Finite Group Databasebeta

← #14676921

Subgroups — #14676921

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×#66948C211yesmaximal, characteristic
2C2×#10622552C211yesmaximal, characteristic, complemented
3C2×#10622601C212yesmaximal, complemented
4C2×#10622601C211yesmaximal, characteristic, complemented
5C2×#10622600C211yesmaximal, characteristic, complemented
6C2×C4⋊C4×Dic11C211yesmaximal, characteristic, complemented
7C2×C4×(C2×D11)⋊C4C211yesmaximal, characteristic, complemented
8#13066858C212yesmaximal, complemented
9#13066856C212yesmaximal, complemented
10#13066852C212yesmaximal, complemented
11C2×C11×#389C211yesmaximal, characteristic, complemented
12C23×D44C2211yescharacteristic
13C23×D44C2212yes—
14C23×C4×D11C2211yescharacteristic
15C22×C11×C4⋊C4C2211yescharacteristic
16C22×C11×C4⋊C4C2212yes—
17C22×C11×C4⋊C4C2211yescharacteristic
18C22×C42×C11C2211yescharacteristic
19C22×(C2×D11)⋊C4C2211yescharacteristic
20C22×(C2×D11)⋊C4C2212yes—
21C22×(C2×D11)⋊C4C2212yes—
22C22×(C2×D11)⋊C4C2212yes—
23C22×(C2×D11)⋊C4C2212yes—
24C22×(C2×D11)⋊C4C2212yes—
25C22×(C2×D11)⋊C4C2211yescharacteristic
26C22×(C2×D11)⋊C4C2212yes—
27C22×C4⋊Dic11C2211yescharacteristic
28C22×C4×Dic11C2212yes—
29C22×C4×Dic11C2211yescharacteristic
30C2×#66948—24no—
31C2×#66948—24no—
32C2×#66948C418yescomplemented
33C11×#389—24no—
34C2×C11×#95C2212yes—
35C2×C11⋊#95C2211yescharacteristic
36C2×C11⋊#95C2211yescharacteristic
37C2×C11⋊#95C2212yes—
38C2×C11⋊#95C2212yes—
39#10622601—28no—
40#10622601—24no—
41#10622600—24no—
42C4⋊C4×Dic11—24no—
43#10622552—24no—
44C4×(C2×D11)⋊C4—24no—
45C24×D11C2312yes—
46C24×D11C2311yescharacteristic
47C23×C4×C11C2312yes—
48C23×C4×C11C2311yescharacteristic
49C23×C4×C11C2311yescharacteristic
50C23×C4×C11C2312yes—
51C23×C4×C11C2311yescharacteristic
52C23×Dic11C2311yescharacteristic
53C23×Dic11C2312yes—
54C23×Dic11C2311yescharacteristic
55C23×Dic11C2311yescharacteristic
56C22×D44—24no—
57C22×D44—24no—
58C22×D44—24no—
59C22×D44—22no—
60C22×D44—24no—
61C22×D44—22no—
62C22×D44—22no—
63C22×D44—22no—
64C22×D44—22no—
65C22×D44—22no—
66C22×D44—42no—
67C22×D44—42no—
68C22×D44C2×C414yes—
69C22×D44C2×C418yes—
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—24no—
79C2×C11×C4⋊C4—22no—
80C2×C11×C4⋊C4—24no—
81C2×C11×C4⋊C4—22no—
82C2×C11×C4⋊C4—42no—
83C2×C11×C4⋊C4C2×C414yes—
84C2×C11×C4⋊C4D414yes—
85C2×C11×C4⋊C4D414yes—
86C2×C42×C11—22no—
87C2×C42×C11—22no—
88C2×C42×C11—22no—
89C2×(C2×D11)⋊C4—22no—
90C2×(C2×D11)⋊C4—24no—
91C2×(C2×D11)⋊C4—24no—
92C2×(C2×D11)⋊C4—22no—
93C2×(C2×D11)⋊C4—22no—
94C2×(C2×D11)⋊C4—22no—
95C2×(C2×D11)⋊C4—22no—
96C2×(C2×D11)⋊C4—24no—
97C2×(C2×D11)⋊C4—24no—
98C2×(C2×D11)⋊C4—24no—
99C2×(C2×D11)⋊C4—24no—
100C2×(C2×D11)⋊C4—24no—
101C2×(C2×D11)⋊C4—24no—
102C2×(C2×D11)⋊C4—24no—
103C2×(C2×D11)⋊C4—24no—
104C2×(C2×D11)⋊C4—24no—
105C2×(C2×D11)⋊C4—24no—
106C2×(C2×D11)⋊C4—42no—
107C2×(C2×D11)⋊C4—42no—
108C2×(C2×D11)⋊C4—42no—
109C2×(C2×D11)⋊C4—42no—
110C2×(C2×D11)⋊C4—42no—
111C2×(C2×D11)⋊C4C2×C418yes—
112C2×(C2×D11)⋊C4D414yescomplemented
113C2×C4⋊Dic11—22no—
114C2×C4⋊Dic11—22no—
115C2×C4⋊Dic11D414yescomplemented
116C2×C4×Dic11—22no—
117C2×C4×Dic11—22no—
118C2×C4×Dic11—24no—
119C2×C4×Dic11—24no—
120C2×C4×Dic11—42no—
121C2×C4×Dic11D414yescomplemented
122#66948—232no—
123C11×#95—24no—
124C11⋊#95—24no—
125C11⋊#95—22no—
126C11⋊#95—22no—
127C11⋊#95—24no—
128#13998—111nomaximal, Sylow
129C24×C11C2411yescharacteristic
130C23×D11—21no—
131C23×D11—21no—
132C23×D11—21no—
133C23×D11—21no—
134C23×D11—21no—
135C23×D11—21no—
136C23×D11—21no—
137C23×D11—21no—
138C23×D11—21no—
139C23×D11—21no—
140C23×D11—21no—
141C23×D11—21no—
142C23×D11—22no—
143C23×D11—22no—
144C23×D11—22no—
145C23×D11—22no—
146C23×D11—22no—
147C23×D11—22no—
148C23×D11—22no—
149C23×D11—22no—
150C23×D11—22no—
151C23×D11—22no—
152C23×D11—22no—
153C23×D11—22no—
154C23×D11—22no—
155C23×D11—22no—
156C23×D11C22×C414yes—
157C23×D11C22×C412yes—
158C23×D11C2×D412yes—
159C23×D11#4112yes—
160C22×C4×C11—22no—
161C22×C4×C11—22no—
162C22×C4×C11—22no—
163C22×C4×C11—22no—
164C22×C4×C11—21no—
165C22×C4×C11—21no—
166C22×C4×C11—21no—
167C22×C4×C11—21no—
168C22×C4×C11—21no—
169C22×C4×C11—21no—
170C22×C4×C11—21no—
171C22×C4×C11—21no—
172C22×C4×C11—21no—
173C22×C4×C11—21no—
174C22×C4×C11—21no—
175C22×C4×C11—21no—
176C22×C4×C11—22no—
177C22×C4×C11—22no—
178C22×C4×C11—22no—
179C22×C4×C11—22no—
180C22×C4×C11—22no—
181C22×C4×C11—22no—
182C22×C4×C11—22no—
183C22×C4×C11C22×C414yes—
184C22×C4×C11C22×C412yes—
185C22×C4×C11C2×D412yes—
186C22×C4×C11C2×D414yes—
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—
195C22×Dic11—21no—
196C22×Dic11—21no—
197C22×Dic11—21no—
198C22×Dic11—21no—
199C22×Dic11—22no—
200C22×Dic11—22no—
201C22×Dic11—21no—
202C22×Dic11—21no—
203C22×Dic11—21no—
204C22×Dic11—21no—
205C22×Dic11—22no—
206C22×Dic11—21no—
207C22×Dic11—22no—
208C22×Dic11—21no—
209C22×Dic11—21no—
210C22×Dic11—21no—
211C22×Dic11—21no—
212C22×Dic11—22no—
213C22×Dic11—21no—
214C22×Dic11—21no—
215C22×Dic11—22no—
216C22×Dic11—21no—
217C22×Dic11C22×C412yes—
218C22×Dic11C2×D412yes—
219C22×Dic11C2×D414yes—
220C22×Dic11C2×D412yes—
221C22×Dic11C2×D412yes—
222C22×Dic11#4112yes—
223C2×D44—216no—
224C2×D44—216no—
225C2×D44—28no—
226C2×D44—28no—
227C2×D44—28no—
228C2×D44—48no—
229C2×D44—48no—
230C2×D44—48no—
231C2×D44—48no—
232C2×D44—48no—
233C2×D44—44no—
234C2×D44—44no—
235C2×D44—44no—
236C2×D44—44no—
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—48no—
245C11×C4⋊C4—44no—
246C11×C4⋊C4C22⋊C4116yescomplemented
247C42×C11—44no—
248(C2×D11)⋊C4—28no—
249(C2×D11)⋊C4—28no—
250(C2×D11)⋊C4—216no—
251(C2×D11)⋊C4—48no—
252(C2×D11)⋊C4—48no—
253(C2×D11)⋊C4—48no—
254(C2×D11)⋊C4—48no—
255(C2×D11)⋊C4—48no—
256C4⋊Dic11—28no—
257C4×Dic11—28no—
258C4×Dic11—48no—
259C22×#121—111no—
260C2×#390—111no—
261C2×#390—112no—
262C2×#390—111no—
263C2×#389D1111yescharacteristic, complemented
264C2×#380—111no—
265C2×C4×C4⋊C4—111no—
266C2×C4×C22⋊C4—111no—
267#1439—112no—
268#1438—112no—
269#1437—112no—
270C23×C11C23×C411yescharacteristic
271C23×C11C22×D411yescharacteristic
272C23×C11C22×D411yescharacteristic
273C23×C11C22×D411yescharacteristic
274C23×C11C22×D411yescharacteristic
275C23×C11C22×D411yescharacteristic
276C23×C11C2×#4111yescharacteristic
277C23×C11C2×#4111yescharacteristic
278C23×C11C2×#4111yescharacteristic
279C23×C11C2×#4111yescharacteristic
280C23×C11C2×#4111yescharacteristic
281C23×C11H(5,𝔽2)11yescharacteristic
282C23×C11H(5,𝔽2)11yescharacteristic
283C23×C11H(5,𝔽2)11yescharacteristic
284C23×C112−1+411yescharacteristic
285C22×D11—22no—
286C22×D11—22no—
287C22×D11—22no—
288C22×D11—22no—
289C22×D11—22no—
290C22×D11—22no—
291C22×D11—22no—
292C22×D11—22no—
293C22×D11—22no—
294C22×D11—22no—
295C22×D11—22no—
296C22×D11—22no—
297C22×D11—22no—
298C22×D11—22no—
299C22×D11—22no—
300C22×D11—22no—
301C22×D11—22no—
302C22×D11—22no—
303C22×D11—24no—
304C22×D11—24no—
305C22×D11—24no—
306C22×D11—24no—
307C22×D11—24no—
308C22×D11—24no—
309C22×D11—24no—
310C22×D11—41no—
311C22×D11—41no—
312C22×D11—41no—
313C22×D11—41no—
314C22×D11—41no—
315C22×D11—41no—
316C22×D11—41no—
317C22×D11—41no—
318C22×D11—41no—
319C22×D11—41no—
320C22×D11—41no—
321C22×D11—41no—
322C22×D11—41no—
323C22×D11—41no—
324C22×D11—41no—
325C22×D11—41no—
326C22×D11—42no—
327C22×D11—42no—
328C22×D11—42no—
329C22×D11—42no—
330C22×D11—42no—
331C22×D11—42no—
332C22×D11—42no—
333C22×D11—42no—
334C22×D11—42no—
335C22×D11—42no—
336C22×D11—42no—
337C22×D11—42no—
338C22×D11—42no—
339C22×D11—42no—
340C22×D11—42no—
341C22×D11—42no—
342C22×D11—42no—
343C22×D11—42no—
344C22×D11—42no—
345C22×D11—42no—
346C22×D11—42no—
347C22×D11—42no—
348C22×D11—42no—
349C22×D11—42no—
350C22×D11—42no—
351C22×D11—42no—
352C22×D11—42no—
353C22×D11—42no—
354C22×D11C4×D414yes—
355C2×C4×C11—24no—
356C2×C4×C11—24no—
357C2×C4×C11—24no—
358C2×C4×C11—24no—
359C2×C4×C11—24no—
360C2×C4×C11—24no—
361C2×C4×C11—22no—
362C2×C4×C11—22no—
363C2×C4×C11—22no—
364C2×C4×C11—22no—
365C2×C4×C11—22no—
366C2×C4×C11—22no—
367C2×C4×C11—41no—
368C2×C4×C11—41no—
369C2×C4×C11—41no—
370C2×C4×C11—41no—
371C2×C4×C11—41no—
372C2×C4×C11—41no—
373C2×C4×C11—41no—
374C2×C4×C11—41no—
375C2×C4×C11—42no—
376C2×C4×C11—42no—
377C2×C4×C11—42no—
378C2×C4×C11—42no—
379C2×C4×C11—42no—
380C2×C4×C11—42no—
381C2×C4×C11—42no—
382C2×C4×C11C2×C22⋊C418yes—
383C2×C4×C11C2×C22⋊C414yes—
384C2×C4×C11C4×D414yes—
385C2×C4×C11C4×D414yes—
386C2×C4×C11#12114yes—
387C2×C4×C11#12114yes—
388C2×C4×C11#12414yes—
389C2×C4×C11#12714yes—
390C2×Dic11—22no—
391C2×Dic11—22no—
392C2×Dic11—22no—
393C2×Dic11—22no—
394C2×Dic11—22no—
395C2×Dic11—22no—
396C2×Dic11—22no—
397C2×Dic11—22no—
398C2×Dic11—22no—
399C2×Dic11—22no—
400C2×Dic11—24no—
401C2×Dic11—22no—
402C2×Dic11—22no—
403C2×Dic11—24no—
404C2×Dic11—24no—
405C2×Dic11—41no—
406C2×Dic11—41no—
407C2×Dic11—41no—
408C2×Dic11—41no—
409C2×Dic11—42no—
410C2×Dic11—42no—
411C2×Dic11—42no—
412C2×Dic11—41no—
413C2×Dic11—41no—
414C2×Dic11—42no—
415C2×Dic11—41no—
416C2×Dic11—41no—
417C2×Dic11#12114yescomplemented
418D44—432no—
419D44—416no—
420C4×D11—416no—
421C23×D4—111no—
422C23×D4—112no—
423C24×C4—111no—
424C2×#121—118no—
425C2×#121—224no—
426C2×#121—224no—
427C22×C4⋊C4—111no—
428C22×C4⋊C4C2×D1111yescharacteristic
429C22×C4⋊C4C2×D1112yes—
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⋊C4—112no—
438C22×C22⋊C4—112no—
439C22×C42—111no—
440C22×C42—112no—
441C22×C42C2×D1111yescharacteristic
442#390—224no—
443#390—224no—
444#390—228no—
445#389—24no—
446#380—224no—
447C4×C4⋊C4—224no—
448C4×C22⋊C4—224no—
449C2×#95—111no—
450C2×#95—112no—
451C2×#95—112no—
452C2×#95—111no—
453C2×#95C2×D1112yes—
454C22×C11C22×C22⋊C411yescharacteristic
455C22×C11C2×C4×D411yescharacteristic
456C22×C11C2×C4×D411yescharacteristic
457C22×C11C2×C4×D411yescharacteristic
458C22×C11C4×#4111yescharacteristic
459C22×C11#51811yescharacteristic
460C22×C11#52011yescharacteristic
461C22×C11C2×#12111yescharacteristic
462C22×C11C2×#12111yescharacteristic
463C22×C11C2×#12111yescharacteristic
464C22×C11#52511yescharacteristic
465C22×C11C2×#12411yescharacteristic
466C22×C11#52911yescharacteristic
467C22×C11C2×#12711yescharacteristic
468C22×C11#53211yescharacteristic
469C22×C11#53511yescharacteristic
470C22×C11#53711yescharacteristic
471C22×C11#54011yescharacteristic
472C22×C11#54211yescharacteristic
473C22×C11D4211yescharacteristic
474C22×C11D4211yescharacteristic
475C22×C11D4211yescharacteristic
476C22×C11#54611yescharacteristic
477C22×C11#54611yescharacteristic
478C22×C11#54611yescharacteristic
479C22×C11#54711yescharacteristic
480C22×C11#54811yescharacteristic
481C22×C11#54811yescharacteristic
482C22×C11#54811yescharacteristic
483C22×C11#55011yescharacteristic
484C22×C11#55011yescharacteristic
485C22×C11#55011yescharacteristic
486C22×C11#55311yescharacteristic
487C22×C11#55311yescharacteristic
488C22×C11#55511yescharacteristic
489C2×D11—24no—
490C2×D11—24no—
491C2×D11—24no—
492C2×D11—42no—
493C2×D11—42no—
494C2×D11—42no—
495C2×D11—42no—
496C2×D11—42no—
497C2×D11—42no—
498C2×D11—42no—
499C2×D11—42no—
500C2×D11—42no—
501C2×D11—42no—
502C2×D11—42no—
503C2×D11—42no—
504C2×D11—44no—
505C2×D11—44no—
506C2×D11—44no—
507C2×D11—44no—
508C2×D11—44no—
509C2×D11—44no—
510C2×D11—44no—
511C2×D11—82no—
512C2×D11—82no—
513C2×D11—82no—
514C2×D11—82no—
515C2×D11—82no—
516C2×D11—82no—
517C2×D11—82no—
518C2×D11—82no—
519C4×C11—28no—
520C4×C11—42no—
521C4×C11—42no—
522C4×C11—82no—
523C4×C11#39018yescomplemented
524Dic11—24no—
525Dic11—42no—
526Dic11—44no—
527Dic11—42no—
528C25—111no—
529C25—112no—
530C22×D4—114no—
531C22×D4—118no—
532C22×D4—224no—
533C22×D4—224no—
534C22×D4—224no—
535C22×D4—222no—
536C22×D4—222no—
537C22×D4—222no—
538C22×D4—222no—
539C22×D4—222no—
540C22×D4—224no—
541C22×D4—222no—
542C22×D4—442no—
543C22×D4—442no—
544C23×C4—111no—
545C23×C4—112no—
546C23×C4—111no—
547C23×C4—111no—
548C23×C4—114no—
549C23×C4—222no—
550C23×C4—222no—
551C23×C4—222no—
552C23×C4—222no—
553C23×C4—222no—
554C23×C4—222no—
555C23×C4C22×D1112yes—
556C23×C4C22×D1111yescharacteristic
557C23×C4C22×D1111yescharacteristic
558C23×C4C22×D1112yes—
559C23×C4C22×D1111yescharacteristic
560#121—2232no—
561C2×C4⋊C4—22no—
562C2×C4⋊C4—24no—
563C2×C4⋊C4—22no—
564C2×C4⋊C4—24no—
565C2×C4⋊C4—22no—
566C2×C4⋊C4—42no—
567C2×C4⋊C4—114no—
568C2×C4⋊C4—222no—
569C2×C4⋊C4—222no—
570C2×C4⋊C4C4×D1114yes—
571C2×C4⋊C4D4414yes—
572C2×C4⋊C4C22⋊D1114yes—
573C2×C22⋊C4—118no—
574C2×C22⋊C4—114no—
575C2×C22⋊C4—222no—
576C2×C22⋊C4—222no—
577C2×C22⋊C4—222no—
578C2×C22⋊C4—222no—
579C2×C22⋊C4—224no—
580C2×C22⋊C4—222no—
581C2×C22⋊C4—224no—
582C2×C22⋊C4—224no—
583C2×C22⋊C4—224no—
584C2×C22⋊C4—224no—
585C2×C22⋊C4—224no—
586C2×C22⋊C4—224no—
587C2×C22⋊C4—224no—
588C2×C22⋊C4—224no—
589C2×C22⋊C4—224no—
590C2×C22⋊C4—224no—
591C2×C22⋊C4—224no—
592C2×C22⋊C4—442no—
593C2×C22⋊C4—442no—
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—24no—
607#95—222no—
608#95—222no—
609#95—224no—
610#95—224no—
611C2×C11C2×#39011yescharacteristic
612C2×C11C4×#12111yescharacteristic
613C2×C11#232411yescharacteristic
614C2×C11D4×C22⋊C411yescharacteristic
615C2×C11#234111yescharacteristic
616C2×C11#236111yescharacteristic
617C2×C11#236311yescharacteristic
618C2×C11#241411yescharacteristic
619C2×C11#241611yescharacteristic
620C2×C11#242611yescharacteristic
621C2×C11#242811yescharacteristic
622C2×C11#249011yescharacteristic
623C2×C11#249111yescharacteristic
624C2×C11#254011yescharacteristic
625C2×C11#254111yescharacteristic
626D11—44no—
627D11—84no—
628C24—112no—
629C24—112no—
630C24—112no—
631C24—114no—
632C24—221no—
633C24—221no—
634C24—221no—
635C24—221no—
636C24—221no—
637C24—221no—
638C24—221no—
639C24—221no—
640C24—221no—
641C24—221no—
642C24—221no—
643C24—221no—
644C24—222no—
645C24—222no—
646C24—222no—
647C24—222no—
648C24—222no—
649C24—222no—
650C24—222no—
651C24—222no—
652C24—222no—
653C24—222no—
654C24—222no—
655C24—222no—
656C24—222no—
657C24—222no—
658C24C23×D1111yescharacteristic
659C2×D4—2216no—
660C2×D4—228no—
661C2×D4—228no—
662C2×D4—2216no—
663C2×D4—228no—
664C2×D4—448no—
665C2×D4—448no—
666C2×D4—448no—
667C2×D4—448no—
668C2×D4—448no—
669C2×D4—444no—
670C2×D4—444no—
671C2×D4—444no—
672C2×D4—444no—
673C22×C4—22no—
674C22×C4—22no—
675C22×C4—22no—
676C22×C4—22no—
677C22×C4—21no—
678C22×C4—21no—
679C22×C4—21no—
680C22×C4—21no—
681C22×C4—21no—
682C22×C4—21no—
683C22×C4—21no—
684C22×C4—21no—
685C22×C4—21no—
686C22×C4—21no—
687C22×C4—21no—
688C22×C4—21no—
689C22×C4—22no—
690C22×C4—22no—
691C22×C4—22no—
692C22×C4—22no—
693C22×C4—22no—
694C22×C4—22no—
695C22×C4—22no—
696C22×C4—112no—
697C22×C4—112no—
698C22×C4—112no—
699C22×C4—112no—
700C22×C4—112no—
701C22×C4—114no—
702C22×C4—221no—
703C22×C4—221no—
704C22×C4—221no—
705C22×C4—221no—
706C22×C4—221no—
707C22×C4—222no—
708C22×C4—221no—
709C22×C4—221no—
710C22×C4—221no—
711C22×C4—222no—
712C22×C4—221no—
713C22×C4—221no—
714C22×C4—221no—
715C22×C4—222no—
716C22×C4—222no—
717C22×C4—221no—
718C22×C4—221no—
719C22×C4—221no—
720C22×C4—222no—
721C22×C4—221no—
722C22×C4—222no—
723C22×C4—221no—
724C22×C4—228no—
725C22×C4—228no—
726C22×C4—228no—
727C22×C4—444no—
728C22×C4—444no—
729C22×C4—444no—
730C22×C4—444no—
731C22×C4C2×C4×D1114yes—
732C22×C4C2×C4×D1112yes—
733C22×C4C2×D4414yes—
734C22×C4C2×D4412yes—
735C22×C4D4×D1112yes—
736C22×C4D4×D1112yes—
737C22×C4D4×D1112yes—
738C22×C4#434312yes—
739C22×C4#434312yes—
740C22×C4#434312yes—
741C22×C4C2×C22⋊D1114yes—
742C22×C4C2×C22⋊D1112yes—
743C4⋊C4—48no—
744C4⋊C4—44no—
745C4⋊C4—228no—
746C4⋊C4(C2×D11)⋊C4116yescomplemented
747C22⋊C4—228no—
748C22⋊C4—228no—
749C22⋊C4—2216no—
750C22⋊C4—448no—
751C22⋊C4—448no—
752C22⋊C4—448no—
753C22⋊C4—448no—
754C22⋊C4—448no—
755C42—44no—
756C42—228no—
757C42—448no—
758C11#1399811yescharacteristic, complemented, Sylow
759C23—114no—
760C23—222no—
761C23—222no—
762C23—222no—
763C23—222no—
764C23—222no—
765C23—222no—
766C23—222no—
767C23—222no—
768C23—222no—
769C23—222no—
770C23—222no—
771C23—222no—
772C23—222no—
773C23—222no—
774C23—222no—
775C23—222no—
776C23—222no—
777C23—222no—
778C23—224no—
779C23—224no—
780C23—224no—
781C23—224no—
782C23—224no—
783C23—224no—
784C23—224no—
785C23—441no—
786C23—441no—
787C23—441no—
788C23—441no—
789C23—441no—
790C23—441no—
791C23—441no—
792C23—441no—
793C23—441no—
794C23—441no—
795C23—441no—
796C23—441no—
797C23—441no—
798C23—441no—
799C23—441no—
800C23—441no—
801C23—442no—
802C23—442no—
803C23—442no—
804C23—442no—
805C23—442no—
806C23—442no—
807C23—442no—
808C23—442no—
809C23—442no—
810C23—442no—
811C23—442no—
812C23—442no—
813C23—442no—
814C23—442no—
815C23—442no—
816C23—442no—
817C23—442no—
818C23—442no—
819C23—442no—
820C23—442no—
821C23—442no—
822C23—442no—
823C23—442no—
824C23—442no—
825C23—442no—
826C23—442no—
827C23—442no—
828C23—442no—
829C23C22×C4×D1111yescharacteristic
830C23C22×D4411yescharacteristic
831C23C2×D4×D1111yescharacteristic
832C23C2×D4×D1111yescharacteristic
833C23C2×D4×D1111yescharacteristic
834C23#6703711yescharacteristic
835C23C2×#434311yescharacteristic
836C23C2×#434311yescharacteristic
837C23C2×#434311yescharacteristic
838C23#6704011yescharacteristic
839C23#41×D1111yescharacteristic
840C23#41×D1111yescharacteristic
841C23#6704211yescharacteristic
842C23#6704211yescharacteristic
843C23C22×C22⋊D1111yescharacteristic
844D4—4432no—
845D4—4416no—
846C2×C4—24no—
847C2×C4—24no—
848C2×C4—24no—
849C2×C4—24no—
850C2×C4—24no—
851C2×C4—24no—
852C2×C4—22no—
853C2×C4—22no—
854C2×C4—22no—
855C2×C4—22no—
856C2×C4—22no—
857C2×C4—22no—
858C2×C4—41no—
859C2×C4—41no—
860C2×C4—41no—
861C2×C4—41no—
862C2×C4—41no—
863C2×C4—41no—
864C2×C4—41no—
865C2×C4—41no—
866C2×C4—42no—
867C2×C4—42no—
868C2×C4—42no—
869C2×C4—42no—
870C2×C4—42no—
871C2×C4—42no—
872C2×C4—42no—
873C2×C4—114no—
874C2×C4—222no—
875C2×C4—222no—
876C2×C4—222no—
877C2×C4—222no—
878C2×C4—222no—
879C2×C4—222no—
880C2×C4—222no—
881C2×C4—222no—
882C2×C4—222no—
883C2×C4—224no—
884C2×C4—222no—
885C2×C4—222no—
886C2×C4—224no—
887C2×C4—222no—
888C2×C4—224no—
889C2×C4—442no—
890C2×C4—441no—
891C2×C4—441no—
892C2×C4—441no—
893C2×C4—441no—
894C2×C4—442no—
895C2×C4—441no—
896C2×C4—441no—
897C2×C4—442no—
898C2×C4—441no—
899C2×C4—441no—
900C2×C4—442no—
901C2×C4—4416no—
902C2×C4#6694614yes—
903C2×C4#6694614yes—
904C2×C4#6694814yes—
905C2×C4#6694814yes—
906C2×C4C2×(C2×D11)⋊C418yes—
907C2×C4C2×(C2×D11)⋊C414yes—
908C2×C4#6699314yes—
909C2×C4#6700014yes—
910C22—224no—
911C22—224no—
912C22—224no—
913C22—442no—
914C22—442no—
915C22—442no—
916C22—442no—
917C22—442no—
918C22—442no—
919C22—442no—
920C22—442no—
921C22—442no—
922C22—442no—
923C22—442no—
924C22—442no—
925C22—444no—
926C22—444no—
927C22—444no—
928C22—444no—
929C22—444no—
930C22—444no—
931C22—444no—
932C22—882no—
933C22—882no—
934C22—882no—
935C22—882no—
936C22—882no—
937C22—882no—
938C22—882no—
939C22—882no—
940C22C2×#6694611yescharacteristic
941C22C2×#6694611yescharacteristic
942C22C2×#6694811yescharacteristic
943C22C2×#6694811yescharacteristic
944C22C4×D4×D1111yescharacteristic
945C22#1062307611yescharacteristic
946C22D4×D4411yescharacteristic
947C22#1062308511yescharacteristic
948C22C4×#434311yescharacteristic
949C22#1062310511yescharacteristic
950C22#1062310711yescharacteristic
951C22#1062310811yescharacteristic
952C22#1062313011yescharacteristic
953C22D11×#12111yescharacteristic
954C22#1062313811yescharacteristic
955C22#1062314011yescharacteristic
956C22#1062315811yescharacteristic
957C22#1062316011yescharacteristic
958C22#1062316111yescharacteristic
959C22#1062316411yescharacteristic
960C22#1062322211yescharacteristic
961C22#1062322611yescharacteristic
962C22#1062322611yescharacteristic
963C22#1062322911yescharacteristic
964C22#1062325611yescharacteristic
965C22#1062325711yescharacteristic
966C22#1062326411yescharacteristic
967C22#1062326511yescharacteristic
968C22C22×(C2×D11)⋊C411yescharacteristic
969C22D4×C22⋊D1111yescharacteristic
970C22C2×#6699311yescharacteristic
971C22C2×#6700011yescharacteristic
972C22#1062334811yescharacteristic
973C22#1062336011yescharacteristic
974C22#1062336511yescharacteristic
975C4—28no—
976C4—42no—
977C4—42no—
978C4—82no—
979C4—224no—
980C4—444no—
981C4—442no—
982C4—442no—
983C4#1062260118yescomplemented
984C2—444no—
985C2—884no—
986C2C2×#1062260111yescharacteristic
987C2#1307112411yescharacteristic
988C2#1307130711yescharacteristic
989C2D4×(C2×D11)⋊C411yescharacteristic
990C2#1307145411yescharacteristic
991C2#1307163111yescharacteristic
992C2#1307165311yescharacteristic
993C2#1307203211yescharacteristic
994C2#1307205411yescharacteristic
995C2#1307218011yescharacteristic
996C2#1307220211yescharacteristic
997C2#1307297111yescharacteristic
998C2#1307298211yescharacteristic
999C2#1307355411yescharacteristic
1000C2#1307355911yescharacteristic
subgroupG/H
center, FrattiniC24C23×D11
commutatorC23×C11C23×C4
FittingC2×C11×#389C2
socle, cosocleC24×C11C24
prime radicalC22×#66948C2
hypercenterC2×#389D11
hypocenterC11#13998
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ C2×#389

Complements

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

NH ≅ G/Ntype
2. C2×#10622552C2semidirect
3. C2×#10622601C2semidirect
4. C2×#10622601C2semidirect
5. C2×#10622600C2semidirect
6. C2×C4⋊C4×Dic11C2semidirect
7. C2×C4×(C2×D11)⋊C4C2semidirect
8. #13066858C2semidirect
9. #13066856C2semidirect
10. #13066852C2semidirect
11. C2×C11×#389C2semidirect
32. C2×#66948C4semidirect
112. C2×(C2×D11)⋊C4D4semidirect
115. C2×C4⋊Dic11D4semidirect
121. C2×C4×Dic11D4semidirect
246. C11×C4⋊C4C22⋊C4semidirect
263. C2×#389D11semidirect
417. C2×Dic11#121semidirect
523. C4×C11#390semidirect
746. C4⋊C4(C2×D11)⋊C4semidirect
758. C11#13998semidirect
983. C4#10622601semidirect

Maximal subgroups

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

subgroupindex
C22×#669482
C2×#106225522
C2×#106226012
C2×#106226002
C2×C4⋊C4×Dic112
C2×C4×(C2×D11)⋊C42
#130668582
#130668562
#130668522
C2×C11×#3892
#1399811