Finite Group Databasebeta

← #25144064

Subgroups — #25144064

Order 11008.

1106 conjugacy classes of subgroups.

The subgroup lattice has 770 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583102C211yesmaximal, characteristic, complemented
2C2×#14583061C211yesmaximal, characteristic
3C2×SD16×Dic43C211yesmaximal, characteristic, complemented
4#19138196C211yesmaximal, characteristic, complemented
5#19137425C211yesmaximal, characteristic
6#19135974C211yesmaximal, characteristic, complemented
7#19135795C211yesmaximal, characteristic, complemented
8#19135792C211yesmaximal, characteristic, complemented
9#19135693C211yesmaximal, characteristic, complemented
10#19135453C211yesmaximal, characteristic, complemented
11#19135204C211yesmaximal, characteristic, complemented
12#19134938C211yesmaximal, characteristic, complemented
13#19134927C211yesmaximal, characteristic, complemented
14#19134840C211yesmaximal, characteristic, complemented
15C2×C43×#452C211yesmaximal, characteristic
16C22×#10621885C2211yescharacteristic
17C22×#10621883C2211yescharacteristic
18C2×#13063323C2211yescharacteristic
19C2×#13063304C2211yescharacteristic
20C2×Q8×Dic43C2211yescharacteristic
21C2×D4×Dic43C2211yescharacteristic
22C2×D4×Dic43C2211yescharacteristic
23#14583102—24no—
24#14583061—24no—
25SD16×Dic43—24no—
26C2×#13063258C2211yescharacteristic
27C2×#13063257C2211yescharacteristic
28C2×Dic43⋊C8C2211yescharacteristic
29C2×#13063250C2211yescharacteristic
30C2×#13063250C2211yescharacteristic
31C2×#13063249C2211yescharacteristic
32C2×#13063249C2211yescharacteristic
33C2×#13063249C2211yescharacteristic
34C2×#13063246C2211yescharacteristic
35C2×C22⋊(C43⋊C8)C2211yescharacteristic
36C2×C8×Dic43C2211yescharacteristic
37#14582832—21no—
38#14582822—21no—
39#14582806C2211yescharacteristic
40#14582806C2211yescharacteristic
41#14582804C2211yescharacteristic
42#14582795C2211yescharacteristic
43#14582794—21no—
44#14582793—21no—
45#14582779—21no—
46#14582779—21no—
47#14582762—21no—
48#14582759C2211yescharacteristic
49C4×C22⋊Dic43C2211yescharacteristic
50C2×C43⋊#95—21no—
51#14582662C2211yescharacteristic
52#14582661C2211yescharacteristic
53#14582653C2211yescharacteristic
54#14582653C2211yescharacteristic
55C22×#41×C43C2211yescharacteristic
56C22×Q16×C43C2211yescharacteristic
57C22×SD16×C43C2211yescharacteristic
58C2×C22⋊Q8×C43C2211yescharacteristic
59C43×#452—24no—
60C2×#103×C43C2211yescharacteristic
61C2×#102×C43C2211yescharacteristic
62C2×C22⋊C8×C43C2211yescharacteristic
63C22×Dic86C2311yescharacteristic
64C23×Dic43—21no—
65C23×Dic43—21no—
66C2×#10621885—22no—
67C2×#10621885—22no—
68C2×#10621885—41no—
69C2×#10621883—22no—
70C2×#10621883—22no—
71C2×#10621883—22no—
72C22×C43⋊C8C2311yescharacteristic
73C22×C43⋊C8C2311yescharacteristic
74#13063323—22no—
75#13063323—41no—
76#13063304—22no—
77#13063304—41no—
78Q8×Dic43—22no—
79Q8×Dic43—41no—
80D4×Dic43—22no—
81D4×Dic43—22no—
82D4×Dic43—41no—
83D4×Dic43—41no—
84C2×C4⋊Dic43—21no—
85C2×C4⋊Dic43C2311yescharacteristic
86C2×C4⋊Dic43C2311yescharacteristic
87C2×C4⋊Dic43C2311yescharacteristic
88C2×Dic43⋊C4—21no—
89C2×Dic43⋊C4—21no—
90C2×Dic43⋊C4—21no—
91C2×Dic43⋊C4—21no—
92C2×C22⋊Dic43—21no—
93C2×C22⋊Dic43—21no—
94C2×C22⋊Dic43—21no—
95C2×C22⋊Dic43—21no—
96C2×C22⋊Dic43D411yescharacteristic
97C2×C22⋊Dic43D411yescharacteristic
98C2×C4×Dic43—21no—
99C2×C4×Dic43C2311yescharacteristic
100C2×C4×Dic43C2311yescharacteristic
101#13063258—41no—
102#13063257—22no—
103Dic43⋊C8—22no—
104#13063250—22no—
105#13063250—41no—
106#13063249—22no—
107#13063249—22no—
108#13063249—22no—
109#13063246D414yes—
110C22⋊(C43⋊C8)—22no—
111C8×Dic43—22no—
112C43⋊#95—21no—
113C43⋊#95—21no—
114C43⋊#95—21no—
115C43⋊#95—21no—
116C43⋊#95—21no—
117C43⋊#95—21no—
118C43⋊#95—21no—
119C43⋊#95—21no—
120C43⋊#95D411yescharacteristic
121C43⋊#95D411yescharacteristic
122C2×#41×C43—22no—
123C2×#41×C43—22no—
124C2×#41×C43—22no—
125C2×#41×C43—22no—
126C2×#41×C43—41no—
127C2×#41×C43—41no—
128C22×Q8×C43C2311yescharacteristic
129C22×Q8×C43C2311yescharacteristic
130C22×D4×C43—21no—
131C22×D4×C43C2311yescharacteristic
132C23×C4×C43—21no—
133C23×C4×C43C2311yescharacteristic
134C2×Q16×C43—22no—
135C2×Q16×C43—22no—
136C2×Q16×C43—41no—
137C2×SD16×C43—22no—
138C2×SD16×C43—22no—
139C2×SD16×C43D414yes—
140C22×C8×C43C2311yescharacteristic
141C22×C8×C43C2311yescharacteristic
142C22⋊Q8×C43—22no—
143C22⋊Q8×C43—41no—
144C2×C4⋊C4×C43—21no—
145C2×C4⋊C4×C43C2311yescharacteristic
146C2×C22⋊C4×C43—21no—
147#103×C43—22no—
148#102×C43—22no—
149C22⋊C8×C43—22no—
150C24×C43—21no—
151C24×C43C2×D411yescharacteristic
152#41×C43—44no—
153#41×C43—44no—
154#41×C43—44no—
155#41×C43—44no—
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×C43—21no—
163C2×Q8×C43—21no—
164C2×Q8×C43—21no—
165C2×Q8×C43—21no—
166C2×Q8×C43C2×D412yes—
167C2×Q8×C43#4112yes—
168C2×D4×C43—24no—
169C2×D4×C43—21no—
170C2×D4×C43—21no—
171C2×D4×C43—21no—
172C2×D4×C43—42no—
173C2×D4×C43—42no—
174C2×D4×C43C2×D412yes—
175C2×D4×C43C2×D412yes—
176C2×D4×C43#4112yes—
177C22×C4×C43—24no—
178C22×C4×C43—21no—
179C22×C4×C43—21no—
180C22×C4×C43—21no—
181C22×C4×C43—21no—
182C22×C4×C43—21no—
183C22×C4×C43—21no—
184C22×C4×C43—21no—
185C22×C4×C43—21no—
186C22×C4×C43—21no—
187C22×C4×C43—42no—
188C22×C4×C43—42no—
189C22×C4×C43C2×D411yescharacteristic
190C22×C4×C43C2411yescharacteristic
191C22×Dic43—21no—
192C22×Dic43—21no—
193C22×Dic43—21no—
194C22×Dic43—21no—
195C22×Dic43—42no—
196C22×Dic43—42no—
197C22×Dic43—42no—
198C22×Dic43—42no—
199C22×Dic43—81no—
200C22×Dic43—81no—
201C22×Dic43C2×D411yescharacteristic
202C22×Dic43C2×D411yescharacteristic
203C22×Dic43C2×D411yescharacteristic
204C22×Dic43C2×D411yescharacteristic
205C2×Dic86—21no—
206C2×Dic86—21no—
207C2×Dic86—21no—
208C2×Dic86—21no—
209C2×Dic86—21no—
210C2×Dic86—21no—
211Q16×C43—44no—
212SD16×C43—28no—
213C2×C8×C43—21no—
214C2×C8×C43—21no—
215C2×C8×C43—21no—
216C2×C8×C43—21no—
217C2×C8×C43—21no—
218C2×C8×C43C2×D412yes—
219C4⋊C4×C43—21no—
220C4⋊C4×C43—21no—
221C4⋊C4×C43—42no—
222C22⋊C4×C43—42no—
223C22⋊Dic43—22no—
224C22⋊Dic43—22no—
225C22⋊Dic43—42no—
226C22⋊Dic43—42no—
227C22⋊Dic43—42no—
228C22⋊Dic43—81no—
229#10621885—44no—
230#10621883—44no—
231C4⋊Dic43—21no—
232C4⋊Dic43—21no—
233C4⋊Dic43—21no—
234C4⋊Dic43—21no—
235C4⋊Dic43—21no—
236C4⋊Dic43—42no—
237C4⋊Dic43C2×D412yes—
238Dic43⋊C4—42no—
239Dic43⋊C4—42no—
240Dic43⋊C4—42no—
241Dic43⋊C4—42no—
242C4×Dic43—21no—
243C4×Dic43—21no—
244C4×Dic43—21no—
245C4×Dic43—21no—
246C4×Dic43—42no—
247C2×C43⋊C8—21no—
248C2×C43⋊C8—21no—
249C2×C43⋊C8—21no—
250C2×C43⋊C8—21no—
251C2×C43⋊C8—21no—
252C2×C43⋊C8C2×D412yes—
253C23×C43—22no—
254C23×C43—22no—
255C23×C43—22no—
256C23×C43—21no—
257C23×C43—21no—
258C23×C43—21no—
259C23×C43—21no—
260C23×C43—21no—
261C23×C43—21no—
262C23×C43—21no—
263C23×C43—41no—
264C23×C43—41no—
265C23×C43—41no—
266C23×C43—41no—
267C23×C43C22×D411yescharacteristic
268Q8×C43—22no—
269Q8×C43—22no—
270Q8×C43—22no—
271Q8×C43—22no—
272Q8×C43—41no—
273Q8×C43—41no—
274Q8×C43—41no—
275Q8×C43—41no—
276D4×C43—22no—
277D4×C43—22no—
278D4×C43—22no—
279D4×C43—48no—
280D4×C43#12114yes—
281C2×C4×C43—21no—
282C2×C4×C43—22no—
283C2×C4×C43—22no—
284C2×C4×C43—21no—
285C2×C4×C43—21no—
286C2×C4×C43—48no—
287C2×C4×C43—41no—
288C2×C4×C43—41no—
289C2×C4×C43—41no—
290C2×C4×C43—41no—
291C2×C4×C43—41no—
292C2×C4×C43—41no—
293C2×C4×C43—41no—
294C2×C4×C43—41no—
295C2×C4×C43—41no—
296C2×C4×C43—41no—
297C2×C4×C43—41no—
298C2×C4×C43C22×D411yescharacteristic
299C2×C4×C43C22×D411yescharacteristic
300C2×C4×C43C2×#4111yescharacteristic
301C2×C4×C43C2×#4111yescharacteristic
302C2×C4×C43H(5,𝔽2)11yescharacteristic
303C2×C4×C43H(5,𝔽2)11yescharacteristic
304C2×Dic43—21no—
305C2×Dic43—21no—
306C2×Dic43—21no—
307C2×Dic43—21no—
308C2×Dic43—21no—
309C2×Dic43—21no—
310C2×Dic43—22no—
311C2×Dic43—21no—
312C2×Dic43—21no—
313C2×Dic43—21no—
314C2×Dic43—21no—
315C2×Dic43—41no—
316C2×Dic43—41no—
317C2×Dic43—41no—
318C2×Dic43—41no—
319C2×Dic43—41no—
320C2×Dic43—41no—
321C2×Dic43—41no—
322C2×Dic43—41no—
323C2×Dic43—41no—
324C2×Dic43—41no—
325C2×Dic43—41no—
326C2×Dic43—84no—
327C2×Dic43—84no—
328C2×Dic43#13512yes—
329C2×Dic43#13712yes—
330Dic86—41no—
331Dic86—41no—
332Dic86—41no—
333Dic86—41no—
334C8×C43—22no—
335C8×C43—41no—
336C43⋊C8—22no—
337C43⋊C8—41no—
338#25154—431nomaximal, Sylow
339C22×C43—24no—
340C22×C43—42no—
341C22×C43—42no—
342C22×C43—42no—
343C22×C43—42no—
344C22×C43—42no—
345C22×C43—42no—
346C22×C43—41no—
347C22×C43—41no—
348C22×C43—41no—
349C22×C43—41no—
350C22×C43—41no—
351C22×C43—41no—
352C22×C43—41no—
353C22×C43#52511yescharacteristic
354C22×C43D4211yescharacteristic
355C22×C43D4211yescharacteristic
356C22×C43C2×#13511yescharacteristic
357C22×C43C2×#13711yescharacteristic
358C22×C43#57711yescharacteristic
359C22×C43#57811yescharacteristic
360C4×C43—41no—
361C4×C43—42no—
362C4×C43—42no—
363C4×C43—81no—
364C4×C43C2×#12111yescharacteristic
365C4×C43#53811yescharacteristic
366C4×C43#54611yescharacteristic
367C4×C43#54611yescharacteristic
368Dic43—22no—
369Dic43—22no—
370Dic43—41no—
371Dic43—41no—
372Dic43—42no—
373Dic43—81no—
374Dic43—81no—
375Dic43—81no—
376C2×#461—431no—
377C2×#452—431no—
378C2×#452D4311yescharacteristic
379C2×C4×SD16—431no—
380#2429—431no—
381#2339—431no—
382#2066—431no—
383#2036—431no—
384#2035—431no—
385#2016—431no—
386#1969—431no—
387#1923—431no—
388#1878—431no—
389#1877—431no—
390#1862—431no—
391C2×C43—44no—
392C2×C43—81no—
393C2×C43#242411yescharacteristic
394C2×C43#310711yescharacteristic
395C2×C43#312011yescharacteristic
396C2×C43#326611yescharacteristic
397C2×C43#327611yescharacteristic
398C2×C43#328211yescharacteristic
399C2×C43#328311yescharacteristic
400C22×#41C2×D4311yescharacteristic
401C22×Q16—431no—
402C22×Q16C2×D4311yescharacteristic
403C22×SD16—431no—
404C22×SD16C2×D4311yescharacteristic
405C2×C4⋊Q8—431no—
406C2×C22⋊Q8—431no—
407C2×C22⋊Q8C2×D4311yescharacteristic
408C2×C4×Q8—431no—
409C2×C4×D4—431no—
410C2×C4×D4—431no—
411#461—864no—
412#452—24no—
413#452—864no—
414C4×SD16—864no—
415C2×#107—431no—
416C2×#106—431no—
417C2×C4⋊C8—431no—
418C2×#103—431no—
419C2×#103—431no—
420C2×#103—431no—
421C2×#103—431no—
422C2×#103—431no—
423C2×#103C2×D4311yescharacteristic
424C2×#102—431no—
425C2×#102C2×D4311yescharacteristic
426C2×C22⋊C8—431no—
427C2×C22⋊C8C2×D4311yescharacteristic
428C2×C4×C8—431no—
429#398—861no—
430#396—861no—
431#391—431no—
432#391—431no—
433#391—431no—
434#389—431no—
435#389—861no—
436#388—861no—
437#386—861no—
438#386—861no—
439#381—861no—
440#380—431no—
441C4×C22⋊C4—431no—
442C2×#95—861no—
443#340—431no—
444#340—431no—
445#336—431no—
446#336—431no—
447C43#2515411yescharacteristic, complemented, Sylow
448C2×#41—22no—
449C2×#41—22no—
450C2×#41—22no—
451C2×#41—22no—
452C2×#41—41no—
453C2×#41—41no—
454C22×Q8—431no—
455C22×Q8C22×D4311yescharacteristic
456C22×Q8C22×D4311yescharacteristic
457C22×D4—21no—
458C22×D4C22×D4311yescharacteristic
459C23×C4—21no—
460C23×C4—861no—
461C23×C4—861no—
462C23×C4C22×D4311yescharacteristic
463C2×Q16—22no—
464C2×Q16—22no—
465C2×Q16—41no—
466C2×Q16—862no—
467C2×Q16—862no—
468C2×Q16—1721no—
469C2×SD16—22no—
470C2×SD16—22no—
471C2×SD16—862no—
472C2×SD16—862no—
473C2×SD16—862no—
474C2×SD16C22⋊D4314yes—
475C22×C8—431no—
476C22×C8—431no—
477C22×C8C22×D4311yescharacteristic
478C22×C8C22×D4311yescharacteristic
479C4⋊Q8—862no—
480C4⋊Q8—1721no—
481C22⋊Q8—22no—
482C22⋊Q8—41no—
483C22⋊Q8—862no—
484C22⋊Q8—1721no—
485C4×Q8—862no—
486C4×Q8—1721no—
487C4×D4—862no—
488C4×D4—862no—
489C4×D4—1721no—
490C4×D4—1721no—
491C2×C4⋊C4—21no—
492C2×C4⋊C4—431no—
493C2×C4⋊C4—431no—
494C2×C4⋊C4—431no—
495C2×C4⋊C4—861no—
496C2×C4⋊C4—861no—
497C2×C4⋊C4—861no—
498C2×C4⋊C4—861no—
499C2×C4⋊C4—861no—
500C2×C4⋊C4C22×D4311yescharacteristic
501C2×C22⋊C4—21no—
502C2×C22⋊C4—431no—
503C2×C22⋊C4—431no—
504C2×C22⋊C4—861no—
505C2×C22⋊C4—861no—
506C2×C22⋊C4—861no—
507C2×C22⋊C4—861no—
508C2×C42—431no—
509C2×C42—431no—
510C2×C42—861no—
511#107—1721no—
512#106—862no—
513C4⋊C8—862no—
514#103—22no—
515#103—862no—
516#103—862no—
517#103—862no—
518#103—862no—
519#103—1721no—
520#102—22no—
521#102—434no—
522C22⋊C8—22no—
523C22⋊C8—862no—
524C4×C8—862no—
525#95—431no—
526#95—431no—
527#95—861no—
528#95—861no—
529#95—861no—
530#95—861no—
531#95—861no—
532#95—861no—
533#95—861no—
534#95—861no—
535C24—21no—
536C24D4×D4311yescharacteristic
537#41—44no—
538#41—44no—
539#41—44no—
540#41—44no—
541C2×Q8—21no—
542C2×Q8—21no—
543C2×Q8—21no—
544C2×Q8—21no—
545C2×Q8—21no—
546C2×Q8—21no—
547C2×Q8—21no—
548C2×Q8—21no—
549C2×Q8—21no—
550C2×Q8—21no—
551C2×Q8—861no—
552C2×Q8—861no—
553C2×Q8—861no—
554C2×Q8—861no—
555C2×Q8—861no—
556C2×Q8—861no—
557C2×Q8#1062190012yes—
558C2×Q8C2×C22⋊D4312yes—
559C2×D4—24no—
560C2×D4—21no—
561C2×D4—21no—
562C2×D4—21no—
563C2×D4—42no—
564C2×D4—42no—
565C2×D4D4×D4312yes—
566C2×D4#1062190012yes—
567C2×D4C2×C22⋊D4312yes—
568C22×C4—24no—
569C22×C4—21no—
570C22×C4—21no—
571C22×C4—21no—
572C22×C4—21no—
573C22×C4—21no—
574C22×C4—21no—
575C22×C4—21no—
576C22×C4—21no—
577C22×C4—21no—
578C22×C4—42no—
579C22×C4—42no—
580C22×C4—431no—
581C22×C4—431no—
582C22×C4—431no—
583C22×C4—431no—
584C22×C4—861no—
585C22×C4—861no—
586C22×C4—861no—
587C22×C4—861no—
588C22×C4—3441no—
589C22×C4—3441no—
590C22×C4—1722no—
591C22×C4—1722no—
592C22×C4—1722no—
593C22×C4—1722no—
594C22×C4D4×D4311yescharacteristic
595C22×C4C23×D4311yescharacteristic
596Q16—44no—
597Q16—1724no—
598SD16—28no—
599SD16—1724no—
600C2×C8—21no—
601C2×C8—21no—
602C2×C8—21no—
603C2×C8—21no—
604C2×C8—21no—
605C2×C8—432no—
606C2×C8—861no—
607C2×C8—861no—
608C2×C8—861no—
609C2×C8—861no—
610C2×C8—861no—
611C2×C8C2×C22⋊D4312yes—
612C4⋊C4—21no—
613C4⋊C4—21no—
614C4⋊C4—42no—
615C4⋊C4—432no—
616C4⋊C4—861no—
617C4⋊C4—861no—
618C4⋊C4—861no—
619C4⋊C4—861no—
620C4⋊C4—861no—
621C4⋊C4—1722no—
622C4⋊C4—1722no—
623C4⋊C4—1722no—
624C4⋊C4—1722no—
625C4⋊C4—1722no—
626C22⋊C4—42no—
627C22⋊C4—862no—
628C22⋊C4—862no—
629C22⋊C4—3441no—
630C22⋊C4—1722no—
631C22⋊C4—1722no—
632C22⋊C4—1722no—
633C42—861no—
634C42—861no—
635C42—861no—
636C42—861no—
637C42—1722no—
638C23—22no—
639C23—22no—
640C23—22no—
641C23—21no—
642C23—21no—
643C23—21no—
644C23—21no—
645C23—21no—
646C23—21no—
647C23—21no—
648C23—41no—
649C23—41no—
650C23—41no—
651C23—41no—
652C23C2×D4×D4311yescharacteristic
653Q8—22no—
654Q8—22no—
655Q8—22no—
656Q8—22no—
657Q8—41no—
658Q8—41no—
659Q8—41no—
660Q8—41no—
661Q8—1721no—
662Q8—1721no—
663Q8—1721no—
664Q8—1721no—
665D4—22no—
666D4—22no—
667D4—22no—
668D4—48no—
669D4#1306329714yes—
670C2×C4—21no—
671C2×C4—22no—
672C2×C4—21no—
673C2×C4—22no—
674C2×C4—21no—
675C2×C4—48no—
676C2×C4—41no—
677C2×C4—41no—
678C2×C4—41no—
679C2×C4—41no—
680C2×C4—41no—
681C2×C4—41no—
682C2×C4—41no—
683C2×C4—41no—
684C2×C4—41no—
685C2×C4—41no—
686C2×C4—41no—
687C2×C4—432no—
688C2×C4—432no—
689C2×C4—861no—
690C2×C4—861no—
691C2×C4—861no—
692C2×C4—861no—
693C2×C4—861no—
694C2×C4—861no—
695C2×C4—861no—
696C2×C4—861no—
697C2×C4—861no—
698C2×C4—862no—
699C2×C4—861no—
700C2×C4—3444no—
701C2×C4—3444no—
702C2×C4—1721no—
703C2×C4—1721no—
704C2×C4—1721no—
705C2×C4—1721no—
706C2×C4—1721no—
707C2×C4—1721no—
708C2×C4—1721no—
709C2×C4—1721no—
710C2×C4—1721no—
711C2×C4—1721no—
712C2×C4—1721no—
713C2×C4C2×D4×D4311yescharacteristic
714C2×C4C22×C22⋊D4311yescharacteristic
715C2×C4C2×#1062190011yescharacteristic
716C2×C4C2×#1062190011yescharacteristic
717C2×C4#1306337011yescharacteristic
718C2×C4#1306337011yescharacteristic
719C8—22no—
720C8—41no—
721C8—862no—
722C8—1721no—
723C22—24no—
724C22—42no—
725C22—42no—
726C22—42no—
727C22—42no—
728C22—42no—
729C22—42no—
730C22—41no—
731C22—41no—
732C22—41no—
733C22—41no—
734C22—41no—
735C22—41no—
736C22—41no—
737C22#1458340511yescharacteristic
738C22#1458353111yescharacteristic
739C22D4×C22⋊D4311yescharacteristic
740C22#135×D4311yescharacteristic
741C22#137×D4311yescharacteristic
742C22#1458370611yescharacteristic
743C22#1458371511yescharacteristic
744C4—41no—
745C4—42no—
746C4—42no—
747C4—81no—
748C4—862no—
749C4—862no—
750C4—3441no—
751C4—3441no—
752C4—3441no—
753C4—1721no—
754C4—1722no—
755C4—1721no—
756C4C2×#1306329711yescharacteristic
757C4#1458348411yescharacteristic
758C4#1458353611yescharacteristic
759C4#1458354311yescharacteristic
760C2—44no—
761C2—81no—
762C2#1913813511yescharacteristic
763C2#1914465911yescharacteristic
764C2#1914480211yescharacteristic
765C2#1914610311yescharacteristic
766C2#1914623511yescharacteristic
767C2#1914629611yescharacteristic
768C2#1914631011yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC2×C43×#452C2
socleC23×C43C22×D4
prime radicalC22×#41×C43C22
hypercenterC2×#452D43
hypocenterC43#25154
LCSG ▷ C22×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×#14583102C2semidirect
3. C2×SD16×Dic43C2semidirect
4. #19138196C2semidirect
6. #19135974C2semidirect
7. #19135795C2semidirect
8. #19135792C2semidirect
9. #19135693C2semidirect
10. #19135453C2semidirect
11. #19135204C2semidirect
12. #19134938C2semidirect
13. #19134927C2semidirect
14. #19134840C2semidirect
447. C43#25154semidirect

Maximal subgroups

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

subgroupindex
C2×#145831022
C2×#145830612
C2×SD16×Dic432
#191381962
#191374252
#191359742
#191357952
#191357922
#191356932
#191354532
#191352042
#191349382
#191349272
#191348402
C2×C43×#4522
#2515443