Finite Group Databasebeta

← #14800972

Subgroups — #14800972

Order 2816.

1264 conjugacy classes of subgroups.

The subgroup lattice has 854 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622662C211yesmaximal, characteristic, complemented
2C2×#10622659C211yesmaximal, characteristic, complemented
3C2×#10622625C211yesmaximal, characteristic, complemented
4C2×#10622614C211yesmaximal, characteristic, complemented
5#13071972C211yesmaximal, characteristic
6#13070001C211yesmaximal, characteristic, complemented
7#13069931C211yesmaximal, characteristic, complemented
8#13069805C211yesmaximal, characteristic, complemented
9#13069617C211yesmaximal, characteristic, complemented
10#13069473C211yesmaximal, characteristic, complemented
11#13069298C211yesmaximal, characteristic, complemented
12#13069052C211yesmaximal, characteristic, complemented
13#13069050C211yesmaximal, characteristic, complemented
14#13068815C211yesmaximal, characteristic, complemented
15C11×#2415C211yesmaximal, characteristic, complemented
16C23×D44C2211yescharacteristic
17C2×C11×C22⋊Q8C2211yescharacteristic
18C2×C11×C22⋊Q8C2211yescharacteristic, complemented
19C2×C4×D4×C11C2211yescharacteristic
20C2×C11×#117C2211yescharacteristic
21C22×#4325C2211yescharacteristic
22C22×#4325C2211yescharacteristic
23C2×#66990—21no—
24C2×#66983C2211yescharacteristic
25C2×#66983C2211yescharacteristic
26C22×#4318C2211yescharacteristic
27C22×#4318C2211yescharacteristic, complemented
28C11×#397—21no—
29C11×#394—21no—
30C11×#391C2211yescharacteristic, complemented
31C11×#389—21no—
32C11×#389C2211yescharacteristic, complemented
33C11×#388—21no—
34C11×#380C2211yescharacteristic, complemented
35C2×#66899C2211yescharacteristic, complemented
36C2×#66899C2211yescharacteristic, complemented
37#10622825C2211yescharacteristic
38C2×C22⋊(C11⋊C8)C2211yescharacteristic
39C2×C22⋊(C11⋊C8)C2211yescharacteristic, complemented
40#10622662—24no—
41#10622659—24no—
42#10622625—24no—
43#10622614—24no—
44#10622604—21no—
45C2×#66873C2211yescharacteristic
46C2×#66873C2211yescharacteristic
47C2×#66873C2211yescharacteristic
48C2×#66873C2211yescharacteristic
49C2×#66873C2211yescharacteristic
50C2×#66873C2211yescharacteristic
51C2×#66872C2211yescharacteristic, complemented
52C2×#66871C2211yescharacteristic, complemented
53#10622573—21no—
54#10622568—21no—
55#10622552C2211yescharacteristic
56#10622552C2211yescharacteristic
57C2×C4⋊(C11⋊C8)C2211yescharacteristic, complemented
58C2×C4×C11⋊C8C2211yescharacteristic, complemented
59#10622167C2211yescharacteristic, complemented
60#10622167C2211yescharacteristic, complemented
61#10622167C2211yescharacteristic, complemented
62#10622167C2211yescharacteristic, complemented
63C24×D11—21no—
64C22×Q8×C11C2311yescharacteristic
65C22×D4×C11D411yescharacteristic
66C23×C4×C11C2311yescharacteristic
67C23×C4×C11C2311yescharacteristic
68C22×C22⋊D11—21no—
69C22×C22⋊D11—21no—
70C22×D44—22no—
71C22×D44—22no—
72C22×D44—22no—
73C22×D44—22no—
74C22×D44—21no—
75C22×D44—41no—
76C22×D44—41no—
77C22×D44C2311yescharacteristic
78C22×D44C2311yescharacteristic
79C11×C22⋊Q8—22no—
80C11×C22⋊Q8—22no—
81C11×C22⋊Q8—22no—
82C11×C22⋊Q8—41no—
83C4×D4×C11—22no—
84C4×D4×C11—22no—
85C11×#117—22no—
86C11×#117—41no—
87C2×C11×C4⋊C4—21no—
88C2×C11×C4⋊C4—21no—
89C2×C11×C4⋊C4—21no—
90C2×C11×C4⋊C4D411yescharacteristic
91C2×C11×C4⋊C4C2311yescharacteristic
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×C11×C22⋊C4D411yescharacteristic
99C2×C11×C22⋊C4D411yescharacteristic
100C2×C42×C11—21no—
101C2×C42×C11C2311yescharacteristic
102C2×C22⋊Dic11—21no—
103C2×#4325—22no—
104C2×#4325—22no—
105C2×#4325—22no—
106C2×#4325—22no—
107C2×#4325—41no—
108C2×#4325—41no—
109#66990—44no—
110#66983—22no—
111#66983—22no—
112#66983—41no—
113#66983—41no—
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⋊Dic11C2311yescharacteristic
121C2×C4⋊Dic11C2311yescharacteristic
122C2×#4318—22no—
123C2×#4318—22no—
124C2×#4318—22no—
125C2×#4318—22no—
126C2×#4318—41no—
127C2×#4318—41no—
128C22×C11⋊C8C2311yescharacteristic
129C22×C11⋊C8C2311yescharacteristic
130C22×C11⋊C8C2311yescharacteristic
131C22×C11⋊C8C2311yescharacteristic
132C11×#95—21no—
133C11×#95—21no—
134C11×#95—21no—
135C11×#95—21no—
136#66899—22no—
137#66899—41no—
138C11⋊#95—21no—
139C22⋊(C11⋊C8)—22no—
140C22⋊(C11⋊C8)D414yescomplemented
141#66873—22no—
142#66873—22no—
143#66873—22no—
144#66873—22no—
145#66873—22no—
146#66873D414yescomplemented
147#66872—41no—
148#66871—22no—
149C4⋊(C11⋊C8)—22no—
150C4×C11⋊C8—22no—
151#25136—111nomaximal, Sylow
152C24×C11C2×D411yescharacteristic
153C24×C11C2×D411yescharacteristic
154C23×D11—21no—
155C23×D11—21no—
156C23×D11—42no—
157C23×D11—42no—
158C23×D11—42no—
159C23×D11—42no—
160C23×D11—42no—
161C23×D11—81no—
162C23×D11—81no—
163C2×Q8×C11—21no—
164C2×Q8×C11—21no—
165C2×Q8×C11—21no—
166C2×Q8×C11—21no—
167C2×Q8×C11—21no—
168C2×Q8×C11—21no—
169C2×D4×C11—22no—
170C2×D4×C11—22no—
171C2×D4×C11—41no—
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×C11—21no—
179C22×C4×C11—21no—
180C22×C4×C11—21no—
181C22×C4×C11—21no—
182C22×C4×C11—21no—
183C22×C4×C11—21no—
184C22×C4×C11—21no—
185C22×C4×C11—21no—
186C22×C4×C11C2×D411yescharacteristic
187C22×C4×C11C2×D411yescharacteristic
188C22×C4×C11C2×D411yescharacteristic
189C22×C4×C11C2×D412yes—
190C22×C4×C11C2×D411yescharacteristic
191C22×C4×C11#4112yes—
192C22×C4×C11C2411yescharacteristic
193C2×C22⋊D11—42no—
194C2×C22⋊D11—42no—
195C2×C22⋊D11—42no—
196C2×C22⋊D11—42no—
197C2×C22⋊D11—81no—
198C2×C22⋊D11—81no—
199C22×Dic11—21no—
200C22×Dic11—21no—
201C2×D44—28no—
202C2×D44—21no—
203C2×D44—21no—
204C2×D44—21no—
205C2×D44—21no—
206C2×D44—21no—
207C2×D44—21no—
208C2×D44—21no—
209C2×D44—21no—
210C2×D44—21no—
211C2×D44—21no—
212C2×D44—42no—
213C2×D44—42no—
214C2×D44—44no—
215C2×D44—44no—
216C2×D44—44no—
217C2×D44—42no—
218C2×D44C2×D412yes—
219C2×D44#4112yes—
220C11×C4⋊C4—22no—
221C11×C4⋊C4—21no—
222C11×C4⋊C4—21no—
223C11×C4⋊C4—21no—
224C11×C4⋊C4—21no—
225C11×C4⋊C4—21no—
226C11×C4⋊C4—42no—
227C11×C4⋊C4—42no—
228C11×C4⋊C4—42no—
229C11×C4⋊C4C2×D412yes—
230C11×C22⋊C4—22no—
231C11×C22⋊C4—22no—
232C11×C22⋊C4—42no—
233C11×C22⋊C4—42no—
234C11×C22⋊C4—42no—
235C11×C22⋊C4—42no—
236C42×C11—21no—
237C42×C11—21no—
238C42×C11—42no—
239C22⋊Dic11—42no—
240#4325—44no—
241#4325—44no—
242(C2×D11)⋊C4—42no—
243(C2×D11)⋊C4—42no—
244(C2×D11)⋊C4—42no—
245(C2×D11)⋊C4—42no—
246(C2×D11)⋊C4—81no—
247(C2×D11)⋊C4—81no—
248C4⋊Dic11—21no—
249C4⋊Dic11—21no—
250C4⋊Dic11—21no—
251C4⋊Dic11—21no—
252#4318—44no—
253#4318—44no—
254C2×C11⋊C8—21no—
255C2×C11⋊C8—21no—
256C2×C11⋊C8—21no—
257C2×C11⋊C8—21no—
258C2×C11⋊C8—21no—
259C2×C11⋊C8—21no—
260C2×C11⋊C8—21no—
261C2×C11⋊C8—21no—
262C2×C11⋊C8—21no—
263C2×C11⋊C8C2×D412yes—
264C2×C11⋊C8C2×D412yes—
265C2×C11⋊C8C2×D412yes—
266C2×#468—111no—
267C2×#450—111no—
268C2×#436—111no—
269C2×#418—111no—
270#2415D1111yescharacteristic, complemented
271#2408—111no—
272#2067—111no—
273#2055—111no—
274#2034—111no—
275#2000—111no—
276#1968—111no—
277#1934—111no—
278#1895—111no—
279#1894—111no—
280#1854—111no—
281C23×C11—21no—
282C23×C11—21no—
283C23×C11—21no—
284C23×C11—21no—
285C23×C11—21no—
286C23×C11—21no—
287C23×C11—21no—
288C23×C11—21no—
289C23×C11—21no—
290C23×C11—21no—
291C23×C11—21no—
292C23×C11—21no—
293C23×C11—21no—
294C23×C11#12112yes—
295C23×C11C22×D411yescharacteristic
296C22×D11—22no—
297C22×D11—22no—
298C22×D11—48no—
299C22×D11—41no—
300C22×D11—41no—
301C22×D11—41no—
302C22×D11—41no—
303C22×D11—41no—
304C22×D11—41no—
305C22×D11—41no—
306C22×D11—41no—
307C22×D11—41no—
308C22×D11—41no—
309C22×D11—41no—
310C22×D11—41no—
311C22×D11—84no—
312C22×D11—84no—
313C22×D11—84no—
314C22×D11—84no—
315C22×D11—84no—
316C22×D11—84no—
317Q8×C11—41no—
318Q8×C11—41no—
319Q8×C11—41no—
320Q8×C11—41no—
321D4×C11—44no—
322C2×C4×C11—21no—
323C2×C4×C11—21no—
324C2×C4×C11—21no—
325C2×C4×C11—21no—
326C2×C4×C11—22no—
327C2×C4×C11—22no—
328C2×C4×C11—22no—
329C2×C4×C11—22no—
330C2×C4×C11—21no—
331C2×C4×C11—21no—
332C2×C4×C11—21no—
333C2×C4×C11—22no—
334C2×C4×C11—21no—
335C2×C4×C11—21no—
336C2×C4×C11—21no—
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×C11—41no—
350C2×C4×C11—41no—
351C2×C4×C11—41no—
352C2×C4×C11#12112yes—
353C2×C4×C11AGL(1,ℤ/8)12yes—
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—
362C2×Dic11—41no—
363C2×Dic11—41no—
364C2×Dic11—41no—
365C2×Dic11—41no—
366C2×Dic11—41no—
367C2×Dic11—41no—
368D44—22no—
369D44—22no—
370D44—22no—
371D44—22no—
372D44—48no—
373D44—41no—
374D44—41no—
375D44—41no—
376D44—41no—
377C11⋊C8—22no—
378C11⋊C8—22no—
379C11⋊C8—22no—
380C11⋊C8—41no—
381C23×D4—111no—
382C22×SD16—111no—
383C22×SD16—111no—
384C22×M16—111no—
385C22×M16—111no—
386C2×C22⋊Q8C2×D1111yescharacteristic
387C2×C22⋊Q8C2×D1111yescharacteristic, complemented
388C2×#121—111no—
389C2×#121—111no—
390C2×#120—221no—
391C2×C4×D4C2×D1111yescharacteristic
392C2×#117C2×D1111yescharacteristic
393#468—224no—
394#450—224no—
395#436—224no—
396C2×#107—111no—
397C2×#106—111no—
398C2×C4⋊C8—111no—
399#418—224no—
400C2×#103—111no—
401C2×#103—111no—
402C2×#102—111no—
403C2×#102—111no—
404C2×#102—111no—
405C2×#102—111no—
406C2×#102—111no—
407C2×#102—111no—
408C2×C22⋊C8—111no—
409C2×C22⋊C8—111no—
410C2×C4×C8—111no—
411#397—21no—
412#394—21no—
413#394—221no—
414#392—221no—
415#391C2×D1111yescharacteristic, complemented
416#390—111no—
417#390—111no—
418#389—21no—
419#389C2×D1111yescharacteristic, complemented
420#388—21no—
421#380—111no—
422#380C2×D1111yescharacteristic, complemented
423#379—221no—
424#340—111no—
425#340—111no—
426#340—111no—
427#340—111no—
428C22×C11—22no—
429C22×C11—22no—
430C22×C11—22no—
431C22×C11—41no—
432C22×C11—41no—
433C22×C11—41no—
434C22×C11—41no—
435C22×C11—41no—
436C22×C11—41no—
437C22×C11—41no—
438C22×C11—41no—
439C22×C11—41no—
440C22×C11—41no—
441C22×C11—41no—
442C22×C11C2×#12111yescharacteristic
443C22×C11D4211yescharacteristic
444C22×C11#54611yescharacteristic
445C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
446C22×C11#57511yescharacteristic
447C22×C11#57711yescharacteristic
448C22×C11#57711yescharacteristic
449C2×D11—42no—
450C2×D11—42no—
451C2×D11—42no—
452C2×D11—42no—
453C2×D11—42no—
454C2×D11—42no—
455C2×D11—816no—
456C2×D11—81no—
457C2×D11—81no—
458C2×D11—81no—
459C2×D11—81no—
460C2×D11—81no—
461C2×D11—81no—
462C2×D11—81no—
463C2×D11—81no—
464C4×C11—22no—
465C4×C11—22no—
466C4×C11—41no—
467C4×C11—42no—
468C4×C11—41no—
469C4×C11—81no—
470C4×C11—81no—
471C4×C11—81no—
472C4×C11#52511yescharacteristic
473C4×C11#53811yescharacteristic
474C4×C11D4211yescharacteristic
475C4×C11#54611yescharacteristic
476Dic11—81no—
477Dic11—81no—
478C25—221no—
479C22×Q8C22×D1111yescharacteristic
480C22×D4—111no—
481C22×D4—111no—
482C22×D4—222no—
483C22×D4—222no—
484C22×D4—221no—
485C22×D4—221no—
486C22×D4—222no—
487C22×D4—222no—
488C22×D4—221no—
489C22×D4—441no—
490C22×D4—441no—
491C22×D4C22⋊D1111yescharacteristic
492C23×C4C22×D1111yescharacteristic
493C23×C4C22×D1111yescharacteristic
494C2×SD16—222no—
495C2×SD16—222no—
496C2×SD16—222no—
497C2×SD16—222no—
498C2×SD16—441no—
499C2×SD16—441no—
500C2×M16—222no—
501C2×M16—222no—
502C2×M16—222no—
503C2×M16—222no—
504C2×M16—441no—
505C2×M16—441no—
506C22×C8—111no—
507C22×C8—111no—
508C22×C8—111no—
509C22×C8—111no—
510C22⋊Q8—22no—
511C22⋊Q8—22no—
512C22⋊Q8—22no—
513C22⋊Q8—41no—
514#121—222no—
515#121—222no—
516#121—441no—
517#121—441no—
518#120—444no—
519C4×D4—22no—
520C4×D4—22no—
521#117—22no—
522#117—41no—
523C2×C4⋊C4—21no—
524C2×C4⋊C4—21no—
525C2×C4⋊C4—21no—
526C2×C4⋊C4—111no—
527C2×C4⋊C4—111no—
528C2×C4⋊C4C22⋊D1111yescharacteristic
529C2×C4⋊C4C22×D1111yescharacteristic
530C2×C4⋊C4C22×D1111yescharacteristic
531C2×C4⋊C4C22×D1111yescharacteristic
532C2×C22⋊C4—21no—
533C2×C22⋊C4—21no—
534C2×C22⋊C4—21no—
535C2×C22⋊C4—21no—
536C2×C22⋊C4—221no—
537C2×C22⋊C4—221no—
538C2×C22⋊C4—221no—
539C2×C22⋊C4—221no—
540C2×C22⋊C4—221no—
541C2×C22⋊C4—221no—
542C2×C22⋊C4—221no—
543C2×C22⋊C4C22⋊D1111yescharacteristic
544C2×C22⋊C4C22⋊D1111yescharacteristic
545C2×C42—21no—
546C2×C42C22×D1111yescharacteristic
547#107—222no—
548#106—441no—
549C4⋊C8—222no—
550#103—222no—
551#103—441no—
552#102—114no—
553#102—222no—
554#102—222no—
555#102—222no—
556#102—222no—
557#102—222no—
558C22⋊C8—114no—
559C22⋊C8—222no—
560C4×C8—222no—
561#95—21no—
562#95—21no—
563#95—21no—
564#95—21no—
565#95—221no—
566C2×C11—42no—
567C2×C11—81no—
568C2×C11#242411yescharacteristic
569C2×C11#305511yescharacteristic
570C2×C11#305711yescharacteristic
571C2×C11#327211yescharacteristic
572C2×C11#327511yescharacteristic
573C2×C11#332311yescharacteristic
574C2×C11#332411yescharacteristic
575D11—82no—
576D11—82no—
577C24—221no—
578C24—221no—
579C24—442no—
580C24—442no—
581C24—442no—
582C24—442no—
583C24—442no—
584C24—881no—
585C24—881no—
586C24C2×C22⋊D1111yescharacteristic
587C24C2×C22⋊D1111yescharacteristic
588C2×Q8—21no—
589C2×Q8—21no—
590C2×Q8—21no—
591C2×Q8—21no—
592C2×Q8—21no—
593C2×Q8—21no—
594C2×D4—22no—
595C2×D4—22no—
596C2×D4—41no—
597C2×D4—112no—
598C2×D4—112no—
599C2×D4—228no—
600C2×D4—221no—
601C2×D4—221no—
602C2×D4—221no—
603C2×D4—221no—
604C2×D4—221no—
605C2×D4—221no—
606C2×D4—221no—
607C2×D4—221no—
608C2×D4—221no—
609C2×D4—221no—
610C2×D4—444no—
611C2×D4—444no—
612C2×D4—442no—
613C2×D4—442no—
614C2×D4—444no—
615C2×D4—442no—
616C2×D4—442no—
617C2×D4—442no—
618C2×D4—442no—
619C2×D4—442no—
620C2×D4—881no—
621C2×D4—881no—
622C22×C4—21no—
623C22×C4—21no—
624C22×C4—21no—
625C22×C4—21no—
626C22×C4—21no—
627C22×C4—21no—
628C22×C4—21no—
629C22×C4—21no—
630C22×C4—21no—
631C22×C4—21no—
632C22×C4—21no—
633C22×C4—21no—
634C22×C4—21no—
635C22×C4—21no—
636C22×C4—221no—
637C22×C4—221no—
638C22×C4D4×D1112yes—
639C22×C4#434112yes—
640C22×C4C2×C22⋊D1111yescharacteristic
641C22×C4C2×C22⋊D1111yescharacteristic
642C22×C4C2×C22⋊D1111yescharacteristic
643C22×C4C2×C22⋊D1111yescharacteristic
644C22×C4C23×D1111yescharacteristic
645SD16—444no—
646SD16—444no—
647M16—444no—
648M16—444no—
649C2×C8—112no—
650C2×C8—112no—
651C2×C8—112no—
652C2×C8—221no—
653C2×C8—221no—
654C2×C8—221no—
655C2×C8—221no—
656C2×C8—221no—
657C2×C8—221no—
658C2×C8—221no—
659C2×C8—221no—
660C2×C8—221no—
661C4⋊C4—22no—
662C4⋊C4—21no—
663C4⋊C4—21no—
664C4⋊C4—21no—
665C4⋊C4—21no—
666C4⋊C4—21no—
667C4⋊C4—42no—
668C4⋊C4—42no—
669C4⋊C4—42no—
670C4⋊C4—221no—
671C4⋊C4—221no—
672C4⋊C4—221no—
673C4⋊C4—221no—
674C4⋊C4D4×D1112yes—
675C22⋊C4—22no—
676C22⋊C4—22no—
677C22⋊C4—42no—
678C22⋊C4—42no—
679C22⋊C4—42no—
680C22⋊C4—42no—
681C22⋊C4—442no—
682C22⋊C4—442no—
683C22⋊C4—442no—
684C22⋊C4—442no—
685C22⋊C4—442no—
686C22⋊C4—881no—
687C22⋊C4—881no—
688C42—21no—
689C42—21no—
690C42—42no—
691C11#2513611yescharacteristic, complemented, Sylow
692C23—21no—
693C23—21no—
694C23—21no—
695C23—21no—
696C23—21no—
697C23—21no—
698C23—21no—
699C23—21no—
700C23—21no—
701C23—21no—
702C23—21no—
703C23—21no—
704C23—21no—
705C23—222no—
706C23—222no—
707C23—448no—
708C23—441no—
709C23—441no—
710C23—441no—
711C23—441no—
712C23—441no—
713C23—441no—
714C23—441no—
715C23—441no—
716C23—441no—
717C23—441no—
718C23—441no—
719C23—441no—
720C23—884no—
721C23—884no—
722C23—884no—
723C23—884no—
724C23—884no—
725C23—884no—
726C23#6699212yes—
727C23C22×C22⋊D1111yescharacteristic
728Q8—41no—
729Q8—41no—
730Q8—41no—
731Q8—41no—
732D4—44no—
733D4—222no—
734D4—222no—
735D4—222no—
736D4—222no—
737D4—448no—
738D4—441no—
739D4—441no—
740D4—441no—
741D4—441no—
742D4—884no—
743D4—884no—
744C2×C4—21no—
745C2×C4—21no—
746C2×C4—21no—
747C2×C4—21no—
748C2×C4—22no—
749C2×C4—22no—
750C2×C4—22no—
751C2×C4—22no—
752C2×C4—22no—
753C2×C4—21no—
754C2×C4—21no—
755C2×C4—21no—
756C2×C4—21no—
757C2×C4—21no—
758C2×C4—21no—
759C2×C4—41no—
760C2×C4—41no—
761C2×C4—41no—
762C2×C4—41no—
763C2×C4—41no—
764C2×C4—41no—
765C2×C4—41no—
766C2×C4—41no—
767C2×C4—41no—
768C2×C4—41no—
769C2×C4—41no—
770C2×C4—41no—
771C2×C4—41no—
772C2×C4—41no—
773C2×C4—41no—
774C2×C4—441no—
775C2×C4—441no—
776C2×C4—441no—
777C2×C4—441no—
778C2×C4—441no—
779C2×C4—441no—
780C2×C4#6699212yes—
781C2×C4#6700212yes—
782C2×C4C2×D4×D1111yescharacteristic
783C2×C4C2×D4×D1111yescharacteristic
784C2×C4C2×#434111yescharacteristic
785C2×C4#6703711yescharacteristic
786C2×C4#41×D1111yescharacteristic
787C2×C4#6704211yescharacteristic
788C8—222no—
789C8—222no—
790C8—222no—
791C8—441no—
792C22—22no—
793C22—22no—
794C22—22no—
795C22—41no—
796C22—41no—
797C22—41no—
798C22—41no—
799C22—41no—
800C22—41no—
801C22—41no—
802C22—41no—
803C22—41no—
804C22—41no—
805C22—41no—
806C22—442no—
807C22—442no—
808C22—442no—
809C22—442no—
810C22—442no—
811C22—442no—
812C22—8816no—
813C22—881no—
814C22—881no—
815C22—881no—
816C22—881no—
817C22—881no—
818C22—881no—
819C22—881no—
820C22—881no—
821C22D4×C22⋊D1111yescharacteristic
822C22C2×#6699211yescharacteristic
823C22C2×#6700211yescharacteristic
824C22#1062335311yescharacteristic
825C22#1062336011yescharacteristic
826C22#1062336811yescharacteristic
827C22#1062336811yescharacteristic
828C4—22no—
829C4—22no—
830C4—41no—
831C4—42no—
832C4—41no—
833C4—81no—
834C4—81no—
835C4—81no—
836C4—881no—
837C4—881no—
838C4#1062313711yescharacteristic
839C4#1062314011yescharacteristic
840C4#1062314111yescharacteristic
841C4#1062314811yescharacteristic
842C2—42no—
843C2—81no—
844C2—882no—
845C2—882no—
846C2#1307215811yescharacteristic
847C2#1307823711yescharacteristic
848C2#1307825711yescharacteristic
849C2#1308021611yescharacteristic
850C2#1308024811yescharacteristic
851C2#1308082611yescharacteristic
852C2#1308084111yescharacteristic
subgroupG/H
centerC23C22×C22⋊D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#2415C2
socleC23×C11C22×D4
prime radical#13071972C2
hypercenter#2415D11
hypocenterC11#25136
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ #2415

Complements

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

NH ≅ G/Ntype
1. C2×#10622662C2semidirect
2. C2×#10622659C2semidirect
3. C2×#10622625C2semidirect
4. C2×#10622614C2semidirect
6. #13070001C2semidirect
7. #13069931C2semidirect
8. #13069805C2semidirect
9. #13069617C2semidirect
10. #13069473C2semidirect
11. #13069298C2semidirect
12. #13069052C2semidirect
13. #13069050C2semidirect
14. #13068815C2semidirect
15. C11×#2415C2semidirect
18. C2×C11×C22⋊Q8C22semidirect
27. C22×#4318C22semidirect
30. C11×#391C22semidirect
32. C11×#389C22semidirect
34. C11×#380C22semidirect
35. C2×#66899C22semidirect
36. C2×#66899C22semidirect
39. C2×C22⋊(C11⋊C8)C22semidirect
51. C2×#66872C22semidirect
52. C2×#66871C22semidirect
57. C2×C4⋊(C11⋊C8)C22semidirect
58. C2×C4×C11⋊C8C22semidirect
59. #10622167C22semidirect
60. #10622167C22semidirect
61. #10622167C22semidirect
62. #10622167C22semidirect
140. C22⋊(C11⋊C8)D4semidirect
146. #66873D4semidirect
270. #2415D11semidirect
387. C2×C22⋊Q8C2×D11semidirect
415. #391C2×D11semidirect
419. #389C2×D11semidirect
422. #380C2×D11semidirect
691. C11#25136semidirect

Maximal subgroups

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

subgroupindex
C2×#106226622
C2×#106226592
C2×#106226252
C2×#106226142
#130719722
#130700012
#130699312
#130698052
#130696172
#130694732
#130692982
#130690522
#130690502
#130688152
C11×#24152
#2513611