Finite Group Databasebeta

← #14800850

Subgroups — #14800850

Order 2816.

1292 conjugacy classes of subgroups.

The subgroup lattice has 860 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622655C211yesmaximal, characteristic, complemented
2C2×#10622831C211yesmaximal, characteristic, complemented
3C2×#10622624C211yesmaximal, characteristic, complemented
4C22×#66896C211yesmaximal, characteristic, complemented
5#13072067C211yesmaximal, characteristic, complemented
6#13070004C211yesmaximal, characteristic, complemented
7#13069933C211yesmaximal, characteristic, complemented
8#13069795C211yesmaximal, characteristic, complemented
9#13069619C211yesmaximal, characteristic, complemented
10#13069496C211yesmaximal, characteristic, complemented
11#13069316C211yesmaximal, characteristic, complemented
12#13069055C211yesmaximal, characteristic, complemented
13#13069037C211yesmaximal, characteristic, complemented
14#13068803C211yesmaximal, characteristic, complemented
15C11×#2408C211yesmaximal, characteristic
16C23×D4×C11C2211yescharacteristic
17C2×C11×#121C2211yescharacteristic
18C2×C11×#121C2211yescharacteristic
19C2×C11×#120—21no—
20C2×C4×D4×C11C2211yescharacteristic
21C22×#4324C2211yescharacteristic
22C22×#4324C2211yescharacteristic
23C22×C4⋊Dic11C2211yescharacteristic
24C2×#66977C2211yescharacteristic
25C2×#66977C2211yescharacteristic, complemented
26C22×#4318C2211yescharacteristic, complemented
27C23×C11⋊C8C2211yescharacteristic
28C11×#394—21no—
29C11×#392—21no—
30C11×#390C2211yescharacteristic
31C11×#390C2211yescharacteristic
32C11×#380C2211yescharacteristic
33C11×#379—21no—
34#10622833—21no—
35#10622831—24no—
36C2×#66896—24no—
37C2×#66896C2211yescharacteristic
38C2×#66896C2211yescharacteristic
39C2×#66896C2211yescharacteristic
40C2×#66896C2211yescharacteristic
41C2×#66896C2211yescharacteristic
42C2×#66896C2211yescharacteristic
43#10622825C2211yescharacteristic, complemented
44C2×C22⋊(C11⋊C8)C2211yescharacteristic
45C2×C22⋊(C11⋊C8)C2211yescharacteristic, complemented
46#10622655—24no—
47#10622624—24no—
48#10622597—21no—
49C2×#66874C2211yescharacteristic, complemented
50C2×#66874C2211yescharacteristic, complemented
51C2×#66871C2211yescharacteristic, complemented
52C2×#66871C2211yescharacteristic, complemented
53#10622561—21no—
54#10622555—21no—
55#10622542C2211yescharacteristic, complemented
56#10622541C2211yescharacteristic, complemented
57C2×C4⋊(C11⋊C8)C2211yescharacteristic, complemented
58C2×#66867C2211yescharacteristic, complemented
59#10622167C2211yescharacteristic, complemented
60#10622167C2211yescharacteristic, complemented
61#10622167C2211yescharacteristic, complemented
62#10622167C2211yescharacteristic, complemented
63C25×C11—21no—
64C22×D4×C11—22no—
65C22×D4×C11—22no—
66C22×D4×C11—21no—
67C22×D4×C11—21no—
68C22×D4×C11—22no—
69C22×D4×C11—21no—
70C22×D4×C11—22no—
71C22×D4×C11—41no—
72C22×D4×C11—41no—
73C22×D4×C11D411yescharacteristic
74C22×D4×C11C2311yescharacteristic
75C22×D4×C11C2311yescharacteristic
76C23×C4×C11C2311yescharacteristic
77C23×C4×C11C2311yescharacteristic
78C23×Dic11—21no—
79C22×Dic22C2311yescharacteristic
80C11×#121—22no—
81C11×#121—22no—
82C11×#121—41no—
83C11×#121—41no—
84C11×#120—44no—
85C4×D4×C11—22no—
86C4×D4×C11—22no—
87C2×C11×C4⋊C4D411yescharacteristic
88C2×C11×C4⋊C4C2311yescharacteristic
89C2×C11×C4⋊C4C2311yescharacteristic
90C2×C11×C22⋊C4—21no—
91C2×C11×C22⋊C4—21no—
92C2×C11×C22⋊C4—21no—
93C2×C11×C22⋊C4—21no—
94C2×C11×C22⋊C4—21no—
95C2×C11×C22⋊C4—21no—
96C2×C11×C22⋊C4—21no—
97C2×C11×C22⋊C4D411yescharacteristic
98C2×C11×C22⋊C4D411yescharacteristic
99C2×C42×C11C2311yescharacteristic
100C2×C22⋊Dic11—21no—
101C2×C22⋊Dic11—21no—
102C2×C22⋊Dic11—21no—
103C2×#4324—22no—
104C2×#4324—22no—
105C2×#4324—22no—
106C2×#4324—22no—
107C2×#4324—41no—
108C2×#4324—41no—
109C2×C4⋊Dic11—22no—
110C2×C4⋊Dic11—21no—
111C2×C4⋊Dic11—41no—
112C2×C4⋊Dic11C2311yescharacteristic
113C2×C4⋊Dic11C2311yescharacteristic
114C2×C4⋊Dic11C2311yescharacteristic
115#66977—22no—
116#66977—22no—
117#66977—22no—
118#66977—41no—
119C2×Dic11⋊C4—21no—
120C2×Dic11⋊C4—21no—
121C2×Dic11⋊C4—21no—
122C2×#4318—22no—
123C2×#4318—22no—
124C2×#4318—41no—
125C22×C11⋊C8—22no—
126C22×C11⋊C8—22no—
127C22×C11⋊C8—41no—
128C22×C11⋊C8C2311yescharacteristic
129C22×C11⋊C8C2311yescharacteristic
130C22×C11⋊C8C2311yescharacteristic
131C22×C11⋊C8C2311yescharacteristic
132C11×#95—21no—
133#66896—22no—
134#66896—22no—
135#66896—22no—
136#66896—22no—
137#66896—22no—
138#66896D414yescomplemented
139C11⋊#95—21no—
140C11⋊#95—21no—
141C11⋊#95—21no—
142C11⋊#95—21no—
143C22⋊(C11⋊C8)—22no—
144C22⋊(C11⋊C8)D414yescomplemented
145#66874—22no—
146#66874—41no—
147#66871—22no—
148#66871—41no—
149C4⋊(C11⋊C8)—22no—
150#66867—22no—
151#25128—111nomaximal, Sylow
152C24×C11—21no—
153C24×C11—21no—
154C24×C11—42no—
155C24×C11—42no—
156C24×C11—42no—
157C24×C11—42no—
158C24×C11—42no—
159C24×C11—81no—
160C24×C11—81no—
161C24×C11C2×D411yescharacteristic
162C24×C11C2×D411yescharacteristic
163C2×D4×C11—28no—
164C2×D4×C11—22no—
165C2×D4×C11—22no—
166C2×D4×C11—22no—
167C2×D4×C11—21no—
168C2×D4×C11—21no—
169C2×D4×C11—21no—
170C2×D4×C11—21no—
171C2×D4×C11—21no—
172C2×D4×C11—21no—
173C2×D4×C11—21no—
174C2×D4×C11—21no—
175C2×D4×C11—21no—
176C2×D4×C11—21no—
177C2×D4×C11—44no—
178C2×D4×C11—44no—
179C2×D4×C11—42no—
180C2×D4×C11—42no—
181C2×D4×C11—44no—
182C2×D4×C11—42no—
183C2×D4×C11—42no—
184C2×D4×C11—42no—
185C2×D4×C11—42no—
186C2×D4×C11—42no—
187C2×D4×C11—81no—
188C2×D4×C11—81no—
189C2×D4×C11C2×D412yes—
190C2×D4×C11#4112yes—
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×C11C2×D411yescharacteristic
204C22×C4×C11C2×D411yescharacteristic
205C22×C4×C11C2×D411yescharacteristic
206C22×C4×C11C2×D411yescharacteristic
207C22×C4×C11C2×D412yes—
208C22×C4×C11#4112yes—
209C22×C4×C11C2411yescharacteristic
210C22×Dic11—21no—
211C22×Dic11—21no—
212C22×Dic11—21no—
213C22×Dic11—21no—
214C22×Dic11—42no—
215C22×Dic11—42no—
216C22×Dic11—81no—
217C2×Dic22—21no—
218C2×Dic22—21no—
219C2×Dic22—21no—
220C2×Dic22—21no—
221C2×Dic22—21no—
222C2×Dic22—21no—
223C11×C4⋊C4—22no—
224C11×C4⋊C4—21no—
225C11×C4⋊C4—21no—
226C11×C4⋊C4—21no—
227C11×C4⋊C4—21no—
228C11×C22⋊C4—22no—
229C11×C22⋊C4—22no—
230C11×C22⋊C4—42no—
231C11×C22⋊C4—42no—
232C11×C22⋊C4—42no—
233C11×C22⋊C4—42no—
234C11×C22⋊C4—42no—
235C11×C22⋊C4—81no—
236C11×C22⋊C4—81no—
237C42×C11—21no—
238C42×C11—21no—
239C22⋊Dic11—42no—
240C22⋊Dic11—42no—
241C22⋊Dic11—81no—
242#4324—44no—
243#4324—44no—
244C4⋊Dic11—21no—
245C4⋊Dic11—21no—
246C4⋊Dic11—21no—
247C4⋊Dic11—21no—
248C4⋊Dic11—21no—
249C4⋊Dic11—42no—
250C4⋊Dic11C2×D412yes—
251Dic11⋊C4—42no—
252Dic11⋊C4—42no—
253Dic11⋊C4—81no—
254#4318—44no—
255C2×C11⋊C8—21no—
256C2×C11⋊C8—21no—
257C2×C11⋊C8—21no—
258C2×C11⋊C8—21no—
259C2×C11⋊C8—21no—
260C2×C11⋊C8—21no—
261C2×C11⋊C8—21no—
262C2×C11⋊C8—21no—
263C2×C11⋊C8—21no—
264C2×C11⋊C8—44no—
265C2×C11⋊C8C2×D412yes—
266C2×C11⋊C8C2×D412yes—
267C2×C11⋊C8C2×D412yes—
268C2×#468—111no—
269C2×#450—111no—
270C2×#435—111no—
271C22×#102—111no—
272#2417—111no—
273#2408D1111yescharacteristic
274#2067—111no—
275#2055—111no—
276#2033—111no—
277#2000—111no—
278#1973—111no—
279#1936—111no—
280#1895—111no—
281#1892—111no—
282#1852—111no—
283C23×C11—21no—
284C23×C11—21no—
285C23×C11—21no—
286C23×C11—21no—
287C23×C11—21no—
288C23×C11—21no—
289C23×C11—22no—
290C23×C11—22no—
291C23×C11—21no—
292C23×C11—21no—
293C23×C11—21no—
294C23×C11—21no—
295C23×C11—21no—
296C23×C11—48no—
297C23×C11—41no—
298C23×C11—41no—
299C23×C11—41no—
300C23×C11—41no—
301C23×C11—41no—
302C23×C11—41no—
303C23×C11—41no—
304C23×C11—41no—
305C23×C11—41no—
306C23×C11—41no—
307C23×C11—41no—
308C23×C11—41no—
309C23×C11—84no—
310C23×C11—84no—
311C23×C11—84no—
312C23×C11—84no—
313C23×C11—84no—
314C23×C11—84no—
315C23×C11#12112yes—
316C23×C11AGL(1,ℤ/8)12yes—
317C23×C11#13712yes—
318C23×C11C22×D411yescharacteristic
319D4×C11—22no—
320D4×C11—22no—
321D4×C11—22no—
322D4×C11—22no—
323D4×C11—48no—
324D4×C11—44no—
325D4×C11—41no—
326D4×C11—41no—
327D4×C11—41no—
328D4×C11—41no—
329D4×C11—84no—
330D4×C11—84no—
331C2×C4×C11—21no—
332C2×C4×C11—21no—
333C2×C4×C11—22no—
334C2×C4×C11—22no—
335C2×C4×C11—22no—
336C2×C4×C11—22no—
337C2×C4×C11—21no—
338C2×C4×C11—21no—
339C2×C4×C11—21no—
340C2×C4×C11—21no—
341C2×C4×C11—21no—
342C2×C4×C11—21no—
343C2×C4×C11—21no—
344C2×C4×C11—21no—
345C2×C4×C11—21no—
346C2×C4×C11—41no—
347C2×C4×C11—41no—
348C2×C4×C11—41no—
349C2×C4×C11—41no—
350C2×C4×C11—41no—
351C2×C4×C11—41no—
352C2×C4×C11—41no—
353C2×C4×C11—41no—
354C2×C4×C11—41no—
355C2×C4×C11—41no—
356C2×C4×C11#12112yes—
357C2×C4×C11C22×D411yescharacteristic
358C2×C4×C11C22×D411yescharacteristic
359C2×C4×C11C2×#4111yescharacteristic
360C2×C4×C11C2×#4111yescharacteristic
361C2×C4×C11H(5,𝔽2)11yescharacteristic
362C2×C4×C11H(5,𝔽2)11yescharacteristic
363C2×Dic11—22no—
364C2×Dic11—41no—
365C2×Dic11—41no—
366C2×Dic11—41no—
367C2×Dic11—41no—
368C2×Dic11—41no—
369C2×Dic11—41no—
370C2×Dic11—41no—
371C2×Dic11—41no—
372C2×Dic11—41no—
373C2×Dic11—41no—
374C2×Dic11—41no—
375C2×Dic11—84no—
376Dic22—41no—
377Dic22—41no—
378Dic22—41no—
379Dic22—41no—
380C11⋊C8—22no—
381C11⋊C8—22no—
382C11⋊C8—22no—
383C11⋊C8—41no—
384C23×D4C2×D1111yescharacteristic
385C22×SD16—111no—
386C22×SD16—111no—
387C22×M16—111no—
388C23×C8—111no—
389C2×C22⋊Q8—111no—
390C2×C22⋊Q8—111no—
391C2×#121C2×D1111yescharacteristic
392C2×#121C2×D1111yescharacteristic
393C2×#120—21no—
394C2×C4×D4C2×D1111yescharacteristic
395C22×C4⋊C4—111no—
396#468—224no—
397#450—224no—
398#435—224no—
399C2×#107—111no—
400C2×#107—111no—
401C2×C4⋊C8—111no—
402C2×#103—111no—
403C2×#103—111no—
404C2×#102—111no—
405C2×#102—111no—
406C2×#102—111no—
407C2×#102—111no—
408C2×#102—111no—
409C2×#102—111no—
410C2×#102—224no—
411C2×C22⋊C8—111no—
412C2×C22⋊C8—111no—
413C2×#97—111no—
414#398—221no—
415#396—221no—
416#394—21no—
417#392—21no—
418#391—111no—
419#390C2×D1111yescharacteristic
420#390C2×D1111yescharacteristic
421#389—111no—
422#386—221no—
423#380—111no—
424#380—221no—
425#380C2×D1111yescharacteristic
426#379—21no—
427#340—111no—
428#340—111no—
429#340—111no—
430#340—111no—
431C22×C11—22no—
432C22×C11—22no—
433C22×C11—22no—
434C22×C11—22no—
435C22×C11—22no—
436C22×C11—22no—
437C22×C11—41no—
438C22×C11—42no—
439C22×C11—42no—
440C22×C11—41no—
441C22×C11—42no—
442C22×C11—41no—
443C22×C11—42no—
444C22×C11—41no—
445C22×C11—41no—
446C22×C11—42no—
447C22×C11—41no—
448C22×C11—42no—
449C22×C11—41no—
450C22×C11—816no—
451C22×C11—81no—
452C22×C11—81no—
453C22×C11—81no—
454C22×C11—81no—
455C22×C11—81no—
456C22×C11—81no—
457C22×C11—81no—
458C22×C11—81no—
459C22×C11#46814yescomplemented
460C22×C11C2×#12111yescharacteristic
461C22×C11D4211yescharacteristic
462C22×C11#54611yescharacteristic
463C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
464C22×C11C2×#13711yescharacteristic
465C22×C11#57611yescharacteristic
466C22×C11#57711yescharacteristic
467C4×C11—22no—
468C4×C11—41no—
469C4×C11—41no—
470C4×C11—41no—
471C4×C11—81no—
472C4×C11—81no—
473C4×C11#52511yescharacteristic
474C4×C11#53811yescharacteristic
475C4×C11D4211yescharacteristic
476C4×C11#54611yescharacteristic
477Dic11—42no—
478Dic11—81no—
479Dic11—81no—
480Dic11—81no—
481C25—21no—
482C22×Q8—111no—
483C22×D4—22no—
484C22×D4—22no—
485C22×D4—21no—
486C22×D4—21no—
487C22×D4—22no—
488C22×D4—22no—
489C22×D4—21no—
490C22×D4—41no—
491C22×D4—41no—
492C22×D4C22⋊D1111yescharacteristic
493C22×D4C22×D1111yescharacteristic
494C22×D4C22×D1111yescharacteristic
495C23×C4—221no—
496C23×C4C22×D1111yescharacteristic
497C23×C4C22×D1111yescharacteristic
498C2×SD16—222no—
499C2×SD16—222no—
500C2×SD16—222no—
501C2×SD16—222no—
502C2×SD16—441no—
503C2×SD16—441no—
504C2×M16—222no—
505C2×M16—222no—
506C2×M16—441no—
507C22×C8—111no—
508C22×C8—111no—
509C22×C8—111no—
510C22×C8—111no—
511C22×C8—222no—
512C22×C8—222no—
513C22×C8—441no—
514C22⋊Q8—222no—
515C22⋊Q8—222no—
516C22⋊Q8—222no—
517C22⋊Q8—441no—
518#121—22no—
519#121—22no—
520#121—41no—
521#121—41no—
522#120—44no—
523C4×D4—22no—
524C4×D4—22no—
525C2×C4⋊C4—111no—
526C2×C4⋊C4—111no—
527C2×C4⋊C4—111no—
528C2×C4⋊C4—222no—
529C2×C4⋊C4—221no—
530C2×C4⋊C4—221no—
531C2×C4⋊C4—221no—
532C2×C4⋊C4—221no—
533C2×C4⋊C4—441no—
534C2×C4⋊C4C22⋊D1111yescharacteristic
535C2×C4⋊C4C22×D1111yescharacteristic
536C2×C4⋊C4C22×D1111yescharacteristic
537C2×C22⋊C4—21no—
538C2×C22⋊C4—21no—
539C2×C22⋊C4—21no—
540C2×C22⋊C4—21no—
541C2×C22⋊C4—21no—
542C2×C22⋊C4—21no—
543C2×C22⋊C4—21no—
544C2×C22⋊C4—221no—
545C2×C22⋊C4—221no—
546C2×C22⋊C4—221no—
547C2×C22⋊C4C22⋊D1111yescharacteristic
548C2×C22⋊C4C22⋊D1111yescharacteristic
549C2×C42C22×D1111yescharacteristic
550#107—222no—
551#107—441no—
552C4⋊C8—222no—
553#103—222no—
554#103—441no—
555#102—114no—
556#102—222no—
557#102—222no—
558#102—222no—
559#102—222no—
560#102—222no—
561C22⋊C8—114no—
562C22⋊C8—222no—
563#97—222no—
564#95—21no—
565#95—221no—
566#95—221no—
567#95—221no—
568#95—221no—
569C2×C11—24no—
570C2×C11—81no—
571C2×C11—82no—
572C2×C11—82no—
573C2×C11#242411yescharacteristic
574C2×C11C2×#46811yescharacteristic
575C2×C11#306211yescharacteristic
576C2×C11#326411yescharacteristic
577C2×C11#326611yescharacteristic
578C2×C11#331011yescharacteristic
579C2×C11#331411yescharacteristic
580C24—21no—
581C24—21no—
582C24—42no—
583C24—42no—
584C24—42no—
585C24—42no—
586C24—42no—
587C24—81no—
588C24—81no—
589C24C2×C22⋊D1111yescharacteristic
590C24C2×C22⋊D1111yescharacteristic
591C2×Q8—221no—
592C2×Q8—221no—
593C2×Q8—221no—
594C2×Q8—221no—
595C2×Q8—221no—
596C2×Q8—221no—
597C2×D4—28no—
598C2×D4—22no—
599C2×D4—22no—
600C2×D4—22no—
601C2×D4—21no—
602C2×D4—21no—
603C2×D4—21no—
604C2×D4—21no—
605C2×D4—21no—
606C2×D4—21no—
607C2×D4—21no—
608C2×D4—21no—
609C2×D4—21no—
610C2×D4—21no—
611C2×D4—44no—
612C2×D4—44no—
613C2×D4—42no—
614C2×D4—42no—
615C2×D4—44no—
616C2×D4—42no—
617C2×D4—42no—
618C2×D4—42no—
619C2×D4—42no—
620C2×D4—42no—
621C2×D4—81no—
622C2×D4—81no—
623C2×D4D4×D1112yes—
624C2×D4#434112yes—
625C22×C4—21no—
626C22×C4—21no—
627C22×C4—21no—
628C22×C4—21no—
629C22×C4—21no—
630C22×C4—21no—
631C22×C4—21no—
632C22×C4—21no—
633C22×C4—21no—
634C22×C4—21no—
635C22×C4—21no—
636C22×C4—21no—
637C22×C4—221no—
638C22×C4—221no—
639C22×C4—221no—
640C22×C4—221no—
641C22×C4—442no—
642C22×C4—442no—
643C22×C4—881no—
644C22×C4D4×D1112yes—
645C22×C4#434112yes—
646C22×C4C2×C22⋊D1111yescharacteristic
647C22×C4C2×C22⋊D1111yescharacteristic
648C22×C4C2×C22⋊D1111yescharacteristic
649C22×C4C2×C22⋊D1111yescharacteristic
650C22×C4C23×D1111yescharacteristic
651SD16—444no—
652SD16—444no—
653M16—444no—
654C2×C8—112no—
655C2×C8—112no—
656C2×C8—112no—
657C2×C8—221no—
658C2×C8—221no—
659C2×C8—221no—
660C2×C8—221no—
661C2×C8—221no—
662C2×C8—221no—
663C2×C8—221no—
664C2×C8—221no—
665C2×C8—221no—
666C2×C8—444no—
667C4⋊C4—22no—
668C4⋊C4—21no—
669C4⋊C4—21no—
670C4⋊C4—21no—
671C4⋊C4—21no—
672C4⋊C4—112no—
673C4⋊C4—221no—
674C4⋊C4—221no—
675C4⋊C4—221no—
676C4⋊C4—221no—
677C4⋊C4—221no—
678C4⋊C4—442no—
679C4⋊C4—442no—
680C4⋊C4—442no—
681C4⋊C4—881no—
682C22⋊C4—22no—
683C22⋊C4—22no—
684C22⋊C4—42no—
685C22⋊C4—42no—
686C22⋊C4—42no—
687C22⋊C4—42no—
688C22⋊C4—42no—
689C22⋊C4—81no—
690C22⋊C4—81no—
691C22⋊C4—442no—
692C22⋊C4—442no—
693C22⋊C4—881no—
694C42—21no—
695C42—21no—
696C11#2512811yescharacteristic, complemented, Sylow
697C23—21no—
698C23—21no—
699C23—21no—
700C23—21no—
701C23—21no—
702C23—22no—
703C23—21no—
704C23—21no—
705C23—22no—
706C23—21no—
707C23—21no—
708C23—21no—
709C23—21no—
710C23—48no—
711C23—41no—
712C23—41no—
713C23—41no—
714C23—41no—
715C23—41no—
716C23—41no—
717C23—41no—
718C23—41no—
719C23—41no—
720C23—41no—
721C23—41no—
722C23—41no—
723C23—84no—
724C23—84no—
725C23—84no—
726C23—84no—
727C23—84no—
728C23—84no—
729C23#6698512yes—
730C23#6699212yes—
731C23#6700412yes—
732C23C22×C22⋊D1111yescharacteristic
733Q8—441no—
734Q8—441no—
735Q8—441no—
736Q8—441no—
737D4—22no—
738D4—22no—
739D4—22no—
740D4—22no—
741D4—48no—
742D4—44no—
743D4—41no—
744D4—41no—
745D4—41no—
746D4—41no—
747D4—84no—
748D4—84no—
749C2×C4—21no—
750C2×C4—21no—
751C2×C4—22no—
752C2×C4—22no—
753C2×C4—22no—
754C2×C4—22no—
755C2×C4—21no—
756C2×C4—21no—
757C2×C4—21no—
758C2×C4—21no—
759C2×C4—21no—
760C2×C4—21no—
761C2×C4—21no—
762C2×C4—21no—
763C2×C4—21no—
764C2×C4—41no—
765C2×C4—41no—
766C2×C4—41no—
767C2×C4—41no—
768C2×C4—41no—
769C2×C4—41no—
770C2×C4—41no—
771C2×C4—41no—
772C2×C4—41no—
773C2×C4—41no—
774C2×C4—222no—
775C2×C4—441no—
776C2×C4—441no—
777C2×C4—441no—
778C2×C4—441no—
779C2×C4—441no—
780C2×C4—441no—
781C2×C4—441no—
782C2×C4—441no—
783C2×C4—441no—
784C2×C4—441no—
785C2×C4—441no—
786C2×C4—884no—
787C2×C4#6699212yes—
788C2×C4C2×D4×D1111yescharacteristic
789C2×C4C2×D4×D1111yescharacteristic
790C2×C4C2×#434111yescharacteristic
791C2×C4C2×#434111yescharacteristic
792C2×C4#6703711yescharacteristic
793C2×C4#6703711yescharacteristic
794C8—222no—
795C8—222no—
796C8—222no—
797C8—441no—
798C22—22no—
799C22—22no—
800C22—22no—
801C22—22no—
802C22—22no—
803C22—22no—
804C22—41no—
805C22—41no—
806C22—42no—
807C22—42no—
808C22—41no—
809C22—42no—
810C22—41no—
811C22—42no—
812C22—41no—
813C22—42no—
814C22—41no—
815C22—42no—
816C22—41no—
817C22—816no—
818C22—81no—
819C22—81no—
820C22—81no—
821C22—81no—
822C22—81no—
823C22—81no—
824C22—81no—
825C22—81no—
826C22#1062265514yescomplemented
827C22C2×#6698511yescharacteristic
828C22D4×C22⋊D1111yescharacteristic
829C22C2×#6699211yescharacteristic
830C22#1062333711yescharacteristic
831C22C2×#6700411yescharacteristic
832C22#1062336611yescharacteristic
833C22#1062336711yescharacteristic
834C4—22no—
835C4—41no—
836C4—41no—
837C4—41no—
838C4—81no—
839C4—81no—
840C4—442no—
841C4—881no—
842C4—881no—
843C4—881no—
844C4#1062311711yescharacteristic
845C4#1062312111yescharacteristic
846C4#1062312211yescharacteristic
847C4#1062312411yescharacteristic
848C2—24no—
849C2—81no—
850C2—82no—
851C2—82no—
852C2#1307215611yescharacteristic
853C2C2×#1062265511yescharacteristic
854C2#1307829211yescharacteristic
855C2#1308009211yescharacteristic
856C2#1308012211yescharacteristic
857C2#1308063711yescharacteristic
858C2#1308069711yescharacteristic
subgroupG/H
centerC23C22×C22⋊D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
Fitting, prime radicalC11×#2408C2
socleC23×C11C22×D4
hypercenter#2408D11
hypocenterC11#25128
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ #2408

Complements

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

NH ≅ G/Ntype
1. C2×#10622655C2semidirect
2. C2×#10622831C2semidirect
3. C2×#10622624C2semidirect
4. C22×#66896C2semidirect
5. #13072067C2semidirect
6. #13070004C2semidirect
7. #13069933C2semidirect
8. #13069795C2semidirect
9. #13069619C2semidirect
10. #13069496C2semidirect
11. #13069316C2semidirect
12. #13069055C2semidirect
13. #13069037C2semidirect
14. #13068803C2semidirect
25. C2×#66977C22semidirect
26. C22×#4318C22semidirect
43. #10622825C22semidirect
45. C2×C22⋊(C11⋊C8)C22semidirect
49. C2×#66874C22semidirect
50. C2×#66874C22semidirect
51. C2×#66871C22semidirect
52. C2×#66871C22semidirect
55. #10622542C22semidirect
56. #10622541C22semidirect
57. C2×C4⋊(C11⋊C8)C22semidirect
58. C2×#66867C22semidirect
59. #10622167C22semidirect
60. #10622167C22semidirect
61. #10622167C22semidirect
62. #10622167C22semidirect
138. #66896D4semidirect
144. C22⋊(C11⋊C8)D4semidirect
459. C22×C11#468semidirect
696. C11#25128semidirect
826. C22#10622655semidirect

Maximal subgroups

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

subgroupindex
C2×#106226552
C2×#106228312
C2×#106226242
C22×#668962
#130720672
#130700042
#130699332
#130697952
#130696192
#130694962
#130693162
#130690552
#130690372
#130688032
C11×#24082
#2512811