Finite Group Databasebeta

← #25140454

Subgroups — #25140454

Order 11008.

1156 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×C4×#10621884C211yesmaximal, characteristic, complemented
3C22⋊C4×D172C211yesmaximal, characteristic
4#19136129C211yesmaximal, characteristic, complemented
5#19136032C211yesmaximal, characteristic, complemented
6#19135910C211yesmaximal, characteristic, complemented
7#19135788C211yesmaximal, characteristic, complemented
8#19135277C211yesmaximal, characteristic, complemented
9#19135203C211yesmaximal, characteristic, complemented
10#19134950C211yesmaximal, characteristic, complemented
11#19134932C211yesmaximal, characteristic, complemented
12#19134855C211yesmaximal, 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—
23C4×#10621884—24no—
24C2×#13063256C2211yescharacteristic, complemented
25C2×#13063256C2211yescharacteristic, 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×C4×C43⋊C8C2211yescharacteristic, 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#13063256—22no—
98#13063256—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—
110C4×C43⋊C8—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—41no—
210C22⋊C4×C43—42no—
211C22⋊C4×C43—81no—
212C22⋊C4×C43SD1614yescomplemented
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×C43C2×SD1612yes—
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—21no—
282C2×C4×C43—22no—
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—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×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×C43C2×SD1612yes—
306C2×C4×C43C2×SD1612yes—
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#24901—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×C43C22×SD1611yescharacteristic
346C22×C43#57511yescharacteristic
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—22no—
366C4×C43—41no—
367C4×C43—42no—
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×C4×SD16—431no—
381#2423D4311yescharacteristic, complemented
382D4×C22⋊C4—431no—
383#2094—431no—
384#2077—431no—
385#2055—431no—
386#2035—431no—
387#1934—431no—
388#1923—431no—
389#1880—431no—
390#1877—431no—
391#1864—431no—
392#1802—431no—
393#1786—431no—
394C2×C43—42no—
395C2×C43#241811yescharacteristic
396C2×C43#310111yescharacteristic
397C2×C43#311811yescharacteristic
398C2×C43#326811yescharacteristic
399C2×C43D4×SD1611yescharacteristic
400C2×C43#329511yescharacteristic
401C2×C43#332311yescharacteristic
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—
413C4×SD16—864no—
414C2×#106—431no—
415C2×#106—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×C4×C8—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#2490111yescharacteristic, 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#106—862no—
508#106—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—
520C4×C8—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—41no—
617C22⋊C4—42no—
618C22⋊C4—81no—
619C22⋊C4—3441no—
620C22⋊C4—3441no—
621C22⋊C4—1722no—
622C22⋊C4—1722no—
623C22⋊C4—1722no—
624C22⋊C4—1722no—
625C22⋊C4—1722no—
626C22⋊C4#1062188414yescomplemented
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—
659C23C2×#1062188412yes—
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—22no—
685C2×C4—21no—
686C2×C4—21no—
687C2×C4—21no—
688C2×C4—41no—
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—3444no—
704C2×C4—3444no—
705C2×C4—1721no—
706C2×C4—1721no—
707C2×C4—1721no—
708C2×C4—1721no—
709C2×C4—1721no—
710C2×C4—1721no—
711C2×C4C2×#1062188412yes—
712C2×C4C2×#1062188412yes—
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
748C22C22×#1062188411yescharacteristic
749C22#1458369711yescharacteristic
750C22#1458370211yescharacteristic
751C22#1458370711yescharacteristic
752C4—22no—
753C4—22no—
754C4—41no—
755C4—42no—
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#1914459911yescharacteristic
772C2#1914477311yescharacteristic
773C2#1914613611yescharacteristic
774C2D4×#1062188411yescharacteristic
775C2#1914641311yescharacteristic
776C2#1914680511yescharacteristic
subgroupG/H
centerC23C22×C22⋊D43
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC43×#2423C2
socleC23×C43C22×D4
prime radicalC23×D172C22
hypercenter#2423D43
hypocenterC43#24901
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×C4×#10621884C2semidirect
4. #19136129C2semidirect
5. #19136032C2semidirect
6. #19135910C2semidirect
7. #19135788C2semidirect
8. #19135277C2semidirect
9. #19135203C2semidirect
10. #19134950C2semidirect
11. #19134932C2semidirect
12. #19134855C2semidirect
13. #19134592C2semidirect
15. C43×#2423C2semidirect
24. C2×#13063256C22semidirect
25. C2×#13063256C22semidirect
26. C2×C4⋊(C43⋊C8)C22semidirect
27. C2×#13063249C22semidirect
28. C2×#13063249C22semidirect
37. C2×C4×C43⋊C8C22semidirect
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
212. C22⋊C4×C43SD16semidirect
381. #2423D43semidirect
408. C2×C4×Q8C2×D43semidirect
430. #391C2×D43semidirect
433. #389C2×D43semidirect
438. #384C2×D43semidirect
449. C43#24901semidirect
626. C22⋊C4#10621884semidirect

Maximal subgroups

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

subgroupindex
C2×#145830492
C2×C4×#106218842
C22⋊C4×D1722
#191361292
#191360322
#191359102
#191357882
#191352772
#191352032
#191349502
#191349322
#191348552
#191345922
#191345252
C43×#24232
#2490143