Finite Group Databasebeta

← #14681104

Subgroups — #14681104

Order 2816.

2594 conjugacy classes of subgroups.

The subgroup lattice has 1360 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#66937C211yesmaximal, characteristic
2C2×#10622552C211yesmaximal, characteristic, complemented
3C2×#10622571C211yesmaximal, characteristic, complemented
4C2×#10622571C211yesmaximal, characteristic, complemented
5C2×#10622563C211yesmaximal, characteristic, complemented
6C2×#10622600C211yesmaximal, characteristic, complemented
7#13066870C211yesmaximal, characteristic, complemented
8#13066862C211yesmaximal, characteristic, complemented
9#13066858C211yesmaximal, characteristic, complemented
10#13066856C211yesmaximal, characteristic, complemented
11#13066855C211yesmaximal, characteristic, complemented
12#13066855C211yesmaximal, characteristic, complemented
13#13066849C211yesmaximal, characteristic, complemented
14(C2×D11)⋊#95C211yesmaximal, characteristic, complemented
15C2×C11×#388C211yesmaximal, characteristic, complemented
16C23×C22⋊D11C2211yescharacteristic
17C23×C22⋊D11C2211yescharacteristic
18C24×Dic11C2211yescharacteristic
19C23×D44C2211yescharacteristic
20C23×C4×D11C2211yescharacteristic
21C22×C11×C4⋊C4C2211yescharacteristic
22C22×C11×C22⋊C4C2211yescharacteristic
23C22×C11×C22⋊C4C2211yescharacteristic
24C22×C11×C22⋊C4C2211yescharacteristic
25C22×C42×C11C2211yescharacteristic
26C22×C22⋊Dic11C2211yescharacteristic
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×C4⋊Dic11C2211yescharacteristic
38C22×Dic11⋊C4C2211yescharacteristic
39C2×#66937—24no—
40C2×#66937—24no—
41C2×#66937C418yescomplemented
42C11×#388—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#10622600—24no—
56#10622571—24no—
57#10622571—24no—
58#10622563—24no—
59#10622552—24no—
60C25×C11C2311yescharacteristic
61C24×D11C2311yescharacteristic
62C24×D11C2311yescharacteristic
63C23×C4×C11C2311yescharacteristic
64C23×C4×C11C2311yescharacteristic
65C23×C4×C11C2311yescharacteristic
66C23×C4×C11C2311yescharacteristic
67C23×C4×C11C2311yescharacteristic
68C23×C4×C11C2311yescharacteristic
69C22×C22⋊D11—22no—
70C22×C22⋊D11—22no—
71C22×C22⋊D11—22no—
72C22×C22⋊D11—22no—
73C22×C22⋊D11—22no—
74C22×C22⋊D11—22no—
75C22×C22⋊D11—22no—
76C22×C22⋊D11—22no—
77C22×C22⋊D11—41no—
78C22×C22⋊D11—41no—
79C22×C22⋊D11—41no—
80C22×C22⋊D11—41no—
81C22×C22⋊D11C2×C414yes—
82C22×C22⋊D11C2×C414yes—
83C23×Dic11—22no—
84C23×Dic11—22no—
85C23×Dic11—22no—
86C23×Dic11—41no—
87C23×Dic11—41no—
88C23×Dic11—41no—
89C23×Dic11—41no—
90C23×Dic11C2311yescharacteristic
91C23×Dic11C2311yescharacteristic
92C23×Dic11C2311yescharacteristic
93C23×Dic11C2311yescharacteristic
94C23×Dic11C2311yescharacteristic
95C23×Dic11C2311yescharacteristic
96C22×D44—22no—
97C22×D44—22no—
98C22×D44—22no—
99C22×D44—22no—
100C22×D44—41no—
101C22×D44—41no—
102C22×D44C2×C414yescomplemented
103C22×C4×D11—22no—
104C22×C4×D11—22no—
105C22×C4×D11—22no—
106C22×C4×D11—22no—
107C22×C4×D11—41no—
108C22×C4×D11—41no—
109C22×C4×D11C2×C414yescomplemented
110C2×C11×C4⋊C4—22no—
111C2×C11×C4⋊C4—22no—
112C2×C11×C4⋊C4—41no—
113C2×C11×C22⋊C4—22no—
114C2×C11×C22⋊C4—22no—
115C2×C11×C22⋊C4—22no—
116C2×C11×C22⋊C4—22no—
117C2×C11×C22⋊C4—41no—
118C2×C11×C22⋊C4—41no—
119C2×C11×C22⋊C4C2×C414yes—
120C2×C11×C22⋊C4D414yes—
121C2×C11×C22⋊C4D414yes—
122C2×C42×C11—22no—
123C2×C42×C11—22no—
124C2×C42×C11—41no—
125C2×C22⋊Dic11—22no—
126C2×C22⋊Dic11—41no—
127C2×C22⋊Dic11—41no—
128C2×(C2×D11)⋊C4—22no—
129C2×(C2×D11)⋊C4—22no—
130C2×(C2×D11)⋊C4—22no—
131C2×(C2×D11)⋊C4—22no—
132C2×(C2×D11)⋊C4—22no—
133C2×(C2×D11)⋊C4—22no—
134C2×(C2×D11)⋊C4—22no—
135C2×(C2×D11)⋊C4—22no—
136C2×(C2×D11)⋊C4—22no—
137C2×(C2×D11)⋊C4—22no—
138C2×(C2×D11)⋊C4—22no—
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)⋊C4—41no—
150C2×(C2×D11)⋊C4—41no—
151C2×(C2×D11)⋊C4—41no—
152C2×(C2×D11)⋊C4—41no—
153C2×(C2×D11)⋊C4C2×C414yescomplemented
154C2×(C2×D11)⋊C4D414yescomplemented
155C2×C4⋊Dic11—22no—
156C2×C4⋊Dic11—22no—
157C2×C4⋊Dic11—22no—
158C2×C4⋊Dic11—22no—
159C2×C4⋊Dic11—41no—
160C2×C4⋊Dic11—41no—
161C2×Dic11⋊C4—22no—
162C2×Dic11⋊C4—22no—
163C2×Dic11⋊C4C2×C414yescomplemented
164#66937—232no—
165C11×#95—22no—
166C11×#95—22no—
167C11⋊#95—22no—
168C11⋊#95—22no—
169C11⋊#95—22no—
170C11⋊#95—22no—
171C11⋊#95—22no—
172C11⋊#95—22no—
173C11⋊#95—22no—
174C11⋊#95—41no—
175C11⋊#95—41no—
176C11⋊#95D414yescomplemented
177#14361—111nomaximal, Sylow
178C24×C11—21no—
179C24×C11—21no—
180C24×C11—21no—
181C24×C11—21no—
182C24×C11—21no—
183C24×C11—21no—
184C24×C11—21no—
185C24×C11—21no—
186C24×C11—21no—
187C24×C11—21no—
188C24×C11—21no—
189C24×C11—21no—
190C24×C11C22×C412yes—
191C24×C11C2×D412yes—
192C24×C11C2×D412yes—
193C24×C11C2411yescharacteristic
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×D11—21no—
214C23×D11—21no—
215C23×D11—21no—
216C23×D11—21no—
217C23×D11—21no—
218C23×D11—21no—
219C23×D11—21no—
220C23×D11C22×C412yes—
221C23×D11C22×C412yes—
222C23×D11C2×D412yes—
223C23×D11#4112yes—
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×C11—21no—
257C22×C4×C11—21no—
258C22×C4×C11C22×C412yes—
259C22×C4×C11C22×C412yes—
260C22×C4×C11C2×D412yes—
261C22×C4×C11C2×D412yes—
262C22×C4×C11C2×D412yes—
263C22×C4×C11C2×D412yes—
264C22×C4×C11C2×D412yes—
265C22×C4×C11C2×D412yes—
266C2×C22⋊D11—28no—
267C2×C22⋊D11—28no—
268C2×C22⋊D11—28no—
269C2×C22⋊D11—28no—
270C2×C22⋊D11—44no—
271C2×C22⋊D11—44no—
272C2×C22⋊D11—44no—
273C2×C22⋊D11—44no—
274C2×C22⋊D11—44no—
275C2×C22⋊D11—44no—
276C2×C22⋊D11—44no—
277C2×C22⋊D11—44no—
278C2×C22⋊D11—44no—
279C2×C22⋊D11—44no—
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×Dic11—21no—
300C22×Dic11—21no—
301C22×Dic11—21no—
302C22×Dic11—21no—
303C22×Dic11—21no—
304C22×Dic11—21no—
305C22×Dic11—21no—
306C22×Dic11—21no—
307C22×Dic11—21no—
308C22×Dic11—21no—
309C22×Dic11—21no—
310C22×Dic11—21no—
311C22×Dic11—21no—
312C22×Dic11—21no—
313C22×Dic11—21no—
314C22×Dic11—21no—
315C22×Dic11—21no—
316C22×Dic11—44no—
317C22×Dic11—44no—
318C22×Dic11—44no—
319C22×Dic11—44no—
320C22×Dic11—44no—
321C22×Dic11—44no—
322C22×Dic11—44no—
323C22×Dic11C22×C412yes—
324C22×Dic11C22×C412yes—
325C22×Dic11C2×D412yes—
326C22×Dic11C2×D412yes—
327C22×Dic11C2×D412yes—
328C22×Dic11#4112yes—
329C2×D44—28no—
330C2×D44—28no—
331C2×D44—44no—
332C2×D44—44no—
333C2×D44—44no—
334C2×D44—44no—
335C2×D44—44no—
336C2×C4×D11—28no—
337C2×C4×D11—28no—
338C2×C4×D11—44no—
339C2×C4×D11—44no—
340C2×C4×D11—44no—
341C2×C4×D11—44no—
342C2×C4×D11—44no—
343C11×C4⋊C4—44no—
344C11×C22⋊C4—44no—
345C11×C22⋊C4—44no—
346C11×C22⋊C4C22⋊C4116yescomplemented
347C42×C11—44no—
348C22⋊Dic11—44no—
349(C2×D11)⋊C4—28no—
350(C2×D11)⋊C4—44no—
351(C2×D11)⋊C4—44no—
352(C2×D11)⋊C4—44no—
353(C2×D11)⋊C4—44no—
354(C2×D11)⋊C4—44no—
355(C2×D11)⋊C4—44no—
356(C2×D11)⋊C4—44no—
357(C2×D11)⋊C4—44no—
358C4⋊Dic11—44no—
359C4⋊Dic11—44no—
360Dic11⋊C4—28no—
361C22×#121—111no—
362C2×#390—111no—
363C2×#388D1111yescharacteristic, complemented
364C2×#386—111no—
365C2×#386—111no—
366C2×#385—111no—
367C2×#380—111no—
368#1441—111no—
369#1439—111no—
370#1439—111no—
371#1438—111no—
372#1438—111no—
373#1438—111no—
374#1436—111no—
375C22⋊#95—111no—
376C23×C11—22no—
377C23×C11—22no—
378C23×C11—22no—
379C23×C11—22no—
380C23×C11—22no—
381C23×C11—22no—
382C23×C11—22no—
383C23×C11—22no—
384C23×C11—22no—
385C23×C11—22no—
386C23×C11—22no—
387C23×C11—22no—
388C23×C11—22no—
389C23×C11—22no—
390C23×C11—22no—
391C23×C11—22no—
392C23×C11—22no—
393C23×C11—22no—
394C23×C11—41no—
395C23×C11—41no—
396C23×C11—41no—
397C23×C11—41no—
398C23×C11—41no—
399C23×C11—41no—
400C23×C11—41no—
401C23×C11—41no—
402C23×C11—41no—
403C23×C11—41no—
404C23×C11—41no—
405C23×C11—41no—
406C23×C11—41no—
407C23×C11—41no—
408C23×C11—41no—
409C23×C11—41no—
410C23×C11C2×C22⋊C414yes—
411C23×C11C23×C411yescharacteristic
412C23×C11C22×D411yescharacteristic
413C23×C11C22×D411yescharacteristic
414C23×C11C22×D411yescharacteristic
415C23×C11C22×D411yescharacteristic
416C23×C11C2×#4111yescharacteristic
417C23×C11C2×#4111yescharacteristic
418C23×C11H(5,𝔽2)11yescharacteristic
419C23×C11H(5,𝔽2)11yescharacteristic
420C23×C11H(5,𝔽2)11yescharacteristic
421C23×C11H(5,𝔽2)11yescharacteristic
422C23×C11H(5,𝔽2)11yescharacteristic
423C23×C11H(5,𝔽2)11yescharacteristic
424C23×C112−1+411yescharacteristic
425C23×C112−1+411yescharacteristic
426C22×D11—22no—
427C22×D11—22no—
428C22×D11—22no—
429C22×D11—22no—
430C22×D11—22no—
431C22×D11—22no—
432C22×D11—22no—
433C22×D11—22no—
434C22×D11—22no—
435C22×D11—22no—
436C22×D11—22no—
437C22×D11—22no—
438C22×D11—22no—
439C22×D11—22no—
440C22×D11—22no—
441C22×D11—22no—
442C22×D11—22no—
443C22×D11—22no—
444C22×D11—22no—
445C22×D11—22no—
446C22×D11—22no—
447C22×D11—22no—
448C22×D11—22no—
449C22×D11—22no—
450C22×D11—22no—
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×D11—41no—
484C22×D11—41no—
485C22×D11—41no—
486C22×D11—41no—
487C22×D11—41no—
488C22×D11—41no—
489C22×D11—41no—
490C22×D11—41no—
491C22×D11—41no—
492C22×D11—41no—
493C22×D11—41no—
494C22×D11—41no—
495C22×D11C4×D414yes—
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—22no—
509C2×C4×C11—22no—
510C2×C4×C11—22no—
511C2×C4×C11—22no—
512C2×C4×C11—22no—
513C2×C4×C11—22no—
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×C11—41no—
531C2×C4×C11—41no—
532C2×C4×C11—41no—
533C2×C4×C11—41no—
534C2×C4×C11—41no—
535C2×C4×C11—41no—
536C2×C4×C11C2×C22⋊C414yes—
537C2×C4×C11C2×C22⋊C414yes—
538C22⋊D11—416no—
539C22⋊D11—416no—
540C2×Dic11—22no—
541C2×Dic11—22no—
542C2×Dic11—22no—
543C2×Dic11—22no—
544C2×Dic11—22no—
545C2×Dic11—22no—
546C2×Dic11—22no—
547C2×Dic11—22no—
548C2×Dic11—22no—
549C2×Dic11—22no—
550C2×Dic11—22no—
551C2×Dic11—22no—
552C2×Dic11—22no—
553C2×Dic11—22no—
554C2×Dic11—22no—
555C2×Dic11—416no—
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—
568C2×Dic11—41no—
569C2×Dic11—41no—
570C2×Dic11—41no—
571C2×Dic11—41no—
572C2×Dic11—41no—
573C2×Dic11—41no—
574C2×Dic11—41no—
575C2×Dic11—41no—
576C2×Dic11—41no—
577C2×Dic11—41no—
578C2×Dic11—41no—
579C2×Dic11—41no—
580C2×Dic11—41no—
581C2×Dic11—41no—
582C2×Dic11C4×D414yes—
583D44—416no—
584C4×D11—416no—
585C23×D4—111no—
586C23×D4—111no—
587C23×D4—111no—
588C24×C4—111no—
589C24×C4—111no—
590C2×#121—118no—
591C2×#121—224no—
592C2×#121—224no—
593C22×C4⋊C4—111no—
594C22×C4⋊C4—111no—
595C22×C4⋊C4—111no—
596C22×C4⋊C4C2×D1111yescharacteristic
597C22×C22⋊C4—111no—
598C22×C22⋊C4—111no—
599C22×C22⋊C4—111no—
600C22×C22⋊C4—111no—
601C22×C22⋊C4—111no—
602C22×C22⋊C4—111no—
603C22×C22⋊C4—111no—
604C22×C22⋊C4—111no—
605C22×C22⋊C4—111no—
606C22×C22⋊C4—111no—
607C22×C22⋊C4C2×D1111yescharacteristic
608C22×C22⋊C4C2×D1111yescharacteristic
609C22×C22⋊C4C2×D1111yescharacteristic
610C22×C42C2×D1111yescharacteristic
611#390—224no—
612#388—24no—
613#386—224no—
614#386—224no—
615#385—224no—
616#380—224no—
617C2×#95—111no—
618C2×#95—111no—
619C2×#95—111no—
620C2×#95—111no—
621C2×#95—111no—
622C2×#95—111no—
623C2×#95—111no—
624C2×#95—111no—
625C2×#95—111no—
626C2×#95—111no—
627C2×#95C2×D1111yescharacteristic
628C2×#95C2×D1111yescharacteristic
629C22×C11—24no—
630C22×C11—24no—
631C22×C11—24no—
632C22×C11—42no—
633C22×C11—42no—
634C22×C11—42no—
635C22×C11—42no—
636C22×C11—42no—
637C22×C11—42no—
638C22×C11—42no—
639C22×C11—42no—
640C22×C11—42no—
641C22×C11—42no—
642C22×C11—42no—
643C22×C11—42no—
644C22×C11C22×C22⋊C411yescharacteristic
645C22×C11C2×C4×D411yescharacteristic
646C22×C11C2×C4×D411yescharacteristic
647C22×C11#51811yescharacteristic
648C22×C11#51811yescharacteristic
649C22×C11#52011yescharacteristic
650C22×C11#52011yescharacteristic
651C22×C11#53411yescharacteristic
652C22×C11#53511yescharacteristic
653C22×C11#53511yescharacteristic
654C22×C11#53611yescharacteristic
655C22×C11#53711yescharacteristic
656C22×C11#53711yescharacteristic
657C22×C11#53711yescharacteristic
658C22×C11#53711yescharacteristic
659C22×C11#53811yescharacteristic
660C22×C11#53911yescharacteristic
661C22×C11#54011yescharacteristic
662C22×C11#54211yescharacteristic
663C22×C11D4211yescharacteristic
664C22×C11D4211yescharacteristic
665C22×C11D4211yescharacteristic
666C22×C11D4211yescharacteristic
667C22×C11D4211yescharacteristic
668C22×C11#54611yescharacteristic
669C22×C11#54611yescharacteristic
670C22×C11#54611yescharacteristic
671C22×C11#54611yescharacteristic
672C22×C11#54711yescharacteristic
673C22×C11#54811yescharacteristic
674C22×C11#55311yescharacteristic
675C22×C11#56011yescharacteristic
676C22×C11#56011yescharacteristic
677C22×C11#56211yescharacteristic
678C22×C11#56211yescharacteristic
679C2×D11—24no—
680C2×D11—24no—
681C2×D11—24no—
682C2×D11—42no—
683C2×D11—42no—
684C2×D11—42no—
685C2×D11—42no—
686C2×D11—42no—
687C2×D11—42no—
688C2×D11—42no—
689C2×D11—42no—
690C2×D11—42no—
691C2×D11—42no—
692C2×D11—42no—
693C2×D11—42no—
694C2×D11—42no—
695C2×D11—42no—
696C2×D11—42no—
697C2×D11—42no—
698C2×D11—42no—
699C2×D11—42no—
700C2×D11—42no—
701C2×D11—81no—
702C2×D11—81no—
703C2×D11—81no—
704C2×D11—81no—
705C2×D11—81no—
706C2×D11—81no—
707C2×D11—81no—
708C2×D11—81no—
709C4×C11—24no—
710C4×C11—24no—
711C4×C11—42no—
712C4×C11—42no—
713C4×C11—81no—
714C4×C11—81no—
715Dic11—24no—
716Dic11—42no—
717Dic11—42no—
718Dic11—42no—
719Dic11—81no—
720Dic11—81no—
721C25—111no—
722C25—111no—
723C25C22×D1111yescharacteristic
724C22×D4—114no—
725C22×D4—114no—
726C22×D4—114no—
727C22×D4—222no—
728C22×D4—222no—
729C22×D4—222no—
730C22×D4—222no—
731C22×D4—222no—
732C22×D4—222no—
733C22×D4—222no—
734C22×D4—222no—
735C22×D4—222no—
736C22×D4—222no—
737C22×D4—222no—
738C22×D4—222no—
739C22×D4—441no—
740C22×D4—441no—
741C22×D4—441no—
742C22×D4—441no—
743C22×D4—441no—
744C22×D4—441no—
745C23×C4—111no—
746C23×C4—111no—
747C23×C4—111no—
748C23×C4—111no—
749C23×C4—114no—
750C23×C4—111no—
751C23×C4—111no—
752C23×C4—222no—
753C23×C4—222no—
754C23×C4—222no—
755C23×C4—222no—
756C23×C4—222no—
757C23×C4—222no—
758C23×C4—222no—
759C23×C4—441no—
760C23×C4—441no—
761C23×C4—441no—
762C23×C4—441no—
763C23×C4—441no—
764C23×C4—441no—
765C23×C4C22×D1111yescharacteristic
766C23×C4C22×D1111yescharacteristic
767C23×C4C22×D1111yescharacteristic
768C23×C4C22×D1111yescharacteristic
769C23×C4C22×D1111yescharacteristic
770C23×C4C22×D1111yescharacteristic
771#121—2232no—
772C2×C4⋊C4—22no—
773C2×C4⋊C4—22no—
774C2×C4⋊C4—41no—
775C2×C4⋊C4—114no—
776C2×C4⋊C4—222no—
777C2×C4⋊C4—222no—
778C2×C4⋊C4—222no—
779C2×C4⋊C4—222no—
780C2×C4⋊C4—222no—
781C2×C4⋊C4—222no—
782C2×C4⋊C4—441no—
783C2×C4⋊C4—441no—
784C2×C22⋊C4—22no—
785C2×C22⋊C4—22no—
786C2×C22⋊C4—22no—
787C2×C22⋊C4—22no—
788C2×C22⋊C4—41no—
789C2×C22⋊C4—41no—
790C2×C22⋊C4—114no—
791C2×C22⋊C4—114no—
792C2×C22⋊C4—222no—
793C2×C22⋊C4—222no—
794C2×C22⋊C4—222no—
795C2×C22⋊C4—222no—
796C2×C22⋊C4—222no—
797C2×C22⋊C4—222no—
798C2×C22⋊C4—222no—
799C2×C22⋊C4—222no—
800C2×C22⋊C4—222no—
801C2×C22⋊C4—222no—
802C2×C22⋊C4—222no—
803C2×C22⋊C4—222no—
804C2×C22⋊C4—441no—
805C2×C22⋊C4—441no—
806C2×C22⋊C4—441no—
807C2×C22⋊C4—441no—
808C2×C22⋊C4—441no—
809C2×C22⋊C4—441no—
810C2×C22⋊C4—441no—
811C2×C22⋊C4—441no—
812C2×C22⋊C4—441no—
813C2×C22⋊C4—441no—
814C2×C22⋊C4—441no—
815C2×C22⋊C4—441no—
816C2×C22⋊C4—441no—
817C2×C22⋊C4—441no—
818C2×C22⋊C4—441no—
819C2×C22⋊C4—441no—
820C2×C22⋊C4C4×D1114yes—
821C2×C22⋊C4D4414yes—
822C2×C22⋊C4C22⋊D1114yes—
823C2×C42—22no—
824C2×C42—22no—
825C2×C42—41no—
826#95—22no—
827#95—22no—
828#95—114no—
829#95—222no—
830#95—222no—
831#95—222no—
832#95—222no—
833#95—222no—
834#95—222no—
835#95—222no—
836#95—441no—
837#95—441no—
838C2×C11—44no—
839C2×C11#231111yescharacteristic
840C2×C11#232411yescharacteristic
841C2×C11#232511yescharacteristic
842C2×C11D4×C22⋊C411yescharacteristic
843C2×C11D4×C22⋊C411yescharacteristic
844C2×C11#236111yescharacteristic
845C2×C11#237711yescharacteristic
846C2×C11#266911yescharacteristic
847C2×C11#267111yescharacteristic
848C2×C11#267211yescharacteristic
849C2×C11#267511yescharacteristic
850C2×C11#267611yescharacteristic
851C2×C11#268111yescharacteristic
852C2×C11#269111yescharacteristic
853C2×C11#270311yescharacteristic
854D11—44no—
855D11—82no—
856C24—21no—
857C24—21no—
858C24—21no—
859C24—21no—
860C24—21no—
861C24—21no—
862C24—21no—
863C24—21no—
864C24—21no—
865C24—21no—
866C24—21no—
867C24—21no—
868C24—112no—
869C24—112no—
870C24—112no—
871C24—112no—
872C24—221no—
873C24—221no—
874C24—221no—
875C24—221no—
876C24—221no—
877C24—221no—
878C24—221no—
879C24—221no—
880C24—221no—
881C24—221no—
882C24—221no—
883C24—221no—
884C24—221no—
885C24—221no—
886C24—221no—
887C24—221no—
888C24—221no—
889C24—221no—
890C24—221no—
891C24—221no—
892C24—221no—
893C24—221no—
894C24—221no—
895C24—221no—
896C24—221no—
897C24—221no—
898C24C2×C4×D1112yes—
899C24C2×D4412yes—
900C24C2×C22⋊D1112yes—
901C24C23×D1111yescharacteristic
902C2×D4—228no—
903C2×D4—228no—
904C2×D4—228no—
905C2×D4—228no—
906C2×D4—228no—
907C2×D4—228no—
908C2×D4—444no—
909C2×D4—444no—
910C2×D4—444no—
911C2×D4—444no—
912C2×D4—444no—
913C2×D4—444no—
914C2×D4—444no—
915C2×D4—444no—
916C2×D4—444no—
917C2×D4—444no—
918C2×D4—444no—
919C2×D4—444no—
920C2×D4—444no—
921C2×D4—444no—
922C2×D4—444no—
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—21no—
943C22×C4—21no—
944C22×C4—21no—
945C22×C4—21no—
946C22×C4—21no—
947C22×C4—21no—
948C22×C4—21no—
949C22×C4—21no—
950C22×C4—21no—
951C22×C4—21no—
952C22×C4—21no—
953C22×C4—21no—
954C22×C4—21no—
955C22×C4—21no—
956C22×C4—21no—
957C22×C4—112no—
958C22×C4—112no—
959C22×C4—112no—
960C22×C4—112no—
961C22×C4—112no—
962C22×C4—112no—
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—221no—
979C22×C4—221no—
980C22×C4—221no—
981C22×C4—221no—
982C22×C4—221no—
983C22×C4—221no—
984C22×C4—221no—
985C22×C4—221no—
986C22×C4—228no—
987C22×C4—221no—
988C22×C4—221no—
989C22×C4—221no—
990C22×C4—221no—
991C22×C4—221no—
992C22×C4—221no—
993C22×C4—221no—
994C22×C4—221no—
995C22×C4—221no—
996C22×C4—221no—
997C22×C4—221no—
998C22×C4—221no—
999C22×C4—221no—
1000C22×C4—221no—
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—
1012C22×C4—444no—
1013C22×C4C2×C4×D1112yes—
1014C22×C4C2×C4×D1112yes—
1015C22×C4C2×D4412yes—
1016C22×C4C2×D4412yes—
1017C22×C4D4×D1112yes—
1018C22×C4D4×D1112yes—
1019C22×C4C2×C22⋊D1112yes—
1020C22×C4C2×C22⋊D1112yes—
1021C4⋊C4—44no—
1022C4⋊C4—228no—
1023C4⋊C4—444no—
1024C4⋊C4—444no—
1025C22⋊C4—44no—
1026C22⋊C4—44no—
1027C22⋊C4—228no—
1028C22⋊C4—444no—
1029C22⋊C4—444no—
1030C22⋊C4—444no—
1031C22⋊C4—444no—
1032C22⋊C4—444no—
1033C22⋊C4—444no—
1034C22⋊C4—444no—
1035C22⋊C4—444no—
1036C22⋊C4—444no—
1037C22⋊C4(C2×D11)⋊C4116yescomplemented
1038C42—44no—
1039C11#1436111yescharacteristic, complemented, Sylow
1040C23—22no—
1041C23—22no—
1042C23—22no—
1043C23—22no—
1044C23—22no—
1045C23—22no—
1046C23—22no—
1047C23—22no—
1048C23—22no—
1049C23—22no—
1050C23—22no—
1051C23—22no—
1052C23—22no—
1053C23—22no—
1054C23—22no—
1055C23—22no—
1056C23—22no—
1057C23—22no—
1058C23—41no—
1059C23—41no—
1060C23—41no—
1061C23—41no—
1062C23—41no—
1063C23—41no—
1064C23—41no—
1065C23—41no—
1066C23—41no—
1067C23—41no—
1068C23—41no—
1069C23—41no—
1070C23—41no—
1071C23—41no—
1072C23—41no—
1073C23—41no—
1074C23—114no—
1075C23—222no—
1076C23—222no—
1077C23—222no—
1078C23—222no—
1079C23—222no—
1080C23—222no—
1081C23—222no—
1082C23—222no—
1083C23—222no—
1084C23—222no—
1085C23—222no—
1086C23—222no—
1087C23—222no—
1088C23—222no—
1089C23—222no—
1090C23—222no—
1091C23—222no—
1092C23—222no—
1093C23—222no—
1094C23—222no—
1095C23—222no—
1096C23—222no—
1097C23—222no—
1098C23—222no—
1099C23—222no—
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—
1120C23—441no—
1121C23—441no—
1122C23—441no—
1123C23—441no—
1124C23—441no—
1125C23—441no—
1126C23—441no—
1127C23—441no—
1128C23—441no—
1129C23—441no—
1130C23—441no—
1131C23—441no—
1132C23—441no—
1133C23—441no—
1134C23—441no—
1135C23—441no—
1136C23—441no—
1137C23—441no—
1138C23—441no—
1139C23—441no—
1140C23—441no—
1141C23—441no—
1142C23—441no—
1143C23—441no—
1144C23C2×(C2×D11)⋊C414yes—
1145C23C22×C4×D1111yescharacteristic
1146C23C22×D4411yescharacteristic
1147C23C2×D4×D1111yescharacteristic
1148C23C2×D4×D1111yescharacteristic
1149C23#6703711yescharacteristic
1150C23#6703711yescharacteristic
1151C23#41×D1111yescharacteristic
1152C23#41×D1111yescharacteristic
1153C23#6704211yescharacteristic
1154C23#6704211yescharacteristic
1155C23#6704211yescharacteristic
1156C23#6704211yescharacteristic
1157C23#6704311yescharacteristic
1158C23#6704311yescharacteristic
1159C23C22×C22⋊D1111yescharacteristic
1160D4—4416no—
1161D4—4416no—
1162D4—4416no—
1163C2×C4—22no—
1164C2×C4—22no—
1165C2×C4—22no—
1166C2×C4—22no—
1167C2×C4—22no—
1168C2×C4—22no—
1169C2×C4—22no—
1170C2×C4—22no—
1171C2×C4—22no—
1172C2×C4—22no—
1173C2×C4—22no—
1174C2×C4—22no—
1175C2×C4—22no—
1176C2×C4—22no—
1177C2×C4—22no—
1178C2×C4—22no—
1179C2×C4—22no—
1180C2×C4—22no—
1181C2×C4—41no—
1182C2×C4—41no—
1183C2×C4—41no—
1184C2×C4—41no—
1185C2×C4—41no—
1186C2×C4—41no—
1187C2×C4—41no—
1188C2×C4—41no—
1189C2×C4—41no—
1190C2×C4—41no—
1191C2×C4—41no—
1192C2×C4—41no—
1193C2×C4—41no—
1194C2×C4—41no—
1195C2×C4—41no—
1196C2×C4—41no—
1197C2×C4—41no—
1198C2×C4—41no—
1199C2×C4—41no—
1200C2×C4—41no—
1201C2×C4—41no—
1202C2×C4—41no—
1203C2×C4—114no—
1204C2×C4—222no—
1205C2×C4—222no—
1206C2×C4—222no—
1207C2×C4—222no—
1208C2×C4—222no—
1209C2×C4—222no—
1210C2×C4—222no—
1211C2×C4—222no—
1212C2×C4—222no—
1213C2×C4—222no—
1214C2×C4—222no—
1215C2×C4—222no—
1216C2×C4—222no—
1217C2×C4—222no—
1218C2×C4—222no—
1219C2×C4—4416no—
1220C2×C4—4416no—
1221C2×C4—441no—
1222C2×C4—441no—
1223C2×C4—441no—
1224C2×C4—441no—
1225C2×C4—441no—
1226C2×C4—441no—
1227C2×C4—441no—
1228C2×C4—441no—
1229C2×C4—441no—
1230C2×C4—441no—
1231C2×C4—441no—
1232C2×C4—441no—
1233C2×C4—441no—
1234C2×C4—441no—
1235C2×C4—441no—
1236C2×C4—441no—
1237C2×C4—441no—
1238C2×C4—441no—
1239C2×C4—441no—
1240C2×C4—441no—
1241C2×C4—441no—
1242C2×C4—441no—
1243C2×C4—441no—
1244C2×C4—441no—
1245C2×C4—441no—
1246C2×C4—441no—
1247C2×C4C2×(C2×D11)⋊C414yes—
1248C2×C4C2×(C2×D11)⋊C414yes—
1249C22—24no—
1250C22—24no—
1251C22—24no—
1252C22—42no—
1253C22—42no—
1254C22—42no—
1255C22—42no—
1256C22—42no—
1257C22—42no—
1258C22—42no—
1259C22—42no—
1260C22—42no—
1261C22—42no—
1262C22—42no—
1263C22—42no—
1264C22—224no—
1265C22—224no—
1266C22—224no—
1267C22—442no—
1268C22—442no—
1269C22—442no—
1270C22—442no—
1271C22—442no—
1272C22—442no—
1273C22—442no—
1274C22—442no—
1275C22—442no—
1276C22—442no—
1277C22—442no—
1278C22—442no—
1279C22—442no—
1280C22—442no—
1281C22—442no—
1282C22—442no—
1283C22—442no—
1284C22—442no—
1285C22—442no—
1286C22—881no—
1287C22—881no—
1288C22—881no—
1289C22—881no—
1290C22—881no—
1291C22—881no—
1292C22—881no—
1293C22—881no—
1294C22#1062305411yescharacteristic
1295C22#1062305411yescharacteristic
1296C22#1062305611yescharacteristic
1297C22#1062305711yescharacteristic
1298C22C4×D4×D1111yescharacteristic
1299C22C4×D4×D1111yescharacteristic
1300C22#1062307611yescharacteristic
1301C22#1062307611yescharacteristic
1302C22D4×D4411yescharacteristic
1303C22D4×D4411yescharacteristic
1304C22#1062308511yescharacteristic
1305C22#1062308511yescharacteristic
1306C22#1062312811yescharacteristic
1307C22#1062313911yescharacteristic
1308C22#1062314011yescharacteristic
1309C22#1062315111yescharacteristic
1310C22#1062318411yescharacteristic
1311C22#1062318611yescharacteristic
1312C22#1062319411yescharacteristic
1313C22#1062319811yescharacteristic
1314C22#1062320511yescharacteristic
1315C22#1062320811yescharacteristic
1316C22#1062320911yescharacteristic
1317C22#1062321511yescharacteristic
1318C22#1062323811yescharacteristic
1319C22#1062324011yescharacteristic
1320C22#1062324111yescharacteristic
1321C22#1062324211yescharacteristic
1322C22C22×(C2×D11)⋊C411yescharacteristic
1323C22D4×C22⋊D1111yescharacteristic
1324C22D4×C22⋊D1111yescharacteristic
1325C22#1062336011yescharacteristic
1326C22#1062336011yescharacteristic
1327C22#1062336411yescharacteristic
1328C22#1062336411yescharacteristic
1329C4—24no—
1330C4—24no—
1331C4—42no—
1332C4—42no—
1333C4—81no—
1334C4—81no—
1335C4—224no—
1336C4—442no—
1337C4—442no—
1338C4—442no—
1339C4—881no—
1340C4—881no—
1341C2—44no—
1342C2—444no—
1343C2—882no—
1344C2#1307120411yescharacteristic
1345C2#1307130411yescharacteristic
1346C2#1307132011yescharacteristic
1347C2D4×(C2×D11)⋊C411yescharacteristic
1348C2D4×(C2×D11)⋊C411yescharacteristic
1349C2#1307162911yescharacteristic
1350C2#1307176911yescharacteristic
1351C2#1307483111yescharacteristic
1352C2#1307485211yescharacteristic
1353C2#1307486511yescharacteristic
1354C2#1307490611yescharacteristic
1355C2#1307491211yescharacteristic
1356C2#1307496611yescharacteristic
1357C2#1307509111yescharacteristic
1358C2#1307525711yescharacteristic
subgroupG/H
center, FrattiniC24C23×D11
commutatorC23×C11C23×C4
FittingC2×C11×#388C2
socle, cosocleC24×C11C24
prime radicalC22×#66937C2
hypercenterC2×#388D11
hypocenterC11#14361
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ C2×#388

Complements

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

NH ≅ G/Ntype
2. C2×#10622552C2semidirect
3. C2×#10622571C2semidirect
4. C2×#10622571C2semidirect
5. C2×#10622563C2semidirect
6. C2×#10622600C2semidirect
7. #13066870C2semidirect
8. #13066862C2semidirect
9. #13066858C2semidirect
10. #13066856C2semidirect
11. #13066855C2semidirect
12. #13066855C2semidirect
13. #13066849C2semidirect
14. (C2×D11)⋊#95C2semidirect
15. C2×C11×#388C2semidirect
41. C2×#66937C4semidirect
102. C22×D44C2×C4semidirect
109. C22×C4×D11C2×C4semidirect
153. C2×(C2×D11)⋊C4C2×C4semidirect
154. C2×(C2×D11)⋊C4D4semidirect
163. C2×Dic11⋊C4C2×C4semidirect
176. C11⋊#95D4semidirect
346. C11×C22⋊C4C22⋊C4semidirect
363. C2×#388D11semidirect
1037. C22⋊C4(C2×D11)⋊C4semidirect
1039. C11#14361semidirect

Maximal subgroups

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

subgroupindex
C22×#669372
C2×#106225522
C2×#106225712
C2×#106225632
C2×#106226002
#130668702
#130668622
#130668582
#130668562
#130668552
#130668492
(C2×D11)⋊#952
C2×C11×#3882
#1436111