Finite Group Databasebeta

← #14782475

Subgroups — #14782475

Order 2816.

1318 conjugacy classes of subgroups.

The subgroup lattice has 784 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622494C211yesmaximal, characteristic, complemented
2C2×#10622450C211yesmaximal, characteristic, complemented
3C2×#10622383C211yesmaximal, characteristic
4C2×#10622383C211yesmaximal, characteristic
5#13071097C211yesmaximal, characteristic, complemented
6D11×#390C211yesmaximal, characteristic
7#13070001C211yesmaximal, characteristic, complemented
8#13070000C211yesmaximal, characteristic, complemented
9#13069999C211yesmaximal, characteristic, complemented
10#13069991C211yesmaximal, characteristic, complemented
11#13069990C211yesmaximal, characteristic, complemented
12#13069989C211yesmaximal, characteristic, complemented
13#13069988C211yesmaximal, characteristic, complemented
14#13068334C211yesmaximal, characteristic, complemented
15C11×#2067C211yesmaximal, characteristic, complemented
16C22×D4×D11C2211yescharacteristic
17C22×#4313C2211yescharacteristic
18C22×#4313C2211yescharacteristic
19C2×#66945C2211yescharacteristic
20C2×#66945C2211yescharacteristic
21C2×C4⋊C4×D11C2211yescharacteristic
22C2×C22⋊C4×D11—21no—
23C2×C22⋊C4×D11—21no—
24C2×C42×D11C2211yescharacteristic
25C2×C11×#107C2211yescharacteristic, complemented
26C2×C11×C4⋊C8C2211yescharacteristic, complemented
27C2×C11×#102C2211yescharacteristic
28C2×C11×#102C2211yescharacteristic
29C11×#390C2211yescharacteristic
30C11×#389C2211yescharacteristic, complemented
31#10622834C2211yescharacteristic
32C2×#66896C2211yescharacteristic
33C2×#66896C2211yescharacteristic
34C2×#66885C2211yescharacteristic
35C2×#66885C2211yescharacteristic
36C2×#66881C2211yescharacteristic, complemented
37C2×Dic11⋊C8C2211yescharacteristic, complemented
38C2×Dic11⋊C8C2211yescharacteristic, complemented
39#10622602—21no—
40#10622601C2211yescharacteristic
41#10622598C2211yescharacteristic, complemented
42C4⋊C4×Dic11—21no—
43#10622586C2211yescharacteristic, complemented
44C2×#66873C2211yescharacteristic
45C2×#66873C2211yescharacteristic
46C2×#66872C2211yescharacteristic, complemented
47C2×#66871C2211yescharacteristic, complemented
48#10622570—21no—
49#10622570—21no—
50#10622552C2211yescharacteristic
51#10622541C2211yescharacteristic, complemented
52C2×C4⋊(C11⋊C8)C2211yescharacteristic, complemented
53#10622494—24no—
54#10622450—24no—
55#10622383—24no—
56#10622383—24no—
57#10622281—21no—
58#10622262—21no—
59C11×#340C2211yescharacteristic, complemented
60#10622189C2211yescharacteristic, complemented
61#10622167C2211yescharacteristic, complemented
62#10622167C2211yescharacteristic, complemented
63C24×D11—21no—
64C22×D4×C11C2311yescharacteristic
65C22×C22⋊D11—21no—
66C2×D4×D11—22no—
67C2×D4×D11—22no—
68C2×D4×D11—22no—
69C2×D4×D11—22no—
70C2×D4×D11—22no—
71C2×D4×D11Q814yes—
72C22×D44C2311yescharacteristic
73C22×C4×D11—21no—
74C22×C4×D11D411yescharacteristic
75C22×C4×D11D411yescharacteristic
76C22×C4×D11C2311yescharacteristic
77C22×C8×C11C2311yescharacteristic
78C22×C8×C11C2311yescharacteristic
79C2×C11×C4⋊C4—21no—
80C2×C11×C4⋊C4C2311yescharacteristic
81C2×C11×C4⋊C4C2311yescharacteristic
82C2×C11×C4⋊C4C2311yescharacteristic
83C2×C11×C22⋊C4—21no—
84C2×C11×C22⋊C4—21no—
85C2×C42×C11C2311yescharacteristic
86C2×C22⋊Dic11—21no—
87C2×C22⋊Dic11—21no—
88C2×(C2×D11)⋊C4—21no—
89C2×(C2×D11)⋊C4—21no—
90C2×(C2×D11)⋊C4—21no—
91C2×(C2×D11)⋊C4—21no—
92C2×(C2×D11)⋊C4—21no—
93C2×(C2×D11)⋊C4—21no—
94C2×C4⋊Dic11—21no—
95C2×C4⋊Dic11C2311yescharacteristic
96C2×C4⋊Dic11C2311yescharacteristic
97C2×C4⋊Dic11C2311yescharacteristic
98C2×Dic11⋊C4—21no—
99C2×Dic11⋊C4—21no—
100C2×Dic11⋊C4—21no—
101C2×C4×Dic11—21no—
102C2×C4×Dic11—21no—
103C2×C4×Dic11D411yescharacteristic
104C2×C4×Dic11D411yescharacteristic
105C2×C4×Dic11C2311yescharacteristic
106C22×C11⋊C8C2311yescharacteristic
107C22×C11⋊C8C2311yescharacteristic
108C2×#4313—22no—
109C2×#4313—22no—
110C2×#4313—22no—
111C2×#4313—22no—
112C2×#4313—22no—
113C2×#4313D414yes—
114#66945—22no—
115#66945—22no—
116#66945—22no—
117#66945D414yes—
118C4⋊C4×D11—22no—
119C4⋊C4×D11—22no—
120C22⋊C4×D11—44no—
121C22⋊C4×D11—44no—
122C42×D11—22no—
123C42×D11—22no—
124C11×#107—22no—
125C11×C4⋊C8—22no—
126C11×#102—22no—
127C11×#102—22no—
128C11×#95—21no—
129#66896—22no—
130#66896—22no—
131C11⋊#95—21no—
132C11⋊#95—21no—
133C11⋊#95—21no—
134#66885—22no—
135#66885—22no—
136#66881—22no—
137Dic11⋊C8—22no—
138Dic11⋊C8—22no—
139#66873—22no—
140#66873—22no—
141#66872—22no—
142#66871—22no—
143C4⋊(C11⋊C8)—22no—
144#23618—111nomaximal, Sylow
145C24×C11—21no—
146C23×D11—21no—
147C23×D11—24no—
148C23×D11—42no—
149C23×D11—42no—
150C23×D11—42no—
151C23×D11—42no—
152C23×D11—42no—
153C23×D11—42no—
154C23×D11C2×D411yescharacteristic
155C2×D4×C11—21no—
156C2×D4×C11—21no—
157C2×D4×C11—21no—
158C2×D4×C11—21no—
159C2×D4×C11—21no—
160C2×D4×C11C2×Q812yes—
161C22×C4×C11—21no—
162C22×C4×C11—21no—
163C22×C4×C11—21no—
164C22×C4×C11C2×D411yescharacteristic
165C22×C4×C11C2×D411yescharacteristic
166C22×C4×C11C2411yescharacteristic
167C2×C22⋊D11—24no—
168C2×C22⋊D11—42no—
169C2×C22⋊D11—42no—
170C22×Dic11—21no—
171C22×Dic11—21no—
172C22×Dic11—21no—
173C22×Dic11C2×D411yescharacteristic
174C22×Dic11C2×D411yescharacteristic
175C22×Dic11C2×D411yescharacteristic
176D4×D11—28no—
177D4×D11—28no—
178D4×D11—44no—
179D4×D11—44no—
180C2×D44—21no—
181C2×D44—21no—
182C2×D44—21no—
183C2×D44—21no—
184C2×D44—21no—
185C2×D44C2×Q812yes—
186C2×C4×D11—22no—
187C2×C4×D11—22no—
188C2×C4×D11—22no—
189C2×C4×D11—22no—
190C2×C4×D11—41no—
191C2×C4×D11—41no—
192C2×C4×D11—42no—
193C2×C4×D11—42no—
194C2×C4×D11—42no—
195C2×C4×D11C2×D412yes—
196C2×C4×D11C2×D412yes—
197C2×C4×D11C2×Q812yes—
198C2×C4×D11#4112yes—
199C2×C4×D11#4112yes—
200C2×C4×D11#4112yes—
201C2×C8×C11—21no—
202C2×C8×C11—21no—
203C2×C8×C11—21no—
204C2×C8×C11—21no—
205C2×C8×C11—21no—
206C2×C8×C11C2×D412yes—
207C11×C4⋊C4—21no—
208C11×C4⋊C4—21no—
209C11×C4⋊C4—21no—
210C11×C4⋊C4—21no—
211C11×C4⋊C4—21no—
212C11×C4⋊C4—42no—
213C11×C4⋊C4C2×D412yes—
214C11×C22⋊C4—42no—
215C11×C22⋊C4—42no—
216C42×C11—21no—
217C42×C11—21no—
218C22⋊Dic11—42no—
219C22⋊Dic11—42no—
220(C2×D11)⋊C4—24no—
221(C2×D11)⋊C4—42no—
222(C2×D11)⋊C4—42no—
223(C2×D11)⋊C4—42no—
224(C2×D11)⋊C4—42no—
225(C2×D11)⋊C4—42no—
226C4⋊Dic11—21no—
227C4⋊Dic11—21no—
228C4⋊Dic11—21no—
229C4⋊Dic11—21no—
230C4⋊Dic11—21no—
231C4⋊Dic11—42no—
232C4⋊Dic11C2×D412yes—
233Dic11⋊C4—42no—
234Dic11⋊C4—42no—
235Dic11⋊C4—42no—
236C4×Dic11—22no—
237C4×Dic11—22no—
238C4×Dic11—24no—
239C4×Dic11—21no—
240C4×Dic11—21no—
241C4×Dic11—42no—
242C2×C11⋊C8—21no—
243C2×C11⋊C8—21no—
244C2×C11⋊C8—21no—
245C2×C11⋊C8—21no—
246C2×C11⋊C8—21no—
247C2×C11⋊C8C2×D412yes—
248#4313—28no—
249#4313—44no—
250C2×#428—111no—
251C2×#423—111no—
252C2×#418—111no—
253C2×#418—111no—
254#2296—111no—
255C2×#390—111no—
256#2067—111no—
257#2067—111no—
258#2067—111no—
259#2067D1111yescharacteristic, complemented
260#2065—111no—
261#2065—111no—
262#2065—111no—
263#2065—111no—
264#1736—111no—
265C23×C11—22no—
266C23×C11—41no—
267C23×C11—41no—
268C23×C11—41no—
269C23×C11—41no—
270C23×C11—41no—
271C23×C11—41no—
272C23×C11C22×D411yescharacteristic
273C22×D11—21no—
274C22×D11—21no—
275C22×D11—21no—
276C22×D11—21no—
277C22×D11—22no—
278C22×D11—48no—
279C22×D11—48no—
280C22×D11—41no—
281C22×D11—41no—
282C22×D11—41no—
283C22×D11—41no—
284C22×D11—41no—
285C22×D11—41no—
286C22×D11—48no—
287C22×D11—84no—
288C22×D11—84no—
289C22×D11—84no—
290C22×D11—84no—
291C22×D11#12112yes—
292C22×D11#12112yes—
293C22×D11C22⋊Q812yes—
294D4×C11—22no—
295D4×C11—22no—
296D4×C11—41no—
297D4×C11—41no—
298C2×C4×C11—21no—
299C2×C4×C11—21no—
300C2×C4×C11—22no—
301C2×C4×C11—21no—
302C2×C4×C11—21no—
303C2×C4×C11—21no—
304C2×C4×C11—41no—
305C2×C4×C11—41no—
306C2×C4×C11—41no—
307C2×C4×C11—41no—
308C2×C4×C11—41no—
309C2×C4×C11—41no—
310C2×C4×C11—41no—
311C2×C4×C11—41no—
312C2×C4×C11AGL(1,ℤ/8)12yes—
313C2×C4×C11C22×D411yescharacteristic
314C2×C4×C11C22×D411yescharacteristic
315C2×C4×C11C22×Q811yescharacteristic
316C2×C4×C11C2×#4111yescharacteristic
317C2×C4×C11C2×#4111yescharacteristic
318C2×C4×C11C2×#4111yescharacteristic
319C22⋊D11—48no—
320C2×Dic11—21no—
321C2×Dic11—21no—
322C2×Dic11—21no—
323C2×Dic11—22no—
324C2×Dic11—21no—
325C2×Dic11—21no—
326C2×Dic11—41no—
327C2×Dic11—41no—
328C2×Dic11—41no—
329C2×Dic11—41no—
330C2×Dic11—41no—
331C2×Dic11—41no—
332C2×Dic11—41no—
333C2×Dic11—41no—
334C2×Dic11#12112yes—
335C2×Dic11#12112yes—
336C2×Dic11C22⋊Q812yes—
337C2×Dic11AGL(1,ℤ/8)12yes—
338D44—22no—
339D44—22no—
340D44—41no—
341D44—41no—
342C4×D11—44no—
343C4×D11—44no—
344C4×D11—84no—
345C4×D11#12114yes—
346C4×D11C22⋊Q814yes—
347C4×D11C22⋊Q814yes—
348C4×D11#12614yes—
349C8×C11—22no—
350C8×C11—41no—
351C11⋊C8—22no—
352C11⋊C8—41no—
353C23×D4—111no—
354C22×M16—111no—
355C22×M16—111no—
356C2×#117—111no—
357C2×#117—111no—
358C22×C4⋊C4—111no—
359C22×C22⋊C4—221no—
360C22×C22⋊C4—221no—
361C22×C42—111no—
362#428—224no—
363C2×#107—111no—
364C2×#107C2×D1111yescharacteristic, complemented
365C2×#106—111no—
366C2×#106—111no—
367#423—224no—
368C2×C4⋊C8—111no—
369C2×C4⋊C8—111no—
370C2×C4⋊C8—111no—
371C2×C4⋊C8C2×D1111yescharacteristic, complemented
372#418—224no—
373#418—224no—
374C2×#102—111no—
375C2×#102—111no—
376C2×#102—111no—
377C2×#102—111no—
378C2×#102—111no—
379C2×#102—111no—
380C2×#102C2×D1111yescharacteristic
381C2×#102C2×D1111yescharacteristic
382#390—111no—
383#390—111no—
384#390—111no—
385#390—221no—
386#390—221no—
387#390C2×D1111yescharacteristic
388#389—111no—
389#389—111no—
390#389—111no—
391#389C2×D1111yescharacteristic, complemented
392#385—221no—
393#385—221no—
394C4×C4⋊C4—221no—
395C4×C4⋊C4—221no—
396#340—111no—
397#340—111no—
398#340—111no—
399#340C2×D1111yescharacteristic, complemented
400C22×C11—42no—
401C22×C11—42no—
402C22×C11—42no—
403C22×C11—81no—
404C22×C11—81no—
405C22×C11—81no—
406C22×C11—81no—
407C22×C11C2×#12111yescharacteristic
408C22×C11C2×#12111yescharacteristic
409C22×C11C2×C22⋊Q811yescharacteristic
410C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
411C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
412C22×C11#57511yescharacteristic
413C22×C11#57511yescharacteristic
414C2×D11—22no—
415C2×D11—22no—
416C2×D11—22no—
417C2×D11—22no—
418C2×D11—22no—
419C2×D11—22no—
420C2×D11—42no—
421C2×D11—42no—
422C2×D11—42no—
423C2×D11—816no—
424C2×D11—81no—
425C2×D11—81no—
426C2×D11—81no—
427C2×D11—81no—
428C2×D11#39614yes—
429C4×C11—22no—
430C4×C11—42no—
431C4×C11—41no—
432C4×C11—81no—
433C4×C11—81no—
434C4×C11C2×#12111yescharacteristic
435C4×C11C2×C22⋊Q811yescharacteristic
436C4×C11C2×C22⋊Q811yescharacteristic
437C4×C11C2×#12611yescharacteristic
438Dic11—22no—
439Dic11—42no—
440Dic11—41no—
441Dic11—81no—
442Dic11—81no—
443Dic11#39614yes—
444C25—221no—
445C22×D4—114no—
446C22×D4—111no—
447C22×D4—222no—
448C22×D4—222no—
449C22×D4—222no—
450C22×D4—222no—
451C22×D4—222no—
452C22×D4—221no—
453C22×D4C22×D1111yescharacteristic
454C23×C4—111no—
455C23×C4—111no—
456C23×C4—111no—
457C23×C4—221no—
458C2×M16—114no—
459C2×M16—222no—
460C2×M16—222no—
461C2×M16—222no—
462C2×M16—222no—
463C2×M16—222no—
464C22×C8—111no—
465C22×C8—111no—
466C22×C8C22×D1111yescharacteristic
467C22×C8C22×D1111yescharacteristic
468#117—114no—
469#117—222no—
470#117—222no—
471#117—222no—
472C2×C4⋊C4—21no—
473C2×C4⋊C4—111no—
474C2×C4⋊C4—111no—
475C2×C4⋊C4—111no—
476C2×C4⋊C4—222no—
477C2×C4⋊C4—222no—
478C2×C4⋊C4—221no—
479C2×C4⋊C4—221no—
480C2×C4⋊C4—221no—
481C2×C4⋊C4—221no—
482C2×C4⋊C4C22×D1111yescharacteristic
483C2×C4⋊C4C22×D1111yescharacteristic
484C2×C4⋊C4C22×D1111yescharacteristic
485C2×C22⋊C4—21no—
486C2×C22⋊C4—21no—
487C2×C22⋊C4—221no—
488C2×C22⋊C4—221no—
489C2×C22⋊C4—221no—
490C2×C22⋊C4—221no—
491C2×C22⋊C4—221no—
492C2×C22⋊C4—221no—
493C2×C22⋊C4—221no—
494C2×C22⋊C4—221no—
495C2×C22⋊C4—444no—
496C2×C22⋊C4—444no—
497C2×C42—111no—
498C2×C42—111no—
499C2×C42—111no—
500C2×C42—222no—
501C2×C42—222no—
502C2×C42—221no—
503C2×C42—221no—
504C2×C42C22×D1111yescharacteristic
505#107—22no—
506#107—222no—
507#106—222no—
508#106—222no—
509C4⋊C8—22no—
510C4⋊C8—222no—
511C4⋊C8—222no—
512C4⋊C8—222no—
513#102—22no—
514#102—22no—
515#102—222no—
516#102—222no—
517#102—222no—
518#102—222no—
519#102—222no—
520#102—222no—
521#95—21no—
522#95—221no—
523#95—221no—
524#95—221no—
525C2×C11—82no—
526C2×C11C2×#39611yescharacteristic
527C2×C11#303811yescharacteristic
528C2×C11#304011yescharacteristic
529C2×C11#305511yescharacteristic
530C2×C11#305511yescharacteristic
531C2×C11#307711yescharacteristic
532C2×C11#307711yescharacteristic
533D11—24no—
534D11—82no—
535C24—21no—
536C24—111no—
537C24—224no—
538C24—221no—
539C24—442no—
540C24—442no—
541C24—442no—
542C24—442no—
543C24—442no—
544C24—442no—
545C2×D4—21no—
546C2×D4—21no—
547C2×D4—21no—
548C2×D4—21no—
549C2×D4—21no—
550C2×D4—112no—
551C2×D4—228no—
552C2×D4—228no—
553C2×D4—224no—
554C2×D4—221no—
555C2×D4—221no—
556C2×D4—221no—
557C2×D4—221no—
558C2×D4—221no—
559C2×D4—444no—
560C2×D4—444no—
561C2×D4—442no—
562C2×D4—442no—
563C2×D4Q8×D1112yes—
564C22×C4—21no—
565C22×C4—21no—
566C22×C4—21no—
567C22×C4—111no—
568C22×C4—112no—
569C22×C4—112no—
570C22×C4—112no—
571C22×C4—112no—
572C22×C4—112no—
573C22×C4—112no—
574C22×C4—111no—
575C22×C4—111no—
576C22×C4—222no—
577C22×C4—222no—
578C22×C4—222no—
579C22×C4—221no—
580C22×C4—222no—
581C22×C4—221no—
582C22×C4—221no—
583C22×C4—441no—
584C22×C4—441no—
585C22×C4—442no—
586C22×C4—442no—
587C22×C4—442no—
588C22×C4D4×D1111yescharacteristic
589C22×C4D4×D1111yescharacteristic
590C22×C4C23×D1111yescharacteristic
591M16—228no—
592M16—444no—
593C2×C8—21no—
594C2×C8—21no—
595C2×C8—21no—
596C2×C8—21no—
597C2×C8—21no—
598C2×C8—112no—
599C2×C8—221no—
600C2×C8—221no—
601C2×C8—221no—
602C2×C8—221no—
603C2×C8—221no—
604C2×C8D4×D1112yes—
605C4⋊C4—21no—
606C4⋊C4—21no—
607C4⋊C4—21no—
608C4⋊C4—21no—
609C4⋊C4—21no—
610C4⋊C4—42no—
611C4⋊C4—112no—
612C4⋊C4—221no—
613C4⋊C4—221no—
614C4⋊C4—221no—
615C4⋊C4—221no—
616C4⋊C4—221no—
617C4⋊C4—442no—
618C4⋊C4—442no—
619C4⋊C4—442no—
620C4⋊C4—442no—
621C4⋊C4D4×D1112yes—
622C22⋊C4—42no—
623C22⋊C4—42no—
624C22⋊C4—224no—
625C22⋊C4—442no—
626C22⋊C4—442no—
627C22⋊C4—442no—
628C22⋊C4—442no—
629C22⋊C4—442no—
630C22⋊C4—442no—
631C22⋊C4—442no—
632C42—21no—
633C42—21no—
634C42—222no—
635C42—222no—
636C42—224no—
637C42—221no—
638C42—221no—
639C42—442no—
640C11#2361811yescharacteristic, complemented, Sylow
641C23—22no—
642C23—41no—
643C23—41no—
644C23—41no—
645C23—41no—
646C23—41no—
647C23—41no—
648C23—112no—
649C23—112no—
650C23—112no—
651C23—221no—
652C23—221no—
653C23—221no—
654C23—221no—
655C23—222no—
656C23—448no—
657C23—448no—
658C23—448no—
659C23—441no—
660C23—441no—
661C23—441no—
662C23—441no—
663C23—441no—
664C23—441no—
665C23—884no—
666C23—884no—
667C23—884no—
668C23—884no—
669C23C2×D4×D1111yescharacteristic
670D4—22no—
671D4—22no—
672D4—41no—
673D4—41no—
674D4—222no—
675D4—222no—
676D4—448no—
677D4—441no—
678D4—441no—
679C2×C4—21no—
680C2×C4—21no—
681C2×C4—21no—
682C2×C4—21no—
683C2×C4—21no—
684C2×C4—22no—
685C2×C4—41no—
686C2×C4—41no—
687C2×C4—41no—
688C2×C4—41no—
689C2×C4—41no—
690C2×C4—41no—
691C2×C4—41no—
692C2×C4—41no—
693C2×C4—112no—
694C2×C4—112no—
695C2×C4—112no—
696C2×C4—114no—
697C2×C4—114no—
698C2×C4—114no—
699C2×C4—114no—
700C2×C4—112no—
701C2×C4—221no—
702C2×C4—221no—
703C2×C4—221no—
704C2×C4—221no—
705C2×C4—221no—
706C2×C4—222no—
707C2×C4—444no—
708C2×C4—444no—
709C2×C4—441no—
710C2×C4—441no—
711C2×C4—441no—
712C2×C4—441no—
713C2×C4—441no—
714C2×C4—441no—
715C2×C4—441no—
716C2×C4—441no—
717C2×C4—884no—
718C2×C4#6696412yes—
719C2×C4C2×D4×D1111yescharacteristic
720C2×C4C2×D4×D1111yescharacteristic
721C2×C4C2×Q8×D1111yescharacteristic
722C2×C4#41×D1111yescharacteristic
723C2×C4#41×D1111yescharacteristic
724C2×C4#41×D1111yescharacteristic
725C8—22no—
726C8—41no—
727C8—222no—
728C8—441no—
729C22—42no—
730C22—42no—
731C22—42no—
732C22—81no—
733C22—81no—
734C22—81no—
735C22—81no—
736C22—114no—
737C22—222no—
738C22—222no—
739C22—222no—
740C22—222no—
741C22—222no—
742C22—222no—
743C22—442no—
744C22—442no—
745C22—442no—
746C22—8816no—
747C22—881no—
748C22—881no—
749C22—881no—
750C22—881no—
751C22D11×#12111yescharacteristic
752C22D11×#12111yescharacteristic
753C22D11×C22⋊Q811yescharacteristic
754C22C2×#6696411yescharacteristic
755C22#1062329911yescharacteristic
756C22D11×AGL(1,ℤ/8)11yescharacteristic
757C22#1062330811yescharacteristic
758C4—22no—
759C4—42no—
760C4—41no—
761C4—81no—
762C4—81no—
763C4—114no—
764C4—222no—
765C4—442no—
766C4—441no—
767C4—881no—
768C4—881no—
769C4D11×#12111yescharacteristic
770C4D11×C22⋊Q811yescharacteristic
771C4D11×C22⋊Q811yescharacteristic
772C4D11×#12611yescharacteristic
773C2—82no—
774C2—224no—
775C2—882no—
776C2D11×#39611yescharacteristic
777C2#1307809111yescharacteristic
778C2#1307810711yescharacteristic
779C2#1307823011yescharacteristic
780C2#1307823211yescharacteristic
781C2#1307840811yescharacteristic
782C2#1307841111yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#2067C2
socleC23×C11C22×D4
prime radicalC22×D4×D11C22
hypercenter#2067D11
hypocenterC11#23618
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ #2067

Complements

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

NH ≅ G/Ntype
1. C2×#10622494C2semidirect
2. C2×#10622450C2semidirect
5. #13071097C2semidirect
7. #13070001C2semidirect
8. #13070000C2semidirect
9. #13069999C2semidirect
10. #13069991C2semidirect
11. #13069990C2semidirect
12. #13069989C2semidirect
13. #13069988C2semidirect
14. #13068334C2semidirect
15. C11×#2067C2semidirect
25. C2×C11×#107C22semidirect
26. C2×C11×C4⋊C8C22semidirect
30. C11×#389C22semidirect
36. C2×#66881C22semidirect
37. C2×Dic11⋊C8C22semidirect
38. C2×Dic11⋊C8C22semidirect
41. #10622598C22semidirect
43. #10622586C22semidirect
46. C2×#66872C22semidirect
47. C2×#66871C22semidirect
51. #10622541C22semidirect
52. C2×C4⋊(C11⋊C8)C22semidirect
59. C11×#340C22semidirect
60. #10622189C22semidirect
61. #10622167C22semidirect
62. #10622167C22semidirect
259. #2067D11semidirect
364. C2×#107C2×D11semidirect
371. C2×C4⋊C8C2×D11semidirect
391. #389C2×D11semidirect
399. #340C2×D11semidirect
640. C11#23618semidirect

Maximal subgroups

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

subgroupindex
C2×#106224942
C2×#106224502
C2×#106223832
#130710972
D11×#3902
#130700012
#130700002
#130699992
#130699912
#130699902
#130699892
#130699882
#130683342
C11×#20672
#2361811