Finite Group Databasebeta

← #35424672

Subgroups — #35424672

Order 21248.

1170 conjugacy classes of subgroups.

The subgroup lattice has 748 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#19127840C211yesmaximal, characteristic
2C2×#19127799C211yesmaximal, characteristic, complemented
3C22×#14581716C211yesmaximal, characteristic, complemented
4#24910477C211yesmaximal, characteristic
5#24908347C211yesmaximal, characteristic, complemented
6#24908156C211yesmaximal, characteristic, complemented
7#24908101C211yesmaximal, characteristic, complemented
8#24907889C211yesmaximal, characteristic
9#24907818C211yesmaximal, characteristic, complemented
10#24907800C211yesmaximal, characteristic, complemented
11#24907717C211yesmaximal, characteristic, complemented
12#24907650C211yesmaximal, characteristic, complemented
13#24907293C211yesmaximal, characteristic, complemented
14#24907241C211yesmaximal, characteristic, complemented
15Q8×C22⋊C4×C83C211yesmaximal, characteristic, complemented
16C22×#13050577C2211yescharacteristic
17C22×#13050577C2211yescharacteristic
18C23×C83⋊C8C2211yescharacteristic
19C2×#14581766C2211yescharacteristic
20C2×C4×D332C2211yescharacteristic
21C2×(C22⋊D83)⋊C4—21no—
22C22×C4⋊Dic83C2211yescharacteristic
23#19127840C418yescomplemented
24#19127799—24no—
25C2×#14581725C2211yescharacteristic
26C2×#14581725C2211yescharacteristic
27C2×#14581716—24no—
28C2×#14581716C2211yescharacteristic
29C2×#14581716C2211yescharacteristic
30C2×#14581716C2211yescharacteristic
31C2×#14581716C2211yescharacteristic
32C2×#14581716C2211yescharacteristic
33C2×#14581716C2211yescharacteristic
34C2×#14581712C2211yescharacteristic
35C2×#14581712C2211yescharacteristic
36C2×C22⋊(C83⋊C8)C2211yescharacteristic
37C2×#14581703C2211yescharacteristic
38C2×#14581703C2211yescharacteristic
39#19127603C2211yescharacteristic
40#19127599C2211yescharacteristic
41#19127593—21no—
42#19127578—21no—
43#19127575—21no—
44C4×C4⋊Dic83C2211yescharacteristic
45#19127463C2211yescharacteristic
46#19127463C2211yescharacteristic
47#19127463C2211yescharacteristic
48#19127463C2211yescharacteristic
49#19127456C2211yescharacteristic
50#19127456C2211yescharacteristic
51C23×Q8×C83C2211yescharacteristic
52C2×C4×Q8×C83C2211yescharacteristic
53C2×C4×Q8×C83C2211yescharacteristic
54#391×C83—21no—
55#391×C83—21no—
56#391×C83C2211yescharacteristic
57#391×C83C2211yescharacteristic
58#380×C83—21no—
59#380×C83C2211yescharacteristic
60C4×C22⋊C4×C83—21no—
61C4×C22⋊C4×C83C2211yescharacteristic
62C22×D332C2311yescharacteristic
63C22×C22⋊D83—21no—
64C23×Dic83—21no—
65C22×C4×D83—21no—
66C2×#13050577—22no—
67C2×#13050577—22no—
68C2×#13050577—41no—
69C2×#13050577—41no—
70C2×#13050577C2×C414yescomplemented
71C2×#13050577C2×C414yescomplemented
72C22×C83⋊C8—22no—
73C22×C83⋊C8—22no—
74C22×C83⋊C8—41no—
75C22×C83⋊C8C2311yescharacteristic
76C22×C83⋊C8C2311yescharacteristic
77C22×C83⋊C8C2311yescharacteristic
78C22×C83⋊C8C2311yescharacteristic
79#14581766—22no—
80#14581766C2×C414yes—
81C4×D332—22no—
82C4×D332—41no—
83(C22⋊D83)⋊C4—44no—
84C2×C4⋊Dic83—22no—
85C2×C4⋊Dic83—21no—
86C2×C4⋊Dic83—41no—
87C2×C4⋊Dic83C2311yescharacteristic
88C2×C4⋊Dic83C2311yescharacteristic
89C2×C4⋊Dic83C2311yescharacteristic
90C2×Dic83⋊C4—21no—
91C2×(C2×D83)⋊C4—21no—
92C2×(C2×D83)⋊C4—21no—
93C2×(C2×D83)⋊C4—21no—
94C2×(C2×D83)⋊C4—21no—
95C2×C4×Dic83—21no—
96#14581725—22no—
97#14581725—41no—
98#14581716—22no—
99#14581716—22no—
100#14581716—22no—
101#14581716C2×C414yescomplemented
102#14581716C2×C414yescomplemented
103#14581716D414yescomplemented
104#14581712—22no—
105#14581712—41no—
106C22⋊(C83⋊C8)C2×C414yescomplemented
107#14581703—22no—
108#14581703—41no—
109C83⋊#95—21no—
110C83⋊#95—21no—
111C22×Q8×C83—21no—
112C22×Q8×C83—22no—
113C22×Q8×C83—22no—
114C22×Q8×C83—22no—
115C22×Q8×C83—41no—
116C22×Q8×C83—41no—
117C22×Q8×C83C2×C414yescomplemented
118C22×Q8×C83C2311yescharacteristic
119C22×Q8×C83C2311yescharacteristic
120C23×C4×C83—21no—
121C23×C4×C83C2311yescharacteristic
122C4×Q8×C83—22no—
123C4×Q8×C83—22no—
124C4×Q8×C83—41no—
125C4×Q8×C83—41no—
126C2×C4⋊C4×C83—21no—
127C2×C4⋊C4×C83—21no—
128C2×C4⋊C4×C83C2311yescharacteristic
129C2×C4⋊C4×C83C2311yescharacteristic
130C2×C22⋊C4×C83—21no—
131C2×C22⋊C4×C83D411yescharacteristic
132C2×C22⋊C4×C83D411yescharacteristic
133C2×C42×C83—21no—
134C2×C42×C83—21no—
135C2×C42×C83C2311yescharacteristic
136C2×C42×C83C2311yescharacteristic
137#95×C83—21no—
138#95×C83—21no—
139#95×C83—21no—
140#95×C83—21no—
141#95×C83—21no—
142#95×C83D411yescharacteristic
143#95×C83D411yescharacteristic
144C23×D83—21no—
145C2×D332—21no—
146C2×D332—21no—
147C2×D332—21no—
148C2×D332—21no—
149C2×D332—21no—
150C2×D332C22×C412yes—
151C2×C22⋊D83—24no—
152C2×C22⋊D83—42no—
153C2×C22⋊D83—42no—
154C22×Dic83—21no—
155C22×Dic83—21no—
156C22×Dic83—21no—
157C22×Dic83—42no—
158C22×Dic83—42no—
159C22×Dic83—81no—
160C2×C4×D83—42no—
161C2×C4×D83—42no—
162C2×C4×D83—81no—
163#13050577—28no—
164#13050577—44no—
165C2×C83⋊C8—21no—
166C2×C83⋊C8—21no—
167C2×C83⋊C8—21no—
168C2×C83⋊C8—21no—
169C2×C83⋊C8—21no—
170C2×C83⋊C8—21no—
171C2×C83⋊C8—21no—
172C2×C83⋊C8—21no—
173C2×C83⋊C8—21no—
174C2×C83⋊C8—44no—
175C2×C83⋊C8C22×C412yes—
176C2×C83⋊C8C22×C412yes—
177C2×C83⋊C8C2×D412yes—
178C4⋊Dic83—21no—
179C4⋊Dic83—21no—
180C4⋊Dic83—21no—
181C4⋊Dic83—21no—
182C4⋊Dic83—42no—
183C4⋊Dic83C22×C412yes—
184C4⋊Dic83C2×D412yes—
185Dic83⋊C4—42no—
186(C2×D83)⋊C4—24no—
187(C2×D83)⋊C4—42no—
188(C2×D83)⋊C4—42no—
189(C2×D83)⋊C4—81no—
190C4×Dic83—42no—
191C24×C83C2×D411yescharacteristic
192C2×Q8×C83—24no—
193C2×Q8×C83—21no—
194C2×Q8×C83—21no—
195C2×Q8×C83—21no—
196C2×Q8×C83—21no—
197C2×Q8×C83—28no—
198C2×Q8×C83—21no—
199C2×Q8×C83—21no—
200C2×Q8×C83—21no—
201C2×Q8×C83—21no—
202C2×Q8×C83—42no—
203C2×Q8×C83—42no—
204C2×Q8×C83—44no—
205C2×Q8×C83—44no—
206C2×Q8×C83—44no—
207C2×Q8×C83C22×C412yes—
208C2×Q8×C83C22×C412yes—
209C2×Q8×C83C2×D412yes—
210C2×Q8×C83#4112yes—
211C22×C4×C83—21no—
212C22×C4×C83—21no—
213C22×C4×C83—21no—
214C22×C4×C83—21no—
215C22×C4×C83—21no—
216C22×C4×C83—24no—
217C22×C4×C83—21no—
218C22×C4×C83—21no—
219C22×C4×C83—21no—
220C22×C4×C83—42no—
221C22×C4×C83—42no—
222C22×C4×C83C22×C412yes—
223C22×C4×C83C2×D411yescharacteristic
224C22×C4×C83C2×D411yescharacteristic
225C22×C4×C83C2×D411yescharacteristic
226C22×C4×C83C2×D411yescharacteristic
227C22×C4×C83C2×D411yescharacteristic
228C22×C4×C83#4112yes—
229C22×C4×C83C2411yescharacteristic
230C4⋊C4×C83—21no—
231C4⋊C4×C83—21no—
232C4⋊C4×C83—21no—
233C4⋊C4×C83—21no—
234C4⋊C4×C83—42no—
235C4⋊C4×C83—42no—
236C22⋊C4×C83—22no—
237C22⋊C4×C83—22no—
238C22⋊C4×C83—42no—
239C42×C83—21no—
240C42×C83—21no—
241C42×C83—21no—
242C42×C83—21no—
243C42×C83—42no—
244C42×C83—42no—
245C23×C83—21no—
246C23×C83—21no—
247C23×C83—21no—
248C23×C83—21no—
249C23×C83C4×D412yes—
250C23×C83AGL(1,ℤ/8)12yes—
251C23×C83#13712yes—
252C23×C83C22×D411yescharacteristic
253C22×D83—22no—
254C22×D83—41no—
255C22×D83—41no—
256C22×D83—41no—
257C22×D83—41no—
258C22×D83—41no—
259C22×D83—41no—
260Q8×C83—22no—
261Q8×C83—22no—
262Q8×C83—22no—
263Q8×C83—22no—
264Q8×C83—22no—
265Q8×C83—48no—
266Q8×C83—41no—
267Q8×C83—41no—
268Q8×C83C4×D414yescomplemented
269C2×C4×C83—22no—
270C2×C4×C83—22no—
271C2×C4×C83—21no—
272C2×C4×C83—22no—
273C2×C4×C83—21no—
274C2×C4×C83—22no—
275C2×C4×C83—22no—
276C2×C4×C83—22no—
277C2×C4×C83—22no—
278C2×C4×C83—22no—
279C2×C4×C83—21no—
280C2×C4×C83—21no—
281C2×C4×C83—21no—
282C2×C4×C83—21no—
283C2×C4×C83—21no—
284C2×C4×C83—21no—
285C2×C4×C83—21no—
286C2×C4×C83—21no—
287C2×C4×C83—21no—
288C2×C4×C83—21no—
289C2×C4×C83—21no—
290C2×C4×C83—21no—
291C2×C4×C83—48no—
292C2×C4×C83—41no—
293C2×C4×C83—41no—
294C2×C4×C83—41no—
295C2×C4×C83—41no—
296C2×C4×C83—41no—
297C2×C4×C83—41no—
298C2×C4×C83—41no—
299C2×C4×C83—41no—
300C2×C4×C83C4×D412yes—
301C2×C4×C83C23×C411yescharacteristic
302C2×C4×C83C22×D411yescharacteristic
303C2×C4×C83C2×#4111yescharacteristic
304C2×C4×C83C2×#4111yescharacteristic
305C2×C4×C83H(5,𝔽2)11yescharacteristic
306C2×C4×C83H(5,𝔽2)11yescharacteristic
307C22⋊D83—48no—
308C2×Dic83—22no—
309C2×Dic83—22no—
310C2×Dic83—41no—
311C2×Dic83—41no—
312C2×Dic83—41no—
313C2×Dic83—41no—
314C2×Dic83—41no—
315C2×Dic83—41no—
316C2×Dic83—41no—
317C2×Dic83—84no—
318D332—22no—
319D332—22no—
320D332—41no—
321D332—41no—
322C4×D83—84no—
323C83⋊C8—22no—
324C83⋊C8—22no—
325C83⋊C8—22no—
326C83⋊C8—41no—
327C22×C83—22no—
328C22×C83—22no—
329C22×C83—22no—
330C22×C83—22no—
331C22×C83—22no—
332C22×C83—22no—
333C22×C83#44014yescomplemented
334C22×C83C2×C4×D411yescharacteristic
335C22×C83D4211yescharacteristic
336C22×C83#54611yescharacteristic
337C22×C83C2×AGL(1,ℤ/8)11yescharacteristic
338C22×C83C2×#13711yescharacteristic
339C22×C83#57711yescharacteristic
340C22×C83#57811yescharacteristic
341C2×D83—42no—
342C2×D83—42no—
343C2×D83—42no—
344C2×D83—81no—
345C2×D83—81no—
346C2×D83—81no—
347C2×D83—81no—
348C4×C83—22no—
349C4×C83—24no—
350C4×C83—42no—
351C4×C83—41no—
352C4×C83—41no—
353C4×C83—41no—
354C4×C83—41no—
355C4×C83—81no—
356C4×C83—81no—
357C4×C83C2×C4×D411yescharacteristic
358C4×C83#51811yescharacteristic
359C4×C83#54611yescharacteristic
360C4×C83#55111yescharacteristic
361Dic83—42no—
362Dic83—42no—
363Dic83—81no—
364#22855—831nomaximal, Sylow
365C2×C83—24no—
366C2×C83#235811yescharacteristic
367C2×C83C2×#44011yescharacteristic
368C2×C83#294711yescharacteristic
369C2×C83#326511yescharacteristic
370C2×C83#327011yescharacteristic
371C2×C83#330811yescharacteristic
372C2×C83#332011yescharacteristic
373D83—82no—
374C2×#448—831no—
375C2×#440—831no—
376C22×#103—831no—
377#2361—831no—
378Q8×C22⋊C4D8311yescharacteristic, complemented
379#1973—831no—
380#1935—831no—
381#1928—831no—
382#1893—831no—
383#1880—831no—
384#1877—831no—
385#1863—831no—
386#1852—831no—
387#1763—831no—
388#1752—831no—
389C83#2285511yescharacteristic, complemented, Sylow
390C23×Q8C2×D8311yescharacteristic
391C22×SD16—831no—
392C22×SD16—831no—
393C23×C8—831no—
394C2×#121—831no—
395C2×C4×Q8C2×D8311yescharacteristic
396C2×C4×Q8C2×D8311yescharacteristic
397C2×C4×D4—831no—
398C2×C4×D4—1661no—
399C22×C4⋊C4—831no—
400#448—838no—
401#440—1664no—
402C2×#107—831no—
403C2×#107—831no—
404C2×#103—831no—
405C2×#103—831no—
406C2×#103—831no—
407C2×#103—831no—
408C2×#103—831no—
409C2×#103—831no—
410C2×#103—1664no—
411C2×#102—831no—
412C2×#102—831no—
413C2×C22⋊C8—831no—
414C2×#97—831no—
415C2×#97—831no—
416#391—21no—
417#391—21no—
418#391C2×D8311yescharacteristic
419#391C2×D8311yescharacteristic
420#390—831no—
421#389—831no—
422#388—1661no—
423#386—1661no—
424#385—1661no—
425#380—21no—
426#380C2×D8311yescharacteristic
427C4×C4⋊C4—831no—
428C4×C22⋊C4—21no—
429C4×C22⋊C4C2×D8311yescharacteristic
430#340—831no—
431#340—831no—
432#340—831no—
433#340—831no—
434#336—831no—
435#336—831no—
436C22×Q8—21no—
437C22×Q8—22no—
438C22×Q8—22no—
439C22×Q8—22no—
440C22×Q8—41no—
441C22×Q8—41no—
442C22×Q8C4×D8314yescomplemented
443C22×Q8C22×D8311yescharacteristic
444C22×Q8C22×D8311yescharacteristic
445C22×D4—831no—
446C22×D4—1661no—
447C23×C4—21no—
448C23×C4—1661no—
449C23×C4—1661no—
450C23×C4C22×D8311yescharacteristic
451C2×SD16—3321no—
452C2×SD16—3321no—
453C2×SD16—834no—
454C2×SD16—834no—
455C2×SD16—1662no—
456C2×SD16—1662no—
457C22×C8—3321no—
458C22×C8—831no—
459C22×C8—831no—
460C22×C8—831no—
461C22×C8—831no—
462C22×C8—1662no—
463C22×C8—1662no—
464#121—834no—
465#121—1662no—
466C4×Q8—22no—
467C4×Q8—22no—
468C4×Q8—41no—
469C4×Q8—41no—
470C4×D4—3321no—
471C4×D4—3324no—
472C4×D4—1662no—
473C2×C4⋊C4—21no—
474C2×C4⋊C4—21no—
475C2×C4⋊C4—3321no—
476C2×C4⋊C4—831no—
477C2×C4⋊C4—831no—
478C2×C4⋊C4—831no—
479C2×C4⋊C4—1661no—
480C2×C4⋊C4—1661no—
481C2×C4⋊C4—1662no—
482C2×C4⋊C4C22×D8311yescharacteristic
483C2×C4⋊C4C22×D8311yescharacteristic
484C2×C22⋊C4—21no—
485C2×C22⋊C4—1661no—
486C2×C22⋊C4—1661no—
487C2×C22⋊C4—1661no—
488C2×C22⋊C4—1661no—
489C2×C22⋊C4C22⋊D8311yescharacteristic
490C2×C22⋊C4C22⋊D8311yescharacteristic
491C2×C42—21no—
492C2×C42—21no—
493C2×C42—1661no—
494C2×C42C22×D8311yescharacteristic
495C2×C42C22×D8311yescharacteristic
496#107—3321no—
497#107—1662no—
498#103—834no—
499#103—834no—
500#103—834no—
501#103—1662no—
502#103—1662no—
503#103—1662no—
504#102—3321no—
505#102—1662no—
506C22⋊C8—834no—
507#97—3321no—
508#97—1662no—
509#95—21no—
510#95—21no—
511#95—21no—
512#95—21no—
513#95—21no—
514#95—1661no—
515#95—1661no—
516#95C22⋊D8311yescharacteristic
517#95C22⋊D8311yescharacteristic
518C24—1661no—
519C24C2×C22⋊D8311yescharacteristic
520C2×Q8—21no—
521C2×Q8—21no—
522C2×Q8—21no—
523C2×Q8—21no—
524C2×Q8—24no—
525C2×Q8—28no—
526C2×Q8—21no—
527C2×Q8—21no—
528C2×Q8—21no—
529C2×Q8—21no—
530C2×Q8—42no—
531C2×Q8—42no—
532C2×Q8—44no—
533C2×Q8—44no—
534C2×Q8—44no—
535C2×Q8C2×C4×D8312yes—
536C2×Q8C2×C4×D8312yes—
537C2×Q8D4×D8312yes—
538C2×Q8#1305058912yes—
539C2×D4—3322no—
540C2×D4—3322no—
541C2×D4—832no—
542C2×D4—1664no—
543C2×D4—1661no—
544C2×D4—1661no—
545C2×D4—1661no—
546C2×D4—1661no—
547C2×D4—1661no—
548C22×C4—21no—
549C22×C4—21no—
550C22×C4—21no—
551C22×C4—21no—
552C22×C4—21no—
553C22×C4—21no—
554C22×C4—24no—
555C22×C4—21no—
556C22×C4—21no—
557C22×C4—42no—
558C22×C4—42no—
559C22×C4—3322no—
560C22×C4—3322no—
561C22×C4—3322no—
562C22×C4—3322no—
563C22×C4—6641no—
564C22×C4—6641no—
565C22×C4—1661no—
566C22×C4—1661no—
567C22×C4—1661no—
568C22×C4C2×C4×D8312yes—
569C22×C4C2×C22⋊D8311yescharacteristic
570C22×C4C2×C22⋊D8311yescharacteristic
571C22×C4C2×C22⋊D8311yescharacteristic
572C22×C4C2×C22⋊D8311yescharacteristic
573C22×C4C2×C22⋊D8311yescharacteristic
574C22×C4#1305059012yes—
575C22×C4C23×D8311yescharacteristic
576SD16—3324no—
577SD16—1668no—
578C2×C8—3324no—
579C2×C8—832no—
580C2×C8—832no—
581C2×C8—832no—
582C2×C8—1661no—
583C2×C8—1661no—
584C2×C8—1661no—
585C2×C8—1661no—
586C2×C8—1661no—
587C2×C8—1661no—
588C2×C8—1661no—
589C2×C8—1661no—
590C2×C8—1661no—
591C4⋊C4—21no—
592C4⋊C4—21no—
593C4⋊C4—21no—
594C4⋊C4—21no—
595C4⋊C4—42no—
596C4⋊C4—42no—
597C4⋊C4—3322no—
598C4⋊C4—3322no—
599C4⋊C4—832no—
600C4⋊C4—832no—
601C4⋊C4—1661no—
602C4⋊C4—1661no—
603C4⋊C4—1661no—
604C4⋊C4—1661no—
605C22⋊C4—22no—
606C22⋊C4—22no—
607C22⋊C4—42no—
608C22⋊C4—3322no—
609C22⋊C4—3322no—
610C22⋊C4—6641no—
611C22⋊C4—1664no—
612C42—21no—
613C42—21no—
614C42—21no—
615C42—21no—
616C42—42no—
617C42—42no—
618C42—3322no—
619C23—21no—
620C23—21no—
621C23—21no—
622C23—21no—
623C23—3321no—
624C23—3321no—
625C23—3321no—
626C23—3321no—
627C23—3321no—
628C23—3321no—
629C23—1662no—
630C23C4×C22⋊D8312yes—
631C23#1458181712yes—
632C23#1458182312yes—
633C23C22×C22⋊D8311yescharacteristic
634Q8—22no—
635Q8—22no—
636Q8—22no—
637Q8—22no—
638Q8—22no—
639Q8—48no—
640Q8—41no—
641Q8—41no—
642Q8(C22⋊D83)⋊C414yescomplemented
643D4—3328no—
644D4—3321no—
645D4—3321no—
646D4—1662no—
647D4—1662no—
648C2×C4—22no—
649C2×C4—21no—
650C2×C4—22no—
651C2×C4—21no—
652C2×C4—22no—
653C2×C4—22no—
654C2×C4—22no—
655C2×C4—22no—
656C2×C4—22no—
657C2×C4—21no—
658C2×C4—21no—
659C2×C4—21no—
660C2×C4—21no—
661C2×C4—22no—
662C2×C4—21no—
663C2×C4—21no—
664C2×C4—21no—
665C2×C4—21no—
666C2×C4—21no—
667C2×C4—21no—
668C2×C4—21no—
669C2×C4—21no—
670C2×C4—48no—
671C2×C4—41no—
672C2×C4—41no—
673C2×C4—41no—
674C2×C4—41no—
675C2×C4—41no—
676C2×C4—41no—
677C2×C4—41no—
678C2×C4—41no—
679C2×C4—3321no—
680C2×C4—3321no—
681C2×C4—3321no—
682C2×C4—3321no—
683C2×C4—3321no—
684C2×C4—3321no—
685C2×C4—3321no—
686C2×C4—6644no—
687C2×C4—6644no—
688C2×C4—1662no—
689C2×C4—1662no—
690C2×C4C4×C22⋊D8312yes—
691C2×C4C22×C4×D8311yescharacteristic
692C2×C4C2×D4×D8311yescharacteristic
693C2×C4C2×#1305058911yescharacteristic
694C2×C4C2×#1305059011yescharacteristic
695C2×C4#1458183711yescharacteristic
696C2×C4#1458183711yescharacteristic
697C8—3321no—
698C8—1662no—
699C8—1662no—
700C8—1662no—
701C22—22no—
702C22—22no—
703C22—22no—
704C22—22no—
705C22—22no—
706C22—22no—
707C22—3322no—
708C22—3322no—
709C22—3322no—
710C22—6641no—
711C22—6641no—
712C22—6641no—
713C22—6641no—
714C22#1912779914yescomplemented
715C22C2×C4×C22⋊D8311yescharacteristic
716C22D4×C22⋊D8311yescharacteristic
717C22#1912834511yescharacteristic
718C22C2×#1458181711yescharacteristic
719C22C2×#1458182311yescharacteristic
720C22#1912850911yescharacteristic
721C22#1912851611yescharacteristic
722C4—22no—
723C4—24no—
724C4—41no—
725C4—42no—
726C4—41no—
727C4—41no—
728C4—41no—
729C4—81no—
730C4—81no—
731C4—3322no—
732C4—3322no—
733C4—6641no—
734C4C2×(C22⋊D83)⋊C411yescharacteristic
735C4#1912817411yescharacteristic
736C4#1912834111yescharacteristic
737C4#1912837711yescharacteristic
738C2—24no—
739C2—6642no—
740C2#2491044211yescharacteristic
741C2C2×#1912779911yescharacteristic
742C2#2491630611yescharacteristic
743C2#2491895911yescharacteristic
744C2#2491903411yescharacteristic
745C2#2491945411yescharacteristic
746C2#2491963411yescharacteristic
subgroupG/H
centerC23C22×C22⋊D83
commutatorC2×C4×C83C23×C4
FrattiniC22×C4C23×D83
FittingQ8×C22⋊C4×C83C2
socleC23×C83C22×D4
prime radicalC2×#14581766C22
cosocleC22×C4×C83C24
hypercenterQ8×C22⋊C4D83
hypocenterC83#22855
LCSG ▷ C2×C4×C83 ▷ C2×C83 ▷ C83
UCSC1 ◁ C23 ◁ C4×C22⋊C4 ◁ Q8×C22⋊C4

Complements

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

NH ≅ G/Ntype
2. C2×#19127799C2semidirect
3. C22×#14581716C2semidirect
5. #24908347C2semidirect
6. #24908156C2semidirect
7. #24908101C2semidirect
9. #24907818C2semidirect
10. #24907800C2semidirect
11. #24907717C2semidirect
12. #24907650C2semidirect
13. #24907293C2semidirect
14. #24907241C2semidirect
15. Q8×C22⋊C4×C83C2semidirect
23. #19127840C4semidirect
70. C2×#13050577C2×C4semidirect
71. C2×#13050577C2×C4semidirect
101. #14581716C2×C4semidirect
102. #14581716C2×C4semidirect
103. #14581716D4semidirect
106. C22⋊(C83⋊C8)C2×C4semidirect
117. C22×Q8×C83C2×C4semidirect
268. Q8×C83C4×D4semidirect
333. C22×C83#440semidirect
378. Q8×C22⋊C4D83semidirect
389. C83#22855semidirect
442. C22×Q8C4×D83semidirect
642. Q8(C22⋊D83)⋊C4semidirect
714. C22#19127799semidirect

Maximal subgroups

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

subgroupindex
C2×#191278402
C2×#191277992
C22×#145817162
#249104772
#249083472
#249081562
#249081012
#249078892
#249078182
#249078002
#249077172
#249076502
#249072932
#249072412
Q8×C22⋊C4×C832
#2285583