Finite Group Databasebeta

← #14797554

Subgroups — #14797554

Order 2816.

1042 conjugacy classes of subgroups.

The subgroup lattice has 760 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×SD16×Dic11C211yesmaximal, characteristic, complemented
2#13072126C211yesmaximal, characteristic, complemented
3#13071457C211yesmaximal, characteristic, complemented
4#13070147C211yesmaximal, characteristic, complemented
5#13070049C211yesmaximal, characteristic, complemented
6#13069924C211yesmaximal, characteristic, complemented
7#13069802C211yesmaximal, characteristic, complemented
8#13069296C211yesmaximal, characteristic, complemented
9#13069219C211yesmaximal, characteristic, complemented
10#13068973C211yesmaximal, characteristic, complemented
11#13068966C211yesmaximal, characteristic, complemented
12#13068882C211yesmaximal, characteristic, complemented
13#13068619C211yesmaximal, characteristic, complemented
14#13068556C211yesmaximal, characteristic, complemented
15C2×C11×#449C211yesmaximal, characteristic
16C22×C11×#41C2211yescharacteristic
17C22×C11×SD16C2211yescharacteristic
18C22×C11×D8C2211yescharacteristic
19C2×C11×#121C2211yescharacteristic
20C2×Q8×Dic11C2211yescharacteristic
21C2×Q8×Dic11C2211yescharacteristic
22C2×#66988—21no—
23C2×D4×Dic11C2211yescharacteristic
24C11×#449—24no—
25C2×C11×#103C2211yescharacteristic
26C2×C11×#102C2211yescharacteristic
27C2×C11×C22⋊C8C2211yescharacteristic
28C2×#66899C2211yescharacteristic
29C2×#66899C2211yescharacteristic
30#10622835—21no—
31#10622834—21no—
32#10622834—21no—
33#10622834C2211yescharacteristic
34#10622834C2211yescharacteristic
35#10622834C2211yescharacteristic
36C2×#66896C2211yescharacteristic
37C2×#66896C2211yescharacteristic
38C2×#66896C2211yescharacteristic
39C2×#66896C2211yescharacteristic
40#10622825—21no—
41#10622825C2211yescharacteristic
42#10622825C2211yescharacteristic
43C4×C22⋊Dic11—21no—
44C4×C22⋊Dic11C2211yescharacteristic
45C2×C22⋊(C11⋊C8)C2211yescharacteristic
46SD16×Dic11—24no—
47C2×#66881C2211yescharacteristic
48C2×Dic11⋊C8C2211yescharacteristic
49C2×C8×Dic11C2211yescharacteristic
50#10622589C2211yescharacteristic
51#10622586C2211yescharacteristic
52C2×#66872C2211yescharacteristic
53#10622565—21no—
54#10622559—21no—
55#10622189C2211yescharacteristic
56#10622189C2211yescharacteristic
57#10622189C2211yescharacteristic
58#10622188C2211yescharacteristic
59#10622188C2211yescharacteristic
60#10622167C2211yescharacteristic
61C2×C11×#41—22no—
62C2×C11×#41—22no—
63C2×C11×#41—22no—
64C2×C11×#41—22no—
65C2×C11×#41—41no—
66C2×C11×#41—41no—
67C22×Q8×C11C2311yescharacteristic
68C22×D4×C11—21no—
69C22×D4×C11—21no—
70C22×D4×C11C2311yescharacteristic
71C22×D4×C11C2311yescharacteristic
72C23×C4×C11—21no—
73C23×C4×C11C2311yescharacteristic
74C23×Dic11—21no—
75C2×C11×SD16—22no—
76C2×C11×SD16—22no—
77C2×C11×SD16D414yes—
78C2×C11×D8—22no—
79C2×C11×D8—22no—
80C2×C11×D8—41no—
81C22×C8×C11C2311yescharacteristic
82C22×C8×C11C2311yescharacteristic
83C11×#121—22no—
84C11×#121—41no—
85C2×C11×C4⋊C4C2311yescharacteristic
86C2×C11×C22⋊C4—21no—
87C2×C22⋊Dic11—21no—
88C2×C22⋊Dic11—21no—
89C2×C22⋊Dic11—21no—
90C2×C22⋊Dic11—21no—
91C2×C22⋊Dic11—21no—
92C2×C22⋊Dic11—21no—
93C2×C22⋊Dic11—21no—
94C2×C22⋊Dic11—21no—
95C2×C22⋊Dic11—21no—
96C2×C22⋊Dic11D411yescharacteristic
97C2×C22⋊Dic11D411yescharacteristic
98Q8×Dic11—22no—
99Q8×Dic11—22no—
100Q8×Dic11—41no—
101Q8×Dic11—41no—
102#66988—44no—
103D4×Dic11—22no—
104D4×Dic11—41no—
105C2×C4⋊Dic11—21no—
106C2×C4⋊Dic11—21no—
107C2×C4⋊Dic11C2311yescharacteristic
108C2×C4⋊Dic11C2311yescharacteristic
109C2×C4⋊Dic11C2311yescharacteristic
110C2×C4⋊Dic11C2311yescharacteristic
111C2×Dic11⋊C4—21no—
112C2×Dic11⋊C4—21no—
113C2×Dic11⋊C4—21no—
114C2×C4×Dic11—21no—
115C2×C4×Dic11—21no—
116C2×C4×Dic11C2311yescharacteristic
117C2×C4×Dic11C2311yescharacteristic
118C22×C11⋊C8C2311yescharacteristic
119C22×C11⋊C8C2311yescharacteristic
120C11×#103—22no—
121C11×#102—22no—
122C11×C22⋊C8—22no—
123#66899—22no—
124#66899—22no—
125#66896—22no—
126#66896—22no—
127#66896—41no—
128#66896—41no—
129C11⋊#95—21no—
130C11⋊#95—21no—
131C11⋊#95—21no—
132C11⋊#95D411yescharacteristic
133C11⋊#95D411yescharacteristic
134C22⋊(C11⋊C8)—41no—
135#66881—22no—
136Dic11⋊C8—41no—
137C8×Dic11—22no—
138#66872—41no—
139#24896—111nomaximal, Sylow
140C24×C11—21no—
141C24×C11—21no—
142C24×C11C2×D411yescharacteristic
143C11×#41—44no—
144C11×#41—44no—
145C11×#41—44no—
146C11×#41—44no—
147C2×Q8×C11—21no—
148C2×Q8×C11—21no—
149C2×Q8×C11—21no—
150C2×Q8×C11C2×D412yes—
151C2×Q8×C11#4112yes—
152C2×Q8×C11#4112yes—
153C2×D4×C11—24no—
154C2×D4×C11—21no—
155C2×D4×C11—21no—
156C2×D4×C11—21no—
157C2×D4×C11—21no—
158C2×D4×C11—21no—
159C2×D4×C11—21no—
160C2×D4×C11—21no—
161C2×D4×C11—21no—
162C2×D4×C11—21no—
163C2×D4×C11—21no—
164C2×D4×C11—42no—
165C2×D4×C11—42no—
166C2×D4×C11—42no—
167C2×D4×C11—42no—
168C2×D4×C11—81no—
169C2×D4×C11C2×D412yes—
170C2×D4×C11#4112yes—
171C22×C4×C11—21no—
172C22×C4×C11—24no—
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—42no—
181C22×C4×C11—42no—
182C22×C4×C11C2×D411yescharacteristic
183C22×C4×C11C2411yescharacteristic
184C22×Dic11—21no—
185C22×Dic11—21no—
186C22×Dic11—21no—
187C22×Dic11—21no—
188C22×Dic11—42no—
189C22×Dic11—42no—
190C22×Dic11—81no—
191C22×Dic11C2×D411yescharacteristic
192C22×Dic11C2×D411yescharacteristic
193C22×Dic11C2×D411yescharacteristic
194C22×Dic11C2×D411yescharacteristic
195C11×SD16—28no—
196C11×D8—44no—
197C2×C8×C11—21no—
198C2×C8×C11—21no—
199C2×C8×C11—21no—
200C2×C8×C11—21no—
201C2×C8×C11—21no—
202C2×C8×C11C2×D412yes—
203C11×C4⋊C4—21no—
204C11×C4⋊C4—21no—
205C11×C22⋊C4—42no—
206C22⋊Dic11—22no—
207C22⋊Dic11—22no—
208C22⋊Dic11—42no—
209C22⋊Dic11—42no—
210C22⋊Dic11—42no—
211C22⋊Dic11—42no—
212C22⋊Dic11—42no—
213C22⋊Dic11—42no—
214C22⋊Dic11—81no—
215C22⋊Dic11—81no—
216C22⋊Dic11—81no—
217C4⋊Dic11—21no—
218C4⋊Dic11—21no—
219C4⋊Dic11—21no—
220C4⋊Dic11—21no—
221C4⋊Dic11—21no—
222C4⋊Dic11—21no—
223C4⋊Dic11—21no—
224C4⋊Dic11—21no—
225C4⋊Dic11—42no—
226C4⋊Dic11—42no—
227Dic11⋊C4—42no—
228Dic11⋊C4—42no—
229Dic11⋊C4—81no—
230C4×Dic11—21no—
231C4×Dic11—21no—
232C4×Dic11—21no—
233C4×Dic11—21no—
234C4×Dic11—42no—
235C4×Dic11—42no—
236C2×C11⋊C8—21no—
237C2×C11⋊C8—21no—
238C2×C11⋊C8—21no—
239C2×C11⋊C8—21no—
240C2×C11⋊C8—21no—
241C2×C11⋊C8—21no—
242C2×#449D1111yescharacteristic
243C2×C4×SD16—111no—
244#2422—111no—
245#2341—111no—
246#2094—111no—
247#2077—111no—
248#2054—111no—
249#2034—111no—
250#1934—111no—
251#1923—111no—
252#1880—111no—
253#1879—111no—
254#1865—111no—
255#1803—111no—
256#1788—111no—
257C23×C11—21no—
258C23×C11—22no—
259C23×C11—22no—
260C23×C11—21no—
261C23×C11—21no—
262C23×C11—21no—
263C23×C11—21no—
264C23×C11—21no—
265C23×C11—21no—
266C23×C11—41no—
267C23×C11—41no—
268C23×C11—41no—
269C23×C11—41no—
270C23×C11—41no—
271C23×C11—41no—
272C23×C11—41no—
273C23×C11—41no—
274C23×C11—41no—
275C23×C11—41no—
276C23×C11—41no—
277C23×C11—41no—
278C23×C11C22×D411yescharacteristic
279Q8×C11—22no—
280Q8×C11—22no—
281Q8×C11—22no—
282Q8×C11#12314yescomplemented
283D4×C11—22no—
284D4×C11—22no—
285D4×C11—22no—
286D4×C11—22no—
287D4×C11—48no—
288D4×C11—41no—
289D4×C11—41no—
290D4×C11—41no—
291D4×C11—41no—
292D4×C11—84no—
293C2×C4×C11—22no—
294C2×C4×C11—22no—
295C2×C4×C11—22no—
296C2×C4×C11—21no—
297C2×C4×C11—21no—
298C2×C4×C11—21no—
299C2×C4×C11—48no—
300C2×C4×C11—41no—
301C2×C4×C11—41no—
302C2×C4×C11—41no—
303C2×C4×C11—41no—
304C2×C4×C11—41no—
305C2×C4×C11—41no—
306C2×C4×C11—41no—
307C2×C4×C11C22×D411yescharacteristic
308C2×C4×C11C2×#4111yescharacteristic
309C2×C4×C11C2×#4111yescharacteristic
310C2×C4×C11C2×#4111yescharacteristic
311C2×C4×C11H(5,𝔽2)11yescharacteristic
312C2×C4×C11H(5,𝔽2)11yescharacteristic
313C2×Dic11—21no—
314C2×Dic11—21no—
315C2×Dic11—21no—
316C2×Dic11—21no—
317C2×Dic11—21no—
318C2×Dic11—21no—
319C2×Dic11—21no—
320C2×Dic11—21no—
321C2×Dic11—21no—
322C2×Dic11—21no—
323C2×Dic11—41no—
324C2×Dic11—41no—
325C2×Dic11—41no—
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—41no—
335C2×Dic11—84no—
336C2×Dic11#13512yes—
337C2×Dic11AGL(1,ℤ/8)12yes—
338C8×C11—22no—
339C8×C11—41no—
340C11⋊C8—41no—
341C11⋊C8—41no—
342C22×#41C2×D1111yescharacteristic
343C22×SD16C2×D1111yescharacteristic
344C22×D8C2×D1111yescharacteristic
345C2×#123—221no—
346C2×#121C2×D1111yescharacteristic
347C2×C4×Q8—111no—
348C2×C4×Q8—111no—
349C2×C4×D4—111no—
350#449—24no—
351C4×SD16—224no—
352C2×#106—111no—
353C2×#106—111no—
354C2×C4⋊C8—111no—
355C2×#103—111no—
356C2×#103—111no—
357C2×#103C2×D1111yescharacteristic
358C2×#102—111no—
359C2×#102—111no—
360C2×#102—111no—
361C2×#102—111no—
362C2×#102C2×D1111yescharacteristic
363C2×C22⋊C8—111no—
364C2×C22⋊C8C2×D1111yescharacteristic
365C2×C4×C8—111no—
366#397—221no—
367#394—221no—
368#390—111no—
369#390—111no—
370#390—111no—
371#390—221no—
372#390—221no—
373#389—111no—
374#385—221no—
375#384—111no—
376#380—111no—
377#380—111no—
378#380—221no—
379C4×C22⋊C4—111no—
380C4×C22⋊C4—221no—
381#340—111no—
382#340—111no—
383#340—111no—
384#340—111no—
385#336—111no—
386#336—111no—
387C22×C11—41no—
388C22×C11—41no—
389C22×C11—42no—
390C22×C11—41no—
391C22×C11—42no—
392C22×C11—42no—
393C22×C11—41no—
394C22×C11—42no—
395C22×C11—41no—
396C22×C11—42no—
397C22×C11—41no—
398C22×C11—42no—
399C22×C11—41no—
400C22×C11—81no—
401C22×C11—81no—
402C22×C11—81no—
403C22×C11—81no—
404C22×C11—81no—
405C22×C11—81no—
406C22×C11—81no—
407C22×C11—81no—
408C22×C11#52511yescharacteristic
409C22×C11D4211yescharacteristic
410C22×C11#54611yescharacteristic
411C22×C11C2×#13511yescharacteristic
412C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
413C22×C11#57711yescharacteristic
414C22×C11#57711yescharacteristic
415C4×C11—24no—
416C4×C11—41no—
417C4×C11—81no—
418C4×C11C2×#12311yescharacteristic
419C4×C11#53811yescharacteristic
420C4×C11#54611yescharacteristic
421C4×C11#55111yescharacteristic
422Dic11—22no—
423Dic11—22no—
424Dic11—41no—
425Dic11—41no—
426Dic11—81no—
427Dic11—81no—
428Dic11—81no—
429Dic11—81no—
430C2×#41—22no—
431C2×#41—22no—
432C2×#41—22no—
433C2×#41—22no—
434C2×#41—41no—
435C2×#41—41no—
436C22×Q8C22×D1111yescharacteristic
437C22×D4—21no—
438C22×D4—21no—
439C22×D4C22×D1111yescharacteristic
440C22×D4C22×D1111yescharacteristic
441C23×C4—21no—
442C23×C4—221no—
443C23×C4C22×D1111yescharacteristic
444C2×SD16—22no—
445C2×SD16—22no—
446C2×SD16C22⋊D1114yes—
447C2×D8—22no—
448C2×D8—22no—
449C2×D8—41no—
450C22×C8—111no—
451C22×C8—111no—
452C22×C8C22×D1111yescharacteristic
453C22×C8C22×D1111yescharacteristic
454#123—444no—
455#121—22no—
456#121—41no—
457C4×Q8—222no—
458C4×Q8—222no—
459C4×Q8—441no—
460C4×Q8—441no—
461C4×D4—222no—
462C4×D4—441no—
463C2×C4⋊C4—111no—
464C2×C4⋊C4—111no—
465C2×C4⋊C4—111no—
466C2×C4⋊C4—111no—
467C2×C4⋊C4—221no—
468C2×C4⋊C4—221no—
469C2×C4⋊C4—221no—
470C2×C4⋊C4—221no—
471C2×C4⋊C4—221no—
472C2×C4⋊C4C22×D1111yescharacteristic
473C2×C22⋊C4—21no—
474C2×C22⋊C4—111no—
475C2×C22⋊C4—111no—
476C2×C22⋊C4—221no—
477C2×C22⋊C4—221no—
478C2×C22⋊C4—221no—
479C2×C22⋊C4—221no—
480C2×C22⋊C4—221no—
481C2×C22⋊C4—221no—
482C2×C22⋊C4—221no—
483C2×C22⋊C4—221no—
484C2×C22⋊C4—221no—
485C2×C42—111no—
486C2×C42—111no—
487C2×C42—221no—
488C2×C42—221no—
489#106—222no—
490#106—441no—
491C4⋊C8—441no—
492#103—22no—
493#103—222no—
494#103—222no—
495#102—22no—
496#102—222no—
497#102—222no—
498#102—441no—
499#102—441no—
500C22⋊C8—22no—
501C22⋊C8—441no—
502C4×C8—222no—
503#95—111no—
504#95—111no—
505#95—221no—
506#95—221no—
507#95—221no—
508C2×C11—81no—
509C2×C11—82no—
510C2×C11—82no—
511C2×C11#241811yescharacteristic
512C2×C11#310611yescharacteristic
513C2×C11#312511yescharacteristic
514C2×C11#326511yescharacteristic
515C2×C11#328411yescharacteristic
516C2×C11#330111yescharacteristic
517C2×C11#333211yescharacteristic
518C24—21no—
519C24—21no—
520C24D4×D1111yescharacteristic
521#41—44no—
522#41—44no—
523#41—44no—
524#41—44no—
525C2×Q8—21no—
526C2×Q8—21no—
527C2×Q8—21no—
528C2×Q8#434112yes—
529C2×Q8#434112yes—
530C2×Q8C2×C22⋊D1112yes—
531C2×D4—24no—
532C2×D4—21no—
533C2×D4—21no—
534C2×D4—21no—
535C2×D4—21no—
536C2×D4—21no—
537C2×D4—21no—
538C2×D4—21no—
539C2×D4—21no—
540C2×D4—21no—
541C2×D4—21no—
542C2×D4—42no—
543C2×D4—42no—
544C2×D4—42no—
545C2×D4—42no—
546C2×D4—81no—
547C2×D4#434112yes—
548C2×D4C2×C22⋊D1112yes—
549C22×C4—21no—
550C22×C4—24no—
551C22×C4—21no—
552C22×C4—21no—
553C22×C4—21no—
554C22×C4—21no—
555C22×C4—21no—
556C22×C4—21no—
557C22×C4—21no—
558C22×C4—42no—
559C22×C4—42no—
560C22×C4—111no—
561C22×C4—111no—
562C22×C4—111no—
563C22×C4—111no—
564C22×C4—221no—
565C22×C4—221no—
566C22×C4—221no—
567C22×C4—221no—
568C22×C4—442no—
569C22×C4—442no—
570C22×C4—881no—
571C22×C4D4×D1111yescharacteristic
572C22×C4C23×D1111yescharacteristic
573SD16—28no—
574D8—44no—
575C2×C8—21no—
576C2×C8—21no—
577C2×C8—21no—
578C2×C8—21no—
579C2×C8—21no—
580C2×C8—221no—
581C2×C8—221no—
582C2×C8—221no—
583C2×C8—221no—
584C2×C8—221no—
585C2×C8—221no—
586C2×C8C2×C22⋊D1112yes—
587C4⋊C4—21no—
588C4⋊C4—21no—
589C4⋊C4—221no—
590C4⋊C4—221no—
591C4⋊C4—221no—
592C4⋊C4—221no—
593C4⋊C4—221no—
594C4⋊C4—221no—
595C4⋊C4—221no—
596C4⋊C4—221no—
597C4⋊C4—442no—
598C4⋊C4—442no—
599C4⋊C4—442no—
600C4⋊C4—442no—
601C4⋊C4—881no—
602C22⋊C4—42no—
603C22⋊C4—222no—
604C22⋊C4—222no—
605C22⋊C4—442no—
606C22⋊C4—442no—
607C22⋊C4—442no—
608C22⋊C4—442no—
609C22⋊C4—442no—
610C22⋊C4—442no—
611C22⋊C4—881no—
612C22⋊C4—881no—
613C22⋊C4—881no—
614C42—221no—
615C42—221no—
616C42—221no—
617C42—221no—
618C42—442no—
619C42—442no—
620C11#2489611yescharacteristic, complemented, Sylow
621C23—21no—
622C23—21no—
623C23—21no—
624C23—21no—
625C23—22no—
626C23—21no—
627C23—21no—
628C23—22no—
629C23—21no—
630C23—41no—
631C23—41no—
632C23—41no—
633C23—41no—
634C23—41no—
635C23—41no—
636C23—41no—
637C23—41no—
638C23—41no—
639C23—41no—
640C23—41no—
641C23—41no—
642C23C2×D4×D1111yescharacteristic
643Q8—22no—
644Q8—22no—
645Q8—22no—
646Q8#6698814yescomplemented
647D4—22no—
648D4—22no—
649D4—22no—
650D4—22no—
651D4—48no—
652D4—41no—
653D4—41no—
654D4—41no—
655D4—41no—
656D4—84no—
657C2×C4—22no—
658C2×C4—22no—
659C2×C4—22no—
660C2×C4—21no—
661C2×C4—21no—
662C2×C4—21no—
663C2×C4—48no—
664C2×C4—41no—
665C2×C4—41no—
666C2×C4—41no—
667C2×C4—41no—
668C2×C4—41no—
669C2×C4—41no—
670C2×C4—41no—
671C2×C4—112no—
672C2×C4—112no—
673C2×C4—221no—
674C2×C4—221no—
675C2×C4—221no—
676C2×C4—221no—
677C2×C4—221no—
678C2×C4—221no—
679C2×C4—221no—
680C2×C4—221no—
681C2×C4—221no—
682C2×C4—221no—
683C2×C4—441no—
684C2×C4—441no—
685C2×C4—441no—
686C2×C4—441no—
687C2×C4—441no—
688C2×C4—441no—
689C2×C4—441no—
690C2×C4—441no—
691C2×C4—441no—
692C2×C4—441no—
693C2×C4—441no—
694C2×C4—441no—
695C2×C4—884no—
696C2×C4C2×#434111yescharacteristic
697C2×C4C2×#434111yescharacteristic
698C2×C4C2×#434111yescharacteristic
699C2×C4#6703711yescharacteristic
700C2×C4#6703711yescharacteristic
701C2×C4C22×C22⋊D1111yescharacteristic
702C8—22no—
703C8—41no—
704C8—441no—
705C8—441no—
706C22—41no—
707C22—42no—
708C22—42no—
709C22—41no—
710C22—41no—
711C22—41no—
712C22—42no—
713C22—41no—
714C22—42no—
715C22—41no—
716C22—42no—
717C22—41no—
718C22—42no—
719C22—81no—
720C22—81no—
721C22—81no—
722C22—81no—
723C22—81no—
724C22—81no—
725C22—81no—
726C22—81no—
727C22#1062311711yescharacteristic
728C22#1062312211yescharacteristic
729C22D11×#13511yescharacteristic
730C22#1062330111yescharacteristic
731C22D11×AGL(1,ℤ/8)11yescharacteristic
732C22#1062330611yescharacteristic
733C22D4×C22⋊D1111yescharacteristic
734C4—24no—
735C4—41no—
736C4—81no—
737C4—222no—
738C4—222no—
739C4—441no—
740C4—441no—
741C4—881no—
742C4—881no—
743C4—881no—
744C4—881no—
745C4#1062311811yescharacteristic
746C4#1062312411yescharacteristic
747C4C2×#6698811yescharacteristic
748C4#1062333711yescharacteristic
749C2—81no—
750C2—82no—
751C2—82no—
752C2#1307207411yescharacteristic
753C2#1307866911yescharacteristic
754C2#1307889411yescharacteristic
755C2#1308010511yescharacteristic
756C2#1308034011yescharacteristic
757C2#1308051111yescharacteristic
758C2#1308093611yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
Fitting, prime radicalC2×C11×#449C2
socleC23×C11C22×D4
hypercenterC2×#449D11
hypocenterC11#24896
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#449

Complements

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

NH ≅ G/Ntype
1. C2×SD16×Dic11C2semidirect
2. #13072126C2semidirect
3. #13071457C2semidirect
4. #13070147C2semidirect
5. #13070049C2semidirect
6. #13069924C2semidirect
7. #13069802C2semidirect
8. #13069296C2semidirect
9. #13069219C2semidirect
10. #13068973C2semidirect
11. #13068966C2semidirect
12. #13068882C2semidirect
13. #13068619C2semidirect
14. #13068556C2semidirect
282. Q8×C11#123semidirect
620. C11#24896semidirect
646. Q8#66988semidirect

Maximal subgroups

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

subgroupindex
C2×SD16×Dic112
#130721262
#130714572
#130701472
#130700492
#130699242
#130698022
#130692962
#130692192
#130689732
#130689662
#130688822
#130686192
#130685562
C2×C11×#4492
#2489611