Finite Group Databasebeta

← #14684409

Subgroups — #14684409

Order 2816.

2018 conjugacy classes of subgroups.

The subgroup lattice has 1300 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622573C211yesmaximal, characteristic
2C2×#10622278C211yesmaximal, characteristic, complemented
3C2×#10622569C211yesmaximal, characteristic, complemented
4#13066876C211yesmaximal, characteristic, complemented
5#13066876C211yesmaximal, characteristic, complemented
6#13066865C211yesmaximal, characteristic, complemented
7#13066864C211yesmaximal, characteristic, complemented
8#13066858C211yesmaximal, characteristic, complemented
9#13066858C211yesmaximal, characteristic, complemented
10#13066856C211yesmaximal, characteristic, complemented
11#13066855C211yesmaximal, characteristic, complemented
12#13066855C211yesmaximal, characteristic, complemented
13#13066855C211yesmaximal, characteristic, complemented
14(C2×D11)⋊#95C211yesmaximal, characteristic, complemented
15C11×#1439C211yesmaximal, characteristic, complemented
16C23×C22⋊D11C2211yescharacteristic
17C23×C22⋊D11C2211yescharacteristic
18C23×D44C2211yescharacteristic
19C23×C4×D11C2211yescharacteristic
20C22×C11×C4⋊C4C2211yescharacteristic
21C22×C11×C22⋊C4C2211yescharacteristic
22C22×C11×C22⋊C4C2211yescharacteristic
23C22×C11×C22⋊C4C2211yescharacteristic
24C22×C22⋊Dic11C2211yescharacteristic
25C22×C22⋊Dic11C2211yescharacteristic
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
35C2×C11×#95C2211yescharacteristic
36C2×C11×#95C2211yescharacteristic
37C2×C11×#95C2211yescharacteristic
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
51#10622573C418yescomplemented
52#10622569—24no—
53#10622278—24no—
54C25×C11C2311yescharacteristic
55C24×D11C2311yescharacteristic
56C24×D11C2311yescharacteristic
57C23×C4×C11C2311yescharacteristic
58C23×C4×C11C2311yescharacteristic
59C23×C4×C11C2311yescharacteristic
60C23×C4×C11C2311yescharacteristic
61C23×C4×C11C2311yescharacteristic
62C23×C4×C11C2311yescharacteristic
63C22×C22⋊D11—22no—
64C22×C22⋊D11—22no—
65C22×C22⋊D11—41no—
66C22×C22⋊D11—41no—
67C22×C22⋊D11—41no—
68C22×C22⋊D11—41no—
69C22×C22⋊D11—41no—
70C22×C22⋊D11—41no—
71C22×C22⋊D11—41no—
72C22×C22⋊D11—41no—
73C22×C22⋊D11—41no—
74C22×C22⋊D11—41no—
75C22×C22⋊D11C2×C414yes—
76C22×C22⋊D11C2×C414yescomplemented
77C23×Dic11C2311yescharacteristic
78C23×Dic11C2311yescharacteristic
79C23×Dic11C2311yescharacteristic
80C23×Dic11C2311yescharacteristic
81C23×Dic11C2311yescharacteristic
82C23×Dic11C2311yescharacteristic
83C22×D44—22no—
84C22×D44—22no—
85C22×D44—41no—
86C22×D44—41no—
87C22×D44—41no—
88C22×D44—41no—
89C22×D44C2×C414yes—
90C22×C4×D11—41no—
91C22×C4×D11—41no—
92C22×C4×D11—41no—
93C22×C4×D11—41no—
94C22×C4×D11—41no—
95C22×C4×D11—41no—
96C22×C4×D11D414yescomplemented
97C2×C11×C4⋊C4—41no—
98C2×C11×C4⋊C4—41no—
99C2×C11×C4⋊C4—41no—
100C2×C11×C22⋊C4—22no—
101C2×C11×C22⋊C4—41no—
102C2×C11×C22⋊C4—41no—
103C2×C11×C22⋊C4—41no—
104C2×C11×C22⋊C4—41no—
105C2×C11×C22⋊C4—41no—
106C2×C11×C22⋊C4—41no—
107C2×C11×C22⋊C4—41no—
108C2×C11×C22⋊C4C2×C414yescomplemented
109C2×C22⋊Dic11—22no—
110C2×C22⋊Dic11—41no—
111C2×C22⋊Dic11—41no—
112C2×C22⋊Dic11—41no—
113C2×C22⋊Dic11—41no—
114C2×C22⋊Dic11—41no—
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—41no—
121C2×(C2×D11)⋊C4—41no—
122C2×(C2×D11)⋊C4—41no—
123C2×(C2×D11)⋊C4—41no—
124C2×(C2×D11)⋊C4—41no—
125C2×(C2×D11)⋊C4—41no—
126C2×(C2×D11)⋊C4—41no—
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)⋊C4C2×C414yes—
141C2×(C2×D11)⋊C4C2×C414yescomplemented
142C11×#95—22no—
143C11×#95—41no—
144C11×#95—41no—
145C11⋊#95—22no—
146C11⋊#95—22no—
147C11⋊#95—22no—
148C11⋊#95—41no—
149C11⋊#95—41no—
150C11⋊#95—41no—
151C11⋊#95—41no—
152C11⋊#95—41no—
153C11⋊#95—41no—
154C11⋊#95—41no—
155C11⋊#95—41no—
156C11⋊#95—41no—
157C11⋊#95C2×C414yescomplemented
158#14621—111nomaximal, Sylow
159C24×C11—21no—
160C24×C11—21no—
161C24×C11—21no—
162C24×C11—21no—
163C24×C11—21no—
164C24×C11—21no—
165C24×C11—21no—
166C24×C11—21no—
167C24×C11—21no—
168C24×C11—21no—
169C24×C11—21no—
170C24×C11—21no—
171C24×C11—21no—
172C24×C11—21no—
173C24×C11C22×C412yes—
174C24×C11C2411yescharacteristic
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×D11C22×C412yes—
202C23×D11C22×C412yes—
203C23×D11C2×D412yes—
204C23×D11#4112yes—
205C22×C4×C11—21no—
206C22×C4×C11—21no—
207C22×C4×C11—21no—
208C22×C4×C11—21no—
209C22×C4×C11—21no—
210C22×C4×C11—21no—
211C22×C4×C11—21no—
212C22×C4×C11—21no—
213C22×C4×C11—21no—
214C22×C4×C11—21no—
215C22×C4×C11—21no—
216C22×C4×C11—21no—
217C22×C4×C11—21no—
218C22×C4×C11—21no—
219C22×C4×C11—21no—
220C22×C4×C11—21no—
221C22×C4×C11—21no—
222C22×C4×C11—21no—
223C22×C4×C11—21no—
224C22×C4×C11—21no—
225C22×C4×C11—21no—
226C22×C4×C11—21no—
227C22×C4×C11—21no—
228C22×C4×C11—21no—
229C22×C4×C11—21no—
230C22×C4×C11—21no—
231C22×C4×C11—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×C11C22×C412yes—
245C22×C4×C11C22×C412yes—
246C22×C4×C11C2×D412yes—
247C2×C22⋊D11—28no—
248C2×C22⋊D11—44no—
249C2×C22⋊D11—44no—
250C2×C22⋊D11—44no—
251C2×C22⋊D11—44no—
252C2×C22⋊D11—44no—
253C2×C22⋊D11—44no—
254C2×C22⋊D11—44no—
255C2×C22⋊D11—44no—
256C2×C22⋊D11—44no—
257C2×C22⋊D11—44no—
258C2×C22⋊D11—44no—
259C2×C22⋊D11—44no—
260C2×C22⋊D11—44no—
261C22×Dic11—21no—
262C22×Dic11—21no—
263C22×Dic11—21no—
264C22×Dic11—21no—
265C22×Dic11—21no—
266C22×Dic11—21no—
267C22×Dic11—21no—
268C22×Dic11—21no—
269C22×Dic11—21no—
270C22×Dic11—21no—
271C22×Dic11—21no—
272C22×Dic11—21no—
273C22×Dic11—21no—
274C22×Dic11—21no—
275C22×Dic11—21no—
276C22×Dic11—21no—
277C22×Dic11—21no—
278C22×Dic11—21no—
279C22×Dic11—21no—
280C22×Dic11—21no—
281C22×Dic11—21no—
282C22×Dic11—21no—
283C22×Dic11—21no—
284C22×Dic11—21no—
285C22×Dic11—21no—
286C22×Dic11—21no—
287C22×Dic11—21no—
288C22×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×Dic11C22×C412yes—
301C22×Dic11C22×C412yes—
302C22×Dic11C2×D412yes—
303C2×D44—28no—
304C2×D44—44no—
305C2×D44—44no—
306C2×D44—44no—
307C2×D44—44no—
308C2×D44—44no—
309C2×D44—44no—
310C2×C4×D11—44no—
311C2×C4×D11—44no—
312C2×C4×D11—44no—
313C2×C4×D11—44no—
314C2×C4×D11—44no—
315C2×C4×D11—44no—
316C2×C4×D11—44no—
317C11×C4⋊C4—44no—
318C11×C22⋊C4—44no—
319C11×C22⋊C4—44no—
320C11×C22⋊C4—44no—
321C22⋊Dic11—44no—
322C22⋊Dic11—44no—
323(C2×D11)⋊C4—44no—
324(C2×D11)⋊C4—44no—
325(C2×D11)⋊C4—44no—
326(C2×D11)⋊C4—44no—
327(C2×D11)⋊C4—44no—
328(C2×D11)⋊C4—44no—
329(C2×D11)⋊C4—44no—
330(C2×D11)⋊C4—44no—
331(C2×D11)⋊C4—44no—
332C2×#392—111no—
333C2×#386—111no—
334C2×#386—111no—
335#1443—111no—
336#1443—111no—
337#1440—111no—
338#1440—111no—
339#1439—111no—
340#1439—111no—
341#1439D1111yescharacteristic, complemented
342#1438—111no—
343#1438—111no—
344#1438—111no—
345#1438—111no—
346C22⋊#95—111no—
347C23×C11—22no—
348C23×C11—22no—
349C23×C11—22no—
350C23×C11—22no—
351C23×C11—22no—
352C23×C11—22no—
353C23×C11—22no—
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×C11—41no—
382C23×C11C23×C411yescharacteristic
383C23×C11C22×D411yescharacteristic
384C23×C11C2×#4111yescharacteristic
385C23×C11H(5,𝔽2)11yescharacteristic
386C23×C11H(5,𝔽2)11yescharacteristic
387C23×C11H(5,𝔽2)11yescharacteristic
388C23×C11H(5,𝔽2)11yescharacteristic
389C23×C11H(5,𝔽2)11yescharacteristic
390C23×C11H(5,𝔽2)11yescharacteristic
391C23×C11H(5,𝔽2)11yescharacteristic
392C23×C11H(5,𝔽2)11yescharacteristic
393C23×C11H(5,𝔽2)11yescharacteristic
394C23×C11H(5,𝔽2)11yescharacteristic
395C23×C11H(5,𝔽2)11yescharacteristic
396C23×C112−1+411yescharacteristic
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—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×D11C4×D414yes—
467C2×C4×C11—22no—
468C2×C4×C11—22no—
469C2×C4×C11—22no—
470C2×C4×C11—22no—
471C2×C4×C11—22no—
472C2×C4×C11—22no—
473C2×C4×C11—22no—
474C2×C4×C11—22no—
475C2×C4×C11—22no—
476C2×C4×C11—41no—
477C2×C4×C11—41no—
478C2×C4×C11—41no—
479C2×C4×C11—41no—
480C2×C4×C11—41no—
481C2×C4×C11—41no—
482C2×C4×C11—41no—
483C2×C4×C11—41no—
484C2×C4×C11—41no—
485C2×C4×C11—41no—
486C2×C4×C11—41no—
487C2×C4×C11—41no—
488C2×C4×C11—41no—
489C2×C4×C11—41no—
490C2×C4×C11—41no—
491C2×C4×C11—41no—
492C2×C4×C11—41no—
493C2×C4×C11—41no—
494C2×C4×C11—41no—
495C2×C4×C11—41no—
496C2×C4×C11—41no—
497C2×C4×C11—41no—
498C2×C4×C11—41no—
499C2×C4×C11—41no—
500C2×C4×C11—41no—
501C2×C4×C11—41no—
502C2×C4×C11—41no—
503C2×C4×C11—41no—
504C2×C4×C11—41no—
505C2×C4×C11—41no—
506C2×C4×C11—41no—
507C2×C4×C11—41no—
508C2×C4×C11—41no—
509C22⋊D11—416no—
510C22⋊D11—416no—
511C2×Dic11—22no—
512C2×Dic11—22no—
513C2×Dic11—22no—
514C2×Dic11—22no—
515C2×Dic11—22no—
516C2×Dic11—22no—
517C2×Dic11—22no—
518C2×Dic11—22no—
519C2×Dic11—22no—
520C2×Dic11—41no—
521C2×Dic11—41no—
522C2×Dic11—41no—
523C2×Dic11—41no—
524C2×Dic11—41no—
525C2×Dic11—41no—
526C2×Dic11—41no—
527C2×Dic11—41no—
528C2×Dic11—41no—
529C2×Dic11—41no—
530C2×Dic11—41no—
531C2×Dic11—41no—
532C2×Dic11—41no—
533C2×Dic11—41no—
534C2×Dic11—41no—
535C2×Dic11—41no—
536C2×Dic11—41no—
537C2×Dic11—41no—
538C2×Dic11—41no—
539C2×Dic11—41no—
540C2×Dic11—41no—
541C2×Dic11—41no—
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—
553D44—416no—
554C4×D11—416no—
555C23×D4—111no—
556C23×D4—111no—
557C23×D4—111no—
558C24×C4—111no—
559C22×C4⋊C4C2×D1111yescharacteristic
560C22×C22⋊C4—111no—
561C22×C22⋊C4—111no—
562C22×C22⋊C4—111no—
563C22×C22⋊C4—111no—
564C22×C22⋊C4—111no—
565C22×C22⋊C4—111no—
566C22×C22⋊C4—111no—
567C22×C22⋊C4—111no—
568C22×C22⋊C4—111no—
569C22×C22⋊C4—111no—
570C22×C22⋊C4—111no—
571C22×C22⋊C4C2×D1111yescharacteristic
572C22×C22⋊C4C2×D1111yescharacteristic
573C22×C22⋊C4C2×D1111yescharacteristic
574#392—118no—
575#386—224no—
576#386—224no—
577C2×#95—111no—
578C2×#95—111no—
579C2×#95—111no—
580C2×#95—111no—
581C2×#95—111no—
582C2×#95—111no—
583C2×#95—111no—
584C2×#95—111no—
585C2×#95—111no—
586C2×#95—111no—
587C2×#95—111no—
588C2×#95—111no—
589C2×#95—111no—
590C2×#95C2×D1111yescharacteristic
591C2×#95C2×D1111yescharacteristic
592C2×#95C2×D1111yescharacteristic
593C22×C11—42no—
594C22×C11—42no—
595C22×C11—42no—
596C22×C11—42no—
597C22×C11—42no—
598C22×C11—42no—
599C22×C11—42no—
600C22×C11—81no—
601C22×C11—81no—
602C22×C11—81no—
603C22×C11—81no—
604C22×C11—81no—
605C22×C11—81no—
606C22×C11—81no—
607C22×C11—81no—
608C22×C11C2×C4×D411yescharacteristic
609C22×C11#51811yescharacteristic
610C22×C11#51811yescharacteristic
611C22×C11#51811yescharacteristic
612C22×C11#51811yescharacteristic
613C22×C11#51811yescharacteristic
614C22×C11#52011yescharacteristic
615C22×C11#53411yescharacteristic
616C22×C11#53411yescharacteristic
617C22×C11#53411yescharacteristic
618C22×C11#53511yescharacteristic
619C22×C11#53511yescharacteristic
620C22×C11#53711yescharacteristic
621C22×C11#53811yescharacteristic
622C22×C11#53811yescharacteristic
623C22×C11#53811yescharacteristic
624C22×C11#53811yescharacteristic
625C22×C11#53811yescharacteristic
626C22×C11#53911yescharacteristic
627C22×C11#56011yescharacteristic
628C22×C11#56011yescharacteristic
629C22×C11#56011yescharacteristic
630C22×C11#56011yescharacteristic
631C22×C11#56011yescharacteristic
632C22×C11#56011yescharacteristic
633C22×C11#56011yescharacteristic
634C22×C11#56011yescharacteristic
635C22×C11#56011yescharacteristic
636C22×C11#56011yescharacteristic
637C22×C11#56011yescharacteristic
638C22×C11H(3,𝔽4)11yescharacteristic
639C22×C11#56211yescharacteristic
640C22×C11#56211yescharacteristic
641C22×C11#56211yescharacteristic
642C22×C11#56211yescharacteristic
643C2×D11—24no—
644C2×D11—24no—
645C2×D11—24no—
646C2×D11—42no—
647C2×D11—42no—
648C2×D11—42no—
649C2×D11—42no—
650C2×D11—42no—
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—81no—
666C2×D11—81no—
667C2×D11—81no—
668C2×D11—81no—
669C2×D11—81no—
670C2×D11—81no—
671C2×D11—81no—
672C2×D11—81no—
673C4×C11—42no—
674C4×C11—42no—
675C4×C11—42no—
676C4×C11—81no—
677C4×C11—81no—
678C4×C11—81no—
679Dic11—42no—
680Dic11—42no—
681Dic11—42no—
682Dic11—81no—
683Dic11—81no—
684Dic11—81no—
685C25—111no—
686C25—111no—
687C25C22×D1111yescharacteristic
688C22×D4—114no—
689C22×D4—114no—
690C22×D4—114no—
691C22×D4—222no—
692C22×D4—222no—
693C22×D4—222no—
694C22×D4—222no—
695C22×D4—441no—
696C22×D4—441no—
697C22×D4—441no—
698C22×D4—441no—
699C22×D4—441no—
700C22×D4—441no—
701C22×D4—441no—
702C22×D4—441no—
703C22×D4—441no—
704C22×D4—441no—
705C22×D4—441no—
706C22×D4—441no—
707C22×D4—441no—
708C22×D4—441no—
709C23×C4—111no—
710C23×C4—111no—
711C23×C4—111no—
712C23×C4—114no—
713C23×C4—111no—
714C23×C4—111no—
715C23×C4—111no—
716C23×C4—441no—
717C23×C4—441no—
718C23×C4—441no—
719C23×C4—441no—
720C23×C4—441no—
721C23×C4—441no—
722C23×C4C22×D1111yescharacteristic
723C23×C4C22×D1111yescharacteristic
724C23×C4C22×D1111yescharacteristic
725C23×C4C22×D1111yescharacteristic
726C23×C4C22×D1111yescharacteristic
727C23×C4C22×D1111yescharacteristic
728C2×C4⋊C4—41no—
729C2×C4⋊C4—41no—
730C2×C4⋊C4—41no—
731C2×C22⋊C4—22no—
732C2×C22⋊C4—41no—
733C2×C22⋊C4—41no—
734C2×C22⋊C4—41no—
735C2×C22⋊C4—41no—
736C2×C22⋊C4—41no—
737C2×C22⋊C4—41no—
738C2×C22⋊C4—41no—
739C2×C22⋊C4—114no—
740C2×C22⋊C4—114no—
741C2×C22⋊C4—222no—
742C2×C22⋊C4—222no—
743C2×C22⋊C4—222no—
744C2×C22⋊C4—222no—
745C2×C22⋊C4—222no—
746C2×C22⋊C4—222no—
747C2×C22⋊C4—441no—
748C2×C22⋊C4—441no—
749C2×C22⋊C4—441no—
750C2×C22⋊C4—441no—
751C2×C22⋊C4—441no—
752C2×C22⋊C4—441no—
753C2×C22⋊C4—441no—
754C2×C22⋊C4—441no—
755C2×C22⋊C4—441no—
756C2×C22⋊C4—441no—
757C2×C22⋊C4—441no—
758C2×C22⋊C4—441no—
759C2×C22⋊C4—441no—
760C2×C22⋊C4—441no—
761C2×C22⋊C4—441no—
762C2×C22⋊C4—441no—
763C2×C22⋊C4—441no—
764C2×C22⋊C4—441no—
765C2×C22⋊C4—441no—
766C2×C22⋊C4—441no—
767C2×C22⋊C4—441no—
768C2×C22⋊C4—441no—
769C2×C22⋊C4—441no—
770C2×C22⋊C4—441no—
771C2×C22⋊C4—441no—
772C2×C22⋊C4C4×D1114yescomplemented
773#95—22no—
774#95—41no—
775#95—41no—
776#95—114no—
777#95—222no—
778#95—222no—
779#95—222no—
780#95—441no—
781#95—441no—
782#95—441no—
783#95—441no—
784#95—441no—
785#95—441no—
786#95—441no—
787#95—441no—
788#95—441no—
789C2×C11—82no—
790C2×C11#232111yescharacteristic
791C2×C11#232111yescharacteristic
792C2×C11#232511yescharacteristic
793C2×C11#237511yescharacteristic
794C2×C11#237711yescharacteristic
795C2×C11#237711yescharacteristic
796C2×C11#238011yescharacteristic
797C2×C11#281211yescharacteristic
798C2×C11#281311yescharacteristic
799C2×C11#281311yescharacteristic
800C2×C11#281511yescharacteristic
801C2×C11#282411yescharacteristic
802C2×C11#282511yescharacteristic
803C2×C11#282511yescharacteristic
804C2×C11#282611yescharacteristic
805D11—44no—
806D11—82no—
807C24—21no—
808C24—21no—
809C24—21no—
810C24—21no—
811C24—21no—
812C24—21no—
813C24—21no—
814C24—21no—
815C24—21no—
816C24—21no—
817C24—21no—
818C24—21no—
819C24—21no—
820C24—21no—
821C24—112no—
822C24—112no—
823C24—112no—
824C24—112no—
825C24—221no—
826C24—221no—
827C24—221no—
828C24—221no—
829C24—221no—
830C24—221no—
831C24—221no—
832C24—221no—
833C24—221no—
834C24—221no—
835C24—221no—
836C24—221no—
837C24—221no—
838C24—221no—
839C24—221no—
840C24—221no—
841C24—221no—
842C24—221no—
843C24—221no—
844C24—221no—
845C24—221no—
846C24—221no—
847C24—221no—
848C24—221no—
849C24—221no—
850C24—221no—
851C24C2×C4×D1112yes—
852C24C23×D1111yescharacteristic
853C2×D4—228no—
854C2×D4—228no—
855C2×D4—444no—
856C2×D4—444no—
857C2×D4—444no—
858C2×D4—444no—
859C2×D4—444no—
860C2×D4—444no—
861C2×D4—444no—
862C2×D4—444no—
863C2×D4—444no—
864C2×D4—444no—
865C2×D4—444no—
866C2×D4—444no—
867C2×D4—444no—
868C2×D4—444no—
869C2×D4—444no—
870C2×D4—444no—
871C2×D4—444no—
872C2×D4—444no—
873C2×D4—444no—
874C22×C4—21no—
875C22×C4—21no—
876C22×C4—21no—
877C22×C4—21no—
878C22×C4—21no—
879C22×C4—21no—
880C22×C4—21no—
881C22×C4—21no—
882C22×C4—21no—
883C22×C4—21no—
884C22×C4—21no—
885C22×C4—21no—
886C22×C4—21no—
887C22×C4—21no—
888C22×C4—21no—
889C22×C4—21no—
890C22×C4—21no—
891C22×C4—21no—
892C22×C4—21no—
893C22×C4—21no—
894C22×C4—21no—
895C22×C4—21no—
896C22×C4—21no—
897C22×C4—21no—
898C22×C4—21no—
899C22×C4—21no—
900C22×C4—21no—
901C22×C4—21no—
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—112no—
914C22×C4—112no—
915C22×C4—112no—
916C22×C4—221no—
917C22×C4—221no—
918C22×C4—221no—
919C22×C4—221no—
920C22×C4—221no—
921C22×C4—221no—
922C22×C4—221no—
923C22×C4—221no—
924C22×C4—221no—
925C22×C4—221no—
926C22×C4—221no—
927C22×C4—221no—
928C22×C4—221no—
929C22×C4—221no—
930C22×C4—221no—
931C22×C4—221no—
932C22×C4—221no—
933C22×C4—221no—
934C22×C4—221no—
935C22×C4—221no—
936C22×C4—221no—
937C22×C4—221no—
938C22×C4—221no—
939C22×C4—221no—
940C22×C4—221no—
941C22×C4—221no—
942C22×C4—221no—
943C22×C4—221no—
944C22×C4—221no—
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—444no—
956C22×C4—444no—
957C22×C4—444no—
958C22×C4—444no—
959C22×C4—444no—
960C22×C4—444no—
961C22×C4—444no—
962C22×C4C2×C4×D1112yes—
963C22×C4C2×C4×D1112yes—
964C22×C4D4×D1112yes—
965C4⋊C4—44no—
966C22⋊C4—44no—
967C22⋊C4—44no—
968C22⋊C4—44no—
969C22⋊C4—444no—
970C22⋊C4—444no—
971C22⋊C4—444no—
972C22⋊C4—444no—
973C22⋊C4—444no—
974C22⋊C4—444no—
975C22⋊C4—444no—
976C22⋊C4—444no—
977C22⋊C4—444no—
978C22⋊C4—444no—
979C22⋊C4—444no—
980C11#1462111yescharacteristic, complemented, Sylow
981C23—22no—
982C23—22no—
983C23—22no—
984C23—22no—
985C23—22no—
986C23—22no—
987C23—22no—
988C23—41no—
989C23—41no—
990C23—41no—
991C23—41no—
992C23—41no—
993C23—41no—
994C23—41no—
995C23—41no—
996C23—41no—
997C23—41no—
998C23—41no—
999C23—41no—
1000C23—41no—
1001C23—41no—
1002C23—41no—
1003C23—41no—
1004C23—41no—
1005C23—41no—
1006C23—41no—
1007C23—41no—
1008C23—41no—
1009C23—41no—
1010C23—41no—
1011C23—41no—
1012C23—41no—
1013C23—41no—
1014C23—41no—
1015C23—41no—
1016C23—114no—
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—441no—
1043C23—441no—
1044C23—441no—
1045C23—441no—
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—
1086C23C22×C4×D1111yescharacteristic
1087C23C2×D4×D1111yescharacteristic
1088C23#6703711yescharacteristic
1089C23#6703711yescharacteristic
1090C23#6703711yescharacteristic
1091C23#6703711yescharacteristic
1092C23#6703711yescharacteristic
1093C23#6703711yescharacteristic
1094C23#6704011yescharacteristic
1095C23#41×D1111yescharacteristic
1096C23#6704211yescharacteristic
1097C23#6704211yescharacteristic
1098C23#6704211yescharacteristic
1099C23#6704211yescharacteristic
1100C23#6704211yescharacteristic
1101D4—4416no—
1102D4—4416no—
1103D4—4416no—
1104C2×C4—22no—
1105C2×C4—22no—
1106C2×C4—22no—
1107C2×C4—22no—
1108C2×C4—22no—
1109C2×C4—22no—
1110C2×C4—22no—
1111C2×C4—22no—
1112C2×C4—22no—
1113C2×C4—41no—
1114C2×C4—41no—
1115C2×C4—41no—
1116C2×C4—41no—
1117C2×C4—41no—
1118C2×C4—41no—
1119C2×C4—41no—
1120C2×C4—41no—
1121C2×C4—41no—
1122C2×C4—41no—
1123C2×C4—41no—
1124C2×C4—41no—
1125C2×C4—41no—
1126C2×C4—41no—
1127C2×C4—41no—
1128C2×C4—41no—
1129C2×C4—41no—
1130C2×C4—41no—
1131C2×C4—41no—
1132C2×C4—41no—
1133C2×C4—41no—
1134C2×C4—41no—
1135C2×C4—41no—
1136C2×C4—41no—
1137C2×C4—41no—
1138C2×C4—41no—
1139C2×C4—41no—
1140C2×C4—41no—
1141C2×C4—41no—
1142C2×C4—41no—
1143C2×C4—41no—
1144C2×C4—41no—
1145C2×C4—41no—
1146C2×C4—222no—
1147C2×C4—222no—
1148C2×C4—222no—
1149C2×C4—222no—
1150C2×C4—222no—
1151C2×C4—222no—
1152C2×C4—222no—
1153C2×C4—222no—
1154C2×C4—222no—
1155C2×C4—4416no—
1156C2×C4—441no—
1157C2×C4—441no—
1158C2×C4—441no—
1159C2×C4—441no—
1160C2×C4—441no—
1161C2×C4—441no—
1162C2×C4—441no—
1163C2×C4—441no—
1164C2×C4—441no—
1165C2×C4—441no—
1166C2×C4—441no—
1167C2×C4—441no—
1168C2×C4—441no—
1169C2×C4—441no—
1170C2×C4—441no—
1171C2×C4—441no—
1172C2×C4—441no—
1173C2×C4—441no—
1174C2×C4—441no—
1175C2×C4—441no—
1176C2×C4—441no—
1177C2×C4—441no—
1178C2×C4—441no—
1179C2×C4—441no—
1180C2×C4—441no—
1181C2×C4—441no—
1182C2×C4—441no—
1183C2×C4—441no—
1184C2×C4—441no—
1185C2×C4—441no—
1186C2×C4—441no—
1187C2×C4—441no—
1188C2×C4—441no—
1189C22—42no—
1190C22—42no—
1191C22—42no—
1192C22—42no—
1193C22—42no—
1194C22—42no—
1195C22—42no—
1196C22—81no—
1197C22—81no—
1198C22—81no—
1199C22—81no—
1200C22—81no—
1201C22—81no—
1202C22—81no—
1203C22—81no—
1204C22—224no—
1205C22—224no—
1206C22—224no—
1207C22—442no—
1208C22—442no—
1209C22—442no—
1210C22—442no—
1211C22—442no—
1212C22—442no—
1213C22—442no—
1214C22—442no—
1215C22—442no—
1216C22—442no—
1217C22—442no—
1218C22—442no—
1219C22—442no—
1220C22—442no—
1221C22—442no—
1222C22—442no—
1223C22—442no—
1224C22—442no—
1225C22—442no—
1226C22—881no—
1227C22—881no—
1228C22—881no—
1229C22—881no—
1230C22—881no—
1231C22—881no—
1232C22—881no—
1233C22—881no—
1234C22#1062301711yescharacteristic
1235C22#1062303511yescharacteristic
1236C22#1062305211yescharacteristic
1237C22C4×D4×D1111yescharacteristic
1238C22#1062307611yescharacteristic
1239C22#1062307611yescharacteristic
1240C22#1062307611yescharacteristic
1241C22#1062312011yescharacteristic
1242C22#1062312611yescharacteristic
1243C22#1062312611yescharacteristic
1244C22#1062313611yescharacteristic
1245C22#1062313811yescharacteristic
1246C22#1062314411yescharacteristic
1247C22#1062315111yescharacteristic
1248C22#1062315111yescharacteristic
1249C22#1062315111yescharacteristic
1250C22#1062315111yescharacteristic
1251C22#1062315111yescharacteristic
1252C22#1062316011yescharacteristic
1253C22#1062316911yescharacteristic
1254C22#1062317811yescharacteristic
1255C22#1062317811yescharacteristic
1256C22#1062317811yescharacteristic
1257C22#1062317811yescharacteristic
1258C22#1062318411yescharacteristic
1259C22#1062318811yescharacteristic
1260C22#1062319711yescharacteristic
1261C22#1062319711yescharacteristic
1262C22#1062319711yescharacteristic
1263C22#1062320911yescharacteristic
1264C22#1062320911yescharacteristic
1265C22#1062321411yescharacteristic
1266C22#1062323511yescharacteristic
1267C22#1062324211yescharacteristic
1268C22#1062324611yescharacteristic
1269C4—42no—
1270C4—42no—
1271C4—42no—
1272C4—81no—
1273C4—81no—
1274C4—81no—
1275C4—442no—
1276C4—442no—
1277C4—442no—
1278C4—881no—
1279C4—881no—
1280C4—881no—
1281C2—82no—
1282C2—444no—
1283C2—882no—
1284C2#1307127511yescharacteristic
1285C2#1307127811yescharacteristic
1286C2#1307131311yescharacteristic
1287C2#1307175611yescharacteristic
1288C2#1307177011yescharacteristic
1289C2#1307177211yescharacteristic
1290C2#1307179111yescharacteristic
1291C2#1307661211yescharacteristic
1292C2#1307661911yescharacteristic
1293C2#1307662511yescharacteristic
1294C2#1307663711yescharacteristic
1295C2#1307669511yescharacteristic
1296C2#1307670111yescharacteristic
1297C2#1307670611yescharacteristic
1298C2#1307671011yescharacteristic
subgroupG/H
center, FrattiniC24C23×D11
commutatorC23×C11C23×C4
FittingC11×#1439C2
socle, cosocleC24×C11C24
prime radicalC2×#10622573C2
hypercenter#1439D11
hypocenterC11#14621
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ #1439

Complements

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

NH ≅ G/Ntype
2. C2×#10622278C2semidirect
3. C2×#10622569C2semidirect
4. #13066876C2semidirect
5. #13066876C2semidirect
6. #13066865C2semidirect
7. #13066864C2semidirect
8. #13066858C2semidirect
9. #13066858C2semidirect
10. #13066856C2semidirect
11. #13066855C2semidirect
12. #13066855C2semidirect
13. #13066855C2semidirect
14. (C2×D11)⋊#95C2semidirect
15. C11×#1439C2semidirect
51. #10622573C4semidirect
76. C22×C22⋊D11C2×C4semidirect
96. C22×C4×D11D4semidirect
108. C2×C11×C22⋊C4C2×C4semidirect
141. C2×(C2×D11)⋊C4C2×C4semidirect
157. C11⋊#95C2×C4semidirect
341. #1439D11semidirect
772. C2×C22⋊C4C4×D11semidirect
980. C11#14621semidirect

Maximal subgroups

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

subgroupindex
C2×#106225732
C2×#106222782
C2×#106225692
#130668762
#130668652
#130668642
#130668582
#130668562
#130668552
(C2×D11)⋊#952
C11×#14392
#1462111