Finite Group Databasebeta

← #14676671

Subgroups — #14676671

Order 2816.

2358 conjugacy classes of subgroups.

The subgroup lattice has 1198 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C4×C22⋊D11C211yesmaximal, characteristic
2C2×#10622570C211yesmaximal, characteristic
3C2×#10622570C211yesmaximal, characteristic
4C2×#10622260C211yesmaximal, characteristic, complemented
5C2×#10622263C211yesmaximal, characteristic, complemented
6#13066862C211yesmaximal, characteristic, complemented
7#13066861C211yesmaximal, characteristic, complemented
8#13066860C211yesmaximal, characteristic, complemented
9#13066859C211yesmaximal, characteristic, complemented
10Dic11⋊#95C211yesmaximal, characteristic, complemented
11#13066839C211yesmaximal, characteristic, complemented
12(C2×D11)⋊#95C211yesmaximal, characteristic, complemented
13(C2×D11)⋊#95C211yesmaximal, characteristic, complemented
14#95×Dic11C211yesmaximal, characteristic, complemented
15C11×C22⋊#95C211yesmaximal, characteristic, complemented
16C24×C4×C11C2211yescharacteristic
17C23×C22⋊D11C2211yescharacteristic
18C23×C4×D11C2211yescharacteristic
19C22×C11×C22⋊C4C2211yescharacteristic
20C22×C11×C22⋊C4C2211yescharacteristic
21C22×C22⋊Dic11C2211yescharacteristic
22C22×C22⋊Dic11C2211yescharacteristic
23C22×C22⋊Dic11C2211yescharacteristic
24C2×C4×C22⋊D11—24no—
25C2×C4×C22⋊D11—24no—
26C2×C4×C22⋊D11—24no—
27C22×(C2×D11)⋊C4C2211yescharacteristic
28C22×(C2×D11)⋊C4C2211yescharacteristic
29C22×(C2×D11)⋊C4C2211yescharacteristic
30C22×(C2×D11)⋊C4C2211yescharacteristic
31C22×(C2×D11)⋊C4C2211yescharacteristic
32C22×C4⋊Dic11C2211yescharacteristic
33C22×Dic11⋊C4C2211yescharacteristic
34C22×Dic11⋊C4C2211yescharacteristic
35C22×Dic11⋊C4C2211yescharacteristic
36C22×Dic11⋊C4C2211yescharacteristic
37C22×C4×Dic11C2211yescharacteristic
38C22×C4×Dic11C2211yescharacteristic
39C22×C4×Dic11C2211yescharacteristic
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
54#10622570—24no—
55#10622570C418yescomplemented
56#10622263—24no—
57#10622260—24no—
58C25×C11C2311yescharacteristic
59C24×D11C2311yescharacteristic
60C23×C4×C11—22no—
61C23×C4×C11—22no—
62C23×C4×C11—22no—
63C23×C4×C11—22no—
64C23×C4×C11—22no—
65C23×C4×C11—41no—
66C23×C4×C11—41no—
67C23×C4×C11C2311yescharacteristic
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⋊D11C2×C414yes—
78C22×C22⋊D11D414yes—
79C22×C22⋊D11Q814yes—
80C23×Dic11C2311yescharacteristic
81C23×Dic11C2311yescharacteristic
82C23×Dic11C2311yescharacteristic
83C23×Dic11C2311yescharacteristic
84C23×Dic11C2311yescharacteristic
85C23×Dic11C2311yescharacteristic
86C23×Dic11C2311yescharacteristic
87C22×C4×D11—22no—
88C22×C4×D11—22no—
89C22×C4×D11—22no—
90C22×C4×D11—22no—
91C22×C4×D11—22no—
92C22×C4×D11—41no—
93C22×C4×D11—41no—
94C2×C11×C22⋊C4—22no—
95C2×C11×C22⋊C4—22no—
96C2×C11×C22⋊C4—41no—
97C2×C11×C22⋊C4—41no—
98C2×C11×C22⋊C4—41no—
99C2×C11×C22⋊C4C2×C414yescomplemented
100C2×C22⋊Dic11—22no—
101C2×C22⋊Dic11—22no—
102C2×C22⋊Dic11—22no—
103C2×C22⋊Dic11—22no—
104C2×C22⋊Dic11—22no—
105C2×C22⋊Dic11—41no—
106C2×C22⋊Dic11—41no—
107C2×C22⋊Dic11—41no—
108C2×C22⋊Dic11C2×C414yescomplemented
109C4×C22⋊D11—232no—
110C2×(C2×D11)⋊C4—22no—
111C2×(C2×D11)⋊C4—22no—
112C2×(C2×D11)⋊C4—22no—
113C2×(C2×D11)⋊C4—22no—
114C2×(C2×D11)⋊C4—22no—
115C2×(C2×D11)⋊C4—22no—
116C2×(C2×D11)⋊C4—22no—
117C2×(C2×D11)⋊C4—41no—
118C2×(C2×D11)⋊C4—41no—
119C2×(C2×D11)⋊C4—41no—
120C2×(C2×D11)⋊C4—41no—
121C2×(C2×D11)⋊C4—41no—
122C2×(C2×D11)⋊C4—41no—
123C2×(C2×D11)⋊C4C2×C414yescomplemented
124C2×(C2×D11)⋊C4C2×C414yescomplemented
125C2×C4⋊Dic11—22no—
126C2×C4⋊Dic11—41no—
127C2×C4⋊Dic11—41no—
128C2×Dic11⋊C4—22no—
129C2×Dic11⋊C4—22no—
130C2×Dic11⋊C4—22no—
131C2×Dic11⋊C4—22no—
132C2×Dic11⋊C4—22no—
133C2×Dic11⋊C4—22no—
134C2×Dic11⋊C4—22no—
135C2×Dic11⋊C4—22no—
136C2×Dic11⋊C4—41no—
137C2×Dic11⋊C4—41no—
138C2×Dic11⋊C4C2×C414yescomplemented
139C2×Dic11⋊C4D414yes—
140C2×C4×Dic11—22no—
141C2×C4×Dic11—22no—
142C2×C4×Dic11—22no—
143C2×C4×Dic11—22no—
144C2×C4×Dic11—22no—
145C2×C4×Dic11—22no—
146C2×C4×Dic11—22no—
147C2×C4×Dic11C2×C414yescomplemented
148C2×C4×Dic11D414yes—
149C11×#95—22no—
150C11×#95—22no—
151C11×#95—22no—
152C11×#95—41no—
153C11⋊#95—22no—
154C11⋊#95—22no—
155C11⋊#95—22no—
156C11⋊#95—22no—
157C11⋊#95—22no—
158C11⋊#95—22no—
159C11⋊#95—22no—
160C11⋊#95—41no—
161C11⋊#95—41no—
162C11⋊#95—41no—
163#13979—111nomaximal, Sylow
164C24×C11—21no—
165C24×C11—21no—
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×C11C22×C412yes—
177C24×C11C2×D412yes—
178C24×C11C2×Q812yes—
179C24×C11C2411yescharacteristic
180C23×D11—21no—
181C23×D11—21no—
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×D11—21no—
191C23×D11—21no—
192C23×D11C22×C412yes—
193C23×D11C2×D412yes—
194C23×D11C2×Q812yes—
195C22×C4×C11—21no—
196C22×C4×C11—21no—
197C22×C4×C11—21no—
198C22×C4×C11—21no—
199C22×C4×C11—28no—
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×C11—21no—
231C22×C4×C11—44no—
232C22×C4×C11—44no—
233C22×C4×C11—44no—
234C22×C4×C11—44no—
235C22×C4×C11—44no—
236C22×C4×C11—44no—
237C22×C4×C11C22×C412yes—
238C22×C4×C11C22×C412yes—
239C22×C4×C11C2×D412yes—
240C22×C4×C11C2×D412yes—
241C22×C4×C11#4112yes—
242C22×C4×C11#4112yes—
243C22×C4×C11#4112yes—
244C2×C22⋊D11—28no—
245C2×C22⋊D11—28no—
246C2×C22⋊D11—28no—
247C2×C22⋊D11—28no—
248C2×C22⋊D11—28no—
249C2×C22⋊D11—28no—
250C2×C22⋊D11C4⋊C4116yescomplemented
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×Dic11—21no—
288C22×Dic11C22×C412yes—
289C22×Dic11C22×C412yes—
290C22×Dic11C22×C412yes—
291C22×Dic11C2×D412yes—
292C22×Dic11C2×D412yes—
293C22×Dic11C2×D412yes—
294C22×Dic11C2×D412yes—
295C22×Dic11C2×D412yes—
296C22×Dic11C2×Q812yes—
297C22×Dic11#4112yes—
298C22×Dic11#4112yes—
299C22×Dic11#4112yes—
300C2×C4×D11—28no—
301C2×C4×D11—44no—
302C2×C4×D11—44no—
303C2×C4×D11—44no—
304C2×C4×D11—44no—
305C2×C4×D11—44no—
306C2×C4×D11—44no—
307C11×C22⋊C4—44no—
308C11×C22⋊C4—44no—
309C22⋊Dic11—28no—
310C22⋊Dic11—44no—
311C22⋊Dic11—44no—
312(C2×D11)⋊C4—28no—
313(C2×D11)⋊C4—44no—
314(C2×D11)⋊C4—44no—
315(C2×D11)⋊C4—44no—
316(C2×D11)⋊C4—44no—
317C4⋊Dic11—44no—
318Dic11⋊C4—28no—
319Dic11⋊C4—28no—
320Dic11⋊C4—44no—
321Dic11⋊C4—44no—
322C4×Dic11—28no—
323C4×Dic11—28no—
324C4×Dic11—44no—
325C22×C4×D4—111no—
326C2×#390—111no—
327C2×#390—111no—
328C2×#389—111no—
329C2×#382—111no—
330#1439—111no—
331#1439—111no—
332#1439—111no—
333#1439—111no—
334C4⋊#95—111no—
335C22⋊#95—111no—
336C22⋊#95—111no—
337C22⋊#95—111no—
338C22⋊#95D1111yescharacteristic, complemented
339C4×#95—111no—
340C23×C11—22no—
341C23×C11—22no—
342C23×C11—22no—
343C23×C11—22no—
344C23×C11—22no—
345C23×C11—22no—
346C23×C11—22no—
347C23×C11—22no—
348C23×C11—22no—
349C23×C11—22no—
350C23×C11—22no—
351C23×C11—22no—
352C23×C11—22no—
353C23×C11—22no—
354C23×C11—22no—
355C23×C11—22no—
356C23×C11—22no—
357C23×C11—22no—
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×C11C2×C4⋊C414yes—
375C23×C11C23×C411yescharacteristic
376C23×C11C22×D411yescharacteristic
377C23×C11C22×D411yescharacteristic
378C23×C11C22×D411yescharacteristic
379C23×C11C22×Q811yescharacteristic
380C23×C11C2×#4111yescharacteristic
381C23×C11C2×#4111yescharacteristic
382C23×C11C2×#4111yescharacteristic
383C23×C11C2×#4111yescharacteristic
384C23×C11C2×#4111yescharacteristic
385C23×C11C2×#4111yescharacteristic
386C23×C11H(5,𝔽2)11yescharacteristic
387C23×C11H(5,𝔽2)11yescharacteristic
388C23×C11H(5,𝔽2)11yescharacteristic
389C23×C11H(5,𝔽2)11yescharacteristic
390C22×D11—22no—
391C22×D11—22no—
392C22×D11—22no—
393C22×D11—22no—
394C22×D11—22no—
395C22×D11—22no—
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—41no—
409C22×D11—41no—
410C22×D11—41no—
411C22×D11—41no—
412C22×D11—41no—
413C22×D11—41no—
414C22×D11—41no—
415C22×D11—41no—
416C22×D11—41no—
417C22×D11—41no—
418C22×D11—41no—
419C22×D11—41no—
420C22×D11—41no—
421C22×D11—41no—
422C22×D11—41no—
423C22×D11—41no—
424C22×D11C2×C4⋊C414yes—
425C2×C4×C11—22no—
426C2×C4×C11—22no—
427C2×C4×C11—22no—
428C2×C4×C11—22no—
429C2×C4×C11—22no—
430C2×C4×C11—22no—
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—416no—
444C2×C4×C11—41no—
445C2×C4×C11—41no—
446C2×C4×C11—41no—
447C2×C4×C11—41no—
448C2×C4×C11—41no—
449C2×C4×C11—41no—
450C2×C4×C11—41no—
451C2×C4×C11—41no—
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#12414yes—
468C22⋊D11—232no—
469C2×Dic11—22no—
470C2×Dic11—22no—
471C2×Dic11—22no—
472C2×Dic11—22no—
473C2×Dic11—22no—
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—41no—
485C2×Dic11—41no—
486C2×Dic11—41no—
487C2×Dic11—41no—
488C2×Dic11—41no—
489C2×Dic11—41no—
490C2×Dic11—41no—
491C2×Dic11—41no—
492C2×Dic11—41no—
493C2×Dic11—41no—
494C2×Dic11—41no—
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×Dic11C2×C4⋊C414yes—
512C2×Dic11C4×D414yes—
513C2×Dic11C4×D414yes—
514C2×Dic11#12014yes—
515C2×Dic11C22⋊Q814yes—
516C2×Dic11C22⋊Q814yes—
517C2×Dic11#12314yes—
518C4×D11—416no—
519C23×D4—111no—
520C24×C4—111no—
521C24×C4C2×D1111yescharacteristic
522C2×C4×D4—224no—
523C2×C4×D4—224no—
524C2×C4×D4—224no—
525C22×C4⋊C4—111no—
526C22×C4⋊C4—111no—
527C22×C4⋊C4—111no—
528C22×C4⋊C4—111no—
529C22×C4⋊C4—111no—
530C22×C22⋊C4—111no—
531C22×C22⋊C4—111no—
532C22×C22⋊C4—111no—
533C22×C22⋊C4—111no—
534C22×C22⋊C4—111no—
535C22×C22⋊C4—111no—
536C22×C22⋊C4—111no—
537C22×C22⋊C4—111no—
538C22×C22⋊C4C2×D1111yescharacteristic
539C22×C22⋊C4C2×D1111yescharacteristic
540C22×C42—111no—
541C22×C42—111no—
542C22×C42—111no—
543#390—118no—
544#390—224no—
545#389—224no—
546#382—224no—
547C2×#95—111no—
548C2×#95—111no—
549C2×#95—111no—
550C2×#95—111no—
551C2×#95—111no—
552C2×#95—111no—
553C2×#95—111no—
554C2×#95—111no—
555C2×#95—111no—
556C2×#95—111no—
557C2×#95C2×D1111yescharacteristic
558C2×#95C2×D1111yescharacteristic
559C2×#95C2×D1111yescharacteristic
560C2×#95C2×D1111yescharacteristic
561C22×C11—24no—
562C22×C11—24no—
563C22×C11—24no—
564C22×C11—42no—
565C22×C11—42no—
566C22×C11—42no—
567C22×C11—42no—
568C22×C11—42no—
569C22×C11—42no—
570C22×C11—42no—
571C22×C11—42no—
572C22×C11—42no—
573C22×C11—42no—
574C22×C11—42no—
575C22×C11—42no—
576C22×C11C22×C4⋊C411yescharacteristic
577C22×C11C2×C4×D411yescharacteristic
578C22×C11C2×C4×D411yescharacteristic
579C22×C11C4×#4111yescharacteristic
580C22×C11C4×#4111yescharacteristic
581C22×C11#51811yescharacteristic
582C22×C11#51811yescharacteristic
583C22×C11C2×#12011yescharacteristic
584C22×C11C2×C22⋊Q811yescharacteristic
585C22×C11C2×C22⋊Q811yescharacteristic
586C22×C11C2×#12311yescharacteristic
587C22×C11C2×#12411yescharacteristic
588C22×C11#52911yescharacteristic
589C22×C11#52911yescharacteristic
590C22×C11#53211yescharacteristic
591C22×C11#53511yescharacteristic
592C22×C11#53511yescharacteristic
593C22×C11#54011yescharacteristic
594C22×C11#54011yescharacteristic
595C22×C11#54611yescharacteristic
596C22×C11#54611yescharacteristic
597C22×C11#54611yescharacteristic
598C22×C11#54611yescharacteristic
599C22×C11#54611yescharacteristic
600C22×C11#54611yescharacteristic
601C22×C11#55011yescharacteristic
602C22×C11#55011yescharacteristic
603C22×C11#55311yescharacteristic
604C22×C11#55311yescharacteristic
605C22×C11#55411yescharacteristic
606C22×C11#55411yescharacteristic
607C22×C11#55411yescharacteristic
608C22×C11#55411yescharacteristic
609C22×C11#55511yescharacteristic
610C22×C11#55511yescharacteristic
611C2×D11—24no—
612C2×D11—24no—
613C2×D11—24no—
614C2×D11—42no—
615C2×D11—42no—
616C2×D11—42no—
617C2×D11—42no—
618C2×D11—42no—
619C2×D11—42no—
620C2×D11—42no—
621C2×D11—42no—
622C2×D11—42no—
623C2×D11—42no—
624C2×D11—42no—
625C2×D11—42no—
626C4×C11—24no—
627C4×C11—42no—
628C4×C11—42no—
629C4×C11—42no—
630C4×C11—42no—
631C4×C11—81no—
632Dic11—42no—
633Dic11—42no—
634Dic11—42no—
635Dic11—42no—
636Dic11—42no—
637Dic11—81no—
638Dic11#38518yes—
639C25—111no—
640C25C22×D1111yescharacteristic
641C22×D4—114no—
642C22×D4—114no—
643C22×D4—114no—
644C22×D4—222no—
645C22×D4—222no—
646C22×D4—222no—
647C22×D4—222no—
648C23×C4—22no—
649C23×C4—22no—
650C23×C4—22no—
651C23×C4—22no—
652C23×C4—22no—
653C23×C4—41no—
654C23×C4—41no—
655C23×C4—111no—
656C23×C4—111no—
657C23×C4—111no—
658C23×C4—111no—
659C23×C4—111no—
660C23×C4—111no—
661C23×C4—111no—
662C23×C4—222no—
663C23×C4—222no—
664C23×C4—222no—
665C23×C4—222no—
666C23×C4—222no—
667C23×C4—441no—
668C23×C4—441no—
669C23×C4C22×D1111yescharacteristic
670C23×C4C22×D1111yescharacteristic
671C23×C4C22×D1111yescharacteristic
672C23×C4C22×D1111yescharacteristic
673C23×C4C22×D1111yescharacteristic
674C23×C4C22×D1111yescharacteristic
675C4×D4—2232no—
676C2×C4⋊C4—114no—
677C2×C4⋊C4—114no—
678C2×C4⋊C4—222no—
679C2×C4⋊C4—222no—
680C2×C4⋊C4—222no—
681C2×C4⋊C4—222no—
682C2×C4⋊C4—222no—
683C2×C4⋊C4—222no—
684C2×C4⋊C4—222no—
685C2×C4⋊C4—222no—
686C2×C4⋊C4—222no—
687C2×C4⋊C4—441no—
688C2×C4⋊C4—441no—
689C2×C4⋊C4—441no—
690C2×C4⋊C4—441no—
691C2×C22⋊C4—22no—
692C2×C22⋊C4—22no—
693C2×C22⋊C4—41no—
694C2×C22⋊C4—41no—
695C2×C22⋊C4—41no—
696C2×C22⋊C4—114no—
697C2×C22⋊C4—114no—
698C2×C22⋊C4—114no—
699C2×C22⋊C4—222no—
700C2×C22⋊C4—222no—
701C2×C22⋊C4—222no—
702C2×C22⋊C4—222no—
703C2×C22⋊C4—222no—
704C2×C22⋊C4—222no—
705C2×C22⋊C4—222no—
706C2×C22⋊C4—222no—
707C2×C22⋊C4—222no—
708C2×C22⋊C4—222no—
709C2×C22⋊C4—222no—
710C2×C22⋊C4—222no—
711C2×C22⋊C4—441no—
712C2×C22⋊C4—441no—
713C2×C22⋊C4—441no—
714C2×C22⋊C4—441no—
715C2×C22⋊C4—441no—
716C2×C22⋊C4—441no—
717C2×C22⋊C4—441no—
718C2×C22⋊C4—441no—
719C2×C22⋊C4—441no—
720C2×C22⋊C4C4×D1114yescomplemented
721C2×C42—114no—
722C2×C42—114no—
723C2×C42—222no—
724C2×C42—222no—
725C2×C42—222no—
726C2×C42—222no—
727C2×C42—222no—
728C2×C42—222no—
729C2×C42—222no—
730#95—22no—
731#95—22no—
732#95—22no—
733#95—41no—
734#95—222no—
735#95—222no—
736#95—222no—
737#95—222no—
738#95—222no—
739#95—222no—
740#95—222no—
741#95—441no—
742#95—441no—
743#95—441no—
744C2×C11—44no—
745C2×C11C2×#38511yescharacteristic
746C2×C11C4×#12411yescharacteristic
747C2×C11#232811yescharacteristic
748C2×C11#234911yescharacteristic
749C2×C11#234911yescharacteristic
750C2×C11#236311yescharacteristic
751C2×C11#236311yescharacteristic
752C2×C11#242011yescharacteristic
753C2×C11#242011yescharacteristic
754C2×C11#243111yescharacteristic
755C2×C11#243511yescharacteristic
756C2×C11#245411yescharacteristic
757C2×C11#245411yescharacteristic
758C2×C11#256311yescharacteristic
759C2×C11#256611yescharacteristic
760D11—44no—
761C24—21no—
762C24—21no—
763C24—21no—
764C24—21no—
765C24—21no—
766C24—21no—
767C24—21no—
768C24—21no—
769C24—21no—
770C24—21no—
771C24—21no—
772C24—21no—
773C24—112no—
774C24—112no—
775C24—112no—
776C24—221no—
777C24—221no—
778C24—221no—
779C24—221no—
780C24—221no—
781C24—221no—
782C24—221no—
783C24—221no—
784C24—221no—
785C24—221no—
786C24—221no—
787C24—221no—
788C24C2×C4×D1112yes—
789C24D4×D1112yes—
790C24Q8×D1112yes—
791C24C23×D1111yescharacteristic
792C2×D4—1116no—
793C2×D4—228no—
794C2×D4—228no—
795C2×D4—228no—
796C2×D4—228no—
797C2×D4—228no—
798C2×D4—228no—
799C22×C4—21no—
800C22×C4—21no—
801C22×C4—21no—
802C22×C4—21no—
803C22×C4—28no—
804C22×C4—21no—
805C22×C4—21no—
806C22×C4—21no—
807C22×C4—21no—
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—44no—
836C22×C4—44no—
837C22×C4—44no—
838C22×C4—44no—
839C22×C4—44no—
840C22×C4—44no—
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—112no—
850C22×C4—112no—
851C22×C4—112no—
852C22×C4—112no—
853C22×C4—228no—
854C22×C4—221no—
855C22×C4—221no—
856C22×C4—221no—
857C22×C4—221no—
858C22×C4—221no—
859C22×C4—221no—
860C22×C4—221no—
861C22×C4—221no—
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—444no—
892C22×C4—444no—
893C22×C4—444no—
894C22×C4—444no—
895C22×C4—444no—
896C22×C4—444no—
897C22×C4C2×C4×D1112yes—
898C22×C4C2×C4×D1112yes—
899C22×C4#433912yes—
900C22×C4#433912yes—
901C22×C4D4×D1112yes—
902C22×C4D4×D1112yes—
903C22×C4#434112yes—
904C4⋊C4—228no—
905C4⋊C4—228no—
906C4⋊C4—444no—
907C4⋊C4—444no—
908C4⋊C4—444no—
909C22⋊C4—44no—
910C22⋊C4—44no—
911C22⋊C4—228no—
912C22⋊C4—228no—
913C22⋊C4—444no—
914C22⋊C4—444no—
915C22⋊C4—444no—
916C22⋊C4—444no—
917C22⋊C4—444no—
918C22⋊C4—444no—
919C42—228no—
920C42—228no—
921C42—444no—
922C11#1397911yescharacteristic, complemented, Sylow
923C23—22no—
924C23—22no—
925C23—22no—
926C23—22no—
927C23—22no—
928C23—22no—
929C23—22no—
930C23—22no—
931C23—22no—
932C23—22no—
933C23—22no—
934C23—22no—
935C23—22no—
936C23—22no—
937C23—22no—
938C23—22no—
939C23—22no—
940C23—22no—
941C23—41no—
942C23—41no—
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—114no—
958C23—222no—
959C23—222no—
960C23—222no—
961C23—222no—
962C23—222no—
963C23—222no—
964C23—222no—
965C23—222no—
966C23—222no—
967C23—222no—
968C23—222no—
969C23—222no—
970C23—222no—
971C23—222no—
972C23—222no—
973C23—222no—
974C23—222no—
975C23—222no—
976C23—441no—
977C23—441no—
978C23—441no—
979C23—441no—
980C23—441no—
981C23—441no—
982C23—441no—
983C23—441no—
984C23—441no—
985C23—441no—
986C23—441no—
987C23—441no—
988C23—441no—
989C23—441no—
990C23—441no—
991C23—441no—
992C23C4⋊C4×D1114yes—
993C23C22×C4×D1111yescharacteristic
994C23C2×#433911yescharacteristic
995C23C2×#433911yescharacteristic
996C23C2×D4×D1111yescharacteristic
997C23C2×D4×D1111yescharacteristic
998C23C2×D4×D1111yescharacteristic
999C23C2×#434111yescharacteristic
1000C23#6703711yescharacteristic
1001C23#6703711yescharacteristic
1002C23#6703711yescharacteristic
1003C23C2×Q8×D1111yescharacteristic
1004C23#41×D1111yescharacteristic
1005C23#41×D1111yescharacteristic
1006C23#41×D1111yescharacteristic
1007C23#6704211yescharacteristic
1008D4—2232no—
1009C2×C4—22no—
1010C2×C4—22no—
1011C2×C4—22no—
1012C2×C4—22no—
1013C2×C4—22no—
1014C2×C4—22no—
1015C2×C4—22no—
1016C2×C4—22no—
1017C2×C4—22no—
1018C2×C4—22no—
1019C2×C4—22no—
1020C2×C4—22no—
1021C2×C4—22no—
1022C2×C4—22no—
1023C2×C4—22no—
1024C2×C4—22no—
1025C2×C4—22no—
1026C2×C4—22no—
1027C2×C4—416no—
1028C2×C4—41no—
1029C2×C4—41no—
1030C2×C4—41no—
1031C2×C4—41no—
1032C2×C4—41no—
1033C2×C4—41no—
1034C2×C4—41no—
1035C2×C4—41no—
1036C2×C4—41no—
1037C2×C4—41no—
1038C2×C4—41no—
1039C2×C4—41no—
1040C2×C4—41no—
1041C2×C4—41no—
1042C2×C4—41no—
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—114no—
1052C2×C4—114no—
1053C2×C4—114no—
1054C2×C4—114no—
1055C2×C4—114no—
1056C2×C4—114no—
1057C2×C4—114no—
1058C2×C4—222no—
1059C2×C4—222no—
1060C2×C4—222no—
1061C2×C4—222no—
1062C2×C4—222no—
1063C2×C4—222no—
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—4416no—
1074C2×C4—441no—
1075C2×C4—441no—
1076C2×C4—441no—
1077C2×C4—441no—
1078C2×C4—441no—
1079C2×C4—441no—
1080C2×C4—441no—
1081C2×C4—441no—
1082C2×C4—441no—
1083C2×C4—441no—
1084C2×C4—441no—
1085C2×C4—441no—
1086C2×C4—441no—
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#6693814yes—
1102C22—24no—
1103C22—24no—
1104C22—24no—
1105C22—42no—
1106C22—42no—
1107C22—42no—
1108C22—42no—
1109C22—42no—
1110C22—42no—
1111C22—42no—
1112C22—42no—
1113C22—42no—
1114C22—42no—
1115C22—42no—
1116C22—42no—
1117C22—224no—
1118C22—224no—
1119C22—224no—
1120C22—442no—
1121C22—442no—
1122C22—442no—
1123C22—442no—
1124C22—442no—
1125C22—442no—
1126C22—442no—
1127C22—442no—
1128C22—442no—
1129C22—442no—
1130C22—442no—
1131C22—442no—
1132C22C4×#433911yescharacteristic
1133C22#1062301711yescharacteristic
1134C22#1062302111yescharacteristic
1135C22#1062302111yescharacteristic
1136C22#1062302111yescharacteristic
1137C22C2×#6693811yescharacteristic
1138C22C2×C4⋊C4×D1111yescharacteristic
1139C22#1062304211yescharacteristic
1140C22#1062304211yescharacteristic
1141C22#1062305911yescharacteristic
1142C22#1062306311yescharacteristic
1143C22C4×#434111yescharacteristic
1144C22#1062306911yescharacteristic
1145C22#1062307111yescharacteristic
1146C22C4×D4×D1111yescharacteristic
1147C22C4×D4×D1111yescharacteristic
1148C22#1062307611yescharacteristic
1149C22#1062307911yescharacteristic
1150C22#1062308411yescharacteristic
1151C22D11×#12011yescharacteristic
1152C22#1062312211yescharacteristic
1153C22#1062312211yescharacteristic
1154C22#1062312311yescharacteristic
1155C22#1062313011yescharacteristic
1156C22#1062313811yescharacteristic
1157C22#1062314611yescharacteristic
1158C22#1062314711yescharacteristic
1159C22D11×C22⋊Q811yescharacteristic
1160C22D11×C22⋊Q811yescharacteristic
1161C22#1062316611yescharacteristic
1162C22#1062316711yescharacteristic
1163C22D11×#12311yescharacteristic
1164C22#1062318511yescharacteristic
1165C22#1062319211yescharacteristic
1166C22#1062319411yescharacteristic
1167C4—24no—
1168C4—42no—
1169C4—42no—
1170C4—42no—
1171C4—42no—
1172C4—81no—
1173C4—118no—
1174C4—442no—
1175C4—442no—
1176C4—442no—
1177C4—442no—
1178C4—442no—
1179C4—881no—
1180C2—44no—
1181C2—444no—
1182C2D11×#38511yescharacteristic
1183C2C4×#6693811yescharacteristic
1184C2#1307133711yescharacteristic
1185C2#1307152211yescharacteristic
1186C2#1307152311yescharacteristic
1187C2#1307165511yescharacteristic
1188C2#1307165711yescharacteristic
1189C2#1307210511yescharacteristic
1190C2#1307210711yescharacteristic
1191C2#1307223311yescharacteristic
1192C2#1307226511yescharacteristic
1193C2#1307248511yescharacteristic
1194C2#1307248711yescharacteristic
1195C2#1307378611yescharacteristic
1196C2#1307381411yescharacteristic
subgroupG/H
center, FrattiniC24C23×D11
commutatorC23×C11C23×C4
FittingC11×C22⋊#95C2
socle, cosocleC24×C11C24
prime radicalC23×C22⋊D11C22
hypercenterC22⋊#95D11
hypocenterC11#13979
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ C22⋊#95

Complements

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

NH ≅ G/Ntype
4. C2×#10622260C2semidirect
5. C2×#10622263C2semidirect
6. #13066862C2semidirect
7. #13066861C2semidirect
8. #13066860C2semidirect
9. #13066859C2semidirect
10. Dic11⋊#95C2semidirect
11. #13066839C2semidirect
12. (C2×D11)⋊#95C2semidirect
13. (C2×D11)⋊#95C2semidirect
14. #95×Dic11C2semidirect
15. C11×C22⋊#95C2semidirect
55. #10622570C4semidirect
99. C2×C11×C22⋊C4C2×C4semidirect
108. C2×C22⋊Dic11C2×C4semidirect
123. C2×(C2×D11)⋊C4C2×C4semidirect
124. C2×(C2×D11)⋊C4C2×C4semidirect
138. C2×Dic11⋊C4C2×C4semidirect
147. C2×C4×Dic11C2×C4semidirect
250. C2×C22⋊D11C4⋊C4semidirect
338. C22⋊#95D11semidirect
720. C2×C22⋊C4C4×D11semidirect
922. C11#13979semidirect

Maximal subgroups

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

subgroupindex
C22×C4×C22⋊D112
C2×#106225702
C2×#106222602
C2×#106222632
#130668622
#130668612
#130668602
#130668592
Dic11⋊#952
#130668392
(C2×D11)⋊#952
#95×Dic112
C11×C22⋊#952
#1397911