Finite Group Databasebeta

← #14769558

Subgroups — #14769558

Order 2816.

1622 conjugacy classes of subgroups.

The subgroup lattice has 884 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#66961C211yesmaximal, characteristic
2C2×#10622323C211yesmaximal, characteristic, complemented
3C2×C4×#4314C211yesmaximal, characteristic, complemented
4#13071456C211yesmaximal, characteristic, complemented
5C22⋊C4×D44C211yesmaximal, characteristic, complemented
6#13069492C211yesmaximal, characteristic, complemented
7#13069482C211yesmaximal, characteristic, complemented
8#13068970C211yesmaximal, characteristic, complemented
9#13068970C211yesmaximal, characteristic, complemented
10#13068963C211yesmaximal, characteristic, complemented
11#13068963C211yesmaximal, characteristic, complemented
12#13068649C211yesmaximal, characteristic, complemented
13#13068557C211yesmaximal, characteristic, complemented
14#13068548C211yesmaximal, characteristic, complemented
15C11×#1753C211yesmaximal, characteristic, complemented
16C22×#4339C2211yescharacteristic
17C23×D44C2211yescharacteristic
18C22×C11×M16C2211yescharacteristic
19C2×#66961—24no—
20C2×#66961—24no—
21C2×#66961C418yescomplemented
22C22×D88C2211yescharacteristic
23C22×D88C2211yescharacteristic
24C22×#4314C2211yescharacteristic
25C22×#4314C2211yescharacteristic
26C2×C22⋊C4×D11—21no—
27C2×C4×D44C2211yescharacteristic
28C2×C4×D44C2211yescharacteristic
29C2×C4×Dic22C2211yescharacteristic, complemented
30C2×C4×Dic22C2211yescharacteristic, complemented
31C2×C11×C22⋊C8C2211yescharacteristic
32C2×C11×#97C2211yescharacteristic, complemented
33C2×C4×C8×C11C2211yescharacteristic, complemented
34C4×C11×C22⋊C4C2211yescharacteristic
35#10622825C2211yescharacteristic
36#10622825C2211yescharacteristic
37C2×#66885C2211yescharacteristic
38C2×#66885C2211yescharacteristic
39C2×#66885C2211yescharacteristic
40C2×#66885C2211yescharacteristic
41C2×#66885C2211yescharacteristic, complemented
42C2×#66885C2211yescharacteristic, complemented
43C2×#66882C2211yescharacteristic, complemented
44C2×#66881C2211yescharacteristic, complemented
45C2×#66880C2211yescharacteristic, complemented
46C2×#66880C2211yescharacteristic, complemented
47#10622570—21no—
48#10622570—21no—
49#10622568—21no—
50#10622552C2211yescharacteristic
51#10622552C2211yescharacteristic
52#10622552C2211yescharacteristic, complemented
53#10622552C2211yescharacteristic, complemented
54#10622323—24no—
55C4×#4314—24no—
56#10622280—21no—
57#10622279—21no—
58#10622278—21no—
59#10622278—21no—
60C11×#336C2211yescharacteristic, complemented
61C11×#336C2211yescharacteristic, complemented
62#10622189C2211yescharacteristic, complemented
63#10622189C2211yescharacteristic, complemented
64C24×D11—21no—
65C23×C4×C11C2311yescharacteristic
66C22×C22⋊D11—21no—
67C2×#4339—22no—
68C2×#4339—22no—
69C2×#4339—22no—
70C2×#4339—41no—
71C2×#4339—41no—
72C2×#4339C2×C414yescomplemented
73C22×D44—22no—
74C22×D44—22no—
75C22×D44—21no—
76C22×D44—22no—
77C22×D44—41no—
78C22×D44—41no—
79C22×D44C2×C414yes—
80C22×D44C2311yescharacteristic
81C22×D44C2311yescharacteristic
82C22×D44C2311yescharacteristic
83C22×C4×D11—21no—
84C22×C4×D11—21no—
85C22×C4×D11—21no—
86C22×Dic22C2311yescharacteristic
87C2×C11×M16—22no—
88C2×C11×M16—22no—
89C2×C11×M16C2×C414yescomplemented
90C22×C8×C11C2311yescharacteristic
91C22×C8×C11C2311yescharacteristic
92C22×C8×C11C2311yescharacteristic
93C22×C8×C11C2311yescharacteristic
94C2×C11×C22⋊C4D411yescharacteristic
95C2×C11×C22⋊C4D411yescharacteristic
96C2×C42×C11C2311yescharacteristic
97C2×C42×C11C2311yescharacteristic
98C2×C22⋊Dic11—21no—
99C2×C22⋊Dic11—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×(C2×D11)⋊C4—21no—
106C2×(C2×D11)⋊C4—21no—
107C2×(C2×D11)⋊C4—21no—
108C2×(C2×D11)⋊C4—21no—
109C2×(C2×D11)⋊C4—21no—
110C2×C4⋊Dic11C2311yescharacteristic
111C2×C4⋊Dic11C2311yescharacteristic
112C2×C4⋊Dic11C2311yescharacteristic
113C2×C4⋊Dic11C2311yescharacteristic
114C2×Dic11⋊C4—21no—
115C2×Dic11⋊C4—21no—
116C2×C4×Dic11—21no—
117C2×C4×Dic11—21no—
118#66961—232no—
119C2×D88—22no—
120C2×D88—22no—
121C2×D88—22no—
122C2×D88—22no—
123C2×D88C2×C414yes—
124C2×D88C2×C414yescomplemented
125C2×#4314—22no—
126C2×#4314—22no—
127C2×#4314C2×C414yes—
128C2×#4314C2×C414yescomplemented
129C2×#4314D414yes—
130C2×#4314D414yes—
131C22⋊C4×D11—44no—
132C4×D44—22no—
133C4×D44—22no—
134C4×D44—41no—
135C4×D44—41no—
136C4×Dic22—22no—
137C4×Dic22—22no—
138C4×Dic22—41no—
139C4×Dic22—41no—
140C11×C22⋊C8—22no—
141C11×#97—22no—
142C4×C8×C11—22no—
143C11×#95D411yescharacteristic
144C11×#95D411yescharacteristic
145C11⋊#95—21no—
146C11⋊#95—21no—
147#66885—22no—
148#66885—22no—
149#66885—41no—
150#66885—41no—
151#66885—41no—
152#66885—41no—
153#66882—22no—
154#66881—22no—
155#66880—22no—
156#66880—22no—
157#22443—111nomaximal, Sylow
158C24×C11C2×D411yescharacteristic
159C23×D11—21no—
160C23×D11—21no—
161C23×D11—21no—
162C23×D11—24no—
163C23×D11—42no—
164C23×D11—42no—
165C23×D11—42no—
166C23×D11—42no—
167C23×D11—81no—
168C23×D11—81no—
169C22×C4×C11—21no—
170C22×C4×C11—21no—
171C22×C4×C11—21no—
172C22×C4×C11—21no—
173C22×C4×C11C22×C412yes—
174C22×C4×C11C2×D411yescharacteristic
175C22×C4×C11C2×D411yescharacteristic
176C22×C4×C11C2×D411yescharacteristic
177C22×C4×C11C2×D411yescharacteristic
178C22×C4×C11C2×D411yescharacteristic
179C22×C4×C11#4112yes—
180C22×C4×C11C2411yescharacteristic
181C2×C22⋊D11—24no—
182C2×C22⋊D11—42no—
183C2×C22⋊D11—42no—
184C22×Dic11—21no—
185C22×Dic11—21no—
186C22×Dic11—21no—
187C22×Dic11—21no—
188C22×Dic11—21no—
189#4339—28no—
190#4339—44no—
191#4339—44no—
192#4339—44no—
193C2×D44—28no—
194C2×D44—24no—
195C2×D44—21no—
196C2×D44—21no—
197C2×D44—21no—
198C2×D44—21no—
199C2×D44—21no—
200C2×D44—21no—
201C2×D44—21no—
202C2×D44—21no—
203C2×D44—21no—
204C2×D44—21no—
205C2×D44—21no—
206C2×D44—21no—
207C2×D44—21no—
208C2×D44—42no—
209C2×D44—42no—
210C2×D44—44no—
211C2×D44—44no—
212C2×D44—44no—
213C2×D44C22×C412yes—
214C2×D44C22×C412yes—
215C2×D44C22×C412yes—
216C2×D44C2×D412yes—
217C2×D44C2×D412yes—
218C2×C4×D11—24no—
219C2×C4×D11—42no—
220C2×C4×D11—42no—
221C2×C4×D11—42no—
222C2×C4×D11—42no—
223C2×C4×D11—42no—
224C2×C4×D11—42no—
225C2×C4×D11—81no—
226C2×C4×D11—81no—
227C2×Dic22—21no—
228C2×Dic22—21no—
229C2×Dic22—21no—
230C2×Dic22C22×C412yes—
231C2×Dic22C2×D412yes—
232C2×Dic22C2×D412yes—
233C11×M16—28no—
234C2×C8×C11—21no—
235C2×C8×C11—21no—
236C2×C8×C11—21no—
237C2×C8×C11—21no—
238C2×C8×C11—21no—
239C2×C8×C11—21no—
240C2×C8×C11—21no—
241C2×C8×C11—21no—
242C2×C8×C11C22×C412yes—
243C2×C8×C11C22×C412yes—
244C2×C8×C11C2×D412yes—
245C2×C8×C11C2×D412yes—
246C11×C22⋊C4—22no—
247C11×C22⋊C4—41no—
248C42×C11—21no—
249C42×C11—21no—
250C42×C11—21no—
251C42×C11—21no—
252C22⋊Dic11—42no—
253C22⋊Dic11—81no—
254(C2×D11)⋊C4—42no—
255(C2×D11)⋊C4—42no—
256(C2×D11)⋊C4—42no—
257(C2×D11)⋊C4—42no—
258(C2×D11)⋊C4—42no—
259(C2×D11)⋊C4—42no—
260(C2×D11)⋊C4—81no—
261(C2×D11)⋊C4—81no—
262(C2×D11)⋊C4—81no—
263(C2×D11)⋊C4—81no—
264C4⋊Dic11—21no—
265C4⋊Dic11—21no—
266C4⋊Dic11—21no—
267C4⋊Dic11—21no—
268C4⋊Dic11—21no—
269C4⋊Dic11—21no—
270C4⋊Dic11—21no—
271C4⋊Dic11—21no—
272Dic11⋊C4—42no—
273Dic11⋊C4—42no—
274C4×Dic11—42no—
275C4×Dic11—42no—
276D88—28no—
277D88—28no—
278#4314—28no—
279#4314C22⋊C4116yescomplemented
280C22×AGL(1,ℤ/8)—111no—
281C2×#440—111no—
282C2×C4×SD16—111no—
283#2341—111no—
284D4×C22⋊C4—111no—
285#1972—111no—
286#1970—111no—
287#1880—111no—
288#1880—111no—
289#1879—111no—
290#1879—111no—
291#1809—111no—
292#1788—111no—
293#1786—111no—
294#1753D1111yescharacteristic, complemented
295C23×C11—21no—
296C23×C11—21no—
297C23×C11—21no—
298C23×C11—21no—
299C23×C11—21no—
300C23×C11—21no—
301C23×C11C4×D412yes—
302C23×C11C22×D411yescharacteristic
303C22×D11—22no—
304C22×D11—22no—
305C22×D11—22no—
306C22×D11—22no—
307C22×D11—22no—
308C22×D11—48no—
309C22×D11—41no—
310C22×D11—41no—
311C22×D11—41no—
312C22×D11—41no—
313C22×D11—48no—
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—84no—
327C22×D11—84no—
328C22×D11—84no—
329C22×D11—84no—
330C22×D11—84no—
331C2×C4×C11—21no—
332C2×C4×C11—21no—
333C2×C4×C11—21no—
334C2×C4×C11—21no—
335C2×C4×C11—22no—
336C2×C4×C11—22no—
337C2×C4×C11—22no—
338C2×C4×C11—22no—
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—21no—
347C2×C4×C11—21no—
348C2×C4×C11C4×D412yes—
349C2×C4×C11AGL(1,ℤ/8)12yescomplemented
350C2×C4×C11C23×C411yescharacteristic
351C2×C4×C11C22×D411yescharacteristic
352C2×C4×C11C22×D411yescharacteristic
353C2×C4×C11C2×#4111yescharacteristic
354C2×C4×C11H(5,𝔽2)11yescharacteristic
355C2×C4×C11H(5,𝔽2)11yescharacteristic
356C22⋊D11—48no—
357C2×Dic11—22no—
358C2×Dic11—22no—
359C2×Dic11—22no—
360C2×Dic11—41no—
361C2×Dic11—41no—
362C2×Dic11—41no—
363C2×Dic11—41no—
364C2×Dic11—41no—
365C2×Dic11—41no—
366C2×Dic11—41no—
367C2×Dic11—41no—
368C2×Dic11—41no—
369C2×Dic11—41no—
370C2×Dic11—41no—
371C2×Dic11—41no—
372D44—22no—
373D44—22no—
374D44—22no—
375D44—22no—
376D44—22no—
377D44—22no—
378D44—22no—
379D44—48no—
380D44—41no—
381D44—41no—
382D44—41no—
383D44—41no—
384D44C2×C22⋊C414yes—
385C4×D11—48no—
386C4×D11—84no—
387C4×D11—84no—
388Dic22—22no—
389Dic22—22no—
390Dic22—22no—
391Dic22C2×C22⋊C414yescomplemented
392C8×C11—22no—
393C8×C11—41no—
394C8×C11—41no—
395C8×C11C2×C22⋊C414yescomplemented
396C22×#41—111no—
397C23×D4—111no—
398C2×AGL(1,ℤ/8)—118no—
399C2×AGL(1,ℤ/8)—224no—
400C2×AGL(1,ℤ/8)—224no—
401C22×SD16—111no—
402C22×SD16—111no—
403C22×D8—111no—
404C22×D8—111no—
405C22×M16C2×D1111yescharacteristic
406C2×C4×Q8—111no—
407C2×C4×Q8—111no—
408C2×C4×D4—111no—
409C2×C4×D4—111no—
410C22×C22⋊C4—221no—
411#440—224no—
412C4×SD16—224no—
413C2×#107—111no—
414C2×#106—111no—
415C2×#103—111no—
416C2×#103—111no—
417C2×#102—111no—
418C2×#102—111no—
419C2×#102—111no—
420C2×#102—111no—
421C2×#102—111no—
422C2×#102—111no—
423C2×C22⋊C8C2×D1111yescharacteristic
424C2×#97C2×D1111yescharacteristic, complemented
425C2×C4×C8C2×D1111yescharacteristic, complemented
426#390—111no—
427#390—111no—
428#390—111no—
429#390—111no—
430#390—221no—
431#390—221no—
432#386—221no—
433#386—221no—
434#380—111no—
435#380—111no—
436#380—221no—
437#379—221no—
438C4×C22⋊C4—221no—
439C4×C22⋊C4C2×D1111yescharacteristic
440#340—111no—
441#340—111no—
442#336C2×D1111yescharacteristic, complemented
443#336C2×D1111yescharacteristic, complemented
444C22×C11—22no—
445C22×C11—22no—
446C22×C11—22no—
447C22×C11—41no—
448C22×C11—41no—
449C22×C11—41no—
450C22×C11—41no—
451C22×C11C2×C4×D411yescharacteristic
452C22×C11D4211yescharacteristic
453C22×C11D4211yescharacteristic
454C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
455C22×C11#57511yescharacteristic
456C22×C11#57611yescharacteristic
457C22×C11#57711yescharacteristic
458C2×D11—24no—
459C2×D11—42no—
460C2×D11—42no—
461C2×D11—42no—
462C2×D11—42no—
463C2×D11—42no—
464C2×D11—42no—
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—
480C4×C11—22no—
481C4×C11—22no—
482C4×C11—41no—
483C4×C11—41no—
484C4×C11—41no—
485C4×C11C22×C22⋊C411yescharacteristic
486C4×C11#51811yescharacteristic
487C4×C11#54611yescharacteristic
488C4×C11#54611yescharacteristic
489Dic11—24no—
490Dic11—81no—
491Dic11—81no—
492Dic11—81no—
493Dic11—81no—
494C25—221no—
495C2×#41—114no—
496C2×#41—222no—
497C2×#41—222no—
498C2×#41—222no—
499C2×#41—441no—
500C2×#41—441no—
501C22×Q8—111no—
502C22×D4—114no—
503C22×D4—111no—
504C22×D4—111no—
505C22×D4—111no—
506C22×D4—222no—
507C22×D4—222no—
508C22×D4—221no—
509C22×D4—221no—
510C22×D4—222no—
511C22×D4—441no—
512C22×D4—441no—
513C23×C4—221no—
514C23×C4—221no—
515C23×C4—221no—
516C23×C4C22×D1111yescharacteristic
517AGL(1,ℤ/8)—2232no—
518C2×SD16—114no—
519C2×SD16—114no—
520C2×SD16—114no—
521C2×SD16—114no—
522C2×SD16—222no—
523C2×SD16—222no—
524C2×D8—114no—
525C2×D8—114no—
526C2×D8—222no—
527C2×D8—222no—
528C2×D8—222no—
529C2×D8—222no—
530C2×M16—22no—
531C2×M16—22no—
532C2×M16C4×D1114yescomplemented
533C22×C8C22×D1111yescharacteristic
534C22×C8C22×D1111yescharacteristic
535C22×C8C22×D1111yescharacteristic
536C22×C8C22×D1111yescharacteristic
537C4×Q8—222no—
538C4×Q8—222no—
539C4×Q8—441no—
540C4×Q8—441no—
541C4×D4—222no—
542C4×D4—222no—
543C4×D4—441no—
544C4×D4—441no—
545C2×C4⋊C4—111no—
546C2×C4⋊C4—111no—
547C2×C4⋊C4—111no—
548C2×C4⋊C4—111no—
549C2×C4⋊C4—221no—
550C2×C4⋊C4—221no—
551C2×C22⋊C4—221no—
552C2×C22⋊C4—221no—
553C2×C22⋊C4—221no—
554C2×C22⋊C4—221no—
555C2×C22⋊C4—221no—
556C2×C22⋊C4—221no—
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—444no—
564C2×C22⋊C4D4411yescharacteristic
565C2×C22⋊C4D4411yescharacteristic
566C2×C42—221no—
567C2×C42—221no—
568C2×C42C22×D1111yescharacteristic
569C2×C42C22×D1111yescharacteristic
570#107—222no—
571#106—222no—
572#103—222no—
573#103—222no—
574#102—222no—
575#102—222no—
576#102—441no—
577#102—441no—
578#102—441no—
579#102—441no—
580C22⋊C8—22no—
581#97—22no—
582C4×C8—22no—
583#95—221no—
584#95—221no—
585#95D4411yescharacteristic
586#95D4411yescharacteristic
587C2×C11—42no—
588C2×C11D4×C22⋊C411yescharacteristic
589C2×C11C4×AGL(1,ℤ/8)11yescharacteristic
590C2×C11#294611yescharacteristic
591C2×C11#326511yescharacteristic
592C2×C11#326811yescharacteristic
593C2×C11#327411yescharacteristic
594C2×C11#327511yescharacteristic
595D11—44no—
596D11—82no—
597D11—82no—
598C24—221no—
599C24—221no—
600C24—221no—
601C24—224no—
602C24—442no—
603C24—442no—
604C24—442no—
605C24—442no—
606C24—881no—
607C24—881no—
608C24C2×D4411yescharacteristic
609#41—228no—
610#41—444no—
611#41—444no—
612#41—444no—
613C2×Q8—112no—
614C2×Q8—112no—
615C2×Q8—112no—
616C2×Q8—221no—
617C2×Q8—221no—
618C2×Q8—221no—
619C2×D4—112no—
620C2×D4—112no—
621C2×D4—112no—
622C2×D4—112no—
623C2×D4—112no—
624C2×D4—228no—
625C2×D4—224no—
626C2×D4—224no—
627C2×D4—221no—
628C2×D4—221no—
629C2×D4—221no—
630C2×D4—221no—
631C2×D4—221no—
632C2×D4—221no—
633C2×D4—221no—
634C2×D4—221no—
635C2×D4—221no—
636C2×D4—221no—
637C2×D4—221no—
638C2×D4—221no—
639C2×D4—221no—
640C2×D4—444no—
641C2×D4—444no—
642C2×D4—444no—
643C2×D4—442no—
644C2×D4—442no—
645C2×D4—442no—
646C2×D4—442no—
647C22×C4—21no—
648C22×C4—21no—
649C22×C4—21no—
650C22×C4—21no—
651C22×C4—221no—
652C22×C4—224no—
653C22×C4—221no—
654C22×C4—221no—
655C22×C4—221no—
656C22×C4—221no—
657C22×C4—442no—
658C22×C4—442no—
659C22×C4—442no—
660C22×C4—442no—
661C22×C4—442no—
662C22×C4—442no—
663C22×C4—881no—
664C22×C4—881no—
665C22×C4C2×C4×D1112yes—
666C22×C4C2×D4411yescharacteristic
667C22×C4C2×D4411yescharacteristic
668C22×C4C2×D4411yescharacteristic
669C22×C4C2×D4411yescharacteristic
670C22×C4C2×D4411yescharacteristic
671C22×C4#433912yes—
672C22×C4C23×D1111yescharacteristic
673SD16—1116no—
674SD16—228no—
675D8—228no—
676D8—228no—
677M16—28no—
678C2×C8—21no—
679C2×C8—21no—
680C2×C8—21no—
681C2×C8—21no—
682C2×C8—21no—
683C2×C8—21no—
684C2×C8—21no—
685C2×C8—21no—
686C2×C8C2×C4×D1112yes—
687C2×C8C2×C4×D1112yes—
688C2×C8D4×D1112yes—
689C2×C8D4×D1112yes—
690C4⋊C4—221no—
691C4⋊C4—221no—
692C4⋊C4—221no—
693C4⋊C4—221no—
694C4⋊C4—221no—
695C4⋊C4—221no—
696C4⋊C4—221no—
697C4⋊C4—221no—
698C4⋊C4—442no—
699C4⋊C4—442no—
700C22⋊C4—22no—
701C22⋊C4—41no—
702C22⋊C4—442no—
703C22⋊C4—442no—
704C22⋊C4—442no—
705C22⋊C4—442no—
706C22⋊C4—442no—
707C22⋊C4—442no—
708C22⋊C4—442no—
709C22⋊C4—881no—
710C22⋊C4—881no—
711C22⋊C4—881no—
712C22⋊C4—881no—
713C22⋊C4—881no—
714C42—21no—
715C42—21no—
716C42—21no—
717C42—21no—
718C42—442no—
719C42—442no—
720C11#2244311yescharacteristic, complemented, Sylow
721C23—21no—
722C23—21no—
723C23—21no—
724C23—21no—
725C23—21no—
726C23—21no—
727C23—222no—
728C23—222no—
729C23—222no—
730C23—222no—
731C23—222no—
732C23—448no—
733C23—448no—
734C23—441no—
735C23—441no—
736C23—441no—
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—884no—
751C23—884no—
752C23—884no—
753C23—884no—
754C23—884no—
755C23C4×D4412yes—
756C23C22×D4411yescharacteristic
757Q8—114no—
758Q8—222no—
759Q8—222no—
760Q8—222no—
761D4—114no—
762D4—222no—
763D4—222no—
764D4—222no—
765D4—222no—
766D4—222no—
767D4—222no—
768D4—222no—
769D4—448no—
770D4—448no—
771D4—441no—
772D4—441no—
773D4—441no—
774D4—441no—
775C2×C4—21no—
776C2×C4—21no—
777C2×C4—21no—
778C2×C4—21no—
779C2×C4—22no—
780C2×C4—22no—
781C2×C4—22no—
782C2×C4—22no—
783C2×C4—21no—
784C2×C4—21no—
785C2×C4—21no—
786C2×C4—21no—
787C2×C4—21no—
788C2×C4—21no—
789C2×C4—21no—
790C2×C4—21no—
791C2×C4—21no—
792C2×C4—222no—
793C2×C4—222no—
794C2×C4—222no—
795C2×C4—448no—
796C2×C4—441no—
797C2×C4—441no—
798C2×C4—441no—
799C2×C4—441no—
800C2×C4—441no—
801C2×C4—441no—
802C2×C4—441no—
803C2×C4—441no—
804C2×C4—441no—
805C2×C4—441no—
806C2×C4—441no—
807C2×C4—441no—
808C2×C4—884no—
809C2×C4—884no—
810C2×C4C4×D4412yes—
811C2×C4#6696112yescomplemented
812C2×C4C22×C4×D1111yescharacteristic
813C2×C4C2×#433911yescharacteristic
814C2×C4C2×D4×D1111yescharacteristic
815C2×C4C2×D4×D1111yescharacteristic
816C2×C4#6704211yescharacteristic
817C2×C4#6704211yescharacteristic
818C8—22no—
819C8—41no—
820C8—41no—
821C8C22⋊C4×D1114yescomplemented
822C22—22no—
823C22—22no—
824C22—22no—
825C22—41no—
826C22—41no—
827C22—41no—
828C22—41no—
829C22—224no—
830C22—442no—
831C22—442no—
832C22—442no—
833C22—442no—
834C22—442no—
835C22—442no—
836C22—442no—
837C22—442no—
838C22—442no—
839C22—442no—
840C22—442no—
841C22—442no—
842C22—8816no—
843C22—881no—
844C22—881no—
845C22—881no—
846C22—881no—
847C22—881no—
848C22—881no—
849C22—881no—
850C22—881no—
851C22C2×C4×D4411yescharacteristic
852C22D4×D4411yescharacteristic
853C22D4×D4411yescharacteristic
854C22C2×#6696111yescharacteristic
855C22#1062327911yescharacteristic
856C22#1062328211yescharacteristic
857C22#1062328311yescharacteristic
858C4—22no—
859C4—22no—
860C4—41no—
861C4—41no—
862C4—41no—
863C4—224no—
864C4—881no—
865C4—881no—
866C4—881no—
867C4—881no—
868C4C2×C22⋊C4×D1111yescharacteristic
869C4#1062305211yescharacteristic
870C4#1062308111yescharacteristic
871C4#1062308111yescharacteristic
872C2—42no—
873C2—444no—
874C2—882no—
875C2—882no—
876C2C22⋊C4×D4411yescharacteristic
877C2C4×#6696111yescharacteristic
878C2#1307745011yescharacteristic
879C2#1308011611yescharacteristic
880C2#1308016111yescharacteristic
881C2#1308023811yescharacteristic
882C2#1308025211yescharacteristic
subgroupG/H
centerC23C22×D44
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#1753C2
socleC23×C11C22×D4
prime radicalC22×#66961C2
cosocleC22×C4×C11C24
hypercenter#1753D11
hypocenterC11#22443
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C4×C22⋊C4 ◁ #1753

Complements

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

NH ≅ G/Ntype
2. C2×#10622323C2semidirect
3. C2×C4×#4314C2semidirect
4. #13071456C2semidirect
5. C22⋊C4×D44C2semidirect
6. #13069492C2semidirect
7. #13069482C2semidirect
8. #13068970C2semidirect
9. #13068970C2semidirect
10. #13068963C2semidirect
11. #13068963C2semidirect
12. #13068649C2semidirect
13. #13068557C2semidirect
14. #13068548C2semidirect
15. C11×#1753C2semidirect
21. C2×#66961C4semidirect
29. C2×C4×Dic22C22semidirect
30. C2×C4×Dic22C22semidirect
32. C2×C11×#97C22semidirect
33. C2×C4×C8×C11C22semidirect
41. C2×#66885C22semidirect
42. C2×#66885C22semidirect
43. C2×#66882C22semidirect
44. C2×#66881C22semidirect
45. C2×#66880C22semidirect
46. C2×#66880C22semidirect
52. #10622552C22semidirect
53. #10622552C22semidirect
60. C11×#336C22semidirect
61. C11×#336C22semidirect
62. #10622189C22semidirect
63. #10622189C22semidirect
72. C2×#4339C2×C4semidirect
89. C2×C11×M16C2×C4semidirect
124. C2×D88C2×C4semidirect
128. C2×#4314C2×C4semidirect
279. #4314C22⋊C4semidirect
294. #1753D11semidirect
349. C2×C4×C11AGL(1,ℤ/8)semidirect
391. Dic22C2×C22⋊C4semidirect
395. C8×C11C2×C22⋊C4semidirect
424. C2×#97C2×D11semidirect
425. C2×C4×C8C2×D11semidirect
442. #336C2×D11semidirect
443. #336C2×D11semidirect
532. C2×M16C4×D11semidirect
720. C11#22443semidirect
811. C2×C4#66961semidirect
821. C8C22⋊C4×D11semidirect

Maximal subgroups

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

subgroupindex
C22×#669612
C2×#106223232
C2×C4×#43142
#130714562
C22⋊C4×D442
#130694922
#130694822
#130689702
#130689632
#130686492
#130685572
#130685482
C11×#17532
#2244311