Finite Group Databasebeta

← #14683138

Subgroups — #14683138

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×#10622573C211yesmaximal, characteristic
2C2×#10622601C211yesmaximal, characteristic, complemented
3C2×#10622570C211yesmaximal, characteristic, complemented
4C2×#10622564C211yesmaximal, characteristic, complemented
5C2×#10622283C211yesmaximal, characteristic, complemented
6C2×#10622278C211yesmaximal, characteristic, complemented
7C2×#10622569C211yesmaximal, characteristic, complemented
8#13066862C211yesmaximal, characteristic, complemented
9#13066860C211yesmaximal, characteristic, complemented
10#13066855C211yesmaximal, characteristic, complemented
11#13066855C211yesmaximal, characteristic, complemented
12#13066848C211yesmaximal, characteristic, complemented
13#13066847C211yesmaximal, characteristic, complemented
14(C2×D11)⋊#95C211yesmaximal, characteristic, complemented
15C11×#1439C211yesmaximal, characteristic, complemented
16C23×C22⋊D11C2211yescharacteristic
17C23×C22⋊D11C2211yescharacteristic
18C23×D44C2211yescharacteristic
19C23×C4×D11C2211yescharacteristic
20C22×C11×C4⋊C4C2211yescharacteristic
21C22×C11×C22⋊C4C2211yescharacteristic
22C22×C11×C22⋊C4C2211yescharacteristic
23C22×C11×C22⋊C4C2211yescharacteristic
24C22×C22⋊Dic11C2211yescharacteristic
25C22×C22⋊Dic11C2211yescharacteristic
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×(C2×D11)⋊C4C2211yescharacteristic
35C22×C4⋊Dic11C2211yescharacteristic
36C22×Dic11⋊C4C2211yescharacteristic
37C22×C4×Dic11C2211yescharacteristic
38C22×C4×Dic11C2211yescharacteristic
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#10622601—24no—
52#10622573C418yescomplemented
53#10622570—24no—
54#10622569—24no—
55#10622564—24no—
56#10622283—24no—
57#10622278—24no—
58C25×C11C2311yescharacteristic
59C24×D11C2311yescharacteristic
60C24×D11C2311yescharacteristic
61C23×C4×C11C2311yescharacteristic
62C23×C4×C11C2311yescharacteristic
63C23×C4×C11C2311yescharacteristic
64C23×C4×C11C2311yescharacteristic
65C23×C4×C11C2311yescharacteristic
66C23×C4×C11C2311yescharacteristic
67C22×C22⋊D11—22no—
68C22×C22⋊D11—22no—
69C22×C22⋊D11—22no—
70C22×C22⋊D11—22no—
71C22×C22⋊D11—41no—
72C22×C22⋊D11—41no—
73C22×C22⋊D11—41no—
74C22×C22⋊D11—41no—
75C22×C22⋊D11—41no—
76C22×C22⋊D11—41no—
77C22×C22⋊D11—41no—
78C22×C22⋊D11—41no—
79C22×C22⋊D11C2×C414yes—
80C22×C22⋊D11C2×C414yescomplemented
81C23×Dic11C2311yescharacteristic
82C23×Dic11C2311yescharacteristic
83C23×Dic11C2311yescharacteristic
84C23×Dic11C2311yescharacteristic
85C23×Dic11C2311yescharacteristic
86C23×Dic11C2311yescharacteristic
87C22×D44—22no—
88C22×D44—22no—
89C22×D44—22no—
90C22×D44—22no—
91C22×D44—41no—
92C22×D44—41no—
93C22×D44C2×C414yes—
94C22×C4×D11—22no—
95C22×C4×D11—22no—
96C22×C4×D11—22no—
97C22×C4×D11—41no—
98C22×C4×D11—41no—
99C22×C4×D11—41no—
100C22×C4×D11—41no—
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—41no—
109C2×C11×C22⋊C4—41no—
110C2×C11×C22⋊C4—41no—
111C2×C11×C22⋊C4—41no—
112C2×C11×C22⋊C4C2×C414yescomplemented
113C2×C22⋊Dic11—22no—
114C2×C22⋊Dic11—22no—
115C2×C22⋊Dic11—22no—
116C2×C22⋊Dic11—22no—
117C2×C22⋊Dic11—41no—
118C2×C22⋊Dic11—41no—
119C2×(C2×D11)⋊C4—22no—
120C2×(C2×D11)⋊C4—22no—
121C2×(C2×D11)⋊C4—22no—
122C2×(C2×D11)⋊C4—22no—
123C2×(C2×D11)⋊C4—22no—
124C2×(C2×D11)⋊C4—22no—
125C2×(C2×D11)⋊C4—22no—
126C2×(C2×D11)⋊C4—22no—
127C2×(C2×D11)⋊C4—22no—
128C2×(C2×D11)⋊C4—22no—
129C2×(C2×D11)⋊C4—22no—
130C2×(C2×D11)⋊C4—22no—
131C2×(C2×D11)⋊C4—41no—
132C2×(C2×D11)⋊C4—41no—
133C2×(C2×D11)⋊C4—41no—
134C2×(C2×D11)⋊C4—41no—
135C2×(C2×D11)⋊C4—41no—
136C2×(C2×D11)⋊C4—41no—
137C2×(C2×D11)⋊C4—41no—
138C2×(C2×D11)⋊C4—41no—
139C2×(C2×D11)⋊C4—41no—
140C2×(C2×D11)⋊C4—41no—
141C2×(C2×D11)⋊C4—41no—
142C2×(C2×D11)⋊C4—41no—
143C2×(C2×D11)⋊C4C2×C414yes—
144C2×(C2×D11)⋊C4C2×C414yescomplemented
145C2×(C2×D11)⋊C4D414yescomplemented
146C2×C4⋊Dic11—22no—
147C2×C4⋊Dic11—22no—
148C2×C4⋊Dic11—41no—
149C2×Dic11⋊C4—22no—
150C2×Dic11⋊C4—22no—
151C2×Dic11⋊C4—41no—
152C2×C4×Dic11—22no—
153C2×C4×Dic11—22no—
154C2×C4×Dic11—22no—
155C2×C4×Dic11—22no—
156C2×C4×Dic11—41no—
157C2×C4×Dic11—41no—
158C11×#95—22no—
159C11×#95—22no—
160C11×#95—41no—
161C11⋊#95—22no—
162C11⋊#95—22no—
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×C11C22×C412yes—
186C24×C11C2411yescharacteristic
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×D11—21no—
201C23×D11—21no—
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×D11C22×C412yes—
214C23×D11C22×C412yes—
215C23×D11C2×D412yes—
216C23×D11#4112yes—
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×C11—21no—
251C22×C4×C11—21no—
252C22×C4×C11—21no—
253C22×C4×C11C22×C412yes—
254C22×C4×C11C22×C412yes—
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×Dic11C22×C412yes—
308C22×Dic11C22×C412yes—
309C22×Dic11C2×D412yes—
310C22×Dic11C2×D412yes—
311C22×Dic11C2×D412yes—
312C22×Dic11C2×D412yes—
313C22×Dic11C2×D412yes—
314C22×Dic11#4112yes—
315C2×D44—28no—
316C2×D44—28no—
317C2×D44—44no—
318C2×D44—44no—
319C2×D44—44no—
320C2×D44—44no—
321C2×D44—44no—
322C2×C4×D11—44no—
323C2×C4×D11—44no—
324C2×C4×D11—44no—
325C2×C4×D11—44no—
326C2×C4×D11—44no—
327C2×C4×D11—44no—
328C2×C4×D11—44no—
329C11×C4⋊C4—44no—
330C11×C22⋊C4—28no—
331C11×C22⋊C4—44no—
332C11×C22⋊C4—44no—
333C22⋊Dic11—44no—
334C22⋊Dic11—44no—
335(C2×D11)⋊C4—28no—
336(C2×D11)⋊C4—44no—
337(C2×D11)⋊C4—44no—
338(C2×D11)⋊C4—44no—
339(C2×D11)⋊C4—44no—
340(C2×D11)⋊C4—44no—
341(C2×D11)⋊C4—44no—
342(C2×D11)⋊C4—44no—
343(C2×D11)⋊C4—44no—
344C4⋊Dic11—44no—
345Dic11⋊C4—44no—
346C4×Dic11—44no—
347C4×Dic11—44no—
348C2×#392—111no—
349C2×#390—111no—
350C2×#390—111no—
351C2×#388—111no—
352C2×#388—111no—
353C2×#386—111no—
354C2×#386—111no—
355#1439—111no—
356#1439—111no—
357#1439D1111yescharacteristic, complemented
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—41no—
371C23×C11—41no—
372C23×C11—41no—
373C23×C11—41no—
374C23×C11—41no—
375C23×C11—41no—
376C23×C11—41no—
377C23×C11—41no—
378C23×C11—41no—
379C23×C11—41no—
380C23×C11—41no—
381C23×C11—41no—
382C23×C11—41no—
383C23×C11—41no—
384C23×C11—41no—
385C23×C11—41no—
386C23×C11—41no—
387C23×C11—41no—
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×C11C23×C411yescharacteristic
399C23×C11C22×D411yescharacteristic
400C23×C11C22×D411yescharacteristic
401C23×C11C22×D411yescharacteristic
402C23×C11C2×#4111yescharacteristic
403C23×C11C2×#4111yescharacteristic
404C23×C11C2×#4111yescharacteristic
405C23×C11H(5,𝔽2)11yescharacteristic
406C23×C11H(5,𝔽2)11yescharacteristic
407C23×C11H(5,𝔽2)11yescharacteristic
408C23×C11H(5,𝔽2)11yescharacteristic
409C23×C11H(5,𝔽2)11yescharacteristic
410C23×C11H(5,𝔽2)11yescharacteristic
411C23×C11H(5,𝔽2)11yescharacteristic
412C23×C112−1+411yescharacteristic
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—22no—
425C22×D11—22no—
426C22×D11—22no—
427C22×D11—22no—
428C22×D11—22no—
429C22×D11—22no—
430C22×D11—22no—
431C22×D11—22no—
432C22×D11—22no—
433C22×D11—22no—
434C22×D11—22no—
435C22×D11—22no—
436C22×D11—22no—
437C22×D11—22no—
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×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×D11C4×D414yes—
483C2×C4×C11—22no—
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—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×C4×C11—41no—
517C2×C4×C11—41no—
518C2×C4×C11—41no—
519C2×C4×C11—41no—
520C2×C4×C11—41no—
521C2×C4×C11—41no—
522C2×C4×C11—41no—
523C2×C4×C11—41no—
524C2×C4×C11C4×D414yes—
525C22⋊D11—416no—
526C22⋊D11—416no—
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—22no—
543C2×Dic11—22no—
544C2×Dic11—22no—
545C2×Dic11—22no—
546C2×Dic11—22no—
547C2×Dic11—22no—
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×Dic11C4×D414yes—
569D44—416no—
570C4×D11—416no—
571C23×D4—111no—
572C23×D4—111no—
573C23×D4—111no—
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⋊C4—111no—
589C22×C22⋊C4C2×D1111yescharacteristic
590C22×C22⋊C4C2×D1111yescharacteristic
591C22×C22⋊C4C2×D1111yescharacteristic
592C22×C42—111no—
593C22×C42—111no—
594#392—118no—
595#390—224no—
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×#95C2×D1111yescharacteristic
611C2×#95C2×D1111yescharacteristic
612C2×#95C2×D1111yescharacteristic
613C22×C11—42no—
614C22×C11—42no—
615C22×C11—42no—
616C22×C11—42no—
617C22×C11—42no—
618C22×C11—42no—
619C22×C11—42no—
620C22×C11—81no—
621C22×C11—81no—
622C22×C11—81no—
623C22×C11—81no—
624C22×C11—81no—
625C22×C11—81no—
626C22×C11—81no—
627C22×C11—81no—
628C22×C11C2×C4×D411yescharacteristic
629C22×C11C2×C4×D411yescharacteristic
630C22×C11C2×C4×D411yescharacteristic
631C22×C11#51811yescharacteristic
632C22×C11#51811yescharacteristic
633C22×C11#51811yescharacteristic
634C22×C11#52011yescharacteristic
635C22×C11#53411yescharacteristic
636C22×C11#53511yescharacteristic
637C22×C11#53511yescharacteristic
638C22×C11#53711yescharacteristic
639C22×C11#53711yescharacteristic
640C22×C11#53711yescharacteristic
641C22×C11#53811yescharacteristic
642C22×C11#53911yescharacteristic
643C22×C11#54011yescharacteristic
644C22×C11#54011yescharacteristic
645C22×C11#54211yescharacteristic
646C22×C11#54211yescharacteristic
647C22×C11D4211yescharacteristic
648C22×C11D4211yescharacteristic
649C22×C11D4211yescharacteristic
650C22×C11#54611yescharacteristic
651C22×C11#54611yescharacteristic
652C22×C11#54611yescharacteristic
653C22×C11#54611yescharacteristic
654C22×C11#55011yescharacteristic
655C22×C11#55011yescharacteristic
656C22×C11#55111yescharacteristic
657C22×C11#55111yescharacteristic
658C22×C11#55911yescharacteristic
659C22×C11#56011yescharacteristic
660C22×C11#56011yescharacteristic
661C22×C11#56011yescharacteristic
662C22×C11H(3,𝔽4)11yescharacteristic
663C2×D11—24no—
664C2×D11—24no—
665C2×D11—24no—
666C2×D11—42no—
667C2×D11—42no—
668C2×D11—42no—
669C2×D11—42no—
670C2×D11—42no—
671C2×D11—42no—
672C2×D11—42no—
673C2×D11—42no—
674C2×D11—42no—
675C2×D11—42no—
676C2×D11—42no—
677C2×D11—42no—
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—
698C4×C11—81no—
699Dic11—24no—
700Dic11—42no—
701Dic11—42no—
702Dic11—42no—
703Dic11—42no—
704Dic11—42no—
705C25—111no—
706C25—111no—
707C25C22×D1111yescharacteristic
708C22×D4—114no—
709C22×D4—114no—
710C22×D4—114no—
711C22×D4—222no—
712C22×D4—222no—
713C22×D4—222no—
714C22×D4—222no—
715C22×D4—222no—
716C22×D4—222no—
717C22×D4—222no—
718C22×D4—222no—
719C22×D4—441no—
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×D4—441no—
729C23×C4—111no—
730C23×C4—111no—
731C23×C4—111no—
732C23×C4—111no—
733C23×C4—111no—
734C23×C4—111no—
735C23×C4—222no—
736C23×C4—222no—
737C23×C4—222no—
738C23×C4—441no—
739C23×C4—441no—
740C23×C4—441no—
741C23×C4—441no—
742C23×C4C22×D1111yescharacteristic
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—41no—
762C2×C22⋊C4—41no—
763C2×C22⋊C4—41no—
764C2×C22⋊C4—41no—
765C2×C22⋊C4—114no—
766C2×C22⋊C4—114no—
767C2×C22⋊C4—114no—
768C2×C22⋊C4—222no—
769C2×C22⋊C4—222no—
770C2×C22⋊C4—222no—
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—441no—
785C2×C22⋊C4—441no—
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⋊C4C4×D1114yescomplemented
799C2×C42—222no—
800C2×C42—222no—
801C2×C42—222no—
802C2×C42—222no—
803C2×C42—441no—
804C2×C42—441no—
805#95—22no—
806#95—22no—
807#95—41no—
808#95—114no—
809#95—114no—
810#95—114no—
811#95—222no—
812#95—222no—
813#95—441no—
814#95—441no—
815#95—441no—
816#95—441no—
817C2×C11—82no—
818C2×C11#232411yescharacteristic
819C2×C11#232411yescharacteristic
820C2×C11#232511yescharacteristic
821C2×C11#235811yescharacteristic
822C2×C11#235811yescharacteristic
823C2×C11#236611yescharacteristic
824C2×C11#237511yescharacteristic
825C2×C11#267011yescharacteristic
826C2×C11#267311yescharacteristic
827C2×C11#267311yescharacteristic
828C2×C11#267511yescharacteristic
829C2×C11#270511yescharacteristic
830C2×C11#270511yescharacteristic
831C2×C11#271211yescharacteristic
832C2×C11#275211yescharacteristic
833D11—44no—
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—112no—
850C24—112no—
851C24—112no—
852C24—112no—
853C24—221no—
854C24—221no—
855C24—221no—
856C24—221no—
857C24—221no—
858C24—221no—
859C24—221no—
860C24—221no—
861C24—221no—
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—
876C24—221no—
877C24—221no—
878C24—221no—
879C24C2×C4×D1112yes—
880C24C23×D1111yescharacteristic
881C2×D4—228no—
882C2×D4—228no—
883C2×D4—228no—
884C2×D4—228no—
885C2×D4—444no—
886C2×D4—444no—
887C2×D4—444no—
888C2×D4—444no—
889C2×D4—444no—
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—21no—
932C22×C4—21no—
933C22×C4—21no—
934C22×C4—21no—
935C22×C4—21no—
936C22×C4—21no—
937C22×C4—21no—
938C22×C4—112no—
939C22×C4—112no—
940C22×C4—112no—
941C22×C4—112no—
942C22×C4—112no—
943C22×C4—112no—
944C22×C4—112no—
945C22×C4—112no—
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×C4C2×C4×D1112yes—
989C22×C4D4×D1112yes—
990C22×C4D4×D1112yes—
991C22×C4D4×D1112yes—
992C22×C4#434112yes—
993C4⋊C4—44no—
994C4⋊C4—444no—
995C4⋊C4—444no—
996C22⋊C4—28no—
997C22⋊C4—44no—
998C22⋊C4—44no—
999C22⋊C4—228no—
1000C22⋊C4—444no—
1001C22⋊C4—444no—
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—444no—
1011C42—444no—
1012C11#1452111yescharacteristic, complemented, Sylow
1013C23—22no—
1014C23—22no—
1015C23—22no—
1016C23—22no—
1017C23—22no—
1018C23—22no—
1019C23—22no—
1020C23—41no—
1021C23—41no—
1022C23—41no—
1023C23—41no—
1024C23—41no—
1025C23—41no—
1026C23—41no—
1027C23—41no—
1028C23—41no—
1029C23—41no—
1030C23—41no—
1031C23—41no—
1032C23—41no—
1033C23—41no—
1034C23—41no—
1035C23—41no—
1036C23—41no—
1037C23—41no—
1038C23—41no—
1039C23—41no—
1040C23—41no—
1041C23—41no—
1042C23—41no—
1043C23—41no—
1044C23—41no—
1045C23—41no—
1046C23—41no—
1047C23—41no—
1048C23—114no—
1049C23—222no—
1050C23—222no—
1051C23—222no—
1052C23—222no—
1053C23—222no—
1054C23—222no—
1055C23—222no—
1056C23—222no—
1057C23—222no—
1058C23—222no—
1059C23—222no—
1060C23—222no—
1061C23—222no—
1062C23—222no—
1063C23—222no—
1064C23—222no—
1065C23—222no—
1066C23—222no—
1067C23—222no—
1068C23—222no—
1069C23—222no—
1070C23—222no—
1071C23—222no—
1072C23—222no—
1073C23—222no—
1074C23—441no—
1075C23—441no—
1076C23—441no—
1077C23—441no—
1078C23—441no—
1079C23—441no—
1080C23—441no—
1081C23—441no—
1082C23—441no—
1083C23—441no—
1084C23—441no—
1085C23—441no—
1086C23—441no—
1087C23—441no—
1088C23—441no—
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—
1117C23—441no—
1118C23C22×C4×D1111yescharacteristic
1119C23C2×D4×D1111yescharacteristic
1120C23C2×D4×D1111yescharacteristic
1121C23C2×D4×D1111yescharacteristic
1122C23C2×#434111yescharacteristic
1123C23#6703711yescharacteristic
1124C23#6703711yescharacteristic
1125C23#6703711yescharacteristic
1126C23#6704011yescharacteristic
1127C23#41×D1111yescharacteristic
1128C23#41×D1111yescharacteristic
1129C23#6704211yescharacteristic
1130C23#6704211yescharacteristic
1131C23#6704211yescharacteristic
1132C23#6704211yescharacteristic
1133D4—4416no—
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—41no—
1171C2×C4—41no—
1172C2×C4—41no—
1173C2×C4—41no—
1174C2×C4—41no—
1175C2×C4—41no—
1176C2×C4—41no—
1177C2×C4—114no—
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—222no—
1193C2×C4—222no—
1194C2×C4—222no—
1195C2×C4—222no—
1196C2×C4—222no—
1197C2×C4—222no—
1198C2×C4—222no—
1199C2×C4—4416no—
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—42no—
1222C22—42no—
1223C22—42no—
1224C22—42no—
1225C22—42no—
1226C22—42no—
1227C22—42no—
1228C22—81no—
1229C22—81no—
1230C22—81no—
1231C22—81no—
1232C22—81no—
1233C22—81no—
1234C22—81no—
1235C22—81no—
1236C22—224no—
1237C22—224no—
1238C22—224no—
1239C22—442no—
1240C22—442no—
1241C22—442no—
1242C22—442no—
1243C22—442no—
1244C22—442no—
1245C22—442no—
1246C22—442no—
1247C22—442no—
1248C22—442no—
1249C22—442no—
1250C22—442no—
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#1062303511yescharacteristic
1268C22#1062305211yescharacteristic
1269C22C4×D4×D1111yescharacteristic
1270C22C4×D4×D1111yescharacteristic
1271C22#1062307611yescharacteristic
1272C22#1062307611yescharacteristic
1273C22#1062312011yescharacteristic
1274C22#1062312211yescharacteristic
1275C22#1062312311yescharacteristic
1276C22#1062313011yescharacteristic
1277C22#1062313811yescharacteristic
1278C22#1062314011yescharacteristic
1279C22#1062314011yescharacteristic
1280C22#1062314011yescharacteristic
1281C22#1062314111yescharacteristic
1282C22#1062315011yescharacteristic
1283C22#1062315111yescharacteristic
1284C22#1062316011yescharacteristic
1285C22#1062316011yescharacteristic
1286C22#1062316011yescharacteristic
1287C22#1062316911yescharacteristic
1288C22#1062317111yescharacteristic
1289C22#1062317411yescharacteristic
1290C22#1062318511yescharacteristic
1291C22#1062318811yescharacteristic
1292C22#1062318911yescharacteristic
1293C22#1062319411yescharacteristic
1294C22#1062319711yescharacteristic
1295C22#1062320711yescharacteristic
1296C22#1062321211yescharacteristic
1297C22#1062321411yescharacteristic
1298C22#1062323611yescharacteristic
1299C22#1062324211yescharacteristic
1300C22#1062324911yescharacteristic
1301C4—24no—
1302C4—42no—
1303C4—42no—
1304C4—42no—
1305C4—81no—
1306C4—81no—
1307C4—224no—
1308C4—442no—
1309C4—442no—
1310C4—442no—
1311C4—442no—
1312C4—442no—
1313C2—82no—
1314C2—444no—
1315C2—882no—
1316C2#1307130511yescharacteristic
1317C2#1307130811yescharacteristic
1318C2#1307131311yescharacteristic
1319C2#1307159411yescharacteristic
1320C2#1307159611yescharacteristic
1321C2#1307167711yescharacteristic
1322C2#1307175611yescharacteristic
1323C2#1307484411yescharacteristic
1324C2#1307488811yescharacteristic
1325C2#1307488911yescharacteristic
1326C2#1307490911yescharacteristic
1327C2#1307529111yescharacteristic
1328C2#1307529411yescharacteristic
1329C2#1307538711yescharacteristic
1330C2#1307587711yescharacteristic
subgroupG/H
center, FrattiniC24C23×D11
commutatorC23×C11C23×C4
FittingC11×#1439C2
socle, cosocleC24×C11C24
prime radicalC2×#10622573C2
hypercenter#1439D11
hypocenterC11#14521
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ #1439

Complements

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

NH ≅ G/Ntype
2. C2×#10622601C2semidirect
3. C2×#10622570C2semidirect
4. C2×#10622564C2semidirect
5. C2×#10622283C2semidirect
6. C2×#10622278C2semidirect
7. C2×#10622569C2semidirect
8. #13066862C2semidirect
9. #13066860C2semidirect
10. #13066855C2semidirect
11. #13066855C2semidirect
12. #13066848C2semidirect
13. #13066847C2semidirect
14. (C2×D11)⋊#95C2semidirect
15. C11×#1439C2semidirect
52. #10622573C4semidirect
80. C22×C22⋊D11C2×C4semidirect
112. C2×C11×C22⋊C4C2×C4semidirect
144. C2×(C2×D11)⋊C4C2×C4semidirect
145. C2×(C2×D11)⋊C4D4semidirect
167. C11⋊#95C2×C4semidirect
168. C11⋊#95D4semidirect
169. C11⋊#95D4semidirect
357. #1439D11semidirect
798. C2×C22⋊C4C4×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×#106225732
C2×#106226012
C2×#106225702
C2×#106225642
C2×#106222832
C2×#106222782
C2×#106225692
#130668622
#130668602
#130668552
#130668482
#130668472
(C2×D11)⋊#952
C11×#14392
#1452111