Finite Group Databasebeta

← #14678215

Subgroups — #14678215

Order 2816.

2158 conjugacy classes of subgroups.

The subgroup lattice has 1176 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#66947C211yesmaximal, characteristic
2C2×#10622601C211yesmaximal, characteristic
3C2×C4⋊C4×Dic11C211yesmaximal, characteristic, complemented
4C2×C4×(C2×D11)⋊C4C211yesmaximal, characteristic, complemented
5#13066866C211yesmaximal, characteristic, complemented
6#13066862C211yesmaximal, characteristic, complemented
7#13066862C211yesmaximal, characteristic, complemented
8#13066856C211yesmaximal, characteristic
9#13066854C211yesmaximal, characteristic, complemented
10#13066852C211yesmaximal, characteristic, complemented
11#13066852C211yesmaximal, characteristic, complemented
12#13066852C211yesmaximal, characteristic, complemented
13#13066851C211yesmaximal, characteristic, complemented
14(C2×D11)⋊#95C211yesmaximal, characteristic, complemented
15C2×C11×#387C211yesmaximal, characteristic, complemented
16C23×D44C2211yescharacteristic
17C23×C4×D11C2211yescharacteristic
18C22×C11×C4⋊C4C2211yescharacteristic
19C22×C11×C4⋊C4C2211yescharacteristic
20C22×C42×C11C2211yescharacteristic
21C22×(C2×D11)⋊C4C2211yescharacteristic
22C22×(C2×D11)⋊C4C2211yescharacteristic
23C22×(C2×D11)⋊C4C2211yescharacteristic
24C22×(C2×D11)⋊C4C2211yescharacteristic
25C22×(C2×D11)⋊C4C2211yescharacteristic
26C22×(C2×D11)⋊C4C2211yescharacteristic
27C22×(C2×D11)⋊C4C2211yescharacteristic
28C22×(C2×D11)⋊C4C2211yescharacteristic
29C22×(C2×D11)⋊C4C2211yescharacteristic
30C22×(C2×D11)⋊C4C2211yescharacteristic
31C22×(C2×D11)⋊C4C2211yescharacteristic
32C22×C4⋊Dic11C2211yescharacteristic
33C22×Dic11⋊C4C2211yescharacteristic
34C22×C4×Dic11C2211yescharacteristic
35C22×C4×Dic11C2211yescharacteristic
36C22×C4×Dic11C2211yescharacteristic
37C2×#66947—24no—
38C2×#66947—24no—
39C2×#66947C418yescomplemented
40C11×#387—24no—
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
54C2×C11⋊#95C2211yescharacteristic
55#10622601—24no—
56C4⋊C4×Dic11—24no—
57C4×(C2×D11)⋊C4—24no—
58C24×D11C2311yescharacteristic
59C24×D11C2311yescharacteristic
60C23×C4×C11C2311yescharacteristic
61C23×C4×C11C2311yescharacteristic
62C23×C4×C11C2311yescharacteristic
63C23×C4×C11C2311yescharacteristic
64C23×C4×C11C2311yescharacteristic
65C23×C4×C11C2311yescharacteristic
66C23×C4×C11C2311yescharacteristic
67C23×Dic11C2311yescharacteristic
68C23×Dic11C2311yescharacteristic
69C23×Dic11C2311yescharacteristic
70C23×Dic11C2311yescharacteristic
71C23×Dic11C2311yescharacteristic
72C23×Dic11C2311yescharacteristic
73C22×D44—22no—
74C22×D44—22no—
75C22×D44—22no—
76C22×D44—22no—
77C22×D44—41no—
78C22×D44—41no—
79C22×D44C2×C414yes—
80C22×C4×D11—22no—
81C22×C4×D11—22no—
82C22×C4×D11—22no—
83C22×C4×D11—22no—
84C22×C4×D11—41no—
85C22×C4×D11—41no—
86C22×C4×D11C2×C414yes—
87C2×C11×C4⋊C4—22no—
88C2×C11×C4⋊C4—22no—
89C2×C11×C4⋊C4—41no—
90C2×C11×C4⋊C4C2×C414yes—
91C2×C11×C4⋊C4D414yes—
92C2×C11×C4⋊C4D414yes—
93C2×C42×C11—22no—
94C2×C42×C11—22no—
95C2×C42×C11—41no—
96C2×(C2×D11)⋊C4—22no—
97C2×(C2×D11)⋊C4—22no—
98C2×(C2×D11)⋊C4—22no—
99C2×(C2×D11)⋊C4—22no—
100C2×(C2×D11)⋊C4—22no—
101C2×(C2×D11)⋊C4—22no—
102C2×(C2×D11)⋊C4—22no—
103C2×(C2×D11)⋊C4—22no—
104C2×(C2×D11)⋊C4—22no—
105C2×(C2×D11)⋊C4—22no—
106C2×(C2×D11)⋊C4—22no—
107C2×(C2×D11)⋊C4—22no—
108C2×(C2×D11)⋊C4—22no—
109C2×(C2×D11)⋊C4—22no—
110C2×(C2×D11)⋊C4—22no—
111C2×(C2×D11)⋊C4—22no—
112C2×(C2×D11)⋊C4—22no—
113C2×(C2×D11)⋊C4—22no—
114C2×(C2×D11)⋊C4—22no—
115C2×(C2×D11)⋊C4—22no—
116C2×(C2×D11)⋊C4—22no—
117C2×(C2×D11)⋊C4—22no—
118C2×(C2×D11)⋊C4—22no—
119C2×(C2×D11)⋊C4—41no—
120C2×(C2×D11)⋊C4—41no—
121C2×(C2×D11)⋊C4—41no—
122C2×(C2×D11)⋊C4—41no—
123C2×(C2×D11)⋊C4—41no—
124C2×(C2×D11)⋊C4—41no—
125C2×(C2×D11)⋊C4C2×C414yes—
126C2×(C2×D11)⋊C4C2×C414yes—
127C2×(C2×D11)⋊C4C2×C414yes—
128C2×(C2×D11)⋊C4D414yes—
129C2×C4⋊Dic11—22no—
130C2×C4⋊Dic11—22no—
131C2×C4⋊Dic11—22no—
132C2×Dic11⋊C4—22no—
133C2×Dic11⋊C4—22no—
134C2×Dic11⋊C4C2×C414yes—
135C2×C4×Dic11—22no—
136C2×C4×Dic11—22no—
137C2×C4×Dic11—22no—
138C2×C4×Dic11—22no—
139C2×C4×Dic11—22no—
140C2×C4×Dic11—22no—
141C2×C4×Dic11—22no—
142C2×C4×Dic11—41no—
143C2×C4×Dic11—41no—
144#66947—232no—
145C11×#95—22no—
146C11×#95—22no—
147C11×#95—22no—
148C11×#95—22no—
149C11⋊#95—22no—
150C11⋊#95—22no—
151C11⋊#95—22no—
152C11⋊#95—22no—
153C11⋊#95—22no—
154C11⋊#95—22no—
155C11⋊#95—41no—
156C11⋊#95—41no—
157C11⋊#95—41no—
158C11⋊#95—41no—
159#14095—111nomaximal, Sylow
160C24×C11C2411yescharacteristic
161C23×D11—21no—
162C23×D11—21no—
163C23×D11—21no—
164C23×D11—21no—
165C23×D11—21no—
166C23×D11—21no—
167C23×D11—21no—
168C23×D11—21no—
169C23×D11—21no—
170C23×D11—21no—
171C23×D11—21no—
172C23×D11—21no—
173C23×D11—21no—
174C23×D11—21no—
175C23×D11—21no—
176C23×D11—21no—
177C23×D11—21no—
178C23×D11—21no—
179C23×D11—21no—
180C23×D11—21no—
181C23×D11—21no—
182C23×D11—21no—
183C23×D11—21no—
184C23×D11—21no—
185C23×D11—21no—
186C23×D11—21no—
187C23×D11C22×C412yes—
188C23×D11C22×C412yes—
189C23×D11C2×D412yes—
190C23×D11#4112yes—
191C22×C4×C11—21no—
192C22×C4×C11—21no—
193C22×C4×C11—21no—
194C22×C4×C11—21no—
195C22×C4×C11—21no—
196C22×C4×C11—21no—
197C22×C4×C11—21no—
198C22×C4×C11—21no—
199C22×C4×C11—21no—
200C22×C4×C11—21no—
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—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×C11C22×C412yes—
230C22×C4×C11C22×C412yes—
231C22×C4×C11C22×C412yes—
232C22×C4×C11C2×D412yes—
233C22×C4×C11C2×D412yes—
234C22×C4×C11C2×D412yes—
235C22×C4×C11C2×D412yes—
236C22×C4×C11C2×D412yes—
237C22×C4×C11C2×D412yes—
238C22×C4×C11C2×D412yes—
239C22×C4×C11#4112yes—
240C22×Dic11—21no—
241C22×Dic11—21no—
242C22×Dic11—21no—
243C22×Dic11—21no—
244C22×Dic11—21no—
245C22×Dic11—21no—
246C22×Dic11—21no—
247C22×Dic11—21no—
248C22×Dic11—21no—
249C22×Dic11—21no—
250C22×Dic11—21no—
251C22×Dic11—21no—
252C22×Dic11—21no—
253C22×Dic11—21no—
254C22×Dic11—21no—
255C22×Dic11—21no—
256C22×Dic11—21no—
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×Dic11C22×C412yes—
275C22×Dic11C22×C412yes—
276C22×Dic11C2×D412yes—
277C22×Dic11#4112yes—
278C22×Dic11#4112yes—
279C22×Dic11#4112yes—
280C22×Dic11#4112yes—
281C22×Dic11#4112yes—
282C2×D44—28no—
283C2×D44—28no—
284C2×D44—44no—
285C2×D44—44no—
286C2×D44—44no—
287C2×D44—44no—
288C2×D44—44no—
289C2×C4×D11—28no—
290C2×C4×D11—28no—
291C2×C4×D11—44no—
292C2×C4×D11—44no—
293C2×C4×D11—44no—
294C2×C4×D11—44no—
295C2×C4×D11—44no—
296C11×C4⋊C4—44no—
297C11×C4⋊C4C22⋊C4116yescomplemented
298C42×C11—44no—
299(C2×D11)⋊C4—28no—
300(C2×D11)⋊C4—28no—
301(C2×D11)⋊C4—28no—
302(C2×D11)⋊C4—28no—
303(C2×D11)⋊C4—28no—
304(C2×D11)⋊C4—44no—
305(C2×D11)⋊C4—44no—
306(C2×D11)⋊C4—44no—
307(C2×D11)⋊C4—44no—
308(C2×D11)⋊C4—44no—
309(C2×D11)⋊C4—44no—
310C4⋊Dic11—28no—
311Dic11⋊C4—28no—
312C4×Dic11—28no—
313C4×Dic11—44no—
314C4×Dic11—44no—
315C22×#123—111no—
316C2×#390—111no—
317C2×#387D1111yescharacteristic, complemented
318C2×C4×C4⋊C4—111no—
319C2×C4×C22⋊C4—111no—
320#1441—111no—
321#1439—111no—
322#1439—111no—
323#1438—111no—
324#1437—111no—
325#1437—111no—
326#1437—111no—
327#1437—111no—
328#1436—111no—
329C22⋊#95—111no—
330C23×C11C23×C411yescharacteristic
331C23×C11C22×D411yescharacteristic
332C23×C11C22×D411yescharacteristic
333C23×C11C22×D411yescharacteristic
334C23×C11C2×#4111yescharacteristic
335C23×C11C2×#4111yescharacteristic
336C23×C11C2×#4111yescharacteristic
337C23×C11C2×#4111yescharacteristic
338C23×C11C2×#4111yescharacteristic
339C23×C11C2×#4111yescharacteristic
340C23×C11C2×#4111yescharacteristic
341C23×C11H(5,𝔽2)11yescharacteristic
342C23×C11H(5,𝔽2)11yescharacteristic
343C23×C11H(5,𝔽2)11yescharacteristic
344C23×C112−1+411yescharacteristic
345C22×D11—22no—
346C22×D11—22no—
347C22×D11—22no—
348C22×D11—22no—
349C22×D11—22no—
350C22×D11—22no—
351C22×D11—22no—
352C22×D11—22no—
353C22×D11—22no—
354C22×D11—22no—
355C22×D11—22no—
356C22×D11—22no—
357C22×D11—22no—
358C22×D11—22no—
359C22×D11—22no—
360C22×D11—22no—
361C22×D11—22no—
362C22×D11—22no—
363C22×D11—22no—
364C22×D11—22no—
365C22×D11—22no—
366C22×D11—22no—
367C22×D11—22no—
368C22×D11—22no—
369C22×D11—22no—
370C22×D11—41no—
371C22×D11—41no—
372C22×D11—41no—
373C22×D11—41no—
374C22×D11—41no—
375C22×D11—41no—
376C22×D11—41no—
377C22×D11—41no—
378C22×D11—41no—
379C22×D11—41no—
380C22×D11—41no—
381C22×D11—41no—
382C22×D11—41no—
383C22×D11—41no—
384C22×D11—41no—
385C22×D11—41no—
386C22×D11—41no—
387C22×D11—41no—
388C22×D11—41no—
389C22×D11—41no—
390C22×D11—41no—
391C22×D11—41no—
392C22×D11—41no—
393C22×D11—41no—
394C22×D11—41no—
395C22×D11—41no—
396C22×D11—41no—
397C22×D11—41no—
398C22×D11—41no—
399C22×D11—41no—
400C22×D11—41no—
401C22×D11—41no—
402C22×D11—41no—
403C22×D11—41no—
404C22×D11—41no—
405C22×D11—41no—
406C22×D11—41no—
407C22×D11—41no—
408C22×D11—41no—
409C22×D11—41no—
410C22×D11—41no—
411C22×D11—41no—
412C22×D11—41no—
413C22×D11—41no—
414C22×D11C4×D414yes—
415C2×C4×C11—22no—
416C2×C4×C11—22no—
417C2×C4×C11—22no—
418C2×C4×C11—22no—
419C2×C4×C11—22no—
420C2×C4×C11—22no—
421C2×C4×C11—22no—
422C2×C4×C11—22no—
423C2×C4×C11—22no—
424C2×C4×C11—22no—
425C2×C4×C11—22no—
426C2×C4×C11—22no—
427C2×C4×C11—22no—
428C2×C4×C11—22no—
429C2×C4×C11—22no—
430C2×C4×C11—22no—
431C2×C4×C11—22no—
432C2×C4×C11—22no—
433C2×C4×C11—22no—
434C2×C4×C11—22no—
435C2×C4×C11—22no—
436C2×C4×C11—22no—
437C2×C4×C11—22no—
438C2×C4×C11—22no—
439C2×C4×C11—41no—
440C2×C4×C11—41no—
441C2×C4×C11—41no—
442C2×C4×C11—41no—
443C2×C4×C11—41no—
444C2×C4×C11—41no—
445C2×C4×C11—41no—
446C2×C4×C11—41no—
447C2×C4×C11—41no—
448C2×C4×C11—41no—
449C2×C4×C11—41no—
450C2×C4×C11—41no—
451C2×C4×C11—41no—
452C2×C4×C11—41no—
453C2×C4×C11—41no—
454C2×C4×C11—41no—
455C2×C4×C11—41no—
456C2×C4×C11—41no—
457C2×C4×C11—41no—
458C2×C4×C11—41no—
459C2×C4×C11—41no—
460C2×C4×C11—41no—
461C2×C4×C11C2×C22⋊C414yes—
462C2×C4×C11C2×C22⋊C414yes—
463C2×C4×C11C2×C22⋊C414yes—
464C2×Dic11—22no—
465C2×Dic11—22no—
466C2×Dic11—22no—
467C2×Dic11—22no—
468C2×Dic11—22no—
469C2×Dic11—22no—
470C2×Dic11—22no—
471C2×Dic11—22no—
472C2×Dic11—22no—
473C2×Dic11—22no—
474C2×Dic11—22no—
475C2×Dic11—22no—
476C2×Dic11—22no—
477C2×Dic11—22no—
478C2×Dic11—22no—
479C2×Dic11—22no—
480C2×Dic11—22no—
481C2×Dic11—22no—
482C2×Dic11—22no—
483C2×Dic11—22no—
484C2×Dic11—22no—
485C2×Dic11—41no—
486C2×Dic11—41no—
487C2×Dic11—41no—
488C2×Dic11—41no—
489C2×Dic11—41no—
490C2×Dic11—41no—
491C2×Dic11—41no—
492C2×Dic11—41no—
493C2×Dic11—41no—
494C2×Dic11—41no—
495C2×Dic11—41no—
496C2×Dic11—41no—
497C2×Dic11—41no—
498C2×Dic11—41no—
499C2×Dic11—41no—
500C2×Dic11—41no—
501C2×Dic11—41no—
502C2×Dic11—41no—
503C2×Dic11—41no—
504C2×Dic11—41no—
505C2×Dic11#12314yescomplemented
506D44—416no—
507C4×D11—416no—
508C23×D4—111no—
509C24×C4—111no—
510C2×#123—118no—
511C2×#123—224no—
512C2×#123—224no—
513C22×C4⋊C4—111no—
514C22×C4⋊C4—111no—
515C22×C4⋊C4C2×D1111yescharacteristic
516C22×C4⋊C4C2×D1111yescharacteristic
517C22×C22⋊C4—111no—
518C22×C22⋊C4—111no—
519C22×C22⋊C4—111no—
520C22×C22⋊C4—111no—
521C22×C22⋊C4—111no—
522C22×C22⋊C4—111no—
523C22×C22⋊C4—111no—
524C22×C22⋊C4—111no—
525C22×C22⋊C4—111no—
526C22×C22⋊C4—111no—
527C22×C22⋊C4—111no—
528C22×C42—111no—
529C22×C42—111no—
530C22×C42—111no—
531C22×C42C2×D1111yescharacteristic
532#390—224no—
533#387—24no—
534C4×C4⋊C4—224no—
535C4×C22⋊C4—224no—
536C2×#95—111no—
537C2×#95—111no—
538C2×#95—111no—
539C2×#95—111no—
540C2×#95—111no—
541C2×#95—111no—
542C2×#95—111no—
543C2×#95—111no—
544C2×#95—111no—
545C2×#95—111no—
546C2×#95C2×D1111yescharacteristic
547C2×#95C2×D1111yescharacteristic
548C2×#95C2×D1111yescharacteristic
549C2×#95C2×D1111yescharacteristic
550C22×C11C22×C22⋊C411yescharacteristic
551C22×C11C2×C4×D411yescharacteristic
552C22×C11C4×#4111yescharacteristic
553C22×C11C4×#4111yescharacteristic
554C22×C11C4×#4111yescharacteristic
555C22×C11#51811yescharacteristic
556C22×C11#52011yescharacteristic
557C22×C11C2×#12311yescharacteristic
558C22×C11#52511yescharacteristic
559C22×C11#52511yescharacteristic
560C22×C11#52511yescharacteristic
561C22×C11#52911yescharacteristic
562C22×C11#52911yescharacteristic
563C22×C11#53211yescharacteristic
564C22×C11#53211yescharacteristic
565C22×C11#53811yescharacteristic
566C22×C11#53911yescharacteristic
567C22×C11#54011yescharacteristic
568C22×C11#54211yescharacteristic
569C22×C11D4211yescharacteristic
570C22×C11D4211yescharacteristic
571C22×C11#54611yescharacteristic
572C22×C11#54611yescharacteristic
573C22×C11#54611yescharacteristic
574C22×C11#54711yescharacteristic
575C22×C11#54811yescharacteristic
576C22×C11#54811yescharacteristic
577C22×C11#55011yescharacteristic
578C22×C11#55011yescharacteristic
579C22×C11#55111yescharacteristic
580C22×C11#55111yescharacteristic
581C22×C11#55211yescharacteristic
582C22×C11#55311yescharacteristic
583C22×C11#55311yescharacteristic
584C22×C11#55911yescharacteristic
585C2×D11—24no—
586C2×D11—24no—
587C2×D11—24no—
588C2×D11—42no—
589C2×D11—42no—
590C2×D11—42no—
591C2×D11—42no—
592C2×D11—42no—
593C2×D11—42no—
594C2×D11—42no—
595C2×D11—42no—
596C2×D11—42no—
597C2×D11—42no—
598C2×D11—42no—
599C2×D11—42no—
600C2×D11—42no—
601C2×D11—42no—
602C2×D11—42no—
603C2×D11—42no—
604C2×D11—42no—
605C2×D11—42no—
606C2×D11—42no—
607C2×D11—81no—
608C2×D11—81no—
609C2×D11—81no—
610C2×D11—81no—
611C2×D11—81no—
612C2×D11—81no—
613C2×D11—81no—
614C2×D11—81no—
615C4×C11—24no—
616C4×C11—24no—
617C4×C11—24no—
618C4×C11—42no—
619C4×C11—42no—
620C4×C11—81no—
621C4×C11—81no—
622Dic11—24no—
623Dic11—42no—
624Dic11—42no—
625Dic11—42no—
626Dic11—42no—
627Dic11—42no—
628C25—111no—
629C25—111no—
630C22×D4—114no—
631C22×D4—222no—
632C22×D4—222no—
633C22×D4—222no—
634C22×D4—222no—
635C22×D4—441no—
636C22×D4—441no—
637C23×C4—111no—
638C23×C4—111no—
639C23×C4—111no—
640C23×C4—111no—
641C23×C4—111no—
642C23×C4—111no—
643C23×C4—114no—
644C23×C4—222no—
645C23×C4—222no—
646C23×C4—222no—
647C23×C4—222no—
648C23×C4—441no—
649C23×C4—441no—
650C23×C4C22×D1111yescharacteristic
651C23×C4C22×D1111yescharacteristic
652C23×C4C22×D1111yescharacteristic
653C23×C4C22×D1111yescharacteristic
654C23×C4C22×D1111yescharacteristic
655C23×C4C22×D1111yescharacteristic
656C23×C4C22×D1111yescharacteristic
657#123—2232no—
658C2×C4⋊C4—22no—
659C2×C4⋊C4—22no—
660C2×C4⋊C4—41no—
661C2×C4⋊C4—114no—
662C2×C4⋊C4—222no—
663C2×C4⋊C4—222no—
664C2×C4⋊C4—222no—
665C2×C4⋊C4—222no—
666C2×C4⋊C4—222no—
667C2×C4⋊C4C4×D1114yes—
668C2×C4⋊C4D4414yes—
669C2×C4⋊C4C22⋊D1114yes—
670C2×C22⋊C4—114no—
671C2×C22⋊C4—114no—
672C2×C22⋊C4—114no—
673C2×C22⋊C4—114no—
674C2×C22⋊C4—222no—
675C2×C22⋊C4—222no—
676C2×C22⋊C4—222no—
677C2×C22⋊C4—222no—
678C2×C22⋊C4—222no—
679C2×C22⋊C4—222no—
680C2×C22⋊C4—222no—
681C2×C22⋊C4—222no—
682C2×C22⋊C4—222no—
683C2×C22⋊C4—222no—
684C2×C22⋊C4—222no—
685C2×C22⋊C4—222no—
686C2×C22⋊C4—222no—
687C2×C22⋊C4—222no—
688C2×C22⋊C4—222no—
689C2×C22⋊C4—222no—
690C2×C22⋊C4—222no—
691C2×C22⋊C4—222no—
692C2×C22⋊C4—222no—
693C2×C22⋊C4—222no—
694C2×C22⋊C4—222no—
695C2×C22⋊C4—222no—
696C2×C22⋊C4—222no—
697C2×C22⋊C4—441no—
698C2×C22⋊C4—441no—
699C2×C22⋊C4—441no—
700C2×C22⋊C4—441no—
701C2×C22⋊C4—441no—
702C2×C22⋊C4—441no—
703C2×C42—22no—
704C2×C42—22no—
705C2×C42—41no—
706C2×C42—222no—
707C2×C42—222no—
708C2×C42—222no—
709C2×C42—222no—
710C2×C42—222no—
711C2×C42—222no—
712C2×C42—222no—
713C2×C42—441no—
714C2×C42—441no—
715#95—22no—
716#95—22no—
717#95—22no—
718#95—22no—
719#95—222no—
720#95—222no—
721#95—222no—
722#95—222no—
723#95—222no—
724#95—222no—
725#95—441no—
726#95—441no—
727#95—441no—
728#95—441no—
729C2×C11#229711yescharacteristic
730C2×C11C4×#12311yescharacteristic
731C2×C11#233511yescharacteristic
732C2×C11D4×C22⋊C411yescharacteristic
733C2×C11#234111yescharacteristic
734C2×C11#235911yescharacteristic
735C2×C11#237411yescharacteristic
736C2×C11#244311yescharacteristic
737C2×C11#244511yescharacteristic
738C2×C11#245611yescharacteristic
739C2×C11#245811yescharacteristic
740C2×C11#246111yescharacteristic
741C2×C11#247111yescharacteristic
742C2×C11#255411yescharacteristic
743C2×C11#255811yescharacteristic
744D11—44no—
745D11—82no—
746C24—112no—
747C24—112no—
748C24—112no—
749C24—112no—
750C24—221no—
751C24—221no—
752C24—221no—
753C24—221no—
754C24—221no—
755C24—221no—
756C24—221no—
757C24—221no—
758C24—221no—
759C24—221no—
760C24—221no—
761C24—221no—
762C24—221no—
763C24—221no—
764C24—221no—
765C24—221no—
766C24—221no—
767C24—221no—
768C24—221no—
769C24—221no—
770C24—221no—
771C24—221no—
772C24—221no—
773C24—221no—
774C24—221no—
775C24—221no—
776C24C23×D1111yescharacteristic
777C2×D4—228no—
778C2×D4—228no—
779C2×D4—444no—
780C2×D4—444no—
781C2×D4—444no—
782C2×D4—444no—
783C2×D4—444no—
784C22×C4—21no—
785C22×C4—21no—
786C22×C4—21no—
787C22×C4—21no—
788C22×C4—21no—
789C22×C4—21no—
790C22×C4—21no—
791C22×C4—21no—
792C22×C4—21no—
793C22×C4—21no—
794C22×C4—21no—
795C22×C4—21no—
796C22×C4—21no—
797C22×C4—21no—
798C22×C4—21no—
799C22×C4—21no—
800C22×C4—21no—
801C22×C4—21no—
802C22×C4—21no—
803C22×C4—21no—
804C22×C4—21no—
805C22×C4—21no—
806C22×C4—21no—
807C22×C4—21no—
808C22×C4—21no—
809C22×C4—21no—
810C22×C4—21no—
811C22×C4—21no—
812C22×C4—21no—
813C22×C4—21no—
814C22×C4—21no—
815C22×C4—21no—
816C22×C4—21no—
817C22×C4—21no—
818C22×C4—21no—
819C22×C4—21no—
820C22×C4—21no—
821C22×C4—21no—
822C22×C4—112no—
823C22×C4—112no—
824C22×C4—112no—
825C22×C4—112no—
826C22×C4—112no—
827C22×C4—112no—
828C22×C4—112no—
829C22×C4—112no—
830C22×C4—228no—
831C22×C4—221no—
832C22×C4—221no—
833C22×C4—221no—
834C22×C4—221no—
835C22×C4—221no—
836C22×C4—221no—
837C22×C4—221no—
838C22×C4—221no—
839C22×C4—221no—
840C22×C4—221no—
841C22×C4—221no—
842C22×C4—221no—
843C22×C4—221no—
844C22×C4—221no—
845C22×C4—221no—
846C22×C4—221no—
847C22×C4—221no—
848C22×C4—221no—
849C22×C4—221no—
850C22×C4—221no—
851C22×C4—221no—
852C22×C4—221no—
853C22×C4—221no—
854C22×C4—221no—
855C22×C4—221no—
856C22×C4—221no—
857C22×C4—221no—
858C22×C4—221no—
859C22×C4—221no—
860C22×C4—221no—
861C22×C4—221no—
862C22×C4—221no—
863C22×C4—221no—
864C22×C4—221no—
865C22×C4—228no—
866C22×C4—444no—
867C22×C4—444no—
868C22×C4—444no—
869C22×C4—444no—
870C22×C4—444no—
871C22×C4C2×C4×D1112yes—
872C22×C4C2×C4×D1112yes—
873C22×C4C2×C4×D1112yes—
874C22×C4C2×D4412yes—
875C22×C4C2×D4412yes—
876C22×C4C2×D4412yes—
877C22×C4D4×D1112yes—
878C22×C4#434312yes—
879C22×C4C2×C22⋊D1112yes—
880C22×C4C2×C22⋊D1112yes—
881C22×C4C2×C22⋊D1112yes—
882C4⋊C4—44no—
883C4⋊C4—228no—
884C4⋊C4—228no—
885C4⋊C4(C2×D11)⋊C4116yescomplemented
886C22⋊C4—228no—
887C22⋊C4—228no—
888C22⋊C4—228no—
889C22⋊C4—228no—
890C22⋊C4—228no—
891C22⋊C4—444no—
892C22⋊C4—444no—
893C22⋊C4—444no—
894C22⋊C4—444no—
895C22⋊C4—444no—
896C22⋊C4—444no—
897C42—44no—
898C42—228no—
899C42—444no—
900C42—444no—
901C11#1409511yescharacteristic, complemented, Sylow
902C23—114no—
903C23—222no—
904C23—222no—
905C23—222no—
906C23—222no—
907C23—222no—
908C23—222no—
909C23—222no—
910C23—222no—
911C23—222no—
912C23—222no—
913C23—222no—
914C23—222no—
915C23—222no—
916C23—222no—
917C23—222no—
918C23—222no—
919C23—222no—
920C23—222no—
921C23—222no—
922C23—222no—
923C23—222no—
924C23—222no—
925C23—222no—
926C23—222no—
927C23—222no—
928C23—441no—
929C23—441no—
930C23—441no—
931C23—441no—
932C23—441no—
933C23—441no—
934C23—441no—
935C23—441no—
936C23—441no—
937C23—441no—
938C23—441no—
939C23—441no—
940C23—441no—
941C23—441no—
942C23—441no—
943C23—441no—
944C23—441no—
945C23—441no—
946C23—441no—
947C23—441no—
948C23—441no—
949C23—441no—
950C23—441no—
951C23—441no—
952C23—441no—
953C23—441no—
954C23—441no—
955C23—441no—
956C23—441no—
957C23—441no—
958C23—441no—
959C23—441no—
960C23—441no—
961C23—441no—
962C23—441no—
963C23—441no—
964C23—441no—
965C23—441no—
966C23—441no—
967C23—441no—
968C23—441no—
969C23—441no—
970C23—441no—
971C23—441no—
972C23C22×C4×D1111yescharacteristic
973C23C22×D4411yescharacteristic
974C23C2×D4×D1111yescharacteristic
975C23#6703711yescharacteristic
976C23C2×#434311yescharacteristic
977C23#6704011yescharacteristic
978C23#41×D1111yescharacteristic
979C23#41×D1111yescharacteristic
980C23#41×D1111yescharacteristic
981C23#41×D1111yescharacteristic
982C23#41×D1111yescharacteristic
983C23#41×D1111yescharacteristic
984C23#6704211yescharacteristic
985C23#6704211yescharacteristic
986C23C22×C22⋊D1111yescharacteristic
987D4—4416no—
988C2×C4—22no—
989C2×C4—22no—
990C2×C4—22no—
991C2×C4—22no—
992C2×C4—22no—
993C2×C4—22no—
994C2×C4—22no—
995C2×C4—22no—
996C2×C4—22no—
997C2×C4—22no—
998C2×C4—22no—
999C2×C4—22no—
1000C2×C4—22no—
1001C2×C4—22no—
1002C2×C4—22no—
1003C2×C4—22no—
1004C2×C4—22no—
1005C2×C4—22no—
1006C2×C4—22no—
1007C2×C4—22no—
1008C2×C4—22no—
1009C2×C4—22no—
1010C2×C4—22no—
1011C2×C4—22no—
1012C2×C4—41no—
1013C2×C4—41no—
1014C2×C4—41no—
1015C2×C4—41no—
1016C2×C4—41no—
1017C2×C4—41no—
1018C2×C4—41no—
1019C2×C4—41no—
1020C2×C4—41no—
1021C2×C4—41no—
1022C2×C4—41no—
1023C2×C4—41no—
1024C2×C4—41no—
1025C2×C4—41no—
1026C2×C4—41no—
1027C2×C4—41no—
1028C2×C4—41no—
1029C2×C4—41no—
1030C2×C4—41no—
1031C2×C4—41no—
1032C2×C4—41no—
1033C2×C4—41no—
1034C2×C4—114no—
1035C2×C4—222no—
1036C2×C4—222no—
1037C2×C4—222no—
1038C2×C4—222no—
1039C2×C4—222no—
1040C2×C4—222no—
1041C2×C4—222no—
1042C2×C4—222no—
1043C2×C4—222no—
1044C2×C4—222no—
1045C2×C4—222no—
1046C2×C4—222no—
1047C2×C4—222no—
1048C2×C4—222no—
1049C2×C4—222no—
1050C2×C4—222no—
1051C2×C4—222no—
1052C2×C4—222no—
1053C2×C4—222no—
1054C2×C4—222no—
1055C2×C4—222no—
1056C2×C4—4416no—
1057C2×C4—441no—
1058C2×C4—441no—
1059C2×C4—441no—
1060C2×C4—441no—
1061C2×C4—441no—
1062C2×C4—441no—
1063C2×C4—441no—
1064C2×C4—441no—
1065C2×C4—441no—
1066C2×C4—441no—
1067C2×C4—441no—
1068C2×C4—441no—
1069C2×C4—441no—
1070C2×C4—441no—
1071C2×C4—441no—
1072C2×C4—441no—
1073C2×C4—441no—
1074C2×C4—441no—
1075C2×C4—441no—
1076C2×C4—441no—
1077C2×C4C2×(C2×D11)⋊C414yes—
1078C2×C4C2×(C2×D11)⋊C414yes—
1079C2×C4C2×(C2×D11)⋊C414yes—
1080C22—224no—
1081C22—224no—
1082C22—224no—
1083C22—442no—
1084C22—442no—
1085C22—442no—
1086C22—442no—
1087C22—442no—
1088C22—442no—
1089C22—442no—
1090C22—442no—
1091C22—442no—
1092C22—442no—
1093C22—442no—
1094C22—442no—
1095C22—442no—
1096C22—442no—
1097C22—442no—
1098C22—442no—
1099C22—442no—
1100C22—442no—
1101C22—442no—
1102C22—881no—
1103C22—881no—
1104C22—881no—
1105C22—881no—
1106C22—881no—
1107C22—881no—
1108C22—881no—
1109C22—881no—
1110C22#1062305311yescharacteristic
1111C22#1062305311yescharacteristic
1112C22#1062305511yescharacteristic
1113C22#1062305511yescharacteristic
1114C22C4×D4×D1111yescharacteristic
1115C22#1062307611yescharacteristic
1116C22D4×D4411yescharacteristic
1117C22#1062308511yescharacteristic
1118C22C4×#434311yescharacteristic
1119C22#1062310511yescharacteristic
1120C22#1062310711yescharacteristic
1121C22#1062310811yescharacteristic
1122C22#1062315811yescharacteristic
1123C22#1062316211yescharacteristic
1124C22#1062316811yescharacteristic
1125C22#1062317111yescharacteristic
1126C22D11×#12311yescharacteristic
1127C22#1062318511yescharacteristic
1128C22#1062319411yescharacteristic
1129C22#1062319511yescharacteristic
1130C22#1062322211yescharacteristic
1131C22#1062322311yescharacteristic
1132C22#1062322411yescharacteristic
1133C22#1062322611yescharacteristic
1134C22#1062323511yescharacteristic
1135C22#1062323611yescharacteristic
1136C22#1062323711yescharacteristic
1137C22#1062324011yescharacteristic
1138C22C22×(C2×D11)⋊C411yescharacteristic
1139C22D4×C22⋊D1111yescharacteristic
1140C22#1062334811yescharacteristic
1141C22#1062336011yescharacteristic
1142C22#1062336311yescharacteristic
1143C22#1062336311yescharacteristic
1144C22#1062336511yescharacteristic
1145C4—24no—
1146C4—24no—
1147C4—24no—
1148C4—42no—
1149C4—42no—
1150C4—81no—
1151C4—81no—
1152C4—224no—
1153C4—442no—
1154C4—442no—
1155C4—442no—
1156C4—442no—
1157C4—442no—
1158C2—444no—
1159C2—882no—
1160C2#1307110411yescharacteristic
1161C2#1307113711yescharacteristic
1162C2#1307141211yescharacteristic
1163C2D4×(C2×D11)⋊C411yescharacteristic
1164C2#1307145411yescharacteristic
1165C2#1307160111yescharacteristic
1166C2#1307174811yescharacteristic
1167C2#1307235611yescharacteristic
1168C2#1307238011yescharacteristic
1169C2#1307250611yescharacteristic
1170C2#1307253611yescharacteristic
1171C2#1307259011yescharacteristic
1172C2#1307272511yescharacteristic
1173C2#1307367411yescharacteristic
1174C2#1307372811yescharacteristic
subgroupG/H
center, FrattiniC24C23×D11
commutatorC23×C11C23×C4
FittingC2×C11×#387C2
socle, cosocleC24×C11C24
prime radicalC23×D44C22
hypercenterC2×#387D11
hypocenterC11#14095
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ C2×#387

Complements

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

NH ≅ G/Ntype
3. C2×C4⋊C4×Dic11C2semidirect
4. C2×C4×(C2×D11)⋊C4C2semidirect
5. #13066866C2semidirect
6. #13066862C2semidirect
7. #13066862C2semidirect
9. #13066854C2semidirect
10. #13066852C2semidirect
11. #13066852C2semidirect
12. #13066852C2semidirect
13. #13066851C2semidirect
14. (C2×D11)⋊#95C2semidirect
15. C2×C11×#387C2semidirect
39. C2×#66947C4semidirect
297. C11×C4⋊C4C22⋊C4semidirect
317. C2×#387D11semidirect
505. C2×Dic11#123semidirect
885. C4⋊C4(C2×D11)⋊C4semidirect
901. C11#14095semidirect

Maximal subgroups

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

subgroupindex
C22×#669472
C2×#106226012
C2×C4⋊C4×Dic112
C2×C4×(C2×D11)⋊C42
#130668662
#130668622
#130668562
#130668542
#130668522
#130668512
(C2×D11)⋊#952
C2×C11×#3872
#1409511