Finite Group Databasebeta

← #25144159

Subgroups — #25144159

Order 11008.

1052 conjugacy classes of subgroups.

The subgroup lattice has 736 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583107C211yesmaximal, characteristic, complemented
2C2×#14583056C211yesmaximal, characteristic
3C2×#14583053C211yesmaximal, characteristic
4#19138188C211yesmaximal, characteristic
5Q8×(C2×D43)⋊C4C211yesmaximal, characteristic
6#19135985C211yesmaximal, characteristic, complemented
7#19135800C211yesmaximal, characteristic
8#19135797C211yesmaximal, characteristic
9#19135696C211yesmaximal, characteristic, complemented
10#19135456C211yesmaximal, characteristic, complemented
11#19135201C211yesmaximal, characteristic
12#19134936C211yesmaximal, characteristic, complemented
13#19134936C211yesmaximal, characteristic, complemented
14#19134851C211yesmaximal, characteristic, complemented
15C2×C4×Q16×C43C211yesmaximal, characteristic, complemented
16C22×Q8×D43C2211yescharacteristic
17C22×Dic172C2211yescharacteristic
18C22×#10621885C2211yescharacteristic
19C22×#10621885C2211yescharacteristic
20C2×#13063323C2211yescharacteristic
21C2×#13063305C2211yescharacteristic
22C2×#13063301C2211yescharacteristic
23C2×Q8×Dic43C2211yescharacteristic
24#14583107—24no—
25#14583056—24no—
26#14583053—24no—
27C2×#13063259C2211yescharacteristic
28C2×Dic43⋊C8C2211yescharacteristic
29C2×#13063250C2211yescharacteristic
30C2×#13063250C2211yescharacteristic
31C2×#13063249C2211yescharacteristic
32C2×#13063249C2211yescharacteristic
33C2×#13063248C2211yescharacteristic
34C2×#13063248C2211yescharacteristic
35C2×(C2×D43)⋊C8C2211yescharacteristic
36C2×(C2×D43)⋊C8C2211yescharacteristic
37#14582829—21no—
38#14582821—21no—
39#14582805—21no—
40#14582805C2211yescharacteristic
41#14582805C2211yescharacteristic
42#14582804—21no—
43#14582804C2211yescharacteristic
44#14582798C2211yescharacteristic
45#14582797—21no—
46#14582790—21no—
47#14582756—21no—
48#14582756C2211yescharacteristic
49C4×(C2×D43)⋊C4—21no—
50C4×(C2×D43)⋊C4C2211yescharacteristic
51#14582661C2211yescharacteristic
52#14582661C2211yescharacteristic
53#14582654C2211yescharacteristic
54#14582653C2211yescharacteristic
55C22×Q16×C43C2211yescharacteristic
56C2×C4×Q8×C43C2211yescharacteristic
57C2×C4×Q8×C43C2211yescharacteristic
58C4×Q16×C43—24no—
59C2×#107×C43C2211yescharacteristic
60C2×#103×C43C2211yescharacteristic
61C2×#103×C43C2211yescharacteristic
62C2×C4×C8×C43C2211yescharacteristic
63C22×Dic86—21no—
64C22×Dic86C2311yescharacteristic
65C22×Dic86C2311yescharacteristic
66C2×Q8×D43—22no—
67C2×Q8×D43—22no—
68C2×Q8×D43—22no—
69C2×Q8×D43—22no—
70C2×Q8×D43—41no—
71C2×Q8×D43—41no—
72C22×C4×D43—21no—
73C22×C4×D43C2311yescharacteristic
74C2×Dic172—22no—
75C2×Dic172—22no—
76C2×Dic172—41no—
77C2×#10621885—22no—
78C2×#10621885—22no—
79C2×#10621885—22no—
80C2×#10621885—22no—
81C2×#10621885—22no—
82C2×#10621885—41no—
83C22×C43⋊C8C2311yescharacteristic
84C22×C43⋊C8C2311yescharacteristic
85#13063323—22no—
86#13063323—41no—
87#13063305—22no—
88#13063305—41no—
89#13063301—22no—
90#13063301—41no—
91Q8×Dic43—22no—
92Q8×Dic43—41no—
93C2×C4⋊Dic43—21no—
94C2×C4⋊Dic43—21no—
95C2×C4⋊Dic43—21no—
96C2×C4⋊Dic43C2311yescharacteristic
97C2×C4⋊Dic43C2311yescharacteristic
98C2×Dic43⋊C4—21no—
99C2×Dic43⋊C4—21no—
100C2×Dic43⋊C4—21no—
101C2×(C2×D43)⋊C4—21no—
102C2×(C2×D43)⋊C4—21no—
103C2×(C2×D43)⋊C4—21no—
104C2×(C2×D43)⋊C4D411yescharacteristic
105C2×(C2×D43)⋊C4D411yescharacteristic
106C2×C4×Dic43—21no—
107C2×C4×Dic43C2311yescharacteristic
108#13063259—41no—
109Dic43⋊C8—22no—
110#13063250—22no—
111#13063250—22no—
112#13063249—22no—
113#13063249—22no—
114#13063248—22no—
115#13063248—41no—
116(C2×D43)⋊C8—22no—
117(C2×D43)⋊C8—22no—
118C43⋊#95—21no—
119C43⋊#95—21no—
120C43⋊#95—21no—
121C43⋊#95—21no—
122C43⋊#95—21no—
123C43⋊#95—21no—
124C43⋊#95—21no—
125C43⋊#95—21no—
126C43⋊#95D411yescharacteristic
127C43⋊#95D411yescharacteristic
128C22×Q8×C43C2311yescharacteristic
129C22×Q8×C43C2311yescharacteristic
130C2×Q16×C43—22no—
131C2×Q16×C43—22no—
132C2×Q16×C43D414yes—
133C22×C8×C43C2311yescharacteristic
134C22×C8×C43C2311yescharacteristic
135C4×Q8×C43—22no—
136C4×Q8×C43—22no—
137C4×Q8×C43—41no—
138C4×Q8×C43—41no—
139C2×C4⋊C4×C43—21no—
140C2×C4⋊C4×C43—21no—
141C2×C4⋊C4×C43C2311yescharacteristic
142C2×C4⋊C4×C43C2311yescharacteristic
143C2×C42×C43—21no—
144C2×C42×C43—21no—
145C2×C42×C43C2311yescharacteristic
146#107×C43—22no—
147#103×C43—22no—
148#103×C43D414yes—
149C4×C8×C43—22no—
150C23×D43C2×D411yescharacteristic
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×C43—21no—
158C2×Q8×C43—21no—
159C2×Q8×C43C2×D412yes—
160C2×Q8×C43C2×D412yes—
161C2×Q8×C43C2×D412yes—
162C2×Q8×C43#4112yes—
163C22×C4×C43—21no—
164C22×C4×C43—21no—
165C22×C4×C43—21no—
166C22×C4×C43—21no—
167C22×C4×C43C2×D411yescharacteristic
168C22×C4×C43C2×D411yescharacteristic
169C22×C4×C43C2411yescharacteristic
170C22×Dic43—21no—
171C22×Dic43—21no—
172C22×Dic43—21no—
173C22×Dic43—21no—
174C22×Dic43C2×D411yescharacteristic
175C22×Dic43C2×D411yescharacteristic
176C22×Dic43C2×D411yescharacteristic
177Q8×D43—44no—
178Q8×D43—44no—
179Q8×D43—44no—
180Q8×D43—44no—
181C2×C4×D43—24no—
182C2×C4×D43—21no—
183C2×C4×D43—21no—
184C2×C4×D43—21no—
185C2×C4×D43—21no—
186C2×C4×D43—21no—
187C2×C4×D43—21no—
188C2×C4×D43—42no—
189C2×C4×D43—42no—
190C2×Dic86—21no—
191C2×Dic86—21no—
192C2×Dic86—21no—
193C2×Dic86—21no—
194C2×Dic86—24no—
195C2×Dic86—21no—
196C2×Dic86—21no—
197C2×Dic86—21no—
198C2×Dic86—21no—
199C2×Dic86—21no—
200C2×Dic86—21no—
201C2×Dic86—21no—
202C2×Dic86—42no—
203C2×Dic86—42no—
204C2×Dic86#4112yes—
205Q16×C43—28no—
206C2×C8×C43—21no—
207C2×C8×C43—21no—
208C2×C8×C43—21no—
209C2×C8×C43—21no—
210C2×C8×C43C2×D412yes—
211C2×C8×C43C2×D412yes—
212C4⋊C4×C43—21no—
213C4⋊C4×C43—21no—
214C4⋊C4×C43—21no—
215C4⋊C4×C43—42no—
216C4⋊C4×C43—42no—
217C4⋊C4×C43C2×D412yes—
218C42×C43—21no—
219C42×C43—21no—
220C42×C43—42no—
221C42×C43—42no—
222#10621885—44no—
223#10621885—44no—
224(C2×D43)⋊C4—41no—
225(C2×D43)⋊C4—42no—
226(C2×D43)⋊C4—42no—
227(C2×D43)⋊C4—42no—
228(C2×D43)⋊C4Q1614yescomplemented
229C4⋊Dic43—21no—
230C4⋊Dic43—21no—
231C4⋊Dic43—21no—
232C4⋊Dic43—21no—
233C4⋊Dic43—42no—
234C4⋊Dic43—42no—
235C4⋊Dic43—42no—
236Dic43⋊C4—42no—
237Dic43⋊C4—42no—
238Dic43⋊C4—42no—
239C4×Dic43—21no—
240C4×Dic43—21no—
241C4×Dic43—42no—
242C2×C43⋊C8—21no—
243C2×C43⋊C8—21no—
244C2×C43⋊C8—21no—
245C2×C43⋊C8—21no—
246C2×C43⋊C8—21no—
247C2×C43⋊C8—21no—
248Dic172—44no—
249C23×C43C22×D411yescharacteristic
250C22×D43—21no—
251C22×D43—21no—
252C22×D43—21no—
253C22×D43—21no—
254C22×D43—21no—
255C22×D43—21no—
256C22×D43C2×Q1612yes—
257Q8×C43—22no—
258Q8×C43—22no—
259Q8×C43—22no—
260Q8×C43—22no—
261Q8×C43—22no—
262Q8×C43—41no—
263Q8×C43—41no—
264Q8×C43#12114yes—
265C2×C4×C43—22no—
266C2×C4×C43—22no—
267C2×C4×C43—21no—
268C2×C4×C43—22no—
269C2×C4×C43—21no—
270C2×C4×C43—22no—
271C2×C4×C43—22no—
272C2×C4×C43—21no—
273C2×C4×C43—21no—
274C2×C4×C43—21no—
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—41no—
282C2×C4×C43C2×Q1612yes—
283C2×C4×C43C22×D411yescharacteristic
284C2×C4×C43C22×D411yescharacteristic
285C2×C4×C43C2×#4111yescharacteristic
286C2×C4×C43C2×#4111yescharacteristic
287C2×C4×C43H(5,𝔽2)11yescharacteristic
288C2×C4×C43H(5,𝔽2)11yescharacteristic
289C2×Dic43—21no—
290C2×Dic43—21no—
291C2×Dic43—21no—
292C2×Dic43—22no—
293C2×Dic43—21no—
294C2×Dic43—21no—
295C2×Dic43—21no—
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×Dic43—41no—
306C2×Dic43—41no—
307C2×Dic43—41no—
308C2×Dic43—41no—
309C2×Dic43C2×Q1612yes—
310C4×D43—48no—
311C4×D43—41no—
312C4×D43—41no—
313C4×D43—41no—
314C4×D43—41no—
315Dic86—22no—
316Dic86—22no—
317Dic86—48no—
318Dic86—41no—
319Dic86—41no—
320Dic86—41no—
321Dic86—41no—
322Dic86—41no—
323Dic86—41no—
324C8×C43—22no—
325C8×C43—22no—
326C43⋊C8—41no—
327C43⋊C8—41no—
328#25161—431nomaximal, Sylow
329C22×C43#52511yescharacteristic
330C22×C43D4211yescharacteristic
331C22×C43D4211yescharacteristic
332C22×C43C22×Q1611yescharacteristic
333C22×C43#57511yescharacteristic
334C22×C43#57811yescharacteristic
335C22×C43#57811yescharacteristic
336C2×D43—22no—
337C2×D43—22no—
338C2×D43—22no—
339C2×D43—41no—
340C2×D43—41no—
341C2×D43—41no—
342C2×D43—41no—
343C4×C43—24no—
344C4×C43—22no—
345C4×C43—42no—
346C4×C43—41no—
347C4×C43—42no—
348C4×C43—81no—
349C4×C43C2×#12111yescharacteristic
350C4×C43#53811yescharacteristic
351C4×C43#54611yescharacteristic
352C4×C43#54611yescharacteristic
353Dic43—22no—
354Dic43—42no—
355Dic43—41no—
356Dic43—41no—
357Dic43—81no—
358Dic43—81no—
359Dic43—81no—
360C2×#462—431no—
361C2×#451—431no—
362C2×#451—431no—
363C2×C4×Q16D4311yescharacteristic, complemented
364#2429—431no—
365Q8×C22⋊C4—431no—
366#2068—431no—
367#2036—431no—
368#2036—431no—
369#2016—431no—
370#1969—431no—
371#1923—431no—
372#1878—431no—
373#1878—431no—
374#1863—431no—
375C2×C43#242411yescharacteristic
376C2×C43#310411yescharacteristic
377C2×C43#312711yescharacteristic
378C2×C43#326911yescharacteristic
379C2×C43#327711yescharacteristic
380C2×C43D4×Q1611yescharacteristic
381C2×C43D4×Q1611yescharacteristic
382D43—42no—
383C23×Q8—431no—
384C22×Q16—431no—
385C22×Q16—431no—
386C22×Q16—431no—
387C22×Q16C2×D4311yescharacteristic
388C2×C4⋊Q8—431no—
389C2×C22⋊Q8—431no—
390C2×C22⋊Q8—431no—
391C2×C4×Q8—431no—
392C2×C4×Q8C2×D4311yescharacteristic
393C2×C4×Q8C2×D4311yescharacteristic
394#462—864no—
395#451—864no—
396#451—864no—
397C4×Q16—24no—
398C2×#107—431no—
399C2×#107C2×D4311yescharacteristic
400C2×C4⋊C8—431no—
401C2×#103—431no—
402C2×#103—431no—
403C2×#103—431no—
404C2×#103—431no—
405C2×#103—431no—
406C2×#103—431no—
407C2×#103C2×D4311yescharacteristic
408C2×#103C2×D4311yescharacteristic
409C2×C22⋊C8—431no—
410C2×C22⋊C8—431no—
411C2×C4×C8C2×D4311yescharacteristic
412#398—861no—
413#396—861no—
414#391—431no—
415#391—431no—
416#391—431no—
417#391—861no—
418#391—861no—
419#389—431no—
420#389—861no—
421#388—861no—
422#380—431no—
423#380—861no—
424C4×C22⋊C4—431no—
425C4×C22⋊C4—861no—
426#340—431no—
427#340—431no—
428#336—431no—
429#336—431no—
430C43#2516111yescharacteristic, complemented, Sylow
431C22×Q8—431no—
432C22×Q8—431no—
433C22×Q8—861no—
434C22×Q8—862no—
435C22×Q8—862no—
436C22×Q8—862no—
437C22×Q8—862no—
438C22×Q8—1721no—
439C22×Q8—1721no—
440C22×Q8C22×D4311yescharacteristic
441C22×Q8C22×D4311yescharacteristic
442C23×C4—431no—
443C23×C4—861no—
444C2×Q16—22no—
445C2×Q16—22no—
446C2×Q16—862no—
447C2×Q16—862no—
448C2×Q16—862no—
449C2×Q16—862no—
450C2×Q16—862no—
451C2×Q16—862no—
452C2×Q16—862no—
453C2×Q16—1721no—
454C2×Q16—1721no—
455C2×Q16D17214yes—
456C22×C8—431no—
457C22×C8—431no—
458C22×C8C22×D4311yescharacteristic
459C22×C8C22×D4311yescharacteristic
460C4⋊Q8—862no—
461C4⋊Q8—1721no—
462C22⋊Q8—862no—
463C22⋊Q8—862no—
464C22⋊Q8—1721no—
465C22⋊Q8—1721no—
466C4×Q8—22no—
467C4×Q8—22no—
468C4×Q8—41no—
469C4×Q8—41no—
470C4×Q8—862no—
471C4×Q8—1721no—
472C2×C4⋊C4—21no—
473C2×C4⋊C4—21no—
474C2×C4⋊C4—431no—
475C2×C4⋊C4—431no—
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⋊C4C22×D4311yescharacteristic
483C2×C4⋊C4C22×D4311yescharacteristic
484C2×C22⋊C4—431no—
485C2×C22⋊C4—431no—
486C2×C22⋊C4—861no—
487C2×C22⋊C4—861no—
488C2×C22⋊C4—861no—
489C2×C42—21no—
490C2×C42—21no—
491C2×C42—431no—
492C2×C42—861no—
493C2×C42C22×D4311yescharacteristic
494#107—22no—
495#107—1721no—
496C4⋊C8—862no—
497#103—22no—
498#103—862no—
499#103—862no—
500#103—862no—
501#103—862no—
502#103—862no—
503#103—1721no—
504#103C22⋊D4314yes—
505C22⋊C8—862no—
506C22⋊C8—862no—
507C4×C8—22no—
508#95—431no—
509#95—431no—
510#95—861no—
511#95—861no—
512#95—861no—
513#95—861no—
514#95—861no—
515#95—861no—
516#95—861no—
517#95—861no—
518C24—431no—
519C2×Q8—21no—
520C2×Q8—21no—
521C2×Q8—21no—
522C2×Q8—21no—
523C2×Q8—21no—
524C2×Q8—21no—
525C2×Q8—21no—
526C2×Q8—21no—
527C2×Q8—432no—
528C2×Q8—864no—
529C2×Q8—861no—
530C2×Q8—861no—
531C2×Q8—861no—
532C2×Q8—861no—
533C2×Q8—861no—
534C2×Q8—861no—
535C2×Q8—861no—
536C2×Q8—861no—
537C2×Q8—861no—
538C2×Q8—861no—
539C2×Q8—861no—
540C2×Q8—1722no—
541C2×Q8—1722no—
542C2×Q8—1724no—
543C2×Q8—1724no—
544C2×Q8—1724no—
545C2×Q8—1724no—
546C2×Q8C2×D17212yes—
547C2×Q8C2×D17212yes—
548C2×Q8#1062189812yes—
549C2×Q8C2×C22⋊D4312yes—
550C22×C4—21no—
551C22×C4—21no—
552C22×C4—21no—
553C22×C4—21no—
554C22×C4—431no—
555C22×C4—431no—
556C22×C4—431no—
557C22×C4—864no—
558C22×C4—861no—
559C22×C4—861no—
560C22×C4—861no—
561C22×C4—861no—
562C22×C4—861no—
563C22×C4—861no—
564C22×C4—861no—
565C22×C4—861no—
566C22×C4—861no—
567C22×C4—861no—
568C22×C4—1722no—
569C22×C4—1722no—
570C22×C4D4×D4311yescharacteristic
571C22×C4D4×D4311yescharacteristic
572C22×C4C23×D4311yescharacteristic
573Q16—28no—
574Q16—1724no—
575Q16—1724no—
576Q16—1724no—
577C2×C8—21no—
578C2×C8—21no—
579C2×C8—21no—
580C2×C8—21no—
581C2×C8—861no—
582C2×C8—861no—
583C2×C8—861no—
584C2×C8—861no—
585C2×C8—861no—
586C2×C8—861no—
587C2×C8C2×D17212yes—
588C2×C8C2×C22⋊D4312yes—
589C4⋊C4—21no—
590C4⋊C4—21no—
591C4⋊C4—21no—
592C4⋊C4—42no—
593C4⋊C4—42no—
594C4⋊C4—861no—
595C4⋊C4—861no—
596C4⋊C4—861no—
597C4⋊C4—861no—
598C4⋊C4—1722no—
599C4⋊C4—1722no—
600C4⋊C4—1722no—
601C4⋊C4—1722no—
602C4⋊C4—1722no—
603C4⋊C4—1722no—
604C4⋊C4C2×C22⋊D4312yes—
605C22⋊C4—434no—
606C22⋊C4—1721no—
607C22⋊C4—1722no—
608C22⋊C4—1722no—
609C22⋊C4—1722no—
610C42—21no—
611C42—21no—
612C42—42no—
613C42—42no—
614C42—861no—
615C42—861no—
616C42—1722no—
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—862no—
633Q8—862no—
634Q8—1728no—
635Q8—1721no—
636Q8—1721no—
637Q8—1721no—
638Q8—1721no—
639Q8—1721no—
640Q8—1721no—
641Q8#1306329914yes—
642C2×C4—22no—
643C2×C4—21no—
644C2×C4—21no—
645C2×C4—22no—
646C2×C4—22no—
647C2×C4—21no—
648C2×C4—21no—
649C2×C4—21no—
650C2×C4—22no—
651C2×C4—22no—
652C2×C4—41no—
653C2×C4—41no—
654C2×C4—41no—
655C2×C4—41no—
656C2×C4—41no—
657C2×C4—41no—
658C2×C4—41no—
659C2×C4—432no—
660C2×C4—861no—
661C2×C4—861no—
662C2×C4—861no—
663C2×C4—862no—
664C2×C4—861no—
665C2×C4—861no—
666C2×C4—861no—
667C2×C4—861no—
668C2×C4—861no—
669C2×C4—1728no—
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×C4—1721no—
681C2×C4—1721no—
682C2×C4—1721no—
683C2×C4—1721no—
684C2×C4—1721no—
685C2×C4Q16×D4312yes—
686C2×C4C22×C22⋊D4311yescharacteristic
687C2×C4C22×D17211yescharacteristic
688C2×C4#41×D4311yescharacteristic
689C2×C4C2×#1062189811yescharacteristic
690C2×C4#1306337011yescharacteristic
691C2×C4#1306337111yescharacteristic
692C8—22no—
693C8—22no—
694C8—1721no—
695C8—1721no—
696C22—862no—
697C22—862no—
698C22—862no—
699C22—1721no—
700C22—1721no—
701C22—1721no—
702C22—1721no—
703C22#1458340811yescharacteristic
704C22D4×C22⋊D4311yescharacteristic
705C22D4×D17211yescharacteristic
706C22C2×Q16×D4311yescharacteristic
707C22#1458369611yescharacteristic
708C22#1458371211yescharacteristic
709C22#1458371311yescharacteristic
710C4—24no—
711C4—22no—
712C4—42no—
713C4—41no—
714C4—42no—
715C4—81no—
716C4—862no—
717C4—3441no—
718C4—3441no—
719C4—3441no—
720C4—1721no—
721C4—1721no—
722C4—1722no—
723C4C2×#1306329911yescharacteristic
724C4#1458348211yescharacteristic
725C4#1458353711yescharacteristic
726C4#1458354411yescharacteristic
727C2—1722no—
728C2#1913812511yescharacteristic
729C2#1914463211yescharacteristic
730C2#1914489211yescharacteristic
731C2#1914615011yescharacteristic
732C2#1914625111yescharacteristic
733C2Q16×C22⋊D4311yescharacteristic
734C2Q16×D17211yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC2×C4×Q16×C43C2
socleC23×C43C22×D4
prime radicalC23×D43C2×D4
hypercenterC2×C4×Q16D43
hypocenterC43#25161
LCSG ▷ C22×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
1. C2×#14583107C2semidirect
6. #19135985C2semidirect
9. #19135696C2semidirect
10. #19135456C2semidirect
12. #19134936C2semidirect
13. #19134936C2semidirect
14. #19134851C2semidirect
15. C2×C4×Q16×C43C2semidirect
228. (C2×D43)⋊C4Q16semidirect
363. C2×C4×Q16D43semidirect
430. C43#25161semidirect

Maximal subgroups

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

subgroupindex
C2×#145831072
C2×#145830562
C2×#145830532
#191381882
Q8×(C2×D43)⋊C42
#191359852
#191358002
#191357972
#191356962
#191354562
#191352012
#191349362
#191348512
C2×C4×Q16×C432
#2516143