Finite Group Databasebeta

← #14800540

Subgroups — #14800540

Order 2816.

1388 conjugacy classes of subgroups.

The subgroup lattice has 900 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622728C211yesmaximal, characteristic, complemented
2C2×#10622345C211yesmaximal, characteristic, complemented
3C22×#66885C211yesmaximal, characteristic, complemented
4#13072056C211yesmaximal, characteristic, complemented
5#13071972C211yesmaximal, characteristic, complemented
6#13070003C211yesmaximal, characteristic, complemented
7#13069927C211yesmaximal, characteristic, complemented
8#13069799C211yesmaximal, characteristic, complemented
9#13069614C211yesmaximal, characteristic, complemented
10#13069482C211yesmaximal, characteristic, complemented
11#13069299C211yesmaximal, characteristic, complemented
12#13069044C211yesmaximal, characteristic, complemented
13#13069044C211yesmaximal, characteristic, complemented
14#13068806C211yesmaximal, characteristic, complemented
15C2×C8×D4×C11C211yesmaximal, characteristic, complemented
16C23×D44C2211yescharacteristic
17C23×C8×C11C2211yescharacteristic
18C23×C8×C11C2211yescharacteristic, complemented
19C2×C4×D4×C11C2211yescharacteristic
20C2×#66992—21no—
21C2×#66990—21no—
22C2×#66983C2211yescharacteristic
23C2×#66983C2211yescharacteristic
24C2×#66983C2211yescharacteristic
25C2×#66983C2211yescharacteristic, complemented
26C22×C4⋊Dic11C2211yescharacteristic
27C22×D88C2211yescharacteristic
28C22×D88C2211yescharacteristic
29C8×D4×C11—24no—
30C2×C11×C4⋊C8C2211yescharacteristic, complemented
31C2×C11×C22⋊C8C2211yescharacteristic
32C2×C11×C22⋊C8C2211yescharacteristic, complemented
33C2×C4×C8×C11C2211yescharacteristic, complemented
34#10622825C2211yescharacteristic
35#10622825C2211yescharacteristic, complemented
36#10622728—24no—
37C2×#66885—24no—
38C2×#66885C2211yescharacteristic
39C2×#66885C2211yescharacteristic
40C2×#66885C2211yescharacteristic
41C2×#66885C2211yescharacteristic
42C2×#66885C2211yescharacteristic
43C2×#66885C2211yescharacteristic
44C2×#66885C2211yescharacteristic, complemented
45C2×#66885C2211yescharacteristic, complemented
46C2×#66882C2211yescharacteristic, complemented
47C2×#66882C2211yescharacteristic, complemented
48#10622607—21no—
49#10622604—21no—
50#10622574—21no—
51#10622573—21no—
52#10622571—21no—
53#10622568—21no—
54#10622552C2211yescharacteristic
55#10622552C2211yescharacteristic
56#10622552C2211yescharacteristic, complemented
57#10622541C2211yescharacteristic, complemented
58#10622345—24no—
59#10622189C2211yescharacteristic, complemented
60#10622189C2211yescharacteristic, complemented
61#10622189C2211yescharacteristic, complemented
62#10622189C2211yescharacteristic, complemented
63C24×D11—21no—
64C22×D4×C11D411yescharacteristic
65C23×C4×C11C2311yescharacteristic
66C23×C4×C11C2311yescharacteristic
67C22×C22⋊D11—21no—
68C22×C22⋊D11—21no—
69C22×C22⋊D11—21no—
70C22×C22⋊D11—21no—
71C23×Dic11—21no—
72C22×D44—22no—
73C22×D44—22no—
74C22×D44—22no—
75C22×D44—22no—
76C22×D44—21no—
77C22×D44—41no—
78C22×D44—41no—
79C22×D44C2311yescharacteristic
80C22×D44C2311yescharacteristic
81C22×D44C2311yescharacteristic
82C22×C8×C11—22no—
83C22×C8×C11—22no—
84C22×C8×C11—22no—
85C22×C8×C11—22no—
86C22×C8×C11—41no—
87C22×C8×C11—41no—
88C22×C8×C11C2311yescharacteristic
89C22×C8×C11C2311yescharacteristic
90C22×C8×C11C2311yescharacteristic
91C22×C8×C11C2311yescharacteristic
92C4×D4×C11—22no—
93C4×D4×C11—22no—
94C2×C11×C4⋊C4D411yescharacteristic
95C2×C11×C22⋊C4D411yescharacteristic
96C2×C11×C22⋊C4D411yescharacteristic
97C2×C42×C11C2311yescharacteristic
98C2×C22⋊Dic11—21no—
99C2×C22⋊Dic11—21no—
100#66992—44no—
101#66990—44no—
102#66983—22no—
103#66983—22no—
104#66983—22no—
105#66983—22no—
106#66983—22no—
107#66983—41no—
108#66983—41no—
109#66983—41no—
110C2×(C2×D11)⋊C4—21no—
111C2×(C2×D11)⋊C4—21no—
112C2×(C2×D11)⋊C4—21no—
113C2×(C2×D11)⋊C4—21no—
114C2×(C2×D11)⋊C4—21no—
115C2×(C2×D11)⋊C4—21no—
116C2×(C2×D11)⋊C4—21no—
117C2×(C2×D11)⋊C4—21no—
118C2×(C2×D11)⋊C4—21no—
119C2×(C2×D11)⋊C4—21no—
120C2×C4⋊Dic11—22no—
121C2×C4⋊Dic11—21no—
122C2×C4⋊Dic11—41no—
123C2×C4⋊Dic11C2311yescharacteristic
124C2×C4⋊Dic11C2311yescharacteristic
125C2×C4⋊Dic11C2311yescharacteristic
126C2×C4⋊Dic11C2311yescharacteristic
127C2×C4⋊Dic11C2311yescharacteristic
128C2×Dic11⋊C4—21no—
129C2×D88—22no—
130C2×D88—22no—
131C2×D88—22no—
132C2×D88—22no—
133C2×D88—41no—
134C2×D88—41no—
135C11×C4⋊C8—22no—
136C11×C22⋊C8—22no—
137C11×C22⋊C8D414yescomplemented
138C4×C8×C11—22no—
139C11⋊#95—21no—
140C11⋊#95—21no—
141C11⋊#95—21no—
142#66885—22no—
143#66885—22no—
144#66885—22no—
145#66885—22no—
146#66885—22no—
147#66885—22no—
148#66885—41no—
149#66885D414yescomplemented
150#66882—22no—
151#66882—41no—
152#25108—111nomaximal, Sylow
153C24×C11C2×D411yescharacteristic
154C24×C11C2×D411yescharacteristic
155C23×D11—21no—
156C23×D11—21no—
157C23×D11—21no—
158C23×D11—42no—
159C23×D11—42no—
160C23×D11—42no—
161C23×D11—42no—
162C23×D11—42no—
163C23×D11—81no—
164C23×D11—81no—
165C2×D4×C11—22no—
166C2×D4×C11—22no—
167C2×D4×C11D814yescomplemented
168C22×C4×C11—21no—
169C22×C4×C11—21no—
170C22×C4×C11—21no—
171C22×C4×C11—21no—
172C22×C4×C11—21no—
173C22×C4×C11—21no—
174C22×C4×C11—21no—
175C22×C4×C11—21no—
176C22×C4×C11—21no—
177C22×C4×C11—21no—
178C22×C4×C11C2×D411yescharacteristic
179C22×C4×C11C2×D411yescharacteristic
180C22×C4×C11C2×D411yescharacteristic
181C22×C4×C11C2×D412yes—
182C22×C4×C11C2×D411yescharacteristic
183C22×C4×C11#4112yes—
184C22×C4×C11C2411yescharacteristic
185C2×C22⋊D11—42no—
186C2×C22⋊D11—42no—
187C2×C22⋊D11—42no—
188C2×C22⋊D11—42no—
189C2×C22⋊D11—42no—
190C2×C22⋊D11—42no—
191C2×C22⋊D11—42no—
192C2×C22⋊D11—42no—
193C2×C22⋊D11—42no—
194C2×C22⋊D11—81no—
195C2×C22⋊D11—81no—
196C2×C22⋊D11—81no—
197C22×Dic11—21no—
198C22×Dic11—21no—
199C22×Dic11—21no—
200C22×Dic11—21no—
201C22×Dic11—21no—
202C22×Dic11—42no—
203C22×Dic11—42no—
204C22×Dic11—81no—
205C2×D44—28no—
206C2×D44—21no—
207C2×D44—21no—
208C2×D44—21no—
209C2×D44—21no—
210C2×D44—21no—
211C2×D44—21no—
212C2×D44—21no—
213C2×D44—21no—
214C2×D44—21no—
215C2×D44—21no—
216C2×D44—21no—
217C2×D44—21no—
218C2×D44—21no—
219C2×D44—21no—
220C2×D44—21no—
221C2×D44—21no—
222C2×D44—42no—
223C2×D44—42no—
224C2×D44—44no—
225C2×D44—44no—
226C2×D44—44no—
227C2×D44—42no—
228C2×D44C2×D412yes—
229C2×D44#4112yes—
230C2×C8×C11—21no—
231C2×C8×C11—21no—
232C2×C8×C11—21no—
233C2×C8×C11—21no—
234C2×C8×C11—21no—
235C2×C8×C11—21no—
236C2×C8×C11—21no—
237C2×C8×C11—21no—
238C2×C8×C11—21no—
239C2×C8×C11—44no—
240C2×C8×C11—44no—
241C2×C8×C11C2×D412yes—
242C2×C8×C11C2×D412yes—
243C2×C8×C11C2×D412yes—
244C11×C4⋊C4—22no—
245C11×C22⋊C4—22no—
246C11×C22⋊C4—22no—
247C42×C11—21no—
248C42×C11—21no—
249C22⋊Dic11—42no—
250C22⋊Dic11—42no—
251(C2×D11)⋊C4—42no—
252(C2×D11)⋊C4—42no—
253(C2×D11)⋊C4—42no—
254(C2×D11)⋊C4—42no—
255(C2×D11)⋊C4—42no—
256(C2×D11)⋊C4—42no—
257(C2×D11)⋊C4—42no—
258(C2×D11)⋊C4—81no—
259(C2×D11)⋊C4—81no—
260(C2×D11)⋊C4—81no—
261C4⋊Dic11—21no—
262C4⋊Dic11—21no—
263C4⋊Dic11—21no—
264C4⋊Dic11—21no—
265C4⋊Dic11—21no—
266C4⋊Dic11—21no—
267C4⋊Dic11—21no—
268C4⋊Dic11—21no—
269C4⋊Dic11—21no—
270C4⋊Dic11—42no—
271C4⋊Dic11C2×D412yes—
272Dic11⋊C4—42no—
273D88—44no—
274D88—44no—
275C2×#466—111no—
276C2×#447—111no—
277C2×C8×D4D1111yescharacteristic, complemented
278C22×#102—111no—
279#2416—111no—
280#2408—111no—
281#2067—111no—
282#2054—111no—
283#2033—111no—
284#1999—111no—
285#1970—111no—
286#1934—111no—
287#1893—111no—
288#1893—111no—
289#1852—111no—
290C23×C11—21no—
291C23×C11—21no—
292C23×C11—21no—
293C23×C11—21no—
294C23×C11—21no—
295C23×C11—21no—
296C23×C11—21no—
297C23×C11—21no—
298C23×C11—21no—
299C23×C11—21no—
300C23×C11#12112yes—
301C23×C11C2×D812yes—
302C23×C11C2×D812yes—
303C23×C11#13512yes—
304C23×C11C22×D411yescharacteristic
305C22×D11—22no—
306C22×D11—22no—
307C22×D11—48no—
308C22×D11—41no—
309C22×D11—41no—
310C22×D11—41no—
311C22×D11—41no—
312C22×D11—41no—
313C22×D11—41no—
314C22×D11—41no—
315C22×D11—41no—
316C22×D11—41no—
317C22×D11—41no—
318C22×D11—41no—
319C22×D11—41no—
320C22×D11—41no—
321C22×D11—41no—
322C22×D11—41no—
323C22×D11—41no—
324C22×D11—41no—
325C22×D11—41no—
326C22×D11—41no—
327C22×D11—84no—
328C22×D11—84no—
329C22×D11—84no—
330C22×D11—84no—
331C22×D11—84no—
332C22×D11—84no—
333D4×C11—28no—
334C2×C4×C11—21no—
335C2×C4×C11—21no—
336C2×C4×C11—21no—
337C2×C4×C11—21no—
338C2×C4×C11—22no—
339C2×C4×C11—22no—
340C2×C4×C11—22no—
341C2×C4×C11—22no—
342C2×C4×C11—21no—
343C2×C4×C11—21no—
344C2×C4×C11—21no—
345C2×C4×C11—21no—
346C2×C4×C11—21no—
347C2×C4×C11—21no—
348C2×C4×C11—41no—
349C2×C4×C11—41no—
350C2×C4×C11—41no—
351C2×C4×C11—41no—
352C2×C4×C11#12112yes—
353C2×C4×C11C2×D812yes—
354C2×C4×C11C22×D411yescharacteristic
355C2×C4×C11C22×D411yescharacteristic
356C2×C4×C11C2×#4111yescharacteristic
357C2×C4×C11C2×#4111yescharacteristic
358C2×C4×C11H(5,𝔽2)11yescharacteristic
359C2×C4×C11H(5,𝔽2)11yescharacteristic
360C22⋊D11—84no—
361C22⋊D11—84no—
362C22⋊D11—84no—
363C22⋊D11—84no—
364C2×Dic11—22no—
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—41no—
376C2×Dic11—41no—
377C2×Dic11—41no—
378C2×Dic11—41no—
379C2×Dic11—84no—
380D44—22no—
381D44—22no—
382D44—22no—
383D44—22no—
384D44—48no—
385D44—41no—
386D44—41no—
387D44—41no—
388D44—41no—
389D44—41no—
390D44—41no—
391D44—41no—
392D44—41no—
393C8×C11—22no—
394C8×C11—22no—
395C8×C11—22no—
396C8×C11—41no—
397C23×D4—111no—
398C22×D8—111no—
399C22×D8—111no—
400C23×C8C2×D1111yescharacteristic
401C23×C8C2×D1111yescharacteristic, complemented
402C2×#121—111no—
403C2×#121—111no—
404C2×#121—111no—
405C2×#121—111no—
406C2×#121—221no—
407C2×#120—221no—
408C2×C4×D4C2×D1111yescharacteristic
409C22×C4⋊C4—111no—
410#466—224no—
411#447—224no—
412C8×D4—24no—
413C2×#107—111no—
414C2×#107—111no—
415C2×C4⋊C8C2×D1111yescharacteristic, complemented
416C2×#102—111no—
417C2×#102—111no—
418C2×#102—111no—
419C2×#102—111no—
420C2×#102—111no—
421C2×#102—111no—
422C2×#102—111no—
423C2×#102—111no—
424C2×#102—224no—
425C2×C22⋊C8C2×D1111yescharacteristic
426C2×C22⋊C8C2×D1111yescharacteristic, complemented
427C2×C4×C8C2×D1111yescharacteristic, complemented
428#396—221no—
429#394—221no—
430#394—221no—
431#392—221no—
432#390—111no—
433#390—111no—
434#390—111no—
435#389—111no—
436#386—221no—
437#380—111no—
438#380—111no—
439#379—221no—
440#340—111no—
441#340—111no—
442#340—111no—
443#340—111no—
444C22×C11—22no—
445C22×C11—22no—
446C22×C11—22no—
447C22×C11—22no—
448C22×C11—22no—
449C22×C11—22no—
450C22×C11—22no—
451C22×C11—22no—
452C22×C11—22no—
453C22×C11—41no—
454C22×C11—41no—
455C22×C11—41no—
456C22×C11—41no—
457C22×C11#46614yescomplemented
458C22×C11C2×#12111yescharacteristic
459C22×C11D4211yescharacteristic
460C22×C11#54611yescharacteristic
461C22×C11C22×D811yescharacteristic
462C22×C11C2×#13511yescharacteristic
463C22×C11#57611yescharacteristic
464C22×C11#57711yescharacteristic
465C2×D11—42no—
466C2×D11—42no—
467C2×D11—42no—
468C2×D11—42no—
469C2×D11—42no—
470C2×D11—42no—
471C2×D11—816no—
472C2×D11—81no—
473C2×D11—81no—
474C2×D11—81no—
475C2×D11—81no—
476C2×D11—81no—
477C2×D11—81no—
478C2×D11—81no—
479C2×D11—81no—
480C2×D11—81no—
481C2×D11—81no—
482C2×D11—81no—
483C2×D11—81no—
484C2×D11—81no—
485C2×D11—81no—
486C2×D11—81no—
487C4×C11—22no—
488C4×C11—22no—
489C4×C11—41no—
490C4×C11—41no—
491C4×C11#52511yescharacteristic
492C4×C11#53811yescharacteristic
493C4×C11D4211yescharacteristic
494C4×C11#54611yescharacteristic
495Dic11—42no—
496Dic11—81no—
497Dic11—81no—
498Dic11—81no—
499Dic11—81no—
500C25—221no—
501C22×D4—111no—
502C22×D4—111no—
503C22×D4—111no—
504C22×D4—222no—
505C22×D4—222no—
506C22×D4—221no—
507C22×D4—221no—
508C22×D4—221no—
509C22×D4—221no—
510C22×D4—221no—
511C22×D4—222no—
512C22×D4—222no—
513C22×D4—441no—
514C22×D4—441no—
515C22×D4D4411yescharacteristic
516C23×C4—221no—
517C23×C4C22×D1111yescharacteristic
518C23×C4C22×D1111yescharacteristic
519C2×D8—222no—
520C2×D8—222no—
521C2×D8—222no—
522C2×D8—222no—
523C2×D8—441no—
524C2×D8—441no—
525C22×C8—22no—
526C22×C8—22no—
527C22×C8—22no—
528C22×C8—22no—
529C22×C8—41no—
530C22×C8—41no—
531C22×C8C22×D1111yescharacteristic
532C22×C8C22×D1111yescharacteristic
533C22×C8C22×D1111yescharacteristic
534C22×C8C22×D1111yescharacteristic
535#121—222no—
536#121—222no—
537#121—222no—
538#121—222no—
539#121—222no—
540#121—441no—
541#121—441no—
542#121—441no—
543#121—444no—
544#120—444no—
545C4×D4—22no—
546C4×D4—22no—
547C2×C4⋊C4—111no—
548C2×C4⋊C4—111no—
549C2×C4⋊C4—111no—
550C2×C4⋊C4—111no—
551C2×C4⋊C4—111no—
552C2×C4⋊C4—222no—
553C2×C4⋊C4—221no—
554C2×C4⋊C4—221no—
555C2×C4⋊C4—441no—
556C2×C4⋊C4D4411yescharacteristic
557C2×C22⋊C4—221no—
558C2×C22⋊C4—221no—
559C2×C22⋊C4—221no—
560C2×C22⋊C4—221no—
561C2×C22⋊C4—221no—
562C2×C22⋊C4—221no—
563C2×C22⋊C4—221no—
564C2×C22⋊C4—221no—
565C2×C22⋊C4—221no—
566C2×C22⋊C4—221no—
567C2×C22⋊C4—221no—
568C2×C22⋊C4—221no—
569C2×C22⋊C4D4411yescharacteristic
570C2×C22⋊C4D4411yescharacteristic
571C2×C42C22×D1111yescharacteristic
572#107—222no—
573#107—441no—
574C4⋊C8—22no—
575#102—114no—
576#102—222no—
577#102—222no—
578#102—222no—
579#102—222no—
580#102—222no—
581#102—222no—
582#102—441no—
583C22⋊C8—22no—
584C22⋊C8C22⋊D1114yescomplemented
585C4×C8—22no—
586#95—221no—
587#95—221no—
588#95—221no—
589C2×C11—24no—
590C2×C11—42no—
591C2×C11#242411yescharacteristic
592C2×C11C2×#46611yescharacteristic
593C2×C11#306211yescharacteristic
594C2×C11D4×D811yescharacteristic
595C2×C11#328211yescharacteristic
596C2×C11#329411yescharacteristic
597C2×C11#329711yescharacteristic
598D11—82no—
599D11—82no—
600D11—161no—
601C24—221no—
602C24—221no—
603C24—221no—
604C24—442no—
605C24—442no—
606C24—442no—
607C24—442no—
608C24—442no—
609C24—881no—
610C24—881no—
611C24C2×D4411yescharacteristic
612C24C2×D4411yescharacteristic
613C2×D4—22no—
614C2×D4—22no—
615C2×D4—112no—
616C2×D4—112no—
617C2×D4—228no—
618C2×D4—221no—
619C2×D4—221no—
620C2×D4—221no—
621C2×D4—221no—
622C2×D4—221no—
623C2×D4—221no—
624C2×D4—221no—
625C2×D4—221no—
626C2×D4—221no—
627C2×D4—221no—
628C2×D4—221no—
629C2×D4—221no—
630C2×D4—221no—
631C2×D4—221no—
632C2×D4—221no—
633C2×D4—221no—
634C2×D4—444no—
635C2×D4—444no—
636C2×D4—442no—
637C2×D4—442no—
638C2×D4—444no—
639C2×D4—442no—
640C2×D4—442no—
641C2×D4—442no—
642C2×D4—442no—
643C2×D4—442no—
644C2×D4—442no—
645C2×D4—442no—
646C2×D4—442no—
647C2×D4—442no—
648C2×D4—442no—
649C2×D4—881no—
650C2×D4—881no—
651C2×D4—881no—
652C2×D4D8814yescomplemented
653C22×C4—21no—
654C22×C4—21no—
655C22×C4—21no—
656C22×C4—21no—
657C22×C4—21no—
658C22×C4—21no—
659C22×C4—21no—
660C22×C4—21no—
661C22×C4—21no—
662C22×C4—21no—
663C22×C4—221no—
664C22×C4—221no—
665C22×C4—221no—
666C22×C4—221no—
667C22×C4—221no—
668C22×C4—442no—
669C22×C4—442no—
670C22×C4—881no—
671C22×C4C2×D4411yescharacteristic
672C22×C4C2×D4411yescharacteristic
673C22×C4C2×D4411yescharacteristic
674C22×C4C2×D4411yescharacteristic
675C22×C4#433912yes—
676C22×C4C2×C22⋊D1112yes—
677C22×C4C23×D1111yescharacteristic
678D8—444no—
679D8—444no—
680C2×C8—21no—
681C2×C8—21no—
682C2×C8—21no—
683C2×C8—21no—
684C2×C8—21no—
685C2×C8—21no—
686C2×C8—21no—
687C2×C8—21no—
688C2×C8—21no—
689C2×C8—44no—
690C2×C8—44no—
691C2×C8D4×D1112yes—
692C2×C8C2×C22⋊D1112yes—
693C2×C8C2×C22⋊D1112yes—
694C4⋊C4—22no—
695C4⋊C4—112no—
696C4⋊C4—221no—
697C4⋊C4—221no—
698C4⋊C4—221no—
699C4⋊C4—221no—
700C4⋊C4—221no—
701C4⋊C4—221no—
702C4⋊C4—221no—
703C4⋊C4—221no—
704C4⋊C4—221no—
705C4⋊C4—442no—
706C4⋊C4—442no—
707C22⋊C4—22no—
708C22⋊C4—22no—
709C22⋊C4—442no—
710C22⋊C4—442no—
711C22⋊C4—442no—
712C22⋊C4—442no—
713C22⋊C4—442no—
714C22⋊C4—442no—
715C22⋊C4—442no—
716C22⋊C4—442no—
717C22⋊C4—442no—
718C22⋊C4—881no—
719C22⋊C4—881no—
720C22⋊C4—881no—
721C42—21no—
722C42—21no—
723C11#2510811yescharacteristic, complemented, Sylow
724C23—21no—
725C23—21no—
726C23—21no—
727C23—21no—
728C23—21no—
729C23—21no—
730C23—21no—
731C23—21no—
732C23—21no—
733C23—21no—
734C23—222no—
735C23—222no—
736C23—448no—
737C23—441no—
738C23—441no—
739C23—441no—
740C23—441no—
741C23—441no—
742C23—441no—
743C23—441no—
744C23—441no—
745C23—441no—
746C23—441no—
747C23—441no—
748C23—441no—
749C23—441no—
750C23—441no—
751C23—441no—
752C23—441no—
753C23—441no—
754C23—441no—
755C23—441no—
756C23—884no—
757C23—884no—
758C23—884no—
759C23—884no—
760C23—884no—
761C23—884no—
762C23C2×D8812yes—
763C23C2×D8812yes—
764C23#6695712yes—
765C23#6698312yes—
766C23C22×D4411yescharacteristic
767D4—28no—
768D4—222no—
769D4—222no—
770D4—222no—
771D4—222no—
772D4—448no—
773D4—441no—
774D4—441no—
775D4—441no—
776D4—441no—
777D4—441no—
778D4—441no—
779D4—441no—
780D4—441no—
781D4—884no—
782D4—884no—
783D4—884no—
784D4—884no—
785C2×C4—21no—
786C2×C4—21no—
787C2×C4—21no—
788C2×C4—21no—
789C2×C4—22no—
790C2×C4—22no—
791C2×C4—22no—
792C2×C4—22no—
793C2×C4—21no—
794C2×C4—21no—
795C2×C4—21no—
796C2×C4—21no—
797C2×C4—21no—
798C2×C4—21no—
799C2×C4—41no—
800C2×C4—41no—
801C2×C4—41no—
802C2×C4—41no—
803C2×C4—222no—
804C2×C4—441no—
805C2×C4—441no—
806C2×C4—441no—
807C2×C4—441no—
808C2×C4—441no—
809C2×C4—441no—
810C2×C4—441no—
811C2×C4—441no—
812C2×C4—441no—
813C2×C4—441no—
814C2×C4—441no—
815C2×C4—441no—
816C2×C4—441no—
817C2×C4—441no—
818C2×C4—884no—
819C2×C4C2×D8812yes—
820C2×C4#6698312yes—
821C2×C4C2×#433911yescharacteristic
822C2×C4C2×D4×D1111yescharacteristic
823C2×C4#6703711yescharacteristic
824C2×C4#41×D1111yescharacteristic
825C2×C4#6704211yescharacteristic
826C2×C4C22×C22⋊D1111yescharacteristic
827C8—22no—
828C8—22no—
829C8—22no—
830C8—41no—
831C22—22no—
832C22—22no—
833C22—22no—
834C22—22no—
835C22—22no—
836C22—22no—
837C22—22no—
838C22—22no—
839C22—22no—
840C22—41no—
841C22—41no—
842C22—41no—
843C22—41no—
844C22—442no—
845C22—442no—
846C22—442no—
847C22—442no—
848C22—442no—
849C22—442no—
850C22—8816no—
851C22—881no—
852C22—881no—
853C22—881no—
854C22—881no—
855C22—881no—
856C22—881no—
857C22—881no—
858C22—881no—
859C22—881no—
860C22—881no—
861C22—881no—
862C22—881no—
863C22—881no—
864C22—881no—
865C22—881no—
866C22#1062272814yescomplemented
867C22D4×D4411yescharacteristic
868C22#1062308511yescharacteristic
869C22C22×D8811yescharacteristic
870C22C2×#6695711yescharacteristic
871C22#1062328211yescharacteristic
872C22#1062328311yescharacteristic
873C22C2×#6698311yescharacteristic
874C4—22no—
875C4—22no—
876C4—41no—
877C4—41no—
878C4—442no—
879C4—881no—
880C4—881no—
881C4—881no—
882C4—881no—
883C4#1062307811yescharacteristic
884C4#1062309111yescharacteristic
885C4D4×C22⋊D1111yescharacteristic
886C4#1062336011yescharacteristic
887C2—24no—
888C2—42no—
889C2—882no—
890C2—882no—
891C2—1761no—
892C2#1307214611yescharacteristic
893C2C2×#1062272811yescharacteristic
894C2#1307829611yescharacteristic
895C2D4×D8811yescharacteristic
896C2#1308032811yescharacteristic
897C2#1308043011yescharacteristic
898C2#1308046811yescharacteristic
subgroupG/H
centerC23C22×D44
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC2×C8×D4×C11C2
socleC23×C11C22×D4
hypercenterC2×C8×D4D11
hypocenterC11#25108
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ C2×C8×D4

Complements

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

NH ≅ G/Ntype
1. C2×#10622728C2semidirect
2. C2×#10622345C2semidirect
3. C22×#66885C2semidirect
4. #13072056C2semidirect
5. #13071972C2semidirect
6. #13070003C2semidirect
7. #13069927C2semidirect
8. #13069799C2semidirect
9. #13069614C2semidirect
10. #13069482C2semidirect
11. #13069299C2semidirect
12. #13069044C2semidirect
13. #13069044C2semidirect
14. #13068806C2semidirect
15. C2×C8×D4×C11C2semidirect
18. C23×C8×C11C22semidirect
25. C2×#66983C22semidirect
30. C2×C11×C4⋊C8C22semidirect
32. C2×C11×C22⋊C8C22semidirect
33. C2×C4×C8×C11C22semidirect
35. #10622825C22semidirect
44. C2×#66885C22semidirect
45. C2×#66885C22semidirect
46. C2×#66882C22semidirect
47. C2×#66882C22semidirect
56. #10622552C22semidirect
57. #10622541C22semidirect
59. #10622189C22semidirect
60. #10622189C22semidirect
61. #10622189C22semidirect
62. #10622189C22semidirect
137. C11×C22⋊C8D4semidirect
149. #66885D4semidirect
167. C2×D4×C11D8semidirect
277. C2×C8×D4D11semidirect
401. C23×C8C2×D11semidirect
415. C2×C4⋊C8C2×D11semidirect
426. C2×C22⋊C8C2×D11semidirect
427. C2×C4×C8C2×D11semidirect
457. C22×C11#466semidirect
584. C22⋊C8C22⋊D11semidirect
652. C2×D4D88semidirect
723. C11#25108semidirect
866. C22#10622728semidirect

Maximal subgroups

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

subgroupindex
C2×#106227282
C2×#106223452
C22×#668852
#130720562
#130719722
#130700032
#130699272
#130697992
#130696142
#130694822
#130692992
#130690442
#130688062
C2×C8×D4×C112
#2510811