Finite Group Databasebeta

← #14683113

Subgroups — #14683113

Order 2816.

2390 conjugacy classes of subgroups.

The subgroup lattice has 1342 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622836C211yesmaximal, characteristic
2C2×#10622570C211yesmaximal, characteristic, complemented
3C2×#10622833C211yesmaximal, characteristic, complemented
4C2×#10622571C211yesmaximal, characteristic, complemented
5C2×#10622569C211yesmaximal, characteristic, complemented
6C2×#10622569C211yesmaximal, characteristic, complemented
7C2×#10622559C211yesmaximal, characteristic, complemented
8#13066874C211yesmaximal, characteristic, complemented
9#13066863C211yesmaximal, characteristic, complemented
10#13066860C211yesmaximal, characteristic, complemented
11#13066859C211yesmaximal, characteristic, complemented
12#13066853C211yesmaximal, characteristic, complemented
13#13066840C211yesmaximal, characteristic, complemented
14(C2×D11)⋊#95C211yesmaximal, characteristic, complemented
15C11×#1438C211yesmaximal, characteristic, complemented
16C23×D4×C11C2211yescharacteristic
17C23×C22⋊D11C2211yescharacteristic
18C23×C22⋊D11C2211yescharacteristic
19C24×Dic11C2211yescharacteristic
20C23×C4×D11C2211yescharacteristic
21C22×C11×C22⋊C4C2211yescharacteristic
22C22×C11×C22⋊C4C2211yescharacteristic
23C22×C11×C22⋊C4C2211yescharacteristic
24C22×C11×C22⋊C4C2211yescharacteristic
25C22×C22⋊Dic11C2211yescharacteristic
26C22×C22⋊Dic11C2211yescharacteristic
27C22×C22⋊Dic11C2211yescharacteristic
28C22×C22⋊Dic11C2211yescharacteristic
29C22×C22⋊Dic11C2211yescharacteristic
30C22×(C2×D11)⋊C4C2211yescharacteristic
31C22×(C2×D11)⋊C4C2211yescharacteristic
32C22×(C2×D11)⋊C4C2211yescharacteristic
33C22×(C2×D11)⋊C4C2211yescharacteristic
34C22×Dic11⋊C4C2211yescharacteristic
35C22×Dic11⋊C4C2211yescharacteristic
36C22×C4×Dic11C2211yescharacteristic
37C2×C11×#95C2211yescharacteristic
38C2×C11×#95C2211yescharacteristic
39#10622836C418yescomplemented
40#10622833—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
53#10622571—24no—
54#10622570—24no—
55#10622569—24no—
56#10622569—24no—
57#10622559—24no—
58C25×C11C2311yescharacteristic
59C25×C11C2311yescharacteristic
60C24×D11C2311yescharacteristic
61C22×D4×C11—22no—
62C22×D4×C11—22no—
63C22×D4×C11—41no—
64C22×D4×C11—41no—
65C22×D4×C11—41no—
66C22×D4×C11—41no—
67C22×D4×C11C2×C414yescomplemented
68C23×C4×C11C2311yescharacteristic
69C23×C4×C11C2311yescharacteristic
70C23×C4×C11C2311yescharacteristic
71C23×C4×C11C2311yescharacteristic
72C23×C4×C11C2311yescharacteristic
73C22×C22⋊D11—22no—
74C22×C22⋊D11—22no—
75C22×C22⋊D11—22no—
76C22×C22⋊D11—22no—
77C22×C22⋊D11—22no—
78C22×C22⋊D11—22no—
79C22×C22⋊D11—22no—
80C22×C22⋊D11—22no—
81C22×C22⋊D11—41no—
82C22×C22⋊D11—41no—
83C22×C22⋊D11—41no—
84C22×C22⋊D11—41no—
85C22×C22⋊D11C2×C414yes—
86C22×C22⋊D11C2×C414yescomplemented
87C23×Dic11—22no—
88C23×Dic11—22no—
89C23×Dic11—22no—
90C23×Dic11—41no—
91C23×Dic11—41no—
92C23×Dic11—41no—
93C23×Dic11—41no—
94C23×Dic11C2311yescharacteristic
95C23×Dic11C2311yescharacteristic
96C23×Dic11C2311yescharacteristic
97C23×Dic11C2311yescharacteristic
98C23×Dic11C2311yescharacteristic
99C23×Dic11C2311yescharacteristic
100C23×Dic11C2311yescharacteristic
101C22×C4×D11—22no—
102C22×C4×D11—22no—
103C22×C4×D11—22no—
104C22×C4×D11—41no—
105C22×C4×D11—41no—
106C22×C4×D11—41no—
107C22×C4×D11—41no—
108C2×C11×C22⋊C4—22no—
109C2×C11×C22⋊C4—22no—
110C2×C11×C22⋊C4—22no—
111C2×C11×C22⋊C4—22no—
112C2×C11×C22⋊C4—22no—
113C2×C11×C22⋊C4—22no—
114C2×C11×C22⋊C4—41no—
115C2×C11×C22⋊C4—41no—
116C2×C11×C22⋊C4—41no—
117C2×C11×C22⋊C4—41no—
118C2×C11×C22⋊C4—41no—
119C2×C11×C22⋊C4—41no—
120C2×C22⋊Dic11—22no—
121C2×C22⋊Dic11—22no—
122C2×C22⋊Dic11—22no—
123C2×C22⋊Dic11—22no—
124C2×C22⋊Dic11—22no—
125C2×C22⋊Dic11—22no—
126C2×C22⋊Dic11—41no—
127C2×C22⋊Dic11—41no—
128C2×C22⋊Dic11—41no—
129C2×C22⋊Dic11—41no—
130C2×C22⋊Dic11—41no—
131C2×C22⋊Dic11—41no—
132C2×C22⋊Dic11C2×C414yescomplemented
133C2×C22⋊Dic11C2×C414yescomplemented
134C2×C22⋊Dic11D414yescomplemented
135C2×(C2×D11)⋊C4—22no—
136C2×(C2×D11)⋊C4—22no—
137C2×(C2×D11)⋊C4—22no—
138C2×(C2×D11)⋊C4—22no—
139C2×(C2×D11)⋊C4—41no—
140C2×(C2×D11)⋊C4—41no—
141C2×(C2×D11)⋊C4—41no—
142C2×(C2×D11)⋊C4—41no—
143C2×(C2×D11)⋊C4—41no—
144C2×(C2×D11)⋊C4—41no—
145C2×(C2×D11)⋊C4C2×C414yescomplemented
146C2×(C2×D11)⋊C4D414yescomplemented
147C2×Dic11⋊C4—22no—
148C2×Dic11⋊C4—22no—
149C2×Dic11⋊C4—22no—
150C2×Dic11⋊C4—41no—
151C2×Dic11⋊C4—41no—
152C2×Dic11⋊C4—41no—
153C2×C4×Dic11—22no—
154C2×C4×Dic11—22no—
155C2×C4×Dic11—41no—
156C11×#95—41no—
157C11×#95—41no—
158C11⋊#95—22no—
159C11⋊#95—22no—
160C11⋊#95—22no—
161C11⋊#95—22no—
162C11⋊#95—22no—
163C11⋊#95—22no—
164C11⋊#95—22no—
165C11⋊#95—22no—
166C11⋊#95—41no—
167C11⋊#95—41no—
168C11⋊#95C2×C414yescomplemented
169C11⋊#95D414yescomplemented
170#14519—111nomaximal, Sylow
171C24×C11—21no—
172C24×C11—21no—
173C24×C11—21no—
174C24×C11—21no—
175C24×C11—21no—
176C24×C11—21no—
177C24×C11—21no—
178C24×C11—21no—
179C24×C11—21no—
180C24×C11—21no—
181C24×C11—21no—
182C24×C11—21no—
183C24×C11—21no—
184C24×C11—21no—
185C24×C11—21no—
186C24×C11—21no—
187C24×C11—21no—
188C24×C11—21no—
189C24×C11—21no—
190C24×C11—21no—
191C24×C11—21no—
192C24×C11—21no—
193C24×C11—21no—
194C24×C11—21no—
195C24×C11—21no—
196C24×C11—21no—
197C24×C11C22×C412yes—
198C24×C11C22×C412yes—
199C24×C11C2×D412yes—
200C24×C11#4112yes—
201C24×C11C2411yescharacteristic
202C23×D11—21no—
203C23×D11—21no—
204C23×D11—21no—
205C23×D11—21no—
206C23×D11—21no—
207C23×D11—21no—
208C23×D11—21no—
209C23×D11—21no—
210C23×D11—21no—
211C23×D11—21no—
212C23×D11—21no—
213C23×D11—21no—
214C23×D11C22×C412yes—
215C23×D11C2×D412yes—
216C23×D11#4112yes—
217C2×D4×C11—28no—
218C2×D4×C11—44no—
219C2×D4×C11—44no—
220C2×D4×C11—44no—
221C2×D4×C11—44no—
222C2×D4×C11—44no—
223C2×D4×C11—44no—
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×C11—21no—
252C22×C4×C11—21no—
253C22×C4×C11—21no—
254C22×C4×C11—21no—
255C22×C4×C11—21no—
256C22×C4×C11C22×C412yes—
257C22×C4×C11C2×D412yes—
258C22×C4×C11C2×D412yes—
259C2×C22⋊D11—28no—
260C2×C22⋊D11—28no—
261C2×C22⋊D11—28no—
262C2×C22⋊D11—28no—
263C2×C22⋊D11—44no—
264C2×C22⋊D11—44no—
265C2×C22⋊D11—44no—
266C2×C22⋊D11—44no—
267C2×C22⋊D11—44no—
268C2×C22⋊D11—44no—
269C2×C22⋊D11—44no—
270C2×C22⋊D11—44no—
271C2×C22⋊D11—44no—
272C2×C22⋊D11—44no—
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—21no—
298C22×Dic11—21no—
299C22×Dic11—21no—
300C22×Dic11—21no—
301C22×Dic11—21no—
302C22×Dic11—21no—
303C22×Dic11—21no—
304C22×Dic11—21no—
305C22×Dic11—21no—
306C22×Dic11—21no—
307C22×Dic11—21no—
308C22×Dic11—21no—
309C22×Dic11—21no—
310C22×Dic11—21no—
311C22×Dic11—21no—
312C22×Dic11—21no—
313C22×Dic11—44no—
314C22×Dic11—44no—
315C22×Dic11—44no—
316C22×Dic11—44no—
317C22×Dic11—44no—
318C22×Dic11—44no—
319C22×Dic11—44no—
320C22×Dic11C22×C412yes—
321C22×Dic11C22×C412yes—
322C22×Dic11C22×C412yes—
323C22×Dic11C2×D412yes—
324C22×Dic11C2×D412yes—
325C22×Dic11C2×D412yes—
326C22×Dic11C2×D412yes—
327C22×Dic11C2×D412yes—
328C22×Dic11#4112yes—
329C2×C4×D11—44no—
330C2×C4×D11—44no—
331C2×C4×D11—44no—
332C2×C4×D11—44no—
333C2×C4×D11—44no—
334C2×C4×D11—44no—
335C2×C4×D11—44no—
336C11×C22⋊C4—44no—
337C11×C22⋊C4—44no—
338C11×C22⋊C4—44no—
339C11×C22⋊C4—44no—
340C22⋊Dic11—28no—
341C22⋊Dic11—44no—
342C22⋊Dic11—44no—
343C22⋊Dic11—44no—
344C22⋊Dic11—44no—
345(C2×D11)⋊C4—44no—
346(C2×D11)⋊C4—44no—
347(C2×D11)⋊C4—44no—
348(C2×D11)⋊C4—44no—
349Dic11⋊C4—44no—
350Dic11⋊C4—44no—
351C4×Dic11—44no—
352C2×#392—111no—
353C2×#390—111no—
354C2×#386—111no—
355C2×#386—111no—
356C2×#386—111no—
357C2×#386—111no—
358C2×#385—111no—
359#1442—111no—
360#1440—111no—
361#1439—111no—
362#1439—111no—
363#1438D1111yescharacteristic, complemented
364#1437—111no—
365#1434—111no—
366C22⋊#95—111no—
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×C11—22no—
385C23×C11—22no—
386C23×C11—22no—
387C23×C11—22no—
388C23×C11—22no—
389C23×C11—22no—
390C23×C11—22no—
391C23×C11—22no—
392C23×C11—41no—
393C23×C11—41no—
394C23×C11—41no—
395C23×C11—41no—
396C23×C11—41no—
397C23×C11—41no—
398C23×C11—41no—
399C23×C11—41no—
400C23×C11—41no—
401C23×C11—41no—
402C23×C11—41no—
403C23×C11—41no—
404C23×C11—41no—
405C23×C11—41no—
406C23×C11—41no—
407C23×C11—41no—
408C23×C11—41no—
409C23×C11—41no—
410C23×C11—41no—
411C23×C11—41no—
412C23×C11—41no—
413C23×C11—41no—
414C23×C11—41no—
415C23×C11—41no—
416C23×C11—41no—
417C23×C11—41no—
418C23×C11—41no—
419C23×C11—41no—
420C23×C11—41no—
421C23×C11—41no—
422C23×C11—41no—
423C23×C11—41no—
424C23×C11—41no—
425C23×C11—41no—
426C23×C11—41no—
427C23×C11—41no—
428C23×C11—41no—
429C23×C11—41no—
430C23×C11—41no—
431C23×C11—41no—
432C23×C11—41no—
433C23×C11—41no—
434C23×C11—41no—
435C23×C11—41no—
436C23×C11C4×D414yes—
437C23×C11C23×C411yescharacteristic
438C23×C11C22×D411yescharacteristic
439C23×C11C22×D411yescharacteristic
440C23×C11C22×D411yescharacteristic
441C23×C11C2×#4111yescharacteristic
442C23×C11C2×#4111yescharacteristic
443C23×C11C2×#4111yescharacteristic
444C23×C11H(5,𝔽2)11yescharacteristic
445C23×C11H(5,𝔽2)11yescharacteristic
446C23×C11H(5,𝔽2)11yescharacteristic
447C23×C11H(5,𝔽2)11yescharacteristic
448C23×C11H(5,𝔽2)11yescharacteristic
449C23×C11H(5,𝔽2)11yescharacteristic
450C23×C11H(5,𝔽2)11yescharacteristic
451C23×C112−1+411yescharacteristic
452C22×D11—22no—
453C22×D11—22no—
454C22×D11—22no—
455C22×D11—22no—
456C22×D11—22no—
457C22×D11—22no—
458C22×D11—22no—
459C22×D11—22no—
460C22×D11—22no—
461C22×D11—22no—
462C22×D11—22no—
463C22×D11—22no—
464C22×D11—22no—
465C22×D11—22no—
466C22×D11—22no—
467C22×D11—22no—
468C22×D11—22no—
469C22×D11—22no—
470C22×D11—41no—
471C22×D11—41no—
472C22×D11—41no—
473C22×D11—41no—
474C22×D11—41no—
475C22×D11—41no—
476C22×D11—41no—
477C22×D11—41no—
478C22×D11—41no—
479C22×D11—41no—
480C22×D11—41no—
481C22×D11—41no—
482C22×D11—41no—
483C22×D11—41no—
484C22×D11—41no—
485C22×D11—41no—
486C22×D11C4×D414yes—
487D4×C11—416no—
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—41no—
498C2×C4×C11—41no—
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—
523C22⋊D11—416no—
524C22⋊D11—416no—
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—22no—
534C2×Dic11—22no—
535C2×Dic11—22no—
536C2×Dic11—22no—
537C2×Dic11—22no—
538C2×Dic11—22no—
539C2×Dic11—22no—
540C2×Dic11—22no—
541C2×Dic11—22no—
542C2×Dic11—22no—
543C2×Dic11—22no—
544C2×Dic11—22no—
545C2×Dic11—22no—
546C2×Dic11—22no—
547C2×Dic11—22no—
548C2×Dic11—22no—
549C2×Dic11—416no—
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—
559C2×Dic11—41no—
560C2×Dic11—41no—
561C2×Dic11—41no—
562C2×Dic11—41no—
563C2×Dic11—41no—
564C2×Dic11—41no—
565C2×Dic11—41no—
566C2×Dic11—41no—
567C2×Dic11—41no—
568C2×Dic11—41no—
569C2×Dic11—41no—
570C2×Dic11—41no—
571C2×Dic11—41no—
572C2×Dic11—41no—
573C2×Dic11—41no—
574C2×Dic11C4×D414yes—
575C4×D11—416no—
576C23×D4—111no—
577C23×D4—111no—
578C23×D4C2×D1111yescharacteristic
579C24×C4—111no—
580C24×C4—111no—
581C22×C4⋊C4—111no—
582C22×C4⋊C4—111no—
583C22×C22⋊C4—111no—
584C22×C22⋊C4—111no—
585C22×C22⋊C4—111no—
586C22×C22⋊C4—111no—
587C22×C22⋊C4—111no—
588C22×C22⋊C4—111no—
589C22×C22⋊C4—111no—
590C22×C22⋊C4—111no—
591C22×C22⋊C4—111no—
592C22×C22⋊C4C2×D1111yescharacteristic
593C22×C22⋊C4C2×D1111yescharacteristic
594C22×C22⋊C4C2×D1111yescharacteristic
595C22×C22⋊C4C2×D1111yescharacteristic
596C22×C42—111no—
597#392—118no—
598#390—224no—
599#386—224no—
600#386—224no—
601#386—224no—
602#386—224no—
603#385—224no—
604C2×#95—111no—
605C2×#95—111no—
606C2×#95—111no—
607C2×#95—111no—
608C2×#95—111no—
609C2×#95—111no—
610C2×#95—111no—
611C2×#95—111no—
612C2×#95—111no—
613C2×#95—111no—
614C2×#95—111no—
615C2×#95—111no—
616C2×#95C2×D1111yescharacteristic
617C2×#95C2×D1111yescharacteristic
618C22×C11—24no—
619C22×C11—24no—
620C22×C11—24no—
621C22×C11—42no—
622C22×C11—42no—
623C22×C11—42no—
624C22×C11—42no—
625C22×C11—42no—
626C22×C11—42no—
627C22×C11—42no—
628C22×C11—42no—
629C22×C11—42no—
630C22×C11—42no—
631C22×C11—42no—
632C22×C11—42no—
633C22×C11—42no—
634C22×C11—42no—
635C22×C11—42no—
636C22×C11—42no—
637C22×C11—42no—
638C22×C11—42no—
639C22×C11—42no—
640C22×C11—81no—
641C22×C11—81no—
642C22×C11—81no—
643C22×C11—81no—
644C22×C11—81no—
645C22×C11—81no—
646C22×C11—81no—
647C22×C11—81no—
648C22×C11C2×C4×D411yescharacteristic
649C22×C11C2×C4×D411yescharacteristic
650C22×C11C2×C4×D411yescharacteristic
651C22×C11#51811yescharacteristic
652C22×C11#51811yescharacteristic
653C22×C11#51811yescharacteristic
654C22×C11#52011yescharacteristic
655C22×C11#53411yescharacteristic
656C22×C11#53411yescharacteristic
657C22×C11#53511yescharacteristic
658C22×C11#53511yescharacteristic
659C22×C11#53511yescharacteristic
660C22×C11#53711yescharacteristic
661C22×C11#53811yescharacteristic
662C22×C11#53811yescharacteristic
663C22×C11#53811yescharacteristic
664C22×C11#53911yescharacteristic
665C22×C11#54011yescharacteristic
666C22×C11#54011yescharacteristic
667C22×C11D4211yescharacteristic
668C22×C11D4211yescharacteristic
669C22×C11D4211yescharacteristic
670C22×C11#54611yescharacteristic
671C22×C11#54611yescharacteristic
672C22×C11#54611yescharacteristic
673C22×C11#54611yescharacteristic
674C22×C11#54711yescharacteristic
675C22×C11#54811yescharacteristic
676C22×C11#55111yescharacteristic
677C22×C11#55111yescharacteristic
678C22×C11#55311yescharacteristic
679C22×C11#56011yescharacteristic
680C22×C11#56011yescharacteristic
681C22×C11#56211yescharacteristic
682C22×C11#56211yescharacteristic
683C2×D11—24no—
684C2×D11—24no—
685C2×D11—24no—
686C2×D11—42no—
687C2×D11—42no—
688C2×D11—42no—
689C2×D11—42no—
690C2×D11—42no—
691C2×D11—42no—
692C2×D11—42no—
693C2×D11—42no—
694C2×D11—42no—
695C2×D11—42no—
696C2×D11—42no—
697C2×D11—42no—
698C4×C11—42no—
699C4×C11—42no—
700C4×C11—42no—
701C4×C11—81no—
702C4×C11—81no—
703Dic11—24no—
704Dic11—42no—
705Dic11—42no—
706Dic11—42no—
707Dic11—42no—
708Dic11—42no—
709Dic11—42no—
710C25—111no—
711C25C22×D1111yescharacteristic
712C25C22×D1111yescharacteristic
713C22×D4—22no—
714C22×D4—22no—
715C22×D4—41no—
716C22×D4—41no—
717C22×D4—41no—
718C22×D4—41no—
719C22×D4—114no—
720C22×D4—114no—
721C22×D4—222no—
722C22×D4—222no—
723C22×D4—222no—
724C22×D4—222no—
725C22×D4—222no—
726C22×D4—222no—
727C22×D4—222no—
728C22×D4—222no—
729C22×D4—441no—
730C22×D4—441no—
731C22×D4—441no—
732C22×D4—441no—
733C22×D4C4×D1114yescomplemented
734C23×C4—111no—
735C23×C4—111no—
736C23×C4—111no—
737C23×C4—111no—
738C23×C4—111no—
739C23×C4—111no—
740C23×C4—111no—
741C23×C4—222no—
742C23×C4—222no—
743C23×C4—222no—
744C23×C4—222no—
745C23×C4—222no—
746C23×C4—222no—
747C23×C4—441no—
748C23×C4—441no—
749C23×C4—441no—
750C23×C4—441no—
751C23×C4—441no—
752C23×C4—441no—
753C23×C4—441no—
754C23×C4—441no—
755C23×C4C22×D1111yescharacteristic
756C23×C4C22×D1111yescharacteristic
757C23×C4C22×D1111yescharacteristic
758C23×C4C22×D1111yescharacteristic
759C23×C4C22×D1111yescharacteristic
760C2×C4⋊C4—222no—
761C2×C4⋊C4—222no—
762C2×C4⋊C4—222no—
763C2×C4⋊C4—441no—
764C2×C4⋊C4—441no—
765C2×C4⋊C4—441no—
766C2×C22⋊C4—22no—
767C2×C22⋊C4—22no—
768C2×C22⋊C4—22no—
769C2×C22⋊C4—22no—
770C2×C22⋊C4—22no—
771C2×C22⋊C4—22no—
772C2×C22⋊C4—41no—
773C2×C22⋊C4—41no—
774C2×C22⋊C4—41no—
775C2×C22⋊C4—41no—
776C2×C22⋊C4—41no—
777C2×C22⋊C4—41no—
778C2×C22⋊C4—114no—
779C2×C22⋊C4—114no—
780C2×C22⋊C4—114no—
781C2×C22⋊C4—114no—
782C2×C22⋊C4—114no—
783C2×C22⋊C4—222no—
784C2×C22⋊C4—222no—
785C2×C22⋊C4—222no—
786C2×C22⋊C4—222no—
787C2×C22⋊C4—222no—
788C2×C22⋊C4—222no—
789C2×C22⋊C4—222no—
790C2×C22⋊C4—222no—
791C2×C22⋊C4—222no—
792C2×C22⋊C4—222no—
793C2×C22⋊C4—441no—
794C2×C22⋊C4—441no—
795C2×C22⋊C4—441no—
796C2×C22⋊C4—441no—
797C2×C22⋊C4—441no—
798C2×C22⋊C4—441no—
799C2×C22⋊C4—441no—
800C2×C22⋊C4—441no—
801C2×C22⋊C4—441no—
802C2×C22⋊C4—441no—
803C2×C22⋊C4—441no—
804C2×C22⋊C4—441no—
805C2×C42—222no—
806C2×C42—222no—
807C2×C42—441no—
808#95—41no—
809#95—41no—
810#95—114no—
811#95—114no—
812#95—222no—
813#95—222no—
814#95—222no—
815#95—222no—
816#95—222no—
817#95—222no—
818#95—222no—
819#95—222no—
820#95—441no—
821#95—441no—
822C2×C11—44no—
823C2×C11—82no—
824C2×C11#232111yescharacteristic
825C2×C11#232511yescharacteristic
826C2×C11#232811yescharacteristic
827C2×C11#235811yescharacteristic
828C2×C11#235811yescharacteristic
829C2×C11#236111yescharacteristic
830C2×C11#237711yescharacteristic
831C2×C11#266911yescharacteristic
832C2×C11#267111yescharacteristic
833C2×C11#267611yescharacteristic
834C2×C11#267811yescharacteristic
835C2×C11#268811yescharacteristic
836C2×C11#269611yescharacteristic
837C2×C11#270611yescharacteristic
838C2×C11#274911yescharacteristic
839D11—44no—
840C24—21no—
841C24—21no—
842C24—21no—
843C24—21no—
844C24—21no—
845C24—21no—
846C24—21no—
847C24—21no—
848C24—21no—
849C24—21no—
850C24—21no—
851C24—21no—
852C24—21no—
853C24—21no—
854C24—21no—
855C24—21no—
856C24—21no—
857C24—21no—
858C24—21no—
859C24—21no—
860C24—21no—
861C24—21no—
862C24—21no—
863C24—21no—
864C24—21no—
865C24—21no—
866C24—112no—
867C24—112no—
868C24—112no—
869C24—221no—
870C24—221no—
871C24—221no—
872C24—221no—
873C24—221no—
874C24—221no—
875C24—221no—
876C24—221no—
877C24—221no—
878C24—221no—
879C24—221no—
880C24—221no—
881C24C2×C4×D1112yes—
882C24C2×C4×D1112yes—
883C24D4×D1112yes—
884C24#434112yes—
885C24C23×D1111yescharacteristic
886C2×D4—28no—
887C2×D4—44no—
888C2×D4—44no—
889C2×D4—44no—
890C2×D4—44no—
891C2×D4—44no—
892C2×D4—44no—
893C2×D4—228no—
894C2×D4—228no—
895C2×D4—228no—
896C2×D4—228no—
897C2×D4—444no—
898C2×D4—444no—
899C2×D4—444no—
900C2×D4—444no—
901C2×D4—444no—
902C2×D4—444no—
903C2×D4—444no—
904C2×D4—444no—
905C2×D4—444no—
906C2×D4—444no—
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—21no—
929C22×C4—21no—
930C22×C4—21no—
931C22×C4—21no—
932C22×C4—21no—
933C22×C4—21no—
934C22×C4—21no—
935C22×C4—21no—
936C22×C4—21no—
937C22×C4—21no—
938C22×C4—21no—
939C22×C4—112no—
940C22×C4—112no—
941C22×C4—112no—
942C22×C4—112no—
943C22×C4—112no—
944C22×C4—112no—
945C22×C4—112no—
946C22×C4—112no—
947C22×C4—112no—
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—221no—
964C22×C4—221no—
965C22×C4—221no—
966C22×C4—221no—
967C22×C4—221no—
968C22×C4—221no—
969C22×C4—221no—
970C22×C4—221no—
971C22×C4—221no—
972C22×C4—221no—
973C22×C4—221no—
974C22×C4—221no—
975C22×C4—221no—
976C22×C4—221no—
977C22×C4—221no—
978C22×C4—221no—
979C22×C4—221no—
980C22×C4—221no—
981C22×C4—221no—
982C22×C4—221no—
983C22×C4—221no—
984C22×C4—221no—
985C22×C4—221no—
986C22×C4—221no—
987C22×C4—221no—
988C22×C4—444no—
989C22×C4—444no—
990C22×C4—444no—
991C22×C4—444no—
992C22×C4—444no—
993C22×C4—444no—
994C22×C4—444no—
995C22×C4—444no—
996C22×C4—444no—
997C22×C4—444no—
998C22×C4—444no—
999C22×C4—444no—
1000C22×C4—444no—
1001C22×C4—444no—
1002C22×C4C2×C4×D1112yes—
1003C22×C4D4×D1112yes—
1004C22×C4D4×D1112yes—
1005C4⋊C4—444no—
1006C4⋊C4—444no—
1007C22⋊C4—44no—
1008C22⋊C4—44no—
1009C22⋊C4—44no—
1010C22⋊C4—44no—
1011C22⋊C4—228no—
1012C22⋊C4—444no—
1013C22⋊C4—444no—
1014C22⋊C4—444no—
1015C22⋊C4—444no—
1016C22⋊C4—444no—
1017C22⋊C4—444no—
1018C22⋊C4—444no—
1019C22⋊C4—444no—
1020C42—444no—
1021C11#1451911yescharacteristic, complemented, Sylow
1022C23—22no—
1023C23—22no—
1024C23—22no—
1025C23—22no—
1026C23—22no—
1027C23—22no—
1028C23—22no—
1029C23—22no—
1030C23—22no—
1031C23—22no—
1032C23—22no—
1033C23—22no—
1034C23—22no—
1035C23—22no—
1036C23—22no—
1037C23—22no—
1038C23—22no—
1039C23—22no—
1040C23—22no—
1041C23—22no—
1042C23—22no—
1043C23—22no—
1044C23—22no—
1045C23—22no—
1046C23—22no—
1047C23—41no—
1048C23—41no—
1049C23—41no—
1050C23—41no—
1051C23—41no—
1052C23—41no—
1053C23—41no—
1054C23—41no—
1055C23—41no—
1056C23—41no—
1057C23—41no—
1058C23—41no—
1059C23—41no—
1060C23—41no—
1061C23—41no—
1062C23—41no—
1063C23—41no—
1064C23—41no—
1065C23—41no—
1066C23—41no—
1067C23—41no—
1068C23—41no—
1069C23—41no—
1070C23—41no—
1071C23—41no—
1072C23—41no—
1073C23—41no—
1074C23—41no—
1075C23—41no—
1076C23—41no—
1077C23—41no—
1078C23—41no—
1079C23—41no—
1080C23—41no—
1081C23—41no—
1082C23—41no—
1083C23—41no—
1084C23—41no—
1085C23—41no—
1086C23—41no—
1087C23—41no—
1088C23—41no—
1089C23—41no—
1090C23—41no—
1091C23—114no—
1092C23—222no—
1093C23—222no—
1094C23—222no—
1095C23—222no—
1096C23—222no—
1097C23—222no—
1098C23—222no—
1099C23—222no—
1100C23—222no—
1101C23—222no—
1102C23—222no—
1103C23—222no—
1104C23—222no—
1105C23—222no—
1106C23—222no—
1107C23—222no—
1108C23—222no—
1109C23—222no—
1110C23—441no—
1111C23—441no—
1112C23—441no—
1113C23—441no—
1114C23—441no—
1115C23—441no—
1116C23—441no—
1117C23—441no—
1118C23—441no—
1119C23—441no—
1120C23—441no—
1121C23—441no—
1122C23—441no—
1123C23—441no—
1124C23—441no—
1125C23—441no—
1126C23(C22⋊D11)⋊C414yes—
1127C23C22×C4×D1111yescharacteristic
1128C23C2×D4×D1111yescharacteristic
1129C23C2×D4×D1111yescharacteristic
1130C23C2×D4×D1111yescharacteristic
1131C23C2×#434111yescharacteristic
1132C23#6703711yescharacteristic
1133C23#6703711yescharacteristic
1134C23#6703711yescharacteristic
1135C23#6703711yescharacteristic
1136C23#6703711yescharacteristic
1137C23#6703711yescharacteristic
1138C23#41×D1111yescharacteristic
1139C23#41×D1111yescharacteristic
1140C23#6704211yescharacteristic
1141C23#6704311yescharacteristic
1142D4—416no—
1143D4—4416no—
1144D4—4416no—
1145C2×C4—22no—
1146C2×C4—22no—
1147C2×C4—22no—
1148C2×C4—22no—
1149C2×C4—22no—
1150C2×C4—22no—
1151C2×C4—22no—
1152C2×C4—22no—
1153C2×C4—22no—
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—41no—
1169C2×C4—41no—
1170C2×C4—41no—
1171C2×C4—41no—
1172C2×C4—41no—
1173C2×C4—41no—
1174C2×C4—41no—
1175C2×C4—41no—
1176C2×C4—41no—
1177C2×C4—41no—
1178C2×C4—41no—
1179C2×C4—41no—
1180C2×C4—114no—
1181C2×C4—222no—
1182C2×C4—222no—
1183C2×C4—222no—
1184C2×C4—222no—
1185C2×C4—222no—
1186C2×C4—222no—
1187C2×C4—222no—
1188C2×C4—222no—
1189C2×C4—222no—
1190C2×C4—222no—
1191C2×C4—222no—
1192C2×C4—222no—
1193C2×C4—222no—
1194C2×C4—222no—
1195C2×C4—222no—
1196C2×C4—222no—
1197C2×C4—222no—
1198C2×C4—222no—
1199C2×C4—222no—
1200C2×C4—222no—
1201C2×C4—222no—
1202C2×C4—222no—
1203C2×C4—222no—
1204C2×C4—222no—
1205C2×C4—4416no—
1206C2×C4—4416no—
1207C2×C4—441no—
1208C2×C4—441no—
1209C2×C4—441no—
1210C2×C4—441no—
1211C2×C4—441no—
1212C2×C4—441no—
1213C2×C4—441no—
1214C2×C4—441no—
1215C2×C4—441no—
1216C2×C4—441no—
1217C2×C4—441no—
1218C2×C4—441no—
1219C2×C4—441no—
1220C2×C4—441no—
1221C2×C4—441no—
1222C2×C4—441no—
1223C2×C4—441no—
1224C2×C4—441no—
1225C2×C4—441no—
1226C2×C4—441no—
1227C2×C4—441no—
1228C2×C4—441no—
1229C2×C4—441no—
1230C2×C4—441no—
1231C22—24no—
1232C22—24no—
1233C22—24no—
1234C22—42no—
1235C22—42no—
1236C22—42no—
1237C22—42no—
1238C22—42no—
1239C22—42no—
1240C22—42no—
1241C22—42no—
1242C22—42no—
1243C22—42no—
1244C22—42no—
1245C22—42no—
1246C22—42no—
1247C22—42no—
1248C22—42no—
1249C22—42no—
1250C22—42no—
1251C22—42no—
1252C22—42no—
1253C22—81no—
1254C22—81no—
1255C22—81no—
1256C22—81no—
1257C22—81no—
1258C22—81no—
1259C22—81no—
1260C22—81no—
1261C22—224no—
1262C22—224no—
1263C22—224no—
1264C22—442no—
1265C22—442no—
1266C22—442no—
1267C22—442no—
1268C22—442no—
1269C22—442no—
1270C22—442no—
1271C22—442no—
1272C22—442no—
1273C22—442no—
1274C22—442no—
1275C22—442no—
1276C22C2×(C22⋊D11)⋊C411yescharacteristic
1277C22#1062301711yescharacteristic
1278C22#1062301711yescharacteristic
1279C22C4×D4×D1111yescharacteristic
1280C22C4×D4×D1111yescharacteristic
1281C22#1062307611yescharacteristic
1282C22#1062307711yescharacteristic
1283C22#1062312011yescharacteristic
1284C22#1062312011yescharacteristic
1285C22#1062312111yescharacteristic
1286C22#1062312211yescharacteristic
1287C22#1062312311yescharacteristic
1288C22#1062312311yescharacteristic
1289C22#1062312411yescharacteristic
1290C22#1062312411yescharacteristic
1291C22#1062312911yescharacteristic
1292C22#1062313211yescharacteristic
1293C22#1062313811yescharacteristic
1294C22#1062313911yescharacteristic
1295C22#1062314011yescharacteristic
1296C22#1062314111yescharacteristic
1297C22#1062314111yescharacteristic
1298C22#1062314111yescharacteristic
1299C22#1062314411yescharacteristic
1300C22#1062314611yescharacteristic
1301C22#1062315111yescharacteristic
1302C22#1062315211yescharacteristic
1303C22#1062318611yescharacteristic
1304C22#1062318911yescharacteristic
1305C22#1062319111yescharacteristic
1306C22#1062319411yescharacteristic
1307C22#1062321011yescharacteristic
1308C22#1062321511yescharacteristic
1309C22#1062324811yescharacteristic
1310C22#1062325111yescharacteristic
1311C4—42no—
1312C4—42no—
1313C4—42no—
1314C4—81no—
1315C4—81no—
1316C4—224no—
1317C4—442no—
1318C4—442no—
1319C4—442no—
1320C4—442no—
1321C4—442no—
1322C4—442no—
1323C2—44no—
1324C2—82no—
1325C2—444no—
1326C2#1307127111yescharacteristic
1327C2#1307131811yescharacteristic
1328C2#1307133711yescharacteristic
1329C2#1307159611yescharacteristic
1330C2#1307159711yescharacteristic
1331C2#1307162711yescharacteristic
1332C2#1307176711yescharacteristic
1333C2#1307483511yescharacteristic
1334C2#1307485811yescharacteristic
1335C2#1307492211yescharacteristic
1336C2#1307494311yescharacteristic
1337C2#1307505811yescharacteristic
1338C2#1307517211yescharacteristic
1339C2#1307530911yescharacteristic
1340C2#1307583211yescharacteristic
subgroupG/H
center, FrattiniC24C23×D11
commutatorC23×C11C23×C4
FittingC11×#1438C2
socle, cosocleC24×C11C24
prime radicalC2×#10622836C2
hypercenter#1438D11
hypocenterC11#14519
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ #1438

Complements

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

NH ≅ G/Ntype
2. C2×#10622570C2semidirect
3. C2×#10622833C2semidirect
4. C2×#10622571C2semidirect
5. C2×#10622569C2semidirect
6. C2×#10622569C2semidirect
7. C2×#10622559C2semidirect
8. #13066874C2semidirect
9. #13066863C2semidirect
10. #13066860C2semidirect
11. #13066859C2semidirect
12. #13066853C2semidirect
13. #13066840C2semidirect
14. (C2×D11)⋊#95C2semidirect
15. C11×#1438C2semidirect
39. #10622836C4semidirect
67. C22×D4×C11C2×C4semidirect
86. C22×C22⋊D11C2×C4semidirect
132. C2×C22⋊Dic11C2×C4semidirect
133. C2×C22⋊Dic11C2×C4semidirect
134. C2×C22⋊Dic11D4semidirect
145. C2×(C2×D11)⋊C4C2×C4semidirect
146. C2×(C2×D11)⋊C4D4semidirect
168. C11⋊#95C2×C4semidirect
169. C11⋊#95D4semidirect
363. #1438D11semidirect
733. C22×D4C4×D11semidirect
1021. C11#14519semidirect

Maximal subgroups

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

subgroupindex
C2×#106228362
C2×#106225702
C2×#106228332
C2×#106225712
C2×#106225692
C2×#106225592
#130668742
#130668632
#130668602
#130668592
#130668532
#130668402
(C2×D11)⋊#952
C11×#14382
#1451911