Finite Group Databasebeta

← #35564605

Subgroups — #35564605

Order 21248.

2414 conjugacy classes of subgroups.

The subgroup lattice has 738 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4×#13050589C211yesmaximal, characteristic
2#24910413C212yesmaximal, complemented
3#24910412C211yesmaximal, characteristic, complemented
4#24910407C212yesmaximal, complemented
5C4⋊C4×Dic166C211yesmaximal, characteristic, complemented
6#24910375C211yesmaximal, characteristic, complemented
7#24910353C214yesmaximal, complemented
8#24910352C212yesmaximal, complemented
9#24910302C212yesmaximal
10#24910104C214yesmaximal, complemented
11#24910100C212yesmaximal, complemented
12#24909868C211yesmaximal, characteristic, complemented
13#24909866C212yesmaximal, complemented
14#24909859C211yesmaximal, characteristic, complemented
15#24909858C212yesmaximal, complemented
16#24909827C212yesmaximal, complemented
17C83×#2354C211yesmaximal, characteristic, complemented
18C22×#13050589C2211yescharacteristic
19C4×#13050589C4116yescomplemented
20C2×C4×Dic166C2212yes—
21C2×C4×Dic166C2211yescharacteristic
22C2×#14581757C2212yes—
23C2×#14581757C2211yescharacteristic
24C2×D4×Dic83C2211yescharacteristic
25C2×C4×C22⋊D83C2212yes—
26C2×(C22⋊D83)⋊C4C2212yes—
27C2×#14581751C2212yes—
28C2×#14581750C2212yes—
29C2×#14581750C2211yescharacteristic
30C2×#14581748C2212yes—
31C22×C4×Dic83C2212yes—
32C2×C42×D83C2211yescharacteristic
33#19127604C2212yes—
34#19127601C2214yes—
35#19127601C2214yes—
36#19127599C2212yes—
37#19127598C2214yes—
38#19127597C2212yes—
39#19127596C2214yes—
40#19127595C2214yes—
41#19127594C2214yes—
42#19127592C2214yes—
43#19127590C2214yes—
44#19127589C2214yes—
45#19127571C2211yescharacteristic
46#19127570C2212yes—
47#19127570C2212yes—
48#19127568C2214yes—
49#19127568C2212yes—
50#19127566C2211yescharacteristic
51#19127566C2212yes—
52#19127566C2211yescharacteristic
53#19127563C2212yes—
54#19127562C2214yes—
55#19127561C2212yes—
56#19127559C2214yes—
57#19127559C2214yes—
58#19127558C2212yes—
59#19127558C2212yes—
60#19127558C2211yescharacteristic
61#19127558C2211yescharacteristic
62C4⋊C4×Dic83C2212yes—
63C4⋊C4×Dic83C2212yes—
64C4⋊C4×Dic83C2212yes—
65C4⋊C4×Dic83C2212yes—
66C4⋊C4×Dic83C2212yes—
67C4×Dic83⋊C4C2214yes—
68C4×Dic83⋊C4C2214yes—
69C4×Dic83⋊C4C2214yes—
70C4×C4⋊Dic83C2211yescharacteristic
71#19127552C2214yes—
72C22⋊C4×Dic83C2214yes—
73C4×(C2×D83)⋊C4C2212yes—
74#19127547C2212yes—
75#19127546C2214yes—
76C2×C4×D4×C83C2211yescharacteristic
77C2×#117×C83C2212yes—
78#390×C83C2212yes—
79#388×C83C2214yes—
80#384×C83C2211yescharacteristic
81#380×C83C2212yes—
82C4×C4⋊C4×C83C2212yes—
83C4×C4⋊C4×C83C2211yescharacteristic
84C2×#13050589—24no—
85C2×#13050589—24no—
86C2×#13050589C2×C418yes—
87C22×Dic166C2311yescharacteristic
88C22×C22⋊D83C2312yes—
89C23×Dic83C2312yes—
90C23×Dic83C2312yes—
91C22×C4×D83C2311yescharacteristic
92C22×C4×D83C2311yescharacteristic
93C22×C4×D83C2311yescharacteristic
94C4×Dic166—28no—
95C4×Dic166C2×C418yes—
96#14581757—28no—
97#14581757C2×C418yes—
98D4×Dic83C2×C418yes—
99C4×C22⋊D83C2×C4116yes—
100(C22⋊D83)⋊C4C2×C4116yes—
101#14581751—44no—
102#14581750—44no—
103#14581750C2×C418yes—
104#14581748C2×C4116yes—
105C2×C4⋊Dic83C2311yescharacteristic
106C2×C4⋊Dic83C2311yescharacteristic
107C2×C4⋊Dic83C2312yes—
108C2×C4⋊Dic83C2312yes—
109C2×C4⋊Dic83C2312yes—
110C2×C4⋊Dic83C2311yescharacteristic
111C2×Dic83⋊C4C2314yes—
112C2×Dic83⋊C4C2314yes—
113C2×Dic83⋊C4C2314yes—
114C2×Dic83⋊C4C2314yes—
115C2×Dic83⋊C4C2312yes—
116C2×Dic83⋊C4C2312yes—
117C2×C22⋊Dic83C2314yes—
118C2×C22⋊Dic83C2314yes—
119C2×C22⋊Dic83C2312yes—
120C2×(C2×D83)⋊C4C2314yes—
121C2×(C2×D83)⋊C4C2312yes—
122C2×(C2×D83)⋊C4C2312yes—
123C2×(C2×D83)⋊C4C2312yes—
124C2×C4×Dic83C2×C4116yes—
125C2×C4×Dic83C2314yes—
126C2×C4×Dic83C2312yes—
127C2×C4×Dic83C2314yes—
128C2×C4×Dic83C2314yes—
129C2×C4×Dic83C2314yes—
130C2×C4×Dic83C2312yes—
131C2×C4×Dic83C2312yes—
132C2×C4×Dic83C2311yescharacteristic
133C2×C4×Dic83C2312yes—
134C2×C4×Dic83C2311yescharacteristic
135C2×C4×Dic83C2311yescharacteristic
136C42×D83C2×C418yes—
137C83⋊#95C2312yes—
138C83⋊#95C2312yes—
139C83⋊#95C2312yes—
140C83⋊#95C2312yes—
141C83⋊#95C2312yes—
142C83⋊#95C2314yes—
143C83⋊#95C2314yes—
144C83⋊#95C2314yes—
145C83⋊#95C2314yes—
146C83⋊#95C2314yes—
147C83⋊#95C2312yes—
148C83⋊#95C2312yes—
149C22×D4×C83C2311yescharacteristic
150C23×C4×C83C2312yes—
151C4×D4×C83C2×C418yes—
152#117×C83—44no—
153C2×C4⋊C4×C83C2311yescharacteristic
154C2×C4⋊C4×C83C2312yes—
155C2×C4⋊C4×C83C2312yes—
156C2×C4⋊C4×C83C2311yescharacteristic
157C2×C4⋊C4×C83C2312yes—
158C2×C4⋊C4×C83C2311yescharacteristic
159C2×C22⋊C4×C83C2314yes—
160C2×C22⋊C4×C83C2314yes—
161C2×C22⋊C4×C83C2312yes—
162C2×C42×C83C2312yes—
163C2×C42×C83C2314yes—
164C2×C42×C83C2311yescharacteristic
165#95×C83C2314yes—
166#95×C83C2312yes—
167C23×D83C2411yescharacteristic
168#13050589—232no—
169C2×Dic166C22×C414yes—
170C2×Dic166#4114yes—
171C2×Dic166#4114yes—
172C2×C22⋊D83—24no—
173C2×C22⋊D83—24no—
174C2×C22⋊D83C22×C418yes—
175C22×Dic83—24no—
176C22×Dic83—24no—
177C22×Dic83—42no—
178C22×Dic83—42no—
179C22×Dic83C22×C418yes—
180C22×Dic83C22×C418yes—
181C22×Dic83C2412yes—
182C22×Dic83C2412yes—
183C22×Dic83C2414yes—
184C22×Dic83C2411yescharacteristic
185C22×Dic83C2411yescharacteristic
186C22×Dic83C2411yescharacteristic
187C22×Dic83C2412yes—
188C22×Dic83C2412yes—
189C2×C4×D83—22no—
190C2×C4×D83—22no—
191C2×C4×D83—22no—
192C2×C4×D83—22no—
193C2×C4×D83—41no—
194C2×C4×D83—41no—
195C2×C4×D83C22×C414yes—
196C2×C4×D83C22×C414yes—
197C2×C4×D83C22×C414yes—
198C4⋊Dic83—24no—
199C4⋊Dic83—24no—
200C4⋊Dic83—22no—
201C4⋊Dic83—22no—
202C4⋊Dic83—42no—
203C4⋊Dic83C22×C414yes—
204Dic83⋊C4—28no—
205Dic83⋊C4—28no—
206Dic83⋊C4—44no—
207Dic83⋊C4—44no—
208Dic83⋊C4C22×C418yes—
209Dic83⋊C4C22×C418yes—
210C22⋊Dic83—44no—
211C22⋊Dic83—44no—
212C22⋊Dic83C22×C418yes—
213(C2×D83)⋊C4—42no—
214(C2×D83)⋊C4—42no—
215(C2×D83)⋊C4—44no—
216(C2×D83)⋊C4C22×C418yes—
217C4×Dic83—24no—
218C4×Dic83—28no—
219C4×Dic83—28no—
220C4×Dic83—44no—
221C4×Dic83—44no—
222C4×Dic83C22×C414yes—
223C4×Dic83C22×C414yes—
224C4×Dic83C22×C414yes—
225C4×Dic83C22×C418yes—
226C4×Dic83C22×C418yes—
227C4×Dic83C22×C418yes—
228C24×C83C2412yes—
229C2×D4×C83—22no—
230C2×D4×C83—22no—
231C2×D4×C83C22×C414yes—
232C22×C4×C83—24no—
233C22×C4×C83—24no—
234C22×C4×C83C22×C418yes—
235C22×C4×C83C2412yes—
236C22×C4×C83C2412yes—
237C22×C4×C83C2414yes—
238C22×C4×C83C2411yescharacteristic
239C22×C4×C83C2412yes—
240C22×C4×C83C2411yescharacteristic
241C22×C4×C83C2411yescharacteristic
242C4⋊C4×C83—24no—
243C4⋊C4×C83—22no—
244C4⋊C4×C83—24no—
245C4⋊C4×C83—22no—
246C4⋊C4×C83—42no—
247C4⋊C4×C83C22×C414yes—
248C22⋊C4×C83—44no—
249C22⋊C4×C83—44no—
250C22⋊C4×C83C22×C418yes—
251C42×C83—24no—
252C42×C83—44no—
253C42×C83C22×C414yes—
254C23×C83—22no—
255C23×C83—22no—
256C23×C83—22no—
257C23×C83—22no—
258C23×C83—22no—
259C23×C83—22no—
260C23×C83C23×C414yes—
261C23×C83C2511yescharacteristic
262C22×D83—21no—
263C22×D83—21no—
264C22×D83—21no—
265C22×D83—21no—
266C22×D83—21no—
267C22×D83—21no—
268C22×D83C23×C412yes—
269D4×C83—28no—
270C2×C4×C83—22no—
271C2×C4×C83—22no—
272C2×C4×C83—21no—
273C2×C4×C83—21no—
274C2×C4×C83—216no—
275C2×C4×C83—22no—
276C2×C4×C83—22no—
277C2×C4×C83—24no—
278C2×C4×C83—22no—
279C2×C4×C83—24no—
280C2×C4×C83—22no—
281C2×C4×C83—22no—
282C2×C4×C83—24no—
283C2×C4×C83—22no—
284C2×C4×C83C23×C412yes—
285C2×C4×C83C23×C414yes—
286C2×C4×C83C23×C412yes—
287C2×C4×C83C23×C412yes—
288C2×C4×C83C2×#4112yes—
289C2×C4×C83C2×#4112yes—
290C2×C4×C83H(5,𝔽2)12yes—
291C2×C4×C832−1+412yes—
292C22⋊D83—216no—
293C2×Dic83—21no—
294C2×Dic83—21no—
295C2×Dic83—21no—
296C2×Dic83—21no—
297C2×Dic83—22no—
298C2×Dic83—22no—
299C2×Dic83—21no—
300C2×Dic83—21no—
301C2×Dic83—216no—
302C2×Dic83—22no—
303C2×Dic83—22no—
304C2×Dic83—24no—
305C2×Dic83—24no—
306C2×Dic83—22no—
307C2×Dic83—22no—
308C2×Dic83—22no—
309C2×Dic83—22no—
310C2×Dic83—24no—
311C2×Dic83—48no—
312C2×Dic83C23×C412yes—
313C2×Dic83C23×C412yes—
314C2×Dic83C23×C414yes—
315C2×Dic83C23×C412yes—
316C2×Dic83C23×C414yes—
317C2×Dic83C2×#4114yes—
318C2×Dic83C2×#4114yes—
319C4×D83—28no—
320C4×D83—28no—
321C4×D83—44no—
322Dic166#117116yescomplemented
323C22×C83—24no—
324C22×C83—24no—
325C22×C83—24no—
326C22×C83—42no—
327C22×C83—42no—
328C22×C83—42no—
329C22×C83—42no—
330C22×C83C24×C411yescharacteristic
331C22×C83C22×#4111yescharacteristic
332C22×C83C22×#4111yescharacteristic
333C22×C83C2×H(5,𝔽2)11yescharacteristic
334C22×C83C2×2−1+411yescharacteristic
335C22×C83#58511yescharacteristic
336C22×C83#58511yescharacteristic
337C2×D83—22no—
338C2×D83—22no—
339C2×D83—22no—
340C2×D83—41no—
341C2×D83—41no—
342C2×D83—41no—
343C2×D83—41no—
344C4×C83—24no—
345C4×C83—22no—
346C4×C83—44no—
347C4×C83—42no—
348C4×C83—42no—
349C4×C83C2×#11714yes—
350C4×C83#52014yes—
351Dic83—22no—
352Dic83—22no—
353Dic83—22no—
354Dic83—24no—
355Dic83—42no—
356Dic83—44no—
357Dic83—42no—
358Dic83C2×#11718yes—
359#34193—831nomaximal, Sylow
360C2×C83—44no—
361C2×C83C22×#11711yescharacteristic
362C2×C83C2×#52011yescharacteristic
363C2×C83#342811yescharacteristic
364C2×C83#351711yescharacteristic
365C2×C83#351711yescharacteristic
366C2×C83#351811yescharacteristic
367C2×C83#351811yescharacteristic
368D83—42no—
369C2×C4×#41—831no—
370#2354—832no—
371#2354—831no—
372#2354—832no—
373#2354D8311yescharacteristic, complemented
374Q8×C4⋊C4—831no—
375Q8×C4⋊C4—831no—
376#2347—834no—
377#2347—832no—
378#2341—832no—
379#2319—832no—
380#2319—834no—
381#2285—831no—
382#2285—832no—
383#2283—832no—
384#2283—831no—
385#2276—832no—
386C83#3419311yescharacteristic, complemented, Sylow
387C22×#41—831no—
388C4×#41—8316no—
389C2×C4×Q8—831no—
390C2×C4×Q8—832no—
391C2×C4×Q8—831no—
392C2×C4×Q8—832no—
393C2×C4×D4—831no—
394C2×C4×D4—832no—
395C2×C4×D4—832no—
396C2×C4×D4C2×D8311yescharacteristic
397C2×#117—832no—
398C2×#117—832no—
399C2×#117—831no—
400C2×#117—832no—
401C2×#117C2×D8312yes—
402C22×C42—832no—
403C22×C42—831no—
404#390—832no—
405#390—834no—
406#390—834no—
407#390C2×D8312yes—
408#389—834no—
409#389—832no—
410#389—832no—
411#389—834no—
412#388—834no—
413#388—834no—
414#388—834no—
415#388—834no—
416#388—834no—
417#388C2×D8314yes—
418#384—832no—
419#384—832no—
420#384—831no—
421#384C2×D8311yescharacteristic
422#383—832no—
423#383—834no—
424#382—831no—
425#382—832no—
426#382—831no—
427#381—834no—
428#381—832no—
429#380—832no—
430#380—832no—
431#380—832no—
432#380—831no—
433#380—831no—
434#380—834no—
435#380—834no—
436#380C2×D8312yes—
437C4×C4⋊C4—832no—
438C4×C4⋊C4—832no—
439C4×C4⋊C4—832no—
440C4×C4⋊C4—832no—
441C4×C4⋊C4—832no—
442C4×C4⋊C4—831no—
443C4×C4⋊C4—834no—
444C4×C4⋊C4—834no—
445C4×C4⋊C4—834no—
446C4×C4⋊C4—834no—
447C4×C4⋊C4C2×D8312yes—
448C4×C4⋊C4C2×D8311yescharacteristic
449C4×C22⋊C4—834no—
450C4×C22⋊C4—832no—
451#376—832no—
452#376—834no—
453C2×#41—838no—
454C2×#41—1664no—
455C2×#41—1664no—
456C22×Q8—831no—
457C22×D4—832no—
458C22×D4C22×D8311yescharacteristic
459C23×C4—832no—
460C23×C4—831no—
461C23×C4—832no—
462C23×C4—831no—
463C23×C4—831no—
464C23×C4C22×D8312yes—
465C4×Q8—838no—
466C4×Q8—838no—
467C4×Q8—1668no—
468C4×Q8—1668no—
469C4×D4—838no—
470C4×D4—8316no—
471C4×D4—8316no—
472C4×D4C4×D8318yes—
473#117—44no—
474#117—3324no—
475#117—3324no—
476#117—838no—
477#117—8316no—
478C2×C4⋊C4—834no—
479C2×C4⋊C4—834no—
480C2×C4⋊C4—832no—
481C2×C4⋊C4—832no—
482C2×C4⋊C4—832no—
483C2×C4⋊C4—831no—
484C2×C4⋊C4—831no—
485C2×C4⋊C4—832no—
486C2×C4⋊C4—834no—
487C2×C4⋊C4—834no—
488C2×C4⋊C4—832no—
489C2×C4⋊C4—831no—
490C2×C4⋊C4C22×D8312yes—
491C2×C4⋊C4C22×D8311yescharacteristic
492C2×C4⋊C4C22×D8312yes—
493C2×C4⋊C4C22×D8311yescharacteristic
494C2×C4⋊C4C22×D8312yes—
495C2×C4⋊C4C22×D8311yescharacteristic
496C2×C22⋊C4—834no—
497C2×C22⋊C4—834no—
498C2×C22⋊C4—834no—
499C2×C22⋊C4—832no—
500C2×C22⋊C4—832no—
501C2×C22⋊C4—832no—
502C2×C22⋊C4—832no—
503C2×C22⋊C4C22×D8314yes—
504C2×C22⋊C4C22×D8314yes—
505C2×C22⋊C4C22×D8312yes—
506C2×C42—834no—
507C2×C42—834no—
508C2×C42—8316no—
509C2×C42—831no—
510C2×C42—832no—
511C2×C42—832no—
512C2×C42—831no—
513C2×C42—832no—
514C2×C42—831no—
515C2×C42—838no—
516C2×C42—834no—
517C2×C42—834no—
518C2×C42—832no—
519C2×C42C22×D8312yes—
520C2×C42C22×D8314yes—
521C2×C42C22×D8311yescharacteristic
522#95—832no—
523#95—834no—
524#95—832no—
525#95—832no—
526#95—832no—
527#95—834no—
528#95—832no—
529#95—834no—
530#95—832no—
531#95—834no—
532#95—834no—
533#95—832no—
534#95C22×D8314yes—
535#95C22×D8312yes—
536C24—831no—
537C24C23×D8312yes—
538#41—16632no—
539C2×Q8—834no—
540C2×Q8—834no—
541C2×Q8—834no—
542C2×D4—22no—
543C2×D4—22no—
544C2×D4—838no—
545C2×D4—1664no—
546C2×D4—1664no—
547C2×D4C2×C4×D8314yes—
548C22×C4—24no—
549C22×C4—24no—
550C22×C4—3321no—
551C22×C4—3321no—
552C22×C4—3322no—
553C22×C4—3322no—
554C22×C4—838no—
555C22×C4—834no—
556C22×C4—832no—
557C22×C4—838no—
558C22×C4—831no—
559C22×C4—831no—
560C22×C4—831no—
561C22×C4—832no—
562C22×C4—834no—
563C22×C4—834no—
564C22×C4—832no—
565C22×C4—832no—
566C22×C4—834no—
567C22×C4—1664no—
568C22×C4—1664no—
569C22×C4—1662no—
570C22×C4—1662no—
571C22×C4—1662no—
572C22×C4—1662no—
573C22×C4C2×C4×D8318yes—
574C22×C4C23×D8312yes—
575C22×C4C23×D8314yes—
576C22×C4C23×D8312yes—
577C22×C4C23×D8312yes—
578C22×C4C23×D8311yescharacteristic
579C22×C4C23×D8311yescharacteristic
580C22×C4C23×D8311yescharacteristic
581C4⋊C4—24no—
582C4⋊C4—22no—
583C4⋊C4—24no—
584C4⋊C4—22no—
585C4⋊C4—42no—
586C4⋊C4—3324no—
587C4⋊C4—3324no—
588C4⋊C4—3322no—
589C4⋊C4—838no—
590C4⋊C4—838no—
591C4⋊C4—834no—
592C4⋊C4—1668no—
593C4⋊C4—1668no—
594C4⋊C4—1664no—
595C4⋊C4—1664no—
596C4⋊C4—1662no—
597C4⋊C4—1662no—
598C4⋊C4C2×C4×D8314yes—
599C22⋊C4—44no—
600C22⋊C4—44no—
601C22⋊C4—3324no—
602C22⋊C4—3322no—
603C22⋊C4—3322no—
604C22⋊C4—3324no—
605C22⋊C4—3324no—
606C22⋊C4—838no—
607C22⋊C4—838no—
608C22⋊C4C2×C4×D8318yes—
609C42—24no—
610C42—44no—
611C42—3324no—
612C42—3324no—
613C42—834no—
614C42—838no—
615C42—834no—
616C42—838no—
617C42—838no—
618C42—834no—
619C42—1668no—
620C42—1668no—
621C42—1664no—
622C42C2×C4×D8314yes—
623C23—22no—
624C23—22no—
625C23—22no—
626C23—22no—
627C23—22no—
628C23—22no—
629C23—832no—
630C23—1661no—
631C23—1661no—
632C23—1661no—
633C23—1661no—
634C23—1661no—
635C23—1661no—
636C23C22×C4×D8314yes—
637C23C24×D8311yescharacteristic
638Q8—8316no—
639D4—28no—
640D4—16616no—
641C2×C4—22no—
642C2×C4—22no—
643C2×C4—21no—
644C2×C4—21no—
645C2×C4—216no—
646C2×C4—22no—
647C2×C4—22no—
648C2×C4—24no—
649C2×C4—22no—
650C2×C4—24no—
651C2×C4—22no—
652C2×C4—22no—
653C2×C4—24no—
654C2×C4—22no—
655C2×C4—3324no—
656C2×C4—3328no—
657C2×C4—834no—
658C2×C4—834no—
659C2×C4—834no—
660C2×C4—832no—
661C2×C4—832no—
662C2×C4—832no—
663C2×C4—834no—
664C2×C4—1662no—
665C2×C4—1662no—
666C2×C4—1664no—
667C2×C4—1662no—
668C2×C4—1664no—
669C2×C4—1662no—
670C2×C4—1662no—
671C2×C4—1662no—
672C2×C4—1664no—
673C2×C4—16616no—
674C2×C4—1661no—
675C2×C4—1661no—
676C2×C4—1661no—
677C2×C4—1661no—
678C2×C4—1662no—
679C2×C4—1661no—
680C2×C4—1662no—
681C2×C4—1661no—
682C2×C4—1668no—
683C2×C4—1668no—
684C2×C4C22×C4×D8314yes—
685C2×C4C22×C4×D8312yes—
686C2×C4C22×C4×D8312yes—
687C2×C4C22×C4×D8312yes—
688C2×C4#41×D8312yes—
689C2×C4#41×D8312yes—
690C2×C4#1458183712yes—
691C2×C4#1458183912yes—
692C22—24no—
693C22—24no—
694C22—24no—
695C22—42no—
696C22—42no—
697C22—42no—
698C22—42no—
699C22—3321no—
700C22—3321no—
701C22—3321no—
702C22—3321no—
703C22—1662no—
704C22—1662no—
705C22—1662no—
706C22C23×C4×D8311yescharacteristic
707C22C2×#41×D8311yescharacteristic
708C22C2×#41×D8311yescharacteristic
709C22C2×#1458183711yescharacteristic
710C22C2×#1458183911yescharacteristic
711C22#1912853611yescharacteristic
712C22#1912853811yescharacteristic
713C4—24no—
714C4—22no—
715C4—44no—
716C4—42no—
717C4—42no—
718C4—3322no—
719C4—3324no—
720C4—3322no—
721C4—838no—
722C4—1662no—
723C4—1662no—
724C4—1662no—
725C4—1664no—
726C4#117×D8314yes—
727C4#1912818014yes—
728C2—44no—
729C2—3322no—
730C2C2×#117×D8311yescharacteristic
731C2C2×#1912818011yescharacteristic
732C2#2492066311yescharacteristic
733C2#2492146611yescharacteristic
734C2#2492146811yescharacteristic
735C2#2492147711yescharacteristic
736C2#2492147911yescharacteristic
subgroupG/H
center, FrattiniC23C24×D83
commutatorC22×C83C24×C4
FittingC83×#2354C2
socle, cosocleC23×C83C25
prime radicalC22×#13050589C22
hypercenter#2354D83
hypocenterC83#34193
LCSG ▷ C22×C83 ▷ C83
UCSC1 ◁ C23 ◁ #2354

Complements

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

NH ≅ G/Ntype
2. #24910413C2semidirect
3. #24910412C2semidirect
4. #24910407C2semidirect
5. C4⋊C4×Dic166C2semidirect
6. #24910375C2semidirect
7. #24910353C2semidirect
8. #24910352C2semidirect
10. #24910104C2semidirect
11. #24910100C2semidirect
12. #24909868C2semidirect
13. #24909866C2semidirect
14. #24909859C2semidirect
15. #24909858C2semidirect
16. #24909827C2semidirect
17. C83×#2354C2semidirect
19. C4×#13050589C4semidirect
322. Dic166#117semidirect
373. #2354D83semidirect
386. C83#34193semidirect

Maximal subgroups

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

subgroupindex
C2×C4×#130505892
#249104132
#249104122
#249104072
C4⋊C4×Dic1662
#249103752
#249103532
#249103522
#249103022
#249101042
#249101002
#249098682
#249098662
#249098592
#249098582
#249098272
C83×#23542
#3419383