Finite Group Databasebeta

← #14676106

Subgroups — #14676106

Order 2816.

2314 conjugacy classes of subgroups.

The subgroup lattice has 840 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×D4×Dic11C211yesmaximal, characteristic
2C2×#10622834C211yesmaximal, characteristic
3C2×#10622556C212yesmaximal, complemented
4#13066863C212yesmaximal, complemented
5#13066863C212yesmaximal, complemented
6#13066846C211yesmaximal, characteristic, complemented
7#13066845C211yesmaximal, characteristic, complemented
8#13066845C211yesmaximal, characteristic, complemented
9#13066838C212yesmaximal, complemented
10C4×C11⋊#95C211yesmaximal, characteristic, complemented
11C2×C11×#390C211yesmaximal, characteristic
12C23×D4×C11C2211yescharacteristic
13C24×Dic11C2212yes—
14C22×C11×C4⋊C4C2211yescharacteristic
15C22×C11×C22⋊C4C2212yes—
16C22×C11×C22⋊C4C2212yes—
17C22×C42×C11C2211yescharacteristic
18C22×C22⋊Dic11C2212yes—
19C22×C22⋊Dic11C2212yes—
20C22×C22⋊Dic11C2212yes—
21C2×D4×Dic11—24no—
22C2×D4×Dic11—24no—
23C2×D4×Dic11C418yescomplemented
24C22×C4⋊Dic11C2211yescharacteristic
25C22×C4⋊Dic11C2211yescharacteristic
26C22×C4×Dic11C2211yescharacteristic
27C22×C4×Dic11C2211yescharacteristic
28C11×#390—24no—
29#10622834—24no—
30C2×C11⋊#95C2211yescharacteristic
31C2×C11⋊#95C2211yescharacteristic
32C2×C11⋊#95C2211yescharacteristic
33C2×C11⋊#95C2212yes—
34C2×C11⋊#95C2212yes—
35C2×C11⋊#95C2212yes—
36C2×C11⋊#95C2212yes—
37C2×C11⋊#95C2212yes—
38C2×C11⋊#95C2212yes—
39C2×C11⋊#95C2211yescharacteristic
40#10622556—28no—
41C25×C11C2312yes—
42C22×D4×C11—22no—
43C22×D4×C11—22no—
44C22×D4×C11—22no—
45C22×D4×C11—22no—
46C22×D4×C11C2×C414yes—
47C22×D4×C11D414yes—
48C22×D4×C11D414yes—
49C23×C4×C11C2312yes—
50C23×C4×C11C2311yescharacteristic
51C23×C4×C11C2311yescharacteristic
52C23×C4×C11C2311yescharacteristic
53C23×Dic11—24no—
54C23×Dic11—24no—
55C23×Dic11—24no—
56C23×Dic11—24no—
57C23×Dic11—42no—
58C23×Dic11—42no—
59C23×Dic11C2×C418yes—
60C23×Dic11C2312yes—
61C23×Dic11C2311yescharacteristic
62C23×Dic11C2312yes—
63C23×Dic11C2311yescharacteristic
64C23×Dic11C2311yescharacteristic
65C23×Dic11C2311yescharacteristic
66C2×C11×C4⋊C4—22no—
67C2×C11×C4⋊C4—22no—
68C2×C11×C4⋊C4—22no—
69C2×C11×C22⋊C4—24no—
70C2×C11×C22⋊C4—24no—
71C2×C11×C22⋊C4—24no—
72C2×C11×C22⋊C4—24no—
73C2×C11×C22⋊C4—42no—
74C2×C11×C22⋊C4—42no—
75C2×C42×C11—22no—
76C2×C42×C11—22no—
77C2×C42×C11—22no—
78C2×C22⋊Dic11—24no—
79C2×C22⋊Dic11—24no—
80C2×C22⋊Dic11—24no—
81C2×C22⋊Dic11—24no—
82C2×C22⋊Dic11—24no—
83C2×C22⋊Dic11—24no—
84C2×C22⋊Dic11—42no—
85C2×C22⋊Dic11—42no—
86C2×C22⋊Dic11C2×C418yes—
87D4×Dic11—232no—
88C2×C4⋊Dic11—22no—
89C2×C4⋊Dic11—22no—
90C2×C4⋊Dic11—22no—
91C2×C4⋊Dic11—22no—
92C2×C4⋊Dic11—22no—
93C2×C4⋊Dic11C2×C414yes—
94C2×C4×Dic11—22no—
95C2×C4×Dic11—22no—
96C2×C4×Dic11—22no—
97C2×C4×Dic11—22no—
98C2×C4×Dic11—22no—
99C2×C4×Dic11C2×C414yes—
100C11⋊#95—24no—
101C11⋊#95—22no—
102C11⋊#95—24no—
103C11⋊#95—24no—
104C11⋊#95—22no—
105C11⋊#95—22no—
106C11⋊#95—42no—
107C11⋊#95—42no—
108C11⋊#95—42no—
109C11⋊#95D414yescomplemented
110#13916—111nomaximal, Sylow
111C24×C11—22no—
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×C11C22×C414yes—
124C24×C11C2×D414yes—
125C24×C11C2×D414yes—
126C24×C11C2411yescharacteristic
127C2×D4×C11—28no—
128C2×D4×C11—28no—
129C2×D4×C11—28no—
130C2×D4×C11—28no—
131C2×D4×C11—28no—
132C2×D4×C11—28no—
133C2×D4×C11C22⋊C4116yes—
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—22no—
147C22×C4×C11—22no—
148C22×C4×C11—22no—
149C22×C4×C11—22no—
150C22×C4×C11—22no—
151C22×C4×C11—22no—
152C22×C4×C11—22no—
153C22×C4×C11C22×C412yes—
154C22×C4×C11C2×D412yes—
155C22×C4×C11C2×D412yes—
156C22×C4×C11C2×D412yes—
157C22×C4×C11#4112yes—
158C22×C4×C11#4112yes—
159C22×C4×C11#4112yes—
160C22×C4×C11#4112yes—
161C22×C4×C11#4112yes—
162C22×Dic11—216no—
163C22×Dic11—216no—
164C22×Dic11—21no—
165C22×Dic11—21no—
166C22×Dic11—22no—
167C22×Dic11—21no—
168C22×Dic11—21no—
169C22×Dic11—21no—
170C22×Dic11—21no—
171C22×Dic11—22no—
172C22×Dic11—22no—
173C22×Dic11—22no—
174C22×Dic11—22no—
175C22×Dic11—21no—
176C22×Dic11—21no—
177C22×Dic11—21no—
178C22×Dic11—21no—
179C22×Dic11—21no—
180C22×Dic11—21no—
181C22×Dic11—21no—
182C22×Dic11—21no—
183C22×Dic11—22no—
184C22×Dic11—22no—
185C22×Dic11—22no—
186C22×Dic11—22no—
187C22×Dic11—21no—
188C22×Dic11—21no—
189C22×Dic11—21no—
190C22×Dic11—21no—
191C22×Dic11—22no—
192C22×Dic11—22no—
193C22×Dic11—21no—
194C22×Dic11—21no—
195C22×Dic11—22no—
196C22×Dic11—22no—
197C22×Dic11—21no—
198C22×Dic11—21no—
199C22×Dic11—48no—
200C22×Dic11—48no—
201C22×Dic11—48no—
202C22×Dic11—48no—
203C22×Dic11—48no—
204C22×Dic11C22×C412yes—
205C22×Dic11C22×C414yes—
206C22×Dic11C22×C412yes—
207C22×Dic11C2×D412yes—
208C22×Dic11C2×D412yes—
209C22×Dic11#4112yes—
210C22×Dic11#4112yes—
211C11×C4⋊C4—44no—
212C11×C22⋊C4—48no—
213C11×C22⋊C4—48no—
214C42×C11—44no—
215C22⋊Dic11—216no—
216C22⋊Dic11—48no—
217C22⋊Dic11—48no—
218C4⋊Dic11—28no—
219C4⋊Dic11—44no—
220C4×Dic11—28no—
221C4×Dic11—44no—
222C22×C4×D4—111no—
223C2×#390—111no—
224C2×#390D1111yescharacteristic
225C2×#381—112no—
226#1440—112no—
227#1440—112no—
228C4⋊#95—111no—
229C4⋊#95—111no—
230C4⋊#95—111no—
231C22⋊#95—112no—
232C4×#95—111no—
233C23×C11—24no—
234C23×C11—24no—
235C23×C11—24no—
236C23×C11—24no—
237C23×C11—24no—
238C23×C11—24no—
239C23×C11—24no—
240C23×C11—24no—
241C23×C11—24no—
242C23×C11—24no—
243C23×C11—24no—
244C23×C11—24no—
245C23×C11—24no—
246C23×C11—24no—
247C23×C11—24no—
248C23×C11—24no—
249C23×C11—24no—
250C23×C11—24no—
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×C11—42no—
267C23×C11C2×C22⋊C418yes—
268C23×C11C23×C411yescharacteristic
269C23×C11C22×D411yescharacteristic
270C23×C11C22×D411yescharacteristic
271C23×C11C22×D411yescharacteristic
272C23×C11C2×#4111yescharacteristic
273C23×C11C2×#4111yescharacteristic
274C23×C11C2×#4111yescharacteristic
275C23×C11C2×#4111yescharacteristic
276C23×C11C2×#4111yescharacteristic
277C23×C11C2×#4111yescharacteristic
278C23×C11C2×#4111yescharacteristic
279C23×C11H(5,𝔽2)11yescharacteristic
280C23×C11H(5,𝔽2)11yescharacteristic
281C23×C11H(5,𝔽2)11yescharacteristic
282C23×C112−1+411yescharacteristic
283D4×C11—232no—
284C2×C4×C11—22no—
285C2×C4×C11—22no—
286C2×C4×C11—22no—
287C2×C4×C11—22no—
288C2×C4×C11—22no—
289C2×C4×C11—22no—
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—42no—
299C2×C4×C11—42no—
300C2×C4×C11—42no—
301C2×C4×C11—42no—
302C2×C4×C11—42no—
303C2×C4×C11—42no—
304C2×C4×C11—42no—
305C2×C4×C11C2×C22⋊C414yes—
306C2×C4×C11#11714yes—
307C2×C4×C11#11714yes—
308C2×C4×C11#12314yes—
309C2×C4×C11#12314yes—
310C2×C4×C11#12314yes—
311C2×C4×C11#12314yes—
312C2×Dic11—22no—
313C2×Dic11—22no—
314C2×Dic11—22no—
315C2×Dic11—22no—
316C2×Dic11—22no—
317C2×Dic11—22no—
318C2×Dic11—22no—
319C2×Dic11—24no—
320C2×Dic11—24no—
321C2×Dic11—22no—
322C2×Dic11—24no—
323C2×Dic11—22no—
324C2×Dic11—22no—
325C2×Dic11—22no—
326C2×Dic11—22no—
327C2×Dic11—22no—
328C2×Dic11—22no—
329C2×Dic11—22no—
330C2×Dic11—432no—
331C2×Dic11—41no—
332C2×Dic11—41no—
333C2×Dic11—41no—
334C2×Dic11—41no—
335C2×Dic11—42no—
336C2×Dic11—42no—
337C2×Dic11—41no—
338C2×Dic11—41no—
339C2×Dic11—41no—
340C2×Dic11—42no—
341C2×Dic11—42no—
342C2×Dic11—41no—
343C2×Dic11—41no—
344C2×Dic11—41no—
345C2×Dic11—41no—
346C2×Dic11—41no—
347C2×Dic11—42no—
348C2×Dic11—42no—
349C2×Dic11—42no—
350C2×Dic11—42no—
351C2×Dic11—42no—
352C2×Dic11—42no—
353C2×Dic11—42no—
354C2×Dic11C4×D414yes—
355C23×D4C2×D1111yescharacteristic
356C24×C4—112no—
357C2×C4×D4—118no—
358C2×C4×D4—224no—
359C2×C4×D4—224no—
360C22×C4⋊C4—111no—
361C22×C4⋊C4—111no—
362C22×C4⋊C4C2×D1111yescharacteristic
363C22×C22⋊C4—112no—
364C22×C22⋊C4—112no—
365C22×C22⋊C4—112no—
366C22×C22⋊C4C2×D1112yes—
367C22×C22⋊C4C2×D1112yes—
368C22×C42—111no—
369C22×C42—111no—
370C22×C42C2×D1111yescharacteristic
371#390—24no—
372#390—224no—
373#381—228no—
374C2×#95—111no—
375C2×#95—111no—
376C2×#95—111no—
377C2×#95—111no—
378C2×#95—112no—
379C2×#95—112no—
380C2×#95—112no—
381C2×#95—112no—
382C2×#95—112no—
383C2×#95—112no—
384C22×C11—28no—
385C22×C11—28no—
386C22×C11—28no—
387C22×C11—44no—
388C22×C11—44no—
389C22×C11—44no—
390C22×C11—44no—
391C22×C11—44no—
392C22×C11—44no—
393C22×C11—44no—
394C22×C11—44no—
395C22×C11—44no—
396C22×C11—44no—
397C22×C11—44no—
398C22×C11—44no—
399C22×C11C22×C22⋊C411yescharacteristic
400C22×C11C2×#11711yescharacteristic
401C22×C11C2×#11711yescharacteristic
402C22×C11C2×C4×D411yescharacteristic
403C22×C11C4×#4111yescharacteristic
404C22×C11#51811yescharacteristic
405C22×C11#52011yescharacteristic
406C22×C11C2×#12311yescharacteristic
407C22×C11C2×#12311yescharacteristic
408C22×C11C2×#12311yescharacteristic
409C22×C11C2×#12311yescharacteristic
410C22×C11#52911yescharacteristic
411C22×C11#52911yescharacteristic
412C22×C11#53211yescharacteristic
413C22×C11#53211yescharacteristic
414C22×C11#54011yescharacteristic
415C22×C11#54011yescharacteristic
416C22×C11#54211yescharacteristic
417C22×C11#54211yescharacteristic
418C22×C11D4211yescharacteristic
419C22×C11D4211yescharacteristic
420C22×C11#54611yescharacteristic
421C22×C11#54611yescharacteristic
422C22×C11#54611yescharacteristic
423C22×C11#54611yescharacteristic
424C22×C11#54711yescharacteristic
425C22×C11#54711yescharacteristic
426C22×C11#54711yescharacteristic
427C22×C11#55011yescharacteristic
428C22×C11#55311yescharacteristic
429C22×C11#55311yescharacteristic
430C22×C11#55511yescharacteristic
431C22×C11#55611yescharacteristic
432C22×C11#55911yescharacteristic
433C22×C11#55911yescharacteristic
434C4×C11—42no—
435C4×C11—42no—
436C4×C11—82no—
437C4×C11#38118yescomplemented
438Dic11—24no—
439Dic11—44no—
440Dic11—42no—
441Dic11—42no—
442Dic11—42no—
443Dic11—82no—
444C25C22×D1112yes—
445C22×D4—22no—
446C22×D4—22no—
447C22×D4—22no—
448C22×D4—22no—
449C22×D4C4×D1114yes—
450C22×D4D4414yes—
451C22×D4C22⋊D1114yes—
452C23×C4—111no—
453C23×C4—111no—
454C23×C4—111no—
455C23×C4—111no—
456C23×C4—112no—
457C23×C4—118no—
458C23×C4—112no—
459C23×C4—224no—
460C23×C4—224no—
461C23×C4—224no—
462C23×C4—224no—
463C23×C4—442no—
464C23×C4—442no—
465C23×C4C22×D1112yes—
466C23×C4C22×D1111yescharacteristic
467C23×C4C22×D1111yescharacteristic
468C23×C4C22×D1111yescharacteristic
469C4×D4—2232no—
470C2×C4⋊C4—22no—
471C2×C4⋊C4—22no—
472C2×C4⋊C4—22no—
473C2×C4⋊C4—114no—
474C2×C4⋊C4—222no—
475C2×C4⋊C4—222no—
476C2×C4⋊C4—222no—
477C2×C4⋊C4—222no—
478C2×C4⋊C4—222no—
479C2×C22⋊C4—24no—
480C2×C22⋊C4—24no—
481C2×C22⋊C4—24no—
482C2×C22⋊C4—24no—
483C2×C22⋊C4—42no—
484C2×C22⋊C4—42no—
485C2×C22⋊C4—118no—
486C2×C22⋊C4—224no—
487C2×C22⋊C4—224no—
488C2×C22⋊C4—224no—
489C2×C22⋊C4—224no—
490C2×C22⋊C4—224no—
491C2×C22⋊C4—224no—
492C2×C22⋊C4—442no—
493C2×C22⋊C4—442no—
494C2×C42—22no—
495C2×C42—22no—
496C2×C42—22no—
497C2×C42—114no—
498C2×C42—222no—
499C2×C42—222no—
500C2×C42—222no—
501C2×C42—222no—
502C2×C42—222no—
503#95—114no—
504#95—222no—
505#95—222no—
506#95—224no—
507#95—224no—
508#95—224no—
509#95—222no—
510#95—442no—
511#95—442no—
512#95—442no—
513C2×C11—48no—
514C2×C11C2×#38111yescharacteristic
515C2×C11#229311yescharacteristic
516C2×C11#231911yescharacteristic
517C2×C11D4×C22⋊C411yescharacteristic
518C2×C11#233911yescharacteristic
519C2×C11#235411yescharacteristic
520C2×C11#235711yescharacteristic
521C2×C11#242011yescharacteristic
522C2×C11#242011yescharacteristic
523C2×C11#242211yescharacteristic
524C2×C11#242211yescharacteristic
525C2×C11#244511yescharacteristic
526C2×C11#244511yescharacteristic
527C2×C11#244711yescharacteristic
528C2×C11#244711yescharacteristic
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—
542C24C2×D4414yes—
543C24C2×C22⋊D1114yes—
544C24C23×D1111yescharacteristic
545C2×D4—28no—
546C2×D4—28no—
547C2×D4—28no—
548C2×D4—28no—
549C2×D4—28no—
550C2×D4—28no—
551C2×D4(C2×D11)⋊C4116yes—
552C22×C4—21no—
553C22×C4—21no—
554C22×C4—21no—
555C22×C4—21no—
556C22×C4—21no—
557C22×C4—21no—
558C22×C4—21no—
559C22×C4—21no—
560C22×C4—21no—
561C22×C4—21no—
562C22×C4—21no—
563C22×C4—21no—
564C22×C4—22no—
565C22×C4—22no—
566C22×C4—22no—
567C22×C4—22no—
568C22×C4—22no—
569C22×C4—22no—
570C22×C4—22no—
571C22×C4—112no—
572C22×C4—112no—
573C22×C4—112no—
574C22×C4—112no—
575C22×C4—114no—
576C22×C4—112no—
577C22×C4—112no—
578C22×C4—2216no—
579C22×C4—221no—
580C22×C4—221no—
581C22×C4—221no—
582C22×C4—221no—
583C22×C4—2216no—
584C22×C4—221no—
585C22×C4—221no—
586C22×C4—221no—
587C22×C4—222no—
588C22×C4—222no—
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—222no—
598C22×C4—221no—
599C22×C4—221no—
600C22×C4—221no—
601C22×C4—222no—
602C22×C4—222no—
603C22×C4—221no—
604C22×C4—221no—
605C22×C4—221no—
606C22×C4—221no—
607C22×C4—222no—
608C22×C4—222no—
609C22×C4—222no—
610C22×C4—222no—
611C22×C4—222no—
612C22×C4—222no—
613C22×C4—222no—
614C22×C4—222no—
615C22×C4—448no—
616C22×C4—448no—
617C22×C4—448no—
618C22×C4—448no—
619C22×C4—448no—
620C22×C4C2×C4×D1112yes—
621C22×C4C2×D4412yes—
622C22×C4D4×D1112yes—
623C22×C4#434112yes—
624C22×C4#434112yes—
625C22×C4#434112yes—
626C22×C4#434112yes—
627C22×C4#434112yes—
628C22×C4C2×C22⋊D1112yes—
629C4⋊C4—44no—
630C4⋊C4—228no—
631C4⋊C4—444no—
632C22⋊C4—48no—
633C22⋊C4—48no—
634C22⋊C4—2216no—
635C22⋊C4—448no—
636C22⋊C4—448no—
637C42—44no—
638C42—228no—
639C42—444no—
640C11#1391611yescharacteristic, complemented, Sylow
641C23—24no—
642C23—24no—
643C23—24no—
644C23—24no—
645C23—24no—
646C23—24no—
647C23—24no—
648C23—24no—
649C23—24no—
650C23—24no—
651C23—24no—
652C23—24no—
653C23—24no—
654C23—24no—
655C23—24no—
656C23—24no—
657C23—24no—
658C23—24no—
659C23—42no—
660C23—42no—
661C23—42no—
662C23—42no—
663C23—42no—
664C23—42no—
665C23—42no—
666C23—42no—
667C23—42no—
668C23—42no—
669C23—42no—
670C23—42no—
671C23—42no—
672C23—42no—
673C23—42no—
674C23—42no—
675C23C2×(C2×D11)⋊C418yes—
676C23C22×C4×D1111yescharacteristic
677C23C22×D4411yescharacteristic
678C23C2×D4×D1111yescharacteristic
679C23C2×#434111yescharacteristic
680C23C2×#434111yescharacteristic
681C23C2×#434111yescharacteristic
682C23C2×#434111yescharacteristic
683C23C2×#434111yescharacteristic
684C23#6703711yescharacteristic
685C23#6703711yescharacteristic
686C23#41×D1111yescharacteristic
687C23#41×D1111yescharacteristic
688C23#6704211yescharacteristic
689C23#6704311yescharacteristic
690C23C22×C22⋊D1111yescharacteristic
691D4—232no—
692C2×C4—22no—
693C2×C4—22no—
694C2×C4—22no—
695C2×C4—22no—
696C2×C4—22no—
697C2×C4—22no—
698C2×C4—41no—
699C2×C4—41no—
700C2×C4—41no—
701C2×C4—41no—
702C2×C4—41no—
703C2×C4—41no—
704C2×C4—41no—
705C2×C4—41no—
706C2×C4—42no—
707C2×C4—42no—
708C2×C4—42no—
709C2×C4—42no—
710C2×C4—42no—
711C2×C4—42no—
712C2×C4—42no—
713C2×C4—114no—
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—224no—
723C2×C4—222no—
724C2×C4—224no—
725C2×C4—224no—
726C2×C4—222no—
727C2×C4—222no—
728C2×C4—222no—
729C2×C4—222no—
730C2×C4—222no—
731C2×C4—222no—
732C2×C4—4432no—
733C2×C4—441no—
734C2×C4—441no—
735C2×C4—441no—
736C2×C4—442no—
737C2×C4—442no—
738C2×C4—441no—
739C2×C4—442no—
740C2×C4—441no—
741C2×C4—441no—
742C2×C4—441no—
743C2×C4—441no—
744C2×C4—441no—
745C2×C4—442no—
746C2×C4—441no—
747C2×C4—441no—
748C2×C4—441no—
749C2×C4—442no—
750C2×C4—442no—
751C2×C4—442no—
752C2×C4—442no—
753C2×C4—442no—
754C2×C4—442no—
755C2×C4—442no—
756C2×C4#6693014yes—
757C2×C4#6693014yes—
758C2×C4#6693914yes—
759C2×C4#6693914yes—
760C2×C4C2×(C2×D11)⋊C414yes—
761C2×C4#6698814yes—
762C2×C4#6698814yes—
763C22—28no—
764C22—28no—
765C22—28no—
766C22—44no—
767C22—44no—
768C22—44no—
769C22—44no—
770C22—44no—
771C22—44no—
772C22—44no—
773C22—44no—
774C22—44no—
775C22—44no—
776C22—44no—
777C22—44no—
778C22C2×#6693011yescharacteristic
779C22C2×#6693011yescharacteristic
780C22C2×#6693911yescharacteristic
781C22C2×#6693911yescharacteristic
782C22C4×#434111yescharacteristic
783C22C4×D4×D1111yescharacteristic
784C22#1062307611yescharacteristic
785C22#1062307711yescharacteristic
786C22D4×D4411yescharacteristic
787C22#1062308511yescharacteristic
788C22#1062308511yescharacteristic
789C22#1062308611yescharacteristic
790C22#1062312711yescharacteristic
791C22#1062313111yescharacteristic
792C22#1062313411yescharacteristic
793C22#1062314211yescharacteristic
794C22#1062314511yescharacteristic
795C22#1062314711yescharacteristic
796C22#1062314911yescharacteristic
797C22#1062315011yescharacteristic
798C22#1062320211yescharacteristic
799C22#1062321111yescharacteristic
800C22#1062321211yescharacteristic
801C22#1062321311yescharacteristic
802C22#1062324411yescharacteristic
803C22#1062324711yescharacteristic
804C22#1062324911yescharacteristic
805C22#1062325011yescharacteristic
806C22C22×(C2×D11)⋊C411yescharacteristic
807C22C2×#6698811yescharacteristic
808C22C2×#6698811yescharacteristic
809C22D4×C22⋊D1111yescharacteristic
810C22#1062333711yescharacteristic
811C22#1062335511yescharacteristic
812C22#1062336011yescharacteristic
813C4—42no—
814C4—42no—
815C4—82no—
816C4—224no—
817C4—442no—
818C4—444no—
819C4—442no—
820C4—442no—
821C4—882no—
822C4#1062255618yescomplemented
823C2—48no—
824C2C2×#1062255611yescharacteristic
825C2#1307107811yescharacteristic
826C2#1307125311yescharacteristic
827C2D4×(C2×D11)⋊C411yescharacteristic
828C2#1307144111yescharacteristic
829C2#1307156411yescharacteristic
830C2#1307158811yescharacteristic
831C2#1307210411yescharacteristic
832C2#1307210611yescharacteristic
833C2#1307212611yescharacteristic
834C2#1307212811yescharacteristic
835C2#1307237711yescharacteristic
836C2#1307237911yescharacteristic
837C2#1307239911yescharacteristic
838C2#1307240111yescharacteristic
subgroupG/H
center, FrattiniC24C23×D11
commutatorC23×C11C23×C4
FittingC2×C11×#390C2
socle, cosocleC24×C11C24
prime radicalC23×D4×C11C22
hypercenterC2×#390D11
hypocenterC11#13916
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ C2×#390

Complements

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

NH ≅ G/Ntype
3. C2×#10622556C2semidirect
4. #13066863C2semidirect
5. #13066863C2semidirect
6. #13066846C2semidirect
7. #13066845C2semidirect
8. #13066845C2semidirect
9. #13066838C2semidirect
10. C4×C11⋊#95C2semidirect
23. C2×D4×Dic11C4semidirect
109. C11⋊#95D4semidirect
437. C4×C11#381semidirect
640. C11#13916semidirect
822. C4#10622556semidirect

Maximal subgroups

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

subgroupindex
C22×D4×Dic112
C2×#106228342
C2×#106225562
#130668632
#130668462
#130668452
#130668382
C4×C11⋊#952
C2×C11×#3902
#1391611