Finite Group Databasebeta

← #25140754

Subgroups — #25140754

Order 11008.

1150 conjugacy classes of subgroups.

The subgroup lattice has 778 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583049C211yesmaximal, characteristic
2C2×#14582997C211yesmaximal, characteristic, complemented
3C22⋊C4×D172C211yesmaximal, characteristic
4#19136124C211yesmaximal, characteristic, complemented
5#19136026C211yesmaximal, characteristic, complemented
6#19135910C211yesmaximal, characteristic, complemented
7#19135795C211yesmaximal, characteristic, complemented
8#19135291C211yesmaximal, characteristic, complemented
9#19135210C211yesmaximal, characteristic, complemented
10#19134950C211yesmaximal, characteristic, complemented
11#19134932C211yesmaximal, characteristic, complemented
12#19134841C211yesmaximal, characteristic, complemented
13#19134592C211yesmaximal, characteristic, complemented
14#19134525C211yesmaximal, characteristic
15C43×#2423C211yesmaximal, characteristic, complemented
16C23×D172C2211yescharacteristic
17C22×#10621884C2211yescharacteristic
18C22×#10621884C2211yescharacteristic
19C2×C4×D172C2211yescharacteristic
20C2×C4×D172C2211yescharacteristic
21C2×C22⋊C4×D43—21no—
22#14583049—24no—
23#14582997—24no—
24C2×#13063258C2211yescharacteristic, complemented
25C2×#13063258C2211yescharacteristic, complemented
26C2×C4⋊(C43⋊C8)C2211yescharacteristic, complemented
27C2×#13063249C2211yescharacteristic, complemented
28C2×#13063249C2211yescharacteristic, complemented
29C2×#13063245C2211yescharacteristic
30C2×#13063245C2211yescharacteristic
31C2×#13063245C2211yescharacteristic
32C2×#13063245C2211yescharacteristic
33C2×#13063245C2211yescharacteristic
34C2×#13063245C2211yescharacteristic
35C2×C22⋊(C43⋊C8)C2211yescharacteristic
36C2×C22⋊(C43⋊C8)C2211yescharacteristic
37C2×#13063236C2211yescharacteristic, complemented
38#14582801C2211yescharacteristic
39#14582801C2211yescharacteristic
40#14582777—21no—
41#14582777—21no—
42#14582759C2211yescharacteristic
43#14582754—21no—
44#14582661C2211yescharacteristic, complemented
45#14582661C2211yescharacteristic, complemented
46#14582661C2211yescharacteristic, complemented
47#14582661C2211yescharacteristic, complemented
48#14582654C2211yescharacteristic, complemented
49#14582654C2211yescharacteristic, complemented
50C2×C22⋊Q8×C43C2211yescharacteristic
51C2×C4×Q8×C43C2211yescharacteristic, complemented
52C43×#399—21no—
53C43×#398—21no—
54C43×#391C2211yescharacteristic, complemented
55C43×#389C2211yescharacteristic, complemented
56C43×#388—21no—
57C43×#387—21no—
58C43×#384C2211yescharacteristic, complemented
59C43×#380C2211yescharacteristic
60C4×C22⋊C4×C43C2211yescharacteristic
61C24×D43—21no—
62C22×D172—21no—
63C22×D172—22no—
64C22×D172—22no—
65C22×D172—22no—
66C22×D172—22no—
67C22×D172—41no—
68C22×D172—41no—
69C22×D172C2311yescharacteristic
70C22×D172C2311yescharacteristic
71C22×C4×D43—21no—
72C22×C4×D43—21no—
73C2×#10621884—22no—
74C2×#10621884—22no—
75C2×#10621884—22no—
76C2×#10621884—22no—
77C2×#10621884—41no—
78C2×#10621884D414yes—
79C22×C43⋊C8C2311yescharacteristic
80C22×C43⋊C8C2311yescharacteristic
81C22×C43⋊C8C2311yescharacteristic
82C22×C43⋊C8C2311yescharacteristic
83C4×D172—22no—
84C4×D172—22no—
85C4×D172—41no—
86C4×D172—41no—
87C2×C4⋊Dic43C2311yescharacteristic
88C2×C4⋊Dic43C2311yescharacteristic
89C2×C22⋊Dic43—21no—
90C2×(C2×D43)⋊C4—21no—
91C2×(C2×D43)⋊C4—21no—
92C2×(C2×D43)⋊C4—21no—
93C2×(C2×D43)⋊C4—21no—
94C2×(C2×D43)⋊C4—21no—
95C2×(C2×D43)⋊C4—21no—
96C22⋊C4×D43—44no—
97#13063258—22no—
98#13063258—41no—
99C4⋊(C43⋊C8)—41no—
100#13063249—22no—
101#13063249—41no—
102#13063245—22no—
103#13063245—22no—
104#13063245—22no—
105#13063245—22no—
106#13063245—22no—
107#13063245—41no—
108C22⋊(C43⋊C8)—22no—
109C22⋊(C43⋊C8)—41no—
110#13063236—22no—
111C43⋊#95—21no—
112C22×Q8×C43C2311yescharacteristic
113C23×C4×C43C2311yescharacteristic
114C22⋊Q8×C43—22no—
115C22⋊Q8×C43—41no—
116C4×Q8×C43—22no—
117C4×Q8×C43—41no—
118C2×C4⋊C4×C43—21no—
119C2×C4⋊C4×C43—21no—
120C2×C4⋊C4×C43—21no—
121C2×C4⋊C4×C43—21no—
122C2×C4⋊C4×C43—21no—
123C2×C4⋊C4×C43C2311yescharacteristic
124C2×C4⋊C4×C43C2311yescharacteristic
125C2×C4⋊C4×C43C2311yescharacteristic
126C2×C22⋊C4×C43—21no—
127C2×C22⋊C4×C43—21no—
128C2×C22⋊C4×C43D411yescharacteristic
129C2×C22⋊C4×C43D411yescharacteristic
130C2×C42×C43—21no—
131C2×C42×C43C2311yescharacteristic
132C2×C42×C43C2311yescharacteristic
133#95×C43—21no—
134#95×C43—21no—
135#95×C43—21no—
136#95×C43—21no—
137#95×C43D411yescharacteristic
138#95×C43D411yescharacteristic
139C24×C43C2×D411yescharacteristic
140C23×D43—21no—
141C23×D43—21no—
142C23×D43—24no—
143C23×D43—42no—
144C23×D43—42no—
145C23×D43—42no—
146C23×D43—42no—
147C23×D43—81no—
148C23×D43—81no—
149C2×Q8×C43—21no—
150C2×Q8×C43—21no—
151C2×Q8×C43—21no—
152C2×Q8×C43—21no—
153C2×Q8×C43—21no—
154C2×Q8×C43C2×D412yes—
155C22×C4×C43—21no—
156C22×C4×C43—21no—
157C22×C4×C43—21no—
158C22×C4×C43—21no—
159C22×C4×C43—21no—
160C22×C4×C43—21no—
161C22×C4×C43—21no—
162C22×C4×C43—21no—
163C22×C4×C43—21no—
164C22×C4×C43—21no—
165C22×C4×C43C2×D411yescharacteristic
166C22×C4×C43C2×D411yescharacteristic
167C22×C4×C43C2×D411yescharacteristic
168C22×C4×C43C2×D411yescharacteristic
169C22×C4×C43C2×D411yescharacteristic
170C22×C4×C43C2411yescharacteristic
171C22×Dic43—21no—
172C22×Dic43—21no—
173C2×D172—21no—
174C2×D172—21no—
175C2×D172—21no—
176C2×D172—24no—
177C2×D172—21no—
178C2×D172—21no—
179C2×D172—21no—
180C2×D172—21no—
181C2×D172—21no—
182C2×D172—42no—
183C2×D172—42no—
184C2×D172—44no—
185C2×D172—44no—
186C2×D172—44no—
187C2×D172—44no—
188C2×D172C2×D412yes—
189C2×D172#4112yes—
190C2×D172#4112yes—
191C2×D172#4112yes—
192C2×C4×D43—42no—
193C2×C4×D43—42no—
194C2×C4×D43—42no—
195C2×C4×D43—42no—
196C2×C4×D43—81no—
197C2×C4×D43—81no—
198C4⋊C4×C43—21no—
199C4⋊C4×C43—21no—
200C4⋊C4×C43—21no—
201C4⋊C4×C43—21no—
202C4⋊C4×C43—21no—
203C4⋊C4×C43—21no—
204C4⋊C4×C43—42no—
205C4⋊C4×C43—42no—
206C4⋊C4×C43—42no—
207C4⋊C4×C43—81no—
208C4⋊C4×C43—81no—
209C22⋊C4×C43—22no—
210C22⋊C4×C43—22no—
211C22⋊C4×C43—42no—
212C22⋊C4×C43—81no—
213C42×C43—21no—
214C42×C43—21no—
215C42×C43—21no—
216C42×C43—21no—
217C42×C43—42no—
218C22⋊Dic43—42no—
219#10621884—28no—
220#10621884—44no—
221(C2×D43)⋊C4—42no—
222(C2×D43)⋊C4—42no—
223(C2×D43)⋊C4—42no—
224(C2×D43)⋊C4—42no—
225(C2×D43)⋊C4—81no—
226(C2×D43)⋊C4—81no—
227C4⋊Dic43—21no—
228C4⋊Dic43—21no—
229C4⋊Dic43—21no—
230C4⋊Dic43—21no—
231C2×C43⋊C8—21no—
232C2×C43⋊C8—21no—
233C2×C43⋊C8—21no—
234C2×C43⋊C8—21no—
235C2×C43⋊C8—21no—
236C2×C43⋊C8—21no—
237C2×C43⋊C8—21no—
238C2×C43⋊C8—21no—
239C2×C43⋊C8—21no—
240C2×C43⋊C8—21no—
241C2×C43⋊C8—21no—
242C2×C43⋊C8C2×D412yes—
243C23×C43—21no—
244C23×C43—21no—
245C23×C43—21no—
246C23×C43—21no—
247C23×C43—21no—
248C23×C43—21no—
249C23×C43#13712yes—
250C23×C43C22×D411yescharacteristic
251C22×D43—22no—
252C22×D43—22no—
253C22×D43—22no—
254C22×D43—22no—
255C22×D43—48no—
256C22×D43—41no—
257C22×D43—41no—
258C22×D43—41no—
259C22×D43—41no—
260C22×D43—48no—
261C22×D43—41no—
262C22×D43—41no—
263C22×D43—41no—
264C22×D43—41no—
265C22×D43—41no—
266C22×D43—41no—
267C22×D43—84no—
268C22×D43—84no—
269C22×D43—84no—
270C22×D43—84no—
271C22×D43—84no—
272Q8×C43—22no—
273Q8×C43—22no—
274Q8×C43—41no—
275Q8×C43—41no—
276C2×C4×C43—21no—
277C2×C4×C43—21no—
278C2×C4×C43—21no—
279C2×C4×C43—21no—
280C2×C4×C43—21no—
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—21no—
289C2×C4×C43—21no—
290C2×C4×C43—21no—
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×C43—41no—
299C2×C4×C43—41no—
300C2×C4×C43—41no—
301C2×C4×C43—41no—
302C2×C4×C43—41no—
303C2×C4×C43—41no—
304C2×C4×C43—41no—
305C2×C4×C43—41no—
306C2×C4×C43AGL(1,ℤ/8)12yes—
307C2×C4×C43C22×D411yescharacteristic
308C2×C4×C43C2×#4111yescharacteristic
309C2×C4×C43C2×#4111yescharacteristic
310C2×C4×C43C2×#4111yescharacteristic
311C2×C4×C43H(5,𝔽2)11yescharacteristic
312C2×C4×C43H(5,𝔽2)11yescharacteristic
313C2×Dic43—41no—
314C2×Dic43—41no—
315C2×Dic43—41no—
316C2×Dic43—41no—
317C2×Dic43—41no—
318C2×Dic43—41no—
319D172—22no—
320D172—22no—
321D172—22no—
322D172—22no—
323D172—22no—
324D172—48no—
325D172—41no—
326D172—41no—
327D172#12314yes—
328C4×D43—84no—
329C4×D43—84no—
330C43⋊C8—22no—
331C43⋊C8—41no—
332C43⋊C8—41no—
333C43⋊C8—41no—
334#24921—431nomaximal, Sylow
335C22×C43—22no—
336C22×C43—22no—
337C22×C43—22no—
338C22×C43—41no—
339C22×C43—41no—
340C22×C43—41no—
341C22×C43—41no—
342C22×C43#52511yescharacteristic
343C22×C43D4211yescharacteristic
344C22×C43#54611yescharacteristic
345C22×C43C2×AGL(1,ℤ/8)11yescharacteristic
346C22×C43C2×#13711yescharacteristic
347C22×C43#57611yescharacteristic
348C22×C43#57711yescharacteristic
349C2×D43—24no—
350C2×D43—42no—
351C2×D43—42no—
352C2×D43—42no—
353C2×D43—42no—
354C2×D43—42no—
355C2×D43—42no—
356C2×D43—42no—
357C2×D43—42no—
358C2×D43—42no—
359C2×D43—816no—
360C2×D43—81no—
361C2×D43—81no—
362C2×D43—81no—
363C2×D43—81no—
364C4×C43—22no—
365C4×C43—41no—
366C4×C43—42no—
367C4×C43—41no—
368C4×C43—41no—
369C4×C43—41no—
370C4×C43—81no—
371C4×C43—81no—
372C4×C43—81no—
373C4×C43C2×#12311yescharacteristic
374C4×C43#53811yescharacteristic
375C4×C43#54611yescharacteristic
376C4×C43#55111yescharacteristic
377Dic43—81no—
378Dic43—81no—
379C2×#450—431no—
380C2×#440—431no—
381#2423D4311yescharacteristic, complemented
382D4×C22⋊C4—431no—
383#2093—431no—
384#2076—431no—
385#2055—431no—
386#2036—431no—
387#1936—431no—
388#1924—431no—
389#1880—431no—
390#1877—431no—
391#1862—431no—
392#1802—431no—
393#1786—431no—
394C2×C43—42no—
395C2×C43#241811yescharacteristic
396C2×C43#311011yescharacteristic
397C2×C43#311811yescharacteristic
398C2×C43#326611yescharacteristic
399C2×C43#327411yescharacteristic
400C2×C43#331011yescharacteristic
401C2×C43#331411yescharacteristic
402D43—44no—
403D43—82no—
404C23×D4—431no—
405C22×SD16—431no—
406C22×SD16—431no—
407C2×C22⋊Q8C2×D4311yescharacteristic
408C2×C4×Q8C2×D4311yescharacteristic, complemented
409C2×C4×D4—431no—
410C2×C4×D4—431no—
411C22×C22⋊C4—861no—
412#450—864no—
413#440—864no—
414C2×#107—431no—
415C2×#107—431no—
416C2×C4⋊C8—431no—
417C2×#103—431no—
418C2×#103—431no—
419C2×#102—431no—
420C2×#102—431no—
421C2×#102—431no—
422C2×#102—431no—
423C2×#102—431no—
424C2×#102—431no—
425C2×C22⋊C8—431no—
426C2×C22⋊C8—431no—
427C2×#97—431no—
428#399—21no—
429#398—21no—
430#391C2×D4311yescharacteristic, complemented
431#390—431no—
432#390—431no—
433#389C2×D4311yescharacteristic, complemented
434#388—21no—
435#387—21no—
436#386—861no—
437#386—861no—
438#384C2×D4311yescharacteristic, complemented
439#380—431no—
440#380C2×D4311yescharacteristic
441#379—861no—
442C4×C22⋊C4C2×D4311yescharacteristic
443#340—431no—
444#340—431no—
445#340—431no—
446#340—431no—
447#336—431no—
448#336—431no—
449C43#2492111yescharacteristic, complemented, Sylow
450C25—861no—
451C22×Q8C22×D4311yescharacteristic
452C22×D4—431no—
453C22×D4—431no—
454C22×D4—862no—
455C22×D4—862no—
456C22×D4—862no—
457C22×D4—862no—
458C22×D4—861no—
459C22×D4—1721no—
460C22×D4—1721no—
461C23×C4—861no—
462C23×C4—861no—
463C23×C4C22×D4311yescharacteristic
464C2×SD16—434no—
465C2×SD16—862no—
466C2×SD16—862no—
467C2×SD16—862no—
468C2×SD16—862no—
469C2×SD16—1721no—
470C22×C8—431no—
471C22×C8—431no—
472C22×C8—431no—
473C22×C8—431no—
474C22⋊Q8—22no—
475C22⋊Q8—41no—
476C4×Q8—22no—
477C4×Q8—41no—
478C4×D4—862no—
479C4×D4—862no—
480C4×D4—1721no—
481C4×D4—1721no—
482C2×C4⋊C4—21no—
483C2×C4⋊C4—21no—
484C2×C4⋊C4—21no—
485C2×C4⋊C4—21no—
486C2×C4⋊C4—21no—
487C2×C4⋊C4—431no—
488C2×C4⋊C4—431no—
489C2×C4⋊C4C22×D4311yescharacteristic
490C2×C4⋊C4C22×D4311yescharacteristic
491C2×C4⋊C4C22×D4311yescharacteristic
492C2×C22⋊C4—21no—
493C2×C22⋊C4—21no—
494C2×C22⋊C4—861no—
495C2×C22⋊C4—861no—
496C2×C22⋊C4—861no—
497C2×C22⋊C4—861no—
498C2×C22⋊C4—861no—
499C2×C22⋊C4—861no—
500C2×C22⋊C4—861no—
501C2×C22⋊C4—1724no—
502C2×C22⋊C4C22⋊D4311yescharacteristic
503C2×C22⋊C4C22⋊D4311yescharacteristic
504C2×C42—21no—
505C2×C42C22×D4311yescharacteristic
506C2×C42C22×D4311yescharacteristic
507#107—862no—
508#107—1721no—
509C4⋊C8—1721no—
510#103—862no—
511#103—1721no—
512#102—862no—
513#102—862no—
514#102—862no—
515#102—862no—
516#102—862no—
517#102—1721no—
518C22⋊C8—862no—
519C22⋊C8—1721no—
520#97—862no—
521#95—21no—
522#95—21no—
523#95—21no—
524#95—21no—
525#95—861no—
526#95C22⋊D4311yescharacteristic
527#95C22⋊D4311yescharacteristic
528C24—864no—
529C24—861no—
530C24—861no—
531C24—3441no—
532C24—3441no—
533C24—1722no—
534C24—1722no—
535C24—1722no—
536C24—1722no—
537C24C2×C22⋊D4311yescharacteristic
538C2×Q8—21no—
539C2×Q8—21no—
540C2×Q8—21no—
541C2×Q8—21no—
542C2×Q8—21no—
543C2×Q8D4×D4312yes—
544C2×D4—432no—
545C2×D4—432no—
546C2×D4—432no—
547C2×D4—432no—
548C2×D4—864no—
549C2×D4—861no—
550C2×D4—861no—
551C2×D4—861no—
552C2×D4—861no—
553C2×D4—861no—
554C2×D4—861no—
555C2×D4—861no—
556C2×D4—861no—
557C2×D4—1722no—
558C2×D4—1722no—
559C2×D4—1724no—
560C2×D4—1724no—
561C2×D4—1724no—
562C2×D4—1724no—
563C22×C4—21no—
564C22×C4—21no—
565C22×C4—21no—
566C22×C4—21no—
567C22×C4—21no—
568C22×C4—21no—
569C22×C4—21no—
570C22×C4—21no—
571C22×C4—21no—
572C22×C4—21no—
573C22×C4—861no—
574C22×C4—861no—
575C22×C4—3441no—
576C22×C4—3441no—
577C22×C4—1722no—
578C22×C4—1722no—
579C22×C4—1722no—
580C22×C4—1722no—
581C22×C4C2×C22⋊D4311yescharacteristic
582C22×C4C2×C22⋊D4311yescharacteristic
583C22×C4C2×C22⋊D4311yescharacteristic
584C22×C4C2×C22⋊D4311yescharacteristic
585C22×C4C2×C22⋊D4311yescharacteristic
586C22×C4C23×D4311yescharacteristic
587SD16—868no—
588SD16—1724no—
589C2×C8—432no—
590C2×C8—861no—
591C2×C8—861no—
592C2×C8—861no—
593C2×C8—861no—
594C2×C8—861no—
595C2×C8—861no—
596C2×C8—861no—
597C2×C8—861no—
598C2×C8—861no—
599C2×C8—861no—
600C2×C8—861no—
601C4⋊C4—21no—
602C4⋊C4—21no—
603C4⋊C4—21no—
604C4⋊C4—21no—
605C4⋊C4—21no—
606C4⋊C4—21no—
607C4⋊C4—42no—
608C4⋊C4—42no—
609C4⋊C4—42no—
610C4⋊C4—81no—
611C4⋊C4—81no—
612C4⋊C4—861no—
613C4⋊C4—861no—
614C4⋊C4—861no—
615C4⋊C4—861no—
616C22⋊C4—22no—
617C22⋊C4—22no—
618C22⋊C4—42no—
619C22⋊C4—81no—
620C22⋊C4—3441no—
621C22⋊C4—3441no—
622C22⋊C4—1722no—
623C22⋊C4—1722no—
624C22⋊C4—1722no—
625C22⋊C4—1722no—
626C22⋊C4—1722no—
627C42—21no—
628C42—21no—
629C42—21no—
630C42—21no—
631C42—42no—
632C23—21no—
633C23—21no—
634C23—21no—
635C23—21no—
636C23—21no—
637C23—21no—
638C23—862no—
639C23—862no—
640C23—862no—
641C23—862no—
642C23—3444no—
643C23—3444no—
644C23—3444no—
645C23—3444no—
646C23—3444no—
647C23—1728no—
648C23—1728no—
649C23—1721no—
650C23—1721no—
651C23—1721no—
652C23—1721no—
653C23—1721no—
654C23—1721no—
655C23—1721no—
656C23—1721no—
657C23—1721no—
658C23—1721no—
659C23#1306335612yes—
660C23C22×C22⋊D4311yescharacteristic
661Q8—22no—
662Q8—22no—
663Q8—41no—
664Q8—41no—
665D4—434no—
666D4—862no—
667D4—862no—
668D4—862no—
669D4—862no—
670D4—862no—
671D4—1728no—
672D4—1721no—
673D4—1721no—
674C2×C4—21no—
675C2×C4—21no—
676C2×C4—21no—
677C2×C4—21no—
678C2×C4—21no—
679C2×C4—21no—
680C2×C4—21no—
681C2×C4—21no—
682C2×C4—21no—
683C2×C4—21no—
684C2×C4—21no—
685C2×C4—22no—
686C2×C4—21no—
687C2×C4—21no—
688C2×C4—21no—
689C2×C4—41no—
690C2×C4—41no—
691C2×C4—41no—
692C2×C4—41no—
693C2×C4—41no—
694C2×C4—41no—
695C2×C4—41no—
696C2×C4—41no—
697C2×C4—41no—
698C2×C4—41no—
699C2×C4—41no—
700C2×C4—41no—
701C2×C4—41no—
702C2×C4—41no—
703C2×C4—41no—
704C2×C4—3444no—
705C2×C4—3444no—
706C2×C4—1721no—
707C2×C4—1721no—
708C2×C4—1721no—
709C2×C4—1721no—
710C2×C4—1721no—
711C2×C4—1721no—
712C2×C4#1306335012yes—
713C2×C4C2×D4×D4311yescharacteristic
714C2×C4#41×D4311yescharacteristic
715C2×C4#41×D4311yescharacteristic
716C2×C4#41×D4311yescharacteristic
717C2×C4#1306337011yescharacteristic
718C2×C4#1306337111yescharacteristic
719C8—862no—
720C8—1721no—
721C8—1721no—
722C8—1721no—
723C22—22no—
724C22—22no—
725C22—22no—
726C22—41no—
727C22—41no—
728C22—41no—
729C22—41no—
730C22—864no—
731C22—34416no—
732C22—3441no—
733C22—3441no—
734C22—3441no—
735C22—3441no—
736C22—1722no—
737C22—1722no—
738C22—1722no—
739C22—1722no—
740C22—1722no—
741C22—1722no—
742C22—1722no—
743C22—1722no—
744C22—1722no—
745C22#1458340611yescharacteristic
746C22D4×C22⋊D4311yescharacteristic
747C22#1458353711yescharacteristic
748C22C2×#1306335011yescharacteristic
749C22C2×#1306335611yescharacteristic
750C22#1458370211yescharacteristic
751C22#1458370711yescharacteristic
752C4—22no—
753C4—41no—
754C4—42no—
755C4—41no—
756C4—41no—
757C4—41no—
758C4—81no—
759C4—81no—
760C4—81no—
761C4—3441no—
762C4—3441no—
763C4#123×D4311yescharacteristic
764C4#1458348511yescharacteristic
765C4#1458354111yescharacteristic
766C4#1458357711yescharacteristic
767C2—42no—
768C2—3442no—
769C2—1724no—
770C2#1913805411yescharacteristic
771C2#1914469011yescharacteristic
772C2#1914477311yescharacteristic
773C2#1914610611yescharacteristic
774C2#1914621511yescharacteristic
775C2#1914661011yescharacteristic
776C2#1914667011yescharacteristic
subgroupG/H
centerC23C22×C22⋊D43
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC43×#2423C2
socleC23×C43C22×D4
prime radicalC23×D172C22
hypercenter#2423D43
hypocenterC43#24921
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C4×C22⋊C4 ◁ #2423

Complements

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

NH ≅ G/Ntype
2. C2×#14582997C2semidirect
4. #19136124C2semidirect
5. #19136026C2semidirect
6. #19135910C2semidirect
7. #19135795C2semidirect
8. #19135291C2semidirect
9. #19135210C2semidirect
10. #19134950C2semidirect
11. #19134932C2semidirect
12. #19134841C2semidirect
13. #19134592C2semidirect
15. C43×#2423C2semidirect
24. C2×#13063258C22semidirect
25. C2×#13063258C22semidirect
26. C2×C4⋊(C43⋊C8)C22semidirect
27. C2×#13063249C22semidirect
28. C2×#13063249C22semidirect
37. C2×#13063236C22semidirect
44. #14582661C22semidirect
45. #14582661C22semidirect
46. #14582661C22semidirect
47. #14582661C22semidirect
48. #14582654C22semidirect
49. #14582654C22semidirect
51. C2×C4×Q8×C43C22semidirect
54. C43×#391C22semidirect
55. C43×#389C22semidirect
58. C43×#384C22semidirect
381. #2423D43semidirect
408. C2×C4×Q8C2×D43semidirect
430. #391C2×D43semidirect
433. #389C2×D43semidirect
438. #384C2×D43semidirect
449. C43#24921semidirect

Maximal subgroups

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

subgroupindex
C2×#145830492
C2×#145829972
C22⋊C4×D1722
#191361242
#191360262
#191359102
#191357952
#191352912
#191352102
#191349502
#191349322
#191348412
#191345922
#191345252
C43×#24232
#2492143