Finite Group Databasebeta

← #14786401

Subgroups — #14786401

Order 2816.

1844 conjugacy classes of subgroups.

The subgroup lattice has 962 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D11×#121C211yesmaximal, characteristic
2C2×#10622495C211yesmaximal, characteristic, complemented
3C2×#10622387C211yesmaximal, characteristic, complemented
4D11×#380C211yesmaximal, characteristic, complemented
5#13069799C211yesmaximal, characteristic, complemented
6#13069798C211yesmaximal, characteristic, complemented
7#13069795C211yesmaximal, characteristic, complemented
8#13068932C211yesmaximal, characteristic, complemented
9#13068930C211yesmaximal, characteristic, complemented
10#13068805C211yesmaximal, characteristic, complemented
11#13068802C211yesmaximal, characteristic, complemented
12#13068545C211yesmaximal, characteristic, complemented
13#13068545C211yesmaximal, characteristic, complemented
14#13068525C211yesmaximal, characteristic, complemented
15C11×#2033C211yesmaximal, characteristic, complemented
16C22×D4×D11—21no—
17C22×D4×D11C2211yescharacteristic
18C23×C4×D11C2211yescharacteristic
19C2×C11×#121C2211yescharacteristic
20C2×#66992—21no—
21C2×#66991C2211yescharacteristic
22C2×#66983C2211yescharacteristic
23D11×#121—24no—
24D11×#121—24no—
25C2×#66948C2211yescharacteristic
26C2×C4⋊C4×D11C2211yescharacteristic
27C2×C4⋊C4×D11C2211yescharacteristic, complemented
28C2×C4⋊C4×D11C2211yescharacteristic, complemented
29C2×#66937—21no—
30C2×C22⋊C4×D11—21no—
31C2×C22⋊C4×D11—21no—
32C2×C11×#107C2211yescharacteristic, complemented
33C2×C11×#102C2211yescharacteristic, complemented
34C2×C11×#102C2211yescharacteristic, complemented
35C2×C11×C22⋊C8C2211yescharacteristic, complemented
36C11×#380C2211yescharacteristic, complemented
37C2×#66896C2211yescharacteristic, complemented
38C2×#66896C2211yescharacteristic, complemented
39#10622825C2211yescharacteristic, complemented
40C2×C22⋊(C11⋊C8)C2211yescharacteristic, complemented
41C2×#66885C2211yescharacteristic, complemented
42C2×#66885C2211yescharacteristic, complemented
43C2×(C2×D11)⋊C8C2211yescharacteristic
44C2×(C2×D11)⋊C8C2211yescharacteristic
45C2×(C2×D11)⋊C8C2211yescharacteristic, complemented
46C2×(C2×D11)⋊C8C2211yescharacteristic, complemented
47C2×#66882C2211yescharacteristic, complemented
48#10622600C2211yescharacteristic
49#10622600C2211yescharacteristic
50C2×#66873C2211yescharacteristic, complemented
51C2×#66873C2211yescharacteristic, complemented
52C2×#66871C2211yescharacteristic, complemented
53C2×#66871C2211yescharacteristic, complemented
54#10622555—21no—
55#10622495—24no—
56#10622387—24no—
57#10622280—21no—
58D11×#95—21no—
59C11×#340C2211yescharacteristic, complemented
60#10622189C2211yescharacteristic, complemented
61#10622167C2211yescharacteristic, complemented
62#10622167C2211yescharacteristic, complemented
63C24×D11—21no—
64C24×D11D411yescharacteristic
65C22×D4×C11—21no—
66C22×D4×C11C2311yescharacteristic
67C23×C4×C11C2311yescharacteristic
68C22×C22⋊D11—21no—
69C22×C22⋊D11—21no—
70C22×C22⋊D11—21no—
71C23×Dic11D411yescharacteristic
72C2×D4×D11—28no—
73C2×D4×D11—22no—
74C2×D4×D11—22no—
75C2×D4×D11—22no—
76C2×D4×D11—22no—
77C2×D4×D11—41no—
78C2×D4×D11—41no—
79C2×D4×D11—44no—
80C2×D4×D11—44no—
81C22×D44—21no—
82C22×D44C2311yescharacteristic
83C22×C4×D11—21no—
84C22×C4×D11—22no—
85C22×C4×D11—22no—
86C22×C4×D11—22no—
87C22×C4×D11—22no—
88C22×C4×D11—21no—
89C22×C4×D11—21no—
90C22×C4×D11—41no—
91C22×C4×D11—41no—
92C22×C4×D11D411yescharacteristic
93C22×C4×D11D411yescharacteristic
94C22×C4×D11C2311yescharacteristic
95C22×C4×D11C2311yescharacteristic
96C22×C8×C11C2311yescharacteristic
97C22×C8×C11C2311yescharacteristic
98C11×#121—22no—
99C11×#121—22no—
100C2×C11×C4⋊C4C2311yescharacteristic
101C2×C11×C4⋊C4C2311yescharacteristic
102C2×C11×C4⋊C4C2311yescharacteristic
103C2×C11×C22⋊C4—21no—
104C2×C11×C22⋊C4—21no—
105C2×C22⋊Dic11—21no—
106C2×C22⋊Dic11—21no—
107#66992—28no—
108#66991—22no—
109#66991D414yes—
110#66983—22no—
111#66983—22no—
112C2×(C2×D11)⋊C4—21no—
113C2×(C2×D11)⋊C4—21no—
114C2×(C2×D11)⋊C4—21no—
115C2×(C2×D11)⋊C4—21no—
116C2×C4⋊Dic11C2311yescharacteristic
117C2×C4⋊Dic11C2311yescharacteristic
118C2×C4⋊Dic11C2311yescharacteristic
119C2×Dic11⋊C4—21no—
120C2×Dic11⋊C4—21no—
121C2×Dic11⋊C4—21no—
122C22×C11⋊C8C2311yescharacteristic
123C22×C11⋊C8C2311yescharacteristic
124#66948—22no—
125#66948D414yes—
126C4⋊C4×D11—22no—
127C4⋊C4×D11—22no—
128C4⋊C4×D11—22no—
129C4⋊C4×D11—22no—
130C4⋊C4×D11—41no—
131C4⋊C4×D11—41no—
132#66937—28no—
133C22⋊C4×D11—28no—
134C22⋊C4×D11—44no—
135C11×#107—22no—
136C11×#102—22no—
137C11×#102—41no—
138C11×C22⋊C8—41no—
139C11×#95—21no—
140#66896—22no—
141#66896—41no—
142C11⋊#95—21no—
143C11⋊#95—21no—
144C11⋊#95—21no—
145C22⋊(C11⋊C8)—41no—
146#66885—22no—
147#66885—41no—
148(C2×D11)⋊C8—22no—
149(C2×D11)⋊C8—22no—
150(C2×D11)⋊C8—22no—
151(C2×D11)⋊C8—22no—
152#66882—22no—
153#66873—22no—
154#66873—41no—
155#66871—22no—
156#66871—22no—
157#24002—111nomaximal, Sylow
158C24×C11—21no—
159C24×C11C2×D411yescharacteristic
160C23×D11—22no—
161C23×D11—22no—
162C23×D11—22no—
163C23×D11—22no—
164C23×D11—24no—
165C23×D11—21no—
166C23×D11—41no—
167C23×D11—41no—
168C23×D11—42no—
169C23×D11—42no—
170C23×D11—42no—
171C23×D11—42no—
172C23×D11—42no—
173C23×D11—42no—
174C23×D11D814yes—
175C23×D11C2×D411yescharacteristic
176C23×D11C2×D411yescharacteristic
177C2×D4×C11—24no—
178C2×D4×C11—21no—
179C2×D4×C11—21no—
180C2×D4×C11—21no—
181C2×D4×C11—21no—
182C2×D4×C11—21no—
183C2×D4×C11—42no—
184C2×D4×C11—42no—
185C2×D4×C11C2×D412yes—
186C22×C4×C11—21no—
187C22×C4×C11—21no—
188C22×C4×C11—21no—
189C22×C4×C11—21no—
190C22×C4×C11—21no—
191C22×C4×C11—21no—
192C22×C4×C11—21no—
193C22×C4×C11—21no—
194C22×C4×C11—21no—
195C22×C4×C11C2×D411yescharacteristic
196C22×C4×C11C2411yescharacteristic
197C2×C22⋊D11—24no—
198C2×C22⋊D11—24no—
199C2×C22⋊D11—24no—
200C2×C22⋊D11—42no—
201C2×C22⋊D11—42no—
202C2×C22⋊D11—42no—
203C2×C22⋊D11—42no—
204C2×C22⋊D11—42no—
205C2×C22⋊D11—42no—
206C22×Dic11—22no—
207C22×Dic11—22no—
208C22×Dic11—21no—
209C22×Dic11—21no—
210C22×Dic11—21no—
211C22×Dic11—41no—
212C22×Dic11C2×D411yescharacteristic
213C22×Dic11C2×D411yescharacteristic
214D4×D11—44no—
215D4×D11—44no—
216D4×D11—432no—
217D4×D11—44no—
218D4×D11—44no—
219C2×D44—24no—
220C2×D44—21no—
221C2×D44—21no—
222C2×D44—21no—
223C2×D44—21no—
224C2×D44—21no—
225C2×D44—42no—
226C2×D44—42no—
227C2×D44C2×D412yes—
228C2×C4×D11—24no—
229C2×C4×D11—22no—
230C2×C4×D11—22no—
231C2×C4×D11—22no—
232C2×C4×D11—22no—
233C2×C4×D11—21no—
234C2×C4×D11—21no—
235C2×C4×D11—21no—
236C2×C4×D11—21no—
237C2×C4×D11—21no—
238C2×C4×D11—21no—
239C2×C4×D11—21no—
240C2×C4×D11—21no—
241C2×C4×D11—41no—
242C2×C4×D11—41no—
243C2×C4×D11—42no—
244C2×C4×D11—42no—
245C2×C4×D11—42no—
246C2×C4×D11—44no—
247C2×C4×D11—44no—
248C2×C4×D11—44no—
249C2×C4×D11—44no—
250C2×C4×D11—42no—
251C2×C4×D11—42no—
252C2×C4×D11—42no—
253C2×C4×D11—42no—
254C2×C4×D11—42no—
255C2×C4×D11C2×D412yes—
256C2×C4×D11C2×D412yes—
257C2×C4×D11#4112yes—
258C2×C4×D11#4112yes—
259C2×C8×C11—21no—
260C2×C8×C11—21no—
261C2×C8×C11—21no—
262C2×C8×C11—21no—
263C2×C8×C11—21no—
264C2×C8×C11—21no—
265C11×C4⋊C4—21no—
266C11×C4⋊C4—21no—
267C11×C4⋊C4—21no—
268C11×C4⋊C4—21no—
269C11×C4⋊C4—21no—
270C11×C4⋊C4C2×D412yes—
271C11×C22⋊C4—24no—
272C11×C22⋊C4—42no—
273C22⋊Dic11—24no—
274C22⋊Dic11—42no—
275(C2×D11)⋊C4—24no—
276(C2×D11)⋊C4—24no—
277(C2×D11)⋊C4—42no—
278(C2×D11)⋊C4—42no—
279C4⋊Dic11—21no—
280C4⋊Dic11—21no—
281C4⋊Dic11—21no—
282C4⋊Dic11—21no—
283C4⋊Dic11—21no—
284C4⋊Dic11C2×D412yes—
285Dic11⋊C4—24no—
286Dic11⋊C4—42no—
287Dic11⋊C4—42no—
288C2×C11⋊C8—21no—
289C2×C11⋊C8—21no—
290C2×C11⋊C8—21no—
291C2×C11⋊C8—21no—
292C2×C11⋊C8—21no—
293C2×C11⋊C8—21no—
294C22×#121—111no—
295C2×#480—111no—
296C2×#480—111no—
297C2×#380—111no—
298#2033—111no—
299#2033—111no—
300#2033—111no—
301#2033D1111yescharacteristic, complemented
302#1874—111no—
303#1874—111no—
304#1852—111no—
305#1852—111no—
306#1786—111no—
307#1786—111no—
308#1779—111no—
309C23×C11—21no—
310C23×C11—21no—
311C23×C11—21no—
312C23×C11—21no—
313C23×C11—21no—
314C23×C11—21no—
315C23×C11—22no—
316C23×C11—41no—
317C23×C11—41no—
318C23×C11—41no—
319C23×C11—41no—
320C23×C11—41no—
321C23×C11—41no—
322C23×C11C2×D812yes—
323C23×C11C22×D411yescharacteristic
324C22×D11—21no—
325C22×D11—21no—
326C22×D11—21no—
327C22×D11—21no—
328C22×D11—21no—
329C22×D11—21no—
330C22×D11—21no—
331C22×D11—21no—
332C22×D11—28no—
333C22×D11—28no—
334C22×D11—22no—
335C22×D11—44no—
336C22×D11—44no—
337C22×D11—44no—
338C22×D11—44no—
339C22×D11—44no—
340C22×D11—48no—
341C22×D11—48no—
342C22×D11—48no—
343C22×D11—41no—
344C22×D11—41no—
345C22×D11—41no—
346C22×D11—41no—
347C22×D11—41no—
348C22×D11—41no—
349C22×D11—84no—
350C22×D11—84no—
351C22×D11—84no—
352C22×D11—84no—
353C22×D11#12012yes—
354C22×D11#12312yes—
355C22×D11C2×D812yes—
356C22×D11C2×D812yes—
357C22×D11AGL(1,ℤ/8)12yes—
358C22×D11#13712yes—
359D4×C11—22no—
360D4×C11—22no—
361D4×C11—48no—
362D4×C11—41no—
363D4×C11—41no—
364C2×C4×C11—22no—
365C2×C4×C11—21no—
366C2×C4×C11—21no—
367C2×C4×C11—21no—
368C2×C4×C11—41no—
369C2×C4×C11—41no—
370C2×C4×C11—41no—
371C2×C4×C11—41no—
372C2×C4×C11—41no—
373C2×C4×C11—41no—
374C2×C4×C11—41no—
375C2×C4×C11—41no—
376C2×C4×C11—41no—
377C2×C4×C11—41no—
378C2×C4×C11—41no—
379C2×C4×C11—41no—
380C2×C4×C11C22×D411yescharacteristic
381C2×C4×C11C22×D411yescharacteristic
382C2×C4×C11C2×#4111yescharacteristic
383C2×C4×C11C2×#4111yescharacteristic
384C2×C4×C11H(5,𝔽2)11yescharacteristic
385C2×C4×C11H(5,𝔽2)11yescharacteristic
386C22⋊D11—48no—
387C22⋊D11—48no—
388C22⋊D11—48no—
389C2×Dic11—21no—
390C2×Dic11—21no—
391C2×Dic11—21no—
392C2×Dic11—21no—
393C2×Dic11—22no—
394C2×Dic11—44no—
395C2×Dic11—41no—
396C2×Dic11—41no—
397C2×Dic11—41no—
398C2×Dic11—41no—
399C2×Dic11—41no—
400C2×Dic11—41no—
401C2×Dic11—41no—
402C2×Dic11—41no—
403C2×Dic11#12012yes—
404C2×Dic11#12312yes—
405D44—22no—
406D44—22no—
407D44—48no—
408D44—41no—
409D44—41no—
410C4×D11—22no—
411C4×D11—22no—
412C4×D11—22no—
413C4×D11—22no—
414C4×D11—22no—
415C4×D11—22no—
416C4×D11—22no—
417C4×D11—22no—
418C4×D11—44no—
419C4×D11—44no—
420C4×D11—48no—
421C4×D11—84no—
422C4×D11—84no—
423C8×C11—41no—
424C8×C11—41no—
425C11⋊C8—41no—
426C11⋊C8—41no—
427C23×D4—111no—
428C23×D4—221no—
429C24×C4—111no—
430C2×#121—111no—
431C2×#121—111no—
432C2×#121—111no—
433C2×#121—221no—
434C2×#121—224no—
435C2×#121—224no—
436C2×#121—221no—
437C2×#121C2×D1111yescharacteristic
438C22×C4⋊C4—111no—
439C22×C4⋊C4—111no—
440C22×C4⋊C4—111no—
441C22×C22⋊C4—221no—
442C22×C22⋊C4—221no—
443#480—224no—
444#480—224no—
445C2×#107—111no—
446C2×#107—111no—
447C2×#107—111no—
448C2×#107C2×D1111yescharacteristic, complemented
449C2×#102—111no—
450C2×#102—111no—
451C2×#102—111no—
452C2×#102—111no—
453C2×#102—111no—
454C2×#102—111no—
455C2×#102C2×D1111yescharacteristic, complemented
456C2×#102C2×D1111yescharacteristic, complemented
457C2×C22⋊C8—111no—
458C2×C22⋊C8—111no—
459C2×C22⋊C8—111no—
460C2×C22⋊C8—111no—
461C2×C22⋊C8—111no—
462C2×C22⋊C8C2×D1111yescharacteristic, complemented
463#380—111no—
464#380—111no—
465#380—111no—
466#380—221no—
467#380—221no—
468#380C2×D1111yescharacteristic, complemented
469C2×#95—221no—
470#340—111no—
471#340—111no—
472#340—111no—
473#340C2×D1111yescharacteristic, complemented
474C22×C11—22no—
475C22×C11—22no—
476C22×C11—22no—
477C22×C11—41no—
478C22×C11—41no—
479C22×C11—41no—
480C22×C11—41no—
481C22×C11—42no—
482C22×C11—42no—
483C22×C11—42no—
484C22×C11—81no—
485C22×C11—81no—
486C22×C11—81no—
487C22×C11—81no—
488C22×C11C2×#12011yescharacteristic
489C22×C11C2×#12311yescharacteristic
490C22×C11#53411yescharacteristic
491C22×C11C22×D811yescharacteristic
492C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
493C22×C11C2×#13711yescharacteristic
494C22×C11#57511yescharacteristic
495C2×D11—22no—
496C2×D11—22no—
497C2×D11—22no—
498C2×D11—22no—
499C2×D11—22no—
500C2×D11—22no—
501C2×D11—22no—
502C2×D11—22no—
503C2×D11—22no—
504C2×D11—22no—
505C2×D11—22no—
506C2×D11—22no—
507C2×D11—416no—
508C2×D11—42no—
509C2×D11—42no—
510C2×D11—42no—
511C2×D11—816no—
512C2×D11—81no—
513C2×D11—81no—
514C2×D11—81no—
515C2×D11—81no—
516C2×D11#44714yes—
517C2×D11#48014yescomplemented
518C4×C11—41no—
519C4×C11—42no—
520C4×C11—81no—
521C4×C11—81no—
522C4×C11#54611yescharacteristic
523C4×C11#54611yescharacteristic
524C4×C11#54611yescharacteristic
525C4×C11#54611yescharacteristic
526Dic11—22no—
527Dic11—22no—
528Dic11—42no—
529Dic11—81no—
530Dic11—81no—
531C25—111no—
532C25—221no—
533C22×D4—21no—
534C22×D4—111no—
535C22×D4—221no—
536C22×D4—222no—
537C22×D4—222no—
538C22×D4—221no—
539C22×D4—222no—
540C22×D4—228no—
541C22×D4—221no—
542C22×D4—221no—
543C22×D4—222no—
544C22×D4—441no—
545C22×D4—441no—
546C22×D4—444no—
547C22×D4—444no—
548C22×D4C22×D1111yescharacteristic
549C23×C4—111no—
550C23×C4—111no—
551C23×C4—111no—
552C23×C4—111no—
553C23×C4—111no—
554C23×C4—222no—
555C23×C4—222no—
556C23×C4—222no—
557C23×C4—222no—
558C23×C4—221no—
559C23×C4—221no—
560C23×C4—221no—
561C23×C4—441no—
562C23×C4—441no—
563C23×C4C22×D1111yescharacteristic
564C22×C8—111no—
565C22×C8—111no—
566C22×C8C22×D1111yescharacteristic
567C22×C8C22×D1111yescharacteristic
568#121—22no—
569#121—22no—
570#121—114no—
571#121—114no—
572#121—228no—
573#121—222no—
574#121—222no—
575#121—222no—
576#121—222no—
577#121—228no—
578C2×C4⋊C4—111no—
579C2×C4⋊C4—111no—
580C2×C4⋊C4—111no—
581C2×C4⋊C4—222no—
582C2×C4⋊C4—222no—
583C2×C4⋊C4—222no—
584C2×C4⋊C4—221no—
585C2×C4⋊C4—222no—
586C2×C4⋊C4—221no—
587C2×C4⋊C4—221no—
588C2×C4⋊C4—441no—
589C2×C4⋊C4—441no—
590C2×C4⋊C4C22×D1111yescharacteristic
591C2×C4⋊C4C22×D1111yescharacteristic
592C2×C4⋊C4C22×D1111yescharacteristic
593C2×C22⋊C4—21no—
594C2×C22⋊C4—21no—
595C2×C22⋊C4—228no—
596C2×C22⋊C4—221no—
597C2×C22⋊C4—221no—
598C2×C22⋊C4—221no—
599C2×C22⋊C4—221no—
600C2×C22⋊C4—221no—
601C2×C22⋊C4—221no—
602C2×C22⋊C4—444no—
603#107—22no—
604#107—222no—
605#107—222no—
606#107—222no—
607#102—22no—
608#102—41no—
609#102—222no—
610#102—222no—
611#102—222no—
612#102—441no—
613#102—441no—
614#102—441no—
615C22⋊C8—41no—
616C22⋊C8—222no—
617C22⋊C8—222no—
618C22⋊C8—222no—
619C22⋊C8—222no—
620C22⋊C8—441no—
621#95—21no—
622#95—221no—
623#95—221no—
624#95—221no—
625C2×C11—42no—
626C2×C11—82no—
627C2×C11#240511yescharacteristic
628C2×C11C2×#44711yescharacteristic
629C2×C11#300711yescharacteristic
630C2×C11C2×#48011yescharacteristic
631C2×C11#309411yescharacteristic
632C2×C11#318611yescharacteristic
633C2×C11#319311yescharacteristic
634D11—24no—
635D11—24no—
636D11—82no—
637C24—21no—
638C24—111no—
639C24—111no—
640C24—114no—
641C24—222no—
642C24—222no—
643C24—222no—
644C24—222no—
645C24—224no—
646C24—221no—
647C24—441no—
648C24—441no—
649C24—442no—
650C24—442no—
651C24—442no—
652C24—442no—
653C24—442no—
654C24—442no—
655C24D4×D1111yescharacteristic
656C2×D4—24no—
657C2×D4—21no—
658C2×D4—21no—
659C2×D4—21no—
660C2×D4—21no—
661C2×D4—21no—
662C2×D4—42no—
663C2×D4—42no—
664C2×D4—112no—
665C2×D4—224no—
666C2×D4—224no—
667C2×D4—224no—
668C2×D4—224no—
669C2×D4—221no—
670C2×D4—221no—
671C2×D4—221no—
672C2×D4—221no—
673C2×D4—221no—
674C2×D4—442no—
675C2×D4—442no—
676C2×D4—442no—
677C2×D4—444no—
678C2×D4—444no—
679C2×D4—444no—
680C2×D4—444no—
681C2×D4—442no—
682C2×D4—4432no—
683C2×D4—442no—
684C2×D4—442no—
685C2×D4—442no—
686C2×D4—442no—
687C2×D4D4×D1112yes—
688C22×C4—21no—
689C22×C4—21no—
690C22×C4—21no—
691C22×C4—21no—
692C22×C4—21no—
693C22×C4—21no—
694C22×C4—21no—
695C22×C4—21no—
696C22×C4—21no—
697C22×C4—111no—
698C22×C4—111no—
699C22×C4—112no—
700C22×C4—112no—
701C22×C4—112no—
702C22×C4—112no—
703C22×C4—222no—
704C22×C4—222no—
705C22×C4—222no—
706C22×C4—222no—
707C22×C4—224no—
708C22×C4—222no—
709C22×C4—222no—
710C22×C4—221no—
711C22×C4—221no—
712C22×C4—221no—
713C22×C4—221no—
714C22×C4—221no—
715C22×C4—221no—
716C22×C4—221no—
717C22×C4—221no—
718C22×C4—221no—
719C22×C4—221no—
720C22×C4—221no—
721C22×C4—441no—
722C22×C4—441no—
723C22×C4—444no—
724C22×C4—444no—
725C22×C4—444no—
726C22×C4—444no—
727C22×C4—442no—
728C22×C4—442no—
729C22×C4—442no—
730C22×C4—442no—
731C22×C4—442no—
732C22×C4—442no—
733C22×C4—442no—
734C22×C4—442no—
735C22×C4—441no—
736C22×C4D4×D1111yescharacteristic
737C22×C4C23×D1111yescharacteristic
738C2×C8—21no—
739C2×C8—21no—
740C2×C8—21no—
741C2×C8—21no—
742C2×C8—21no—
743C2×C8—21no—
744C2×C8—221no—
745C2×C8—221no—
746C2×C8—221no—
747C2×C8—221no—
748C2×C8—221no—
749C2×C8—221no—
750C4⋊C4—21no—
751C4⋊C4—21no—
752C4⋊C4—21no—
753C4⋊C4—21no—
754C4⋊C4—21no—
755C4⋊C4—112no—
756C4⋊C4—224no—
757C4⋊C4—221no—
758C4⋊C4—221no—
759C4⋊C4—221no—
760C4⋊C4—221no—
761C4⋊C4—221no—
762C4⋊C4—442no—
763C4⋊C4—442no—
764C4⋊C4D4×D1112yes—
765C22⋊C4—24no—
766C22⋊C4—42no—
767C22⋊C4—224no—
768C22⋊C4—224no—
769C22⋊C4—224no—
770C22⋊C4—442no—
771C22⋊C4—442no—
772C22⋊C4—442no—
773C11#2400211yescharacteristic, complemented, Sylow
774C23—21no—
775C23—21no—
776C23—21no—
777C23—21no—
778C23—21no—
779C23—21no—
780C23—22no—
781C23—41no—
782C23—41no—
783C23—41no—
784C23—41no—
785C23—41no—
786C23—41no—
787C23—112no—
788C23—112no—
789C23—112no—
790C23—112no—
791C23—112no—
792C23—112no—
793C23—228no—
794C23—228no—
795C23—221no—
796C23—221no—
797C23—221no—
798C23—221no—
799C23—221no—
800C23—221no—
801C23—221no—
802C23—221no—
803C23—222no—
804C23—444no—
805C23—444no—
806C23—444no—
807C23—444no—
808C23—444no—
809C23—448no—
810C23—448no—
811C23—448no—
812C23—441no—
813C23—441no—
814C23—441no—
815C23—441no—
816C23—441no—
817C23—441no—
818C23—884no—
819C23—884no—
820C23—884no—
821C23—884no—
822C23D8×D1112yes—
823C23C2×D4×D1111yescharacteristic
824D4—22no—
825D4—22no—
826D4—48no—
827D4—41no—
828D4—41no—
829D4—222no—
830D4—222no—
831D4—448no—
832D4—448no—
833D4—448no—
834D4—448no—
835D4—441no—
836D4—441no—
837C2×C4—21no—
838C2×C4—22no—
839C2×C4—21no—
840C2×C4—21no—
841C2×C4—41no—
842C2×C4—41no—
843C2×C4—41no—
844C2×C4—41no—
845C2×C4—41no—
846C2×C4—41no—
847C2×C4—41no—
848C2×C4—41no—
849C2×C4—41no—
850C2×C4—41no—
851C2×C4—41no—
852C2×C4—41no—
853C2×C4—112no—
854C2×C4—112no—
855C2×C4—221no—
856C2×C4—221no—
857C2×C4—221no—
858C2×C4—221no—
859C2×C4—222no—
860C2×C4—222no—
861C2×C4—222no—
862C2×C4—222no—
863C2×C4—222no—
864C2×C4—222no—
865C2×C4—222no—
866C2×C4—222no—
867C2×C4—222no—
868C2×C4—444no—
869C2×C4—444no—
870C2×C4—448no—
871C2×C4—444no—
872C2×C4—441no—
873C2×C4—441no—
874C2×C4—441no—
875C2×C4—441no—
876C2×C4—441no—
877C2×C4—441no—
878C2×C4—441no—
879C2×C4—441no—
880C2×C4—884no—
881C2×C4—884no—
882C2×C4C2×D4×D1111yescharacteristic
883C2×C4C2×D4×D1111yescharacteristic
884C2×C4#6703711yescharacteristic
885C2×C4#41×D1111yescharacteristic
886C2×C4#41×D1111yescharacteristic
887C2×C4#6704211yescharacteristic
888C8—41no—
889C8—41no—
890C8—441no—
891C8—441no—
892C22—22no—
893C22—22no—
894C22—22no—
895C22—41no—
896C22—41no—
897C22—41no—
898C22—41no—
899C22—42no—
900C22—42no—
901C22—42no—
902C22—81no—
903C22—81no—
904C22—81no—
905C22—81no—
906C22—114no—
907C22—114no—
908C22—222no—
909C22—222no—
910C22—222no—
911C22—222no—
912C22—222no—
913C22—222no—
914C22—222no—
915C22—222no—
916C22—222no—
917C22—222no—
918C22—222no—
919C22—222no—
920C22—4416no—
921C22—442no—
922C22—442no—
923C22—442no—
924C22—8816no—
925C22—881no—
926C22—881no—
927C22—881no—
928C22—881no—
929C22D11×#12011yescharacteristic
930C22#1062313611yescharacteristic
931C22D11×#12311yescharacteristic
932C22C2×D8×D1111yescharacteristic
933C22#1062329911yescharacteristic
934C22D11×AGL(1,ℤ/8)11yescharacteristic
935C22D11×#13711yescharacteristic
936C4—42no—
937C4—41no—
938C4—81no—
939C4—81no—
940C4—222no—
941C4—222no—
942C4—442no—
943C4—881no—
944C4—881no—
945C4#1062314111yescharacteristic
946C4#1062314311yescharacteristic
947C4#1062318511yescharacteristic
948C4#1062320711yescharacteristic
949C2—42no—
950C2—82no—
951C2—224no—
952C2—224no—
953C2—882no—
954C2#1307193811yescharacteristic
955C2D11×#44711yescharacteristic
956C2#1307787311yescharacteristic
957C2D11×#48011yescharacteristic
958C2#1307855511yescharacteristic
959C2#1307936311yescharacteristic
960C2#1307941711yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#2033C2
socleC23×C11C22×D4
prime radicalC2×D11×#121C2
hypercenter#2033D11
hypocenterC11#24002
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ #2033

Complements

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

NH ≅ G/Ntype
2. C2×#10622495C2semidirect
3. C2×#10622387C2semidirect
4. D11×#380C2semidirect
5. #13069799C2semidirect
6. #13069798C2semidirect
7. #13069795C2semidirect
8. #13068932C2semidirect
9. #13068930C2semidirect
10. #13068805C2semidirect
11. #13068802C2semidirect
12. #13068545C2semidirect
13. #13068545C2semidirect
14. #13068525C2semidirect
15. C11×#2033C2semidirect
27. C2×C4⋊C4×D11C22semidirect
28. C2×C4⋊C4×D11C22semidirect
32. C2×C11×#107C22semidirect
33. C2×C11×#102C22semidirect
34. C2×C11×#102C22semidirect
35. C2×C11×C22⋊C8C22semidirect
36. C11×#380C22semidirect
37. C2×#66896C22semidirect
38. C2×#66896C22semidirect
39. #10622825C22semidirect
40. C2×C22⋊(C11⋊C8)C22semidirect
41. C2×#66885C22semidirect
42. C2×#66885C22semidirect
45. C2×(C2×D11)⋊C8C22semidirect
46. C2×(C2×D11)⋊C8C22semidirect
47. C2×#66882C22semidirect
50. C2×#66873C22semidirect
51. C2×#66873C22semidirect
52. C2×#66871C22semidirect
53. C2×#66871C22semidirect
59. C11×#340C22semidirect
60. #10622189C22semidirect
61. #10622167C22semidirect
62. #10622167C22semidirect
301. #2033D11semidirect
448. C2×#107C2×D11semidirect
455. C2×#102C2×D11semidirect
456. C2×#102C2×D11semidirect
462. C2×C22⋊C8C2×D11semidirect
468. #380C2×D11semidirect
473. #340C2×D11semidirect
517. C2×D11#480semidirect
773. C11#24002semidirect

Maximal subgroups

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

subgroupindex
C2×D11×#1212
C2×#106224952
C2×#106223872
D11×#3802
#130697992
#130697982
#130697952
#130689322
#130689302
#130688052
#130688022
#130685452
#130685252
C11×#20332
#2400211