Finite Group Databasebeta

← #14684407

Subgroups — #14684407

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×#10622836C211yesmaximal, characteristic
2C2×#10622826C211yesmaximal, characteristic, complemented
3#13066877C211yesmaximal, characteristic, complemented
4#13066876C211yesmaximal, characteristic, complemented
5#13066864C211yesmaximal, characteristic, complemented
6#13066863C211yesmaximal, characteristic, complemented
7#13066860C211yesmaximal, characteristic, complemented
8#13066859C211yesmaximal, characteristic, complemented
9#13066859C211yesmaximal, characteristic, complemented
10#13066857C211yesmaximal, characteristic, complemented
11#13066855C211yesmaximal, characteristic, complemented
12#13066855C211yesmaximal, characteristic, complemented
13#13066855C211yesmaximal, characteristic, complemented
14#13066839C211yesmaximal, characteristic, complemented
15C2×C11×#386C211yesmaximal, characteristic, complemented
16C23×D4×C11C2211yescharacteristic
17C24×C4×C11C2211yescharacteristic
18C23×C22⋊D11C2211yescharacteristic
19C23×C22⋊D11C2211yescharacteristic
20C22×C11×C22⋊C4C2211yescharacteristic
21C22×C11×C22⋊C4C2211yescharacteristic
22C22×C11×C22⋊C4C2211yescharacteristic
23C22×C22⋊Dic11C2211yescharacteristic
24C22×C22⋊Dic11C2211yescharacteristic
25C22×C22⋊Dic11C2211yescharacteristic
26C22×C22⋊Dic11C2211yescharacteristic
27C22×C22⋊Dic11C2211yescharacteristic
28C22×C22⋊Dic11C2211yescharacteristic
29C22×(C2×D11)⋊C4C2211yescharacteristic
30C22×(C2×D11)⋊C4C2211yescharacteristic
31C22×(C2×D11)⋊C4C2211yescharacteristic
32C22×(C2×D11)⋊C4C2211yescharacteristic
33C22×(C2×D11)⋊C4C2211yescharacteristic
34C22×Dic11⋊C4C2211yescharacteristic
35C11×#386—24no—
36C2×C11×#95C2211yescharacteristic
37C2×C11×#95C2211yescharacteristic
38#10622836C418yescomplemented
39#10622826—24no—
40C2×C11⋊#95C2211yescharacteristic
41C2×C11⋊#95C2211yescharacteristic
42C2×C11⋊#95C2211yescharacteristic
43C2×C11⋊#95C2211yescharacteristic
44C2×C11⋊#95C2211yescharacteristic
45C2×C11⋊#95C2211yescharacteristic
46C2×C11⋊#95C2211yescharacteristic
47C2×C11⋊#95C2211yescharacteristic
48C2×C11⋊#95C2211yescharacteristic
49C2×C11⋊#95C2211yescharacteristic
50C2×C11⋊#95C2211yescharacteristic
51C2×C11⋊#95C2211yescharacteristic
52C2×C11⋊#95C2211yescharacteristic
53C2×C11⋊#95C2211yescharacteristic
54C25×C11C2311yescharacteristic
55C25×C11C2311yescharacteristic
56C24×D11C2311yescharacteristic
57C22×D4×C11—22no—
58C22×D4×C11—22no—
59C22×D4×C11—41no—
60C22×D4×C11—41no—
61C22×D4×C11—41no—
62C22×D4×C11—41no—
63C22×D4×C11C2×C414yes—
64C23×C4×C11—41no—
65C23×C4×C11—41no—
66C23×C4×C11—41no—
67C23×C4×C11—41no—
68C23×C4×C11—41no—
69C23×C4×C11—41no—
70C23×C4×C11D414yescomplemented
71C23×C4×C11C2311yescharacteristic
72C23×C4×C11C2311yescharacteristic
73C23×C4×C11C2311yescharacteristic
74C23×C4×C11C2311yescharacteristic
75C23×C4×C11C2311yescharacteristic
76C22×C22⋊D11—22no—
77C22×C22⋊D11—22no—
78C22×C22⋊D11—41no—
79C22×C22⋊D11—41no—
80C22×C22⋊D11—41no—
81C22×C22⋊D11—41no—
82C22×C22⋊D11—41no—
83C22×C22⋊D11—41no—
84C22×C22⋊D11—41no—
85C22×C22⋊D11—41no—
86C22×C22⋊D11—41no—
87C22×C22⋊D11—41no—
88C22×C22⋊D11C2×C414yes—
89C22×C22⋊D11C2×C414yescomplemented
90C23×Dic11C2311yescharacteristic
91C23×Dic11C2311yescharacteristic
92C23×Dic11C2311yescharacteristic
93C23×Dic11C2311yescharacteristic
94C23×Dic11C2311yescharacteristic
95C23×Dic11C2311yescharacteristic
96C23×Dic11C2311yescharacteristic
97C2×C11×C22⋊C4—22no—
98C2×C11×C22⋊C4—22no—
99C2×C11×C22⋊C4—22no—
100C2×C11×C22⋊C4—41no—
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×C22⋊Dic11—22no—
107C2×C22⋊Dic11—22no—
108C2×C22⋊Dic11—41no—
109C2×C22⋊Dic11—41no—
110C2×C22⋊Dic11—41no—
111C2×C22⋊Dic11—41no—
112C2×C22⋊Dic11—41no—
113C2×C22⋊Dic11—41no—
114C2×C22⋊Dic11—41no—
115C2×C22⋊Dic11—41no—
116C2×C22⋊Dic11—41no—
117C2×C22⋊Dic11—41no—
118C2×C22⋊Dic11—41no—
119C2×C22⋊Dic11—41no—
120C2×C22⋊Dic11—41no—
121C2×C22⋊Dic11—41no—
122C2×C22⋊Dic11C2×C414yes—
123C2×C22⋊Dic11C2×C414yescomplemented
124C2×(C2×D11)⋊C4—22no—
125C2×(C2×D11)⋊C4—22no—
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)⋊C4C2×C414yescomplemented
139C2×Dic11⋊C4—41no—
140C2×Dic11⋊C4—41no—
141C2×Dic11⋊C4—41no—
142C11×#95—22no—
143C11×#95—22no—
144C11⋊#95—22no—
145C11⋊#95—22no—
146C11⋊#95—41no—
147C11⋊#95—41no—
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×C11—21no—
174C24×C11—21no—
175C24×C11—21no—
176C24×C11—21no—
177C24×C11—21no—
178C24×C11—21no—
179C24×C11—21no—
180C24×C11—21no—
181C24×C11—21no—
182C24×C11—21no—
183C24×C11—21no—
184C24×C11—21no—
185C24×C11C22×C412yes—
186C24×C11C22×C412yes—
187C24×C11C2×D412yes—
188C24×C11#4112yes—
189C24×C11C2411yescharacteristic
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×D11C22×C412yes—
205C2×D4×C11—28no—
206C2×D4×C11—44no—
207C2×D4×C11—44no—
208C2×D4×C11—44no—
209C2×D4×C11—44no—
210C2×D4×C11—44no—
211C2×D4×C11—44no—
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×C11—44no—
245C22×C4×C11—44no—
246C22×C4×C11—44no—
247C22×C4×C11—44no—
248C22×C4×C11—44no—
249C22×C4×C11—44no—
250C22×C4×C11—44no—
251C22×C4×C11C22×C412yes—
252C22×C4×C11C2×D412yes—
253C22×C4×C11C2×D412yes—
254C2×C22⋊D11—28no—
255C2×C22⋊D11—44no—
256C2×C22⋊D11—44no—
257C2×C22⋊D11—44no—
258C2×C22⋊D11—44no—
259C2×C22⋊D11—44no—
260C2×C22⋊D11—44no—
261C2×C22⋊D11—44no—
262C2×C22⋊D11—44no—
263C2×C22⋊D11—44no—
264C2×C22⋊D11—44no—
265C2×C22⋊D11—44no—
266C2×C22⋊D11—44no—
267C2×C22⋊D11—44no—
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×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×Dic11C22×C412yes—
315C22×Dic11C22×C412yes—
316C22×Dic11C22×C412yes—
317C11×C22⋊C4—44no—
318C11×C22⋊C4—44no—
319C11×C22⋊C4—44no—
320C22⋊Dic11—44no—
321C22⋊Dic11—44no—
322C22⋊Dic11—44no—
323C22⋊Dic11—44no—
324C22⋊Dic11—44no—
325C22⋊Dic11—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—
331Dic11⋊C4—44no—
332C2×#392—111no—
333C2×#386—111no—
334C2×#386D1111yescharacteristic, complemented
335#1443—111no—
336#1443—111no—
337#1440—111no—
338#1440—111no—
339#1439—111no—
340#1439—111no—
341#1439—111no—
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—22no—
355C23×C11—22no—
356C23×C11—22no—
357C23×C11—22no—
358C23×C11—22no—
359C23×C11—22no—
360C23×C11—22no—
361C23×C11—22no—
362C23×C11—22no—
363C23×C11—22no—
364C23×C11—22no—
365C23×C11—22no—
366C23×C11—22no—
367C23×C11—22no—
368C23×C11—22no—
369C23×C11—22no—
370C23×C11—22no—
371C23×C11—22no—
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×C11—41no—
383C23×C11—41no—
384C23×C11—41no—
385C23×C11—41no—
386C23×C11—41no—
387C23×C11—41no—
388C23×C11—41no—
389C23×C11—41no—
390C23×C11—41no—
391C23×C11—41no—
392C23×C11—41no—
393C23×C11—41no—
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×C11—41no—
411C23×C11—41no—
412C23×C11—41no—
413C23×C11—41no—
414C23×C11—41no—
415C23×C11—41no—
416C23×C11C4×D414yes—
417C23×C11C23×C411yescharacteristic
418C23×C11C22×D411yescharacteristic
419C23×C11C2×#4111yescharacteristic
420C23×C11H(5,𝔽2)11yescharacteristic
421C23×C11H(5,𝔽2)11yescharacteristic
422C23×C11H(5,𝔽2)11yescharacteristic
423C23×C11H(5,𝔽2)11yescharacteristic
424C23×C11H(5,𝔽2)11yescharacteristic
425C23×C11H(5,𝔽2)11yescharacteristic
426C23×C11H(5,𝔽2)11yescharacteristic
427C23×C11H(5,𝔽2)11yescharacteristic
428C23×C11H(5,𝔽2)11yescharacteristic
429C23×C11H(5,𝔽2)11yescharacteristic
430C23×C11H(5,𝔽2)11yescharacteristic
431C23×C112−1+411yescharacteristic
432C22×D11—22no—
433C22×D11—22no—
434C22×D11—22no—
435C22×D11—22no—
436C22×D11—22no—
437C22×D11—22no—
438C22×D11—22no—
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—
467D4×C11—416no—
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—22no—
477C2×C4×C11—416no—
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—
504C22⋊D11—416no—
505C22⋊D11—416no—
506C2×Dic11—22no—
507C2×Dic11—22no—
508C2×Dic11—22no—
509C2×Dic11—22no—
510C2×Dic11—22no—
511C2×Dic11—22no—
512C2×Dic11—22no—
513C2×Dic11—22no—
514C2×Dic11—22no—
515C2×Dic11—41no—
516C2×Dic11—41no—
517C2×Dic11—41no—
518C2×Dic11—41no—
519C2×Dic11—41no—
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—
553C2×Dic11—41no—
554C2×Dic11—41no—
555C23×D4—111no—
556C23×D4—111no—
557C23×D4C2×D1111yescharacteristic
558C24×C4C2×D1111yescharacteristic
559C22×C4⋊C4—111no—
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—24no—
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×#95—111no—
591C2×#95C2×D1111yescharacteristic
592C2×#95C2×D1111yescharacteristic
593C22×C11—24no—
594C22×C11—24no—
595C22×C11—24no—
596C22×C11—42no—
597C22×C11—42no—
598C22×C11—42no—
599C22×C11—42no—
600C22×C11—42no—
601C22×C11—42no—
602C22×C11—42no—
603C22×C11—42no—
604C22×C11—42no—
605C22×C11—42no—
606C22×C11—42no—
607C22×C11—42no—
608C22×C11—42no—
609C22×C11—42no—
610C22×C11—42no—
611C22×C11—42no—
612C22×C11—42no—
613C22×C11—42no—
614C22×C11—42no—
615C22×C11—81no—
616C22×C11—81no—
617C22×C11—81no—
618C22×C11—81no—
619C22×C11—81no—
620C22×C11—81no—
621C22×C11—81no—
622C22×C11—81no—
623C22×C11C2×C4×D411yescharacteristic
624C22×C11#51811yescharacteristic
625C22×C11#51811yescharacteristic
626C22×C11#51811yescharacteristic
627C22×C11#51811yescharacteristic
628C22×C11#51811yescharacteristic
629C22×C11#52011yescharacteristic
630C22×C11#53411yescharacteristic
631C22×C11#53411yescharacteristic
632C22×C11#53411yescharacteristic
633C22×C11#53511yescharacteristic
634C22×C11#53511yescharacteristic
635C22×C11#53711yescharacteristic
636C22×C11#53811yescharacteristic
637C22×C11#53811yescharacteristic
638C22×C11#53811yescharacteristic
639C22×C11#53811yescharacteristic
640C22×C11#53811yescharacteristic
641C22×C11#53911yescharacteristic
642C22×C11#56011yescharacteristic
643C22×C11#56011yescharacteristic
644C22×C11#56011yescharacteristic
645C22×C11#56011yescharacteristic
646C22×C11#56011yescharacteristic
647C22×C11#56011yescharacteristic
648C22×C11#56011yescharacteristic
649C22×C11#56011yescharacteristic
650C22×C11#56011yescharacteristic
651C22×C11#56011yescharacteristic
652C22×C11#56011yescharacteristic
653C22×C11H(3,𝔽4)11yescharacteristic
654C22×C11#56211yescharacteristic
655C22×C11#56211yescharacteristic
656C22×C11#56211yescharacteristic
657C22×C11#56211yescharacteristic
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—
678Dic11—42no—
679Dic11—42no—
680Dic11—42no—
681Dic11—81no—
682Dic11—81no—
683Dic11—81no—
684Dic11—81no—
685C25—111no—
686C25C22×D1111yescharacteristic
687C25C22×D1111yescharacteristic
688C22×D4—22no—
689C22×D4—22no—
690C22×D4—41no—
691C22×D4—41no—
692C22×D4—41no—
693C22×D4—41no—
694C22×D4—114no—
695C22×D4—114no—
696C22×D4—222no—
697C22×D4—222no—
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×D4C4×D1114yes—
709C23×C4—41no—
710C23×C4—41no—
711C23×C4—41no—
712C23×C4—41no—
713C23×C4—41no—
714C23×C4—41no—
715C23×C4—111no—
716C23×C4—111no—
717C23×C4—111no—
718C23×C4—111no—
719C23×C4—111no—
720C23×C4—111no—
721C23×C4—111no—
722C23×C4C22⋊D1114yescomplemented
723C23×C4C22×D1111yescharacteristic
724C23×C4C22×D1111yescharacteristic
725C23×C4C22×D1111yescharacteristic
726C23×C4C22×D1111yescharacteristic
727C23×C4C22×D1111yescharacteristic
728C2×C4⋊C4—441no—
729C2×C4⋊C4—441no—
730C2×C4⋊C4—441no—
731C2×C22⋊C4—22no—
732C2×C22⋊C4—22no—
733C2×C22⋊C4—22no—
734C2×C22⋊C4—41no—
735C2×C22⋊C4—41no—
736C2×C22⋊C4—41no—
737C2×C22⋊C4—41no—
738C2×C22⋊C4—41no—
739C2×C22⋊C4—41no—
740C2×C22⋊C4—114no—
741C2×C22⋊C4—114no—
742C2×C22⋊C4—114no—
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⋊C4—441no—
773#95—22no—
774#95—22no—
775#95—114no—
776#95—222no—
777#95—222no—
778#95—441no—
779#95—441no—
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—44no—
790C2×C11—82no—
791C2×C11#232111yescharacteristic
792C2×C11#232111yescharacteristic
793C2×C11#232511yescharacteristic
794C2×C11#237511yescharacteristic
795C2×C11#237711yescharacteristic
796C2×C11#237711yescharacteristic
797C2×C11#238011yescharacteristic
798C2×C11#281211yescharacteristic
799C2×C11#281311yescharacteristic
800C2×C11#281311yescharacteristic
801C2×C11#281511yescharacteristic
802C2×C11#282411yescharacteristic
803C2×C11#282511yescharacteristic
804C2×C11#282511yescharacteristic
805C2×C11#282611yescharacteristic
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—21no—
822C24—21no—
823C24—21no—
824C24—21no—
825C24—21no—
826C24—21no—
827C24—21no—
828C24—21no—
829C24—21no—
830C24—21no—
831C24—21no—
832C24—21no—
833C24—112no—
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—
848C24C2×C4×D1112yes—
849C24C2×C4×D1112yes—
850C24#433912yes—
851C24C2×C22⋊D1112yes—
852C24C23×D1111yescharacteristic
853C2×D4—28no—
854C2×D4—44no—
855C2×D4—44no—
856C2×D4—44no—
857C2×D4—44no—
858C2×D4—44no—
859C2×D4—44no—
860C2×D4—228no—
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—44no—
907C22×C4—44no—
908C22×C4—44no—
909C22×C4—44no—
910C22×C4—44no—
911C22×C4—44no—
912C22×C4—44no—
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—221no—
956C22×C4—221no—
957C22×C4—221no—
958C22×C4—221no—
959C22×C4—221no—
960C22×C4—221no—
961C22×C4—221no—
962C22×C4C2×C4×D1112yes—
963C22×C4C2×C22⋊D1112yes—
964C22×C4C2×C22⋊D1112yes—
965C4⋊C4—444no—
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—22no—
989C23—22no—
990C23—22no—
991C23—22no—
992C23—22no—
993C23—22no—
994C23—22no—
995C23—22no—
996C23—22no—
997C23—22no—
998C23—22no—
999C23—22no—
1000C23—22no—
1001C23—22no—
1002C23—22no—
1003C23—22no—
1004C23—22no—
1005C23—22no—
1006C23—41no—
1007C23—41no—
1008C23—41no—
1009C23—41no—
1010C23—41no—
1011C23—41no—
1012C23—41no—
1013C23—41no—
1014C23—41no—
1015C23—41no—
1016C23—41no—
1017C23—41no—
1018C23—41no—
1019C23—41no—
1020C23—41no—
1021C23—41no—
1022C23—41no—
1023C23—41no—
1024C23—41no—
1025C23—41no—
1026C23—41no—
1027C23—41no—
1028C23—41no—
1029C23—41no—
1030C23—41no—
1031C23—41no—
1032C23—41no—
1033C23—41no—
1034C23—41no—
1035C23—41no—
1036C23—41no—
1037C23—41no—
1038C23—41no—
1039C23—41no—
1040C23—41no—
1041C23—41no—
1042C23—41no—
1043C23—41no—
1044C23—41no—
1045C23—41no—
1046C23—41no—
1047C23—41no—
1048C23—41no—
1049C23—41no—
1050C23—222no—
1051C23—222no—
1052C23—222no—
1053C23—222no—
1054C23—222no—
1055C23—222no—
1056C23—222no—
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—
1085C23C4×C22⋊D1114yes—
1086C23C22×C4×D1111yescharacteristic
1087C23C2×#433911yescharacteristic
1088C23#6703711yescharacteristic
1089C23#6703711yescharacteristic
1090C23#6703711yescharacteristic
1091C23#6703711yescharacteristic
1092C23#6703711yescharacteristic
1093C23#6703711yescharacteristic
1094C23#6703711yescharacteristic
1095C23#6703711yescharacteristic
1096C23#6704211yescharacteristic
1097C23#6704211yescharacteristic
1098C23#6704211yescharacteristic
1099C23#6704311yescharacteristic
1100C23C22×C22⋊D1111yescharacteristic
1101D4—416no—
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—416no—
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—222no—
1141C2×C4—222no—
1142C2×C4—222no—
1143C2×C4—222no—
1144C2×C4—222no—
1145C2×C4—222no—
1146C2×C4—222no—
1147C2×C4—222no—
1148C2×C4—222no—
1149C2×C4—441no—
1150C2×C4—441no—
1151C2×C4—441no—
1152C2×C4—441no—
1153C2×C4—441no—
1154C2×C4—441no—
1155C2×C4—441no—
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—24no—
1190C22—24no—
1191C22—24no—
1192C22—42no—
1193C22—42no—
1194C22—42no—
1195C22—42no—
1196C22—42no—
1197C22—42no—
1198C22—42no—
1199C22—42no—
1200C22—42no—
1201C22—42no—
1202C22—42no—
1203C22—42no—
1204C22—42no—
1205C22—42no—
1206C22—42no—
1207C22—42no—
1208C22—42no—
1209C22—42no—
1210C22—42no—
1211C22—81no—
1212C22—81no—
1213C22—81no—
1214C22—81no—
1215C22—81no—
1216C22—81no—
1217C22—81no—
1218C22—81no—
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#1062301711yescharacteristic
1236C22#1062302511yescharacteristic
1237C22#1062302511yescharacteristic
1238C22#1062307611yescharacteristic
1239C22#1062307611yescharacteristic
1240C22#1062307611yescharacteristic
1241C22#1062307711yescharacteristic
1242C22#1062309111yescharacteristic
1243C22#1062309111yescharacteristic
1244C22#1062309111yescharacteristic
1245C22#1062309511yescharacteristic
1246C22#1062312511yescharacteristic
1247C22#1062312611yescharacteristic
1248C22#1062312611yescharacteristic
1249C22#1062312611yescharacteristic
1250C22#1062315111yescharacteristic
1251C22#1062315111yescharacteristic
1252C22#1062315111yescharacteristic
1253C22#1062315111yescharacteristic
1254C22#1062315111yescharacteristic
1255C22#1062315111yescharacteristic
1256C22#1062315211yescharacteristic
1257C22#1062315211yescharacteristic
1258C22#1062319711yescharacteristic
1259C22#1062319711yescharacteristic
1260C22#1062319811yescharacteristic
1261C22#1062319811yescharacteristic
1262C22C2×C4×C22⋊D1111yescharacteristic
1263C22#1062333511yescharacteristic
1264C22#1062333511yescharacteristic
1265C22#1062333511yescharacteristic
1266C22#1062333611yescharacteristic
1267C22#1062336111yescharacteristic
1268C22#1062336411yescharacteristic
1269C4—42no—
1270C4—42no—
1271C4—42no—
1272C4—81no—
1273C4—81no—
1274C4—442no—
1275C4—442no—
1276C4—442no—
1277C4—881no—
1278C4—881no—
1279C4—881no—
1280C4—881no—
1281C2—44no—
1282C2—82no—
1283C2—882no—
1284C2#1307127011yescharacteristic
1285C2#1307127411yescharacteristic
1286C2#1307131411yescharacteristic
1287C2#1307175411yescharacteristic
1288C2#1307176811yescharacteristic
1289C2#1307177411yescharacteristic
1290C2#1307179111yescharacteristic
1291C2#1307661111yescharacteristic
1292C2#1307661611yescharacteristic
1293C2#1307661811yescharacteristic
1294C2#1307663811yescharacteristic
1295C2#1307669311yescharacteristic
1296C2#1307670211yescharacteristic
1297C2#1307670211yescharacteristic
1298C2#1307671111yescharacteristic
subgroupG/H
center, FrattiniC24C23×D11
commutatorC23×C11C23×C4
FittingC2×C11×#386C2
socle, cosocleC24×C11C24
prime radicalC2×#10622836C2
hypercenterC2×#386D11
hypocenterC11#14621
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ C2×#386

Complements

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

NH ≅ G/Ntype
2. C2×#10622826C2semidirect
3. #13066877C2semidirect
4. #13066876C2semidirect
5. #13066864C2semidirect
6. #13066863C2semidirect
7. #13066860C2semidirect
8. #13066859C2semidirect
9. #13066859C2semidirect
10. #13066857C2semidirect
11. #13066855C2semidirect
12. #13066855C2semidirect
13. #13066855C2semidirect
14. #13066839C2semidirect
15. C2×C11×#386C2semidirect
38. #10622836C4semidirect
70. C23×C4×C11D4semidirect
89. C22×C22⋊D11C2×C4semidirect
123. C2×C22⋊Dic11C2×C4semidirect
138. C2×(C2×D11)⋊C4C2×C4semidirect
157. C11⋊#95C2×C4semidirect
334. C2×#386D11semidirect
722. C23×C4C22⋊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×#106228362
C2×#106228262
#130668772
#130668762
#130668642
#130668632
#130668602
#130668592
#130668572
#130668552
#130668392
C2×C11×#3862
#1462111