Finite Group Databasebeta

← #14676575

Subgroups — #14676575

Order 2816.

3058 conjugacy classes of subgroups.

The subgroup lattice has 1388 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#66992C211yesmaximal, characteristic
2C22×C4×C22⋊D11C211yesmaximal, characteristic, complemented
3C2×#10622570C211yesmaximal, characteristic, complemented
4C2×#10622569C211yesmaximal, characteristic, complemented
5C2×#10622555C211yesmaximal, characteristic, complemented
6C2×C22⋊C4×Dic11C211yesmaximal, characteristic, complemented
7#13066864C211yesmaximal, characteristic, complemented
8#13066863C211yesmaximal, characteristic, complemented
9#13066857C211yesmaximal, characteristic, complemented
10#13066855C211yesmaximal, characteristic, complemented
11Dic11⋊#95C211yesmaximal, characteristic, complemented
12Dic11⋊#95C211yesmaximal, characteristic, complemented
13#13066839C211yesmaximal, characteristic, complemented
14(C2×D11)⋊#95C211yesmaximal, characteristic, complemented
15C2×C11×#386C211yesmaximal, characteristic, complemented
16C23×D4×C11C2211yescharacteristic
17C24×C4×C11C2211yescharacteristic
18C23×C22⋊D11C2211yescharacteristic
19C23×C22⋊D11C2211yescharacteristic
20C24×Dic11C2211yescharacteristic
21C23×C4×D11C2211yescharacteristic
22C22×C11×C22⋊C4C2211yescharacteristic
23C22×C11×C22⋊C4C2211yescharacteristic
24C22×C11×C22⋊C4C2211yescharacteristic
25C22×C22⋊Dic11C2211yescharacteristic
26C22×C22⋊Dic11C2211yescharacteristic
27C22×C22⋊Dic11C2211yescharacteristic
28C22×C22⋊Dic11C2211yescharacteristic
29C22×C22⋊Dic11C2211yescharacteristic
30C2×#66992—24no—
31C2×#66992—24no—
32C2×#66992C418yescomplemented
33C2×C4×C22⋊D11—24no—
34C2×C4×C22⋊D11—24no—
35C2×C4×C22⋊D11—24no—
36C22×(C2×D11)⋊C4C2211yescharacteristic
37C22×(C2×D11)⋊C4C2211yescharacteristic
38C22×(C2×D11)⋊C4C2211yescharacteristic
39C22×(C2×D11)⋊C4C2211yescharacteristic
40C22×Dic11⋊C4C2211yescharacteristic
41C22×Dic11⋊C4C2211yescharacteristic
42C22×Dic11⋊C4C2211yescharacteristic
43C22×C4×Dic11C2211yescharacteristic
44C22×C4×Dic11C2211yescharacteristic
45C11×#386—24no—
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
56C2×C11⋊#95C2211yescharacteristic
57C2×C11⋊#95C2211yescharacteristic
58#10622570—24no—
59#10622569—24no—
60#10622555—24no—
61C22⋊C4×Dic11—24no—
62C25×C11C2311yescharacteristic
63C25×C11C2311yescharacteristic
64C24×D11C2311yescharacteristic
65C22×D4×C11—22no—
66C22×D4×C11—22no—
67C22×D4×C11—22no—
68C22×D4×C11—22no—
69C22×D4×C11—41no—
70C22×D4×C11—41no—
71C22×D4×C11C2×C414yescomplemented
72C23×C4×C11—22no—
73C23×C4×C11—22no—
74C23×C4×C11—22no—
75C23×C4×C11—22no—
76C23×C4×C11—22no—
77C23×C4×C11—41no—
78C23×C4×C11—41no—
79C23×C4×C11C2311yescharacteristic
80C23×C4×C11C2311yescharacteristic
81C23×C4×C11C2311yescharacteristic
82C23×C4×C11C2311yescharacteristic
83C23×C4×C11C2311yescharacteristic
84C22×C22⋊D11—22no—
85C22×C22⋊D11—22no—
86C22×C22⋊D11—22no—
87C22×C22⋊D11—22no—
88C22×C22⋊D11—22no—
89C22×C22⋊D11—22no—
90C22×C22⋊D11—22no—
91C22×C22⋊D11—22no—
92C22×C22⋊D11—41no—
93C22×C22⋊D11—41no—
94C22×C22⋊D11C2×C414yes—
95C22×C22⋊D11C2×C414yescomplemented
96C22×C22⋊D11D414yes—
97C22×C22⋊D11D414yes—
98C23×Dic11—22no—
99C23×Dic11—22no—
100C23×Dic11—22no—
101C23×Dic11—22no—
102C23×Dic11—22no—
103C23×Dic11—22no—
104C23×Dic11C2×C414yescomplemented
105C23×Dic11C2311yescharacteristic
106C23×Dic11C2311yescharacteristic
107C23×Dic11C2311yescharacteristic
108C23×Dic11C2311yescharacteristic
109C23×Dic11C2311yescharacteristic
110C23×Dic11C2311yescharacteristic
111C23×Dic11C2311yescharacteristic
112C22×C4×D11—22no—
113C22×C4×D11—22no—
114C22×C4×D11—22no—
115C22×C4×D11—22no—
116C22×C4×D11—22no—
117C22×C4×D11—41no—
118C22×C4×D11—41no—
119C2×C11×C22⋊C4—22no—
120C2×C11×C22⋊C4—22no—
121C2×C11×C22⋊C4—22no—
122C2×C11×C22⋊C4—22no—
123C2×C11×C22⋊C4—22no—
124C2×C11×C22⋊C4—22no—
125C2×C11×C22⋊C4—41no—
126C2×C11×C22⋊C4—41no—
127C2×C11×C22⋊C4D414yescomplemented
128C2×C22⋊Dic11—22no—
129C2×C22⋊Dic11—22no—
130C2×C22⋊Dic11—22no—
131C2×C22⋊Dic11—22no—
132C2×C22⋊Dic11—22no—
133C2×C22⋊Dic11—22no—
134C2×C22⋊Dic11—22no—
135C2×C22⋊Dic11—22no—
136C2×C22⋊Dic11—22no—
137C2×C22⋊Dic11—22no—
138C2×C22⋊Dic11—22no—
139C2×C22⋊Dic11—22no—
140C2×C22⋊Dic11—41no—
141C2×C22⋊Dic11—41no—
142C2×C22⋊Dic11C2×C414yescomplemented
143#66992—232no—
144C4×C22⋊D11—232no—
145C2×(C2×D11)⋊C4—22no—
146C2×(C2×D11)⋊C4—22no—
147C2×(C2×D11)⋊C4—22no—
148C2×(C2×D11)⋊C4—22no—
149C2×(C2×D11)⋊C4—22no—
150C2×(C2×D11)⋊C4—22no—
151C2×(C2×D11)⋊C4—22no—
152C2×(C2×D11)⋊C4—22no—
153C2×(C2×D11)⋊C4—22no—
154C2×(C2×D11)⋊C4—41no—
155C2×(C2×D11)⋊C4—41no—
156C2×(C2×D11)⋊C4C2×C414yescomplemented
157C2×Dic11⋊C4—22no—
158C2×Dic11⋊C4—22no—
159C2×Dic11⋊C4—22no—
160C2×Dic11⋊C4—22no—
161C2×Dic11⋊C4—22no—
162C2×Dic11⋊C4—22no—
163C2×Dic11⋊C4—22no—
164C2×Dic11⋊C4C2×C414yescomplemented
165C2×Dic11⋊C4D414yescomplemented
166C2×C4×Dic11—22no—
167C2×C4×Dic11—22no—
168C2×C4×Dic11—22no—
169C2×C4×Dic11—22no—
170C2×C4×Dic11—22no—
171C2×C4×Dic11D414yescomplemented
172C11×#95—22no—
173C11×#95—22no—
174C11⋊#95—22no—
175C11⋊#95—22no—
176C11⋊#95—22no—
177C11⋊#95—22no—
178C11⋊#95—22no—
179C11⋊#95—22no—
180C11⋊#95—41no—
181C11⋊#95—41no—
182C11⋊#95—41no—
183C11⋊#95—41no—
184#13970—111nomaximal, Sylow
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×C11—21no—
198C24×C11—21no—
199C24×C11—21no—
200C24×C11—21no—
201C24×C11—21no—
202C24×C11—21no—
203C24×C11—21no—
204C24×C11—21no—
205C24×C11—21no—
206C24×C11—21no—
207C24×C11—21no—
208C24×C11—21no—
209C24×C11C22×C412yes—
210C24×C11C22×C412yes—
211C24×C11C2×D412yes—
212C24×C11C2×D412yes—
213C24×C11C2×D412yes—
214C24×C11#4112yes—
215C24×C11C2411yescharacteristic
216C23×D11—21no—
217C23×D11—21no—
218C23×D11—21no—
219C23×D11—21no—
220C23×D11—21no—
221C23×D11—21no—
222C23×D11—21no—
223C23×D11—21no—
224C23×D11—21no—
225C23×D11—21no—
226C23×D11—21no—
227C23×D11—21no—
228C23×D11C22×C412yes—
229C23×D11C2×D412yes—
230C23×D11C2×D412yes—
231C2×D4×C11—28no—
232C2×D4×C11—28no—
233C2×D4×C11—44no—
234C2×D4×C11—44no—
235C2×D4×C11—44no—
236C2×D4×C11—44no—
237C2×D4×C11—44no—
238C22×C4×C11—21no—
239C22×C4×C11—21no—
240C22×C4×C11—21no—
241C22×C4×C11—21no—
242C22×C4×C11—28no—
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×C11—21no—
254C22×C4×C11—21no—
255C22×C4×C11—21no—
256C22×C4×C11—21no—
257C22×C4×C11—21no—
258C22×C4×C11—21no—
259C22×C4×C11—21no—
260C22×C4×C11—21no—
261C22×C4×C11—21no—
262C22×C4×C11—21no—
263C22×C4×C11—21no—
264C22×C4×C11—21no—
265C22×C4×C11—21no—
266C22×C4×C11—21no—
267C22×C4×C11—21no—
268C22×C4×C11—44no—
269C22×C4×C11—44no—
270C22×C4×C11—44no—
271C22×C4×C11—44no—
272C22×C4×C11—44no—
273C22×C4×C11—44no—
274C22×C4×C11C22×C412yes—
275C22×C4×C11C2×D412yes—
276C22×C4×C11C2×D412yes—
277C22×C4×C11C2×D412yes—
278C22×C4×C11C2×D412yes—
279C22×C4×C11#4112yes—
280C2×C22⋊D11—28no—
281C2×C22⋊D11—28no—
282C2×C22⋊D11—28no—
283C2×C22⋊D11—28no—
284C2×C22⋊D11—28no—
285C2×C22⋊D11—28no—
286C2×C22⋊D11—28no—
287C2×C22⋊D11—28no—
288C2×C22⋊D11—44no—
289C2×C22⋊D11—44no—
290C2×C22⋊D11—44no—
291C2×C22⋊D11—44no—
292C2×C22⋊D11—44no—
293C2×C22⋊D11C22⋊C4116yescomplemented
294C22×Dic11—28no—
295C22×Dic11—28no—
296C22×Dic11—28no—
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—21no—
315C22×Dic11—21no—
316C22×Dic11—21no—
317C22×Dic11—21no—
318C22×Dic11—21no—
319C22×Dic11—21no—
320C22×Dic11—21no—
321C22×Dic11—21no—
322C22×Dic11—21no—
323C22×Dic11—21no—
324C22×Dic11—21no—
325C22×Dic11—21no—
326C22×Dic11—21no—
327C22×Dic11—21no—
328C22×Dic11—21no—
329C22×Dic11—21no—
330C22×Dic11—21no—
331C22×Dic11—21no—
332C22×Dic11—21no—
333C22×Dic11—21no—
334C22×Dic11—44no—
335C22×Dic11—44no—
336C22×Dic11—44no—
337C22×Dic11—44no—
338C22×Dic11C22×C412yes—
339C22×Dic11C22×C412yes—
340C22×Dic11C22×C412yes—
341C22×Dic11C2×D412yes—
342C22×Dic11C2×D412yes—
343C22×Dic11C2×D412yes—
344C22×Dic11C2×D412yes—
345C22×Dic11C2×D412yes—
346C22×Dic11C2×D412yes—
347C22×Dic11#4112yes—
348C22×Dic11#4112yes—
349C22×Dic11#4112yes—
350C2×C4×D11—28no—
351C2×C4×D11—44no—
352C2×C4×D11—44no—
353C2×C4×D11—44no—
354C2×C4×D11—44no—
355C2×C4×D11—44no—
356C2×C4×D11—44no—
357C11×C22⋊C4—28no—
358C11×C22⋊C4—44no—
359C11×C22⋊C4—44no—
360C22⋊Dic11—28no—
361C22⋊Dic11—28no—
362C22⋊Dic11—28no—
363C22⋊Dic11—44no—
364C22⋊Dic11—44no—
365(C2×D11)⋊C4—28no—
366(C2×D11)⋊C4—28no—
367(C2×D11)⋊C4—44no—
368(C2×D11)⋊C4—44no—
369Dic11⋊C4—28no—
370Dic11⋊C4—28no—
371Dic11⋊C4—44no—
372C4×Dic11—28no—
373C4×Dic11—44no—
374C22×#121—111no—
375C22×C4×D4—111no—
376C2×#390—111no—
377C2×#386—111no—
378C2×#386D1111yescharacteristic, complemented
379C2×#380—111no—
380C2×C4×C22⋊C4—111no—
381#1440—111no—
382#1440—111no—
383#1438—111no—
384#1438—111no—
385C4⋊#95—111no—
386C4⋊#95—111no—
387C22⋊#95—111no—
388C22⋊#95—111no—
389C23×C11—22no—
390C23×C11—22no—
391C23×C11—22no—
392C23×C11—22no—
393C23×C11—22no—
394C23×C11—22no—
395C23×C11—22no—
396C23×C11—22no—
397C23×C11—22no—
398C23×C11—22no—
399C23×C11—22no—
400C23×C11—22no—
401C23×C11—22no—
402C23×C11—22no—
403C23×C11—22no—
404C23×C11—22no—
405C23×C11—22no—
406C23×C11—22no—
407C23×C11—22no—
408C23×C11—22no—
409C23×C11—22no—
410C23×C11—22no—
411C23×C11—22no—
412C23×C11—22no—
413C23×C11—22no—
414C23×C11—22no—
415C23×C11—22no—
416C23×C11—22no—
417C23×C11—22no—
418C23×C11—22no—
419C23×C11—22no—
420C23×C11—22no—
421C23×C11—22no—
422C23×C11—22no—
423C23×C11—22no—
424C23×C11—22no—
425C23×C11—41no—
426C23×C11—41no—
427C23×C11—41no—
428C23×C11—41no—
429C23×C11—41no—
430C23×C11—41no—
431C23×C11—41no—
432C23×C11—41no—
433C23×C11—41no—
434C23×C11—41no—
435C23×C11—41no—
436C23×C11—41no—
437C23×C11—41no—
438C23×C11—41no—
439C23×C11—41no—
440C23×C11—41no—
441C23×C11—41no—
442C23×C11—41no—
443C23×C11—41no—
444C23×C11—41no—
445C23×C11—41no—
446C23×C11—41no—
447C23×C11—41no—
448C23×C11—41no—
449C23×C11—41no—
450C23×C11—41no—
451C23×C11—41no—
452C23×C11—41no—
453C23×C11—41no—
454C23×C11—41no—
455C23×C11—41no—
456C23×C11—41no—
457C23×C11C2×C22⋊C414yes—
458C23×C11C4×D414yescomplemented
459C23×C11C23×C411yescharacteristic
460C23×C11C22×D411yescharacteristic
461C23×C11C22×D411yescharacteristic
462C23×C11C22×D411yescharacteristic
463C23×C11C22×D411yescharacteristic
464C23×C11C22×D411yescharacteristic
465C23×C11C2×#4111yescharacteristic
466C23×C11C2×#4111yescharacteristic
467C23×C11C2×#4111yescharacteristic
468C23×C11C2×#4111yescharacteristic
469C23×C11C2×#4111yescharacteristic
470C23×C11H(5,𝔽2)11yescharacteristic
471C23×C11H(5,𝔽2)11yescharacteristic
472C23×C11H(5,𝔽2)11yescharacteristic
473C23×C112−1+411yescharacteristic
474C22×D11—22no—
475C22×D11—22no—
476C22×D11—22no—
477C22×D11—22no—
478C22×D11—22no—
479C22×D11—22no—
480C22×D11—22no—
481C22×D11—22no—
482C22×D11—22no—
483C22×D11—22no—
484C22×D11—22no—
485C22×D11—22no—
486C22×D11—22no—
487C22×D11—22no—
488C22×D11—22no—
489C22×D11—22no—
490C22×D11—22no—
491C22×D11—22no—
492C22×D11—41no—
493C22×D11—41no—
494C22×D11—41no—
495C22×D11—41no—
496C22×D11—41no—
497C22×D11—41no—
498C22×D11—41no—
499C22×D11—41no—
500C22×D11—41no—
501C22×D11—41no—
502C22×D11—41no—
503C22×D11—41no—
504C22×D11—41no—
505C22×D11—41no—
506C22×D11—41no—
507C22×D11—41no—
508C22×D11C2×C22⋊C414yes—
509D4×C11—416no—
510C2×C4×C11—22no—
511C2×C4×C11—22no—
512C2×C4×C11—22no—
513C2×C4×C11—22no—
514C2×C4×C11—22no—
515C2×C4×C11—22no—
516C2×C4×C11—22no—
517C2×C4×C11—22no—
518C2×C4×C11—22no—
519C2×C4×C11—22no—
520C2×C4×C11—22no—
521C2×C4×C11—22no—
522C2×C4×C11—22no—
523C2×C4×C11—22no—
524C2×C4×C11—22no—
525C2×C4×C11—416no—
526C2×C4×C11—41no—
527C2×C4×C11—41no—
528C2×C4×C11—41no—
529C2×C4×C11—41no—
530C2×C4×C11—41no—
531C2×C4×C11—41no—
532C2×C4×C11—41no—
533C2×C4×C11—41no—
534C2×C4×C11—41no—
535C2×C4×C11—41no—
536C2×C4×C11—41no—
537C2×C4×C11—41no—
538C2×C4×C11—41no—
539C2×C4×C11—41no—
540C2×C4×C11—41no—
541C2×C4×C11—41no—
542C2×C4×C11—41no—
543C2×C4×C11—41no—
544C2×C4×C11—41no—
545C2×C4×C11#12114yescomplemented
546C22⋊D11—232no—
547C22⋊D11—416no—
548C2×Dic11—22no—
549C2×Dic11—22no—
550C2×Dic11—22no—
551C2×Dic11—22no—
552C2×Dic11—22no—
553C2×Dic11—22no—
554C2×Dic11—22no—
555C2×Dic11—22no—
556C2×Dic11—22no—
557C2×Dic11—22no—
558C2×Dic11—22no—
559C2×Dic11—22no—
560C2×Dic11—22no—
561C2×Dic11—22no—
562C2×Dic11—22no—
563C2×Dic11—41no—
564C2×Dic11—41no—
565C2×Dic11—41no—
566C2×Dic11—41no—
567C2×Dic11—41no—
568C2×Dic11—41no—
569C2×Dic11—41no—
570C2×Dic11—41no—
571C2×Dic11—41no—
572C2×Dic11—41no—
573C2×Dic11—41no—
574C2×Dic11—41no—
575C2×Dic11—41no—
576C2×Dic11—41no—
577C2×Dic11—41no—
578C2×Dic11—41no—
579C2×Dic11—41no—
580C2×Dic11—41no—
581C2×Dic11—41no—
582C2×Dic11—41no—
583C2×Dic11—416no—
584C2×Dic11—41no—
585C2×Dic11—41no—
586C2×Dic11—41no—
587C2×Dic11—41no—
588C2×Dic11—41no—
589C2×Dic11—41no—
590C2×Dic11—41no—
591C2×Dic11C2×C22⋊C414yes—
592C2×Dic11C4×D414yes—
593C2×Dic11C4×D414yes—
594C2×Dic11#12014yes—
595C2×Dic11#12114yes—
596C2×Dic11#12114yes—
597C2×Dic11#12314yes—
598C4×D11—416no—
599C23×D4—111no—
600C23×D4—111no—
601C23×D4C2×D1111yescharacteristic
602C24×C4—111no—
603C24×C4—111no—
604C24×C4C2×D1111yescharacteristic
605C2×#121—118no—
606C2×#121—224no—
607C2×#121—224no—
608C2×C4×D4—224no—
609C2×C4×D4—224no—
610C2×C4×D4—224no—
611C22×C4⋊C4—111no—
612C22×C4⋊C4—111no—
613C22×C4⋊C4—111no—
614C22×C22⋊C4—111no—
615C22×C22⋊C4—111no—
616C22×C22⋊C4—111no—
617C22×C22⋊C4—111no—
618C22×C22⋊C4—111no—
619C22×C22⋊C4—111no—
620C22×C22⋊C4—111no—
621C22×C22⋊C4—111no—
622C22×C22⋊C4—111no—
623C22×C22⋊C4C2×D1111yescharacteristic
624C22×C22⋊C4C2×D1111yescharacteristic
625C22×C22⋊C4C2×D1111yescharacteristic
626C22×C42—111no—
627C22×C42—111no—
628#390—224no—
629#386—24no—
630#386—224no—
631#380—224no—
632C4×C22⋊C4—224no—
633C2×#95—111no—
634C2×#95—111no—
635C2×#95—111no—
636C2×#95—111no—
637C2×#95—111no—
638C2×#95—111no—
639C2×#95—111no—
640C2×#95—111no—
641C2×#95—111no—
642C2×#95—111no—
643C2×#95C2×D1111yescharacteristic
644C2×#95C2×D1111yescharacteristic
645C22×C11—24no—
646C22×C11—24no—
647C22×C11—24no—
648C22×C11—24no—
649C22×C11—24no—
650C22×C11—24no—
651C22×C11—42no—
652C22×C11—42no—
653C22×C11—42no—
654C22×C11—42no—
655C22×C11—42no—
656C22×C11—42no—
657C22×C11—42no—
658C22×C11—42no—
659C22×C11—42no—
660C22×C11—42no—
661C22×C11—42no—
662C22×C11—42no—
663C22×C11—42no—
664C22×C11—42no—
665C22×C11—42no—
666C22×C11—42no—
667C22×C11—42no—
668C22×C11—42no—
669C22×C11—42no—
670C22×C11—42no—
671C22×C11—42no—
672C22×C11—42no—
673C22×C11—42no—
674C22×C11—42no—
675C22×C11C22×C22⋊C411yescharacteristic
676C22×C11C2×C4×D411yescharacteristic
677C22×C11C2×C4×D411yescharacteristic
678C22×C11C2×C4×D411yescharacteristic
679C22×C11C4×#4111yescharacteristic
680C22×C11#51811yescharacteristic
681C22×C11#52011yescharacteristic
682C22×C11C2×#12011yescharacteristic
683C22×C11C2×#12111yescharacteristic
684C22×C11C2×#12111yescharacteristic
685C22×C11C2×#12111yescharacteristic
686C22×C11C2×#12311yescharacteristic
687C22×C11#52511yescharacteristic
688C22×C11#52911yescharacteristic
689C22×C11#53211yescharacteristic
690C22×C11#53511yescharacteristic
691C22×C11#53711yescharacteristic
692C22×C11#54011yescharacteristic
693C22×C11#54211yescharacteristic
694C22×C11D4211yescharacteristic
695C22×C11D4211yescharacteristic
696C22×C11D4211yescharacteristic
697C22×C11#54611yescharacteristic
698C22×C11#54611yescharacteristic
699C22×C11#54611yescharacteristic
700C22×C11#54611yescharacteristic
701C22×C11#54611yescharacteristic
702C22×C11#54711yescharacteristic
703C22×C11#54711yescharacteristic
704C22×C11#54711yescharacteristic
705C22×C11#54811yescharacteristic
706C22×C11#55011yescharacteristic
707C22×C11#55311yescharacteristic
708C22×C11#55311yescharacteristic
709C22×C11#55511yescharacteristic
710C2×D11—24no—
711C2×D11—24no—
712C2×D11—24no—
713C2×D11—42no—
714C2×D11—42no—
715C2×D11—42no—
716C2×D11—42no—
717C2×D11—42no—
718C2×D11—42no—
719C2×D11—42no—
720C2×D11—42no—
721C2×D11—42no—
722C2×D11—42no—
723C2×D11—42no—
724C2×D11—42no—
725C4×C11—24no—
726C4×C11—42no—
727C4×C11—42no—
728C4×C11—42no—
729C4×C11—81no—
730Dic11—42no—
731Dic11—42no—
732Dic11—42no—
733Dic11—42no—
734Dic11—42no—
735Dic11—81no—
736Dic11#38618yescomplemented
737C25—111no—
738C25C22×D1111yescharacteristic
739C25C22×D1111yescharacteristic
740C22×D4—22no—
741C22×D4—22no—
742C22×D4—22no—
743C22×D4—22no—
744C22×D4—41no—
745C22×D4—41no—
746C22×D4—114no—
747C22×D4—114no—
748C22×D4—114no—
749C22×D4—114no—
750C22×D4—222no—
751C22×D4—222no—
752C22×D4—222no—
753C22×D4—222no—
754C22×D4—222no—
755C22×D4—222no—
756C22×D4—222no—
757C22×D4—222no—
758C22×D4—441no—
759C22×D4—441no—
760C22×D4C4×D1114yescomplemented
761C23×C4—22no—
762C23×C4—22no—
763C23×C4—22no—
764C23×C4—22no—
765C23×C4—22no—
766C23×C4—41no—
767C23×C4—41no—
768C23×C4—111no—
769C23×C4—114no—
770C23×C4—111no—
771C23×C4—111no—
772C23×C4—111no—
773C23×C4—111no—
774C23×C4—111no—
775C23×C4—111no—
776C23×C4—222no—
777C23×C4—222no—
778C23×C4—222no—
779C23×C4—222no—
780C23×C4—222no—
781C23×C4—222no—
782C23×C4—222no—
783C23×C4—222no—
784C23×C4—222no—
785C23×C4—222no—
786C23×C4—222no—
787C23×C4—441no—
788C23×C4—441no—
789C23×C4C22×D1111yescharacteristic
790C23×C4C22×D1111yescharacteristic
791C23×C4C22×D1111yescharacteristic
792C23×C4C22×D1111yescharacteristic
793C23×C4C22×D1111yescharacteristic
794#121—2232no—
795C4×D4—2232no—
796C2×C4⋊C4—114no—
797C2×C4⋊C4—114no—
798C2×C4⋊C4—222no—
799C2×C4⋊C4—222no—
800C2×C4⋊C4—222no—
801C2×C4⋊C4—222no—
802C2×C4⋊C4—222no—
803C2×C4⋊C4—222no—
804C2×C4⋊C4—222no—
805C2×C22⋊C4—22no—
806C2×C22⋊C4—22no—
807C2×C22⋊C4—22no—
808C2×C22⋊C4—22no—
809C2×C22⋊C4—22no—
810C2×C22⋊C4—22no—
811C2×C22⋊C4—41no—
812C2×C22⋊C4—41no—
813C2×C22⋊C4—114no—
814C2×C22⋊C4—114no—
815C2×C22⋊C4—222no—
816C2×C22⋊C4—222no—
817C2×C22⋊C4—222no—
818C2×C22⋊C4—222no—
819C2×C22⋊C4—222no—
820C2×C22⋊C4—222no—
821C2×C22⋊C4—222no—
822C2×C22⋊C4—222no—
823C2×C22⋊C4—222no—
824C2×C22⋊C4—222no—
825C2×C22⋊C4—222no—
826C2×C22⋊C4—222no—
827C2×C22⋊C4—222no—
828C2×C22⋊C4—222no—
829C2×C22⋊C4—222no—
830C2×C22⋊C4—222no—
831C2×C22⋊C4—222no—
832C2×C22⋊C4—222no—
833C2×C22⋊C4—222no—
834C2×C22⋊C4—222no—
835C2×C22⋊C4—222no—
836C2×C22⋊C4—441no—
837C2×C22⋊C4—441no—
838C2×C22⋊C4—441no—
839C2×C22⋊C4—441no—
840C2×C22⋊C4C22⋊D1114yescomplemented
841C2×C42—114no—
842C2×C42—222no—
843C2×C42—222no—
844C2×C42—222no—
845C2×C42—222no—
846C2×C42—222no—
847#95—22no—
848#95—22no—
849#95—222no—
850#95—222no—
851#95—222no—
852#95—222no—
853#95—222no—
854#95—222no—
855#95—441no—
856#95—441no—
857#95—441no—
858#95—441no—
859C2×C11—44no—
860C2×C11—44no—
861C2×C11C2×#38611yescharacteristic
862C2×C11C4×#12111yescharacteristic
863C2×C11#232411yescharacteristic
864C2×C11D4×C22⋊C411yescharacteristic
865C2×C11#233911yescharacteristic
866C2×C11#236111yescharacteristic
867C2×C11#236311yescharacteristic
868C2×C11#240711yescharacteristic
869C2×C11#240811yescharacteristic
870C2×C11#242011yescharacteristic
871C2×C11#242211yescharacteristic
872C2×C11#242711yescharacteristic
873C2×C11#242811yescharacteristic
874C2×C11#253511yescharacteristic
875C2×C11#253711yescharacteristic
876D11—44no—
877C24—21no—
878C24—21no—
879C24—21no—
880C24—21no—
881C24—21no—
882C24—21no—
883C24—21no—
884C24—21no—
885C24—21no—
886C24—21no—
887C24—21no—
888C24—21no—
889C24—21no—
890C24—21no—
891C24—21no—
892C24—21no—
893C24—21no—
894C24—21no—
895C24—21no—
896C24—21no—
897C24—21no—
898C24—21no—
899C24—21no—
900C24—21no—
901C24—112no—
902C24—112no—
903C24—112no—
904C24—221no—
905C24—221no—
906C24—221no—
907C24—221no—
908C24—221no—
909C24—221no—
910C24—221no—
911C24—221no—
912C24—221no—
913C24—221no—
914C24—221no—
915C24—221no—
916C24C2×C4×D1112yes—
917C24C2×C4×D1112yes—
918C24#433912yes—
919C24D4×D1112yes—
920C24D4×D1112yes—
921C24C2×C22⋊D1112yes—
922C24C23×D1111yescharacteristic
923C2×D4—28no—
924C2×D4—28no—
925C2×D4—44no—
926C2×D4—44no—
927C2×D4—44no—
928C2×D4—44no—
929C2×D4—44no—
930C2×D4—1116no—
931C2×D4—228no—
932C2×D4—228no—
933C2×D4—228no—
934C2×D4—228no—
935C2×D4—228no—
936C2×D4—228no—
937C2×D4—228no—
938C2×D4—228no—
939C2×D4—444no—
940C2×D4—444no—
941C2×D4—444no—
942C2×D4—444no—
943C2×D4—444no—
944C22×C4—21no—
945C22×C4—21no—
946C22×C4—21no—
947C22×C4—21no—
948C22×C4—28no—
949C22×C4—21no—
950C22×C4—21no—
951C22×C4—21no—
952C22×C4—21no—
953C22×C4—21no—
954C22×C4—21no—
955C22×C4—21no—
956C22×C4—21no—
957C22×C4—21no—
958C22×C4—21no—
959C22×C4—21no—
960C22×C4—21no—
961C22×C4—21no—
962C22×C4—21no—
963C22×C4—21no—
964C22×C4—21no—
965C22×C4—21no—
966C22×C4—21no—
967C22×C4—21no—
968C22×C4—21no—
969C22×C4—21no—
970C22×C4—21no—
971C22×C4—21no—
972C22×C4—21no—
973C22×C4—21no—
974C22×C4—44no—
975C22×C4—44no—
976C22×C4—44no—
977C22×C4—44no—
978C22×C4—44no—
979C22×C4—44no—
980C22×C4—112no—
981C22×C4—112no—
982C22×C4—112no—
983C22×C4—112no—
984C22×C4—112no—
985C22×C4—112no—
986C22×C4—112no—
987C22×C4—112no—
988C22×C4—112no—
989C22×C4—112no—
990C22×C4—112no—
991C22×C4—112no—
992C22×C4—228no—
993C22×C4—228no—
994C22×C4—228no—
995C22×C4—228no—
996C22×C4—221no—
997C22×C4—221no—
998C22×C4—221no—
999C22×C4—221no—
1000C22×C4—221no—
1001C22×C4—221no—
1002C22×C4—221no—
1003C22×C4—221no—
1004C22×C4—221no—
1005C22×C4—221no—
1006C22×C4—221no—
1007C22×C4—221no—
1008C22×C4—221no—
1009C22×C4—221no—
1010C22×C4—221no—
1011C22×C4—221no—
1012C22×C4—221no—
1013C22×C4—221no—
1014C22×C4—221no—
1015C22×C4—221no—
1016C22×C4—221no—
1017C22×C4—221no—
1018C22×C4—221no—
1019C22×C4—221no—
1020C22×C4—221no—
1021C22×C4—221no—
1022C22×C4—221no—
1023C22×C4—221no—
1024C22×C4—221no—
1025C22×C4—221no—
1026C22×C4—221no—
1027C22×C4—221no—
1028C22×C4—221no—
1029C22×C4—221no—
1030C22×C4—221no—
1031C22×C4—221no—
1032C22×C4—221no—
1033C22×C4—444no—
1034C22×C4—444no—
1035C22×C4—444no—
1036C22×C4—444no—
1037C22×C4—444no—
1038C22×C4—444no—
1039C22×C4—444no—
1040C22×C4—444no—
1041C22×C4—444no—
1042C22×C4—444no—
1043C22×C4C2×C4×D1112yes—
1044C22×C4D4×D1112yes—
1045C22×C4D4×D1112yes—
1046C22×C4#434112yes—
1047C22×C4C2×C22⋊D1112yes—
1048C22×C4C2×C22⋊D1112yes—
1049C4⋊C4—228no—
1050C4⋊C4—228no—
1051C4⋊C4—444no—
1052C22⋊C4—28no—
1053C22⋊C4—44no—
1054C22⋊C4—44no—
1055C22⋊C4—228no—
1056C22⋊C4—228no—
1057C22⋊C4—228no—
1058C22⋊C4—228no—
1059C22⋊C4—228no—
1060C22⋊C4—444no—
1061C22⋊C4—444no—
1062C22⋊C4—444no—
1063C22⋊C4—444no—
1064C42—228no—
1065C42—444no—
1066C11#1397011yescharacteristic, complemented, Sylow
1067C23—22no—
1068C23—22no—
1069C23—22no—
1070C23—22no—
1071C23—22no—
1072C23—22no—
1073C23—22no—
1074C23—22no—
1075C23—22no—
1076C23—22no—
1077C23—22no—
1078C23—22no—
1079C23—22no—
1080C23—22no—
1081C23—22no—
1082C23—22no—
1083C23—22no—
1084C23—22no—
1085C23—22no—
1086C23—22no—
1087C23—22no—
1088C23—22no—
1089C23—22no—
1090C23—22no—
1091C23—22no—
1092C23—22no—
1093C23—22no—
1094C23—22no—
1095C23—22no—
1096C23—22no—
1097C23—22no—
1098C23—22no—
1099C23—22no—
1100C23—22no—
1101C23—22no—
1102C23—22no—
1103C23—41no—
1104C23—41no—
1105C23—41no—
1106C23—41no—
1107C23—41no—
1108C23—41no—
1109C23—41no—
1110C23—41no—
1111C23—41no—
1112C23—41no—
1113C23—41no—
1114C23—41no—
1115C23—41no—
1116C23—41no—
1117C23—41no—
1118C23—41no—
1119C23—41no—
1120C23—41no—
1121C23—41no—
1122C23—41no—
1123C23—41no—
1124C23—41no—
1125C23—41no—
1126C23—41no—
1127C23—41no—
1128C23—41no—
1129C23—41no—
1130C23—41no—
1131C23—41no—
1132C23—41no—
1133C23—41no—
1134C23—41no—
1135C23—114no—
1136C23—222no—
1137C23—222no—
1138C23—222no—
1139C23—222no—
1140C23—222no—
1141C23—222no—
1142C23—222no—
1143C23—222no—
1144C23—222no—
1145C23—222no—
1146C23—222no—
1147C23—222no—
1148C23—222no—
1149C23—222no—
1150C23—222no—
1151C23—222no—
1152C23—222no—
1153C23—222no—
1154C23—441no—
1155C23—441no—
1156C23—441no—
1157C23—441no—
1158C23—441no—
1159C23—441no—
1160C23—441no—
1161C23—441no—
1162C23—441no—
1163C23—441no—
1164C23—441no—
1165C23—441no—
1166C23—441no—
1167C23—441no—
1168C23—441no—
1169C23—441no—
1170C23C22⋊C4×D1114yes—
1171C23C4×C22⋊D1114yescomplemented
1172C23C22×C4×D1111yescharacteristic
1173C23C2×#433911yescharacteristic
1174C23C2×D4×D1111yescharacteristic
1175C23C2×D4×D1111yescharacteristic
1176C23C2×D4×D1111yescharacteristic
1177C23C2×D4×D1111yescharacteristic
1178C23C2×#434111yescharacteristic
1179C23#6703711yescharacteristic
1180C23#6703711yescharacteristic
1181C23#6703711yescharacteristic
1182C23#41×D1111yescharacteristic
1183C23#41×D1111yescharacteristic
1184C23#41×D1111yescharacteristic
1185C23#6704311yescharacteristic
1186C23C22×C22⋊D1111yescharacteristic
1187D4—416no—
1188D4—2232no—
1189D4—4416no—
1190C2×C4—22no—
1191C2×C4—22no—
1192C2×C4—22no—
1193C2×C4—22no—
1194C2×C4—22no—
1195C2×C4—22no—
1196C2×C4—22no—
1197C2×C4—22no—
1198C2×C4—22no—
1199C2×C4—22no—
1200C2×C4—22no—
1201C2×C4—22no—
1202C2×C4—22no—
1203C2×C4—22no—
1204C2×C4—22no—
1205C2×C4—416no—
1206C2×C4—41no—
1207C2×C4—41no—
1208C2×C4—41no—
1209C2×C4—41no—
1210C2×C4—41no—
1211C2×C4—41no—
1212C2×C4—41no—
1213C2×C4—41no—
1214C2×C4—41no—
1215C2×C4—41no—
1216C2×C4—41no—
1217C2×C4—41no—
1218C2×C4—41no—
1219C2×C4—41no—
1220C2×C4—41no—
1221C2×C4—41no—
1222C2×C4—41no—
1223C2×C4—41no—
1224C2×C4—41no—
1225C2×C4—114no—
1226C2×C4—114no—
1227C2×C4—114no—
1228C2×C4—114no—
1229C2×C4—114no—
1230C2×C4—114no—
1231C2×C4—114no—
1232C2×C4—222no—
1233C2×C4—222no—
1234C2×C4—222no—
1235C2×C4—222no—
1236C2×C4—222no—
1237C2×C4—222no—
1238C2×C4—222no—
1239C2×C4—222no—
1240C2×C4—222no—
1241C2×C4—222no—
1242C2×C4—222no—
1243C2×C4—222no—
1244C2×C4—222no—
1245C2×C4—222no—
1246C2×C4—222no—
1247C2×C4—4416no—
1248C2×C4—4416no—
1249C2×C4—441no—
1250C2×C4—441no—
1251C2×C4—441no—
1252C2×C4—441no—
1253C2×C4—441no—
1254C2×C4—441no—
1255C2×C4—441no—
1256C2×C4—441no—
1257C2×C4—441no—
1258C2×C4—441no—
1259C2×C4—441no—
1260C2×C4—441no—
1261C2×C4—441no—
1262C2×C4—441no—
1263C2×C4—441no—
1264C2×C4—441no—
1265C2×C4—441no—
1266C2×C4—441no—
1267C2×C4—441no—
1268C2×C4—441no—
1269C2×C4—441no—
1270C2×C4—441no—
1271C2×C4—441no—
1272C2×C4—441no—
1273C2×C4—441no—
1274C2×C4—441no—
1275C2×C4—441no—
1276C2×C4#6699214yescomplemented
1277C22—24no—
1278C22—24no—
1279C22—24no—
1280C22—24no—
1281C22—24no—
1282C22—24no—
1283C22—42no—
1284C22—42no—
1285C22—42no—
1286C22—42no—
1287C22—42no—
1288C22—42no—
1289C22—42no—
1290C22—42no—
1291C22—42no—
1292C22—42no—
1293C22—42no—
1294C22—42no—
1295C22—42no—
1296C22—42no—
1297C22—42no—
1298C22—42no—
1299C22—42no—
1300C22—42no—
1301C22—42no—
1302C22—42no—
1303C22—42no—
1304C22—42no—
1305C22—42no—
1306C22—42no—
1307C22—224no—
1308C22—224no—
1309C22—224no—
1310C22—442no—
1311C22—442no—
1312C22—442no—
1313C22—442no—
1314C22—442no—
1315C22—442no—
1316C22—442no—
1317C22—442no—
1318C22—442no—
1319C22—442no—
1320C22—442no—
1321C22—442no—
1322C22C2×C22⋊C4×D1111yescharacteristic
1323C22#1062301711yescharacteristic
1324C22#1062302111yescharacteristic
1325C22#1062302111yescharacteristic
1326C22C4×#434111yescharacteristic
1327C22#1062306911yescharacteristic
1328C22#1062307111yescharacteristic
1329C22C4×D4×D1111yescharacteristic
1330C22C4×D4×D1111yescharacteristic
1331C22#1062307711yescharacteristic
1332C22#1062307811yescharacteristic
1333C22#1062308311yescharacteristic
1334C22D11×#12011yescharacteristic
1335C22#1062312211yescharacteristic
1336C22#1062312211yescharacteristic
1337C22#1062312311yescharacteristic
1338C22#1062313011yescharacteristic
1339C22D11×#12111yescharacteristic
1340C22D11×#12111yescharacteristic
1341C22#1062313911yescharacteristic
1342C22#1062314111yescharacteristic
1343C22#1062314211yescharacteristic
1344C22#1062314611yescharacteristic
1345C22#1062314711yescharacteristic
1346C22D11×#12311yescharacteristic
1347C22#1062318611yescharacteristic
1348C22#1062319211yescharacteristic
1349C22#1062319311yescharacteristic
1350C22C2×C4×C22⋊D1111yescharacteristic
1351C22D4×C22⋊D1111yescharacteristic
1352C22D4×C22⋊D1111yescharacteristic
1353C22D4×C22⋊D1111yescharacteristic
1354C22C2×#6699211yescharacteristic
1355C22#1062335511yescharacteristic
1356C22#1062336311yescharacteristic
1357C4—24no—
1358C4—42no—
1359C4—42no—
1360C4—42no—
1361C4—81no—
1362C4—118no—
1363C4—442no—
1364C4—442no—
1365C4—442no—
1366C4—442no—
1367C4—442no—
1368C4—881no—
1369C2—44no—
1370C2—44no—
1371C2—444no—
1372C2D11×#38611yescharacteristic
1373C2C4×#6699211yescharacteristic
1374C2#1307130611yescharacteristic
1375C2C22⋊C4×C22⋊D1111yescharacteristic
1376C2#1307144211yescharacteristic
1377C2#1307163311yescharacteristic
1378C2#1307165711yescharacteristic
1379C2#1307195811yescharacteristic
1380C2#1307196911yescharacteristic
1381C2#1307210511yescharacteristic
1382C2#1307212711yescharacteristic
1383C2#1307219011yescharacteristic
1384C2#1307220111yescharacteristic
1385C2#1307351611yescharacteristic
1386C2#1307353011yescharacteristic
subgroupG/H
center, FrattiniC24C23×D11
commutatorC23×C11C23×C4
FittingC2×C11×#386C2
socle, cosocleC24×C11C24
prime radicalC22×#66992C2
hypercenterC2×#386D11
hypocenterC11#13970
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ C2×#386

Complements

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

NH ≅ G/Ntype
2. C22×C4×C22⋊D11C2semidirect
3. C2×#10622570C2semidirect
4. C2×#10622569C2semidirect
5. C2×#10622555C2semidirect
6. C2×C22⋊C4×Dic11C2semidirect
7. #13066864C2semidirect
8. #13066863C2semidirect
9. #13066857C2semidirect
10. #13066855C2semidirect
11. Dic11⋊#95C2semidirect
12. Dic11⋊#95C2semidirect
13. #13066839C2semidirect
14. (C2×D11)⋊#95C2semidirect
15. C2×C11×#386C2semidirect
32. C2×#66992C4semidirect
71. C22×D4×C11C2×C4semidirect
95. C22×C22⋊D11C2×C4semidirect
104. C23×Dic11C2×C4semidirect
127. C2×C11×C22⋊C4D4semidirect
142. C2×C22⋊Dic11C2×C4semidirect
156. C2×(C2×D11)⋊C4C2×C4semidirect
164. C2×Dic11⋊C4C2×C4semidirect
165. C2×Dic11⋊C4D4semidirect
171. C2×C4×Dic11D4semidirect
293. C2×C22⋊D11C22⋊C4semidirect
378. C2×#386D11semidirect
458. C23×C11C4×D4semidirect
545. C2×C4×C11#121semidirect
736. Dic11#386semidirect
760. C22×D4C4×D11semidirect
840. C2×C22⋊C4C22⋊D11semidirect
1066. C11#13970semidirect
1171. C23C4×C22⋊D11semidirect
1276. C2×C4#66992semidirect

Maximal subgroups

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

subgroupindex
C22×#669922
C22×C4×C22⋊D112
C2×#106225702
C2×#106225692
C2×#106225552
C2×C22⋊C4×Dic112
#130668642
#130668632
#130668572
#130668552
Dic11⋊#952
#130668392
(C2×D11)⋊#952
C2×C11×#3862
#1397011