Finite Group Databasebeta

← #14684411

Subgroups — #14684411

Order 2816.

2018 conjugacy classes of subgroups.

The subgroup lattice has 1300 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622284C211yesmaximal, characteristic
2C2×#10622278C211yesmaximal, characteristic, complemented
3C2×#10622278C211yesmaximal, characteristic, complemented
4#13066878C211yesmaximal, characteristic, complemented
5#13066864C211yesmaximal, characteristic, complemented
6#13066864C211yesmaximal, characteristic, complemented
7#13066860C211yesmaximal, characteristic, complemented
8#13066860C211yesmaximal, characteristic, complemented
9#13066860C211yesmaximal, characteristic, complemented
10#13066856C211yesmaximal, characteristic, complemented
11#13066856C211yesmaximal, characteristic, complemented
12#13066856C211yesmaximal, characteristic, complemented
13#13066856C211yesmaximal, characteristic, complemented
14(C2×D11)⋊#95C211yesmaximal, characteristic, complemented
15C11×#1443C211yesmaximal, characteristic, complemented
16C23×D44C2211yescharacteristic
17C23×D44C2211yescharacteristic
18C23×D44C2211yescharacteristic
19C23×C4×D11C2211yescharacteristic
20C22×(C2×D11)⋊C4C2211yescharacteristic
21C22×(C2×D11)⋊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×(C2×D11)⋊C4C2211yescharacteristic
31C22×(C2×D11)⋊C4C2211yescharacteristic
32C22×(C2×D11)⋊C4C2211yescharacteristic
33C22×(C2×D11)⋊C4C2211yescharacteristic
34C22×Dic11⋊C4C2211yescharacteristic
35C2×C11×#95C2211yescharacteristic
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
51#10622284C418yescomplemented
52#10622278—24no—
53#10622278—24no—
54C24×D11C2311yescharacteristic
55C24×D11C2311yescharacteristic
56C24×D11C2311yescharacteristic
57C23×C4×C11C2311yescharacteristic
58C23×C4×C11C2311yescharacteristic
59C23×C4×C11C2311yescharacteristic
60C23×C4×C11C2311yescharacteristic
61C23×C4×C11C2311yescharacteristic
62C23×C4×C11C2311yescharacteristic
63C23×C4×C11C2311yescharacteristic
64C23×Dic11C2311yescharacteristic
65C23×Dic11C2311yescharacteristic
66C23×Dic11C2311yescharacteristic
67C23×Dic11C2311yescharacteristic
68C23×Dic11C2311yescharacteristic
69C22×D44—22no—
70C22×D44—22no—
71C22×D44—22no—
72C22×D44—22no—
73C22×D44—41no—
74C22×D44—41no—
75C22×D44—41no—
76C22×D44—41no—
77C22×D44—41no—
78C22×D44—41no—
79C22×D44—41no—
80C22×D44—41no—
81C22×D44—41no—
82C22×D44—41no—
83C22×D44—41no—
84C22×D44—41no—
85C22×D44—41no—
86C22×D44—41no—
87C22×D44C2×C414yes—
88C22×D44C2×C414yes—
89C22×D44C2×C414yescomplemented
90C22×C4×D11—41no—
91C22×C4×D11—41no—
92C22×C4×D11—41no—
93C22×C4×D11—41no—
94C22×C4×D11—41no—
95C22×C4×D11—41no—
96C22×C4×D11D414yescomplemented
97C2×(C2×D11)⋊C4—22no—
98C2×(C2×D11)⋊C4—22no—
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—41no—
105C2×(C2×D11)⋊C4—41no—
106C2×(C2×D11)⋊C4—41no—
107C2×(C2×D11)⋊C4—41no—
108C2×(C2×D11)⋊C4—41no—
109C2×(C2×D11)⋊C4—41no—
110C2×(C2×D11)⋊C4—41no—
111C2×(C2×D11)⋊C4—41no—
112C2×(C2×D11)⋊C4—41no—
113C2×(C2×D11)⋊C4—41no—
114C2×(C2×D11)⋊C4—41no—
115C2×(C2×D11)⋊C4—41no—
116C2×(C2×D11)⋊C4—41no—
117C2×(C2×D11)⋊C4—41no—
118C2×(C2×D11)⋊C4—41no—
119C2×(C2×D11)⋊C4—41no—
120C2×(C2×D11)⋊C4—41no—
121C2×(C2×D11)⋊C4—41no—
122C2×(C2×D11)⋊C4—41no—
123C2×(C2×D11)⋊C4—41no—
124C2×(C2×D11)⋊C4—41no—
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)⋊C4—41no—
132C2×(C2×D11)⋊C4—41no—
133C2×(C2×D11)⋊C4—41no—
134C2×(C2×D11)⋊C4—41no—
135C2×(C2×D11)⋊C4—41no—
136C2×(C2×D11)⋊C4C2×C414yes—
137C2×(C2×D11)⋊C4C2×C414yescomplemented
138C2×(C2×D11)⋊C4C2×C414yescomplemented
139C2×Dic11⋊C4—41no—
140C2×Dic11⋊C4—41no—
141C2×Dic11⋊C4—41no—
142C11×#95—22no—
143C11×#95—22no—
144C11×#95—41no—
145C11×#95—41no—
146C11×#95—41no—
147C11×#95—41no—
148C11×#95C2×C414yescomplemented
149C11⋊#95—22no—
150C11⋊#95—22no—
151C11⋊#95—41no—
152C11⋊#95—41no—
153C11⋊#95—41no—
154C11⋊#95—41no—
155C11⋊#95—41no—
156C11⋊#95—41no—
157C11⋊#95—41no—
158#14621—111nomaximal, Sylow
159C24×C11C2411yescharacteristic
160C23×D11—21no—
161C23×D11—21no—
162C23×D11—21no—
163C23×D11—21no—
164C23×D11—21no—
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×D11—21no—
186C23×D11—21no—
187C23×D11—21no—
188C23×D11—21no—
189C23×D11—21no—
190C23×D11—21no—
191C23×D11—21no—
192C23×D11—21no—
193C23×D11—21no—
194C23×D11—21no—
195C23×D11—21no—
196C23×D11—21no—
197C23×D11—21no—
198C23×D11—21no—
199C23×D11—21no—
200C23×D11C22×C412yes—
201C23×D11C22×C412yes—
202C23×D11C22×C412yes—
203C23×D11C2×D412yes—
204C23×D11#4112yes—
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×C11—21no—
240C22×C4×C11—21no—
241C22×C4×C11—21no—
242C22×C4×C11—21no—
243C22×C4×C11—21no—
244C22×C4×C11—21no—
245C22×C4×C11—21no—
246C22×C4×C11—21no—
247C22×C4×C11—21no—
248C22×C4×C11—21no—
249C22×C4×C11—21no—
250C22×C4×C11C22×C412yes—
251C22×C4×C11C22×C412yes—
252C22×C4×C11C22×C412yes—
253C22×C4×C11C2×D412yes—
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×Dic11—21no—
283C22×Dic11—21no—
284C22×Dic11—21no—
285C22×Dic11—21no—
286C22×Dic11—21no—
287C22×Dic11C22×C412yes—
288C22×Dic11C2×D412yes—
289C2×D44—28no—
290C2×D44—28no—
291C2×D44—44no—
292C2×D44—44no—
293C2×D44—44no—
294C2×D44—44no—
295C2×D44—44no—
296C2×D44—44no—
297C2×D44—44no—
298C2×D44—44no—
299C2×D44—44no—
300C2×D44—44no—
301C2×D44—44no—
302C2×D44—44no—
303C2×D44—44no—
304C2×D44—44no—
305C2×D44—44no—
306C2×D44—44no—
307C2×D44—44no—
308C2×D44—44no—
309C2×D44—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—
317(C2×D11)⋊C4—44no—
318(C2×D11)⋊C4—44no—
319(C2×D11)⋊C4—44no—
320(C2×D11)⋊C4—44no—
321(C2×D11)⋊C4—44no—
322(C2×D11)⋊C4—44no—
323(C2×D11)⋊C4—44no—
324(C2×D11)⋊C4—44no—
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—
330(C2×D11)⋊C4—44no—
331Dic11⋊C4—44no—
332C2×#392—111no—
333C2×#386—111no—
334C2×#386—111no—
335#1443—111no—
336#1443D1111yescharacteristic, complemented
337#1440—111no—
338#1440—111no—
339#1439—111no—
340#1439—111no—
341#1439—111no—
342#1438—111no—
343#1438—111no—
344#1438—111no—
345#1438—111no—
346C22⋊#95—111no—
347C23×C11C23×C411yescharacteristic
348C23×C11C22×D411yescharacteristic
349C23×C11C2×#4111yescharacteristic
350C23×C11H(5,𝔽2)11yescharacteristic
351C23×C11H(5,𝔽2)11yescharacteristic
352C23×C11H(5,𝔽2)11yescharacteristic
353C23×C11H(5,𝔽2)11yescharacteristic
354C23×C11H(5,𝔽2)11yescharacteristic
355C23×C11H(5,𝔽2)11yescharacteristic
356C23×C11H(5,𝔽2)11yescharacteristic
357C23×C11H(5,𝔽2)11yescharacteristic
358C23×C11H(5,𝔽2)11yescharacteristic
359C23×C11H(5,𝔽2)11yescharacteristic
360C23×C11H(5,𝔽2)11yescharacteristic
361C23×C112−1+411yescharacteristic
362C22×D11—22no—
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—41no—
395C22×D11—41no—
396C22×D11—41no—
397C22×D11—41no—
398C22×D11—41no—
399C22×D11—41no—
400C22×D11—41no—
401C22×D11—41no—
402C22×D11—41no—
403C22×D11—41no—
404C22×D11—41no—
405C22×D11—41no—
406C22×D11—41no—
407C22×D11—41no—
408C22×D11—41no—
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×D11—41no—
426C22×D11—41no—
427C22×D11—41no—
428C22×D11—41no—
429C22×D11—41no—
430C22×D11—41no—
431C22×D11—41no—
432C22×D11—41no—
433C22×D11—41no—
434C22×D11—41no—
435C22×D11—41no—
436C22×D11—41no—
437C22×D11—41no—
438C22×D11—41no—
439C22×D11—41no—
440C22×D11—41no—
441C22×D11—41no—
442C22×D11—41no—
443C22×D11—41no—
444C22×D11—41no—
445C22×D11—41no—
446C22×D11—41no—
447C22×D11—41no—
448C22×D11—41no—
449C22×D11—41no—
450C22×D11—41no—
451C22×D11—41no—
452C22×D11—41no—
453C22×D11—41no—
454C22×D11—41no—
455C22×D11—41no—
456C22×D11—41no—
457C22×D11—41no—
458C22×D11—41no—
459C22×D11—41no—
460C22×D11—41no—
461C22×D11—41no—
462C22×D11—41no—
463C22×D11—41no—
464C22×D11—41no—
465C22×D11—41no—
466C22×D11C4×D414yes—
467C2×C4×C11—22no—
468C2×C4×C11—22no—
469C2×C4×C11—22no—
470C2×C4×C11—22no—
471C2×C4×C11—22no—
472C2×C4×C11—22no—
473C2×C4×C11—22no—
474C2×C4×C11—22no—
475C2×C4×C11—22no—
476C2×C4×C11—22no—
477C2×C4×C11—22no—
478C2×C4×C11—22no—
479C2×C4×C11—41no—
480C2×C4×C11—41no—
481C2×C4×C11—41no—
482C2×C4×C11—41no—
483C2×C4×C11—41no—
484C2×C4×C11—41no—
485C2×C4×C11—41no—
486C2×C4×C11—41no—
487C2×C4×C11—41no—
488C2×C4×C11—41no—
489C2×C4×C11—41no—
490C2×C4×C11—41no—
491C2×C4×C11—41no—
492C2×C4×C11—41no—
493C2×C4×C11—41no—
494C2×C4×C11—41no—
495C2×C4×C11—41no—
496C2×C4×C11—41no—
497C2×C4×C11—41no—
498C2×C4×C11—41no—
499C2×C4×C11—41no—
500C2×C4×C11—41no—
501C2×C4×C11—41no—
502C2×C4×C11—41no—
503C2×C4×C11—41no—
504C2×C4×C11—41no—
505C2×C4×C11—41no—
506C2×C4×C11—41no—
507C2×C4×C11—41no—
508C2×C4×C11—41no—
509C2×C4×C11—41no—
510C2×C4×C11—41no—
511C2×C4×C11—41no—
512C2×C4×C11—41no—
513C2×C4×C11—41no—
514C2×C4×C11—41no—
515C2×C4×C11—41no—
516C2×Dic11—22no—
517C2×Dic11—22no—
518C2×Dic11—22no—
519C2×Dic11—22no—
520C2×Dic11—22no—
521C2×Dic11—22no—
522C2×Dic11—41no—
523C2×Dic11—41no—
524C2×Dic11—41no—
525C2×Dic11—41no—
526C2×Dic11—41no—
527C2×Dic11—41no—
528C2×Dic11—41no—
529C2×Dic11—41no—
530C2×Dic11—41no—
531C2×Dic11—41no—
532C2×Dic11—41no—
533C2×Dic11—41no—
534C2×Dic11—41no—
535C2×Dic11—41no—
536C2×Dic11—41no—
537C2×Dic11—41no—
538C2×Dic11—41no—
539C2×Dic11—41no—
540C2×Dic11—41no—
541C2×Dic11—41no—
542C2×Dic11—41no—
543C2×Dic11—41no—
544C2×Dic11—41no—
545C2×Dic11—41no—
546C2×Dic11—41no—
547C2×Dic11—41no—
548C2×Dic11—41no—
549C2×Dic11—41no—
550C2×Dic11—41no—
551D44—416no—
552D44—416no—
553D44—416no—
554C4×D11—416no—
555C23×D4—111no—
556C23×D4—111no—
557C23×D4—111no—
558C24×C4—111no—
559C22×C4⋊C4—111no—
560C22×C22⋊C4—111no—
561C22×C22⋊C4—111no—
562C22×C22⋊C4—111no—
563C22×C22⋊C4—111no—
564C22×C22⋊C4—111no—
565C22×C22⋊C4—111no—
566C22×C22⋊C4—111no—
567C22×C22⋊C4—111no—
568C22×C22⋊C4—111no—
569C22×C22⋊C4—111no—
570C22×C22⋊C4—111no—
571C22×C22⋊C4—111no—
572C22×C22⋊C4—111no—
573C22×C22⋊C4—111no—
574#392—118no—
575#386—224no—
576#386—224no—
577C2×#95—111no—
578C2×#95—111no—
579C2×#95—111no—
580C2×#95—111no—
581C2×#95—111no—
582C2×#95—111no—
583C2×#95—111no—
584C2×#95—111no—
585C2×#95—111no—
586C2×#95C2×D1111yescharacteristic
587C2×#95C2×D1111yescharacteristic
588C2×#95C2×D1111yescharacteristic
589C2×#95C2×D1111yescharacteristic
590C2×#95C2×D1111yescharacteristic
591C2×#95C2×D1111yescharacteristic
592C2×#95C2×D1111yescharacteristic
593C22×C11C2×C4×D411yescharacteristic
594C22×C11#51811yescharacteristic
595C22×C11#51811yescharacteristic
596C22×C11#51811yescharacteristic
597C22×C11#51811yescharacteristic
598C22×C11#51811yescharacteristic
599C22×C11#52011yescharacteristic
600C22×C11#53411yescharacteristic
601C22×C11#53411yescharacteristic
602C22×C11#53411yescharacteristic
603C22×C11#53511yescharacteristic
604C22×C11#53511yescharacteristic
605C22×C11#53711yescharacteristic
606C22×C11#53811yescharacteristic
607C22×C11#53811yescharacteristic
608C22×C11#53811yescharacteristic
609C22×C11#53811yescharacteristic
610C22×C11#53811yescharacteristic
611C22×C11#53911yescharacteristic
612C22×C11#56011yescharacteristic
613C22×C11#56011yescharacteristic
614C22×C11#56011yescharacteristic
615C22×C11#56011yescharacteristic
616C22×C11#56011yescharacteristic
617C22×C11#56011yescharacteristic
618C22×C11#56011yescharacteristic
619C22×C11#56011yescharacteristic
620C22×C11#56011yescharacteristic
621C22×C11#56011yescharacteristic
622C22×C11#56011yescharacteristic
623C22×C11H(3,𝔽4)11yescharacteristic
624C22×C11#56211yescharacteristic
625C22×C11#56211yescharacteristic
626C22×C11#56211yescharacteristic
627C22×C11#56211yescharacteristic
628C2×D11—24no—
629C2×D11—24no—
630C2×D11—24no—
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—42no—
641C2×D11—42no—
642C2×D11—42no—
643C2×D11—42no—
644C2×D11—42no—
645C2×D11—42no—
646C2×D11—42no—
647C2×D11—42no—
648C2×D11—42no—
649C2×D11—42no—
650C2×D11—42no—
651C2×D11—42no—
652C2×D11—42no—
653C2×D11—42no—
654C2×D11—42no—
655C2×D11—42no—
656C2×D11—42no—
657C2×D11—81no—
658C2×D11—81no—
659C2×D11—81no—
660C2×D11—81no—
661C2×D11—81no—
662C2×D11—81no—
663C2×D11—81no—
664C2×D11—81no—
665C2×D11—81no—
666C2×D11—81no—
667C2×D11—81no—
668C2×D11—81no—
669C2×D11—81no—
670C2×D11—81no—
671C2×D11—81no—
672C2×D11—81no—
673C4×C11—42no—
674C4×C11—42no—
675C4×C11—42no—
676C4×C11—42no—
677C4×C11—81no—
678C4×C11—81no—
679C4×C11—81no—
680Dic11—42no—
681Dic11—42no—
682Dic11—81no—
683Dic11—81no—
684Dic11—81no—
685C25—111no—
686C25—111no—
687C25—111no—
688C22×D4—114no—
689C22×D4—114no—
690C22×D4—114no—
691C22×D4—222no—
692C22×D4—222no—
693C22×D4—222no—
694C22×D4—222no—
695C22×D4—441no—
696C22×D4—441no—
697C22×D4—441no—
698C22×D4—441no—
699C22×D4—441no—
700C22×D4—441no—
701C22×D4—441no—
702C22×D4—441no—
703C22×D4—441no—
704C22×D4—441no—
705C22×D4—441no—
706C22×D4—441no—
707C22×D4—441no—
708C22×D4—441no—
709C23×C4—111no—
710C23×C4—111no—
711C23×C4—114no—
712C23×C4—111no—
713C23×C4—111no—
714C23×C4—111no—
715C23×C4—441no—
716C23×C4—441no—
717C23×C4—441no—
718C23×C4—441no—
719C23×C4—441no—
720C23×C4—441no—
721C23×C4C22×D1111yescharacteristic
722C23×C4C22×D1111yescharacteristic
723C23×C4C22×D1111yescharacteristic
724C23×C4C22×D1111yescharacteristic
725C23×C4C22×D1111yescharacteristic
726C23×C4C22×D1111yescharacteristic
727C23×C4C22×D1111yescharacteristic
728C2×C4⋊C4—441no—
729C2×C4⋊C4—441no—
730C2×C4⋊C4—441no—
731C2×C22⋊C4—114no—
732C2×C22⋊C4—114no—
733C2×C22⋊C4—114no—
734C2×C22⋊C4—222no—
735C2×C22⋊C4—222no—
736C2×C22⋊C4—222no—
737C2×C22⋊C4—222no—
738C2×C22⋊C4—222no—
739C2×C22⋊C4—222no—
740C2×C22⋊C4—222no—
741C2×C22⋊C4—441no—
742C2×C22⋊C4—441no—
743C2×C22⋊C4—441no—
744C2×C22⋊C4—441no—
745C2×C22⋊C4—441no—
746C2×C22⋊C4—441no—
747C2×C22⋊C4—441no—
748C2×C22⋊C4—441no—
749C2×C22⋊C4—441no—
750C2×C22⋊C4—441no—
751C2×C22⋊C4—441no—
752C2×C22⋊C4—441no—
753C2×C22⋊C4—441no—
754C2×C22⋊C4—441no—
755C2×C22⋊C4—441no—
756C2×C22⋊C4—441no—
757C2×C22⋊C4—441no—
758C2×C22⋊C4—441no—
759C2×C22⋊C4—441no—
760C2×C22⋊C4—441no—
761C2×C22⋊C4—441no—
762C2×C22⋊C4—441no—
763C2×C22⋊C4—441no—
764C2×C22⋊C4—441no—
765C2×C22⋊C4—441no—
766C2×C22⋊C4—441no—
767C2×C22⋊C4—441no—
768C2×C22⋊C4—441no—
769C2×C22⋊C4—441no—
770C2×C22⋊C4—441no—
771C2×C22⋊C4—441no—
772C2×C22⋊C4—441no—
773#95—22no—
774#95—22no—
775#95—41no—
776#95—41no—
777#95—41no—
778#95—41no—
779#95—222no—
780#95—222no—
781#95—441no—
782#95—441no—
783#95—441no—
784#95—441no—
785#95—441no—
786#95—441no—
787#95—441no—
788#95C4×D1114yescomplemented
789C2×C11#232111yescharacteristic
790C2×C11#232111yescharacteristic
791C2×C11#232511yescharacteristic
792C2×C11#237511yescharacteristic
793C2×C11#237711yescharacteristic
794C2×C11#237711yescharacteristic
795C2×C11#238011yescharacteristic
796C2×C11#281211yescharacteristic
797C2×C11#281311yescharacteristic
798C2×C11#281311yescharacteristic
799C2×C11#281511yescharacteristic
800C2×C11#282411yescharacteristic
801C2×C11#282511yescharacteristic
802C2×C11#282511yescharacteristic
803C2×C11#282611yescharacteristic
804D11—44no—
805D11—82no—
806D11—82no—
807C24—112no—
808C24—112no—
809C24—112no—
810C24—112no—
811C24—112no—
812C24—221no—
813C24—221no—
814C24—221no—
815C24—221no—
816C24—221no—
817C24—221no—
818C24—221no—
819C24—221no—
820C24—221no—
821C24—221no—
822C24—221no—
823C24—221no—
824C24—221no—
825C24—221no—
826C24—221no—
827C24—221no—
828C24—221no—
829C24—221no—
830C24—221no—
831C24—221no—
832C24—221no—
833C24—221no—
834C24—221no—
835C24—221no—
836C24—221no—
837C24—221no—
838C24—221no—
839C24—221no—
840C24—221no—
841C24—221no—
842C24—221no—
843C24—221no—
844C24—221no—
845C24—221no—
846C24—221no—
847C24—221no—
848C24—221no—
849C24—221no—
850C24—221no—
851C24—221no—
852C24C23×D1111yescharacteristic
853C2×D4—228no—
854C2×D4—228no—
855C2×D4—444no—
856C2×D4—444no—
857C2×D4—444no—
858C2×D4—444no—
859C2×D4—444no—
860C2×D4—444no—
861C2×D4—444no—
862C2×D4—444no—
863C2×D4—444no—
864C2×D4—444no—
865C2×D4—444no—
866C2×D4—444no—
867C2×D4—444no—
868C2×D4—444no—
869C2×D4—444no—
870C2×D4—444no—
871C2×D4—444no—
872C2×D4—444no—
873C2×D4—444no—
874C22×C4—21no—
875C22×C4—21no—
876C22×C4—21no—
877C22×C4—21no—
878C22×C4—21no—
879C22×C4—21no—
880C22×C4—21no—
881C22×C4—21no—
882C22×C4—21no—
883C22×C4—21no—
884C22×C4—21no—
885C22×C4—21no—
886C22×C4—21no—
887C22×C4—21no—
888C22×C4—21no—
889C22×C4—21no—
890C22×C4—21no—
891C22×C4—21no—
892C22×C4—21no—
893C22×C4—21no—
894C22×C4—21no—
895C22×C4—21no—
896C22×C4—21no—
897C22×C4—21no—
898C22×C4—21no—
899C22×C4—21no—
900C22×C4—21no—
901C22×C4—21no—
902C22×C4—21no—
903C22×C4—21no—
904C22×C4—21no—
905C22×C4—21no—
906C22×C4—21no—
907C22×C4—21no—
908C22×C4—21no—
909C22×C4—21no—
910C22×C4—21no—
911C22×C4—21no—
912C22×C4—21no—
913C22×C4—21no—
914C22×C4—21no—
915C22×C4—21no—
916C22×C4—21no—
917C22×C4—21no—
918C22×C4—21no—
919C22×C4—112no—
920C22×C4—112no—
921C22×C4—221no—
922C22×C4—221no—
923C22×C4—221no—
924C22×C4—221no—
925C22×C4—221no—
926C22×C4—221no—
927C22×C4—221no—
928C22×C4—221no—
929C22×C4—221no—
930C22×C4—221no—
931C22×C4—221no—
932C22×C4—221no—
933C22×C4—221no—
934C22×C4—221no—
935C22×C4—221no—
936C22×C4—221no—
937C22×C4—221no—
938C22×C4—221no—
939C22×C4—221no—
940C22×C4—221no—
941C22×C4—221no—
942C22×C4—221no—
943C22×C4—221no—
944C22×C4—221no—
945C22×C4—221no—
946C22×C4—221no—
947C22×C4—221no—
948C22×C4—221no—
949C22×C4—221no—
950C22×C4—221no—
951C22×C4—221no—
952C22×C4—221no—
953C22×C4—221no—
954C22×C4—444no—
955C22×C4—444no—
956C22×C4—444no—
957C22×C4—444no—
958C22×C4—444no—
959C22×C4—444no—
960C22×C4—444no—
961C22×C4C2×C4×D1112yes—
962C22×C4C2×C4×D1112yes—
963C22×C4C2×C4×D1112yes—
964C22×C4D4×D1112yes—
965C4⋊C4—444no—
966C22⋊C4—444no—
967C22⋊C4—444no—
968C22⋊C4—444no—
969C22⋊C4—444no—
970C22⋊C4—444no—
971C22⋊C4—444no—
972C22⋊C4—444no—
973C22⋊C4—444no—
974C22⋊C4—444no—
975C22⋊C4—444no—
976C22⋊C4—444no—
977C22⋊C4—444no—
978C22⋊C4—444no—
979C22⋊C4—444no—
980C11#1462111yescharacteristic, complemented, Sylow
981C23—114no—
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—222no—
1002C23—222no—
1003C23—222no—
1004C23—222no—
1005C23—222no—
1006C23—222no—
1007C23—222no—
1008C23—222no—
1009C23—222no—
1010C23—222no—
1011C23—222no—
1012C23—222no—
1013C23—222no—
1014C23—441no—
1015C23—441no—
1016C23—441no—
1017C23—441no—
1018C23—441no—
1019C23—441no—
1020C23—441no—
1021C23—441no—
1022C23—441no—
1023C23—441no—
1024C23—441no—
1025C23—441no—
1026C23—441no—
1027C23—441no—
1028C23—441no—
1029C23—441no—
1030C23—441no—
1031C23—441no—
1032C23—441no—
1033C23—441no—
1034C23—441no—
1035C23—441no—
1036C23—441no—
1037C23—441no—
1038C23—441no—
1039C23—441no—
1040C23—441no—
1041C23—441no—
1042C23—441no—
1043C23—441no—
1044C23—441no—
1045C23—441no—
1046C23—441no—
1047C23—441no—
1048C23—441no—
1049C23—441no—
1050C23—441no—
1051C23—441no—
1052C23—441no—
1053C23—441no—
1054C23—441no—
1055C23—441no—
1056C23—441no—
1057C23—441no—
1058C23—441no—
1059C23—441no—
1060C23—441no—
1061C23—441no—
1062C23—441no—
1063C23—441no—
1064C23—441no—
1065C23—441no—
1066C23—441no—
1067C23—441no—
1068C23—441no—
1069C23—441no—
1070C23—441no—
1071C23—441no—
1072C23—441no—
1073C23—441no—
1074C23—441no—
1075C23—441no—
1076C23—441no—
1077C23—441no—
1078C23—441no—
1079C23—441no—
1080C23—441no—
1081C23—441no—
1082C23—441no—
1083C23—441no—
1084C23—441no—
1085C23—441no—
1086C23C22×C4×D1111yescharacteristic
1087C23C2×D4×D1111yescharacteristic
1088C23#6703711yescharacteristic
1089C23#6703711yescharacteristic
1090C23#6704011yescharacteristic
1091C23#41×D1111yescharacteristic
1092C23#6704211yescharacteristic
1093C23#6704211yescharacteristic
1094C23#6704211yescharacteristic
1095C23#6704211yescharacteristic
1096C23#6704211yescharacteristic
1097C23#6704211yescharacteristic
1098C23#6704211yescharacteristic
1099C23#6704211yescharacteristic
1100C23#6704211yescharacteristic
1101D4—4416no—
1102D4—4416no—
1103D4—4416no—
1104C2×C4—22no—
1105C2×C4—22no—
1106C2×C4—22no—
1107C2×C4—22no—
1108C2×C4—22no—
1109C2×C4—22no—
1110C2×C4—22no—
1111C2×C4—22no—
1112C2×C4—22no—
1113C2×C4—22no—
1114C2×C4—22no—
1115C2×C4—22no—
1116C2×C4—41no—
1117C2×C4—41no—
1118C2×C4—41no—
1119C2×C4—41no—
1120C2×C4—41no—
1121C2×C4—41no—
1122C2×C4—41no—
1123C2×C4—41no—
1124C2×C4—41no—
1125C2×C4—41no—
1126C2×C4—41no—
1127C2×C4—41no—
1128C2×C4—41no—
1129C2×C4—41no—
1130C2×C4—41no—
1131C2×C4—41no—
1132C2×C4—41no—
1133C2×C4—41no—
1134C2×C4—41no—
1135C2×C4—41no—
1136C2×C4—41no—
1137C2×C4—41no—
1138C2×C4—41no—
1139C2×C4—41no—
1140C2×C4—41no—
1141C2×C4—41no—
1142C2×C4—41no—
1143C2×C4—41no—
1144C2×C4—41no—
1145C2×C4—41no—
1146C2×C4—41no—
1147C2×C4—41no—
1148C2×C4—41no—
1149C2×C4—41no—
1150C2×C4—41no—
1151C2×C4—41no—
1152C2×C4—41no—
1153C2×C4—222no—
1154C2×C4—222no—
1155C2×C4—222no—
1156C2×C4—222no—
1157C2×C4—222no—
1158C2×C4—222no—
1159C2×C4—4416no—
1160C2×C4—441no—
1161C2×C4—441no—
1162C2×C4—441no—
1163C2×C4—441no—
1164C2×C4—441no—
1165C2×C4—441no—
1166C2×C4—441no—
1167C2×C4—441no—
1168C2×C4—441no—
1169C2×C4—441no—
1170C2×C4—441no—
1171C2×C4—441no—
1172C2×C4—441no—
1173C2×C4—441no—
1174C2×C4—441no—
1175C2×C4—441no—
1176C2×C4—441no—
1177C2×C4—441no—
1178C2×C4—441no—
1179C2×C4—441no—
1180C2×C4—441no—
1181C2×C4—441no—
1182C2×C4—441no—
1183C2×C4—441no—
1184C2×C4—441no—
1185C2×C4—441no—
1186C2×C4—441no—
1187C2×C4—441no—
1188C2×C4—441no—
1189C22—224no—
1190C22—224no—
1191C22—224no—
1192C22—442no—
1193C22—442no—
1194C22—442no—
1195C22—442no—
1196C22—442no—
1197C22—442no—
1198C22—442no—
1199C22—442no—
1200C22—442no—
1201C22—442no—
1202C22—442no—
1203C22—442no—
1204C22—442no—
1205C22—442no—
1206C22—442no—
1207C22—442no—
1208C22—442no—
1209C22—442no—
1210C22—442no—
1211C22—442no—
1212C22—442no—
1213C22—442no—
1214C22—442no—
1215C22—442no—
1216C22—442no—
1217C22—442no—
1218C22—881no—
1219C22—881no—
1220C22—881no—
1221C22—881no—
1222C22—881no—
1223C22—881no—
1224C22—881no—
1225C22—881no—
1226C22—881no—
1227C22—881no—
1228C22—881no—
1229C22—881no—
1230C22—881no—
1231C22—881no—
1232C22—881no—
1233C22—881no—
1234C22#1062305211yescharacteristic
1235C22#1062305211yescharacteristic
1236C22#1062305211yescharacteristic
1237C22C4×D4×D1111yescharacteristic
1238C22#1062307611yescharacteristic
1239C22#1062307611yescharacteristic
1240C22#1062310511yescharacteristic
1241C22#1062313611yescharacteristic
1242C22#1062313811yescharacteristic
1243C22#1062315111yescharacteristic
1244C22#1062316011yescharacteristic
1245C22#1062317811yescharacteristic
1246C22#1062317811yescharacteristic
1247C22#1062318411yescharacteristic
1248C22#1062318411yescharacteristic
1249C22#1062318811yescharacteristic
1250C22#1062319711yescharacteristic
1251C22#1062319711yescharacteristic
1252C22#1062319711yescharacteristic
1253C22#1062320511yescharacteristic
1254C22#1062320911yescharacteristic
1255C22#1062321411yescharacteristic
1256C22#1062322311yescharacteristic
1257C22#1062323111yescharacteristic
1258C22#1062323111yescharacteristic
1259C22#1062323511yescharacteristic
1260C22#1062323511yescharacteristic
1261C22#1062323511yescharacteristic
1262C22#1062324211yescharacteristic
1263C22#1062324211yescharacteristic
1264C22#1062324211yescharacteristic
1265C22#1062324211yescharacteristic
1266C22#1062324211yescharacteristic
1267C22#1062324211yescharacteristic
1268C22#1062324211yescharacteristic
1269C4—42no—
1270C4—42no—
1271C4—42no—
1272C4—42no—
1273C4—81no—
1274C4—81no—
1275C4—81no—
1276C4—442no—
1277C4—442no—
1278C4—881no—
1279C4—881no—
1280C4—881no—
1281C2—444no—
1282C2—882no—
1283C2—882no—
1284C2#1307126911yescharacteristic
1285C2#1307127811yescharacteristic
1286C2#1307131511yescharacteristic
1287C2#1307175611yescharacteristic
1288C2#1307177111yescharacteristic
1289C2#1307177111yescharacteristic
1290C2#1307179211yescharacteristic
1291C2#1307661411yescharacteristic
1292C2#1307662111yescharacteristic
1293C2#1307662511yescharacteristic
1294C2#1307663911yescharacteristic
1295C2#1307669711yescharacteristic
1296C2#1307670311yescharacteristic
1297C2#1307670611yescharacteristic
1298C2#1307671311yescharacteristic
subgroupG/H
center, FrattiniC24C23×D11
commutatorC23×C11C23×C4
FittingC11×#1443C2
socle, cosocleC24×C11C24
prime radicalC2×#10622284C2
hypercenter#1443D11
hypocenterC11#14621
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ #1443

Complements

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

NH ≅ G/Ntype
2. C2×#10622278C2semidirect
3. C2×#10622278C2semidirect
4. #13066878C2semidirect
5. #13066864C2semidirect
6. #13066864C2semidirect
7. #13066860C2semidirect
8. #13066860C2semidirect
9. #13066860C2semidirect
10. #13066856C2semidirect
11. #13066856C2semidirect
12. #13066856C2semidirect
13. #13066856C2semidirect
14. (C2×D11)⋊#95C2semidirect
15. C11×#1443C2semidirect
51. #10622284C4semidirect
89. C22×D44C2×C4semidirect
96. C22×C4×D11D4semidirect
137. C2×(C2×D11)⋊C4C2×C4semidirect
138. C2×(C2×D11)⋊C4C2×C4semidirect
148. C11×#95C2×C4semidirect
336. #1443D11semidirect
788. #95C4×D11semidirect
980. C11#14621semidirect

Maximal subgroups

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

subgroupindex
C2×#106222842
C2×#106222782
#130668782
#130668642
#130668602
#130668562
(C2×D11)⋊#952
C11×#14432
#1462111