Finite Group Databasebeta

← #14683132

Subgroups — #14683132

Order 2816.

2282 conjugacy classes of subgroups.

The subgroup lattice has 1332 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622836C211yesmaximal, characteristic
2C2×#10622570C211yesmaximal, characteristic, complemented
3C2×#10622553C211yesmaximal, characteristic, complemented
4C2×#10622557C211yesmaximal, characteristic, complemented
5C2×#10622833C211yesmaximal, characteristic, complemented
6C2×#10622571C211yesmaximal, characteristic, complemented
7#13066859C211yesmaximal, characteristic, complemented
8#13066859C211yesmaximal, characteristic, complemented
9#13066858C211yesmaximal, characteristic, complemented
10#13066855C211yesmaximal, characteristic, complemented
11#13066855C211yesmaximal, characteristic, complemented
12#13066849C211yesmaximal, characteristic, complemented
13#13066848C211yesmaximal, characteristic, complemented
14#13066838C211yesmaximal, characteristic, complemented
15C2×C11×#390C211yesmaximal, characteristic, complemented
16C23×D4×C11C2211yescharacteristic
17C23×C22⋊D11C2211yescharacteristic
18C23×C22⋊D11C2211yescharacteristic
19C24×Dic11C2211yescharacteristic
20C22×C11×C4⋊C4C2211yescharacteristic
21C22×C11×C22⋊C4C2211yescharacteristic
22C22×C11×C22⋊C4C2211yescharacteristic
23C22×C11×C22⋊C4C2211yescharacteristic
24C22×C11×C22⋊C4C2211yescharacteristic
25C22×C42×C11C2211yescharacteristic
26C22×C22⋊Dic11C2211yescharacteristic
27C22×C22⋊Dic11C2211yescharacteristic
28C22×C22⋊Dic11C2211yescharacteristic
29C22×C22⋊Dic11C2211yescharacteristic
30C22×C22⋊Dic11C2211yescharacteristic
31C22×(C2×D11)⋊C4C2211yescharacteristic
32C22×(C2×D11)⋊C4C2211yescharacteristic
33C22×(C2×D11)⋊C4C2211yescharacteristic
34C22×(C2×D11)⋊C4C2211yescharacteristic
35C22×(C2×D11)⋊C4C2211yescharacteristic
36C22×Dic11⋊C4C2211yescharacteristic
37C22×Dic11⋊C4C2211yescharacteristic
38C22×C4×Dic11C2211yescharacteristic
39C11×#390—24no—
40#10622836C418yescomplemented
41#10622833—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
54#10622571—24no—
55#10622570—24no—
56#10622557—24no—
57#10622553—24no—
58C25×C11C2311yescharacteristic
59C25×C11C2311yescharacteristic
60C24×D11C2311yescharacteristic
61C22×D4×C11—22no—
62C22×D4×C11—22no—
63C22×D4×C11—22no—
64C22×D4×C11—22no—
65C22×D4×C11—41no—
66C22×D4×C11—41no—
67C22×D4×C11C2×C414yes—
68C23×C4×C11C2311yescharacteristic
69C23×C4×C11C2311yescharacteristic
70C23×C4×C11C2311yescharacteristic
71C23×C4×C11C2311yescharacteristic
72C23×C4×C11C2311yescharacteristic
73C22×C22⋊D11—22no—
74C22×C22⋊D11—22no—
75C22×C22⋊D11—22no—
76C22×C22⋊D11—22no—
77C22×C22⋊D11—41no—
78C22×C22⋊D11—41no—
79C22×C22⋊D11—41no—
80C22×C22⋊D11—41no—
81C22×C22⋊D11—41no—
82C22×C22⋊D11—41no—
83C22×C22⋊D11—41no—
84C22×C22⋊D11—41no—
85C22×C22⋊D11C2×C414yes—
86C22×C22⋊D11C2×C414yescomplemented
87C23×Dic11—22no—
88C23×Dic11—22no—
89C23×Dic11—22no—
90C23×Dic11—41no—
91C23×Dic11—41no—
92C23×Dic11—41no—
93C23×Dic11—41no—
94C23×Dic11C2311yescharacteristic
95C23×Dic11C2311yescharacteristic
96C23×Dic11C2311yescharacteristic
97C23×Dic11C2311yescharacteristic
98C23×Dic11C2311yescharacteristic
99C23×Dic11C2311yescharacteristic
100C23×Dic11C2311yescharacteristic
101C2×C11×C4⋊C4—22no—
102C2×C11×C4⋊C4—22no—
103C2×C11×C4⋊C4—41no—
104C2×C11×C22⋊C4—22no—
105C2×C11×C22⋊C4—22no—
106C2×C11×C22⋊C4—22no—
107C2×C11×C22⋊C4—22no—
108C2×C11×C22⋊C4—22no—
109C2×C11×C22⋊C4—41no—
110C2×C11×C22⋊C4—41no—
111C2×C11×C22⋊C4—41no—
112C2×C11×C22⋊C4—41no—
113C2×C11×C22⋊C4—41no—
114C2×C11×C22⋊C4—41no—
115C2×C11×C22⋊C4D414yescomplemented
116C2×C42×C11—22no—
117C2×C42×C11—22no—
118C2×C42×C11—41no—
119C2×C22⋊Dic11—22no—
120C2×C22⋊Dic11—22no—
121C2×C22⋊Dic11—22no—
122C2×C22⋊Dic11—22no—
123C2×C22⋊Dic11—22no—
124C2×C22⋊Dic11—22no—
125C2×C22⋊Dic11—22no—
126C2×C22⋊Dic11—41no—
127C2×C22⋊Dic11—41no—
128C2×C22⋊Dic11—41no—
129C2×C22⋊Dic11—41no—
130C2×C22⋊Dic11—41no—
131C2×C22⋊Dic11—41no—
132C2×C22⋊Dic11C2×C414yes—
133C2×C22⋊Dic11C2×C414yescomplemented
134C2×(C2×D11)⋊C4—22no—
135C2×(C2×D11)⋊C4—22no—
136C2×(C2×D11)⋊C4—22no—
137C2×(C2×D11)⋊C4—22no—
138C2×(C2×D11)⋊C4—22no—
139C2×(C2×D11)⋊C4—22no—
140C2×(C2×D11)⋊C4—22no—
141C2×(C2×D11)⋊C4—22no—
142C2×(C2×D11)⋊C4—41no—
143C2×(C2×D11)⋊C4—41no—
144C2×(C2×D11)⋊C4—41no—
145C2×(C2×D11)⋊C4—41no—
146C2×(C2×D11)⋊C4—41no—
147C2×(C2×D11)⋊C4—41no—
148C2×(C2×D11)⋊C4C2×C414yescomplemented
149C2×Dic11⋊C4—22no—
150C2×Dic11⋊C4—22no—
151C2×Dic11⋊C4—22no—
152C2×Dic11⋊C4—22no—
153C2×Dic11⋊C4—41no—
154C2×Dic11⋊C4—41no—
155C2×C4×Dic11—22no—
156C2×C4×Dic11—22no—
157C2×C4×Dic11—41no—
158C11⋊#95—22no—
159C11⋊#95—22no—
160C11⋊#95—22no—
161C11⋊#95—22no—
162C11⋊#95—41no—
163C11⋊#95—41no—
164C11⋊#95—41no—
165C11⋊#95—41no—
166C11⋊#95—41no—
167C11⋊#95C2×C414yescomplemented
168C11⋊#95D414yescomplemented
169C11⋊#95D414yescomplemented
170#14521—111nomaximal, Sylow
171C24×C11—21no—
172C24×C11—21no—
173C24×C11—21no—
174C24×C11—21no—
175C24×C11—21no—
176C24×C11—21no—
177C24×C11—21no—
178C24×C11—21no—
179C24×C11—21no—
180C24×C11—21no—
181C24×C11—21no—
182C24×C11—21no—
183C24×C11—21no—
184C24×C11—21no—
185C24×C11—21no—
186C24×C11—21no—
187C24×C11—21no—
188C24×C11—21no—
189C24×C11—21no—
190C24×C11—21no—
191C24×C11—21no—
192C24×C11—21no—
193C24×C11—21no—
194C24×C11—21no—
195C24×C11—21no—
196C24×C11—21no—
197C24×C11C22×C412yes—
198C24×C11C22×C412yes—
199C24×C11C2×D412yes—
200C24×C11#4112yes—
201C24×C11C2411yescharacteristic
202C23×D11—21no—
203C23×D11—21no—
204C23×D11—21no—
205C23×D11—21no—
206C23×D11—21no—
207C23×D11—21no—
208C23×D11—21no—
209C23×D11—21no—
210C23×D11—21no—
211C23×D11—21no—
212C23×D11—21no—
213C23×D11—21no—
214C23×D11—21no—
215C23×D11—21no—
216C23×D11C22×C412yes—
217C2×D4×C11—28no—
218C2×D4×C11—28no—
219C2×D4×C11—44no—
220C2×D4×C11—44no—
221C2×D4×C11—44no—
222C2×D4×C11—44no—
223C2×D4×C11—44no—
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×C11—21no—
251C22×C4×C11—21no—
252C22×C4×C11—21no—
253C22×C4×C11C22×C412yes—
254C22×C4×C11C2×D412yes—
255C22×C4×C11C2×D412yes—
256C22×C4×C11C2×D412yes—
257C22×C4×C11C2×D412yes—
258C22×C4×C11#4112yes—
259C2×C22⋊D11—28no—
260C2×C22⋊D11—28no—
261C2×C22⋊D11—44no—
262C2×C22⋊D11—44no—
263C2×C22⋊D11—44no—
264C2×C22⋊D11—44no—
265C2×C22⋊D11—44no—
266C2×C22⋊D11—44no—
267C2×C22⋊D11—44no—
268C2×C22⋊D11—44no—
269C2×C22⋊D11—44no—
270C2×C22⋊D11—44no—
271C2×C22⋊D11—44no—
272C2×C22⋊D11—44no—
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—21no—
299C22×Dic11—21no—
300C22×Dic11—21no—
301C22×Dic11—21no—
302C22×Dic11—21no—
303C22×Dic11—21no—
304C22×Dic11—21no—
305C22×Dic11—21no—
306C22×Dic11—21no—
307C22×Dic11—21no—
308C22×Dic11—21no—
309C22×Dic11—21no—
310C22×Dic11—21no—
311C22×Dic11—21no—
312C22×Dic11—21no—
313C22×Dic11—21no—
314C22×Dic11—44no—
315C22×Dic11—44no—
316C22×Dic11—44no—
317C22×Dic11—44no—
318C22×Dic11—44no—
319C22×Dic11—44no—
320C22×Dic11—44no—
321C22×Dic11C22×C412yes—
322C22×Dic11C22×C412yes—
323C22×Dic11C22×C412yes—
324C22×Dic11C2×D412yes—
325C22×Dic11C2×D412yes—
326C22×Dic11C2×D412yes—
327C22×Dic11C2×D412yes—
328C22×Dic11#4112yes—
329C11×C4⋊C4—44no—
330C11×C22⋊C4—44no—
331C11×C22⋊C4—44no—
332C11×C22⋊C4—44no—
333C11×C22⋊C4—44no—
334C42×C11—44no—
335C22⋊Dic11—28no—
336C22⋊Dic11—44no—
337C22⋊Dic11—44no—
338C22⋊Dic11—44no—
339C22⋊Dic11—44no—
340(C2×D11)⋊C4—28no—
341(C2×D11)⋊C4—44no—
342(C2×D11)⋊C4—44no—
343(C2×D11)⋊C4—44no—
344(C2×D11)⋊C4—44no—
345Dic11⋊C4—44no—
346Dic11⋊C4—44no—
347C4×Dic11—44no—
348C2×#392—111no—
349C2×#390—111no—
350C2×#390D1111yescharacteristic, complemented
351C2×#388—111no—
352C2×#388—111no—
353C2×#386—111no—
354C2×#386—111no—
355#1439—111no—
356#1439—111no—
357#1439—111no—
358#1438—111no—
359#1438—111no—
360#1436—111no—
361#1436—111no—
362C22⋊#95—111no—
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×C11—22no—
385C23×C11—22no—
386C23×C11—22no—
387C23×C11—22no—
388C23×C11—41no—
389C23×C11—41no—
390C23×C11—41no—
391C23×C11—41no—
392C23×C11—41no—
393C23×C11—41no—
394C23×C11—41no—
395C23×C11—41no—
396C23×C11—41no—
397C23×C11—41no—
398C23×C11—41no—
399C23×C11—41no—
400C23×C11—41no—
401C23×C11—41no—
402C23×C11—41no—
403C23×C11—41no—
404C23×C11—41no—
405C23×C11—41no—
406C23×C11—41no—
407C23×C11—41no—
408C23×C11—41no—
409C23×C11—41no—
410C23×C11—41no—
411C23×C11—41no—
412C23×C11—41no—
413C23×C11—41no—
414C23×C11—41no—
415C23×C11—41no—
416C23×C11—41no—
417C23×C11—41no—
418C23×C11—41no—
419C23×C11—41no—
420C23×C11—41no—
421C23×C11—41no—
422C23×C11—41no—
423C23×C11—41no—
424C23×C11—41no—
425C23×C11—41no—
426C23×C11—41no—
427C23×C11—41no—
428C23×C11—41no—
429C23×C11—41no—
430C23×C11—41no—
431C23×C11—41no—
432C23×C11C4×D414yes—
433C23×C11C23×C411yescharacteristic
434C23×C11C22×D411yescharacteristic
435C23×C11C22×D411yescharacteristic
436C23×C11C22×D411yescharacteristic
437C23×C11C2×#4111yescharacteristic
438C23×C11C2×#4111yescharacteristic
439C23×C11C2×#4111yescharacteristic
440C23×C11H(5,𝔽2)11yescharacteristic
441C23×C11H(5,𝔽2)11yescharacteristic
442C23×C11H(5,𝔽2)11yescharacteristic
443C23×C11H(5,𝔽2)11yescharacteristic
444C23×C11H(5,𝔽2)11yescharacteristic
445C23×C11H(5,𝔽2)11yescharacteristic
446C23×C11H(5,𝔽2)11yescharacteristic
447C23×C112−1+411yescharacteristic
448C22×D11—22no—
449C22×D11—22no—
450C22×D11—22no—
451C22×D11—22no—
452C22×D11—22no—
453C22×D11—22no—
454C22×D11—22no—
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×D11—41no—
467C22×D11—41no—
468C22×D11—41no—
469C22×D11—41no—
470C22×D11—41no—
471C22×D11—41no—
472C22×D11—41no—
473C22×D11—41no—
474C22×D11—41no—
475C22×D11—41no—
476C22×D11—41no—
477C22×D11—41no—
478C22×D11—41no—
479C22×D11—41no—
480C22×D11—41no—
481C22×D11—41no—
482C22×D11—41no—
483D4×C11—416no—
484C2×C4×C11—22no—
485C2×C4×C11—22no—
486C2×C4×C11—22no—
487C2×C4×C11—22no—
488C2×C4×C11—22no—
489C2×C4×C11—22no—
490C2×C4×C11—22no—
491C2×C4×C11—22no—
492C2×C4×C11—22no—
493C2×C4×C11—22no—
494C2×C4×C11—22no—
495C2×C4×C11—22no—
496C2×C4×C11—22no—
497C2×C4×C11—22no—
498C2×C4×C11—22no—
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×C4×C11—41no—
517C2×C4×C11—41no—
518C2×C4×C11C4×D414yes—
519C22⋊D11—416no—
520C22⋊D11—416no—
521C2×Dic11—22no—
522C2×Dic11—22no—
523C2×Dic11—22no—
524C2×Dic11—22no—
525C2×Dic11—22no—
526C2×Dic11—22no—
527C2×Dic11—22no—
528C2×Dic11—22no—
529C2×Dic11—22no—
530C2×Dic11—22no—
531C2×Dic11—22no—
532C2×Dic11—22no—
533C2×Dic11—22no—
534C2×Dic11—22no—
535C2×Dic11—22no—
536C2×Dic11—22no—
537C2×Dic11—22no—
538C2×Dic11—22no—
539C2×Dic11—22no—
540C2×Dic11—22no—
541C2×Dic11—22no—
542C2×Dic11—416no—
543C2×Dic11—41no—
544C2×Dic11—41no—
545C2×Dic11—41no—
546C2×Dic11—41no—
547C2×Dic11—41no—
548C2×Dic11—41no—
549C2×Dic11—41no—
550C2×Dic11—41no—
551C2×Dic11—41no—
552C2×Dic11—41no—
553C2×Dic11—41no—
554C2×Dic11—41no—
555C2×Dic11—41no—
556C2×Dic11—41no—
557C2×Dic11—41no—
558C2×Dic11—41no—
559C2×Dic11—41no—
560C2×Dic11—41no—
561C2×Dic11—41no—
562C2×Dic11—41no—
563C2×Dic11—41no—
564C2×Dic11—41no—
565C2×Dic11—41no—
566C2×Dic11—41no—
567C2×Dic11—41no—
568C2×Dic11—41no—
569C2×Dic11—41no—
570C2×Dic11C4×D414yes—
571C23×D4—111no—
572C23×D4—111no—
573C23×D4C2×D1111yescharacteristic
574C24×C4—111no—
575C22×C4⋊C4—111no—
576C22×C4⋊C4—111no—
577C22×C4⋊C4C2×D1111yescharacteristic
578C22×C22⋊C4—111no—
579C22×C22⋊C4—111no—
580C22×C22⋊C4—111no—
581C22×C22⋊C4—111no—
582C22×C22⋊C4—111no—
583C22×C22⋊C4—111no—
584C22×C22⋊C4—111no—
585C22×C22⋊C4—111no—
586C22×C22⋊C4—111no—
587C22×C22⋊C4—111no—
588C22×C22⋊C4C2×D1111yescharacteristic
589C22×C22⋊C4C2×D1111yescharacteristic
590C22×C22⋊C4C2×D1111yescharacteristic
591C22×C22⋊C4C2×D1111yescharacteristic
592C22×C42—111no—
593C22×C42C2×D1111yescharacteristic
594#392—118no—
595#390—24no—
596#390—224no—
597#388—224no—
598#388—224no—
599#386—224no—
600#386—224no—
601C2×#95—111no—
602C2×#95—111no—
603C2×#95—111no—
604C2×#95—111no—
605C2×#95—111no—
606C2×#95—111no—
607C2×#95—111no—
608C2×#95—111no—
609C2×#95—111no—
610C2×#95—111no—
611C2×#95—111no—
612C2×#95—111no—
613C22×C11—24no—
614C22×C11—24no—
615C22×C11—24no—
616C22×C11—42no—
617C22×C11—42no—
618C22×C11—42no—
619C22×C11—42no—
620C22×C11—42no—
621C22×C11—42no—
622C22×C11—42no—
623C22×C11—42no—
624C22×C11—42no—
625C22×C11—42no—
626C22×C11—42no—
627C22×C11—42no—
628C22×C11—42no—
629C22×C11—42no—
630C22×C11—42no—
631C22×C11—42no—
632C22×C11—42no—
633C22×C11—42no—
634C22×C11—42no—
635C22×C11—81no—
636C22×C11—81no—
637C22×C11—81no—
638C22×C11—81no—
639C22×C11—81no—
640C22×C11—81no—
641C22×C11—81no—
642C22×C11—81no—
643C22×C11C2×C4×D411yescharacteristic
644C22×C11C2×C4×D411yescharacteristic
645C22×C11C2×C4×D411yescharacteristic
646C22×C11#51811yescharacteristic
647C22×C11#51811yescharacteristic
648C22×C11#51811yescharacteristic
649C22×C11#52011yescharacteristic
650C22×C11#53411yescharacteristic
651C22×C11#53511yescharacteristic
652C22×C11#53511yescharacteristic
653C22×C11#53711yescharacteristic
654C22×C11#53711yescharacteristic
655C22×C11#53711yescharacteristic
656C22×C11#53811yescharacteristic
657C22×C11#53911yescharacteristic
658C22×C11#54011yescharacteristic
659C22×C11#54011yescharacteristic
660C22×C11#54211yescharacteristic
661C22×C11#54211yescharacteristic
662C22×C11D4211yescharacteristic
663C22×C11D4211yescharacteristic
664C22×C11D4211yescharacteristic
665C22×C11#54611yescharacteristic
666C22×C11#54611yescharacteristic
667C22×C11#54611yescharacteristic
668C22×C11#54611yescharacteristic
669C22×C11#55011yescharacteristic
670C22×C11#55011yescharacteristic
671C22×C11#55111yescharacteristic
672C22×C11#55111yescharacteristic
673C22×C11#55911yescharacteristic
674C22×C11#56011yescharacteristic
675C22×C11#56011yescharacteristic
676C22×C11#56011yescharacteristic
677C22×C11H(3,𝔽4)11yescharacteristic
678C2×D11—42no—
679C2×D11—42no—
680C2×D11—42no—
681C2×D11—42no—
682C2×D11—42no—
683C2×D11—42no—
684C2×D11—42no—
685C2×D11—81no—
686C2×D11—81no—
687C2×D11—81no—
688C2×D11—81no—
689C2×D11—81no—
690C2×D11—81no—
691C2×D11—81no—
692C2×D11—81no—
693C4×C11—24no—
694C4×C11—42no—
695C4×C11—42no—
696C4×C11—42no—
697C4×C11—81no—
698Dic11—24no—
699Dic11—42no—
700Dic11—42no—
701Dic11—42no—
702Dic11—42no—
703Dic11—42no—
704Dic11—81no—
705C25—111no—
706C25C22×D1111yescharacteristic
707C25C22×D1111yescharacteristic
708C22×D4—22no—
709C22×D4—22no—
710C22×D4—22no—
711C22×D4—22no—
712C22×D4—41no—
713C22×D4—41no—
714C22×D4—114no—
715C22×D4—114no—
716C22×D4—222no—
717C22×D4—222no—
718C22×D4—222no—
719C22×D4—222no—
720C22×D4—441no—
721C22×D4—441no—
722C22×D4—441no—
723C22×D4—441no—
724C22×D4—441no—
725C22×D4—441no—
726C22×D4—441no—
727C22×D4—441no—
728C22×D4C4×D1114yes—
729C23×C4—111no—
730C23×C4—111no—
731C23×C4—111no—
732C23×C4—111no—
733C23×C4—111no—
734C23×C4—111no—
735C23×C4—111no—
736C23×C4—222no—
737C23×C4—222no—
738C23×C4—222no—
739C23×C4—441no—
740C23×C4—441no—
741C23×C4—441no—
742C23×C4—441no—
743C23×C4C22×D1111yescharacteristic
744C23×C4C22×D1111yescharacteristic
745C23×C4C22×D1111yescharacteristic
746C23×C4C22×D1111yescharacteristic
747C23×C4C22×D1111yescharacteristic
748C2×C4⋊C4—22no—
749C2×C4⋊C4—22no—
750C2×C4⋊C4—41no—
751C2×C4⋊C4—222no—
752C2×C4⋊C4—222no—
753C2×C4⋊C4—222no—
754C2×C4⋊C4—222no—
755C2×C4⋊C4—441no—
756C2×C4⋊C4—441no—
757C2×C22⋊C4—22no—
758C2×C22⋊C4—22no—
759C2×C22⋊C4—22no—
760C2×C22⋊C4—22no—
761C2×C22⋊C4—22no—
762C2×C22⋊C4—41no—
763C2×C22⋊C4—41no—
764C2×C22⋊C4—41no—
765C2×C22⋊C4—41no—
766C2×C22⋊C4—41no—
767C2×C22⋊C4—41no—
768C2×C22⋊C4—114no—
769C2×C22⋊C4—114no—
770C2×C22⋊C4—114no—
771C2×C22⋊C4—222no—
772C2×C22⋊C4—222no—
773C2×C22⋊C4—222no—
774C2×C22⋊C4—222no—
775C2×C22⋊C4—222no—
776C2×C22⋊C4—222no—
777C2×C22⋊C4—222no—
778C2×C22⋊C4—222no—
779C2×C22⋊C4—222no—
780C2×C22⋊C4—222no—
781C2×C22⋊C4—222no—
782C2×C22⋊C4—222no—
783C2×C22⋊C4—222no—
784C2×C22⋊C4—222no—
785C2×C22⋊C4—222no—
786C2×C22⋊C4—441no—
787C2×C22⋊C4—441no—
788C2×C22⋊C4—441no—
789C2×C22⋊C4—441no—
790C2×C22⋊C4—441no—
791C2×C22⋊C4—441no—
792C2×C22⋊C4—441no—
793C2×C22⋊C4—441no—
794C2×C22⋊C4—441no—
795C2×C22⋊C4—441no—
796C2×C22⋊C4—441no—
797C2×C22⋊C4—441no—
798C2×C22⋊C4C22⋊D1114yescomplemented
799C2×C42—22no—
800C2×C42—22no—
801C2×C42—41no—
802C2×C42—222no—
803C2×C42—222no—
804C2×C42—441no—
805#95—114no—
806#95—114no—
807#95—114no—
808#95—222no—
809#95—222no—
810#95—222no—
811#95—222no—
812#95—441no—
813#95—441no—
814#95—441no—
815#95—441no—
816#95—441no—
817C2×C11—44no—
818C2×C11—82no—
819C2×C11#232411yescharacteristic
820C2×C11#232411yescharacteristic
821C2×C11#232511yescharacteristic
822C2×C11#235811yescharacteristic
823C2×C11#235811yescharacteristic
824C2×C11#236611yescharacteristic
825C2×C11#237511yescharacteristic
826C2×C11#267011yescharacteristic
827C2×C11#267311yescharacteristic
828C2×C11#267311yescharacteristic
829C2×C11#267511yescharacteristic
830C2×C11#270511yescharacteristic
831C2×C11#270511yescharacteristic
832C2×C11#271211yescharacteristic
833C2×C11#275211yescharacteristic
834D11—82no—
835C24—21no—
836C24—21no—
837C24—21no—
838C24—21no—
839C24—21no—
840C24—21no—
841C24—21no—
842C24—21no—
843C24—21no—
844C24—21no—
845C24—21no—
846C24—21no—
847C24—21no—
848C24—21no—
849C24—21no—
850C24—21no—
851C24—21no—
852C24—21no—
853C24—21no—
854C24—21no—
855C24—21no—
856C24—21no—
857C24—21no—
858C24—21no—
859C24—21no—
860C24—21no—
861C24—112no—
862C24—221no—
863C24—221no—
864C24—221no—
865C24—221no—
866C24—221no—
867C24—221no—
868C24—221no—
869C24—221no—
870C24—221no—
871C24—221no—
872C24—221no—
873C24—221no—
874C24—221no—
875C24—221no—
876C24C2×C4×D1112yes—
877C24C2×C4×D1112yes—
878C24#433912yes—
879C24C2×C22⋊D1112yes—
880C24C23×D1111yescharacteristic
881C2×D4—28no—
882C2×D4—28no—
883C2×D4—44no—
884C2×D4—44no—
885C2×D4—44no—
886C2×D4—44no—
887C2×D4—44no—
888C2×D4—228no—
889C2×D4—228no—
890C2×D4—444no—
891C2×D4—444no—
892C2×D4—444no—
893C2×D4—444no—
894C2×D4—444no—
895C2×D4—444no—
896C2×D4—444no—
897C2×D4—444no—
898C2×D4—444no—
899C2×D4—444no—
900C2×D4—444no—
901C2×D4—444no—
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—21no—
920C22×C4—21no—
921C22×C4—21no—
922C22×C4—21no—
923C22×C4—21no—
924C22×C4—21no—
925C22×C4—21no—
926C22×C4—21no—
927C22×C4—21no—
928C22×C4—21no—
929C22×C4—21no—
930C22×C4—21no—
931C22×C4—112no—
932C22×C4—112no—
933C22×C4—112no—
934C22×C4—112no—
935C22×C4—112no—
936C22×C4—112no—
937C22×C4—112no—
938C22×C4—112no—
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—221no—
955C22×C4—221no—
956C22×C4—221no—
957C22×C4—221no—
958C22×C4—221no—
959C22×C4—221no—
960C22×C4—221no—
961C22×C4—221no—
962C22×C4—221no—
963C22×C4—221no—
964C22×C4—221no—
965C22×C4—221no—
966C22×C4—221no—
967C22×C4—221no—
968C22×C4—221no—
969C22×C4—221no—
970C22×C4—221no—
971C22×C4—221no—
972C22×C4—221no—
973C22×C4—221no—
974C22×C4—221no—
975C22×C4—221no—
976C22×C4—221no—
977C22×C4—221no—
978C22×C4—221no—
979C22×C4—221no—
980C22×C4—444no—
981C22×C4—444no—
982C22×C4—444no—
983C22×C4—444no—
984C22×C4—444no—
985C22×C4—444no—
986C22×C4—444no—
987C22×C4C2×C4×D1112yes—
988C22×C4D4×D1112yes—
989C22×C4D4×D1112yes—
990C22×C4#434112yes—
991C22×C4C2×C22⋊D1112yes—
992C22×C4C2×C22⋊D1112yes—
993C4⋊C4—44no—
994C4⋊C4—444no—
995C4⋊C4—444no—
996C22⋊C4—44no—
997C22⋊C4—44no—
998C22⋊C4—44no—
999C22⋊C4—44no—
1000C22⋊C4—228no—
1001C22⋊C4—228no—
1002C22⋊C4—444no—
1003C22⋊C4—444no—
1004C22⋊C4—444no—
1005C22⋊C4—444no—
1006C22⋊C4—444no—
1007C22⋊C4—444no—
1008C22⋊C4—444no—
1009C22⋊C4—444no—
1010C42—44no—
1011C42—444no—
1012C11#1452111yescharacteristic, complemented, Sylow
1013C23—22no—
1014C23—22no—
1015C23—22no—
1016C23—22no—
1017C23—22no—
1018C23—22no—
1019C23—22no—
1020C23—22no—
1021C23—22no—
1022C23—22no—
1023C23—22no—
1024C23—22no—
1025C23—22no—
1026C23—22no—
1027C23—22no—
1028C23—22no—
1029C23—22no—
1030C23—22no—
1031C23—22no—
1032C23—22no—
1033C23—22no—
1034C23—22no—
1035C23—22no—
1036C23—22no—
1037C23—22no—
1038C23—41no—
1039C23—41no—
1040C23—41no—
1041C23—41no—
1042C23—41no—
1043C23—41no—
1044C23—41no—
1045C23—41no—
1046C23—41no—
1047C23—41no—
1048C23—41no—
1049C23—41no—
1050C23—41no—
1051C23—41no—
1052C23—41no—
1053C23—41no—
1054C23—41no—
1055C23—41no—
1056C23—41no—
1057C23—41no—
1058C23—41no—
1059C23—41no—
1060C23—41no—
1061C23—41no—
1062C23—41no—
1063C23—41no—
1064C23—41no—
1065C23—41no—
1066C23—41no—
1067C23—41no—
1068C23—41no—
1069C23—41no—
1070C23—41no—
1071C23—41no—
1072C23—41no—
1073C23—41no—
1074C23—41no—
1075C23—41no—
1076C23—41no—
1077C23—41no—
1078C23—41no—
1079C23—41no—
1080C23—41no—
1081C23—41no—
1082C23—222no—
1083C23—222no—
1084C23—222no—
1085C23—222no—
1086C23—222no—
1087C23—222no—
1088C23—222no—
1089C23—441no—
1090C23—441no—
1091C23—441no—
1092C23—441no—
1093C23—441no—
1094C23—441no—
1095C23—441no—
1096C23—441no—
1097C23—441no—
1098C23—441no—
1099C23—441no—
1100C23—441no—
1101C23—441no—
1102C23—441no—
1103C23—441no—
1104C23—441no—
1105C23—441no—
1106C23—441no—
1107C23—441no—
1108C23—441no—
1109C23—441no—
1110C23—441no—
1111C23—441no—
1112C23—441no—
1113C23—441no—
1114C23—441no—
1115C23—441no—
1116C23—441no—
1117C23C4×C22⋊D1114yes—
1118C23C22×C4×D1111yescharacteristic
1119C23C2×#433911yescharacteristic
1120C23C2×D4×D1111yescharacteristic
1121C23C2×D4×D1111yescharacteristic
1122C23C2×#434111yescharacteristic
1123C23#6703711yescharacteristic
1124C23#6703711yescharacteristic
1125C23#6703711yescharacteristic
1126C23#6703711yescharacteristic
1127C23#6703711yescharacteristic
1128C23#41×D1111yescharacteristic
1129C23#6704211yescharacteristic
1130C23#6704211yescharacteristic
1131C23#6704311yescharacteristic
1132C23C22×C22⋊D1111yescharacteristic
1133D4—416no—
1134D4—4416no—
1135D4—4416no—
1136C2×C4—22no—
1137C2×C4—22no—
1138C2×C4—22no—
1139C2×C4—22no—
1140C2×C4—22no—
1141C2×C4—22no—
1142C2×C4—22no—
1143C2×C4—22no—
1144C2×C4—22no—
1145C2×C4—22no—
1146C2×C4—22no—
1147C2×C4—22no—
1148C2×C4—22no—
1149C2×C4—22no—
1150C2×C4—22no—
1151C2×C4—41no—
1152C2×C4—41no—
1153C2×C4—41no—
1154C2×C4—41no—
1155C2×C4—41no—
1156C2×C4—41no—
1157C2×C4—41no—
1158C2×C4—41no—
1159C2×C4—41no—
1160C2×C4—41no—
1161C2×C4—41no—
1162C2×C4—41no—
1163C2×C4—41no—
1164C2×C4—41no—
1165C2×C4—41no—
1166C2×C4—41no—
1167C2×C4—41no—
1168C2×C4—41no—
1169C2×C4—41no—
1170C2×C4—114no—
1171C2×C4—222no—
1172C2×C4—222no—
1173C2×C4—222no—
1174C2×C4—222no—
1175C2×C4—222no—
1176C2×C4—222no—
1177C2×C4—222no—
1178C2×C4—222no—
1179C2×C4—222no—
1180C2×C4—222no—
1181C2×C4—222no—
1182C2×C4—222no—
1183C2×C4—222no—
1184C2×C4—222no—
1185C2×C4—222no—
1186C2×C4—222no—
1187C2×C4—222no—
1188C2×C4—222no—
1189C2×C4—222no—
1190C2×C4—222no—
1191C2×C4—222no—
1192C2×C4—4416no—
1193C2×C4—441no—
1194C2×C4—441no—
1195C2×C4—441no—
1196C2×C4—441no—
1197C2×C4—441no—
1198C2×C4—441no—
1199C2×C4—441no—
1200C2×C4—441no—
1201C2×C4—441no—
1202C2×C4—441no—
1203C2×C4—441no—
1204C2×C4—441no—
1205C2×C4—441no—
1206C2×C4—441no—
1207C2×C4—441no—
1208C2×C4—441no—
1209C2×C4—441no—
1210C2×C4—441no—
1211C2×C4—441no—
1212C2×C4—441no—
1213C2×C4—441no—
1214C2×C4—441no—
1215C2×C4—441no—
1216C2×C4—441no—
1217C2×C4—441no—
1218C2×C4—441no—
1219C2×C4—441no—
1220C2×C4(C22⋊D11)⋊C414yes—
1221C22—24no—
1222C22—24no—
1223C22—24no—
1224C22—42no—
1225C22—42no—
1226C22—42no—
1227C22—42no—
1228C22—42no—
1229C22—42no—
1230C22—42no—
1231C22—42no—
1232C22—42no—
1233C22—42no—
1234C22—42no—
1235C22—42no—
1236C22—42no—
1237C22—42no—
1238C22—42no—
1239C22—42no—
1240C22—42no—
1241C22—42no—
1242C22—42no—
1243C22—81no—
1244C22—81no—
1245C22—81no—
1246C22—81no—
1247C22—81no—
1248C22—81no—
1249C22—81no—
1250C22—81no—
1251C22—442no—
1252C22—442no—
1253C22—442no—
1254C22—442no—
1255C22—442no—
1256C22—442no—
1257C22—442no—
1258C22—881no—
1259C22—881no—
1260C22—881no—
1261C22—881no—
1262C22—881no—
1263C22—881no—
1264C22—881no—
1265C22—881no—
1266C22C2×(C22⋊D11)⋊C411yescharacteristic
1267C22#1062301711yescharacteristic
1268C22#1062302111yescharacteristic
1269C22#1062302611yescharacteristic
1270C22C4×D4×D1111yescharacteristic
1271C22#1062307611yescharacteristic
1272C22#1062307611yescharacteristic
1273C22#1062307711yescharacteristic
1274C22#1062308111yescharacteristic
1275C22#1062308711yescharacteristic
1276C22#1062309111yescharacteristic
1277C22#1062309511yescharacteristic
1278C22#1062312811yescharacteristic
1279C22#1062313011yescharacteristic
1280C22#1062313811yescharacteristic
1281C22#1062313911yescharacteristic
1282C22#1062314011yescharacteristic
1283C22#1062314611yescharacteristic
1284C22#1062315111yescharacteristic
1285C22#1062315111yescharacteristic
1286C22#1062320011yescharacteristic
1287C22#1062321211yescharacteristic
1288C22#1062321311yescharacteristic
1289C22#1062321411yescharacteristic
1290C22#1062324611yescharacteristic
1291C22#1062324911yescharacteristic
1292C22#1062325011yescharacteristic
1293C22#1062325111yescharacteristic
1294C22C2×C4×C22⋊D1111yescharacteristic
1295C22D4×C22⋊D1111yescharacteristic
1296C22D4×C22⋊D1111yescharacteristic
1297C22#1062333511yescharacteristic
1298C22#1062333711yescharacteristic
1299C22#1062336011yescharacteristic
1300C22#1062336411yescharacteristic
1301C4—24no—
1302C4—42no—
1303C4—42no—
1304C4—42no—
1305C4—81no—
1306C4—224no—
1307C4—442no—
1308C4—442no—
1309C4—442no—
1310C4—442no—
1311C4—442no—
1312C4—881no—
1313C2—44no—
1314C2—82no—
1315C2—882no—
1316C2#1307130211yescharacteristic
1317C2#1307131211yescharacteristic
1318C2#1307131411yescharacteristic
1319C2#1307159311yescharacteristic
1320C2#1307159511yescharacteristic
1321C2#1307167711yescharacteristic
1322C2#1307175311yescharacteristic
1323C2#1307483911yescharacteristic
1324C2#1307487611yescharacteristic
1325C2#1307487811yescharacteristic
1326C2#1307490611yescharacteristic
1327C2#1307528411yescharacteristic
1328C2#1307529211yescharacteristic
1329C2#1307538211yescharacteristic
1330C2#1307587811yescharacteristic
subgroupG/H
center, FrattiniC24C23×D11
commutatorC23×C11C23×C4
FittingC2×C11×#390C2
socle, cosocleC24×C11C24
prime radicalC2×#10622836C2
hypercenterC2×#390D11
hypocenterC11#14521
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ C2×#390

Complements

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

NH ≅ G/Ntype
2. C2×#10622570C2semidirect
3. C2×#10622553C2semidirect
4. C2×#10622557C2semidirect
5. C2×#10622833C2semidirect
6. C2×#10622571C2semidirect
7. #13066859C2semidirect
8. #13066859C2semidirect
9. #13066858C2semidirect
10. #13066855C2semidirect
11. #13066855C2semidirect
12. #13066849C2semidirect
13. #13066848C2semidirect
14. #13066838C2semidirect
15. C2×C11×#390C2semidirect
40. #10622836C4semidirect
86. C22×C22⋊D11C2×C4semidirect
115. C2×C11×C22⋊C4D4semidirect
133. C2×C22⋊Dic11C2×C4semidirect
148. C2×(C2×D11)⋊C4C2×C4semidirect
167. C11⋊#95C2×C4semidirect
168. C11⋊#95D4semidirect
169. C11⋊#95D4semidirect
350. C2×#390D11semidirect
798. C2×C22⋊C4C22⋊D11semidirect
1012. C11#14521semidirect

Maximal subgroups

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

subgroupindex
C2×#106228362
C2×#106225702
C2×#106225532
C2×#106225572
C2×#106228332
C2×#106225712
#130668592
#130668582
#130668552
#130668492
#130668482
#130668382
C2×C11×#3902
#1452111