Finite Group Databasebeta

← #25102385

Subgroups — #25102385

Order 11008.

1344 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×#14583375C211yesmaximal, characteristic
2C2×#14583053C211yesmaximal, characteristic
3C2×#14583004C211yesmaximal, characteristic, complemented
4#19137271C211yesmaximal, characteristic
5#19134938C211yesmaximal, characteristic, complemented
6#19134933C211yesmaximal, characteristic, complemented
7#19134904C211yesmaximal, characteristic
8#19134861C211yesmaximal, characteristic, complemented
9#19134846C211yesmaximal, characteristic, complemented
10#19134791C211yesmaximal, characteristic
11#19134528C211yesmaximal, characteristic
12#19134425C211yesmaximal, characteristic, complemented
13C4×#13063250C211yesmaximal, characteristic, complemented
14#19134362C211yesmaximal, characteristic
15C2×C4×Q16×C43C211yesmaximal, characteristic, complemented
16C22×Q8×D43C2211yescharacteristic
17C22×#10621885C2211yescharacteristic
18C2×#13063301C2211yescharacteristic
19#14583375—24no—
20#14583375—24no—
21C2×Q8×Dic43C2211yescharacteristic
22C2×C4×Dic86—21no—
23C2×C4×Dic86C2211yescharacteristic
24C2×#13063290—21no—
25C2×#13063290C2211yescharacteristic
26C2×#13063283—21no—
27C2×#13063283C2211yescharacteristic
28C2×#13063282—21no—
29C2×#13063282C2211yescharacteristic
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#14582794—21no—
45#14582790—21no—
46#14582789—21no—
47#14582783—21no—
48#14582756C2211yescharacteristic
49C4×C4⋊Dic43C2211yescharacteristic
50#14582662C2211yescharacteristic
51#14582662C2211yescharacteristic
52#14582661C2211yescharacteristic
53#14582661C2211yescharacteristic
54#14582653C2211yescharacteristic
55#14582653C2211yescharacteristic
56C22×Q16×C43C2211yescharacteristic
57C2×C4×Q8×C43C2211yescharacteristic
58C2×C4×Q8×C43C2211yescharacteristic
59C4×Q16×C43—24no—
60C2×#107×C43C2211yescharacteristic
61C2×#103×C43C2211yescharacteristic
62C2×#103×C43C2211yescharacteristic
63C2×C4×C8×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×D43C2311yescharacteristic
74C2×#10621885—22no—
75C2×#10621885—22no—
76C2×#10621885C2×C414yes—
77C22×C43⋊C8C2311yescharacteristic
78C22×C43⋊C8C2311yescharacteristic
79#13063301—22no—
80#13063301C2×C414yes—
81Q8×Dic43—22no—
82Q8×Dic43—22no—
83C4×Dic86—28no—
84C4×Dic86—22no—
85C4×Dic86D414yes—
86#13063290—28no—
87#13063290—22no—
88#13063290—22no—
89#13063283—28no—
90#13063283—22no—
91#13063283—22no—
92#13063282—28no—
93#13063282—22no—
94#13063282—22no—
95C2×C4⋊Dic43—21no—
96C2×C4⋊Dic43C2311yescharacteristic
97C2×C4⋊Dic43C2311yescharacteristic
98C2×C4⋊Dic43C2311yescharacteristic
99C2×Dic43⋊C4—21no—
100C2×Dic43⋊C4—21no—
101C2×Dic43⋊C4—21no—
102C2×Dic43⋊C4—21no—
103C2×Dic43⋊C4D411yescharacteristic
104C2×Dic43⋊C4D411yescharacteristic
105C2×(C2×D43)⋊C4—21no—
106C2×(C2×D43)⋊C4—21no—
107C2×(C2×D43)⋊C4—21no—
108C2×(C2×D43)⋊C4D411yescharacteristic
109C2×(C2×D43)⋊C4D411yescharacteristic
110C2×C4×Dic43—21no—
111C2×C4×Dic43—21no—
112C2×C4×Dic43—21no—
113C2×C4×Dic43—21no—
114C2×C4×Dic43—21no—
115C2×C4×Dic43C2311yescharacteristic
116#13063256—22no—
117#13063250—22no—
118#13063250C2×C414yes—
119#13063249—22no—
120#13063249—22no—
121#13063249C2×C414yes—
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×C414yes—
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#107×C43—22no—
150#103×C43—22no—
151#103×C43—22no—
152C4×C8×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—21no—
187C2×C4×D43—21no—
188C2×C4×D43—21no—
189C2×C4×D43—21no—
190C2×C4×D43—24no—
191C2×C4×D43C22×C412yes—
192C2×C4×D43#4112yes—
193C2×Dic86—24no—
194C2×Dic86—24no—
195C2×Dic86—21no—
196C2×Dic86—21no—
197C2×Dic86—21no—
198C2×Dic86—24no—
199C2×Dic86C22×C412yes—
200C2×Dic86C2×D412yes—
201C2×Dic86#4112yes—
202Q16×C43—28no—
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—42no—
214C4⋊C4×C43C2×D412yes—
215C42×C43—24no—
216C42×C43—42no—
217C42×C43C2×D412yes—
218C42×C43C2×D412yes—
219#10621885—28no—
220(C2×D43)⋊C4—24no—
221(C2×D43)⋊C4—22no—
222(C2×D43)⋊C4—22no—
223(C2×D43)⋊C4—24no—
224(C2×D43)⋊C4—81no—
225C4⋊Dic43—24no—
226C4⋊Dic43—21no—
227C4⋊Dic43—21no—
228C4⋊Dic43—21no—
229C4⋊Dic43—21no—
230C4⋊Dic43C22×C412yes—
231C4⋊Dic43C2×D412yes—
232Dic43⋊C4—24no—
233Dic43⋊C4—24no—
234Dic43⋊C4—22no—
235Dic43⋊C4—22no—
236Dic43⋊C4—24no—
237Dic43⋊C4—81no—
238C4×Dic43—24no—
239C4×Dic43—24no—
240C4×Dic43—24no—
241C4×Dic43—24no—
242C4×Dic43—21no—
243C4×Dic43—21no—
244C4×Dic43—81no—
245C2×C43⋊C8—21no—
246C2×C43⋊C8—21no—
247C2×C43⋊C8—21no—
248C2×C43⋊C8—21no—
249C2×C43⋊C8—21no—
250C2×C43⋊C8C22×C412yes—
251C23×C43C22×D411yescharacteristic
252C22×D43—21no—
253C22×D43—21no—
254C22×D43—21no—
255C22×D43—21no—
256C22×D43—21no—
257C22×D43—21no—
258C22×D43C4×D412yes—
259Q8×C43—22no—
260Q8×C43—22no—
261Q8×C43—22no—
262Q8×C43—22no—
263Q8×C43—22no—
264Q8×C43—41no—
265Q8×C43—41no—
266Q8×C43C4×D414yes—
267C2×C4×C43—22no—
268C2×C4×C43—22no—
269C2×C4×C43—22no—
270C2×C4×C43—21no—
271C2×C4×C43—21no—
272C2×C4×C43—21no—
273C2×C4×C43—21no—
274C2×C4×C43—22no—
275C2×C4×C43—22no—
276C2×C4×C43—41no—
277C2×C4×C43—41no—
278C2×C4×C43—41no—
279C2×C4×C43—41no—
280C2×C4×C43—41no—
281C2×C4×C43—41no—
282C2×C4×C43—41no—
283C2×C4×C43#12012yes—
284C2×C4×C43#12012yes—
285C2×C4×C43C23×C411yescharacteristic
286C2×C4×C43C22×D411yescharacteristic
287C2×C4×C43C22×D411yescharacteristic
288C2×C4×C43C2×#4111yescharacteristic
289C2×C4×C43C2×#4111yescharacteristic
290C2×C4×C43C2×#4111yescharacteristic
291C2×Dic43—22no—
292C2×Dic43—21no—
293C2×Dic43—22no—
294C2×Dic43—21no—
295C2×Dic43—22no—
296C2×Dic43—22no—
297C2×Dic43—21no—
298C2×Dic43—21no—
299C2×Dic43—22no—
300C2×Dic43—21no—
301C2×Dic43—21no—
302C2×Dic43—21no—
303C2×Dic43—21no—
304C2×Dic43—41no—
305C2×Dic43—41no—
306C2×Dic43—41no—
307C2×Dic43—41no—
308C2×Dic43—41no—
309C2×Dic43—41no—
310C2×Dic43—41no—
311C2×Dic43C4×D412yes—
312C4×D43—216no—
313C4×D43—22no—
314C4×D43—22no—
315C4×D43—22no—
316C4×D43—22no—
317Dic86—216no—
318Dic86—22no—
319Dic86—22no—
320Dic86—22no—
321Dic86C4×D414yes—
322C8×C43—22no—
323C8×C43—41no—
324C43⋊C8—22no—
325C43⋊C8—41no—
326#21463—431nomaximal, Sylow
327C22×C43C2×C4×D411yescharacteristic
328C22×C43C2×#12011yescharacteristic
329C22×C43#52511yescharacteristic
330C22×C43#57711yescharacteristic
331C22×C43#57811yescharacteristic
332C22×C43#57811yescharacteristic
333C22×C43#57811yescharacteristic
334C2×D43—22no—
335C2×D43—22no—
336C2×D43—22no—
337C2×D43—41no—
338C2×D43—41no—
339C2×D43—41no—
340C2×D43—41no—
341C4×C43—22no—
342C4×C43—22no—
343C4×C43—24no—
344C4×C43—42no—
345C4×C43—42no—
346C4×C43—81no—
347C4×C43C2×C4×D411yescharacteristic
348C4×C43C2×C4×D411yescharacteristic
349C4×C43#52511yescharacteristic
350C4×C43#52511yescharacteristic
351Dic43—22no—
352Dic43—24no—
353Dic43—42no—
354Dic43—41no—
355Dic43—42no—
356Dic43—41no—
357Dic43—81no—
358C2×#519—431no—
359C2×#451—431no—
360C2×#441—431no—
361C2×C4×Q16D4311yescharacteristic, complemented
362#2323—431no—
363#1878—431no—
364#1878—431no—
365#1873—431no—
366#1865—431no—
367#1863—431no—
368#1854—431no—
369#1787—431no—
370#1763—431no—
371C4×#103—431no—
372#1750—431no—
373C2×C43C4×#12011yescharacteristic
374C2×C43#294711yescharacteristic
375C2×C43#295011yescharacteristic
376C2×C43#301111yescharacteristic
377C2×C43#301311yescharacteristic
378C2×C43#312111yescharacteristic
379C2×C43#312711yescharacteristic
380D43—42no—
381C23×Q8—431no—
382C22×Q16—431no—
383C22×Q16C2×D4311yescharacteristic
384C2×C22⋊Q8—431no—
385#519—864no—
386#519—864no—
387C2×C4×Q8—431no—
388C2×C4×Q8—431no—
389C2×C4×Q8—431no—
390C2×C4×Q8—861no—
391C2×C4×Q8—861no—
392C2×C4×Q8C2×D4311yescharacteristic
393C2×C4×Q8C2×D4311yescharacteristic
394C2×#117—431no—
395C2×#117—431no—
396C2×#117—861no—
397C2×#117—861no—
398#451—438no—
399#441—864no—
400C4×Q16—24no—
401C2×#107C2×D4311yescharacteristic
402C2×#106—431no—
403C2×#103—431no—
404C2×#103—431no—
405C2×#103—431no—
406C2×#103—431no—
407C2×#103—431no—
408C2×#103—431no—
409C2×#103C2×D4311yescharacteristic
410C2×#103C2×D4311yescharacteristic
411C2×C22⋊C8—431no—
412C2×C22⋊C8—431no—
413C2×#97—431no—
414C2×C4×C8C2×D4311yescharacteristic
415#391—431no—
416#389—431no—
417#389—861no—
418#388—861no—
419#388—861no—
420#387—861no—
421#380—431no—
422C4×C4⋊C4—431no—
423#340—431no—
424#340—431no—
425#340—431no—
426#340—431no—
427#336—431no—
428#336—431no—
429C43#2146311yescharacteristic, complemented, Sylow
430C22×Q8—434no—
431C22×Q8—431no—
432C22×Q8—861no—
433C22×Q8—862no—
434C22×Q8—862no—
435C22×Q8—862no—
436C22×Q8—862no—
437C22×Q8—862no—
438C22×Q8C22×D4311yescharacteristic
439C22×Q8C22×D4311yescharacteristic
440C23×C4—431no—
441C23×C4—861no—
442C2×Q16—22no—
443C2×Q16—22no—
444C2×Q16—434no—
445C2×Q16—862no—
446C2×Q16—862no—
447C2×Q16C4×D4314yes—
448C22×C8—431no—
449C22×C8—431no—
450C22×C8C22×D4311yescharacteristic
451C22×C8C22×D4311yescharacteristic
452C22⋊Q8—434no—
453C22⋊Q8—862no—
454C4×Q8—22no—
455C4×Q8—22no—
456C4×Q8—22no—
457C4×Q8—434no—
458C4×Q8—868no—
459C4×Q8—862no—
460C4×Q8—868no—
461C4×Q8—862no—
462C4×Q8—862no—
463C4×Q8—862no—
464C4×Q8—862no—
465C4×Q8C22⋊D4314yes—
466#117—868no—
467#117—862no—
468#117—868no—
469#117—862no—
470#117—862no—
471#117—862no—
472C2×C4⋊C4—21no—
473C2×C4⋊C4—21no—
474C2×C4⋊C4—431no—
475C2×C4⋊C4—431no—
476C2×C4⋊C4—431no—
477C2×C4⋊C4—431no—
478C2×C4⋊C4—431no—
479C2×C4⋊C4—861no—
480C2×C4⋊C4—861no—
481C2×C4⋊C4—861no—
482C2×C4⋊C4—861no—
483C2×C4⋊C4—861no—
484C2×C4⋊C4C22×D4311yescharacteristic
485C2×C4⋊C4C22×D4311yescharacteristic
486C2×C22⋊C4—431no—
487C2×C22⋊C4—431no—
488C2×C22⋊C4—861no—
489C2×C22⋊C4—861no—
490C2×C22⋊C4—861no—
491C2×C42—21no—
492C2×C42—21no—
493C2×C42—431no—
494C2×C42—861no—
495C2×C42—861no—
496C2×C42—861no—
497C2×C42—861no—
498C2×C42—861no—
499C2×C42C22×D4311yescharacteristic
500#107—22no—
501#106—862no—
502#103—22no—
503#103—22no—
504#103—434no—
505#103—434no—
506#103—862no—
507#103—862no—
508#103—862no—
509#103—862no—
510C22⋊C8—434no—
511C22⋊C8—862no—
512#97—862no—
513C4×C8—22no—
514#95—861no—
515#95—861no—
516#95—861no—
517#95—861no—
518#95—861no—
519C24—431no—
520C2×Q8—21no—
521C2×Q8—21no—
522C2×Q8—21no—
523C2×Q8—21no—
524C2×Q8—21no—
525C2×Q8—21no—
526C2×Q8—21no—
527C2×Q8—21no—
528C2×Q8—432no—
529C2×Q8—432no—
530C2×Q8—432no—
531C2×Q8—864no—
532C2×Q8—864no—
533C2×Q8—864no—
534C2×Q8—868no—
535C2×Q8—868no—
536C2×Q8—868no—
537C2×Q8—868no—
538C2×Q8—861no—
539C2×Q8—861no—
540C2×Q8—861no—
541C2×Q8C2×C4×D4312yes—
542C2×Q8C2×C4×D4312yes—
543C2×Q8#1062189812yes—
544C2×Q8C2×C22⋊D4312yes—
545C22×C4—21no—
546C22×C4—21no—
547C22×C4—21no—
548C22×C4—21no—
549C22×C4—431no—
550C22×C4—432no—
551C22×C4—432no—
552C22×C4—431no—
553C22×C4—431no—
554C22×C4—864no—
555C22×C4—864no—
556C22×C4—864no—
557C22×C4—861no—
558C22×C4—861no—
559C22×C4—861no—
560C22×C4—861no—
561C22×C4—861no—
562C22×C4—861no—
563C22×C4—861no—
564C22×C4—861no—
565C22×C4D4×D4311yescharacteristic
566C22×C4D4×D4311yescharacteristic
567C22×C4C23×D4311yescharacteristic
568Q16—28no—
569Q16—868no—
570C2×C8—21no—
571C2×C8—21no—
572C2×C8—21no—
573C2×C8—21no—
574C2×C8—21no—
575C2×C8—432no—
576C2×C8—861no—
577C2×C8—861no—
578C2×C8—861no—
579C2×C8—861no—
580C2×C8—861no—
581C2×C8C2×C4×D4312yes—
582C4⋊C4—24no—
583C4⋊C4—21no—
584C4⋊C4—21no—
585C4⋊C4—21no—
586C4⋊C4—42no—
587C4⋊C4—432no—
588C4⋊C4—432no—
589C4⋊C4—864no—
590C4⋊C4—864no—
591C4⋊C4—864no—
592C4⋊C4—862no—
593C4⋊C4—862no—
594C4⋊C4—864no—
595C4⋊C4—861no—
596C4⋊C4—861no—
597C4⋊C4—861no—
598C4⋊C4—861no—
599C4⋊C4—3441no—
600C4⋊C4C2×C22⋊D4312yes—
601C22⋊C4—864no—
602C22⋊C4—864no—
603C22⋊C4—862no—
604C22⋊C4—862no—
605C22⋊C4—3441no—
606C42—24no—
607C42—42no—
608C42—864no—
609C42—864no—
610C42—864no—
611C42—864no—
612C42—861no—
613C42—861no—
614C42—3441no—
615C42D4×D4312yes—
616C42C2×C22⋊D4312yes—
617C23—432no—
618C23—861no—
619C23—861no—
620C23—861no—
621C23—861no—
622C23—861no—
623C23—861no—
624C23C2×D4×D4311yescharacteristic
625Q8—22no—
626Q8—22no—
627Q8—22no—
628Q8—22no—
629Q8—22no—
630Q8—41no—
631Q8—41no—
632Q8—434no—
633Q8—8616no—
634Q8—862no—
635Q8—862no—
636Q8—862no—
637Q8C4×C22⋊D4314yes—
638C2×C4—22no—
639C2×C4—22no—
640C2×C4—22no—
641C2×C4—21no—
642C2×C4—21no—
643C2×C4—21no—
644C2×C4—21no—
645C2×C4—22no—
646C2×C4—22no—
647C2×C4—41no—
648C2×C4—41no—
649C2×C4—41no—
650C2×C4—41no—
651C2×C4—41no—
652C2×C4—41no—
653C2×C4—41no—
654C2×C4—432no—
655C2×C4—8616no—
656C2×C4—862no—
657C2×C4—861no—
658C2×C4—862no—
659C2×C4—861no—
660C2×C4—862no—
661C2×C4—862no—
662C2×C4—862no—
663C2×C4—862no—
664C2×C4—862no—
665C2×C4—862no—
666C2×C4—862no—
667C2×C4—861no—
668C2×C4—861no—
669C2×C4—861no—
670C2×C4—861no—
671C2×C4—861no—
672C2×C4—861no—
673C2×C4—1721no—
674C2×C4—1721no—
675C2×C4—1721no—
676C2×C4—1721no—
677C2×C4—1721no—
678C2×C4—1721no—
679C2×C4—1721no—
680C2×C4#1306329312yes—
681C2×C4#1306329312yes—
682C2×C4C22×C4×D4311yescharacteristic
683C2×C4C2×D4×D4311yescharacteristic
684C2×C4C22×C22⋊D4311yescharacteristic
685C2×C4#41×D4311yescharacteristic
686C2×C4#41×D4311yescharacteristic
687C2×C4C2×#1062189811yescharacteristic
688C8—22no—
689C8—41no—
690C8—862no—
691C8—1721no—
692C22—862no—
693C22—862no—
694C22—862no—
695C22—1721no—
696C22—1721no—
697C22—1721no—
698C22—1721no—
699C22C4×D4×D4311yescharacteristic
700C22C2×#1306329311yescharacteristic
701C22#1458340811yescharacteristic
702C22#1458370611yescharacteristic
703C22#1458371211yescharacteristic
704C22#1458371211yescharacteristic
705C22#1458371311yescharacteristic
706C4—24no—
707C4—22no—
708C4—22no—
709C4—42no—
710C4—42no—
711C4—81no—
712C4—862no—
713C4—864no—
714C4—3441no—
715C4—1722no—
716C4—1721no—
717C4—1722no—
718C4—1721no—
719C4C4×D4×D4311yescharacteristic
720C4C2×C4×C22⋊D4311yescharacteristic
721C4#1458340611yescharacteristic
722C4#1458340811yescharacteristic
723C2—1722no—
724C2C4×#1306329311yescharacteristic
725C2#1914343311yescharacteristic
726C2#1914345811yescharacteristic
727C2#1914388611yescharacteristic
728C2#1914390611yescharacteristic
729C2#1914483011yescharacteristic
730C2#1914489211yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC2×C4×Q16×C43C2
socleC23×C43C22×D4
prime radicalC23×D43C2×D4
cosocleC22×C4×C43C24
hypercenterC2×C4×Q16D43
hypocenterC43#21463
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×C4×Q16

Complements

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

NH ≅ G/Ntype
3. C2×#14583004C2semidirect
5. #19134938C2semidirect
6. #19134933C2semidirect
8. #19134861C2semidirect
9. #19134846C2semidirect
12. #19134425C2semidirect
13. C4×#13063250C2semidirect
15. C2×C4×Q16×C43C2semidirect
30. #14583053C4semidirect
361. C2×C4×Q16D43semidirect
429. C43#21463semidirect

Maximal subgroups

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

subgroupindex
C2×#145833752
C2×#145830532
C2×#145830042
#191372712
#191349382
#191349332
#191349042
#191348612
#191348462
#191347912
#191345282
#191344252
C4×#130632502
#191343622
C2×C4×Q16×C432
#2146343