Finite Group Databasebeta

← #14680200

Subgroups — #14680200

Order 2816.

1926 conjugacy classes of subgroups.

The subgroup lattice has 832 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#66925C211yesmaximal, characteristic
2C2×#10622598C211yesmaximal, characteristic, complemented
3C2×#10622541C211yesmaximal, characteristic, complemented
4C2×#10622600C211yesmaximal, characteristic
5C2×#10622600C211yesmaximal, characteristic
6#13066880C212yesmaximal, complemented
7#13066871C212yesmaximal, complemented
8#13066862C212yesmaximal
9#13066860C212yesmaximal
10#13066845C211yesmaximal, characteristic, complemented
11C11×C4⋊#95C211yesmaximal, characteristic, complemented
12C23×C4×D11C2211yescharacteristic
13C22×C11×C4⋊C4C2211yescharacteristic
14C22×C11×C4⋊C4C2211yescharacteristic
15C22×C42×C11C2211yescharacteristic
16C22×(C2×D11)⋊C4C2211yescharacteristic
17C22×(C2×D11)⋊C4C2211yescharacteristic
18C22×(C2×D11)⋊C4C2212yes—
19C22×(C2×D11)⋊C4C2212yes—
20C22×C4⋊Dic11C2211yescharacteristic
21C22×C4⋊Dic11C2211yescharacteristic
22C22×C4⋊Dic11C2212yes—
23C22×Dic11⋊C4C2211yescharacteristic
24C22×Dic11⋊C4C2211yescharacteristic
25C22×Dic11⋊C4C2212yes—
26C22×C4×Dic11C2211yescharacteristic
27C2×#66925—24no—
28C2×#66925—24no—
29C2×#66925—24no—
30C2×C11×#95C2212yes—
31C2×C11×#95C2212yes—
32C2×C11⋊#95C2212yes—
33C2×C11⋊#95C2212yes—
34C2×C11⋊#95C2212yes—
35C2×C11⋊#95C2212yes—
36C2×C11⋊#95C2212yes—
37C2×C11⋊#95C2212yes—
38#10622600—24no—
39#10622600C418yescomplemented
40#10622598—24no—
41#10622541—24no—
42C24×D11C2311yescharacteristic
43C23×C4×C11C2312yes—
44C23×C4×C11C2312yes—
45C23×C4×C11C2311yescharacteristic
46C23×C4×C11C2311yescharacteristic
47C23×C4×C11C2311yescharacteristic
48C23×Dic11C2312yes—
49C23×Dic11C2312yes—
50C23×Dic11C2311yescharacteristic
51C23×Dic11C2311yescharacteristic
52C23×Dic11C2311yescharacteristic
53C22×C4×D11—22no—
54C22×C4×D11—22no—
55C22×C4×D11—22no—
56C22×C4×D11—22no—
57C22×C4×D11C2×C414yes—
58C22×C4×D11D414yes—
59C22×C4×D11Q814yes—
60C2×C11×C4⋊C4—22no—
61C2×C11×C4⋊C4—22no—
62C2×C11×C4⋊C4—22no—
63C2×C11×C4⋊C4—22no—
64C2×C11×C4⋊C4—22no—
65C2×C11×C4⋊C4C2×C414yes—
66C2×C42×C11—22no—
67C2×C42×C11—22no—
68C2×C42×C11D414yes—
69C2×(C2×D11)⋊C4—22no—
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—42no—
77C2×(C2×D11)⋊C4—42no—
78C2×(C2×D11)⋊C4—42no—
79C2×(C2×D11)⋊C4—42no—
80C2×(C2×D11)⋊C4C2×C418yes—
81C2×C4⋊Dic11—22no—
82C2×C4⋊Dic11—22no—
83C2×C4⋊Dic11—22no—
84C2×C4⋊Dic11—22no—
85C2×C4⋊Dic11—22no—
86C2×C4⋊Dic11—24no—
87C2×C4⋊Dic11—42no—
88C2×C4⋊Dic11—42no—
89C2×C4⋊Dic11C2×C414yes—
90C2×Dic11⋊C4—22no—
91C2×Dic11⋊C4—22no—
92C2×Dic11⋊C4—22no—
93C2×Dic11⋊C4—22no—
94C2×Dic11⋊C4—22no—
95C2×Dic11⋊C4—22no—
96C2×Dic11⋊C4—24no—
97C2×Dic11⋊C4—42no—
98C2×Dic11⋊C4—42no—
99C2×C4×Dic11—22no—
100C2×C4×Dic11—22no—
101C2×C4×Dic11D414yes—
102#66925—232no—
103C11×#95—42no—
104C11×#95—42no—
105C11⋊#95—24no—
106C11⋊#95—24no—
107C11⋊#95—24no—
108C11⋊#95—42no—
109C11⋊#95—42no—
110C11⋊#95C2×C418yes—
111#14264—111nomaximal, Sylow
112C24×C11C2411yescharacteristic
113C23×D11—21no—
114C23×D11—21no—
115C23×D11—21no—
116C23×D11—21no—
117C23×D11—21no—
118C23×D11—21no—
119C23×D11—21no—
120C23×D11—21no—
121C23×D11—21no—
122C23×D11—21no—
123C23×D11—21no—
124C23×D11—21no—
125C23×D11C22×C412yes—
126C23×D11C2×D412yes—
127C23×D11C2×Q812yes—
128C22×C4×C11—22no—
129C22×C4×C11—21no—
130C22×C4×C11—21no—
131C22×C4×C11—21no—
132C22×C4×C11—21no—
133C22×C4×C11—22no—
134C22×C4×C11—21no—
135C22×C4×C11—21no—
136C22×C4×C11—22no—
137C22×C4×C11—22no—
138C22×C4×C11—21no—
139C22×C4×C11—21no—
140C22×C4×C11—22no—
141C22×C4×C11—22no—
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×C414yes—
154C22×C4×C11C22×C412yes—
155C22×C4×C11C2×D412yes—
156C22×C4×C11C2×D412yes—
157C22×C4×C11C2×D412yes—
158C22×C4×C11C2×D412yes—
159C22×C4×C11C2×D412yes—
160C22×C4×C11C2×Q812yes—
161C22×C4×C11#4112yes—
162C22×C4×C11#4112yes—
163C22×Dic11—21no—
164C22×Dic11—21no—
165C22×Dic11—22no—
166C22×Dic11—21no—
167C22×Dic11—21no—
168C22×Dic11—21no—
169C22×Dic11—21no—
170C22×Dic11—22no—
171C22×Dic11—22no—
172C22×Dic11—22no—
173C22×Dic11—21no—
174C22×Dic11—21no—
175C22×Dic11—22no—
176C22×Dic11—21no—
177C22×Dic11—21no—
178C22×Dic11—22no—
179C22×Dic11—22no—
180C22×Dic11—22no—
181C22×Dic11—21no—
182C22×Dic11—21no—
183C22×Dic11—22no—
184C22×Dic11—22no—
185C22×Dic11—22no—
186C22×Dic11—21no—
187C22×Dic11—22no—
188C22×Dic11—21no—
189C22×Dic11—21no—
190C22×Dic11—21no—
191C22×Dic11—22no—
192C22×Dic11C22×C414yes—
193C22×Dic11C22×C412yes—
194C22×Dic11C2×D412yes—
195C22×Dic11C2×D412yes—
196C22×Dic11C2×D412yes—
197C22×Dic11C2×Q812yes—
198C2×C4×D11—28no—
199C2×C4×D11—28no—
200C2×C4×D11—28no—
201C2×C4×D11—28no—
202C2×C4×D11—28no—
203C2×C4×D11—28no—
204C2×C4×D11C4⋊C4116yescomplemented
205C11×C4⋊C4—28no—
206C11×C4⋊C4—44no—
207C42×C11—28no—
208(C2×D11)⋊C4—28no—
209(C2×D11)⋊C4—28no—
210(C2×D11)⋊C4—48no—
211(C2×D11)⋊C4—48no—
212C4⋊Dic11—28no—
213C4⋊Dic11—48no—
214C4⋊Dic11—44no—
215Dic11⋊C4—28no—
216Dic11⋊C4—28no—
217Dic11⋊C4—48no—
218C4×Dic11—28no—
219C22×#117—111no—
220C2×#389—111no—
221C2×#389—111no—
222C2×#380—111no—
223C2×#380—111no—
224#1444—112no—
225#1442—112no—
226#1439—112no—
227#1439—112no—
228C4⋊#95—111no—
229C4⋊#95D1111yescharacteristic, complemented
230C23×C11C23×C411yescharacteristic
231C23×C11C22×D411yescharacteristic
232C23×C11C22×D411yescharacteristic
233C23×C11C22×D411yescharacteristic
234C23×C11C22×Q811yescharacteristic
235C23×C11C2×#4111yescharacteristic
236C23×C11C2×#4111yescharacteristic
237C23×C11H(5,𝔽2)11yescharacteristic
238C23×C11H(5,𝔽2)11yescharacteristic
239C23×C11H(5,𝔽2)11yescharacteristic
240C23×C11H(5,𝔽2)11yescharacteristic
241C23×C112−1+411yescharacteristic
242C23×C112−1+411yescharacteristic
243C23×C112−1+411yescharacteristic
244C23×C112−1+411yescharacteristic
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—22no—
255C22×D11—22no—
256C22×D11—22no—
257C22×D11—22no—
258C22×D11—22no—
259C22×D11—22no—
260C22×D11—22no—
261C22×D11—22no—
262C22×D11—22no—
263C22×D11—41no—
264C22×D11—41no—
265C22×D11—41no—
266C22×D11—41no—
267C22×D11—41no—
268C22×D11—41no—
269C22×D11—41no—
270C22×D11—41no—
271C22×D11—41no—
272C22×D11—41no—
273C22×D11—41no—
274C22×D11—41no—
275C22×D11—41no—
276C22×D11—41no—
277C22×D11—41no—
278C22×D11—41no—
279C22×D11C2×C4⋊C414yes—
280C2×C4×C11—24no—
281C2×C4×C11—24no—
282C2×C4×C11—24no—
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—42no—
290C2×C4×C11—41no—
291C2×C4×C11—41no—
292C2×C4×C11—41no—
293C2×C4×C11—41no—
294C2×C4×C11—42no—
295C2×C4×C11—41no—
296C2×C4×C11—41no—
297C2×C4×C11—41no—
298C2×C4×C11—41no—
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×C11—42no—
306C2×C4×C11—42no—
307C2×C4×C11—42no—
308C2×C4×C11C2×C4⋊C414yes—
309C2×C4×C11C4×D414yes—
310C2×C4×C11C4×D414yes—
311C2×C4×C11#12014yes—
312C2×C4×C11C22⋊Q814yes—
313C2×C4×C11C22⋊Q814yes—
314C2×C4×C11#12314yes—
315C2×Dic11—22no—
316C2×Dic11—22no—
317C2×Dic11—22no—
318C2×Dic11—22no—
319C2×Dic11—22no—
320C2×Dic11—22no—
321C2×Dic11—24no—
322C2×Dic11—24no—
323C2×Dic11—24no—
324C2×Dic11—22no—
325C2×Dic11—22no—
326C2×Dic11—22no—
327C2×Dic11—22no—
328C2×Dic11—22no—
329C2×Dic11—22no—
330C2×Dic11—42no—
331C2×Dic11—41no—
332C2×Dic11—41no—
333C2×Dic11—41no—
334C2×Dic11—41no—
335C2×Dic11—42no—
336C2×Dic11—41no—
337C2×Dic11—41no—
338C2×Dic11—41no—
339C2×Dic11—41no—
340C2×Dic11—42no—
341C2×Dic11—42no—
342C2×Dic11—42no—
343C2×Dic11—42no—
344C2×Dic11—42no—
345C2×Dic11—42no—
346C2×Dic11—42no—
347C2×Dic11—42no—
348C2×Dic11—42no—
349C2×Dic11C2×C4⋊C414yes—
350C4×D11—232no—
351C24×C4—111no—
352C2×#117—224no—
353C2×#117—224no—
354C2×#117—224no—
355C22×C4⋊C4—111no—
356C22×C4⋊C4—111no—
357C22×C4⋊C4—111no—
358C22×C4⋊C4—111no—
359C22×C4⋊C4—112no—
360C22×C4⋊C4—112no—
361C22×C4⋊C4C2×D1111yescharacteristic
362C22×C4⋊C4C2×D1111yescharacteristic
363C22×C22⋊C4—112no—
364C22×C22⋊C4—111no—
365C22×C22⋊C4—111no—
366C22×C22⋊C4—112no—
367C22×C42—111no—
368C22×C42C2×D1111yescharacteristic
369#389—224no—
370#389—224no—
371#380—118no—
372#380—224no—
373C2×#95—112no—
374C2×#95—112no—
375C2×#95—112no—
376C2×#95—112no—
377C2×#95—112no—
378C2×#95—112no—
379C2×#95C2×D1112yes—
380C2×#95C2×D1112yes—
381C22×C11C22×C4⋊C411yescharacteristic
382C22×C11C2×C4×D411yescharacteristic
383C22×C11C2×C4×D411yescharacteristic
384C22×C11#51811yescharacteristic
385C22×C11#51911yescharacteristic
386C22×C11#52011yescharacteristic
387C22×C11#52011yescharacteristic
388C22×C11C2×#12011yescharacteristic
389C22×C11C2×C22⋊Q811yescharacteristic
390C22×C11C2×C22⋊Q811yescharacteristic
391C22×C11C2×#12311yescharacteristic
392C22×C11#53511yescharacteristic
393C22×C11#53511yescharacteristic
394C22×C11#53511yescharacteristic
395C22×C11#53611yescharacteristic
396C22×C11#53611yescharacteristic
397C22×C11#53611yescharacteristic
398C22×C11#53711yescharacteristic
399C22×C11#53711yescharacteristic
400C22×C11#53711yescharacteristic
401C22×C11#53711yescharacteristic
402C22×C11#53711yescharacteristic
403C22×C11#53711yescharacteristic
404C22×C11#54011yescharacteristic
405C22×C11#54011yescharacteristic
406C22×C11#54111yescharacteristic
407C22×C11#54111yescharacteristic
408C22×C11#54211yescharacteristic
409C22×C11#54211yescharacteristic
410C22×C11#54211yescharacteristic
411C22×C11#54211yescharacteristic
412C22×C11#54411yescharacteristic
413C22×C11#54411yescharacteristic
414C22×C11#54411yescharacteristic
415C22×C11#54411yescharacteristic
416C2×D11—24no—
417C2×D11—24no—
418C2×D11—24no—
419C2×D11—42no—
420C2×D11—42no—
421C2×D11—42no—
422C2×D11—42no—
423C2×D11—42no—
424C2×D11—42no—
425C2×D11—42no—
426C2×D11—42no—
427C2×D11—42no—
428C2×D11—42no—
429C2×D11—42no—
430C2×D11—42no—
431C4×C11—44no—
432C4×C11—42no—
433C4×C11—42no—
434C4×C11—82no—
435C4×C11#38518yes—
436Dic11—24no—
437Dic11—44no—
438Dic11—42no—
439Dic11—42no—
440Dic11—82no—
441C25—111no—
442C23×C4—111no—
443C23×C4—114no—
444C23×C4—114no—
445C23×C4—114no—
446C23×C4—111no—
447C23×C4—112no—
448C23×C4—111no—
449C23×C4—112no—
450C23×C4—222no—
451C23×C4—222no—
452C23×C4—222no—
453C23×C4—222no—
454C23×C4C22×D1112yes—
455C23×C4C22×D1112yes—
456C23×C4C22×D1111yescharacteristic
457C23×C4C22×D1111yescharacteristic
458C23×C4C22×D1111yescharacteristic
459#117—2232no—
460C2×C4⋊C4—22no—
461C2×C4⋊C4—22no—
462C2×C4⋊C4—22no—
463C2×C4⋊C4—22no—
464C2×C4⋊C4—22no—
465C2×C4⋊C4—114no—
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⋊C4—222no—
474C2×C4⋊C4—224no—
475C2×C4⋊C4—224no—
476C2×C4⋊C4—222no—
477C2×C4⋊C4—222no—
478C2×C4⋊C4—222no—
479C2×C4⋊C4—442no—
480C2×C4⋊C4—442no—
481C2×C4⋊C4—442no—
482C2×C4⋊C4—442no—
483C2×C4⋊C4C4×D1114yes—
484C2×C22⋊C4—118no—
485C2×C22⋊C4—222no—
486C2×C22⋊C4—222no—
487C2×C22⋊C4—222no—
488C2×C22⋊C4—222no—
489C2×C22⋊C4—222no—
490C2×C22⋊C4—222no—
491C2×C22⋊C4—224no—
492C2×C22⋊C4—442no—
493C2×C22⋊C4—442no—
494C2×C22⋊C4—442no—
495C2×C22⋊C4—442no—
496C2×C42—22no—
497C2×C42—22no—
498C2×C42—114no—
499C2×C42—222no—
500C2×C42—222no—
501C2×C42D4414yes—
502#95—42no—
503#95—42no—
504#95—118no—
505#95—224no—
506#95—224no—
507#95—224no—
508#95—442no—
509#95—442no—
510C2×C11C2×#38511yescharacteristic
511C2×C11#231611yescharacteristic
512C2×C11#231711yescharacteristic
513C2×C11#232311yescharacteristic
514C2×C11#232311yescharacteristic
515C2×C11#232411yescharacteristic
516C2×C11#232411yescharacteristic
517C2×C11#261511yescharacteristic
518C2×C11#261611yescharacteristic
519C2×C11#262411yescharacteristic
520C2×C11#262511yescharacteristic
521C2×C11#262811yescharacteristic
522C2×C11#262811yescharacteristic
523C2×C11#262911yescharacteristic
524C2×C11#262911yescharacteristic
525D11—44no—
526C24—112no—
527C24—112no—
528C24—112no—
529C24—221no—
530C24—221no—
531C24—221no—
532C24—221no—
533C24—221no—
534C24—221no—
535C24—221no—
536C24—221no—
537C24—221no—
538C24—221no—
539C24—221no—
540C24—221no—
541C24C23×D1111yescharacteristic
542C22×C4—22no—
543C22×C4—21no—
544C22×C4—21no—
545C22×C4—21no—
546C22×C4—21no—
547C22×C4—22no—
548C22×C4—21no—
549C22×C4—21no—
550C22×C4—22no—
551C22×C4—22no—
552C22×C4—21no—
553C22×C4—21no—
554C22×C4—22no—
555C22×C4—21no—
556C22×C4—21no—
557C22×C4—21no—
558C22×C4—21no—
559C22×C4—22no—
560C22×C4—22no—
561C22×C4—22no—
562C22×C4—22no—
563C22×C4—22no—
564C22×C4—22no—
565C22×C4—22no—
566C22×C4—22no—
567C22×C4—112no—
568C22×C4—112no—
569C22×C4—112no—
570C22×C4—1116no—
571C22×C4—114no—
572C22×C4—112no—
573C22×C4—112no—
574C22×C4—221no—
575C22×C4—221no—
576C22×C4—221no—
577C22×C4—221no—
578C22×C4—228no—
579C22×C4—228no—
580C22×C4—228no—
581C22×C4—228no—
582C22×C4—228no—
583C22×C4—228no—
584C22×C4—222no—
585C22×C4—221no—
586C22×C4—221no—
587C22×C4—222no—
588C22×C4—221no—
589C22×C4—221no—
590C22×C4—221no—
591C22×C4—222no—
592C22×C4—221no—
593C22×C4—222no—
594C22×C4—221no—
595C22×C4—221no—
596C22×C4—221no—
597C22×C4—222no—
598C22×C4—222no—
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×C4C2×C4×D1114yes—
610C22×C4C2×C4×D1112yes—
611C22×C4C2×D4412yes—
612C22×C4C2×D4412yes—
613C22×C4C2×D4412yes—
614C22×C4#433912yes—
615C22×C4D4×D1112yes—
616C22×C4D4×D1112yes—
617C22×C4#434112yes—
618C22×C4Q8×D1112yes—
619C4⋊C4—28no—
620C4⋊C4—44no—
621C4⋊C4—228no—
622C4⋊C4—228no—
623C4⋊C4—228no—
624C4⋊C4—448no—
625C4⋊C4—448no—
626C4⋊C4—444no—
627C22⋊C4—228no—
628C22⋊C4—228no—
629C22⋊C4—448no—
630C22⋊C4—448no—
631C42—28no—
632C42—228no—
633C11#1426411yescharacteristic, complemented, Sylow
634C23—114no—
635C23—222no—
636C23—222no—
637C23—222no—
638C23—222no—
639C23—222no—
640C23—222no—
641C23—222no—
642C23—222no—
643C23—222no—
644C23—222no—
645C23—222no—
646C23—222no—
647C23—222no—
648C23—222no—
649C23—222no—
650C23—222no—
651C23—222no—
652C23—222no—
653C23—441no—
654C23—441no—
655C23—441no—
656C23—441no—
657C23—441no—
658C23—441no—
659C23—441no—
660C23—441no—
661C23—441no—
662C23—441no—
663C23—441no—
664C23—441no—
665C23—441no—
666C23—441no—
667C23—441no—
668C23—441no—
669C23C22×C4×D1111yescharacteristic
670C23C22×D4411yescharacteristic
671C23C2×#433911yescharacteristic
672C23C2×D4×D1111yescharacteristic
673C23C2×D4×D1111yescharacteristic
674C23C2×#434111yescharacteristic
675C23#6703711yescharacteristic
676C23#6703711yescharacteristic
677C23C2×Q8×D1111yescharacteristic
678C23#6704011yescharacteristic
679C23#6704011yescharacteristic
680C23#6704211yescharacteristic
681C23#6704211yescharacteristic
682C23#6704311yescharacteristic
683C23#6704311yescharacteristic
684C2×C4—24no—
685C2×C4—22no—
686C2×C4—22no—
687C2×C4—22no—
688C2×C4—22no—
689C2×C4—22no—
690C2×C4—22no—
691C2×C4—24no—
692C2×C4—24no—
693C2×C4—42no—
694C2×C4—42no—
695C2×C4—41no—
696C2×C4—41no—
697C2×C4—41no—
698C2×C4—41no—
699C2×C4—42no—
700C2×C4—41no—
701C2×C4—41no—
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—42no—
712C2×C4—114no—
713C2×C4—222no—
714C2×C4—222no—
715C2×C4—222no—
716C2×C4—222no—
717C2×C4—222no—
718C2×C4—222no—
719C2×C4—2232no—
720C2×C4—224no—
721C2×C4—222no—
722C2×C4—222no—
723C2×C4—224no—
724C2×C4—224no—
725C2×C4—222no—
726C2×C4—222no—
727C2×C4—222no—
728C2×C4—222no—
729C2×C4—441no—
730C2×C4—441no—
731C2×C4—442no—
732C2×C4—442no—
733C2×C4—441no—
734C2×C4—441no—
735C2×C4—442no—
736C2×C4—442no—
737C2×C4—441no—
738C2×C4—441no—
739C2×C4—441no—
740C2×C4—441no—
741C2×C4—442no—
742C2×C4—442no—
743C2×C4—442no—
744C2×C4—442no—
745C2×C4—442no—
746C2×C4—442no—
747C2×C4—442no—
748C2×C4C4×D4414yes—
749C2×C4(C22⋊D11)⋊C414yes—
750C2×C4#6693514yes—
751C2×C4#6693614yes—
752C2×C4C4⋊C4×D1114yes—
753C2×C4#6694914yes—
754C2×C4#6695014yes—
755C22—224no—
756C22—224no—
757C22—224no—
758C22—442no—
759C22—442no—
760C22—442no—
761C22—442no—
762C22—442no—
763C22—442no—
764C22—442no—
765C22—442no—
766C22—442no—
767C22—442no—
768C22—442no—
769C22—442no—
770C22C2×C4×D4411yescharacteristic
771C22C2×(C22⋊D11)⋊C411yescharacteristic
772C22C2×#6693511yescharacteristic
773C22C2×#6693611yescharacteristic
774C22C2×C4⋊C4×D1111yescharacteristic
775C22C2×#6694911yescharacteristic
776C22C2×#6695011yescharacteristic
777C22#1062304111yescharacteristic
778C22#1062304111yescharacteristic
779C22#1062305611yescharacteristic
780C22#1062305711yescharacteristic
781C22#1062307611yescharacteristic
782C22#1062307711yescharacteristic
783C22#1062309211yescharacteristic
784C22#1062309311yescharacteristic
785C22#1062310311yescharacteristic
786C22#1062310511yescharacteristic
787C22#1062311311yescharacteristic
788C22#1062311411yescharacteristic
789C22#1062313811yescharacteristic
790C22#1062313811yescharacteristic
791C22#1062313911yescharacteristic
792C22#1062313911yescharacteristic
793C22#1062315911yescharacteristic
794C22#1062315911yescharacteristic
795C22#1062316011yescharacteristic
796C22#1062316011yescharacteristic
797C22#1062321311yescharacteristic
798C22#1062321311yescharacteristic
799C22#1062322011yescharacteristic
800C22#1062322011yescharacteristic
801C22#1062325011yescharacteristic
802C22#1062326011yescharacteristic
803C22#1062326011yescharacteristic
804C22#1062326211yescharacteristic
805C4—42no—
806C4—42no—
807C4—44no—
808C4—82no—
809C4—224no—
810C4—442no—
811C4—442no—
812C4—444no—
813C4—882no—
814C4#1062228118yes—
815C2—444no—
816C2C2×#1062228111yescharacteristic
817C2#1307123111yescharacteristic
818C2#1307123811yescharacteristic
819C2#1307129911yescharacteristic
820C2#1307130111yescharacteristic
821C2#1307131011yescharacteristic
822C2#1307131211yescharacteristic
823C2#1307434211yescharacteristic
824C2#1307434711yescharacteristic
825C2#1307440811yescharacteristic
826C2#1307441611yescharacteristic
827C2#1307444011yescharacteristic
828C2#1307444311yescharacteristic
829C2#1307444911yescharacteristic
830C2#1307445111yescharacteristic
subgroupG/H
center, FrattiniC24C23×D11
commutatorC23×C11C23×C4
FittingC11×C4⋊#95C2
socle, cosocleC24×C11C24
prime radicalC24×D11C23
hypercenterC4⋊#95D11
hypocenterC11#14264
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ C4⋊#95

Complements

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

NH ≅ G/Ntype
2. C2×#10622598C2semidirect
3. C2×#10622541C2semidirect
6. #13066880C2semidirect
7. #13066871C2semidirect
10. #13066845C2semidirect
11. C11×C4⋊#95C2semidirect
39. #10622600C4semidirect
204. C2×C4×D11C4⋊C4semidirect
229. C4⋊#95D11semidirect
633. C11#14264semidirect

Maximal subgroups

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

subgroupindex
C22×#669252
C2×#106225982
C2×#106225412
C2×#106226002
#130668802
#130668712
#130668622
#130668602
#130668452
C11×C4⋊#952
#1426411