Finite Group Databasebeta

← #14677208

Subgroups — #14677208

Order 2816.

1954 conjugacy classes of subgroups.

The subgroup lattice has 834 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622552C211yesmaximal, characteristic
2C2×#10622601C211yesmaximal, characteristic
3C2×#10622601C211yesmaximal, characteristic
4C2×#10622553C212yesmaximal, complemented
5C2×C4×Dic11⋊C4C211yesmaximal, characteristic, complemented
6#13066864C212yesmaximal, complemented
7#13066860C212yesmaximal, complemented
8#13066854C212yesmaximal, complemented
9#13066845C211yesmaximal, characteristic, complemented
10#13066845C211yesmaximal, characteristic, complemented
11C2×C4×C11×C4⋊C4C211yesmaximal, characteristic, complemented
12C23×D44C2211yescharacteristic
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)⋊C4C2212yes—
20C22×(C2×D11)⋊C4C2212yes—
21C22×(C2×D11)⋊C4C2212yes—
22C22×(C2×D11)⋊C4C2212yes—
23C22×C4⋊Dic11C2211yescharacteristic
24C22×Dic11⋊C4C2211yescharacteristic
25C22×Dic11⋊C4C2211yescharacteristic
26C22×C4×Dic11C2211yescharacteristic
27C22×C4×Dic11C2211yescharacteristic
28C4×C11×C4⋊C4—24no—
29C2×C11×#95C2212yes—
30C2×C11⋊#95C2212yes—
31C2×C11⋊#95C2212yes—
32C2×C11⋊#95C2211yescharacteristic
33C2×C11⋊#95C2211yescharacteristic
34C2×C11⋊#95C2212yes—
35C2×C11⋊#95C2212yes—
36#10622601—24no—
37#10622601C418yescomplemented
38#10622553—28no—
39#10622552—24no—
40C4×Dic11⋊C4—24no—
41C24×D11C2312yes—
42C23×C4×C11C2312yes—
43C23×C4×C11C2311yescharacteristic
44C23×C4×C11C2312yes—
45C23×C4×C11C2311yescharacteristic
46C23×C4×C11C2311yescharacteristic
47C23×Dic11C2312yes—
48C23×Dic11C2311yescharacteristic
49C23×Dic11C2311yescharacteristic
50C23×Dic11C2311yescharacteristic
51C23×Dic11C2311yescharacteristic
52C22×D44—22no—
53C22×D44—22no—
54C22×D44—22no—
55C22×D44—22no—
56C22×D44—22no—
57C22×D44—22no—
58C22×D44C2×C414yes—
59C2×C11×C4⋊C4—22no—
60C2×C11×C4⋊C4—22no—
61C2×C11×C4⋊C4—22no—
62C2×C11×C4⋊C4—22no—
63C2×C11×C4⋊C4C2×C414yes—
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×C11D414yes—
71C2×(C2×D11)⋊C4—24no—
72C2×(C2×D11)⋊C4—24no—
73C2×(C2×D11)⋊C4—24no—
74C2×(C2×D11)⋊C4—24no—
75C2×(C2×D11)⋊C4—24no—
76C2×(C2×D11)⋊C4—24no—
77C2×(C2×D11)⋊C4—24no—
78C2×(C2×D11)⋊C4—24no—
79C2×(C2×D11)⋊C4—24no—
80C2×(C2×D11)⋊C4—24no—
81C2×(C2×D11)⋊C4—42no—
82C2×(C2×D11)⋊C4—42no—
83C2×(C2×D11)⋊C4—42no—
84C2×(C2×D11)⋊C4—42no—
85C2×(C2×D11)⋊C4—42no—
86C2×(C2×D11)⋊C4—42no—
87C2×(C2×D11)⋊C4C2×C418yes—
88C2×(C2×D11)⋊C4C2×C418yes—
89C2×C4⋊Dic11—22no—
90C2×C4⋊Dic11—22no—
91C2×C4⋊Dic11—22no—
92C2×Dic11⋊C4—22no—
93C2×Dic11⋊C4—22no—
94C2×Dic11⋊C4—22no—
95C2×Dic11⋊C4—22no—
96C2×Dic11⋊C4—22no—
97C2×Dic11⋊C4D414yescomplemented
98C2×C4×Dic11—22no—
99C2×C4×Dic11—22no—
100C2×C4×Dic11—22no—
101C2×C4×Dic11—22no—
102C2×C4×Dic11—22no—
103C2×C4×Dic11C2×C414yes—
104C11×#95—24no—
105C11⋊#95—22no—
106C11⋊#95—22no—
107C11⋊#95—24no—
108C11⋊#95—24no—
109C11⋊#95—42no—
110C11⋊#95—42no—
111#14022—111nomaximal, Sylow
112C24×C11C2411yescharacteristic
113C23×D11—22no—
114C23×D11—22no—
115C23×D11—22no—
116C23×D11—22no—
117C23×D11—22no—
118C23×D11—22no—
119C23×D11—22no—
120C23×D11—22no—
121C23×D11—22no—
122C23×D11—22no—
123C23×D11—22no—
124C23×D11—22no—
125C23×D11—22no—
126C23×D11—22no—
127C23×D11C22×C414yes—
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—21no—
135C22×C4×C11—22no—
136C22×C4×C11—21no—
137C22×C4×C11—21no—
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—22no—
145C22×C4×C11—22no—
146C22×C4×C11—21no—
147C22×C4×C11—21no—
148C22×C4×C11—22no—
149C22×C4×C11—22no—
150C22×C4×C11C22×C414yes—
151C22×C4×C11C22×C412yes—
152C22×C4×C11C2×D412yes—
153C22×C4×C11C2×D414yes—
154C22×C4×C11C2×D412yes—
155C22×C4×C11C2×D412yes—
156C22×C4×C11C2×D412yes—
157C22×C4×C11C2×D412yes—
158C22×C4×C11#4112yes—
159C22×C4×C11#4112yes—
160C22×C4×C11#4112yes—
161C22×C4×C11#4112yes—
162C22×C4×C11#4112yes—
163C22×Dic11—21no—
164C22×Dic11—21no—
165C22×Dic11—21no—
166C22×Dic11—21no—
167C22×Dic11—21no—
168C22×Dic11—21no—
169C22×Dic11—22no—
170C22×Dic11—22no—
171C22×Dic11—21no—
172C22×Dic11—21no—
173C22×Dic11—21no—
174C22×Dic11—21no—
175C22×Dic11—21no—
176C22×Dic11—21no—
177C22×Dic11—21no—
178C22×Dic11—21no—
179C22×Dic11—22no—
180C22×Dic11—22no—
181C22×Dic11—22no—
182C22×Dic11—21no—
183C22×Dic11—21no—
184C22×Dic11—21no—
185C22×Dic11—21no—
186C22×Dic11—21no—
187C22×Dic11—21no—
188C22×Dic11—22no—
189C22×Dic11—22no—
190C22×Dic11—21no—
191C22×Dic11—21no—
192C22×Dic11C22×C412yes—
193C22×Dic11C22×C412yes—
194C22×Dic11C2×D412yes—
195C22×Dic11C2×D412yes—
196C22×Dic11#4112yes—
197C22×Dic11#4112yes—
198C2×D44—28no—
199C2×D44—28no—
200C2×D44—28no—
201C2×D44—44no—
202C2×D44—44no—
203C2×D44—44no—
204C2×D44—44no—
205C11×C4⋊C4—28no—
206C11×C4⋊C4—28no—
207C42×C11—28no—
208C42×C11—48no—
209(C2×D11)⋊C4—216no—
210(C2×D11)⋊C4—48no—
211(C2×D11)⋊C4—48no—
212(C2×D11)⋊C4—48no—
213(C2×D11)⋊C4—48no—
214(C2×D11)⋊C4—48no—
215C4⋊Dic11—44no—
216Dic11⋊C4—28no—
217Dic11⋊C4—28no—
218C4×Dic11—28no—
219C4×Dic11—44no—
220C2×#390—111no—
221C2×#390—111no—
222C2×#390—111no—
223C2×#388—112no—
224C2×C4×C4⋊C4—111no—
225C2×C4×C4⋊C4D1111yescharacteristic, complemented
226#1440—112no—
227#1439—112no—
228#1437—112no—
229C4⋊#95—111no—
230C4⋊#95—111no—
231C23×C11C23×C411yescharacteristic
232C23×C11C22×D411yescharacteristic
233C23×C11C22×D411yescharacteristic
234C23×C11C22×D411yescharacteristic
235C23×C11C2×#4111yescharacteristic
236C23×C11C2×#4111yescharacteristic
237C23×C11C2×#4111yescharacteristic
238C23×C11C2×#4111yescharacteristic
239C23×C11C2×#4111yescharacteristic
240C23×C11C2×#4111yescharacteristic
241C23×C11C2×#4111yescharacteristic
242C23×C11H(5,𝔽2)11yescharacteristic
243C23×C11H(5,𝔽2)11yescharacteristic
244C23×C11H(5,𝔽2)11yescharacteristic
245C23×C112−1+411yescharacteristic
246C22×D11—24no—
247C22×D11—24no—
248C22×D11—24no—
249C22×D11—24no—
250C22×D11—24no—
251C22×D11—24no—
252C22×D11—24no—
253C22×D11—42no—
254C22×D11—42no—
255C22×D11—42no—
256C22×D11—42no—
257C22×D11—42no—
258C22×D11—42no—
259C22×D11—42no—
260C22×D11—42no—
261C22×D11—42no—
262C22×D11—42no—
263C22×D11—42no—
264C22×D11—42no—
265C22×D11—42no—
266C22×D11—42no—
267C22×D11—42no—
268C22×D11—42no—
269C22×D11—42no—
270C22×D11—42no—
271C22×D11—42no—
272C22×D11—42no—
273C22×D11—42no—
274C22×D11—42no—
275C22×D11—42no—
276C22×D11—42no—
277C22×D11—42no—
278C22×D11—42no—
279C22×D11—42no—
280C22×D11—42no—
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—22no—
291C2×C4×C11—24no—
292C2×C4×C11—22no—
293C2×C4×C11—22no—
294C2×C4×C11—24no—
295C2×C4×C11—24no—
296C2×C4×C11—42no—
297C2×C4×C11—42no—
298C2×C4×C11—42no—
299C2×C4×C11—41no—
300C2×C4×C11—42no—
301C2×C4×C11—42no—
302C2×C4×C11—42no—
303C2×C4×C11—41no—
304C2×C4×C11—41no—
305C2×C4×C11—41no—
306C2×C4×C11—42no—
307C2×C4×C11—42no—
308C2×C4×C11#11714yes—
309C2×C4×C11C4×D414yes—
310C2×C4×C11C4×D414yes—
311C2×C4×C11#12114yes—
312C2×C4×C11#12114yes—
313C2×C4×C11#12314yes—
314C2×C4×C11#12414yes—
315C2×C4×C11#12614yes—
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—22no—
326C2×Dic11—22no—
327C2×Dic11—22no—
328C2×Dic11—22no—
329C2×Dic11—22no—
330C2×Dic11—22no—
331C2×Dic11—41no—
332C2×Dic11—41no—
333C2×Dic11—41no—
334C2×Dic11—41no—
335C2×Dic11—41no—
336C2×Dic11—41no—
337C2×Dic11—41no—
338C2×Dic11—41no—
339C2×Dic11—41no—
340C2×Dic11—41no—
341C2×Dic11—41no—
342C2×Dic11—41no—
343C2×Dic11—42no—
344C2×Dic11—42no—
345C2×Dic11—42no—
346C2×Dic11—42no—
347C2×Dic11—42no—
348C2×Dic11—42no—
349C2×Dic11—42no—
350C2×Dic11C4×D414yes—
351D44—416no—
352C23×D4—111no—
353C22×C4⋊C4—111no—
354C22×C4⋊C4—111no—
355C22×C4⋊C4—111no—
356C22×C4⋊C4C2×D1111yescharacteristic
357C22×C4⋊C4C2×D1111yescharacteristic
358C22×C22⋊C4—112no—
359C22×C22⋊C4—112no—
360C22×C22⋊C4—112no—
361C22×C22⋊C4—112no—
362C22×C22⋊C4—112no—
363C22×C22⋊C4—112no—
364C22×C42—111no—
365C22×C42—111no—
366C22×C42C2×D1112yes—
367C22×C42C2×D1111yescharacteristic
368#390—118no—
369#390—224no—
370#390—224no—
371#388—228no—
372C4×C4⋊C4—24no—
373C4×C4⋊C4—224no—
374C2×#95—112no—
375C2×#95—112no—
376C2×#95—111no—
377C2×#95—111no—
378C2×#95—112no—
379C2×#95—112no—
380C2×#95C2×D1112yes—
381C22×C11C2×#11711yescharacteristic
382C22×C11C2×C4×D411yescharacteristic
383C22×C11C2×C4×D411yescharacteristic
384C22×C11C2×C4×D411yescharacteristic
385C22×C11C4×#4111yescharacteristic
386C22×C11#51811yescharacteristic
387C22×C11#52011yescharacteristic
388C22×C11C2×#12111yescharacteristic
389C22×C11C2×#12111yescharacteristic
390C22×C11C2×#12311yescharacteristic
391C22×C11#52511yescharacteristic
392C22×C11C2×#12411yescharacteristic
393C22×C11C2×#12611yescharacteristic
394C22×C11#52911yescharacteristic
395C22×C11#53211yescharacteristic
396C22×C11#53511yescharacteristic
397C22×C11#53711yescharacteristic
398C22×C11#54011yescharacteristic
399C22×C11#54211yescharacteristic
400C22×C11D4211yescharacteristic
401C22×C11#54611yescharacteristic
402C22×C11#54711yescharacteristic
403C22×C11#54811yescharacteristic
404C22×C11#55011yescharacteristic
405C22×C11#55011yescharacteristic
406C22×C11#55011yescharacteristic
407C22×C11#55311yescharacteristic
408C22×C11#55311yescharacteristic
409C22×C11#55511yescharacteristic
410C22×C11#55611yescharacteristic
411C22×C11#55611yescharacteristic
412C22×C11#55911yescharacteristic
413C22×C11#55911yescharacteristic
414C22×C11#55911yescharacteristic
415C22×C11#55911yescharacteristic
416C2×D11—44no—
417C2×D11—44no—
418C2×D11—44no—
419C2×D11—44no—
420C2×D11—44no—
421C2×D11—44no—
422C2×D11—44no—
423C2×D11—82no—
424C2×D11—82no—
425C2×D11—82no—
426C2×D11—82no—
427C2×D11—82no—
428C2×D11—82no—
429C2×D11—82no—
430C2×D11—82no—
431C4×C11—24no—
432C4×C11—44no—
433C4×C11—42no—
434C4×C11—44no—
435C4×C11#38818yescomplemented
436Dic11—24no—
437Dic11—42no—
438Dic11—42no—
439Dic11—42no—
440Dic11—82no—
441C25—112no—
442C22×D4—114no—
443C22×D4—222no—
444C22×D4—222no—
445C22×D4—222no—
446C22×D4—222no—
447C22×D4—222no—
448C22×D4—222no—
449C23×C4—111no—
450C23×C4—111no—
451C23×C4—111no—
452C23×C4—111no—
453C23×C4—112no—
454C23×C4C22×D1112yes—
455C23×C4C22×D1111yescharacteristic
456C23×C4C22×D1112yes—
457C23×C4C22×D1111yescharacteristic
458C23×C4C22×D1111yescharacteristic
459C2×C4⋊C4—22no—
460C2×C4⋊C4—22no—
461C2×C4⋊C4—22no—
462C2×C4⋊C4—22no—
463C2×C4⋊C4—114no—
464C2×C4⋊C4—222no—
465C2×C4⋊C4—222no—
466C2×C4⋊C4—222no—
467C2×C4⋊C4—222no—
468C2×C4⋊C4—222no—
469C2×C4⋊C4—222no—
470C2×C4⋊C4—222no—
471C2×C4⋊C4—222no—
472C2×C4⋊C4C4×D1114yes—
473C2×C4⋊C4C22⋊D1114yes—
474C2×C22⋊C4—118no—
475C2×C22⋊C4—118no—
476C2×C22⋊C4—224no—
477C2×C22⋊C4—224no—
478C2×C22⋊C4—224no—
479C2×C22⋊C4—224no—
480C2×C22⋊C4—224no—
481C2×C22⋊C4—224no—
482C2×C22⋊C4—224no—
483C2×C22⋊C4—224no—
484C2×C22⋊C4—224no—
485C2×C22⋊C4—224no—
486C2×C22⋊C4—442no—
487C2×C22⋊C4—442no—
488C2×C22⋊C4—442no—
489C2×C22⋊C4—442no—
490C2×C22⋊C4—442no—
491C2×C22⋊C4—442no—
492C2×C42—22no—
493C2×C42—22no—
494C2×C42—24no—
495C2×C42—24no—
496C2×C42—42no—
497C2×C42—114no—
498C2×C42—222no—
499C2×C42—222no—
500C2×C42—222no—
501C2×C42—222no—
502C2×C42—222no—
503C2×C42D4414yes—
504#95—24no—
505#95—224no—
506#95—224no—
507#95—222no—
508#95—222no—
509#95—442no—
510#95—442no—
511C2×C11C2×#38811yescharacteristic
512C2×C11C4×#12111yescharacteristic
513C2×C11#232411yescharacteristic
514C2×C11#235411yescharacteristic
515C2×C11#235711yescharacteristic
516C2×C11#236611yescharacteristic
517C2×C11#236711yescharacteristic
518C2×C11#241411yescharacteristic
519C2×C11#241611yescharacteristic
520C2×C11#244511yescharacteristic
521C2×C11#244811yescharacteristic
522C2×C11#251211yescharacteristic
523C2×C11#251311yescharacteristic
524C2×C11#254811yescharacteristic
525C2×C11#259211yescharacteristic
526D11—84no—
527C24—114no—
528C24—222no—
529C24—222no—
530C24—222no—
531C24—222no—
532C24—222no—
533C24—222no—
534C24—222no—
535C24—222no—
536C24—222no—
537C24—222no—
538C24—222no—
539C24—222no—
540C24—222no—
541C24—222no—
542C24C23×D1111yescharacteristic
543C2×D4—228no—
544C2×D4—228no—
545C2×D4—228no—
546C2×D4—444no—
547C2×D4—444no—
548C2×D4—444no—
549C2×D4—444no—
550C22×C4—21no—
551C22×C4—21no—
552C22×C4—21no—
553C22×C4—21no—
554C22×C4—21no—
555C22×C4—22no—
556C22×C4—22no—
557C22×C4—22no—
558C22×C4—22no—
559C22×C4—22no—
560C22×C4—22no—
561C22×C4—22no—
562C22×C4—22no—
563C22×C4—22no—
564C22×C4—21no—
565C22×C4—21no—
566C22×C4—22no—
567C22×C4—22no—
568C22×C4—21no—
569C22×C4—21no—
570C22×C4—21no—
571C22×C4—22no—
572C22×C4—112no—
573C22×C4—112no—
574C22×C4—112no—
575C22×C4—112no—
576C22×C4—112no—
577C22×C4—112no—
578C22×C4—221no—
579C22×C4—221no—
580C22×C4—221no—
581C22×C4—221no—
582C22×C4—221no—
583C22×C4—221no—
584C22×C4—221no—
585C22×C4—221no—
586C22×C4—221no—
587C22×C4—221no—
588C22×C4—221no—
589C22×C4—221no—
590C22×C4—221no—
591C22×C4—221no—
592C22×C4—221no—
593C22×C4—221no—
594C22×C4—221no—
595C22×C4—221no—
596C22×C4—221no—
597C22×C4—221no—
598C22×C4—221no—
599C22×C4—221no—
600C22×C4—222no—
601C22×C4—222no—
602C22×C4—222no—
603C22×C4—222no—
604C22×C4—222no—
605C22×C4—222no—
606C22×C4—222no—
607C22×C4C2×C4×D1114yes—
608C22×C4C2×C4×D1112yes—
609C22×C4C2×D4412yes—
610C22×C4C2×D4412yes—
611C22×C4C2×D4412yes—
612C22×C4#433912yes—
613C22×C4#433912yes—
614C22×C4#433912yes—
615C22×C4#433912yes—
616C22×C4D4×D1112yes—
617C22×C4#434312yes—
618C22×C4C2×C22⋊D1114yes—
619C22×C4C2×C22⋊D1112yes—
620C4⋊C4—28no—
621C4⋊C4—28no—
622C4⋊C4—228no—
623C4⋊C4—228no—
624C4⋊C4—444no—
625C22⋊C4—2216no—
626C22⋊C4—448no—
627C22⋊C4—448no—
628C22⋊C4—448no—
629C22⋊C4—448no—
630C22⋊C4—448no—
631C42—28no—
632C42—48no—
633C42—228no—
634C42—444no—
635C11#1402211yescharacteristic, complemented, Sylow
636C23—224no—
637C23—224no—
638C23—224no—
639C23—224no—
640C23—224no—
641C23—224no—
642C23—224no—
643C23—442no—
644C23—442no—
645C23—442no—
646C23—442no—
647C23—442no—
648C23—442no—
649C23—442no—
650C23—442no—
651C23—442no—
652C23—442no—
653C23—442no—
654C23—442no—
655C23—442no—
656C23—442no—
657C23—442no—
658C23—442no—
659C23—442no—
660C23—442no—
661C23—442no—
662C23—442no—
663C23—442no—
664C23—442no—
665C23—442no—
666C23—442no—
667C23—442no—
668C23—442no—
669C23—442no—
670C23—442no—
671C23C22×C4×D1111yescharacteristic
672C23C22×D4411yescharacteristic
673C23C2×#433911yescharacteristic
674C23C2×#433911yescharacteristic
675C23C2×#433911yescharacteristic
676C23C2×#433911yescharacteristic
677C23C2×D4×D1111yescharacteristic
678C23#6703711yescharacteristic
679C23C2×#434311yescharacteristic
680C23#6704011yescharacteristic
681C23#41×D1111yescharacteristic
682C23#41×D1111yescharacteristic
683C23#6704211yescharacteristic
684C23#6704211yescharacteristic
685C23C22×C22⋊D1111yescharacteristic
686D4—4416no—
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—24no—
696C2×C4—24no—
697C2×C4—22no—
698C2×C4—24no—
699C2×C4—24no—
700C2×C4—24no—
701C2×C4—24no—
702C2×C4—41no—
703C2×C4—41no—
704C2×C4—42no—
705C2×C4—42no—
706C2×C4—42no—
707C2×C4—42no—
708C2×C4—42no—
709C2×C4—42no—
710C2×C4—42no—
711C2×C4—41no—
712C2×C4—42no—
713C2×C4—41no—
714C2×C4—114no—
715C2×C4—222no—
716C2×C4—222no—
717C2×C4—222no—
718C2×C4—222no—
719C2×C4—222no—
720C2×C4—222no—
721C2×C4—222no—
722C2×C4—222no—
723C2×C4—222no—
724C2×C4—222no—
725C2×C4—222no—
726C2×C4—222no—
727C2×C4—222no—
728C2×C4—222no—
729C2×C4—222no—
730C2×C4—441no—
731C2×C4—441no—
732C2×C4—441no—
733C2×C4—441no—
734C2×C4—441no—
735C2×C4—441no—
736C2×C4—441no—
737C2×C4—441no—
738C2×C4—441no—
739C2×C4—441no—
740C2×C4—441no—
741C2×C4—441no—
742C2×C4—442no—
743C2×C4—442no—
744C2×C4—442no—
745C2×C4—442no—
746C2×C4—442no—
747C2×C4—442no—
748C2×C4—442no—
749C2×C4#6692514yes—
750C2×C4C4×D4414yes—
751C2×C4#6692814yes—
752C2×C4#6692914yes—
753C2×C4#6694814yes—
754C2×C4C4×C22⋊D1114yes—
755C2×C4#6698214yes—
756C2×C4#6698314yes—
757C22—444no—
758C22—444no—
759C22—444no—
760C22—444no—
761C22—444no—
762C22—444no—
763C22—444no—
764C22—882no—
765C22—882no—
766C22—882no—
767C22—882no—
768C22—882no—
769C22—882no—
770C22—882no—
771C22—882no—
772C22C2×#6692511yescharacteristic
773C22C2×C4×D4411yescharacteristic
774C22C2×#6692811yescharacteristic
775C22C2×#6692911yescharacteristic
776C22C2×#6694811yescharacteristic
777C22#1062303811yescharacteristic
778C22#1062304111yescharacteristic
779C22#1062304511yescharacteristic
780C22#1062305511yescharacteristic
781C22#1062305611yescharacteristic
782C22#1062306111yescharacteristic
783C22#1062306311yescharacteristic
784C22C4×D4×D1111yescharacteristic
785C22#1062307611yescharacteristic
786C22#1062307911yescharacteristic
787C22#1062308411yescharacteristic
788C22#1062308411yescharacteristic
789C22#1062309011yescharacteristic
790C22#1062309011yescharacteristic
791C22#1062309311yescharacteristic
792C22#1062309911yescharacteristic
793C22#1062309911yescharacteristic
794C22C4×#434311yescharacteristic
795C22#1062310511yescharacteristic
796C22#1062311111yescharacteristic
797C22#1062311311yescharacteristic
798C22#1062311611yescharacteristic
799C22#1062311611yescharacteristic
800C22C2×C4×C22⋊D1111yescharacteristic
801C22C2×#6698211yescharacteristic
802C22C2×#6698311yescharacteristic
803C22D4×C22⋊D1111yescharacteristic
804C22#1062334811yescharacteristic
805C22#1062336011yescharacteristic
806C22#1062336511yescharacteristic
807C4—24no—
808C4—44no—
809C4—42no—
810C4—44no—
811C4—224no—
812C4—442no—
813C4—442no—
814C4—442no—
815C4—882no—
816C4#1062255318yescomplemented
817C2—884no—
818C2C2×#1062255311yescharacteristic
819C2C4×#6694811yescharacteristic
820C2#1307131011yescharacteristic
821C2#1307156111yescharacteristic
822C2#1307158511yescharacteristic
823C2#1307167811yescharacteristic
824C2#1307168311yescharacteristic
825C2#1307202811yescharacteristic
826C2#1307205011yescharacteristic
827C2#1307237511yescharacteristic
828C2#1307240811yescharacteristic
829C2#1307319611yescharacteristic
830C2#1307320711yescharacteristic
831C2#1307361811yescharacteristic
832C2#1307409911yescharacteristic
subgroupG/H
center, FrattiniC24C23×D11
commutatorC23×C11C23×C4
FittingC2×C4×C11×C4⋊C4C2
socle, cosocleC24×C11C24
prime radicalC23×D44C22
hypercenterC2×C4×C4⋊C4D11
hypocenterC11#14022
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ C2×C4×C4⋊C4

Complements

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

NH ≅ G/Ntype
4. C2×#10622553C2semidirect
5. C2×C4×Dic11⋊C4C2semidirect
6. #13066864C2semidirect
7. #13066860C2semidirect
8. #13066854C2semidirect
9. #13066845C2semidirect
10. #13066845C2semidirect
11. C2×C4×C11×C4⋊C4C2semidirect
37. #10622601C4semidirect
97. C2×Dic11⋊C4D4semidirect
225. C2×C4×C4⋊C4D11semidirect
435. C4×C11#388semidirect
635. C11#14022semidirect
816. C4#10622553semidirect

Maximal subgroups

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

subgroupindex
C2×#106225522
C2×#106226012
C2×#106225532
C2×C4×Dic11⋊C42
#130668642
#130668602
#130668542
#130668452
C2×C4×C11×C4⋊C42
#1402211