Finite Group Databasebeta

← #14676629

Subgroups — #14676629

Order 2816.

2690 conjugacy classes of subgroups.

The subgroup lattice has 1234 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×(C22⋊D11)⋊C4C211yesmaximal, characteristic
2C2×#10622826C211yesmaximal, characteristic
3C2×#10622571C211yesmaximal, characteristic
4C2×#10622559C211yesmaximal, characteristic, complemented
5C2×#10622602C211yesmaximal, characteristic, complemented
6C22×C11⋊#95C211yesmaximal, characteristic, complemented
7#13066879C211yesmaximal, characteristic, complemented
8#13066874C211yesmaximal, characteristic, complemented
9#13066860C211yesmaximal, characteristic, complemented
10#13066858C211yesmaximal, characteristic, complemented
11#13066848C211yesmaximal, characteristic, complemented
12#13066847C211yesmaximal, characteristic, complemented
13#13066838C211yesmaximal, characteristic, complemented
14(C2×D11)⋊#95C211yesmaximal, characteristic, complemented
15C2×C11×#380C211yesmaximal, characteristic, complemented
16C24×C4×C11C2211yescharacteristic
17C23×C22⋊D11C2211yescharacteristic
18C24×Dic11C2211yescharacteristic
19C24×Dic11C2211yescharacteristic
20C23×C4×D11C2211yescharacteristic
21C22×C11×C4⋊C4C2211yescharacteristic
22C22×C11×C4⋊C4C2211yescharacteristic
23C22×C11×C22⋊C4C2211yescharacteristic
24C22×C11×C22⋊C4C2211yescharacteristic
25C22×C22⋊Dic11C2211yescharacteristic
26C22×(C2×D11)⋊C4C2211yescharacteristic
27C22×(C2×D11)⋊C4C2211yescharacteristic
28C22×(C2×D11)⋊C4C2211yescharacteristic
29C22×(C2×D11)⋊C4C2211yescharacteristic
30C22×(C2×D11)⋊C4C2211yescharacteristic
31C22×Dic11⋊C4C2211yescharacteristic
32C22×Dic11⋊C4C2211yescharacteristic
33C22×Dic11⋊C4C2211yescharacteristic
34C22×C4×Dic11C2211yescharacteristic
35C2×(C22⋊D11)⋊C4—24no—
36C2×(C22⋊D11)⋊C4—24no—
37C2×(C22⋊D11)⋊C4—24no—
38C11×#380—24no—
39C2×C11×#95C2211yescharacteristic
40C2×C11×#95C2211yescharacteristic
41#10622826C418yescomplemented
42C2×C11⋊#95—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
55C2×C11⋊#95C2211yescharacteristic
56C2×C11⋊#95C2211yescharacteristic
57#10622602—24no—
58#10622571—24no—
59#10622559—24no—
60C25×C11C2311yescharacteristic
61C24×D11C2311yescharacteristic
62C23×C4×C11—22no—
63C23×C4×C11—22no—
64C23×C4×C11—22no—
65C23×C4×C11—22no—
66C23×C4×C11—41no—
67C23×C4×C11—41no—
68C23×C4×C11C2×C414yescomplemented
69C23×C4×C11C2311yescharacteristic
70C23×C4×C11C2311yescharacteristic
71C23×C4×C11C2311yescharacteristic
72C23×C4×C11C2311yescharacteristic
73C23×C4×C11C2311yescharacteristic
74C23×C4×C11C2311yescharacteristic
75C22×C22⋊D11—22no—
76C22×C22⋊D11—22no—
77C22×C22⋊D11—22no—
78C22×C22⋊D11—22no—
79C22×C22⋊D11C2×C414yes—
80C22×C22⋊D11D414yes—
81C22×C22⋊D11Q814yes—
82C23×Dic11—22no—
83C23×Dic11—22no—
84C23×Dic11—22no—
85C23×Dic11—22no—
86C23×Dic11—22no—
87C23×Dic11—22no—
88C23×Dic11—22no—
89C23×Dic11—22no—
90C23×Dic11—22no—
91C23×Dic11—41no—
92C23×Dic11—41no—
93C23×Dic11—41no—
94C23×Dic11—41no—
95C23×Dic11D414yes—
96C23×Dic11C2311yescharacteristic
97C23×Dic11C2311yescharacteristic
98C23×Dic11C2311yescharacteristic
99C23×Dic11C2311yescharacteristic
100C23×Dic11C2311yescharacteristic
101C23×Dic11C2311yescharacteristic
102C23×Dic11C2311yescharacteristic
103C22×C4×D11—22no—
104C22×C4×D11—22no—
105C22×C4×D11—22no—
106C22×C4×D11—22no—
107C22×C4×D11—22no—
108C22×C4×D11—41no—
109C22×C4×D11—41no—
110C2×C11×C4⋊C4—22no—
111C2×C11×C4⋊C4—22no—
112C2×C11×C4⋊C4—22no—
113C2×C11×C4⋊C4—22no—
114C2×C11×C4⋊C4—41no—
115C2×C11×C4⋊C4—41no—
116C2×C11×C22⋊C4—22no—
117C2×C11×C22⋊C4—22no—
118C2×C11×C22⋊C4—22no—
119C2×C11×C22⋊C4—22no—
120C2×C11×C22⋊C4—22no—
121C2×C11×C22⋊C4D414yes—
122C2×C22⋊Dic11—22no—
123C2×C22⋊Dic11—22no—
124C2×C22⋊Dic11C2×C414yescomplemented
125C2×(C2×D11)⋊C4—22no—
126C2×(C2×D11)⋊C4—22no—
127C2×(C2×D11)⋊C4—22no—
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—41no—
135C2×(C2×D11)⋊C4—41no—
136C2×(C2×D11)⋊C4—41no—
137C2×(C2×D11)⋊C4—41no—
138C2×(C2×D11)⋊C4C2×C414yescomplemented
139C2×(C2×D11)⋊C4C2×C414yescomplemented
140C2×Dic11⋊C4—22no—
141C2×Dic11⋊C4—22no—
142C2×Dic11⋊C4—22no—
143C2×Dic11⋊C4—22no—
144C2×Dic11⋊C4—22no—
145C2×Dic11⋊C4—22no—
146C2×Dic11⋊C4—22no—
147C2×Dic11⋊C4—41no—
148C2×Dic11⋊C4—41no—
149C2×C4×Dic11—22no—
150C2×C4×Dic11—22no—
151C2×C4×Dic11—22no—
152(C22⋊D11)⋊C4—232no—
153C11×#95—22no—
154C11×#95—22no—
155C11⋊#95—22no—
156C11⋊#95—22no—
157C11⋊#95—22no—
158C11⋊#95—22no—
159C11⋊#95—22no—
160C11⋊#95—22no—
161C11⋊#95—22no—
162C11⋊#95—22no—
163C11⋊#95—22no—
164C11⋊#95—41no—
165C11⋊#95—41no—
166C11⋊#95C2×C414yescomplemented
167C11⋊#95C2×C414yescomplemented
168C11⋊#95D414yescomplemented
169#13975—111nomaximal, Sylow
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×C11C22×C412yes—
179C24×C11C2×D412yes—
180C24×C11C2×D412yes—
181C24×C11C2×D412yes—
182C24×C11C2×Q812yes—
183C24×C11#4112yes—
184C24×C11#4112yes—
185C24×C11C2411yescharacteristic
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×D11C22×C412yes—
199C23×D11C2×D412yes—
200C23×D11C2×Q812yes—
201C22×C4×C11—21no—
202C22×C4×C11—21no—
203C22×C4×C11—21no—
204C22×C4×C11—21no—
205C22×C4×C11—28no—
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—28no—
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—44no—
240C22×C4×C11—44no—
241C22×C4×C11—44no—
242C22×C4×C11—44no—
243C22×C4×C11—44no—
244C22×C4×C11C22×C412yes—
245C22×C4×C11C22×C412yes—
246C22×C4×C11C2×D412yes—
247C22×C4×C11C2×D412yes—
248C22×C4×C11C2×D412yes—
249C22×C4×C11#4112yes—
250C2×C22⋊D11—28no—
251C2×C22⋊D11—28no—
252C2×C22⋊D11—28no—
253C2×C22⋊D11—28no—
254C2×C22⋊D11—28no—
255C2×C22⋊D11—28no—
256C2×C22⋊D11C4⋊C4116yescomplemented
257C22×Dic11—28no—
258C22×Dic11—28no—
259C22×Dic11—28no—
260C22×Dic11—21no—
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—44no—
299C22×Dic11—44no—
300C22×Dic11—44no—
301C22×Dic11—44no—
302C22×Dic11—44no—
303C22×Dic11—44no—
304C22×Dic11—44no—
305C22×Dic11—44no—
306C22×Dic11—44no—
307C22×Dic11—44no—
308C22×Dic11—44no—
309C22×Dic11C22×C412yes—
310C22×Dic11C22×C412yes—
311C22×Dic11C22×C412yes—
312C22×Dic11C2×D412yes—
313C22×Dic11C2×D412yes—
314C22×Dic11C2×D412yes—
315C22×Dic11C2×D412yes—
316C22×Dic11C2×D412yes—
317C22×Dic11C2×Q812yes—
318C22×Dic11#4112yes—
319C22×Dic11#4112yes—
320C2×C4×D11—28no—
321C2×C4×D11—44no—
322C2×C4×D11—44no—
323C2×C4×D11—44no—
324C2×C4×D11—44no—
325C2×C4×D11—44no—
326C2×C4×D11—44no—
327C11×C4⋊C4—44no—
328C11×C4⋊C4—44no—
329C11×C22⋊C4—28no—
330C11×C22⋊C4—44no—
331C22⋊Dic11—28no—
332(C2×D11)⋊C4—28no—
333(C2×D11)⋊C4—28no—
334(C2×D11)⋊C4—44no—
335(C2×D11)⋊C4—44no—
336(C2×D11)⋊C4—44no—
337Dic11⋊C4—28no—
338Dic11⋊C4—44no—
339Dic11⋊C4—44no—
340C4×Dic11—28no—
341C22×C4×D4—111no—
342C2×#386—111no—
343C2×#386—111no—
344C2×#385—111no—
345C2×#385—111no—
346C2×#380D1111yescharacteristic, complemented
347C22×#95—111no—
348#1444—111no—
349#1442—111no—
350#1439—111no—
351#1439—111no—
352#1436—111no—
353#1436—111no—
354C22⋊#95—111no—
355C22⋊#95—111no—
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—22no—
373C23×C11—22no—
374C23×C11—22no—
375C23×C11—22no—
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×C11C2×C4⋊C414yes—
385C23×C11C4×D414yes—
386C23×C11C4×D414yes—
387C23×C11#12014yes—
388C23×C11C22⋊Q814yes—
389C23×C11C22⋊Q814yes—
390C23×C11#12314yes—
391C23×C11C23×C411yescharacteristic
392C23×C11C22×D411yescharacteristic
393C23×C11C22×D411yescharacteristic
394C23×C11C22×D411yescharacteristic
395C23×C11C22×D411yescharacteristic
396C23×C11C22×Q811yescharacteristic
397C23×C11C2×#4111yescharacteristic
398C23×C11C2×#4111yescharacteristic
399C23×C11C2×#4111yescharacteristic
400C23×C11C2×#4111yescharacteristic
401C23×C11C2×#4111yescharacteristic
402C23×C11H(5,𝔽2)11yescharacteristic
403C23×C11H(5,𝔽2)11yescharacteristic
404C23×C11H(5,𝔽2)11yescharacteristic
405C23×C112−1+411yescharacteristic
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—22no—
423C22×D11—22no—
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×D11C2×C4⋊C414yes—
441C2×C4×C11—22no—
442C2×C4×C11—22no—
443C2×C4×C11—22no—
444C2×C4×C11—22no—
445C2×C4×C11—22no—
446C2×C4×C11—22no—
447C2×C4×C11—22no—
448C2×C4×C11—22no—
449C2×C4×C11—22no—
450C2×C4×C11—22no—
451C2×C4×C11—22no—
452C2×C4×C11—22no—
453C2×C4×C11—22no—
454C2×C4×C11—22no—
455C2×C4×C11—22no—
456C2×C4×C11—416no—
457C2×C4×C11—41no—
458C2×C4×C11—41no—
459C2×C4×C11—41no—
460C2×C4×C11—41no—
461C2×C4×C11—41no—
462C2×C4×C11—41no—
463C2×C4×C11—41no—
464C2×C4×C11—41no—
465C2×C4×C11—41no—
466C2×C4×C11—41no—
467C2×C4×C11—41no—
468C2×C4×C11—41no—
469C2×C4×C11—41no—
470C2×C4×C11—41no—
471C2×C4×C11—41no—
472C2×C4×C11—41no—
473C2×C4×C11—41no—
474C2×C4×C11—41no—
475C2×C4×C11—41no—
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×C11C4×D414yescomplemented
484C22⋊D11—232no—
485C2×Dic11—22no—
486C2×Dic11—22no—
487C2×Dic11—22no—
488C2×Dic11—22no—
489C2×Dic11—22no—
490C2×Dic11—22no—
491C2×Dic11—22no—
492C2×Dic11—22no—
493C2×Dic11—22no—
494C2×Dic11—22no—
495C2×Dic11—22no—
496C2×Dic11—22no—
497C2×Dic11—22no—
498C2×Dic11—22no—
499C2×Dic11—22no—
500C2×Dic11—22no—
501C2×Dic11—22no—
502C2×Dic11—22no—
503C2×Dic11—22no—
504C2×Dic11—22no—
505C2×Dic11—22no—
506C2×Dic11—22no—
507C2×Dic11—22no—
508C2×Dic11—22no—
509C2×Dic11—22no—
510C2×Dic11—22no—
511C2×Dic11—22no—
512C2×Dic11—416no—
513C2×Dic11—416no—
514C2×Dic11—41no—
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×Dic11C2×C4⋊C414yes—
535C2×Dic11#12114yes—
536C4×D11—416no—
537C23×D4—111no—
538C24×C4—111no—
539C24×C4—111no—
540C24×C4—111no—
541C24×C4C2×D1111yescharacteristic
542C2×C4×D4—224no—
543C2×C4×D4—224no—
544C2×C4×D4—224no—
545C22×C4⋊C4—111no—
546C22×C4⋊C4—111no—
547C22×C4⋊C4—111no—
548C22×C4⋊C4C2×D1111yescharacteristic
549C22×C4⋊C4C2×D1111yescharacteristic
550C22×C22⋊C4—111no—
551C22×C22⋊C4—111no—
552C22×C22⋊C4—111no—
553C22×C22⋊C4—111no—
554C22×C22⋊C4—111no—
555C22×C22⋊C4—111no—
556C22×C22⋊C4C2×D1111yescharacteristic
557C22×C22⋊C4C2×D1111yescharacteristic
558C22×C42—111no—
559#386—118no—
560#386—224no—
561#385—224no—
562#385—224no—
563#380—24no—
564C2×#95—111no—
565C2×#95—111no—
566C2×#95—111no—
567C2×#95—111no—
568C2×#95—111no—
569C2×#95—111no—
570C2×#95—111no—
571C2×#95—111no—
572C2×#95—111no—
573C2×#95—111no—
574C2×#95—111no—
575C2×#95—111no—
576C2×#95—111no—
577C2×#95—111no—
578C2×#95—224no—
579C2×#95C2×D1111yescharacteristic
580C2×#95C2×D1111yescharacteristic
581C22×C11—24no—
582C22×C11—24no—
583C22×C11—24no—
584C22×C11—24no—
585C22×C11—24no—
586C22×C11—24no—
587C22×C11—24no—
588C22×C11—24no—
589C22×C11—24no—
590C22×C11—24no—
591C22×C11—24no—
592C22×C11—24no—
593C22×C11—24no—
594C22×C11—24no—
595C22×C11#38518yescomplemented
596C22×C11C22×C4⋊C411yescharacteristic
597C22×C11C2×C4×D411yescharacteristic
598C22×C11C2×C4×D411yescharacteristic
599C22×C11C2×C4×D411yescharacteristic
600C22×C11C4×#4111yescharacteristic
601C22×C11#51811yescharacteristic
602C22×C11#52011yescharacteristic
603C22×C11C2×#12011yescharacteristic
604C22×C11C2×#12111yescharacteristic
605C22×C11C2×C22⋊Q811yescharacteristic
606C22×C11C2×C22⋊Q811yescharacteristic
607C22×C11C2×#12311yescharacteristic
608C22×C11#52511yescharacteristic
609C22×C11#52911yescharacteristic
610C22×C11#53211yescharacteristic
611C22×C11#53411yescharacteristic
612C22×C11#53711yescharacteristic
613C22×C11#53811yescharacteristic
614C22×C11#53911yescharacteristic
615C22×C11D4211yescharacteristic
616C22×C11D4211yescharacteristic
617C22×C11#54611yescharacteristic
618C22×C11#54611yescharacteristic
619C22×C11#54611yescharacteristic
620C22×C11#54611yescharacteristic
621C22×C11#54611yescharacteristic
622C22×C11#54711yescharacteristic
623C22×C11#54711yescharacteristic
624C22×C11D4×Q811yescharacteristic
625C22×C11#55111yescharacteristic
626C22×C11#55111yescharacteristic
627C22×C11#55211yescharacteristic
628C22×C11#55411yescharacteristic
629C22×C11#55411yescharacteristic
630C22×C11#55411yescharacteristic
631C2×D11—24no—
632C2×D11—24no—
633C2×D11—24no—
634C2×D11—42no—
635C2×D11—42no—
636C2×D11—42no—
637C2×D11—42no—
638C2×D11—42no—
639C2×D11—42no—
640C2×D11—42no—
641C2×D11—42no—
642C2×D11—42no—
643C2×D11—42no—
644C2×D11—42no—
645C2×D11—42no—
646C4×C11—24no—
647C4×C11—42no—
648C4×C11—42no—
649C4×C11—42no—
650C4×C11—81no—
651C4×C11—81no—
652Dic11—24no—
653Dic11—24no—
654Dic11—42no—
655Dic11—42no—
656Dic11—42no—
657Dic11—42no—
658Dic11—42no—
659C25—111no—
660C25C22×D1111yescharacteristic
661C22×D4—114no—
662C22×D4—114no—
663C22×D4—114no—
664C22×D4—222no—
665C22×D4—222no—
666C22×D4—222no—
667C22×D4—222no—
668C23×C4—22no—
669C23×C4—22no—
670C23×C4—22no—
671C23×C4—22no—
672C23×C4—41no—
673C23×C4—41no—
674C23×C4—111no—
675C23×C4—111no—
676C23×C4—111no—
677C23×C4—111no—
678C23×C4—111no—
679C23×C4—111no—
680C23×C4—111no—
681C23×C4—114no—
682C23×C4—222no—
683C23×C4—222no—
684C23×C4—222no—
685C23×C4—222no—
686C23×C4—222no—
687C23×C4—222no—
688C23×C4—222no—
689C23×C4—222no—
690C23×C4—222no—
691C23×C4—222no—
692C23×C4—222no—
693C23×C4—222no—
694C23×C4—222no—
695C23×C4—222no—
696C23×C4—441no—
697C23×C4—441no—
698C23×C4—441no—
699C23×C4—441no—
700C23×C4—441no—
701C23×C4—441no—
702C23×C4C4×D1114yescomplemented
703C23×C4C22×D1111yescharacteristic
704C23×C4C22×D1111yescharacteristic
705C23×C4C22×D1111yescharacteristic
706C23×C4C22×D1111yescharacteristic
707C23×C4C22×D1111yescharacteristic
708C23×C4C22×D1111yescharacteristic
709C4×D4—2232no—
710C2×C4⋊C4—22no—
711C2×C4⋊C4—22no—
712C2×C4⋊C4—22no—
713C2×C4⋊C4—22no—
714C2×C4⋊C4—41no—
715C2×C4⋊C4—41no—
716C2×C4⋊C4—222no—
717C2×C4⋊C4—222no—
718C2×C4⋊C4—222no—
719C2×C4⋊C4—222no—
720C2×C4⋊C4—222no—
721C2×C4⋊C4—222no—
722C2×C4⋊C4—222no—
723C2×C4⋊C4—441no—
724C2×C4⋊C4—441no—
725C2×C22⋊C4—22no—
726C2×C22⋊C4—22no—
727C2×C22⋊C4—22no—
728C2×C22⋊C4—22no—
729C2×C22⋊C4—22no—
730C2×C22⋊C4—114no—
731C2×C22⋊C4—114no—
732C2×C22⋊C4—114no—
733C2×C22⋊C4—222no—
734C2×C22⋊C4—222no—
735C2×C22⋊C4—222no—
736C2×C22⋊C4—222no—
737C2×C22⋊C4—222no—
738C2×C22⋊C4—222no—
739C2×C22⋊C4—222no—
740C2×C22⋊C4—222no—
741C2×C22⋊C4—222no—
742C2×C22⋊C4—222no—
743C2×C22⋊C4—222no—
744C2×C22⋊C4—441no—
745C2×C22⋊C4—441no—
746C2×C22⋊C4—441no—
747C2×C22⋊C4—441no—
748C2×C22⋊C4C22⋊D1114yes—
749C2×C42—222no—
750C2×C42—222no—
751C2×C42—222no—
752#95—22no—
753#95—22no—
754#95—114no—
755#95—114no—
756#95—114no—
757#95—222no—
758#95—222no—
759#95—222no—
760#95—222no—
761#95—222no—
762#95—222no—
763#95—222no—
764#95—222no—
765#95—222no—
766#95—441no—
767#95—441no—
768C2×C11—28no—
769C2×C11C2×#38511yescharacteristic
770C2×C11C4×#12111yescharacteristic
771C2×C11#232511yescharacteristic
772C2×C11D4×C4⋊C411yescharacteristic
773C2×C11#234911yescharacteristic
774C2×C11#235811yescharacteristic
775C2×C11#235911yescharacteristic
776C2×C11#241011yescharacteristic
777C2×C11#241711yescharacteristic
778C2×C11#241811yescharacteristic
779C2×C11#241911yescharacteristic
780C2×C11#243011yescharacteristic
781C2×C11#244911yescharacteristic
782C2×C11#245011yescharacteristic
783C2×C11#256411yescharacteristic
784D11—44no—
785C24—21no—
786C24—21no—
787C24—21no—
788C24—21no—
789C24—21no—
790C24—21no—
791C24—21no—
792C24—21no—
793C24—112no—
794C24—112no—
795C24—112no—
796C24—221no—
797C24—221no—
798C24—221no—
799C24—221no—
800C24—221no—
801C24—221no—
802C24—221no—
803C24—221no—
804C24—221no—
805C24—221no—
806C24—221no—
807C24—221no—
808C24C2×C4×D1112yes—
809C24#433912yes—
810C24D4×D1112yes—
811C24D4×D1112yes—
812C24Q8×D1112yes—
813C24#434312yes—
814C24C2×C22⋊D1112yes—
815C24C23×D1111yescharacteristic
816C2×D4—1116no—
817C2×D4—228no—
818C2×D4—228no—
819C2×D4—228no—
820C2×D4—228no—
821C2×D4—228no—
822C2×D4—228no—
823C22×C4—21no—
824C22×C4—21no—
825C22×C4—21no—
826C22×C4—21no—
827C22×C4—28no—
828C22×C4—21no—
829C22×C4—21no—
830C22×C4—21no—
831C22×C4—21no—
832C22×C4—21no—
833C22×C4—21no—
834C22×C4—21no—
835C22×C4—21no—
836C22×C4—21no—
837C22×C4—21no—
838C22×C4—21no—
839C22×C4—21no—
840C22×C4—21no—
841C22×C4—21no—
842C22×C4—21no—
843C22×C4—21no—
844C22×C4—21no—
845C22×C4—21no—
846C22×C4—28no—
847C22×C4—21no—
848C22×C4—21no—
849C22×C4—21no—
850C22×C4—21no—
851C22×C4—21no—
852C22×C4—21no—
853C22×C4—21no—
854C22×C4—21no—
855C22×C4—21no—
856C22×C4—21no—
857C22×C4—21no—
858C22×C4—21no—
859C22×C4—21no—
860C22×C4—21no—
861C22×C4—44no—
862C22×C4—44no—
863C22×C4—44no—
864C22×C4—44no—
865C22×C4—44no—
866C22×C4—112no—
867C22×C4—112no—
868C22×C4—112no—
869C22×C4—112no—
870C22×C4—112no—
871C22×C4—112no—
872C22×C4—112no—
873C22×C4—112no—
874C22×C4—112no—
875C22×C4—112no—
876C22×C4—112no—
877C22×C4—228no—
878C22×C4—228no—
879C22×C4—221no—
880C22×C4—221no—
881C22×C4—221no—
882C22×C4—221no—
883C22×C4—221no—
884C22×C4—221no—
885C22×C4—221no—
886C22×C4—221no—
887C22×C4—228no—
888C22×C4—228no—
889C22×C4—221no—
890C22×C4—221no—
891C22×C4—221no—
892C22×C4—221no—
893C22×C4—221no—
894C22×C4—221no—
895C22×C4—221no—
896C22×C4—221no—
897C22×C4—221no—
898C22×C4—221no—
899C22×C4—221no—
900C22×C4—221no—
901C22×C4—221no—
902C22×C4—221no—
903C22×C4—221no—
904C22×C4—221no—
905C22×C4—221no—
906C22×C4—221no—
907C22×C4—221no—
908C22×C4—221no—
909C22×C4—221no—
910C22×C4—221no—
911C22×C4—221no—
912C22×C4—221no—
913C22×C4—221no—
914C22×C4—221no—
915C22×C4—221no—
916C22×C4—221no—
917C22×C4—221no—
918C22×C4—221no—
919C22×C4—444no—
920C22×C4—444no—
921C22×C4—444no—
922C22×C4—444no—
923C22×C4—444no—
924C22×C4—444no—
925C22×C4—444no—
926C22×C4—444no—
927C22×C4—444no—
928C22×C4—444no—
929C22×C4—444no—
930C22×C4—444no—
931C22×C4—444no—
932C22×C4—444no—
933C22×C4—444no—
934C22×C4—444no—
935C22×C4—444no—
936C22×C4C2×C4×D1112yes—
937C22×C4C2×C4×D1112yes—
938C22×C4D4×D1112yes—
939C22×C4#434112yes—
940C22×C4C2×C22⋊D1112yes—
941C22×C4C2×C22⋊D1112yes—
942C4⋊C4—44no—
943C4⋊C4—44no—
944C4⋊C4—228no—
945C4⋊C4—444no—
946C4⋊C4—444no—
947C22⋊C4—28no—
948C22⋊C4—44no—
949C22⋊C4—228no—
950C22⋊C4—228no—
951C22⋊C4—228no—
952C22⋊C4—444no—
953C22⋊C4—444no—
954C22⋊C4—444no—
955C42—228no—
956C11#1397511yescharacteristic, complemented, Sylow
957C23—22no—
958C23—22no—
959C23—22no—
960C23—22no—
961C23—22no—
962C23—22no—
963C23—22no—
964C23—22no—
965C23—22no—
966C23—22no—
967C23—22no—
968C23—22no—
969C23—22no—
970C23—22no—
971C23—22no—
972C23—22no—
973C23—22no—
974C23—22no—
975C23—22no—
976C23—22no—
977C23—22no—
978C23—22no—
979C23—22no—
980C23—22no—
981C23—22no—
982C23—22no—
983C23—22no—
984C23—22no—
985C23—114no—
986C23—222no—
987C23—222no—
988C23—222no—
989C23—222no—
990C23—222no—
991C23—222no—
992C23—222no—
993C23—222no—
994C23—222no—
995C23—222no—
996C23—222no—
997C23—222no—
998C23—222no—
999C23—222no—
1000C23—222no—
1001C23—222no—
1002C23—222no—
1003C23—222no—
1004C23—441no—
1005C23—441no—
1006C23—441no—
1007C23—441no—
1008C23—441no—
1009C23—441no—
1010C23—441no—
1011C23—441no—
1012C23—441no—
1013C23—441no—
1014C23—441no—
1015C23—441no—
1016C23—441no—
1017C23—441no—
1018C23—441no—
1019C23—441no—
1020C23C4⋊C4×D1114yes—
1021C23#6694614yes—
1022C23#6694714yes—
1023C23#6694914yes—
1024C23C4×C22⋊D1114yes—
1025C23#6699014yes—
1026C23#6699914yes—
1027C23C22×C4×D1111yescharacteristic
1028C23C2×#433911yescharacteristic
1029C23C2×D4×D1111yescharacteristic
1030C23C2×D4×D1111yescharacteristic
1031C23C2×D4×D1111yescharacteristic
1032C23C2×#434111yescharacteristic
1033C23#6703711yescharacteristic
1034C23#6703711yescharacteristic
1035C23C2×Q8×D1111yescharacteristic
1036C23C2×#434311yescharacteristic
1037C23#41×D1111yescharacteristic
1038C23#41×D1111yescharacteristic
1039C23#6704211yescharacteristic
1040C23#6704311yescharacteristic
1041C23C22×C22⋊D1111yescharacteristic
1042D4—2232no—
1043C2×C4—22no—
1044C2×C4—22no—
1045C2×C4—22no—
1046C2×C4—22no—
1047C2×C4—22no—
1048C2×C4—22no—
1049C2×C4—22no—
1050C2×C4—22no—
1051C2×C4—22no—
1052C2×C4—22no—
1053C2×C4—22no—
1054C2×C4—22no—
1055C2×C4—22no—
1056C2×C4—22no—
1057C2×C4—22no—
1058C2×C4—416no—
1059C2×C4—41no—
1060C2×C4—41no—
1061C2×C4—41no—
1062C2×C4—41no—
1063C2×C4—41no—
1064C2×C4—41no—
1065C2×C4—41no—
1066C2×C4—41no—
1067C2×C4—41no—
1068C2×C4—41no—
1069C2×C4—41no—
1070C2×C4—41no—
1071C2×C4—41no—
1072C2×C4—41no—
1073C2×C4—41no—
1074C2×C4—41no—
1075C2×C4—41no—
1076C2×C4—41no—
1077C2×C4—41no—
1078C2×C4—41no—
1079C2×C4—41no—
1080C2×C4—41no—
1081C2×C4—41no—
1082C2×C4—41no—
1083C2×C4—41no—
1084C2×C4—41no—
1085C2×C4—114no—
1086C2×C4—114no—
1087C2×C4—222no—
1088C2×C4—222no—
1089C2×C4—222no—
1090C2×C4—222no—
1091C2×C4—222no—
1092C2×C4—222no—
1093C2×C4—222no—
1094C2×C4—222no—
1095C2×C4—222no—
1096C2×C4—222no—
1097C2×C4—222no—
1098C2×C4—222no—
1099C2×C4—222no—
1100C2×C4—222no—
1101C2×C4—222no—
1102C2×C4—222no—
1103C2×C4—222no—
1104C2×C4—222no—
1105C2×C4—222no—
1106C2×C4—222no—
1107C2×C4—222no—
1108C2×C4—222no—
1109C2×C4—222no—
1110C2×C4—222no—
1111C2×C4—222no—
1112C2×C4—222no—
1113C2×C4—222no—
1114C2×C4—4416no—
1115C2×C4—4416no—
1116C2×C4—4416no—
1117C2×C4—441no—
1118C2×C4—441no—
1119C2×C4—441no—
1120C2×C4—441no—
1121C2×C4—441no—
1122C2×C4—441no—
1123C2×C4—441no—
1124C2×C4—441no—
1125C2×C4—441no—
1126C2×C4—441no—
1127C2×C4—441no—
1128C2×C4—441no—
1129C2×C4—441no—
1130C2×C4—441no—
1131C2×C4—441no—
1132C2×C4—441no—
1133C2×C4—441no—
1134C2×C4—441no—
1135C2×C4—441no—
1136C2×C4—441no—
1137C2×C4(C22⋊D11)⋊C414yescomplemented
1138C22—24no—
1139C22—24no—
1140C22—24no—
1141C22—24no—
1142C22—24no—
1143C22—24no—
1144C22—24no—
1145C22—24no—
1146C22—24no—
1147C22—24no—
1148C22—24no—
1149C22—24no—
1150C22—24no—
1151C22—24no—
1152C22—224no—
1153C22—224no—
1154C22—224no—
1155C22—442no—
1156C22—442no—
1157C22—442no—
1158C22—442no—
1159C22—442no—
1160C22—442no—
1161C22—442no—
1162C22—442no—
1163C22—442no—
1164C22—442no—
1165C22—442no—
1166C22—442no—
1167C22#1062260218yescomplemented
1168C22C2×(C22⋊D11)⋊C411yescharacteristic
1169C22#1062301711yescharacteristic
1170C22#1062302111yescharacteristic
1171C22#1062302611yescharacteristic
1172C22C2×C4⋊C4×D1111yescharacteristic
1173C22C2×#6694611yescharacteristic
1174C22C2×#6694711yescharacteristic
1175C22C2×#6694911yescharacteristic
1176C22#1062305311yescharacteristic
1177C22#1062305411yescharacteristic
1178C22#1062305811yescharacteristic
1179C22#1062306211yescharacteristic
1180C22#1062312711yescharacteristic
1181C22#1062312811yescharacteristic
1182C22D11×#12111yescharacteristic
1183C22#1062313611yescharacteristic
1184C22#1062314011yescharacteristic
1185C22#1062314111yescharacteristic
1186C22#1062314111yescharacteristic
1187C22#1062314211yescharacteristic
1188C22#1062315511yescharacteristic
1189C22#1062315811yescharacteristic
1190C22#1062316311yescharacteristic
1191C22#1062316611yescharacteristic
1192C22#1062316711yescharacteristic
1193C22#1062316711yescharacteristic
1194C22#1062317511yescharacteristic
1195C22#1062317611yescharacteristic
1196C22C2×C4×C22⋊D1111yescharacteristic
1197C22C2×#6699011yescharacteristic
1198C22D4×C22⋊D1111yescharacteristic
1199C22#1062333711yescharacteristic
1200C22C2×#6699911yescharacteristic
1201C22#1062335511yescharacteristic
1202C22#1062336011yescharacteristic
1203C4—24no—
1204C4—42no—
1205C4—42no—
1206C4—42no—
1207C4—81no—
1208C4—81no—
1209C4—224no—
1210C4—224no—
1211C4—442no—
1212C4—442no—
1213C4—442no—
1214C4—442no—
1215C4—442no—
1216C2—28no—
1217C2—444no—
1218C2C2×#1062260211yescharacteristic
1219C2#1307112211yescharacteristic
1220C2#1307131611yescharacteristic
1221C2#1307151211yescharacteristic
1222C2#1307152011yescharacteristic
1223C2#1307159511yescharacteristic
1224C2#1307160811yescharacteristic
1225C2#1307198711yescharacteristic
1226C2#1307206611yescharacteristic
1227C2#1307208411yescharacteristic
1228C2#1307209911yescharacteristic
1229C2#1307222211yescharacteristic
1230C2#1307242111yescharacteristic
1231C2#1307243611yescharacteristic
1232C2#1307379411yescharacteristic
subgroupG/H
center, FrattiniC24C23×D11
commutatorC23×C11C23×C4
FittingC2×C11×#380C2
socle, cosocleC24×C11C24
prime radicalC23×C22⋊D11C22
hypercenterC2×#380D11
hypocenterC11#13975
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ C2×#380

Complements

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

NH ≅ G/Ntype
4. C2×#10622559C2semidirect
5. C2×#10622602C2semidirect
6. C22×C11⋊#95C2semidirect
7. #13066879C2semidirect
8. #13066874C2semidirect
9. #13066860C2semidirect
10. #13066858C2semidirect
11. #13066848C2semidirect
12. #13066847C2semidirect
13. #13066838C2semidirect
14. (C2×D11)⋊#95C2semidirect
15. C2×C11×#380C2semidirect
41. #10622826C4semidirect
68. C23×C4×C11C2×C4semidirect
124. C2×C22⋊Dic11C2×C4semidirect
138. C2×(C2×D11)⋊C4C2×C4semidirect
139. C2×(C2×D11)⋊C4C2×C4semidirect
166. C11⋊#95C2×C4semidirect
167. C11⋊#95C2×C4semidirect
168. C11⋊#95D4semidirect
256. C2×C22⋊D11C4⋊C4semidirect
346. C2×#380D11semidirect
483. C2×C4×C11C4×D4semidirect
595. C22×C11#385semidirect
702. C23×C4C4×D11semidirect
956. C11#13975semidirect
1137. C2×C4(C22⋊D11)⋊C4semidirect
1167. C22#10622602semidirect

Maximal subgroups

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

subgroupindex
C22×(C22⋊D11)⋊C42
C2×#106228262
C2×#106225712
C2×#106225592
C2×#106226022
C22×C11⋊#952
#130668792
#130668742
#130668602
#130668582
#130668482
#130668472
#130668382
(C2×D11)⋊#952
C2×C11×#3802
#1397511