825C211yesmaximal, characteristic
4C2×C4×C4⋊Dic11C211yesmaximal, characteristic, complemented
5#13066877C212yesmaximal, complemented
6#13066859C212yesmaximal
7#13066853C212yesmaximal
8#13066847C212yesmaximal, 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⋊Dic11C2211yescharacteristic
22C22×C4⋊Dic11C2211yescharacteristic
23C22×Dic11⋊C4C2212yes—
24C22×C4×Dic11C2212yes—
25C4×C11×C22⋊C4—24no—
26C2×C11×#95C2211yescharacteristic
27C2×C11×#95C2211yescharacteristic
28#10622825—24no—
29#10622825C418yescomplemented
30C2×C11⋊#95C2212yes—
31C2×C11⋊#95C2212yes—
32C2×C11⋊#95C2212yes—
33C2×C11⋊#95C2212yes—
34C2×C11⋊#95C2212yes—
35C2×C11⋊#95C2212yes—
36C2×C11⋊#95C2212yes—
37C2×C11⋊#95C2212yes—
38C4×C4⋊Dic11—24no—
39#10622541—24no—
40C25×C11C2311yescharacteristic
41C23×C4×C11—22no—
42C23×C4×C11—22no—
43C23×C4×C11—22no—
44C23×C4×C11—22no—
45C23×C4×C11—22no—
46C23×C4×C11—22no—
47C23×C4×C11C2×C414yes—
48C23×C4×C11C2311yescharacteristic
49C23×C4×C11C2311yescharacteristic
50C23×C4×C11C2311yescharacteristic
51C23×C4×C11C2311yescharacteristic
52C23×C4×C11C2311yescharacteristic
53C23×C4×C11C2311yescharacteristic
54C23×Dic11C2312yes—
55C23×Dic11C2312yes—
56C23×Dic11C2312yes—
57C23×Dic11C2312yes—
58C2×C11×C22⋊C4—22no—
59C2×C11×C22⋊C4—22no—
60C2×C11×C22⋊C4—22no—
61C2×C11×C22⋊C4—22no—
62C2×C11×C22⋊C4—22no—
63C2×C11×C22⋊C4Q814yes—
64C2×C42×C11—22no—
65C2×C42×C11—22no—
66C2×C42×C11—22no—
67C2×C42×C11—22no—
68C2×C42×C11—22no—
69C2×C42×C11D414yes—
70C2×C22⋊Dic11—24no—
71C2×C22⋊Dic11—24no—
72C2×C22⋊Dic11—42no—
73C2×C22⋊Dic11—42no—
74C2×C22⋊Dic11—42no—
75C2×C22⋊Dic11C2×C418yes—
76C2×C4⋊Dic11—22no—
77C2×C4⋊Dic11—22no—
78C2×C4⋊Dic11—22no—
79C2×C4⋊Dic11—22no—
80C2×C4⋊Dic11—22no—
81C2×C4⋊Dic11—22no—
82C2×C4⋊Dic11—22no—
83C2×C4⋊Dic11—22no—
84C2×C4⋊Dic11—22no—
85C2×C4⋊Dic11C2×C414yes—
86C2×C4⋊Dic11C2×C414yes—
87C2×C4⋊Dic11D414yes—
88C2×Dic11⋊C4—24no—
89C2×Dic11⋊C4—24no—
90C2×Dic11⋊C4—42no—
91C2×C4×Dic11—24no—
92C2×C4×Dic11—42no—
93C2×C4×Dic11—42no—
94C11×#95—22no—
95C11×#95—22no—
96C11⋊#95—24no—
97C11⋊#95—24no—
98C11⋊#95—24no—
99C11⋊#95—24no—
100C11⋊#95—42no—
101C11⋊#95—42no—
102C11⋊#95—42no—
103C11⋊#95C2×C418yes—
104#13993—111nomaximal, Sylow
105C24×C11—21no—
106C24×C11—21no—
107C24×C11—21no—
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×C11C22×C412yes—
118C24×C11C2×Q812yes—
119C24×C11#4112yes—
120C24×C11C2411yescharacteristic
121C22×C4×C11—21no—
122C22×C4×C11—21no—
123C22×C4×C11—21no—
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—21no—
149C22×C4×C11—28no—
150C22×C4×C11—28no—
151C22×C4×C11—28no—
152C22×C4×C11—44no—
153C22×C4×C11—44no—
154C22×C4×C11—44no—
155C22×C4×C11—44no—
156C22×C4×C11C22×C412yes—
157C22×C4×C11C22×C412yes—
158C22×C4×C11C2×D412yes—
159C22×C4×C11C2×D412yes—
160C22×C4×C11C2×D412yes—
161C22×C4×C11C2×D412yes—
162C22×C4×C11C2×Q812yes—
163C22×C4×C11C2×Q812yes—
164C22×C4×C11#4112yes—
165C22×C4×C11#4112yes—
166C22×C4×C11#4112yes—
167C22×C4×C11#4112yes—
168C22×C4×C11#4112yes—
169C22×C4×C11#4112yes—
170C22×Dic11—22no—
171C22×Dic11—22no—
172C22×Dic11—22no—
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×Dic11C22×C414yes—
196C22×Dic11C22×C414yes—
197C22×Dic11C2×D414yes—
198C11×C22⋊C4—28no—
199C11×C22⋊C4—28no—
200C42×C11—28no—
201C42×C11—44no—
202C22⋊Dic11—48no—
203C22⋊Dic11—48no—
204C4⋊Dic11—28no—
205C4⋊Dic11—28no—
206C4⋊Dic11—28no—
207C4⋊Dic11—44no—
208Dic11⋊C4—48no—
209C4×Dic11—48no—
210C2×#389—111no—
211C2×#380—111no—
212C2×#380—111no—
213C2×C4×C4⋊C4—111no—
214C2×C4×C22⋊C4D1111yescharacteristic
215#1443—112no—
216#1439—112no—
217#1437—112no—
218#1436—112no—
219C4⋊#95—111no—
220C4⋊#95—111no—
221C23×C11—22no—
222C23×C11—22no—
223C23×C11—22no—
224C23×C11—22no—
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—41no—
240C23×C11—41no—
241C23×C11—41no—
242C23×C11—41no—
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×C11C4×Q814yes—
256C23×C11C23×C411yescharacteristic
257C23×C11C22×D411yescharacteristic
258C23×C11C22×D411yescharacteristic
259C23×C11C22×Q811yescharacteristic
260C23×C11C2×#4111yescharacteristic
261C23×C11C2×#4111yescharacteristic
262C23×C11C2×#4111yescharacteristic
263C23×C11C2×#4111yescharacteristic
264C23×C11C2×#4111yescharacteristic
265C23×C11C2×#4111yescharacteristic
266C23×C11C2×#4111yescharacteristic
267C23×C11H(5,𝔽2)11yescharacteristic
268C23×C11H(5,𝔽2)11yescharacteristic
269C23×C11H(5,𝔽2)11yescharacteristic
270C23×C112−1+411yescharacteristic
271C2×C4×C11—22no—
272C2×C4×C11—22no—
273C2×C4×C11—22no—
274C2×C4×C11—22no—
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—41no—
290C2×C4×C11—41no—
291C2×C4×C11—41no—
292C2×C4×C11—41no—
293C2×C4×C11—41no—
294C2×C4×C11—41no—
295C2×C4×C11—41no—
296C2×C4×C11—41no—
297C2×C4×C11—41no—
298C2×C4×C11—41no—
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—416no—
306C2×C4×C11#11714yes—
307C2×C4×C11C4×D414yes—
308C2×C4×C11C4×D414yes—
309C2×C4×C11#12114yes—
310C2×C4×C11C22⋊Q814yes—
311C2×C4×C11#12314yes—
312C2×C4×C11#12414yes—
313C2×C4×C11#12614yes—
314C2×Dic11—24no—
315C2×Dic11—24no—
316C2×Dic11—24no—
317C2×Dic11—24no—
318C2×Dic11—24no—
319C2×Dic11—24no—
320C2×Dic11—24no—
321C2×Dic11—24no—
322C2×Dic11—24no—
323C2×Dic11—42no—
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—
342C24×C4C2×D1111yescharacteristic
343C22×C4⋊C4—111no—
344C22×C4⋊C4—111no—
345C22×C4⋊C4—111no—
346C22×C4⋊C4—111no—
347C22×C4⋊C4—112no—
348C22×C22⋊C4—112no—
349C22×C22⋊C4—112no—
350C22×C22⋊C4C2×D1111yescharacteristic
351C22×C22⋊C4C2×D1111yescharacteristic
352C22×C42—112no—
353C22×C42C2×D1111yescharacteristic
354C22×C42C2×D1111yescharacteristic
355#389—224no—
356#380—118no—
357#380—224no—
358C4×C4⋊C4—224no—
359C4×C22⋊C4—24no—
360C2×#95—112no—
361C2×#95—112no—
362C2×#95—112no—
363C2×#95—112no—
364C2×#95—112no—
365C2×#95—112no—
366C2×#95—112no—
367C2×#95—112no—
368C2×#95C2×D1111yescharacteristic
369C2×#95C2×D1111yescharacteristic
370C22×C11—24no—
371C22×C11—24no—
372C22×C11—24no—
373C22×C11—42no—
374C22×C11—42no—
375C22×C11—42no—
376C22×C11—42no—
377C22×C11—42no—
378C22×C11—42no—
379C22×C11—42no—
380C22×C11—42no—
381C22×C11—42no—
382C22×C11—42no—
383C22×C11—42no—
384C22×C11—42no—
385C22×C11C2×#11711yescharacteristic
386C22×C11C2×C4×D411yescharacteristic
387C22×C11C2×C4×D411yescharacteristic
388C22×C11C2×C4×Q811yescharacteristic
389C22×C11C4×#4111yescharacteristic
390C22×C11#51811yescharacteristic
391C22×C11#52011yescharacteristic
392C22×C11C2×#12111yescharacteristic
393C22×C11C2×C22⋊Q811yescharacteristic
394C22×C11C2×#12311yescharacteristic
395C22×C11#52511yescharacteristic
396C22×C11C2×#12411yescharacteristic
397C22×C11C2×#12611yescharacteristic
398C22×C11#52911yescharacteristic
399C22×C11#53311yescharacteristic
400C22×C11#53511yescharacteristic
401C22×C11#53711yescharacteristic
402C22×C11#54011yescharacteristic
403C22×C11#54211yescharacteristic
404C22×C11#54611yescharacteristic
405C22×C11#54611yescharacteristic
406C22×C11D4×Q811yescharacteristic
407C22×C11#55011yescharacteristic
408C22×C11#55211yescharacteristic
409C22×C11#55311yescharacteristic
410C22×C11#55311yescharacteristic
411C22×C11#55311yescharacteristic
412C22×C11#55311yescharacteristic
413C22×C11#55311yescharacteristic
414C22×C11#55411yescharacteristic
415C22×C11#55411yescharacteristic
416C22×C11#55411yescharacteristic
417C22×C11#55511yescharacteristic
418C22×C11#55611yescharacteristic
419C22×C11#55611yescharacteristic
420C4×C11—24no—
421C4×C11—42no—
422C4×C11—42no—
423C4×C11—42no—
424C4×C11—42no—
425C4×C11#38818yes—
426Dic11—44no—
427Dic11—44no—
428Dic11—44no—
429Dic11—82no—
430C25C22×D1111yescharacteristic
431C23×C4—22no—
432C23×C4—22no—
433C23×C4—22no—
434C23×C4—22no—
435C23×C4—22no—
436C23×C4—22no—
437C23×C4—112no—
438C23×C4—112no—
439C23×C4—112no—
440C23×C4—112no—
441C23×C4C4×D1114yes—
442C23×C4C22×D1111yescharacteristic
443C23×C4C22×D1111yescharacteristic
444C23×C4C22×D1111yescharacteristic
445C23×C4C22×D1111yescharacteristic
446C23×C4C22×D1111yescharacteristic
447C23×C4C22×D1111yescharacteristic
448C2×C4⋊C4—114no—
449C2×C4⋊C4—114no—
450C2×C4⋊C4—114no—
451C2×C4⋊C4—222no—
452C2×C4⋊C4—222no—
453C2×C4⋊C4—222no—
454C2×C4⋊C4—222no—
455C2×C4⋊C4—222no—
456C2×C4⋊C4—222no—
457C2×C4⋊C4—224no—
458C2×C4⋊C4—224no—
459C2×C4⋊C4—222no—
460C2×C4⋊C4—222no—
461C2×C4⋊C4—222no—
462C2×C4⋊C4—442no—
463C2×C22⋊C4—22no—
464C2×C22⋊C4—22no—
465C2×C22⋊C4—22no—
466C2×C22⋊C4—22no—
467C2×C22⋊C4—22no—
468C2×C22⋊C4—118no—
469C2×C22⋊C4—224no—
470C2×C22⋊C4—224no—
471C2×C22⋊C4—442no—
472C2×C22⋊C4—442no—
473C2×C22⋊C4—442no—
474C2×C22⋊C4Dic2214yes—
475C2×C42—22no—
476C2×C42—22no—
477C2×C42—22no—
478C2×C42—22no—
479C2×C42—22no—
480C2×C42—224no—
481C2×C42—442no—
482C2×C42—442no—
483C2×C42C22⋊D1114yes—
484#95—22no—
485#95—22no—
486#95—118no—
487#95—224no—
488#95—224no—
489#95—224no—
490#95—224no—
491#95—442no—
492#95—442no—
493#95—442no—
494C2×C11—44no—
495C2×C11C2×#38811yescharacteristic
496C2×C11C4×C22⋊Q811yescharacteristic
497C2×C11#232411yescharacteristic
498C2×C11#234511yescharacteristic
499C2×C11#234711yescharacteristic
500C2×C11#236011yescharacteristic
501C2×C11#236311yescharacteristic
502C2×C11#248511yescharacteristic
503C2×C11#248711yescharacteristic
504C2×C11#249011yescharacteristic
505C2×C11#249211yescharacteristic
506C2×C11#249411yescharacteristic
507C2×C11#249711yescharacteristic
508C2×C11#253511yescharacteristic
509C2×C11#253811yescharacteristic
510C24—21no—
511C24—21no—
512C24—21no—
513C24—21no—
514C24—21no—
515C24—21no—
516C24—21no—
517C24—21no—
518C24—21no—
519C24—21no—
520C24—21no—
521C24—21no—
522C24C2×Dic2212yes—
523C24C2×C4×D1112yes—
524C24#433912yes—
525C24C23×D1111yescharacteristic
526C22×C4—21no—
527C22×C4—21no—
528C22×C4—21no—
529C22×C4—21no—
530C22×C4—21no—
531C22×C4—21no—
532C22×C4—21no—
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—28no—
555C22×C4—28no—
556C22×C4—28no—
557C22×C4—44no—
558C22×C4—44no—
559C22×C4—44no—
560C22×C4—44no—
561C22×C4—114no—
562C22×C4—114no—
563C22×C4—114no—
564C22×C4—222no—
565C22×C4—222no—
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×C4C2×Dic2212yes—
590C22×C4C2×Dic2212yes—
591C22×C4C2×C4×D1112yes—
592C22×C4C2×C4×D1112yes—
593C22×C4#433912yes—
594C22×C4#433912yes—
595C22×C4#433912yes—
596C22×C4D4×D1112yes—
597C22×C4#434112yes—
598C22×C4#434112yes—
599C22×C4#434112yes—
600C22×C4C2×C22⋊D1112yes—
601C22×C4C2×C22⋊D1112yes—
602C22×C4C2×C22⋊D1112yes—
603C4⋊C4—228no—
604C4⋊C4—228no—
605C4⋊C4—228no—
606C4⋊C4—448no—
607C4⋊C4—444no—
608C22⋊C4—28no—
609C22⋊C4—28no—
610C22⋊C4—448no—
611C22⋊C4—448no—
612C42—28no—
613C42—44no—
614C42—448no—
615C11#1399311yescharacteristic, complemented, Sylow
616C23—22no—
617C23—22no—
618C23—22no—
619C23—22no—
620C23—22no—
621C23—22no—
622C23—22no—
623C23—22no—
624C23—22no—
625C23—22no—
626C23—22no—
627C23—22no—
628C23—22no—
629C23—22no—
630C23—22no—
631C23—22no—
632C23—22no—
633C23—22no—
634C23—41no—
635C23—41no—
636C23—41no—
637C23—41no—
638C23—41no—
639C23—41no—
640C23—41no—
641C23—41no—
642C23—41no—
643C23—41no—
644C23—41no—
645C23—41no—
646C23—41no—
647C23—41no—
648C23—41no—
649C23—41no—
650C23C4×Dic2214yes—
651C23C22×Dic2211yescharacteristic
652C23C22×C4×D1111yescharacteristic
653C23C2×#433911yescharacteristic
654C23C2×#433911yescharacteristic
655C23C2×#433911yescharacteristic
656C23C2×#433911yescharacteristic
657C23C2×D4×D1111yescharacteristic
658C23C2×#434111yescharacteristic
659C23C2×#434111yescharacteristic
660C23C2×#434111yescharacteristic
661C23#6704211yescharacteristic
662C23#6704211yescharacteristic
663C23#6704211yescharacteristic
664C23#6704311yescharacteristic
665C23C22×C22⋊D1111yescharacteristic
666C2×C4—22no—
667C2×C4—22no—
668C2×C4—22no—
669C2×C4—22no—
670C2×C4—22no—
671C2×C4—22no—
672C2×C4—22no—
673C2×C4—22no—
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—41no—
685C2×C4—41no—
686C2×C4—41no—
687C2×C4—41no—
688C2×C4—41no—
689C2×C4—41no—
690C2×C4—41no—
691C2×C4—41no—
692C2×C4—41no—
693C2×C4—41no—
694C2×C4—41no—
695C2×C4—41no—
696C2×C4—41no—
697C2×C4—41no—
698C2×C4—41no—
699C2×C4—41no—
700C2×C4—416no—
701C2×C4—224no—
702C2×C4—224no—
703C2×C4—224no—
704C2×C4—224no—
705C2×C4—224no—
706C2×C4—224no—
707C2×C4—224no—
708C2×C4—224no—
709C2×C4—224no—
710C2×C4—442no—
711C2×C4—442no—
712C2×C4—442no—
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#6693014yes—
730C2×C4#6693214yes—
731C2×C4(C22⋊D11)⋊C414yes—
732C2×C4#6693814yes—
733C2×C4#6697714yes—
734C2×C4C4×C22⋊D1114yes—
735C2×C4#6698814yes—
736C2×C4#6699114yes—
737C22—24no—
738C22—24no—
739C22—24no—
740C22—42no—
741C22—42no—
742C22—42no—
743C22—42no—
744C22—42no—
745C22—42no—
746C22—42no—
747C22—42no—
748C22—42no—
749C22—42no—
750C22—42no—
751C22—42no—
752C22C2×C4×Dic2211yescharacteristic
753C22#1062300111yescharacteristic
754C22C4×#433911yescharacteristic
755C22#1062301011yescharacteristic
756C22C2×#6693011yescharacteristic
757C22C2×#6693211yescharacteristic
758C22C2×(C22⋊D11)⋊C411yescharacteristic
759C22C2×#6693811yescharacteristic
760C22#1062305211yescharacteristic
761C22#1062305411yescharacteristic
762C22#1062306511yescharacteristic
763C22#1062306611yescharacteristic
764C22D4×Dic2211yescharacteristic
765C22#1062307211yescharacteristic
766C22#1062307311yescharacteristic
767C22#1062307311yescharacteristic
768C22#1062307411yescharacteristic
769C22#1062307411yescharacteristic
770C22#1062307411yescharacteristic
771C22#1062308111yescharacteristic
772C22#1062308111yescharacteristic
773C22#1062308411yescharacteristic
774C22#1062309411yescharacteristic
775C22#1062309611yescharacteristic
776C22#1062309611yescharacteristic
777C22#1062309611yescharacteristic
778C22#1062309611yescharacteristic
779C22#1062309611yescharacteristic
780C22C2×#6697711yescharacteristic
781C22C2×C4×C22⋊D1111yescharacteristic
782C22#1062332211yescharacteristic
783C22C2×#6698811yescharacteristic
784C22C2×#6699111yescharacteristic
785C22#1062336111yescharacteristic
786C22#1062336411yescharacteristic
787C4—24no—
788C4—42no—
789C4—42no—
790C4—42no—
791C4—42no—
792C4—444no—
793C4—444no—
794C4—444no—
795C4—882no—
796C4#1062255718yes—
797C2—44no—
798C2C2×#1062255711yescharacteristic
799C2C4×#6697711yescharacteristic
800C2#1307130911yescharacteristic
801C2#1307149111yescharacteristic
802C2#1307150711yescharacteristic
803C2#1307161911yescharacteristic
804C2#1307165211yescharacteristic
805C2#1307291311yescharacteristic
806C2#1307293311yescharacteristic
807C2#1307296811yescharacteristic
808C2#1307299011yescharacteristic
809C2#1307301611yescharacteristic
810C2#1307304911yescharacteristic
811C2#1307351711yescharacteristic
812C2#1307353811yescharacteristic
subgroupG/H
center, FrattiniC24C23×D11
commutatorC23×C11C23×C4
FittingC2×C4×C11×C22⋊C4C2
socle, cosocleC24×C11C24
prime radicalC25×C11C23
hypercenterC2×C4×C22⋊C4D11
hypocenterC11#13993
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ C2×C4×C22⋊C4

Complements

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

NH ≅ G/Ntype
1. C2×#10622541C2semidirect
4. C2×C4×C4⋊Dic11C2semidirect
5. #13066877C2semidirect
8. #13066847C2semidirect
9. #13066846C2semidirect
10. #13066846C2semidirect
29. #10622825C4semidirect
615. C11#13993semidirect

Maximal subgroups

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

subgroupindex
C2×#106225412
C2×#106228252
C2×C4×C4⋊Dic112
#130668772
#130668592
#130668532
#130668472
#130668462
C2×C4×C11×C22⋊C42
#1399311