Finite Group Databasebeta

← #14676799

Subgroups — #14676799

Order 2816.

2170 conjugacy classes of subgroups.

The subgroup lattice has 1184 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622282C211yesmaximal, characteristic, complemented
2C2×#10622278C211yesmaximal, characteristic
3C2×#10622278C211yesmaximal, characteristic
4C2×#10622602C211yesmaximal, characteristic, complemented
5C2×#10622600C211yesmaximal, characteristic, complemented
6C2×#10622279C211yesmaximal, characteristic, complemented
7C2×#10622279C211yesmaximal, characteristic, complemented
8#13066864C211yesmaximal, characteristic, complemented
9#13066862C211yesmaximal, characteristic, complemented
10#13066856C211yesmaximal, characteristic
11#13066852C211yesmaximal, characteristic, complemented
12#13066850C211yesmaximal, characteristic, complemented
13#13066847C211yesmaximal, characteristic, complemented
14#13066842C211yesmaximal, characteristic, complemented
15C11×#1442C211yesmaximal, characteristic, complemented
16C23×D44C2211yescharacteristic
17C23×C4×D11C2211yescharacteristic
18C23×C4×D11C2211yescharacteristic
19C22×C11×C4⋊C4C2211yescharacteristic
20C22×(C2×D11)⋊C4C2211yescharacteristic
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×C4⋊Dic11C2211yescharacteristic
31C22×Dic11⋊C4C2211yescharacteristic
32C22×C4×Dic11C2211yescharacteristic
33C22×C4×Dic11C2211yescharacteristic
34C22×C4×Dic11C2211yescharacteristic
35C2×C11×#95C2211yescharacteristic
36C2×C11×#95C2211yescharacteristic
37C2×C11×#95C2211yescharacteristic
38C2×C11×#95C2211yescharacteristic
39C2×C11×#95C2211yescharacteristic
40C2×C11×#95C2211yescharacteristic
41C2×C11⋊#95C2211yescharacteristic
42C2×C11⋊#95C2211yescharacteristic
43C2×C11⋊#95C2211yescharacteristic
44C2×C11⋊#95C2211yescharacteristic
45C2×C11⋊#95C2211yescharacteristic
46C2×C11⋊#95C2211yescharacteristic
47C2×C11⋊#95C2211yescharacteristic
48C2×C11⋊#95C2211yescharacteristic
49C2×C11⋊#95C2211yescharacteristic
50C2×C11⋊#95C2211yescharacteristic
51#10622602—24no—
52#10622600—24no—
53#10622282—24no—
54#10622279—24no—
55#10622279—24no—
56#10622278—24no—
57#10622278C418yescomplemented
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—22no—
85C22×C4×D11—22no—
86C22×C4×D11—22no—
87C22×C4×D11—22no—
88C22×C4×D11—22no—
89C22×C4×D11—41no—
90C22×C4×D11—41no—
91C22×C4×D11—41no—
92C22×C4×D11—41no—
93C22×C4×D11C2×C414yescomplemented
94C2×C11×C4⋊C4—22no—
95C2×C11×C4⋊C4—22no—
96C2×C11×C4⋊C4—41no—
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)⋊C4C2×C414yes—
124C2×(C2×D11)⋊C4C2×C414yes—
125C2×(C2×D11)⋊C4C2×C414yescomplemented
126C2×(C2×D11)⋊C4D414yes—
127C2×C4⋊Dic11—22no—
128C2×C4⋊Dic11—22no—
129C2×C4⋊Dic11—41no—
130C2×Dic11⋊C4—22no—
131C2×Dic11⋊C4—22no—
132C2×Dic11⋊C4—22no—
133C2×C4×Dic11—22no—
134C2×C4×Dic11—22no—
135C2×C4×Dic11—22no—
136C2×C4×Dic11—22no—
137C2×C4×Dic11—22no—
138C2×C4×Dic11—22no—
139C2×C4×Dic11—41no—
140C2×C4×Dic11—41no—
141C2×C4×Dic11—41no—
142C11×#95—22no—
143C11×#95—22no—
144C11×#95—22no—
145C11×#95—22no—
146C11×#95—41no—
147C11×#95C2×C414yescomplemented
148C11⋊#95—22no—
149C11⋊#95—22no—
150C11⋊#95—22no—
151C11⋊#95—22no—
152C11⋊#95—22no—
153C11⋊#95—41no—
154C11⋊#95—41no—
155C11⋊#95C2×C414yescomplemented
156C11⋊#95D414yescomplemented
157C11⋊#95D414yescomplemented
158#13988—111nomaximal, Sylow
159C24×C11C2411yescharacteristic
160C23×D11—21no—
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×D11C22×C412yes—
185C23×D11C22×C412yes—
186C23×D11C2×D412yes—
187C23×D11#4112yes—
188C23×D11#4112yes—
189C23×D11#4112yes—
190C22×C4×C11—21no—
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×C11—21no—
230C22×C4×C11—21no—
231C22×C4×C11C22×C412yes—
232C22×C4×C11C22×C412yes—
233C22×C4×C11C22×C412yes—
234C22×C4×C11C2×D412yes—
235C22×C4×C11C2×D412yes—
236C22×C4×C11C2×D412yes—
237C22×C4×C11#4112yes—
238C22×C4×C11#4112yes—
239C22×Dic11—21no—
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×Dic11C22×C412yes—
273C22×Dic11C22×C412yes—
274C22×Dic11C2×D412yes—
275C22×Dic11C2×D412yes—
276C22×Dic11C2×D412yes—
277C22×Dic11C2×D412yes—
278C22×Dic11C2×D412yes—
279C22×Dic11#4112yes—
280C22×Dic11#4112yes—
281C2×D44—28no—
282C2×D44—28no—
283C2×D44—44no—
284C2×D44—44no—
285C2×D44—44no—
286C2×D44—44no—
287C2×D44—44no—
288C2×C4×D11—28no—
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—
296C2×C4×D11—44no—
297C2×C4×D11—44no—
298C2×C4×D11—44no—
299C2×C4×D11—44no—
300C2×C4×D11—44no—
301C2×C4×D11—44no—
302C11×C4⋊C4—44no—
303(C2×D11)⋊C4—28no—
304(C2×D11)⋊C4—28no—
305(C2×D11)⋊C4—28no—
306(C2×D11)⋊C4—28no—
307(C2×D11)⋊C4—28no—
308(C2×D11)⋊C4—28no—
309(C2×D11)⋊C4—44no—
310(C2×D11)⋊C4—44no—
311(C2×D11)⋊C4—44no—
312(C2×D11)⋊C4—44no—
313C4⋊Dic11—44no—
314Dic11⋊C4—44no—
315C4×Dic11—44no—
316C4×Dic11—44no—
317C4×Dic11—44no—
318C2×#388—111no—
319C2×#386—111no—
320C2×#386—111no—
321C2×#385—111no—
322C2×#380—111no—
323C2×C4×C22⋊C4—111no—
324C2×C4×C22⋊C4—111no—
325#1442D1111yescharacteristic, complemented
326#1440—111no—
327#1439—111no—
328#1438—111no—
329#1437—111no—
330#1436—111no—
331#1436—111no—
332#1434—111no—
333C23×C11C23×C411yescharacteristic
334C23×C11C22×D411yescharacteristic
335C23×C11C22×D411yescharacteristic
336C23×C11C22×D411yescharacteristic
337C23×C11C2×#4111yescharacteristic
338C23×C11C2×#4111yescharacteristic
339C23×C11C2×#4111yescharacteristic
340C23×C11C2×#4111yescharacteristic
341C23×C11C2×#4111yescharacteristic
342C23×C11C2×#4111yescharacteristic
343C23×C11C2×#4111yescharacteristic
344C23×C11H(5,𝔽2)11yescharacteristic
345C23×C11H(5,𝔽2)11yescharacteristic
346C23×C11H(5,𝔽2)11yescharacteristic
347C23×C112−1+411yescharacteristic
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—22no—
371C22×D11—22no—
372C22×D11—22no—
373C22×D11—22no—
374C22×D11—22no—
375C22×D11—22no—
376C22×D11—22no—
377C22×D11—22no—
378C22×D11—22no—
379C22×D11—22no—
380C22×D11—22no—
381C22×D11—22no—
382C22×D11—22no—
383C22×D11—22no—
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×D11—41no—
415C22×D11—41no—
416C22×D11#11714yes—
417C22×D11C4×D414yes—
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×C11—41no—
462C2×C4×C11—41no—
463C2×C4×C11—41no—
464C2×C4×C11—41no—
465C2×C4×C11—41no—
466C2×C4×C11C4×D414yes—
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—22no—
486C2×Dic11—22no—
487C2×Dic11—22no—
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—41no—
506C2×Dic11—41no—
507C2×Dic11C4×D414yes—
508C2×Dic11#12114yes—
509D44—416no—
510C4×D11—416no—
511C4×D11—416no—
512C23×D4—111no—
513C24×C4—111no—
514C24×C4—111no—
515C22×C4⋊C4—111no—
516C22×C4⋊C4—111no—
517C22×C4⋊C4C2×D1111yescharacteristic
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—
531#388—224no—
532#386—118no—
533#386—224no—
534#385—224no—
535#380—224no—
536C4×C22⋊C4—224no—
537C4×C22⋊C4—224no—
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×#95—111no—
547C2×#95—111no—
548C2×#95C2×D1111yescharacteristic
549C2×#95C2×D1111yescharacteristic
550C2×#95C2×D1111yescharacteristic
551C2×#95C2×D1111yescharacteristic
552C2×#95C2×D1111yescharacteristic
553C2×#95C2×D1111yescharacteristic
554C22×C11C2×#11711yescharacteristic
555C22×C11C2×C4×D411yescharacteristic
556C22×C11C2×C4×D411yescharacteristic
557C22×C11C2×C4×D411yescharacteristic
558C22×C11C4×#4111yescharacteristic
559C22×C11#51811yescharacteristic
560C22×C11#52011yescharacteristic
561C22×C11C2×#12111yescharacteristic
562C22×C11#52511yescharacteristic
563C22×C11#52511yescharacteristic
564C22×C11#52511yescharacteristic
565C22×C11#52911yescharacteristic
566C22×C11#52911yescharacteristic
567C22×C11#52911yescharacteristic
568C22×C11#53211yescharacteristic
569C22×C11#53811yescharacteristic
570C22×C11#53911yescharacteristic
571C22×C11#54011yescharacteristic
572C22×C11#54211yescharacteristic
573C22×C11D4211yescharacteristic
574C22×C11D4211yescharacteristic
575C22×C11#54611yescharacteristic
576C22×C11#54611yescharacteristic
577C22×C11#54611yescharacteristic
578C22×C11#54611yescharacteristic
579C22×C11#54611yescharacteristic
580C22×C11#54711yescharacteristic
581C22×C11#54811yescharacteristic
582C22×C11#54811yescharacteristic
583C22×C11#55111yescharacteristic
584C22×C11#55111yescharacteristic
585C22×C11#55111yescharacteristic
586C22×C11#55211yescharacteristic
587C22×C11#55311yescharacteristic
588C22×C11#55311yescharacteristic
589C2×D11—24no—
590C2×D11—24no—
591C2×D11—24no—
592C2×D11—24no—
593C2×D11—24no—
594C2×D11—24no—
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—42no—
608C2×D11—42no—
609C2×D11—42no—
610C2×D11—42no—
611C2×D11—42no—
612C2×D11—42no—
613C2×D11—42no—
614C2×D11—42no—
615C2×D11—42no—
616C2×D11—42no—
617C2×D11—42no—
618C2×D11—42no—
619C4×C11—24no—
620C4×C11—42no—
621C4×C11—42no—
622C4×C11—42no—
623C4×C11—42no—
624C4×C11—42no—
625C4×C11—81no—
626Dic11—24no—
627Dic11—24no—
628Dic11—42no—
629Dic11—42no—
630Dic11—42no—
631Dic11—81no—
632C25—111no—
633C25—111no—
634C22×D4—114no—
635C22×D4—222no—
636C22×D4—222no—
637C22×D4—222no—
638C22×D4—222no—
639C22×D4—441no—
640C22×D4—441no—
641C23×C4—111no—
642C23×C4—111no—
643C23×C4—111no—
644C23×C4—111no—
645C23×C4—111no—
646C23×C4—114no—
647C23×C4—111no—
648C23×C4—222no—
649C23×C4—222no—
650C23×C4—222no—
651C23×C4—222no—
652C23×C4—222no—
653C23×C4—222no—
654C23×C4—222no—
655C23×C4—222no—
656C23×C4—222no—
657C23×C4—441no—
658C23×C4—441no—
659C23×C4—441no—
660C23×C4—441no—
661C23×C4C22×D1111yescharacteristic
662C23×C4C22×D1111yescharacteristic
663C23×C4C22×D1111yescharacteristic
664C23×C4C22×D1111yescharacteristic
665C23×C4C22×D1111yescharacteristic
666C23×C4C22×D1111yescharacteristic
667C23×C4C22×D1111yescharacteristic
668C2×C4⋊C4—22no—
669C2×C4⋊C4—22no—
670C2×C4⋊C4—41no—
671C2×C4⋊C4—222no—
672C2×C4⋊C4—222no—
673C2×C4⋊C4—222no—
674C2×C4⋊C4—222no—
675C2×C4⋊C4—222no—
676C2×C4⋊C4—441no—
677C2×C22⋊C4—114no—
678C2×C22⋊C4—114no—
679C2×C22⋊C4—114no—
680C2×C22⋊C4—114no—
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—222no—
698C2×C22⋊C4—222no—
699C2×C22⋊C4—222no—
700C2×C22⋊C4—222no—
701C2×C22⋊C4—222no—
702C2×C22⋊C4—222no—
703C2×C22⋊C4—441no—
704C2×C22⋊C4—441no—
705C2×C22⋊C4—441no—
706C2×C22⋊C4—441no—
707C2×C42—222no—
708C2×C42—222no—
709C2×C42—222no—
710C2×C42—222no—
711C2×C42—222no—
712C2×C42—222no—
713C2×C42—441no—
714C2×C42—441no—
715C2×C42—441no—
716#95—22no—
717#95—22no—
718#95—22no—
719#95—22no—
720#95—41no—
721#95—114no—
722#95—114no—
723#95—114no—
724#95—222no—
725#95—222no—
726#95—222no—
727#95—222no—
728#95—222no—
729#95—441no—
730#95—441no—
731#95C4×D1114yescomplemented
732C2×C11#229011yescharacteristic
733C2×C11C4×#12111yescharacteristic
734C2×C11#233511yescharacteristic
735C2×C11#234211yescharacteristic
736C2×C11#235211yescharacteristic
737C2×C11#235811yescharacteristic
738C2×C11#236111yescharacteristic
739C2×C11#242411yescharacteristic
740C2×C11#242711yescharacteristic
741C2×C11#245711yescharacteristic
742C2×C11#246311yescharacteristic
743C2×C11#246411yescharacteristic
744C2×C11#247711yescharacteristic
745C2×C11#255311yescharacteristic
746C2×C11#257811yescharacteristic
747D11—44no—
748D11—44no—
749C24—112no—
750C24—112no—
751C24—112no—
752C24—112no—
753C24—112no—
754C24—112no—
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—
776C24—221no—
777C24—221no—
778C24—221no—
779C24C23×D1111yescharacteristic
780C2×D4—228no—
781C2×D4—228no—
782C2×D4—444no—
783C2×D4—444no—
784C2×D4—444no—
785C2×D4—444no—
786C2×D4—444no—
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—21no—
823C22×C4—21no—
824C22×C4—21no—
825C22×C4—21no—
826C22×C4—21no—
827C22×C4—21no—
828C22×C4—112no—
829C22×C4—112no—
830C22×C4—112no—
831C22×C4—112no—
832C22×C4—112no—
833C22×C4—112no—
834C22×C4—112no—
835C22×C4—112no—
836C22×C4—112no—
837C22×C4—228no—
838C22×C4—228no—
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—221no—
867C22×C4—221no—
868C22×C4—221no—
869C22×C4—221no—
870C22×C4—221no—
871C22×C4—221no—
872C22×C4—221no—
873C22×C4—444no—
874C22×C4—444no—
875C22×C4—444no—
876C22×C4—444no—
877C22×C4—444no—
878C22×C4—444no—
879C22×C4—444no—
880C22×C4—444no—
881C22×C4—444no—
882C22×C4—444no—
883C22×C4—444no—
884C22×C4C2×C4×D1112yes—
885C22×C4C2×C4×D1112yes—
886C22×C4C2×C4×D1112yes—
887C22×C4D4×D1112yes—
888C22×C4D4×D1112yes—
889C22×C4D4×D1112yes—
890C22×C4#434312yes—
891C22×C4#434312yes—
892C4⋊C4—44no—
893C4⋊C4—444no—
894C4⋊C4—444no—
895C22⋊C4—228no—
896C22⋊C4—228no—
897C22⋊C4—228no—
898C22⋊C4—228no—
899C22⋊C4—228no—
900C22⋊C4—228no—
901C22⋊C4—444no—
902C22⋊C4—444no—
903C22⋊C4—444no—
904C22⋊C4—444no—
905C42—444no—
906C42—444no—
907C42—444no—
908C11#1398811yescharacteristic, complemented, Sylow
909C23—114no—
910C23—114no—
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—222no—
929C23—222no—
930C23—222no—
931C23—222no—
932C23—222no—
933C23—222no—
934C23—222no—
935C23—222no—
936C23—222no—
937C23—222no—
938C23—222no—
939C23—222no—
940C23—222no—
941C23—222no—
942C23—222no—
943C23—222no—
944C23—222no—
945C23—222no—
946C23—222no—
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—
972C23—441no—
973C23—441no—
974C23—441no—
975C23—441no—
976C23—441no—
977C23—441no—
978C23—441no—
979C23C22×C4×D1111yescharacteristic
980C23C2×D4×D1111yescharacteristic
981C23C2×D4×D1111yescharacteristic
982C23C2×D4×D1111yescharacteristic
983C23#6703711yescharacteristic
984C23C2×#434311yescharacteristic
985C23C2×#434311yescharacteristic
986C23#41×D1111yescharacteristic
987C23#41×D1111yescharacteristic
988C23#41×D1111yescharacteristic
989C23#41×D1111yescharacteristic
990C23#41×D1111yescharacteristic
991C23#6704211yescharacteristic
992C23#6704211yescharacteristic
993C23#6704311yescharacteristic
994D4—4416no—
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—22no—
1013C2×C4—22no—
1014C2×C4—22no—
1015C2×C4—22no—
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—41no—
1035C2×C4—41no—
1036C2×C4—41no—
1037C2×C4—41no—
1038C2×C4—41no—
1039C2×C4—41no—
1040C2×C4—41no—
1041C2×C4—41no—
1042C2×C4—41no—
1043C2×C4—114no—
1044C2×C4—114no—
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—222no—
1057C2×C4—222no—
1058C2×C4—222no—
1059C2×C4—222no—
1060C2×C4—222no—
1061C2×C4—222no—
1062C2×C4—222no—
1063C2×C4—222no—
1064C2×C4—222no—
1065C2×C4—222no—
1066C2×C4—4416no—
1067C2×C4—4416no—
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×C4—441no—
1078C2×C4—441no—
1079C2×C4—441no—
1080C2×C4—441no—
1081C2×C4—441no—
1082C2×C4—441no—
1083C2×C4—441no—
1084C2×C4—441no—
1085C2×C4—441no—
1086C2×C4—441no—
1087C2×C4#6694614yes—
1088C22—224no—
1089C22—224no—
1090C22—224no—
1091C22—224no—
1092C22—224no—
1093C22—224no—
1094C22—442no—
1095C22—442no—
1096C22—442no—
1097C22—442no—
1098C22—442no—
1099C22—442no—
1100C22—442no—
1101C22—442no—
1102C22—442no—
1103C22—442no—
1104C22—442no—
1105C22—442no—
1106C22—442no—
1107C22—442no—
1108C22—442no—
1109C22—442no—
1110C22—442no—
1111C22—442no—
1112C22—442no—
1113C22—442no—
1114C22—442no—
1115C22—442no—
1116C22—442no—
1117C22—442no—
1118C22C2×#6694611yescharacteristic
1119C22D11×#11711yescharacteristic
1120C22#1062305411yescharacteristic
1121C22C4×D4×D1111yescharacteristic
1122C22C4×D4×D1111yescharacteristic
1123C22#1062307611yescharacteristic
1124C22C4×#434311yescharacteristic
1125C22#1062312111yescharacteristic
1126C22D11×#12111yescharacteristic
1127C22#1062314011yescharacteristic
1128C22#1062314311yescharacteristic
1129C22#1062315811yescharacteristic
1130C22#1062315811yescharacteristic
1131C22#1062316111yescharacteristic
1132C22#1062316811yescharacteristic
1133C22#1062317611yescharacteristic
1134C22#1062318511yescharacteristic
1135C22#1062318511yescharacteristic
1136C22#1062318611yescharacteristic
1137C22#1062318711yescharacteristic
1138C22#1062318811yescharacteristic
1139C22#1062320711yescharacteristic
1140C22#1062320811yescharacteristic
1141C22#1062320811yescharacteristic
1142C22#1062321011yescharacteristic
1143C22#1062322211yescharacteristic
1144C22#1062322211yescharacteristic
1145C22#1062322511yescharacteristic
1146C22#1062322611yescharacteristic
1147C22#1062322911yescharacteristic
1148C22#1062323611yescharacteristic
1149C22#1062323711yescharacteristic
1150C22#1062324011yescharacteristic
1151C22#1062324111yescharacteristic
1152C22#1062325611yescharacteristic
1153C4—24no—
1154C4—42no—
1155C4—42no—
1156C4—42no—
1157C4—42no—
1158C4—42no—
1159C4—81no—
1160C4—224no—
1161C4—224no—
1162C4—442no—
1163C4—442no—
1164C4—442no—
1165C4—881no—
1166C2—444no—
1167C2—444no—
1168C2#1307105411yescharacteristic
1169C2#1307112411yescharacteristic
1170C2#1307140511yescharacteristic
1171C2#1307146011yescharacteristic
1172C2#1307154211yescharacteristic
1173C2#1307159211yescharacteristic
1174C2#1307162911yescharacteristic
1175C2#1307214511yescharacteristic
1176C2#1307218811yescharacteristic
1177C2#1307252611yescharacteristic
1178C2#1307261311yescharacteristic
1179C2#1307262511yescharacteristic
1180C2#1307281211yescharacteristic
1181C2#1307366411yescharacteristic
1182C2#1307394511yescharacteristic
subgroupG/H
center, FrattiniC24C23×D11
commutatorC23×C11C23×C4
FittingC11×#1442C2
socle, cosocleC24×C11C24
prime radicalC23×D44C22
hypercenter#1442D11
hypocenterC11#13988
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ #1442

Complements

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

NH ≅ G/Ntype
1. C2×#10622282C2semidirect
4. C2×#10622602C2semidirect
5. C2×#10622600C2semidirect
6. C2×#10622279C2semidirect
7. C2×#10622279C2semidirect
8. #13066864C2semidirect
9. #13066862C2semidirect
11. #13066852C2semidirect
12. #13066850C2semidirect
13. #13066847C2semidirect
14. #13066842C2semidirect
15. C11×#1442C2semidirect
57. #10622278C4semidirect
93. C22×C4×D11C2×C4semidirect
125. C2×(C2×D11)⋊C4C2×C4semidirect
147. C11×#95C2×C4semidirect
155. C11⋊#95C2×C4semidirect
156. C11⋊#95D4semidirect
157. C11⋊#95D4semidirect
325. #1442D11semidirect
731. #95C4×D11semidirect
908. C11#13988semidirect

Maximal subgroups

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

subgroupindex
C2×#106222822
C2×#106222782
C2×#106226022
C2×#106226002
C2×#106222792
#130668642
#130668622
#130668562
#130668522
#130668502
#130668472
#130668422
C11×#14422
#1398811