Finite Group Databasebeta

← #14676549

Subgroups — #14676549

Order 2816.

2742 conjugacy classes of subgroups.

The subgroup lattice has 1224 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#66947C211yesmaximal, characteristic
2C22×#66946C211yesmaximal, characteristic
3C2×#10622278C211yesmaximal, characteristic
4C2×#10622277C211yesmaximal, characteristic, complemented
5C2×D11×#95C211yesmaximal, characteristic, complemented
6#13066866C211yesmaximal, characteristic, complemented
7#13066864C211yesmaximal, characteristic, complemented
8#13066864C211yesmaximal, characteristic, complemented
9#13066851C211yesmaximal, characteristic, complemented
10#13066848C211yesmaximal, characteristic, complemented
11(C2×D11)⋊#95C211yesmaximal, characteristic, complemented
12(C2×D11)⋊#95C211yesmaximal, characteristic, complemented
13(C2×D11)⋊#95C211yesmaximal, characteristic, complemented
14(C2×D11)⋊#95C211yesmaximal, characteristic, complemented
15C11×#1441C211yesmaximal, characteristic, complemented
16C23×D44C2211yescharacteristic
17C23×C4×D11C2211yescharacteristic
18C23×C4×D11C2211yescharacteristic
19C23×C4×D11C2211yescharacteristic
20C23×C4×D11C2211yescharacteristic
21C22×C11×C4⋊C4C2211yescharacteristic
22C22×C11×C4⋊C4C2211yescharacteristic
23C22×(C2×D11)⋊C4C2211yescharacteristic
24C22×(C2×D11)⋊C4C2211yescharacteristic
25C22×(C2×D11)⋊C4C2211yescharacteristic
26C22×(C2×D11)⋊C4C2211yescharacteristic
27C22×(C2×D11)⋊C4C2211yescharacteristic
28C22×(C2×D11)⋊C4C2211yescharacteristic
29C22×(C2×D11)⋊C4C2211yescharacteristic
30C22×(C2×D11)⋊C4C2211yescharacteristic
31C22×Dic11⋊C4C2211yescharacteristic
32C22×C4×Dic11C2211yescharacteristic
33C2×#66947—24no—
34C2×#66947—24no—
35C2×#66947C418yescomplemented
36C2×#66946—24no—
37C2×#66946—24no—
38C2×#66946—24no—
39C2×C11×#95C2211yescharacteristic
40C2×C11×#95C2211yescharacteristic
41C2×C11×#95C2211yescharacteristic
42C2×C11×#95C2211yescharacteristic
43C2×C11×#95C2211yescharacteristic
44C2×C11⋊#95C2211yescharacteristic
45C2×C11⋊#95C2211yescharacteristic
46C2×C11⋊#95C2211yescharacteristic
47C2×C11⋊#95C2211yescharacteristic
48C2×C11⋊#95C2211yescharacteristic
49C2×C11⋊#95C2211yescharacteristic
50C2×C11⋊#95C2211yescharacteristic
51C2×C11⋊#95C2211yescharacteristic
52C2×C11⋊#95C2211yescharacteristic
53C2×C11⋊#95C2211yescharacteristic
54C2×C11⋊#95C2211yescharacteristic
55C2×C11⋊#95C2211yescharacteristic
56C2×C11⋊#95C2211yescharacteristic
57#10622278—24no—
58#10622277—24no—
59D11×#95—24no—
60C24×D11C2311yescharacteristic
61C24×D11C2311yescharacteristic
62C23×C4×C11C2311yescharacteristic
63C23×C4×C11C2311yescharacteristic
64C23×C4×C11C2311yescharacteristic
65C23×C4×C11C2311yescharacteristic
66C23×C4×C11C2311yescharacteristic
67C23×C4×C11C2311yescharacteristic
68C23×C4×C11C2311yescharacteristic
69C23×Dic11C2311yescharacteristic
70C23×Dic11C2311yescharacteristic
71C23×Dic11C2311yescharacteristic
72C23×Dic11C2311yescharacteristic
73C23×Dic11C2311yescharacteristic
74C23×Dic11C2311yescharacteristic
75C22×D44—22no—
76C22×D44—22no—
77C22×D44—22no—
78C22×D44—22no—
79C22×D44C2×C414yes—
80C22×D44D414yes—
81C22×D44D414yes—
82C22×C4×D11—22no—
83C22×C4×D11—22no—
84C22×C4×D11—22no—
85C22×C4×D11—22no—
86C22×C4×D11—22no—
87C22×C4×D11—22no—
88C22×C4×D11—22no—
89C22×C4×D11—22no—
90C22×C4×D11—22no—
91C22×C4×D11—22no—
92C22×C4×D11—22no—
93C22×C4×D11—22no—
94C22×C4×D11—22no—
95C22×C4×D11—22no—
96C22×C4×D11—22no—
97C22×C4×D11—22no—
98C22×C4×D11—22no—
99C22×C4×D11—22no—
100C22×C4×D11—22no—
101C22×C4×D11—22no—
102C22×C4×D11—41no—
103C22×C4×D11—41no—
104C22×C4×D11—41no—
105C22×C4×D11—41no—
106C22×C4×D11—41no—
107C22×C4×D11—41no—
108C22×C4×D11C2×C414yescomplemented
109C22×C4×D11D414yes—
110C2×C11×C4⋊C4—22no—
111C2×C11×C4⋊C4—22no—
112C2×C11×C4⋊C4—22no—
113C2×C11×C4⋊C4—22no—
114C2×C11×C4⋊C4—22no—
115C2×C11×C4⋊C4C2×C414yescomplemented
116C2×(C2×D11)⋊C4—22no—
117C2×(C2×D11)⋊C4—22no—
118C2×(C2×D11)⋊C4—22no—
119C2×(C2×D11)⋊C4—22no—
120C2×(C2×D11)⋊C4—22no—
121C2×(C2×D11)⋊C4—22no—
122C2×(C2×D11)⋊C4—22no—
123C2×(C2×D11)⋊C4—22no—
124C2×(C2×D11)⋊C4—22no—
125C2×(C2×D11)⋊C4—22no—
126C2×(C2×D11)⋊C4—22no—
127C2×(C2×D11)⋊C4—22no—
128C2×(C2×D11)⋊C4—22no—
129C2×(C2×D11)⋊C4—22no—
130C2×(C2×D11)⋊C4—22no—
131C2×(C2×D11)⋊C4—22no—
132C2×(C2×D11)⋊C4—22no—
133C2×(C2×D11)⋊C4—22no—
134C2×(C2×D11)⋊C4—41no—
135C2×(C2×D11)⋊C4—41no—
136C2×(C2×D11)⋊C4C2×C414yescomplemented
137C2×(C2×D11)⋊C4C2×C414yescomplemented
138C2×(C2×D11)⋊C4C2×C414yescomplemented
139C2×(C2×D11)⋊C4D414yes—
140C2×Dic11⋊C4—22no—
141C2×Dic11⋊C4—22no—
142C2×Dic11⋊C4C2×C414yescomplemented
143C2×C4×Dic11—22no—
144C2×C4×Dic11—22no—
145C2×C4×Dic11—22no—
146#66947—232no—
147#66946—232no—
148C11×#95—22no—
149C11×#95—22no—
150C11×#95—22no—
151C11×#95—41no—
152C11×#95—41no—
153C11⋊#95—22no—
154C11⋊#95—22no—
155C11⋊#95—22no—
156C11⋊#95—22no—
157C11⋊#95—22no—
158C11⋊#95—22no—
159C11⋊#95—22no—
160C11⋊#95—22no—
161C11⋊#95—22no—
162C11⋊#95—22no—
163C11⋊#95—22no—
164C11⋊#95—41no—
165C11⋊#95—41no—
166#13968—111nomaximal, Sylow
167C24×C11C2411yescharacteristic
168C23×D11—21no—
169C23×D11—21no—
170C23×D11—21no—
171C23×D11—21no—
172C23×D11—21no—
173C23×D11—21no—
174C23×D11—21no—
175C23×D11—21no—
176C23×D11—21no—
177C23×D11—21no—
178C23×D11—21no—
179C23×D11—21no—
180C23×D11—21no—
181C23×D11—21no—
182C23×D11—21no—
183C23×D11—21no—
184C23×D11—21no—
185C23×D11—21no—
186C23×D11—21no—
187C23×D11—21no—
188C23×D11C22×C412yes—
189C23×D11C22×C412yes—
190C23×D11C2×D412yes—
191C23×D11C2×D412yes—
192C23×D11C2×D412yes—
193C23×D11C2×D412yes—
194C23×D11C2×D412yes—
195C23×D11C2×D412yes—
196C23×D11#4112yes—
197C23×D11#4112yes—
198C22×C4×C11—21no—
199C22×C4×C11—21no—
200C22×C4×C11—21no—
201C22×C4×C11—21no—
202C22×C4×C11—21no—
203C22×C4×C11—21no—
204C22×C4×C11—21no—
205C22×C4×C11—21no—
206C22×C4×C11—21no—
207C22×C4×C11—21no—
208C22×C4×C11—21no—
209C22×C4×C11—21no—
210C22×C4×C11—21no—
211C22×C4×C11—21no—
212C22×C4×C11—21no—
213C22×C4×C11—21no—
214C22×C4×C11—21no—
215C22×C4×C11—21no—
216C22×C4×C11—21no—
217C22×C4×C11—21no—
218C22×C4×C11—21no—
219C22×C4×C11—21no—
220C22×C4×C11—21no—
221C22×C4×C11—21no—
222C22×C4×C11—21no—
223C22×C4×C11—21no—
224C22×C4×C11—21no—
225C22×C4×C11—21no—
226C22×C4×C11—21no—
227C22×C4×C11—21no—
228C22×C4×C11—21no—
229C22×C4×C11—21no—
230C22×C4×C11—21no—
231C22×C4×C11—21no—
232C22×C4×C11—21no—
233C22×C4×C11—21no—
234C22×C4×C11—21no—
235C22×C4×C11—21no—
236C22×C4×C11—21no—
237C22×C4×C11—21no—
238C22×C4×C11—21no—
239C22×C4×C11C22×C412yes—
240C22×C4×C11C22×C412yes—
241C22×C4×C11C22×C412yes—
242C22×C4×C11C2×D412yes—
243C22×C4×C11C2×D412yes—
244C22×C4×C11C2×D412yes—
245C22×C4×C11C2×D412yes—
246C22×C4×C11#4112yes—
247C22×Dic11—21no—
248C22×Dic11—21no—
249C22×Dic11—21no—
250C22×Dic11—21no—
251C22×Dic11—21no—
252C22×Dic11—21no—
253C22×Dic11—21no—
254C22×Dic11—21no—
255C22×Dic11—21no—
256C22×Dic11—21no—
257C22×Dic11—21no—
258C22×Dic11—21no—
259C22×Dic11—21no—
260C22×Dic11—21no—
261C22×Dic11—21no—
262C22×Dic11—21no—
263C22×Dic11—21no—
264C22×Dic11—21no—
265C22×Dic11—21no—
266C22×Dic11—21no—
267C22×Dic11—21no—
268C22×Dic11—21no—
269C22×Dic11—21no—
270C22×Dic11—21no—
271C22×Dic11—21no—
272C22×Dic11—21no—
273C22×Dic11—21no—
274C22×Dic11—21no—
275C22×Dic11—21no—
276C22×Dic11—21no—
277C22×Dic11—21no—
278C22×Dic11—21no—
279C22×Dic11—21no—
280C22×Dic11—21no—
281C22×Dic11—21no—
282C22×Dic11C22×C412yes—
283C22×Dic11C22×C412yes—
284C22×Dic11C2×D412yes—
285C22×Dic11C2×D412yes—
286C22×Dic11#4112yes—
287C22×Dic11#4112yes—
288C22×Dic11#4112yes—
289C2×D44—28no—
290C2×D44—28no—
291C2×D44—28no—
292C2×D44—28no—
293C2×D44—28no—
294C2×D44—28no—
295C2×D44C22⋊C4116yes—
296C2×C4×D11—28no—
297C2×C4×D11—28no—
298C2×C4×D11—28no—
299C2×C4×D11—28no—
300C2×C4×D11—28no—
301C2×C4×D11—28no—
302C2×C4×D11—28no—
303C2×C4×D11—44no—
304C2×C4×D11—44no—
305C2×C4×D11—44no—
306C2×C4×D11—44no—
307C2×C4×D11—44no—
308C2×C4×D11—44no—
309C2×C4×D11—44no—
310C2×C4×D11—44no—
311C2×C4×D11—44no—
312C2×C4×D11—44no—
313C2×C4×D11—44no—
314C2×C4×D11—44no—
315C2×C4×D11—44no—
316C2×C4×D11—44no—
317C2×C4×D11—44no—
318C2×C4×D11—44no—
319C2×C4×D11—44no—
320C2×C4×D11—44no—
321C2×C4×D11—44no—
322C2×C4×D11—44no—
323C2×C4×D11—44no—
324C11×C4⋊C4—28no—
325C11×C4⋊C4—28no—
326(C2×D11)⋊C4—28no—
327(C2×D11)⋊C4—28no—
328(C2×D11)⋊C4—28no—
329(C2×D11)⋊C4—28no—
330(C2×D11)⋊C4—28no—
331(C2×D11)⋊C4—44no—
332(C2×D11)⋊C4—44no—
333(C2×D11)⋊C4—44no—
334Dic11⋊C4—28no—
335C4×Dic11—28no—
336C22×#123—111no—
337C22×C4×D4—111no—
338C2×#386—111no—
339C2×#381—111no—
340C22×#95—111no—
341#1441—111no—
342#1441D1111yescharacteristic, complemented
343#1440—111no—
344#1440—111no—
345#1436—111no—
346#1436—111no—
347C22⋊#95—111no—
348C22⋊#95—111no—
349C22⋊#95—111no—
350C22⋊#95—111no—
351C23×C11C23×C411yescharacteristic
352C23×C11C22×D411yescharacteristic
353C23×C11C22×D411yescharacteristic
354C23×C11C22×D411yescharacteristic
355C23×C11C22×D411yescharacteristic
356C23×C11C2×#4111yescharacteristic
357C23×C11C2×#4111yescharacteristic
358C23×C11C2×#4111yescharacteristic
359C23×C11C2×#4111yescharacteristic
360C23×C11C2×#4111yescharacteristic
361C23×C11C2×#4111yescharacteristic
362C23×C11H(5,𝔽2)11yescharacteristic
363C23×C11H(5,𝔽2)11yescharacteristic
364C23×C112−1+411yescharacteristic
365C23×C112−1+411yescharacteristic
366C22×D11—22no—
367C22×D11—22no—
368C22×D11—22no—
369C22×D11—22no—
370C22×D11—22no—
371C22×D11—22no—
372C22×D11—22no—
373C22×D11—22no—
374C22×D11—22no—
375C22×D11—22no—
376C22×D11—22no—
377C22×D11—22no—
378C22×D11—22no—
379C22×D11—22no—
380C22×D11—22no—
381C22×D11—22no—
382C22×D11—22no—
383C22×D11—22no—
384C22×D11—22no—
385C22×D11—22no—
386C22×D11—22no—
387C22×D11—22no—
388C22×D11—22no—
389C22×D11—22no—
390C22×D11—22no—
391C22×D11—22no—
392C22×D11—22no—
393C22×D11—22no—
394C22×D11—22no—
395C22×D11—22no—
396C22×D11—22no—
397C22×D11—22no—
398C22×D11—22no—
399C22×D11—22no—
400C22×D11—22no—
401C22×D11—22no—
402C22×D11—22no—
403C22×D11—22no—
404C22×D11—22no—
405C22×D11—22no—
406C22×D11—22no—
407C22×D11—22no—
408C22×D11—22no—
409C22×D11—22no—
410C22×D11—22no—
411C22×D11—22no—
412C22×D11—41no—
413C22×D11—41no—
414C22×D11—41no—
415C22×D11—41no—
416C22×D11—41no—
417C22×D11—41no—
418C22×D11—41no—
419C22×D11—41no—
420C22×D11—41no—
421C22×D11—41no—
422C22×D11—41no—
423C22×D11—41no—
424C22×D11—41no—
425C22×D11—41no—
426C22×D11—41no—
427C22×D11—41no—
428C22×D11C2×C22⋊C414yes—
429C22×D11C2×C22⋊C414yes—
430C22×D11C4×D414yes—
431C22×D11C4×D414yes—
432C22×D11#12014yes—
433C22×D11#12114yes—
434C22×D11#12114yes—
435C22×D11#12314yes—
436C2×C4×C11—22no—
437C2×C4×C11—22no—
438C2×C4×C11—22no—
439C2×C4×C11—22no—
440C2×C4×C11—22no—
441C2×C4×C11—22no—
442C2×C4×C11—22no—
443C2×C4×C11—22no—
444C2×C4×C11—22no—
445C2×C4×C11—22no—
446C2×C4×C11—22no—
447C2×C4×C11—22no—
448C2×C4×C11—22no—
449C2×C4×C11—22no—
450C2×C4×C11—22no—
451C2×C4×C11—22no—
452C2×C4×C11—22no—
453C2×C4×C11—22no—
454C2×C4×C11—22no—
455C2×C4×C11—22no—
456C2×C4×C11—22no—
457C2×C4×C11—41no—
458C2×C4×C11—41no—
459C2×C4×C11—41no—
460C2×C4×C11—41no—
461C2×C4×C11—41no—
462C2×C4×C11—41no—
463C2×C4×C11—41no—
464C2×C4×C11—41no—
465C2×C4×C11—41no—
466C2×C4×C11—41no—
467C2×C4×C11—41no—
468C2×C4×C11—41no—
469C2×C4×C11—41no—
470C2×C4×C11—41no—
471C2×C4×C11—41no—
472C2×C4×C11—41no—
473C2×C4×C11—41no—
474C2×C4×C11—41no—
475C2×C4×C11—41no—
476C2×C4×C11—41no—
477C2×C4×C11—41no—
478C2×C4×C11—41no—
479C2×C4×C11—41no—
480C2×C4×C11—41no—
481C2×C4×C11—41no—
482C2×C4×C11—41no—
483C2×C4×C11—41no—
484C2×C4×C11C2×C22⋊C414yes—
485C2×Dic11—22no—
486C2×Dic11—22no—
487C2×Dic11—22no—
488C2×Dic11—22no—
489C2×Dic11—22no—
490C2×Dic11—22no—
491C2×Dic11—22no—
492C2×Dic11—22no—
493C2×Dic11—22no—
494C2×Dic11—22no—
495C2×Dic11—22no—
496C2×Dic11—22no—
497C2×Dic11—22no—
498C2×Dic11—22no—
499C2×Dic11—22no—
500C2×Dic11—22no—
501C2×Dic11—22no—
502C2×Dic11—22no—
503C2×Dic11—41no—
504C2×Dic11—41no—
505C2×Dic11—41no—
506C2×Dic11—41no—
507C2×Dic11—41no—
508C2×Dic11—41no—
509C2×Dic11—41no—
510C2×Dic11—41no—
511C2×Dic11—41no—
512C2×Dic11—41no—
513C2×Dic11—41no—
514C2×Dic11—41no—
515C2×Dic11—41no—
516C2×Dic11—41no—
517C2×Dic11—41no—
518C2×Dic11—41no—
519C2×Dic11—41no—
520C2×Dic11—41no—
521C2×Dic11—41no—
522C2×Dic11—41no—
523C2×Dic11—41no—
524C2×Dic11—41no—
525C2×Dic11—41no—
526C2×Dic11#12314yescomplemented
527D44—232no—
528C4×D11—416no—
529C4×D11—416no—
530C4×D11—416no—
531C4×D11—416no—
532C23×D4—111no—
533C24×C4—111no—
534C24×C4—111no—
535C24×C4—111no—
536C24×C4—111no—
537C2×#123—118no—
538C2×#123—224no—
539C2×#123—224no—
540C2×C4×D4—224no—
541C2×C4×D4—224no—
542C2×C4×D4—224no—
543C22×C4⋊C4—111no—
544C22×C4⋊C4C2×D1111yescharacteristic
545C22×C4⋊C4C2×D1111yescharacteristic
546C22×C22⋊C4—111no—
547C22×C22⋊C4—111no—
548C22×C22⋊C4—111no—
549C22×C22⋊C4—111no—
550C22×C22⋊C4—111no—
551C22×C22⋊C4—111no—
552C22×C22⋊C4—111no—
553C22×C22⋊C4—111no—
554C22×C42—111no—
555#386—224no—
556#381—224no—
557C2×#95—111no—
558C2×#95—111no—
559C2×#95—111no—
560C2×#95—111no—
561C2×#95—111no—
562C2×#95—111no—
563C2×#95—111no—
564C2×#95—111no—
565C2×#95—111no—
566C2×#95—111no—
567C2×#95—111no—
568C2×#95—111no—
569C2×#95—111no—
570C2×#95—224no—
571C2×#95C2×D1111yescharacteristic
572C2×#95C2×D1111yescharacteristic
573C2×#95C2×D1111yescharacteristic
574C2×#95C2×D1111yescharacteristic
575C2×#95C2×D1111yescharacteristic
576C22×C11C22×C22⋊C411yescharacteristic
577C22×C11C2×C4×D411yescharacteristic
578C22×C11C2×C4×D411yescharacteristic
579C22×C11C4×#4111yescharacteristic
580C22×C11C4×#4111yescharacteristic
581C22×C11#52011yescharacteristic
582C22×C11#52011yescharacteristic
583C22×C11C2×#12011yescharacteristic
584C22×C11C2×#12111yescharacteristic
585C22×C11C2×#12111yescharacteristic
586C22×C11C2×#12311yescharacteristic
587C22×C11C2×#12311yescharacteristic
588C22×C11#52511yescharacteristic
589C22×C11#52911yescharacteristic
590C22×C11#52911yescharacteristic
591C22×C11#53411yescharacteristic
592C22×C11#53611yescharacteristic
593C22×C11#53911yescharacteristic
594C22×C11#53911yescharacteristic
595C22×C11#54611yescharacteristic
596C22×C11#54611yescharacteristic
597C22×C11#54611yescharacteristic
598C22×C11#54611yescharacteristic
599C22×C11#54611yescharacteristic
600C22×C11#54611yescharacteristic
601C22×C11#54711yescharacteristic
602C22×C11#54711yescharacteristic
603C22×C11#54711yescharacteristic
604C22×C11#54711yescharacteristic
605C22×C11#54711yescharacteristic
606C22×C11#54711yescharacteristic
607C22×C11#55111yescharacteristic
608C22×C11#55111yescharacteristic
609C22×C11#55211yescharacteristic
610C22×C11#55211yescharacteristic
611C2×D11—24no—
612C2×D11—24no—
613C2×D11—24no—
614C2×D11—24no—
615C2×D11—24no—
616C2×D11—24no—
617C2×D11—24no—
618C2×D11—24no—
619C2×D11—24no—
620C2×D11—24no—
621C2×D11—24no—
622C2×D11—24no—
623C2×D11—24no—
624C2×D11—24no—
625C2×D11—24no—
626C2×D11—24no—
627C2×D11—24no—
628C2×D11—42no—
629C2×D11—42no—
630C2×D11—42no—
631C2×D11—42no—
632C2×D11—42no—
633C2×D11—42no—
634C2×D11—42no—
635C2×D11—42no—
636C2×D11—42no—
637C2×D11—42no—
638C2×D11—42no—
639C2×D11—42no—
640C2×D11#38618yes—
641C4×C11—24no—
642C4×C11—42no—
643C4×C11—42no—
644C4×C11—42no—
645C4×C11—42no—
646C4×C11—42no—
647C4×C11—81no—
648Dic11—24no—
649Dic11—42no—
650Dic11—42no—
651Dic11—42no—
652Dic11—42no—
653Dic11—81no—
654C25—111no—
655C25—111no—
656C22×D4—114no—
657C22×D4—114no—
658C22×D4—114no—
659C22×D4—222no—
660C22×D4—222no—
661C22×D4—222no—
662C22×D4—222no—
663C23×C4—111no—
664C23×C4—111no—
665C23×C4—111no—
666C23×C4—111no—
667C23×C4—111no—
668C23×C4—114no—
669C23×C4—114no—
670C23×C4—111no—
671C23×C4—222no—
672C23×C4—222no—
673C23×C4—222no—
674C23×C4—222no—
675C23×C4—222no—
676C23×C4—222no—
677C23×C4—222no—
678C23×C4—222no—
679C23×C4—222no—
680C23×C4—222no—
681C23×C4—222no—
682C23×C4—222no—
683C23×C4—222no—
684C23×C4—222no—
685C23×C4—222no—
686C23×C4—222no—
687C23×C4—222no—
688C23×C4—222no—
689C23×C4—222no—
690C23×C4—222no—
691C23×C4—441no—
692C23×C4—441no—
693C23×C4—441no—
694C23×C4—441no—
695C23×C4—441no—
696C23×C4—441no—
697C23×C4C22×D1111yescharacteristic
698C23×C4C22×D1111yescharacteristic
699C23×C4C22×D1111yescharacteristic
700C23×C4C22×D1111yescharacteristic
701C23×C4C22×D1111yescharacteristic
702C23×C4C22×D1111yescharacteristic
703C23×C4C22×D1111yescharacteristic
704#123—2232no—
705C4×D4—2232no—
706C2×C4⋊C4—22no—
707C2×C4⋊C4—22no—
708C2×C4⋊C4—22no—
709C2×C4⋊C4—22no—
710C2×C4⋊C4—22no—
711C2×C4⋊C4—114no—
712C2×C4⋊C4—222no—
713C2×C4⋊C4—222no—
714C2×C4⋊C4C4×D1114yescomplemented
715C2×C22⋊C4—114no—
716C2×C22⋊C4—114no—
717C2×C22⋊C4—114no—
718C2×C22⋊C4—114no—
719C2×C22⋊C4—222no—
720C2×C22⋊C4—222no—
721C2×C22⋊C4—222no—
722C2×C22⋊C4—222no—
723C2×C22⋊C4—222no—
724C2×C22⋊C4—222no—
725C2×C22⋊C4—222no—
726C2×C22⋊C4—222no—
727C2×C22⋊C4—222no—
728C2×C22⋊C4—222no—
729C2×C22⋊C4—222no—
730C2×C22⋊C4—222no—
731C2×C22⋊C4—222no—
732C2×C22⋊C4—222no—
733C2×C22⋊C4—222no—
734C2×C22⋊C4—222no—
735C2×C22⋊C4—222no—
736C2×C22⋊C4—222no—
737C2×C22⋊C4—441no—
738C2×C22⋊C4—441no—
739C2×C42—222no—
740C2×C42—222no—
741C2×C42—222no—
742#95—22no—
743#95—22no—
744#95—22no—
745#95—41no—
746#95—41no—
747#95—222no—
748#95—222no—
749#95—222no—
750#95—222no—
751#95—222no—
752#95—222no—
753#95—222no—
754#95—222no—
755#95—222no—
756#95—222no—
757#95—222no—
758#95—441no—
759#95—441no—
760C2×C11C2×#38611yescharacteristic
761C2×C11C4×#12311yescharacteristic
762C2×C11#232211yescharacteristic
763C2×C11#233911yescharacteristic
764C2×C11#233911yescharacteristic
765C2×C11#235911yescharacteristic
766C2×C11#235911yescharacteristic
767C2×C11#240511yescharacteristic
768C2×C11#240611yescharacteristic
769C2×C11#241911yescharacteristic
770C2×C11#241911yescharacteristic
771C2×C11#242511yescharacteristic
772C2×C11#242511yescharacteristic
773C2×C11#248611yescharacteristic
774C2×C11#253411yescharacteristic
775D11—28no—
776D11—44no—
777C24—112no—
778C24—112no—
779C24—112no—
780C24—112no—
781C24—112no—
782C24—112no—
783C24—112no—
784C24—112no—
785C24—112no—
786C24—112no—
787C24—221no—
788C24—221no—
789C24—221no—
790C24—221no—
791C24—221no—
792C24—221no—
793C24—221no—
794C24—221no—
795C24—221no—
796C24—221no—
797C24—221no—
798C24—221no—
799C24—221no—
800C24—221no—
801C24—221no—
802C24—221no—
803C24—221no—
804C24—221no—
805C24—221no—
806C24—221no—
807C24C23×D1111yescharacteristic
808C2×D4—1116no—
809C2×D4—228no—
810C2×D4—228no—
811C2×D4—228no—
812C2×D4—228no—
813C2×D4—228no—
814C2×D4—228no—
815C22×C4—21no—
816C22×C4—21no—
817C22×C4—21no—
818C22×C4—21no—
819C22×C4—21no—
820C22×C4—21no—
821C22×C4—21no—
822C22×C4—21no—
823C22×C4—21no—
824C22×C4—21no—
825C22×C4—21no—
826C22×C4—21no—
827C22×C4—21no—
828C22×C4—21no—
829C22×C4—21no—
830C22×C4—21no—
831C22×C4—21no—
832C22×C4—21no—
833C22×C4—21no—
834C22×C4—21no—
835C22×C4—21no—
836C22×C4—21no—
837C22×C4—21no—
838C22×C4—21no—
839C22×C4—21no—
840C22×C4—21no—
841C22×C4—21no—
842C22×C4—21no—
843C22×C4—21no—
844C22×C4—21no—
845C22×C4—21no—
846C22×C4—21no—
847C22×C4—21no—
848C22×C4—21no—
849C22×C4—21no—
850C22×C4—21no—
851C22×C4—21no—
852C22×C4—21no—
853C22×C4—21no—
854C22×C4—21no—
855C22×C4—21no—
856C22×C4—112no—
857C22×C4—112no—
858C22×C4—112no—
859C22×C4—112no—
860C22×C4—112no—
861C22×C4—112no—
862C22×C4—112no—
863C22×C4—228no—
864C22×C4—228no—
865C22×C4—228no—
866C22×C4—228no—
867C22×C4—228no—
868C22×C4—228no—
869C22×C4—228no—
870C22×C4—221no—
871C22×C4—221no—
872C22×C4—221no—
873C22×C4—221no—
874C22×C4—221no—
875C22×C4—221no—
876C22×C4—221no—
877C22×C4—221no—
878C22×C4—221no—
879C22×C4—221no—
880C22×C4—221no—
881C22×C4—221no—
882C22×C4—221no—
883C22×C4—221no—
884C22×C4—221no—
885C22×C4—221no—
886C22×C4—221no—
887C22×C4—221no—
888C22×C4—221no—
889C22×C4—221no—
890C22×C4—221no—
891C22×C4—221no—
892C22×C4—221no—
893C22×C4—221no—
894C22×C4—221no—
895C22×C4—221no—
896C22×C4—221no—
897C22×C4—221no—
898C22×C4—221no—
899C22×C4—221no—
900C22×C4—221no—
901C22×C4—221no—
902C22×C4—221no—
903C22×C4—221no—
904C22×C4—221no—
905C22×C4—444no—
906C22×C4—444no—
907C22×C4—444no—
908C22×C4—444no—
909C22×C4—444no—
910C22×C4—444no—
911C22×C4—444no—
912C22×C4—444no—
913C22×C4—444no—
914C22×C4—444no—
915C22×C4—444no—
916C22×C4—444no—
917C22×C4—444no—
918C22×C4—444no—
919C22×C4—444no—
920C22×C4—444no—
921C22×C4—444no—
922C22×C4—444no—
923C22×C4—444no—
924C22×C4—444no—
925C22×C4—444no—
926C22×C4C2×C4×D1112yes—
927C22×C4C2×C4×D1112yes—
928C22×C4C2×C4×D1112yes—
929C22×C4D4×D1112yes—
930C22×C4D4×D1112yes—
931C22×C4D4×D1112yes—
932C22×C4D4×D1112yes—
933C22×C4#434312yes—
934C4⋊C4—28no—
935C4⋊C4—28no—
936C4⋊C4—228no—
937C22⋊C4—228no—
938C22⋊C4—228no—
939C22⋊C4—228no—
940C22⋊C4—228no—
941C22⋊C4—228no—
942C22⋊C4—444no—
943C22⋊C4—444no—
944C22⋊C4—444no—
945C42—228no—
946C11#1396811yescharacteristic, complemented, Sylow
947C23—114no—
948C23—114no—
949C23—114no—
950C23—114no—
951C23—114no—
952C23—114no—
953C23—114no—
954C23—114no—
955C23—222no—
956C23—222no—
957C23—222no—
958C23—222no—
959C23—222no—
960C23—222no—
961C23—222no—
962C23—222no—
963C23—222no—
964C23—222no—
965C23—222no—
966C23—222no—
967C23—222no—
968C23—222no—
969C23—222no—
970C23—222no—
971C23—222no—
972C23—222no—
973C23—222no—
974C23—222no—
975C23—222no—
976C23—222no—
977C23—222no—
978C23—222no—
979C23—222no—
980C23—222no—
981C23—222no—
982C23—222no—
983C23—222no—
984C23—222no—
985C23—222no—
986C23—222no—
987C23—222no—
988C23—222no—
989C23—222no—
990C23—222no—
991C23—222no—
992C23—222no—
993C23—222no—
994C23—222no—
995C23—222no—
996C23—222no—
997C23—222no—
998C23—222no—
999C23—222no—
1000C23—222no—
1001C23—441no—
1002C23—441no—
1003C23—441no—
1004C23—441no—
1005C23—441no—
1006C23—441no—
1007C23—441no—
1008C23—441no—
1009C23—441no—
1010C23—441no—
1011C23—441no—
1012C23—441no—
1013C23—441no—
1014C23—441no—
1015C23—441no—
1016C23—441no—
1017C23C22×C4×D1111yescharacteristic
1018C23C2×D4×D1111yescharacteristic
1019C23C2×D4×D1111yescharacteristic
1020C23C2×D4×D1111yescharacteristic
1021C23C2×D4×D1111yescharacteristic
1022C23#6703711yescharacteristic
1023C23C2×#434311yescharacteristic
1024C23#6704011yescharacteristic
1025C23#6704011yescharacteristic
1026C23#41×D1111yescharacteristic
1027C23#41×D1111yescharacteristic
1028C23#41×D1111yescharacteristic
1029C23#41×D1111yescharacteristic
1030C23#41×D1111yescharacteristic
1031C23#6704211yescharacteristic
1032D4—2232no—
1033C2×C4—22no—
1034C2×C4—22no—
1035C2×C4—22no—
1036C2×C4—22no—
1037C2×C4—22no—
1038C2×C4—22no—
1039C2×C4—22no—
1040C2×C4—22no—
1041C2×C4—22no—
1042C2×C4—22no—
1043C2×C4—22no—
1044C2×C4—22no—
1045C2×C4—22no—
1046C2×C4—22no—
1047C2×C4—22no—
1048C2×C4—22no—
1049C2×C4—22no—
1050C2×C4—22no—
1051C2×C4—22no—
1052C2×C4—22no—
1053C2×C4—22no—
1054C2×C4—41no—
1055C2×C4—41no—
1056C2×C4—41no—
1057C2×C4—41no—
1058C2×C4—41no—
1059C2×C4—41no—
1060C2×C4—41no—
1061C2×C4—41no—
1062C2×C4—41no—
1063C2×C4—41no—
1064C2×C4—41no—
1065C2×C4—41no—
1066C2×C4—41no—
1067C2×C4—41no—
1068C2×C4—41no—
1069C2×C4—41no—
1070C2×C4—41no—
1071C2×C4—41no—
1072C2×C4—41no—
1073C2×C4—41no—
1074C2×C4—41no—
1075C2×C4—41no—
1076C2×C4—41no—
1077C2×C4—41no—
1078C2×C4—41no—
1079C2×C4—41no—
1080C2×C4—41no—
1081C2×C4—114no—
1082C2×C4—222no—
1083C2×C4—222no—
1084C2×C4—222no—
1085C2×C4—222no—
1086C2×C4—222no—
1087C2×C4—222no—
1088C2×C4—222no—
1089C2×C4—222no—
1090C2×C4—222no—
1091C2×C4—222no—
1092C2×C4—222no—
1093C2×C4—222no—
1094C2×C4—222no—
1095C2×C4—222no—
1096C2×C4—222no—
1097C2×C4—222no—
1098C2×C4—222no—
1099C2×C4—222no—
1100C2×C4—4416no—
1101C2×C4—4416no—
1102C2×C4—4416no—
1103C2×C4—4416no—
1104C2×C4—441no—
1105C2×C4—441no—
1106C2×C4—441no—
1107C2×C4—441no—
1108C2×C4—441no—
1109C2×C4—441no—
1110C2×C4—441no—
1111C2×C4—441no—
1112C2×C4—441no—
1113C2×C4—441no—
1114C2×C4—441no—
1115C2×C4—441no—
1116C2×C4—441no—
1117C2×C4—441no—
1118C2×C4—441no—
1119C2×C4—441no—
1120C2×C4—441no—
1121C2×C4—441no—
1122C2×C4—441no—
1123C2×C4—441no—
1124C2×C4—441no—
1125C2×C4—441no—
1126C2×C4—441no—
1127C2×C4C22⋊C4×D1114yes—
1128C22—118no—
1129C22—224no—
1130C22—224no—
1131C22—224no—
1132C22—224no—
1133C22—224no—
1134C22—224no—
1135C22—224no—
1136C22—224no—
1137C22—224no—
1138C22—224no—
1139C22—224no—
1140C22—224no—
1141C22—224no—
1142C22—224no—
1143C22—224no—
1144C22—224no—
1145C22—224no—
1146C22—442no—
1147C22—442no—
1148C22—442no—
1149C22—442no—
1150C22—442no—
1151C22—442no—
1152C22—442no—
1153C22—442no—
1154C22—442no—
1155C22—442no—
1156C22—442no—
1157C22—442no—
1158C22C2×C22⋊C4×D1111yescharacteristic
1159C22#1062303511yescharacteristic
1160C22#1062305311yescharacteristic
1161C22C4×D4×D1111yescharacteristic
1162C22C4×D4×D1111yescharacteristic
1163C22C4×#434311yescharacteristic
1164C22#1062310511yescharacteristic
1165C22D11×#12011yescharacteristic
1166C22D11×#12111yescharacteristic
1167C22D11×#12111yescharacteristic
1168C22#1062313611yescharacteristic
1169C22#1062314111yescharacteristic
1170C22#1062314311yescharacteristic
1171C22#1062314311yescharacteristic
1172C22#1062315811yescharacteristic
1173C22#1062316111yescharacteristic
1174C22#1062316211yescharacteristic
1175C22#1062316211yescharacteristic
1176C22#1062316211yescharacteristic
1177C22#1062316211yescharacteristic
1178C22#1062316811yescharacteristic
1179C22#1062316911yescharacteristic
1180C22D11×#12311yescharacteristic
1181C22D11×#12311yescharacteristic
1182C22#1062318511yescharacteristic
1183C22#1062320711yescharacteristic
1184C22#1062322211yescharacteristic
1185C22#1062322311yescharacteristic
1186C22#1062322411yescharacteristic
1187C22#1062322411yescharacteristic
1188C22#1062323611yescharacteristic
1189C22#1062323711yescharacteristic
1190C22#1062325511yescharacteristic
1191C22#1062325711yescharacteristic
1192C22#1062325711yescharacteristic
1193C4—24no—
1194C4—42no—
1195C4—42no—
1196C4—42no—
1197C4—42no—
1198C4—42no—
1199C4—81no—
1200C4—224no—
1201C4—442no—
1202C4—442no—
1203C4—442no—
1204C4—442no—
1205C4—881no—
1206C2—228no—
1207C2—444no—
1208C2D11×#38611yescharacteristic
1209C2#1307113711yescharacteristic
1210C2#1307128011yescharacteristic
1211C2#1307144411yescharacteristic
1212C2#1307144511yescharacteristic
1213C2#1307160111yescharacteristic
1214C2#1307160311yescharacteristic
1215C2#1307193811yescharacteristic
1216C2#1307195211yescharacteristic
1217C2#1307209411yescharacteristic
1218C2#1307209611yescharacteristic
1219C2#1307216011yescharacteristic
1220C2#1307216211yescharacteristic
1221C2#1307291911yescharacteristic
1222C2#1307350711yescharacteristic
subgroupG/H
center, FrattiniC24C23×D11
commutatorC23×C11C23×C4
FittingC11×#1441C2
socle, cosocleC24×C11C24
prime radicalC23×D44C22
hypercenter#1441D11
hypocenterC11#13968
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ #1441

Complements

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

NH ≅ G/Ntype
4. C2×#10622277C2semidirect
5. C2×D11×#95C2semidirect
6. #13066866C2semidirect
7. #13066864C2semidirect
8. #13066864C2semidirect
9. #13066851C2semidirect
10. #13066848C2semidirect
11. (C2×D11)⋊#95C2semidirect
12. (C2×D11)⋊#95C2semidirect
13. (C2×D11)⋊#95C2semidirect
14. (C2×D11)⋊#95C2semidirect
15. C11×#1441C2semidirect
35. C2×#66947C4semidirect
108. C22×C4×D11C2×C4semidirect
115. C2×C11×C4⋊C4C2×C4semidirect
136. C2×(C2×D11)⋊C4C2×C4semidirect
137. C2×(C2×D11)⋊C4C2×C4semidirect
138. C2×(C2×D11)⋊C4C2×C4semidirect
142. C2×Dic11⋊C4C2×C4semidirect
342. #1441D11semidirect
526. C2×Dic11#123semidirect
714. C2×C4⋊C4C4×D11semidirect
946. C11#13968semidirect

Maximal subgroups

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

subgroupindex
C22×#669472
C22×#669462
C2×#106222782
C2×#106222772
C2×D11×#952
#130668662
#130668642
#130668512
#130668482
(C2×D11)⋊#952
C11×#14412
#1396811