Finite Group Databasebeta

← #14676635

Subgroups — #14676635

Order 2816.

2690 conjugacy classes of subgroups.

The subgroup lattice has 1234 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C4×C22⋊D11C211yesmaximal, characteristic
2C2×#10622571C211yesmaximal, characteristic
3C2×#10622571C211yesmaximal, characteristic
4C2×#10622602C211yesmaximal, characteristic, complemented
5C2×#10622555C211yesmaximal, characteristic, complemented
6C22×C11⋊#95C211yesmaximal, characteristic, complemented
7#13066879C211yesmaximal, characteristic, complemented
8#13066874C211yesmaximal, characteristic, complemented
9#13066860C211yesmaximal, characteristic, complemented
10#13066858C211yesmaximal, characteristic, complemented
11#13066848C211yesmaximal, characteristic, complemented
12#13066847C211yesmaximal, characteristic, complemented
13#13066838C211yesmaximal, characteristic, complemented
14(C2×D11)⋊#95C211yesmaximal, characteristic, complemented
15C2×C11×#385C211yesmaximal, characteristic, complemented
16C24×C4×C11C2211yescharacteristic
17C23×C22⋊D11C2211yescharacteristic
18C24×Dic11C2211yescharacteristic
19C24×Dic11C2211yescharacteristic
20C23×C4×D11C2211yescharacteristic
21C22×C11×C4⋊C4C2211yescharacteristic
22C22×C11×C4⋊C4C2211yescharacteristic
23C22×C11×C22⋊C4C2211yescharacteristic
24C22×C11×C22⋊C4C2211yescharacteristic
25C22×C22⋊Dic11C2211yescharacteristic
26C2×C4×C22⋊D11—24no—
27C2×C4×C22⋊D11—24no—
28C2×C4×C22⋊D11—24no—
29C22×(C2×D11)⋊C4C2211yescharacteristic
30C22×(C2×D11)⋊C4C2211yescharacteristic
31C22×(C2×D11)⋊C4C2211yescharacteristic
32C22×(C2×D11)⋊C4C2211yescharacteristic
33C22×(C2×D11)⋊C4C2211yescharacteristic
34C22×Dic11⋊C4C2211yescharacteristic
35C22×Dic11⋊C4C2211yescharacteristic
36C22×Dic11⋊C4C2211yescharacteristic
37C22×C4×Dic11C2211yescharacteristic
38C11×#385—24no—
39C2×C11×#95C2211yescharacteristic
40C2×C11×#95C2211yescharacteristic
41C2×C11⋊#95—24no—
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
56#10622602—24no—
57#10622571—24no—
58#10622571C418yescomplemented
59#10622555—24no—
60C25×C11C2311yescharacteristic
61C24×D11C2311yescharacteristic
62C23×C4×C11—22no—
63C23×C4×C11—22no—
64C23×C4×C11—22no—
65C23×C4×C11—22no—
66C23×C4×C11—41no—
67C23×C4×C11—41no—
68C23×C4×C11D414yes—
69C23×C4×C11C2311yescharacteristic
70C23×C4×C11C2311yescharacteristic
71C23×C4×C11C2311yescharacteristic
72C23×C4×C11C2311yescharacteristic
73C23×C4×C11C2311yescharacteristic
74C23×C4×C11C2311yescharacteristic
75C22×C22⋊D11—22no—
76C22×C22⋊D11—22no—
77C22×C22⋊D11—22no—
78C22×C22⋊D11—22no—
79C22×C22⋊D11C2×C414yes—
80C22×C22⋊D11D414yes—
81C22×C22⋊D11Q814yes—
82C23×Dic11—22no—
83C23×Dic11—22no—
84C23×Dic11—22no—
85C23×Dic11—22no—
86C23×Dic11—22no—
87C23×Dic11—22no—
88C23×Dic11—22no—
89C23×Dic11—22no—
90C23×Dic11—22no—
91C23×Dic11—41no—
92C23×Dic11—41no—
93C23×Dic11—41no—
94C23×Dic11—41no—
95C23×Dic11C2×C414yescomplemented
96C23×Dic11C2311yescharacteristic
97C23×Dic11C2311yescharacteristic
98C23×Dic11C2311yescharacteristic
99C23×Dic11C2311yescharacteristic
100C23×Dic11C2311yescharacteristic
101C23×Dic11C2311yescharacteristic
102C23×Dic11C2311yescharacteristic
103C22×C4×D11—22no—
104C22×C4×D11—22no—
105C22×C4×D11—22no—
106C22×C4×D11—22no—
107C22×C4×D11—22no—
108C22×C4×D11—41no—
109C22×C4×D11—41no—
110C2×C11×C4⋊C4—22no—
111C2×C11×C4⋊C4—22no—
112C2×C11×C4⋊C4—22no—
113C2×C11×C4⋊C4—22no—
114C2×C11×C4⋊C4—41no—
115C2×C11×C4⋊C4—41no—
116C2×C11×C22⋊C4—22no—
117C2×C11×C22⋊C4—22no—
118C2×C11×C22⋊C4—22no—
119C2×C11×C22⋊C4—22no—
120C2×C11×C22⋊C4—22no—
121C2×C11×C22⋊C4C2×C414yescomplemented
122C2×C22⋊Dic11—22no—
123C2×C22⋊Dic11—22no—
124C2×C22⋊Dic11D414yes—
125C4×C22⋊D11—232no—
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—22no—
135C2×(C2×D11)⋊C4—41no—
136C2×(C2×D11)⋊C4—41no—
137C2×(C2×D11)⋊C4—41no—
138C2×(C2×D11)⋊C4—41no—
139C2×(C2×D11)⋊C4C2×C414yescomplemented
140C2×(C2×D11)⋊C4C2×C414yescomplemented
141C2×Dic11⋊C4—22no—
142C2×Dic11⋊C4—22no—
143C2×Dic11⋊C4—22no—
144C2×Dic11⋊C4—22no—
145C2×Dic11⋊C4—22no—
146C2×Dic11⋊C4—22no—
147C2×Dic11⋊C4—22no—
148C2×Dic11⋊C4—41no—
149C2×Dic11⋊C4—41no—
150C2×C4×Dic11—22no—
151C2×C4×Dic11—22no—
152C2×C4×Dic11—22no—
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—
166C11⋊#95C2×C414yescomplemented
167C11⋊#95C2×C414yescomplemented
168C11⋊#95D414yescomplemented
169#13975—111nomaximal, Sylow
170C24×C11—21no—
171C24×C11—21no—
172C24×C11—21no—
173C24×C11—21no—
174C24×C11—21no—
175C24×C11—21no—
176C24×C11—21no—
177C24×C11—21no—
178C24×C11C22×C412yes—
179C24×C11C2×D412yes—
180C24×C11C2×D412yes—
181C24×C11C2×D412yes—
182C24×C11C2×Q812yes—
183C24×C11#4112yes—
184C24×C11#4112yes—
185C24×C11C2411yescharacteristic
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×D11C22×C412yes—
199C23×D11C2×D412yes—
200C23×D11C2×Q812yes—
201C22×C4×C11—21no—
202C22×C4×C11—21no—
203C22×C4×C11—21no—
204C22×C4×C11—21no—
205C22×C4×C11—28no—
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—28no—
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—44no—
240C22×C4×C11—44no—
241C22×C4×C11—44no—
242C22×C4×C11—44no—
243C22×C4×C11—44no—
244C22×C4×C11C22×C412yes—
245C22×C4×C11C22×C412yes—
246C22×C4×C11C2×D412yes—
247C22×C4×C11C2×D412yes—
248C22×C4×C11C2×D412yes—
249C22×C4×C11#4112yes—
250C2×C22⋊D11—28no—
251C2×C22⋊D11—28no—
252C2×C22⋊D11—28no—
253C2×C22⋊D11—28no—
254C2×C22⋊D11—28no—
255C2×C22⋊D11—28no—
256C2×C22⋊D11C4⋊C4116yescomplemented
257C22×Dic11—28no—
258C22×Dic11—28no—
259C22×Dic11—28no—
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×Dic11—21no—
288C22×Dic11—21no—
289C22×Dic11—21no—
290C22×Dic11—21no—
291C22×Dic11—21no—
292C22×Dic11—21no—
293C22×Dic11—21no—
294C22×Dic11—21no—
295C22×Dic11—21no—
296C22×Dic11—21no—
297C22×Dic11—21no—
298C22×Dic11—44no—
299C22×Dic11—44no—
300C22×Dic11—44no—
301C22×Dic11—44no—
302C22×Dic11—44no—
303C22×Dic11—44no—
304C22×Dic11—44no—
305C22×Dic11—44no—
306C22×Dic11—44no—
307C22×Dic11—44no—
308C22×Dic11—44no—
309C22×Dic11C22×C412yes—
310C22×Dic11C22×C412yes—
311C22×Dic11C22×C412yes—
312C22×Dic11C2×D412yes—
313C22×Dic11C2×D412yes—
314C22×Dic11C2×D412yes—
315C22×Dic11C2×D412yes—
316C22×Dic11C2×D412yes—
317C22×Dic11C2×Q812yes—
318C22×Dic11#4112yes—
319C22×Dic11#4112yes—
320C2×C4×D11—28no—
321C2×C4×D11—44no—
322C2×C4×D11—44no—
323C2×C4×D11—44no—
324C2×C4×D11—44no—
325C2×C4×D11—44no—
326C2×C4×D11—44no—
327C11×C4⋊C4—44no—
328C11×C4⋊C4—44no—
329C11×C22⋊C4—28no—
330C11×C22⋊C4—44no—
331C22⋊Dic11—28no—
332(C2×D11)⋊C4—28no—
333(C2×D11)⋊C4—28no—
334(C2×D11)⋊C4—44no—
335(C2×D11)⋊C4—44no—
336(C2×D11)⋊C4—44no—
337Dic11⋊C4—28no—
338Dic11⋊C4—44no—
339Dic11⋊C4—44no—
340C4×Dic11—28no—
341C22×C4×D4—111no—
342C2×#386—111no—
343C2×#386—111no—
344C2×#385—111no—
345C2×#385D1111yescharacteristic, complemented
346C2×#380—111no—
347C22×#95—111no—
348#1444—111no—
349#1442—111no—
350#1439—111no—
351#1439—111no—
352#1436—111no—
353#1436—111no—
354C22⋊#95—111no—
355C22⋊#95—111no—
356C23×C11—22no—
357C23×C11—22no—
358C23×C11—22no—
359C23×C11—22no—
360C23×C11—22no—
361C23×C11—22no—
362C23×C11—22no—
363C23×C11—22no—
364C23×C11—22no—
365C23×C11—22no—
366C23×C11—22no—
367C23×C11—22no—
368C23×C11—22no—
369C23×C11—22no—
370C23×C11—22no—
371C23×C11—22no—
372C23×C11—22no—
373C23×C11—22no—
374C23×C11—22no—
375C23×C11—22no—
376C23×C11—22no—
377C23×C11—22no—
378C23×C11—22no—
379C23×C11—22no—
380C23×C11—22no—
381C23×C11—22no—
382C23×C11—22no—
383C23×C11—22no—
384C23×C11C2×C4⋊C414yes—
385C23×C11C4×D414yes—
386C23×C11C4×D414yes—
387C23×C11#12014yes—
388C23×C11C22⋊Q814yes—
389C23×C11C22⋊Q814yes—
390C23×C11#12314yes—
391C23×C11C23×C411yescharacteristic
392C23×C11C22×D411yescharacteristic
393C23×C11C22×D411yescharacteristic
394C23×C11C22×D411yescharacteristic
395C23×C11C22×D411yescharacteristic
396C23×C11C22×Q811yescharacteristic
397C23×C11C2×#4111yescharacteristic
398C23×C11C2×#4111yescharacteristic
399C23×C11C2×#4111yescharacteristic
400C23×C11C2×#4111yescharacteristic
401C23×C11C2×#4111yescharacteristic
402C23×C11H(5,𝔽2)11yescharacteristic
403C23×C11H(5,𝔽2)11yescharacteristic
404C23×C11H(5,𝔽2)11yescharacteristic
405C23×C112−1+411yescharacteristic
406C22×D11—22no—
407C22×D11—22no—
408C22×D11—22no—
409C22×D11—22no—
410C22×D11—22no—
411C22×D11—22no—
412C22×D11—22no—
413C22×D11—22no—
414C22×D11—22no—
415C22×D11—22no—
416C22×D11—22no—
417C22×D11—22no—
418C22×D11—22no—
419C22×D11—22no—
420C22×D11—22no—
421C22×D11—22no—
422C22×D11—22no—
423C22×D11—22no—
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×D11C2×C4⋊C414yes—
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—416no—
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#12114yes—
484C22⋊D11—232no—
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—22no—
504C2×Dic11—22no—
505C2×Dic11—22no—
506C2×Dic11—22no—
507C2×Dic11—22no—
508C2×Dic11—22no—
509C2×Dic11—22no—
510C2×Dic11—22no—
511C2×Dic11—22no—
512C2×Dic11—416no—
513C2×Dic11—416no—
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—41no—
527C2×Dic11—41no—
528C2×Dic11—41no—
529C2×Dic11—41no—
530C2×Dic11—41no—
531C2×Dic11—41no—
532C2×Dic11—41no—
533C2×Dic11—41no—
534C2×Dic11C2×C4⋊C414yes—
535C2×Dic11C4×D414yescomplemented
536C4×D11—416no—
537C23×D4—111no—
538C24×C4—111no—
539C24×C4—111no—
540C24×C4—111no—
541C24×C4C2×D1111yescharacteristic
542C2×C4×D4—224no—
543C2×C4×D4—224no—
544C2×C4×D4—224no—
545C22×C4⋊C4—111no—
546C22×C4⋊C4—111no—
547C22×C4⋊C4—111no—
548C22×C4⋊C4C2×D1111yescharacteristic
549C22×C4⋊C4C2×D1111yescharacteristic
550C22×C22⋊C4—111no—
551C22×C22⋊C4—111no—
552C22×C22⋊C4—111no—
553C22×C22⋊C4—111no—
554C22×C22⋊C4—111no—
555C22×C22⋊C4—111no—
556C22×C22⋊C4C2×D1111yescharacteristic
557C22×C22⋊C4C2×D1111yescharacteristic
558C22×C42—111no—
559#386—118no—
560#386—224no—
561#385—24no—
562#385—224no—
563#380—224no—
564C2×#95—111no—
565C2×#95—111no—
566C2×#95—111no—
567C2×#95—111no—
568C2×#95—111no—
569C2×#95—111no—
570C2×#95—111no—
571C2×#95—111no—
572C2×#95—111no—
573C2×#95—111no—
574C2×#95—111no—
575C2×#95—111no—
576C2×#95—111no—
577C2×#95—111no—
578C2×#95—224no—
579C2×#95C2×D1111yescharacteristic
580C2×#95C2×D1111yescharacteristic
581C22×C11—24no—
582C22×C11—24no—
583C22×C11—24no—
584C22×C11—24no—
585C22×C11—24no—
586C22×C11—24no—
587C22×C11—24no—
588C22×C11—24no—
589C22×C11—24no—
590C22×C11—24no—
591C22×C11—24no—
592C22×C11—24no—
593C22×C11—24no—
594C22×C11—24no—
595C22×C11#38518yescomplemented
596C22×C11C22×C4⋊C411yescharacteristic
597C22×C11C2×C4×D411yescharacteristic
598C22×C11C2×C4×D411yescharacteristic
599C22×C11C2×C4×D411yescharacteristic
600C22×C11C4×#4111yescharacteristic
601C22×C11#51811yescharacteristic
602C22×C11#52011yescharacteristic
603C22×C11C2×#12011yescharacteristic
604C22×C11C2×#12111yescharacteristic
605C22×C11C2×C22⋊Q811yescharacteristic
606C22×C11C2×C22⋊Q811yescharacteristic
607C22×C11C2×#12311yescharacteristic
608C22×C11#52511yescharacteristic
609C22×C11#52911yescharacteristic
610C22×C11#53211yescharacteristic
611C22×C11#53411yescharacteristic
612C22×C11#53711yescharacteristic
613C22×C11#53811yescharacteristic
614C22×C11#53911yescharacteristic
615C22×C11D4211yescharacteristic
616C22×C11D4211yescharacteristic
617C22×C11#54611yescharacteristic
618C22×C11#54611yescharacteristic
619C22×C11#54611yescharacteristic
620C22×C11#54611yescharacteristic
621C22×C11#54611yescharacteristic
622C22×C11#54711yescharacteristic
623C22×C11#54711yescharacteristic
624C22×C11D4×Q811yescharacteristic
625C22×C11#55111yescharacteristic
626C22×C11#55111yescharacteristic
627C22×C11#55211yescharacteristic
628C22×C11#55411yescharacteristic
629C22×C11#55411yescharacteristic
630C22×C11#55411yescharacteristic
631C2×D11—24no—
632C2×D11—24no—
633C2×D11—24no—
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—
646C4×C11—24no—
647C4×C11—42no—
648C4×C11—42no—
649C4×C11—42no—
650C4×C11—81no—
651C4×C11—81no—
652Dic11—24no—
653Dic11—24no—
654Dic11—42no—
655Dic11—42no—
656Dic11—42no—
657Dic11—42no—
658Dic11—42no—
659C25—111no—
660C25C22×D1111yescharacteristic
661C22×D4—114no—
662C22×D4—114no—
663C22×D4—114no—
664C22×D4—222no—
665C22×D4—222no—
666C22×D4—222no—
667C22×D4—222no—
668C23×C4—22no—
669C23×C4—22no—
670C23×C4—22no—
671C23×C4—22no—
672C23×C4—41no—
673C23×C4—41no—
674C23×C4—111no—
675C23×C4—111no—
676C23×C4—111no—
677C23×C4—111no—
678C23×C4—111no—
679C23×C4—111no—
680C23×C4—111no—
681C23×C4—114no—
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—222no—
692C23×C4—222no—
693C23×C4—222no—
694C23×C4—222no—
695C23×C4—222no—
696C23×C4—441no—
697C23×C4—441no—
698C23×C4—441no—
699C23×C4—441no—
700C23×C4—441no—
701C23×C4—441no—
702C23×C4C22⋊D1114yes—
703C23×C4C22×D1111yescharacteristic
704C23×C4C22×D1111yescharacteristic
705C23×C4C22×D1111yescharacteristic
706C23×C4C22×D1111yescharacteristic
707C23×C4C22×D1111yescharacteristic
708C23×C4C22×D1111yescharacteristic
709C4×D4—2232no—
710C2×C4⋊C4—22no—
711C2×C4⋊C4—22no—
712C2×C4⋊C4—22no—
713C2×C4⋊C4—22no—
714C2×C4⋊C4—41no—
715C2×C4⋊C4—41no—
716C2×C4⋊C4—222no—
717C2×C4⋊C4—222no—
718C2×C4⋊C4—222no—
719C2×C4⋊C4—222no—
720C2×C4⋊C4—222no—
721C2×C4⋊C4—222no—
722C2×C4⋊C4—222no—
723C2×C4⋊C4—441no—
724C2×C4⋊C4—441no—
725C2×C22⋊C4—22no—
726C2×C22⋊C4—22no—
727C2×C22⋊C4—22no—
728C2×C22⋊C4—22no—
729C2×C22⋊C4—22no—
730C2×C22⋊C4—114no—
731C2×C22⋊C4—114no—
732C2×C22⋊C4—114no—
733C2×C22⋊C4—222no—
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—222no—
742C2×C22⋊C4—222no—
743C2×C22⋊C4—222no—
744C2×C22⋊C4—441no—
745C2×C22⋊C4—441no—
746C2×C22⋊C4—441no—
747C2×C22⋊C4—441no—
748C2×C22⋊C4C4×D1114yescomplemented
749C2×C42—222no—
750C2×C42—222no—
751C2×C42—222no—
752#95—22no—
753#95—22no—
754#95—114no—
755#95—114no—
756#95—114no—
757#95—222no—
758#95—222no—
759#95—222no—
760#95—222no—
761#95—222no—
762#95—222no—
763#95—222no—
764#95—222no—
765#95—222no—
766#95—441no—
767#95—441no—
768C2×C11—28no—
769C2×C11C2×#38511yescharacteristic
770C2×C11C4×#12111yescharacteristic
771C2×C11#232511yescharacteristic
772C2×C11D4×C4⋊C411yescharacteristic
773C2×C11#234911yescharacteristic
774C2×C11#235811yescharacteristic
775C2×C11#235911yescharacteristic
776C2×C11#241011yescharacteristic
777C2×C11#241711yescharacteristic
778C2×C11#241811yescharacteristic
779C2×C11#241911yescharacteristic
780C2×C11#243011yescharacteristic
781C2×C11#244911yescharacteristic
782C2×C11#245011yescharacteristic
783C2×C11#256411yescharacteristic
784D11—44no—
785C24—21no—
786C24—21no—
787C24—21no—
788C24—21no—
789C24—21no—
790C24—21no—
791C24—21no—
792C24—21no—
793C24—112no—
794C24—112no—
795C24—112no—
796C24—221no—
797C24—221no—
798C24—221no—
799C24—221no—
800C24—221no—
801C24—221no—
802C24—221no—
803C24—221no—
804C24—221no—
805C24—221no—
806C24—221no—
807C24—221no—
808C24C2×C4×D1112yes—
809C24#433912yes—
810C24D4×D1112yes—
811C24D4×D1112yes—
812C24Q8×D1112yes—
813C24#434312yes—
814C24C2×C22⋊D1112yes—
815C24C23×D1111yescharacteristic
816C2×D4—1116no—
817C2×D4—228no—
818C2×D4—228no—
819C2×D4—228no—
820C2×D4—228no—
821C2×D4—228no—
822C2×D4—228no—
823C22×C4—21no—
824C22×C4—21no—
825C22×C4—21no—
826C22×C4—21no—
827C22×C4—28no—
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—28no—
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—21no—
857C22×C4—21no—
858C22×C4—21no—
859C22×C4—21no—
860C22×C4—21no—
861C22×C4—44no—
862C22×C4—44no—
863C22×C4—44no—
864C22×C4—44no—
865C22×C4—44no—
866C22×C4—112no—
867C22×C4—112no—
868C22×C4—112no—
869C22×C4—112no—
870C22×C4—112no—
871C22×C4—112no—
872C22×C4—112no—
873C22×C4—112no—
874C22×C4—112no—
875C22×C4—112no—
876C22×C4—112no—
877C22×C4—228no—
878C22×C4—228no—
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—228no—
888C22×C4—228no—
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—221no—
906C22×C4—221no—
907C22×C4—221no—
908C22×C4—221no—
909C22×C4—221no—
910C22×C4—221no—
911C22×C4—221no—
912C22×C4—221no—
913C22×C4—221no—
914C22×C4—221no—
915C22×C4—221no—
916C22×C4—221no—
917C22×C4—221no—
918C22×C4—221no—
919C22×C4—444no—
920C22×C4—444no—
921C22×C4—444no—
922C22×C4—444no—
923C22×C4—444no—
924C22×C4—444no—
925C22×C4—444no—
926C22×C4—444no—
927C22×C4—444no—
928C22×C4—444no—
929C22×C4—444no—
930C22×C4—444no—
931C22×C4—444no—
932C22×C4—444no—
933C22×C4—444no—
934C22×C4—444no—
935C22×C4—444no—
936C22×C4C2×C4×D1112yes—
937C22×C4C2×C4×D1112yes—
938C22×C4D4×D1112yes—
939C22×C4#434112yes—
940C22×C4C2×C22⋊D1112yes—
941C22×C4C2×C22⋊D1112yes—
942C4⋊C4—44no—
943C4⋊C4—44no—
944C4⋊C4—228no—
945C4⋊C4—444no—
946C4⋊C4—444no—
947C22⋊C4—28no—
948C22⋊C4—44no—
949C22⋊C4—228no—
950C22⋊C4—228no—
951C22⋊C4—228no—
952C22⋊C4—444no—
953C22⋊C4—444no—
954C22⋊C4—444no—
955C42—228no—
956C11#1397511yescharacteristic, complemented, Sylow
957C23—22no—
958C23—22no—
959C23—22no—
960C23—22no—
961C23—22no—
962C23—22no—
963C23—22no—
964C23—22no—
965C23—22no—
966C23—22no—
967C23—22no—
968C23—22no—
969C23—22no—
970C23—22no—
971C23—22no—
972C23—22no—
973C23—22no—
974C23—22no—
975C23—22no—
976C23—22no—
977C23—22no—
978C23—22no—
979C23—22no—
980C23—22no—
981C23—22no—
982C23—22no—
983C23—22no—
984C23—22no—
985C23—114no—
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—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—
1017C23—441no—
1018C23—441no—
1019C23—441no—
1020C23C4⋊C4×D1114yes—
1021C23#6694614yes—
1022C23#6694714yes—
1023C23#6694914yes—
1024C23C4×C22⋊D1114yes—
1025C23#6699014yes—
1026C23#6699914yes—
1027C23C22×C4×D1111yescharacteristic
1028C23C2×#433911yescharacteristic
1029C23C2×D4×D1111yescharacteristic
1030C23C2×D4×D1111yescharacteristic
1031C23C2×D4×D1111yescharacteristic
1032C23C2×#434111yescharacteristic
1033C23#6703711yescharacteristic
1034C23#6703711yescharacteristic
1035C23C2×Q8×D1111yescharacteristic
1036C23C2×#434311yescharacteristic
1037C23#41×D1111yescharacteristic
1038C23#41×D1111yescharacteristic
1039C23#6704211yescharacteristic
1040C23#6704311yescharacteristic
1041C23C22×C22⋊D1111yescharacteristic
1042D4—2232no—
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—22no—
1055C2×C4—22no—
1056C2×C4—22no—
1057C2×C4—22no—
1058C2×C4—416no—
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—41no—
1082C2×C4—41no—
1083C2×C4—41no—
1084C2×C4—41no—
1085C2×C4—114no—
1086C2×C4—114no—
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—222no—
1101C2×C4—222no—
1102C2×C4—222no—
1103C2×C4—222no—
1104C2×C4—222no—
1105C2×C4—222no—
1106C2×C4—222no—
1107C2×C4—222no—
1108C2×C4—222no—
1109C2×C4—222no—
1110C2×C4—222no—
1111C2×C4—222no—
1112C2×C4—222no—
1113C2×C4—222no—
1114C2×C4—4416no—
1115C2×C4—4416no—
1116C2×C4—4416no—
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×C4—441no—
1128C2×C4—441no—
1129C2×C4—441no—
1130C2×C4—441no—
1131C2×C4—441no—
1132C2×C4—441no—
1133C2×C4—441no—
1134C2×C4—441no—
1135C2×C4—441no—
1136C2×C4—441no—
1137C2×C4#6699214yes—
1138C22—24no—
1139C22—24no—
1140C22—24no—
1141C22—24no—
1142C22—24no—
1143C22—24no—
1144C22—24no—
1145C22—24no—
1146C22—24no—
1147C22—24no—
1148C22—24no—
1149C22—24no—
1150C22—24no—
1151C22—24no—
1152C22—224no—
1153C22—224no—
1154C22—224no—
1155C22—442no—
1156C22—442no—
1157C22—442no—
1158C22—442no—
1159C22—442no—
1160C22—442no—
1161C22—442no—
1162C22—442no—
1163C22—442no—
1164C22—442no—
1165C22—442no—
1166C22—442no—
1167C22#1062260218yescomplemented
1168C22C2×C4⋊C4×D1111yescharacteristic
1169C22C2×#6694611yescharacteristic
1170C22C2×#6694711yescharacteristic
1171C22C2×#6694911yescharacteristic
1172C22C4×#434111yescharacteristic
1173C22#1062306911yescharacteristic
1174C22C4×D4×D1111yescharacteristic
1175C22#1062307611yescharacteristic
1176C22#1062307711yescharacteristic
1177C22#1062307811yescharacteristic
1178C22#1062309111yescharacteristic
1179C22#1062309511yescharacteristic
1180C22#1062312111yescharacteristic
1181C22#1062312111yescharacteristic
1182C22#1062312211yescharacteristic
1183C22#1062312211yescharacteristic
1184C22#1062316111yescharacteristic
1185C22#1062316311yescharacteristic
1186C22#1062316611yescharacteristic
1187C22#1062316711yescharacteristic
1188C22#1062316711yescharacteristic
1189C22#1062316811yescharacteristic
1190C22#1062316811yescharacteristic
1191C22#1062317311yescharacteristic
1192C22#1062318511yescharacteristic
1193C22#1062318511yescharacteristic
1194C22#1062318611yescharacteristic
1195C22#1062318611yescharacteristic
1196C22C2×C4×C22⋊D1111yescharacteristic
1197C22C2×#6699011yescharacteristic
1198C22C2×#6699211yescharacteristic
1199C22#1062333511yescharacteristic
1200C22C2×#6699911yescharacteristic
1201C22#1062336311yescharacteristic
1202C22#1062336411yescharacteristic
1203C4—24no—
1204C4—42no—
1205C4—42no—
1206C4—42no—
1207C4—81no—
1208C4—81no—
1209C4—224no—
1210C4—224no—
1211C4—442no—
1212C4—442no—
1213C4—442no—
1214C4—442no—
1215C4—442no—
1216C2—28no—
1217C2—444no—
1218C2C2×#1062260211yescharacteristic
1219C2C4×#6699211yescharacteristic
1220C2#1307131411yescharacteristic
1221C2#1307151411yescharacteristic
1222C2#1307152211yescharacteristic
1223C2#1307159211yescharacteristic
1224C2#1307160611yescharacteristic
1225C2#1307199111yescharacteristic
1226C2#1307206811yescharacteristic
1227C2#1307208011yescharacteristic
1228C2#1307209511yescharacteristic
1229C2#1307222811yescharacteristic
1230C2#1307242711yescharacteristic
1231C2#1307244211yescharacteristic
1232C2#1307379811yescharacteristic
subgroupG/H
center, FrattiniC24C23×D11
commutatorC23×C11C23×C4
FittingC2×C11×#385C2
socle, cosocleC24×C11C24
prime radicalC23×C22⋊D11C22
hypercenterC2×#385D11
hypocenterC11#13975
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ C2×#385

Complements

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

NH ≅ G/Ntype
4. C2×#10622602C2semidirect
5. C2×#10622555C2semidirect
6. C22×C11⋊#95C2semidirect
7. #13066879C2semidirect
8. #13066874C2semidirect
9. #13066860C2semidirect
10. #13066858C2semidirect
11. #13066848C2semidirect
12. #13066847C2semidirect
13. #13066838C2semidirect
14. (C2×D11)⋊#95C2semidirect
15. C2×C11×#385C2semidirect
58. #10622571C4semidirect
95. C23×Dic11C2×C4semidirect
121. C2×C11×C22⋊C4C2×C4semidirect
139. C2×(C2×D11)⋊C4C2×C4semidirect
140. C2×(C2×D11)⋊C4C2×C4semidirect
166. C11⋊#95C2×C4semidirect
167. C11⋊#95C2×C4semidirect
168. C11⋊#95D4semidirect
256. C2×C22⋊D11C4⋊C4semidirect
345. C2×#385D11semidirect
535. C2×Dic11C4×D4semidirect
595. C22×C11#385semidirect
748. C2×C22⋊C4C4×D11semidirect
956. C11#13975semidirect
1167. C22#10622602semidirect

Maximal subgroups

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

subgroupindex
C22×C4×C22⋊D112
C2×#106225712
C2×#106226022
C2×#106225552
C22×C11⋊#952
#130668792
#130668742
#130668602
#130668582
#130668482
#130668472
#130668382
(C2×D11)⋊#952
C2×C11×#3852
#1397511