Finite Group Databasebeta

← #14774049

Subgroups — #14774049

Order 2816.

1170 conjugacy classes of subgroups.

The subgroup lattice has 748 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622777C211yesmaximal, characteristic, complemented
2C22×#66899C211yesmaximal, characteristic, complemented
3#13071636C211yesmaximal, characteristic
4Q8×C22⋊Dic11C211yesmaximal, characteristic, complemented
5#13069499C211yesmaximal, characteristic, complemented
6#13069308C211yesmaximal, characteristic, complemented
7#13069259C211yesmaximal, characteristic, complemented
8#13069045C211yesmaximal, characteristic
9#13068973C211yesmaximal, characteristic, complemented
10#13068952C211yesmaximal, characteristic, complemented
11#13068872C211yesmaximal, characteristic, complemented
12#13068806C211yesmaximal, characteristic, complemented
13#13068448C211yesmaximal, characteristic, complemented
14#13068395C211yesmaximal, characteristic, complemented
15C2×C11×#448C211yesmaximal, characteristic
16C23×Q8×C11C2211yescharacteristic
17C22×C11×SD16C2211yescharacteristic
18C22×C11×SD16C2211yescharacteristic
19C2×C11×#121C2211yescharacteristic
20C2×Q8×Dic11C2211yescharacteristic
21C2×Q8×Dic11C2211yescharacteristic
22C2×D4×Dic11—21no—
23C2×D4×Dic11C2211yescharacteristic
24C22×C4⋊Dic11C2211yescharacteristic
25C23×C11⋊C8C2211yescharacteristic
26C11×#448C418yescomplemented
27C2×C11×#103C2211yescharacteristic
28C2×C11×#103C2211yescharacteristic
29C2×C11×C22⋊C8C2211yescharacteristic
30#10622843—21no—
31#10622843—21no—
32#10622843C2211yescharacteristic
33#10622843C2211yescharacteristic
34C2×#66899—24no—
35C2×#66899C2211yescharacteristic
36C2×#66899C2211yescharacteristic
37C2×#66899C2211yescharacteristic
38C2×#66899C2211yescharacteristic
39#10622834C2211yescharacteristic
40#10622833—21no—
41C2×#66896C2211yescharacteristic
42C2×#66896C2211yescharacteristic
43#10622825—21no—
44#10622825C2211yescharacteristic
45C4×C22⋊Dic11—21no—
46C4×C22⋊Dic11C2211yescharacteristic
47#10622777—24no—
48C2×#66882C2211yescharacteristic
49C2×#66882C2211yescharacteristic
50C2×#66879C2211yescharacteristic
51C2×#66879C2211yescharacteristic
52#10622598C2211yescharacteristic
53C4⋊C4×Dic11C2211yescharacteristic
54#10622564—21no—
55#10622563—21no—
56#10622189C2211yescharacteristic
57#10622189C2211yescharacteristic
58#10622188C2211yescharacteristic
59#10622188C2211yescharacteristic
60#10622167C2211yescharacteristic
61#10622167C2211yescharacteristic
62C22×Q8×C11—21no—
63C22×Q8×C11—22no—
64C22×Q8×C11—22no—
65C22×Q8×C11—22no—
66C22×Q8×C11—41no—
67C22×Q8×C11—41no—
68C22×Q8×C11C2×C414yescomplemented
69C22×Q8×C11C2311yescharacteristic
70C22×Q8×C11C2311yescharacteristic
71C22×D4×C11—21no—
72C22×D4×C11C2311yescharacteristic
73C23×C4×C11—21no—
74C23×C4×C11C2311yescharacteristic
75C23×Dic11—21no—
76C23×Dic11—21no—
77C2×C11×SD16—22no—
78C2×C11×SD16—22no—
79C2×C11×SD16—41no—
80C2×C11×SD16—41no—
81C2×C11×SD16C2×C414yescomplemented
82C2×C11×SD16C2×C414yescomplemented
83C22×C8×C11C2311yescharacteristic
84C22×C8×C11C2311yescharacteristic
85C11×#121—22no—
86C11×#121C2×C414yes—
87C2×C11×C4⋊C4C2311yescharacteristic
88C2×C11×C22⋊C4—21no—
89C2×C22⋊Dic11—21no—
90C2×C22⋊Dic11—21no—
91C2×C22⋊Dic11—21no—
92C2×C22⋊Dic11—21no—
93C2×C22⋊Dic11D411yescharacteristic
94C2×C22⋊Dic11D411yescharacteristic
95Q8×Dic11—22no—
96Q8×Dic11—22no—
97Q8×Dic11—41no—
98Q8×Dic11—41no—
99D4×Dic11—22no—
100D4×Dic11—41no—
101D4×Dic11—44no—
102C2×C4⋊Dic11—22no—
103C2×C4⋊Dic11—21no—
104C2×C4⋊Dic11—21no—
105C2×C4⋊Dic11—21no—
106C2×C4⋊Dic11—21no—
107C2×C4⋊Dic11—41no—
108C2×C4⋊Dic11C2311yescharacteristic
109C2×C4⋊Dic11C2311yescharacteristic
110C2×C4⋊Dic11C2311yescharacteristic
111C2×C4⋊Dic11C2311yescharacteristic
112C2×C4×Dic11—21no—
113C2×C4×Dic11—21no—
114C2×C4×Dic11—21no—
115C2×C4×Dic11C2311yescharacteristic
116C2×C4×Dic11C2311yescharacteristic
117C22×C11⋊C8—22no—
118C22×C11⋊C8—22no—
119C22×C11⋊C8—41no—
120C22×C11⋊C8C2311yescharacteristic
121C22×C11⋊C8C2311yescharacteristic
122C11×#103C2×C414yescomplemented
123C11×#103C2×C414yescomplemented
124C11×C22⋊C8C2×C414yescomplemented
125#66899—22no—
126#66899—22no—
127#66899—22no—
128#66899D414yescomplemented
129#66896—22no—
130#66896—41no—
131C11⋊#95—21no—
132C11⋊#95—21no—
133C11⋊#95—21no—
134C11⋊#95—21no—
135C11⋊#95—21no—
136C11⋊#95—21no—
137C11⋊#95—21no—
138C11⋊#95D411yescharacteristic
139C11⋊#95D411yescharacteristic
140#66882—22no—
141#66882—41no—
142#66879—22no—
143#66879—41no—
144#22855—111nomaximal, Sylow
145C24×C11—21no—
146C24×C11C2×D411yescharacteristic
147C2×Q8×C11—24no—
148C2×Q8×C11—21no—
149C2×Q8×C11—21no—
150C2×Q8×C11—21no—
151C2×Q8×C11—21no—
152C2×Q8×C11—28no—
153C2×Q8×C11—21no—
154C2×Q8×C11—21no—
155C2×Q8×C11—21no—
156C2×Q8×C11—21no—
157C2×Q8×C11—42no—
158C2×Q8×C11—42no—
159C2×Q8×C11—44no—
160C2×Q8×C11—44no—
161C2×Q8×C11—44no—
162C2×Q8×C11C22×C412yes—
163C2×Q8×C11C22×C412yes—
164C2×Q8×C11C2×D412yes—
165C2×Q8×C11#4112yes—
166C2×D4×C11—24no—
167C2×D4×C11—21no—
168C2×D4×C11—21no—
169C2×D4×C11—21no—
170C2×D4×C11—21no—
171C2×D4×C11—21no—
172C2×D4×C11—42no—
173C2×D4×C11—42no—
174C2×D4×C11C22×C412yes—
175C22×C4×C11—21no—
176C22×C4×C11—21no—
177C22×C4×C11—21no—
178C22×C4×C11—21no—
179C22×C4×C11—21no—
180C22×C4×C11—24no—
181C22×C4×C11—21no—
182C22×C4×C11—21no—
183C22×C4×C11—42no—
184C22×C4×C11—42no—
185C22×C4×C11C22×C412yes—
186C22×C4×C11C2×D411yescharacteristic
187C22×C4×C11#4112yes—
188C22×C4×C11C2411yescharacteristic
189C22×Dic11—21no—
190C22×Dic11—21no—
191C22×Dic11—21no—
192C22×Dic11—21no—
193C22×Dic11—42no—
194C22×Dic11—42no—
195C22×Dic11—42no—
196C22×Dic11—42no—
197C22×Dic11—81no—
198C22×Dic11—81no—
199C22×Dic11C2×D411yescharacteristic
200C22×Dic11C2×D411yescharacteristic
201C22×Dic11C2×D411yescharacteristic
202C22×Dic11C2×D411yescharacteristic
203C11×SD16—28no—
204C11×SD16—44no—
205C2×C8×C11—21no—
206C2×C8×C11—21no—
207C2×C8×C11—21no—
208C2×C8×C11—21no—
209C2×C8×C11C22×C412yes—
210C2×C8×C11C22×C412yes—
211C11×C4⋊C4—21no—
212C11×C4⋊C4C22×C412yes—
213C11×C22⋊C4—24no—
214C22⋊Dic11—22no—
215C22⋊Dic11—22no—
216C22⋊Dic11—42no—
217C22⋊Dic11—42no—
218C22⋊Dic11—42no—
219C22⋊Dic11—81no—
220C4⋊Dic11—21no—
221C4⋊Dic11—21no—
222C4⋊Dic11—21no—
223C4⋊Dic11—21no—
224C4⋊Dic11—21no—
225C4⋊Dic11—21no—
226C4⋊Dic11—21no—
227C4⋊Dic11—42no—
228C4⋊Dic11—42no—
229C4⋊Dic11—42no—
230C4⋊Dic11—42no—
231C4⋊Dic11C2×D412yes—
232C4×Dic11—21no—
233C4×Dic11—21no—
234C4×Dic11—21no—
235C4×Dic11—21no—
236C4×Dic11—42no—
237C4×Dic11—42no—
238C4×Dic11—42no—
239C2×C11⋊C8—21no—
240C2×C11⋊C8—21no—
241C2×C11⋊C8—21no—
242C2×C11⋊C8—21no—
243C2×C11⋊C8—21no—
244C2×C11⋊C8—44no—
245C2×C11⋊C8C2×D412yes—
246C2×#448D1111yescharacteristic
247C2×#440—111no—
248C22×#103—111no—
249#2361—111no—
250Q8×C22⋊C4—111no—
251#1973—111no—
252#1935—111no—
253#1928—111no—
254#1893—111no—
255#1880—111no—
256#1877—111no—
257#1863—111no—
258#1852—111no—
259#1763—111no—
260#1752—111no—
261C23×C11—21no—
262C23×C11—21no—
263C23×C11—21no—
264C23×C11—21no—
265C23×C11—22no—
266C23×C11—41no—
267C23×C11—41no—
268C23×C11—41no—
269C23×C11—41no—
270C23×C11—41no—
271C23×C11—41no—
272C23×C11C4×D412yes—
273C23×C11AGL(1,ℤ/8)12yes—
274C23×C11#13712yes—
275C23×C11C22×D411yescharacteristic
276Q8×C11—22no—
277Q8×C11—22no—
278Q8×C11—22no—
279Q8×C11—22no—
280Q8×C11—22no—
281Q8×C11—48no—
282Q8×C11—41no—
283Q8×C11—41no—
284Q8×C11C4×D414yescomplemented
285D4×C11—22no—
286D4×C11—22no—
287D4×C11—48no—
288D4×C11—41no—
289D4×C11—41no—
290C2×C4×C11—22no—
291C2×C4×C11—22no—
292C2×C4×C11—21no—
293C2×C4×C11—22no—
294C2×C4×C11—21no—
295C2×C4×C11—22no—
296C2×C4×C11—22no—
297C2×C4×C11—22no—
298C2×C4×C11—22no—
299C2×C4×C11—22no—
300C2×C4×C11—22no—
301C2×C4×C11—48no—
302C2×C4×C11—41no—
303C2×C4×C11—41no—
304C2×C4×C11—41no—
305C2×C4×C11—41no—
306C2×C4×C11C4×D412yes—
307C2×C4×C11C23×C411yescharacteristic
308C2×C4×C11C22×D411yescharacteristic
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—22no—
316C2×Dic11—21no—
317C2×Dic11—21no—
318C2×Dic11—21no—
319C2×Dic11—21no—
320C2×Dic11—21no—
321C2×Dic11—21no—
322C2×Dic11—21no—
323C2×Dic11—21no—
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—41no—
335C2×Dic11—41no—
336C2×Dic11—41no—
337C2×Dic11—84no—
338C2×Dic11—84no—
339C8×C11—22no—
340C8×C11—22no—
341C11⋊C8—22no—
342C11⋊C8—41no—
343C23×Q8C2×D1111yescharacteristic
344C22×SD16C2×D1111yescharacteristic
345C22×SD16C2×D1111yescharacteristic
346C23×C8—111no—
347C2×#121C2×D1111yescharacteristic
348C2×C4×Q8—111no—
349C2×C4×Q8—111no—
350C2×C4×D4—111no—
351C2×C4×D4—221no—
352C22×C4⋊C4—111no—
353#448Dic1118yescomplemented
354#440—224no—
355C2×#107—111no—
356C2×#107—111no—
357C2×#103—111no—
358C2×#103—111no—
359C2×#103—111no—
360C2×#103—111no—
361C2×#103—224no—
362C2×#103C2×D1111yescharacteristic
363C2×#103C2×D1111yescharacteristic
364C2×#102—111no—
365C2×#102—111no—
366C2×C22⋊C8C2×D1111yescharacteristic
367C2×#97—111no—
368C2×#97—111no—
369#391—111no—
370#391—111no—
371#391—221no—
372#391—221no—
373#390—111no—
374#389—111no—
375#388—221no—
376#386—221no—
377#385—221no—
378#380—111no—
379#380—221no—
380C4×C4⋊C4—111no—
381C4×C22⋊C4—111no—
382C4×C22⋊C4—221no—
383#340—111no—
384#340—111no—
385#340—111no—
386#340—111no—
387#336—111no—
388#336—111no—
389C22×C11—22no—
390C22×C11—22no—
391C22×C11—22no—
392C22×C11—22no—
393C22×C11—22no—
394C22×C11—22no—
395C22×C11—42no—
396C22×C11—42no—
397C22×C11—42no—
398C22×C11—81no—
399C22×C11—81no—
400C22×C11—81no—
401C22×C11—81no—
402C22×C11#44014yescomplemented
403C22×C11C2×C4×D411yescharacteristic
404C22×C11D4211yescharacteristic
405C22×C11#54611yescharacteristic
406C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
407C22×C11C2×#13711yescharacteristic
408C22×C11#57711yescharacteristic
409C22×C11#57811yescharacteristic
410C4×C11—22no—
411C4×C11—24no—
412C4×C11—42no—
413C4×C11—42no—
414C4×C11C2×C4×D411yescharacteristic
415C4×C11#51811yescharacteristic
416C4×C11#54611yescharacteristic
417C4×C11#55111yescharacteristic
418Dic11—41no—
419Dic11—42no—
420Dic11—41no—
421Dic11—41no—
422Dic11—41no—
423Dic11—81no—
424Dic11—81no—
425Dic11—81no—
426C22×Q8—21no—
427C22×Q8—22no—
428C22×Q8—22no—
429C22×Q8—22no—
430C22×Q8—41no—
431C22×Q8—41no—
432C22×Q8C2×Dic1114yescomplemented
433C22×Q8C22×D1111yescharacteristic
434C22×Q8C22×D1111yescharacteristic
435C22×D4—21no—
436C22×D4C22×D1111yescharacteristic
437C23×C4—21no—
438C23×C4—221no—
439C23×C4—221no—
440C23×C4C22×D1111yescharacteristic
441C2×SD16—22no—
442C2×SD16—22no—
443C2×SD16—41no—
444C2×SD16—41no—
445C2×SD16C2×Dic1114yescomplemented
446C2×SD16C2×Dic1114yescomplemented
447C22×C8—111no—
448C22×C8—111no—
449C22×C8—222no—
450C22×C8—222no—
451C22×C8—441no—
452C22×C8C22×D1111yescharacteristic
453C22×C8C22×D1111yescharacteristic
454#121—22no—
455#121C2×Dic1114yes—
456C4×Q8—222no—
457C4×Q8—222no—
458C4×Q8—441no—
459C4×Q8—441no—
460C4×D4—222no—
461C4×D4—441no—
462C4×D4—444no—
463C2×C4⋊C4—111no—
464C2×C4⋊C4—111no—
465C2×C4⋊C4—111no—
466C2×C4⋊C4—111no—
467C2×C4⋊C4—222no—
468C2×C4⋊C4—221no—
469C2×C4⋊C4—221no—
470C2×C4⋊C4—221no—
471C2×C4⋊C4—221no—
472C2×C4⋊C4—441no—
473C2×C4⋊C4C22×D1111yescharacteristic
474C2×C22⋊C4—21no—
475C2×C22⋊C4—111no—
476C2×C22⋊C4—111no—
477C2×C22⋊C4—221no—
478C2×C22⋊C4—221no—
479C2×C22⋊C4—221no—
480C2×C22⋊C4—221no—
481C2×C42—111no—
482C2×C42—111no—
483C2×C42—221no—
484C2×C42—221no—
485C2×C42—221no—
486#107—222no—
487#107—441no—
488#103—114no—
489#103—222no—
490#103—222no—
491#103—222no—
492#103C2×Dic1114yescomplemented
493#103C2×Dic1114yescomplemented
494#102—222no—
495#102—441no—
496C22⋊C8C2×Dic1114yescomplemented
497#97—222no—
498#97—441no—
499#95—111no—
500#95—111no—
501#95—221no—
502#95—221no—
503#95—221no—
504#95—221no—
505#95—221no—
506#95—221no—
507#95—221no—
508C2×C11—24no—
509C2×C11—82no—
510C2×C11#235811yescharacteristic
511C2×C11C2×#44011yescharacteristic
512C2×C11#294711yescharacteristic
513C2×C11#326511yescharacteristic
514C2×C11#327011yescharacteristic
515C2×C11#330811yescharacteristic
516C2×C11#332011yescharacteristic
517C24—21no—
518C24D4×D1111yescharacteristic
519C2×Q8—24no—
520C2×Q8—21no—
521C2×Q8—21no—
522C2×Q8—21no—
523C2×Q8—21no—
524C2×Q8—28no—
525C2×Q8—21no—
526C2×Q8—21no—
527C2×Q8—21no—
528C2×Q8—21no—
529C2×Q8—42no—
530C2×Q8—42no—
531C2×Q8—44no—
532C2×Q8—44no—
533C2×Q8—44no—
534C2×Q8D4×D1112yes—
535C2×Q8#434112yes—
536C2×Q8C22×Dic1112yes—
537C2×Q8C22×Dic1112yes—
538C2×D4—24no—
539C2×D4—21no—
540C2×D4—21no—
541C2×D4—21no—
542C2×D4—21no—
543C2×D4—21no—
544C2×D4—42no—
545C2×D4—42no—
546C2×D4C22×Dic1112yes—
547C22×C4—21no—
548C22×C4—21no—
549C22×C4—21no—
550C22×C4—21no—
551C22×C4—21no—
552C22×C4—24no—
553C22×C4—21no—
554C22×C4—21no—
555C22×C4—42no—
556C22×C4—42no—
557C22×C4—111no—
558C22×C4—111no—
559C22×C4—111no—
560C22×C4—111no—
561C22×C4—221no—
562C22×C4—221no—
563C22×C4—221no—
564C22×C4—221no—
565C22×C4—442no—
566C22×C4—442no—
567C22×C4—442no—
568C22×C4—442no—
569C22×C4—881no—
570C22×C4—881no—
571C22×C4D4×D1111yescharacteristic
572C22×C4#434112yes—
573C22×C4C22×Dic1112yes—
574C22×C4C23×D1111yescharacteristic
575SD16—28no—
576SD16—44no—
577C2×C8—21no—
578C2×C8—21no—
579C2×C8—21no—
580C2×C8—21no—
581C2×C8—112no—
582C2×C8—221no—
583C2×C8—221no—
584C2×C8—221no—
585C2×C8—221no—
586C2×C8—221no—
587C2×C8—444no—
588C2×C8C22×Dic1112yes—
589C2×C8C22×Dic1112yes—
590C4⋊C4—21no—
591C4⋊C4—112no—
592C4⋊C4—221no—
593C4⋊C4—221no—
594C4⋊C4—221no—
595C4⋊C4—221no—
596C4⋊C4—221no—
597C4⋊C4—221no—
598C4⋊C4—221no—
599C4⋊C4—442no—
600C4⋊C4—442no—
601C4⋊C4—442no—
602C4⋊C4—442no—
603C4⋊C4C22×Dic1112yes—
604C22⋊C4—24no—
605C22⋊C4—222no—
606C22⋊C4—222no—
607C22⋊C4—442no—
608C22⋊C4—442no—
609C22⋊C4—442no—
610C22⋊C4—881no—
611C42—221no—
612C42—221no—
613C42—221no—
614C42—221no—
615C42—442no—
616C42—442no—
617C42—442no—
618C11#2285511yescharacteristic, complemented, Sylow
619C23—21no—
620C23—21no—
621C23—21no—
622C23—21no—
623C23—22no—
624C23—41no—
625C23—41no—
626C23—41no—
627C23—41no—
628C23—41no—
629C23—41no—
630C23#6696712yes—
631C23#6696812yes—
632C23D4×Dic1112yes—
633C23C2×D4×D1111yescharacteristic
634Q8—22no—
635Q8—22no—
636Q8—22no—
637Q8—22no—
638Q8—22no—
639Q8—48no—
640Q8—41no—
641Q8—41no—
642Q8D4×Dic1114yescomplemented
643D4—22no—
644D4—22no—
645D4—48no—
646D4—41no—
647D4—41no—
648C2×C4—22no—
649C2×C4—22no—
650C2×C4—21no—
651C2×C4—22no—
652C2×C4—21no—
653C2×C4—22no—
654C2×C4—22no—
655C2×C4—22no—
656C2×C4—22no—
657C2×C4—22no—
658C2×C4—22no—
659C2×C4—48no—
660C2×C4—41no—
661C2×C4—41no—
662C2×C4—41no—
663C2×C4—41no—
664C2×C4—221no—
665C2×C4—221no—
666C2×C4—221no—
667C2×C4—221no—
668C2×C4—221no—
669C2×C4—221no—
670C2×C4—221no—
671C2×C4—221no—
672C2×C4—221no—
673C2×C4—221no—
674C2×C4—222no—
675C2×C4—221no—
676C2×C4—221no—
677C2×C4—441no—
678C2×C4—441no—
679C2×C4—441no—
680C2×C4—441no—
681C2×C4—441no—
682C2×C4—441no—
683C2×C4—441no—
684C2×C4—441no—
685C2×C4—441no—
686C2×C4—441no—
687C2×C4—441no—
688C2×C4—884no—
689C2×C4—884no—
690C2×C4D4×Dic1112yes—
691C2×C4C2×D4×D1111yescharacteristic
692C2×C4C2×#434111yescharacteristic
693C2×C4C2×#434111yescharacteristic
694C2×C4#6703711yescharacteristic
695C2×C4#6703711yescharacteristic
696C2×C4C23×Dic1111yescharacteristic
697C8—22no—
698C8—22no—
699C8—222no—
700C8—441no—
701C22—22no—
702C22—22no—
703C22—22no—
704C22—22no—
705C22—22no—
706C22—22no—
707C22—42no—
708C22—42no—
709C22—42no—
710C22—81no—
711C22—81no—
712C22—81no—
713C22—81no—
714C22#1062277714yescomplemented
715C22#1062312111yescharacteristic
716C22#1062312211yescharacteristic
717C22C2×#6696711yescharacteristic
718C22C2×#6696811yescharacteristic
719C22#1062330911yescharacteristic
720C22#1062331011yescharacteristic
721C22C2×D4×Dic1111yescharacteristic
722C4—22no—
723C4—24no—
724C4—42no—
725C4—42no—
726C4—441no—
727C4—441no—
728C4—442no—
729C4—441no—
730C4—441no—
731C4—881no—
732C4—881no—
733C4—881no—
734C4#1062311811yescharacteristic
735C4#1062312211yescharacteristic
736C4C2×D4×Dic1111yescharacteristic
737C4#1062332911yescharacteristic
738C2—24no—
739C2—82no—
740C2#1307160011yescharacteristic
741C2C2×#1062277711yescharacteristic
742C2#1307746011yescharacteristic
743C2#1308010411yescharacteristic
744C2#1308017911yescharacteristic
745C2#1308061111yescharacteristic
746C2#1308079111yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC2×C11×#448C2
socleC23×C11C22×D4
prime radicalC2×C11×#121C22
cosocleC22×C4×C11C24
hypercenterC2×#448D11
hypocenterC11#22855
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#448

Complements

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

NH ≅ G/Ntype
1. C2×#10622777C2semidirect
2. C22×#66899C2semidirect
4. Q8×C22⋊Dic11C2semidirect
5. #13069499C2semidirect
6. #13069308C2semidirect
7. #13069259C2semidirect
9. #13068973C2semidirect
10. #13068952C2semidirect
11. #13068872C2semidirect
12. #13068806C2semidirect
13. #13068448C2semidirect
14. #13068395C2semidirect
26. C11×#448C4semidirect
68. C22×Q8×C11C2×C4semidirect
81. C2×C11×SD16C2×C4semidirect
82. C2×C11×SD16C2×C4semidirect
122. C11×#103C2×C4semidirect
123. C11×#103C2×C4semidirect
124. C11×C22⋊C8C2×C4semidirect
128. #66899D4semidirect
284. Q8×C11C4×D4semidirect
353. #448Dic11semidirect
402. C22×C11#440semidirect
432. C22×Q8C2×Dic11semidirect
445. C2×SD16C2×Dic11semidirect
446. C2×SD16C2×Dic11semidirect
492. #103C2×Dic11semidirect
493. #103C2×Dic11semidirect
496. C22⋊C8C2×Dic11semidirect
618. C11#22855semidirect
642. Q8D4×Dic11semidirect
714. C22#10622777semidirect

Maximal subgroups

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

subgroupindex
C2×#106227772
C22×#668992
#130716362
Q8×C22⋊Dic112
#130694992
#130693082
#130692592
#130690452
#130689732
#130689522
#130688722
#130688062
#130684482
#130683952
C2×C11×#4482
#2285511