Finite Group Databasebeta

← #14675271

Subgroups — #14675271

Order 2816.

2882 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×C22⋊C4×Dic11C211yesmaximal, characteristic, complemented
5C2×C4×(C2×D11)⋊C4C211yesmaximal, characteristic, complemented
6C22×C11⋊#95C211yesmaximal, characteristic, complemented
7#13066854C211yesmaximal, characteristic, complemented
8#13066852C211yesmaximal, characteristic, complemented
9#13066851C211yesmaximal, characteristic, complemented
10#13066849C211yesmaximal, characteristic, complemented
11#13066840C211yesmaximal, characteristic, complemented
12#13066838C211yesmaximal, characteristic, complemented
13(C2×D11)⋊#95C211yesmaximal, characteristic, complemented
14C4×C11⋊#95C211yesmaximal, characteristic, complemented
15C2×C4×C11×C22⋊C4C211yesmaximal, characteristic, complemented
16C24×C4×C11C2211yescharacteristic
17C23×C22⋊D11C2211yescharacteristic
18C24×Dic11C2211yescharacteristic
19C24×Dic11C2211yescharacteristic
20C23×C4×D11C2211yescharacteristic
21C22×C11×C22⋊C4C2211yescharacteristic
22C22×C11×C22⋊C4C2211yescharacteristic
23C22×C42×C11C2211yescharacteristic
24C22×C42×C11C2211yescharacteristic
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×C4×Dic11C2211yescharacteristic
33C22×C4×Dic11C2211yescharacteristic
34C22×C4×Dic11C2211yescharacteristic
35C2×(C22⋊D11)⋊C4—24no—
36C2×(C22⋊D11)⋊C4—24no—
37C2×(C22⋊D11)⋊C4C418yescomplemented
38C4×C11×C22⋊C4—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#10622571C418yescomplemented
58C22⋊C4×Dic11—24no—
59C4×(C2×D11)⋊C4—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⋊D11C2×C414yes—
81C22×C22⋊D11C2×C414yes—
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—41no—
91C23×Dic11—41no—
92C23×Dic11—41no—
93C23×Dic11—41no—
94C23×Dic11C2×C414yes—
95C23×Dic11C2×C414yescomplemented
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—41no—
108C22×C4×D11—41no—
109C22×C4×D11C2×C414yescomplemented
110C2×C11×C22⋊C4—22no—
111C2×C11×C22⋊C4—22no—
112C2×C11×C22⋊C4C2×C414yes—
113C2×C11×C22⋊C4C2×C414yescomplemented
114C2×C11×C22⋊C4D414yes—
115C2×C11×C22⋊C4D414yes—
116C2×C42×C11—22no—
117C2×C42×C11—22no—
118C2×C42×C11—22no—
119C2×C42×C11—22no—
120C2×C42×C11—41no—
121C2×C42×C11—41no—
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—41no—
132C2×(C2×D11)⋊C4—41no—
133C2×(C2×D11)⋊C4—41no—
134C2×(C2×D11)⋊C4—41no—
135C2×(C2×D11)⋊C4C2×C414yescomplemented
136C2×(C2×D11)⋊C4C2×C414yescomplemented
137C2×(C2×D11)⋊C4C2×C414yescomplemented
138C2×(C2×D11)⋊C4C2×C414yescomplemented
139C2×(C2×D11)⋊C4C2×C414yescomplemented
140C2×Dic11⋊C4—22no—
141C2×Dic11⋊C4—22no—
142C2×Dic11⋊C4C2×C414yescomplemented
143C2×C4×Dic11—22no—
144C2×C4×Dic11—22no—
145C2×C4×Dic11—22no—
146C2×C4×Dic11—22no—
147C2×C4×Dic11—22no—
148C2×C4×Dic11—22no—
149C2×C4×Dic11—41no—
150C2×C4×Dic11—41no—
151C2×C4×Dic11C2×C414yescomplemented
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—41no—
163C11⋊#95—41no—
164C11⋊#95C2×C414yescomplemented
165C11⋊#95C2×C414yescomplemented
166C11⋊#95C2×C414yescomplemented
167C11⋊#95C2×C414yescomplemented
168C11⋊#95D414yescomplemented
169#13813—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×C11C22×C412yes—
180C24×C11C22×C412yes—
181C24×C11C2×D412yes—
182C24×C11C2×D412yes—
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×D11C22×C412yes—
200C23×D11C22×C412yes—
201C22×C4×C11—21no—
202C22×C4×C11—21no—
203C22×C4×C11—21no—
204C22×C4×C11—21no—
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—28no—
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—28no—
233C22×C4×C11—44no—
234C22×C4×C11—44no—
235C22×C4×C11—44no—
236C22×C4×C11—44no—
237C22×C4×C11—44no—
238C22×C4×C11C22×C412yes—
239C22×C4×C11C22×C412yes—
240C22×C4×C11C22×C412yes—
241C22×C4×C11C22×C412yes—
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×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⋊D11C42116yescomplemented
257C22×Dic11—28no—
258C22×Dic11—28no—
259C22×Dic11—28no—
260C22×Dic11—28no—
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—44no—
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×Dic11C22×C412yes—
308C22×Dic11C22×C412yes—
309C22×Dic11C22×C412yes—
310C22×Dic11C22×C412yes—
311C22×Dic11C22×C412yes—
312C22×Dic11C22×C412yes—
313C22×Dic11C22×C412yes—
314C22×Dic11C22×C412yes—
315C22×Dic11C22×C412yes—
316C22×Dic11C2×D412yes—
317C22×Dic11C2×D412yes—
318C22×Dic11#4112yes—
319C22×Dic11#4112yes—
320C2×C4×D11—28no—
321C2×C4×D11—28no—
322C2×C4×D11—44no—
323C2×C4×D11—44no—
324C2×C4×D11—44no—
325C2×C4×D11—44no—
326C2×C4×D11—44no—
327C11×C22⋊C4—28no—
328C11×C22⋊C4C22⋊C4116yescomplemented
329C42×C11—44no—
330C42×C11—44no—
331C22⋊Dic11—28no—
332(C2×D11)⋊C4—28no—
333(C2×D11)⋊C4—28no—
334(C2×D11)⋊C4—28no—
335(C2×D11)⋊C4—44no—
336(C2×D11)⋊C4—44no—
337Dic11⋊C4—28no—
338C4×Dic11—28no—
339C4×Dic11—44no—
340C4×Dic11—44no—
341C22×C4×D4—111no—
342C2×#386—111no—
343C2×#386—111no—
344C2×C4×C22⋊C4—111no—
345C2×C4×C22⋊C4—111no—
346C2×C4×C22⋊C4D1111yescharacteristic, complemented
347C22×#95—111no—
348#1437—111no—
349#1437—111no—
350#1436—111no—
351#1436—111no—
352#1434—111no—
353C22⋊#95—111no—
354C22⋊#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—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×C4214yes—
385C23×C11C2×C22⋊C414yes—
386C23×C11#11714yes—
387C23×C11C4×D414yes—
388C23×C11C4×D414yes—
389C23×C11C4×D414yes—
390C23×C11C4×D414yes—
391C23×C11C23×C411yescharacteristic
392C23×C11C23×C411yescharacteristic
393C23×C11C23×C411yescharacteristic
394C23×C11C22×D411yescharacteristic
395C23×C11C22×D411yescharacteristic
396C23×C11C22×D411yescharacteristic
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×C4214yes—
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—22no—
460C2×C4×C11—22no—
461C2×C4×C11—22no—
462C2×C4×C11—22no—
463C2×C4×C11—22no—
464C2×C4×C11—22no—
465C2×C4×C11—22no—
466C2×C4×C11—22no—
467C2×C4×C11—22no—
468C2×C4×C11—416no—
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×C11C2×C22⋊C414yes—
482C2×C4×C11C2×C22⋊C414yes—
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—22no—
513C2×Dic11—22no—
514C2×Dic11—22no—
515C2×Dic11—416no—
516C2×Dic11—416no—
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×Dic11C2×C4214yes—
534C2×Dic11C4×D414yes—
535C2×Dic11C4×D414yescomplemented
536C4×D11—416no—
537C23×D4—111no—
538C24×C4—111no—
539C24×C4—111no—
540C24×C4—111no—
541C24×C4C2×D1111yescharacteristic
542C2×C4×D4—118no—
543C2×C4×D4—224no—
544C2×C4×D4—224no—
545C22×C4⋊C4—111no—
546C22×C22⋊C4—111no—
547C22×C22⋊C4—111no—
548C22×C22⋊C4—111no—
549C22×C22⋊C4—111no—
550C22×C22⋊C4—111no—
551C22×C22⋊C4—111no—
552C22×C22⋊C4C2×D1111yescharacteristic
553C22×C22⋊C4C2×D1111yescharacteristic
554C22×C42—111no—
555C22×C42—111no—
556C22×C42—111no—
557C22×C42C2×D1111yescharacteristic
558C22×C42C2×D1111yescharacteristic
559#386—118no—
560#386—118no—
561C4×C22⋊C4—24no—
562C4×C22⋊C4—224no—
563C4×C22⋊C4—224no—
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×C11C4×C22⋊C418yescomplemented
596C22×C11C22×C4211yescharacteristic
597C22×C11C22×C22⋊C411yescharacteristic
598C22×C11C2×#11711yescharacteristic
599C22×C11C2×C4×D411yescharacteristic
600C22×C11C2×C4×D411yescharacteristic
601C22×C11C2×C4×D411yescharacteristic
602C22×C11C2×C4×D411yescharacteristic
603C22×C11C2×C4×D411yescharacteristic
604C22×C11C2×C4×D411yescharacteristic
605C22×C11C2×C4×D411yescharacteristic
606C22×C11C4×#4111yescharacteristic
607C22×C11C4×#4111yescharacteristic
608C22×C11C4×#4111yescharacteristic
609C22×C11#51811yescharacteristic
610C22×C11#51811yescharacteristic
611C22×C11#51811yescharacteristic
612C22×C11#52011yescharacteristic
613C22×C11#52011yescharacteristic
614C22×C11#52011yescharacteristic
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×C11#54811yescharacteristic
625C22×C11#55111yescharacteristic
626C22×C11#55111yescharacteristic
627C22×C11#55211yescharacteristic
628C22×C11#55311yescharacteristic
629C22×C11#55311yescharacteristic
630C22×C11#55311yescharacteristic
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—24no—
648C4×C11—24no—
649C4×C11—42no—
650C4×C11—42no—
651C4×C11—42no—
652Dic11—24no—
653Dic11—24no—
654Dic11—24no—
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—114no—
683C23×C4—114no—
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—114no—
711C2×C4⋊C4—222no—
712C2×C4⋊C4—222no—
713C2×C22⋊C4—22no—
714C2×C22⋊C4—22no—
715C2×C22⋊C4—114no—
716C2×C22⋊C4—114no—
717C2×C22⋊C4—114no—
718C2×C22⋊C4—114no—
719C2×C22⋊C4—114no—
720C2×C22⋊C4—114no—
721C2×C22⋊C4—222no—
722C2×C22⋊C4—222no—
723C2×C22⋊C4—222no—
724C2×C22⋊C4—222no—
725C2×C22⋊C4—222no—
726C2×C22⋊C4—222no—
727C2×C22⋊C4—222no—
728C2×C22⋊C4—222no—
729C2×C22⋊C4—441no—
730C2×C22⋊C4—441no—
731C2×C22⋊C4—441no—
732C2×C22⋊C4—441no—
733C2×C22⋊C4C4×D1114yes—
734C2×C22⋊C4C4×D1114yescomplemented
735C2×C22⋊C4D4414yes—
736C2×C22⋊C4C22⋊D1114yes—
737C2×C42—22no—
738C2×C42—22no—
739C2×C42—22no—
740C2×C42—22no—
741C2×C42—41no—
742C2×C42—41no—
743C2×C42—114no—
744C2×C42—222no—
745C2×C42—222no—
746C2×C42—222no—
747C2×C42—222no—
748C2×C42—222no—
749C2×C42—222no—
750C2×C42—441no—
751C2×C42—441no—
752#95—22no—
753#95—22no—
754#95—114no—
755#95—114no—
756#95—114no—
757#95—114no—
758#95—114no—
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×C4×C22⋊C411yescharacteristic
770C2×C11C42×D411yescharacteristic
771C2×C11#227511yescharacteristic
772C2×C11D4×C22⋊C411yescharacteristic
773C2×C11#233911yescharacteristic
774C2×C11#235211yescharacteristic
775C2×C11#235311yescharacteristic
776C2×C11#235811yescharacteristic
777C2×C11#235811yescharacteristic
778C2×C11#235911yescharacteristic
779C2×C11#235911yescharacteristic
780C2×C11#236111yescharacteristic
781C2×C11#236111yescharacteristic
782C2×C11#236411yescharacteristic
783C2×C11#236411yescharacteristic
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—
809C24C2×C4×D1112yes—
810C24C2×C4×D1112yes—
811C24C2×D4412yes—
812C24#433912yes—
813C24#433912yes—
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—21no—
828C22×C4—21no—
829C22×C4—21no—
830C22×C4—21no—
831C22×C4—21no—
832C22×C4—21no—
833C22×C4—21no—
834C22×C4—21no—
835C22×C4—28no—
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—28no—
855C22×C4—44no—
856C22×C4—44no—
857C22×C4—44no—
858C22×C4—44no—
859C22×C4—44no—
860C22×C4—112no—
861C22×C4—112no—
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—228no—
874C22×C4—228no—
875C22×C4—228no—
876C22×C4—221no—
877C22×C4—221no—
878C22×C4—221no—
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—221no—
888C22×C4—228no—
889C22×C4—228no—
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—228no—
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×C4—444no—
926C22×C4—444no—
927C22×C4—444no—
928C22×C4—444no—
929C22×C4—444no—
930C22×C4C2×C4×D1112yes—
931C22×C4C2×C4×D1112yes—
932C22×C4C2×C4×D1112yes—
933C22×C4C2×C4×D1112yes—
934C22×C4C2×C4×D1112yes—
935C22×C4C2×C4×D1112yes—
936C22×C4C2×D4412yes—
937C22×C4C2×D4412yes—
938C22×C4D4×D1112yes—
939C22×C4#434112yes—
940C22×C4C2×C22⋊D1112yes—
941C22×C4C2×C22⋊D1112yes—
942C4⋊C4—228no—
943C22⋊C4—28no—
944C22⋊C4—228no—
945C22⋊C4—228no—
946C22⋊C4—228no—
947C22⋊C4—228no—
948C22⋊C4—444no—
949C22⋊C4—444no—
950C22⋊C4(C2×D11)⋊C4116yescomplemented
951C42—44no—
952C42—44no—
953C42—228no—
954C42—444no—
955C42—444no—
956C11#1381311yescharacteristic, 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—
1020C23C42×D1114yes—
1021C23#6692514yes—
1022C23C4×D4414yes—
1023C23C4×D4414yes—
1024C23C2×(C2×D11)⋊C414yes—
1025C23C4×C22⋊D1114yes—
1026C23C4×C22⋊D1114yes—
1027C23C22×C4×D1111yescharacteristic
1028C23C22×C4×D1111yescharacteristic
1029C23C22×C4×D1111yescharacteristic
1030C23C22×D4411yescharacteristic
1031C23C2×#433911yescharacteristic
1032C23C2×#433911yescharacteristic
1033C23C2×D4×D1111yescharacteristic
1034C23C2×#434111yescharacteristic
1035C23#6703711yescharacteristic
1036C23#6703711yescharacteristic
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—22no—
1059C2×C4—22no—
1060C2×C4—22no—
1061C2×C4—22no—
1062C2×C4—22no—
1063C2×C4—22no—
1064C2×C4—22no—
1065C2×C4—22no—
1066C2×C4—22no—
1067C2×C4—22no—
1068C2×C4—22no—
1069C2×C4—22no—
1070C2×C4—416no—
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—114no—
1084C2×C4—114no—
1085C2×C4—114no—
1086C2×C4—222no—
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—222no—
1115C2×C4—222no—
1116C2×C4—4416no—
1117C2×C4—4416no—
1118C2×C4—4416no—
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(C22⋊D11)⋊C414yescomplemented
1136C2×C4C2×(C2×D11)⋊C414yes—
1137C2×C4C2×(C2×D11)⋊C414yes—
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—
1167C22C4×(C2×D11)⋊C418yescomplemented
1168C22C2×C42×D1111yescharacteristic
1169C22C2×#6692511yescharacteristic
1170C22C2×C4×D4411yescharacteristic
1171C22C2×C4×D4411yescharacteristic
1172C22C2×(C22⋊D11)⋊C411yescharacteristic
1173C22#1062301711yescharacteristic
1174C22#1062302111yescharacteristic
1175C22#1062302611yescharacteristic
1176C22#1062305311yescharacteristic
1177C22#1062305411yescharacteristic
1178C22#1062305811yescharacteristic
1179C22#1062306211yescharacteristic
1180C22C4×#434111yescharacteristic
1181C22C4×#434111yescharacteristic
1182C22#1062307111yescharacteristic
1183C22#1062307111yescharacteristic
1184C22C4×D4×D1111yescharacteristic
1185C22C4×D4×D1111yescharacteristic
1186C22#1062307611yescharacteristic
1187C22#1062307611yescharacteristic
1188C22#1062307711yescharacteristic
1189C22#1062307711yescharacteristic
1190C22D4×D4411yescharacteristic
1191C22#1062308311yescharacteristic
1192C22#1062308511yescharacteristic
1193C22#1062308511yescharacteristic
1194C22#1062308611yescharacteristic
1195C22#1062309611yescharacteristic
1196C22C22×(C2×D11)⋊C411yescharacteristic
1197C22C2×C4×C22⋊D1111yescharacteristic
1198C22C2×C4×C22⋊D1111yescharacteristic
1199C22D4×C22⋊D1111yescharacteristic
1200C22#1062333711yescharacteristic
1201C22#1062335511yescharacteristic
1202C22#1062336011yescharacteristic
1203C4—24no—
1204C4—24no—
1205C4—24no—
1206C4—42no—
1207C4—42no—
1208C4—42no—
1209C4—224no—
1210C4—224no—
1211C4—224no—
1212C4—442no—
1213C4—442no—
1214C4—442no—
1215C4—442no—
1216C2—28no—
1217C2—444no—
1218C2C2×C4×(C2×D11)⋊C411yescharacteristic
1219C2C4×(C22⋊D11)⋊C411yescharacteristic
1220C2#1307097511yescharacteristic
1221C2D4×(C2×D11)⋊C411yescharacteristic
1222C2#1307144111yescharacteristic
1223C2#1307153911yescharacteristic
1224C2#1307155011yescharacteristic
1225C2#1307159511yescharacteristic
1226C2#1307159811yescharacteristic
1227C2#1307160811yescharacteristic
1228C2#1307161011yescharacteristic
1229C2#1307163011yescharacteristic
1230C2#1307163311yescharacteristic
1231C2#1307166111yescharacteristic
1232C2#1307166611yescharacteristic
subgroupG/H
center, FrattiniC24C23×D11
commutatorC22×C11C22×C42
FittingC2×C4×C11×C22⋊C4C2
socle, cosocleC24×C11C24
prime radicalC23×C22⋊D11C22
hypercenterC2×C4×C22⋊C4D11
hypocenterC11#13813
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C24 ◁ C2×C4×C22⋊C4

Complements

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

NH ≅ G/Ntype
4. C2×C22⋊C4×Dic11C2semidirect
5. C2×C4×(C2×D11)⋊C4C2semidirect
6. C22×C11⋊#95C2semidirect
7. #13066854C2semidirect
8. #13066852C2semidirect
9. #13066851C2semidirect
10. #13066849C2semidirect
11. #13066840C2semidirect
12. #13066838C2semidirect
13. (C2×D11)⋊#95C2semidirect
14. C4×C11⋊#95C2semidirect
15. C2×C4×C11×C22⋊C4C2semidirect
37. C2×(C22⋊D11)⋊C4C4semidirect
41. #10622826C4semidirect
57. #10622571C4semidirect
68. C23×C4×C11C2×C4semidirect
95. C23×Dic11C2×C4semidirect
109. C22×C4×D11C2×C4semidirect
113. C2×C11×C22⋊C4C2×C4semidirect
124. C2×C22⋊Dic11C2×C4semidirect
135. C2×(C2×D11)⋊C4C2×C4semidirect
136. C2×(C2×D11)⋊C4C2×C4semidirect
137. C2×(C2×D11)⋊C4C2×C4semidirect
138. C2×(C2×D11)⋊C4C2×C4semidirect
139. C2×(C2×D11)⋊C4C2×C4semidirect
142. C2×Dic11⋊C4C2×C4semidirect
151. C2×C4×Dic11C2×C4semidirect
164. C11⋊#95C2×C4semidirect
165. C11⋊#95C2×C4semidirect
166. C11⋊#95C2×C4semidirect
167. C11⋊#95C2×C4semidirect
168. C11⋊#95D4semidirect
256. C2×C22⋊D11C42semidirect
328. C11×C22⋊C4C22⋊C4semidirect
346. C2×C4×C22⋊C4D11semidirect
483. C2×C4×C11C4×D4semidirect
535. C2×Dic11C4×D4semidirect
595. C22×C11C4×C22⋊C4semidirect
702. C23×C4C4×D11semidirect
734. C2×C22⋊C4C4×D11semidirect
950. C22⋊C4(C2×D11)⋊C4semidirect
956. C11#13813semidirect
1135. C2×C4(C22⋊D11)⋊C4semidirect
1167. C22C4×(C2×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×#106228262
C2×#106225712
C2×C22⋊C4×Dic112
C2×C4×(C2×D11)⋊C42
C22×C11⋊#952
#130668542
#130668522
#130668512
#130668492
#130668402
#130668382
(C2×D11)⋊#952
C4×C11⋊#952
C2×C4×C11×C22⋊C42
#1381311