Finite Group Databasebeta

← #14769550

Subgroups — #14769550

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×#10622502C211yesmaximal, characteristic, complemented
3C2×#10622465C211yesmaximal, characteristic, complemented
4#13071453C211yesmaximal, characteristic, complemented
5#13071436C211yesmaximal, characteristic, complemented
6#13069490C211yesmaximal, characteristic, complemented
7#13069480C211yesmaximal, characteristic, complemented
8#13068972C211yesmaximal, characteristic, complemented
9#13068972C211yesmaximal, characteristic, complemented
10#13068965C211yesmaximal, characteristic, complemented
11#13068965C211yesmaximal, characteristic, complemented
12#13068554C211yesmaximal, characteristic, complemented
13#13068546C211yesmaximal, characteristic, complemented
14#13068397C211yesmaximal, characteristic, complemented
15C11×#1809C211yesmaximal, 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×#66946C2211yescharacteristic
27C2×#66946C2211yescharacteristic
28C2×#66940C2211yescharacteristic, complemented
29C2×#66940C2211yescharacteristic, complemented
30C2×C22⋊C4×D11—21no—
31C2×C11×#107C2211yescharacteristic, complemented
32C2×C11×#106C2211yescharacteristic, complemented
33C11×#380C2211yescharacteristic
34C11×#380C2211yescharacteristic
35C4×C22⋊Dic11C2211yescharacteristic
36C2×C22⋊(C11⋊C8)C2211yescharacteristic
37C2×#66879C2211yescharacteristic, complemented
38C2×C8×Dic11C2211yescharacteristic, complemented
39#10622601C2211yescharacteristic
40#10622601C2211yescharacteristic
41#10622601C2211yescharacteristic, complemented
42#10622601C2211yescharacteristic, complemented
43C2×#66874C2211yescharacteristic, complemented
44C2×#66874C2211yescharacteristic, complemented
45C2×#66873C2211yescharacteristic
46C2×#66873C2211yescharacteristic
47C2×#66873C2211yescharacteristic
48C2×#66873C2211yescharacteristic
49C2×#66873C2211yescharacteristic, complemented
50C2×#66873C2211yescharacteristic, complemented
51#10622570—21no—
52#10622570—21no—
53#10622568—21no—
54#10622502—24no—
55#10622465—24no—
56#10622280—21no—
57#10622279—21no—
58#10622278—21no—
59#10622278—21no—
60C11×#340C2211yescharacteristic, complemented
61C11×#340C2211yescharacteristic, complemented
62#10622188C2211yescharacteristic, complemented
63#10622188C2211yescharacteristic, 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
92C2×C11×C4⋊C4C2311yescharacteristic
93C2×C11×C4⋊C4C2311yescharacteristic
94C2×C11×C4⋊C4C2311yescharacteristic
95C2×C11×C4⋊C4C2311yescharacteristic
96C2×C11×C22⋊C4—21no—
97C2×C11×C22⋊C4—21no—
98C2×C22⋊Dic11D411yescharacteristic
99C2×C22⋊Dic11D411yescharacteristic
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×Dic11⋊C4—21no—
111C2×Dic11⋊C4—21no—
112C2×C4×Dic11—21no—
113C2×C4×Dic11—21no—
114C2×C4×Dic11C2311yescharacteristic
115C2×C4×Dic11C2311yescharacteristic
116C22×C11⋊C8C2311yescharacteristic
117C22×C11⋊C8C2311yescharacteristic
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—
131#66946—22no—
132#66946—22no—
133#66946—41no—
134#66946—41no—
135#66940—22no—
136#66940—22no—
137#66940—41no—
138#66940—41no—
139C22⋊C4×D11—44no—
140C11×#107—22no—
141C11×#106—22no—
142C11×#95—21no—
143C11×#95—21no—
144C11⋊#95D411yescharacteristic
145C11⋊#95D411yescharacteristic
146C22⋊(C11⋊C8)—22no—
147#66879—22no—
148C8×Dic11—22no—
149#66874—22no—
150#66874—22no—
151#66873—22no—
152#66873—22no—
153#66873—41no—
154#66873—41no—
155#66873—41no—
156#66873—41no—
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×C11—21no—
174C22×C4×C11—21no—
175C22×C4×C11—21no—
176C22×C4×C11—21no—
177C22×C4×C11C22×C412yes—
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×Dic11C2×D411yescharacteristic
186C22×Dic11C2×D411yescharacteristic
187C22×Dic11C2×D411yescharacteristic
188C22×Dic11C2×D411yescharacteristic
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×C11C22×C412yes—
237C2×C8×C11C22×C412yes—
238C2×C8×C11C2×D412yes—
239C2×C8×C11C2×D412yes—
240C11×C4⋊C4—21no—
241C11×C4⋊C4—21no—
242C11×C4⋊C4—21no—
243C11×C4⋊C4—21no—
244C11×C4⋊C4—21no—
245C11×C4⋊C4—21no—
246C11×C4⋊C4—21no—
247C11×C4⋊C4—21no—
248C11×C22⋊C4—42no—
249C11×C22⋊C4—81no—
250C22⋊Dic11—22no—
251C22⋊Dic11—41no—
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—
261(C2×D11)⋊C4—81no—
262Dic11⋊C4—42no—
263Dic11⋊C4—42no—
264C4×Dic11—21no—
265C4×Dic11—21no—
266C4×Dic11—21no—
267C4×Dic11—21no—
268C4×Dic11—42no—
269C4×Dic11—42no—
270C2×C11⋊C8—21no—
271C2×C11⋊C8—21no—
272C2×C11⋊C8—21no—
273C2×C11⋊C8—21no—
274C2×C11⋊C8—21no—
275C2×C11⋊C8—21no—
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#1809D1111yescharacteristic, complemented
292#1788—111no—
293#1786—111no—
294#1753—111no—
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—22no—
334C2×C4×C11—22no—
335C2×C4×C11—22no—
336C2×C4×C11—22no—
337C2×C4×C11—41no—
338C2×C4×C11—41no—
339C2×C4×C11—41no—
340C2×C4×C11—41no—
341C2×C4×C11—41no—
342C2×C4×C11—41no—
343C2×C4×C11—41no—
344C2×C4×C11—41no—
345C2×C4×C11—41no—
346C2×C4×C11—41no—
347C2×C4×C11—41no—
348C2×C4×C11—41no—
349C2×C4×C11C4×D412yes—
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—21no—
359C2×Dic11—22no—
360C2×Dic11—22no—
361C2×Dic11—21no—
362C2×Dic11—21no—
363C2×Dic11—21no—
364C2×Dic11—21no—
365C2×Dic11—21no—
366C2×Dic11—21no—
367C2×Dic11—21no—
368C2×Dic11—21no—
369C2×Dic11—21no—
370C2×Dic11—21no—
371C2×Dic11AGL(1,ℤ/8)12yescomplemented
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×C11C2×C22⋊C414yescomplemented
394C11⋊C8—41no—
395C11⋊C8—41no—
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×#107C2×D1111yescharacteristic, complemented
414C2×#106C2×D1111yescharacteristic, complemented
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⋊C8—111no—
424C2×#97—111no—
425C2×C4×C8—111no—
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—221no—
435#380C2×D1111yescharacteristic
436#380C2×D1111yescharacteristic
437#379—221no—
438C4×C22⋊C4—111no—
439C4×C22⋊C4—221no—
440#340C2×D1111yescharacteristic, complemented
441#340C2×D1111yescharacteristic, complemented
442#336—111no—
443#336—111no—
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—81no—
482C4×C11—81no—
483C4×C11—81no—
484C4×C11—81no—
485C4×C11C22×C22⋊C411yescharacteristic
486C4×C11#51811yescharacteristic
487C4×C11#54611yescharacteristic
488C4×C11#54611yescharacteristic
489Dic11—24no—
490Dic11—22no—
491Dic11—41no—
492Dic11—41no—
493Dic11—41no—
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×C8—111no—
534C22×C8—111no—
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—221no—
546C2×C4⋊C4—221no—
547C2×C4⋊C4C22×D1111yescharacteristic
548C2×C4⋊C4C22×D1111yescharacteristic
549C2×C4⋊C4C22×D1111yescharacteristic
550C2×C4⋊C4C22×D1111yescharacteristic
551C2×C22⋊C4—21no—
552C2×C22⋊C4—21no—
553C2×C22⋊C4—111no—
554C2×C22⋊C4—111no—
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—221no—
564C2×C22⋊C4—221no—
565C2×C22⋊C4—444no—
566C2×C42—111no—
567C2×C42—111no—
568C2×C42—221no—
569C2×C42—221no—
570#107—22no—
571#106—22no—
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—222no—
581#97—222no—
582C4×C8—222no—
583#95—21no—
584#95—21no—
585#95—111no—
586#95—111no—
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—
608C24D4×D1111yescharacteristic
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—21no—
652C22×C4—21no—
653C22×C4—21no—
654C22×C4—21no—
655C22×C4—111no—
656C22×C4—111no—
657C22×C4—111no—
658C22×C4—111no—
659C22×C4—221no—
660C22×C4—224no—
661C22×C4—442no—
662C22×C4—442no—
663C22×C4—442no—
664C22×C4—442no—
665C22×C4—442no—
666C22×C4—442no—
667C22×C4—881no—
668C22×C4—881no—
669C22×C4C2×C4×D1112yes—
670C22×C4D4×D1111yescharacteristic
671C22×C4#434312yes—
672C22×C4C23×D1111yescharacteristic
673SD16—1116no—
674SD16—228no—
675D8—228no—
676D8—228no—
677M16—28no—
678C2×C8—21no—
679C2×C8—21no—
680C2×C8—221no—
681C2×C8—221no—
682C2×C8—221no—
683C2×C8—221no—
684C2×C8—221no—
685C2×C8—221no—
686C2×C8C2×C4×D1112yes—
687C2×C8C2×C4×D1112yes—
688C2×C8D4×D1112yes—
689C2×C8D4×D1112yes—
690C4⋊C4—21no—
691C4⋊C4—21no—
692C4⋊C4—21no—
693C4⋊C4—21no—
694C4⋊C4—21no—
695C4⋊C4—21no—
696C4⋊C4—21no—
697C4⋊C4—21no—
698C4⋊C4—442no—
699C4⋊C4—442no—
700C22⋊C4—42no—
701C22⋊C4—81no—
702C22⋊C4—222no—
703C22⋊C4—442no—
704C22⋊C4—442no—
705C22⋊C4—442no—
706C22⋊C4—442no—
707C22⋊C4—442no—
708C22⋊C4—442no—
709C22⋊C4—441no—
710C22⋊C4—881no—
711C22⋊C4—881no—
712C22⋊C4—881no—
713C22⋊C4—881no—
714C42—221no—
715C42—221no—
716C42—221no—
717C42—221no—
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—
755C23#6694612yes—
756C23C2×D4×D1111yescharacteristic
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—22no—
778C2×C4—22no—
779C2×C4—22no—
780C2×C4—22no—
781C2×C4—41no—
782C2×C4—41no—
783C2×C4—41no—
784C2×C4—41no—
785C2×C4—41no—
786C2×C4—41no—
787C2×C4—41no—
788C2×C4—41no—
789C2×C4—41no—
790C2×C4—41no—
791C2×C4—41no—
792C2×C4—41no—
793C2×C4—112no—
794C2×C4—222no—
795C2×C4—221no—
796C2×C4—221no—
797C2×C4—222no—
798C2×C4—222no—
799C2×C4—221no—
800C2×C4—221no—
801C2×C4—221no—
802C2×C4—221no—
803C2×C4—221no—
804C2×C4—221no—
805C2×C4—221no—
806C2×C4—221no—
807C2×C4—221no—
808C2×C4—448no—
809C2×C4—884no—
810C2×C4—884no—
811C2×C4#6694612yes—
812C2×C4C22×C4×D1111yescharacteristic
813C2×C4C2×D4×D1111yescharacteristic
814C2×C4C2×D4×D1111yescharacteristic
815C2×C4C2×#434311yescharacteristic
816C2×C4#6704211yescharacteristic
817C2×C4#6704211yescharacteristic
818C8—22no—
819C8—441no—
820C8—441no—
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×#6694611yescharacteristic
852C22#1062314011yescharacteristic
853C22#1062314011yescharacteristic
854C22D11×AGL(1,ℤ/8)11yescharacteristic
855C22#1062330511yescharacteristic
856C22#1062330811yescharacteristic
857C22#1062330911yescharacteristic
858C4—22no—
859C4—81no—
860C4—81no—
861C4—81no—
862C4—81no—
863C4—222no—
864C4—224no—
865C4—441no—
866C4—441no—
867C4—441no—
868C4C2×C22⋊C4×D1111yescharacteristic
869C4#1062305211yescharacteristic
870C4#1062316111yescharacteristic
871C4#1062316111yescharacteristic
872C2—42no—
873C2—444no—
874C2—882no—
875C2—882no—
876C2#1307143611yescharacteristic
877C2#1307742311yescharacteristic
878C2#1307744611yescharacteristic
879C2#1308011811yescharacteristic
880C2#1308016311yescharacteristic
881C2#1308023311yescharacteristic
882C2#1308024411yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#1809C2
socleC23×C11C22×D4
prime radicalC22×#66961C2
cosocleC22×C4×C11C24
hypercenter#1809D11
hypocenterC11#22443
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1809

Complements

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

NH ≅ G/Ntype
2. C2×#10622502C2semidirect
3. C2×#10622465C2semidirect
4. #13071453C2semidirect
5. #13071436C2semidirect
6. #13069490C2semidirect
7. #13069480C2semidirect
8. #13068972C2semidirect
9. #13068972C2semidirect
10. #13068965C2semidirect
11. #13068965C2semidirect
12. #13068554C2semidirect
13. #13068546C2semidirect
14. #13068397C2semidirect
15. C11×#1809C2semidirect
21. C2×#66961C4semidirect
28. C2×#66940C22semidirect
29. C2×#66940C22semidirect
31. C2×C11×#107C22semidirect
32. C2×C11×#106C22semidirect
37. C2×#66879C22semidirect
38. C2×C8×Dic11C22semidirect
41. #10622601C22semidirect
42. #10622601C22semidirect
43. C2×#66874C22semidirect
44. C2×#66874C22semidirect
49. C2×#66873C22semidirect
50. C2×#66873C22semidirect
60. C11×#340C22semidirect
61. C11×#340C22semidirect
62. #10622188C22semidirect
63. #10622188C22semidirect
72. C2×#4339C2×C4semidirect
89. C2×C11×M16C2×C4semidirect
124. C2×D88C2×C4semidirect
128. C2×#4314C2×C4semidirect
279. #4314C22⋊C4semidirect
291. #1809D11semidirect
371. C2×Dic11AGL(1,ℤ/8)semidirect
391. Dic22C2×C22⋊C4semidirect
393. C8×C11C2×C22⋊C4semidirect
413. C2×#107C2×D11semidirect
414. C2×#106C2×D11semidirect
440. #340C2×D11semidirect
441. #340C2×D11semidirect
532. C2×M16C4×D11semidirect
720. C11#22443semidirect
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×#106225022
C2×#106224652
#130714532
#130714362
#130694902
#130694802
#130689722
#130689652
#130685542
#130685462
#130683972
C11×#18092
#2244311