Finite Group Databasebeta

← #14690473

Subgroups — #14690473

Order 2816.

1906 conjugacy classes of subgroups.

The subgroup lattice has 836 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622607C212yesmaximal, complemented
2C2×#10622552C211yesmaximal, characteristic
3C2×#10622601C211yesmaximal, characteristic
4C2×#10622601C211yesmaximal, characteristic
5C2×#10622598C211yesmaximal, characteristic, complemented
6C2×#10622586C211yesmaximal, characteristic, complemented
7#13066862C212yesmaximal, complemented
8#13066860C212yesmaximal, complemented
9#13066858C212yesmaximal, complemented
10C4×C11⋊#95C211yesmaximal, characteristic, complemented
11C2×C11×#389C211yesmaximal, characteristic, complemented
12C23×D44C2211yescharacteristic
13C22×C11×C4⋊C4C2212yes—
14C22×C11×C4⋊C4C2211yescharacteristic
15C22×C11×C4⋊C4C2211yescharacteristic
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⋊Dic11C2212yes—
24C22×C4⋊Dic11C2211yescharacteristic
25C22×Dic11⋊C4C2212yes—
26C22×C4×Dic11C2211yescharacteristic
27C22×C4×Dic11C2211yescharacteristic
28C11×#389—24no—
29C2×C11×#95C2212yes—
30C2×C11⋊#95C2211yescharacteristic
31C2×C11⋊#95C2211yescharacteristic
32C2×C11⋊#95C2211yescharacteristic
33C2×C11⋊#95C2212yes—
34C2×C11⋊#95C2212yes—
35C2×C11⋊#95C2211yescharacteristic
36#10622607—28no—
37#10622601—24no—
38#10622601—24no—
39#10622598—24no—
40#10622586—24no—
41#10622552—24no—
42C24×D11C2312yes—
43C23×C4×C11C2312yes—
44C23×C4×C11C2312yes—
45C23×C4×C11C2311yescharacteristic
46C23×C4×C11C2311yescharacteristic
47C23×C4×C11C2311yescharacteristic
48C23×Dic11C2311yescharacteristic
49C23×Dic11C2311yescharacteristic
50C23×Dic11C2312yes—
51C23×Dic11C2311yescharacteristic
52C23×Dic11C2311yescharacteristic
53C22×D44—22no—
54C22×D44—22no—
55C22×D44—22no—
56C22×D44—22no—
57C22×D44—22no—
58C22×D44—22no—
59C22×D44Q814yes—
60C2×C11×C4⋊C4—22no—
61C2×C11×C4⋊C4—22no—
62C2×C11×C4⋊C4—22no—
63C2×C11×C4⋊C4—22no—
64C2×C11×C4⋊C4—24no—
65C2×C11×C4⋊C4—24no—
66C2×C11×C4⋊C4—42no—
67C2×C11×C4⋊C4D414yes—
68C2×C11×C4⋊C4D414yes—
69C2×C42×C11—22no—
70C2×C42×C11—22no—
71C2×C42×C11—22no—
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—24no—
82C2×(C2×D11)⋊C4—24no—
83C2×(C2×D11)⋊C4—24no—
84C2×(C2×D11)⋊C4—42no—
85C2×(C2×D11)⋊C4—42no—
86C2×(C2×D11)⋊C4—42no—
87C2×(C2×D11)⋊C4—42no—
88C2×(C2×D11)⋊C4—42no—
89C2×(C2×D11)⋊C4—42no—
90C2×C4⋊Dic11—22no—
91C2×C4⋊Dic11—22no—
92C2×C4⋊Dic11—24no—
93C2×C4⋊Dic11—24no—
94C2×C4⋊Dic11—42no—
95C2×C4⋊Dic11D414yes—
96C2×Dic11⋊C4—24no—
97C2×Dic11⋊C4—24no—
98C2×Dic11⋊C4—42no—
99C2×C4×Dic11—22no—
100C2×C4×Dic11—22no—
101C2×C4×Dic11—22no—
102C2×C4×Dic11—22no—
103C2×C4×Dic11—22no—
104C2×C4×Dic11—22no—
105C11×#95—24no—
106C11⋊#95—24no—
107C11⋊#95—22no—
108C11⋊#95—24no—
109C11⋊#95—22no—
110C11⋊#95—22no—
111C11⋊#95D414yescomplemented
112#15141—111nomaximal, Sylow
113C24×C11C2411yescharacteristic
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×D11—22no—
128C23×D11C2×Q814yes—
129C22×C4×C11—22no—
130C22×C4×C11—21no—
131C22×C4×C11—22no—
132C22×C4×C11—22no—
133C22×C4×C11—22no—
134C22×C4×C11—21no—
135C22×C4×C11—21no—
136C22×C4×C11—21no—
137C22×C4×C11—21no—
138C22×C4×C11—21no—
139C22×C4×C11—22no—
140C22×C4×C11—22no—
141C22×C4×C11—21no—
142C22×C4×C11—21no—
143C22×C4×C11—22no—
144C22×C4×C11—22no—
145C22×C4×C11—22no—
146C22×C4×C11—22no—
147C22×C4×C11—21no—
148C22×C4×C11—21no—
149C22×C4×C11—22no—
150C22×C4×C11—22no—
151C22×C4×C11—21no—
152C22×C4×C11—21no—
153C22×C4×C11C2×D414yes—
154C22×C4×C11C2×D412yes—
155C22×C4×C11C2×D414yes—
156C22×C4×C11C2×D412yes—
157C22×C4×C11C2×D412yes—
158C22×C4×C11C2×D412yes—
159C22×C4×C11C2×Q812yes—
160C22×C4×C11#4112yes—
161C22×C4×C11#4112yes—
162C22×C4×C11#4112yes—
163C22×C4×C11#4112yes—
164C22×Dic11—21no—
165C22×Dic11—21no—
166C22×Dic11—22no—
167C22×Dic11—21no—
168C22×Dic11—21no—
169C22×Dic11—21no—
170C22×Dic11—21no—
171C22×Dic11—21no—
172C22×Dic11—21no—
173C22×Dic11—22no—
174C22×Dic11—21no—
175C22×Dic11—21no—
176C22×Dic11—21no—
177C22×Dic11—21no—
178C22×Dic11—21no—
179C22×Dic11—21no—
180C22×Dic11—21no—
181C22×Dic11—21no—
182C22×Dic11—22no—
183C22×Dic11—22no—
184C22×Dic11—21no—
185C22×Dic11—22no—
186C22×Dic11—21no—
187C22×Dic11—22no—
188C22×Dic11—21no—
189C22×Dic11—21no—
190C22×Dic11—21no—
191C22×Dic11—21no—
192C22×Dic11—21no—
193C22×Dic11—21no—
194C22×Dic11C2×D414yes—
195C22×Dic11C2×D412yes—
196C22×Dic11C2×D412yes—
197C22×Dic11#4112yes—
198C22×Dic11#4112yes—
199C2×D44—28no—
200C2×D44—28no—
201C2×D44—28no—
202C2×D44—44no—
203C2×D44—44no—
204C2×D44—44no—
205C2×D44—44no—
206C11×C4⋊C4—28no—
207C11×C4⋊C4—28no—
208C11×C4⋊C4—48no—
209C42×C11—44no—
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—
215(C2×D11)⋊C4—48no—
216C4⋊Dic11—28no—
217C4⋊Dic11—48no—
218Dic11⋊C4—48no—
219C4×Dic11—44no—
220C4×Dic11—44no—
221C2×#396—112no—
222C2×#390—111no—
223C2×#390—111no—
224C2×#390—111no—
225C2×#389—111no—
226C2×#389—111no—
227C2×#389D1111yescharacteristic, complemented
228#1439—112no—
229#1439—112no—
230#1439—112no—
231C4×#95—111no—
232C23×C11C22×D411yescharacteristic
233C23×C11C22×D411yescharacteristic
234C23×C11C22×D411yescharacteristic
235C23×C11C22×D411yescharacteristic
236C23×C11C22×Q811yescharacteristic
237C23×C11C2×#4111yescharacteristic
238C23×C11C2×#4111yescharacteristic
239C23×C11C2×#4111yescharacteristic
240C23×C11C2×#4111yescharacteristic
241C23×C11C2×#4111yescharacteristic
242C23×C11C2×#4111yescharacteristic
243C23×C11H(5,𝔽2)11yescharacteristic
244C23×C11H(5,𝔽2)11yescharacteristic
245C23×C11H(5,𝔽2)11yescharacteristic
246C23×C112−1+411yescharacteristic
247C22×D11—24no—
248C22×D11—24no—
249C22×D11—24no—
250C22×D11—24no—
251C22×D11—24no—
252C22×D11—24no—
253C22×D11—24no—
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—
281C22×D11—42no—
282C2×C4×C11—24no—
283C2×C4×C11—24no—
284C2×C4×C11—22no—
285C2×C4×C11—22no—
286C2×C4×C11—24no—
287C2×C4×C11—22no—
288C2×C4×C11—24no—
289C2×C4×C11—22no—
290C2×C4×C11—22no—
291C2×C4×C11—24no—
292C2×C4×C11—24no—
293C2×C4×C11—22no—
294C2×C4×C11—41no—
295C2×C4×C11—41no—
296C2×C4×C11—42no—
297C2×C4×C11—42no—
298C2×C4×C11—42no—
299C2×C4×C11—41no—
300C2×C4×C11—42no—
301C2×C4×C11—41no—
302C2×C4×C11—42no—
303C2×C4×C11—42no—
304C2×C4×C11—41no—
305C2×C4×C11—41no—
306C2×C4×C11—41no—
307C2×C4×C11—42no—
308C2×C4×C11—42no—
309C2×C4×C11—41no—
310C2×C4×C11#12114yes—
311C2×C4×C11#12114yes—
312C2×C4×C11#12114yes—
313C2×C4×C11C22⋊Q814yes—
314C2×C4×C11C22⋊Q814yes—
315C2×C4×C11C22⋊Q814yes—
316C2×C4×C11#12614yes—
317C2×Dic11—24no—
318C2×Dic11—22no—
319C2×Dic11—22no—
320C2×Dic11—22no—
321C2×Dic11—22no—
322C2×Dic11—22no—
323C2×Dic11—22no—
324C2×Dic11—24no—
325C2×Dic11—22no—
326C2×Dic11—22no—
327C2×Dic11—22no—
328C2×Dic11—22no—
329C2×Dic11—24no—
330C2×Dic11—22no—
331C2×Dic11—22no—
332C2×Dic11—41no—
333C2×Dic11—41no—
334C2×Dic11—41no—
335C2×Dic11—41no—
336C2×Dic11—42no—
337C2×Dic11—41no—
338C2×Dic11—41no—
339C2×Dic11—42no—
340C2×Dic11—41no—
341C2×Dic11—41no—
342C2×Dic11—42no—
343C2×Dic11—41no—
344C2×Dic11—41no—
345C2×Dic11—41no—
346C2×Dic11—41no—
347C2×Dic11—41no—
348C2×Dic11—42no—
349C2×Dic11—41no—
350C2×Dic11—41no—
351C2×Dic11—41no—
352D44—416no—
353C23×D4—111no—
354C22×C4⋊C4—111no—
355C22×C4⋊C4—112no—
356C22×C4⋊C4—112no—
357C22×C4⋊C4C2×D1112yes—
358C22×C4⋊C4C2×D1111yescharacteristic
359C22×C4⋊C4C2×D1111yescharacteristic
360C22×C22⋊C4—112no—
361C22×C22⋊C4—112no—
362C22×C22⋊C4—112no—
363C22×C22⋊C4—112no—
364C22×C22⋊C4—112no—
365C22×C22⋊C4—112no—
366C22×C42—111no—
367C22×C42—111no—
368C22×C42C2×D1111yescharacteristic
369#396—228no—
370#390—224no—
371#390—224no—
372#390—224no—
373#389—24no—
374#389—224no—
375#389—224no—
376C2×#95—111no—
377C2×#95—111no—
378C2×#95—111no—
379C2×#95—111no—
380C2×#95—112no—
381C2×#95—112no—
382C2×#95C2×D1112yes—
383C22×C11C2×#12111yescharacteristic
384C22×C11C2×#12111yescharacteristic
385C22×C11C2×#12111yescharacteristic
386C22×C11C2×C22⋊Q811yescharacteristic
387C22×C11C2×C22⋊Q811yescharacteristic
388C22×C11C2×C22⋊Q811yescharacteristic
389C22×C11C2×#12611yescharacteristic
390C22×C11#52911yescharacteristic
391C22×C11#52911yescharacteristic
392C22×C11#52911yescharacteristic
393C22×C11#53211yescharacteristic
394C22×C11#53211yescharacteristic
395C22×C11#53211yescharacteristic
396C22×C11#54011yescharacteristic
397C22×C11#54011yescharacteristic
398C22×C11#54011yescharacteristic
399C22×C11#54211yescharacteristic
400C22×C11#54211yescharacteristic
401C22×C11#54211yescharacteristic
402C22×C11D4211yescharacteristic
403C22×C11D4211yescharacteristic
404C22×C11D4211yescharacteristic
405C22×C11#54611yescharacteristic
406C22×C11#54611yescharacteristic
407C22×C11#54611yescharacteristic
408C22×C11#54811yescharacteristic
409C22×C11#54811yescharacteristic
410C22×C11#54811yescharacteristic
411C22×C11D4×Q811yescharacteristic
412C22×C11#55011yescharacteristic
413C22×C11#55011yescharacteristic
414C22×C11#55011yescharacteristic
415C22×C11#55411yescharacteristic
416C22×C11#55411yescharacteristic
417C22×C11#55411yescharacteristic
418C2×D11—44no—
419C2×D11—44no—
420C2×D11—44no—
421C2×D11—44no—
422C2×D11—44no—
423C2×D11—44no—
424C2×D11—44no—
425C2×D11—82no—
426C2×D11—82no—
427C2×D11—82no—
428C2×D11—82no—
429C2×D11—82no—
430C2×D11—82no—
431C2×D11—82no—
432C2×D11—82no—
433C4×C11—42no—
434C4×C11—44no—
435C4×C11—44no—
436C4×C11—42no—
437C4×C11#39618yescomplemented
438Dic11—42no—
439Dic11—42no—
440Dic11—42no—
441Dic11—44no—
442Dic11—42no—
443C25—112no—
444C22×D4—114no—
445C22×D4—222no—
446C22×D4—222no—
447C22×D4—222no—
448C22×D4—222no—
449C22×D4—222no—
450C22×D4—222no—
451C23×C4—112no—
452C23×C4—111no—
453C23×C4—111no—
454C23×C4—111no—
455C23×C4—111no—
456C23×C4C22×D1112yes—
457C23×C4C22×D1111yescharacteristic
458C23×C4C22×D1111yescharacteristic
459C23×C4C22×D1112yes—
460C23×C4C22×D1111yescharacteristic
461C2×C4⋊C4—22no—
462C2×C4⋊C4—22no—
463C2×C4⋊C4—22no—
464C2×C4⋊C4—22no—
465C2×C4⋊C4—24no—
466C2×C4⋊C4—24no—
467C2×C4⋊C4—42no—
468C2×C4⋊C4—114no—
469C2×C4⋊C4—222no—
470C2×C4⋊C4—222no—
471C2×C4⋊C4—224no—
472C2×C4⋊C4—224no—
473C2×C4⋊C4—224no—
474C2×C4⋊C4—224no—
475C2×C4⋊C4—442no—
476C2×C4⋊C4—442no—
477C2×C4⋊C4D4414yes—
478C2×C4⋊C4C22⋊D1114yes—
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—224no—
487C2×C22⋊C4—224no—
488C2×C22⋊C4—224no—
489C2×C22⋊C4—224no—
490C2×C22⋊C4—224no—
491C2×C22⋊C4—442no—
492C2×C22⋊C4—442no—
493C2×C22⋊C4—442no—
494C2×C22⋊C4—442no—
495C2×C22⋊C4—442no—
496C2×C22⋊C4—442no—
497C2×C42—22no—
498C2×C42—22no—
499C2×C42—22no—
500C2×C42—222no—
501C2×C42—222no—
502C2×C42—222no—
503C2×C42—222no—
504C2×C42—222no—
505C2×C42—222no—
506#95—24no—
507#95—114no—
508#95—222no—
509#95—222no—
510#95—224no—
511#95—224no—
512#95—222no—
513C2×C11C2×#39611yescharacteristic
514C2×C11#242611yescharacteristic
515C2×C11#242611yescharacteristic
516C2×C11#242611yescharacteristic
517C2×C11#242811yescharacteristic
518C2×C11#242811yescharacteristic
519C2×C11#242811yescharacteristic
520C2×C11#245211yescharacteristic
521C2×C11#245211yescharacteristic
522C2×C11#245211yescharacteristic
523C2×C11#245411yescharacteristic
524C2×C11#245411yescharacteristic
525C2×C11#245411yescharacteristic
526C2×C11#264411yescharacteristic
527C2×C11#286011yescharacteristic
528D11—84no—
529C24—114no—
530C24—222no—
531C24—222no—
532C24—222no—
533C24—222no—
534C24—222no—
535C24—222no—
536C24—222no—
537C24—222no—
538C24—222no—
539C24—222no—
540C24—222no—
541C24—222no—
542C24—222no—
543C24—222no—
544C24C23×D1111yescharacteristic
545C2×D4—228no—
546C2×D4—228no—
547C2×D4—228no—
548C2×D4—444no—
549C2×D4—444no—
550C2×D4—444no—
551C2×D4—444no—
552C22×C4—22no—
553C22×C4—22no—
554C22×C4—21no—
555C22×C4—21no—
556C22×C4—22no—
557C22×C4—22no—
558C22×C4—21no—
559C22×C4—21no—
560C22×C4—22no—
561C22×C4—22no—
562C22×C4—22no—
563C22×C4—21no—
564C22×C4—21no—
565C22×C4—21no—
566C22×C4—21no—
567C22×C4—22no—
568C22×C4—22no—
569C22×C4—21no—
570C22×C4—21no—
571C22×C4—22no—
572C22×C4—22no—
573C22×C4—21no—
574C22×C4—22no—
575C22×C4—21no—
576C22×C4—112no—
577C22×C4—112no—
578C22×C4—114no—
579C22×C4—112no—
580C22×C4—112no—
581C22×C4—221no—
582C22×C4—222no—
583C22×C4—221no—
584C22×C4—221no—
585C22×C4—221no—
586C22×C4—221no—
587C22×C4—221no—
588C22×C4—221no—
589C22×C4—221no—
590C22×C4—222no—
591C22×C4—221no—
592C22×C4—221no—
593C22×C4—221no—
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—221no—
603C22×C4—221no—
604C22×C4—221no—
605C22×C4—222no—
606C22×C4—222no—
607C22×C4—221no—
608C22×C4—221no—
609C22×C4—221no—
610C22×C4—221no—
611C22×C4C2×D4414yes—
612C22×C4C2×D4412yes—
613C22×C4#433912yes—
614C22×C4D4×D1112yes—
615C22×C4D4×D1112yes—
616C22×C4#434112yes—
617C22×C4Q8×D1112yes—
618C22×C4#434312yes—
619C22×C4#434312yes—
620C22×C4C2×C22⋊D1114yes—
621C22×C4C2×C22⋊D1112yes—
622C4⋊C4—28no—
623C4⋊C4—28no—
624C4⋊C4—48no—
625C4⋊C4—228no—
626C4⋊C4—448no—
627C4⋊C4—448no—
628C22⋊C4—448no—
629C22⋊C4—448no—
630C22⋊C4—448no—
631C22⋊C4—448no—
632C22⋊C4—448no—
633C22⋊C4—448no—
634C42—44no—
635C42—444no—
636C42—444no—
637C11#1514111yescharacteristic, complemented, Sylow
638C23—224no—
639C23—224no—
640C23—224no—
641C23—224no—
642C23—224no—
643C23—224no—
644C23—224no—
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—
671C23—442no—
672C23—442no—
673C23C22×D4411yescharacteristic
674C23C2×#433911yescharacteristic
675C23C2×D4×D1111yescharacteristic
676C23C2×D4×D1111yescharacteristic
677C23C2×#434111yescharacteristic
678C23#6703711yescharacteristic
679C23C2×Q8×D1111yescharacteristic
680C23C2×#434311yescharacteristic
681C23C2×#434311yescharacteristic
682C23#6704011yescharacteristic
683C23#41×D1111yescharacteristic
684C23#41×D1111yescharacteristic
685C23#6704211yescharacteristic
686C23#6704211yescharacteristic
687C23C22×C22⋊D1111yescharacteristic
688D4—4416no—
689C2×C4—24no—
690C2×C4—24no—
691C2×C4—22no—
692C2×C4—24no—
693C2×C4—24no—
694C2×C4—24no—
695C2×C4—22no—
696C2×C4—24no—
697C2×C4—22no—
698C2×C4—22no—
699C2×C4—22no—
700C2×C4—22no—
701C2×C4—42no—
702C2×C4—41no—
703C2×C4—41no—
704C2×C4—42no—
705C2×C4—42no—
706C2×C4—41no—
707C2×C4—41no—
708C2×C4—42no—
709C2×C4—42no—
710C2×C4—42no—
711C2×C4—41no—
712C2×C4—42no—
713C2×C4—41no—
714C2×C4—42no—
715C2×C4—41no—
716C2×C4—41no—
717C2×C4—222no—
718C2×C4—224no—
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—224no—
728C2×C4—222no—
729C2×C4—224no—
730C2×C4—222no—
731C2×C4—222no—
732C2×C4—442no—
733C2×C4—441no—
734C2×C4—441no—
735C2×C4—441no—
736C2×C4—441no—
737C2×C4—441no—
738C2×C4—442no—
739C2×C4—441no—
740C2×C4—441no—
741C2×C4—441no—
742C2×C4—441no—
743C2×C4—441no—
744C2×C4—442no—
745C2×C4—441no—
746C2×C4—441no—
747C2×C4—441no—
748C2×C4—441no—
749C2×C4—441no—
750C2×C4—441no—
751C2×C4—442no—
752C2×C4#6694814yes—
753C2×C4#6694914yes—
754C2×C4#6695014yes—
755C2×C4#6695114yes—
756C2×C4#6698314yes—
757C2×C4#6699214yes—
758C2×C4#6699914yes—
759C22—444no—
760C22—444no—
761C22—444no—
762C22—444no—
763C22—444no—
764C22—444no—
765C22—444no—
766C22—882no—
767C22—882no—
768C22—882no—
769C22—882no—
770C22—882no—
771C22—882no—
772C22—882no—
773C22—882no—
774C22C2×#6694811yescharacteristic
775C22C2×#6694911yescharacteristic
776C22C2×#6695011yescharacteristic
777C22C2×#6695111yescharacteristic
778C22#1062307911yescharacteristic
779C22D4×D4411yescharacteristic
780C22#1062308511yescharacteristic
781C22#1062309311yescharacteristic
782C22#1062310711yescharacteristic
783C22#1062310811yescharacteristic
784C22#1062311111yescharacteristic
785C22#1062311311yescharacteristic
786C22#1062312711yescharacteristic
787C22#1062313011yescharacteristic
788C22#1062314011yescharacteristic
789C22#1062315011yescharacteristic
790C22#1062315511yescharacteristic
791C22#1062316111yescharacteristic
792C22#1062316411yescharacteristic
793C22#1062317411yescharacteristic
794C22#1062322111yescharacteristic
795C22#1062322111yescharacteristic
796C22#1062322211yescharacteristic
797C22#1062322911yescharacteristic
798C22#1062325611yescharacteristic
799C22#1062325811yescharacteristic
800C22#1062326111yescharacteristic
801C22#1062326411yescharacteristic
802C22C2×#6698311yescharacteristic
803C22D4×C22⋊D1111yescharacteristic
804C22C2×#6699211yescharacteristic
805C22C2×#6699911yescharacteristic
806C22#1062334811yescharacteristic
807C22#1062336011yescharacteristic
808C22#1062336511yescharacteristic
809C4—42no—
810C4—44no—
811C4—44no—
812C4—42no—
813C4—442no—
814C4—442no—
815C4—442no—
816C4—442no—
817C4—444no—
818C4#1062260718yescomplemented
819C2—884no—
820C2C2×#1062260711yescharacteristic
821C2#1307217611yescharacteristic
822C2#1307218011yescharacteristic
823C2#1307218411yescharacteristic
824C2#1307219811yescharacteristic
825C2#1307220211yescharacteristic
826C2#1307220611yescharacteristic
827C2#1307246211yescharacteristic
828C2#1307246411yescharacteristic
829C2#1307246711yescharacteristic
830C2#1307248411yescharacteristic
831C2#1307248611yescharacteristic
832C2#1307248911yescharacteristic
833C2#1307457911yescharacteristic
834C2#1307698411yescharacteristic
subgroupG/H
center, FrattiniC24C23×D11
commutator, socle, cosocleC24×C11C24
FittingC2×C11×#389C2
prime radicalC23×D44C22
hypercenterC2×#389D11
hypocenterC11#15141
LCSG ▷ C24×C11 ▷ C11
UCSC1 ◁ C24 ◁ C2×#389

Complements

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

NH ≅ G/Ntype
1. C2×#10622607C2semidirect
5. C2×#10622598C2semidirect
6. C2×#10622586C2semidirect
7. #13066862C2semidirect
8. #13066860C2semidirect
9. #13066858C2semidirect
10. C4×C11⋊#95C2semidirect
11. C2×C11×#389C2semidirect
111. C11⋊#95D4semidirect
227. C2×#389D11semidirect
437. C4×C11#396semidirect
637. C11#15141semidirect
818. C4#10622607semidirect

Maximal subgroups

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

subgroupindex
C2×#106226072
C2×#106225522
C2×#106226012
C2×#106225982
C2×#106225862
#130668622
#130668602
#130668582
C4×C11⋊#952
C2×C11×#3892
#1514111