Finite Group Databasebeta

← #14677014

Subgroups — #14677014

Order 2816.

1946 conjugacy classes of subgroups.

The subgroup lattice has 1158 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622557C211yesmaximal, characteristic, complemented
2C2×#10622833C211yesmaximal, characteristic
3C2×#10622556C211yesmaximal, characteristic, complemented
4C2×C22⋊C4×Dic11C211yesmaximal, characteristic, complemented
5#13066875C211yesmaximal, characteristic, complemented
6#13066863C211yesmaximal, characteristic, complemented
7#13066859C211yesmaximal, characteristic, complemented
8#13066857C211yesmaximal, characteristic
9#13066853C211yesmaximal, characteristic, complemented
10#13066853C211yesmaximal, characteristic, complemented
11#13066853C211yesmaximal, characteristic, complemented
12#13066849C211yesmaximal, characteristic, complemented
13#13066848C211yesmaximal, characteristic, complemented
14C4×C11⋊#95C211yesmaximal, characteristic, complemented
15C2×C11×#390C211yesmaximal, characteristic
16C23×D4×C11C2211yescharacteristic
17C24×Dic11C2211yescharacteristic
18C22×C11×C4⋊C4C2211yescharacteristic
19C22×C11×C22⋊C4C2211yescharacteristic
20C22×C11×C22⋊C4C2211yescharacteristic
21C22×C11×C22⋊C4C2211yescharacteristic
22C22×C11×C22⋊C4C2211yescharacteristic
23C22×C42×C11C2211yescharacteristic
24C22×C22⋊Dic11C2211yescharacteristic
25C22×C22⋊Dic11C2211yescharacteristic
26C22×C22⋊Dic11C2211yescharacteristic
27C22×C22⋊Dic11C2211yescharacteristic
28C22×C22⋊Dic11C2211yescharacteristic
29C22×C22⋊Dic11C2211yescharacteristic
30C22×C22⋊Dic11C2211yescharacteristic
31C22×Dic11⋊C4C2211yescharacteristic
32C22×C4×Dic11C2211yescharacteristic
33C22×C4×Dic11C2211yescharacteristic
34C22×C4×Dic11C2211yescharacteristic
35C11×#390—24no—
36#10622833C418yescomplemented
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
51C2×C11⋊#95C2211yescharacteristic
52C2×C11⋊#95C2211yescharacteristic
53#10622557—24no—
54#10622556—24no—
55C22⋊C4×Dic11—24no—
56C25×C11C2311yescharacteristic
57C25×C11C2311yescharacteristic
58C22×D4×C11—22no—
59C22×D4×C11—22no—
60C22×D4×C11—22no—
61C22×D4×C11—22no—
62C22×D4×C11—41no—
63C22×D4×C11—41no—
64C22×D4×C11C2×C414yes—
65C23×C4×C11C2311yescharacteristic
66C23×C4×C11C2311yescharacteristic
67C23×C4×C11C2311yescharacteristic
68C23×C4×C11C2311yescharacteristic
69C23×C4×C11C2311yescharacteristic
70C23×Dic11—22no—
71C23×Dic11—22no—
72C23×Dic11—22no—
73C23×Dic11—22no—
74C23×Dic11—41no—
75C23×Dic11—41no—
76C23×Dic11C2×C414yes—
77C23×Dic11C2311yescharacteristic
78C23×Dic11C2311yescharacteristic
79C23×Dic11C2311yescharacteristic
80C23×Dic11C2311yescharacteristic
81C23×Dic11C2311yescharacteristic
82C23×Dic11C2311yescharacteristic
83C23×Dic11C2311yescharacteristic
84C23×Dic11C2311yescharacteristic
85C2×C11×C4⋊C4—22no—
86C2×C11×C4⋊C4—22no—
87C2×C11×C4⋊C4—41no—
88C2×C11×C22⋊C4—22no—
89C2×C11×C22⋊C4—22no—
90C2×C11×C22⋊C4—22no—
91C2×C11×C22⋊C4—22no—
92C2×C11×C22⋊C4—22no—
93C2×C11×C22⋊C4—22no—
94C2×C11×C22⋊C4—22no—
95C2×C11×C22⋊C4—22no—
96C2×C11×C22⋊C4—22no—
97C2×C11×C22⋊C4—41no—
98C2×C11×C22⋊C4—41no—
99C2×C11×C22⋊C4D414yes—
100C2×C42×C11—22no—
101C2×C42×C11—22no—
102C2×C42×C11—41no—
103C2×C22⋊Dic11—22no—
104C2×C22⋊Dic11—22no—
105C2×C22⋊Dic11—22no—
106C2×C22⋊Dic11—22no—
107C2×C22⋊Dic11—22no—
108C2×C22⋊Dic11—22no—
109C2×C22⋊Dic11—22no—
110C2×C22⋊Dic11—22no—
111C2×C22⋊Dic11—22no—
112C2×C22⋊Dic11—22no—
113C2×C22⋊Dic11—41no—
114C2×C22⋊Dic11—41no—
115C2×C22⋊Dic11—41no—
116C2×C22⋊Dic11—41no—
117C2×C22⋊Dic11—41no—
118C2×C22⋊Dic11—41no—
119C2×C22⋊Dic11—41no—
120C2×C22⋊Dic11—41no—
121C2×C22⋊Dic11C2×C414yes—
122C2×C22⋊Dic11C2×C414yes—
123C2×C22⋊Dic11C2×C414yes—
124C2×Dic11⋊C4—22no—
125C2×Dic11⋊C4—22no—
126C2×Dic11⋊C4—41no—
127C2×C4×Dic11—22no—
128C2×C4×Dic11—22no—
129C2×C4×Dic11—22no—
130C2×C4×Dic11—22no—
131C2×C4×Dic11—22no—
132C2×C4×Dic11—41no—
133C2×C4×Dic11—41no—
134C2×C4×Dic11—41no—
135C2×C4×Dic11—41no—
136C11⋊#95—22no—
137C11⋊#95—22no—
138C11⋊#95—22no—
139C11⋊#95—22no—
140C11⋊#95—22no—
141C11⋊#95—22no—
142C11⋊#95—22no—
143C11⋊#95—22no—
144C11⋊#95—22no—
145C11⋊#95—22no—
146C11⋊#95—41no—
147C11⋊#95—41no—
148C11⋊#95—41no—
149C11⋊#95C2×C414yes—
150C11⋊#95C2×C414yes—
151C11⋊#95D414yescomplemented
152#14007—111nomaximal, Sylow
153C24×C11—21no—
154C24×C11—21no—
155C24×C11—21no—
156C24×C11—21no—
157C24×C11—21no—
158C24×C11—21no—
159C24×C11—21no—
160C24×C11—21no—
161C24×C11—21no—
162C24×C11—21no—
163C24×C11—21no—
164C24×C11—21no—
165C24×C11—21no—
166C24×C11—21no—
167C24×C11—21no—
168C24×C11—21no—
169C24×C11—21no—
170C24×C11—21no—
171C24×C11—21no—
172C24×C11—21no—
173C24×C11—21no—
174C24×C11—21no—
175C24×C11—21no—
176C24×C11—21no—
177C24×C11—21no—
178C24×C11—21no—
179C24×C11C22×C412yes—
180C24×C11C22×C412yes—
181C24×C11C2×D412yes—
182C24×C11#4112yes—
183C24×C11C2411yescharacteristic
184C2×D4×C11—28no—
185C2×D4×C11—28no—
186C2×D4×C11—44no—
187C2×D4×C11—44no—
188C2×D4×C11—44no—
189C2×D4×C11—44no—
190C2×D4×C11—44no—
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×C11C22×C412yes—
219C22×C4×C11C2×D412yes—
220C22×C4×C11C2×D412yes—
221C22×C4×C11C2×D412yes—
222C22×C4×C11#4112yes—
223C22×C4×C11#4112yes—
224C22×C4×C11#4112yes—
225C22×C4×C11#4112yes—
226C22×Dic11—28no—
227C22×Dic11—28no—
228C22×Dic11—21no—
229C22×Dic11—21no—
230C22×Dic11—21no—
231C22×Dic11—21no—
232C22×Dic11—21no—
233C22×Dic11—21no—
234C22×Dic11—21no—
235C22×Dic11—21no—
236C22×Dic11—21no—
237C22×Dic11—21no—
238C22×Dic11—21no—
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×Dic11—21no—
273C22×Dic11—21no—
274C22×Dic11—21no—
275C22×Dic11—44no—
276C22×Dic11—44no—
277C22×Dic11—44no—
278C22×Dic11—44no—
279C22×Dic11—44no—
280C22×Dic11C22×C412yes—
281C22×Dic11C22×C412yes—
282C22×Dic11C22×C412yes—
283C22×Dic11C22×C412yes—
284C22×Dic11C2×D412yes—
285C22×Dic11C2×D412yes—
286C22×Dic11#4112yes—
287C22×Dic11#4112yes—
288C22×Dic11#4112yes—
289C11×C4⋊C4—44no—
290C11×C22⋊C4—28no—
291C11×C22⋊C4—44no—
292C11×C22⋊C4—44no—
293C11×C22⋊C4—44no—
294C42×C11—44no—
295C22⋊Dic11—28no—
296C22⋊Dic11—28no—
297C22⋊Dic11—44no—
298C22⋊Dic11—44no—
299C22⋊Dic11—44no—
300C22⋊Dic11—44no—
301C22⋊Dic11—44no—
302Dic11⋊C4—44no—
303C4×Dic11—44no—
304C4×Dic11—44no—
305C4×Dic11—44no—
306C2×#390D1111yescharacteristic
307C2×#388—111no—
308C2×#386—111no—
309C2×#381—111no—
310C2×C4×C22⋊C4—111no—
311#1442—111no—
312#1440—111no—
313#1439—111no—
314#1438—111no—
315#1437—111no—
316#1437—111no—
317#1437—111no—
318#1436—111no—
319#1436—111no—
320C4×#95—111no—
321C23×C11—22no—
322C23×C11—22no—
323C23×C11—22no—
324C23×C11—22no—
325C23×C11—22no—
326C23×C11—22no—
327C23×C11—22no—
328C23×C11—22no—
329C23×C11—22no—
330C23×C11—22no—
331C23×C11—22no—
332C23×C11—22no—
333C23×C11—22no—
334C23×C11—22no—
335C23×C11—22no—
336C23×C11—22no—
337C23×C11—22no—
338C23×C11—22no—
339C23×C11—22no—
340C23×C11—22no—
341C23×C11—22no—
342C23×C11—22no—
343C23×C11—22no—
344C23×C11—22no—
345C23×C11—22no—
346C23×C11—41no—
347C23×C11—41no—
348C23×C11—41no—
349C23×C11—41no—
350C23×C11—41no—
351C23×C11—41no—
352C23×C11—41no—
353C23×C11—41no—
354C23×C11—41no—
355C23×C11—41no—
356C23×C11—41no—
357C23×C11—41no—
358C23×C11—41no—
359C23×C11—41no—
360C23×C11—41no—
361C23×C11—41no—
362C23×C11—41no—
363C23×C11—41no—
364C23×C11—41no—
365C23×C11—41no—
366C23×C11—41no—
367C23×C11—41no—
368C23×C11—41no—
369C23×C11—41no—
370C23×C11—41no—
371C23×C11—41no—
372C23×C11—41no—
373C23×C11—41no—
374C23×C11—41no—
375C23×C11—41no—
376C23×C11—41no—
377C23×C11—41no—
378C23×C11—41no—
379C23×C11—41no—
380C23×C11—41no—
381C23×C11—41no—
382C23×C11—41no—
383C23×C11—41no—
384C23×C11—41no—
385C23×C11—41no—
386C23×C11—41no—
387C23×C11—41no—
388C23×C11—41no—
389C23×C11—41no—
390C23×C11C4×D414yes—
391C23×C11C23×C411yescharacteristic
392C23×C11C22×D411yescharacteristic
393C23×C11C22×D411yescharacteristic
394C23×C11C2×#4111yescharacteristic
395C23×C11C2×#4111yescharacteristic
396C23×C11C2×#4111yescharacteristic
397C23×C11C2×#4111yescharacteristic
398C23×C11C2×#4111yescharacteristic
399C23×C11C2×#4111yescharacteristic
400C23×C11C2×#4111yescharacteristic
401C23×C11C2×#4111yescharacteristic
402C23×C11H(5,𝔽2)11yescharacteristic
403C23×C11H(5,𝔽2)11yescharacteristic
404C23×C11H(5,𝔽2)11yescharacteristic
405C23×C11H(5,𝔽2)11yescharacteristic
406D4×C11—416no—
407C2×C4×C11—22no—
408C2×C4×C11—22no—
409C2×C4×C11—22no—
410C2×C4×C11—22no—
411C2×C4×C11—22no—
412C2×C4×C11—22no—
413C2×C4×C11—22no—
414C2×C4×C11—22no—
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—41no—
426C2×C4×C11—41no—
427C2×C4×C11—41no—
428C2×C4×C11—41no—
429C2×C4×C11—41no—
430C2×C4×C11—41no—
431C2×C4×C11—41no—
432C2×C4×C11—41no—
433C2×C4×C11—41no—
434C2×C4×C11—41no—
435C2×C4×C11—41no—
436C2×C4×C11—41no—
437C2×C4×C11—41no—
438C2×C4×C11—41no—
439C2×C4×C11—41no—
440C2×C4×C11#11714yes—
441C2×C4×C11#12314yes—
442C2×Dic11—22no—
443C2×Dic11—22no—
444C2×Dic11—22no—
445C2×Dic11—22no—
446C2×Dic11—22no—
447C2×Dic11—22no—
448C2×Dic11—22no—
449C2×Dic11—22no—
450C2×Dic11—22no—
451C2×Dic11—22no—
452C2×Dic11—22no—
453C2×Dic11—22no—
454C2×Dic11—22no—
455C2×Dic11—22no—
456C2×Dic11—22no—
457C2×Dic11—22no—
458C2×Dic11—22no—
459C2×Dic11—22no—
460C2×Dic11—22no—
461C2×Dic11—22no—
462C2×Dic11—22no—
463C2×Dic11—22no—
464C2×Dic11—22no—
465C2×Dic11—22no—
466C2×Dic11—416no—
467C2×Dic11—41no—
468C2×Dic11—41no—
469C2×Dic11—41no—
470C2×Dic11—41no—
471C2×Dic11—41no—
472C2×Dic11—41no—
473C2×Dic11—41no—
474C2×Dic11—41no—
475C2×Dic11—41no—
476C2×Dic11—41no—
477C2×Dic11—41no—
478C2×Dic11—41no—
479C2×Dic11—41no—
480C2×Dic11—41no—
481C2×Dic11—41no—
482C2×Dic11—41no—
483C2×Dic11—41no—
484C2×Dic11—41no—
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×Dic11C4×D414yes—
499C23×D4C2×D1111yescharacteristic
500C24×C4—111no—
501C22×C4⋊C4—111no—
502C22×C4⋊C4C2×D1111yescharacteristic
503C22×C22⋊C4—111no—
504C22×C22⋊C4—111no—
505C22×C22⋊C4—111no—
506C22×C22⋊C4—111no—
507C22×C22⋊C4—111no—
508C22×C22⋊C4—111no—
509C22×C22⋊C4—111no—
510C22×C22⋊C4C2×D1111yescharacteristic
511C22×C22⋊C4C2×D1111yescharacteristic
512C22×C22⋊C4C2×D1111yescharacteristic
513C22×C22⋊C4C2×D1111yescharacteristic
514C22×C42—111no—
515C22×C42—111no—
516C22×C42—111no—
517C22×C42C2×D1111yescharacteristic
518#390—24no—
519#388—224no—
520#386—118no—
521#381—224no—
522C4×C22⋊C4—224no—
523C2×#95—111no—
524C2×#95—111no—
525C2×#95—111no—
526C2×#95—111no—
527C2×#95—111no—
528C2×#95—111no—
529C2×#95—111no—
530C2×#95—111no—
531C2×#95—111no—
532C2×#95—111no—
533C2×#95—111no—
534C2×#95—111no—
535C2×#95—111no—
536C2×#95—111no—
537C2×#95—111no—
538C2×#95—111no—
539C22×C11—24no—
540C22×C11—24no—
541C22×C11—24no—
542C22×C11—42no—
543C22×C11—42no—
544C22×C11—42no—
545C22×C11—42no—
546C22×C11—42no—
547C22×C11—42no—
548C22×C11—42no—
549C22×C11—42no—
550C22×C11—42no—
551C22×C11—42no—
552C22×C11—42no—
553C22×C11—42no—
554C22×C11—42no—
555C22×C11—42no—
556C22×C11—42no—
557C22×C11—42no—
558C22×C11—42no—
559C22×C11—42no—
560C22×C11—42no—
561C22×C11—81no—
562C22×C11—81no—
563C22×C11—81no—
564C22×C11—81no—
565C22×C11—81no—
566C22×C11—81no—
567C22×C11—81no—
568C22×C11—81no—
569C22×C11C2×#11711yescharacteristic
570C22×C11C2×C4×D411yescharacteristic
571C22×C11C2×C4×D411yescharacteristic
572C22×C11C4×#4111yescharacteristic
573C22×C11C4×#4111yescharacteristic
574C22×C11#51811yescharacteristic
575C22×C11#51811yescharacteristic
576C22×C11C2×#12311yescharacteristic
577C22×C11#52511yescharacteristic
578C22×C11#52911yescharacteristic
579C22×C11#52911yescharacteristic
580C22×C11#52911yescharacteristic
581C22×C11#52911yescharacteristic
582C22×C11#53211yescharacteristic
583C22×C11#53211yescharacteristic
584C22×C11#53811yescharacteristic
585C22×C11#53811yescharacteristic
586C22×C11#54011yescharacteristic
587C22×C11#54011yescharacteristic
588C22×C11D4211yescharacteristic
589C22×C11#54611yescharacteristic
590C22×C11#54611yescharacteristic
591C22×C11#54611yescharacteristic
592C22×C11#54611yescharacteristic
593C22×C11#54611yescharacteristic
594C22×C11#55011yescharacteristic
595C22×C11#55111yescharacteristic
596C22×C11#55111yescharacteristic
597C22×C11#55111yescharacteristic
598C22×C11#55311yescharacteristic
599C22×C11#55311yescharacteristic
600C22×C11#55311yescharacteristic
601C22×C11#55511yescharacteristic
602C22×C11#55911yescharacteristic
603C22×C11#55911yescharacteristic
604C4×C11—24no—
605C4×C11—24no—
606C4×C11—42no—
607C4×C11—42no—
608C4×C11—81no—
609Dic11—24no—
610Dic11—42no—
611Dic11—42no—
612Dic11—42no—
613Dic11—42no—
614Dic11—42no—
615Dic11—42no—
616Dic11—81no—
617C25C22×D1111yescharacteristic
618C25C22×D1111yescharacteristic
619C22×D4—22no—
620C22×D4—22no—
621C22×D4—22no—
622C22×D4—22no—
623C22×D4—41no—
624C22×D4—41no—
625C22×D4C4×D1114yes—
626C23×C4—111no—
627C23×C4—111no—
628C23×C4—111no—
629C23×C4—111no—
630C23×C4—111no—
631C23×C4—111no—
632C23×C4—111no—
633C23×C4—114no—
634C23×C4—111no—
635C23×C4—222no—
636C23×C4—222no—
637C23×C4—222no—
638C23×C4—222no—
639C23×C4—441no—
640C23×C4—441no—
641C23×C4C22×D1111yescharacteristic
642C23×C4C22×D1111yescharacteristic
643C23×C4C22×D1111yescharacteristic
644C23×C4C22×D1111yescharacteristic
645C23×C4C22×D1111yescharacteristic
646C2×C4⋊C4—22no—
647C2×C4⋊C4—22no—
648C2×C4⋊C4—41no—
649C2×C4⋊C4—222no—
650C2×C4⋊C4—222no—
651C2×C4⋊C4—441no—
652C2×C22⋊C4—22no—
653C2×C22⋊C4—22no—
654C2×C22⋊C4—22no—
655C2×C22⋊C4—22no—
656C2×C22⋊C4—22no—
657C2×C22⋊C4—22no—
658C2×C22⋊C4—22no—
659C2×C22⋊C4—22no—
660C2×C22⋊C4—22no—
661C2×C22⋊C4—41no—
662C2×C22⋊C4—41no—
663C2×C22⋊C4—114no—
664C2×C22⋊C4—114no—
665C2×C22⋊C4—114no—
666C2×C22⋊C4—222no—
667C2×C22⋊C4—222no—
668C2×C22⋊C4—222no—
669C2×C22⋊C4—222no—
670C2×C22⋊C4—222no—
671C2×C22⋊C4—222no—
672C2×C22⋊C4—222no—
673C2×C22⋊C4—222no—
674C2×C22⋊C4—222no—
675C2×C22⋊C4—222no—
676C2×C22⋊C4—441no—
677C2×C22⋊C4—441no—
678C2×C22⋊C4—441no—
679C2×C22⋊C4—441no—
680C2×C22⋊C4—441no—
681C2×C22⋊C4—441no—
682C2×C22⋊C4—441no—
683C2×C22⋊C4—441no—
684C2×C22⋊C4C22⋊D1114yes—
685C2×C42—22no—
686C2×C42—22no—
687C2×C42—41no—
688C2×C42—222no—
689C2×C42—222no—
690C2×C42—222no—
691C2×C42—222no—
692C2×C42—222no—
693C2×C42—441no—
694C2×C42—441no—
695C2×C42—441no—
696C2×C42—441no—
697#95—114no—
698#95—114no—
699#95—114no—
700#95—222no—
701#95—222no—
702#95—222no—
703#95—222no—
704#95—222no—
705#95—222no—
706#95—222no—
707#95—222no—
708#95—222no—
709#95—222no—
710#95—441no—
711#95—441no—
712#95—441no—
713C2×C11—44no—
714C2×C11—82no—
715C2×C11#229311yescharacteristic
716C2×C11C4×#12311yescharacteristic
717C2×C11#233311yescharacteristic
718C2×C11#234211yescharacteristic
719C2×C11#235711yescharacteristic
720C2×C11#235811yescharacteristic
721C2×C11#236311yescharacteristic
722C2×C11#244411yescharacteristic
723C2×C11#244511yescharacteristic
724C2×C11#245911yescharacteristic
725C2×C11#246411yescharacteristic
726C2×C11#251611yescharacteristic
727C2×C11#252611yescharacteristic
728C2×C11#255411yescharacteristic
729C2×C11#255711yescharacteristic
730C24—21no—
731C24—21no—
732C24—21no—
733C24—21no—
734C24—21no—
735C24—21no—
736C24—21no—
737C24—21no—
738C24—21no—
739C24—21no—
740C24—21no—
741C24—21no—
742C24—21no—
743C24—21no—
744C24—21no—
745C24—21no—
746C24—21no—
747C24—21no—
748C24—21no—
749C24—21no—
750C24—21no—
751C24—21no—
752C24—21no—
753C24—21no—
754C24—21no—
755C24—21no—
756C24C2×C4×D1112yes—
757C24C2×C4×D1112yes—
758C24#433912yes—
759C24C2×C22⋊D1112yes—
760C24C23×D1111yescharacteristic
761C2×D4—28no—
762C2×D4—28no—
763C2×D4—44no—
764C2×D4—44no—
765C2×D4—44no—
766C2×D4—44no—
767C2×D4—44no—
768C22×C4—21no—
769C22×C4—21no—
770C22×C4—21no—
771C22×C4—21no—
772C22×C4—21no—
773C22×C4—21no—
774C22×C4—21no—
775C22×C4—21no—
776C22×C4—21no—
777C22×C4—21no—
778C22×C4—21no—
779C22×C4—21no—
780C22×C4—21no—
781C22×C4—21no—
782C22×C4—21no—
783C22×C4—21no—
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—112no—
796C22×C4—112no—
797C22×C4—112no—
798C22×C4—112no—
799C22×C4—112no—
800C22×C4—112no—
801C22×C4—112no—
802C22×C4—112no—
803C22×C4—112no—
804C22×C4—228no—
805C22×C4—221no—
806C22×C4—221no—
807C22×C4—221no—
808C22×C4—221no—
809C22×C4—228no—
810C22×C4—221no—
811C22×C4—221no—
812C22×C4—221no—
813C22×C4—221no—
814C22×C4—221no—
815C22×C4—221no—
816C22×C4—221no—
817C22×C4—221no—
818C22×C4—221no—
819C22×C4—221no—
820C22×C4—221no—
821C22×C4—221no—
822C22×C4—221no—
823C22×C4—221no—
824C22×C4—221no—
825C22×C4—221no—
826C22×C4—221no—
827C22×C4—221no—
828C22×C4—221no—
829C22×C4—221no—
830C22×C4—221no—
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—444no—
854C22×C4—444no—
855C22×C4—444no—
856C22×C4—444no—
857C22×C4—444no—
858C22×C4C2×C4×D1112yes—
859C22×C4D4×D1112yes—
860C22×C4#434112yes—
861C22×C4#434112yes—
862C22×C4#434112yes—
863C22×C4#434112yes—
864C22×C4C2×C22⋊D1112yes—
865C22×C4C2×C22⋊D1112yes—
866C4⋊C4—44no—
867C4⋊C4—444no—
868C22⋊C4—28no—
869C22⋊C4—44no—
870C22⋊C4—44no—
871C22⋊C4—44no—
872C22⋊C4—228no—
873C22⋊C4—228no—
874C22⋊C4—444no—
875C22⋊C4—444no—
876C22⋊C4—444no—
877C22⋊C4—444no—
878C22⋊C4—444no—
879C42—44no—
880C42—444no—
881C42—444no—
882C42—444no—
883C11#1400711yescharacteristic, complemented, Sylow
884C23—22no—
885C23—22no—
886C23—22no—
887C23—22no—
888C23—22no—
889C23—22no—
890C23—22no—
891C23—22no—
892C23—22no—
893C23—22no—
894C23—22no—
895C23—22no—
896C23—22no—
897C23—22no—
898C23—22no—
899C23—22no—
900C23—22no—
901C23—22no—
902C23—22no—
903C23—22no—
904C23—22no—
905C23—22no—
906C23—22no—
907C23—22no—
908C23—22no—
909C23—41no—
910C23—41no—
911C23—41no—
912C23—41no—
913C23—41no—
914C23—41no—
915C23—41no—
916C23—41no—
917C23—41no—
918C23—41no—
919C23—41no—
920C23—41no—
921C23—41no—
922C23—41no—
923C23—41no—
924C23—41no—
925C23—41no—
926C23—41no—
927C23—41no—
928C23—41no—
929C23—41no—
930C23—41no—
931C23—41no—
932C23—41no—
933C23—41no—
934C23—41no—
935C23—41no—
936C23—41no—
937C23—41no—
938C23—41no—
939C23—41no—
940C23—41no—
941C23—41no—
942C23—41no—
943C23—41no—
944C23—41no—
945C23—41no—
946C23—41no—
947C23—41no—
948C23—41no—
949C23—41no—
950C23—41no—
951C23—41no—
952C23—41no—
953C23C4×C22⋊D1114yes—
954C23C22×C4×D1111yescharacteristic
955C23C2×#433911yescharacteristic
956C23C2×D4×D1111yescharacteristic
957C23C2×#434111yescharacteristic
958C23C2×#434111yescharacteristic
959C23C2×#434111yescharacteristic
960C23C2×#434111yescharacteristic
961C23#6703711yescharacteristic
962C23#6703711yescharacteristic
963C23#6703711yescharacteristic
964C23#41×D1111yescharacteristic
965C23#41×D1111yescharacteristic
966C23#41×D1111yescharacteristic
967C23#6704211yescharacteristic
968C23C22×C22⋊D1111yescharacteristic
969D4—416no—
970C2×C4—22no—
971C2×C4—22no—
972C2×C4—22no—
973C2×C4—22no—
974C2×C4—22no—
975C2×C4—22no—
976C2×C4—22no—
977C2×C4—22no—
978C2×C4—22no—
979C2×C4—22no—
980C2×C4—22no—
981C2×C4—22no—
982C2×C4—22no—
983C2×C4—22no—
984C2×C4—22no—
985C2×C4—22no—
986C2×C4—22no—
987C2×C4—22no—
988C2×C4—41no—
989C2×C4—41no—
990C2×C4—41no—
991C2×C4—41no—
992C2×C4—41no—
993C2×C4—41no—
994C2×C4—41no—
995C2×C4—41no—
996C2×C4—41no—
997C2×C4—41no—
998C2×C4—41no—
999C2×C4—41no—
1000C2×C4—41no—
1001C2×C4—41no—
1002C2×C4—41no—
1003C2×C4—114no—
1004C2×C4—222no—
1005C2×C4—222no—
1006C2×C4—222no—
1007C2×C4—222no—
1008C2×C4—222no—
1009C2×C4—222no—
1010C2×C4—222no—
1011C2×C4—222no—
1012C2×C4—222no—
1013C2×C4—222no—
1014C2×C4—222no—
1015C2×C4—222no—
1016C2×C4—222no—
1017C2×C4—222no—
1018C2×C4—222no—
1019C2×C4—222no—
1020C2×C4—222no—
1021C2×C4—222no—
1022C2×C4—222no—
1023C2×C4—222no—
1024C2×C4—222no—
1025C2×C4—222no—
1026C2×C4—222no—
1027C2×C4—222no—
1028C2×C4—4416no—
1029C2×C4—441no—
1030C2×C4—441no—
1031C2×C4—441no—
1032C2×C4—441no—
1033C2×C4—441no—
1034C2×C4—441no—
1035C2×C4—441no—
1036C2×C4—441no—
1037C2×C4—441no—
1038C2×C4—441no—
1039C2×C4—441no—
1040C2×C4—441no—
1041C2×C4—441no—
1042C2×C4—441no—
1043C2×C4—441no—
1044C2×C4—441no—
1045C2×C4—441no—
1046C2×C4—441no—
1047C2×C4—441no—
1048C2×C4—441no—
1049C2×C4—441no—
1050C2×C4—441no—
1051C2×C4—441no—
1052C2×C4—441no—
1053C2×C4—441no—
1054C2×C4—441no—
1055C2×C4—441no—
1056C2×C4—441no—
1057C2×C4—441no—
1058C2×C4—441no—
1059C2×C4—441no—
1060C2×C4#6693014yes—
1061C2×C4#6698814yes—
1062C22—24no—
1063C22—24no—
1064C22—24no—
1065C22—42no—
1066C22—42no—
1067C22—42no—
1068C22—42no—
1069C22—42no—
1070C22—42no—
1071C22—42no—
1072C22—42no—
1073C22—42no—
1074C22—42no—
1075C22—42no—
1076C22—42no—
1077C22—42no—
1078C22—42no—
1079C22—42no—
1080C22—42no—
1081C22—42no—
1082C22—42no—
1083C22—42no—
1084C22—81no—
1085C22—81no—
1086C22—81no—
1087C22—81no—
1088C22—81no—
1089C22—81no—
1090C22—81no—
1091C22—81no—
1092C22C2×#6693011yescharacteristic
1093C22#1062301711yescharacteristic
1094C22#1062302611yescharacteristic
1095C22#1062302611yescharacteristic
1096C22C4×#434111yescharacteristic
1097C22C4×#434111yescharacteristic
1098C22#1062306911yescharacteristic
1099C22#1062306911yescharacteristic
1100C22C4×D4×D1111yescharacteristic
1101C22#1062307611yescharacteristic
1102C22#1062308111yescharacteristic
1103C22#1062308711yescharacteristic
1104C22#1062312711yescharacteristic
1105C22#1062313111yescharacteristic
1106C22#1062313211yescharacteristic
1107C22#1062314111yescharacteristic
1108C22#1062314511yescharacteristic
1109C22#1062314611yescharacteristic
1110C22#1062314811yescharacteristic
1111C22#1062314911yescharacteristic
1112C22#1062320111yescharacteristic
1113C22#1062320911yescharacteristic
1114C22#1062321111yescharacteristic
1115C22#1062321211yescharacteristic
1116C22#1062324411yescharacteristic
1117C22#1062324711yescharacteristic
1118C22#1062324911yescharacteristic
1119C22#1062325011yescharacteristic
1120C22C2×C4×C22⋊D1111yescharacteristic
1121C22C2×#6698811yescharacteristic
1122C22D4×C22⋊D1111yescharacteristic
1123C22#1062333711yescharacteristic
1124C22#1062333711yescharacteristic
1125C22#1062335911yescharacteristic
1126C22#1062336011yescharacteristic
1127C4—24no—
1128C4—24no—
1129C4—42no—
1130C4—42no—
1131C4—81no—
1132C4—224no—
1133C4—442no—
1134C4—442no—
1135C4—442no—
1136C4—442no—
1137C4—442no—
1138C4—442no—
1139C4—881no—
1140C2—44no—
1141C2—82no—
1142C2#1307107811yescharacteristic
1143C2C4×#6698811yescharacteristic
1144C2#1307137511yescharacteristic
1145C2#1307146111yescharacteristic
1146C2#1307158811yescharacteristic
1147C2#1307159311yescharacteristic
1148C2#1307165111yescharacteristic
1149C2#1307236211yescharacteristic
1150C2#1307237711yescharacteristic
1151C2#1307254911yescharacteristic
1152C2#1307261811yescharacteristic
1153C2#1307324711yescharacteristic
1154C2#1307339311yescharacteristic
1155C2#1307367311yescharacteristic
1156C2#1307372011yescharacteristic
subgroupG/H
center, FrattiniC24C23×D11
commutatorC23×C11C23×C4
FittingC2×C11×#390C2
socle, cosocleC24×C11C24
prime radicalC23×D4×C11C22
hypercenterC2×#390D11
hypocenterC11#14007
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ C2×#390

Complements

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

NH ≅ G/Ntype
1. C2×#10622557C2semidirect
3. C2×#10622556C2semidirect
4. C2×C22⋊C4×Dic11C2semidirect
5. #13066875C2semidirect
6. #13066863C2semidirect
7. #13066859C2semidirect
9. #13066853C2semidirect
10. #13066853C2semidirect
11. #13066853C2semidirect
12. #13066849C2semidirect
13. #13066848C2semidirect
14. C4×C11⋊#95C2semidirect
36. #10622833C4semidirect
151. C11⋊#95D4semidirect
883. C11#14007semidirect

Maximal subgroups

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

subgroupindex
C2×#106225572
C2×#106228332
C2×#106225562
C2×C22⋊C4×Dic112
#130668752
#130668632
#130668592
#130668572
#130668532
#130668492
#130668482
C4×C11⋊#952
C2×C11×#3902
#1400711