Finite Group Databasebeta

← #14769249

Subgroups — #14769249

Order 2816.

1670 conjugacy classes of subgroups.

The subgroup lattice has 904 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623337C211yesmaximal, characteristic
2C2×#10622724C211yesmaximal, characteristic, complemented
3C2×#10622384C211yesmaximal, characteristic, complemented
4C4⋊C4×C22⋊D11C211yesmaximal, characteristic, complemented
5#13069547C211yesmaximal, characteristic, complemented
6#13069431C211yesmaximal, characteristic, complemented
7#13069051C211yesmaximal, characteristic, complemented
8#13069039C211yesmaximal, characteristic, complemented
9#13068930C211yesmaximal, characteristic, complemented
10#13068923C211yesmaximal, characteristic, complemented
11#13068614C211yesmaximal, characteristic, complemented
12#13068553C211yesmaximal, characteristic, complemented
13#13068547C211yesmaximal, characteristic, complemented
14#13068443C211yesmaximal, characteristic, complemented
15C22×C11×#102C211yesmaximal, characteristic, complemented
16C23×D4×C11C2211yescharacteristic
17C22×#4341C2211yescharacteristic
18C23×C8×C11C2211yescharacteristic
19C22×C11×C4⋊C4C2211yescharacteristic
20C2×#67006—21no—
21C22×C22⋊Dic11—21no—
22#10623337—24no—
23#10623337C418yescomplemented
24C2×#66992—21no—
25C2×#66991C2211yescharacteristic
26C2×#66989C2211yescharacteristic
27C2×#66988—21no—
28C2×D4×Dic11C2211yescharacteristic
29C2×C4×C22⋊D11—21no—
30C2×C4×C22⋊D11C2211yescharacteristic
31C2×#66977C2211yescharacteristic
32C22×#4313C2211yescharacteristic, complemented
33C2×C4⋊C4×D11C2211yescharacteristic, complemented
34C2×C11×#102—24no—
35C2×C11×#102C2211yescharacteristic
36C2×C11×#102C2211yescharacteristic
37C2×C11×#102C2211yescharacteristic
38C2×C11×#102C2211yescharacteristic
39C2×#66896C2211yescharacteristic
40C2×#66896C2211yescharacteristic
41C2×#66896C2211yescharacteristic
42C2×#66896C2211yescharacteristic
43#10622825C2211yescharacteristic
44#10622823—21no—
45C2×C22⋊(C11⋊C8)C2211yescharacteristic
46#10622724—24no—
47C2×(C2×D11)⋊C8C2211yescharacteristic, complemented
48C2×#66880C2211yescharacteristic, complemented
49C2×#66880C2211yescharacteristic, complemented
50C2×#66879C2211yescharacteristic, complemented
51C2×Dic11⋊C8C2211yescharacteristic, complemented
52#10622602—21no—
53#10622600C2211yescharacteristic, complemented
54#10622589C2211yescharacteristic, complemented
55C4⋊C4×Dic11C2211yescharacteristic, complemented
56#10622585—21no—
57C2×#66874C2211yescharacteristic, complemented
58C2×#66874C2211yescharacteristic, complemented
59#10622384—24no—
60#10622189C2211yescharacteristic, complemented
61#10622189C2211yescharacteristic, complemented
62#10622167C2211yescharacteristic, complemented
63#10622167C2211yescharacteristic, complemented
64C25×C11—21no—
65C22×D4×C11—22no—
66C22×D4×C11—22no—
67C22×D4×C11—21no—
68C22×D4×C11—22no—
69C22×D4×C11—41no—
70C22×D4×C11—41no—
71C22×D4×C11C2×C414yescomplemented
72C22×D4×C11C2311yescharacteristic
73C22×D4×C11C2311yescharacteristic
74C23×C4×C11—21no—
75C23×C4×C11C2311yescharacteristic
76C22×C22⋊D11—21no—
77C22×C22⋊D11—21no—
78C22×C22⋊D11D411yescharacteristic
79C23×Dic11—21no—
80C23×Dic11—21no—
81C2×#4341—22no—
82C2×#4341—22no—
83C2×#4341—22no—
84C2×#4341—41no—
85C2×#4341—41no—
86C2×#4341C2×C414yescomplemented
87C22×C4×D11—21no—
88C22×C4×D11C2311yescharacteristic
89C22×Dic22C2311yescharacteristic
90C22×C8×C11—22no—
91C22×C8×C11—22no—
92C22×C8×C11—41no—
93C22×C8×C11C2311yescharacteristic
94C22×C8×C11C2311yescharacteristic
95C2×C11×C4⋊C4—22no—
96C2×C11×C4⋊C4—21no—
97C2×C11×C4⋊C4—41no—
98C2×C11×C4⋊C4C2311yescharacteristic
99C2×C11×C4⋊C4C2311yescharacteristic
100#67006—28no—
101C2×C22⋊Dic11—21no—
102C2×C22⋊Dic11—21no—
103C2×C22⋊Dic11—21no—
104C2×C22⋊Dic11—21no—
105C2×C22⋊Dic11—21no—
106C2×C22⋊Dic11—28no—
107C2×C22⋊Dic11—21no—
108C2×C22⋊Dic11D411yescharacteristic
109#66992—28no—
110#66991—22no—
111#66991C2×C414yescomplemented
112#66989—22no—
113#66989C2×C414yescomplemented
114#66988—28no—
115D4×Dic11—22no—
116D4×Dic11C2×C414yescomplemented
117C4×C22⋊D11—44no—
118C4×C22⋊D11C2×C414yes—
119C4×C22⋊D11D414yes—
120C2×(C2×D11)⋊C4—21no—
121C2×(C2×D11)⋊C4D411yescharacteristic
122C2×C4⋊Dic11C2311yescharacteristic
123C2×C4⋊Dic11C2311yescharacteristic
124C2×C4⋊Dic11C2311yescharacteristic
125#66977—22no—
126#66977C2×C414yescomplemented
127C2×Dic11⋊C4—21no—
128C2×Dic11⋊C4—21no—
129C2×Dic11⋊C4—21no—
130C2×Dic11⋊C4—21no—
131C2×Dic11⋊C4D411yescharacteristic
132C2×C4×Dic11—21no—
133C2×C4×Dic11C2311yescharacteristic
134C22×C11⋊C8C2311yescharacteristic
135C22×C11⋊C8C2311yescharacteristic
136C2×#4313—22no—
137C2×#4313—22no—
138C2×#4313—41no—
139C4⋊C4×D11—22no—
140C4⋊C4×D11—41no—
141C11×#102—22no—
142C11×#102—22no—
143C11×#102—22no—
144C11×#102D414yescomplemented
145#66896—22no—
146#66896—22no—
147#66896—41no—
148#66896—41no—
149C11⋊#95—21no—
150C11⋊#95—21no—
151C11⋊#95—21no—
152C22⋊(C11⋊C8)—22no—
153(C2×D11)⋊C8—22no—
154#66880—22no—
155#66880—41no—
156#66879—22no—
157Dic11⋊C8—22no—
158#66874—22no—
159#66874—41no—
160#22419—111nomaximal, Sylow
161C24×C11—21no—
162C24×C11—21no—
163C24×C11—24no—
164C24×C11—42no—
165C24×C11—42no—
166C24×C11—42no—
167C24×C11—42no—
168C24×C11—81no—
169C24×C11—81no—
170C24×C11C2×D411yescharacteristic
171C23×D11C2×D411yescharacteristic
172C2×D4×C11—28no—
173C2×D4×C11—24no—
174C2×D4×C11—21no—
175C2×D4×C11—21no—
176C2×D4×C11—21no—
177C2×D4×C11—21no—
178C2×D4×C11—21no—
179C2×D4×C11—21no—
180C2×D4×C11—21no—
181C2×D4×C11—21no—
182C2×D4×C11—44no—
183C2×D4×C11—44no—
184C2×D4×C11—44no—
185C2×D4×C11—42no—
186C2×D4×C11—42no—
187C2×D4×C11C22×C412yes—
188C2×D4×C11C22×C412yes—
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—42no—
198C22×C4×C11—42no—
199C22×C4×C11—81no—
200C22×C4×C11C22×C412yes—
201C22×C4×C11C2×D411yescharacteristic
202C22×C4×C11C2×D412yes—
203C22×C4×C11C2411yescharacteristic
204C2×C22⋊D11—22no—
205C2×C22⋊D11—22no—
206C2×C22⋊D11—24no—
207C2×C22⋊D11—24no—
208C2×C22⋊D11—42no—
209C2×C22⋊D11—42no—
210C2×C22⋊D11—81no—
211C2×C22⋊D11—81no—
212C2×C22⋊D11C22⋊C414yes—
213C22×Dic11—24no—
214C22×Dic11—24no—
215C22×Dic11—21no—
216C22×Dic11—21no—
217C22×Dic11—21no—
218C22×Dic11—21no—
219C22×Dic11—42no—
220C22×Dic11—42no—
221C22×Dic11—81no—
222C22×Dic11—81no—
223C22×Dic11C2×D411yescharacteristic
224C22×Dic11C2×D411yescharacteristic
225C22×Dic11C2×D411yescharacteristic
226#4341—28no—
227#4341—44no—
228#4341—44no—
229#4341—44no—
230C2×C4×D11—21no—
231C2×C4×D11—21no—
232C2×C4×D11—21no—
233C2×C4×D11—21no—
234C2×C4×D11—42no—
235C2×C4×D11—42no—
236C2×C4×D11—81no—
237C2×C4×D11C22×C412yes—
238C2×C4×D11C2×D412yes—
239C2×Dic22—21no—
240C2×Dic22—21no—
241C2×Dic22—21no—
242C2×Dic22—21no—
243C2×Dic22—21no—
244C2×Dic22C22×C412yes—
245C2×C8×C11—21no—
246C2×C8×C11—21no—
247C2×C8×C11—21no—
248C2×C8×C11—21no—
249C2×C8×C11—21no—
250C2×C8×C11—44no—
251C2×C8×C11C2×D412yes—
252C11×C4⋊C4—21no—
253C11×C4⋊C4—21no—
254C11×C4⋊C4—21no—
255C11×C4⋊C4—42no—
256C11×C4⋊C4C2×D412yes—
257C22⋊Dic11—24no—
258C22⋊Dic11—24no—
259C22⋊Dic11—24no—
260C22⋊Dic11—24no—
261C22⋊Dic11—24no—
262C22⋊Dic11—42no—
263C22⋊Dic11C22⋊C414yes—
264(C2×D11)⋊C4—42no—
265(C2×D11)⋊C4C22⋊C414yes—
266C4⋊Dic11—21no—
267C4⋊Dic11—21no—
268C4⋊Dic11—21no—
269C4⋊Dic11—21no—
270C4⋊Dic11—21no—
271C4⋊Dic11C22×C412yes—
272Dic11⋊C4—24no—
273Dic11⋊C4—42no—
274Dic11⋊C4—42no—
275Dic11⋊C4—81no—
276Dic11⋊C4C22⋊C414yes—
277C4×Dic11—42no—
278C4×Dic11C22×C412yes—
279C4×Dic11C2×D412yes—
280C2×C11⋊C8—21no—
281C2×C11⋊C8—21no—
282C2×C11⋊C8—21no—
283C2×C11⋊C8—21no—
284C2×C11⋊C8—21no—
285C2×C11⋊C8—21no—
286#4313—44no—
287C2×#546—111no—
288C2×#435—111no—
289C2×#417—111no—
290C22×#102D1111yescharacteristic, complemented
291D4×C4⋊C4—111no—
292#1983—111no—
293#1959—111no—
294#1895—111no—
295#1892—111no—
296#1874—111no—
297#1872—111no—
298#1802—111no—
299#1788—111no—
300#1786—111no—
301#1762—111no—
302C23×C11—21no—
303C23×C11—21no—
304C23×C11—21no—
305C23×C11—21no—
306C23×C11—22no—
307C23×C11—22no—
308C23×C11—22no—
309C23×C11—22no—
310C23×C11—48no—
311C23×C11—41no—
312C23×C11—41no—
313C23×C11—41no—
314C23×C11—41no—
315C23×C11—41no—
316C23×C11—41no—
317C23×C11—41no—
318C23×C11—41no—
319C23×C11—41no—
320C23×C11—41no—
321C23×C11—48no—
322C23×C11—84no—
323C23×C11—84no—
324C23×C11—84no—
325C23×C11—84no—
326C23×C11—84no—
327C23×C11C2×C22⋊C412yes—
328C23×C11AGL(1,ℤ/8)12yes—
329C23×C11#13712yes—
330C23×C11C22×D411yescharacteristic
331C22×D11—21no—
332C22×D11—21no—
333C22×D11—21no—
334C22×D11—21no—
335C22×D11—21no—
336C22×D11—21no—
337C22×D11C2×C22⋊C412yes—
338D4×C11—22no—
339D4×C11—22no—
340D4×C11—22no—
341D4×C11—22no—
342D4×C11—22no—
343D4×C11—48no—
344D4×C11—41no—
345D4×C11—41no—
346D4×C11C4×D414yescomplemented
347C2×C4×C11—21no—
348C2×C4×C11—21no—
349C2×C4×C11—22no—
350C2×C4×C11—22no—
351C2×C4×C11—22no—
352C2×C4×C11—22no—
353C2×C4×C11—22no—
354C2×C4×C11—41no—
355C2×C4×C11—41no—
356C2×C4×C11—41no—
357C2×C4×C11—41no—
358C2×C4×C11—41no—
359C2×C4×C11—84no—
360C2×C4×C11C2×C22⋊C412yes—
361C2×C4×C11C23×C411yescharacteristic
362C2×C4×C11C22×D411yescharacteristic
363C2×C4×C11C22×D411yescharacteristic
364C2×C4×C11C2×#4111yescharacteristic
365C2×C4×C11H(5,𝔽2)11yescharacteristic
366C2×C4×C11H(5,𝔽2)11yescharacteristic
367C22⋊D11—28no—
368C22⋊D11—48no—
369C22⋊D11—84no—
370C2×Dic11—21no—
371C2×Dic11—21no—
372C2×Dic11—21no—
373C2×Dic11—21no—
374C2×Dic11—21no—
375C2×Dic11—21no—
376C2×Dic11—22no—
377C2×Dic11—22no—
378C2×Dic11—48no—
379C2×Dic11—41no—
380C2×Dic11—41no—
381C2×Dic11—41no—
382C2×Dic11—41no—
383C2×Dic11—41no—
384C2×Dic11—41no—
385C2×Dic11—41no—
386C2×Dic11—41no—
387C2×Dic11—41no—
388C2×Dic11—41no—
389C2×Dic11—84no—
390C2×Dic11C2×C22⋊C412yes—
391C2×Dic11C2×C22⋊C412yes—
392C2×Dic11C2×C22⋊C412yes—
393C4×D11—22no—
394C4×D11—22no—
395C4×D11—22no—
396C4×D11—22no—
397C4×D11—84no—
398Dic22—22no—
399Dic22—22no—
400Dic22—41no—
401Dic22—41no—
402C8×C11—22no—
403C8×C11—41no—
404C11⋊C8—41no—
405C11⋊C8—41no—
406C22×#41—111no—
407C23×D4C2×D1111yescharacteristic
408C22×M16—111no—
409C23×C8C2×D1111yescharacteristic
410#546—118no—
411#546—224no—
412C2×#124—111no—
413C2×#123—221no—
414C2×C22⋊Q8—111no—
415C2×#121—111no—
416C2×#121—221no—
417C2×#120—221no—
418C2×C4×D4—111no—
419C2×C4×D4—111no—
420C2×C4×D4—221no—
421C22×C4⋊C4—111no—
422C22×C4⋊C4C2×D1111yescharacteristic
423C22×C22⋊C4—221no—
424#435—224no—
425C2×C4⋊C8—111no—
426#417—224no—
427C2×#103—111no—
428C2×#103—111no—
429C2×#103—111no—
430C2×#103—111no—
431C2×#102—24no—
432C2×#102—111no—
433C2×#102—111no—
434C2×#102—111no—
435C2×#102—111no—
436C2×#102C2×D1111yescharacteristic
437C2×#102C2×D1111yescharacteristic
438C2×#102C2×D1111yescharacteristic
439C2×#102C2×D1111yescharacteristic
440C2×C22⋊C8—111no—
441C2×C22⋊C8—111no—
442C2×#97—111no—
443#389—221no—
444#385—221no—
445#385—221no—
446#384—111no—
447#380—111no—
448#380—111no—
449C4×C4⋊C4—111no—
450#340—111no—
451#340—111no—
452#340—111no—
453#340—111no—
454C22×C11—22no—
455C22×C11—22no—
456C22×C11—22no—
457C22×C11—22no—
458C22×C11—22no—
459C22×C11—22no—
460C22×C11—24no—
461C22×C11—42no—
462C22×C11—42no—
463C22×C11—42no—
464C22×C11—42no—
465C22×C11—42no—
466C22×C11—42no—
467C22×C11—42no—
468C22×C11—42no—
469C22×C11—42no—
470C22×C11—816no—
471C22×C11—81no—
472C22×C11—81no—
473C22×C11—81no—
474C22×C11—81no—
475C22×C11#41714yescomplemented
476C22×C11C22×C22⋊C411yescharacteristic
477C22×C11D4211yescharacteristic
478C22×C11#54611yescharacteristic
479C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
480C22×C11C2×#13711yescharacteristic
481C22×C11#57611yescharacteristic
482C22×C11#57711yescharacteristic
483C2×D11—22no—
484C2×D11—22no—
485C2×D11—22no—
486C2×D11—41no—
487C2×D11—41no—
488C2×D11—41no—
489C2×D11—41no—
490C4×C11—22no—
491C4×C11—42no—
492C4×C11—81no—
493C4×C11C2×C4×D411yescharacteristic
494C4×C11#51811yescharacteristic
495C4×C11D4211yescharacteristic
496C4×C11#54611yescharacteristic
497Dic11—22no—
498Dic11—22no—
499Dic11—22no—
500Dic11—42no—
501Dic11—42no—
502Dic11—81no—
503Dic11—81no—
504C25—21no—
505C2×#41—114no—
506C2×#41—222no—
507C2×#41—222no—
508C2×#41—222no—
509C2×#41—441no—
510C2×#41—441no—
511C22×Q8—111no—
512C22×D4—22no—
513C22×D4—22no—
514C22×D4—21no—
515C22×D4—22no—
516C22×D4—41no—
517C22×D4—41no—
518C22×D4—111no—
519C22×D4—221no—
520C22×D4—221no—
521C22×D4C4×D1114yescomplemented
522C22×D4C22×D1111yescharacteristic
523C22×D4C22×D1111yescharacteristic
524C23×C4—21no—
525C23×C4—111no—
526C23×C4—221no—
527C23×C4—221no—
528C23×C4—221no—
529C23×C4C22×D1111yescharacteristic
530C2×M16—222no—
531C2×M16—222no—
532C2×M16—441no—
533C22×C8—22no—
534C22×C8—22no—
535C22×C8—41no—
536C22×C8—111no—
537C22×C8—111no—
538C22×C8C22×D1111yescharacteristic
539C22×C8C22×D1111yescharacteristic
540#124—114no—
541#124—222no—
542#123—228no—
543C22⋊Q8—114no—
544C22⋊Q8—222no—
545#121—114no—
546#121—228no—
547#121—222no—
548#120—228no—
549C4×D4—114no—
550C4×D4—114no—
551C4×D4—114no—
552C4×D4—222no—
553C4×D4—444no—
554C2×C4⋊C4—22no—
555C2×C4⋊C4—21no—
556C2×C4⋊C4—41no—
557C2×C4⋊C4—111no—
558C2×C4⋊C4—111no—
559C2×C4⋊C4—111no—
560C2×C4⋊C4—111no—
561C2×C4⋊C4—221no—
562C2×C4⋊C4—222no—
563C2×C4⋊C4—221no—
564C2×C4⋊C4—221no—
565C2×C4⋊C4—221no—
566C2×C4⋊C4—441no—
567C2×C4⋊C4C22×D1111yescharacteristic
568C2×C4⋊C4C22×D1111yescharacteristic
569C2×C22⋊C4—111no—
570C2×C22⋊C4—111no—
571C2×C22⋊C4—228no—
572C2×C22⋊C4—221no—
573C2×C22⋊C4—221no—
574C2×C22⋊C4—221no—
575C2×C22⋊C4—221no—
576C2×C22⋊C4—221no—
577C2×C22⋊C4—221no—
578C2×C22⋊C4—221no—
579C2×C42—111no—
580C2×C42—221no—
581C4⋊C8—222no—
582#103—222no—
583#103—222no—
584#103—441no—
585#103—441no—
586#102—22no—
587#102—22no—
588#102—22no—
589#102—222no—
590#102—222no—
591#102—441no—
592#102—441no—
593#102C22⋊D1114yescomplemented
594C22⋊C8—222no—
595C22⋊C8—222no—
596#97—222no—
597#95—221no—
598#95—221no—
599#95—221no—
600C2×C11—24no—
601C2×C11—44no—
602C2×C11—82no—
603C2×C11D4×C22⋊C411yescharacteristic
604C2×C11C2×#41711yescharacteristic
605C2×C11#289711yescharacteristic
606C2×C11#326411yescharacteristic
607C2×C11#326611yescharacteristic
608C2×C11#330611yescharacteristic
609C2×C11#331411yescharacteristic
610D11—42no—
611C24—21no—
612C24—21no—
613C24—24no—
614C24—42no—
615C24—42no—
616C24—42no—
617C24—42no—
618C24—81no—
619C24—81no—
620C24—111no—
621C24D4×D1111yescharacteristic
622#41—228no—
623#41—444no—
624#41—444no—
625#41—444no—
626C2×Q8—112no—
627C2×Q8—221no—
628C2×Q8—221no—
629C2×Q8—221no—
630C2×Q8—221no—
631C2×Q8—221no—
632C2×D4—28no—
633C2×D4—24no—
634C2×D4—21no—
635C2×D4—21no—
636C2×D4—21no—
637C2×D4—21no—
638C2×D4—21no—
639C2×D4—21no—
640C2×D4—21no—
641C2×D4—21no—
642C2×D4—44no—
643C2×D4—44no—
644C2×D4—44no—
645C2×D4—42no—
646C2×D4—42no—
647C2×D4—114no—
648C2×D4—222no—
649C2×D4—222no—
650C2×D4—224no—
651C2×D4—224no—
652C2×D4—442no—
653C2×D4—442no—
654C2×D4—881no—
655C2×D4—881no—
656C2×D4C2×C4×D1112yes—
657C2×D4C2×C4×D1112yes—
658C2×D4#433912yes—
659C2×D4C2×C22⋊D1112yes—
660C22×C4—21no—
661C22×C4—21no—
662C22×C4—21no—
663C22×C4—21no—
664C22×C4—21no—
665C22×C4—21no—
666C22×C4—42no—
667C22×C4—42no—
668C22×C4—81no—
669C22×C4—111no—
670C22×C4—111no—
671C22×C4—111no—
672C22×C4—112no—
673C22×C4—112no—
674C22×C4—224no—
675C22×C4—224no—
676C22×C4—221no—
677C22×C4—221no—
678C22×C4—221no—
679C22×C4—221no—
680C22×C4—221no—
681C22×C4—221no—
682C22×C4—221no—
683C22×C4—221no—
684C22×C4—442no—
685C22×C4—442no—
686C22×C4—442no—
687C22×C4—442no—
688C22×C4—881no—
689C22×C4—881no—
690C22×C4—881no—
691C22×C4C2×C4×D1112yes—
692C22×C4D4×D1111yescharacteristic
693C22×C4D4×D1112yes—
694C22×C4C23×D1111yescharacteristic
695M16—444no—
696C2×C8—21no—
697C2×C8—21no—
698C2×C8—21no—
699C2×C8—21no—
700C2×C8—21no—
701C2×C8—44no—
702C2×C8—221no—
703C2×C8—221no—
704C2×C8—221no—
705C2×C8—221no—
706C2×C8—221no—
707C2×C8—221no—
708C2×C8C2×C22⋊D1112yes—
709C4⋊C4—21no—
710C4⋊C4—21no—
711C4⋊C4—21no—
712C4⋊C4—42no—
713C4⋊C4—114no—
714C4⋊C4—112no—
715C4⋊C4—224no—
716C4⋊C4—221no—
717C4⋊C4—221no—
718C4⋊C4—221no—
719C4⋊C4—221no—
720C4⋊C4—221no—
721C4⋊C4—442no—
722C4⋊C4—442no—
723C4⋊C4—881no—
724C4⋊C4C2×C22⋊D1112yes—
725C22⋊C4—114no—
726C22⋊C4—114no—
727C22⋊C4—224no—
728C22⋊C4—224no—
729C22⋊C4—224no—
730C22⋊C4—224no—
731C22⋊C4—224no—
732C22⋊C4—442no—
733C22⋊C4—442no—
734C42—112no—
735C42—112no—
736C42—442no—
737C11#2241911yescharacteristic, complemented, Sylow
738C23—21no—
739C23—21no—
740C23—21no—
741C23—21no—
742C23—22no—
743C23—22no—
744C23—22no—
745C23—22no—
746C23—48no—
747C23—41no—
748C23—41no—
749C23—41no—
750C23—41no—
751C23—41no—
752C23—41no—
753C23—41no—
754C23—41no—
755C23—41no—
756C23—41no—
757C23—48no—
758C23—84no—
759C23—84no—
760C23—84no—
761C23—84no—
762C23—84no—
763C23—112no—
764C23—221no—
765C23—221no—
766C23—221no—
767C23—221no—
768C23—221no—
769C23—221no—
770C23C22⋊C4×D1112yes—
771C23#6696412yes—
772C23#6696812yes—
773C23C2×D4×D1111yescharacteristic
774Q8—222no—
775Q8—222no—
776Q8—441no—
777Q8—441no—
778D4—22no—
779D4—22no—
780D4—22no—
781D4—22no—
782D4—22no—
783D4—48no—
784D4—41no—
785D4—41no—
786D4—228no—
787D4—448no—
788D4—884no—
789D4C4×C22⋊D1114yescomplemented
790C2×C4—21no—
791C2×C4—21no—
792C2×C4—22no—
793C2×C4—22no—
794C2×C4—22no—
795C2×C4—22no—
796C2×C4—22no—
797C2×C4—41no—
798C2×C4—41no—
799C2×C4—41no—
800C2×C4—41no—
801C2×C4—41no—
802C2×C4—84no—
803C2×C4—112no—
804C2×C4—112no—
805C2×C4—112no—
806C2×C4—221no—
807C2×C4—221no—
808C2×C4—221no—
809C2×C4—221no—
810C2×C4—221no—
811C2×C4—221no—
812C2×C4—222no—
813C2×C4—222no—
814C2×C4—222no—
815C2×C4—222no—
816C2×C4—222no—
817C2×C4—222no—
818C2×C4—448no—
819C2×C4—441no—
820C2×C4—441no—
821C2×C4—441no—
822C2×C4—441no—
823C2×C4—441no—
824C2×C4—441no—
825C2×C4—441no—
826C2×C4—441no—
827C2×C4—441no—
828C2×C4—441no—
829C2×C4—884no—
830C2×C4—884no—
831C2×C4C22⋊C4×D1112yes—
832C2×C4C22×C4×D1111yescharacteristic
833C2×C4C2×#433911yescharacteristic
834C2×C4C2×D4×D1111yescharacteristic
835C2×C4#6703711yescharacteristic
836C2×C4#6703711yescharacteristic
837C2×C4C22×C22⋊D1111yescharacteristic
838C8—22no—
839C8—41no—
840C8—441no—
841C8—441no—
842C22—22no—
843C22—22no—
844C22—22no—
845C22—22no—
846C22—22no—
847C22—22no—
848C22—24no—
849C22—42no—
850C22—42no—
851C22—42no—
852C22—42no—
853C22—42no—
854C22—42no—
855C22—42no—
856C22—42no—
857C22—42no—
858C22—816no—
859C22—81no—
860C22—81no—
861C22—81no—
862C22—81no—
863C22—222no—
864C22—222no—
865C22—222no—
866C22—441no—
867C22—441no—
868C22—441no—
869C22—441no—
870C22#1062238414yescomplemented
871C22C2×C22⋊C4×D1111yescharacteristic
872C22#1062302111yescharacteristic
873C22C2×#6696411yescharacteristic
874C22#1062328811yescharacteristic
875C22C2×#6696811yescharacteristic
876C22#1062329311yescharacteristic
877C22D4×C22⋊D1111yescharacteristic
878C4—22no—
879C4—42no—
880C4—81no—
881C4—222no—
882C4—222no—
883C4—222no—
884C4—442no—
885C4—442no—
886C4—881no—
887C4—881no—
888C4#1062301711yescharacteristic
889C4#1062302111yescharacteristic
890C4C2×C4×C22⋊D1111yescharacteristic
891C4D4×C22⋊D1111yescharacteristic
892C2—24no—
893C2—44no—
894C2—82no—
895C2—442no—
896C2C22⋊C4×C22⋊D1111yescharacteristic
897C2C2×#1062238411yescharacteristic
898C2#1307713711yescharacteristic
899C2#1308009611yescharacteristic
900C2#1308012611yescharacteristic
901C2#1308057311yescharacteristic
902C2#1308069311yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC22×C11×#102C2
socleC23×C11C22×D4
prime radicalC2×#10623337C2
cosocleC22×C4×C11C24
hypercenterC22×#102D11
hypocenterC11#22419
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ C22×#102

Complements

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

NH ≅ G/Ntype
2. C2×#10622724C2semidirect
3. C2×#10622384C2semidirect
4. C4⋊C4×C22⋊D11C2semidirect
5. #13069547C2semidirect
6. #13069431C2semidirect
7. #13069051C2semidirect
8. #13069039C2semidirect
9. #13068930C2semidirect
10. #13068923C2semidirect
11. #13068614C2semidirect
12. #13068553C2semidirect
13. #13068547C2semidirect
14. #13068443C2semidirect
15. C22×C11×#102C2semidirect
23. #10623337C4semidirect
32. C22×#4313C22semidirect
33. C2×C4⋊C4×D11C22semidirect
47. C2×(C2×D11)⋊C8C22semidirect
48. C2×#66880C22semidirect
49. C2×#66880C22semidirect
50. C2×#66879C22semidirect
51. C2×Dic11⋊C8C22semidirect
53. #10622600C22semidirect
54. #10622589C22semidirect
55. C4⋊C4×Dic11C22semidirect
57. C2×#66874C22semidirect
58. C2×#66874C22semidirect
60. #10622189C22semidirect
61. #10622189C22semidirect
62. #10622167C22semidirect
63. #10622167C22semidirect
71. C22×D4×C11C2×C4semidirect
86. C2×#4341C2×C4semidirect
111. #66991C2×C4semidirect
113. #66989C2×C4semidirect
116. D4×Dic11C2×C4semidirect
126. #66977C2×C4semidirect
144. C11×#102D4semidirect
290. C22×#102D11semidirect
346. D4×C11C4×D4semidirect
475. C22×C11#417semidirect
521. C22×D4C4×D11semidirect
593. #102C22⋊D11semidirect
737. C11#22419semidirect
789. D4C4×C22⋊D11semidirect
870. C22#10622384semidirect

Maximal subgroups

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

subgroupindex
C2×#106233372
C2×#106227242
C2×#106223842
C4⋊C4×C22⋊D112
#130695472
#130694312
#130690512
#130690392
#130689302
#130689232
#130686142
#130685532
#130685472
#130684432
C22×C11×#1022
#2241911