Finite Group Databasebeta

← #25117290

Subgroups — #25117290

Order 11008.

1190 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×#14583042C211yesmaximal, characteristic
2C2×C4×#10621883C211yesmaximal, characteristic, complemented
3C2×#14582898C211yesmaximal, characteristic, complemented
4#19137435C211yesmaximal, characteristic, complemented
5#19135470C211yesmaximal, characteristic, complemented
6#19135277C211yesmaximal, characteristic, complemented
7#19135222C211yesmaximal, characteristic, complemented
8#19135034C211yesmaximal, characteristic, complemented
9#19134953C211yesmaximal, characteristic, complemented
10#19134943C211yesmaximal, characteristic, complemented
11#19134862C211yesmaximal, characteristic, complemented
12#19134788C211yesmaximal, characteristic, complemented
13#19134428C211yesmaximal, characteristic, complemented
14#19134379C211yesmaximal, characteristic, complemented
15C43×#2361C211yesmaximal, characteristic, complemented
16C22×#10621898C2211yescharacteristic
17C22×#10621883C2211yescharacteristic
18C22×#10621882C2211yescharacteristic
19C22×#10621877C2211yescharacteristic
20C2×C4×Dic86C2211yescharacteristic
21C2×C4×Dic86C2211yescharacteristic
22#14583042C418yescomplemented
23C4×#10621883—24no—
24C2×#13063256C2211yescharacteristic
25C2×#13063256C2211yescharacteristic
26#14582898—24no—
27C2×#13063248C2211yescharacteristic
28C2×#13063248C2211yescharacteristic
29C2×#13063248C2211yescharacteristic
30C2×#13063246C2211yescharacteristic
31C2×#13063246C2211yescharacteristic
32C2×#13063245C2211yescharacteristic
33C2×#13063245C2211yescharacteristic
34C2×#13063245C2211yescharacteristic
35C2×C22⋊(C43⋊C8)C2211yescharacteristic
36C2×#13063236C2211yescharacteristic
37C2×C4×C43⋊C8C2211yescharacteristic
38#14582801C2211yescharacteristic
39#14582801C2211yescharacteristic
40#14582799—21no—
41#14582799—21no—
42#14582759C2211yescharacteristic
43#14582758—21no—
44#14582746—21no—
45#14582661C2211yescharacteristic
46#14582661C2211yescharacteristic
47#14582661C2211yescharacteristic
48#14582661C2211yescharacteristic
49#14582654C2211yescharacteristic
50#14582654C2211yescharacteristic
51C2×#121×C43C2211yescharacteristic
52C2×C4×D4×C43—21no—
53C2×C4×D4×C43C2211yescharacteristic
54C22×C4⋊C4×C43C2211yescharacteristic
55C43×#390C2211yescharacteristic
56C43×#389C2211yescharacteristic
57C43×#388—21no—
58C43×#386—21no—
59C43×#385—21no—
60C4×C4⋊C4×C43C2211yescharacteristic
61C4×C22⋊C4×C43C2211yescharacteristic
62C2×#10621898—22no—
63C2×#10621898—22no—
64C2×#10621898—22no—
65C2×#10621898—41no—
66C2×#10621898—41no—
67C2×#10621898C2×C414yescomplemented
68C22×Dic86C2311yescharacteristic
69C22×D172C2311yescharacteristic
70C22×C22⋊D43—21no—
71C22×C4×D43—21no—
72C2×#10621883—22no—
73C2×#10621883—22no—
74C2×#10621883C2×C414yescomplemented
75C2×#10621882—41no—
76C2×#10621882—41no—
77C2×#10621882C2×C414yescomplemented
78C2×#10621877—22no—
79C2×#10621877—22no—
80C2×#10621877—41no—
81C22×C43⋊C8C2311yescharacteristic
82C22×C43⋊C8C2311yescharacteristic
83C22×C43⋊C8C2311yescharacteristic
84C22×C43⋊C8C2311yescharacteristic
85C4×Dic86—22no—
86C4×Dic86—22no—
87C4×Dic86—41no—
88C4×Dic86—41no—
89C2×C4⋊Dic43C2311yescharacteristic
90C2×C4⋊Dic43C2311yescharacteristic
91C2×Dic43⋊C4—21no—
92C2×Dic43⋊C4—21no—
93C2×C22⋊Dic43—21no—
94C2×(C2×D43)⋊C4—21no—
95C2×(C2×D43)⋊C4—21no—
96C2×(C2×D43)⋊C4—21no—
97C2×(C2×D43)⋊C4—21no—
98C2×C4×Dic43—21no—
99C2×C4×Dic43—21no—
100#13063256—22no—
101#13063256—41no—
102#13063248—22no—
103#13063248C2×C414yescomplemented
104#13063248D414yescomplemented
105#13063246—22no—
106#13063246—41no—
107#13063245—22no—
108#13063245—22no—
109#13063245C2×C414yescomplemented
110C22⋊(C43⋊C8)C2×C414yescomplemented
111#13063236—41no—
112C4×C43⋊C8—22no—
113C43⋊#95—21no—
114C22×D4×C43—21no—
115C22×D4×C43C2311yescharacteristic
116C23×C4×C43—21no—
117C23×C4×C43—21no—
118C23×C4×C43C2311yescharacteristic
119#121×C43—22no—
120#121×C43C2×C414yes—
121C4×D4×C43—22no—
122C4×D4×C43—41no—
123C4×D4×C43—44no—
124C2×C4⋊C4×C43—22no—
125C2×C4⋊C4×C43—21no—
126C2×C4⋊C4×C43—21no—
127C2×C4⋊C4×C43—41no—
128C2×C4⋊C4×C43C2311yescharacteristic
129C2×C4⋊C4×C43C2311yescharacteristic
130C2×C4⋊C4×C43C2311yescharacteristic
131C2×C22⋊C4×C43—21no—
132C2×C22⋊C4×C43—21no—
133C2×C22⋊C4×C43—21no—
134C2×C22⋊C4×C43—21no—
135C2×C22⋊C4×C43D411yescharacteristic
136C2×C22⋊C4×C43D411yescharacteristic
137C2×C42×C43—21no—
138C2×C42×C43C2311yescharacteristic
139C2×C42×C43C2311yescharacteristic
140#95×C43—21no—
141#95×C43—21no—
142#95×C43D411yescharacteristic
143#95×C43D411yescharacteristic
144C24×C43—21no—
145C24×C43C2×D411yescharacteristic
146C23×D43—21no—
147C2×D4×C43—21no—
148C2×D4×C43—24no—
149C2×D4×C43—21no—
150C2×D4×C43—21no—
151C2×D4×C43—21no—
152C2×D4×C43—21no—
153C2×D4×C43—42no—
154C2×D4×C43—42no—
155C2×D4×C43C22×C412yes—
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—42no—
164C22×C4×C43—42no—
165C22×C4×C43—42no—
166C22×C4×C43—42no—
167C22×C4×C43—81no—
168C22×C4×C43—81no—
169C22×C4×C43C22×C412yes—
170C22×C4×C43C2×D411yescharacteristic
171C22×C4×C43C2×D411yescharacteristic
172C22×C4×C43C2×D411yescharacteristic
173C22×C4×C43C2×D411yescharacteristic
174C22×C4×C43C2×D411yescharacteristic
175C22×C4×C43#4112yes—
176C22×C4×C43C2411yescharacteristic
177C2×C22⋊D43—24no—
178C2×C22⋊D43—42no—
179C2×C22⋊D43—42no—
180C22×Dic43—21no—
181C22×Dic43—21no—
182C22×Dic43—21no—
183#10621898—28no—
184#10621898—44no—
185#10621898—44no—
186#10621898—44no—
187C2×D172—21no—
188C2×D172—21no—
189C2×D172—21no—
190C2×D172—21no—
191C2×D172—21no—
192C2×D172C22×C412yes—
193C2×C4×D43—24no—
194C2×C4×D43—42no—
195C2×C4×D43—42no—
196C2×Dic86—21no—
197C2×Dic86—21no—
198C2×Dic86—21no—
199C2×Dic86C22×C412yes—
200C2×Dic86C2×D412yes—
201C2×Dic86#4112yes—
202C4⋊C4×C43—21no—
203C4⋊C4×C43—21no—
204C4⋊C4×C43—21no—
205C4⋊C4×C43—21no—
206C4⋊C4×C43—42no—
207C4⋊C4×C43—42no—
208C4⋊C4×C43C22×C412yes—
209C4⋊C4×C43C2×D412yes—
210C22⋊C4×C43—24no—
211C22⋊C4×C43—22no—
212C22⋊C4×C43—41no—
213C22⋊C4×C43—42no—
214C22⋊C4×C43—42no—
215C22⋊C4×C43—81no—
216C42×C43—21no—
217C42×C43—21no—
218C42×C43—21no—
219C42×C43—21no—
220C42×C43—42no—
221C22⋊Dic43—81no—
222#10621883—28no—
223#10621882—44no—
224(C2×D43)⋊C4—42no—
225(C2×D43)⋊C4—42no—
226(C2×D43)⋊C4—81no—
227(C2×D43)⋊C4—81no—
228C4⋊Dic43—21no—
229C4⋊Dic43—21no—
230C4⋊Dic43—21no—
231C4⋊Dic43—21no—
232Dic43⋊C4—42no—
233Dic43⋊C4—42no—
234C4×Dic43—42no—
235C4×Dic43—42no—
236#10621877—44no—
237C2×C43⋊C8—21no—
238C2×C43⋊C8—21no—
239C2×C43⋊C8—21no—
240C2×C43⋊C8—21no—
241C2×C43⋊C8—21no—
242C2×C43⋊C8—21no—
243C2×C43⋊C8—21no—
244C2×C43⋊C8—21no—
245C2×C43⋊C8—21no—
246C2×C43⋊C8C22×C412yes—
247C2×C43⋊C8C22×C412yes—
248C2×C43⋊C8C2×D412yes—
249C23×C43—21no—
250C23×C43—21no—
251C23×C43—21no—
252C23×C43—21no—
253C23×C43—21no—
254C23×C43—21no—
255C23×C43—22no—
256C23×C43—41no—
257C23×C43—41no—
258C23×C43—41no—
259C23×C43—41no—
260C23×C43—41no—
261C23×C43—41no—
262C23×C43C4×D412yes—
263C23×C43C22×D411yescharacteristic
264C22×D43—22no—
265C22×D43—41no—
266C22×D43—41no—
267C22×D43—41no—
268C22×D43—41no—
269C22×D43—41no—
270C22×D43—41no—
271D4×C43—22no—
272D4×C43—22no—
273D4×C43—48no—
274D4×C43—41no—
275D4×C43—41no—
276C2×C4×C43—21no—
277C2×C4×C43—21no—
278C2×C4×C43—21no—
279C2×C4×C43—21no—
280C2×C4×C43—22no—
281C2×C4×C43—22no—
282C2×C4×C43—22no—
283C2×C4×C43—22no—
284C2×C4×C43—22no—
285C2×C4×C43—21no—
286C2×C4×C43—22no—
287C2×C4×C43—21no—
288C2×C4×C43—21no—
289C2×C4×C43—21no—
290C2×C4×C43—21no—
291C2×C4×C43—21no—
292C2×C4×C43—21no—
293C2×C4×C43—21no—
294C2×C4×C43—21no—
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—84no—
303C2×C4×C43—84no—
304C2×C4×C43C4×D412yes—
305C2×C4×C43AGL(1,ℤ/8)12yes—
306C2×C4×C43C23×C411yescharacteristic
307C2×C4×C43C22×D411yescharacteristic
308C2×C4×C43C2×#4111yescharacteristic
309C2×C4×C43C2×#4111yescharacteristic
310C2×C4×C43H(5,𝔽2)11yescharacteristic
311C2×C4×C43H(5,𝔽2)11yescharacteristic
312C22⋊D43—48no—
313C2×Dic43—22no—
314C2×Dic43—22no—
315C2×Dic43—22no—
316C2×Dic43—41no—
317C2×Dic43—41no—
318C2×Dic43—41no—
319C2×Dic43—41no—
320C2×Dic43—41no—
321C2×Dic43—41no—
322D172—22no—
323D172—22no—
324D172—41no—
325D172—41no—
326C4×D43—48no—
327Dic86—22no—
328Dic86—22no—
329Dic86—22no—
330Dic86C4×D414yescomplemented
331C43⋊C8—22no—
332C43⋊C8—22no—
333C43⋊C8—22no—
334C43⋊C8—41no—
335#22883—431nomaximal, Sylow
336C22×C43—22no—
337C22×C43—22no—
338C22×C43—22no—
339C22×C43—41no—
340C22×C43—41no—
341C22×C43—41no—
342C22×C43—41no—
343C22×C43—42no—
344C22×C43—42no—
345C22×C43—42no—
346C22×C43—81no—
347C22×C43—81no—
348C22×C43—81no—
349C22×C43—81no—
350C22×C43C2×C4×D411yescharacteristic
351C22×C43D4211yescharacteristic
352C22×C43#54611yescharacteristic
353C22×C43C2×AGL(1,ℤ/8)11yescharacteristic
354C22×C43#57511yescharacteristic
355C22×C43#57711yescharacteristic
356C22×C43#57711yescharacteristic
357C2×D43—42no—
358C2×D43—42no—
359C2×D43—42no—
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—42no—
369C4×C43—41no—
370C4×C43—41no—
371C4×C43—81no—
372C4×C43C2×C4×D411yescharacteristic
373C4×C43#51811yescharacteristic
374C4×C43#54611yescharacteristic
375C4×C43#55111yescharacteristic
376Dic43—24no—
377Dic43—81no—
378Dic43—81no—
379C2×#449—431no—
380C2×C4×SD16—431no—
381C2×#417—431no—
382#2361D4311yescharacteristic, complemented
383#2341—431no—
384#1972—431no—
385#1934—431no—
386#1926—431no—
387#1895—431no—
388#1880—431no—
389#1879—431no—
390#1865—431no—
391#1853—431no—
392#1763—431no—
393#1753—431no—
394C2×C43—42no—
395C2×C43—82no—
396C2×C43#235811yescharacteristic
397C2×C43C4×AGL(1,ℤ/8)11yescharacteristic
398C2×C43#295211yescharacteristic
399C2×C43#326511yescharacteristic
400C2×C43#327111yescharacteristic
401C2×C43#332611yescharacteristic
402C2×C43#333211yescharacteristic
403D43—82no—
404C22×#41—431no—
405C22×SD16—431no—
406C22×D8—431no—
407C22×M16—431no—
408C2×#121C2×D4311yescharacteristic
409C2×C4×Q8—431no—
410C2×C4×Q8—431no—
411C2×C4×D4—21no—
412C2×C4×D4C2×D4311yescharacteristic
413C22×C4⋊C4C2×D4311yescharacteristic
414#449—438no—
415C4×SD16—864no—
416C2×#106—431no—
417C2×#106—431no—
418#417—864no—
419C2×#103—431no—
420C2×#103—431no—
421C2×#103—431no—
422C2×#102—431no—
423C2×#102—431no—
424C2×#102—431no—
425C2×#102—431no—
426C2×#102—431no—
427C2×C22⋊C8—431no—
428C2×#97—431no—
429C2×C4×C8—431no—
430#390—431no—
431#390—431no—
432#390—861no—
433#390—861no—
434#390C2×D4311yescharacteristic
435#389C2×D4311yescharacteristic
436#388—21no—
437#386—21no—
438#385—21no—
439#380—431no—
440#380—861no—
441C4×C4⋊C4C2×D4311yescharacteristic
442C4×C22⋊C4—861no—
443C4×C22⋊C4C2×D4311yescharacteristic
444#340—431no—
445#340—431no—
446#340—431no—
447#340—431no—
448#336—431no—
449#336—431no—
450C43#2288311yescharacteristic, complemented, Sylow
451C2×#41—434no—
452C2×#41—862no—
453C2×#41—862no—
454C2×#41—862no—
455C2×#41—1721no—
456C2×#41—1721no—
457C22×Q8—431no—
458C22×D4—21no—
459C22×D4—431no—
460C22×D4—861no—
461C22×D4C22×D4311yescharacteristic
462C23×C4—21no—
463C23×C4—21no—
464C23×C4—861no—
465C23×C4C22×D4311yescharacteristic
466C2×SD16—434no—
467C2×SD16—862no—
468C2×SD16—862no—
469C2×D8—434no—
470C2×D8—1721no—
471C2×D8—1721no—
472C2×M16—862no—
473C2×M16—862no—
474C2×M16—1721no—
475C22×C8—431no—
476C22×C8—431no—
477C22×C8—431no—
478C22×C8—431no—
479#121—22no—
480#121C4×D4314yes—
481C4×Q8—862no—
482C4×Q8—862no—
483C4×Q8—1721no—
484C4×Q8—1721no—
485C4×D4—22no—
486C4×D4—41no—
487C4×D4—44no—
488C2×C4⋊C4—22no—
489C2×C4⋊C4—21no—
490C2×C4⋊C4—21no—
491C2×C4⋊C4—41no—
492C2×C4⋊C4—431no—
493C2×C4⋊C4—431no—
494C2×C4⋊C4—861no—
495C2×C4⋊C4—861no—
496C2×C4⋊C4C22×D4311yescharacteristic
497C2×C4⋊C4C22×D4311yescharacteristic
498C2×C4⋊C4C22×D4311yescharacteristic
499C2×C22⋊C4—21no—
500C2×C22⋊C4—21no—
501C2×C22⋊C4—21no—
502C2×C22⋊C4—21no—
503C2×C22⋊C4—861no—
504C2×C22⋊C4—861no—
505C2×C22⋊C4—861no—
506C2×C22⋊C4—861no—
507C2×C22⋊C4—861no—
508C2×C22⋊C4C22⋊D4311yescharacteristic
509C2×C22⋊C4C22⋊D4311yescharacteristic
510C2×C42—21no—
511C2×C42—861no—
512C2×C42—861no—
513C2×C42C22×D4311yescharacteristic
514C2×C42C22×D4311yescharacteristic
515#106—862no—
516#106—1721no—
517#103—434no—
518#103—434no—
519#103—862no—
520#102—434no—
521#102—862no—
522#102—862no—
523#102—862no—
524#102—1721no—
525C22⋊C8—434no—
526#97—1721no—
527C4×C8—862no—
528#95—21no—
529#95—21no—
530#95—861no—
531#95C22⋊D4311yescharacteristic
532#95C22⋊D4311yescharacteristic
533C24—21no—
534C24—861no—
535C24C2×C22⋊D4311yescharacteristic
536#41—868no—
537#41—1724no—
538#41—1724no—
539#41—1724no—
540C2×Q8—432no—
541C2×Q8—432no—
542C2×Q8—432no—
543C2×Q8—861no—
544C2×Q8—861no—
545C2×Q8—861no—
546C2×D4—24no—
547C2×D4—21no—
548C2×D4—21no—
549C2×D4—21no—
550C2×D4—21no—
551C2×D4—21no—
552C2×D4—42no—
553C2×D4—42no—
554C2×D4—432no—
555C2×D4—864no—
556C2×D4—861no—
557C2×D4—861no—
558C2×D4—861no—
559C2×D4—861no—
560C2×D4—861no—
561C2×D4—1722no—
562C2×D4—1722no—
563C2×D4C2×C4×D4312yes—
564C22×C4—21no—
565C22×C4—21no—
566C22×C4—21no—
567C22×C4—21no—
568C22×C4—21no—
569C22×C4—21no—
570C22×C4—21no—
571C22×C4—42no—
572C22×C4—42no—
573C22×C4—42no—
574C22×C4—42no—
575C22×C4—81no—
576C22×C4—81no—
577C22×C4—861no—
578C22×C4—864no—
579C22×C4—861no—
580C22×C4—861no—
581C22×C4—1722no—
582C22×C4—1722no—
583C22×C4C2×C4×D4312yes—
584C22×C4#1062189812yes—
585C22×C4C2×C22⋊D4311yescharacteristic
586C22×C4C2×C22⋊D4311yescharacteristic
587C22×C4C2×C22⋊D4311yescharacteristic
588C22×C4C2×C22⋊D4311yescharacteristic
589C22×C4C2×C22⋊D4311yescharacteristic
590C22×C4C23×D4311yescharacteristic
591SD16—868no—
592D8—1724no—
593M16—1724no—
594C2×C8—432no—
595C2×C8—432no—
596C2×C8—432no—
597C2×C8—861no—
598C2×C8—861no—
599C2×C8—861no—
600C2×C8—861no—
601C2×C8—861no—
602C2×C8—861no—
603C2×C8—861no—
604C2×C8—861no—
605C2×C8—861no—
606C4⋊C4—21no—
607C4⋊C4—21no—
608C4⋊C4—21no—
609C4⋊C4—21no—
610C4⋊C4—42no—
611C4⋊C4—42no—
612C4⋊C4—861no—
613C4⋊C4—861no—
614C4⋊C4—861no—
615C4⋊C4—861no—
616C4⋊C4—1722no—
617C4⋊C4—1722no—
618C4⋊C4C2×C4×D4312yes—
619C4⋊C4D4×D4312yes—
620C22⋊C4—24no—
621C22⋊C4—22no—
622C22⋊C4—41no—
623C22⋊C4—42no—
624C22⋊C4—42no—
625C22⋊C4—81no—
626C22⋊C4—3441no—
627C22⋊C4—3441no—
628C22⋊C4—3441no—
629C22⋊C4—1722no—
630C22⋊C4—1722no—
631C42—21no—
632C42—21no—
633C42—21no—
634C42—21no—
635C42—42no—
636C42—1722no—
637C42—1722no—
638C23—21no—
639C23—21no—
640C23—21no—
641C23—21no—
642C23—21no—
643C23—21no—
644C23—22no—
645C23—41no—
646C23—41no—
647C23—41no—
648C23—41no—
649C23—41no—
650C23—41no—
651C23—862no—
652C23—1721no—
653C23—1721no—
654C23—1721no—
655C23—1721no—
656C23—1721no—
657C23—1721no—
658C23C4×C22⋊D4312yes—
659C23C22×C22⋊D4311yescharacteristic
660Q8—434no—
661Q8—862no—
662Q8—862no—
663Q8—862no—
664D4—22no—
665D4—22no—
666D4—48no—
667D4—41no—
668D4—41no—
669D4—862no—
670D4—862no—
671D4—1728no—
672D4—1721no—
673D4—1721no—
674C2×C4—21no—
675C2×C4—21no—
676C2×C4—21no—
677C2×C4—21no—
678C2×C4—22no—
679C2×C4—22no—
680C2×C4—22no—
681C2×C4—22no—
682C2×C4—22no—
683C2×C4—21no—
684C2×C4—21no—
685C2×C4—21no—
686C2×C4—21no—
687C2×C4—21no—
688C2×C4—21no—
689C2×C4—21no—
690C2×C4—22no—
691C2×C4—21no—
692C2×C4—21no—
693C2×C4—41no—
694C2×C4—41no—
695C2×C4—41no—
696C2×C4—41no—
697C2×C4—41no—
698C2×C4—41no—
699C2×C4—41no—
700C2×C4—84no—
701C2×C4—84no—
702C2×C4—862no—
703C2×C4—862no—
704C2×C4—862no—
705C2×C4—1728no—
706C2×C4—1721no—
707C2×C4—1721no—
708C2×C4—1721no—
709C2×C4—1721no—
710C2×C4—1721no—
711C2×C4—1721no—
712C2×C4C4×C22⋊D4312yes—
713C2×C4#1306335112yes—
714C2×C4C22×C4×D4311yescharacteristic
715C2×C4C2×D4×D4311yescharacteristic
716C2×C4#41×D4311yescharacteristic
717C2×C4C2×#1062189811yescharacteristic
718C2×C4#1306337011yescharacteristic
719C2×C4#1306337111yescharacteristic
720C8—862no—
721C8—862no—
722C8—862no—
723C8—1721no—
724C22—22no—
725C22—22no—
726C22—22no—
727C22—41no—
728C22—41no—
729C22—41no—
730C22—41no—
731C22—42no—
732C22—42no—
733C22—42no—
734C22—81no—
735C22—81no—
736C22—81no—
737C22—81no—
738C22—3441no—
739C22—3441no—
740C22—3441no—
741C22—3441no—
742C22—1722no—
743C22—1722no—
744C22—1722no—
745C22C2×C4×C22⋊D4311yescharacteristic
746C22D4×C22⋊D4311yescharacteristic
747C22#1458353711yescharacteristic
748C22C2×#1306335111yescharacteristic
749C22#1458369711yescharacteristic
750C22#1458370711yescharacteristic
751C22#1458371011yescharacteristic
752C4—22no—
753C4—22no—
754C4—41no—
755C4—42no—
756C4—41no—
757C4—41no—
758C4—42no—
759C4—81no—
760C4—864no—
761C4—3441no—
762C4—3441no—
763C4C4×D4×D4311yescharacteristic
764C4#1458337111yescharacteristic
765C4#1458354511yescharacteristic
766C4#1458357811yescharacteristic
767C2—42no—
768C2—82no—
769C2—3442no—
770C2#1913757211yescharacteristic
771C2C4×#1306335111yescharacteristic
772C2#1914347611yescharacteristic
773C2#1914608611yescharacteristic
774C2#1914618111yescharacteristic
775C2#1914684211yescharacteristic
776C2#1914691611yescharacteristic
subgroupG/H
centerC23C22×C22⋊D43
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC43×#2361C2
socleC23×C43C22×D4
prime radicalC2×#14583042C2
cosocleC22×C4×C43C24
hypercenter#2361D43
hypocenterC43#22883
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C4×C22⋊C4 ◁ #2361

Complements

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

NH ≅ G/Ntype
2. C2×C4×#10621883C2semidirect
3. C2×#14582898C2semidirect
4. #19137435C2semidirect
5. #19135470C2semidirect
6. #19135277C2semidirect
7. #19135222C2semidirect
8. #19135034C2semidirect
9. #19134953C2semidirect
10. #19134943C2semidirect
11. #19134862C2semidirect
12. #19134788C2semidirect
13. #19134428C2semidirect
14. #19134379C2semidirect
15. C43×#2361C2semidirect
22. #14583042C4semidirect
67. C2×#10621898C2×C4semidirect
74. C2×#10621883C2×C4semidirect
77. C2×#10621882C2×C4semidirect
103. #13063248C2×C4semidirect
104. #13063248D4semidirect
109. #13063245C2×C4semidirect
110. C22⋊(C43⋊C8)C2×C4semidirect
330. Dic86C4×D4semidirect
382. #2361D43semidirect
450. C43#22883semidirect

Maximal subgroups

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

subgroupindex
C2×#145830422
C2×C4×#106218832
C2×#145828982
#191374352
#191354702
#191352772
#191352222
#191350342
#191349532
#191349432
#191348622
#191347882
#191344282
#191343792
C43×#23612
#2288343