Finite Group Databasebeta

← #25112341

Subgroups — #25112341

Order 11008.

1386 conjugacy classes of subgroups.

The subgroup lattice has 766 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×Q16×D43C211yesmaximal, characteristic
2C2×#14583004C211yesmaximal, characteristic, complemented
3C2×#14583003C211yesmaximal, characteristic, complemented
4#19137429C211yesmaximal, characteristic
5Q8×(C2×D43)⋊C4C211yesmaximal, characteristic
6#19135465C211yesmaximal, characteristic, complemented
7#19135463C211yesmaximal, characteristic, complemented
8#19134938C211yesmaximal, characteristic, complemented
9#19134937C211yesmaximal, characteristic, complemented
10#19134935C211yesmaximal, characteristic, complemented
11#19134619C211yesmaximal, characteristic
12#19134528C211yesmaximal, characteristic
13#19134528C211yesmaximal, characteristic
14#19134370C211yesmaximal, characteristic
15C43×#1878C211yesmaximal, characteristic, complemented
16C22×Q8×D43C2211yescharacteristic
17C22×Q8×D43C2211yescharacteristic
18C22×Dic172C2211yescharacteristic
19C22×#10621885C2211yescharacteristic
20C22×#10621885C2211yescharacteristic
21C2×Q16×D43—24no—
22C2×Q16×D43—24no—
23C2×Q16×D43C418yescomplemented
24C22×C8×D43C2211yescharacteristic
25C2×Q8×Dic43C2211yescharacteristic
26C2×C4×Dic86C2211yescharacteristic
27C2×#13063290C2211yescharacteristic
28#14583004—24no—
29#14583003—24no—
30C2×#13063256C2211yescharacteristic
31C2×#13063256C2211yescharacteristic
32C2×#13063250C2211yescharacteristic
33C2×#13063250C2211yescharacteristic
34C2×#13063249C2211yescharacteristic
35C2×#13063249C2211yescharacteristic
36C2×#13063248C2211yescharacteristic
37C2×#13063248C2211yescharacteristic
38C2×(C2×D43)⋊C8C2211yescharacteristic
39C2×#13063236C2211yescharacteristic
40C2×#13063235C2211yescharacteristic
41#14582806C2211yescharacteristic
42#14582805—21no—
43#14582805C2211yescharacteristic
44#14582804—21no—
45#14582804C2211yescharacteristic
46#14582803—21no—
47#14582803—21no—
48#14582758—21no—
49#14582756—21no—
50#14582756C2211yescharacteristic
51#14582756C2211yescharacteristic
52C4×(C2×D43)⋊C4—21no—
53C4×(C2×D43)⋊C4C2211yescharacteristic
54#14582746—21no—
55#14582662C2211yescharacteristic
56#14582653C2211yescharacteristic
57C22×Q16×C43C2211yescharacteristic
58C2×C4×Q8×C43C2211yescharacteristic
59C2×#103×C43C2211yescharacteristic
60C2×#103×C43C2211yescharacteristic
61C43×#391C2211yescharacteristic
62C43×#340C2211yescharacteristic
63C43×#336C2211yescharacteristic
64C22×Dic86—21no—
65C22×Dic86—21no—
66C22×Dic86C2311yescharacteristic
67C22×Dic86C2311yescharacteristic
68C2×Q8×D43—22no—
69C2×Q8×D43—22no—
70C2×Q8×D43—22no—
71C2×Q8×D43—22no—
72C2×Q8×D43—22no—
73C2×Q8×D43—22no—
74C2×Q8×D43—41no—
75C2×Q8×D43—41no—
76C2×Q8×D43—41no—
77C2×Q8×D43—41no—
78C2×Q8×D43C2×C414yes—
79C2×Q8×D43C2×C414yes—
80C22×C4×D43—21no—
81C22×C4×D43—21no—
82C22×C4×D43C2311yescharacteristic
83C2×Dic172—22no—
84C2×Dic172—22no—
85C2×Dic172C2×C414yes—
86C2×#10621885—22no—
87C2×#10621885—22no—
88C2×#10621885C2×C414yes—
89C2×#10621885C2×C414yes—
90C2×#10621885D414yes—
91C2×#10621885D414yes—
92Q16×D43—232no—
93C22×C43⋊C8C2311yescharacteristic
94C22×C43⋊C8C2311yescharacteristic
95C2×C8×D43—22no—
96C2×C8×D43—22no—
97C2×C8×D43C2×C414yes—
98Q8×Dic43—22no—
99Q8×Dic43—41no—
100C4×Dic86—22no—
101C4×Dic86—41no—
102#13063290—22no—
103#13063290—41no—
104C2×C4⋊Dic43—21no—
105C2×C4⋊Dic43C2311yescharacteristic
106C2×C4⋊Dic43C2311yescharacteristic
107C2×Dic43⋊C4—21no—
108C2×Dic43⋊C4—21no—
109C2×(C2×D43)⋊C4—21no—
110C2×(C2×D43)⋊C4—21no—
111C2×(C2×D43)⋊C4D411yescharacteristic
112C2×(C2×D43)⋊C4D411yescharacteristic
113C2×C4×Dic43—21no—
114C2×C4×Dic43—21no—
115C2×C4×Dic43—21no—
116C2×C4×Dic43C2311yescharacteristic
117#13063256—22no—
118#13063256—22no—
119#13063250—22no—
120#13063250—41no—
121#13063249—22no—
122#13063249—41no—
123#13063248—22no—
124#13063248—41no—
125(C2×D43)⋊C8—22no—
126#13063236—22no—
127#13063235—22no—
128C43⋊#95—21no—
129C43⋊#95—21no—
130C43⋊#95—21no—
131C43⋊#95—21no—
132C43⋊#95—21no—
133C43⋊#95—21no—
134C43⋊#95—21no—
135C43⋊#95—21no—
136C43⋊#95D411yescharacteristic
137C43⋊#95D411yescharacteristic
138C22×Q8×C43C2311yescharacteristic
139C22×Q8×C43C2311yescharacteristic
140C2×Q16×C43—22no—
141C2×Q16×C43—22no—
142C2×Q16×C43C2×C414yes—
143C22×C8×C43C2311yescharacteristic
144C22×C8×C43C2311yescharacteristic
145C4×Q8×C43—22no—
146C4×Q8×C43—41no—
147C2×C4⋊C4×C43—21no—
148C2×C4⋊C4×C43C2311yescharacteristic
149C2×C4⋊C4×C43C2311yescharacteristic
150C2×C42×C43—21no—
151C2×C42×C43C2311yescharacteristic
152#103×C43—22no—
153#103×C43—41no—
154#95×C43—21no—
155#95×C43—21no—
156C23×D43C2×D411yescharacteristic
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×C43C22×C412yes—
166C2×Q8×C43C22×C412yes—
167C2×Q8×C43C2×D412yes—
168C2×Q8×C43C2×D412yes—
169C22×C4×C43—21no—
170C22×C4×C43—21no—
171C22×C4×C43—21no—
172C22×C4×C43—21no—
173C22×C4×C43C2×D411yescharacteristic
174C22×C4×C43C2×D411yescharacteristic
175C22×C4×C43C2411yescharacteristic
176C22×Dic43—21no—
177C22×Dic43—21no—
178C22×Dic43—21no—
179C22×Dic43—21no—
180C22×Dic43C2×D411yescharacteristic
181C22×Dic43C2×D411yescharacteristic
182C22×Dic43C2×D411yescharacteristic
183Q8×D43—28no—
184Q8×D43—28no—
185Q8×D43—44no—
186Q8×D43—44no—
187Q8×D43—44no—
188Q8×D43—44no—
189Q8×D43—44no—
190Q8×D43—44no—
191C2×C4×D43—21no—
192C2×C4×D43—21no—
193C2×C4×D43—21no—
194C2×C4×D43—21no—
195C2×C4×D43—24no—
196C2×C4×D43—24no—
197C2×C4×D43—42no—
198C2×C4×D43—42no—
199C2×C4×D43—42no—
200C2×C4×D43—42no—
201C2×C4×D43C22×C412yes—
202C2×C4×D43#4112yes—
203C2×Dic86—21no—
204C2×Dic86—21no—
205C2×Dic86—21no—
206C2×Dic86—21no—
207C2×Dic86—21no—
208C2×Dic86—21no—
209C2×Dic86—21no—
210C2×Dic86—21no—
211C2×Dic86—24no—
212C2×Dic86—24no—
213C2×Dic86—42no—
214C2×Dic86—42no—
215C2×Dic86—42no—
216C2×Dic86—42no—
217C2×Dic86C22×C412yes—
218C2×Dic86C22×C412yes—
219C2×Dic86C2×D412yes—
220C2×Dic86C2×D412yes—
221Q16×C43—28no—
222C2×C8×C43—21no—
223C2×C8×C43—21no—
224C2×C8×C43—21no—
225C2×C8×C43—21no—
226C2×C8×C43—21no—
227C2×C8×C43C22×C412yes—
228C4⋊C4×C43—21no—
229C4⋊C4×C43—21no—
230C4⋊C4×C43—21no—
231C4⋊C4×C43—21no—
232C4⋊C4×C43—42no—
233C42×C43—21no—
234C42×C43—21no—
235C42×C43—42no—
236#10621885—28no—
237#10621885C22⋊C4116yescomplemented
238(C2×D43)⋊C4—22no—
239(C2×D43)⋊C4—22no—
240(C2×D43)⋊C4—42no—
241(C2×D43)⋊C4—42no—
242C4⋊Dic43—21no—
243C4⋊Dic43—21no—
244C4⋊Dic43—21no—
245C4⋊Dic43—21no—
246C4⋊Dic43—42no—
247Dic43⋊C4—42no—
248Dic43⋊C4—42no—
249C4×Dic43—21no—
250C4×Dic43—21no—
251C4×Dic43—42no—
252C4×Dic43—42no—
253C4×Dic43—42no—
254C2×C43⋊C8—21no—
255C2×C43⋊C8—21no—
256C2×C43⋊C8—21no—
257C2×C43⋊C8C22×C412yes—
258C2×C43⋊C8C2×D412yes—
259C2×C43⋊C8C2×D412yes—
260Dic172—28no—
261C8×D43—28no—
262C23×C43C22×D411yescharacteristic
263C22×D43—21no—
264C22×D43—21no—
265C22×D43—21no—
266C22×D43—21no—
267C22×D43C4×D412yes—
268C22×D43#13712yes—
269C22×D43#13712yes—
270Q8×C43—22no—
271Q8×C43—22no—
272Q8×C43—22no—
273Q8×C43—22no—
274Q8×C43—22no—
275Q8×C43—41no—
276Q8×C43—41no—
277Q8×C43C2×C22⋊C414yes—
278C2×C4×C43—22no—
279C2×C4×C43—22no—
280C2×C4×C43—22no—
281C2×C4×C43—22no—
282C2×C4×C43—21no—
283C2×C4×C43—21no—
284C2×C4×C43—21no—
285C2×C4×C43—21no—
286C2×C4×C43—21no—
287C2×C4×C43—21no—
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×C43C23×C411yescharacteristic
297C2×C4×C43C22×D411yescharacteristic
298C2×C4×C43C22×D411yescharacteristic
299C2×C4×C43C2×#4111yescharacteristic
300C2×C4×C43H(5,𝔽2)11yescharacteristic
301C2×C4×C43H(5,𝔽2)11yescharacteristic
302C2×Dic43—22no—
303C2×Dic43—22no—
304C2×Dic43—22no—
305C2×Dic43—21no—
306C2×Dic43—21no—
307C2×Dic43—22no—
308C2×Dic43—21no—
309C2×Dic43—21no—
310C2×Dic43—21no—
311C2×Dic43—21no—
312C2×Dic43—21no—
313C2×Dic43—21no—
314C2×Dic43—41no—
315C2×Dic43—41no—
316C2×Dic43—41no—
317C2×Dic43—41no—
318C2×Dic43—41no—
319C2×Dic43—41no—
320C2×Dic43—41no—
321C2×Dic43—41no—
322C2×Dic43C4×D412yes—
323C4×D43—22no—
324C4×D43—22no—
325C4×D43—22no—
326C4×D43—22no—
327C4×D43—48no—
328C4×D43—48no—
329Dic86—22no—
330Dic86—22no—
331Dic86—22no—
332Dic86—22no—
333Dic86—22no—
334Dic86—48no—
335Dic86—48no—
336Dic86—41no—
337Dic86—41no—
338Dic86C2×C22⋊C414yes—
339C8×C43—22no—
340C8×C43—41no—
341C43⋊C8—41no—
342C43⋊C8C2×C22⋊C414yes—
343#22440—431nomaximal, Sylow
344C22×C43C2×C4×D411yescharacteristic
345C22×C43D4211yescharacteristic
346C22×C43D4211yescharacteristic
347C22×C43C2×#13711yescharacteristic
348C22×C43C2×#13711yescharacteristic
349C22×C43#57811yescharacteristic
350C22×C43#57811yescharacteristic
351C2×D43—22no—
352C2×D43—22no—
353C2×D43—22no—
354C2×D43—22no—
355C2×D43—22no—
356C2×D43—22no—
357C2×D43#44114yescomplemented
358C4×C43—24no—
359C4×C43—42no—
360C4×C43—41no—
361C4×C43—41no—
362C4×C43—81no—
363C4×C43—81no—
364C4×C43C22×C22⋊C411yescharacteristic
365C4×C43#51811yescharacteristic
366C4×C43#54611yescharacteristic
367C4×C43#54611yescharacteristic
368Dic43—24no—
369Dic43—22no—
370Dic43—42no—
371Dic43—41no—
372Dic43—41no—
373Dic43—81no—
374Dic43—81no—
375C23×Q16—431no—
376C2×#441—431no—
377C2×#441—431no—
378Q8×C22⋊C4—431no—
379Q8×C22⋊C4—431no—
380#1971—431no—
381#1971—431no—
382#1878—431no—
383#1878—431no—
384#1878—431no—
385#1878D4311yescharacteristic, complemented
386#1807—431no—
387#1787—431no—
388#1787—431no—
389#1752—431no—
390C2×C43D4×C22⋊C411yescharacteristic
391C2×C43C2×#44111yescharacteristic
392C2×C43#295011yescharacteristic
393C2×C43#327011yescharacteristic
394C2×C43#327011yescharacteristic
395C2×C43#327011yescharacteristic
396C2×C43#327011yescharacteristic
397D43—24no—
398C23×Q8—431no—
399C23×Q8—431no—
400C22×Q16—431no—
401C22×Q16—431no—
402C22×Q16—438no—
403C22×Q16—431no—
404C22×Q16—864no—
405C22×Q16—864no—
406C22×Q16C2×D4311yescharacteristic
407C23×C8—431no—
408C2×C4×Q8—431no—
409C2×C4×Q8—431no—
410C2×C4×Q8—431no—
411C2×C4×Q8C2×D4311yescharacteristic
412#441—864no—
413#441—864no—
414C2×#106—431no—
415C2×#106—431no—
416C2×#103—431no—
417C2×#103—431no—
418C2×#103—431no—
419C2×#103—431no—
420C2×#103—431no—
421C2×#103—431no—
422C2×#103C2×D4311yescharacteristic
423C2×#103C2×D4311yescharacteristic
424C2×C22⋊C8—431no—
425C2×#97—431no—
426C2×#97—431no—
427#391—431no—
428#391—431no—
429#391—431no—
430#391—861no—
431#391—861no—
432#391—861no—
433#391—861no—
434#391C2×D4311yescharacteristic
435#380—431no—
436#380—431no—
437#380—861no—
438#380—861no—
439C4×C22⋊C4—431no—
440C4×C22⋊C4—861no—
441C4×C22⋊C4—861no—
442#340—431no—
443#340C2×D4311yescharacteristic
444#336—431no—
445#336C2×D4311yescharacteristic
446C43#2244011yescharacteristic, complemented, Sylow
447C22×Q8—434no—
448C22×Q8—434no—
449C22×Q8—431no—
450C22×Q8—431no—
451C22×Q8—861no—
452C22×Q8—861no—
453C22×Q8—862no—
454C22×Q8—862no—
455C22×Q8—862no—
456C22×Q8—862no—
457C22×Q8—862no—
458C22×Q8—862no—
459C22×Q8—1721no—
460C22×Q8—1721no—
461C22×Q8—1721no—
462C22×Q8—1721no—
463C22×Q8C22×D4311yescharacteristic
464C22×Q8C22×D4311yescharacteristic
465C23×C4—431no—
466C23×C4—861no—
467C23×C4—861no—
468C2×Q16—22no—
469C2×Q16—22no—
470C2×Q16—434no—
471C2×Q16—434no—
472C2×Q16—434no—
473C2×Q16—434no—
474C2×Q16—434no—
475C2×Q16—862no—
476C2×Q16—862no—
477C2×Q16—862no—
478C2×Q16—862no—
479C2×Q16—8632no—
480C2×Q16C4×D4314yes—
481C22×C8—431no—
482C22×C8—434no—
483C22×C8—431no—
484C22×C8—862no—
485C22×C8—862no—
486C22×C8C22×D4311yescharacteristic
487C22×C8C22×D4311yescharacteristic
488C4×Q8—22no—
489C4×Q8—41no—
490C4×Q8—862no—
491C4×Q8—862no—
492C4×Q8—862no—
493C4×Q8—1721no—
494C4×Q8—1721no—
495C4×Q8—1721no—
496C2×C4⋊C4—21no—
497C2×C4⋊C4—431no—
498C2×C4⋊C4—431no—
499C2×C4⋊C4—861no—
500C2×C4⋊C4—861no—
501C2×C4⋊C4—861no—
502C2×C4⋊C4C22×D4311yescharacteristic
503C2×C4⋊C4C22×D4311yescharacteristic
504C2×C22⋊C4—431no—
505C2×C22⋊C4—431no—
506C2×C22⋊C4—861no—
507C2×C22⋊C4—861no—
508C2×C42—21no—
509C2×C42—431no—
510C2×C42—861no—
511C2×C42—861no—
512C2×C42—861no—
513C2×C42C22×D4311yescharacteristic
514#106—862no—
515#106—862no—
516#103—22no—
517#103—41no—
518#103—862no—
519#103—862no—
520#103—862no—
521#103—1721no—
522#103—1721no—
523#103—1721no—
524C22⋊C8—862no—
525#97—862no—
526#97—862no—
527#95—21no—
528#95—21no—
529#95—431no—
530#95—431no—
531#95—861no—
532#95—861no—
533#95—861no—
534#95—861no—
535#95—861no—
536#95—861no—
537#95—861no—
538#95—861no—
539C24—431no—
540C2×Q8—21no—
541C2×Q8—21no—
542C2×Q8—21no—
543C2×Q8—21no—
544C2×Q8—21no—
545C2×Q8—21no—
546C2×Q8—21no—
547C2×Q8—21no—
548C2×Q8—432no—
549C2×Q8—432no—
550C2×Q8—432no—
551C2×Q8—432no—
552C2×Q8—864no—
553C2×Q8—864no—
554C2×Q8—861no—
555C2×Q8—861no—
556C2×Q8—861no—
557C2×Q8—861no—
558C2×Q8—868no—
559C2×Q8—868no—
560C2×Q8—861no—
561C2×Q8—861no—
562C2×Q8—861no—
563C2×Q8—861no—
564C2×Q8—1722no—
565C2×Q8—1722no—
566C2×Q8—1722no—
567C2×Q8—1722no—
568C2×Q8—1724no—
569C2×Q8—1724no—
570C2×Q8—1724no—
571C2×Q8—1724no—
572C2×Q8—1724no—
573C2×Q8—1724no—
574C2×Q8C2×C4×D4312yes—
575C2×Q8C2×C4×D4312yes—
576C2×Q8D4×D4312yes—
577C2×Q8D4×D4312yes—
578C22×C4—21no—
579C22×C4—21no—
580C22×C4—21no—
581C22×C4—21no—
582C22×C4—431no—
583C22×C4—432no—
584C22×C4—432no—
585C22×C4—431no—
586C22×C4—431no—
587C22×C4—864no—
588C22×C4—864no—
589C22×C4—861no—
590C22×C4—861no—
591C22×C4—861no—
592C22×C4—861no—
593C22×C4—861no—
594C22×C4—861no—
595C22×C4—861no—
596C22×C4—861no—
597C22×C4—1722no—
598C22×C4—1722no—
599C22×C4—1722no—
600C22×C4—1722no—
601C22×C4D4×D4311yescharacteristic
602C22×C4D4×D4311yescharacteristic
603C22×C4C23×D4311yescharacteristic
604Q16—28no—
605Q16—4316no—
606Q16—868no—
607Q16—868no—
608C2×C8—21no—
609C2×C8—21no—
610C2×C8—21no—
611C2×C8—21no—
612C2×C8—21no—
613C2×C8—432no—
614C2×C8—432no—
615C2×C8—432no—
616C2×C8—868no—
617C2×C8—861no—
618C2×C8—861no—
619C2×C8—861no—
620C2×C8C2×C4×D4312yes—
621C4⋊C4—21no—
622C4⋊C4—21no—
623C4⋊C4—21no—
624C4⋊C4—21no—
625C4⋊C4—42no—
626C4⋊C4—861no—
627C4⋊C4—861no—
628C4⋊C4—861no—
629C4⋊C4—861no—
630C4⋊C4—1722no—
631C4⋊C4—1722no—
632C4⋊C4—1722no—
633C22⋊C4—862no—
634C22⋊C4—862no—
635C22⋊C4—1722no—
636C22⋊C4—1722no—
637C42—21no—
638C42—21no—
639C42—42no—
640C42—861no—
641C42—861no—
642C42—1722no—
643C42—1722no—
644C42—1722no—
645C23—432no—
646C23—432no—
647C23—432no—
648C23—861no—
649C23—861no—
650C23—861no—
651C23—861no—
652C23C2×D4×D4311yescharacteristic
653Q8—22no—
654Q8—22no—
655Q8—22no—
656Q8—22no—
657Q8—22no—
658Q8—41no—
659Q8—41no—
660Q8—434no—
661Q8—862no—
662Q8—862no—
663Q8—862no—
664Q8—862no—
665Q8—862no—
666Q8—1728no—
667Q8—1728no—
668Q8—1721no—
669Q8—1721no—
670Q8C22⋊C4×D4314yes—
671C2×C4—22no—
672C2×C4—22no—
673C2×C4—22no—
674C2×C4—22no—
675C2×C4—21no—
676C2×C4—21no—
677C2×C4—21no—
678C2×C4—21no—
679C2×C4—21no—
680C2×C4—21no—
681C2×C4—41no—
682C2×C4—41no—
683C2×C4—41no—
684C2×C4—41no—
685C2×C4—41no—
686C2×C4—41no—
687C2×C4—41no—
688C2×C4—41no—
689C2×C4—432no—
690C2×C4—862no—
691C2×C4—862no—
692C2×C4—861no—
693C2×C4—862no—
694C2×C4—861no—
695C2×C4—862no—
696C2×C4—862no—
697C2×C4—862no—
698C2×C4—862no—
699C2×C4—862no—
700C2×C4—861no—
701C2×C4—861no—
702C2×C4—861no—
703C2×C4—861no—
704C2×C4—861no—
705C2×C4—861no—
706C2×C4—1728no—
707C2×C4—1728no—
708C2×C4—1721no—
709C2×C4—1721no—
710C2×C4—1721no—
711C2×C4—1721no—
712C2×C4—1721no—
713C2×C4—1721no—
714C2×C4—1721no—
715C2×C4—1721no—
716C2×C4C22×C4×D4311yescharacteristic
717C2×C4C2×D4×D4311yescharacteristic
718C2×C4C2×D4×D4311yescharacteristic
719C2×C4#41×D4311yescharacteristic
720C2×C4#1306337011yescharacteristic
721C2×C4#1306337111yescharacteristic
722C8—22no—
723C8—41no—
724C8—434no—
725C8—1721no—
726C22—434no—
727C22—862no—
728C22—862no—
729C22—862no—
730C22—862no—
731C22—862no—
732C22—862no—
733C22C4×D4×D4311yescharacteristic
734C22#1458353111yescharacteristic
735C22#1458353311yescharacteristic
736C22#137×D4311yescharacteristic
737C22#137×D4311yescharacteristic
738C22#1458371211yescharacteristic
739C22#1458371311yescharacteristic
740C4—24no—
741C4—42no—
742C4—41no—
743C4—41no—
744C4—81no—
745C4—81no—
746C4—862no—
747C4—864no—
748C4—3441no—
749C4—3441no—
750C4—1722no—
751C4—1721no—
752C4—1721no—
753C4C2×C22⋊C4×D4311yescharacteristic
754C4#1458337111yescharacteristic
755C4#1458353811yescharacteristic
756C4#1458354111yescharacteristic
757C2—864no—
758C2#1913741311yescharacteristic
759C2#441×D4311yescharacteristic
760C2#1914345811yescharacteristic
761C2#1914616011yescharacteristic
762C2#1914616311yescharacteristic
763C2#1914616811yescharacteristic
764C2#1914617111yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC43×#1878C2
socleC23×C43C22×D4
prime radicalC23×D43C2×D4
cosocleC22×C4×C43C24
hypercenter#1878D43
hypocenterC43#22440
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1878

Complements

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

NH ≅ G/Ntype
2. C2×#14583004C2semidirect
3. C2×#14583003C2semidirect
6. #19135465C2semidirect
7. #19135463C2semidirect
8. #19134938C2semidirect
9. #19134937C2semidirect
10. #19134935C2semidirect
15. C43×#1878C2semidirect
23. C2×Q16×D43C4semidirect
237. #10621885C22⋊C4semidirect
357. C2×D43#441semidirect
385. #1878D43semidirect
446. C43#22440semidirect

Maximal subgroups

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

subgroupindex
C22×Q16×D432
C2×#145830042
C2×#145830032
#191374292
Q8×(C2×D43)⋊C42
#191354652
#191354632
#191349382
#191349372
#191349352
#191346192
#191345282
#191343702
C43×#18782
#2244043