Finite Group Databasebeta

← #14685010

Subgroups — #14685010

Order 2816.

2746 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×C42×D11C211yesmaximal, characteristic, complemented
2C2×#10622558C211yesmaximal, characteristic, complemented
3C2×#10622564C211yesmaximal, characteristic, complemented
4C2×#10622569C211yesmaximal, characteristic
5C2×#10622569C211yesmaximal, characteristic
6C2×#10622569C211yesmaximal, characteristic
7C2×#10622281C211yesmaximal, characteristic, complemented
8#13066853C211yesmaximal, characteristic, complemented
9#13066850C211yesmaximal, characteristic, complemented
10#13066849C211yesmaximal, characteristic, complemented
11#13066842C211yesmaximal, characteristic, complemented
12#13066841C211yesmaximal, characteristic, complemented
13(C2×D11)⋊#95C211yesmaximal, characteristic, complemented
14(C2×D11)⋊#95C211yesmaximal, characteristic, complemented
15C11×#1437C211yesmaximal, characteristic, complemented
16C23×C22⋊D11C2211yescharacteristic
17C23×C4×D11C2211yescharacteristic
18C23×C4×D11C2211yescharacteristic
19C23×C4×D11C2211yescharacteristic
20C22×C11×C22⋊C4C2211yescharacteristic
21C22×C11×C22⋊C4C2211yescharacteristic
22C22×C11×C22⋊C4C2211yescharacteristic
23C22×C42×C11C2211yescharacteristic
24C22×C22⋊Dic11C2211yescharacteristic
25C22×C22⋊Dic11C2211yescharacteristic
26C22×C22⋊Dic11C2211yescharacteristic
27C22×(C2×D11)⋊C4C2211yescharacteristic
28C22×(C2×D11)⋊C4C2211yescharacteristic
29C22×(C2×D11)⋊C4C2211yescharacteristic
30C22×C4⋊Dic11C2211yescharacteristic
31C22×Dic11⋊C4C2211yescharacteristic
32C22×C4×Dic11C2211yescharacteristic
33C22×C4×Dic11C2211yescharacteristic
34C22×C4×Dic11C2211yescharacteristic
35C2×C42×D11—24no—
36C2×C42×D11—24no—
37C2×C42×D11—24no—
38C2×C11×#95C2211yescharacteristic
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
54#10622569—24no—
55#10622569—24no—
56#10622569C418yescomplemented
57#10622564—24no—
58#10622558—24no—
59#10622281—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—22no—
98C22×C4×D11—22no—
99C22×C4×D11—22no—
100C22×C4×D11C2×C414yes—
101C22×C4×D11D414yes—
102C22×C4×D11D414yes—
103C2×C11×C22⋊C4—22no—
104C2×C11×C22⋊C4—22no—
105C2×C11×C22⋊C4—22no—
106C2×C11×C22⋊C4—22no—
107C2×C11×C22⋊C4—22no—
108C2×C11×C22⋊C4—22no—
109C2×C11×C22⋊C4—22no—
110C2×C11×C22⋊C4—22no—
111C2×C11×C22⋊C4C2×C414yescomplemented
112C2×C42×C11—22no—
113C2×C42×C11—22no—
114C2×C42×C11—22no—
115C2×C22⋊Dic11—22no—
116C2×C22⋊Dic11—22no—
117C2×C22⋊Dic11—22no—
118C2×C22⋊Dic11—22no—
119C2×C22⋊Dic11—22no—
120C2×C22⋊Dic11—22no—
121C2×C22⋊Dic11—22no—
122C2×C22⋊Dic11—22no—
123C2×C22⋊Dic11C2×C414yescomplemented
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—22no—
132C2×(C2×D11)⋊C4C2×C414yes—
133C2×C4⋊Dic11—22no—
134C2×C4⋊Dic11—22no—
135C2×C4⋊Dic11—22no—
136C2×Dic11⋊C4—22no—
137C2×Dic11⋊C4—22no—
138C2×Dic11⋊C4—22no—
139C2×C4×Dic11—22no—
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×Dic11D414yescomplemented
147C2×C4×Dic11D414yescomplemented
148C42×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—22no—
162C11⋊#95—22no—
163C11⋊#95C2×C414yescomplemented
164C11⋊#95C2×C414yescomplemented
165#14696—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×C11C22×C412yes—
230C22×C4×C11C22×C412yes—
231C22×C4×C11C2×D412yes—
232C22×C4×C11C2×D412yes—
233C22×C4×C11C2×D412yes—
234C22×C4×C11C2×D412yes—
235C22×C4×C11#4112yes—
236C22×C4×C11#4112yes—
237C22×C4×C11#4112yes—
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×Dic11C22×C412yes—
285C22×Dic11C22×C412yes—
286C22×Dic11C22×C412yes—
287C22×Dic11C2×D412yes—
288C22×Dic11C2×D412yes—
289C22×Dic11C2×D412yes—
290C22×Dic11C2×D412yes—
291C22×Dic11C2×D412yes—
292C22×Dic11C2×D412yes—
293C22×Dic11#4112yes—
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—28no—
306C2×C4×D11—28no—
307C2×C4×D11—28no—
308C2×C4×D11—28no—
309C2×C4×D11—28no—
310C2×C4×D11—28no—
311C2×C4×D11—28no—
312C2×C4×D11—28no—
313C2×C4×D11—28no—
314C2×C4×D11—28no—
315C2×C4×D11—28no—
316C11×C22⋊C4—28no—
317C11×C22⋊C4—44no—
318C11×C22⋊C4—44no—
319C42×C11—28no—
320C22⋊Dic11—28no—
321C22⋊Dic11—44no—
322C22⋊Dic11—44no—
323(C2×D11)⋊C4—28no—
324(C2×D11)⋊C4—44no—
325(C2×D11)⋊C4—44no—
326C4⋊Dic11—44no—
327Dic11⋊C4—44no—
328C4×Dic11—28no—
329C4×Dic11—28no—
330C4×Dic11—28no—
331C23×C42—111no—
332C2×#388—111no—
333C2×#388—111no—
334C2×#386—111no—
335C2×#386—111no—
336C2×#386—111no—
337C2×#385—111no—
338#1437—111no—
339#1437D1111yescharacteristic, complemented
340#1436—111no—
341#1436—111no—
342#1434—111no—
343#1434—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×C11C2×#4111yescharacteristic
393C23×C11C2×#4111yescharacteristic
394C23×C11C2×#4111yescharacteristic
395C23×C11C2×#4111yescharacteristic
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×C11C4×D414yes—
471C2×C4×C11#12114yes—
472C2×C4×C11#12314yes—
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—22no—
496C2×Dic11—22no—
497C2×Dic11—22no—
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×Dic11C4×D414yes—
521C2×Dic11#12014yes—
522C2×Dic11#12114yes—
523C4×D11—232no—
524C4×D11—232no—
525C4×D11—232no—
526C23×D4—111no—
527C24×C4—111no—
528C24×C4—111no—
529C24×C4—111no—
530C22×C4⋊C4—111no—
531C22×C4⋊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×C22⋊C4C2×D1111yescharacteristic
541C22×C42—111no—
542C22×C42—111no—
543C22×C42—111no—
544C22×C42—224no—
545C22×C42—224no—
546C22×C42—224no—
547C22×C42C2×D1111yescharacteristic
548#388—224no—
549#388—224no—
550#386—118no—
551#386—224no—
552#386—224no—
553#385—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×#95C2×D1111yescharacteristic
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×C11C4×#4111yescharacteristic
591C22×C11C4×#4111yescharacteristic
592C22×C11C2×#12011yescharacteristic
593C22×C11C2×#12111yescharacteristic
594C22×C11C2×#12111yescharacteristic
595C22×C11C2×#12111yescharacteristic
596C22×C11C2×#12311yescharacteristic
597C22×C11C2×#12311yescharacteristic
598C22×C11#52511yescharacteristic
599C22×C11#52511yescharacteristic
600C22×C11#52511yescharacteristic
601C22×C11#52511yescharacteristic
602C22×C11#52511yescharacteristic
603C22×C11#52511yescharacteristic
604C22×C11#52511yescharacteristic
605C22×C11#52511yescharacteristic
606C22×C11#52511yescharacteristic
607C22×C11#52511yescharacteristic
608C22×C11C2×#12411yescharacteristic
609C22×C11C2×#12611yescharacteristic
610C22×C11#52911yescharacteristic
611C22×C11#52911yescharacteristic
612C22×C11#52911yescharacteristic
613C22×C11#52911yescharacteristic
614C22×C11#52911yescharacteristic
615C22×C11#52911yescharacteristic
616C22×C11#52911yescharacteristic
617C22×C11#52911yescharacteristic
618C22×C11#53211yescharacteristic
619C22×C11#53211yescharacteristic
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—24no—
638C4×C11—42no—
639C4×C11—81no—
640C4×C11—81no—
641Dic11—24no—
642Dic11—24no—
643Dic11—24no—
644Dic11—42no—
645Dic11—42no—
646Dic11—81no—
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—114no—
663C23×C4—114no—
664C23×C4—114no—
665C23×C4—111no—
666C23×C4—111no—
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—222no—
682C23×C4—222no—
683C23×C4—222no—
684C23×C4—222no—
685C23×C4C22×D1111yescharacteristic
686C23×C4C22×D1111yescharacteristic
687C23×C4C22×D1111yescharacteristic
688C23×C4C22×D1111yescharacteristic
689C23×C4C22×D1111yescharacteristic
690C23×C4C22×D1111yescharacteristic
691C2×C4⋊C4—222no—
692C2×C4⋊C4—222no—
693C2×C4⋊C4—222no—
694C2×C4⋊C4—222no—
695C2×C4⋊C4—222no—
696C2×C4⋊C4—222no—
697C2×C22⋊C4—22no—
698C2×C22⋊C4—22no—
699C2×C22⋊C4—22no—
700C2×C22⋊C4—22no—
701C2×C22⋊C4—22no—
702C2×C22⋊C4—22no—
703C2×C22⋊C4—22no—
704C2×C22⋊C4—22no—
705C2×C22⋊C4—114no—
706C2×C22⋊C4—114no—
707C2×C22⋊C4—222no—
708C2×C22⋊C4—222no—
709C2×C22⋊C4—222no—
710C2×C22⋊C4—222no—
711C2×C22⋊C4—222no—
712C2×C22⋊C4—222no—
713C2×C22⋊C4—222no—
714C2×C22⋊C4—222no—
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⋊C4C4×D1114yescomplemented
724C2×C42—22no—
725C2×C42—22no—
726C2×C42—22no—
727C2×C42—114no—
728C2×C42—114no—
729C2×C42—2232no—
730C2×C42—222no—
731C2×C42—222no—
732C2×C42—222no—
733C2×C42—222no—
734C2×C42—222no—
735C2×C42—222no—
736C2×C42—222no—
737#95—22no—
738#95—22no—
739#95—22no—
740#95—114no—
741#95—114no—
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—222no—
752#95—222no—
753C2×C11—82no—
754C2×C11C2×#38811yescharacteristic
755C2×C11#229011yescharacteristic
756C2×C11#229011yescharacteristic
757C2×C11C4×#12011yescharacteristic
758C2×C11C4×#12111yescharacteristic
759C2×C11C4×#12111yescharacteristic
760C2×C11C4×#12311yescharacteristic
761C2×C11#284711yescharacteristic
762C2×C11#284911yescharacteristic
763C2×C11#285011yescharacteristic
764C2×C11#285011yescharacteristic
765C2×C11#285211yescharacteristic
766C2×C11#285211yescharacteristic
767C2×C11#285311yescharacteristic
768C2×C11#285411yescharacteristic
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—112no—
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—228no—
852C22×C4—228no—
853C22×C4—228no—
854C22×C4—228no—
855C22×C4—228no—
856C22×C4—228no—
857C22×C4—228no—
858C22×C4—228no—
859C22×C4—228no—
860C22×C4—228no—
861C22×C4—228no—
862C22×C4—228no—
863C22×C4—228no—
864C22×C4—228no—
865C22×C4—228no—
866C22×C4—228no—
867C22×C4—228no—
868C22×C4—228no—
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—228no—
882C22×C4—228no—
883C22×C4—228no—
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—221no—
893C22×C4—221no—
894C22×C4—221no—
895C22×C4—221no—
896C22×C4—221no—
897C22×C4—221no—
898C22×C4—221no—
899C22×C4—221no—
900C22×C4—221no—
901C22×C4—221no—
902C22×C4—221no—
903C22×C4—221no—
904C22×C4—221no—
905C22×C4—221no—
906C22×C4—221no—
907C22×C4—221no—
908C22×C4—221no—
909C22×C4—221no—
910C22×C4C2×C4×D1112yes—
911C22×C4C2×C4×D1112yes—
912C22×C4#433912yes—
913C22×C4#433912yes—
914C22×C4D4×D1112yes—
915C22×C4D4×D1112yes—
916C22×C4D4×D1112yes—
917C22×C4D4×D1112yes—
918C22×C4#434112yes—
919C22×C4#434112yes—
920C4⋊C4—444no—
921C4⋊C4—444no—
922C22⋊C4—28no—
923C22⋊C4—44no—
924C22⋊C4—44no—
925C22⋊C4—228no—
926C22⋊C4—228no—
927C22⋊C4—444no—
928C22⋊C4—444no—
929C22⋊C4—444no—
930C22⋊C4—444no—
931C42—28no—
932C42—228no—
933C42—228no—
934C42—228no—
935C11#1469611yescharacteristic, 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×#433911yescharacteristic
1009C23C2×D4×D1111yescharacteristic
1010C23C2×D4×D1111yescharacteristic
1011C23C2×D4×D1111yescharacteristic
1012C23C2×D4×D1111yescharacteristic
1013C23C2×#434111yescharacteristic
1014C23C2×#434111yescharacteristic
1015C23#41×D1111yescharacteristic
1016C23#41×D1111yescharacteristic
1017C23#41×D1111yescharacteristic
1018C23#41×D1111yescharacteristic
1019C23#41×D1111yescharacteristic
1020C23#41×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—114no—
1062C2×C4—114no—
1063C2×C4—114no—
1064C2×C4—2232no—
1065C2×C4—2232no—
1066C2×C4—2232no—
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—222no—
1086C2×C4—222no—
1087C2×C4—222no—
1088C2×C4—222no—
1089C2×C4—222no—
1090C2×C4—222no—
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(C22⋊D11)⋊C414yes—
1114C2×C4#6693614yes—
1115C2×C4#6693714yes—
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—
1146C22C4×#433911yescharacteristic
1147C22C2×(C22⋊D11)⋊C411yescharacteristic
1148C22C2×#6693611yescharacteristic
1149C22C2×#6693711yescharacteristic
1150C22D11×#11711yescharacteristic
1151C22#1062305911yescharacteristic
1152C22#1062305911yescharacteristic
1153C22C4×#434111yescharacteristic
1154C22C4×D4×D1111yescharacteristic
1155C22C4×D4×D1111yescharacteristic
1156C22C4×D4×D1111yescharacteristic
1157C22#1062307811yescharacteristic
1158C22#1062307811yescharacteristic
1159C22#1062307811yescharacteristic
1160C22#1062307811yescharacteristic
1161C22#1062307911yescharacteristic
1162C22#1062308811yescharacteristic
1163C22#1062308811yescharacteristic
1164C22#1062308811yescharacteristic
1165C22D11×#12011yescharacteristic
1166C22D11×#12111yescharacteristic
1167C22D11×#12111yescharacteristic
1168C22#1062313711yescharacteristic
1169C22#1062313711yescharacteristic
1170C22#1062313711yescharacteristic
1171C22#1062313711yescharacteristic
1172C22D11×#12311yescharacteristic
1173C22#1062318711yescharacteristic
1174C22#1062318711yescharacteristic
1175C22D11×#12411yescharacteristic
1176C22#1062321111yescharacteristic
1177C22#1062321111yescharacteristic
1178C22D11×#12611yescharacteristic
1179C22#1062323711yescharacteristic
1180C22#1062324711yescharacteristic
1181C4—24no—
1182C4—24no—
1183C4—24no—
1184C4—42no—
1185C4—81no—
1186C4—81no—
1187C4—224no—
1188C4—224no—
1189C4—224no—
1190C4—442no—
1191C4—442no—
1192C4—881no—
1193C4—881no—
1194C2—82no—
1195C2—228no—
1196C2D11×#38811yescharacteristic
1197C2#1307105811yescharacteristic
1198C2#1307106211yescharacteristic
1199C2#1307112111yescharacteristic
1200C2C4×#6693711yescharacteristic
1201C2#1307113211yescharacteristic
1202C2C4×#6693611yescharacteristic
1203C2#1307689711yescharacteristic
1204C2#1307690711yescharacteristic
1205C2#1307691411yescharacteristic
1206C2#1307691611yescharacteristic
1207C2#1307693011yescharacteristic
1208C2#1307693011yescharacteristic
1209C2#1307693611yescharacteristic
1210C2#1307694611yescharacteristic
subgroupG/H
center, FrattiniC24C23×D11
commutatorC23×C11C23×C4
FittingC11×#1437C2
socle, cosocleC24×C11C24
prime radicalC23×C22⋊D11C22
hypercenter#1437D11
hypocenterC11#14696
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ #1437

Complements

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

NH ≅ G/Ntype
1. C22×C42×D11C2semidirect
2. C2×#10622558C2semidirect
3. C2×#10622564C2semidirect
7. C2×#10622281C2semidirect
8. #13066853C2semidirect
9. #13066850C2semidirect
10. #13066849C2semidirect
11. #13066842C2semidirect
12. #13066841C2semidirect
13. (C2×D11)⋊#95C2semidirect
14. (C2×D11)⋊#95C2semidirect
15. C11×#1437C2semidirect
56. #10622569C4semidirect
111. C2×C11×C22⋊C4C2×C4semidirect
123. C2×C22⋊Dic11C2×C4semidirect
146. C2×C4×Dic11D4semidirect
147. C2×C4×Dic11D4semidirect
163. C11⋊#95C2×C4semidirect
164. C11⋊#95C2×C4semidirect
339. #1437D11semidirect
634. C2×D11#388semidirect
723. C2×C22⋊C4C4×D11semidirect
935. C11#14696semidirect

Maximal subgroups

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

subgroupindex
C22×C42×D112
C2×#106225582
C2×#106225642
C2×#106225692
C2×#106222812
#130668532
#130668502
#130668492
#130668422
#130668412
(C2×D11)⋊#952
C11×#14372
#1469611