Finite Group Databasebeta

← #14677178

Subgroups — #14677178

Order 2816.

2538 conjugacy classes of subgroups.

The subgroup lattice has 1212 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C4⋊C4×D11C211yesmaximal, characteristic, complemented
2C2×#10622558C211yesmaximal, characteristic, complemented
3C2×#10622569C211yesmaximal, characteristic
4C2×#10622569C211yesmaximal, characteristic
5C2×#10622569C211yesmaximal, characteristic
6C2×C4×(C2×D11)⋊C4C211yesmaximal, characteristic, complemented
7#13066874C211yesmaximal, characteristic, complemented
8#13066872C211yesmaximal, characteristic, complemented
9#13066861C211yesmaximal, characteristic, complemented
10#13066859C211yesmaximal, characteristic, complemented
11#13066849C211yesmaximal, characteristic, complemented
12#13066848C211yesmaximal, characteristic, complemented
13(C2×D11)⋊#95C211yesmaximal, characteristic, complemented
14(C2×D11)⋊#95C211yesmaximal, characteristic, complemented
15C2×C11×#388C211yesmaximal, characteristic, complemented
16C23×C22⋊D11C2211yescharacteristic
17C23×C4×D11C2211yescharacteristic
18C23×C4×D11C2211yescharacteristic
19C23×C4×D11C2211yescharacteristic
20C22×C11×C4⋊C4C2211yescharacteristic
21C22×C11×C22⋊C4C2211yescharacteristic
22C22×C11×C22⋊C4C2211yescharacteristic
23C22×C11×C22⋊C4C2211yescharacteristic
24C22×C42×C11C2211yescharacteristic
25C22×C22⋊Dic11C2211yescharacteristic
26C22×C22⋊Dic11C2211yescharacteristic
27C22×C22⋊Dic11C2211yescharacteristic
28C22×(C2×D11)⋊C4C2211yescharacteristic
29C22×(C2×D11)⋊C4C2211yescharacteristic
30C22×(C2×D11)⋊C4C2211yescharacteristic
31C22×C4⋊Dic11C2211yescharacteristic
32C22×Dic11⋊C4C2211yescharacteristic
33C22×Dic11⋊C4C2211yescharacteristic
34C22×C4×Dic11C2211yescharacteristic
35C2×C4⋊C4×D11—24no—
36C2×C4⋊C4×D11—24no—
37C2×C4⋊C4×D11—24no—
38C11×#388—24no—
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
51C2×C11⋊#95C2211yescharacteristic
52C2×C11⋊#95C2211yescharacteristic
53C2×C11⋊#95C2211yescharacteristic
54C2×C11⋊#95C2211yescharacteristic
55#10622569—24no—
56#10622569—24no—
57#10622569C418yescomplemented
58#10622558—24no—
59C4×(C2×D11)⋊C4—24no—
60C25×C11C2311yescharacteristic
61C24×D11C2311yescharacteristic
62C23×C4×C11C2311yescharacteristic
63C23×C4×C11C2311yescharacteristic
64C23×C4×C11C2311yescharacteristic
65C23×C4×C11C2311yescharacteristic
66C23×C4×C11C2311yescharacteristic
67C23×C4×C11C2311yescharacteristic
68C22×C22⋊D11—22no—
69C22×C22⋊D11—22no—
70C22×C22⋊D11—22no—
71C22×C22⋊D11—22no—
72C22×C22⋊D11—22no—
73C22×C22⋊D11—22no—
74C22×C22⋊D11C2×C414yes—
75C23×Dic11C2311yescharacteristic
76C23×Dic11C2311yescharacteristic
77C23×Dic11C2311yescharacteristic
78C23×Dic11C2311yescharacteristic
79C23×Dic11C2311yescharacteristic
80C23×Dic11C2311yescharacteristic
81C23×Dic11C2311yescharacteristic
82C22×C4×D11—22no—
83C22×C4×D11—22no—
84C22×C4×D11—22no—
85C22×C4×D11—22no—
86C22×C4×D11—22no—
87C22×C4×D11—22no—
88C22×C4×D11—22no—
89C22×C4×D11—22no—
90C22×C4×D11—22no—
91C22×C4×D11—22no—
92C22×C4×D11—22no—
93C22×C4×D11—22no—
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—
101C22×C4×D11C2×C414yes—
102C22×C4×D11D414yes—
103C2×C11×C4⋊C4—22no—
104C2×C11×C4⋊C4—22no—
105C2×C11×C4⋊C4D414yescomplemented
106C2×C11×C22⋊C4—22no—
107C2×C11×C22⋊C4—22no—
108C2×C11×C22⋊C4—22no—
109C2×C11×C22⋊C4—22no—
110C2×C11×C22⋊C4—22no—
111C2×C11×C22⋊C4—22no—
112C2×C11×C22⋊C4—22no—
113C2×C11×C22⋊C4—41no—
114C2×C11×C22⋊C4C2×C414yescomplemented
115C2×C42×C11—22no—
116C2×C42×C11—22no—
117C2×C42×C11—41no—
118C2×C22⋊Dic11—22no—
119C2×C22⋊Dic11—22no—
120C2×C22⋊Dic11—22no—
121C2×C22⋊Dic11—22no—
122C2×C22⋊Dic11—22no—
123C2×C22⋊Dic11—41no—
124C2×C22⋊Dic11—41no—
125C2×C22⋊Dic11—41no—
126C2×C22⋊Dic11C2×C414yescomplemented
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)⋊C4C2×C414yes—
135C2×(C2×D11)⋊C4D414yes—
136C2×C4⋊Dic11—22no—
137C2×C4⋊Dic11—22no—
138C2×C4⋊Dic11—22no—
139C2×Dic11⋊C4—22no—
140C2×Dic11⋊C4—22no—
141C2×Dic11⋊C4—22no—
142C2×Dic11⋊C4—22no—
143C2×Dic11⋊C4—22no—
144C2×Dic11⋊C4D414yescomplemented
145C2×C4×Dic11—22no—
146C2×C4×Dic11—22no—
147C2×C4×Dic11—41no—
148C4⋊C4×D11—232no—
149C11×#95—22no—
150C11×#95—22no—
151C11⋊#95—22no—
152C11⋊#95—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—41no—
162C11⋊#95—41no—
163C11⋊#95C2×C414yescomplemented
164C11⋊#95C2×C414yescomplemented
165#14019—111nomaximal, Sylow
166C24×C11—21no—
167C24×C11—21no—
168C24×C11—21no—
169C24×C11—21no—
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×C11—21no—
179C24×C11—21no—
180C24×C11C22×C412yes—
181C24×C11C2411yescharacteristic
182C23×D11—21no—
183C23×D11—21no—
184C23×D11—21no—
185C23×D11—21no—
186C23×D11—21no—
187C23×D11—21no—
188C23×D11—21no—
189C23×D11—21no—
190C23×D11C22×C412yes—
191C23×D11C2×D412yes—
192C23×D11C2×D412yes—
193C23×D11#4112yes—
194C23×D11#4112yes—
195C23×D11#4112yes—
196C23×D11#4112yes—
197C22×C4×C11—21no—
198C22×C4×C11—21no—
199C22×C4×C11—21no—
200C22×C4×C11—21no—
201C22×C4×C11—21no—
202C22×C4×C11—21no—
203C22×C4×C11—21no—
204C22×C4×C11—21no—
205C22×C4×C11—21no—
206C22×C4×C11—21no—
207C22×C4×C11—21no—
208C22×C4×C11—21no—
209C22×C4×C11—21no—
210C22×C4×C11—21no—
211C22×C4×C11—21no—
212C22×C4×C11—21no—
213C22×C4×C11—21no—
214C22×C4×C11—21no—
215C22×C4×C11—21no—
216C22×C4×C11—21no—
217C22×C4×C11—21no—
218C22×C4×C11—21no—
219C22×C4×C11—21no—
220C22×C4×C11—21no—
221C22×C4×C11—21no—
222C22×C4×C11—21no—
223C22×C4×C11—21no—
224C22×C4×C11—21no—
225C22×C4×C11—21no—
226C22×C4×C11—21no—
227C22×C4×C11—21no—
228C22×C4×C11—21no—
229C22×C4×C11—21no—
230C22×C4×C11C22×C412yes—
231C22×C4×C11C22×C412yes—
232C22×C4×C11C2×D412yes—
233C22×C4×C11C2×D412yes—
234C22×C4×C11C2×D412yes—
235C22×C4×C11C2×D412yes—
236C22×C4×C11C2×D412yes—
237C22×C4×C11C2×D412yes—
238C22×C4×C11#4112yes—
239C2×C22⋊D11—28no—
240C2×C22⋊D11—28no—
241C2×C22⋊D11—28no—
242C2×C22⋊D11—44no—
243C2×C22⋊D11—44no—
244C2×C22⋊D11—44no—
245C2×C22⋊D11—44no—
246C22×Dic11—21no—
247C22×Dic11—21no—
248C22×Dic11—21no—
249C22×Dic11—21no—
250C22×Dic11—21no—
251C22×Dic11—21no—
252C22×Dic11—21no—
253C22×Dic11—21no—
254C22×Dic11—21no—
255C22×Dic11—21no—
256C22×Dic11—21no—
257C22×Dic11—21no—
258C22×Dic11—21no—
259C22×Dic11—21no—
260C22×Dic11—21no—
261C22×Dic11—21no—
262C22×Dic11—21no—
263C22×Dic11—21no—
264C22×Dic11—21no—
265C22×Dic11—21no—
266C22×Dic11—21no—
267C22×Dic11—21no—
268C22×Dic11—21no—
269C22×Dic11—21no—
270C22×Dic11—21no—
271C22×Dic11—21no—
272C22×Dic11—21no—
273C22×Dic11—21no—
274C22×Dic11—21no—
275C22×Dic11—21no—
276C22×Dic11—21no—
277C22×Dic11—21no—
278C22×Dic11—21no—
279C22×Dic11—21no—
280C22×Dic11—21no—
281C22×Dic11—21no—
282C22×Dic11—21no—
283C22×Dic11—21no—
284C22×Dic11—21no—
285C22×Dic11—21no—
286C22×Dic11—21no—
287C22×Dic11C22×C412yes—
288C22×Dic11C22×C412yes—
289C22×Dic11C22×C412yes—
290C22×Dic11C2×D412yes—
291C22×Dic11C2×D412yes—
292C22×Dic11C2×D412yes—
293C22×Dic11C2×D412yes—
294C22×Dic11#4112yes—
295C2×C4×D11—28no—
296C2×C4×D11—28no—
297C2×C4×D11—28no—
298C2×C4×D11—28no—
299C2×C4×D11—28no—
300C2×C4×D11—28no—
301C2×C4×D11—28no—
302C2×C4×D11—28no—
303C2×C4×D11—28no—
304C2×C4×D11—28no—
305C2×C4×D11—44no—
306C2×C4×D11—44no—
307C2×C4×D11—44no—
308C2×C4×D11—44no—
309C2×C4×D11—44no—
310C2×C4×D11—44no—
311C2×C4×D11—44no—
312C2×C4×D11—44no—
313C2×C4×D11—44no—
314C2×C4×D11—44no—
315C2×C4×D11—44no—
316C11×C4⋊C4—28no—
317C11×C22⋊C4—28no—
318C11×C22⋊C4—44no—
319C11×C22⋊C4—44no—
320C42×C11—44no—
321C22⋊Dic11—28no—
322C22⋊Dic11—44no—
323C22⋊Dic11—44no—
324(C2×D11)⋊C4—28no—
325(C2×D11)⋊C4—28no—
326(C2×D11)⋊C4—44no—
327C4⋊Dic11—28no—
328Dic11⋊C4—28no—
329Dic11⋊C4—28no—
330C4×Dic11—44no—
331C23×C4⋊C4—111no—
332C2×#388—111no—
333C2×#388D1111yescharacteristic, complemented
334C2×#386—111no—
335C2×#386—111no—
336C2×#386—111no—
337C2×C4×C22⋊C4—111no—
338#1442—111no—
339#1442—111no—
340#1439—111no—
341#1439—111no—
342#1436—111no—
343#1436—111no—
344C22⋊#95—111no—
345C22⋊#95—111no—
346C23×C11—22no—
347C23×C11—22no—
348C23×C11—22no—
349C23×C11—22no—
350C23×C11—22no—
351C23×C11—22no—
352C23×C11—22no—
353C23×C11—41no—
354C23×C11—41no—
355C23×C11—41no—
356C23×C11—41no—
357C23×C11—41no—
358C23×C11—41no—
359C23×C11—41no—
360C23×C11—41no—
361C23×C11—41no—
362C23×C11—41no—
363C23×C11—41no—
364C23×C11—41no—
365C23×C11—41no—
366C23×C11—41no—
367C23×C11—41no—
368C23×C11—41no—
369C23×C11—41no—
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×C11C23×C411yescharacteristic
382C23×C11C22×D411yescharacteristic
383C23×C11C22×D411yescharacteristic
384C23×C11C22×D411yescharacteristic
385C23×C11C22×D411yescharacteristic
386C23×C11C2×#4111yescharacteristic
387C23×C11C2×#4111yescharacteristic
388C23×C11C2×#4111yescharacteristic
389C23×C11C2×#4111yescharacteristic
390C23×C11C2×#4111yescharacteristic
391C23×C11C2×#4111yescharacteristic
392C23×C11H(5,𝔽2)11yescharacteristic
393C23×C11H(5,𝔽2)11yescharacteristic
394C23×C112−1+411yescharacteristic
395C23×C112−1+411yescharacteristic
396C22×D11—22no—
397C22×D11—22no—
398C22×D11—22no—
399C22×D11—22no—
400C22×D11—22no—
401C22×D11—22no—
402C22×D11—22no—
403C22×D11—22no—
404C22×D11—22no—
405C22×D11—22no—
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#11714yes—
425C22×D11C4×D414yes—
426C22×D11C4×D414yes—
427C22×D11#12114yes—
428C22×D11#12314yes—
429C22×D11#12414yes—
430C22×D11#12614yes—
431C2×C4×C11—22no—
432C2×C4×C11—22no—
433C2×C4×C11—22no—
434C2×C4×C11—22no—
435C2×C4×C11—22no—
436C2×C4×C11—22no—
437C2×C4×C11—22no—
438C2×C4×C11—22no—
439C2×C4×C11—22no—
440C2×C4×C11—22no—
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—41no—
453C2×C4×C11—41no—
454C2×C4×C11—41no—
455C2×C4×C11—41no—
456C2×C4×C11—41no—
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×C11C4×D414yes—
472C2×C4×C11#12014yes—
473C22⋊D11—416no—
474C2×Dic11—22no—
475C2×Dic11—22no—
476C2×Dic11—22no—
477C2×Dic11—22no—
478C2×Dic11—22no—
479C2×Dic11—22no—
480C2×Dic11—22no—
481C2×Dic11—22no—
482C2×Dic11—22no—
483C2×Dic11—22no—
484C2×Dic11—22no—
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—41no—
496C2×Dic11—41no—
497C2×Dic11—41no—
498C2×Dic11—41no—
499C2×Dic11—41no—
500C2×Dic11—41no—
501C2×Dic11—41no—
502C2×Dic11—41no—
503C2×Dic11—41no—
504C2×Dic11—41no—
505C2×Dic11—41no—
506C2×Dic11—41no—
507C2×Dic11—41no—
508C2×Dic11—41no—
509C2×Dic11—41no—
510C2×Dic11—41no—
511C2×Dic11—41no—
512C2×Dic11—41no—
513C2×Dic11—41no—
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×Dic11C4×D414yes—
523C4×D11—232no—
524C4×D11—416no—
525C4×D11—416no—
526C23×D4—111no—
527C24×C4—111no—
528C24×C4—111no—
529C24×C4—111no—
530C22×C4⋊C4—111no—
531C22×C4⋊C4—111no—
532C22×C4⋊C4—111no—
533C22×C4⋊C4—224no—
534C22×C4⋊C4—224no—
535C22×C4⋊C4—224no—
536C22×C4⋊C4C2×D1111yescharacteristic
537C22×C22⋊C4—111no—
538C22×C22⋊C4—111no—
539C22×C22⋊C4—111no—
540C22×C22⋊C4—111no—
541C22×C22⋊C4—111no—
542C22×C22⋊C4—111no—
543C22×C22⋊C4C2×D1111yescharacteristic
544C22×C22⋊C4C2×D1111yescharacteristic
545C22×C22⋊C4C2×D1111yescharacteristic
546C22×C42—111no—
547C22×C42C2×D1111yescharacteristic
548#388—24no—
549#388—224no—
550#386—118no—
551#386—224no—
552#386—224no—
553C4×C22⋊C4—224no—
554C2×#95—111no—
555C2×#95—111no—
556C2×#95—111no—
557C2×#95—111no—
558C2×#95—111no—
559C2×#95—111no—
560C2×#95—111no—
561C2×#95—111no—
562C2×#95—111no—
563C2×#95—111no—
564C2×#95—111no—
565C2×#95—111no—
566C2×#95—111no—
567C2×#95—111no—
568C2×#95C2×D1111yescharacteristic
569C2×#95C2×D1111yescharacteristic
570C22×C11—42no—
571C22×C11—42no—
572C22×C11—42no—
573C22×C11—42no—
574C22×C11—42no—
575C22×C11—42no—
576C22×C11—42no—
577C22×C11—81no—
578C22×C11—81no—
579C22×C11—81no—
580C22×C11—81no—
581C22×C11—81no—
582C22×C11—81no—
583C22×C11—81no—
584C22×C11—81no—
585C22×C11C2×#11711yescharacteristic
586C22×C11C2×C4×D411yescharacteristic
587C22×C11C2×C4×D411yescharacteristic
588C22×C11C2×C4×D411yescharacteristic
589C22×C11C2×C4×D411yescharacteristic
590C22×C11#52011yescharacteristic
591C22×C11#52011yescharacteristic
592C22×C11C2×#12011yescharacteristic
593C22×C11C2×#12111yescharacteristic
594C22×C11C2×#12311yescharacteristic
595C22×C11#52511yescharacteristic
596C22×C11#52511yescharacteristic
597C22×C11#52511yescharacteristic
598C22×C11C2×#12411yescharacteristic
599C22×C11C2×#12611yescharacteristic
600C22×C11#53411yescharacteristic
601C22×C11#53611yescharacteristic
602C22×C11#53911yescharacteristic
603C22×C11#53911yescharacteristic
604C22×C11D4211yescharacteristic
605C22×C11D4211yescharacteristic
606C22×C11#54611yescharacteristic
607C22×C11#54611yescharacteristic
608C22×C11#54711yescharacteristic
609C22×C11#54711yescharacteristic
610C22×C11#54811yescharacteristic
611C22×C11#54811yescharacteristic
612C22×C11#54811yescharacteristic
613C22×C11#54811yescharacteristic
614C22×C11#55211yescharacteristic
615C22×C11#55211yescharacteristic
616C22×C11#55311yescharacteristic
617C22×C11#55311yescharacteristic
618C22×C11#55311yescharacteristic
619C22×C11#55311yescharacteristic
620C2×D11—24no—
621C2×D11—24no—
622C2×D11—24no—
623C2×D11—24no—
624C2×D11—24no—
625C2×D11—24no—
626C2×D11—24no—
627C2×D11—24no—
628C2×D11—24no—
629C2×D11—24no—
630C2×D11—24no—
631C2×D11—24no—
632C2×D11—24no—
633C2×D11—24no—
634C2×D11#38818yescomplemented
635C4×C11—24no—
636C4×C11—24no—
637C4×C11—42no—
638C4×C11—42no—
639C4×C11—42no—
640C4×C11—81no—
641Dic11—24no—
642Dic11—42no—
643Dic11—42no—
644Dic11—42no—
645Dic11—42no—
646Dic11—42no—
647Dic11—81no—
648C25—111no—
649C25C22×D1111yescharacteristic
650C22×D4—114no—
651C22×D4—222no—
652C22×D4—222no—
653C22×D4—222no—
654C22×D4—222no—
655C22×D4—222no—
656C22×D4—222no—
657C23×C4—111no—
658C23×C4—111no—
659C23×C4—111no—
660C23×C4—111no—
661C23×C4—111no—
662C23×C4—111no—
663C23×C4—114no—
664C23×C4—114no—
665C23×C4—111no—
666C23×C4—222no—
667C23×C4—222no—
668C23×C4—222no—
669C23×C4—222no—
670C23×C4—222no—
671C23×C4—222no—
672C23×C4—222no—
673C23×C4—222no—
674C23×C4—222no—
675C23×C4—222no—
676C23×C4—222no—
677C23×C4—222no—
678C23×C4—222no—
679C23×C4—222no—
680C23×C4—222no—
681C23×C4—441no—
682C23×C4—441no—
683C23×C4—441no—
684C23×C4—441no—
685C23×C4C22×D1111yescharacteristic
686C23×C4C22×D1111yescharacteristic
687C23×C4C22×D1111yescharacteristic
688C23×C4C22×D1111yescharacteristic
689C23×C4C22×D1111yescharacteristic
690C23×C4C22×D1111yescharacteristic
691C2×C4⋊C4—22no—
692C2×C4⋊C4—22no—
693C2×C4⋊C4—114no—
694C2×C4⋊C4—2232no—
695C2×C4⋊C4—222no—
696C2×C4⋊C4—222no—
697C2×C4⋊C4—222no—
698C2×C4⋊C4—222no—
699C2×C4⋊C4—222no—
700C2×C4⋊C4—222no—
701C2×C4⋊C4—222no—
702C2×C4⋊C4—222no—
703C2×C4⋊C4C22⋊D1114yescomplemented
704C2×C22⋊C4—22no—
705C2×C22⋊C4—22no—
706C2×C22⋊C4—22no—
707C2×C22⋊C4—22no—
708C2×C22⋊C4—22no—
709C2×C22⋊C4—22no—
710C2×C22⋊C4—22no—
711C2×C22⋊C4—41no—
712C2×C22⋊C4—114no—
713C2×C22⋊C4—114no—
714C2×C22⋊C4—114no—
715C2×C22⋊C4—222no—
716C2×C22⋊C4—222no—
717C2×C22⋊C4—222no—
718C2×C22⋊C4—222no—
719C2×C22⋊C4—222no—
720C2×C22⋊C4—222no—
721C2×C22⋊C4—222no—
722C2×C22⋊C4—222no—
723C2×C22⋊C4—222no—
724C2×C22⋊C4—222no—
725C2×C22⋊C4—222no—
726C2×C22⋊C4—222no—
727C2×C22⋊C4—441no—
728C2×C22⋊C4—441no—
729C2×C22⋊C4—441no—
730C2×C22⋊C4C4×D1114yescomplemented
731C2×C42—22no—
732C2×C42—22no—
733C2×C42—41no—
734C2×C42—222no—
735C2×C42—222no—
736C2×C42—441no—
737#95—22no—
738#95—22no—
739#95—114no—
740#95—114no—
741#95—222no—
742#95—222no—
743#95—222no—
744#95—222no—
745#95—222no—
746#95—222no—
747#95—222no—
748#95—222no—
749#95—222no—
750#95—222no—
751#95—441no—
752#95—441no—
753C2×C11—82no—
754C2×C11C2×#38811yescharacteristic
755C2×C11C4×#12011yescharacteristic
756C2×C11#232211yescharacteristic
757C2×C11#235211yescharacteristic
758C2×C11#235211yescharacteristic
759C2×C11#236111yescharacteristic
760C2×C11#236111yescharacteristic
761C2×C11#241011yescharacteristic
762C2×C11#241311yescharacteristic
763C2×C11#243611yescharacteristic
764C2×C11#244311yescharacteristic
765C2×C11#244311yescharacteristic
766C2×C11#248111yescharacteristic
767C2×C11#248111yescharacteristic
768C2×C11#259111yescharacteristic
769D11—28no—
770C24—21no—
771C24—21no—
772C24—21no—
773C24—21no—
774C24—21no—
775C24—21no—
776C24—21no—
777C24—21no—
778C24—21no—
779C24—21no—
780C24—21no—
781C24—21no—
782C24—21no—
783C24—21no—
784C24—112no—
785C24—112no—
786C24—112no—
787C24—112no—
788C24—112no—
789C24—112no—
790C24—112no—
791C24—221no—
792C24—221no—
793C24—221no—
794C24—221no—
795C24—221no—
796C24—221no—
797C24—221no—
798C24—221no—
799C24C2×C4×D1112yes—
800C24C23×D1111yescharacteristic
801C2×D4—228no—
802C2×D4—228no—
803C2×D4—228no—
804C2×D4—444no—
805C2×D4—444no—
806C2×D4—444no—
807C2×D4—444no—
808C22×C4—21no—
809C22×C4—21no—
810C22×C4—21no—
811C22×C4—21no—
812C22×C4—21no—
813C22×C4—21no—
814C22×C4—21no—
815C22×C4—21no—
816C22×C4—21no—
817C22×C4—21no—
818C22×C4—21no—
819C22×C4—21no—
820C22×C4—21no—
821C22×C4—21no—
822C22×C4—21no—
823C22×C4—21no—
824C22×C4—21no—
825C22×C4—21no—
826C22×C4—21no—
827C22×C4—21no—
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—112no—
842C22×C4—112no—
843C22×C4—112no—
844C22×C4—112no—
845C22×C4—112no—
846C22×C4—112no—
847C22×C4—112no—
848C22×C4—112no—
849C22×C4—228no—
850C22×C4—228no—
851C22×C4—228no—
852C22×C4—228no—
853C22×C4—228no—
854C22×C4—228no—
855C22×C4—228no—
856C22×C4—228no—
857C22×C4—221no—
858C22×C4—221no—
859C22×C4—221no—
860C22×C4—221no—
861C22×C4—228no—
862C22×C4—221no—
863C22×C4—221no—
864C22×C4—221no—
865C22×C4—221no—
866C22×C4—221no—
867C22×C4—221no—
868C22×C4—221no—
869C22×C4—221no—
870C22×C4—221no—
871C22×C4—221no—
872C22×C4—221no—
873C22×C4—221no—
874C22×C4—221no—
875C22×C4—221no—
876C22×C4—221no—
877C22×C4—221no—
878C22×C4—221no—
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—221no—
888C22×C4—221no—
889C22×C4—221no—
890C22×C4—221no—
891C22×C4—221no—
892C22×C4—228no—
893C22×C4—221no—
894C22×C4—221no—
895C22×C4—221no—
896C22×C4—221no—
897C22×C4—221no—
898C22×C4—221no—
899C22×C4—221no—
900C22×C4—444no—
901C22×C4—444no—
902C22×C4—444no—
903C22×C4—444no—
904C22×C4—444no—
905C22×C4—444no—
906C22×C4—444no—
907C22×C4—444no—
908C22×C4—444no—
909C22×C4—444no—
910C22×C4—444no—
911C22×C4C2×C4×D1112yes—
912C22×C4C2×C4×D1112yes—
913C22×C4#433912yes—
914C22×C4D4×D1112yes—
915C22×C4D4×D1112yes—
916C22×C4D4×D1112yes—
917C22×C4C2×C22⋊D1112yes—
918C22×C4C2×C22⋊D1112yes—
919C22×C4C2×C22⋊D1112yes—
920C4⋊C4—28no—
921C4⋊C4—228no—
922C4⋊C4—228no—
923C4⋊C4—228no—
924C22⋊C4—28no—
925C22⋊C4—44no—
926C22⋊C4—44no—
927C22⋊C4—228no—
928C22⋊C4—228no—
929C22⋊C4—228no—
930C22⋊C4—444no—
931C22⋊C4—444no—
932C22⋊C4—444no—
933C42—44no—
934C42—444no—
935C11#1401911yescharacteristic, complemented, Sylow
936C23—22no—
937C23—22no—
938C23—22no—
939C23—22no—
940C23—22no—
941C23—22no—
942C23—22no—
943C23—41no—
944C23—41no—
945C23—41no—
946C23—41no—
947C23—41no—
948C23—41no—
949C23—41no—
950C23—41no—
951C23—41no—
952C23—41no—
953C23—41no—
954C23—41no—
955C23—41no—
956C23—41no—
957C23—41no—
958C23—41no—
959C23—41no—
960C23—41no—
961C23—41no—
962C23—41no—
963C23—41no—
964C23—41no—
965C23—41no—
966C23—41no—
967C23—41no—
968C23—41no—
969C23—41no—
970C23—41no—
971C23—114no—
972C23—114no—
973C23—114no—
974C23—114no—
975C23—114no—
976C23—114no—
977C23—114no—
978C23—222no—
979C23—222no—
980C23—222no—
981C23—222no—
982C23—222no—
983C23—222no—
984C23—222no—
985C23—222no—
986C23—222no—
987C23—222no—
988C23—222no—
989C23—222no—
990C23—222no—
991C23—222no—
992C23—222no—
993C23—222no—
994C23—222no—
995C23—222no—
996C23—222no—
997C23—222no—
998C23—222no—
999C23—222no—
1000C23—222no—
1001C23—222no—
1002C23—222no—
1003C23—222no—
1004C23—222no—
1005C23—222no—
1006C23C22×C4×D1111yescharacteristic
1007C23C2×#433911yescharacteristic
1008C23C2×D4×D1111yescharacteristic
1009C23C2×D4×D1111yescharacteristic
1010C23C2×D4×D1111yescharacteristic
1011C23#6703711yescharacteristic
1012C23#41×D1111yescharacteristic
1013C23#41×D1111yescharacteristic
1014C23#41×D1111yescharacteristic
1015C23#41×D1111yescharacteristic
1016C23#41×D1111yescharacteristic
1017C23#6704211yescharacteristic
1018C23#6704311yescharacteristic
1019C23#6704311yescharacteristic
1020C23C22×C22⋊D1111yescharacteristic
1021D4—4416no—
1022C2×C4—22no—
1023C2×C4—22no—
1024C2×C4—22no—
1025C2×C4—22no—
1026C2×C4—22no—
1027C2×C4—22no—
1028C2×C4—22no—
1029C2×C4—22no—
1030C2×C4—22no—
1031C2×C4—22no—
1032C2×C4—22no—
1033C2×C4—22no—
1034C2×C4—22no—
1035C2×C4—22no—
1036C2×C4—22no—
1037C2×C4—22no—
1038C2×C4—22no—
1039C2×C4—22no—
1040C2×C4—22no—
1041C2×C4—22no—
1042C2×C4—22no—
1043C2×C4—41no—
1044C2×C4—41no—
1045C2×C4—41no—
1046C2×C4—41no—
1047C2×C4—41no—
1048C2×C4—41no—
1049C2×C4—41no—
1050C2×C4—41no—
1051C2×C4—41no—
1052C2×C4—41no—
1053C2×C4—41no—
1054C2×C4—41no—
1055C2×C4—41no—
1056C2×C4—41no—
1057C2×C4—41no—
1058C2×C4—41no—
1059C2×C4—41no—
1060C2×C4—41no—
1061C2×C4—41no—
1062C2×C4—114no—
1063C2×C4—2232no—
1064C2×C4—222no—
1065C2×C4—222no—
1066C2×C4—222no—
1067C2×C4—222no—
1068C2×C4—222no—
1069C2×C4—222no—
1070C2×C4—222no—
1071C2×C4—222no—
1072C2×C4—222no—
1073C2×C4—222no—
1074C2×C4—222no—
1075C2×C4—222no—
1076C2×C4—222no—
1077C2×C4—222no—
1078C2×C4—222no—
1079C2×C4—222no—
1080C2×C4—222no—
1081C2×C4—222no—
1082C2×C4—222no—
1083C2×C4—222no—
1084C2×C4—222no—
1085C2×C4—4416no—
1086C2×C4—4416no—
1087C2×C4—441no—
1088C2×C4—441no—
1089C2×C4—441no—
1090C2×C4—441no—
1091C2×C4—441no—
1092C2×C4—441no—
1093C2×C4—441no—
1094C2×C4—441no—
1095C2×C4—441no—
1096C2×C4—441no—
1097C2×C4—441no—
1098C2×C4—441no—
1099C2×C4—441no—
1100C2×C4—441no—
1101C2×C4—441no—
1102C2×C4—441no—
1103C2×C4—441no—
1104C2×C4—441no—
1105C2×C4—441no—
1106C2×C4—441no—
1107C2×C4—441no—
1108C2×C4—441no—
1109C2×C4—441no—
1110C2×C4—441no—
1111C2×C4—441no—
1112C2×C4—441no—
1113C2×C4—441no—
1114C2×C4C4×C22⋊D1114yes—
1115C2×C4#6699014yes—
1116C22—42no—
1117C22—42no—
1118C22—42no—
1119C22—42no—
1120C22—42no—
1121C22—42no—
1122C22—42no—
1123C22—81no—
1124C22—81no—
1125C22—81no—
1126C22—81no—
1127C22—81no—
1128C22—81no—
1129C22—81no—
1130C22—81no—
1131C22—118no—
1132C22—224no—
1133C22—224no—
1134C22—224no—
1135C22—224no—
1136C22—224no—
1137C22—224no—
1138C22—224no—
1139C22—224no—
1140C22—224no—
1141C22—224no—
1142C22—224no—
1143C22—224no—
1144C22—224no—
1145C22—224no—
1146C22D11×#11711yescharacteristic
1147C22#1062305411yescharacteristic
1148C22#1062306011yescharacteristic
1149C22#1062306111yescharacteristic
1150C22C4×D4×D1111yescharacteristic
1151C22C4×D4×D1111yescharacteristic
1152C22C4×D4×D1111yescharacteristic
1153C22#1062307711yescharacteristic
1154C22#1062307811yescharacteristic
1155C22#1062307811yescharacteristic
1156C22#1062308211yescharacteristic
1157C22#1062308911yescharacteristic
1158C22D11×#12111yescharacteristic
1159C22#1062313611yescharacteristic
1160C22#1062314011yescharacteristic
1161C22#1062314111yescharacteristic
1162C22D11×#12311yescharacteristic
1163C22#1062318611yescharacteristic
1164C22#1062319111yescharacteristic
1165C22#1062319211yescharacteristic
1166C22D11×#12411yescharacteristic
1167C22#1062320611yescharacteristic
1168C22#1062320811yescharacteristic
1169C22#1062320811yescharacteristic
1170C22D11×#12611yescharacteristic
1171C22#1062323811yescharacteristic
1172C22#1062323911yescharacteristic
1173C22#1062324011yescharacteristic
1174C22C2×C4×C22⋊D1111yescharacteristic
1175C22C2×#6699011yescharacteristic
1176C22D4×C22⋊D1111yescharacteristic
1177C22#1062335911yescharacteristic
1178C22#1062336011yescharacteristic
1179C22#1062336211yescharacteristic
1180C22#1062336211yescharacteristic
1181C4—24no—
1182C4—24no—
1183C4—42no—
1184C4—42no—
1185C4—42no—
1186C4—81no—
1187C4—224no—
1188C4—442no—
1189C4—442no—
1190C4—442no—
1191C4—442no—
1192C4—442no—
1193C4—881no—
1194C2—82no—
1195C2—228no—
1196C2D11×#38811yescharacteristic
1197C2C4×#6699011yescharacteristic
1198C2#1307128611yescharacteristic
1199C2#1307154411yescharacteristic
1200C2#1307154611yescharacteristic
1201C2#1307162811yescharacteristic
1202C2#1307162911yescharacteristic
1203C2#1307198711yescharacteristic
1204C2#1307202211yescharacteristic
1205C2#1307227111yescharacteristic
1206C2#1307234811yescharacteristic
1207C2#1307235811yescharacteristic
1208C2#1307287311yescharacteristic
1209C2#1307288311yescharacteristic
1210C2#1307409411yescharacteristic
subgroupG/H
center, FrattiniC24C23×D11
commutatorC23×C11C23×C4
FittingC2×C11×#388C2
socle, cosocleC24×C11C24
prime radicalC23×C22⋊D11C22
hypercenterC2×#388D11
hypocenterC11#14019
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ C2×#388

Complements

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

NH ≅ G/Ntype
1. C22×C4⋊C4×D11C2semidirect
2. C2×#10622558C2semidirect
6. C2×C4×(C2×D11)⋊C4C2semidirect
7. #13066874C2semidirect
8. #13066872C2semidirect
9. #13066861C2semidirect
10. #13066859C2semidirect
11. #13066849C2semidirect
12. #13066848C2semidirect
13. (C2×D11)⋊#95C2semidirect
14. (C2×D11)⋊#95C2semidirect
15. C2×C11×#388C2semidirect
57. #10622569C4semidirect
105. C2×C11×C4⋊C4D4semidirect
114. C2×C11×C22⋊C4C2×C4semidirect
126. C2×C22⋊Dic11C2×C4semidirect
144. C2×Dic11⋊C4D4semidirect
163. C11⋊#95C2×C4semidirect
164. C11⋊#95C2×C4semidirect
333. C2×#388D11semidirect
634. C2×D11#388semidirect
703. C2×C4⋊C4C22⋊D11semidirect
730. C2×C22⋊C4C4×D11semidirect
935. C11#14019semidirect

Maximal subgroups

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

subgroupindex
C22×C4⋊C4×D112
C2×#106225582
C2×#106225692
C2×C4×(C2×D11)⋊C42
#130668742
#130668722
#130668612
#130668592
#130668492
#130668482
(C2×D11)⋊#952
C2×C11×#3882
#1401911