Finite Group Databasebeta

← #14681917

Subgroups — #14681917

Order 2816.

2386 conjugacy classes of subgroups.

The subgroup lattice has 1334 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#66948C211yesmaximal, characteristic
2C2×#10622552C211yesmaximal, characteristic, complemented
3C2×#10622601C211yesmaximal, characteristic, complemented
4C2×#10622594C211yesmaximal, characteristic, complemented
5#13066862C211yesmaximal, characteristic, complemented
6#13066858C211yesmaximal, characteristic, complemented
7#13066856C211yesmaximal, characteristic, complemented
8#13066856C211yesmaximal, characteristic, complemented
9#13066856C211yesmaximal, characteristic, complemented
10#13066856C211yesmaximal, characteristic, complemented
11#13066854C211yesmaximal, characteristic, complemented
12#13066852C211yesmaximal, characteristic, complemented
13(C2×D11)⋊#95C211yesmaximal, characteristic, complemented
14(C2×D11)⋊#95C211yesmaximal, characteristic, complemented
15C2×C11×#387C211yesmaximal, characteristic, complemented
16C23×D44C2211yescharacteristic
17C23×D44C2211yescharacteristic
18C23×D44C2211yescharacteristic
19C23×C4×D11C2211yescharacteristic
20C22×C11×C4⋊C4C2211yescharacteristic
21C22×C11×C4⋊C4C2211yescharacteristic
22C22×C42×C11C2211yescharacteristic
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×(C2×D11)⋊C4C2211yescharacteristic
37C22×C4⋊Dic11C2211yescharacteristic
38C22×C4×Dic11C2211yescharacteristic
39C2×#66948—24no—
40C2×#66948—24no—
41C2×#66948C418yescomplemented
42C11×#387—24no—
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#10622601—24no—
56#10622594—24no—
57#10622552—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—22no—
82C22×D44—22no—
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×C414yes—
94C22×C4×D11—22no—
95C22×C4×D11—22no—
96C22×C4×D11—41no—
97C22×C4×D11—41no—
98C22×C4×D11—41no—
99C22×C4×D11—41no—
100C22×C4×D11C2×C414yes—
101C2×C11×C4⋊C4—22no—
102C2×C11×C4⋊C4—22no—
103C2×C11×C4⋊C4—41no—
104C2×C11×C4⋊C4C2×C414yes—
105C2×C11×C4⋊C4D414yes—
106C2×C11×C4⋊C4D414yes—
107C2×C42×C11—22no—
108C2×C42×C11—22no—
109C2×C42×C11—41no—
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)⋊C4—41no—
146C2×(C2×D11)⋊C4—41no—
147C2×(C2×D11)⋊C4—41no—
148C2×(C2×D11)⋊C4—41no—
149C2×(C2×D11)⋊C4C2×C414yes—
150C2×(C2×D11)⋊C4C2×C414yes—
151C2×(C2×D11)⋊C4D414yescomplemented
152C2×C4⋊Dic11—22no—
153C2×C4⋊Dic11—22no—
154C2×C4⋊Dic11—41no—
155C2×C4×Dic11—22no—
156C2×C4×Dic11—22no—
157C2×C4×Dic11—41no—
158#66948—232no—
159C11×#95—22no—
160C11×#95—22no—
161C11×#95—22no—
162C11×#95—22no—
163C11⋊#95—22no—
164C11⋊#95—22no—
165C11⋊#95—22no—
166C11⋊#95—22no—
167C11⋊#95—41no—
168C11⋊#95—41no—
169C11⋊#95—41no—
170C11⋊#95—41no—
171#14418—111nomaximal, Sylow
172C24×C11C2411yescharacteristic
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×D11—21no—
213C23×D11C22×C412yes—
214C23×D11C22×C412yes—
215C23×D11C22×C412yes—
216C23×D11C2×D412yes—
217C23×D11#4112yes—
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×C11C2×D412yes—
265C22×C4×C11C2×D412yes—
266C22×C4×C11#4112yes—
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×Dic11—21no—
298C22×Dic11—21no—
299C22×Dic11C22×C412yes—
300C22×Dic11C2×D412yes—
301C22×Dic11#4112yes—
302C2×D44—28no—
303C2×D44—28no—
304C2×D44—28no—
305C2×D44—28no—
306C2×D44—28no—
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×D44—44no—
323C2×C4×D11—28no—
324C2×C4×D11—44no—
325C2×C4×D11—44no—
326C2×C4×D11—44no—
327C2×C4×D11—44no—
328C2×C4×D11—44no—
329C2×C4×D11—44no—
330C11×C4⋊C4—44no—
331C11×C4⋊C4C22⋊C4116yescomplemented
332C42×C11—44no—
333(C2×D11)⋊C4—28no—
334(C2×D11)⋊C4—28no—
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—
345(C2×D11)⋊C4—44no—
346(C2×D11)⋊C4—44no—
347C4⋊Dic11—44no—
348C4×Dic11—44no—
349C22×#121—111no—
350C2×#390—111no—
351C2×#390—111no—
352C2×#387—111no—
353C2×#387D1111yescharacteristic, complemented
354#1439—111no—
355#1439—111no—
356#1438—111no—
357#1438—111no—
358#1438—111no—
359#1438—111no—
360#1437—111no—
361#1437—111no—
362C22⋊#95—111no—
363C22⋊#95—111no—
364C23×C11C23×C411yescharacteristic
365C23×C11C22×D411yescharacteristic
366C23×C11C22×D411yescharacteristic
367C23×C11C22×D411yescharacteristic
368C23×C11C2×#4111yescharacteristic
369C23×C11C2×#4111yescharacteristic
370C23×C11C2×#4111yescharacteristic
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×C11H(5,𝔽2)11yescharacteristic
378C23×C112−1+411yescharacteristic
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—22no—
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×D11—41no—
483C22×D11C4×D414yes—
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—22no—
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×C11C2×C22⋊C414yes—
531C2×C4×C11C2×C22⋊C414yes—
532C2×C4×C11C2×C22⋊C414yes—
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—41no—
543C2×Dic11—41no—
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—
567C2×Dic11—41no—
568D44—416no—
569D44—416no—
570D44—416no—
571C4×D11—416no—
572C23×D4—111no—
573C23×D4—111no—
574C23×D4—111no—
575C24×C4—111no—
576C2×#121—118no—
577C2×#121—224no—
578C2×#121—224no—
579C22×C4⋊C4—111no—
580C22×C4⋊C4C2×D1111yescharacteristic
581C22×C4⋊C4C2×D1111yescharacteristic
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×C22⋊C4—111no—
593C22×C22⋊C4—111no—
594C22×C22⋊C4—111no—
595C22×C22⋊C4—111no—
596C22×C42—111no—
597C22×C42C2×D1111yescharacteristic
598#390—224no—
599#390—224no—
600#387—24no—
601#387—224no—
602C2×#95—111no—
603C2×#95—111no—
604C2×#95—111no—
605C2×#95—111no—
606C2×#95—111no—
607C2×#95—111no—
608C2×#95—111no—
609C2×#95—111no—
610C2×#95C2×D1111yescharacteristic
611C2×#95C2×D1111yescharacteristic
612C2×#95C2×D1111yescharacteristic
613C2×#95C2×D1111yescharacteristic
614C22×C11C22×C22⋊C411yescharacteristic
615C22×C11C2×C4×D411yescharacteristic
616C22×C11C4×#4111yescharacteristic
617C22×C11#51811yescharacteristic
618C22×C11#51811yescharacteristic
619C22×C11#51811yescharacteristic
620C22×C11#52011yescharacteristic
621C22×C11#53411yescharacteristic
622C22×C11#53511yescharacteristic
623C22×C11#53511yescharacteristic
624C22×C11#53511yescharacteristic
625C22×C11#53511yescharacteristic
626C22×C11#53711yescharacteristic
627C22×C11#53811yescharacteristic
628C22×C11#53811yescharacteristic
629C22×C11#53811yescharacteristic
630C22×C11#53911yescharacteristic
631C22×C11#54011yescharacteristic
632C22×C11#54011yescharacteristic
633C22×C11D4211yescharacteristic
634C22×C11D4211yescharacteristic
635C22×C11#54611yescharacteristic
636C22×C11#54611yescharacteristic
637C22×C11#54611yescharacteristic
638C22×C11#54611yescharacteristic
639C22×C11#54811yescharacteristic
640C22×C11#54811yescharacteristic
641C22×C11#55011yescharacteristic
642C22×C11#55011yescharacteristic
643C22×C11#55311yescharacteristic
644C22×C11#55311yescharacteristic
645C22×C11#56011yescharacteristic
646C22×C11#56011yescharacteristic
647C22×C11#56211yescharacteristic
648C22×C11#56211yescharacteristic
649C2×D11—24no—
650C2×D11—24no—
651C2×D11—24no—
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—42no—
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—
693C2×D11—81no—
694C4×C11—24no—
695C4×C11—24no—
696C4×C11—24no—
697C4×C11—42no—
698C4×C11—42no—
699C4×C11—81no—
700C4×C11—81no—
701Dic11—42no—
702Dic11—42no—
703Dic11—42no—
704Dic11—81no—
705Dic11—81no—
706C25—111no—
707C25—111no—
708C25—111no—
709C22×D4—114no—
710C22×D4—114no—
711C22×D4—114no—
712C22×D4—222no—
713C22×D4—222no—
714C22×D4—222no—
715C22×D4—222no—
716C22×D4—222no—
717C22×D4—222no—
718C22×D4—222no—
719C22×D4—222no—
720C22×D4—222no—
721C22×D4—222no—
722C22×D4—441no—
723C22×D4—441no—
724C22×D4—441no—
725C22×D4—441no—
726C22×D4—441no—
727C22×D4—441no—
728C22×D4—441no—
729C22×D4—441no—
730C23×C4—111no—
731C23×C4—111no—
732C23×C4—111no—
733C23×C4—114no—
734C23×C4—111no—
735C23×C4—111no—
736C23×C4—222no—
737C23×C4—222no—
738C23×C4—441no—
739C23×C4—441no—
740C23×C4—441no—
741C23×C4—441no—
742C23×C4C22×D1111yescharacteristic
743C23×C4C22×D1111yescharacteristic
744C23×C4C22×D1111yescharacteristic
745C23×C4C22×D1111yescharacteristic
746C23×C4C22×D1111yescharacteristic
747C23×C4C22×D1111yescharacteristic
748C23×C4C22×D1111yescharacteristic
749#121—2232no—
750C2×C4⋊C4—22no—
751C2×C4⋊C4—22no—
752C2×C4⋊C4—41no—
753C2×C4⋊C4—222no—
754C2×C4⋊C4—222no—
755C2×C4⋊C4—441no—
756C2×C4⋊C4C4×D1114yes—
757C2×C4⋊C4D4414yes—
758C2×C4⋊C4C22⋊D1114yes—
759C2×C22⋊C4—114no—
760C2×C22⋊C4—114no—
761C2×C22⋊C4—114no—
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—441no—
780C2×C22⋊C4—441no—
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×C22⋊C4—441no—
800C2×C22⋊C4—441no—
801C2×C42—22no—
802C2×C42—22no—
803C2×C42—41no—
804C2×C42—222no—
805C2×C42—222no—
806C2×C42—441no—
807#95—22no—
808#95—22no—
809#95—22no—
810#95—22no—
811#95—222no—
812#95—222no—
813#95—222no—
814#95—222no—
815#95—441no—
816#95—441no—
817#95—441no—
818#95—441no—
819C2×C11#230911yescharacteristic
820C2×C11#232511yescharacteristic
821C2×C11#233311yescharacteristic
822C2×C11D4×C22⋊C411yescharacteristic
823C2×C11#234111yescharacteristic
824C2×C11#236411yescharacteristic
825C2×C11#237711yescharacteristic
826C2×C11#267311yescharacteristic
827C2×C11#267311yescharacteristic
828C2×C11#267611yescharacteristic
829C2×C11#267611yescharacteristic
830C2×C11#271111yescharacteristic
831C2×C11#271111yescharacteristic
832C2×C11#271411yescharacteristic
833C2×C11#271411yescharacteristic
834D11—44no—
835D11—82no—
836D11—82no—
837C24—112no—
838C24—112no—
839C24—112no—
840C24—112no—
841C24—112no—
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—
880C24—221no—
881C24—221no—
882C24C23×D1111yescharacteristic
883C2×D4—228no—
884C2×D4—228no—
885C2×D4—228no—
886C2×D4—228no—
887C2×D4—228no—
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—
902C2×D4—444no—
903C2×D4—444no—
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—21no—
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—228no—
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—221no—
977C22×C4—221no—
978C22×C4—444no—
979C22×C4—444no—
980C22×C4—444no—
981C22×C4—444no—
982C22×C4—444no—
983C22×C4—444no—
984C22×C4C2×C4×D1112yes—
985C22×C4C2×C4×D1112yes—
986C22×C4C2×C4×D1112yes—
987C22×C4C2×D4412yes—
988C22×C4C2×D4412yes—
989C22×C4C2×D4412yes—
990C22×C4D4×D1112yes—
991C22×C4#434312yes—
992C22×C4C2×C22⋊D1112yes—
993C22×C4C2×C22⋊D1112yes—
994C22×C4C2×C22⋊D1112yes—
995C4⋊C4—44no—
996C4⋊C4—444no—
997C4⋊C4(C2×D11)⋊C4116yescomplemented
998C22⋊C4—228no—
999C22⋊C4—228no—
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—
1010C22⋊C4—444no—
1011C22⋊C4—444no—
1012C42—44no—
1013C42—444no—
1014C11#1441811yescharacteristic, complemented, Sylow
1015C23—114no—
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—222no—
1047C23—222no—
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—
1118C23—441no—
1119C23—441no—
1120C23C22×C4×D1111yescharacteristic
1121C23C22×D4411yescharacteristic
1122C23C2×D4×D1111yescharacteristic
1123C23#6703711yescharacteristic
1124C23C2×#434311yescharacteristic
1125C23#6704011yescharacteristic
1126C23#41×D1111yescharacteristic
1127C23#41×D1111yescharacteristic
1128C23#6704211yescharacteristic
1129C23#6704211yescharacteristic
1130C23#6704211yescharacteristic
1131C23#6704211yescharacteristic
1132C23#6704211yescharacteristic
1133C23#6704211yescharacteristic
1134C23C22×C22⋊D1111yescharacteristic
1135D4—4416no—
1136D4—4416no—
1137D4—4416no—
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—22no—
1161C2×C4—22no—
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—41no—
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—4416no—
1194C2×C4—441no—
1195C2×C4—441no—
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×C4—441no—
1220C2×C4C2×(C2×D11)⋊C414yes—
1221C2×C4C2×(C2×D11)⋊C414yes—
1222C2×C4C2×(C2×D11)⋊C414yes—
1223C22—224no—
1224C22—224no—
1225C22—224no—
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—442no—
1251C22—442no—
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—
1266C22—881no—
1267C22—881no—
1268C22#1062305211yescharacteristic
1269C22#1062305211yescharacteristic
1270C22#1062305611yescharacteristic
1271C22#1062305611yescharacteristic
1272C22C4×D4×D1111yescharacteristic
1273C22#1062307611yescharacteristic
1274C22D4×D4411yescharacteristic
1275C22#1062308511yescharacteristic
1276C22C4×#434311yescharacteristic
1277C22#1062310511yescharacteristic
1278C22#1062310711yescharacteristic
1279C22#1062310811yescharacteristic
1280C22#1062316011yescharacteristic
1281C22#1062316111yescharacteristic
1282C22#1062317511yescharacteristic
1283C22#1062317811yescharacteristic
1284C22#1062318411yescharacteristic
1285C22#1062318511yescharacteristic
1286C22#1062319411yescharacteristic
1287C22#1062319711yescharacteristic
1288C22#1062322311yescharacteristic
1289C22#1062322611yescharacteristic
1290C22#1062322911yescharacteristic
1291C22#1062323111yescharacteristic
1292C22#1062323511yescharacteristic
1293C22#1062323511yescharacteristic
1294C22#1062324011yescharacteristic
1295C22#1062324211yescharacteristic
1296C22C22×(C2×D11)⋊C411yescharacteristic
1297C22D4×C22⋊D1111yescharacteristic
1298C22#1062334811yescharacteristic
1299C22#1062336011yescharacteristic
1300C22#1062336111yescharacteristic
1301C22#1062336111yescharacteristic
1302C22#1062336511yescharacteristic
1303C4—24no—
1304C4—24no—
1305C4—24no—
1306C4—42no—
1307C4—42no—
1308C4—81no—
1309C4—81no—
1310C4—442no—
1311C4—442no—
1312C4—442no—
1313C4—881no—
1314C4—881no—
1315C2—444no—
1316C2—882no—
1317C2—882no—
1318C2#1307119611yescharacteristic
1319C2#1307131511yescharacteristic
1320C2#1307138011yescharacteristic
1321C2D4×(C2×D11)⋊C411yescharacteristic
1322C2#1307145411yescharacteristic
1323C2#1307166211yescharacteristic
1324C2#1307177111yescharacteristic
1325C2#1307488211yescharacteristic
1326C2#1307488511yescharacteristic
1327C2#1307491311yescharacteristic
1328C2#1307491511yescharacteristic
1329C2#1307536911yescharacteristic
1330C2#1307537111yescharacteristic
1331C2#1307540811yescharacteristic
1332C2#1307541011yescharacteristic
subgroupG/H
center, FrattiniC24C23×D11
commutatorC23×C11C23×C4
FittingC2×C11×#387C2
socle, cosocleC24×C11C24
prime radicalC22×#66948C2
hypercenterC2×#387D11
hypocenterC11#14418
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ C2×#387

Complements

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

NH ≅ G/Ntype
2. C2×#10622552C2semidirect
3. C2×#10622601C2semidirect
4. C2×#10622594C2semidirect
5. #13066862C2semidirect
6. #13066858C2semidirect
7. #13066856C2semidirect
8. #13066856C2semidirect
9. #13066856C2semidirect
10. #13066856C2semidirect
11. #13066854C2semidirect
12. #13066852C2semidirect
13. (C2×D11)⋊#95C2semidirect
14. (C2×D11)⋊#95C2semidirect
15. C2×C11×#387C2semidirect
41. C2×#66948C4semidirect
151. C2×(C2×D11)⋊C4D4semidirect
331. C11×C4⋊C4C22⋊C4semidirect
353. C2×#387D11semidirect
997. C4⋊C4(C2×D11)⋊C4semidirect
1014. C11#14418semidirect

Maximal subgroups

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

subgroupindex
C22×#669482
C2×#106225522
C2×#106226012
C2×#106225942
#130668622
#130668582
#130668562
#130668542
#130668522
(C2×D11)⋊#952
C2×C11×#3872
#1441811