Finite Group Databasebeta

← #14769552

Subgroups — #14769552

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×#66964C211yesmaximal, characteristic
2C2×#10622502C211yesmaximal, characteristic, complemented
3C2×C4×#4314C211yesmaximal, characteristic, complemented
4#13071455C211yesmaximal, characteristic, complemented
5#13071437C211yesmaximal, characteristic, complemented
6#13069493C211yesmaximal, characteristic, complemented
7#13068974C211yesmaximal, characteristic, complemented
8#13068968C211yesmaximal, characteristic, complemented
9#13068967C211yesmaximal, characteristic, complemented
10#13068961C211yesmaximal, characteristic, complemented
11#13068650C211yesmaximal, characteristic, complemented
12#13068553C211yesmaximal, characteristic, complemented
13#13068545C211yesmaximal, characteristic, complemented
14#13068399C211yesmaximal, characteristic, complemented
15C11×#1970C211yesmaximal, characteristic, complemented
16C22×#4341C2211yescharacteristic
17C22×D4×D11C2211yescharacteristic
18C22×C11×D8C2211yescharacteristic
19C22×#4324C2211yescharacteristic
20C22×#4323C2211yescharacteristic
21C2×#66964—24no—
22C2×#66964—24no—
23C2×#66964C418yescomplemented
24C22×#4314C2211yescharacteristic
25C22×#4313C2211yescharacteristic
26C2×#66946C2211yescharacteristic
27C2×#66940C2211yescharacteristic, complemented
28C2×C22⋊C4×D11—21no—
29C2×C4×D44C2211yescharacteristic
30C2×C4×Dic22C2211yescharacteristic, complemented
31C2×C11×#107C2211yescharacteristic, complemented
32C2×C11×#102C2211yescharacteristic
33C2×C11×#102C2211yescharacteristic, complemented
34C2×C4×C8×C11C2211yescharacteristic, complemented
35C11×#390C2211yescharacteristic
36C11×#390C2211yescharacteristic, complemented
37#10622834C2211yescharacteristic
38#10622834C2211yescharacteristic, complemented
39C2×#66896C2211yescharacteristic
40C2×#66896C2211yescharacteristic, complemented
41C2×#66885C2211yescharacteristic
42C2×(C2×D11)⋊C8C2211yescharacteristic
43C2×#66881C2211yescharacteristic, complemented
44C2×#66880C2211yescharacteristic, complemented
45C2×#66879C2211yescharacteristic, complemented
46#10622600C2211yescharacteristic
47#10622600C2211yescharacteristic
48C2×#66874C2211yescharacteristic, complemented
49C2×#66873C2211yescharacteristic
50#10622570—21no—
51#10622570—21no—
52#10622569—21no—
53#10622569—21no—
54#10622568—21no—
55#10622555—21no—
56C22⋊C4×Dic11—21no—
57C4×(C2×D11)⋊C4C2211yescharacteristic
58#10622502—24no—
59C4×#4314—24no—
60#10622188C2211yescharacteristic, complemented
61#10622167C2211yescharacteristic, complemented
62#10622167C2211yescharacteristic, complemented
63#10622162C2211yescharacteristic, complemented
64C24×D11—21no—
65C22×D4×C11C2311yescharacteristic
66C22×D4×C11C2311yescharacteristic
67C22×C22⋊D11—21no—
68C22×C22⋊D11—21no—
69C23×Dic11—21no—
70C2×#4341—22no—
71C2×#4341—22no—
72C2×#4341—22no—
73C2×#4341—41no—
74C2×#4341—41no—
75C2×#4341C2×C414yescomplemented
76C2×D4×D11—22no—
77C2×D4×D11—22no—
78C2×D4×D11—22no—
79C2×D4×D11—41no—
80C2×D4×D11—41no—
81C2×D4×D11C2×C414yes—
82C22×D44C2311yescharacteristic
83C22×C4×D11—21no—
84C22×C4×D11—21no—
85C22×C4×D11C2311yescharacteristic
86C22×Dic22C2311yescharacteristic
87C2×C11×D8—22no—
88C2×C11×D8—22no—
89C2×C11×D8C2×C414yescomplemented
90C22×C8×C11C2311yescharacteristic
91C22×C8×C11C2311yescharacteristic
92C2×C11×C4⋊C4C2311yescharacteristic
93C2×C11×C4⋊C4C2311yescharacteristic
94C2×C11×C22⋊C4—21no—
95C2×C11×C22⋊C4—21no—
96C2×C11×C22⋊C4—21no—
97C2×C11×C22⋊C4—21no—
98C2×C42×C11C2311yescharacteristic
99C2×C22⋊Dic11—21no—
100C2×C22⋊Dic11—21no—
101C2×C22⋊Dic11—21no—
102C2×C22⋊Dic11—21no—
103C2×#4324—22no—
104C2×#4324—22no—
105C2×#4324C2×C414yescomplemented
106C2×#4323—22no—
107C2×#4323—22no—
108C2×#4323C2×C414yes—
109C2×(C2×D11)⋊C4—21no—
110C2×(C2×D11)⋊C4—21no—
111C2×(C2×D11)⋊C4—21no—
112C2×(C2×D11)⋊C4—21no—
113C2×(C2×D11)⋊C4D411yescharacteristic
114C2×(C2×D11)⋊C4D411yescharacteristic
115C2×C4⋊Dic11C2311yescharacteristic
116C2×C4⋊Dic11C2311yescharacteristic
117C2×Dic11⋊C4—21no—
118C2×Dic11⋊C4—21no—
119C2×C4×Dic11—21no—
120C2×C4×Dic11—21no—
121C2×C4×Dic11C2311yescharacteristic
122C22×C11⋊C8C2311yescharacteristic
123C22×C11⋊C8C2311yescharacteristic
124#66964—232no—
125C2×#4314C2×C414yes—
126C2×#4314D414yes—
127C2×#4314D414yes—
128C2×#4313—22no—
129C2×#4313—22no—
130C2×#4313C2×C414yescomplemented
131#66946—22no—
132#66946—41no—
133#66940—22no—
134#66940—41no—
135C22⋊C4×D11—44no—
136C4×D44—22no—
137C4×D44—41no—
138C4×Dic22—22no—
139C4×Dic22—41no—
140C11×#107—22no—
141C11×#102—41no—
142C11×#102—41no—
143C4×C8×C11—22no—
144#66896—41no—
145#66896—41no—
146C11⋊#95—21no—
147C11⋊#95—21no—
148C11⋊#95D411yescharacteristic
149C11⋊#95D411yescharacteristic
150#66885—22no—
151(C2×D11)⋊C8—22no—
152#66881—22no—
153#66880—22no—
154#66879—22no—
155#66874—22no—
156#66873—22no—
157#22443—111nomaximal, Sylow
158C24×C11—21no—
159C24×C11—21no—
160C23×D11—21no—
161C23×D11—24no—
162C23×D11—42no—
163C23×D11—42no—
164C23×D11—42no—
165C23×D11—42no—
166C23×D11—81no—
167C23×D11—81no—
168C23×D11C2×D411yescharacteristic
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—21no—
178C2×D4×C11—21no—
179C2×D4×C11C22×C412yes—
180C2×D4×C11C22×C412yes—
181C22×C4×C11—21no—
182C22×C4×C11—21no—
183C22×C4×C11C2×D411yescharacteristic
184C22×C4×C11C2×D411yescharacteristic
185C22×C4×C11C2411yescharacteristic
186C2×C22⋊D11—24no—
187C2×C22⋊D11—24no—
188C2×C22⋊D11—42no—
189C2×C22⋊D11—42no—
190C2×C22⋊D11—42no—
191C2×C22⋊D11—42no—
192C22×Dic11—24no—
193C22×Dic11—21no—
194C22×Dic11—21no—
195C22×Dic11—21no—
196C22×Dic11—42no—
197C22×Dic11—42no—
198C22×Dic11C2×D411yescharacteristic
199C22×Dic11C2×D411yescharacteristic
200C22×Dic11C2×D411yescharacteristic
201#4341—28no—
202#4341—44no—
203#4341—44no—
204#4341—44no—
205D4×D11—28no—
206D4×D11—44no—
207D4×D11—44no—
208D4×D11—44no—
209C2×D44—21no—
210C2×D44—21no—
211C2×D44—21no—
212C2×D44C22×C412yes—
213C2×D44C2×D412yes—
214C2×D44C2×D412yes—
215C2×C4×D11—21no—
216C2×C4×D11—21no—
217C2×C4×D11—21no—
218C2×C4×D11—21no—
219C2×C4×D11—42no—
220C2×C4×D11—42no—
221C2×C4×D11—42no—
222C2×C4×D11—42no—
223C2×C4×D11—81no—
224C2×C4×D11—81no—
225C2×C4×D11C22×C412yes—
226C2×C4×D11#4112yes—
227C2×Dic22—21no—
228C2×Dic22—21no—
229C2×Dic22—21no—
230C2×Dic22C22×C412yes—
231C2×Dic22C2×D412yes—
232C2×Dic22C2×D412yes—
233C11×D8—28no—
234C2×C8×C11—21no—
235C2×C8×C11—21no—
236C2×C8×C11—21no—
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×C22⋊C4—42no—
245C11×C22⋊C4—42no—
246C11×C22⋊C4—81no—
247C11×C22⋊C4—81no—
248C42×C11—21no—
249C42×C11—21no—
250C22⋊Dic11—42no—
251C22⋊Dic11—42no—
252C22⋊Dic11—81no—
253C22⋊Dic11—81no—
254#4324—28no—
255#4323—28no—
256(C2×D11)⋊C4—22no—
257(C2×D11)⋊C4—41no—
258(C2×D11)⋊C4—42no—
259(C2×D11)⋊C4—42no—
260(C2×D11)⋊C4—42no—
261(C2×D11)⋊C4—81no—
262C4⋊Dic11—21no—
263C4⋊Dic11—21no—
264C4⋊Dic11—21no—
265C4⋊Dic11—21no—
266Dic11⋊C4—42no—
267Dic11⋊C4—42no—
268C4×Dic11—21no—
269C4×Dic11—21no—
270C4×Dic11—42no—
271C4×Dic11—42no—
272C2×C11⋊C8—21no—
273C2×C11⋊C8—21no—
274C2×C11⋊C8—21no—
275C2×C11⋊C8—21no—
276C2×C11⋊C8—21no—
277C2×C11⋊C8C22×C412yes—
278#4314C22⋊C4116yescomplemented
279#4313—28no—
280C22×AGL(1,ℤ/8)—111no—
281C2×#440—111no—
282C2×C4×SD16—111no—
283#2341—111no—
284D4×C22⋊C4—111no—
285#1972—111no—
286#1970D1111yescharacteristic, complemented
287#1880—111no—
288#1880—111no—
289#1879—111no—
290#1879—111no—
291#1809—111no—
292#1788—111no—
293#1786—111no—
294#1753—111no—
295C23×C11—22no—
296C23×C11—22no—
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×C11C22×D411yescharacteristic
310C22×D11—22no—
311C22×D11—22no—
312C22×D11—22no—
313C22×D11—21no—
314C22×D11—21no—
315C22×D11—21no—
316C22×D11—21no—
317C22×D11—21no—
318C22×D11—21no—
319C22×D11—48no—
320C22×D11—48no—
321C22×D11—41no—
322C22×D11—41no—
323C22×D11—41no—
324C22×D11—41no—
325C22×D11—84no—
326C22×D11—84no—
327C22×D11—84no—
328C22×D11—84no—
329C22×D11—84no—
330C22×D11C4×D412yes—
331D4×C11—22no—
332D4×C11—22no—
333D4×C11—22no—
334D4×C11—22no—
335D4×C11—41no—
336D4×C11—41no—
337D4×C11—41no—
338D4×C11—41no—
339C2×C4×C11—21no—
340C2×C4×C11—21no—
341C2×C4×C11—21no—
342C2×C4×C11—21no—
343C2×C4×C11—21no—
344C2×C4×C11—41no—
345C2×C4×C11—41no—
346C2×C4×C11—41no—
347C2×C4×C11—41no—
348C2×C4×C11—41no—
349C2×C4×C11—41no—
350C2×C4×C11AGL(1,ℤ/8)12yescomplemented
351C2×C4×C11C23×C411yescharacteristic
352C2×C4×C11C22×D411yescharacteristic
353C2×C4×C11C22×D411yescharacteristic
354C2×C4×C11C2×#4111yescharacteristic
355C2×C4×C11H(5,𝔽2)11yescharacteristic
356C2×C4×C11H(5,𝔽2)11yescharacteristic
357C22⋊D11—48no—
358C22⋊D11—48no—
359C2×Dic11—22no—
360C2×Dic11—22no—
361C2×Dic11—22no—
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—48no—
371C2×Dic11—41no—
372C2×Dic11—41no—
373C2×Dic11—41no—
374C2×Dic11—41no—
375C2×Dic11—41no—
376C2×Dic11—41no—
377C2×Dic11C4×D412yes—
378D44—22no—
379D44—22no—
380D44—22no—
381D44C2×C22⋊C414yes—
382C4×D11—22no—
383C4×D11—22no—
384C4×D11—22no—
385C4×D11—22no—
386C4×D11—84no—
387C4×D11—84no—
388Dic22—22no—
389Dic22—22no—
390Dic22—22no—
391Dic22C2×C22⋊C414yescomplemented
392C8×C11—41no—
393C8×C11C2×C22⋊C414yescomplemented
394C11⋊C8—22no—
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×D8C2×D1111yescharacteristic
405C22×M16—111no—
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×#106—111no—
415C2×#103—111no—
416C2×#103—111no—
417C2×#102—111no—
418C2×#102—111no—
419C2×#102—111no—
420C2×#102—111no—
421C2×#102C2×D1111yescharacteristic
422C2×#102C2×D1111yescharacteristic, complemented
423C2×C22⋊C8—111no—
424C2×#97—111no—
425C2×C4×C8C2×D1111yescharacteristic, complemented
426#390—111no—
427#390—111no—
428#390—221no—
429#390—221no—
430#390C2×D1111yescharacteristic
431#390C2×D1111yescharacteristic, complemented
432#386—221no—
433#386—221no—
434#380—111no—
435#380—111no—
436#380—221no—
437#379—221no—
438C4×C22⋊C4—111no—
439C4×C22⋊C4—221no—
440#340—111no—
441#340—111no—
442#336—111no—
443#336—111no—
444C22×C11—42no—
445C22×C11—42no—
446C22×C11—42no—
447C22×C11—42no—
448C22×C11—42no—
449C22×C11—42no—
450C22×C11—81no—
451C22×C11—81no—
452C22×C11—81no—
453C22×C11—81no—
454C22×C11—81no—
455C22×C11—81no—
456C22×C11—81no—
457C22×C11—81no—
458C22×C11C2×C4×D411yescharacteristic
459C22×C11D4211yescharacteristic
460C22×C11D4211yescharacteristic
461C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
462C22×C11#57511yescharacteristic
463C22×C11#57611yescharacteristic
464C22×C11#57711yescharacteristic
465C2×D11—24no—
466C2×D11—22no—
467C2×D11—22no—
468C2×D11—22no—
469C2×D11—42no—
470C2×D11—42no—
471C2×D11—41no—
472C2×D11—42no—
473C2×D11—41no—
474C2×D11—42no—
475C2×D11—41no—
476C2×D11—42no—
477C2×D11—41no—
478C2×D11—42no—
479C2×D11—816no—
480C4×C11—22no—
481C4×C11—41no—
482C4×C11—81no—
483C4×C11—81no—
484C4×C11C22×C22⋊C411yescharacteristic
485C4×C11#51811yescharacteristic
486C4×C11#54611yescharacteristic
487C4×C11#54611yescharacteristic
488Dic11—24no—
489Dic11—22no—
490Dic11—41no—
491Dic11—41no—
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—222no—
505C22×D4—221no—
506C22×D4—222no—
507C22×D4—222no—
508C22×D4—221no—
509C22×D4—441no—
510C22×D4—441no—
511C22×D4C22×D1111yescharacteristic
512C22×D4C22×D1111yescharacteristic
513C23×C4—111no—
514C23×C4—221no—
515C23×C4—221no—
516C23×C4—221no—
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—22no—
525C2×D8—22no—
526C2×D8—114no—
527C2×D8—222no—
528C2×D8—222no—
529C2×D8C4×D1114yescomplemented
530C2×M16—114no—
531C2×M16—222no—
532C2×M16—222no—
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—111no—
546C2×C4⋊C4—111no—
547C2×C4⋊C4—221no—
548C2×C4⋊C4—221no—
549C2×C4⋊C4C22×D1111yescharacteristic
550C2×C4⋊C4C22×D1111yescharacteristic
551C2×C22⋊C4—21no—
552C2×C22⋊C4—21no—
553C2×C22⋊C4—21no—
554C2×C22⋊C4—21no—
555C2×C22⋊C4—111no—
556C2×C22⋊C4—111no—
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—221no—
568C2×C42—221no—
569C2×C42C22×D1111yescharacteristic
570#107—22no—
571#106—222no—
572#103—222no—
573#103—222no—
574#102—41no—
575#102—41no—
576#102—222no—
577#102—222no—
578#102—441no—
579#102—441no—
580C22⋊C8—222no—
581#97—222no—
582C4×C8—22no—
583#95—111no—
584#95—111no—
585#95—221no—
586#95—221no—
587C2×C11—82no—
588C2×C11—82no—
589C2×C11D4×C22⋊C411yescharacteristic
590C2×C11C4×AGL(1,ℤ/8)11yescharacteristic
591C2×C11#294611yescharacteristic
592C2×C11#326511yescharacteristic
593C2×C11#326811yescharacteristic
594C2×C11#327411yescharacteristic
595C2×C11#327511yescharacteristic
596D11—42no—
597D11—44no—
598C24—21no—
599C24—21no—
600C24—111no—
601C24—224no—
602C24—221no—
603C24—442no—
604C24—442no—
605C24—442no—
606C24—442no—
607C24—881no—
608C24—881no—
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—21no—
620C2×D4—21no—
621C2×D4—21no—
622C2×D4—21no—
623C2×D4—21no—
624C2×D4—21no—
625C2×D4—21no—
626C2×D4—21no—
627C2×D4—21no—
628C2×D4—21no—
629C2×D4—112no—
630C2×D4—112no—
631C2×D4—112no—
632C2×D4—224no—
633C2×D4—228no—
634C2×D4—224no—
635C2×D4—221no—
636C2×D4—221no—
637C2×D4—221no—
638C2×D4—444no—
639C2×D4—444no—
640C2×D4—444no—
641C2×D4—442no—
642C2×D4—442no—
643C2×D4—442no—
644C2×D4—442no—
645C2×D4C2×C4×D1112yes—
646C2×D4C2×C4×D1112yes—
647C22×C4—21no—
648C22×C4—21no—
649C22×C4—111no—
650C22×C4—112no—
651C22×C4—112no—
652C22×C4—111no—
653C22×C4—111no—
654C22×C4—224no—
655C22×C4—221no—
656C22×C4—221no—
657C22×C4—221no—
658C22×C4—221no—
659C22×C4—221no—
660C22×C4—221no—
661C22×C4—221no—
662C22×C4—442no—
663C22×C4—442no—
664C22×C4—442no—
665C22×C4—442no—
666C22×C4—442no—
667C22×C4—442no—
668C22×C4—881no—
669C22×C4—881no—
670C22×C4D4×D1111yescharacteristic
671C22×C4D4×D1111yescharacteristic
672C22×C4C23×D1111yescharacteristic
673SD16—1116no—
674SD16—228no—
675D8—28no—
676D8—228no—
677M16—228no—
678C2×C8—21no—
679C2×C8—21no—
680C2×C8—21no—
681C2×C8—112no—
682C2×C8—221no—
683C2×C8—221no—
684C2×C8—221no—
685C2×C8—221no—
686C2×C8—221no—
687C2×C8C2×C4×D1112yes—
688C2×C8D4×D1112yes—
689C2×C8D4×D1112yes—
690C4⋊C4—21no—
691C4⋊C4—21no—
692C4⋊C4—21no—
693C4⋊C4—21no—
694C4⋊C4—221no—
695C4⋊C4—221no—
696C4⋊C4—221no—
697C4⋊C4—221no—
698C4⋊C4—442no—
699C4⋊C4—442no—
700C22⋊C4—42no—
701C22⋊C4—42no—
702C22⋊C4—81no—
703C22⋊C4—81no—
704C22⋊C4—222no—
705C22⋊C4—441no—
706C22⋊C4—442no—
707C22⋊C4—442no—
708C22⋊C4—442no—
709C22⋊C4—442no—
710C22⋊C4—442no—
711C22⋊C4—881no—
712C22⋊C4—881no—
713C22⋊C4—881no—
714C42—21no—
715C42—21no—
716C42—221no—
717C42—221no—
718C42—442no—
719C42—442no—
720C11#2244311yescharacteristic, complemented, Sylow
721C23—22no—
722C23—22no—
723C23—41no—
724C23—41no—
725C23—41no—
726C23—41no—
727C23—41no—
728C23—41no—
729C23—41no—
730C23—41no—
731C23—41no—
732C23—41no—
733C23—41no—
734C23—41no—
735C23—112no—
736C23—222no—
737C23—221no—
738C23—221no—
739C23—221no—
740C23—221no—
741C23—221no—
742C23—222no—
743C23—222no—
744C23—221no—
745C23—448no—
746C23—448no—
747C23—441no—
748C23—441no—
749C23—441no—
750C23—441no—
751C23—884no—
752C23—884no—
753C23—884no—
754C23—884no—
755C23—884no—
756C23C2×D4×D1111yescharacteristic
757Q8—114no—
758Q8—222no—
759Q8—222no—
760Q8—222no—
761D4—22no—
762D4—22no—
763D4—22no—
764D4—22no—
765D4—41no—
766D4—41no—
767D4—41no—
768D4—41no—
769D4—114no—
770D4—222no—
771D4—222no—
772D4—222no—
773D4—448no—
774D4—448no—
775C2×C4—21no—
776C2×C4—21no—
777C2×C4—21no—
778C2×C4—21no—
779C2×C4—21no—
780C2×C4—41no—
781C2×C4—41no—
782C2×C4—41no—
783C2×C4—41no—
784C2×C4—41no—
785C2×C4—41no—
786C2×C4—112no—
787C2×C4—222no—
788C2×C4—221no—
789C2×C4—222no—
790C2×C4—222no—
791C2×C4—221no—
792C2×C4—222no—
793C2×C4—222no—
794C2×C4—222no—
795C2×C4—222no—
796C2×C4—221no—
797C2×C4—221no—
798C2×C4—221no—
799C2×C4—221no—
800C2×C4—221no—
801C2×C4—221no—
802C2×C4—448no—
803C2×C4—441no—
804C2×C4—441no—
805C2×C4—441no—
806C2×C4—441no—
807C2×C4—441no—
808C2×C4—441no—
809C2×C4—884no—
810C2×C4—884no—
811C2×C4#6696412yescomplemented
812C2×C4C22×C4×D1111yescharacteristic
813C2×C4C2×D4×D1111yescharacteristic
814C2×C4C2×D4×D1111yescharacteristic
815C2×C4#6703711yescharacteristic
816C2×C4#41×D1111yescharacteristic
817C2×C4#6704211yescharacteristic
818C8—41no—
819C8—222no—
820C8—441no—
821C8C22⋊C4×D1114yescomplemented
822C22—42no—
823C22—42no—
824C22—42no—
825C22—42no—
826C22—42no—
827C22—42no—
828C22—81no—
829C22—81no—
830C22—81no—
831C22—81no—
832C22—81no—
833C22—81no—
834C22—81no—
835C22—81no—
836C22—222no—
837C22—224no—
838C22—222no—
839C22—222no—
840C22—442no—
841C22—441no—
842C22—441no—
843C22—442no—
844C22—442no—
845C22—442no—
846C22—441no—
847C22—441no—
848C22—442no—
849C22—442no—
850C22—8816no—
851C22C4×D4×D1111yescharacteristic
852C22#1062314011yescharacteristic
853C22#1062324811yescharacteristic
854C22C2×#6696411yescharacteristic
855C22#1062328811yescharacteristic
856C22#1062329911yescharacteristic
857C22#1062330111yescharacteristic
858C4—22no—
859C4—41no—
860C4—81no—
861C4—81no—
862C4—222no—
863C4—224no—
864C4—441no—
865C4—441no—
866C4—881no—
867C4—881no—
868C4C2×C22⋊C4×D1111yescharacteristic
869C4#1062307611yescharacteristic
870C4#1062314311yescharacteristic
871C4#1062320711yescharacteristic
872C2—82no—
873C2—82no—
874C2—442no—
875C2—444no—
876C2#1307143711yescharacteristic
877C2C4×#6696411yescharacteristic
878C2#1307744111yescharacteristic
879C2#1308010811yescharacteristic
880C2#1308015311yescharacteristic
881C2#1308023511yescharacteristic
882C2#1308024611yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#1970C2
socleC23×C11C22×D4
prime radicalC22×#66964C2
cosocleC22×C4×C11C24
hypercenter#1970D11
hypocenterC11#22443
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1970

Complements

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

NH ≅ G/Ntype
2. C2×#10622502C2semidirect
3. C2×C4×#4314C2semidirect
4. #13071455C2semidirect
5. #13071437C2semidirect
6. #13069493C2semidirect
7. #13068974C2semidirect
8. #13068968C2semidirect
9. #13068967C2semidirect
10. #13068961C2semidirect
11. #13068650C2semidirect
12. #13068553C2semidirect
13. #13068545C2semidirect
14. #13068399C2semidirect
15. C11×#1970C2semidirect
23. C2×#66964C4semidirect
27. C2×#66940C22semidirect
30. C2×C4×Dic22C22semidirect
31. C2×C11×#107C22semidirect
33. C2×C11×#102C22semidirect
34. C2×C4×C8×C11C22semidirect
36. C11×#390C22semidirect
38. #10622834C22semidirect
40. C2×#66896C22semidirect
43. C2×#66881C22semidirect
44. C2×#66880C22semidirect
45. C2×#66879C22semidirect
48. C2×#66874C22semidirect
60. #10622188C22semidirect
61. #10622167C22semidirect
62. #10622167C22semidirect
63. #10622162C22semidirect
75. C2×#4341C2×C4semidirect
89. C2×C11×D8C2×C4semidirect
105. C2×#4324C2×C4semidirect
130. C2×#4313C2×C4semidirect
278. #4314C22⋊C4semidirect
286. #1970D11semidirect
350. C2×C4×C11AGL(1,ℤ/8)semidirect
391. Dic22C2×C22⋊C4semidirect
393. C8×C11C2×C22⋊C4semidirect
413. C2×#107C2×D11semidirect
422. C2×#102C2×D11semidirect
425. C2×C4×C8C2×D11semidirect
431. #390C2×D11semidirect
529. C2×D8C4×D11semidirect
720. C11#22443semidirect
811. C2×C4#66964semidirect
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×#669642
C2×#106225022
C2×C4×#43142
#130714552
#130714372
#130694932
#130689742
#130689682
#130689672
#130689612
#130686502
#130685532
#130685452
#130683992
C11×#19702
#2244311