Finite Group Databasebeta

← #14677212

Subgroups — #14677212

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×#10622834C211yesmaximal, characteristic
2C2×#10622834C211yesmaximal, characteristic
3C2×#10622557C212yesmaximal, complemented
4C2×C4⋊C4×Dic11C211yesmaximal, characteristic, complemented
5C2×C4×Dic11⋊C4C211yesmaximal, characteristic, complemented
6#13066863C212yesmaximal, complemented
7#13066859C212yesmaximal, complemented
8#13066853C212yesmaximal, complemented
9#13066846C211yesmaximal, characteristic, complemented
10#13066845C211yesmaximal, characteristic, complemented
11C2×C11×#390C211yesmaximal, characteristic
12C23×D4×C11C2211yescharacteristic
13C22×C11×C4⋊C4C2211yescharacteristic
14C22×C11×C22⋊C4C2212yes—
15C22×C11×C22⋊C4C2212yes—
16C22×C42×C11C2211yescharacteristic
17C22×C22⋊Dic11C2212yes—
18C22×C22⋊Dic11C2212yes—
19C22×C22⋊Dic11C2212yes—
20C22×C22⋊Dic11C2212yes—
21C22×C4⋊Dic11C2211yescharacteristic
22C22×C4⋊Dic11C2211yescharacteristic
23C22×Dic11⋊C4C2211yescharacteristic
24C22×Dic11⋊C4C2211yescharacteristic
25C22×C4×Dic11C2212yes—
26C22×C4×Dic11C2211yescharacteristic
27C22×C4×Dic11C2211yescharacteristic
28C11×#390—24no—
29#10622834—24no—
30#10622834C418yescomplemented
31C2×C11⋊#95C2212yes—
32C2×C11⋊#95C2212yes—
33C2×C11⋊#95C2211yescharacteristic
34C2×C11⋊#95C2211yescharacteristic
35C2×C11⋊#95C2212yes—
36C2×C11⋊#95C2212yes—
37C2×C11⋊#95C2212yes—
38C4⋊C4×Dic11—24no—
39#10622557—28no—
40C4×Dic11⋊C4—24no—
41C25×C11C2312yes—
42C22×D4×C11—22no—
43C22×D4×C11—22no—
44C22×D4×C11—22no—
45C22×D4×C11—22no—
46C22×D4×C11—22no—
47C22×D4×C11—22no—
48C22×D4×C11C2×C414yes—
49C23×C4×C11C2312yes—
50C23×C4×C11C2311yescharacteristic
51C23×C4×C11C2311yescharacteristic
52C23×C4×C11C2311yescharacteristic
53C23×Dic11C2312yes—
54C23×Dic11C2312yes—
55C23×Dic11C2311yescharacteristic
56C23×Dic11C2311yescharacteristic
57C23×Dic11C2311yescharacteristic
58C23×Dic11C2311yescharacteristic
59C2×C11×C4⋊C4—22no—
60C2×C11×C4⋊C4—22no—
61C2×C11×C4⋊C4D414yes—
62C2×C11×C22⋊C4—24no—
63C2×C11×C22⋊C4—24no—
64C2×C11×C22⋊C4—24no—
65C2×C11×C22⋊C4—24no—
66C2×C11×C22⋊C4—42no—
67C2×C11×C22⋊C4—42no—
68C2×C42×C11—22no—
69C2×C42×C11—22no—
70C2×C42×C11—22no—
71C2×C22⋊Dic11—24no—
72C2×C22⋊Dic11—24no—
73C2×C22⋊Dic11—24no—
74C2×C22⋊Dic11—24no—
75C2×C22⋊Dic11—24no—
76C2×C22⋊Dic11—24no—
77C2×C22⋊Dic11—42no—
78C2×C22⋊Dic11—42no—
79C2×C22⋊Dic11—42no—
80C2×C22⋊Dic11—42no—
81C2×C22⋊Dic11C2×C418yes—
82C2×C22⋊Dic11C2×C418yes—
83C2×C4⋊Dic11—22no—
84C2×C4⋊Dic11—22no—
85C2×C4⋊Dic11—22no—
86C2×C4⋊Dic11—22no—
87C2×C4⋊Dic11—22no—
88C2×C4⋊Dic11C2×C414yes—
89C2×Dic11⋊C4—22no—
90C2×Dic11⋊C4—22no—
91C2×Dic11⋊C4—22no—
92C2×Dic11⋊C4—22no—
93C2×Dic11⋊C4—22no—
94C2×Dic11⋊C4D414yescomplemented
95C2×C4×Dic11—22no—
96C2×C4×Dic11—22no—
97C2×C4×Dic11—22no—
98C2×C4×Dic11—22no—
99C2×C4×Dic11—24no—
100C2×C4×Dic11—24no—
101C2×C4×Dic11—42no—
102C2×C4×Dic11C2×C414yes—
103C2×C4×Dic11D414yes—
104C11⋊#95—24no—
105C11⋊#95—24no—
106C11⋊#95—22no—
107C11⋊#95—22no—
108C11⋊#95—24no—
109C11⋊#95—42no—
110C11⋊#95—42no—
111#14022—111nomaximal, Sylow
112C24×C11—22no—
113C24×C11—22no—
114C24×C11—22no—
115C24×C11—22no—
116C24×C11—22no—
117C24×C11—22no—
118C24×C11—22no—
119C24×C11—22no—
120C24×C11—22no—
121C24×C11—22no—
122C24×C11—22no—
123C24×C11—22no—
124C24×C11—22no—
125C24×C11—22no—
126C24×C11C22×C414yes—
127C24×C11C2411yescharacteristic
128C2×D4×C11—28no—
129C2×D4×C11—28no—
130C2×D4×C11—28no—
131C2×D4×C11—44no—
132C2×D4×C11—44no—
133C2×D4×C11—44no—
134C2×D4×C11—44no—
135C22×C4×C11—22no—
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—22no—
145C22×C4×C11—22no—
146C22×C4×C11—22no—
147C22×C4×C11—21no—
148C22×C4×C11—22no—
149C22×C4×C11—22no—
150C22×C4×C11—21no—
151C22×C4×C11—21no—
152C22×C4×C11—21no—
153C22×C4×C11C22×C412yes—
154C22×C4×C11C2×D412yes—
155C22×C4×C11C2×D414yes—
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—22no—
168C22×Dic11—22no—
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—22no—
183C22×Dic11—22no—
184C22×Dic11—21no—
185C22×Dic11—21no—
186C22×Dic11—22no—
187C22×Dic11—22no—
188C22×Dic11—21no—
189C22×Dic11—21no—
190C22×Dic11—21no—
191C22×Dic11—21no—
192C22×Dic11—22no—
193C22×Dic11—22no—
194C22×Dic11—21no—
195C22×Dic11—21no—
196C22×Dic11C22×C412yes—
197C22×Dic11C22×C414yes—
198C22×Dic11C22×C412yes—
199C22×Dic11C2×D412yes—
200C22×Dic11C2×D412yes—
201C22×Dic11C2×D412yes—
202C22×Dic11C2×D412yes—
203C22×Dic11#4112yes—
204C22×Dic11#4112yes—
205C11×C4⋊C4—28no—
206C11×C22⋊C4—48no—
207C11×C22⋊C4—48no—
208C42×C11—44no—
209C22⋊Dic11—216no—
210C22⋊Dic11—48no—
211C22⋊Dic11—48no—
212C22⋊Dic11—48no—
213C4⋊Dic11—28no—
214C4⋊Dic11—44no—
215Dic11⋊C4—28no—
216Dic11⋊C4—28no—
217C4×Dic11—28no—
218C4×Dic11—28no—
219C4×Dic11—48no—
220C2×#390—111no—
221C2×#390—111no—
222C2×#390D1111yescharacteristic
223C2×#388—112no—
224C2×C4×C4⋊C4—111no—
225C2×C4×C4⋊C4—111no—
226#1440—112no—
227#1439—112no—
228#1437—112no—
229C4⋊#95—111no—
230C4⋊#95—111no—
231C23×C11—24no—
232C23×C11—24no—
233C23×C11—24no—
234C23×C11—24no—
235C23×C11—24no—
236C23×C11—24no—
237C23×C11—24no—
238C23×C11—42no—
239C23×C11—42no—
240C23×C11—42no—
241C23×C11—42no—
242C23×C11—42no—
243C23×C11—42no—
244C23×C11—42no—
245C23×C11—42no—
246C23×C11—42no—
247C23×C11—42no—
248C23×C11—42no—
249C23×C11—42no—
250C23×C11—42no—
251C23×C11—42no—
252C23×C11—42no—
253C23×C11—42no—
254C23×C11—42no—
255C23×C11—42no—
256C23×C11—42no—
257C23×C11—42no—
258C23×C11—42no—
259C23×C11—42no—
260C23×C11—42no—
261C23×C11—42no—
262C23×C11—42no—
263C23×C11—42no—
264C23×C11—42no—
265C23×C11—42no—
266C23×C11C23×C411yescharacteristic
267C23×C11C22×D411yescharacteristic
268C23×C11C22×D411yescharacteristic
269C23×C11C22×D411yescharacteristic
270C23×C11C2×#4111yescharacteristic
271C23×C11C2×#4111yescharacteristic
272C23×C11C2×#4111yescharacteristic
273C23×C11C2×#4111yescharacteristic
274C23×C11C2×#4111yescharacteristic
275C23×C11C2×#4111yescharacteristic
276C23×C11C2×#4111yescharacteristic
277C23×C11H(5,𝔽2)11yescharacteristic
278C23×C11H(5,𝔽2)11yescharacteristic
279C23×C11H(5,𝔽2)11yescharacteristic
280C23×C112−1+411yescharacteristic
281D4×C11—416no—
282C2×C4×C11—22no—
283C2×C4×C11—24no—
284C2×C4×C11—22no—
285C2×C4×C11—24no—
286C2×C4×C11—22no—
287C2×C4×C11—22no—
288C2×C4×C11—24no—
289C2×C4×C11—22no—
290C2×C4×C11—22no—
291C2×C4×C11—41no—
292C2×C4×C11—41no—
293C2×C4×C11—42no—
294C2×C4×C11—41no—
295C2×C4×C11—41no—
296C2×C4×C11—42no—
297C2×C4×C11—41no—
298C2×C4×C11—42no—
299C2×C4×C11—41no—
300C2×C4×C11—41no—
301C2×C4×C11—41no—
302C2×C4×C11—42no—
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—22no—
323C2×Dic11—24no—
324C2×Dic11—24no—
325C2×Dic11—22no—
326C2×Dic11—24no—
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—42no—
336C2×Dic11—41no—
337C2×Dic11—42no—
338C2×Dic11—42no—
339C2×Dic11—41no—
340C2×Dic11—41no—
341C2×Dic11—41no—
342C2×Dic11—42no—
343C2×Dic11—42no—
344C2×Dic11—42no—
345C2×Dic11—42no—
346C2×Dic11—42no—
347C2×Dic11—42no—
348C2×Dic11—42no—
349C2×Dic11—42no—
350C2×Dic11C4×D414yes—
351C2×Dic11#12114yes—
352C23×D4C2×D1111yescharacteristic
353C22×C4⋊C4—111no—
354C22×C4⋊C4—111no—
355C22×C4⋊C4—111no—
356C22×C4⋊C4—111no—
357C22×C4⋊C4C2×D1111yescharacteristic
358C22×C22⋊C4—112no—
359C22×C22⋊C4—112no—
360C22×C22⋊C4—112no—
361C22×C22⋊C4—112no—
362C22×C22⋊C4C2×D1112yes—
363C22×C22⋊C4C2×D1112yes—
364C22×C42—111no—
365C22×C42—111no—
366C22×C42—112no—
367C22×C42C2×D1111yescharacteristic
368#390—24no—
369#390—118no—
370#390—224no—
371#388—228no—
372C4×C4⋊C4—224no—
373C4×C4⋊C4—224no—
374C2×#95—112no—
375C2×#95—112no—
376C2×#95—111no—
377C2×#95—112no—
378C2×#95—111no—
379C2×#95—112no—
380C2×#95—112no—
381C22×C11—44no—
382C22×C11—44no—
383C22×C11—44no—
384C22×C11—44no—
385C22×C11—44no—
386C22×C11—44no—
387C22×C11—44no—
388C22×C11—82no—
389C22×C11—82no—
390C22×C11—82no—
391C22×C11—82no—
392C22×C11—82no—
393C22×C11—82no—
394C22×C11—82no—
395C22×C11—82no—
396C22×C11C2×#11711yescharacteristic
397C22×C11C2×C4×D411yescharacteristic
398C22×C11C2×C4×D411yescharacteristic
399C22×C11C2×C4×D411yescharacteristic
400C22×C11C4×#4111yescharacteristic
401C22×C11#51811yescharacteristic
402C22×C11#52011yescharacteristic
403C22×C11C2×#12111yescharacteristic
404C22×C11C2×#12111yescharacteristic
405C22×C11C2×#12311yescharacteristic
406C22×C11#52511yescharacteristic
407C22×C11C2×#12411yescharacteristic
408C22×C11C2×#12611yescharacteristic
409C22×C11#52911yescharacteristic
410C22×C11#53211yescharacteristic
411C22×C11#53511yescharacteristic
412C22×C11#53711yescharacteristic
413C22×C11#54011yescharacteristic
414C22×C11#54211yescharacteristic
415C22×C11D4211yescharacteristic
416C22×C11#54611yescharacteristic
417C22×C11#54711yescharacteristic
418C22×C11#54811yescharacteristic
419C22×C11#55011yescharacteristic
420C22×C11#55011yescharacteristic
421C22×C11#55011yescharacteristic
422C22×C11#55311yescharacteristic
423C22×C11#55311yescharacteristic
424C22×C11#55511yescharacteristic
425C22×C11#55611yescharacteristic
426C22×C11#55611yescharacteristic
427C22×C11#55911yescharacteristic
428C22×C11#55911yescharacteristic
429C22×C11#55911yescharacteristic
430C22×C11#55911yescharacteristic
431C4×C11—42no—
432C4×C11—42no—
433C4×C11—44no—
434C4×C11#38818yescomplemented
435Dic11—24no—
436Dic11—24no—
437Dic11—42no—
438Dic11—44no—
439Dic11—42no—
440Dic11—82no—
441C25C22×D1112yes—
442C22×D4—22no—
443C22×D4—22no—
444C22×D4—22no—
445C22×D4—22no—
446C22×D4—22no—
447C22×D4—22no—
448C22×D4C4×D1114yes—
449C23×C4—111no—
450C23×C4—111no—
451C23×C4—112no—
452C23×C4—111no—
453C23×C4—111no—
454C23×C4—112no—
455C23×C4C22×D1111yescharacteristic
456C23×C4C22×D1111yescharacteristic
457C23×C4C22×D1112yes—
458C23×C4C22×D1111yescharacteristic
459C2×C4⋊C4—22no—
460C2×C4⋊C4—22no—
461C2×C4⋊C4—114no—
462C2×C4⋊C4—114no—
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—222no—
470C2×C4⋊C4—222no—
471C2×C4⋊C4—222no—
472C2×C4⋊C4—222no—
473C2×C4⋊C4C22⋊D1114yes—
474C2×C22⋊C4—24no—
475C2×C22⋊C4—24no—
476C2×C22⋊C4—24no—
477C2×C22⋊C4—24no—
478C2×C22⋊C4—42no—
479C2×C22⋊C4—42no—
480C2×C22⋊C4—118no—
481C2×C22⋊C4—118no—
482C2×C22⋊C4—224no—
483C2×C22⋊C4—224no—
484C2×C22⋊C4—224no—
485C2×C22⋊C4—224no—
486C2×C22⋊C4—224no—
487C2×C22⋊C4—224no—
488C2×C22⋊C4—442no—
489C2×C22⋊C4—442no—
490C2×C22⋊C4—442no—
491C2×C22⋊C4—442no—
492C2×C42—22no—
493C2×C42—22no—
494C2×C42—22no—
495C2×C42—114no—
496C2×C42—114no—
497C2×C42—222no—
498C2×C42—222no—
499C2×C42—222no—
500C2×C42—222no—
501C2×C42—224no—
502C2×C42—224no—
503C2×C42—442no—
504#95—222no—
505#95—222no—
506#95—224no—
507#95—224no—
508#95—224no—
509#95—442no—
510#95—442no—
511C2×C11—84no—
512C2×C11C2×#38811yescharacteristic
513C2×C11C4×#12111yescharacteristic
514C2×C11#232411yescharacteristic
515C2×C11#235411yescharacteristic
516C2×C11#235711yescharacteristic
517C2×C11#236611yescharacteristic
518C2×C11#236711yescharacteristic
519C2×C11#241411yescharacteristic
520C2×C11#241611yescharacteristic
521C2×C11#244511yescharacteristic
522C2×C11#244811yescharacteristic
523C2×C11#251211yescharacteristic
524C2×C11#251311yescharacteristic
525C2×C11#254811yescharacteristic
526C2×C11#259211yescharacteristic
527C24—22no—
528C24—22no—
529C24—22no—
530C24—22no—
531C24—22no—
532C24—22no—
533C24—22no—
534C24—22no—
535C24—22no—
536C24—22no—
537C24—22no—
538C24—22no—
539C24—22no—
540C24—22no—
541C24C2×C4×D1114yes—
542C24C23×D1111yescharacteristic
543C2×D4—28no—
544C2×D4—28no—
545C2×D4—28no—
546C2×D4—44no—
547C2×D4—44no—
548C2×D4—44no—
549C2×D4—44no—
550C22×C4—21no—
551C22×C4—21no—
552C22×C4—22no—
553C22×C4—21no—
554C22×C4—21no—
555C22×C4—22no—
556C22×C4—22no—
557C22×C4—22no—
558C22×C4—22no—
559C22×C4—22no—
560C22×C4—21no—
561C22×C4—21no—
562C22×C4—21no—
563C22×C4—21no—
564C22×C4—21no—
565C22×C4—21no—
566C22×C4—21no—
567C22×C4—21no—
568C22×C4—112no—
569C22×C4—112no—
570C22×C4—112no—
571C22×C4—112no—
572C22×C4—112no—
573C22×C4—112no—
574C22×C4—112no—
575C22×C4—114no—
576C22×C4—112no—
577C22×C4—221no—
578C22×C4—221no—
579C22×C4—221no—
580C22×C4—221no—
581C22×C4—221no—
582C22×C4—221no—
583C22×C4—221no—
584C22×C4—221no—
585C22×C4—222no—
586C22×C4—221no—
587C22×C4—222no—
588C22×C4—221no—
589C22×C4—221no—
590C22×C4—221no—
591C22×C4—221no—
592C22×C4—222no—
593C22×C4—221no—
594C22×C4—221no—
595C22×C4—222no—
596C22×C4—221no—
597C22×C4—222no—
598C22×C4—221no—
599C22×C4—221no—
600C22×C4—221no—
601C22×C4—221no—
602C22×C4—222no—
603C22×C4—222no—
604C22×C4—222no—
605C22×C4—222no—
606C22×C4—222no—
607C22×C4—222no—
608C22×C4—222no—
609C22×C4—222no—
610C22×C4C2×C4×D1112yes—
611C22×C4#433912yes—
612C22×C4D4×D1112yes—
613C22×C4D4×D1112yes—
614C22×C4#434112yes—
615C22×C4#434112yes—
616C22×C4#434112yes—
617C22×C4#434112yes—
618C22×C4C2×C22⋊D1114yes—
619C22×C4C2×C22⋊D1112yes—
620C4⋊C4—28no—
621C4⋊C4—228no—
622C4⋊C4—228no—
623C4⋊C4—228no—
624C4⋊C4—444no—
625C22⋊C4—48no—
626C22⋊C4—48no—
627C22⋊C4—2216no—
628C22⋊C4—448no—
629C22⋊C4—448no—
630C22⋊C4—448no—
631C42—44no—
632C42—228no—
633C42—228no—
634C42—448no—
635C11#1402211yescharacteristic, complemented, Sylow
636C23—24no—
637C23—24no—
638C23—24no—
639C23—24no—
640C23—24no—
641C23—24no—
642C23—24no—
643C23—42no—
644C23—42no—
645C23—42no—
646C23—42no—
647C23—42no—
648C23—42no—
649C23—42no—
650C23—42no—
651C23—42no—
652C23—42no—
653C23—42no—
654C23—42no—
655C23—42no—
656C23—42no—
657C23—42no—
658C23—42no—
659C23—42no—
660C23—42no—
661C23—42no—
662C23—42no—
663C23—42no—
664C23—42no—
665C23—42no—
666C23—42no—
667C23—42no—
668C23—42no—
669C23—42no—
670C23—42no—
671C23C22×C4×D1111yescharacteristic
672C23C2×#433911yescharacteristic
673C23C2×D4×D1111yescharacteristic
674C23C2×D4×D1111yescharacteristic
675C23C2×#434111yescharacteristic
676C23C2×#434111yescharacteristic
677C23C2×#434111yescharacteristic
678C23C2×#434111yescharacteristic
679C23#6703711yescharacteristic
680C23#6703711yescharacteristic
681C23#41×D1111yescharacteristic
682C23#41×D1111yescharacteristic
683C23#6704211yescharacteristic
684C23#6704311yescharacteristic
685C23C22×C22⋊D1111yescharacteristic
686D4—416no—
687C2×C4—24no—
688C2×C4—24no—
689C2×C4—22no—
690C2×C4—22no—
691C2×C4—24no—
692C2×C4—22no—
693C2×C4—22no—
694C2×C4—22no—
695C2×C4—22no—
696C2×C4—42no—
697C2×C4—42no—
698C2×C4—42no—
699C2×C4—42no—
700C2×C4—41no—
701C2×C4—41no—
702C2×C4—41no—
703C2×C4—41no—
704C2×C4—41no—
705C2×C4—41no—
706C2×C4—41no—
707C2×C4—41no—
708C2×C4—114no—
709C2×C4—114no—
710C2×C4—222no—
711C2×C4—222no—
712C2×C4—222no—
713C2×C4—222no—
714C2×C4—222no—
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—224no—
724C2×C4—224no—
725C2×C4—222no—
726C2×C4—222no—
727C2×C4—224no—
728C2×C4—222no—
729C2×C4—222no—
730C2×C4—222no—
731C2×C4—441no—
732C2×C4—442no—
733C2×C4—441no—
734C2×C4—442no—
735C2×C4—442no—
736C2×C4—442no—
737C2×C4—441no—
738C2×C4—441no—
739C2×C4—441no—
740C2×C4—441no—
741C2×C4—441no—
742C2×C4—441no—
743C2×C4—442no—
744C2×C4—442no—
745C2×C4—442no—
746C2×C4—442no—
747C2×C4—442no—
748C2×C4—442no—
749C2×C4—442no—
750C2×C4#6693014yes—
751C2×C4#6693214yes—
752C2×C4(C22⋊D11)⋊C414yes—
753C2×C4#6693814yes—
754C2×C4C4×C22⋊D1114yes—
755C2×C4#6698814yes—
756C2×C4#6699114yes—
757C22—44no—
758C22—44no—
759C22—44no—
760C22—44no—
761C22—44no—
762C22—44no—
763C22—44no—
764C22—82no—
765C22—82no—
766C22—82no—
767C22—82no—
768C22—82no—
769C22—82no—
770C22—82no—
771C22—82no—
772C22C2×#6693011yescharacteristic
773C22C2×#6693211yescharacteristic
774C22C2×(C22⋊D11)⋊C411yescharacteristic
775C22C2×#6693811yescharacteristic
776C22C4×#434111yescharacteristic
777C22#1062307311yescharacteristic
778C22C4×D4×D1111yescharacteristic
779C22#1062307611yescharacteristic
780C22#1062307711yescharacteristic
781C22#1062308411yescharacteristic
782C22#1062309011yescharacteristic
783C22#1062309011yescharacteristic
784C22D11×#12111yescharacteristic
785C22#1062313711yescharacteristic
786C22#1062313811yescharacteristic
787C22#1062313911yescharacteristic
788C22#1062314211yescharacteristic
789C22#1062314511yescharacteristic
790C22#1062314711yescharacteristic
791C22#1062314911yescharacteristic
792C22#1062320211yescharacteristic
793C22#1062321111yescharacteristic
794C22#1062321211yescharacteristic
795C22#1062321311yescharacteristic
796C22#1062324411yescharacteristic
797C22#1062324711yescharacteristic
798C22#1062324911yescharacteristic
799C22#1062325011yescharacteristic
800C22C2×C4×C22⋊D1111yescharacteristic
801C22C2×#6698811yescharacteristic
802C22C2×#6699111yescharacteristic
803C22D4×C22⋊D1111yescharacteristic
804C22#1062333711yescharacteristic
805C22#1062336211yescharacteristic
806C22#1062336511yescharacteristic
807C4—42no—
808C4—42no—
809C4—44no—
810C4—224no—
811C4—224no—
812C4—444no—
813C4—442no—
814C4—442no—
815C4—882no—
816C4#1062255718yescomplemented
817C2—84no—
818C2C2×#1062255711yescharacteristic
819C2#1307113211yescharacteristic
820C2#1307131211yescharacteristic
821C2#1307156411yescharacteristic
822C2#1307158811yescharacteristic
823C2#1307167811yescharacteristic
824C2#1307168911yescharacteristic
825C2#1307203011yescharacteristic
826C2#1307205211yescharacteristic
827C2#1307237711yescharacteristic
828C2#1307241011yescharacteristic
829C2#1307320411yescharacteristic
830C2#1307321511yescharacteristic
831C2#1307361711yescharacteristic
832C2#1307410111yescharacteristic
subgroupG/H
center, FrattiniC24C23×D11
commutatorC23×C11C23×C4
FittingC2×C11×#390C2
socle, cosocleC24×C11C24
prime radicalC23×D4×C11C22
hypercenterC2×#390D11
hypocenterC11#14022
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ C2×#390

Complements

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

NH ≅ G/Ntype
3. C2×#10622557C2semidirect
4. C2×C4⋊C4×Dic11C2semidirect
5. C2×C4×Dic11⋊C4C2semidirect
6. #13066863C2semidirect
7. #13066859C2semidirect
8. #13066853C2semidirect
9. #13066846C2semidirect
10. #13066845C2semidirect
30. #10622834C4semidirect
94. C2×Dic11⋊C4D4semidirect
434. C4×C11#388semidirect
635. C11#14022semidirect
816. C4#10622557semidirect

Maximal subgroups

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

subgroupindex
C2×#106228342
C2×#106225572
C2×C4⋊C4×Dic112
C2×C4×Dic11⋊C42
#130668632
#130668592
#130668532
#130668462
#130668452
C2×C11×#3902
#1402211