Finite Group Databasebeta

← #14677141

Subgroups — #14677141

Order 2816.

2590 conjugacy classes of subgroups.

The subgroup lattice has 1218 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#66946C211yesmaximal, characteristic
2C2×#10622278C211yesmaximal, characteristic
3C2×#10622278C211yesmaximal, characteristic
4C2×#10622281C211yesmaximal, characteristic, complemented
5C2×D11×#95C211yesmaximal, characteristic, complemented
6#13066875C211yesmaximal, characteristic, complemented
7#13066862C211yesmaximal, characteristic, complemented
8#13066860C211yesmaximal, characteristic, complemented
9#13066850C211yesmaximal, characteristic, complemented
10#13066847C211yesmaximal, 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×#1442C211yesmaximal, characteristic, complemented
16C23×D44C2211yescharacteristic
17C23×C4×D11C2211yescharacteristic
18C23×C4×D11C2211yescharacteristic
19C23×C4×D11C2211yescharacteristic
20C23×C4×D11C2211yescharacteristic
21C22×C11×C4⋊C4C2211yescharacteristic
22C22×(C2×D11)⋊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×C4⋊Dic11C2211yescharacteristic
31C22×Dic11⋊C4C2211yescharacteristic
32C22×C4×Dic11C2211yescharacteristic
33C2×#66946—24no—
34C2×#66946—24no—
35C2×#66946—24no—
36C2×C11×#95C2211yescharacteristic
37C2×C11×#95C2211yescharacteristic
38C2×C11×#95C2211yescharacteristic
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
54#10622281—24no—
55#10622278—24no—
56#10622278C418yescomplemented
57D11×#95—24no—
58C24×D11C2311yescharacteristic
59C24×D11C2311yescharacteristic
60C23×C4×C11C2311yescharacteristic
61C23×C4×C11C2311yescharacteristic
62C23×C4×C11C2311yescharacteristic
63C23×C4×C11C2311yescharacteristic
64C23×C4×C11C2311yescharacteristic
65C23×C4×C11C2311yescharacteristic
66C23×C4×C11C2311yescharacteristic
67C23×Dic11C2311yescharacteristic
68C23×Dic11C2311yescharacteristic
69C23×Dic11C2311yescharacteristic
70C23×Dic11C2311yescharacteristic
71C23×Dic11C2311yescharacteristic
72C23×Dic11C2311yescharacteristic
73C22×D44—22no—
74C22×D44—22no—
75C22×D44—22no—
76C22×D44—22no—
77C22×D44C2×C414yes—
78C22×D44D414yes—
79C22×D44Q814yes—
80C22×C4×D11—22no—
81C22×C4×D11—22no—
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—41no—
97C22×C4×D11—41no—
98C22×C4×D11—41no—
99C22×C4×D11—41no—
100C22×C4×D11—41no—
101C22×C4×D11—41no—
102C22×C4×D11—41no—
103C22×C4×D11—41no—
104C22×C4×D11—41no—
105C22×C4×D11—41no—
106C22×C4×D11C2×C414yescomplemented
107C22×C4×D11D414yes—
108C2×C11×C4⋊C4—22no—
109C2×C11×C4⋊C4—22no—
110C2×C11×C4⋊C4—22no—
111C2×(C2×D11)⋊C4—22no—
112C2×(C2×D11)⋊C4—22no—
113C2×(C2×D11)⋊C4—22no—
114C2×(C2×D11)⋊C4—22no—
115C2×(C2×D11)⋊C4—22no—
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—41no—
126C2×(C2×D11)⋊C4—41no—
127C2×(C2×D11)⋊C4—41no—
128C2×(C2×D11)⋊C4—41no—
129C2×(C2×D11)⋊C4—41no—
130C2×(C2×D11)⋊C4—41no—
131C2×(C2×D11)⋊C4C2×C414yescomplemented
132C2×(C2×D11)⋊C4C2×C414yescomplemented
133C2×(C2×D11)⋊C4C2×C414yescomplemented
134C2×(C2×D11)⋊C4D414yes—
135C2×C4⋊Dic11—22no—
136C2×C4⋊Dic11—22no—
137C2×C4⋊Dic11—41no—
138C2×Dic11⋊C4—22no—
139C2×Dic11⋊C4—22no—
140C2×Dic11⋊C4—41no—
141C2×C4×Dic11—22no—
142C2×C4×Dic11—22no—
143C2×C4×Dic11—22no—
144#66946—232no—
145C11×#95—22no—
146C11×#95—22no—
147C11×#95—22no—
148C11×#95—41no—
149C11×#95—41no—
150C11×#95C2×C414yescomplemented
151C11⋊#95—22no—
152C11⋊#95—22no—
153C11⋊#95—22no—
154C11⋊#95—22no—
155C11⋊#95—22no—
156C11⋊#95—22no—
157C11⋊#95—22no—
158C11⋊#95—41no—
159C11⋊#95—41no—
160C11⋊#95—41no—
161C11⋊#95—41no—
162C11⋊#95C2×C414yescomplemented
163#14016—111nomaximal, Sylow
164C24×C11C2411yescharacteristic
165C23×D11—21no—
166C23×D11—21no—
167C23×D11—21no—
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×D11C22×C412yes—
186C23×D11C22×C412yes—
187C23×D11C2×D412yes—
188C23×D11C2×D412yes—
189C23×D11C2×D412yes—
190C23×D11C2×D412yes—
191C23×D11C2×Q812yes—
192C23×D11C2×Q812yes—
193C23×D11#4112yes—
194C23×D11#4112yes—
195C22×C4×C11—21no—
196C22×C4×C11—21no—
197C22×C4×C11—21no—
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×C11C22×C412yes—
237C22×C4×C11C22×C412yes—
238C22×C4×C11C22×C412yes—
239C22×C4×C11C2×D412yes—
240C22×C4×C11C2×D412yes—
241C22×C4×C11C2×D412yes—
242C22×C4×C11C2×Q812yes—
243C22×C4×C11#4112yes—
244C22×Dic11—21no—
245C22×Dic11—21no—
246C22×Dic11—21no—
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×Dic11C22×C412yes—
280C22×Dic11C22×C412yes—
281C22×Dic11C2×D412yes—
282C22×Dic11C2×D412yes—
283C22×Dic11#4112yes—
284C22×Dic11#4112yes—
285C22×Dic11#4112yes—
286C2×D44—28no—
287C2×D44—28no—
288C2×D44—28no—
289C2×D44—28no—
290C2×D44—28no—
291C2×D44—28no—
292C2×D44C4⋊C4116yescomplemented
293C2×C4×D11—28no—
294C2×C4×D11—28no—
295C2×C4×D11—28no—
296C2×C4×D11—28no—
297C2×C4×D11—28no—
298C2×C4×D11—44no—
299C2×C4×D11—44no—
300C2×C4×D11—44no—
301C2×C4×D11—44no—
302C2×C4×D11—44no—
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—
321C11×C4⋊C4—28no—
322(C2×D11)⋊C4—28no—
323(C2×D11)⋊C4—28no—
324(C2×D11)⋊C4—28no—
325(C2×D11)⋊C4—44no—
326(C2×D11)⋊C4—44no—
327(C2×D11)⋊C4—44no—
328(C2×D11)⋊C4—44no—
329(C2×D11)⋊C4—44no—
330C4⋊Dic11—44no—
331Dic11⋊C4—44no—
332C4×Dic11—28no—
333C22×C4×D4—111no—
334C2×#386—111no—
335C2×#386—111no—
336C2×#385—111no—
337C22×#95—111no—
338#1442—111no—
339#1442D1111yescharacteristic, complemented
340#1439—111no—
341#1439—111no—
342#1436—111no—
343#1436—111no—
344C22⋊#95—111no—
345C22⋊#95—111no—
346C22⋊#95—111no—
347C22⋊#95—111no—
348C23×C11C23×C411yescharacteristic
349C23×C11C22×D411yescharacteristic
350C23×C11C22×D411yescharacteristic
351C23×C11C22×D411yescharacteristic
352C23×C11C22×Q811yescharacteristic
353C23×C11C2×#4111yescharacteristic
354C23×C11C2×#4111yescharacteristic
355C23×C11C2×#4111yescharacteristic
356C23×C11C2×#4111yescharacteristic
357C23×C11C2×#4111yescharacteristic
358C23×C11C2×#4111yescharacteristic
359C23×C11H(5,𝔽2)11yescharacteristic
360C23×C11H(5,𝔽2)11yescharacteristic
361C23×C11H(5,𝔽2)11yescharacteristic
362C23×C11H(5,𝔽2)11yescharacteristic
363C22×D11—22no—
364C22×D11—22no—
365C22×D11—22no—
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—41no—
410C22×D11—41no—
411C22×D11—41no—
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×D11C2×C4⋊C414yes—
426C22×D11C2×C4⋊C414yes—
427C22×D11C4×D414yes—
428C22×D11C4×D414yes—
429C22×D11#12014yes—
430C22×D11C22⋊Q814yes—
431C22×D11C22⋊Q814yes—
432C22×D11#12314yes—
433C2×C4×C11—22no—
434C2×C4×C11—22no—
435C2×C4×C11—22no—
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—41no—
455C2×C4×C11—41no—
456C2×C4×C11—41no—
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×C11C2×C4⋊C414yes—
482C2×Dic11—22no—
483C2×Dic11—22no—
484C2×Dic11—22no—
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—41no—
501C2×Dic11—41no—
502C2×Dic11—41no—
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#12314yes—
524D44—232no—
525C4×D11—416no—
526C4×D11—416no—
527C4×D11—416no—
528C4×D11—416no—
529C23×D4—111no—
530C24×C4—111no—
531C24×C4—111no—
532C24×C4—111no—
533C24×C4—111no—
534C2×C4×D4—224no—
535C2×C4×D4—224no—
536C2×C4×D4—224no—
537C22×C4⋊C4—111no—
538C22×C4⋊C4—111no—
539C22×C4⋊C4C2×D1111yescharacteristic
540C22×C22⋊C4—111no—
541C22×C22⋊C4—111no—
542C22×C22⋊C4—111no—
543C22×C22⋊C4—111no—
544C22×C22⋊C4—111no—
545C22×C22⋊C4—111no—
546C22×C22⋊C4—111no—
547C22×C22⋊C4—111no—
548C22×C42—111no—
549#386—118no—
550#386—224no—
551#385—224no—
552C2×#95—111no—
553C2×#95—111no—
554C2×#95—111no—
555C2×#95—111no—
556C2×#95—111no—
557C2×#95—111no—
558C2×#95—111no—
559C2×#95—111no—
560C2×#95—111no—
561C2×#95—111no—
562C2×#95—111no—
563C2×#95—111no—
564C2×#95—224no—
565C2×#95C2×D1111yescharacteristic
566C2×#95C2×D1111yescharacteristic
567C2×#95C2×D1111yescharacteristic
568C2×#95C2×D1111yescharacteristic
569C2×#95C2×D1111yescharacteristic
570C2×#95C2×D1111yescharacteristic
571C22×C11C22×C4⋊C411yescharacteristic
572C22×C11C2×C4×D411yescharacteristic
573C22×C11C2×C4×D411yescharacteristic
574C22×C11C4×#4111yescharacteristic
575C22×C11C4×#4111yescharacteristic
576C22×C11#51811yescharacteristic
577C22×C11#51811yescharacteristic
578C22×C11C2×#12011yescharacteristic
579C22×C11C2×C22⋊Q811yescharacteristic
580C22×C11C2×C22⋊Q811yescharacteristic
581C22×C11C2×#12311yescharacteristic
582C22×C11C2×#12311yescharacteristic
583C22×C11#52511yescharacteristic
584C22×C11#52911yescharacteristic
585C22×C11#52911yescharacteristic
586C22×C11#53411yescharacteristic
587C22×C11#53511yescharacteristic
588C22×C11#53811yescharacteristic
589C22×C11#53811yescharacteristic
590C22×C11#54611yescharacteristic
591C22×C11#54611yescharacteristic
592C22×C11#54611yescharacteristic
593C22×C11#54611yescharacteristic
594C22×C11#54611yescharacteristic
595C22×C11#54611yescharacteristic
596C22×C11#54611yescharacteristic
597C22×C11#54611yescharacteristic
598C22×C11#55311yescharacteristic
599C22×C11#55311yescharacteristic
600C22×C11#55311yescharacteristic
601C22×C11#55311yescharacteristic
602C22×C11#55411yescharacteristic
603C22×C11#55411yescharacteristic
604C22×C11#55411yescharacteristic
605C22×C11#55411yescharacteristic
606C2×D11—24no—
607C2×D11—24no—
608C2×D11—24no—
609C2×D11—24no—
610C2×D11—24no—
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—42no—
624C2×D11—42no—
625C2×D11—42no—
626C2×D11—42no—
627C2×D11—42no—
628C2×D11—42no—
629C2×D11—42no—
630C2×D11—42no—
631C2×D11—42no—
632C2×D11—42no—
633C2×D11—42no—
634C2×D11—42no—
635C2×D11#38518yes—
636C4×C11—24no—
637C4×C11—42no—
638C4×C11—42no—
639C4×C11—42no—
640C4×C11—42no—
641C4×C11—42no—
642C4×C11—81no—
643Dic11—24no—
644Dic11—42no—
645Dic11—42no—
646Dic11—42no—
647Dic11—42no—
648Dic11—81no—
649C25—111no—
650C25—111no—
651C22×D4—114no—
652C22×D4—114no—
653C22×D4—114no—
654C22×D4—222no—
655C22×D4—222no—
656C22×D4—222no—
657C22×D4—222no—
658C23×C4—111no—
659C23×C4—111no—
660C23×C4—111no—
661C23×C4—111no—
662C23×C4—111no—
663C23×C4—114no—
664C23×C4—114no—
665C23×C4—111no—
666C23×C4—222no—
667C23×C4—222no—
668C23×C4—222no—
669C23×C4—222no—
670C23×C4—222no—
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—441no—
683C23×C4—441no—
684C23×C4—441no—
685C23×C4—441no—
686C23×C4—441no—
687C23×C4—441no—
688C23×C4—441no—
689C23×C4—441no—
690C23×C4—441no—
691C23×C4—441no—
692C23×C4C22×D1111yescharacteristic
693C23×C4C22×D1111yescharacteristic
694C23×C4C22×D1111yescharacteristic
695C23×C4C22×D1111yescharacteristic
696C23×C4C22×D1111yescharacteristic
697C23×C4C22×D1111yescharacteristic
698C23×C4C22×D1111yescharacteristic
699C4×D4—2232no—
700C2×C4⋊C4—22no—
701C2×C4⋊C4—22no—
702C2×C4⋊C4—22no—
703C2×C4⋊C4—222no—
704C2×C4⋊C4—222no—
705C2×C4⋊C4—222no—
706C2×C4⋊C4—222no—
707C2×C4⋊C4—441no—
708C2×C4⋊C4—441no—
709C2×C22⋊C4—114no—
710C2×C22⋊C4—114no—
711C2×C22⋊C4—114no—
712C2×C22⋊C4—114no—
713C2×C22⋊C4—222no—
714C2×C22⋊C4—222no—
715C2×C22⋊C4—222no—
716C2×C22⋊C4—222no—
717C2×C22⋊C4—222no—
718C2×C22⋊C4—222no—
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—441no—
728C2×C22⋊C4—441no—
729C2×C22⋊C4—441no—
730C2×C22⋊C4—441no—
731C2×C22⋊C4—441no—
732C2×C22⋊C4—441no—
733C2×C42—222no—
734C2×C42—222no—
735C2×C42—222no—
736#95—22no—
737#95—22no—
738#95—22no—
739#95—41no—
740#95—41no—
741#95—114no—
742#95—222no—
743#95—222no—
744#95—222no—
745#95—222no—
746#95—222no—
747#95—222no—
748#95—222no—
749#95—441no—
750#95—441no—
751#95—441no—
752#95—441no—
753#95C4×D1114yescomplemented
754C2×C11C2×#38511yescharacteristic
755C2×C11C4×#12311yescharacteristic
756C2×C11#232111yescharacteristic
757C2×C11#234911yescharacteristic
758C2×C11#234911yescharacteristic
759C2×C11#236411yescharacteristic
760C2×C11#236411yescharacteristic
761C2×C11#240411yescharacteristic
762C2×C11#240511yescharacteristic
763C2×C11#244411yescharacteristic
764C2×C11#244411yescharacteristic
765C2×C11#245011yescharacteristic
766C2×C11#245011yescharacteristic
767C2×C11#248711yescharacteristic
768C2×C11#257911yescharacteristic
769D11—28no—
770D11—44no—
771C24—112no—
772C24—112no—
773C24—112no—
774C24—112no—
775C24—112no—
776C24—112no—
777C24—112no—
778C24—112no—
779C24—112no—
780C24—112no—
781C24—221no—
782C24—221no—
783C24—221no—
784C24—221no—
785C24—221no—
786C24—221no—
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—
801C24C23×D1111yescharacteristic
802C2×D4—1116no—
803C2×D4—228no—
804C2×D4—228no—
805C2×D4—228no—
806C2×D4—228no—
807C2×D4—228no—
808C2×D4—228no—
809C22×C4—21no—
810C22×C4—21no—
811C22×C4—21no—
812C22×C4—21no—
813C22×C4—21no—
814C22×C4—21no—
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—112no—
851C22×C4—112no—
852C22×C4—112no—
853C22×C4—112no—
854C22×C4—112no—
855C22×C4—112no—
856C22×C4—112no—
857C22×C4—228no—
858C22×C4—228no—
859C22×C4—228no—
860C22×C4—228no—
861C22×C4—228no—
862C22×C4—221no—
863C22×C4—221no—
864C22×C4—221no—
865C22×C4—221no—
866C22×C4—221no—
867C22×C4—221no—
868C22×C4—221no—
869C22×C4—221no—
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—444no—
898C22×C4—444no—
899C22×C4—444no—
900C22×C4—444no—
901C22×C4—444no—
902C22×C4—444no—
903C22×C4—444no—
904C22×C4—444no—
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×C4C2×C4×D1112yes—
921C22×C4C2×C4×D1112yes—
922C22×C4C2×C4×D1112yes—
923C22×C4D4×D1112yes—
924C22×C4D4×D1112yes—
925C22×C4D4×D1112yes—
926C22×C4Q8×D1112yes—
927C22×C4#434312yes—
928C4⋊C4—28no—
929C4⋊C4—444no—
930C4⋊C4—444no—
931C22⋊C4—228no—
932C22⋊C4—228no—
933C22⋊C4—228no—
934C22⋊C4—444no—
935C22⋊C4—444no—
936C22⋊C4—444no—
937C22⋊C4—444no—
938C22⋊C4—444no—
939C42—228no—
940C11#1401611yescharacteristic, complemented, Sylow
941C23—114no—
942C23—114no—
943C23—114no—
944C23—114no—
945C23—114no—
946C23—114no—
947C23—114no—
948C23—114no—
949C23—222no—
950C23—222no—
951C23—222no—
952C23—222no—
953C23—222no—
954C23—222no—
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—441no—
996C23—441no—
997C23—441no—
998C23—441no—
999C23—441no—
1000C23—441no—
1001C23—441no—
1002C23—441no—
1003C23—441no—
1004C23—441no—
1005C23—441no—
1006C23—441no—
1007C23—441no—
1008C23—441no—
1009C23—441no—
1010C23—441no—
1011C23C22×C4×D1111yescharacteristic
1012C23C2×D4×D1111yescharacteristic
1013C23C2×D4×D1111yescharacteristic
1014C23C2×D4×D1111yescharacteristic
1015C23#6703711yescharacteristic
1016C23C2×Q8×D1111yescharacteristic
1017C23C2×#434311yescharacteristic
1018C23#41×D1111yescharacteristic
1019C23#41×D1111yescharacteristic
1020C23#41×D1111yescharacteristic
1021C23#41×D1111yescharacteristic
1022C23#41×D1111yescharacteristic
1023C23#6704211yescharacteristic
1024C23#6704211yescharacteristic
1025C23#6704211yescharacteristic
1026D4—2232no—
1027C2×C4—22no—
1028C2×C4—22no—
1029C2×C4—22no—
1030C2×C4—22no—
1031C2×C4—22no—
1032C2×C4—22no—
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—41no—
1049C2×C4—41no—
1050C2×C4—41no—
1051C2×C4—41no—
1052C2×C4—41no—
1053C2×C4—41no—
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—114no—
1076C2×C4—222no—
1077C2×C4—222no—
1078C2×C4—222no—
1079C2×C4—222no—
1080C2×C4—222no—
1081C2×C4—222no—
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—4416no—
1095C2×C4—4416no—
1096C2×C4—4416no—
1097C2×C4—4416no—
1098C2×C4—441no—
1099C2×C4—441no—
1100C2×C4—441no—
1101C2×C4—441no—
1102C2×C4—441no—
1103C2×C4—441no—
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×C4C4⋊C4×D1114yes—
1122C22—118no—
1123C22—224no—
1124C22—224no—
1125C22—224no—
1126C22—224no—
1127C22—224no—
1128C22—224no—
1129C22—224no—
1130C22—224no—
1131C22—224no—
1132C22—224no—
1133C22—224no—
1134C22—224no—
1135C22—224no—
1136C22—224no—
1137C22—224no—
1138C22—224no—
1139C22—224no—
1140C22—442no—
1141C22—442no—
1142C22—442no—
1143C22—442no—
1144C22—442no—
1145C22—442no—
1146C22—442no—
1147C22—442no—
1148C22—442no—
1149C22—442no—
1150C22—442no—
1151C22—442no—
1152C22C2×C4⋊C4×D1111yescharacteristic
1153C22#1062305211yescharacteristic
1154C22#1062305311yescharacteristic
1155C22C4×D4×D1111yescharacteristic
1156C22C4×D4×D1111yescharacteristic
1157C22#1062307611yescharacteristic
1158C22C4×#434311yescharacteristic
1159C22D11×#12011yescharacteristic
1160C22#1062313611yescharacteristic
1161C22#1062314111yescharacteristic
1162C22#1062314311yescharacteristic
1163C22D11×C22⋊Q811yescharacteristic
1164C22D11×C22⋊Q811yescharacteristic
1165C22#1062315811yescharacteristic
1166C22#1062316111yescharacteristic
1167C22#1062316111yescharacteristic
1168C22D11×#12311yescharacteristic
1169C22D11×#12311yescharacteristic
1170C22#1062318511yescharacteristic
1171C22#1062318811yescharacteristic
1172C22#1062319211yescharacteristic
1173C22#1062320511yescharacteristic
1174C22#1062320711yescharacteristic
1175C22#1062320711yescharacteristic
1176C22#1062320711yescharacteristic
1177C22#1062322111yescharacteristic
1178C22#1062322111yescharacteristic
1179C22#1062322111yescharacteristic
1180C22#1062322211yescharacteristic
1181C22#1062322611yescharacteristic
1182C22#1062323511yescharacteristic
1183C22#1062323711yescharacteristic
1184C22#1062324011yescharacteristic
1185C22#1062324011yescharacteristic
1186C22#1062326111yescharacteristic
1187C4—24no—
1188C4—42no—
1189C4—42no—
1190C4—42no—
1191C4—42no—
1192C4—42no—
1193C4—81no—
1194C4—224no—
1195C4—442no—
1196C4—442no—
1197C4—442no—
1198C4—442no—
1199C4—881no—
1200C2—228no—
1201C2—444no—
1202C2D11×#38511yescharacteristic
1203C2#1307113711yescharacteristic
1204C2#1307126911yescharacteristic
1205C2#1307152411yescharacteristic
1206C2#1307152511yescharacteristic
1207C2#1307166011yescharacteristic
1208C2#1307166211yescharacteristic
1209C2#1307193611yescharacteristic
1210C2#1307193811yescharacteristic
1211C2#1307236711yescharacteristic
1212C2#1307236911yescharacteristic
1213C2#1307244111yescharacteristic
1214C2#1307244311yescharacteristic
1215C2#1307292811yescharacteristic
1216C2#1307396411yescharacteristic
subgroupG/H
center, FrattiniC24C23×D11
commutatorC23×C11C23×C4
FittingC11×#1442C2
socle, cosocleC24×C11C24
prime radicalC23×D44C22
hypercenter#1442D11
hypocenterC11#14016
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ #1442

Complements

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

NH ≅ G/Ntype
4. C2×#10622281C2semidirect
5. C2×D11×#95C2semidirect
6. #13066875C2semidirect
7. #13066862C2semidirect
8. #13066860C2semidirect
9. #13066850C2semidirect
10. #13066847C2semidirect
11. (C2×D11)⋊#95C2semidirect
12. (C2×D11)⋊#95C2semidirect
13. (C2×D11)⋊#95C2semidirect
14. (C2×D11)⋊#95C2semidirect
15. C11×#1442C2semidirect
56. #10622278C4semidirect
106. C22×C4×D11C2×C4semidirect
131. C2×(C2×D11)⋊C4C2×C4semidirect
132. C2×(C2×D11)⋊C4C2×C4semidirect
133. C2×(C2×D11)⋊C4C2×C4semidirect
150. C11×#95C2×C4semidirect
162. C11⋊#95C2×C4semidirect
292. C2×D44C4⋊C4semidirect
339. #1442D11semidirect
753. #95C4×D11semidirect
940. C11#14016semidirect

Maximal subgroups

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

subgroupindex
C22×#669462
C2×#106222782
C2×#106222812
C2×D11×#952
#130668752
#130668622
#130668602
#130668502
#130668472
(C2×D11)⋊#952
C11×#14422
#1401611