Finite Group Databasebeta

← #14683134

Subgroups — #14683134

Order 2816.

2282 conjugacy classes of subgroups.

The subgroup lattice has 1332 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622284C211yesmaximal, characteristic
2C2×#10622552C211yesmaximal, characteristic, complemented
3C2×#10622601C211yesmaximal, characteristic, complemented
4C2×#10622553C211yesmaximal, characteristic, complemented
5C2×#10622282C211yesmaximal, characteristic, complemented
6C2×#10622278C211yesmaximal, characteristic, complemented
7C2×#10622278C211yesmaximal, characteristic, complemented
8#13066862C211yesmaximal, characteristic, complemented
9#13066860C211yesmaximal, characteristic, complemented
10#13066858C211yesmaximal, characteristic, complemented
11#13066856C211yesmaximal, characteristic, complemented
12#13066856C211yesmaximal, characteristic, complemented
13#13066850C211yesmaximal, characteristic, complemented
14(C2×D11)⋊#95C211yesmaximal, characteristic, complemented
15C11×#1436C211yesmaximal, characteristic, complemented
16C23×D44C2211yescharacteristic
17C23×D44C2211yescharacteristic
18C23×D44C2211yescharacteristic
19C23×C4×D11C2211yescharacteristic
20C22×C11×C4⋊C4C2211yescharacteristic
21C22×C42×C11C2211yescharacteristic
22C22×(C2×D11)⋊C4C2211yescharacteristic
23C22×(C2×D11)⋊C4C2211yescharacteristic
24C22×(C2×D11)⋊C4C2211yescharacteristic
25C22×(C2×D11)⋊C4C2211yescharacteristic
26C22×(C2×D11)⋊C4C2211yescharacteristic
27C22×(C2×D11)⋊C4C2211yescharacteristic
28C22×(C2×D11)⋊C4C2211yescharacteristic
29C22×(C2×D11)⋊C4C2211yescharacteristic
30C22×(C2×D11)⋊C4C2211yescharacteristic
31C22×(C2×D11)⋊C4C2211yescharacteristic
32C22×(C2×D11)⋊C4C2211yescharacteristic
33C22×(C2×D11)⋊C4C2211yescharacteristic
34C22×(C2×D11)⋊C4C2211yescharacteristic
35C22×(C2×D11)⋊C4C2211yescharacteristic
36C22×C4⋊Dic11C2211yescharacteristic
37C22×Dic11⋊C4C2211yescharacteristic
38C22×C4×Dic11C2211yescharacteristic
39C2×C11×#95C2211yescharacteristic
40C2×C11×#95C2211yescharacteristic
41C2×C11×#95C2211yescharacteristic
42C2×C11×#95C2211yescharacteristic
43C2×C11×#95C2211yescharacteristic
44C2×C11⋊#95C2211yescharacteristic
45C2×C11⋊#95C2211yescharacteristic
46C2×C11⋊#95C2211yescharacteristic
47C2×C11⋊#95C2211yescharacteristic
48C2×C11⋊#95C2211yescharacteristic
49C2×C11⋊#95C2211yescharacteristic
50C2×C11⋊#95C2211yescharacteristic
51#10622601—24no—
52#10622553—24no—
53#10622552—24no—
54#10622284C418yescomplemented
55#10622282—24no—
56#10622278—24no—
57#10622278—24no—
58C24×D11C2311yescharacteristic
59C24×D11C2311yescharacteristic
60C24×D11C2311yescharacteristic
61C23×C4×C11C2311yescharacteristic
62C23×C4×C11C2311yescharacteristic
63C23×C4×C11C2311yescharacteristic
64C23×C4×C11C2311yescharacteristic
65C23×C4×C11C2311yescharacteristic
66C23×C4×C11C2311yescharacteristic
67C23×C4×C11C2311yescharacteristic
68C23×Dic11C2311yescharacteristic
69C23×Dic11C2311yescharacteristic
70C23×Dic11C2311yescharacteristic
71C23×Dic11C2311yescharacteristic
72C23×Dic11C2311yescharacteristic
73C22×D44—22no—
74C22×D44—22no—
75C22×D44—22no—
76C22×D44—22no—
77C22×D44—22no—
78C22×D44—22no—
79C22×D44—22no—
80C22×D44—22no—
81C22×D44—41no—
82C22×D44—41no—
83C22×D44—41no—
84C22×D44—41no—
85C22×D44—41no—
86C22×D44—41no—
87C22×D44—41no—
88C22×D44—41no—
89C22×D44—41no—
90C22×D44—41no—
91C22×D44C2×C414yes—
92C22×D44C2×C414yes—
93C22×D44C2×C414yescomplemented
94C22×C4×D11—22no—
95C22×C4×D11—22no—
96C22×C4×D11—22no—
97C22×C4×D11—41no—
98C22×C4×D11—41no—
99C22×C4×D11—41no—
100C22×C4×D11—41no—
101C2×C11×C4⋊C4—22no—
102C2×C11×C4⋊C4—22no—
103C2×C11×C4⋊C4—41no—
104C2×C42×C11—22no—
105C2×C42×C11—22no—
106C2×C42×C11—41no—
107C2×(C2×D11)⋊C4—22no—
108C2×(C2×D11)⋊C4—22no—
109C2×(C2×D11)⋊C4—22no—
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—22no—
118C2×(C2×D11)⋊C4—22no—
119C2×(C2×D11)⋊C4—22no—
120C2×(C2×D11)⋊C4—22no—
121C2×(C2×D11)⋊C4—22no—
122C2×(C2×D11)⋊C4—22no—
123C2×(C2×D11)⋊C4—22no—
124C2×(C2×D11)⋊C4—22no—
125C2×(C2×D11)⋊C4—22no—
126C2×(C2×D11)⋊C4—22no—
127C2×(C2×D11)⋊C4—41no—
128C2×(C2×D11)⋊C4—41no—
129C2×(C2×D11)⋊C4—41no—
130C2×(C2×D11)⋊C4—41no—
131C2×(C2×D11)⋊C4—41no—
132C2×(C2×D11)⋊C4—41no—
133C2×(C2×D11)⋊C4—41no—
134C2×(C2×D11)⋊C4—41no—
135C2×(C2×D11)⋊C4—41no—
136C2×(C2×D11)⋊C4—41no—
137C2×(C2×D11)⋊C4—41no—
138C2×(C2×D11)⋊C4—41no—
139C2×(C2×D11)⋊C4—41no—
140C2×(C2×D11)⋊C4—41no—
141C2×(C2×D11)⋊C4—41no—
142C2×(C2×D11)⋊C4—41no—
143C2×(C2×D11)⋊C4—41no—
144C2×(C2×D11)⋊C4—41no—
145C2×(C2×D11)⋊C4C2×C414yes—
146C2×(C2×D11)⋊C4C2×C414yescomplemented
147C2×(C2×D11)⋊C4C2×C414yescomplemented
148C2×(C2×D11)⋊C4D414yescomplemented
149C2×C4⋊Dic11—22no—
150C2×C4⋊Dic11—22no—
151C2×C4⋊Dic11—41no—
152C2×Dic11⋊C4—22no—
153C2×Dic11⋊C4—22no—
154C2×Dic11⋊C4—41no—
155C2×C4×Dic11—22no—
156C2×C4×Dic11—22no—
157C2×C4×Dic11—41no—
158C11×#95—22no—
159C11×#95—41no—
160C11×#95—41no—
161C11×#95C2×C414yescomplemented
162C11×#95D414yescomplemented
163C11⋊#95—22no—
164C11⋊#95—22no—
165C11⋊#95—22no—
166C11⋊#95—41no—
167C11⋊#95—41no—
168C11⋊#95—41no—
169C11⋊#95D414yescomplemented
170#14521—111nomaximal, Sylow
171C24×C11C2411yescharacteristic
172C23×D11—21no—
173C23×D11—21no—
174C23×D11—21no—
175C23×D11—21no—
176C23×D11—21no—
177C23×D11—21no—
178C23×D11—21no—
179C23×D11—21no—
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×D11—21no—
193C23×D11—21no—
194C23×D11—21no—
195C23×D11—21no—
196C23×D11—21no—
197C23×D11—21no—
198C23×D11—21no—
199C23×D11—21no—
200C23×D11—21no—
201C23×D11—21no—
202C23×D11—21no—
203C23×D11—21no—
204C23×D11—21no—
205C23×D11—21no—
206C23×D11—21no—
207C23×D11—21no—
208C23×D11—21no—
209C23×D11—21no—
210C23×D11—21no—
211C23×D11—21no—
212C23×D11C22×C412yes—
213C23×D11C22×C412yes—
214C23×D11C22×C412yes—
215C23×D11C2×D412yes—
216C23×D11#4112yes—
217C22×C4×C11—21no—
218C22×C4×C11—21no—
219C22×C4×C11—21no—
220C22×C4×C11—21no—
221C22×C4×C11—21no—
222C22×C4×C11—21no—
223C22×C4×C11—21no—
224C22×C4×C11—21no—
225C22×C4×C11—21no—
226C22×C4×C11—21no—
227C22×C4×C11—21no—
228C22×C4×C11—21no—
229C22×C4×C11—21no—
230C22×C4×C11—21no—
231C22×C4×C11—21no—
232C22×C4×C11—21no—
233C22×C4×C11—21no—
234C22×C4×C11—21no—
235C22×C4×C11—21no—
236C22×C4×C11—21no—
237C22×C4×C11—21no—
238C22×C4×C11—21no—
239C22×C4×C11—21no—
240C22×C4×C11—21no—
241C22×C4×C11—21no—
242C22×C4×C11—21no—
243C22×C4×C11—21no—
244C22×C4×C11—21no—
245C22×C4×C11—21no—
246C22×C4×C11—21no—
247C22×C4×C11—21no—
248C22×C4×C11—21no—
249C22×C4×C11—21no—
250C22×C4×C11—21no—
251C22×C4×C11—21no—
252C22×C4×C11—21no—
253C22×C4×C11—21no—
254C22×C4×C11—21no—
255C22×C4×C11—21no—
256C22×C4×C11C22×C412yes—
257C22×C4×C11C22×C412yes—
258C22×C4×C11C22×C412yes—
259C22×C4×C11C2×D412yes—
260C22×C4×C11C2×D412yes—
261C22×C4×C11C2×D412yes—
262C22×C4×C11C2×D412yes—
263C22×C4×C11C2×D412yes—
264C22×C4×C11#4112yes—
265C22×C4×C11#4112yes—
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×Dic11—21no—
289C22×Dic11—21no—
290C22×Dic11—21no—
291C22×Dic11—21no—
292C22×Dic11—21no—
293C22×Dic11—21no—
294C22×Dic11—21no—
295C22×Dic11—21no—
296C22×Dic11—21no—
297C22×Dic11C22×C412yes—
298C22×Dic11C2×D412yes—
299C22×Dic11C2×D412yes—
300C22×Dic11C2×D412yes—
301C2×D44—28no—
302C2×D44—28no—
303C2×D44—28no—
304C2×D44—28no—
305C2×D44—44no—
306C2×D44—44no—
307C2×D44—44no—
308C2×D44—44no—
309C2×D44—44no—
310C2×D44—44no—
311C2×D44—44no—
312C2×D44—44no—
313C2×D44—44no—
314C2×D44—44no—
315C2×D44—44no—
316C2×D44—44no—
317C2×D44—44no—
318C2×D44—44no—
319C2×D44—44no—
320C2×D44—44no—
321C2×D44—44no—
322C2×C4×D11—44no—
323C2×C4×D11—44no—
324C2×C4×D11—44no—
325C2×C4×D11—44no—
326C2×C4×D11—44no—
327C2×C4×D11—44no—
328C2×C4×D11—44no—
329C11×C4⋊C4—44no—
330C42×C11—44no—
331(C2×D11)⋊C4—28no—
332(C2×D11)⋊C4—28no—
333(C2×D11)⋊C4—44no—
334(C2×D11)⋊C4—44no—
335(C2×D11)⋊C4—44no—
336(C2×D11)⋊C4—44no—
337(C2×D11)⋊C4—44no—
338(C2×D11)⋊C4—44no—
339(C2×D11)⋊C4—44no—
340(C2×D11)⋊C4—44no—
341(C2×D11)⋊C4—44no—
342(C2×D11)⋊C4—44no—
343(C2×D11)⋊C4—44no—
344(C2×D11)⋊C4—44no—
345C4⋊Dic11—44no—
346Dic11⋊C4—44no—
347C4×Dic11—44no—
348C2×#392—111no—
349C2×#390—111no—
350C2×#390—111no—
351C2×#388—111no—
352C2×#388—111no—
353C2×#386—111no—
354C2×#386—111no—
355#1439—111no—
356#1439—111no—
357#1439—111no—
358#1438—111no—
359#1438—111no—
360#1436—111no—
361#1436D1111yescharacteristic, complemented
362C22⋊#95—111no—
363C23×C11C23×C411yescharacteristic
364C23×C11C22×D411yescharacteristic
365C23×C11C22×D411yescharacteristic
366C23×C11C22×D411yescharacteristic
367C23×C11C2×#4111yescharacteristic
368C23×C11C2×#4111yescharacteristic
369C23×C11C2×#4111yescharacteristic
370C23×C11H(5,𝔽2)11yescharacteristic
371C23×C11H(5,𝔽2)11yescharacteristic
372C23×C11H(5,𝔽2)11yescharacteristic
373C23×C11H(5,𝔽2)11yescharacteristic
374C23×C11H(5,𝔽2)11yescharacteristic
375C23×C11H(5,𝔽2)11yescharacteristic
376C23×C11H(5,𝔽2)11yescharacteristic
377C23×C112−1+411yescharacteristic
378C22×D11—22no—
379C22×D11—22no—
380C22×D11—22no—
381C22×D11—22no—
382C22×D11—22no—
383C22×D11—22no—
384C22×D11—22no—
385C22×D11—22no—
386C22×D11—22no—
387C22×D11—22no—
388C22×D11—22no—
389C22×D11—22no—
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—22no—
409C22×D11—22no—
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×D11—41no—
425C22×D11—41no—
426C22×D11—41no—
427C22×D11—41no—
428C22×D11—41no—
429C22×D11—41no—
430C22×D11—41no—
431C22×D11—41no—
432C22×D11—41no—
433C22×D11—41no—
434C22×D11—41no—
435C22×D11—41no—
436C22×D11—41no—
437C22×D11—41no—
438C22×D11—41no—
439C22×D11—41no—
440C22×D11—41no—
441C22×D11—41no—
442C22×D11—41no—
443C22×D11—41no—
444C22×D11—41no—
445C22×D11—41no—
446C22×D11—41no—
447C22×D11—41no—
448C22×D11—41no—
449C22×D11—41no—
450C22×D11—41no—
451C22×D11—41no—
452C22×D11—41no—
453C22×D11—41no—
454C22×D11—41no—
455C22×D11—41no—
456C22×D11—41no—
457C22×D11—41no—
458C22×D11—41no—
459C22×D11—41no—
460C22×D11—41no—
461C22×D11—41no—
462C22×D11—41no—
463C22×D11—41no—
464C22×D11—41no—
465C22×D11—41no—
466C22×D11—41no—
467C22×D11—41no—
468C22×D11—41no—
469C22×D11—41no—
470C22×D11—41no—
471C22×D11—41no—
472C22×D11—41no—
473C22×D11—41no—
474C22×D11—41no—
475C22×D11—41no—
476C22×D11—41no—
477C22×D11—41no—
478C22×D11—41no—
479C22×D11—41no—
480C22×D11—41no—
481C22×D11—41no—
482C22×D11C4×D414yes—
483C2×C4×C11—22no—
484C2×C4×C11—22no—
485C2×C4×C11—22no—
486C2×C4×C11—22no—
487C2×C4×C11—22no—
488C2×C4×C11—22no—
489C2×C4×C11—22no—
490C2×C4×C11—22no—
491C2×C4×C11—22no—
492C2×C4×C11—22no—
493C2×C4×C11—22no—
494C2×C4×C11—22no—
495C2×C4×C11—22no—
496C2×C4×C11—22no—
497C2×C4×C11—22no—
498C2×C4×C11—22no—
499C2×C4×C11—22no—
500C2×C4×C11—22no—
501C2×C4×C11—22no—
502C2×C4×C11—22no—
503C2×C4×C11—22no—
504C2×C4×C11—22no—
505C2×C4×C11—22no—
506C2×C4×C11—22no—
507C2×C4×C11—41no—
508C2×C4×C11—41no—
509C2×C4×C11—41no—
510C2×C4×C11—41no—
511C2×C4×C11—41no—
512C2×C4×C11—41no—
513C2×C4×C11—41no—
514C2×C4×C11—41no—
515C2×C4×C11—41no—
516C2×C4×C11—41no—
517C2×C4×C11—41no—
518C2×C4×C11—41no—
519C2×C4×C11—41no—
520C2×C4×C11—41no—
521C2×C4×C11—41no—
522C2×C4×C11—41no—
523C2×C4×C11—41no—
524C2×C4×C11—41no—
525C2×C4×C11—41no—
526C2×C4×C11—41no—
527C2×C4×C11—41no—
528C2×C4×C11—41no—
529C2×C4×C11—41no—
530C2×C4×C11C4×D414yes—
531C2×C4×C11C4×D414yes—
532C2×Dic11—22no—
533C2×Dic11—22no—
534C2×Dic11—22no—
535C2×Dic11—22no—
536C2×Dic11—22no—
537C2×Dic11—22no—
538C2×Dic11—22no—
539C2×Dic11—22no—
540C2×Dic11—22no—
541C2×Dic11—22no—
542C2×Dic11—22no—
543C2×Dic11—22no—
544C2×Dic11—41no—
545C2×Dic11—41no—
546C2×Dic11—41no—
547C2×Dic11—41no—
548C2×Dic11—41no—
549C2×Dic11—41no—
550C2×Dic11—41no—
551C2×Dic11—41no—
552C2×Dic11—41no—
553C2×Dic11—41no—
554C2×Dic11—41no—
555C2×Dic11—41no—
556C2×Dic11—41no—
557C2×Dic11—41no—
558C2×Dic11—41no—
559C2×Dic11—41no—
560C2×Dic11—41no—
561C2×Dic11—41no—
562C2×Dic11—41no—
563C2×Dic11—41no—
564C2×Dic11—41no—
565C2×Dic11—41no—
566C2×Dic11—41no—
567D44—416no—
568D44—416no—
569D44—416no—
570C4×D11—416no—
571C23×D4—111no—
572C23×D4—111no—
573C23×D4—111no—
574C24×C4—111no—
575C22×C4⋊C4—111no—
576C22×C4⋊C4—111no—
577C22×C4⋊C4C2×D1111yescharacteristic
578C22×C22⋊C4—111no—
579C22×C22⋊C4—111no—
580C22×C22⋊C4—111no—
581C22×C22⋊C4—111no—
582C22×C22⋊C4—111no—
583C22×C22⋊C4—111no—
584C22×C22⋊C4—111no—
585C22×C22⋊C4—111no—
586C22×C22⋊C4—111no—
587C22×C22⋊C4—111no—
588C22×C22⋊C4—111no—
589C22×C22⋊C4—111no—
590C22×C22⋊C4—111no—
591C22×C22⋊C4—111no—
592C22×C42—111no—
593C22×C42C2×D1111yescharacteristic
594#392—118no—
595#390—224no—
596#390—224no—
597#388—224no—
598#388—224no—
599#386—224no—
600#386—224no—
601C2×#95—111no—
602C2×#95—111no—
603C2×#95—111no—
604C2×#95—111no—
605C2×#95—111no—
606C2×#95—111no—
607C2×#95—111no—
608C2×#95C2×D1111yescharacteristic
609C2×#95C2×D1111yescharacteristic
610C2×#95C2×D1111yescharacteristic
611C2×#95C2×D1111yescharacteristic
612C2×#95C2×D1111yescharacteristic
613C22×C11C2×C4×D411yescharacteristic
614C22×C11C2×C4×D411yescharacteristic
615C22×C11C2×C4×D411yescharacteristic
616C22×C11#51811yescharacteristic
617C22×C11#51811yescharacteristic
618C22×C11#51811yescharacteristic
619C22×C11#52011yescharacteristic
620C22×C11#53411yescharacteristic
621C22×C11#53511yescharacteristic
622C22×C11#53511yescharacteristic
623C22×C11#53711yescharacteristic
624C22×C11#53711yescharacteristic
625C22×C11#53711yescharacteristic
626C22×C11#53811yescharacteristic
627C22×C11#53911yescharacteristic
628C22×C11#54011yescharacteristic
629C22×C11#54011yescharacteristic
630C22×C11#54211yescharacteristic
631C22×C11#54211yescharacteristic
632C22×C11D4211yescharacteristic
633C22×C11D4211yescharacteristic
634C22×C11D4211yescharacteristic
635C22×C11#54611yescharacteristic
636C22×C11#54611yescharacteristic
637C22×C11#54611yescharacteristic
638C22×C11#54611yescharacteristic
639C22×C11#55011yescharacteristic
640C22×C11#55011yescharacteristic
641C22×C11#55111yescharacteristic
642C22×C11#55111yescharacteristic
643C22×C11#55911yescharacteristic
644C22×C11#56011yescharacteristic
645C22×C11#56011yescharacteristic
646C22×C11#56011yescharacteristic
647C22×C11H(3,𝔽4)11yescharacteristic
648C2×D11—24no—
649C2×D11—24no—
650C2×D11—24no—
651C2×D11—42no—
652C2×D11—42no—
653C2×D11—42no—
654C2×D11—42no—
655C2×D11—42no—
656C2×D11—42no—
657C2×D11—42no—
658C2×D11—42no—
659C2×D11—42no—
660C2×D11—42no—
661C2×D11—42no—
662C2×D11—42no—
663C2×D11—42no—
664C2×D11—42no—
665C2×D11—42no—
666C2×D11—42no—
667C2×D11—42no—
668C2×D11—42no—
669C2×D11—42no—
670C2×D11—42no—
671C2×D11—42no—
672C2×D11—42no—
673C2×D11—42no—
674C2×D11—42no—
675C2×D11—42no—
676C2×D11—42no—
677C2×D11—81no—
678C2×D11—81no—
679C2×D11—81no—
680C2×D11—81no—
681C2×D11—81no—
682C2×D11—81no—
683C2×D11—81no—
684C2×D11—81no—
685C2×D11—81no—
686C2×D11—81no—
687C2×D11—81no—
688C2×D11—81no—
689C2×D11—81no—
690C2×D11—81no—
691C2×D11—81no—
692C2×D11—81no—
693C4×C11—24no—
694C4×C11—24no—
695C4×C11—42no—
696C4×C11—42no—
697C4×C11—42no—
698C4×C11—42no—
699C4×C11—81no—
700Dic11—42no—
701Dic11—42no—
702Dic11—42no—
703Dic11—42no—
704Dic11—81no—
705C25—111no—
706C25—111no—
707C25—111no—
708C22×D4—114no—
709C22×D4—114no—
710C22×D4—114no—
711C22×D4—222no—
712C22×D4—222no—
713C22×D4—222no—
714C22×D4—222no—
715C22×D4—222no—
716C22×D4—222no—
717C22×D4—222no—
718C22×D4—222no—
719C22×D4—441no—
720C22×D4—441no—
721C22×D4—441no—
722C22×D4—441no—
723C22×D4—441no—
724C22×D4—441no—
725C22×D4—441no—
726C22×D4—441no—
727C22×D4—441no—
728C22×D4—441no—
729C23×C4—111no—
730C23×C4—111no—
731C23×C4—111no—
732C23×C4—111no—
733C23×C4—111no—
734C23×C4—222no—
735C23×C4—222no—
736C23×C4—222no—
737C23×C4—441no—
738C23×C4—441no—
739C23×C4—441no—
740C23×C4—441no—
741C23×C4C22×D1111yescharacteristic
742C23×C4C22×D1111yescharacteristic
743C23×C4C22×D1111yescharacteristic
744C23×C4C22×D1111yescharacteristic
745C23×C4C22×D1111yescharacteristic
746C23×C4C22×D1111yescharacteristic
747C23×C4C22×D1111yescharacteristic
748C2×C4⋊C4—22no—
749C2×C4⋊C4—22no—
750C2×C4⋊C4—41no—
751C2×C4⋊C4—222no—
752C2×C4⋊C4—222no—
753C2×C4⋊C4—222no—
754C2×C4⋊C4—222no—
755C2×C4⋊C4—441no—
756C2×C4⋊C4—441no—
757C2×C22⋊C4—114no—
758C2×C22⋊C4—114no—
759C2×C22⋊C4—114no—
760C2×C22⋊C4—114no—
761C2×C22⋊C4—222no—
762C2×C22⋊C4—222no—
763C2×C22⋊C4—222no—
764C2×C22⋊C4—222no—
765C2×C22⋊C4—222no—
766C2×C22⋊C4—222no—
767C2×C22⋊C4—222no—
768C2×C22⋊C4—222no—
769C2×C22⋊C4—222no—
770C2×C22⋊C4—222no—
771C2×C22⋊C4—222no—
772C2×C22⋊C4—222no—
773C2×C22⋊C4—222no—
774C2×C22⋊C4—222no—
775C2×C22⋊C4—222no—
776C2×C22⋊C4—222no—
777C2×C22⋊C4—222no—
778C2×C22⋊C4—222no—
779C2×C22⋊C4—222no—
780C2×C22⋊C4—222no—
781C2×C22⋊C4—441no—
782C2×C22⋊C4—441no—
783C2×C22⋊C4—441no—
784C2×C22⋊C4—441no—
785C2×C22⋊C4—441no—
786C2×C22⋊C4—441no—
787C2×C22⋊C4—441no—
788C2×C22⋊C4—441no—
789C2×C22⋊C4—441no—
790C2×C22⋊C4—441no—
791C2×C22⋊C4—441no—
792C2×C22⋊C4—441no—
793C2×C22⋊C4—441no—
794C2×C22⋊C4—441no—
795C2×C22⋊C4—441no—
796C2×C22⋊C4—441no—
797C2×C22⋊C4—441no—
798C2×C22⋊C4—441no—
799C2×C42—22no—
800C2×C42—22no—
801C2×C42—41no—
802C2×C42—222no—
803C2×C42—222no—
804C2×C42—441no—
805#95—22no—
806#95—41no—
807#95—41no—
808#95—114no—
809#95—222no—
810#95—222no—
811#95—222no—
812#95—441no—
813#95—441no—
814#95—441no—
815#95C4×D1114yescomplemented
816#95D4414yescomplemented
817C2×C11#232411yescharacteristic
818C2×C11#232411yescharacteristic
819C2×C11#232511yescharacteristic
820C2×C11#235811yescharacteristic
821C2×C11#235811yescharacteristic
822C2×C11#236611yescharacteristic
823C2×C11#237511yescharacteristic
824C2×C11#267011yescharacteristic
825C2×C11#267311yescharacteristic
826C2×C11#267311yescharacteristic
827C2×C11#267511yescharacteristic
828C2×C11#270511yescharacteristic
829C2×C11#270511yescharacteristic
830C2×C11#271211yescharacteristic
831C2×C11#275211yescharacteristic
832D11—44no—
833D11—82no—
834D11—82no—
835C24—112no—
836C24—112no—
837C24—112no—
838C24—112no—
839C24—112no—
840C24—221no—
841C24—221no—
842C24—221no—
843C24—221no—
844C24—221no—
845C24—221no—
846C24—221no—
847C24—221no—
848C24—221no—
849C24—221no—
850C24—221no—
851C24—221no—
852C24—221no—
853C24—221no—
854C24—221no—
855C24—221no—
856C24—221no—
857C24—221no—
858C24—221no—
859C24—221no—
860C24—221no—
861C24—221no—
862C24—221no—
863C24—221no—
864C24—221no—
865C24—221no—
866C24—221no—
867C24—221no—
868C24—221no—
869C24—221no—
870C24—221no—
871C24—221no—
872C24—221no—
873C24—221no—
874C24—221no—
875C24—221no—
876C24—221no—
877C24—221no—
878C24—221no—
879C24—221no—
880C24C23×D1111yescharacteristic
881C2×D4—228no—
882C2×D4—228no—
883C2×D4—228no—
884C2×D4—228no—
885C2×D4—444no—
886C2×D4—444no—
887C2×D4—444no—
888C2×D4—444no—
889C2×D4—444no—
890C2×D4—444no—
891C2×D4—444no—
892C2×D4—444no—
893C2×D4—444no—
894C2×D4—444no—
895C2×D4—444no—
896C2×D4—444no—
897C2×D4—444no—
898C2×D4—444no—
899C2×D4—444no—
900C2×D4—444no—
901C2×D4—444no—
902C22×C4—21no—
903C22×C4—21no—
904C22×C4—21no—
905C22×C4—21no—
906C22×C4—21no—
907C22×C4—21no—
908C22×C4—21no—
909C22×C4—21no—
910C22×C4—21no—
911C22×C4—21no—
912C22×C4—21no—
913C22×C4—21no—
914C22×C4—21no—
915C22×C4—21no—
916C22×C4—21no—
917C22×C4—21no—
918C22×C4—21no—
919C22×C4—21no—
920C22×C4—21no—
921C22×C4—21no—
922C22×C4—21no—
923C22×C4—21no—
924C22×C4—21no—
925C22×C4—21no—
926C22×C4—21no—
927C22×C4—21no—
928C22×C4—21no—
929C22×C4—21no—
930C22×C4—21no—
931C22×C4—21no—
932C22×C4—21no—
933C22×C4—21no—
934C22×C4—21no—
935C22×C4—21no—
936C22×C4—21no—
937C22×C4—21no—
938C22×C4—21no—
939C22×C4—21no—
940C22×C4—21no—
941C22×C4—112no—
942C22×C4—112no—
943C22×C4—112no—
944C22×C4—112no—
945C22×C4—221no—
946C22×C4—221no—
947C22×C4—221no—
948C22×C4—221no—
949C22×C4—221no—
950C22×C4—221no—
951C22×C4—221no—
952C22×C4—221no—
953C22×C4—221no—
954C22×C4—221no—
955C22×C4—221no—
956C22×C4—221no—
957C22×C4—221no—
958C22×C4—221no—
959C22×C4—221no—
960C22×C4—221no—
961C22×C4—221no—
962C22×C4—221no—
963C22×C4—221no—
964C22×C4—221no—
965C22×C4—221no—
966C22×C4—221no—
967C22×C4—221no—
968C22×C4—221no—
969C22×C4—221no—
970C22×C4—221no—
971C22×C4—221no—
972C22×C4—221no—
973C22×C4—221no—
974C22×C4—221no—
975C22×C4—221no—
976C22×C4—444no—
977C22×C4—444no—
978C22×C4—444no—
979C22×C4—444no—
980C22×C4—444no—
981C22×C4—444no—
982C22×C4—444no—
983C22×C4C2×C4×D1112yes—
984C22×C4C2×C4×D1112yes—
985C22×C4C2×C4×D1112yes—
986C22×C4C2×D4412yes—
987C22×C4C2×D4412yes—
988C22×C4C2×D4412yes—
989C22×C4#433912yes—
990C22×C4D4×D1112yes—
991C22×C4D4×D1112yes—
992C22×C4#434312yes—
993C4⋊C4—44no—
994C4⋊C4—444no—
995C4⋊C4—444no—
996C22⋊C4—228no—
997C22⋊C4—228no—
998C22⋊C4—444no—
999C22⋊C4—444no—
1000C22⋊C4—444no—
1001C22⋊C4—444no—
1002C22⋊C4—444no—
1003C22⋊C4—444no—
1004C22⋊C4—444no—
1005C22⋊C4—444no—
1006C22⋊C4—444no—
1007C22⋊C4—444no—
1008C22⋊C4—444no—
1009C22⋊C4—444no—
1010C42—44no—
1011C42—444no—
1012C11#1452111yescharacteristic, complemented, Sylow
1013C23—114no—
1014C23—222no—
1015C23—222no—
1016C23—222no—
1017C23—222no—
1018C23—222no—
1019C23—222no—
1020C23—222no—
1021C23—222no—
1022C23—222no—
1023C23—222no—
1024C23—222no—
1025C23—222no—
1026C23—222no—
1027C23—222no—
1028C23—222no—
1029C23—222no—
1030C23—222no—
1031C23—222no—
1032C23—222no—
1033C23—222no—
1034C23—222no—
1035C23—222no—
1036C23—222no—
1037C23—222no—
1038C23—222no—
1039C23—222no—
1040C23—222no—
1041C23—222no—
1042C23—222no—
1043C23—222no—
1044C23—222no—
1045C23—222no—
1046C23—441no—
1047C23—441no—
1048C23—441no—
1049C23—441no—
1050C23—441no—
1051C23—441no—
1052C23—441no—
1053C23—441no—
1054C23—441no—
1055C23—441no—
1056C23—441no—
1057C23—441no—
1058C23—441no—
1059C23—441no—
1060C23—441no—
1061C23—441no—
1062C23—441no—
1063C23—441no—
1064C23—441no—
1065C23—441no—
1066C23—441no—
1067C23—441no—
1068C23—441no—
1069C23—441no—
1070C23—441no—
1071C23—441no—
1072C23—441no—
1073C23—441no—
1074C23—441no—
1075C23—441no—
1076C23—441no—
1077C23—441no—
1078C23—441no—
1079C23—441no—
1080C23—441no—
1081C23—441no—
1082C23—441no—
1083C23—441no—
1084C23—441no—
1085C23—441no—
1086C23—441no—
1087C23—441no—
1088C23—441no—
1089C23—441no—
1090C23—441no—
1091C23—441no—
1092C23—441no—
1093C23—441no—
1094C23—441no—
1095C23—441no—
1096C23—441no—
1097C23—441no—
1098C23—441no—
1099C23—441no—
1100C23—441no—
1101C23—441no—
1102C23—441no—
1103C23—441no—
1104C23—441no—
1105C23—441no—
1106C23—441no—
1107C23—441no—
1108C23—441no—
1109C23—441no—
1110C23—441no—
1111C23—441no—
1112C23—441no—
1113C23—441no—
1114C23—441no—
1115C23—441no—
1116C23—441no—
1117C23—441no—
1118C23C22×C4×D1111yescharacteristic
1119C23C22×D4411yescharacteristic
1120C23C2×#433911yescharacteristic
1121C23C2×D4×D1111yescharacteristic
1122C23C2×D4×D1111yescharacteristic
1123C23#6703711yescharacteristic
1124C23#6703711yescharacteristic
1125C23C2×#434311yescharacteristic
1126C23#6704011yescharacteristic
1127C23#41×D1111yescharacteristic
1128C23#6704211yescharacteristic
1129C23#6704211yescharacteristic
1130C23#6704211yescharacteristic
1131C23#6704211yescharacteristic
1132C23#6704211yescharacteristic
1133D4—4416no—
1134D4—4416no—
1135D4—4416no—
1136C2×C4—22no—
1137C2×C4—22no—
1138C2×C4—22no—
1139C2×C4—22no—
1140C2×C4—22no—
1141C2×C4—22no—
1142C2×C4—22no—
1143C2×C4—22no—
1144C2×C4—22no—
1145C2×C4—22no—
1146C2×C4—22no—
1147C2×C4—22no—
1148C2×C4—22no—
1149C2×C4—22no—
1150C2×C4—22no—
1151C2×C4—22no—
1152C2×C4—22no—
1153C2×C4—22no—
1154C2×C4—22no—
1155C2×C4—22no—
1156C2×C4—22no—
1157C2×C4—22no—
1158C2×C4—22no—
1159C2×C4—22no—
1160C2×C4—41no—
1161C2×C4—41no—
1162C2×C4—41no—
1163C2×C4—41no—
1164C2×C4—41no—
1165C2×C4—41no—
1166C2×C4—41no—
1167C2×C4—41no—
1168C2×C4—41no—
1169C2×C4—41no—
1170C2×C4—41no—
1171C2×C4—41no—
1172C2×C4—41no—
1173C2×C4—41no—
1174C2×C4—41no—
1175C2×C4—41no—
1176C2×C4—41no—
1177C2×C4—41no—
1178C2×C4—41no—
1179C2×C4—41no—
1180C2×C4—41no—
1181C2×C4—41no—
1182C2×C4—41no—
1183C2×C4—222no—
1184C2×C4—222no—
1185C2×C4—222no—
1186C2×C4—222no—
1187C2×C4—222no—
1188C2×C4—222no—
1189C2×C4—222no—
1190C2×C4—222no—
1191C2×C4—222no—
1192C2×C4—222no—
1193C2×C4—222no—
1194C2×C4—222no—
1195C2×C4—4416no—
1196C2×C4—441no—
1197C2×C4—441no—
1198C2×C4—441no—
1199C2×C4—441no—
1200C2×C4—441no—
1201C2×C4—441no—
1202C2×C4—441no—
1203C2×C4—441no—
1204C2×C4—441no—
1205C2×C4—441no—
1206C2×C4—441no—
1207C2×C4—441no—
1208C2×C4—441no—
1209C2×C4—441no—
1210C2×C4—441no—
1211C2×C4—441no—
1212C2×C4—441no—
1213C2×C4—441no—
1214C2×C4—441no—
1215C2×C4—441no—
1216C2×C4—441no—
1217C2×C4—441no—
1218C2×C4—441no—
1219C2×C4C4×D4414yes—
1220C2×C4#6694614yes—
1221C22—224no—
1222C22—224no—
1223C22—224no—
1224C22—442no—
1225C22—442no—
1226C22—442no—
1227C22—442no—
1228C22—442no—
1229C22—442no—
1230C22—442no—
1231C22—442no—
1232C22—442no—
1233C22—442no—
1234C22—442no—
1235C22—442no—
1236C22—442no—
1237C22—442no—
1238C22—442no—
1239C22—442no—
1240C22—442no—
1241C22—442no—
1242C22—442no—
1243C22—442no—
1244C22—442no—
1245C22—442no—
1246C22—442no—
1247C22—442no—
1248C22—442no—
1249C22—442no—
1250C22—881no—
1251C22—881no—
1252C22—881no—
1253C22—881no—
1254C22—881no—
1255C22—881no—
1256C22—881no—
1257C22—881no—
1258C22—881no—
1259C22—881no—
1260C22—881no—
1261C22—881no—
1262C22—881no—
1263C22—881no—
1264C22—881no—
1265C22—881no—
1266C22C2×C4×D4411yescharacteristic
1267C22#1062302111yescharacteristic
1268C22C2×#6694611yescharacteristic
1269C22#1062304111yescharacteristic
1270C22#1062305211yescharacteristic
1271C22#1062305611yescharacteristic
1272C22#1062305811yescharacteristic
1273C22C4×D4×D1111yescharacteristic
1274C22#1062307611yescharacteristic
1275C22#1062307611yescharacteristic
1276C22D4×D4411yescharacteristic
1277C22D4×D4411yescharacteristic
1278C22#1062308411yescharacteristic
1279C22#1062308511yescharacteristic
1280C22#1062309311yescharacteristic
1281C22#1062310511yescharacteristic
1282C22#1062310811yescharacteristic
1283C22#1062311311yescharacteristic
1284C22#1062311611yescharacteristic
1285C22#1062312111yescharacteristic
1286C22#1062313811yescharacteristic
1287C22#1062315111yescharacteristic
1288C22#1062316011yescharacteristic
1289C22#1062316011yescharacteristic
1290C22#1062316111yescharacteristic
1291C22#1062316811yescharacteristic
1292C22#1062318411yescharacteristic
1293C22#1062318511yescharacteristic
1294C22#1062319711yescharacteristic
1295C22#1062321411yescharacteristic
1296C22#1062322311yescharacteristic
1297C22#1062322911yescharacteristic
1298C22#1062323511yescharacteristic
1299C22#1062324211yescharacteristic
1300C22#1062326411yescharacteristic
1301C4—24no—
1302C4—24no—
1303C4—42no—
1304C4—42no—
1305C4—42no—
1306C4—42no—
1307C4—81no—
1308C4—442no—
1309C4—442no—
1310C4—442no—
1311C4—442no—
1312C4—881no—
1313C2—444no—
1314C2—882no—
1315C2—882no—
1316C2#1307130711yescharacteristic
1317C2#1307131011yescharacteristic
1318C2#1307131511yescharacteristic
1319C2#1307159211yescharacteristic
1320C2#1307159811yescharacteristic
1321C2#1307168011yescharacteristic
1322C2#1307175611yescharacteristic
1323C2#1307484011yescharacteristic
1324C2#1307488511yescharacteristic
1325C2#1307488611yescharacteristic
1326C2#1307490711yescharacteristic
1327C2#1307528711yescharacteristic
1328C2#1307529011yescharacteristic
1329C2#1307538611yescharacteristic
1330C2#1307587911yescharacteristic
subgroupG/H
center, FrattiniC24C23×D11
commutatorC23×C11C23×C4
FittingC11×#1436C2
socle, cosocleC24×C11C24
prime radicalC2×#10622284C2
hypercenter#1436D11
hypocenterC11#14521
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ #1436

Complements

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

NH ≅ G/Ntype
2. C2×#10622552C2semidirect
3. C2×#10622601C2semidirect
4. C2×#10622553C2semidirect
5. C2×#10622282C2semidirect
6. C2×#10622278C2semidirect
7. C2×#10622278C2semidirect
8. #13066862C2semidirect
9. #13066860C2semidirect
10. #13066858C2semidirect
11. #13066856C2semidirect
12. #13066856C2semidirect
13. #13066850C2semidirect
14. (C2×D11)⋊#95C2semidirect
15. C11×#1436C2semidirect
54. #10622284C4semidirect
93. C22×D44C2×C4semidirect
146. C2×(C2×D11)⋊C4C2×C4semidirect
147. C2×(C2×D11)⋊C4C2×C4semidirect
148. C2×(C2×D11)⋊C4D4semidirect
161. C11×#95C2×C4semidirect
162. C11×#95D4semidirect
169. C11⋊#95D4semidirect
361. #1436D11semidirect
815. #95C4×D11semidirect
816. #95D44semidirect
1012. C11#14521semidirect

Maximal subgroups

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

subgroupindex
C2×#106222842
C2×#106225522
C2×#106226012
C2×#106225532
C2×#106222822
C2×#106222782
#130668622
#130668602
#130668582
#130668562
#130668502
(C2×D11)⋊#952
C11×#14362
#1452111