Finite Group Databasebeta

← #25102269

Subgroups — #25102269

Order 11008.

1436 conjugacy classes of subgroups.

The subgroup lattice has 750 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4×Q8×D43C211yesmaximal, characteristic
2C2×#14583053C211yesmaximal, characteristic
3C2×#14583004C211yesmaximal, characteristic, complemented
4C4×#13063301C211yesmaximal, characteristic
5#19134938C211yesmaximal, characteristic, complemented
6#19134933C211yesmaximal, characteristic, complemented
7#19134899C211yesmaximal, characteristic
8#19134861C211yesmaximal, characteristic, complemented
9#19134860C211yesmaximal, characteristic, complemented
10#19134786C211yesmaximal, characteristic
11#19134528C211yesmaximal, characteristic
12#19134426C211yesmaximal, characteristic, complemented
13#19134425C211yesmaximal, characteristic, complemented
14#19134358C211yesmaximal, characteristic
15C2×C43×#441C211yesmaximal, characteristic, complemented
16C22×Q8×D43C2211yescharacteristic
17C22×#10621885C2211yescharacteristic
18C2×#13063301C2211yescharacteristic
19C2×Q8×Dic43C2211yescharacteristic
20C2×C4×Dic86—21no—
21C2×C4×Dic86C2211yescharacteristic
22C2×#13063290—21no—
23C2×#13063290C2211yescharacteristic
24C4×Q8×D43—24no—
25C4×Q8×D43—24no—
26C2×C4⋊C4×D43—21no—
27C2×C4⋊C4×D43C2211yescharacteristic
28C2×C42×D43—21no—
29C2×C42×D43C2211yescharacteristic
30#14583053C418yescomplemented
31#14583004—24no—
32C2×#13063256C2211yescharacteristic
33C2×#13063250C2211yescharacteristic
34C2×#13063250C2211yescharacteristic
35C2×#13063249C2211yescharacteristic
36C2×#13063249C2211yescharacteristic
37C2×#13063249C2211yescharacteristic
38C2×#13063248C2211yescharacteristic
39C2×(C2×D43)⋊C8C2211yescharacteristic
40C2×(C2×D43)⋊C8C2211yescharacteristic
41C2×#13063236C2211yescharacteristic
42#14582806C2211yescharacteristic
43#14582795C2211yescharacteristic
44#14582780—21no—
45#14582770—21no—
46#14582756C2211yescharacteristic
47C4×Dic43⋊C4—21no—
48C4×C4⋊Dic43C2211yescharacteristic
49C4×(C2×D43)⋊C4—21no—
50#14582662C2211yescharacteristic
51#14582662C2211yescharacteristic
52#14582661C2211yescharacteristic
53#14582661C2211yescharacteristic
54#14582653C2211yescharacteristic
55#14582653C2211yescharacteristic
56C22×Q16×C43C2211yescharacteristic
57C2×C4×Q8×C43C2211yescharacteristic
58C2×C4×Q8×C43C2211yescharacteristic
59C43×#441—24no—
60C2×#106×C43C2211yescharacteristic
61C2×#103×C43C2211yescharacteristic
62C2×#103×C43C2211yescharacteristic
63C2×#97×C43C2211yescharacteristic
64C22×Dic86—21no—
65C22×Dic86C2311yescharacteristic
66C2×Q8×D43—22no—
67C2×Q8×D43—22no—
68C2×Q8×D43—22no—
69C2×Q8×D43—22no—
70C2×Q8×D43—22no—
71C2×Q8×D43C2×C414yes—
72C22×C4×D43—21no—
73C22×C4×D43—21no—
74C22×C4×D43D411yescharacteristic
75C22×C4×D43D411yescharacteristic
76C22×C4×D43C2311yescharacteristic
77C2×#10621885—22no—
78C2×#10621885—22no—
79C2×#10621885C2×C414yescomplemented
80C22×C43⋊C8C2311yescharacteristic
81C22×C43⋊C8C2311yescharacteristic
82#13063301—22no—
83#13063301C2×C414yes—
84Q8×Dic43—22no—
85Q8×Dic43—22no—
86C4×Dic86—28no—
87C4×Dic86—22no—
88C4×Dic86D414yes—
89#13063290—28no—
90#13063290—22no—
91#13063290—22no—
92C2×C4⋊Dic43—21no—
93C2×C4⋊Dic43C2311yescharacteristic
94C2×C4⋊Dic43C2311yescharacteristic
95C2×C4⋊Dic43C2311yescharacteristic
96C2×Dic43⋊C4—21no—
97C2×Dic43⋊C4—21no—
98C2×Dic43⋊C4—21no—
99C2×Dic43⋊C4—21no—
100C2×Dic43⋊C4—21no—
101C4⋊C4×D43—28no—
102C4⋊C4×D43—22no—
103C4⋊C4×D43—22no—
104C2×(C2×D43)⋊C4—21no—
105C2×(C2×D43)⋊C4—21no—
106C2×C4×Dic43—21no—
107C2×C4×Dic43—21no—
108C2×C4×Dic43—21no—
109C2×C4×Dic43—21no—
110C2×C4×Dic43D411yescharacteristic
111C2×C4×Dic43D411yescharacteristic
112C2×C4×Dic43C2311yescharacteristic
113C42×D43—28no—
114C42×D43—22no—
115C42×D43—22no—
116#13063256—22no—
117#13063250—22no—
118#13063250C2×C414yescomplemented
119#13063249—22no—
120#13063249—22no—
121#13063249C2×C414yescomplemented
122#13063248—22no—
123(C2×D43)⋊C8—22no—
124(C2×D43)⋊C8C2×C414yes—
125#13063236—22no—
126C43⋊#95—21no—
127C43⋊#95—21no—
128C43⋊#95—21no—
129C43⋊#95—21no—
130C43⋊#95—21no—
131C22×Q8×C43C2311yescharacteristic
132C22×Q8×C43C2311yescharacteristic
133C2×Q16×C43—22no—
134C2×Q16×C43—22no—
135C2×Q16×C43C2×C414yescomplemented
136C22×C8×C43C2311yescharacteristic
137C22×C8×C43C2311yescharacteristic
138C4×Q8×C43—22no—
139C4×Q8×C43—22no—
140C4×Q8×C43—22no—
141C4×Q8×C43D414yes—
142C2×C4⋊C4×C43—21no—
143C2×C4⋊C4×C43—21no—
144C2×C4⋊C4×C43C2311yescharacteristic
145C2×C4⋊C4×C43C2311yescharacteristic
146C2×C42×C43—21no—
147C2×C42×C43—21no—
148C2×C42×C43C2311yescharacteristic
149#106×C43—22no—
150#103×C43—22no—
151#103×C43—22no—
152#97×C43—22no—
153C23×D43C2×D411yescharacteristic
154C2×Q8×C43—21no—
155C2×Q8×C43—21no—
156C2×Q8×C43—21no—
157C2×Q8×C43—21no—
158C2×Q8×C43—21no—
159C2×Q8×C43—21no—
160C2×Q8×C43—21no—
161C2×Q8×C43—21no—
162C2×Q8×C43C22×C412yes—
163C2×Q8×C43C22×C412yes—
164C2×Q8×C43C2×D412yes—
165C2×Q8×C43#4112yes—
166C22×C4×C43—21no—
167C22×C4×C43—21no—
168C22×C4×C43—21no—
169C22×C4×C43—21no—
170C22×C4×C43C2×D411yescharacteristic
171C22×C4×C43C2×D411yescharacteristic
172C22×C4×C43C2411yescharacteristic
173C22×Dic43—21no—
174C22×Dic43—21no—
175C22×Dic43—21no—
176C22×Dic43—21no—
177C22×Dic43C2×D411yescharacteristic
178C22×Dic43C2×D411yescharacteristic
179C22×Dic43C2×D411yescharacteristic
180Q8×D43—28no—
181Q8×D43—28no—
182Q8×D43—28no—
183Q8×D43—28no—
184C2×C4×D43—24no—
185C2×C4×D43—24no—
186C2×C4×D43—22no—
187C2×C4×D43—21no—
188C2×C4×D43—21no—
189C2×C4×D43—21no—
190C2×C4×D43—21no—
191C2×C4×D43—22no—
192C2×C4×D43—24no—
193C2×C4×D43—22no—
194C2×C4×D43—24no—
195C2×C4×D43—22no—
196C2×C4×D43—22no—
197C2×C4×D43—41no—
198C2×C4×D43—42no—
199C2×C4×D43—42no—
200C2×C4×D43C22×C412yes—
201C2×C4×D43#4112yes—
202C2×Dic86—24no—
203C2×Dic86—24no—
204C2×Dic86—21no—
205C2×Dic86—21no—
206C2×Dic86—21no—
207C2×Dic86—24no—
208C2×Dic86C22×C412yes—
209C2×Dic86C2×D412yes—
210C2×Dic86#4112yes—
211Q16×C43—28no—
212C2×C8×C43—21no—
213C2×C8×C43—21no—
214C2×C8×C43—21no—
215C2×C8×C43—21no—
216C2×C8×C43—21no—
217C2×C8×C43C22×C412yes—
218C4⋊C4×C43—24no—
219C4⋊C4×C43—21no—
220C4⋊C4×C43—21no—
221C4⋊C4×C43—21no—
222C4⋊C4×C43—42no—
223C4⋊C4×C43C2×D412yes—
224C42×C43—24no—
225C42×C43—42no—
226C42×C43C2×D412yes—
227C42×C43C2×D412yes—
228#10621885—28no—
229(C2×D43)⋊C4—24no—
230(C2×D43)⋊C4—42no—
231C4⋊Dic43—24no—
232C4⋊Dic43—21no—
233C4⋊Dic43—21no—
234C4⋊Dic43—21no—
235C4⋊Dic43—21no—
236C4⋊Dic43C22×C412yes—
237C4⋊Dic43C2×D412yes—
238Dic43⋊C4—24no—
239Dic43⋊C4—24no—
240Dic43⋊C4—24no—
241Dic43⋊C4—24no—
242Dic43⋊C4—42no—
243C4×Dic43—24no—
244C4×Dic43—24no—
245C4×Dic43—24no—
246C4×Dic43—22no—
247C4×Dic43—22no—
248C4×Dic43—21no—
249C4×Dic43—21no—
250C4×Dic43—42no—
251C2×C43⋊C8—21no—
252C2×C43⋊C8—21no—
253C2×C43⋊C8—21no—
254C2×C43⋊C8—21no—
255C2×C43⋊C8—21no—
256C2×C43⋊C8C22×C412yes—
257C23×C43C22×D411yescharacteristic
258C22×D43—21no—
259C22×D43—21no—
260C22×D43—21no—
261C22×D43—21no—
262C22×D43C4×D412yes—
263C22×D43#13712yes—
264C22×D43#13712yes—
265Q8×C43—22no—
266Q8×C43—22no—
267Q8×C43—22no—
268Q8×C43—22no—
269Q8×C43—22no—
270Q8×C43—41no—
271Q8×C43—41no—
272Q8×C43C4×D414yes—
273C2×C4×C43—22no—
274C2×C4×C43—22no—
275C2×C4×C43—22no—
276C2×C4×C43—21no—
277C2×C4×C43—21no—
278C2×C4×C43—21no—
279C2×C4×C43—21no—
280C2×C4×C43—22no—
281C2×C4×C43—22no—
282C2×C4×C43—41no—
283C2×C4×C43—41no—
284C2×C4×C43—41no—
285C2×C4×C43—41no—
286C2×C4×C43—41no—
287C2×C4×C43—41no—
288C2×C4×C43—41no—
289C2×C4×C43#12012yes—
290C2×C4×C43#12012yes—
291C2×C4×C43C23×C411yescharacteristic
292C2×C4×C43C22×D411yescharacteristic
293C2×C4×C43C22×D411yescharacteristic
294C2×C4×C43C2×#4111yescharacteristic
295C2×C4×C43C2×#4111yescharacteristic
296C2×C4×C43C2×#4111yescharacteristic
297C2×Dic43—22no—
298C2×Dic43—21no—
299C2×Dic43—21no—
300C2×Dic43—22no—
301C2×Dic43—21no—
302C2×Dic43—22no—
303C2×Dic43—21no—
304C2×Dic43—22no—
305C2×Dic43—21no—
306C2×Dic43—22no—
307C2×Dic43—21no—
308C2×Dic43—21no—
309C2×Dic43—41no—
310C2×Dic43—41no—
311C2×Dic43—41no—
312C2×Dic43—41no—
313C2×Dic43—41no—
314C2×Dic43—41no—
315C2×Dic43—41no—
316C2×Dic43C4×D412yes—
317C2×Dic43#13712yes—
318C4×D43—28no—
319C4×D43—216no—
320C4×D43—22no—
321C4×D43—22no—
322C4×D43—22no—
323C4×D43—22no—
324C4×D43—44no—
325C4×D43—48no—
326Dic86—216no—
327Dic86—22no—
328Dic86—22no—
329Dic86—22no—
330Dic86C4×D414yes—
331C8×C43—22no—
332C8×C43—41no—
333C43⋊C8—22no—
334C43⋊C8—41no—
335#21455—431nomaximal, Sylow
336C22×C43C2×C4×D411yescharacteristic
337C22×C43C2×#12011yescharacteristic
338C22×C43#52511yescharacteristic
339C22×C43C2×#13711yescharacteristic
340C22×C43C2×#13711yescharacteristic
341C22×C43C2×#13711yescharacteristic
342C22×C43#57511yescharacteristic
343C2×D43—22no—
344C2×D43—22no—
345C2×D43—22no—
346C2×D43—22no—
347C2×D43—22no—
348C2×D43—22no—
349C2×D43#44114yescomplemented
350C4×C43—22no—
351C4×C43—22no—
352C4×C43—24no—
353C4×C43—42no—
354C4×C43—42no—
355C4×C43—81no—
356C4×C43C2×C4×D411yescharacteristic
357C4×C43C2×C4×D411yescharacteristic
358C4×C43#52511yescharacteristic
359C4×C43#52511yescharacteristic
360Dic43—22no—
361Dic43—22no—
362Dic43—24no—
363Dic43—42no—
364Dic43—41no—
365Dic43—42no—
366Dic43—81no—
367C22×C4×Q8—431no—
368C2×#451—431no—
369C2×#441—431no—
370C2×#441D4311yescharacteristic, complemented
371C4×C22⋊Q8—431no—
372#1878—431no—
373#1878—431no—
374#1872—431no—
375#1865—431no—
376#1865—431no—
377#1853—431no—
378#1787—431no—
379#1763—431no—
380#1763—431no—
381#1749—431no—
382C2×C43C4×#12011yescharacteristic
383C2×C43C2×#44111yescharacteristic
384C2×C43C4×#13711yescharacteristic
385C2×C43#300411yescharacteristic
386C2×C43#300711yescharacteristic
387C2×C43#311311yescharacteristic
388C2×C43#311711yescharacteristic
389D43—24no—
390C23×Q8—431no—
391C22×Q16—431no—
392C22×Q16C2×D4311yescharacteristic
393C2×C22⋊Q8—431no—
394C2×C4×Q8—431no—
395C2×C4×Q8—431no—
396C2×C4×Q8—431no—
397C2×C4×Q8—861no—
398C2×C4×Q8—861no—
399C2×C4×Q8—864no—
400C2×C4×Q8—864no—
401C2×C4×Q8C2×D4311yescharacteristic
402C2×C4×Q8C2×D4311yescharacteristic
403C22×C4⋊C4—431no—
404C22×C4⋊C4—861no—
405C22×C42—431no—
406C22×C42—861no—
407#451—438no—
408#441—24no—
409#441—864no—
410C2×#106—431no—
411C2×#106C2×D4311yescharacteristic
412C2×#103—431no—
413C2×#103—431no—
414C2×#103—431no—
415C2×#103—431no—
416C2×#103—431no—
417C2×#103—431no—
418C2×#103C2×D4311yescharacteristic
419C2×#103C2×D4311yescharacteristic
420C2×C22⋊C8—431no—
421C2×C22⋊C8—431no—
422C2×#97—431no—
423C2×#97C2×D4311yescharacteristic
424#391—431no—
425#389—431no—
426#387—861no—
427#385—861no—
428#380—431no—
429C4×C4⋊C4—431no—
430C4×C4⋊C4—861no—
431C4×C22⋊C4—861no—
432#340—431no—
433#340—431no—
434#340—431no—
435#340—431no—
436#336—431no—
437#336—431no—
438C43#2145511yescharacteristic, complemented, Sylow
439C22×Q8—434no—
440C22×Q8—431no—
441C22×Q8—861no—
442C22×Q8—862no—
443C22×Q8—862no—
444C22×Q8—862no—
445C22×Q8—862no—
446C22×Q8—862no—
447C22×Q8C22×D4311yescharacteristic
448C22×Q8C22×D4311yescharacteristic
449C23×C4—431no—
450C23×C4—431no—
451C23×C4—431no—
452C23×C4—861no—
453C23×C4—861no—
454C2×Q16—22no—
455C2×Q16—22no—
456C2×Q16—434no—
457C2×Q16—862no—
458C2×Q16—862no—
459C2×Q16C4×D4314yescomplemented
460C22×C8—431no—
461C22×C8—431no—
462C22×C8C22×D4311yescharacteristic
463C22×C8C22×D4311yescharacteristic
464C22⋊Q8—434no—
465C22⋊Q8—862no—
466C4×Q8—22no—
467C4×Q8—22no—
468C4×Q8—22no—
469C4×Q8—434no—
470C4×Q8—868no—
471C4×Q8—862no—
472C4×Q8—868no—
473C4×Q8—862no—
474C4×Q8—862no—
475C4×Q8—862no—
476C4×Q8—862no—
477C4×Q8C22⋊D4314yes—
478C2×C4⋊C4—21no—
479C2×C4⋊C4—21no—
480C2×C4⋊C4—431no—
481C2×C4⋊C4—431no—
482C2×C4⋊C4—431no—
483C2×C4⋊C4—862no—
484C2×C4⋊C4—868no—
485C2×C4⋊C4—861no—
486C2×C4⋊C4—861no—
487C2×C4⋊C4—861no—
488C2×C4⋊C4—861no—
489C2×C4⋊C4—861no—
490C2×C4⋊C4—862no—
491C2×C4⋊C4—861no—
492C2×C4⋊C4C22×D4311yescharacteristic
493C2×C4⋊C4C22×D4311yescharacteristic
494C2×C22⋊C4—861no—
495C2×C22⋊C4—861no—
496C2×C42—21no—
497C2×C42—21no—
498C2×C42—431no—
499C2×C42—431no—
500C2×C42—431no—
501C2×C42—868no—
502C2×C42—861no—
503C2×C42—861no—
504C2×C42—861no—
505C2×C42—862no—
506C2×C42—862no—
507C2×C42—861no—
508C2×C42C22×D4311yescharacteristic
509#106—22no—
510#106—862no—
511#103—22no—
512#103—22no—
513#103—434no—
514#103—434no—
515#103—862no—
516#103—862no—
517#103—862no—
518#103—862no—
519C22⋊C8—434no—
520C22⋊C8—862no—
521#97—22no—
522#97—862no—
523#95—861no—
524#95—861no—
525#95—861no—
526#95—861no—
527#95—861no—
528C24—431no—
529C2×Q8—21no—
530C2×Q8—21no—
531C2×Q8—21no—
532C2×Q8—21no—
533C2×Q8—21no—
534C2×Q8—21no—
535C2×Q8—21no—
536C2×Q8—21no—
537C2×Q8—432no—
538C2×Q8—432no—
539C2×Q8—432no—
540C2×Q8—864no—
541C2×Q8—864no—
542C2×Q8—864no—
543C2×Q8—868no—
544C2×Q8—868no—
545C2×Q8—868no—
546C2×Q8—868no—
547C2×Q8—861no—
548C2×Q8—861no—
549C2×Q8—861no—
550C2×Q8C2×C4×D4312yes—
551C2×Q8C2×C4×D4312yes—
552C2×Q8#1062189812yes—
553C2×Q8C2×C22⋊D4312yes—
554C22×C4—21no—
555C22×C4—21no—
556C22×C4—21no—
557C22×C4—21no—
558C22×C4—431no—
559C22×C4—431no—
560C22×C4—432no—
561C22×C4—432no—
562C22×C4—431no—
563C22×C4—862no—
564C22×C4—862no—
565C22×C4—864no—
566C22×C4—864no—
567C22×C4—864no—
568C22×C4—862no—
569C22×C4—864no—
570C22×C4—861no—
571C22×C4—862no—
572C22×C4—861no—
573C22×C4—861no—
574C22×C4—861no—
575C22×C4—861no—
576C22×C4—861no—
577C22×C4—861no—
578C22×C4—862no—
579C22×C4—861no—
580C22×C4—1721no—
581C22×C4—1722no—
582C22×C4—1722no—
583C22×C4D4×D4311yescharacteristic
584C22×C4D4×D4311yescharacteristic
585C22×C4C23×D4311yescharacteristic
586Q16—28no—
587Q16—868no—
588C2×C8—21no—
589C2×C8—21no—
590C2×C8—21no—
591C2×C8—21no—
592C2×C8—21no—
593C2×C8—432no—
594C2×C8—861no—
595C2×C8—861no—
596C2×C8—861no—
597C2×C8—861no—
598C2×C8—861no—
599C2×C8C2×C4×D4312yes—
600C4⋊C4—24no—
601C4⋊C4—21no—
602C4⋊C4—21no—
603C4⋊C4—21no—
604C4⋊C4—42no—
605C4⋊C4—432no—
606C4⋊C4—432no—
607C4⋊C4—864no—
608C4⋊C4—864no—
609C4⋊C4—864no—
610C4⋊C4—864no—
611C4⋊C4—864no—
612C4⋊C4—861no—
613C4⋊C4—861no—
614C4⋊C4—861no—
615C4⋊C4—861no—
616C4⋊C4—1722no—
617C4⋊C4C2×C22⋊D4312yes—
618C22⋊C4—864no—
619C22⋊C4—1722no—
620C42—24no—
621C42—42no—
622C42—864no—
623C42—864no—
624C42—862no—
625C42—862no—
626C42—864no—
627C42—861no—
628C42—861no—
629C42—1722no—
630C42D4×D4312yes—
631C42C2×C22⋊D4312yes—
632C23—432no—
633C23—432no—
634C23—432no—
635C23—861no—
636C23—861no—
637C23—861no—
638C23—861no—
639C23C2×D4×D4311yescharacteristic
640Q8—22no—
641Q8—22no—
642Q8—22no—
643Q8—22no—
644Q8—22no—
645Q8—41no—
646Q8—41no—
647Q8—434no—
648Q8—8616no—
649Q8—862no—
650Q8—862no—
651Q8—862no—
652Q8C4×C22⋊D4314yes—
653C2×C4—22no—
654C2×C4—22no—
655C2×C4—22no—
656C2×C4—21no—
657C2×C4—21no—
658C2×C4—21no—
659C2×C4—21no—
660C2×C4—22no—
661C2×C4—22no—
662C2×C4—41no—
663C2×C4—41no—
664C2×C4—41no—
665C2×C4—41no—
666C2×C4—41no—
667C2×C4—41no—
668C2×C4—41no—
669C2×C4—432no—
670C2×C4—432no—
671C2×C4—8616no—
672C2×C4—868no—
673C2×C4—862no—
674C2×C4—861no—
675C2×C4—861no—
676C2×C4—862no—
677C2×C4—861no—
678C2×C4—862no—
679C2×C4—861no—
680C2×C4—862no—
681C2×C4—862no—
682C2×C4—862no—
683C2×C4—862no—
684C2×C4—862no—
685C2×C4—862no—
686C2×C4—861no—
687C2×C4—861no—
688C2×C4—861no—
689C2×C4—1724no—
690C2×C4—1728no—
691C2×C4—1721no—
692C2×C4—1721no—
693C2×C4—1721no—
694C2×C4—1721no—
695C2×C4—1721no—
696C2×C4—1721no—
697C2×C4—1721no—
698C2×C4#1306329312yes—
699C2×C4#1306329312yes—
700C2×C4C22×C4×D4311yescharacteristic
701C2×C4C2×D4×D4311yescharacteristic
702C2×C4C22×C22⋊D4311yescharacteristic
703C2×C4#41×D4311yescharacteristic
704C2×C4#41×D4311yescharacteristic
705C2×C4C2×#1062189811yescharacteristic
706C8—22no—
707C8—41no—
708C8—862no—
709C8—1721no—
710C22—434no—
711C22—862no—
712C22—862no—
713C22—862no—
714C22—862no—
715C22—862no—
716C22—862no—
717C22C4×D4×D4311yescharacteristic
718C22C2×#1306329311yescharacteristic
719C22#1458340811yescharacteristic
720C22#137×D4311yescharacteristic
721C22#137×D4311yescharacteristic
722C22#137×D4311yescharacteristic
723C22#1458369811yescharacteristic
724C4—24no—
725C4—22no—
726C4—22no—
727C4—42no—
728C4—42no—
729C4—81no—
730C4—862no—
731C4—864no—
732C4—862no—
733C4—3441no—
734C4—1721no—
735C4—1722no—
736C4—1722no—
737C4C4×D4×D4311yescharacteristic
738C4C2×C4×C22⋊D4311yescharacteristic
739C4#1458340611yescharacteristic
740C4#1458340811yescharacteristic
741C2—864no—
742C2C4×#1306329311yescharacteristic
743C2#441×D4311yescharacteristic
744C2#1914341111yescharacteristic
745C2#1914382711yescharacteristic
746C2#1914385111yescharacteristic
747C2#1914472311yescharacteristic
748C2#1914477011yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC2×C43×#441C2
socleC23×C43C22×D4
prime radicalC23×D43C2×D4
cosocleC22×C4×C43C24
hypercenterC2×#441D43
hypocenterC43#21455
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#441

Complements

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

NH ≅ G/Ntype
3. C2×#14583004C2semidirect
5. #19134938C2semidirect
6. #19134933C2semidirect
8. #19134861C2semidirect
9. #19134860C2semidirect
12. #19134426C2semidirect
13. #19134425C2semidirect
15. C2×C43×#441C2semidirect
30. #14583053C4semidirect
79. C2×#10621885C2×C4semidirect
118. #13063250C2×C4semidirect
121. #13063249C2×C4semidirect
135. C2×Q16×C43C2×C4semidirect
349. C2×D43#441semidirect
370. C2×#441D43semidirect
438. C43#21455semidirect
459. C2×Q16C4×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×#145830532
C2×#145830042
C4×#130633012
#191349382
#191349332
#191348992
#191348612
#191348602
#191347862
#191345282
#191344262
#191344252
#191343582
C2×C43×#4412
#2145543