Finite Group Databasebeta

← #14762879

Subgroups — #14762879

Order 2816.

1326 conjugacy classes of subgroups.

The subgroup lattice has 832 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623057C211yesmaximal, characteristic
2C2×#10622340C211yesmaximal, characteristic
3#13071205C211yesmaximal, characteristic
4#13069048C211yesmaximal, characteristic, complemented
5#13069048C211yesmaximal, characteristic, complemented
6#13069038C211yesmaximal, characteristic, complemented
7#13069038C211yesmaximal, characteristic, complemented
8#13068927C211yesmaximal, characteristic, complemented
9#13068927C211yesmaximal, characteristic, complemented
10#13068922C211yesmaximal, characteristic, complemented
11#13068922C211yesmaximal, characteristic, complemented
12#13068711C211yesmaximal, characteristic, complemented
13#13068552C211yesmaximal, characteristic, complemented
14#13068550C211yesmaximal, characteristic, complemented
15C11×#1825C211yesmaximal, characteristic, complemented
16C22×#4339C2211yescharacteristic
17C23×Dic22C2211yescharacteristic
18C2×C11×#117C2211yescharacteristic
19C22×#4313C2211yescharacteristic
20C22×C8×D11C2211yescharacteristic
21#10623057—24no—
22#10623057C418yescomplemented
23C2×#66950C2211yescharacteristic
24C2×#66950C2211yescharacteristic
25C2×#66950C2211yescharacteristic
26C2×#66950C2211yescharacteristic
27C2×#66945C2211yescharacteristic
28C2×C4⋊C4×D11C2211yescharacteristic
29C2×#66939—21no—
30C2×#66939—21no—
31C2×#66928—21no—
32C2×#66922—21no—
33C2×C11×C22⋊C8C2211yescharacteristic
34C11×#380C2211yescharacteristic
35#10622825C2211yescharacteristic
36C2×C22⋊(C11⋊C8)C2211yescharacteristic
37C2×(C2×D11)⋊C8C2211yescharacteristic
38C2×(C2×D11)⋊C8C2211yescharacteristic
39C2×#66880C2211yescharacteristic
40C2×#66880C2211yescharacteristic
41C2×#66880C2211yescharacteristic
42C2×#66880C2211yescharacteristic
43#10622600C2211yescharacteristic
44#10622600C2211yescharacteristic
45C2×#66874C2211yescharacteristic
46C2×#66874C2211yescharacteristic
47C2×#66874C2211yescharacteristic
48C2×#66874C2211yescharacteristic
49#10622570—21no—
50#10622569—21no—
51#10622340—24no—
52#10622278—21no—
53#10622259—21no—
54C11×#340C2211yescharacteristic
55C11×#340C2211yescharacteristic
56C11×#340C2211yescharacteristic
57C11×#340C2211yescharacteristic
58#10622167C2211yescharacteristic
59#10622167C2211yescharacteristic
60#10622167C2211yescharacteristic
61#10622167C2211yescharacteristic
62C23×C4×C11C2311yescharacteristic
63C22×C22⋊D11D411yescharacteristic
64C22×C22⋊D11D411yescharacteristic
65C23×Dic11—21no—
66C2×#4339—41no—
67C2×#4339—41no—
68C2×#4339—41no—
69C2×#4339—41no—
70C2×#4339C2×C414yes—
71C2×#4339D414yes—
72C22×D44D411yescharacteristic
73C22×C4×D11—21no—
74C22×C4×D11C2311yescharacteristic
75C22×C4×D11C2311yescharacteristic
76C22×Dic22—21no—
77C22×Dic22—22no—
78C22×Dic22—41no—
79C22×Dic22—41no—
80C22×Dic22—41no—
81C22×Dic22—41no—
82C22×Dic22C2×C414yescomplemented
83C22×Dic22D411yescharacteristic
84C22×Dic22C2311yescharacteristic
85C22×Dic22C2311yescharacteristic
86C22×C8×C11C2311yescharacteristic
87C22×C8×C11C2311yescharacteristic
88C11×#117—22no—
89C11×#117C2×C414yescomplemented
90C2×C11×C4⋊C4C2311yescharacteristic
91C2×C11×C4⋊C4C2311yescharacteristic
92C2×C11×C4⋊C4C2311yescharacteristic
93C2×C11×C4⋊C4C2311yescharacteristic
94C2×C11×C22⋊C4—21no—
95C2×C11×C22⋊C4—21no—
96C2×C42×C11—21no—
97C2×C22⋊Dic11—21no—
98C2×(C2×D11)⋊C4—21no—
99C2×(C2×D11)⋊C4—21no—
100C2×(C2×D11)⋊C4—21no—
101C2×(C2×D11)⋊C4—21no—
102C2×(C2×D11)⋊C4—21no—
103C2×(C2×D11)⋊C4—21no—
104C2×(C2×D11)⋊C4—21no—
105C2×C4⋊Dic11—21no—
106C2×C4⋊Dic11—21no—
107C2×C4⋊Dic11—21no—
108C2×C4⋊Dic11—21no—
109C2×C4⋊Dic11C2311yescharacteristic
110C2×C4⋊Dic11C2311yescharacteristic
111C2×Dic11⋊C4—21no—
112C2×C4×Dic11—21no—
113C22×C11⋊C8C2311yescharacteristic
114C22×C11⋊C8C2311yescharacteristic
115C2×#4313—22no—
116C2×#4313—41no—
117C2×#4313—41no—
118C2×C8×D11—22no—
119C2×C8×D11—41no—
120C2×C8×D11—41no—
121#66950—22no—
122#66950—22no—
123#66950—22no—
124#66950—22no—
125#66950C2×C414yes—
126#66950C2×C414yes—
127#66950C2×C414yescomplemented
128#66950C2×C414yescomplemented
129#66945—41no—
130#66945—41no—
131C4⋊C4×D11—41no—
132C4⋊C4×D11—41no—
133#66939—28no—
134#66939—28no—
135#66928—28no—
136#66922—28no—
137C11×C22⋊C8—22no—
138C11×#95—21no—
139C11⋊#95—21no—
140C11⋊#95—21no—
141C11⋊#95—21no—
142C22⋊(C11⋊C8)—22no—
143(C2×D11)⋊C8—22no—
144(C2×D11)⋊C8—22no—
145#66880—41no—
146#66880—41no—
147#66880—41no—
148#66880—41no—
149#66874—41no—
150#66874—41no—
151#66874—41no—
152#66874—41no—
153#21771—111nomaximal, Sylow
154C24×C11C2×D411yescharacteristic
155C23×D11C2×D411yescharacteristic
156C23×D11C2×D411yescharacteristic
157C22×C4×C11—21no—
158C22×C4×C11—21no—
159C22×C4×C11—21no—
160C22×C4×C11—21no—
161C22×C4×C11—21no—
162C22×C4×C11—21no—
163C22×C4×C11—21no—
164C22×C4×C11—21no—
165C22×C4×C11C22×C412yes—
166C22×C4×C11C2×D411yescharacteristic
167C22×C4×C11C2×D412yes—
168C22×C4×C11C2411yescharacteristic
169C2×C22⋊D11—41no—
170C2×C22⋊D11—41no—
171C2×C22⋊D11—41no—
172C2×C22⋊D11—41no—
173C2×C22⋊D11C22⋊C414yes—
174C2×C22⋊D11C22⋊C414yes—
175C22×Dic11—24no—
176C22×Dic11—21no—
177C22×Dic11—21no—
178C22×Dic11—21no—
179C22×Dic11—21no—
180C22×Dic11—42no—
181C22×Dic11—42no—
182C22×Dic11C2×D411yescharacteristic
183C22×Dic11C2×D411yescharacteristic
184#4339—44no—
185#4339—44no—
186#4339—44no—
187#4339—44no—
188C2×D44—41no—
189C2×D44—41no—
190C2×D44C22⋊C414yes—
191C2×C4×D11—21no—
192C2×C4×D11—21no—
193C2×C4×D11—21no—
194C2×C4×D11—21no—
195C2×C4×D11—21no—
196C2×C4×D11—21no—
197C2×C4×D11—21no—
198C2×C4×D11—21no—
199C2×C4×D11—42no—
200C2×C4×D11—81no—
201C2×C4×D11—81no—
202C2×C4×D11C22×C412yes—
203C2×C4×D11C22×C412yes—
204C2×C4×D11C2×D412yes—
205C2×C4×D11C2×D412yes—
206C2×Dic22—24no—
207C2×Dic22—21no—
208C2×Dic22—21no—
209C2×Dic22—21no—
210C2×Dic22—21no—
211C2×Dic22—21no—
212C2×Dic22—21no—
213C2×Dic22—21no—
214C2×Dic22—21no—
215C2×Dic22—21no—
216C2×Dic22—21no—
217C2×Dic22—44no—
218C2×Dic22—44no—
219C2×Dic22—41no—
220C2×Dic22—41no—
221C2×Dic22—42no—
222C2×Dic22—42no—
223C2×Dic22—44no—
224C2×Dic22—44no—
225C2×Dic22C22⋊C414yes—
226C2×Dic22C22×C412yes—
227C2×Dic22C22×C412yes—
228C2×C8×C11—21no—
229C2×C8×C11—21no—
230C2×C8×C11—21no—
231C2×C8×C11—21no—
232C2×C8×C11—21no—
233C2×C8×C11—21no—
234C11×C4⋊C4—21no—
235C11×C4⋊C4—21no—
236C11×C4⋊C4—21no—
237C11×C4⋊C4—21no—
238C11×C4⋊C4—21no—
239C11×C4⋊C4—21no—
240C11×C4⋊C4C22×C412yes—
241C11×C4⋊C4C22×C412yes—
242C11×C22⋊C4—24no—
243C11×C22⋊C4—81no—
244C42×C11—24no—
245C22⋊Dic11—81no—
246(C2×D11)⋊C4—24no—
247(C2×D11)⋊C4—24no—
248(C2×D11)⋊C4—24no—
249(C2×D11)⋊C4—24no—
250(C2×D11)⋊C4—42no—
251(C2×D11)⋊C4—81no—
252(C2×D11)⋊C4—81no—
253C4⋊Dic11—24no—
254C4⋊Dic11—24no—
255C4⋊Dic11—24no—
256C4⋊Dic11—24no—
257C4⋊Dic11—21no—
258C4⋊Dic11—21no—
259C4⋊Dic11—21no—
260C4⋊Dic11—21no—
261Dic11⋊C4—42no—
262C4×Dic11—42no—
263C2×C11⋊C8—21no—
264C2×C11⋊C8—21no—
265C2×C11⋊C8—21no—
266C2×C11⋊C8—21no—
267C2×C11⋊C8—21no—
268C2×C11⋊C8—21no—
269#4313—44no—
270C8×D11—44no—
271C2×#536—111no—
272C2×#408—111no—
273#2311—111no—
274#1894—111no—
275#1894—111no—
276#1892—111no—
277#1892—111no—
278#1873—111no—
279#1873—111no—
280#1872—111no—
281#1872—111no—
282#1825—111no—
283#1825D1111yescharacteristic, complemented
284#1787—111no—
285#1787—111no—
286C23×C11—21no—
287C23×C11—21no—
288C23×C11—21no—
289C23×C11—21no—
290C23×C11—21no—
291C23×C11—21no—
292C23×C11C2×C22⋊C412yes—
293C23×C11C22×D411yescharacteristic
294C22×D11—21no—
295C22×D11—21no—
296C22×D11—21no—
297C22×D11—21no—
298C22×D11—21no—
299C22×D11—21no—
300C22×D11—21no—
301C22×D11—21no—
302C22×D11—21no—
303C22×D11—21no—
304C22×D11—21no—
305C22×D11—21no—
306C22×D11C2×C22⋊C412yes—
307C22×D11C2×C22⋊C412yes—
308C2×C4×C11—21no—
309C2×C4×C11—21no—
310C2×C4×C11—22no—
311C2×C4×C11—22no—
312C2×C4×C11—22no—
313C2×C4×C11—22no—
314C2×C4×C11—22no—
315C2×C4×C11—22no—
316C2×C4×C11—41no—
317C2×C4×C11—41no—
318C2×C4×C11—41no—
319C2×C4×C11—41no—
320C2×C4×C11—41no—
321C2×C4×C11—41no—
322C2×C4×C11—41no—
323C2×C4×C11—41no—
324C2×C4×C11—41no—
325C2×C4×C11—41no—
326C2×C4×C11C2×C22⋊C412yes—
327C2×C4×C11C23×C411yescharacteristic
328C2×C4×C11C22×D411yescharacteristic
329C2×C4×C11H(5,𝔽2)11yescharacteristic
330C2×C4×C11H(5,𝔽2)11yescharacteristic
331C2×C4×C11H(5,𝔽2)11yescharacteristic
332C2×C4×C11H(5,𝔽2)11yescharacteristic
333C22⋊D11—44no—
334C22⋊D11—44no—
335C2×Dic11—21no—
336C2×Dic11—21no—
337C2×Dic11—21no—
338C2×Dic11—21no—
339C2×Dic11—22no—
340C2×Dic11—22no—
341C2×Dic11—48no—
342C2×Dic11—41no—
343C2×Dic11—41no—
344C2×Dic11—41no—
345C2×Dic11—41no—
346C2×Dic11—41no—
347C2×Dic11—41no—
348C2×Dic11—41no—
349C2×Dic11—41no—
350C2×Dic11—41no—
351C2×Dic11—41no—
352C2×Dic11C2×C22⋊C412yes—
353C2×Dic11C2×C22⋊C412yes—
354D44—44no—
355C4×D11—22no—
356C4×D11—22no—
357C4×D11—22no—
358C4×D11—22no—
359C4×D11—22no—
360C4×D11—22no—
361C4×D11—22no—
362C4×D11—22no—
363C4×D11—84no—
364Dic22—22no—
365Dic22—22no—
366Dic22—22no—
367Dic22—22no—
368Dic22—44no—
369Dic22—48no—
370Dic22—41no—
371Dic22—41no—
372Dic22—41no—
373Dic22—41no—
374C8×C11—41no—
375C8×C11—41no—
376C11⋊C8—41no—
377C11⋊C8—41no—
378C22×#41—111no—
379C23×Q8—111no—
380C22×M16—111no—
381C23×C8—111no—
382#536—118no—
383#536—224no—
384C2×C4⋊Q8—221no—
385C2×#124—221no—
386C2×#123—221no—
387C2×#123—221no—
388C2×C22⋊Q8—111no—
389C2×C22⋊Q8—111no—
390C2×C22⋊Q8—111no—
391C2×C22⋊Q8—111no—
392C2×#117—111no—
393C2×#117C2×D1111yescharacteristic
394C22×C4⋊C4—111no—
395C2×#103—111no—
396C2×#103—111no—
397C2×#103—111no—
398C2×#103—111no—
399C2×#103—111no—
400C2×#103—111no—
401C2×#103—111no—
402C2×#103—111no—
403#408—224no—
404C2×C22⋊C8—111no—
405C2×C22⋊C8—111no—
406C2×C22⋊C8—111no—
407C2×C22⋊C8C2×D1111yescharacteristic
408#391—221no—
409#390—221no—
410#386—221no—
411#386—221no—
412#380—111no—
413#380—111no—
414#380—111no—
415#380C2×D1111yescharacteristic
416#340—111no—
417#340—111no—
418#340—111no—
419#340—111no—
420#340C2×D1111yescharacteristic
421#340C2×D1111yescharacteristic
422#340C2×D1111yescharacteristic
423#340C2×D1111yescharacteristic
424C22×C11—22no—
425C22×C11—22no—
426C22×C11—22no—
427C22×C11—41no—
428C22×C11—41no—
429C22×C11—41no—
430C22×C11—41no—
431C22×C11C22×C22⋊C411yescharacteristic
432C22×C11#53411yescharacteristic
433C22×C11#53411yescharacteristic
434C22×C11#57711yescharacteristic
435C22×C11#57711yescharacteristic
436C22×C11#57811yescharacteristic
437C22×C11#57811yescharacteristic
438C2×D11—22no—
439C2×D11—22no—
440C2×D11—22no—
441C2×D11—22no—
442C2×D11—22no—
443C2×D11—22no—
444C2×D11—41no—
445C2×D11—41no—
446C2×D11—41no—
447C2×D11—41no—
448C2×D11—41no—
449C2×D11—41no—
450C2×D11—41no—
451C2×D11—41no—
452C4×C11—22no—
453C4×C11—42no—
454C4×C11—42no—
455C4×C11—81no—
456C4×C11—81no—
457C4×C11#51811yescharacteristic
458C4×C11#51811yescharacteristic
459C4×C11#53411yescharacteristic
460C4×C11#53411yescharacteristic
461Dic11—22no—
462Dic11—22no—
463Dic11—42no—
464Dic11—42no—
465Dic11—81no—
466Dic11—81no—
467C2×#41—114no—
468C2×#41—114no—
469C2×#41—441no—
470C2×#41—441no—
471C2×#41—441no—
472C2×#41—441no—
473C22×Q8—111no—
474C22×Q8—114no—
475C22×Q8—111no—
476C22×Q8—111no—
477C22×Q8—221no—
478C22×Q8—222no—
479C22×Q8—441no—
480C22×Q8—441no—
481C22×Q8—441no—
482C22×Q8—441no—
483C22×D4—111no—
484C22×D4—111no—
485C22×D4—111no—
486C23×C4—111no—
487C23×C4—111no—
488C23×C4—221no—
489C23×C4—221no—
490C23×C4C22×D1111yescharacteristic
491C2×M16—222no—
492C2×M16—441no—
493C2×M16—441no—
494C22×C8—111no—
495C22×C8—111no—
496C22×C8—222no—
497C22×C8—441no—
498C22×C8—441no—
499C22×C8C22×D1111yescharacteristic
500C22×C8C22×D1111yescharacteristic
501C4⋊Q8—228no—
502#124—228no—
503#123—228no—
504#123—228no—
505C22⋊Q8—114no—
506C22⋊Q8—114no—
507C22⋊Q8—114no—
508C22⋊Q8—114no—
509C22⋊Q8—222no—
510C22⋊Q8—222no—
511C22⋊Q8—222no—
512C22⋊Q8—222no—
513#117—22no—
514#117—441no—
515#117—441no—
516#117C4×D1114yescomplemented
517C2×C4⋊C4—111no—
518C2×C4⋊C4—111no—
519C2×C4⋊C4—221no—
520C2×C4⋊C4—221no—
521C2×C4⋊C4—221no—
522C2×C4⋊C4—221no—
523C2×C4⋊C4—221no—
524C2×C4⋊C4—441no—
525C2×C4⋊C4—441no—
526C2×C4⋊C4C22×D1111yescharacteristic
527C2×C4⋊C4C22×D1111yescharacteristic
528C2×C4⋊C4C22×D1111yescharacteristic
529C2×C4⋊C4C22×D1111yescharacteristic
530C2×C22⋊C4—21no—
531C2×C22⋊C4—21no—
532C2×C22⋊C4—221no—
533C2×C22⋊C4—221no—
534C2×C22⋊C4—221no—
535C2×C22⋊C4—221no—
536C2×C22⋊C4—221no—
537C2×C22⋊C4—221no—
538C2×C22⋊C4—221no—
539C2×C22⋊C4—221no—
540C2×C42—21no—
541C2×C42—221no—
542#103—441no—
543#103—441no—
544#103—441no—
545#103—441no—
546#103—441no—
547#103—441no—
548#103—441no—
549#103—441no—
550C22⋊C8—22no—
551C22⋊C8—222no—
552C22⋊C8—222no—
553C22⋊C8—222no—
554#95—21no—
555#95—221no—
556#95—221no—
557#95—221no—
558C2×C11—42no—
559C2×C11#230811yescharacteristic
560C2×C11#289811yescharacteristic
561C2×C11#289811yescharacteristic
562C2×C11#320011yescharacteristic
563C2×C11#320111yescharacteristic
564C2×C11#320111yescharacteristic
565C2×C11#320211yescharacteristic
566D11—42no—
567D11—42no—
568C24—111no—
569C24—111no—
570C24D4×D1111yescharacteristic
571#41—444no—
572#41—444no—
573#41—444no—
574#41—444no—
575C2×Q8—114no—
576C2×Q8—112no—
577C2×Q8—112no—
578C2×Q8—224no—
579C2×Q8—221no—
580C2×Q8—221no—
581C2×Q8—221no—
582C2×Q8—221no—
583C2×Q8—221no—
584C2×Q8—221no—
585C2×Q8—221no—
586C2×Q8—221no—
587C2×Q8—221no—
588C2×Q8—221no—
589C2×Q8—441no—
590C2×Q8—441no—
591C2×Q8—444no—
592C2×Q8—444no—
593C2×Q8—442no—
594C2×Q8—442no—
595C2×Q8—444no—
596C2×Q8—444no—
597C2×D4—114no—
598C2×D4—114no—
599C2×D4—114no—
600C2×D4—441no—
601C2×D4—441no—
602C2×D4—441no—
603C2×D4—441no—
604C2×D4—441no—
605C2×D4—441no—
606C22×C4—21no—
607C22×C4—21no—
608C22×C4—21no—
609C22×C4—21no—
610C22×C4—21no—
611C22×C4—21no—
612C22×C4—21no—
613C22×C4—21no—
614C22×C4—111no—
615C22×C4—111no—
616C22×C4—112no—
617C22×C4—112no—
618C22×C4—112no—
619C22×C4—112no—
620C22×C4—221no—
621C22×C4—221no—
622C22×C4—221no—
623C22×C4—221no—
624C22×C4—221no—
625C22×C4—221no—
626C22×C4—221no—
627C22×C4—221no—
628C22×C4—224no—
629C22×C4—221no—
630C22×C4—221no—
631C22×C4—221no—
632C22×C4—221no—
633C22×C4—442no—
634C22×C4—442no—
635C22×C4—442no—
636C22×C4—881no—
637C22×C4—881no—
638C22×C4C2×C4×D1112yes—
639C22×C4D4×D1111yescharacteristic
640C22×C4D4×D1112yes—
641C22×C4C23×D1111yescharacteristic
642M16—444no—
643C2×C8—21no—
644C2×C8—21no—
645C2×C8—21no—
646C2×C8—21no—
647C2×C8—21no—
648C2×C8—21no—
649C2×C8—221no—
650C2×C8—221no—
651C2×C8—221no—
652C2×C8—221no—
653C2×C8—221no—
654C2×C8—221no—
655C2×C8—444no—
656C4⋊C4—21no—
657C4⋊C4—21no—
658C4⋊C4—21no—
659C4⋊C4—21no—
660C4⋊C4—21no—
661C4⋊C4—21no—
662C4⋊C4—224no—
663C4⋊C4—224no—
664C4⋊C4—224no—
665C4⋊C4—224no—
666C4⋊C4—221no—
667C4⋊C4—221no—
668C4⋊C4—221no—
669C4⋊C4—221no—
670C4⋊C4—442no—
671C4⋊C4C2×C4×D1112yes—
672C4⋊C4C2×C4×D1112yes—
673C22⋊C4—24no—
674C22⋊C4—81no—
675C22⋊C4—224no—
676C22⋊C4—224no—
677C22⋊C4—224no—
678C22⋊C4—224no—
679C22⋊C4—442no—
680C22⋊C4—881no—
681C22⋊C4—881no—
682C22⋊C4—881no—
683C42—24no—
684C42—442no—
685C11#2177111yescharacteristic, complemented, Sylow
686C23—21no—
687C23—21no—
688C23—21no—
689C23—21no—
690C23—21no—
691C23—21no—
692C23—112no—
693C23—112no—
694C23—221no—
695C23—221no—
696C23—221no—
697C23—221no—
698C23—221no—
699C23—221no—
700C23—221no—
701C23—221no—
702C23—221no—
703C23—221no—
704C23—221no—
705C23—221no—
706C23C22⋊C4×D1112yes—
707C23C2×D4×D1111yescharacteristic
708Q8—222no—
709Q8—222no—
710Q8—222no—
711Q8—222no—
712Q8—444no—
713Q8—448no—
714Q8—441no—
715Q8—441no—
716Q8—441no—
717Q8—441no—
718D4—444no—
719D4—444no—
720D4—444no—
721C2×C4—21no—
722C2×C4—21no—
723C2×C4—22no—
724C2×C4—22no—
725C2×C4—22no—
726C2×C4—22no—
727C2×C4—22no—
728C2×C4—22no—
729C2×C4—41no—
730C2×C4—41no—
731C2×C4—41no—
732C2×C4—41no—
733C2×C4—41no—
734C2×C4—41no—
735C2×C4—41no—
736C2×C4—41no—
737C2×C4—41no—
738C2×C4—41no—
739C2×C4—112no—
740C2×C4—112no—
741C2×C4—221no—
742C2×C4—221no—
743C2×C4—221no—
744C2×C4—221no—
745C2×C4—222no—
746C2×C4—222no—
747C2×C4—222no—
748C2×C4—222no—
749C2×C4—222no—
750C2×C4—222no—
751C2×C4—222no—
752C2×C4—222no—
753C2×C4—222no—
754C2×C4—222no—
755C2×C4—448no—
756C2×C4—441no—
757C2×C4—441no—
758C2×C4—441no—
759C2×C4—441no—
760C2×C4—441no—
761C2×C4—441no—
762C2×C4—441no—
763C2×C4—441no—
764C2×C4—441no—
765C2×C4—441no—
766C2×C4—884no—
767C2×C4C22⋊C4×D1112yes—
768C2×C4C22×C4×D1111yescharacteristic
769C2×C4C2×D4×D1111yescharacteristic
770C2×C4#6704211yescharacteristic
771C2×C4#6704211yescharacteristic
772C2×C4#6704211yescharacteristic
773C2×C4#6704211yescharacteristic
774C8—41no—
775C8—41no—
776C8—441no—
777C8—441no—
778C22—22no—
779C22—22no—
780C22—22no—
781C22—41no—
782C22—41no—
783C22—41no—
784C22—41no—
785C22—222no—
786C22—222no—
787C22—222no—
788C22—222no—
789C22—222no—
790C22—222no—
791C22—441no—
792C22—441no—
793C22—441no—
794C22—441no—
795C22—441no—
796C22—441no—
797C22—441no—
798C22—441no—
799C22C2×C22⋊C4×D1111yescharacteristic
800C22#1062318411yescharacteristic
801C22#1062318411yescharacteristic
802C22#1062330111yescharacteristic
803C22#1062330211yescharacteristic
804C22#1062330611yescharacteristic
805C22#1062331011yescharacteristic
806C4—22no—
807C4—42no—
808C4—42no—
809C4—81no—
810C4—81no—
811C4—222no—
812C4—222no—
813C4—442no—
814C4—442no—
815C4—881no—
816C4—881no—
817C4#1062305211yescharacteristic
818C4#1062305211yescharacteristic
819C4#1062318411yescharacteristic
820C4#1062318411yescharacteristic
821C2—42no—
822C2—442no—
823C2—442no—
824C2#1307119311yescharacteristic
825C2#1307714511yescharacteristic
826C2#1307714711yescharacteristic
827C2#1307949011yescharacteristic
828C2#1307949611yescharacteristic
829C2#1307950411yescharacteristic
830C2#1307951011yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#1825C2
socleC23×C11C22×D4
prime radicalC22×#4339C22
cosocleC22×C4×C11C24
hypercenter#1825D11
hypocenterC11#21771
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1825

Complements

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

NH ≅ G/Ntype
4. #13069048C2semidirect
5. #13069048C2semidirect
6. #13069038C2semidirect
7. #13069038C2semidirect
8. #13068927C2semidirect
9. #13068927C2semidirect
10. #13068922C2semidirect
11. #13068922C2semidirect
12. #13068711C2semidirect
13. #13068552C2semidirect
14. #13068550C2semidirect
15. C11×#1825C2semidirect
22. #10623057C4semidirect
82. C22×Dic22C2×C4semidirect
89. C11×#117C2×C4semidirect
127. #66950C2×C4semidirect
128. #66950C2×C4semidirect
283. #1825D11semidirect
516. #117C4×D11semidirect
685. C11#21771semidirect

Maximal subgroups

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

subgroupindex
C2×#106230572
C2×#106223402
#130712052
#130690482
#130690382
#130689272
#130689222
#130687112
#130685522
#130685502
C11×#18252
#2177111