Finite Group Databasebeta

← #14676916

Subgroups — #14676916

Order 2816.

2682 conjugacy classes of subgroups.

The subgroup lattice has 1002 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#66991C211yesmaximal, characteristic
2C2×#10622834C211yesmaximal, characteristic, complemented
3C2×#10622570C212yesmaximal, complemented
4C2×#10622541C211yesmaximal, characteristic, complemented
5C2×#10622600C211yesmaximal, characteristic, complemented
6C2×C4⋊C4×Dic11C211yesmaximal, characteristic, complemented
7C2×C4×(C2×D11)⋊C4C211yesmaximal, characteristic, complemented
8#13066859C212yesmaximal, complemented
9#13066855C212yesmaximal, complemented
10#13066853C212yesmaximal, complemented
11C2×C11×#390C211yesmaximal, characteristic, complemented
12C23×D4×C11C2211yescharacteristic
13C23×C22⋊D11C2212yes—
14C23×C4×D11C2211yescharacteristic
15C22×C11×C4⋊C4C2211yescharacteristic
16C22×C11×C22⋊C4C2212yes—
17C22×C11×C22⋊C4C2212yes—
18C22×C42×C11C2211yescharacteristic
19C22×C22⋊Dic11C2212yes—
20C22×C22⋊Dic11C2212yes—
21C22×C22⋊Dic11C2212yes—
22C2×#66991—24no—
23C2×#66991—24no—
24C2×#66991C418yescomplemented
25C22×(C2×D11)⋊C4C2211yescharacteristic
26C22×(C2×D11)⋊C4C2212yes—
27C22×(C2×D11)⋊C4C2211yescharacteristic
28C22×C4⋊Dic11C2211yescharacteristic
29C22×C4⋊Dic11C2211yescharacteristic
30C22×Dic11⋊C4C2212yes—
31C22×C4×Dic11C2212yes—
32C22×C4×Dic11C2211yescharacteristic
33C11×#390—24no—
34#10622834—24no—
35C2×C11⋊#95C2211yescharacteristic
36C2×C11⋊#95C2211yescharacteristic
37C2×C11⋊#95C2212yes—
38C2×C11⋊#95C2212yes—
39C2×C11⋊#95C2212yes—
40#10622600—24no—
41C4⋊C4×Dic11—24no—
42#10622570—28no—
43C4×(C2×D11)⋊C4—24no—
44#10622541—24no—
45C25×C11C2312yes—
46C24×D11C2311yescharacteristic
47C22×D4×C11—22no—
48C22×D4×C11—22no—
49C22×D4×C11—22no—
50C22×D4×C11—22no—
51C22×D4×C11—22no—
52C22×D4×C11—22no—
53C22×D4×C11C2×C414yes—
54C23×C4×C11C2312yes—
55C23×C4×C11C2311yescharacteristic
56C23×C4×C11C2311yescharacteristic
57C23×C4×C11C2311yescharacteristic
58C22×C22⋊D11—24no—
59C22×C22⋊D11—24no—
60C22×C22⋊D11—24no—
61C22×C22⋊D11—24no—
62C22×C22⋊D11—42no—
63C22×C22⋊D11—42no—
64C22×C22⋊D11C2×C418yes—
65C23×Dic11C2312yes—
66C23×Dic11C2311yescharacteristic
67C23×Dic11C2311yescharacteristic
68C23×Dic11C2312yes—
69C23×Dic11C2311yescharacteristic
70C22×C4×D11—22no—
71C22×C4×D11—22no—
72C22×C4×D11—22no—
73C22×C4×D11—22no—
74C22×C4×D11—22no—
75C22×C4×D11—22no—
76C22×C4×D11C2×C414yes—
77C2×C11×C4⋊C4—22no—
78C2×C11×C4⋊C4—22no—
79C2×C11×C4⋊C4D414yescomplemented
80C2×C11×C22⋊C4—24no—
81C2×C11×C22⋊C4—24no—
82C2×C11×C22⋊C4—24no—
83C2×C11×C22⋊C4—24no—
84C2×C11×C22⋊C4—42no—
85C2×C11×C22⋊C4—42no—
86C2×C42×C11—22no—
87C2×C42×C11—22no—
88C2×C42×C11—22no—
89C2×C22⋊Dic11—24no—
90C2×C22⋊Dic11—24no—
91C2×C22⋊Dic11—24no—
92C2×C22⋊Dic11—24no—
93C2×C22⋊Dic11—24no—
94C2×C22⋊Dic11—24no—
95C2×C22⋊Dic11—42no—
96C2×C22⋊Dic11—42no—
97C2×C22⋊Dic11C2×C418yes—
98#66991—232no—
99C2×(C2×D11)⋊C4—22no—
100C2×(C2×D11)⋊C4—22no—
101C2×(C2×D11)⋊C4—22no—
102C2×(C2×D11)⋊C4—22no—
103C2×(C2×D11)⋊C4—22no—
104C2×(C2×D11)⋊C4—24no—
105C2×(C2×D11)⋊C4—24no—
106C2×(C2×D11)⋊C4—42no—
107C2×(C2×D11)⋊C4D414yescomplemented
108C2×C4⋊Dic11—22no—
109C2×C4⋊Dic11—22no—
110C2×C4⋊Dic11—22no—
111C2×C4⋊Dic11C2×C414yes—
112C2×C4⋊Dic11D414yes—
113C2×C4⋊Dic11D414yes—
114C2×Dic11⋊C4—24no—
115C2×Dic11⋊C4—24no—
116C2×Dic11⋊C4—42no—
117C2×C4×Dic11—22no—
118C2×C4×Dic11—22no—
119C2×C4×Dic11—24no—
120C2×C4×Dic11—24no—
121C2×C4×Dic11—42no—
122C2×C4×Dic11D414yescomplemented
123C11⋊#95—24no—
124C11⋊#95—24no—
125C11⋊#95—22no—
126C11⋊#95—22no—
127C11⋊#95—24no—
128#13998—111nomaximal, Sylow
129C24×C11—22no—
130C24×C11—22no—
131C24×C11—22no—
132C24×C11—22no—
133C24×C11—22no—
134C24×C11—22no—
135C24×C11—22no—
136C24×C11—22no—
137C24×C11—22no—
138C24×C11—22no—
139C24×C11—22no—
140C24×C11—22no—
141C24×C11—22no—
142C24×C11—22no—
143C24×C11C22×C414yes—
144C24×C11C2411yescharacteristic
145C23×D11—21no—
146C23×D11—21no—
147C23×D11—21no—
148C23×D11—21no—
149C23×D11—21no—
150C23×D11—21no—
151C23×D11—21no—
152C23×D11—21no—
153C23×D11—21no—
154C23×D11—21no—
155C23×D11—21no—
156C23×D11—21no—
157C23×D11C22×C412yes—
158C23×D11C2×D412yes—
159C23×D11#4112yes—
160C2×D4×C11—28no—
161C2×D4×C11—28no—
162C2×D4×C11—28no—
163C2×D4×C11—44no—
164C2×D4×C11—44no—
165C2×D4×C11—44no—
166C2×D4×C11—44no—
167C22×C4×C11—21no—
168C22×C4×C11—22no—
169C22×C4×C11—21no—
170C22×C4×C11—21no—
171C22×C4×C11—22no—
172C22×C4×C11—21no—
173C22×C4×C11—21no—
174C22×C4×C11—21no—
175C22×C4×C11—21no—
176C22×C4×C11—21no—
177C22×C4×C11—22no—
178C22×C4×C11—22no—
179C22×C4×C11—22no—
180C22×C4×C11—21no—
181C22×C4×C11—22no—
182C22×C4×C11—21no—
183C22×C4×C11—21no—
184C22×C4×C11—21no—
185C22×C4×C11C22×C412yes—
186C22×C4×C11C2×D412yes—
187C22×C4×C11C2×D414yes—
188C22×C4×C11C2×D412yes—
189C22×C4×C11C2×D412yes—
190C22×C4×C11C2×D412yes—
191C22×C4×C11C2×D412yes—
192C22×C4×C11#4112yes—
193C22×C4×C11#4112yes—
194C22×C4×C11#4112yes—
195C2×C22⋊D11—216no—
196C2×C22⋊D11—216no—
197C2×C22⋊D11—48no—
198C2×C22⋊D11—48no—
199C2×C22⋊D11—48no—
200C2×C22⋊D11—48no—
201C2×C22⋊D11—48no—
202C22×Dic11—21no—
203C22×Dic11—22no—
204C22×Dic11—21no—
205C22×Dic11—21no—
206C22×Dic11—21no—
207C22×Dic11—21no—
208C22×Dic11—21no—
209C22×Dic11—22no—
210C22×Dic11—22no—
211C22×Dic11—22no—
212C22×Dic11—22no—
213C22×Dic11—21no—
214C22×Dic11—22no—
215C22×Dic11—21no—
216C22×Dic11—21no—
217C22×Dic11—21no—
218C22×Dic11—21no—
219C22×Dic11—21no—
220C22×Dic11—22no—
221C22×Dic11—21no—
222C22×Dic11—22no—
223C22×Dic11—22no—
224C22×Dic11—21no—
225C22×Dic11—21no—
226C22×Dic11—22no—
227C22×Dic11—22no—
228C22×Dic11—21no—
229C22×Dic11C22×C412yes—
230C22×Dic11C22×C414yes—
231C22×Dic11C2×D412yes—
232C22×Dic11C2×D414yes—
233C22×Dic11C2×D414yes—
234C22×Dic11C2×D412yes—
235C22×Dic11C2×D412yes—
236C22×Dic11#4112yes—
237C2×C4×D11—28no—
238C2×C4×D11—28no—
239C2×C4×D11—28no—
240C2×C4×D11—44no—
241C2×C4×D11—44no—
242C2×C4×D11—44no—
243C2×C4×D11—44no—
244C11×C4⋊C4—28no—
245C11×C22⋊C4—48no—
246C11×C22⋊C4—48no—
247C42×C11—44no—
248C22⋊Dic11—216no—
249C22⋊Dic11—48no—
250C22⋊Dic11—48no—
251(C2×D11)⋊C4—28no—
252(C2×D11)⋊C4—28no—
253(C2×D11)⋊C4—48no—
254C4⋊Dic11—44no—
255C4⋊Dic11C22⋊C4116yescomplemented
256Dic11⋊C4—48no—
257C4×Dic11—28no—
258C4×Dic11—48no—
259C22×#121—111no—
260C2×#390—111no—
261C2×#390—112no—
262C2×#390D1111yescharacteristic, complemented
263C2×#389—111no—
264C2×#380—111no—
265C2×C4×C4⋊C4—111no—
266C2×C4×C22⋊C4—111no—
267#1439—112no—
268#1438—112no—
269#1437—112no—
270C23×C11—24no—
271C23×C11—24no—
272C23×C11—24no—
273C23×C11—24no—
274C23×C11—24no—
275C23×C11—24no—
276C23×C11—24no—
277C23×C11—42no—
278C23×C11—42no—
279C23×C11—42no—
280C23×C11—42no—
281C23×C11—42no—
282C23×C11—42no—
283C23×C11—42no—
284C23×C11—42no—
285C23×C11—42no—
286C23×C11—42no—
287C23×C11—42no—
288C23×C11—42no—
289C23×C11—42no—
290C23×C11—42no—
291C23×C11—42no—
292C23×C11—42no—
293C23×C11—42no—
294C23×C11—42no—
295C23×C11—42no—
296C23×C11—42no—
297C23×C11—42no—
298C23×C11—42no—
299C23×C11—42no—
300C23×C11—42no—
301C23×C11—42no—
302C23×C11—42no—
303C23×C11—42no—
304C23×C11—42no—
305C23×C11C23×C411yescharacteristic
306C23×C11C22×D411yescharacteristic
307C23×C11C22×D411yescharacteristic
308C23×C11C22×D411yescharacteristic
309C23×C11C22×D411yescharacteristic
310C23×C11C22×D411yescharacteristic
311C23×C11C2×#4111yescharacteristic
312C23×C11C2×#4111yescharacteristic
313C23×C11C2×#4111yescharacteristic
314C23×C11C2×#4111yescharacteristic
315C23×C11C2×#4111yescharacteristic
316C23×C11H(5,𝔽2)11yescharacteristic
317C23×C11H(5,𝔽2)11yescharacteristic
318C23×C11H(5,𝔽2)11yescharacteristic
319C23×C112−1+411yescharacteristic
320C22×D11—22no—
321C22×D11—22no—
322C22×D11—22no—
323C22×D11—22no—
324C22×D11—22no—
325C22×D11—22no—
326C22×D11—22no—
327C22×D11—22no—
328C22×D11—22no—
329C22×D11—22no—
330C22×D11—22no—
331C22×D11—22no—
332C22×D11—22no—
333C22×D11—22no—
334C22×D11—22no—
335C22×D11—22no—
336C22×D11—22no—
337C22×D11—22no—
338C22×D11—41no—
339C22×D11—41no—
340C22×D11—41no—
341C22×D11—41no—
342C22×D11—41no—
343C22×D11—41no—
344C22×D11—41no—
345C22×D11—41no—
346C22×D11—41no—
347C22×D11—41no—
348C22×D11—41no—
349C22×D11—41no—
350C22×D11—41no—
351C22×D11—41no—
352C22×D11—41no—
353C22×D11—41no—
354C22×D11C4×D414yes—
355D4×C11—416no—
356C2×C4×C11—22no—
357C2×C4×C11—24no—
358C2×C4×C11—22no—
359C2×C4×C11—22no—
360C2×C4×C11—24no—
361C2×C4×C11—22no—
362C2×C4×C11—22no—
363C2×C4×C11—24no—
364C2×C4×C11—22no—
365C2×C4×C11—41no—
366C2×C4×C11—41no—
367C2×C4×C11—42no—
368C2×C4×C11—41no—
369C2×C4×C11—41no—
370C2×C4×C11—42no—
371C2×C4×C11—42no—
372C2×C4×C11—41no—
373C2×C4×C11—41no—
374C2×C4×C11—42no—
375C2×C4×C11—41no—
376C2×C4×C11—41no—
377C2×C4×C11C2×C22⋊C414yes—
378C2×C4×C11C4×D414yes—
379C2×C4×C11C4×D414yes—
380C2×C4×C11#12114yes—
381C2×C4×C11#12114yes—
382C2×C4×C11#12414yes—
383C2×C4×C11#12714yes—
384C22⋊D11—432no—
385C2×Dic11—24no—
386C2×Dic11—24no—
387C2×Dic11—22no—
388C2×Dic11—22no—
389C2×Dic11—22no—
390C2×Dic11—24no—
391C2×Dic11—24no—
392C2×Dic11—24no—
393C2×Dic11—24no—
394C2×Dic11—22no—
395C2×Dic11—22no—
396C2×Dic11—22no—
397C2×Dic11—22no—
398C2×Dic11—22no—
399C2×Dic11—22no—
400C2×Dic11—22no—
401C2×Dic11—22no—
402C2×Dic11—22no—
403C2×Dic11—41no—
404C2×Dic11—41no—
405C2×Dic11—41no—
406C2×Dic11—41no—
407C2×Dic11—41no—
408C2×Dic11—41no—
409C2×Dic11—41no—
410C2×Dic11—41no—
411C2×Dic11—42no—
412C2×Dic11—42no—
413C2×Dic11—42no—
414C2×Dic11—42no—
415C2×Dic11—42no—
416C2×Dic11—42no—
417C2×Dic11—42no—
418C2×Dic11C2×C22⋊C418yes—
419C2×Dic11#12114yescomplemented
420C4×D11—416no—
421C23×D4—112no—
422C23×D4C2×D1111yescharacteristic
423C24×C4—111no—
424C2×#121—118no—
425C2×#121—224no—
426C2×#121—224no—
427C22×C4⋊C4—111no—
428C22×C4⋊C4—111no—
429C22×C4⋊C4—112no—
430C22×C4⋊C4C2×D1111yescharacteristic
431C22×C22⋊C4—112no—
432C22×C22⋊C4—111no—
433C22×C22⋊C4—112no—
434C22×C22⋊C4—111no—
435C22×C22⋊C4—112no—
436C22×C22⋊C4—112no—
437C22×C22⋊C4C2×D1112yes—
438C22×C22⋊C4C2×D1112yes—
439C22×C42—111no—
440C22×C42—112no—
441C22×C42C2×D1111yescharacteristic
442#390—24no—
443#390—224no—
444#390—228no—
445#389—224no—
446#380—224no—
447C4×C4⋊C4—224no—
448C4×C22⋊C4—224no—
449C2×#95—111no—
450C2×#95—112no—
451C2×#95—112no—
452C2×#95—112no—
453C2×#95—111no—
454C22×C11—44no—
455C22×C11—44no—
456C22×C11—44no—
457C22×C11—44no—
458C22×C11—44no—
459C22×C11—44no—
460C22×C11—44no—
461C22×C11—82no—
462C22×C11—82no—
463C22×C11—82no—
464C22×C11—82no—
465C22×C11—82no—
466C22×C11—82no—
467C22×C11—82no—
468C22×C11—82no—
469C22×C11C22×C22⋊C411yescharacteristic
470C22×C11C2×C4×D411yescharacteristic
471C22×C11C2×C4×D411yescharacteristic
472C22×C11C2×C4×D411yescharacteristic
473C22×C11C4×#4111yescharacteristic
474C22×C11#51811yescharacteristic
475C22×C11#52011yescharacteristic
476C22×C11C2×#12111yescharacteristic
477C22×C11C2×#12111yescharacteristic
478C22×C11C2×#12111yescharacteristic
479C22×C11#52511yescharacteristic
480C22×C11C2×#12411yescharacteristic
481C22×C11#52911yescharacteristic
482C22×C11C2×#12711yescharacteristic
483C22×C11#53211yescharacteristic
484C22×C11#53511yescharacteristic
485C22×C11#53711yescharacteristic
486C22×C11#54011yescharacteristic
487C22×C11#54211yescharacteristic
488C22×C11D4211yescharacteristic
489C22×C11D4211yescharacteristic
490C22×C11D4211yescharacteristic
491C22×C11#54611yescharacteristic
492C22×C11#54611yescharacteristic
493C22×C11#54611yescharacteristic
494C22×C11#54711yescharacteristic
495C22×C11#54811yescharacteristic
496C22×C11#54811yescharacteristic
497C22×C11#54811yescharacteristic
498C22×C11#55011yescharacteristic
499C22×C11#55011yescharacteristic
500C22×C11#55011yescharacteristic
501C22×C11#55311yescharacteristic
502C22×C11#55311yescharacteristic
503C22×C11#55511yescharacteristic
504C2×D11—24no—
505C2×D11—24no—
506C2×D11—24no—
507C2×D11—42no—
508C2×D11—42no—
509C2×D11—42no—
510C2×D11—42no—
511C2×D11—42no—
512C2×D11—42no—
513C2×D11—42no—
514C2×D11—42no—
515C2×D11—42no—
516C2×D11—42no—
517C2×D11—42no—
518C2×D11—42no—
519C4×C11—44no—
520C4×C11—42no—
521C4×C11—42no—
522C4×C11#39018yescomplemented
523Dic11—28no—
524Dic11—24no—
525Dic11—42no—
526Dic11—42no—
527Dic11—82no—
528C25—111no—
529C25C22×D1112yes—
530C22×D4—22no—
531C22×D4—22no—
532C22×D4—22no—
533C22×D4—22no—
534C22×D4—22no—
535C22×D4—22no—
536C22×D4—118no—
537C22×D4—224no—
538C22×D4—224no—
539C22×D4—224no—
540C22×D4—224no—
541C22×D4—442no—
542C22×D4—442no—
543C22×D4C4×D1114yes—
544C23×C4—111no—
545C23×C4—112no—
546C23×C4—111no—
547C23×C4—111no—
548C23×C4—114no—
549C23×C4—112no—
550C23×C4—222no—
551C23×C4—222no—
552C23×C4—222no—
553C23×C4—222no—
554C23×C4—222no—
555C23×C4—222no—
556C23×C4C22×D1111yescharacteristic
557C23×C4C22×D1111yescharacteristic
558C23×C4C22×D1112yes—
559C23×C4C22×D1111yescharacteristic
560#121—2232no—
561C2×C4⋊C4—22no—
562C2×C4⋊C4—22no—
563C2×C4⋊C4—114no—
564C2×C4⋊C4—114no—
565C2×C4⋊C4—114no—
566C2×C4⋊C4—224no—
567C2×C4⋊C4—222no—
568C2×C4⋊C4—224no—
569C2×C4⋊C4—222no—
570C2×C4⋊C4—222no—
571C2×C4⋊C4—442no—
572C2×C4⋊C4C22⋊D1114yescomplemented
573C2×C22⋊C4—24no—
574C2×C22⋊C4—24no—
575C2×C22⋊C4—24no—
576C2×C22⋊C4—24no—
577C2×C22⋊C4—42no—
578C2×C22⋊C4—42no—
579C2×C22⋊C4—118no—
580C2×C22⋊C4—114no—
581C2×C22⋊C4—222no—
582C2×C22⋊C4—222no—
583C2×C22⋊C4—222no—
584C2×C22⋊C4—222no—
585C2×C22⋊C4—224no—
586C2×C22⋊C4—224no—
587C2×C22⋊C4—222no—
588C2×C22⋊C4—224no—
589C2×C22⋊C4—224no—
590C2×C22⋊C4—224no—
591C2×C22⋊C4—224no—
592C2×C22⋊C4—224no—
593C2×C22⋊C4—224no—
594C2×C22⋊C4—442no—
595C2×C22⋊C4—442no—
596C2×C22⋊C4—442no—
597C2×C42—22no—
598C2×C42—22no—
599C2×C42—22no—
600C2×C42—114no—
601C2×C42—222no—
602C2×C42—222no—
603C2×C42—224no—
604C2×C42—224no—
605C2×C42—442no—
606#95—222no—
607#95—222no—
608#95—224no—
609#95—224no—
610#95—224no—
611C2×C11—84no—
612C2×C11C2×#39011yescharacteristic
613C2×C11C4×#12111yescharacteristic
614C2×C11#232411yescharacteristic
615C2×C11D4×C22⋊C411yescharacteristic
616C2×C11#234111yescharacteristic
617C2×C11#236111yescharacteristic
618C2×C11#236311yescharacteristic
619C2×C11#241411yescharacteristic
620C2×C11#241611yescharacteristic
621C2×C11#242611yescharacteristic
622C2×C11#242811yescharacteristic
623C2×C11#249011yescharacteristic
624C2×C11#249111yescharacteristic
625C2×C11#254011yescharacteristic
626C2×C11#254111yescharacteristic
627D11—44no—
628C24—22no—
629C24—22no—
630C24—22no—
631C24—22no—
632C24—22no—
633C24—22no—
634C24—22no—
635C24—22no—
636C24—22no—
637C24—22no—
638C24—22no—
639C24—22no—
640C24—22no—
641C24—22no—
642C24—112no—
643C24—112no—
644C24—112no—
645C24—221no—
646C24—221no—
647C24—221no—
648C24—221no—
649C24—221no—
650C24—221no—
651C24—221no—
652C24—221no—
653C24—221no—
654C24—221no—
655C24—221no—
656C24—221no—
657C24C2×C4×D1114yes—
658C24C23×D1111yescharacteristic
659C2×D4—28no—
660C2×D4—28no—
661C2×D4—28no—
662C2×D4—44no—
663C2×D4—44no—
664C2×D4—44no—
665C2×D4—44no—
666C2×D4—2216no—
667C2×D4—2216no—
668C2×D4—448no—
669C2×D4—448no—
670C2×D4—448no—
671C2×D4—448no—
672C2×D4—448no—
673C22×C4—21no—
674C22×C4—21no—
675C22×C4—21no—
676C22×C4—22no—
677C22×C4—21no—
678C22×C4—22no—
679C22×C4—22no—
680C22×C4—22no—
681C22×C4—22no—
682C22×C4—21no—
683C22×C4—21no—
684C22×C4—22no—
685C22×C4—21no—
686C22×C4—21no—
687C22×C4—21no—
688C22×C4—21no—
689C22×C4—21no—
690C22×C4—21no—
691C22×C4—114no—
692C22×C4—112no—
693C22×C4—114no—
694C22×C4—114no—
695C22×C4—112no—
696C22×C4—112no—
697C22×C4—112no—
698C22×C4—112no—
699C22×C4—221no—
700C22×C4—221no—
701C22×C4—222no—
702C22×C4—221no—
703C22×C4—222no—
704C22×C4—222no—
705C22×C4—222no—
706C22×C4—221no—
707C22×C4—221no—
708C22×C4—221no—
709C22×C4—221no—
710C22×C4—221no—
711C22×C4—221no—
712C22×C4—221no—
713C22×C4—221no—
714C22×C4—221no—
715C22×C4—221no—
716C22×C4—221no—
717C22×C4—221no—
718C22×C4—221no—
719C22×C4—228no—
720C22×C4—228no—
721C22×C4—228no—
722C22×C4—222no—
723C22×C4—222no—
724C22×C4—222no—
725C22×C4—222no—
726C22×C4—222no—
727C22×C4—222no—
728C22×C4—222no—
729C22×C4—444no—
730C22×C4—444no—
731C22×C4—444no—
732C22×C4—444no—
733C22×C4C2×C4×D1112yes—
734C22×C4#433912yes—
735C22×C4D4×D1112yes—
736C22×C4D4×D1112yes—
737C22×C4D4×D1112yes—
738C22×C4D4×D1112yes—
739C22×C4#434112yes—
740C22×C4#434112yes—
741C22×C4C2×C22⋊D1114yes—
742C22×C4C2×C22⋊D1112yes—
743C4⋊C4—28no—
744C4⋊C4—1116no—
745C4⋊C4—448no—
746C4⋊C4—444no—
747C22⋊C4—48no—
748C22⋊C4—48no—
749C22⋊C4—228no—
750C22⋊C4—228no—
751C22⋊C4—2216no—
752C22⋊C4—448no—
753C22⋊C4—448no—
754C22⋊C4—448no—
755C42—44no—
756C42—228no—
757C42—448no—
758C11#1399811yescharacteristic, complemented, Sylow
759C23—24no—
760C23—24no—
761C23—24no—
762C23—24no—
763C23—24no—
764C23—24no—
765C23—24no—
766C23—42no—
767C23—42no—
768C23—42no—
769C23—42no—
770C23—42no—
771C23—42no—
772C23—42no—
773C23—42no—
774C23—42no—
775C23—42no—
776C23—42no—
777C23—42no—
778C23—42no—
779C23—42no—
780C23—42no—
781C23—42no—
782C23—42no—
783C23—42no—
784C23—42no—
785C23—42no—
786C23—42no—
787C23—42no—
788C23—42no—
789C23—42no—
790C23—42no—
791C23—42no—
792C23—42no—
793C23—42no—
794C23—114no—
795C23—222no—
796C23—222no—
797C23—222no—
798C23—222no—
799C23—222no—
800C23—222no—
801C23—222no—
802C23—222no—
803C23—222no—
804C23—222no—
805C23—222no—
806C23—222no—
807C23—222no—
808C23—222no—
809C23—222no—
810C23—222no—
811C23—222no—
812C23—222no—
813C23—441no—
814C23—441no—
815C23—441no—
816C23—441no—
817C23—441no—
818C23—441no—
819C23—441no—
820C23—441no—
821C23—441no—
822C23—441no—
823C23—441no—
824C23—441no—
825C23—441no—
826C23—441no—
827C23—441no—
828C23—441no—
829C23C22×C4×D1111yescharacteristic
830C23C2×#433911yescharacteristic
831C23C2×D4×D1111yescharacteristic
832C23C2×D4×D1111yescharacteristic
833C23C2×D4×D1111yescharacteristic
834C23C2×D4×D1111yescharacteristic
835C23C2×#434111yescharacteristic
836C23C2×#434111yescharacteristic
837C23#6703711yescharacteristic
838C23#6703711yescharacteristic
839C23#41×D1111yescharacteristic
840C23#41×D1111yescharacteristic
841C23#6704211yescharacteristic
842C23#6704311yescharacteristic
843C23C22×C22⋊D1111yescharacteristic
844D4—416no—
845D4—4432no—
846C2×C4—22no—
847C2×C4—24no—
848C2×C4—24no—
849C2×C4—22no—
850C2×C4—24no—
851C2×C4—22no—
852C2×C4—22no—
853C2×C4—22no—
854C2×C4—22no—
855C2×C4—42no—
856C2×C4—42no—
857C2×C4—42no—
858C2×C4—42no—
859C2×C4—41no—
860C2×C4—41no—
861C2×C4—41no—
862C2×C4—41no—
863C2×C4—41no—
864C2×C4—41no—
865C2×C4—41no—
866C2×C4—41no—
867C2×C4—118no—
868C2×C4—114no—
869C2×C4—222no—
870C2×C4—224no—
871C2×C4—222no—
872C2×C4—224no—
873C2×C4—224no—
874C2×C4—222no—
875C2×C4—222no—
876C2×C4—222no—
877C2×C4—224no—
878C2×C4—224no—
879C2×C4—224no—
880C2×C4—222no—
881C2×C4—222no—
882C2×C4—222no—
883C2×C4—222no—
884C2×C4—222no—
885C2×C4—222no—
886C2×C4—222no—
887C2×C4—441no—
888C2×C4—441no—
889C2×C4—441no—
890C2×C4—441no—
891C2×C4—441no—
892C2×C4—441no—
893C2×C4—441no—
894C2×C4—441no—
895C2×C4—4416no—
896C2×C4—442no—
897C2×C4—442no—
898C2×C4—442no—
899C2×C4—442no—
900C2×C4—442no—
901C2×C4—442no—
902C2×C4—442no—
903C2×C4C22⋊C4×D1114yes—
904C2×C4(C22⋊D11)⋊C414yes—
905C2×C4#6693714yes—
906C2×C4#6693814yes—
907C2×C4C4×C22⋊D1114yes—
908C2×C4#6699214yes—
909C2×C4#6699314yes—
910C22—44no—
911C22—44no—
912C22—44no—
913C22—44no—
914C22—44no—
915C22—44no—
916C22—44no—
917C22—82no—
918C22—82no—
919C22—82no—
920C22—82no—
921C22—82no—
922C22—82no—
923C22—82no—
924C22—82no—
925C22—224no—
926C22—224no—
927C22—224no—
928C22—442no—
929C22—442no—
930C22—442no—
931C22—442no—
932C22—442no—
933C22—442no—
934C22—442no—
935C22—442no—
936C22—442no—
937C22—442no—
938C22—442no—
939C22—442no—
940C22C2×C22⋊C4×D1111yescharacteristic
941C22C2×(C22⋊D11)⋊C411yescharacteristic
942C22C2×#6693711yescharacteristic
943C22C2×#6693811yescharacteristic
944C22C4×#434111yescharacteristic
945C22C4×D4×D1111yescharacteristic
946C22#1062307611yescharacteristic
947C22#1062307711yescharacteristic
948C22#1062308211yescharacteristic
949C22#1062308911yescharacteristic
950C22#1062308911yescharacteristic
951C22#1062309411yescharacteristic
952C22#1062312911yescharacteristic
953C22#1062313011yescharacteristic
954C22D11×#12111yescharacteristic
955C22#1062313711yescharacteristic
956C22#1062313811yescharacteristic
957C22#1062313911yescharacteristic
958C22#1062314011yescharacteristic
959C22#1062314311yescharacteristic
960C22#1062320711yescharacteristic
961C22#1062320811yescharacteristic
962C22#1062321111yescharacteristic
963C22#1062321311yescharacteristic
964C22#1062324711yescharacteristic
965C22#1062324811yescharacteristic
966C22#1062324911yescharacteristic
967C22#1062325011yescharacteristic
968C22C2×C4×C22⋊D1111yescharacteristic
969C22D4×C22⋊D1111yescharacteristic
970C22C2×#6699211yescharacteristic
971C22C2×#6699311yescharacteristic
972C22#1062333711yescharacteristic
973C22#1062336211yescharacteristic
974C22#1062336511yescharacteristic
975C4—44no—
976C4—42no—
977C4—42no—
978C4—228no—
979C4—224no—
980C4—442no—
981C4—442no—
982C4—882no—
983C4#1062257018yescomplemented
984C2—84no—
985C2—444no—
986C2C2×#1062257011yescharacteristic
987C2#1307113211yescharacteristic
988C2#1307131211yescharacteristic
989C2#1307143711yescharacteristic
990C2#1307145511yescharacteristic
991C2#1307162811yescharacteristic
992C2#1307165011yescharacteristic
993C2#1307203711yescharacteristic
994C2#1307205911yescharacteristic
995C2#1307218511yescharacteristic
996C2#1307220711yescharacteristic
997C2#1307296611yescharacteristic
998C2#1307297711yescharacteristic
999C2#1307355211yescharacteristic
1000C2#1307355911yescharacteristic
subgroupG/H
center, FrattiniC24C23×D11
commutatorC23×C11C23×C4
FittingC2×C11×#390C2
socle, cosocleC24×C11C24
prime radicalC22×#66991C2
hypercenterC2×#390D11
hypocenterC11#13998
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ C2×#390

Complements

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

NH ≅ G/Ntype
2. C2×#10622834C2semidirect
3. C2×#10622570C2semidirect
4. C2×#10622541C2semidirect
5. C2×#10622600C2semidirect
6. C2×C4⋊C4×Dic11C2semidirect
7. C2×C4×(C2×D11)⋊C4C2semidirect
8. #13066859C2semidirect
9. #13066855C2semidirect
10. #13066853C2semidirect
11. C2×C11×#390C2semidirect
24. C2×#66991C4semidirect
79. C2×C11×C4⋊C4D4semidirect
107. C2×(C2×D11)⋊C4D4semidirect
122. C2×C4×Dic11D4semidirect
255. C4⋊Dic11C22⋊C4semidirect
262. C2×#390D11semidirect
419. C2×Dic11#121semidirect
522. C4×C11#390semidirect
572. C2×C4⋊C4C22⋊D11semidirect
758. C11#13998semidirect
983. C4#10622570semidirect

Maximal subgroups

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

subgroupindex
C22×#669912
C2×#106228342
C2×#106225702
C2×#106225412
C2×#106226002
C2×C4⋊C4×Dic112
C2×C4×(C2×D11)⋊C42
#130668592
#130668552
#130668532
C2×C11×#3902
#1399811