Finite Group Databasebeta

← #14676650

Subgroups — #14676650

Order 2816.

2558 conjugacy classes of subgroups.

The subgroup lattice has 1230 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×(C22⋊D11)⋊C4C211yesmaximal, characteristic
2C2×#10622570C211yesmaximal, characteristic
3C2×#10622570C211yesmaximal, characteristic
4C2×#10622260C211yesmaximal, characteristic, complemented
5C2×#10622563C211yesmaximal, characteristic, complemented
6C2×#10622281C211yesmaximal, characteristic, complemented
7C2×#10622559C211yesmaximal, characteristic, complemented
8C2×#10622602C211yesmaximal, characteristic, complemented
9C2×#10622589C211yesmaximal, characteristic, complemented
10#13066862C211yesmaximal, characteristic, complemented
11#13066860C211yesmaximal, characteristic, complemented
12#13066859C211yesmaximal, characteristic, complemented
13Dic11⋊#95C211yesmaximal, characteristic, complemented
14#95×Dic11C211yesmaximal, characteristic, complemented
15C11×#1439C211yesmaximal, characteristic, complemented
16C23×C22⋊D11C2211yescharacteristic
17C24×Dic11C2211yescharacteristic
18C23×C4×D11C2211yescharacteristic
19C22×C11×C4⋊C4C2211yescharacteristic
20C22×C11×C22⋊C4C2211yescharacteristic
21C22×C11×C22⋊C4C2211yescharacteristic
22C22×C11×C22⋊C4C2211yescharacteristic
23C22×C22⋊Dic11C2211yescharacteristic
24C22×C22⋊Dic11C2211yescharacteristic
25C22×(C2×D11)⋊C4C2211yescharacteristic
26C22×(C2×D11)⋊C4C2211yescharacteristic
27C22×(C2×D11)⋊C4C2211yescharacteristic
28C22×(C2×D11)⋊C4C2211yescharacteristic
29C22×(C2×D11)⋊C4C2211yescharacteristic
30C22×C4⋊Dic11C2211yescharacteristic
31C22×C4⋊Dic11C2211yescharacteristic
32C22×Dic11⋊C4C2211yescharacteristic
33C22×Dic11⋊C4C2211yescharacteristic
34C22×Dic11⋊C4C2211yescharacteristic
35C22×Dic11⋊C4C2211yescharacteristic
36C22×Dic11⋊C4C2211yescharacteristic
37C22×Dic11⋊C4C2211yescharacteristic
38C22×C4×Dic11C2211yescharacteristic
39C22×C4×Dic11C2211yescharacteristic
40C22×C4×Dic11C2211yescharacteristic
41C2×(C22⋊D11)⋊C4—24no—
42C2×(C22⋊D11)⋊C4—24no—
43C2×(C22⋊D11)⋊C4—24no—
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
54#10622602—24no—
55#10622589—24no—
56#10622570—24no—
57#10622570C418yescomplemented
58#10622563—24no—
59#10622559—24no—
60#10622281—24no—
61#10622260—24no—
62C25×C11C2311yescharacteristic
63C24×D11C2311yescharacteristic
64C23×C4×C11C2311yescharacteristic
65C23×C4×C11C2311yescharacteristic
66C23×C4×C11C2311yescharacteristic
67C23×C4×C11C2311yescharacteristic
68C23×C4×C11C2311yescharacteristic
69C23×C4×C11C2311yescharacteristic
70C22×C22⋊D11—22no—
71C22×C22⋊D11—22no—
72C22×C22⋊D11—22no—
73C22×C22⋊D11—22no—
74C22×C22⋊D11C2×C414yes—
75C22×C22⋊D11D414yes—
76C22×C22⋊D11Q814yes—
77C23×Dic11—22no—
78C23×Dic11—22no—
79C23×Dic11—22no—
80C23×Dic11—22no—
81C23×Dic11—22no—
82C23×Dic11—41no—
83C23×Dic11—41no—
84C23×Dic11C2311yescharacteristic
85C23×Dic11C2311yescharacteristic
86C23×Dic11C2311yescharacteristic
87C23×Dic11C2311yescharacteristic
88C23×Dic11C2311yescharacteristic
89C23×Dic11C2311yescharacteristic
90C23×Dic11C2311yescharacteristic
91C22×C4×D11—22no—
92C22×C4×D11—22no—
93C22×C4×D11—22no—
94C22×C4×D11—22no—
95C22×C4×D11—22no—
96C22×C4×D11—41no—
97C22×C4×D11—41no—
98C2×C11×C4⋊C4—22no—
99C2×C11×C4⋊C4—22no—
100C2×C11×C4⋊C4—41no—
101C2×C11×C22⋊C4—22no—
102C2×C11×C22⋊C4—22no—
103C2×C11×C22⋊C4—22no—
104C2×C11×C22⋊C4—22no—
105C2×C11×C22⋊C4—22no—
106C2×C11×C22⋊C4—22no—
107C2×C11×C22⋊C4—22no—
108C2×C11×C22⋊C4—41no—
109C2×C11×C22⋊C4C2×C414yescomplemented
110C2×C22⋊Dic11—22no—
111C2×C22⋊Dic11—22no—
112C2×C22⋊Dic11—22no—
113C2×C22⋊Dic11—22no—
114C2×C22⋊Dic11—41no—
115C2×C22⋊Dic11C2×C414yescomplemented
116C2×(C2×D11)⋊C4—22no—
117C2×(C2×D11)⋊C4—22no—
118C2×(C2×D11)⋊C4—22no—
119C2×(C2×D11)⋊C4—22no—
120C2×(C2×D11)⋊C4—22no—
121C2×(C2×D11)⋊C4—22no—
122C2×(C2×D11)⋊C4—22no—
123C2×(C2×D11)⋊C4—22no—
124C2×(C2×D11)⋊C4—22no—
125C2×(C2×D11)⋊C4—22no—
126C2×(C2×D11)⋊C4—22no—
127C2×(C2×D11)⋊C4—41no—
128C2×(C2×D11)⋊C4—41no—
129C2×(C2×D11)⋊C4C2×C414yescomplemented
130C2×(C2×D11)⋊C4C2×C414yescomplemented
131C2×C4⋊Dic11—22no—
132C2×C4⋊Dic11—22no—
133C2×C4⋊Dic11—22no—
134C2×C4⋊Dic11—22no—
135C2×C4⋊Dic11—22no—
136C2×C4⋊Dic11—41no—
137C2×Dic11⋊C4—22no—
138C2×Dic11⋊C4—22no—
139C2×Dic11⋊C4—22no—
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—22no—
148C2×Dic11⋊C4—22no—
149C2×Dic11⋊C4—22no—
150C2×Dic11⋊C4—22no—
151C2×Dic11⋊C4—41no—
152C2×Dic11⋊C4—41no—
153C2×Dic11⋊C4C2×C414yescomplemented
154C2×Dic11⋊C4D414yes—
155C2×C4×Dic11—22no—
156C2×C4×Dic11—22no—
157C2×C4×Dic11—22no—
158C2×C4×Dic11—22no—
159C2×C4×Dic11—22no—
160C2×C4×Dic11—22no—
161C2×C4×Dic11—22no—
162C2×C4×Dic11C2×C414yescomplemented
163C2×C4×Dic11D414yes—
164(C22⋊D11)⋊C4—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⋊#95D414yescomplemented
174C11⋊#95D414yescomplemented
175#13977—111nomaximal, Sylow
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×C11—21no—
186C24×C11—21no—
187C24×C11—21no—
188C24×C11C22×C412yes—
189C24×C11C2×D412yes—
190C24×C11C2×Q812yes—
191C24×C11C2411yescharacteristic
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—
205C23×D11C2×D412yes—
206C23×D11C2×Q812yes—
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×C11C22×C412yes—
243C22×C4×C11C22×C412yes—
244C22×C4×C11C2×D412yes—
245C22×C4×C11C2×D412yes—
246C22×C4×C11C2×D412yes—
247C22×C4×C11C2×D412yes—
248C22×C4×C11#4112yes—
249C2×C22⋊D11—28no—
250C2×C22⋊D11—28no—
251C2×C22⋊D11—28no—
252C2×C22⋊D11—28no—
253C2×C22⋊D11—28no—
254C2×C22⋊D11—28no—
255C2×C22⋊D11C4⋊C4116yescomplemented
256C22×Dic11—28no—
257C22×Dic11—21no—
258C22×Dic11—21no—
259C22×Dic11—21no—
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—44no—
291C22×Dic11—44no—
292C22×Dic11—44no—
293C22×Dic11—44no—
294C22×Dic11—44no—
295C22×Dic11—44no—
296C22×Dic11C22×C412yes—
297C22×Dic11C22×C412yes—
298C22×Dic11C22×C412yes—
299C22×Dic11C2×D412yes—
300C22×Dic11C2×D412yes—
301C22×Dic11C2×D412yes—
302C22×Dic11C2×D412yes—
303C22×Dic11C2×D412yes—
304C22×Dic11C2×D412yes—
305C22×Dic11C2×D412yes—
306C22×Dic11C2×D412yes—
307C22×Dic11C2×D412yes—
308C22×Dic11C2×Q812yes—
309C22×Dic11#4112yes—
310C22×Dic11#4112yes—
311C22×Dic11#4112yes—
312C2×C4×D11—28no—
313C2×C4×D11—44no—
314C2×C4×D11—44no—
315C2×C4×D11—44no—
316C2×C4×D11—44no—
317C2×C4×D11—44no—
318C2×C4×D11—44no—
319C11×C4⋊C4—44no—
320C11×C22⋊C4—28no—
321C11×C22⋊C4—28no—
322C11×C22⋊C4—44no—
323C22⋊Dic11—28no—
324C22⋊Dic11—44no—
325(C2×D11)⋊C4—28no—
326(C2×D11)⋊C4—28no—
327(C2×D11)⋊C4—28no—
328(C2×D11)⋊C4—44no—
329(C2×D11)⋊C4—44no—
330C4⋊Dic11—44no—
331C4⋊Dic11—44no—
332Dic11⋊C4—28no—
333Dic11⋊C4—28no—
334Dic11⋊C4—44no—
335Dic11⋊C4—44no—
336Dic11⋊C4—44no—
337Dic11⋊C4—44no—
338C4×Dic11—28no—
339C4×Dic11—28no—
340C4×Dic11—44no—
341C22×C4×D4—111no—
342C2×#390—111no—
343C2×#390—111no—
344C2×#389—111no—
345C2×#385—111no—
346C2×#385—111no—
347C2×#385—111no—
348C2×#385—111no—
349C2×#384—111no—
350#1439—111no—
351#1439—111no—
352#1439—111no—
353#1439D1111yescharacteristic, complemented
354C4⋊#95—111no—
355C4×#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—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×C11C2×C4⋊C414yes—
391C23×C11C23×C411yescharacteristic
392C23×C11C22×D411yescharacteristic
393C23×C11C22×D411yescharacteristic
394C23×C11C22×D411yescharacteristic
395C23×C11C22×D411yescharacteristic
396C23×C11C22×D411yescharacteristic
397C23×C11C22×Q811yescharacteristic
398C23×C11C2×#4111yescharacteristic
399C23×C11C2×#4111yescharacteristic
400C23×C11C2×#4111yescharacteristic
401C23×C11C2×#4111yescharacteristic
402C23×C11H(5,𝔽2)11yescharacteristic
403C23×C11H(5,𝔽2)11yescharacteristic
404C23×C112−1+411yescharacteristic
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—22no—
457C2×C4×C11—22no—
458C2×C4×C11—22no—
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×C11C4×D414yescomplemented
483C22⋊D11—232no—
484C2×Dic11—22no—
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—416no—
506C2×Dic11—41no—
507C2×Dic11—41no—
508C2×Dic11—41no—
509C2×Dic11—41no—
510C2×Dic11—41no—
511C2×Dic11—41no—
512C2×Dic11—41no—
513C2×Dic11—41no—
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×Dic11C2×C4⋊C414yes—
526C2×Dic11C4×D414yes—
527C2×Dic11C4×D414yes—
528C2×Dic11C4×D414yescomplemented
529C2×Dic11#12014yes—
530C2×Dic11C22⋊Q814yes—
531C2×Dic11C22⋊Q814yes—
532C2×Dic11#12314yes—
533C2×Dic11#12714yes—
534C4×D11—416no—
535C23×D4—111no—
536C24×C4—111no—
537C24×C4—111no—
538C2×C4×D4—224no—
539C2×C4×D4—224no—
540C2×C4×D4—224no—
541C22×C4⋊C4—111no—
542C22×C4⋊C4—111no—
543C22×C4⋊C4—111no—
544C22×C4⋊C4—111no—
545C22×C4⋊C4—111no—
546C22×C4⋊C4—111no—
547C22×C4⋊C4—111no—
548C22×C4⋊C4—111no—
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⋊C4—111no—
557C22×C22⋊C4C2×D1111yescharacteristic
558C22×C22⋊C4C2×D1111yescharacteristic
559C22×C22⋊C4C2×D1111yescharacteristic
560C22×C42—111no—
561C22×C42—111no—
562C22×C42—111no—
563#390—118no—
564#390—224no—
565#389—224no—
566#385—224no—
567#385—224no—
568#385—224no—
569#385—224no—
570#384—224no—
571C2×#95—111no—
572C2×#95—111no—
573C2×#95—111no—
574C2×#95—111no—
575C2×#95—111no—
576C2×#95—111no—
577C2×#95—111no—
578C2×#95C2×D1111yescharacteristic
579C2×#95C2×D1111yescharacteristic
580C2×#95C2×D1111yescharacteristic
581C22×C11—24no—
582C22×C11—24no—
583C22×C11—24no—
584C22×C11—42no—
585C22×C11—42no—
586C22×C11—42no—
587C22×C11—42no—
588C22×C11—42no—
589C22×C11—42no—
590C22×C11—42no—
591C22×C11—42no—
592C22×C11—42no—
593C22×C11—42no—
594C22×C11—42no—
595C22×C11—42no—
596C22×C11C22×C4⋊C411yescharacteristic
597C22×C11C2×C4×D411yescharacteristic
598C22×C11C2×C4×D411yescharacteristic
599C22×C11C2×C4×D411yescharacteristic
600C22×C11C2×C4×D411yescharacteristic
601C22×C11#52011yescharacteristic
602C22×C11#52011yescharacteristic
603C22×C11C2×#12011yescharacteristic
604C22×C11C2×C22⋊Q811yescharacteristic
605C22×C11C2×C22⋊Q811yescharacteristic
606C22×C11C2×#12311yescharacteristic
607C22×C11C2×#12711yescharacteristic
608C22×C11#53211yescharacteristic
609C22×C11#53211yescharacteristic
610C22×C11#53211yescharacteristic
611C22×C11#53511yescharacteristic
612C22×C11#53611yescharacteristic
613C22×C11#54211yescharacteristic
614C22×C11#54211yescharacteristic
615C22×C11D4211yescharacteristic
616C22×C11D4211yescharacteristic
617C22×C11D4211yescharacteristic
618C22×C11D4211yescharacteristic
619C22×C11#54711yescharacteristic
620C22×C11#54711yescharacteristic
621C22×C11#54711yescharacteristic
622C22×C11#54711yescharacteristic
623C22×C11#54811yescharacteristic
624C22×C11#54811yescharacteristic
625C22×C11D4×Q811yescharacteristic
626C22×C11D4×Q811yescharacteristic
627C22×C11#55311yescharacteristic
628C22×C11#55311yescharacteristic
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—42no—
651C4×C11—81no—
652Dic11—24no—
653Dic11—24no—
654Dic11—42no—
655Dic11—42no—
656Dic11—42no—
657Dic11—81no—
658Dic11#38518yescomplemented
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—111no—
669C23×C4—111no—
670C23×C4—111no—
671C23×C4—111no—
672C23×C4—111no—
673C23×C4—111no—
674C23×C4—111no—
675C23×C4—222no—
676C23×C4—222no—
677C23×C4—222no—
678C23×C4—222no—
679C23×C4—222no—
680C23×C4—222no—
681C23×C4—222no—
682C23×C4—222no—
683C23×C4—222no—
684C23×C4—222no—
685C23×C4—441no—
686C23×C4—441no—
687C23×C4—441no—
688C23×C4—441no—
689C23×C4C22×D1111yescharacteristic
690C23×C4C22×D1111yescharacteristic
691C23×C4C22×D1111yescharacteristic
692C23×C4C22×D1111yescharacteristic
693C23×C4C22×D1111yescharacteristic
694C23×C4C22×D1111yescharacteristic
695C4×D4—2232no—
696C2×C4⋊C4—22no—
697C2×C4⋊C4—22no—
698C2×C4⋊C4—41no—
699C2×C4⋊C4—114no—
700C2×C4⋊C4—114no—
701C2×C4⋊C4—222no—
702C2×C4⋊C4—222no—
703C2×C4⋊C4—222no—
704C2×C4⋊C4—222no—
705C2×C4⋊C4—222no—
706C2×C4⋊C4—222no—
707C2×C4⋊C4—222no—
708C2×C4⋊C4—222no—
709C2×C4⋊C4—222no—
710C2×C4⋊C4—222no—
711C2×C4⋊C4—222no—
712C2×C4⋊C4—222no—
713C2×C4⋊C4—222no—
714C2×C4⋊C4—222no—
715C2×C4⋊C4—222no—
716C2×C4⋊C4—222no—
717C2×C4⋊C4—222no—
718C2×C4⋊C4—222no—
719C2×C4⋊C4—222no—
720C2×C4⋊C4—441no—
721C2×C4⋊C4—441no—
722C2×C4⋊C4—441no—
723C2×C22⋊C4—22no—
724C2×C22⋊C4—22no—
725C2×C22⋊C4—22no—
726C2×C22⋊C4—22no—
727C2×C22⋊C4—22no—
728C2×C22⋊C4—22no—
729C2×C22⋊C4—22no—
730C2×C22⋊C4—41no—
731C2×C22⋊C4—114no—
732C2×C22⋊C4—114no—
733C2×C22⋊C4—114no—
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—222no—
745C2×C22⋊C4—222no—
746C2×C22⋊C4—222no—
747C2×C22⋊C4—222no—
748C2×C22⋊C4—222no—
749C2×C22⋊C4—441no—
750C2×C22⋊C4—441no—
751C2×C22⋊C4—441no—
752C2×C22⋊C4C4×D1114yescomplemented
753C2×C42—114no—
754C2×C42—114no—
755C2×C42—222no—
756C2×C42—222no—
757C2×C42—222no—
758C2×C42—222no—
759C2×C42—222no—
760C2×C42—222no—
761C2×C42—222no—
762#95—22no—
763#95—22no—
764#95—22no—
765#95—114no—
766#95—114no—
767#95—222no—
768#95—222no—
769#95—222no—
770#95—222no—
771#95—222no—
772C2×C11—44no—
773C2×C11C2×#38511yescharacteristic
774C2×C11C4×#12711yescharacteristic
775C2×C11#232611yescharacteristic
776C2×C11D4×C4⋊C411yescharacteristic
777C2×C11D4×C4⋊C411yescharacteristic
778C2×C11#236111yescharacteristic
779C2×C11#236111yescharacteristic
780C2×C11#242211yescharacteristic
781C2×C11#242211yescharacteristic
782C2×C11#243211yescharacteristic
783C2×C11#243311yescharacteristic
784C2×C11#245211yescharacteristic
785C2×C11#245211yescharacteristic
786C2×C11#254211yescharacteristic
787C2×C11#256611yescharacteristic
788D11—44no—
789C24—21no—
790C24—21no—
791C24—21no—
792C24—21no—
793C24—21no—
794C24—21no—
795C24—21no—
796C24—21no—
797C24—21no—
798C24—21no—
799C24—21no—
800C24—21no—
801C24—112no—
802C24—112no—
803C24—112no—
804C24—221no—
805C24—221no—
806C24—221no—
807C24—221no—
808C24—221no—
809C24—221no—
810C24—221no—
811C24—221no—
812C24—221no—
813C24—221no—
814C24—221no—
815C24—221no—
816C24C2×C4×D1112yes—
817C24D4×D1112yes—
818C24Q8×D1112yes—
819C24C23×D1111yescharacteristic
820C2×D4—1116no—
821C2×D4—228no—
822C2×D4—228no—
823C2×D4—228no—
824C2×D4—228no—
825C2×D4—228no—
826C2×D4—228no—
827C22×C4—21no—
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—21no—
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—21no—
862C22×C4—112no—
863C22×C4—112no—
864C22×C4—112no—
865C22×C4—112no—
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—112no—
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—221no—
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—444no—
914C22×C4—444no—
915C22×C4—444no—
916C22×C4—444no—
917C22×C4—444no—
918C22×C4—444no—
919C22×C4—444no—
920C22×C4—444no—
921C22×C4—444no—
922C22×C4—444no—
923C22×C4—444no—
924C22×C4—444no—
925C22×C4C2×C4×D1112yes—
926C22×C4C2×C4×D1112yes—
927C22×C4D4×D1112yes—
928C22×C4D4×D1112yes—
929C22×C4D4×D1112yes—
930C22×C4D4×D1112yes—
931C22×C4#434112yes—
932C4⋊C4—44no—
933C4⋊C4—228no—
934C4⋊C4—228no—
935C4⋊C4—444no—
936C4⋊C4—444no—
937C4⋊C4—444no—
938C4⋊C4—444no—
939C4⋊C4—444no—
940C4⋊C4—444no—
941C22⋊C4—28no—
942C22⋊C4—28no—
943C22⋊C4—44no—
944C22⋊C4—228no—
945C22⋊C4—228no—
946C22⋊C4—228no—
947C22⋊C4—228no—
948C22⋊C4—444no—
949C22⋊C4—444no—
950C22⋊C4—444no—
951C42—228no—
952C42—228no—
953C42—444no—
954C11#1397711yescharacteristic, complemented, Sylow
955C23—22no—
956C23—22no—
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—41no—
974C23—41no—
975C23—41no—
976C23—41no—
977C23—41no—
978C23—41no—
979C23—41no—
980C23—41no—
981C23—41no—
982C23—41no—
983C23—41no—
984C23—41no—
985C23—41no—
986C23—41no—
987C23—41no—
988C23—41no—
989C23—114no—
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—222no—
1005C23—222no—
1006C23—222no—
1007C23—222no—
1008C23—441no—
1009C23—441no—
1010C23—441no—
1011C23—441no—
1012C23—441no—
1013C23—441no—
1014C23—441no—
1015C23—441no—
1016C23—441no—
1017C23—441no—
1018C23—441no—
1019C23—441no—
1020C23—441no—
1021C23—441no—
1022C23—441no—
1023C23—441no—
1024C23C4⋊C4×D1114yes—
1025C23C22×C4×D1111yescharacteristic
1026C23C2×D4×D1111yescharacteristic
1027C23C2×D4×D1111yescharacteristic
1028C23C2×D4×D1111yescharacteristic
1029C23C2×D4×D1111yescharacteristic
1030C23C2×D4×D1111yescharacteristic
1031C23C2×#434111yescharacteristic
1032C23#6703711yescharacteristic
1033C23C2×Q8×D1111yescharacteristic
1034C23#41×D1111yescharacteristic
1035C23#41×D1111yescharacteristic
1036C23#41×D1111yescharacteristic
1037C23#6704211yescharacteristic
1038C23#6704311yescharacteristic
1039C23#6704311yescharacteristic
1040D4—2232no—
1041C2×C4—22no—
1042C2×C4—22no—
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—22no—
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—114no—
1083C2×C4—114no—
1084C2×C4—114no—
1085C2×C4—114no—
1086C2×C4—114no—
1087C2×C4—114no—
1088C2×C4—114no—
1089C2×C4—114no—
1090C2×C4—114no—
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—4416no—
1113C2×C4—4416no—
1114C2×C4—441no—
1115C2×C4—441no—
1116C2×C4—441no—
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(C22⋊D11)⋊C414yescomplemented
1134C22—24no—
1135C22—24no—
1136C22—24no—
1137C22—42no—
1138C22—42no—
1139C22—42no—
1140C22—42no—
1141C22—42no—
1142C22—42no—
1143C22—42no—
1144C22—42no—
1145C22—42no—
1146C22—42no—
1147C22—42no—
1148C22—42no—
1149C22—224no—
1150C22—224no—
1151C22—224no—
1152C22—442no—
1153C22—442no—
1154C22—442no—
1155C22—442no—
1156C22—442no—
1157C22—442no—
1158C22—442no—
1159C22—442no—
1160C22—442no—
1161C22—442no—
1162C22—442no—
1163C22—442no—
1164C22C2×(C22⋊D11)⋊C411yescharacteristic
1165C22C2×C4⋊C4×D1111yescharacteristic
1166C22#1062305411yescharacteristic
1167C22C4×D4×D1111yescharacteristic
1168C22C4×D4×D1111yescharacteristic
1169C22C4×D4×D1111yescharacteristic
1170C22#1062307711yescharacteristic
1171C22D11×#12011yescharacteristic
1172C22#1062312111yescharacteristic
1173C22#1062312111yescharacteristic
1174C22#1062312711yescharacteristic
1175C22#1062312711yescharacteristic
1176C22#1062312911yescharacteristic
1177C22#1062313211yescharacteristic
1178C22#1062313811yescharacteristic
1179C22#1062314011yescharacteristic
1180C22#1062314011yescharacteristic
1181C22#1062314211yescharacteristic
1182C22D11×C22⋊Q811yescharacteristic
1183C22D11×C22⋊Q811yescharacteristic
1184C22#1062316311yescharacteristic
1185C22#1062316311yescharacteristic
1186C22#1062316611yescharacteristic
1187C22#1062316711yescharacteristic
1188C22#1062317911yescharacteristic
1189C22D11×#12311yescharacteristic
1190C22#1062318611yescharacteristic
1191C22#1062318611yescharacteristic
1192C22#1062318611yescharacteristic
1193C22#1062319911yescharacteristic
1194C22#1062320011yescharacteristic
1195C22#1062320811yescharacteristic
1196C22#1062324011yescharacteristic
1197C22#1062324111yescharacteristic
1198C22D11×#12711yescharacteristic
1199C4—24no—
1200C4—42no—
1201C4—42no—
1202C4—42no—
1203C4—42no—
1204C4—81no—
1205C4—118no—
1206C4—224no—
1207C4—224no—
1208C4—442no—
1209C4—442no—
1210C4—442no—
1211C4—881no—
1212C2—44no—
1213C2—444no—
1214C2D11×#38511yescharacteristic
1215C2#1307118011yescharacteristic
1216C2#1307132511yescharacteristic
1217C2#1307151211yescharacteristic
1218C2#1307151411yescharacteristic
1219C2#1307162711yescharacteristic
1220C2#1307162911yescharacteristic
1221C2#1307212311yescharacteristic
1222C2#1307212511yescharacteristic
1223C2#1307223911yescharacteristic
1224C2#1307224811yescharacteristic
1225C2#1307245911yescharacteristic
1226C2#1307246111yescharacteristic
1227C2#1307356411yescharacteristic
1228C2#1307381111yescharacteristic
subgroupG/H
center, FrattiniC24C23×D11
commutatorC23×C11C23×C4
FittingC11×#1439C2
socle, cosocleC24×C11C24
prime radicalC23×C22⋊D11C22
hypercenter#1439D11
hypocenterC11#13977
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ #1439

Complements

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

NH ≅ G/Ntype
4. C2×#10622260C2semidirect
5. C2×#10622563C2semidirect
6. C2×#10622281C2semidirect
7. C2×#10622559C2semidirect
8. C2×#10622602C2semidirect
9. C2×#10622589C2semidirect
10. #13066862C2semidirect
11. #13066860C2semidirect
12. #13066859C2semidirect
13. Dic11⋊#95C2semidirect
14. #95×Dic11C2semidirect
15. C11×#1439C2semidirect
57. #10622570C4semidirect
109. C2×C11×C22⋊C4C2×C4semidirect
115. C2×C22⋊Dic11C2×C4semidirect
129. C2×(C2×D11)⋊C4C2×C4semidirect
130. C2×(C2×D11)⋊C4C2×C4semidirect
153. C2×Dic11⋊C4C2×C4semidirect
162. C2×C4×Dic11C2×C4semidirect
173. C11⋊#95D4semidirect
174. C11⋊#95D4semidirect
255. C2×C22⋊D11C4⋊C4semidirect
353. #1439D11semidirect
482. C2×C4×C11C4×D4semidirect
528. C2×Dic11C4×D4semidirect
658. Dic11#385semidirect
752. C2×C22⋊C4C4×D11semidirect
954. C11#13977semidirect
1133. C2×C4(C22⋊D11)⋊C4semidirect

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×#106225702
C2×#106222602
C2×#106225632
C2×#106222812
C2×#106225592
C2×#106226022
C2×#106225892
#130668622
#130668602
#130668592
Dic11⋊#952
#95×Dic112
C11×#14392
#1397711