Finite Group Databasebeta

← #25097563

Subgroups — #25097563

Order 11008.

1446 conjugacy classes of subgroups.

The subgroup lattice has 732 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4×Q8×D43C211yesmaximal, characteristic
2C2×#14582938C211yesmaximal, characteristic
3C2×#14582906C211yesmaximal, characteristic
4C2×#14582906C211yesmaximal, characteristic
5#19137076C211yesmaximal, characteristic
6#19134862C211yesmaximal, characteristic, complemented
7#19134861C211yesmaximal, characteristic, complemented
8#19134860C211yesmaximal, characteristic, complemented
9#19134852C211yesmaximal, characteristic, complemented
10#19134851C211yesmaximal, characteristic, complemented
11#19134850C211yesmaximal, characteristic, complemented
12#19134849C211yesmaximal, characteristic, complemented
13#19134313C211yesmaximal, characteristic
14#19134287C211yesmaximal, characteristic
15C43×#1865C211yesmaximal, characteristic, complemented
16C22×Q8×D43C2211yescharacteristic
17C22×#10621872C2211yescharacteristic
18C22×#10621872C2211yescharacteristic
19C2×Q8×Dic43C2211yescharacteristic
20C2×C4×Dic86—21no—
21C2×C4×Dic86C2211yescharacteristic
22C2×#13063290—21no—
23C2×#13063290C2211yescharacteristic
24C4×Q8×D43—24no—
25C4×Q8×D43—24no—
26C2×#13063283C2211yescharacteristic
27C2×#13063283C2211yescharacteristic
28C2×C4⋊C4×D43—21no—
29C2×C4⋊C4×D43C2211yescharacteristic
30C2×C42×D43—21no—
31C2×C42×D43C2211yescharacteristic
32#14582938—24no—
33C2×#13063259C2211yescharacteristic
34C2×#13063258C2211yescharacteristic
35C2×#13063256C2211yescharacteristic
36#14582906—24no—
37#14582906C418yescomplemented
38C2×#13063250C2211yescharacteristic
39C2×#13063250C2211yescharacteristic
40C2×#13063249C2211yescharacteristic
41C2×#13063249C2211yescharacteristic
42C2×#13063248C2211yescharacteristic
43C2×#13063248C2211yescharacteristic
44#14582798C2211yescharacteristic
45#14582797C2211yescharacteristic
46#14582795C2211yescharacteristic
47#14582773—21no—
48#14582770—21no—
49C4⋊C4×Dic43—21no—
50#14582750—21no—
51#14582662C2211yescharacteristic
52#14582661C2211yescharacteristic
53#14582661C2211yescharacteristic
54#14582654C2211yescharacteristic
55#14582653C2211yescharacteristic
56#14582653C2211yescharacteristic
57C2×C4×Q8×C43C2211yescharacteristic
58C2×#106×C43C2211yescharacteristic
59C2×#103×C43C2211yescharacteristic
60C2×#103×C43C2211yescharacteristic
61C43×#389C2211yescharacteristic
62C43×#340C2211yescharacteristic
63C43×#336C2211yescharacteristic
64C22×Dic86—21no—
65C22×Dic86C2311yescharacteristic
66C2×Q8×D43—22no—
67C2×Q8×D43—22no—
68C2×Q8×D43—22no—
69C2×Q8×D43C2×C414yes—
70C2×Q8×D43D414yes—
71C2×Q8×D43Q814yes—
72C22×C4×D43—21no—
73C22×C4×D43—21no—
74C22×C4×D43D411yescharacteristic
75C22×C4×D43D411yescharacteristic
76C22×C4×D43C2311yescharacteristic
77C2×#10621872—22no—
78C2×#10621872—22no—
79C2×#10621872—22no—
80C2×#10621872—22no—
81C2×#10621872—22no—
82C2×#10621872C2×C414yes—
83C22×C43⋊C8C2311yescharacteristic
84C22×C43⋊C8C2311yescharacteristic
85Q8×Dic43—22no—
86Q8×Dic43—22no—
87C4×Dic86—28no—
88C4×Dic86—22no—
89C4×Dic86—22no—
90#13063290—28no—
91#13063290—22no—
92#13063290—22no—
93#13063283—22no—
94#13063283—22no—
95#13063283—22no—
96#13063283C2×C414yes—
97C2×C4⋊Dic43—21no—
98C2×C4⋊Dic43—21no—
99C2×C4⋊Dic43C2311yescharacteristic
100C2×C4⋊Dic43C2311yescharacteristic
101C2×C4⋊Dic43C2311yescharacteristic
102C2×Dic43⋊C4—21no—
103C2×Dic43⋊C4—21no—
104C2×Dic43⋊C4—21no—
105C2×Dic43⋊C4—21no—
106C2×Dic43⋊C4—21no—
107C4⋊C4×D43—28no—
108C4⋊C4×D43—22no—
109C4⋊C4×D43D414yes—
110C2×(C2×D43)⋊C4—21no—
111C2×(C2×D43)⋊C4—21no—
112C2×C4×Dic43—21no—
113C2×C4×Dic43—21no—
114C2×C4×Dic43—21no—
115C2×C4×Dic43—21no—
116C2×C4×Dic43—21no—
117C2×C4×Dic43D411yescharacteristic
118C2×C4×Dic43D411yescharacteristic
119C2×C4×Dic43C2311yescharacteristic
120C42×D43—28no—
121C42×D43—22no—
122C42×D43—22no—
123#13063259—22no—
124#13063258—22no—
125#13063256—22no—
126#13063250—22no—
127#13063250C2×C414yescomplemented
128#13063249—22no—
129#13063249C2×C414yescomplemented
130#13063248—22no—
131#13063248C2×C414yescomplemented
132C43⋊#95—21no—
133C43⋊#95—21no—
134C43⋊#95—21no—
135C22×Q8×C43C2311yescharacteristic
136C22×C8×C43C2311yescharacteristic
137C22×C8×C43C2311yescharacteristic
138C4×Q8×C43—22no—
139C4×Q8×C43—22no—
140C2×C4⋊C4×C43—21no—
141C2×C4⋊C4×C43—21no—
142C2×C4⋊C4×C43C2311yescharacteristic
143C2×C4⋊C4×C43C2311yescharacteristic
144C2×C4⋊C4×C43C2311yescharacteristic
145C2×C42×C43—21no—
146C2×C42×C43C2311yescharacteristic
147#106×C43—22no—
148#103×C43—22no—
149#103×C43C2×C414yescomplemented
150#95×C43—21no—
151C23×D43C2×D411yescharacteristic
152C2×Q8×C43—21no—
153C2×Q8×C43—21no—
154C2×Q8×C43—21no—
155C2×Q8×C43C22×C412yes—
156C2×Q8×C43C2×D412yes—
157C2×Q8×C43C2×Q812yes—
158C22×C4×C43—21no—
159C22×C4×C43—21no—
160C22×C4×C43—21no—
161C22×C4×C43—21no—
162C22×C4×C43C2×D411yescharacteristic
163C22×C4×C43C2×D411yescharacteristic
164C22×C4×C43C2411yescharacteristic
165C22×Dic43—21no—
166C22×Dic43—21no—
167C22×Dic43—21no—
168C22×Dic43—21no—
169C22×Dic43C2×D411yescharacteristic
170C22×Dic43C2×D411yescharacteristic
171C22×Dic43C2×D411yescharacteristic
172Q8×D43—28no—
173Q8×D43—28no—
174Q8×D43—28no—
175Q8×D43C4⋊C4116yescomplemented
176C2×C4×D43—22no—
177C2×C4×D43—22no—
178C2×C4×D43—24no—
179C2×C4×D43—22no—
180C2×C4×D43—24no—
181C2×C4×D43—22no—
182C2×C4×D43—24no—
183C2×C4×D43—24no—
184C2×C4×D43—41no—
185C2×C4×D43—41no—
186C2×C4×D43—42no—
187C2×C4×D43—42no—
188C2×C4×D43C22×C412yes—
189C2×C4×D43C2×D412yes—
190C2×C4×D43C2×D412yes—
191C2×C4×D43C2×Q812yes—
192C2×C4×D43#4112yes—
193C2×C4×D43#4112yes—
194C2×Dic86—21no—
195C2×Dic86—21no—
196C2×Dic86—21no—
197C2×Dic86—24no—
198C2×Dic86—24no—
199C2×Dic86—24no—
200C2×Dic86C22×C412yes—
201C2×Dic86C2×D412yes—
202C2×Dic86C2×Q812yes—
203C2×C8×C43—21no—
204C2×C8×C43—21no—
205C2×C8×C43—21no—
206C2×C8×C43—21no—
207C2×C8×C43—21no—
208C2×C8×C43C22×C412yes—
209C4⋊C4×C43—24no—
210C4⋊C4×C43—21no—
211C4⋊C4×C43—21no—
212C4⋊C4×C43—21no—
213C4⋊C4×C43—21no—
214C4⋊C4×C43—42no—
215C4⋊C4×C43C22×C412yes—
216C4⋊C4×C43C2×D412yes—
217C42×C43—24no—
218C42×C43—21no—
219C42×C43—21no—
220(C2×D43)⋊C4—24no—
221(C2×D43)⋊C4—42no—
222C4⋊Dic43—24no—
223C4⋊Dic43—21no—
224C4⋊Dic43—21no—
225C4⋊Dic43—21no—
226C4⋊Dic43—21no—
227C4⋊Dic43—42no—
228C4⋊Dic43C22×C412yes—
229C4⋊Dic43C2×D412yes—
230Dic43⋊C4—24no—
231Dic43⋊C4—24no—
232Dic43⋊C4—24no—
233Dic43⋊C4—42no—
234Dic43⋊C4—42no—
235C4×Dic43—24no—
236C4×Dic43—24no—
237C4×Dic43—24no—
238C4×Dic43—21no—
239C4×Dic43—21no—
240C4×Dic43—24no—
241C4×Dic43—22no—
242C4×Dic43—22no—
243C4×Dic43—42no—
244C2×C43⋊C8—21no—
245C2×C43⋊C8—21no—
246C2×C43⋊C8—21no—
247C2×C43⋊C8—21no—
248C2×C43⋊C8—21no—
249C2×C43⋊C8C22×C412yes—
250#10621872—28no—
251#10621872—44no—
252C23×C43C22×D411yescharacteristic
253C22×D43—21no—
254C22×D43—21no—
255C22×D43—21no—
256C22×D43—21no—
257C22×D43C4×D412yes—
258C22×D43#12012yes—
259C22×D43C22⋊Q812yes—
260Q8×C43—22no—
261Q8×C43—22no—
262Q8×C43—22no—
263Q8×C43C2×C4⋊C414yes—
264C2×C4×C43—22no—
265C2×C4×C43—21no—
266C2×C4×C43—22no—
267C2×C4×C43—22no—
268C2×C4×C43—21no—
269C2×C4×C43—22no—
270C2×C4×C43—21no—
271C2×C4×C43—22no—
272C2×C4×C43—21no—
273C2×C4×C43—21no—
274C2×C4×C43—41no—
275C2×C4×C43—41no—
276C2×C4×C43—41no—
277C2×C4×C43—41no—
278C2×C4×C43—41no—
279C2×C4×C43—41no—
280C2×C4×C43—41no—
281C2×C4×C43#13712yes—
282C2×C4×C43C23×C411yescharacteristic
283C2×C4×C43C22×D411yescharacteristic
284C2×C4×C43C22×D411yescharacteristic
285C2×C4×C43C22×Q811yescharacteristic
286C2×C4×C43C2×#4111yescharacteristic
287C2×C4×C43C2×#4111yescharacteristic
288C2×Dic43—22no—
289C2×Dic43—21no—
290C2×Dic43—22no—
291C2×Dic43—22no—
292C2×Dic43—21no—
293C2×Dic43—22no—
294C2×Dic43—21no—
295C2×Dic43—22no—
296C2×Dic43—21no—
297C2×Dic43—21no—
298C2×Dic43—41no—
299C2×Dic43—41no—
300C2×Dic43—41no—
301C2×Dic43—41no—
302C2×Dic43—41no—
303C2×Dic43—41no—
304C2×Dic43—41no—
305C2×Dic43C4×D412yes—
306C2×Dic43#12012yes—
307C2×Dic43C22⋊Q812yes—
308C2×Dic43#13712yes—
309C4×D43—28no—
310C4×D43—216no—
311C4×D43—44no—
312C4×D43—48no—
313C4×D43C2×C4⋊C414yes—
314C4×D43C4×D414yes—
315C4×D43C22⋊Q814yes—
316C4×D43#12314yes—
317Dic86—22no—
318Dic86—22no—
319Dic86—22no—
320Dic86—216no—
321Dic86C2×C4⋊C414yes—
322C8×C43—22no—
323C8×C43—41no—
324C43⋊C8—22no—
325C43⋊C8—41no—
326#20874—431nomaximal, Sylow
327C22×C43C2×C4×D411yescharacteristic
328C22×C43C2×#12011yescharacteristic
329C22×C43C2×C22⋊Q811yescharacteristic
330C22×C43C2×#13711yescharacteristic
331C22×C43C2×#13711yescharacteristic
332C22×C43#57511yescharacteristic
333C22×C43#57511yescharacteristic
334C2×D43—22no—
335C2×D43—22no—
336C2×D43—22no—
337C2×D43—22no—
338C2×D43—22no—
339C2×D43—22no—
340C2×D43#38514yes—
341C4×C43—22no—
342C4×C43—24no—
343C4×C43—42no—
344C4×C43—41no—
345C4×C43—42no—
346C4×C43—81no—
347C4×C43C22×C4⋊C411yescharacteristic
348C4×C43C2×C4×D411yescharacteristic
349C4×C43C2×C22⋊Q811yescharacteristic
350C4×C43C2×#12311yescharacteristic
351Dic43—22no—
352Dic43—24no—
353Dic43—42no—
354Dic43—41no—
355Dic43—42no—
356Dic43—81no—
357Dic43#38514yes—
358C22×C4×Q8—431no—
359C2×#428—431no—
360C2×#419—431no—
361C2×#419—431no—
362#2296—431no—
363#1865—431no—
364#1865—431no—
365#1865—431no—
366#1865D4311yescharacteristic, complemented
367#1863—431no—
368#1863—431no—
369#1863—431no—
370#1863—431no—
371#1736—431no—
372#1728—431no—
373C2×C43C2×#38511yescharacteristic
374C2×C43C4×#13711yescharacteristic
375C2×C43C4×#13711yescharacteristic
376C2×C43#300411yescharacteristic
377C2×C43#300511yescharacteristic
378C2×C43#307811yescharacteristic
379C2×C43#307811yescharacteristic
380D43—24no—
381C23×Q8—431no—
382C22×M16—431no—
383C22×M16—431no—
384C2×C4×Q8—431no—
385C2×C4×Q8—431no—
386C2×C4×Q8—431no—
387C2×C4×Q8—861no—
388C2×C4×Q8—861no—
389C2×C4×Q8—864no—
390C2×C4×Q8—864no—
391C2×C4×Q8C2×D4311yescharacteristic
392C2×#117—431no—
393C2×#117—431no—
394C22×C4⋊C4—431no—
395C22×C4⋊C4—861no—
396C22×C42—431no—
397C22×C42—861no—
398#428—864no—
399C2×#107—431no—
400C2×#107—431no—
401C2×#106—431no—
402C2×#106C2×D4311yescharacteristic
403#419—438no—
404#419—864no—
405C2×#103—431no—
406C2×#103—431no—
407C2×#103—431no—
408C2×#103—431no—
409C2×#103—431no—
410C2×#103—431no—
411C2×#103C2×D4311yescharacteristic
412C2×#103C2×D4311yescharacteristic
413#389—431no—
414#389—431no—
415#389—431no—
416#389C2×D4311yescharacteristic
417#385—861no—
418#385—861no—
419C4×C4⋊C4—861no—
420C4×C4⋊C4—861no—
421#340—431no—
422#340—431no—
423#340—431no—
424#340C2×D4311yescharacteristic
425#336—431no—
426#336—431no—
427#336—431no—
428#336C2×D4311yescharacteristic
429C43#2087411yescharacteristic, complemented, Sylow
430C22×Q8—434no—
431C22×Q8—434no—
432C22×Q8—434no—
433C22×Q8—431no—
434C22×Q8—861no—
435C22×Q8—862no—
436C22×Q8—862no—
437C22×Q8—862no—
438C22×Q8C22×D4311yescharacteristic
439C23×C4—431no—
440C23×C4—431no—
441C23×C4—431no—
442C23×C4—861no—
443C23×C4—861no—
444C2×M16—434no—
445C2×M16—862no—
446C2×M16—862no—
447C2×M16—862no—
448C2×M16—862no—
449C2×M16—862no—
450C22×C8—431no—
451C22×C8—431no—
452C22×C8C22×D4311yescharacteristic
453C22×C8C22×D4311yescharacteristic
454C4×Q8—22no—
455C4×Q8—22no—
456C4×Q8—862no—
457C4×Q8—862no—
458C4×Q8—868no—
459C4×Q8—862no—
460C4×Q8—868no—
461C4×Q8—862no—
462C4×Q8—862no—
463C4×Q8—862no—
464#117—434no—
465#117—862no—
466#117—862no—
467#117—862no—
468C2×C4⋊C4—21no—
469C2×C4⋊C4—21no—
470C2×C4⋊C4—431no—
471C2×C4⋊C4—431no—
472C2×C4⋊C4—434no—
473C2×C4⋊C4—431no—
474C2×C4⋊C4—862no—
475C2×C4⋊C4—868no—
476C2×C4⋊C4—861no—
477C2×C4⋊C4—861no—
478C2×C4⋊C4—861no—
479C2×C4⋊C4—861no—
480C2×C4⋊C4—861no—
481C2×C4⋊C4—861no—
482C2×C4⋊C4—861no—
483C2×C4⋊C4C22×D4311yescharacteristic
484C2×C4⋊C4C22×D4311yescharacteristic
485C2×C4⋊C4C22×D4311yescharacteristic
486C2×C22⋊C4—861no—
487C2×C22⋊C4—861no—
488C2×C42—21no—
489C2×C42—431no—
490C2×C42—431no—
491C2×C42—431no—
492C2×C42—862no—
493C2×C42—862no—
494C2×C42—868no—
495C2×C42—861no—
496C2×C42—861no—
497C2×C42—861no—
498C2×C42—861no—
499C2×C42—861no—
500C2×C42C22×D4311yescharacteristic
501#107—862no—
502#107—862no—
503#106—22no—
504#106—862no—
505#103—22no—
506#103—434no—
507#103—434no—
508#103—434no—
509#103—862no—
510#103—862no—
511#103—862no—
512#103C4×D4314yescomplemented
513#95—21no—
514#95—861no—
515#95—861no—
516#95—861no—
517C24—431no—
518C2×Q8—21no—
519C2×Q8—21no—
520C2×Q8—21no—
521C2×Q8—4316no—
522C2×Q8—432no—
523C2×Q8—432no—
524C2×Q8—432no—
525C2×Q8—864no—
526C2×Q8—864no—
527C2×Q8—864no—
528C2×Q8—868no—
529C2×Q8—868no—
530C2×Q8—868no—
531C2×Q8—861no—
532C2×Q8—861no—
533C2×Q8—861no—
534C2×Q8C2×C4×D4312yes—
535C2×Q8D4×D4312yes—
536C2×Q8Q8×D4312yes—
537C22×C4—21no—
538C22×C4—21no—
539C22×C4—21no—
540C22×C4—21no—
541C22×C4—431no—
542C22×C4—432no—
543C22×C4—432no—
544C22×C4—432no—
545C22×C4—432no—
546C22×C4—432no—
547C22×C4—432no—
548C22×C4—431no—
549C22×C4—431no—
550C22×C4—862no—
551C22×C4—862no—
552C22×C4—864no—
553C22×C4—864no—
554C22×C4—864no—
555C22×C4—864no—
556C22×C4—862no—
557C22×C4—861no—
558C22×C4—862no—
559C22×C4—861no—
560C22×C4—861no—
561C22×C4—861no—
562C22×C4—1721no—
563C22×C4—1721no—
564C22×C4—1722no—
565C22×C4—1722no—
566C22×C4D4×D4311yescharacteristic
567C22×C4D4×D4311yescharacteristic
568C22×C4C23×D4311yescharacteristic
569M16—868no—
570M16—1724no—
571C2×C8—21no—
572C2×C8—21no—
573C2×C8—21no—
574C2×C8—21no—
575C2×C8—21no—
576C2×C8—432no—
577C2×C8—861no—
578C2×C8—861no—
579C2×C8—861no—
580C2×C8—861no—
581C2×C8—861no—
582C2×C8C2×C4×D4312yes—
583C4⋊C4—24no—
584C4⋊C4—21no—
585C4⋊C4—21no—
586C4⋊C4—21no—
587C4⋊C4—21no—
588C4⋊C4—42no—
589C4⋊C4—432no—
590C4⋊C4—432no—
591C4⋊C4—864no—
592C4⋊C4—864no—
593C4⋊C4—864no—
594C4⋊C4—864no—
595C4⋊C4—861no—
596C4⋊C4—861no—
597C4⋊C4—861no—
598C4⋊C4—861no—
599C4⋊C4—1722no—
600C4⋊C4—1722no—
601C4⋊C4—1722no—
602C4⋊C4C2×C4×D4312yes—
603C4⋊C4D4×D4312yes—
604C22⋊C4—864no—
605C22⋊C4—1722no—
606C42—24no—
607C42—21no—
608C42—21no—
609C42—862no—
610C42—862no—
611C42—864no—
612C42—864no—
613C42—864no—
614C42—864no—
615C42—861no—
616C42—861no—
617C42—1722no—
618C23—432no—
619C23—432no—
620C23—432no—
621C23—861no—
622C23—861no—
623C23—861no—
624C23—861no—
625C23C2×D4×D4311yescharacteristic
626Q8—22no—
627Q8—22no—
628Q8—22no—
629Q8—434no—
630Q8—8616no—
631Q8—862no—
632Q8—862no—
633Q8—862no—
634Q8C4⋊C4×D4314yes—
635C2×C4—22no—
636C2×C4—21no—
637C2×C4—22no—
638C2×C4—22no—
639C2×C4—21no—
640C2×C4—22no—
641C2×C4—21no—
642C2×C4—22no—
643C2×C4—21no—
644C2×C4—21no—
645C2×C4—41no—
646C2×C4—41no—
647C2×C4—41no—
648C2×C4—41no—
649C2×C4—41no—
650C2×C4—41no—
651C2×C4—41no—
652C2×C4—432no—
653C2×C4—432no—
654C2×C4—432no—
655C2×C4—434no—
656C2×C4—434no—
657C2×C4—434no—
658C2×C4—434no—
659C2×C4—432no—
660C2×C4—8616no—
661C2×C4—868no—
662C2×C4—862no—
663C2×C4—861no—
664C2×C4—862no—
665C2×C4—862no—
666C2×C4—861no—
667C2×C4—862no—
668C2×C4—862no—
669C2×C4—861no—
670C2×C4—861no—
671C2×C4—861no—
672C2×C4—1724no—
673C2×C4—1728no—
674C2×C4—1721no—
675C2×C4—1721no—
676C2×C4—1721no—
677C2×C4—1721no—
678C2×C4—1721no—
679C2×C4—1721no—
680C2×C4—1721no—
681C2×C4#1306335412yes—
682C2×C4C22×C4×D4311yescharacteristic
683C2×C4C2×D4×D4311yescharacteristic
684C2×C4C2×D4×D4311yescharacteristic
685C2×C4C2×Q8×D4311yescharacteristic
686C2×C4#41×D4311yescharacteristic
687C2×C4#41×D4311yescharacteristic
688C8—22no—
689C8—41no—
690C8—862no—
691C8—1721no—
692C22—434no—
693C22—862no—
694C22—862no—
695C22—862no—
696C22—862no—
697C22—862no—
698C22—862no—
699C22C4×D4×D4311yescharacteristic
700C22#120×D4311yescharacteristic
701C22C22⋊Q8×D4311yescharacteristic
702C22#137×D4311yescharacteristic
703C22C2×#1306335411yescharacteristic
704C22#1458369611yescharacteristic
705C22#1458369811yescharacteristic
706C4—22no—
707C4—24no—
708C4—41no—
709C4—42no—
710C4—42no—
711C4—81no—
712C4—434no—
713C4—862no—
714C4—864no—
715C4—3441no—
716C4—1721no—
717C4—1722no—
718C4—1722no—
719C4C2×C4⋊C4×D4311yescharacteristic
720C4C4×D4×D4311yescharacteristic
721C4C22⋊Q8×D4311yescharacteristic
722C4#123×D4311yescharacteristic
723C2—864no—
724C2#385×D4311yescharacteristic
725C2C4×#1306335411yescharacteristic
726C2#1914341111yescharacteristic
727C2#1914382611yescharacteristic
728C2#1914383811yescharacteristic
729C2#1914439511yescharacteristic
730C2#1914439811yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC43×#1865C2
socleC23×C43C22×D4
prime radicalC23×D43C2×D4
cosocleC22×C4×C43C24
hypercenter#1865D43
hypocenterC43#20874
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1865

Complements

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

NH ≅ G/Ntype
6. #19134862C2semidirect
7. #19134861C2semidirect
8. #19134860C2semidirect
9. #19134852C2semidirect
10. #19134851C2semidirect
11. #19134850C2semidirect
12. #19134849C2semidirect
15. C43×#1865C2semidirect
37. #14582906C4semidirect
127. #13063250C2×C4semidirect
129. #13063249C2×C4semidirect
131. #13063248C2×C4semidirect
149. #103×C43C2×C4semidirect
175. Q8×D43C4⋊C4semidirect
366. #1865D43semidirect
429. C43#20874semidirect
512. #103C4×D43semidirect

Maximal subgroups

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

subgroupindex
C2×C4×Q8×D432
C2×#145829382
C2×#145829062
#191370762
#191348622
#191348612
#191348602
#191348522
#191348512
#191348502
#191348492
#191343132
#191342872
C43×#18652
#2087443