Finite Group Databasebeta

← #25099056

Subgroups — #25099056

Order 11008.

1238 conjugacy classes of subgroups.

The subgroup lattice has 758 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14582936C211yesmaximal, characteristic, complemented
2C2×#14582902C211yesmaximal, characteristic
3C2×#102×D43C211yesmaximal, characteristic
4#19137174C211yesmaximal, characteristic
5#19136949C211yesmaximal, characteristic, complemented
6#19135225C211yesmaximal, characteristic, complemented
7#19135222C211yesmaximal, characteristic, complemented
8#19135220C211yesmaximal, characteristic, complemented
9#19135219C211yesmaximal, characteristic, complemented
10#19135217C211yesmaximal, characteristic, complemented
11#19135216C211yesmaximal, characteristic, complemented
12#19135214C211yesmaximal, characteristic, complemented
13#19134313C211yesmaximal, characteristic, complemented
14#19134290C211yesmaximal, characteristic, complemented
15C43×#1925C211yesmaximal, characteristic, complemented
16C22×D4×D43C2211yescharacteristic
17C22×#10621872C2211yescharacteristic
18C22×C8×D43C2211yescharacteristic
19C2×#13063283C2211yescharacteristic
20C2×#13063283C2211yescharacteristic
21C2×#13063282C2211yescharacteristic
22C2×C4⋊C4×D43C2211yescharacteristic
23#14582936—24no—
24C2×#13063259C2211yescharacteristic, complemented
25C2×#13063256C2211yescharacteristic, complemented
26C2×#13063256C2211yescharacteristic, complemented
27#14582902—24no—
28C2×#13063247C2211yescharacteristic
29C2×#13063247C2211yescharacteristic
30C2×#13063246C2211yescharacteristic
31C2×#13063246C2211yescharacteristic
32C2×#13063245C2211yescharacteristic
33C2×#13063245C2211yescharacteristic
34#102×D43C418yescomplemented
35#14582802C2211yescharacteristic
36#14582801C2211yescharacteristic
37#14582800C2211yescharacteristic
38#14582799—21no—
39#14582799—21no—
40#14582754—21no—
41#14582754—21no—
42C4⋊C4×Dic43C2211yescharacteristic, complemented
43C4⋊C4×Dic43C2211yescharacteristic, complemented
44C4×Dic43⋊C4—21no—
45C4×C4⋊Dic43C2211yescharacteristic, complemented
46#14582750—21no—
47C4×(C2×D43)⋊C4—21no—
48#14582746—21no—
49#14582662C2211yescharacteristic, complemented
50#14582661C2211yescharacteristic, complemented
51#14582661C2211yescharacteristic, complemented
52#14582654C2211yescharacteristic, complemented
53#14582653C2211yescharacteristic, complemented
54#14582653C2211yescharacteristic, complemented
55C2×#107×C43C2211yescharacteristic, complemented
56C2×#102×C43C2211yescharacteristic
57C2×#102×C43C2211yescharacteristic
58C43×#390C2211yescharacteristic
59C4×C4⋊C4×C43C2211yescharacteristic, complemented
60C43×#340C2211yescharacteristic, complemented
61C43×#336C2211yescharacteristic, complemented
62C24×D43—21no—
63C22×D172C2311yescharacteristic
64C22×C22⋊D43—21no—
65C2×D4×D43—22no—
66C2×D4×D43—22no—
67C2×D4×D43—22no—
68C2×D4×D43—22no—
69C2×D4×D43—22no—
70C2×D4×D43C2×C414yes—
71C22×C4×D43—21no—
72C22×C4×D43C2311yescharacteristic
73C2×#10621872—22no—
74C2×#10621872—22no—
75C2×#10621872—22no—
76C22×C43⋊C8C2311yescharacteristic
77C22×C43⋊C8C2311yescharacteristic
78C2×C8×D43—22no—
79C2×C8×D43—22no—
80C2×C8×D43C2×C414yes—
81#13063283—22no—
82#13063283—22no—
83#13063283—22no—
84#13063283D414yes—
85#13063282—22no—
86#13063282—22no—
87C2×C4⋊Dic43C2311yescharacteristic
88C2×C4⋊Dic43C2311yescharacteristic
89C2×C4⋊Dic43C2311yescharacteristic
90C2×Dic43⋊C4—21no—
91C2×Dic43⋊C4D411yescharacteristic
92C2×Dic43⋊C4D411yescharacteristic
93C4⋊C4×D43—22no—
94C4⋊C4×D43C2×C414yes—
95C2×C22⋊Dic43—21no—
96C2×C22⋊Dic43—21no—
97C2×(C2×D43)⋊C4—21no—
98C2×(C2×D43)⋊C4—21no—
99C2×(C2×D43)⋊C4—21no—
100C2×(C2×D43)⋊C4—21no—
101C2×(C2×D43)⋊C4—21no—
102C2×(C2×D43)⋊C4—21no—
103C2×(C2×D43)⋊C4D411yescharacteristic
104C2×(C2×D43)⋊C4D411yescharacteristic
105C2×C4×Dic43—21no—
106C2×C4×Dic43—21no—
107C2×C4×Dic43—21no—
108C2×C4×Dic43—21no—
109C2×C4×Dic43—21no—
110C2×C4×Dic43C2311yescharacteristic
111#13063259—22no—
112#13063256—22no—
113#13063256—22no—
114#13063247—22no—
115#13063247C2×C414yes—
116#13063246—22no—
117#13063246C2×C414yes—
118#13063245—22no—
119#13063245C2×C414yes—
120C43⋊#95—21no—
121C43⋊#95—21no—
122C43⋊#95—21no—
123C22×D4×C43C2311yescharacteristic
124C22×C8×C43C2311yescharacteristic
125C22×C8×C43C2311yescharacteristic
126C2×C4⋊C4×C43C2311yescharacteristic
127C2×C4⋊C4×C43C2311yescharacteristic
128C2×C4⋊C4×C43C2311yescharacteristic
129C2×C22⋊C4×C43—21no—
130C2×C22⋊C4×C43—21no—
131C2×C42×C43—21no—
132C2×C42×C43C2311yescharacteristic
133#107×C43—22no—
134#102×C43—22no—
135#102×C43C2×C414yes—
136#95×C43—21no—
137C24×C43—21no—
138C23×D43—21no—
139C23×D43—24no—
140C23×D43—42no—
141C23×D43—42no—
142C23×D43—81no—
143C23×D43—81no—
144C23×D43—81no—
145C23×D43—81no—
146C23×D43C2×D411yescharacteristic
147C2×D4×C43—21no—
148C2×D4×C43—21no—
149C2×D4×C43—21no—
150C2×D4×C43—21no—
151C2×D4×C43—21no—
152C2×D4×C43C22×C412yes—
153C22×C4×C43—21no—
154C22×C4×C43—21no—
155C22×C4×C43—21no—
156C22×C4×C43C2×D411yescharacteristic
157C22×C4×C43C2×D411yescharacteristic
158C22×C4×C43C2411yescharacteristic
159C2×C22⋊D43—24no—
160C2×C22⋊D43—42no—
161C2×C22⋊D43—42no—
162C22×Dic43—21no—
163C22×Dic43—21no—
164C22×Dic43—21no—
165C22×Dic43C2×D411yescharacteristic
166C22×Dic43C2×D411yescharacteristic
167C22×Dic43C2×D411yescharacteristic
168D4×D43—28no—
169D4×D43—28no—
170D4×D43—44no—
171D4×D43—44no—
172C2×D172—21no—
173C2×D172—21no—
174C2×D172—21no—
175C2×D172—21no—
176C2×D172—21no—
177C2×D172C22×C412yes—
178C2×C4×D43—24no—
179C2×C4×D43—81no—
180C2×C4×D43—81no—
181C2×C4×D43C22×C412yes—
182C2×C4×D43C2×D412yes—
183C2×C4×D43#4112yes—
184C2×C4×D43#4112yes—
185C2×C4×D43#4112yes—
186C2×C4×D43#4112yes—
187C2×C8×C43—21no—
188C2×C8×C43—21no—
189C2×C8×C43—21no—
190C2×C8×C43—21no—
191C2×C8×C43—21no—
192C2×C8×C43C22×C412yes—
193C4⋊C4×C43—21no—
194C4⋊C4×C43—21no—
195C4⋊C4×C43—21no—
196C4⋊C4×C43—21no—
197C4⋊C4×C43C22×C412yes—
198C4⋊C4×C43C2×D412yes—
199C22⋊C4×C43—81no—
200C22⋊C4×C43—81no—
201C42×C43—21no—
202C42×C43—21no—
203C42×C43—81no—
204C22⋊Dic43—81no—
205C22⋊Dic43—81no—
206(C2×D43)⋊C4—24no—
207(C2×D43)⋊C4—22no—
208(C2×D43)⋊C4—22no—
209(C2×D43)⋊C4—42no—
210(C2×D43)⋊C4—81no—
211(C2×D43)⋊C4—81no—
212(C2×D43)⋊C4—81no—
213(C2×D43)⋊C4—81no—
214C4⋊Dic43—21no—
215C4⋊Dic43—21no—
216C4⋊Dic43—21no—
217C4⋊Dic43—21no—
218C4⋊Dic43C22×C412yes—
219C4⋊Dic43C2×D412yes—
220Dic43⋊C4—24no—
221Dic43⋊C4—22no—
222Dic43⋊C4—22no—
223C4×Dic43—21no—
224C4×Dic43—21no—
225C4×Dic43—24no—
226C4×Dic43—42no—
227C4×Dic43—81no—
228C4×Dic43—81no—
229C4×Dic43—81no—
230C2×C43⋊C8—21no—
231C2×C43⋊C8—21no—
232C2×C43⋊C8—21no—
233C2×C43⋊C8—21no—
234C2×C43⋊C8—21no—
235C2×C43⋊C8C22×C412yes—
236#10621872—44no—
237C8×D43—28no—
238C23×C43—22no—
239C23×C43—41no—
240C23×C43—41no—
241C23×C43—41no—
242C23×C43—41no—
243C23×C43—41no—
244C23×C43—41no—
245C23×C43C22×D411yescharacteristic
246C22×D43—21no—
247C22×D43—21no—
248C22×D43—21no—
249C22×D43—21no—
250C22×D43—22no—
251C22×D43—41no—
252C22×D43—41no—
253C22×D43—41no—
254C22×D43—41no—
255C22×D43—41no—
256C22×D43—41no—
257C22×D43—48no—
258C22×D43—84no—
259C22×D43—84no—
260C22×D43—84no—
261C22×D43—84no—
262C22×D43—84no—
263C22×D43—84no—
264C22×D43C4×D412yes—
265C22×D43#12112yes—
266C22×D43#12312yes—
267D4×C43—22no—
268D4×C43—22no—
269D4×C43—41no—
270D4×C43—41no—
271C2×C4×C43—22no—
272C2×C4×C43—22no—
273C2×C4×C43—21no—
274C2×C4×C43—21no—
275C2×C4×C43—21no—
276C2×C4×C43—21no—
277C2×C4×C43—21no—
278C2×C4×C43—21no—
279C2×C4×C43—41no—
280C2×C4×C43—41no—
281C2×C4×C43—41no—
282C2×C4×C43—41no—
283C2×C4×C43—41no—
284C2×C4×C43—41no—
285C2×C4×C43—41no—
286C2×C4×C43C23×C411yescharacteristic
287C2×C4×C43C22×D411yescharacteristic
288C2×C4×C43C2×#4111yescharacteristic
289C2×C4×C43C2×#4111yescharacteristic
290C2×C4×C43C2×#4111yescharacteristic
291C2×C4×C43C2×#4111yescharacteristic
292C22⋊D43—48no—
293C2×Dic43—22no—
294C2×Dic43—22no—
295C2×Dic43—21no—
296C2×Dic43—21no—
297C2×Dic43—21no—
298C2×Dic43—21no—
299C2×Dic43—21no—
300C2×Dic43—21no—
301C2×Dic43—41no—
302C2×Dic43—41no—
303C2×Dic43—41no—
304C2×Dic43—41no—
305C2×Dic43—41no—
306C2×Dic43—41no—
307C2×Dic43—41no—
308C2×Dic43C4×D412yes—
309C2×Dic43#12112yes—
310C2×Dic43#12312yes—
311D172—22no—
312D172—22no—
313D172—41no—
314D172—41no—
315C4×D43—84no—
316C4×D43#11714yes—
317C4×D43C4×D414yes—
318C4×D43#12414yes—
319C4×D43#12614yes—
320C8×C43—22no—
321C8×C43—41no—
322C43⋊C8—22no—
323C43⋊C8—41no—
324#21065—431nomaximal, Sylow
325C22×C43—42no—
326C22×C43—42no—
327C22×C43—42no—
328C22×C43—81no—
329C22×C43—81no—
330C22×C43—81no—
331C22×C43—81no—
332C22×C43C2×C4×D411yescharacteristic
333C22×C43C2×#12111yescharacteristic
334C22×C43C2×#12311yescharacteristic
335C22×C43#57611yescharacteristic
336C22×C43#57611yescharacteristic
337C22×C43#57711yescharacteristic
338C22×C43#57711yescharacteristic
339C2×D43—22no—
340C2×D43—22no—
341C2×D43—22no—
342C2×D43—22no—
343C2×D43—22no—
344C2×D43—22no—
345C2×D43—42no—
346C2×D43—42no—
347C2×D43—42no—
348C2×D43—816no—
349C2×D43—81no—
350C2×D43—81no—
351C2×D43—81no—
352C2×D43—81no—
353C2×D43#38814yes—
354C4×C43—41no—
355C4×C43—41no—
356C4×C43—42no—
357C4×C43—42no—
358C4×C43—81no—
359C4×C43C2×#11711yescharacteristic
360C4×C43C2×C4×D411yescharacteristic
361C4×C43C2×#12411yescharacteristic
362C4×C43C2×#12611yescharacteristic
363Dic43—41no—
364Dic43—41no—
365Dic43—42no—
366Dic43—42no—
367Dic43—81no—
368Dic43#38814yes—
369C2×#427—431no—
370C2×#418—431no—
371C22×#102—431no—
372#2309—431no—
373#2274—431no—
374#1926—431no—
375#1926—431no—
376#1926—431no—
377#1926—431no—
378#1925—431no—
379#1925—431no—
380#1925—431no—
381#1925D4311yescharacteristic, complemented
382#1736—431no—
383#1729—431no—
384C2×C43—82no—
385C2×C43C2×#38811yescharacteristic
386C2×C43#294811yescharacteristic
387C2×C43#294911yescharacteristic
388C2×C43#304511yescharacteristic
389C2×C43#304511yescharacteristic
390C2×C43#309611yescharacteristic
391C2×C43#309611yescharacteristic
392D43—24no—
393D43—82no—
394C23×D4—431no—
395C22×M16—431no—
396C23×C8—431no—
397C2×#117—431no—
398C2×#117—431no—
399C2×#117—431no—
400C22×C4⋊C4—431no—
401#427—864no—
402C2×#107—431no—
403C2×#107C2×D4311yescharacteristic, complemented
404C2×#106—431no—
405C2×#106—431no—
406#418—864no—
407C2×#102—431no—
408C2×#102—431no—
409C2×#102—431no—
410C2×#102—438no—
411C2×#102—431no—
412C2×#102—431no—
413C2×#102—431no—
414C2×#102C2×D4311yescharacteristic
415C2×#102C2×D4311yescharacteristic
416#390—431no—
417#390—431no—
418#390—431no—
419#390—861no—
420#390—861no—
421#390C2×D4311yescharacteristic
422#379—861no—
423#379—861no—
424C4×C4⋊C4—431no—
425C4×C4⋊C4—431no—
426C4×C4⋊C4—431no—
427C4×C4⋊C4—861no—
428C4×C4⋊C4—861no—
429C4×C4⋊C4C2×D4311yescharacteristic, complemented
430C4×C22⋊C4—861no—
431C4×C22⋊C4—861no—
432#340—431no—
433#340—431no—
434#340—431no—
435#340C2×D4311yescharacteristic, complemented
436#336—431no—
437#336—431no—
438#336—431no—
439#336C2×D4311yescharacteristic, complemented
440C43#2106511yescharacteristic, complemented, Sylow
441C25—861no—
442C22×D4—434no—
443C22×D4—431no—
444C22×D4—862no—
445C22×D4—862no—
446C22×D4—862no—
447C22×D4—862no—
448C22×D4—862no—
449C22×D4—861no—
450C22×D4C22×D4311yescharacteristic
451C23×C4—431no—
452C23×C4—861no—
453C2×M16—862no—
454C2×M16—862no—
455C2×M16—862no—
456C22×C8—431no—
457C22×C8—434no—
458C22×C8—431no—
459C22×C8—862no—
460C22×C8—862no—
461C22×C8C22×D4311yescharacteristic
462C22×C8C22×D4311yescharacteristic
463#117—434no—
464#117—862no—
465#117—862no—
466#117—862no—
467#117—862no—
468#117—862no—
469C2×C4⋊C4—431no—
470C2×C4⋊C4—431no—
471C2×C4⋊C4—434no—
472C2×C4⋊C4—431no—
473C2×C4⋊C4—431no—
474C2×C4⋊C4—431no—
475C2×C4⋊C4—862no—
476C2×C4⋊C4—861no—
477C2×C4⋊C4C22×D4311yescharacteristic
478C2×C4⋊C4C22×D4311yescharacteristic
479C2×C4⋊C4C22×D4311yescharacteristic
480C2×C22⋊C4—21no—
481C2×C22⋊C4—21no—
482C2×C22⋊C4—431no—
483C2×C22⋊C4—431no—
484C2×C22⋊C4—861no—
485C2×C22⋊C4—861no—
486C2×C22⋊C4—861no—
487C2×C22⋊C4—861no—
488C2×C22⋊C4—861no—
489C2×C22⋊C4—861no—
490C2×C22⋊C4—861no—
491C2×C22⋊C4—861no—
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#107—862no—
502#106—862no—
503#106—862no—
504#102—22no—
505#102—434no—
506#102—434no—
507#102—434no—
508#102—862no—
509#102—862no—
510#102—862no—
511#102C4×D4314yes—
512#95—21no—
513#95—861no—
514#95—861no—
515#95—861no—
516C24—21no—
517C24—431no—
518C24—864no—
519C24—861no—
520C24—3441no—
521C24—3441no—
522C24—3441no—
523C24—3441no—
524C24—1722no—
525C24—1722no—
526C2×D4—21no—
527C2×D4—21no—
528C2×D4—21no—
529C2×D4—21no—
530C2×D4—21no—
531C2×D4—432no—
532C2×D4—868no—
533C2×D4—868no—
534C2×D4—864no—
535C2×D4—861no—
536C2×D4—861no—
537C2×D4—861no—
538C2×D4—861no—
539C2×D4—861no—
540C2×D4—1724no—
541C2×D4—1724no—
542C2×D4—1722no—
543C2×D4—1722no—
544C2×D4C2×C4×D4312yes—
545C22×C4—21no—
546C22×C4—21no—
547C22×C4—21no—
548C22×C4—431no—
549C22×C4—432no—
550C22×C4—432no—
551C22×C4—432no—
552C22×C4—432no—
553C22×C4—432no—
554C22×C4—432no—
555C22×C4—431no—
556C22×C4—431no—
557C22×C4—864no—
558C22×C4—861no—
559C22×C4—861no—
560C22×C4—861no—
561C22×C4—3441no—
562C22×C4—3441no—
563C22×C4D4×D4311yescharacteristic
564C22×C4D4×D4311yescharacteristic
565C22×C4C23×D4311yescharacteristic
566M16—1724no—
567C2×C8—21no—
568C2×C8—21no—
569C2×C8—21no—
570C2×C8—21no—
571C2×C8—21no—
572C2×C8—432no—
573C2×C8—868no—
574C2×C8—861no—
575C2×C8—861no—
576C2×C8—861no—
577C2×C8—861no—
578C2×C8—861no—
579C2×C8C2×C4×D4312yes—
580C4⋊C4—21no—
581C4⋊C4—21no—
582C4⋊C4—21no—
583C4⋊C4—21no—
584C4⋊C4—432no—
585C4⋊C4—432no—
586C4⋊C4—864no—
587C4⋊C4—862no—
588C4⋊C4—862no—
589C4⋊C4—861no—
590C4⋊C4—861no—
591C4⋊C4—861no—
592C4⋊C4—861no—
593C4⋊C4C2×C4×D4312yes—
594C4⋊C4D4×D4312yes—
595C22⋊C4—81no—
596C22⋊C4—81no—
597C22⋊C4—862no—
598C22⋊C4—862no—
599C22⋊C4—864no—
600C22⋊C4—3441no—
601C22⋊C4—3441no—
602C22⋊C4—3441no—
603C22⋊C4—3441no—
604C22⋊C4—3441no—
605C22⋊C4—3441no—
606C22⋊C4—1722no—
607C42—21no—
608C42—21no—
609C42—81no—
610C42—864no—
611C42—861no—
612C42—861no—
613C42—3441no—
614C42—3441no—
615C42—3441no—
616C42—1722no—
617C23—22no—
618C23—41no—
619C23—41no—
620C23—41no—
621C23—41no—
622C23—41no—
623C23—41no—
624C23—432no—
625C23—432no—
626C23—432no—
627C23—861no—
628C23—861no—
629C23—861no—
630C23—861no—
631C23—862no—
632C23—3444no—
633C23—3444no—
634C23—3444no—
635C23—3444no—
636C23—3444no—
637C23—3444no—
638C23—1728no—
639C23—1721no—
640C23—1721no—
641C23—1721no—
642C23—1721no—
643C23—1721no—
644C23—1721no—
645C23C2×D4×D4311yescharacteristic
646D4—22no—
647D4—22no—
648D4—41no—
649D4—41no—
650D4—862no—
651D4—862no—
652D4—1728no—
653D4—1721no—
654D4—1721no—
655C2×C4—22no—
656C2×C4—22no—
657C2×C4—21no—
658C2×C4—21no—
659C2×C4—21no—
660C2×C4—21no—
661C2×C4—21no—
662C2×C4—21no—
663C2×C4—41no—
664C2×C4—41no—
665C2×C4—41no—
666C2×C4—41no—
667C2×C4—41no—
668C2×C4—41no—
669C2×C4—41no—
670C2×C4—432no—
671C2×C4—432no—
672C2×C4—432no—
673C2×C4—434no—
674C2×C4—434no—
675C2×C4—434no—
676C2×C4—434no—
677C2×C4—862no—
678C2×C4—862no—
679C2×C4—861no—
680C2×C4—861no—
681C2×C4—861no—
682C2×C4—861no—
683C2×C4—861no—
684C2×C4—861no—
685C2×C4—3444no—
686C2×C4—1721no—
687C2×C4—1721no—
688C2×C4—1721no—
689C2×C4—1721no—
690C2×C4—1721no—
691C2×C4—1721no—
692C2×C4—1721no—
693C2×C4C22×C4×D4311yescharacteristic
694C2×C4C2×D4×D4311yescharacteristic
695C2×C4#41×D4311yescharacteristic
696C2×C4#41×D4311yescharacteristic
697C2×C4#41×D4311yescharacteristic
698C2×C4#41×D4311yescharacteristic
699C8—22no—
700C8—41no—
701C8—862no—
702C8—1721no—
703C22—42no—
704C22—42no—
705C22—42no—
706C22—81no—
707C22—81no—
708C22—81no—
709C22—81no—
710C22—434no—
711C22—862no—
712C22—862no—
713C22—862no—
714C22—862no—
715C22—862no—
716C22—862no—
717C22—34416no—
718C22—3441no—
719C22—3441no—
720C22—3441no—
721C22—3441no—
722C22—1722no—
723C22—1722no—
724C22—1722no—
725C22C4×D4×D4311yescharacteristic
726C22#121×D4311yescharacteristic
727C22#123×D4311yescharacteristic
728C22#1458370011yescharacteristic
729C22#1458370111yescharacteristic
730C22#1458370811yescharacteristic
731C22#1458370911yescharacteristic
732C4—42no—
733C4—41no—
734C4—41no—
735C4—42no—
736C4—81no—
737C4—434no—
738C4—3441no—
739C4—1722no—
740C4—1721no—
741C4—1721no—
742C4—1722no—
743C4#117×D4311yescharacteristic
744C4C4×D4×D4311yescharacteristic
745C4#124×D4311yescharacteristic
746C4#126×D4311yescharacteristic
747C2—82no—
748C2—864no—
749C2—3442no—
750C2#388×D4311yescharacteristic
751C2#1914344211yescharacteristic
752C2#1914345111yescharacteristic
753C2#1914412911yescharacteristic
754C2#1914413711yescharacteristic
755C2#1914454611yescharacteristic
756C2#1914455011yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC43×#1925C2
socleC23×C43C22×D4
prime radicalC22×D4×D43C22
cosocleC22×C4×C43C24
hypercenter#1925D43
hypocenterC43#21065
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1925

Complements

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

NH ≅ G/Ntype
1. C2×#14582936C2semidirect
5. #19136949C2semidirect
6. #19135225C2semidirect
7. #19135222C2semidirect
8. #19135220C2semidirect
9. #19135219C2semidirect
10. #19135217C2semidirect
11. #19135216C2semidirect
12. #19135214C2semidirect
13. #19134313C2semidirect
14. #19134290C2semidirect
15. C43×#1925C2semidirect
24. C2×#13063259C22semidirect
25. C2×#13063256C22semidirect
26. C2×#13063256C22semidirect
34. #102×D43C4semidirect
42. C4⋊C4×Dic43C22semidirect
43. C4⋊C4×Dic43C22semidirect
45. C4×C4⋊Dic43C22semidirect
49. #14582662C22semidirect
50. #14582661C22semidirect
51. #14582661C22semidirect
52. #14582654C22semidirect
53. #14582653C22semidirect
54. #14582653C22semidirect
55. C2×#107×C43C22semidirect
59. C4×C4⋊C4×C43C22semidirect
60. C43×#340C22semidirect
61. C43×#336C22semidirect
381. #1925D43semidirect
403. C2×#107C2×D43semidirect
429. C4×C4⋊C4C2×D43semidirect
435. #340C2×D43semidirect
439. #336C2×D43semidirect
440. C43#21065semidirect

Maximal subgroups

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

subgroupindex
C2×#145829362
C2×#145829022
C2×#102×D432
#191371742
#191369492
#191352252
#191352222
#191352202
#191352192
#191352172
#191352162
#191352142
#191343132
#191342902
C43×#19252
#2106543