Finite Group Databasebeta

← #14683125

Subgroups — #14683125

Order 2816.

2182 conjugacy classes of subgroups.

The subgroup lattice has 1316 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622284C211yesmaximal, characteristic
2C2×#10622552C211yesmaximal, characteristic, complemented
3C2×#10622283C211yesmaximal, characteristic, complemented
4C2×#10622278C211yesmaximal, characteristic, complemented
5C2×#10622278C211yesmaximal, characteristic, complemented
6#13066873C211yesmaximal, characteristic, complemented
7#13066864C211yesmaximal, characteristic, complemented
8#13066856C211yesmaximal, characteristic, complemented
9#13066856C211yesmaximal, characteristic, complemented
10#13066856C211yesmaximal, characteristic, complemented
11#13066854C211yesmaximal, characteristic, complemented
12#13066852C211yesmaximal, characteristic, complemented
13#13066852C211yesmaximal, characteristic, complemented
14(C2×D11)⋊#95C211yesmaximal, characteristic, complemented
15C11×#1434C211yesmaximal, characteristic, complemented
16C23×D44C2211yescharacteristic
17C23×D44C2211yescharacteristic
18C23×D44C2211yescharacteristic
19C23×C4×D11C2211yescharacteristic
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×(C2×D11)⋊C4C2211yescharacteristic
33C22×(C2×D11)⋊C4C2211yescharacteristic
34C22×(C2×D11)⋊C4C2211yescharacteristic
35C22×C4⋊Dic11C2211yescharacteristic
36C22×C4×Dic11C2211yescharacteristic
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#10622552—24no—
52#10622284C418yescomplemented
53#10622283—24no—
54#10622278—24no—
55#10622278—24no—
56C24×D11C2311yescharacteristic
57C24×D11C2311yescharacteristic
58C24×D11C2311yescharacteristic
59C23×C4×C11C2311yescharacteristic
60C23×C4×C11C2311yescharacteristic
61C23×C4×C11C2311yescharacteristic
62C23×C4×C11C2311yescharacteristic
63C23×C4×C11C2311yescharacteristic
64C23×C4×C11C2311yescharacteristic
65C23×C4×C11C2311yescharacteristic
66C23×Dic11C2311yescharacteristic
67C23×Dic11C2311yescharacteristic
68C23×Dic11C2311yescharacteristic
69C23×Dic11C2311yescharacteristic
70C23×Dic11C2311yescharacteristic
71C22×D44—22no—
72C22×D44—22no—
73C22×D44—22no—
74C22×D44—22no—
75C22×D44—22no—
76C22×D44—22no—
77C22×D44—41no—
78C22×D44—41no—
79C22×D44—41no—
80C22×D44—41no—
81C22×D44—41no—
82C22×D44—41no—
83C22×D44—41no—
84C22×D44—41no—
85C22×D44—41no—
86C22×D44—41no—
87C22×D44—41no—
88C22×D44—41no—
89C22×D44C2×C414yes—
90C22×D44C2×C414yes—
91C22×D44C2×C414yescomplemented
92C22×C4×D11—22no—
93C22×C4×D11—22no—
94C22×C4×D11—22no—
95C22×C4×D11—41no—
96C22×C4×D11—41no—
97C22×C4×D11—41no—
98C22×C4×D11—41no—
99C2×C42×C11—22no—
100C2×C42×C11—22no—
101C2×C42×C11—41no—
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—22no—
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)⋊C4—41no—
126C2×(C2×D11)⋊C4—41no—
127C2×(C2×D11)⋊C4—41no—
128C2×(C2×D11)⋊C4—41no—
129C2×(C2×D11)⋊C4—41no—
130C2×(C2×D11)⋊C4—41no—
131C2×(C2×D11)⋊C4—41no—
132C2×(C2×D11)⋊C4—41no—
133C2×(C2×D11)⋊C4—41no—
134C2×(C2×D11)⋊C4—41no—
135C2×(C2×D11)⋊C4—41no—
136C2×(C2×D11)⋊C4—41no—
137C2×(C2×D11)⋊C4—41no—
138C2×(C2×D11)⋊C4—41no—
139C2×(C2×D11)⋊C4—41no—
140C2×(C2×D11)⋊C4C2×C414yes—
141C2×(C2×D11)⋊C4C2×C414yescomplemented
142C2×(C2×D11)⋊C4C2×C414yescomplemented
143C2×(C2×D11)⋊C4D414yescomplemented
144C2×C4⋊Dic11—22no—
145C2×C4⋊Dic11—22no—
146C2×C4⋊Dic11—41no—
147C2×C4×Dic11—22no—
148C2×C4×Dic11—41no—
149C2×C4×Dic11—41no—
150C11×#95—22no—
151C11×#95—41no—
152C11×#95—41no—
153C11×#95—41no—
154C11×#95C2×C414yescomplemented
155C11×#95D414yescomplemented
156C11⋊#95—22no—
157C11⋊#95—22no—
158C11⋊#95—22no—
159C11⋊#95—41no—
160C11⋊#95—41no—
161C11⋊#95—41no—
162C11⋊#95—41no—
163C11⋊#95—41no—
164#14520—111nomaximal, Sylow
165C24×C11C2411yescharacteristic
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×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×D11—21no—
199C23×D11—21no—
200C23×D11—21no—
201C23×D11—21no—
202C23×D11—21no—
203C23×D11—21no—
204C23×D11—21no—
205C23×D11—21no—
206C23×D11C22×C412yes—
207C23×D11C22×C412yes—
208C23×D11C22×C412yes—
209C23×D11C2×D412yes—
210C23×D11#4112yes—
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×C11—21no—
243C22×C4×C11—21no—
244C22×C4×C11—21no—
245C22×C4×C11—21no—
246C22×C4×C11—21no—
247C22×C4×C11—21no—
248C22×C4×C11—21no—
249C22×C4×C11—21no—
250C22×C4×C11—21no—
251C22×C4×C11C22×C412yes—
252C22×C4×C11C22×C412yes—
253C22×C4×C11C22×C412yes—
254C22×C4×C11C2×D412yes—
255C22×C4×C11C2×D412yes—
256C22×C4×C11C2×D412yes—
257C22×C4×C11C2×D412yes—
258C22×C4×C11#4112yes—
259C22×C4×C11#4112yes—
260C22×Dic11—21no—
261C22×Dic11—21no—
262C22×Dic11—21no—
263C22×Dic11—21no—
264C22×Dic11—21no—
265C22×Dic11—21no—
266C22×Dic11—21no—
267C22×Dic11—21no—
268C22×Dic11—21no—
269C22×Dic11—21no—
270C22×Dic11—21no—
271C22×Dic11—21no—
272C22×Dic11—21no—
273C22×Dic11—21no—
274C22×Dic11—21no—
275C22×Dic11—21no—
276C22×Dic11—21no—
277C22×Dic11—21no—
278C22×Dic11—21no—
279C22×Dic11—21no—
280C22×Dic11—21no—
281C22×Dic11—21no—
282C22×Dic11—21no—
283C22×Dic11—21no—
284C22×Dic11—21no—
285C22×Dic11—21no—
286C22×Dic11—21no—
287C22×Dic11—21no—
288C22×Dic11—21no—
289C22×Dic11—21no—
290C22×Dic11—21no—
291C22×Dic11—21no—
292C22×Dic11C22×C412yes—
293C22×Dic11C2×D412yes—
294C22×Dic11#4112yes—
295C2×D44—28no—
296C2×D44—28no—
297C2×D44—28no—
298C2×D44—44no—
299C2×D44—44no—
300C2×D44—44no—
301C2×D44—44no—
302C2×D44—44no—
303C2×D44—44no—
304C2×D44—44no—
305C2×D44—44no—
306C2×D44—44no—
307C2×D44—44no—
308C2×D44—44no—
309C2×D44—44no—
310C2×D44—44no—
311C2×D44—44no—
312C2×D44—44no—
313C2×D44—44no—
314C2×D44—44no—
315C2×D44—44no—
316C2×C4×D11—44no—
317C2×C4×D11—44no—
318C2×C4×D11—44no—
319C2×C4×D11—44no—
320C2×C4×D11—44no—
321C2×C4×D11—44no—
322C2×C4×D11—44no—
323C42×C11—44no—
324(C2×D11)⋊C4—28no—
325(C2×D11)⋊C4—44no—
326(C2×D11)⋊C4—44no—
327(C2×D11)⋊C4—44no—
328(C2×D11)⋊C4—44no—
329(C2×D11)⋊C4—44no—
330(C2×D11)⋊C4—44no—
331(C2×D11)⋊C4—44no—
332(C2×D11)⋊C4—44no—
333(C2×D11)⋊C4—44no—
334(C2×D11)⋊C4—44no—
335(C2×D11)⋊C4—44no—
336(C2×D11)⋊C4—44no—
337(C2×D11)⋊C4—44no—
338C4⋊Dic11—44no—
339C4×Dic11—44no—
340C2×#392—111no—
341C2×#390—111no—
342C2×#388—111no—
343C2×#386—111no—
344C2×#386—111no—
345#1442—111no—
346#1440—111no—
347#1438—111no—
348#1438—111no—
349#1438—111no—
350#1437—111no—
351#1437—111no—
352#1437—111no—
353#1434D1111yescharacteristic, complemented
354C22⋊#95—111no—
355C23×C11C23×C411yescharacteristic
356C23×C11C22×D411yescharacteristic
357C23×C11C22×D411yescharacteristic
358C23×C11C2×#4111yescharacteristic
359C23×C11C2×#4111yescharacteristic
360C23×C11C2×#4111yescharacteristic
361C23×C11C2×#4111yescharacteristic
362C23×C11H(5,𝔽2)11yescharacteristic
363C23×C11H(5,𝔽2)11yescharacteristic
364C23×C11H(5,𝔽2)11yescharacteristic
365C23×C11H(5,𝔽2)11yescharacteristic
366C23×C11H(5,𝔽2)11yescharacteristic
367C23×C11H(5,𝔽2)11yescharacteristic
368C23×C11H(5,𝔽2)11yescharacteristic
369C23×C11H(5,𝔽2)11yescharacteristic
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—22no—
385C22×D11—22no—
386C22×D11—22no—
387C22×D11—22no—
388C22×D11—22no—
389C22×D11—22no—
390C22×D11—22no—
391C22×D11—22no—
392C22×D11—22no—
393C22×D11—22no—
394C22×D11—22no—
395C22×D11—22no—
396C22×D11—22no—
397C22×D11—22no—
398C22×D11—22no—
399C22×D11—22no—
400C22×D11—22no—
401C22×D11—22no—
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—41no—
417C22×D11—41no—
418C22×D11—41no—
419C22×D11—41no—
420C22×D11—41no—
421C22×D11—41no—
422C22×D11—41no—
423C22×D11—41no—
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×D11—41no—
441C22×D11—41no—
442C22×D11—41no—
443C22×D11—41no—
444C22×D11—41no—
445C22×D11—41no—
446C22×D11—41no—
447C22×D11—41no—
448C22×D11—41no—
449C22×D11—41no—
450C22×D11—41no—
451C22×D11—41no—
452C22×D11—41no—
453C22×D11—41no—
454C22×D11—41no—
455C22×D11—41no—
456C22×D11—41no—
457C22×D11—41no—
458C22×D11—41no—
459C22×D11—41no—
460C22×D11—41no—
461C22×D11—41no—
462C22×D11—41no—
463C22×D11—41no—
464C22×D11—41no—
465C22×D11—41no—
466C22×D11—41no—
467C22×D11—41no—
468C22×D11—41no—
469C22×D11—41no—
470C22×D11—41no—
471C22×D11—41no—
472C22×D11—41no—
473C22×D11—41no—
474C22×D11C4×D414yes—
475C2×C4×C11—22no—
476C2×C4×C11—22no—
477C2×C4×C11—22no—
478C2×C4×C11—22no—
479C2×C4×C11—22no—
480C2×C4×C11—22no—
481C2×C4×C11—22no—
482C2×C4×C11—22no—
483C2×C4×C11—22no—
484C2×C4×C11—22no—
485C2×C4×C11—22no—
486C2×C4×C11—22no—
487C2×C4×C11—22no—
488C2×C4×C11—22no—
489C2×C4×C11—22no—
490C2×C4×C11—22no—
491C2×C4×C11—22no—
492C2×C4×C11—22no—
493C2×C4×C11—22no—
494C2×C4×C11—22no—
495C2×C4×C11—22no—
496C2×C4×C11—22no—
497C2×C4×C11—22no—
498C2×C4×C11—22no—
499C2×C4×C11—41no—
500C2×C4×C11—41no—
501C2×C4×C11—41no—
502C2×C4×C11—41no—
503C2×C4×C11—41no—
504C2×C4×C11—41no—
505C2×C4×C11—41no—
506C2×C4×C11—41no—
507C2×C4×C11—41no—
508C2×C4×C11—41no—
509C2×C4×C11—41no—
510C2×C4×C11—41no—
511C2×C4×C11—41no—
512C2×C4×C11—41no—
513C2×C4×C11—41no—
514C2×C4×C11—41no—
515C2×C4×C11—41no—
516C2×C4×C11—41no—
517C2×C4×C11—41no—
518C2×C4×C11—41no—
519C2×C4×C11—41no—
520C2×C4×C11—41no—
521C2×C4×C11—41no—
522C2×C4×C11—41no—
523C2×C4×C11C4×D414yes—
524C2×Dic11—22no—
525C2×Dic11—22no—
526C2×Dic11—22no—
527C2×Dic11—22no—
528C2×Dic11—22no—
529C2×Dic11—22no—
530C2×Dic11—22no—
531C2×Dic11—22no—
532C2×Dic11—22no—
533C2×Dic11—41no—
534C2×Dic11—41no—
535C2×Dic11—41no—
536C2×Dic11—41no—
537C2×Dic11—41no—
538C2×Dic11—41no—
539C2×Dic11—41no—
540C2×Dic11—41no—
541C2×Dic11—41no—
542C2×Dic11—41no—
543C2×Dic11—41no—
544C2×Dic11—41no—
545C2×Dic11—41no—
546C2×Dic11—41no—
547C2×Dic11—41no—
548C2×Dic11—41no—
549C2×Dic11—41no—
550C2×Dic11—41no—
551C2×Dic11—41no—
552C2×Dic11—41no—
553C2×Dic11—41no—
554C2×Dic11—41no—
555C2×Dic11—41no—
556C2×Dic11—41no—
557C2×Dic11—41no—
558C2×Dic11—41no—
559D44—416no—
560D44—416no—
561D44—416no—
562C4×D11—416no—
563C23×D4—111no—
564C23×D4—111no—
565C23×D4—111no—
566C24×C4—111no—
567C22×C4⋊C4—111no—
568C22×C22⋊C4—111no—
569C22×C22⋊C4—111no—
570C22×C22⋊C4—111no—
571C22×C22⋊C4—111no—
572C22×C22⋊C4—111no—
573C22×C22⋊C4—111no—
574C22×C22⋊C4—111no—
575C22×C22⋊C4—111no—
576C22×C22⋊C4—111no—
577C22×C22⋊C4—111no—
578C22×C22⋊C4—111no—
579C22×C22⋊C4—111no—
580C22×C22⋊C4—111no—
581C22×C22⋊C4—111no—
582C22×C42—111no—
583C22×C42C2×D1111yescharacteristic
584#392—118no—
585#390—224no—
586#388—224no—
587#386—224no—
588#386—224no—
589C2×#95—111no—
590C2×#95—111no—
591C2×#95—111no—
592C2×#95—111no—
593C2×#95—111no—
594C2×#95—111no—
595C2×#95—111no—
596C2×#95—111no—
597C2×#95C2×D1111yescharacteristic
598C2×#95C2×D1111yescharacteristic
599C2×#95C2×D1111yescharacteristic
600C2×#95C2×D1111yescharacteristic
601C2×#95C2×D1111yescharacteristic
602C2×#95C2×D1111yescharacteristic
603C22×C11C2×C4×D411yescharacteristic
604C22×C11C2×C4×D411yescharacteristic
605C22×C11C4×#4111yescharacteristic
606C22×C11#51811yescharacteristic
607C22×C11#51811yescharacteristic
608C22×C11#51811yescharacteristic
609C22×C11#51811yescharacteristic
610C22×C11#53411yescharacteristic
611C22×C11#53511yescharacteristic
612C22×C11#53511yescharacteristic
613C22×C11#53511yescharacteristic
614C22×C11#53811yescharacteristic
615C22×C11#53811yescharacteristic
616C22×C11#53811yescharacteristic
617C22×C11#53811yescharacteristic
618C22×C11#54011yescharacteristic
619C22×C11#54011yescharacteristic
620C22×C11#54011yescharacteristic
621C22×C11#54011yescharacteristic
622C22×C11D4211yescharacteristic
623C22×C11#54611yescharacteristic
624C22×C11#54611yescharacteristic
625C22×C11#54611yescharacteristic
626C22×C11#54611yescharacteristic
627C22×C11#54611yescharacteristic
628C22×C11#55011yescharacteristic
629C22×C11#55111yescharacteristic
630C22×C11#55311yescharacteristic
631C22×C11#55311yescharacteristic
632C22×C11#55311yescharacteristic
633C22×C11#55511yescharacteristic
634C22×C11#56011yescharacteristic
635C22×C11#56011yescharacteristic
636C22×C11#56011yescharacteristic
637C22×C11H(3,𝔽4)11yescharacteristic
638C2×D11—24no—
639C2×D11—24no—
640C2×D11—24no—
641C2×D11—42no—
642C2×D11—42no—
643C2×D11—42no—
644C2×D11—42no—
645C2×D11—42no—
646C2×D11—42no—
647C2×D11—42no—
648C2×D11—42no—
649C2×D11—42no—
650C2×D11—42no—
651C2×D11—42no—
652C2×D11—42no—
653C2×D11—42no—
654C2×D11—42no—
655C2×D11—42no—
656C2×D11—42no—
657C2×D11—42no—
658C2×D11—42no—
659C2×D11—42no—
660C2×D11—42no—
661C2×D11—42no—
662C2×D11—42no—
663C2×D11—42no—
664C2×D11—42no—
665C2×D11—42no—
666C2×D11—42no—
667C2×D11—81no—
668C2×D11—81no—
669C2×D11—81no—
670C2×D11—81no—
671C2×D11—81no—
672C2×D11—81no—
673C2×D11—81no—
674C2×D11—81no—
675C2×D11—81no—
676C2×D11—81no—
677C2×D11—81no—
678C2×D11—81no—
679C2×D11—81no—
680C2×D11—81no—
681C2×D11—81no—
682C2×D11—81no—
683C4×C11—24no—
684C4×C11—42no—
685C4×C11—42no—
686C4×C11—42no—
687C4×C11—42no—
688C4×C11—42no—
689C4×C11—42no—
690Dic11—42no—
691Dic11—42no—
692Dic11—42no—
693Dic11—81no—
694Dic11—81no—
695C25—111no—
696C25—111no—
697C25—111no—
698C22×D4—114no—
699C22×D4—114no—
700C22×D4—114no—
701C22×D4—222no—
702C22×D4—222no—
703C22×D4—222no—
704C22×D4—222no—
705C22×D4—222no—
706C22×D4—222no—
707C22×D4—441no—
708C22×D4—441no—
709C22×D4—441no—
710C22×D4—441no—
711C22×D4—441no—
712C22×D4—441no—
713C22×D4—441no—
714C22×D4—441no—
715C22×D4—441no—
716C22×D4—441no—
717C22×D4—441no—
718C22×D4—441no—
719C23×C4—111no—
720C23×C4—111no—
721C23×C4—111no—
722C23×C4—111no—
723C23×C4—111no—
724C23×C4—222no—
725C23×C4—222no—
726C23×C4—222no—
727C23×C4—441no—
728C23×C4—441no—
729C23×C4—441no—
730C23×C4—441no—
731C23×C4C22×D1111yescharacteristic
732C23×C4C22×D1111yescharacteristic
733C23×C4C22×D1111yescharacteristic
734C23×C4C22×D1111yescharacteristic
735C23×C4C22×D1111yescharacteristic
736C23×C4C22×D1111yescharacteristic
737C23×C4C22×D1111yescharacteristic
738C2×C4⋊C4—222no—
739C2×C4⋊C4—222no—
740C2×C4⋊C4—441no—
741C2×C22⋊C4—114no—
742C2×C22⋊C4—114no—
743C2×C22⋊C4—114no—
744C2×C22⋊C4—114no—
745C2×C22⋊C4—222no—
746C2×C22⋊C4—222no—
747C2×C22⋊C4—222no—
748C2×C22⋊C4—222no—
749C2×C22⋊C4—222no—
750C2×C22⋊C4—222no—
751C2×C22⋊C4—222no—
752C2×C22⋊C4—222no—
753C2×C22⋊C4—222no—
754C2×C22⋊C4—222no—
755C2×C22⋊C4—222no—
756C2×C22⋊C4—222no—
757C2×C22⋊C4—222no—
758C2×C22⋊C4—222no—
759C2×C22⋊C4—222no—
760C2×C22⋊C4—222no—
761C2×C22⋊C4—222no—
762C2×C22⋊C4—222no—
763C2×C22⋊C4—441no—
764C2×C22⋊C4—441no—
765C2×C22⋊C4—441no—
766C2×C22⋊C4—441no—
767C2×C22⋊C4—441no—
768C2×C22⋊C4—441no—
769C2×C22⋊C4—441no—
770C2×C22⋊C4—441no—
771C2×C22⋊C4—441no—
772C2×C22⋊C4—441no—
773C2×C22⋊C4—441no—
774C2×C22⋊C4—441no—
775C2×C22⋊C4—441no—
776C2×C22⋊C4—441no—
777C2×C22⋊C4—441no—
778C2×C22⋊C4—441no—
779C2×C22⋊C4—441no—
780C2×C22⋊C4—441no—
781C2×C22⋊C4—441no—
782C2×C22⋊C4—441no—
783C2×C42—22no—
784C2×C42—22no—
785C2×C42—41no—
786C2×C42—222no—
787C2×C42—441no—
788C2×C42—441no—
789#95—22no—
790#95—41no—
791#95—41no—
792#95—41no—
793#95—222no—
794#95—222no—
795#95—222no—
796#95—441no—
797#95—441no—
798#95—441no—
799#95—441no—
800#95—441no—
801#95C4×D1114yescomplemented
802#95D4414yescomplemented
803C2×C11#232111yescharacteristic
804C2×C11#232811yescharacteristic
805C2×C11#233311yescharacteristic
806C2×C11#235811yescharacteristic
807C2×C11#236311yescharacteristic
808C2×C11#236411yescharacteristic
809C2×C11#237511yescharacteristic
810C2×C11#267011yescharacteristic
811C2×C11#267311yescharacteristic
812C2×C11#269911yescharacteristic
813C2×C11#270311yescharacteristic
814C2×C11#270311yescharacteristic
815C2×C11#271411yescharacteristic
816C2×C11#275311yescharacteristic
817C2×C11#275611yescharacteristic
818D11—44no—
819D11—82no—
820D11—82no—
821C24—112no—
822C24—112no—
823C24—112no—
824C24—112no—
825C24—112no—
826C24—221no—
827C24—221no—
828C24—221no—
829C24—221no—
830C24—221no—
831C24—221no—
832C24—221no—
833C24—221no—
834C24—221no—
835C24—221no—
836C24—221no—
837C24—221no—
838C24—221no—
839C24—221no—
840C24—221no—
841C24—221no—
842C24—221no—
843C24—221no—
844C24—221no—
845C24—221no—
846C24—221no—
847C24—221no—
848C24—221no—
849C24—221no—
850C24—221no—
851C24—221no—
852C24—221no—
853C24—221no—
854C24—221no—
855C24—221no—
856C24—221no—
857C24—221no—
858C24—221no—
859C24—221no—
860C24—221no—
861C24—221no—
862C24—221no—
863C24—221no—
864C24—221no—
865C24—221no—
866C24C23×D1111yescharacteristic
867C2×D4—228no—
868C2×D4—228no—
869C2×D4—228no—
870C2×D4—444no—
871C2×D4—444no—
872C2×D4—444no—
873C2×D4—444no—
874C2×D4—444no—
875C2×D4—444no—
876C2×D4—444no—
877C2×D4—444no—
878C2×D4—444no—
879C2×D4—444no—
880C2×D4—444no—
881C2×D4—444no—
882C2×D4—444no—
883C2×D4—444no—
884C2×D4—444no—
885C2×D4—444no—
886C2×D4—444no—
887C2×D4—444no—
888C22×C4—21no—
889C22×C4—21no—
890C22×C4—21no—
891C22×C4—21no—
892C22×C4—21no—
893C22×C4—21no—
894C22×C4—21no—
895C22×C4—21no—
896C22×C4—21no—
897C22×C4—21no—
898C22×C4—21no—
899C22×C4—21no—
900C22×C4—21no—
901C22×C4—21no—
902C22×C4—21no—
903C22×C4—21no—
904C22×C4—21no—
905C22×C4—21no—
906C22×C4—21no—
907C22×C4—21no—
908C22×C4—21no—
909C22×C4—21no—
910C22×C4—21no—
911C22×C4—21no—
912C22×C4—21no—
913C22×C4—21no—
914C22×C4—21no—
915C22×C4—21no—
916C22×C4—21no—
917C22×C4—21no—
918C22×C4—21no—
919C22×C4—21no—
920C22×C4—21no—
921C22×C4—21no—
922C22×C4—21no—
923C22×C4—21no—
924C22×C4—21no—
925C22×C4—21no—
926C22×C4—21no—
927C22×C4—21no—
928C22×C4—112no—
929C22×C4—112no—
930C22×C4—112no—
931C22×C4—221no—
932C22×C4—221no—
933C22×C4—221no—
934C22×C4—221no—
935C22×C4—221no—
936C22×C4—221no—
937C22×C4—221no—
938C22×C4—221no—
939C22×C4—221no—
940C22×C4—221no—
941C22×C4—221no—
942C22×C4—221no—
943C22×C4—221no—
944C22×C4—221no—
945C22×C4—221no—
946C22×C4—221no—
947C22×C4—221no—
948C22×C4—221no—
949C22×C4—221no—
950C22×C4—221no—
951C22×C4—221no—
952C22×C4—221no—
953C22×C4—221no—
954C22×C4—221no—
955C22×C4—221no—
956C22×C4—221no—
957C22×C4—221no—
958C22×C4—221no—
959C22×C4—221no—
960C22×C4—221no—
961C22×C4—221no—
962C22×C4—221no—
963C22×C4—444no—
964C22×C4—444no—
965C22×C4—444no—
966C22×C4—444no—
967C22×C4—444no—
968C22×C4—444no—
969C22×C4—444no—
970C22×C4C2×C4×D1112yes—
971C22×C4C2×C4×D1112yes—
972C22×C4C2×C4×D1112yes—
973C22×C4C2×D4412yes—
974C22×C4C2×D4412yes—
975C22×C4C2×D4412yes—
976C22×C4#433912yes—
977C22×C4D4×D1112yes—
978C22×C4#434312yes—
979C4⋊C4—444no—
980C22⋊C4—228no—
981C22⋊C4—444no—
982C22⋊C4—444no—
983C22⋊C4—444no—
984C22⋊C4—444no—
985C22⋊C4—444no—
986C22⋊C4—444no—
987C22⋊C4—444no—
988C22⋊C4—444no—
989C22⋊C4—444no—
990C22⋊C4—444no—
991C22⋊C4—444no—
992C22⋊C4—444no—
993C22⋊C4—444no—
994C42—44no—
995C42—444no—
996C11#1452011yescharacteristic, complemented, Sylow
997C23—114no—
998C23—222no—
999C23—222no—
1000C23—222no—
1001C23—222no—
1002C23—222no—
1003C23—222no—
1004C23—222no—
1005C23—222no—
1006C23—222no—
1007C23—222no—
1008C23—222no—
1009C23—222no—
1010C23—222no—
1011C23—222no—
1012C23—222no—
1013C23—222no—
1014C23—222no—
1015C23—222no—
1016C23—222no—
1017C23—222no—
1018C23—222no—
1019C23—222no—
1020C23—222no—
1021C23—222no—
1022C23—222no—
1023C23—222no—
1024C23—222no—
1025C23—222no—
1026C23—222no—
1027C23—222no—
1028C23—222no—
1029C23—222no—
1030C23—441no—
1031C23—441no—
1032C23—441no—
1033C23—441no—
1034C23—441no—
1035C23—441no—
1036C23—441no—
1037C23—441no—
1038C23—441no—
1039C23—441no—
1040C23—441no—
1041C23—441no—
1042C23—441no—
1043C23—441no—
1044C23—441no—
1045C23—441no—
1046C23—441no—
1047C23—441no—
1048C23—441no—
1049C23—441no—
1050C23—441no—
1051C23—441no—
1052C23—441no—
1053C23—441no—
1054C23—441no—
1055C23—441no—
1056C23—441no—
1057C23—441no—
1058C23—441no—
1059C23—441no—
1060C23—441no—
1061C23—441no—
1062C23—441no—
1063C23—441no—
1064C23—441no—
1065C23—441no—
1066C23—441no—
1067C23—441no—
1068C23—441no—
1069C23—441no—
1070C23—441no—
1071C23—441no—
1072C23—441no—
1073C23—441no—
1074C23—441no—
1075C23—441no—
1076C23—441no—
1077C23—441no—
1078C23—441no—
1079C23—441no—
1080C23—441no—
1081C23—441no—
1082C23—441no—
1083C23—441no—
1084C23—441no—
1085C23—441no—
1086C23—441no—
1087C23—441no—
1088C23—441no—
1089C23—441no—
1090C23—441no—
1091C23—441no—
1092C23—441no—
1093C23—441no—
1094C23—441no—
1095C23—441no—
1096C23—441no—
1097C23—441no—
1098C23—441no—
1099C23—441no—
1100C23—441no—
1101C23—441no—
1102C23C22×C4×D1111yescharacteristic
1103C23C22×D4411yescharacteristic
1104C23C2×#433911yescharacteristic
1105C23C2×D4×D1111yescharacteristic
1106C23#6703711yescharacteristic
1107C23#6703711yescharacteristic
1108C23C2×#434311yescharacteristic
1109C23#41×D1111yescharacteristic
1110C23#41×D1111yescharacteristic
1111C23#6704211yescharacteristic
1112C23#6704211yescharacteristic
1113C23#6704211yescharacteristic
1114C23#6704211yescharacteristic
1115C23#6704211yescharacteristic
1116C23#6704211yescharacteristic
1117D4—4416no—
1118D4—4416no—
1119D4—4416no—
1120C2×C4—22no—
1121C2×C4—22no—
1122C2×C4—22no—
1123C2×C4—22no—
1124C2×C4—22no—
1125C2×C4—22no—
1126C2×C4—22no—
1127C2×C4—22no—
1128C2×C4—22no—
1129C2×C4—22no—
1130C2×C4—22no—
1131C2×C4—22no—
1132C2×C4—22no—
1133C2×C4—22no—
1134C2×C4—22no—
1135C2×C4—22no—
1136C2×C4—22no—
1137C2×C4—22no—
1138C2×C4—22no—
1139C2×C4—22no—
1140C2×C4—22no—
1141C2×C4—22no—
1142C2×C4—22no—
1143C2×C4—22no—
1144C2×C4—41no—
1145C2×C4—41no—
1146C2×C4—41no—
1147C2×C4—41no—
1148C2×C4—41no—
1149C2×C4—41no—
1150C2×C4—41no—
1151C2×C4—41no—
1152C2×C4—41no—
1153C2×C4—41no—
1154C2×C4—41no—
1155C2×C4—41no—
1156C2×C4—41no—
1157C2×C4—41no—
1158C2×C4—41no—
1159C2×C4—41no—
1160C2×C4—41no—
1161C2×C4—41no—
1162C2×C4—41no—
1163C2×C4—41no—
1164C2×C4—41no—
1165C2×C4—41no—
1166C2×C4—41no—
1167C2×C4—41no—
1168C2×C4—222no—
1169C2×C4—222no—
1170C2×C4—222no—
1171C2×C4—222no—
1172C2×C4—222no—
1173C2×C4—222no—
1174C2×C4—222no—
1175C2×C4—222no—
1176C2×C4—222no—
1177C2×C4—4416no—
1178C2×C4—441no—
1179C2×C4—441no—
1180C2×C4—441no—
1181C2×C4—441no—
1182C2×C4—441no—
1183C2×C4—441no—
1184C2×C4—441no—
1185C2×C4—441no—
1186C2×C4—441no—
1187C2×C4—441no—
1188C2×C4—441no—
1189C2×C4—441no—
1190C2×C4—441no—
1191C2×C4—441no—
1192C2×C4—441no—
1193C2×C4—441no—
1194C2×C4—441no—
1195C2×C4—441no—
1196C2×C4—441no—
1197C2×C4—441no—
1198C2×C4—441no—
1199C2×C4—441no—
1200C2×C4—441no—
1201C2×C4—441no—
1202C2×C4—441no—
1203C2×C4—441no—
1204C2×C4C4×D4414yes—
1205C22—224no—
1206C22—224no—
1207C22—224no—
1208C22—442no—
1209C22—442no—
1210C22—442no—
1211C22—442no—
1212C22—442no—
1213C22—442no—
1214C22—442no—
1215C22—442no—
1216C22—442no—
1217C22—442no—
1218C22—442no—
1219C22—442no—
1220C22—442no—
1221C22—442no—
1222C22—442no—
1223C22—442no—
1224C22—442no—
1225C22—442no—
1226C22—442no—
1227C22—442no—
1228C22—442no—
1229C22—442no—
1230C22—442no—
1231C22—442no—
1232C22—442no—
1233C22—442no—
1234C22—881no—
1235C22—881no—
1236C22—881no—
1237C22—881no—
1238C22—881no—
1239C22—881no—
1240C22—881no—
1241C22—881no—
1242C22—881no—
1243C22—881no—
1244C22—881no—
1245C22—881no—
1246C22—881no—
1247C22—881no—
1248C22—881no—
1249C22—881no—
1250C22C2×C4×D4411yescharacteristic
1251C22#1062302111yescharacteristic
1252C22#1062304511yescharacteristic
1253C22#1062305211yescharacteristic
1254C22#1062305211yescharacteristic
1255C22#1062305611yescharacteristic
1256C22#1062305611yescharacteristic
1257C22#1062305811yescharacteristic
1258C22#1062306311yescharacteristic
1259C22#1062306611yescharacteristic
1260C22#1062306611yescharacteristic
1261C22C4×D4×D1111yescharacteristic
1262C22#1062307611yescharacteristic
1263C22#1062307611yescharacteristic
1264C22D4×D4411yescharacteristic
1265C22#1062308511yescharacteristic
1266C22#1062308511yescharacteristic
1267C22C4×#434311yescharacteristic
1268C22#1062310811yescharacteristic
1269C22#1062313811yescharacteristic
1270C22#1062315111yescharacteristic
1271C22#1062316111yescharacteristic
1272C22#1062317511yescharacteristic
1273C22#1062318411yescharacteristic
1274C22#1062318511yescharacteristic
1275C22#1062319411yescharacteristic
1276C22#1062319711yescharacteristic
1277C22#1062320911yescharacteristic
1278C22#1062321411yescharacteristic
1279C22#1062322611yescharacteristic
1280C22#1062322911yescharacteristic
1281C22#1062323511yescharacteristic
1282C22#1062323511yescharacteristic
1283C22#1062324011yescharacteristic
1284C22#1062324211yescharacteristic
1285C4—24no—
1286C4—42no—
1287C4—42no—
1288C4—42no—
1289C4—42no—
1290C4—42no—
1291C4—42no—
1292C4—442no—
1293C4—442no—
1294C4—442no—
1295C4—881no—
1296C4—881no—
1297C2—444no—
1298C2—882no—
1299C2—882no—
1300C2#1307127811yescharacteristic
1301C2#1307134111yescharacteristic
1302C2#1307138011yescharacteristic
1303C2#1307159811yescharacteristic
1304C2#1307165611yescharacteristic
1305C2#1307166211yescharacteristic
1306C2#1307175611yescharacteristic
1307C2#1307484011yescharacteristic
1308C2#1307488511yescharacteristic
1309C2#1307520311yescharacteristic
1310C2#1307525711yescharacteristic
1311C2#1307525911yescharacteristic
1312C2#1307541011yescharacteristic
1313C2#1307588911yescharacteristic
1314C2#1307593411yescharacteristic
subgroupG/H
center, FrattiniC24C23×D11
commutatorC23×C11C23×C4
FittingC11×#1434C2
socle, cosocleC24×C11C24
prime radicalC2×#10622284C2
hypercenter#1434D11
hypocenterC11#14520
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ #1434

Complements

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

NH ≅ G/Ntype
2. C2×#10622552C2semidirect
3. C2×#10622283C2semidirect
4. C2×#10622278C2semidirect
5. C2×#10622278C2semidirect
6. #13066873C2semidirect
7. #13066864C2semidirect
8. #13066856C2semidirect
9. #13066856C2semidirect
10. #13066856C2semidirect
11. #13066854C2semidirect
12. #13066852C2semidirect
13. #13066852C2semidirect
14. (C2×D11)⋊#95C2semidirect
15. C11×#1434C2semidirect
52. #10622284C4semidirect
91. C22×D44C2×C4semidirect
141. C2×(C2×D11)⋊C4C2×C4semidirect
142. C2×(C2×D11)⋊C4C2×C4semidirect
143. C2×(C2×D11)⋊C4D4semidirect
154. C11×#95C2×C4semidirect
155. C11×#95D4semidirect
353. #1434D11semidirect
801. #95C4×D11semidirect
802. #95D44semidirect
996. C11#14520semidirect

Maximal subgroups

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

subgroupindex
C2×#106222842
C2×#106225522
C2×#106222832
C2×#106222782
#130668732
#130668642
#130668562
#130668542
#130668522
(C2×D11)⋊#952
C11×#14342
#1452011