Finite Group Databasebeta

← #25117233

Subgroups — #25117233

Order 11008.

1106 conjugacy classes of subgroups.

The subgroup lattice has 738 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×Q16×Dic43C211yesmaximal, characteristic, complemented
2C2×#14582900C211yesmaximal, characteristic
3#19137604C211yesmaximal, characteristic, complemented
4#19137436C211yesmaximal, characteristic
5#19135478C211yesmaximal, characteristic, complemented
6#19135280C211yesmaximal, characteristic, complemented
7#19135217C211yesmaximal, characteristic, complemented
8#19135029C211yesmaximal, characteristic, complemented
9#19134952C211yesmaximal, characteristic, complemented
10#19134938C211yesmaximal, characteristic, complemented
11#19134851C211yesmaximal, characteristic, complemented
12#19134785C211yesmaximal, characteristic, complemented
13#19134427C211yesmaximal, characteristic, complemented
14#19134381C211yesmaximal, characteristic, complemented
15C2×C43×#452C211yesmaximal, characteristic
16C22×#10621877C2211yescharacteristic
17C2×Q8×Dic43C2211yescharacteristic
18C2×Q8×Dic43C2211yescharacteristic
19C2×Q8×Dic43C2211yescharacteristic
20C22×C4⋊Dic43C2211yescharacteristic
21Q16×Dic43—24no—
22C2×#13063259C2211yescharacteristic
23C2×#13063259C2211yescharacteristic
24#14582900—24no—
25C2×#13063249C2211yescharacteristic
26C2×#13063249C2211yescharacteristic
27C2×#13063249C2211yescharacteristic
28C2×#13063249C2211yescharacteristic
29C2×#13063246C2211yescharacteristic
30C2×#13063246C2211yescharacteristic
31C2×#13063235C2211yescharacteristic
32C2×C8×Dic43C2211yescharacteristic
33#14582806C2211yescharacteristic
34#14582802—21no—
35#14582802—21no—
36#14582802C2211yescharacteristic
37#14582802C2211yescharacteristic
38#14582798—21no—
39#14582798C2211yescharacteristic
40#14582785—21no—
41#14582774—21no—
42#14582759—21no—
43#14582759C2211yescharacteristic
44C4⋊C4×Dic43C2211yescharacteristic
45C22⋊C4×Dic43—21no—
46C4×C22⋊Dic43—21no—
47C4×C22⋊Dic43C2211yescharacteristic
48#14582662C2211yescharacteristic
49#14582662C2211yescharacteristic
50#14582661C2211yescharacteristic
51#14582661C2211yescharacteristic
52#14582653C2211yescharacteristic
53#14582653C2211yescharacteristic
54C22×#41×C43C2211yescharacteristic
55C22×Q16×C43C2211yescharacteristic
56C22×SD16×C43C2211yescharacteristic
57C2×C22⋊Q8×C43C2211yescharacteristic
58C43×#452C418yescomplemented
59C2×#103×C43C2211yescharacteristic
60C2×#102×C43C2211yescharacteristic
61C2×C22⋊C8×C43C2211yescharacteristic
62C23×Dic43—21no—
63C2×#10621877—22no—
64C2×#10621877—22no—
65C2×#10621877—41no—
66C22×C43⋊C8C2311yescharacteristic
67C22×C43⋊C8C2311yescharacteristic
68Q8×Dic43—22no—
69Q8×Dic43—22no—
70Q8×Dic43—22no—
71Q8×Dic43—41no—
72Q8×Dic43—41no—
73Q8×Dic43—41no—
74C2×C4⋊Dic43—22no—
75C2×C4⋊Dic43—21no—
76C2×C4⋊Dic43—21no—
77C2×C4⋊Dic43—21no—
78C2×C4⋊Dic43—21no—
79C2×C4⋊Dic43—21no—
80C2×C4⋊Dic43—41no—
81C2×C4⋊Dic43C2311yescharacteristic
82C2×C4⋊Dic43C2311yescharacteristic
83C2×C4⋊Dic43C2311yescharacteristic
84C2×C4⋊Dic43C2311yescharacteristic
85C2×C22⋊Dic43—21no—
86C2×C22⋊Dic43—21no—
87C2×C22⋊Dic43—21no—
88C2×C22⋊Dic43—21no—
89C2×C22⋊Dic43—21no—
90C2×C22⋊Dic43D411yescharacteristic
91C2×C22⋊Dic43D411yescharacteristic
92C2×C4×Dic43—21no—
93C2×C4×Dic43—21no—
94C2×C4×Dic43—21no—
95C2×C4×Dic43—21no—
96C2×C4×Dic43C2311yescharacteristic
97C2×C4×Dic43C2311yescharacteristic
98#13063259—22no—
99#13063259—41no—
100#13063249—22no—
101#13063249—22no—
102#13063249—41no—
103#13063249D414yes—
104#13063246—22no—
105#13063246—22no—
106#13063235—41no—
107C8×Dic43—22no—
108C43⋊#95—21no—
109C43⋊#95—21no—
110C43⋊#95—21no—
111C43⋊#95—21no—
112C43⋊#95—21no—
113C43⋊#95D411yescharacteristic
114C43⋊#95D411yescharacteristic
115C2×#41×C43—22no—
116C2×#41×C43—22no—
117C2×#41×C43—22no—
118C2×#41×C43—41no—
119C2×#41×C43—41no—
120C2×#41×C43C2×C414yes—
121C22×Q8×C43C2311yescharacteristic
122C22×Q8×C43C2311yescharacteristic
123C22×D4×C43—21no—
124C22×D4×C43C2311yescharacteristic
125C23×C4×C43—21no—
126C23×C4×C43C2311yescharacteristic
127C2×Q16×C43—22no—
128C2×Q16×C43—22no—
129C2×Q16×C43C2×C414yescomplemented
130C2×SD16×C43—41no—
131C2×SD16×C43—41no—
132C2×SD16×C43C2×C414yescomplemented
133C22×C8×C43C2311yescharacteristic
134C22×C8×C43C2311yescharacteristic
135C22⋊Q8×C43—22no—
136C22⋊Q8×C43C2×C414yes—
137C2×C4⋊C4×C43—21no—
138C2×C4⋊C4×C43C2311yescharacteristic
139C2×C22⋊C4×C43—21no—
140#103×C43C2×C414yescomplemented
141#102×C43C2×C414yescomplemented
142C22⋊C8×C43C2×C414yes—
143C24×C43—21no—
144C24×C43C2×D411yescharacteristic
145#41×C43—28no—
146#41×C43—44no—
147#41×C43—44no—
148#41×C43—44no—
149C2×Q8×C43—21no—
150C2×Q8×C43—21no—
151C2×Q8×C43—21no—
152C2×Q8×C43—21no—
153C2×Q8×C43—21no—
154C2×Q8×C43—21no—
155C2×Q8×C43—21no—
156C2×Q8×C43—21no—
157C2×Q8×C43C22×C412yes—
158C2×Q8×C43C22×C412yes—
159C2×Q8×C43C2×D412yes—
160C2×Q8×C43#4112yes—
161C2×D4×C43—21no—
162C2×D4×C43—24no—
163C2×D4×C43—21no—
164C2×D4×C43—21no—
165C2×D4×C43—21no—
166C2×D4×C43—21no—
167C2×D4×C43—42no—
168C2×D4×C43—42no—
169C2×D4×C43C22×C412yes—
170C22×C4×C43—21no—
171C22×C4×C43—21no—
172C22×C4×C43—21no—
173C22×C4×C43—21no—
174C22×C4×C43—24no—
175C22×C4×C43—21no—
176C22×C4×C43—21no—
177C22×C4×C43—21no—
178C22×C4×C43—42no—
179C22×C4×C43—42no—
180C22×C4×C43C22×C412yes—
181C22×C4×C43C2×D411yescharacteristic
182C22×C4×C43#4112yes—
183C22×C4×C43C2411yescharacteristic
184C22×Dic43—21no—
185C22×Dic43—21no—
186C22×Dic43—21no—
187C22×Dic43—21no—
188C22×Dic43—42no—
189C22×Dic43—42no—
190C22×Dic43—81no—
191C22×Dic43C2×D411yescharacteristic
192C22×Dic43C2×D411yescharacteristic
193C22×Dic43C2×D411yescharacteristic
194C22×Dic43C2×D411yescharacteristic
195Q16×C43—28no—
196SD16×C43—44no—
197C2×C8×C43—21no—
198C2×C8×C43—21no—
199C2×C8×C43—21no—
200C2×C8×C43—21no—
201C2×C8×C43C22×C412yes—
202C2×C8×C43C22×C412yes—
203C4⋊C4×C43—24no—
204C4⋊C4×C43—21no—
205C4⋊C4×C43C22×C412yes—
206C22⋊C4×C43—24no—
207C22⋊Dic43—22no—
208C22⋊Dic43—41no—
209C22⋊Dic43—42no—
210C22⋊Dic43—42no—
211C22⋊Dic43—81no—
212C22⋊Dic43—81no—
213C22⋊Dic43—81no—
214C4⋊Dic43—21no—
215C4⋊Dic43—21no—
216C4⋊Dic43—21no—
217C4⋊Dic43—21no—
218C4⋊Dic43—21no—
219C4⋊Dic43—21no—
220C4⋊Dic43—21no—
221C4⋊Dic43—42no—
222C4⋊Dic43—42no—
223C4⋊Dic43—42no—
224C4⋊Dic43—42no—
225C4⋊Dic43—81no—
226C4⋊Dic43C2×D412yes—
227C4×Dic43—21no—
228C4×Dic43—21no—
229C4×Dic43—21no—
230C4×Dic43—21no—
231C4×Dic43—42no—
232C4×Dic43—42no—
233C4×Dic43—42no—
234C4×Dic43—81no—
235#10621877—44no—
236C2×C43⋊C8—21no—
237C2×C43⋊C8—21no—
238C2×C43⋊C8—21no—
239C2×C43⋊C8—21no—
240C2×C43⋊C8—21no—
241C2×C43⋊C8C2×D412yes—
242C23×C43—21no—
243C23×C43—21no—
244C23×C43—21no—
245C23×C43—21no—
246C23×C43—21no—
247C23×C43—21no—
248C23×C43—22no—
249C23×C43—41no—
250C23×C43—41no—
251C23×C43—41no—
252C23×C43—41no—
253C23×C43—41no—
254C23×C43—41no—
255C23×C43C4×D412yes—
256C23×C43C22×D411yescharacteristic
257Q8×C43—22no—
258Q8×C43—22no—
259Q8×C43—22no—
260Q8×C43—22no—
261Q8×C43—22no—
262Q8×C43—41no—
263Q8×C43—41no—
264Q8×C43C4×D414yes—
265D4×C43—22no—
266D4×C43—22no—
267D4×C43—48no—
268D4×C43—41no—
269D4×C43—41no—
270C2×C4×C43—22no—
271C2×C4×C43—22no—
272C2×C4×C43—21no—
273C2×C4×C43—22no—
274C2×C4×C43—21no—
275C2×C4×C43—22no—
276C2×C4×C43—22no—
277C2×C4×C43—22no—
278C2×C4×C43—22no—
279C2×C4×C43—22no—
280C2×C4×C43—22no—
281C2×C4×C43—48no—
282C2×C4×C43—41no—
283C2×C4×C43—41no—
284C2×C4×C43—41no—
285C2×C4×C43—41no—
286C2×C4×C43C4×D412yes—
287C2×C4×C43C23×C411yescharacteristic
288C2×C4×C43C22×D411yescharacteristic
289C2×C4×C43C2×#4111yescharacteristic
290C2×C4×C43C2×#4111yescharacteristic
291C2×C4×C43H(5,𝔽2)11yescharacteristic
292C2×C4×C43H(5,𝔽2)11yescharacteristic
293C2×Dic43—21no—
294C2×Dic43—21no—
295C2×Dic43—21no—
296C2×Dic43—22no—
297C2×Dic43—21no—
298C2×Dic43—21no—
299C2×Dic43—21no—
300C2×Dic43—21no—
301C2×Dic43—21no—
302C2×Dic43—21no—
303C2×Dic43—21no—
304C2×Dic43—21no—
305C2×Dic43—41no—
306C2×Dic43—41no—
307C2×Dic43—41no—
308C2×Dic43—41no—
309C2×Dic43—41no—
310C2×Dic43—41no—
311C2×Dic43—41no—
312C2×Dic43—41no—
313C2×Dic43—41no—
314C2×Dic43—41no—
315C2×Dic43—41no—
316C2×Dic43—84no—
317C2×Dic43#13712yes—
318C8×C43—22no—
319C8×C43—22no—
320C43⋊C8—22no—
321C43⋊C8—41no—
322#22879—431nomaximal, Sylow
323C22×C43—22no—
324C22×C43—22no—
325C22×C43—22no—
326C22×C43—41no—
327C22×C43—41no—
328C22×C43—41no—
329C22×C43—41no—
330C22×C43—42no—
331C22×C43—42no—
332C22×C43—42no—
333C22×C43—81no—
334C22×C43—81no—
335C22×C43—81no—
336C22×C43—81no—
337C22×C43C2×C4×D411yescharacteristic
338C22×C43D4211yescharacteristic
339C22×C43#54611yescharacteristic
340C22×C43C2×#13711yescharacteristic
341C22×C43#57511yescharacteristic
342C22×C43#57611yescharacteristic
343C22×C43#57811yescharacteristic
344C4×C43—22no—
345C4×C43—24no—
346C4×C43—42no—
347C4×C43—42no—
348C4×C43C2×C4×D411yescharacteristic
349C4×C43#51811yescharacteristic
350C4×C43#54611yescharacteristic
351C4×C43#55111yescharacteristic
352Dic43—22no—
353Dic43—41no—
354Dic43—41no—
355Dic43—42no—
356Dic43—41no—
357Dic43—81no—
358Dic43—81no—
359Dic43—81no—
360C2×#452D4311yescharacteristic
361C2×C4×Q16—431no—
362C2×#417—431no—
363#2360—431no—
364#2341—431no—
365#1973—431no—
366#1934—431no—
367#1925—431no—
368#1894—431no—
369#1880—431no—
370#1878—431no—
371#1863—431no—
372#1852—431no—
373#1763—431no—
374#1753—431no—
375C2×C43—42no—
376C2×C43—82no—
377C2×C43#235811yescharacteristic
378C2×C43C4×#13711yescharacteristic
379C2×C43#295111yescharacteristic
380C2×C43#326811yescharacteristic
381C2×C43#327011yescharacteristic
382C2×C43#332711yescharacteristic
383C2×C43#333311yescharacteristic
384C22×#41C2×D4311yescharacteristic
385C22×Q16C2×D4311yescharacteristic
386C22×SD16C2×D4311yescharacteristic
387C22×M16—431no—
388C2×C22⋊Q8C2×D4311yescharacteristic
389C2×C4×Q8—431no—
390C2×C4×Q8—431no—
391C2×C4×Q8—431no—
392C22×C4⋊C4—431no—
393#452Dic4318yescomplemented
394C4×Q16—864no—
395C2×#107—431no—
396C2×#107—431no—
397#417—864no—
398C2×#103—431no—
399C2×#103—431no—
400C2×#103—431no—
401C2×#103—431no—
402C2×#103C2×D4311yescharacteristic
403C2×#102—431no—
404C2×#102—431no—
405C2×#102C2×D4311yescharacteristic
406C2×C22⋊C8C2×D4311yescharacteristic
407C2×#97—431no—
408C2×C4×C8—431no—
409#391—431no—
410#390—431no—
411#390—431no—
412#390—861no—
413#390—861no—
414#389—431no—
415#389—861no—
416#387—861no—
417#385—861no—
418#380—431no—
419#380—861no—
420C4×C4⋊C4—431no—
421C4×C22⋊C4—431no—
422C4×C22⋊C4—861no—
423C4×C22⋊C4—861no—
424#340—431no—
425#340—431no—
426#340—431no—
427#340—431no—
428#336—431no—
429#336—431no—
430C43#2287911yescharacteristic, complemented, Sylow
431C2×#41—22no—
432C2×#41—22no—
433C2×#41—22no—
434C2×#41—41no—
435C2×#41—41no—
436C2×#41C2×Dic4314yes—
437C22×Q8C22×D4311yescharacteristic
438C22×Q8C22×D4311yescharacteristic
439C22×D4—21no—
440C22×D4C22×D4311yescharacteristic
441C23×C4—21no—
442C23×C4—861no—
443C23×C4C22×D4311yescharacteristic
444C2×Q16—22no—
445C2×Q16—22no—
446C2×Q16C2×Dic4314yescomplemented
447C2×SD16—41no—
448C2×SD16—41no—
449C2×SD16C2×Dic4314yescomplemented
450C2×M16—862no—
451C2×M16—862no—
452C2×M16—1721no—
453C22×C8—431no—
454C22×C8—431no—
455C22×C8C22×D4311yescharacteristic
456C22×C8C22×D4311yescharacteristic
457C22⋊Q8—22no—
458C22⋊Q8C2×Dic4314yes—
459C4×Q8—862no—
460C4×Q8—862no—
461C4×Q8—862no—
462C4×Q8—1721no—
463C4×Q8—1721no—
464C4×Q8—1721no—
465C2×C4⋊C4—21no—
466C2×C4⋊C4—431no—
467C2×C4⋊C4—431no—
468C2×C4⋊C4—431no—
469C2×C4⋊C4—431no—
470C2×C4⋊C4—862no—
471C2×C4⋊C4—861no—
472C2×C4⋊C4—861no—
473C2×C4⋊C4—861no—
474C2×C4⋊C4—861no—
475C2×C4⋊C4—861no—
476C2×C4⋊C4—1721no—
477C2×C4⋊C4C22×D4311yescharacteristic
478C2×C22⋊C4—21no—
479C2×C22⋊C4—431no—
480C2×C22⋊C4—431no—
481C2×C22⋊C4—861no—
482C2×C22⋊C4—861no—
483C2×C22⋊C4—861no—
484C2×C22⋊C4—861no—
485C2×C22⋊C4—861no—
486C2×C42—431no—
487C2×C42—431no—
488C2×C42—861no—
489C2×C42—861no—
490C2×C42—861no—
491C2×C42—861no—
492#107—862no—
493#107—1721no—
494#103—434no—
495#103—862no—
496#103—862no—
497#103—1721no—
498#103C2×Dic4314yescomplemented
499#102—862no—
500#102—862no—
501#102C2×Dic4314yescomplemented
502C22⋊C8C2×Dic4314yes—
503#97—1721no—
504C4×C8—862no—
505#95—431no—
506#95—431no—
507#95—861no—
508#95—861no—
509#95—861no—
510#95—861no—
511#95—861no—
512C24—21no—
513C24D4×D4311yescharacteristic
514#41—28no—
515#41—44no—
516#41—44no—
517#41—44no—
518C2×Q8—21no—
519C2×Q8—21no—
520C2×Q8—21no—
521C2×Q8—21no—
522C2×Q8—21no—
523C2×Q8—21no—
524C2×Q8—21no—
525C2×Q8—21no—
526C2×Q8D4×D4312yes—
527C2×Q8#1062190012yes—
528C2×Q8C22×Dic4312yes—
529C2×Q8C22×Dic4312yes—
530C2×D4—24no—
531C2×D4—21no—
532C2×D4—21no—
533C2×D4—21no—
534C2×D4—21no—
535C2×D4—21no—
536C2×D4—42no—
537C2×D4—42no—
538C2×D4C22×Dic4312yes—
539C22×C4—21no—
540C22×C4—21no—
541C22×C4—21no—
542C22×C4—21no—
543C22×C4—21no—
544C22×C4—21no—
545C22×C4—21no—
546C22×C4—24no—
547C22×C4—42no—
548C22×C4—42no—
549C22×C4—431no—
550C22×C4—431no—
551C22×C4—431no—
552C22×C4—431no—
553C22×C4—861no—
554C22×C4—861no—
555C22×C4—861no—
556C22×C4—861no—
557C22×C4—3441no—
558C22×C4—1722no—
559C22×C4—1722no—
560C22×C4D4×D4311yescharacteristic
561C22×C4#1062190012yes—
562C22×C4C22×Dic4312yes—
563C22×C4C23×D4311yescharacteristic
564Q16—28no—
565SD16—44no—
566M16—1724no—
567C2×C8—21no—
568C2×C8—21no—
569C2×C8—21no—
570C2×C8—21no—
571C2×C8—432no—
572C2×C8—861no—
573C2×C8—861no—
574C2×C8—861no—
575C2×C8—861no—
576C2×C8—861no—
577C2×C8C22×Dic4312yes—
578C2×C8C22×Dic4312yes—
579C4⋊C4—24no—
580C4⋊C4—21no—
581C4⋊C4—432no—
582C4⋊C4—861no—
583C4⋊C4—861no—
584C4⋊C4—861no—
585C4⋊C4—861no—
586C4⋊C4—861no—
587C4⋊C4—861no—
588C4⋊C4—861no—
589C4⋊C4—3441no—
590C4⋊C4—1722no—
591C4⋊C4—1722no—
592C4⋊C4—1722no—
593C4⋊C4—1722no—
594C4⋊C4C22×Dic4312yes—
595C22⋊C4—24no—
596C22⋊C4—862no—
597C22⋊C4—3441no—
598C22⋊C4—3441no—
599C22⋊C4—3441no—
600C22⋊C4—1722no—
601C22⋊C4—1721no—
602C22⋊C4—1722no—
603C42—861no—
604C42—861no—
605C42—861no—
606C42—861no—
607C42—3441no—
608C42—1722no—
609C42—1722no—
610C42—1722no—
611C23—21no—
612C23—21no—
613C23—21no—
614C23—21no—
615C23—21no—
616C23—21no—
617C23—22no—
618C23—41no—
619C23—41no—
620C23—41no—
621C23—41no—
622C23—41no—
623C23—41no—
624C23D4×Dic4312yes—
625C23C2×D4×D4311yescharacteristic
626Q8—22no—
627Q8—22no—
628Q8—22no—
629Q8—22no—
630Q8—22no—
631Q8—41no—
632Q8—41no—
633Q8D4×Dic4314yes—
634D4—22no—
635D4—22no—
636D4—48no—
637D4—41no—
638D4—41no—
639C2×C4—22no—
640C2×C4—22no—
641C2×C4—21no—
642C2×C4—22no—
643C2×C4—21no—
644C2×C4—22no—
645C2×C4—22no—
646C2×C4—22no—
647C2×C4—22no—
648C2×C4—22no—
649C2×C4—22no—
650C2×C4—48no—
651C2×C4—41no—
652C2×C4—41no—
653C2×C4—41no—
654C2×C4—41no—
655C2×C4—432no—
656C2×C4—861no—
657C2×C4—861no—
658C2×C4—861no—
659C2×C4—861no—
660C2×C4—861no—
661C2×C4—861no—
662C2×C4—861no—
663C2×C4—861no—
664C2×C4—861no—
665C2×C4—862no—
666C2×C4—861no—
667C2×C4—861no—
668C2×C4—3444no—
669C2×C4—1721no—
670C2×C4—1721no—
671C2×C4—1721no—
672C2×C4—1721no—
673C2×C4—1721no—
674C2×C4—1721no—
675C2×C4—1721no—
676C2×C4—1721no—
677C2×C4—1721no—
678C2×C4—1721no—
679C2×C4—1721no—
680C2×C4D4×Dic4312yes—
681C2×C4C23×Dic4311yescharacteristic
682C2×C4C2×D4×D4311yescharacteristic
683C2×C4C2×#1062190011yescharacteristic
684C2×C4C2×#1062190011yescharacteristic
685C2×C4#1306337011yescharacteristic
686C2×C4#1306337011yescharacteristic
687C8—22no—
688C8—22no—
689C8—862no—
690C8—1721no—
691C22—22no—
692C22—22no—
693C22—22no—
694C22—41no—
695C22—41no—
696C22—41no—
697C22—41no—
698C22—42no—
699C22—42no—
700C22—42no—
701C22—81no—
702C22—81no—
703C22—81no—
704C22—81no—
705C22C2×D4×Dic4311yescharacteristic
706C22#1458353111yescharacteristic
707C22#1458353611yescharacteristic
708C22#137×D4311yescharacteristic
709C22#1458369811yescharacteristic
710C22#1458370111yescharacteristic
711C22#1458371311yescharacteristic
712C4—22no—
713C4—24no—
714C4—42no—
715C4—42no—
716C4—862no—
717C4—3441no—
718C4—3441no—
719C4—3441no—
720C4—1721no—
721C4—1721no—
722C4—1722no—
723C4—1721no—
724C4C2×D4×Dic4311yescharacteristic
725C4#1458337411yescharacteristic
726C4#1458353611yescharacteristic
727C4#1458358011yescharacteristic
728C2—42no—
729C2—82no—
730C2#1913757911yescharacteristic
731C2#137×Dic4311yescharacteristic
732C2#1914347111yescharacteristic
733C2#1914613811yescharacteristic
734C2#1914616311yescharacteristic
735C2#1914685611yescharacteristic
736C2#1914692611yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC2×C43×#452C2
socleC23×C43C22×D4
prime radicalC22×#41×C43C22
cosocleC22×C4×C43C24
hypercenterC2×#452D43
hypocenterC43#22879
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#452

Complements

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

NH ≅ G/Ntype
1. C2×Q16×Dic43C2semidirect
3. #19137604C2semidirect
5. #19135478C2semidirect
6. #19135280C2semidirect
7. #19135217C2semidirect
8. #19135029C2semidirect
9. #19134952C2semidirect
10. #19134938C2semidirect
11. #19134851C2semidirect
12. #19134785C2semidirect
13. #19134427C2semidirect
14. #19134381C2semidirect
58. C43×#452C4semidirect
129. C2×Q16×C43C2×C4semidirect
132. C2×SD16×C43C2×C4semidirect
140. #103×C43C2×C4semidirect
141. #102×C43C2×C4semidirect
393. #452Dic43semidirect
430. C43#22879semidirect
446. C2×Q16C2×Dic43semidirect
449. C2×SD16C2×Dic43semidirect
498. #103C2×Dic43semidirect
501. #102C2×Dic43semidirect

Maximal subgroups

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

subgroupindex
C2×Q16×Dic432
C2×#145829002
#191376042
#191374362
#191354782
#191352802
#191352172
#191350292
#191349522
#191349382
#191348512
#191347852
#191344272
#191343812
C2×C43×#4522
#2287943