Finite Group Databasebeta

← #14676605

Subgroups — #14676605

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×#10622600C211yesmaximal, characteristic
3C2×#10622600C211yesmaximal, characteristic
4C2×C4×(C2×D11)⋊C4C211yesmaximal, characteristic
5#13066871C212yesmaximal, complemented
6#13066860C212yesmaximal
7#13066854C212yesmaximal
8#13066845C211yesmaximal, characteristic, complemented
9#13066845C211yesmaximal, characteristic, complemented
10#13066843C212yesmaximal, 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)⋊C4C2211yescharacteristic
18C22×(C2×D11)⋊C4C2212yes—
19C22×(C2×D11)⋊C4C2211yescharacteristic
20C22×(C2×D11)⋊C4C2212yes—
21C22×C4⋊Dic11C2211yescharacteristic
22C22×C4⋊Dic11C2211yescharacteristic
23C22×Dic11⋊C4C2212yes—
24C22×C4×Dic11C2211yescharacteristic
25C4×C11×C4⋊C4—24no—
26C2×C11×#95C2212yes—
27C2×C11⋊#95C2211yescharacteristic
28C2×C11⋊#95C2212yes—
29C2×C11⋊#95C2212yes—
30C2×C11⋊#95C2212yes—
31C2×C11⋊#95C2211yescharacteristic
32C2×C11⋊#95C2212yes—
33C2×C11⋊#95C2212yes—
34C2×C11⋊#95C2212yes—
35C2×C11⋊#95C2212yes—
36#10622600—24no—
37#10622600C418yescomplemented
38C4×(C2×D11)⋊C4—24no—
39#10622541—24no—
40C24×D11C2311yescharacteristic
41C23×C4×C11C2312yes—
42C23×C4×C11C2311yescharacteristic
43C23×C4×C11C2312yes—
44C23×C4×C11C2311yescharacteristic
45C23×C4×C11C2311yescharacteristic
46C23×Dic11C2312yes—
47C23×Dic11C2312yes—
48C23×Dic11C2311yescharacteristic
49C23×Dic11C2311yescharacteristic
50C23×Dic11C2311yescharacteristic
51C22×C4×D11—22no—
52C22×C4×D11—22no—
53C22×C4×D11—22no—
54C22×C4×D11—22no—
55C22×C4×D11—22no—
56C22×C4×D11—22no—
57C22×C4×D11C2×C414yes—
58C2×C11×C4⋊C4—22no—
59C2×C11×C4⋊C4—22no—
60C2×C11×C4⋊C4—22no—
61C2×C11×C4⋊C4—22no—
62C2×C11×C4⋊C4C2×C414yes—
63C2×C11×C4⋊C4D414yes—
64C2×C42×C11—22no—
65C2×C42×C11—22no—
66C2×C42×C11—24no—
67C2×C42×C11—24no—
68C2×C42×C11—42no—
69C2×C42×C11D414yes—
70C2×(C2×D11)⋊C4—22no—
71C2×(C2×D11)⋊C4—22no—
72C2×(C2×D11)⋊C4—22no—
73C2×(C2×D11)⋊C4—22no—
74C2×(C2×D11)⋊C4—22no—
75C2×(C2×D11)⋊C4—24no—
76C2×(C2×D11)⋊C4—24no—
77C2×(C2×D11)⋊C4—42no—
78C2×(C2×D11)⋊C4—42no—
79C2×(C2×D11)⋊C4—42no—
80C2×(C2×D11)⋊C4C2×C418yes—
81C2×(C2×D11)⋊C4Q814yes—
82C2×C4⋊Dic11—22no—
83C2×C4⋊Dic11—22no—
84C2×C4⋊Dic11—22no—
85C2×C4⋊Dic11—22no—
86C2×C4⋊Dic11—22no—
87C2×C4⋊Dic11C2×C414yes—
88C2×Dic11⋊C4—24no—
89C2×Dic11⋊C4—42no—
90C2×Dic11⋊C4—42no—
91C2×C4×Dic11—22no—
92C2×C4×Dic11—22no—
93C2×C4×Dic11—22no—
94C11×#95—24no—
95C11⋊#95—24no—
96C11⋊#95—22no—
97C11⋊#95—22no—
98C11⋊#95—24no—
99C11⋊#95—24no—
100C11⋊#95—42no—
101C11⋊#95—42no—
102C11⋊#95—42no—
103C11⋊#95C2×C418yes—
104#13973—111nomaximal, Sylow
105C24×C11C2411yescharacteristic
106C23×D11—21no—
107C23×D11—21no—
108C23×D11—21no—
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×D11C22×C412yes—
119C23×D11C2×Q812yes—
120C23×D11#4112yes—
121C22×C4×C11—21no—
122C22×C4×C11—21no—
123C22×C4×C11—21no—
124C22×C4×C11—21no—
125C22×C4×C11—21no—
126C22×C4×C11—22no—
127C22×C4×C11—22no—
128C22×C4×C11—21no—
129C22×C4×C11—21no—
130C22×C4×C11—22no—
131C22×C4×C11—22no—
132C22×C4×C11—21no—
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—21no—
141C22×C4×C11—21no—
142C22×C4×C11—22no—
143C22×C4×C11C22×C414yes—
144C22×C4×C11C22×C412yes—
145C22×C4×C11C2×D412yes—
146C22×C4×C11C2×D414yes—
147C22×C4×C11C2×D412yes—
148C22×C4×C11C2×D412yes—
149C22×C4×C11C2×D412yes—
150C22×C4×C11C2×Q812yes—
151C22×C4×C11#4112yes—
152C22×C4×C11#4112yes—
153C22×C4×C11#4112yes—
154C22×C4×C11#4112yes—
155C22×C4×C11#4112yes—
156C22×Dic11—21no—
157C22×Dic11—21no—
158C22×Dic11—21no—
159C22×Dic11—21no—
160C22×Dic11—22no—
161C22×Dic11—22no—
162C22×Dic11—22no—
163C22×Dic11—21no—
164C22×Dic11—21no—
165C22×Dic11—21no—
166C22×Dic11—21no—
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—21no—
178C22×Dic11—21no—
179C22×Dic11—21no—
180C22×Dic11—22no—
181C22×Dic11—22no—
182C22×Dic11—22no—
183C22×Dic11—22no—
184C22×Dic11—22no—
185C22×Dic11—22no—
186C22×Dic11—21no—
187C22×Dic11C22×C412yes—
188C22×Dic11C22×C414yes—
189C22×Dic11C2×Q812yes—
190C22×Dic11#4112yes—
191C2×C4×D11—28no—
192C2×C4×D11—28no—
193C2×C4×D11—28no—
194C2×C4×D11—44no—
195C2×C4×D11—44no—
196C2×C4×D11—44no—
197C2×C4×D11—44no—
198C11×C4⋊C4—28no—
199C11×C4⋊C4—28no—
200C42×C11—28no—
201C42×C11—48no—
202(C2×D11)⋊C4—28no—
203(C2×D11)⋊C4—28no—
204(C2×D11)⋊C4—48no—
205(C2×D11)⋊C4—48no—
206C4⋊Dic11—28no—
207C4⋊Dic11—44no—
208Dic11⋊C4—48no—
209C4×Dic11—44no—
210C2×#389—111no—
211C2×#380—111no—
212C2×#380—111no—
213C2×C4×C4⋊C4D1111yescharacteristic, complemented
214C2×C4×C22⋊C4—111no—
215#1442—112no—
216#1439—112no—
217#1437—112no—
218C4⋊#95—111no—
219C4⋊#95—111no—
220#1434—112no—
221C23×C11C23×C411yescharacteristic
222C23×C11C22×D411yescharacteristic
223C23×C11C22×D411yescharacteristic
224C23×C11C22×Q811yescharacteristic
225C23×C11C2×#4111yescharacteristic
226C23×C11C2×#4111yescharacteristic
227C23×C11C2×#4111yescharacteristic
228C23×C11C2×#4111yescharacteristic
229C23×C11C2×#4111yescharacteristic
230C23×C11C2×#4111yescharacteristic
231C23×C11C2×#4111yescharacteristic
232C23×C11H(5,𝔽2)11yescharacteristic
233C23×C11H(5,𝔽2)11yescharacteristic
234C23×C11H(5,𝔽2)11yescharacteristic
235C23×C112−1+411yescharacteristic
236C22×D11—22no—
237C22×D11—22no—
238C22×D11—22no—
239C22×D11—22no—
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—41no—
255C22×D11—41no—
256C22×D11—41no—
257C22×D11—41no—
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×D11C4×Q814yes—
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—24no—
278C2×C4×C11—24no—
279C2×C4×C11—24no—
280C2×C4×C11—22no—
281C2×C4×C11—24no—
282C2×C4×C11—22no—
283C2×C4×C11—22no—
284C2×C4×C11—24no—
285C2×C4×C11—24no—
286C2×C4×C11—42no—
287C2×C4×C11—42no—
288C2×C4×C11—42no—
289C2×C4×C11—41no—
290C2×C4×C11—42no—
291C2×C4×C11—41no—
292C2×C4×C11—41no—
293C2×C4×C11—42no—
294C2×C4×C11—42no—
295C2×C4×C11—41no—
296C2×C4×C11—42no—
297C2×C4×C11—42no—
298C2×C4×C11#11714yes—
299C2×C4×C11C4×D414yes—
300C2×C4×C11C4×D414yes—
301C2×C4×C11#12114yes—
302C2×C4×C11C22⋊Q814yes—
303C2×C4×C11#12314yes—
304C2×C4×C11#12414yes—
305C2×C4×C11#12614yes—
306C2×Dic11—22no—
307C2×Dic11—24no—
308C2×Dic11—22no—
309C2×Dic11—22no—
310C2×Dic11—24no—
311C2×Dic11—24no—
312C2×Dic11—22no—
313C2×Dic11—22no—
314C2×Dic11—22no—
315C2×Dic11—22no—
316C2×Dic11—22no—
317C2×Dic11—22no—
318C2×Dic11—41no—
319C2×Dic11—41no—
320C2×Dic11—41no—
321C2×Dic11—41no—
322C2×Dic11—41no—
323C2×Dic11—41no—
324C2×Dic11—42no—
325C2×Dic11—41no—
326C2×Dic11—41no—
327C2×Dic11—42no—
328C2×Dic11—42no—
329C2×Dic11—42no—
330C2×Dic11—41no—
331C2×Dic11—41no—
332C2×Dic11—41no—
333C2×Dic11—41no—
334C2×Dic11—42no—
335C2×Dic11—42no—
336C2×Dic11—42no—
337C2×Dic11—42no—
338C2×Dic11—42no—
339C2×Dic11—42no—
340C2×Dic11—42no—
341C4×D11—416no—
342C24×C4—111no—
343C22×C4⋊C4—111no—
344C22×C4⋊C4—111no—
345C22×C4⋊C4—112no—
346C22×C4⋊C4C2×D1111yescharacteristic
347C22×C4⋊C4C2×D1111yescharacteristic
348C22×C22⋊C4—111no—
349C22×C22⋊C4—112no—
350C22×C22⋊C4—111no—
351C22×C22⋊C4—112no—
352C22×C42—111no—
353C22×C42C2×D1112yes—
354C22×C42C2×D1111yescharacteristic
355#389—224no—
356#380—118no—
357#380—224no—
358C4×C4⋊C4—24no—
359C4×C22⋊C4—224no—
360C2×#95—112no—
361C2×#95—111no—
362C2×#95—112no—
363C2×#95—112no—
364C2×#95—112no—
365C2×#95—111no—
366C2×#95—112no—
367C2×#95—112no—
368C2×#95—112no—
369C2×#95C2×D1112yes—
370C22×C11C2×#11711yescharacteristic
371C22×C11C2×C4×D411yescharacteristic
372C22×C11C2×C4×D411yescharacteristic
373C22×C11C2×C4×Q811yescharacteristic
374C22×C11C4×#4111yescharacteristic
375C22×C11#51811yescharacteristic
376C22×C11#52011yescharacteristic
377C22×C11C2×#12111yescharacteristic
378C22×C11C2×C22⋊Q811yescharacteristic
379C22×C11C2×#12311yescharacteristic
380C22×C11#52511yescharacteristic
381C22×C11C2×#12411yescharacteristic
382C22×C11C2×#12611yescharacteristic
383C22×C11#52911yescharacteristic
384C22×C11#53311yescharacteristic
385C22×C11#53511yescharacteristic
386C22×C11#53711yescharacteristic
387C22×C11#54011yescharacteristic
388C22×C11#54211yescharacteristic
389C22×C11#54611yescharacteristic
390C22×C11#54611yescharacteristic
391C22×C11D4×Q811yescharacteristic
392C22×C11#55011yescharacteristic
393C22×C11#55211yescharacteristic
394C22×C11#55211yescharacteristic
395C22×C11#55211yescharacteristic
396C22×C11#55311yescharacteristic
397C22×C11#55311yescharacteristic
398C22×C11#55311yescharacteristic
399C22×C11#55411yescharacteristic
400C22×C11#55411yescharacteristic
401C22×C11#55411yescharacteristic
402C22×C11#55511yescharacteristic
403C22×C11#55511yescharacteristic
404C22×C11#55511yescharacteristic
405C2×D11—24no—
406C2×D11—24no—
407C2×D11—24no—
408C2×D11—42no—
409C2×D11—42no—
410C2×D11—42no—
411C2×D11—42no—
412C2×D11—42no—
413C2×D11—42no—
414C2×D11—42no—
415C2×D11—42no—
416C2×D11—42no—
417C2×D11—42no—
418C2×D11—42no—
419C2×D11—42no—
420C4×C11—24no—
421C4×C11—44no—
422C4×C11—42no—
423C4×C11—44no—
424C4×C11#38818yes—
425Dic11—42no—
426Dic11—42no—
427Dic11—44no—
428Dic11—42no—
429Dic11—82no—
430C25—111no—
431C23×C4—112no—
432C23×C4—111no—
433C23×C4—111no—
434C23×C4—111no—
435C23×C4—114no—
436C23×C4—112no—
437C23×C4—222no—
438C23×C4—222no—
439C23×C4—222no—
440C23×C4—222no—
441C23×C4—222no—
442C23×C4—222no—
443C23×C4C22×D1112yes—
444C23×C4C22×D1111yescharacteristic
445C23×C4C22×D1112yes—
446C23×C4C22×D1111yescharacteristic
447C23×C4C22×D1111yescharacteristic
448C2×C4⋊C4—22no—
449C2×C4⋊C4—22no—
450C2×C4⋊C4—22no—
451C2×C4⋊C4—22no—
452C2×C4⋊C4—114no—
453C2×C4⋊C4—222no—
454C2×C4⋊C4—222no—
455C2×C4⋊C4—224no—
456C2×C4⋊C4—222no—
457C2×C4⋊C4—222no—
458C2×C4⋊C4—222no—
459C2×C4⋊C4—442no—
460C2×C4⋊C4—442no—
461C2×C4⋊C4C4×D1114yes—
462C2×C4⋊C4C22⋊D1114yes—
463C2×C22⋊C4—114no—
464C2×C22⋊C4—118no—
465C2×C22⋊C4—222no—
466C2×C22⋊C4—222no—
467C2×C22⋊C4—222no—
468C2×C22⋊C4—222no—
469C2×C22⋊C4—222no—
470C2×C22⋊C4—224no—
471C2×C22⋊C4—224no—
472C2×C22⋊C4—442no—
473C2×C22⋊C4—442no—
474C2×C22⋊C4—442no—
475C2×C42—22no—
476C2×C42—22no—
477C2×C42—24no—
478C2×C42—24no—
479C2×C42—42no—
480C2×C42—222no—
481C2×C42—222no—
482C2×C42—222no—
483C2×C42D4414yes—
484#95—24no—
485#95—118no—
486#95—224no—
487#95—222no—
488#95—222no—
489#95—224no—
490#95—224no—
491#95—442no—
492#95—442no—
493#95—442no—
494C2×C11C2×#38811yescharacteristic
495C2×C11C4×C22⋊Q811yescharacteristic
496C2×C11#232411yescharacteristic
497C2×C11#234511yescharacteristic
498C2×C11#234611yescharacteristic
499C2×C11#236011yescharacteristic
500C2×C11#236311yescharacteristic
501C2×C11#241411yescharacteristic
502C2×C11#241711yescharacteristic
503C2×C11#242011yescharacteristic
504C2×C11#242311yescharacteristic
505C2×C11#249511yescharacteristic
506C2×C11#249711yescharacteristic
507C2×C11#256211yescharacteristic
508C2×C11#256311yescharacteristic
509D11—44no—
510C24—112no—
511C24—112no—
512C24—112no—
513C24—221no—
514C24—221no—
515C24—221no—
516C24—221no—
517C24—221no—
518C24—221no—
519C24—221no—
520C24—221no—
521C24—221no—
522C24—221no—
523C24—221no—
524C24—221no—
525C24C23×D1111yescharacteristic
526C22×C4—21no—
527C22×C4—21no—
528C22×C4—21no—
529C22×C4—21no—
530C22×C4—21no—
531C22×C4—22no—
532C22×C4—22no—
533C22×C4—22no—
534C22×C4—22no—
535C22×C4—22no—
536C22×C4—22no—
537C22×C4—22no—
538C22×C4—22no—
539C22×C4—21no—
540C22×C4—21no—
541C22×C4—22no—
542C22×C4—22no—
543C22×C4—22no—
544C22×C4—21no—
545C22×C4—21no—
546C22×C4—21no—
547C22×C4—22no—
548C22×C4—112no—
549C22×C4—114no—
550C22×C4—112no—
551C22×C4—112no—
552C22×C4—221no—
553C22×C4—221no—
554C22×C4—221no—
555C22×C4—222no—
556C22×C4—221no—
557C22×C4—221no—
558C22×C4—221no—
559C22×C4—221no—
560C22×C4—222no—
561C22×C4—221no—
562C22×C4—221no—
563C22×C4—221no—
564C22×C4—221no—
565C22×C4—221no—
566C22×C4—221no—
567C22×C4—222no—
568C22×C4—222no—
569C22×C4—221no—
570C22×C4—221no—
571C22×C4—221no—
572C22×C4—221no—
573C22×C4—222no—
574C22×C4—222no—
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—444no—
587C22×C4—444no—
588C22×C4—444no—
589C22×C4—444no—
590C22×C4C2×C4×D1114yes—
591C22×C4C2×C4×D1112yes—
592C22×C4C2×D4412yes—
593C22×C4C2×D4412yes—
594C22×C4C2×D4412yes—
595C22×C4#433912yes—
596C22×C4#433912yes—
597C22×C4#433912yes—
598C22×C4#433912yes—
599C22×C4#434112yes—
600C22×C4Q8×D1112yes—
601C22×C4C2×C22⋊D1114yes—
602C22×C4C2×C22⋊D1112yes—
603C4⋊C4—28no—
604C4⋊C4—28no—
605C4⋊C4—228no—
606C4⋊C4—448no—
607C4⋊C4—444no—
608C22⋊C4—228no—
609C22⋊C4—228no—
610C22⋊C4—448no—
611C22⋊C4—448no—
612C42—28no—
613C42—48no—
614C42—444no—
615C11#1397311yescharacteristic, complemented, Sylow
616C23—114no—
617C23—222no—
618C23—222no—
619C23—222no—
620C23—222no—
621C23—222no—
622C23—222no—
623C23—222no—
624C23—222no—
625C23—222no—
626C23—222no—
627C23—222no—
628C23—222no—
629C23—222no—
630C23—222no—
631C23—222no—
632C23—222no—
633C23—222no—
634C23—222no—
635C23—441no—
636C23—441no—
637C23—441no—
638C23—441no—
639C23—441no—
640C23—441no—
641C23—441no—
642C23—441no—
643C23—441no—
644C23—441no—
645C23—441no—
646C23—441no—
647C23—441no—
648C23—441no—
649C23—441no—
650C23—441no—
651C23C22×C4×D1111yescharacteristic
652C23C22×D4411yescharacteristic
653C23C2×#433911yescharacteristic
654C23C2×#433911yescharacteristic
655C23C2×#433911yescharacteristic
656C23C2×#433911yescharacteristic
657C23C2×#434111yescharacteristic
658C23#6703711yescharacteristic
659C23C2×Q8×D1111yescharacteristic
660C23#6704011yescharacteristic
661C23#41×D1111yescharacteristic
662C23#41×D1111yescharacteristic
663C23#6704211yescharacteristic
664C23#6704211yescharacteristic
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—24no—
675C2×C4—24no—
676C2×C4—22no—
677C2×C4—24no—
678C2×C4—24no—
679C2×C4—24no—
680C2×C4—24no—
681C2×C4—41no—
682C2×C4—41no—
683C2×C4—42no—
684C2×C4—42no—
685C2×C4—42no—
686C2×C4—42no—
687C2×C4—42no—
688C2×C4—42no—
689C2×C4—42no—
690C2×C4—41no—
691C2×C4—42no—
692C2×C4—41no—
693C2×C4—222no—
694C2×C4—224no—
695C2×C4—222no—
696C2×C4—222no—
697C2×C4—222no—
698C2×C4—222no—
699C2×C4—224no—
700C2×C4—222no—
701C2×C4—224no—
702C2×C4—222no—
703C2×C4—222no—
704C2×C4—222no—
705C2×C4—441no—
706C2×C4—441no—
707C2×C4—441no—
708C2×C4—441no—
709C2×C4—441no—
710C2×C4—442no—
711C2×C4—442no—
712C2×C4—441no—
713C2×C4—441no—
714C2×C4—441no—
715C2×C4—441no—
716C2×C4—442no—
717C2×C4—441no—
718C2×C4—441no—
719C2×C4—441no—
720C2×C4—442no—
721C2×C4—4416no—
722C2×C4—442no—
723C2×C4—442no—
724C2×C4—442no—
725C2×C4—442no—
726C2×C4—442no—
727C2×C4—442no—
728C2×C4—442no—
729C2×C4#6692514yes—
730C2×C4C4×D4414yes—
731C2×C4#6692814yes—
732C2×C4#6692914yes—
733C2×C4#6695014yes—
734C2×C4C4×C22⋊D1114yes—
735C2×C4#6698214yes—
736C2×C4#6698314yes—
737C22—224no—
738C22—224no—
739C22—224no—
740C22—442no—
741C22—442no—
742C22—442no—
743C22—442no—
744C22—442no—
745C22—442no—
746C22—442no—
747C22—442no—
748C22—442no—
749C22—442no—
750C22—442no—
751C22—442no—
752C22C2×#6692511yescharacteristic
753C22C2×C4×D4411yescharacteristic
754C22C2×#6692811yescharacteristic
755C22C2×#6692911yescharacteristic
756C22C2×#6695011yescharacteristic
757C22#1062304111yescharacteristic
758C22#1062304211yescharacteristic
759C22#1062304411yescharacteristic
760C22#1062305511yescharacteristic
761C22#1062305611yescharacteristic
762C22#1062306111yescharacteristic
763C22#1062306311yescharacteristic
764C22C4×#434111yescharacteristic
765C22#1062307611yescharacteristic
766C22#1062308811yescharacteristic
767C22#1062308911yescharacteristic
768C22#1062308911yescharacteristic
769C22#1062309311yescharacteristic
770C22#1062309411yescharacteristic
771C22#1062309411yescharacteristic
772C22C4×Q8×D1111yescharacteristic
773C22#1062310511yescharacteristic
774C22#1062310911yescharacteristic
775C22#1062311011yescharacteristic
776C22#1062311011yescharacteristic
777C22#1062311211yescharacteristic
778C22#1062311211yescharacteristic
779C22#1062311311yescharacteristic
780C22C2×C4×C22⋊D1111yescharacteristic
781C22C2×#6698211yescharacteristic
782C22C2×#6698311yescharacteristic
783C22#1062333711yescharacteristic
784C22Q8×C22⋊D1111yescharacteristic
785C22#1062336011yescharacteristic
786C22#1062336511yescharacteristic
787C4—24no—
788C4—44no—
789C4—42no—
790C4—44no—
791C4—442no—
792C4—442no—
793C4—442no—
794C4—444no—
795C4—882no—
796C4#1062255318yes—
797C2—444no—
798C2C2×#1062255311yescharacteristic
799C2C4×#6695011yescharacteristic
800C2#1307131011yescharacteristic
801C2#1307148911yescharacteristic
802C2#1307149711yescharacteristic
803C2#1307161711yescharacteristic
804C2#1307165011yescharacteristic
805C2#1307202811yescharacteristic
806C2#1307206111yescharacteristic
807C2#1307210211yescharacteristic
808C2#1307213511yescharacteristic
809C2#1307302111yescharacteristic
810C2#1307304311yescharacteristic
811C2#1307377711yescharacteristic
812C2#1307378511yescharacteristic
subgroupG/H
center, FrattiniC24C23×D11
commutatorC23×C11C23×C4
FittingC2×C4×C11×C4⋊C4C2
socle, cosocleC24×C11C24
prime radicalC24×D11C23
hypercenterC2×C4×C4⋊C4D11
hypocenterC11#13973
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ C2×C4×C4⋊C4

Complements

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

NH ≅ G/Ntype
1. C2×#10622541C2semidirect
5. #13066871C2semidirect
8. #13066845C2semidirect
9. #13066845C2semidirect
10. #13066843C2semidirect
11. C2×C4×C11×C4⋊C4C2semidirect
37. #10622600C4semidirect
213. C2×C4×C4⋊C4D11semidirect
615. C11#13973semidirect

Maximal subgroups

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

subgroupindex
C2×#106225412
C2×#106226002
C2×C4×(C2×D11)⋊C42
#130668712
#130668602
#130668542
#130668452
#130668432
C2×C4×C11×C4⋊C42
#1397311