Finite Group Databasebeta

← #35414169

Subgroups — #35414169

Order 21248.

1086 conjugacy classes of subgroups.

The subgroup lattice has 716 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#19128322C211yesmaximal, characteristic
2#24910086C211yesmaximal, characteristic, complemented
3#24908436C211yesmaximal, characteristic, complemented
4#24908424C211yesmaximal, characteristic, complemented
5#24908279C211yesmaximal, characteristic, complemented
6#24908274C211yesmaximal, characteristic, complemented
7#24907783C211yesmaximal, characteristic
8#24907778C211yesmaximal, characteristic
9#24907773C211yesmaximal, characteristic, complemented
10#24907768C211yesmaximal, characteristic, complemented
11#24907479C211yesmaximal, characteristic, complemented
12#24907474C211yesmaximal, characteristic, complemented
13#24907469C211yesmaximal, characteristic, complemented
14#24907464C211yesmaximal, characteristic, complemented
15C2×#433×C83C211yesmaximal, characteristic, complemented
16#19128322—24no—
17#19128322C418yescomplemented
18C2×#14581792C2211yescharacteristic
19C2×#14581787—21no—
20C2×#14581780C2211yescharacteristic
21C2×#14581778—21no—
22C2×#14581774—21no—
23C2×#14581771C2211yescharacteristic
24C2×#14581770—21no—
25C2×#14581766C2211yescharacteristic
26C2×C4×Dic166C2211yescharacteristic
27C2×C4×D332C2211yescharacteristic
28C2×#14581751C2211yescharacteristic
29C22×C4⋊Dic83C2211yescharacteristic
30C2×#14581717C2211yescharacteristic
31C2×#14581717C2211yescharacteristic
32C2×#14581717C2211yescharacteristic
33C2×#14581717C2211yescharacteristic
34C2×#14581714C2211yescharacteristic
35C2×#14581714C2211yescharacteristic
36C2×#14581714C2211yescharacteristic
37C2×#14581714C2211yescharacteristic
38#19127600—21no—
39#19127600—21no—
40#19127576—21no—
41#19127576—21no—
42#19127571C2211yescharacteristic
43#19127571C2211yescharacteristic
44#19127567C2211yescharacteristic
45#19127567C2211yescharacteristic
46#19127464C2211yescharacteristic
47#19127464C2211yescharacteristic
48#19127464C2211yescharacteristic
49#19127464C2211yescharacteristic
50#19127464C2211yescharacteristic
51#19127464C2211yescharacteristic
52#19127464C2211yescharacteristic
53#19127464C2211yescharacteristic
54C2×#117×C83C2211yescharacteristic
55#433×C83—24no—
56C2×C4⋊C8×C83C2211yescharacteristic
57C2×C4⋊C8×C83C2211yescharacteristic
58C2×C22⋊C8×C83C2211yescharacteristic
59C2×C22⋊C8×C83C2211yescharacteristic
60C2×#97×C83C2211yescharacteristic
61C2×C4×C8×C83C2211yescharacteristic
62C22×Dic166—21no—
63C22×Dic166C2311yescharacteristic
64C22×D332C2311yescharacteristic
65C22×C22⋊D83—21no—
66C23×Dic83—21no—
67C22×C4×D83—21no—
68#14581792—22no—
69#14581792C2×C414yescomplemented
70#14581787—28no—
71#14581780—22no—
72#14581780C2×C414yescomplemented
73#14581778—28no—
74#14581774—28no—
75#14581771—22no—
76#14581771C2×C414yes—
77#14581770—28no—
78#14581766—22no—
79#14581766C2×C414yes—
80C4×Dic166—22no—
81C4×Dic166C2×C414yescomplemented
82C4×D332—22no—
83C4×D332C2×C414yescomplemented
84#14581751—41no—
85#14581751—41no—
86C2×C4⋊Dic83—21no—
87C2×C4⋊Dic83—21no—
88C2×C4⋊Dic83—21no—
89C2×C4⋊Dic83—21no—
90C2×C4⋊Dic83—21no—
91C2×C4⋊Dic83—21no—
92C2×C4⋊Dic83—41no—
93C2×C4⋊Dic83—41no—
94C2×C4⋊Dic83C2311yescharacteristic
95C2×C4⋊Dic83C2311yescharacteristic
96C2×C4⋊Dic83C2311yescharacteristic
97C2×C4⋊Dic83C2311yescharacteristic
98C2×C4⋊Dic83C2311yescharacteristic
99C2×C4⋊Dic83C2311yescharacteristic
100C2×Dic83⋊C4—21no—
101C2×Dic83⋊C4—21no—
102C2×C22⋊Dic83—21no—
103C2×C22⋊Dic83—21no—
104C2×(C2×D83)⋊C4—21no—
105C2×(C2×D83)⋊C4—21no—
106C2×(C2×D83)⋊C4—21no—
107C2×(C2×D83)⋊C4—21no—
108C2×C4×Dic83—21no—
109C2×C4×Dic83—21no—
110#14581717—41no—
111#14581717—41no—
112#14581717—41no—
113#14581717—41no—
114#14581714—41no—
115#14581714—41no—
116#14581714—41no—
117#14581714—41no—
118C83⋊#95—21no—
119C83⋊#95—21no—
120C83⋊#95—21no—
121C83⋊#95—21no—
122C23×C4×C83C2311yescharacteristic
123C22×C8×C83C2311yescharacteristic
124C22×C8×C83C2311yescharacteristic
125C22×C8×C83C2311yescharacteristic
126C22×C8×C83C2311yescharacteristic
127#117×C83C2×C414yes—
128#117×C83D414yes—
129C2×C4⋊C4×C83D411yescharacteristic
130C2×C4⋊C4×C83D411yescharacteristic
131C2×C22⋊C4×C83D411yescharacteristic
132C2×C22⋊C4×C83D411yescharacteristic
133C2×C42×C83C2311yescharacteristic
134C2×C42×C83C2311yescharacteristic
135C4⋊C8×C83—22no—
136C4⋊C8×C83—22no—
137C22⋊C8×C83—22no—
138C22⋊C8×C83—22no—
139#97×C83—22no—
140C4×C8×C83—22no—
141C23×D83—21no—
142C2×Dic166—21no—
143C2×Dic166—21no—
144C2×Dic166—21no—
145C2×Dic166—21no—
146C2×Dic166—21no—
147C2×Dic166—24no—
148C2×Dic166—81no—
149C2×Dic166—81no—
150C2×Dic166C22×C412yes—
151C2×D332—21no—
152C2×D332—21no—
153C2×D332—21no—
154C2×D332—21no—
155C2×D332—21no—
156C2×D332C22×C412yes—
157C2×C22⋊D83—24no—
158C2×C22⋊D83—81no—
159C2×C22⋊D83—81no—
160C22×Dic83—21no—
161C22×Dic83—21no—
162C22×Dic83—21no—
163C22×Dic83—21no—
164C22×Dic83—21no—
165C22×Dic83—21no—
166C22×Dic83—21no—
167C22×Dic83—42no—
168C22×Dic83—81no—
169C22×Dic83—81no—
170C2×C4×D83—24no—
171C2×C4×D83—81no—
172C2×C4×D83—81no—
173C4⋊Dic83—24no—
174C4⋊Dic83—21no—
175C4⋊Dic83—21no—
176C4⋊Dic83—21no—
177C4⋊Dic83—21no—
178C4⋊Dic83—21no—
179C4⋊Dic83—21no—
180C4⋊Dic83—21no—
181C4⋊Dic83—21no—
182C4⋊Dic83—21no—
183C4⋊Dic83—21no—
184C4⋊Dic83—42no—
185C4⋊Dic83—81no—
186C4⋊Dic83—81no—
187C4⋊Dic83—81no—
188C4⋊Dic83—81no—
189C4⋊Dic83C22×C412yes—
190C4⋊Dic83C22×C412yes—
191Dic83⋊C4—24no—
192Dic83⋊C4—24no—
193C22⋊Dic83—24no—
194C22⋊Dic83—42no—
195(C2×D83)⋊C4—24no—
196(C2×D83)⋊C4—24no—
197(C2×D83)⋊C4—24no—
198(C2×D83)⋊C4—24no—
199C4×Dic83—24no—
200C4×Dic83—42no—
201C24×C83C2×D411yescharacteristic
202C22×C4×C83—21no—
203C22×C4×C83—21no—
204C22×C4×C83—21no—
205C22×C4×C83—21no—
206C22×C4×C83C22×C412yes—
207C22×C4×C83C2×D412yes—
208C22×C4×C83C2×D411yescharacteristic
209C22×C4×C83C2×D411yescharacteristic
210C22×C4×C83C2×D411yescharacteristic
211C22×C4×C83C2×D411yescharacteristic
212C22×C4×C83C2×D411yescharacteristic
213C22×C4×C83C2411yescharacteristic
214C2×C8×C83—21no—
215C2×C8×C83—21no—
216C2×C8×C83—21no—
217C2×C8×C83—21no—
218C2×C8×C83—21no—
219C2×C8×C83—21no—
220C2×C8×C83—21no—
221C2×C8×C83—21no—
222C2×C8×C83—21no—
223C2×C8×C83—21no—
224C2×C8×C83—21no—
225C2×C8×C83—21no—
226C4⋊C4×C83C22⋊C414yes—
227C4⋊C4×C83C22⋊C414yes—
228C22⋊C4×C83C22⋊C414yes—
229C22⋊C4×C83C22⋊C414yes—
230C42×C83C22×C412yes—
231C42×C83C22×C412yes—
232C42×C83C2×D412yes—
233C42×C83C2×D412yes—
234C23×C83—21no—
235C23×C83—21no—
236C23×C83—21no—
237C23×C83—21no—
238C23×C83—21no—
239C23×C83—21no—
240C23×C83C2×C22⋊C412yes—
241C23×C83C22×D411yescharacteristic
242C22×D83—22no—
243C22×D83—41no—
244C22×D83—41no—
245C22×D83—41no—
246C22×D83—41no—
247C22×D83—41no—
248C22×D83—41no—
249C2×C4×C83—21no—
250C2×C4×C83—21no—
251C2×C4×C83—21no—
252C2×C4×C83—21no—
253C2×C4×C83—21no—
254C2×C4×C83—21no—
255C2×C4×C83—21no—
256C2×C4×C83—21no—
257C2×C4×C83—21no—
258C2×C4×C83—21no—
259C2×C4×C83—22no—
260C2×C4×C83—22no—
261C2×C4×C83—22no—
262C2×C4×C83—22no—
263C2×C4×C83C2×C22⋊C412yes—
264C2×C4×C83C2×C22⋊C412yes—
265C2×C4×C83C2×C22⋊C412yes—
266C2×C4×C83C2×C22⋊C412yes—
267C2×C4×C83C2×C22⋊C412yes—
268C2×C4×C83C23×C411yescharacteristic
269C2×C4×C83C22×D411yescharacteristic
270C2×C4×C83H(5,𝔽2)11yescharacteristic
271C2×C4×C83H(5,𝔽2)11yescharacteristic
272C2×C4×C832−1+411yescharacteristic
273C2×C4×C832−1+411yescharacteristic
274C22⋊D83—84no—
275C2×Dic83—22no—
276C2×Dic83—22no—
277C2×Dic83—22no—
278C2×Dic83—41no—
279C2×Dic83—41no—
280C2×Dic83—41no—
281C2×Dic83—41no—
282C2×Dic83—41no—
283C2×Dic83—41no—
284C2×Dic83—41no—
285C2×Dic83—41no—
286C2×Dic83—41no—
287C2×Dic83—41no—
288C2×Dic83—41no—
289C2×Dic83—41no—
290C2×Dic83—41no—
291C2×Dic83—41no—
292C2×Dic83—41no—
293C2×Dic83—41no—
294C2×Dic83—41no—
295C2×Dic83—41no—
296C2×Dic83—84no—
297D332—22no—
298D332—22no—
299D332—41no—
300D332—41no—
301C4×D83—84no—
302Dic166—22no—
303Dic166—22no—
304Dic166—41no—
305Dic166—41no—
306Dic166—84no—
307C8×C83—41no—
308C8×C83—41no—
309C8×C83—41no—
310C8×C83—41no—
311C22×C83—22no—
312C22×C83—22no—
313C22×C83—22no—
314C22×C83—41no—
315C22×C83—41no—
316C22×C83—41no—
317C22×C83—41no—
318C22×C83C22×C22⋊C411yescharacteristic
319C22×C83#53511yescharacteristic
320C22×C83#53611yescharacteristic
321C22×C83#57611yescharacteristic
322C22×C83#57711yescharacteristic
323C22×C83#57711yescharacteristic
324C22×C83#57811yescharacteristic
325C2×D83—42no—
326C2×D83—42no—
327C2×D83—42no—
328C2×D83—81no—
329C2×D83—81no—
330C2×D83—81no—
331C2×D83—81no—
332C4×C83—22no—
333C4×C83—22no—
334C4×C83—22no—
335C4×C83—22no—
336C4×C83—22no—
337C4×C83#52011yescharacteristic
338C4×C83#52011yescharacteristic
339C4×C83#53711yescharacteristic
340C4×C83#53711yescharacteristic
341Dic83—42no—
342Dic83—42no—
343Dic83—42no—
344Dic83—81no—
345Dic83—81no—
346Dic83—81no—
347Dic83—81no—
348#21871—831nomaximal, Sylow
349C2×C83—42no—
350C2×C83#231111yescharacteristic
351C2×C83#289711yescharacteristic
352C2×C83#289811yescharacteristic
353C2×C83#322411yescharacteristic
354C2×C83#322511yescharacteristic
355C2×C83#324311yescharacteristic
356C2×C83#324411yescharacteristic
357D83—82no—
358C2×#542—831no—
359C2×#433D8311yescharacteristic, complemented
360#2317—831no—
361#1993—831no—
362#1990—831no—
363#1959—831no—
364#1958—831no—
365#1875—831no—
366#1874—831no—
367#1873—831no—
368#1872—831no—
369#1805—831no—
370#1804—831no—
371#1803—831no—
372#1802—831no—
373C83#2187111yescharacteristic, complemented, Sylow
374#542—838no—
375#542—1664no—
376C2×C4⋊Q8—831no—
377C2×#126—1661no—
378C2×#124—831no—
379C2×#124—1661no—
380C2×#123—1661no—
381C2×C22⋊Q8—831no—
382C2×C22⋊Q8—1661no—
383C2×#121—831no—
384C2×C4×Q8—831no—
385C2×C4×D4—831no—
386C2×#117—831no—
387C2×#117C2×D8311yescharacteristic
388C22×C4⋊C4—831no—
389#433—24no—
390C2×C4⋊C8C2×D8311yescharacteristic
391C2×C4⋊C8C2×D8311yescharacteristic
392C2×#103—831no—
393C2×#103—831no—
394C2×#103—831no—
395C2×#103—831no—
396C2×#102—831no—
397C2×#102—831no—
398C2×#102—831no—
399C2×#102—831no—
400C2×C22⋊C8C2×D8311yescharacteristic
401C2×C22⋊C8C2×D8311yescharacteristic
402C2×#97C2×D8311yescharacteristic
403C2×C4×C8C2×D8311yescharacteristic
404#389—1661no—
405#389—1661no—
406#385—1661no—
407#385—1661no—
408#384—831no—
409#384—831no—
410#382—831no—
411#382—831no—
412#340—831no—
413#340—831no—
414#340—831no—
415#340—831no—
416#340—831no—
417#340—831no—
418#340—831no—
419#340—831no—
420C22×Q8—831no—
421C22×Q8—1661no—
422C22×D4—831no—
423C22×D4—1661no—
424C23×C4—1661no—
425C23×C4—1661no—
426C23×C4C22×D8311yescharacteristic
427C22×C8C22×D8311yescharacteristic
428C22×C8C22×D8311yescharacteristic
429C22×C8C22×D8311yescharacteristic
430C22×C8C22×D8311yescharacteristic
431C4⋊Q8—834no—
432C4⋊Q8—1662no—
433#126—1668no—
434#124—834no—
435#124—1668no—
436#124—1662no—
437#123—1668no—
438C22⋊Q8—834no—
439C22⋊Q8—1662no—
440C22⋊Q8—1668no—
441#121—834no—
442#121—1662no—
443C4×Q8—834no—
444C4×Q8—1662no—
445C4×D4—834no—
446C4×D4—1662no—
447#117—3321no—
448#117—3321no—
449#117C4×D8314yes—
450#117C22⋊D8314yes—
451C2×C4⋊C4—3321no—
452C2×C4⋊C4—3321no—
453C2×C4⋊C4—831no—
454C2×C4⋊C4—831no—
455C2×C4⋊C4—831no—
456C2×C4⋊C4—831no—
457C2×C4⋊C4—831no—
458C2×C4⋊C4—831no—
459C2×C4⋊C4—1661no—
460C2×C4⋊C4—1661no—
461C2×C4⋊C4—1661no—
462C2×C4⋊C4—1661no—
463C2×C4⋊C4—1661no—
464C2×C4⋊C4—1661no—
465C2×C4⋊C4—1661no—
466C2×C4⋊C4—1661no—
467C2×C4⋊C4D33211yescharacteristic
468C2×C4⋊C4D33211yescharacteristic
469C2×C22⋊C4—1661no—
470C2×C22⋊C4—1661no—
471C2×C22⋊C4—1661no—
472C2×C22⋊C4—1661no—
473C2×C22⋊C4—1661no—
474C2×C22⋊C4—1661no—
475C2×C22⋊C4D33211yescharacteristic
476C2×C22⋊C4D33211yescharacteristic
477C2×C42—1661no—
478C2×C42—1661no—
479C2×C42C22×D8311yescharacteristic
480C2×C42C22×D8311yescharacteristic
481C4⋊C8—22no—
482C4⋊C8—22no—
483#103—3321no—
484#103—3321no—
485#103—3321no—
486#103—3321no—
487#102—3321no—
488#102—3321no—
489#102—3321no—
490#102—3321no—
491C22⋊C8—22no—
492C22⋊C8—22no—
493#97—22no—
494C4×C8—22no—
495#95—1661no—
496#95—1661no—
497#95—1661no—
498#95—1661no—
499C24—1661no—
500C24C2×D33211yescharacteristic
501C2×Q8—832no—
502C2×Q8—6641no—
503C2×Q8—6641no—
504C2×Q8—1661no—
505C2×Q8—1661no—
506C2×Q8—1661no—
507C2×Q8—1661no—
508C2×Q8—1661no—
509C2×Q8—1664no—
510C2×D4—832no—
511C2×D4—6641no—
512C2×D4—6641no—
513C2×D4—1664no—
514C2×D4—1661no—
515C2×D4—1661no—
516C2×D4—1661no—
517C2×D4—1661no—
518C2×D4—1661no—
519C22×C4—21no—
520C22×C4—21no—
521C22×C4—21no—
522C22×C4—21no—
523C22×C4—3322no—
524C22×C4—6641no—
525C22×C4—6641no—
526C22×C4—6641no—
527C22×C4—6641no—
528C22×C4—1661no—
529C22×C4—1661no—
530C22×C4—1661no—
531C22×C4—1661no—
532C22×C4—1661no—
533C22×C4—1661no—
534C22×C4—1661no—
535C22×C4—1664no—
536C22×C4C2×C4×D8312yes—
537C22×C4C2×C22⋊D8312yes—
538C22×C4C2×D33211yescharacteristic
539C22×C4C2×D33211yescharacteristic
540C22×C4C2×D33211yescharacteristic
541C22×C4C2×D33211yescharacteristic
542C22×C4C2×D33211yescharacteristic
543C22×C4C23×D8311yescharacteristic
544C2×C8—21no—
545C2×C8—21no—
546C2×C8—21no—
547C2×C8—21no—
548C2×C8—21no—
549C2×C8—21no—
550C2×C8—21no—
551C2×C8—21no—
552C2×C8—21no—
553C2×C8—21no—
554C2×C8—21no—
555C2×C8—21no—
556C4⋊C4—3322no—
557C4⋊C4—832no—
558C4⋊C4—832no—
559C4⋊C4—6641no—
560C4⋊C4—6641no—
561C4⋊C4—6641no—
562C4⋊C4—6641no—
563C4⋊C4—1661no—
564C4⋊C4—1661no—
565C4⋊C4—1661no—
566C4⋊C4—1661no—
567C4⋊C4—1661no—
568C4⋊C4—1661no—
569C4⋊C4—1661no—
570C4⋊C4—1661no—
571C4⋊C4—1661no—
572C4⋊C4—1661no—
573C4⋊C4—1664no—
574C4⋊C4—1664no—
575C4⋊C4—1664no—
576C4⋊C4(C2×D83)⋊C414yes—
577C4⋊C4(C2×D83)⋊C414yes—
578C22⋊C4—3322no—
579C22⋊C4—1664no—
580C22⋊C4—1664no—
581C22⋊C4—1664no—
582C22⋊C4—1664no—
583C22⋊C4—1664no—
584C22⋊C4(C2×D83)⋊C414yes—
585C22⋊C4(C2×D83)⋊C414yes—
586C42—3322no—
587C42—1664no—
588C42C2×C4×D8312yes—
589C42C2×C4×D8312yes—
590C42C2×C22⋊D8312yes—
591C42C2×C22⋊D8312yes—
592C23—21no—
593C23—21no—
594C23—21no—
595C23—21no—
596C23—21no—
597C23—21no—
598C23—3321no—
599C23—3321no—
600C23—3321no—
601C23—3321no—
602C23—3321no—
603C23—3321no—
604C23—1662no—
605C23C2×(C2×D83)⋊C412yes—
606C23C22×D33211yescharacteristic
607Q8—3321no—
608Q8—3321no—
609Q8—6644no—
610Q8—1662no—
611Q8—1662no—
612D4—3321no—
613D4—3321no—
614D4—6644no—
615D4—1662no—
616D4—1662no—
617C2×C4—21no—
618C2×C4—21no—
619C2×C4—21no—
620C2×C4—21no—
621C2×C4—21no—
622C2×C4—21no—
623C2×C4—21no—
624C2×C4—21no—
625C2×C4—21no—
626C2×C4—21no—
627C2×C4—22no—
628C2×C4—22no—
629C2×C4—22no—
630C2×C4—22no—
631C2×C4—3321no—
632C2×C4—3321no—
633C2×C4—3321no—
634C2×C4—3321no—
635C2×C4—3321no—
636C2×C4—3321no—
637C2×C4—3321no—
638C2×C4—3321no—
639C2×C4—3321no—
640C2×C4—3321no—
641C2×C4—3321no—
642C2×C4—3321no—
643C2×C4—3321no—
644C2×C4—3321no—
645C2×C4—3321no—
646C2×C4—3321no—
647C2×C4—3321no—
648C2×C4—3321no—
649C2×C4—6644no—
650C2×C4—6644no—
651C2×C4—1662no—
652C2×C4—1662no—
653C2×C4—1662no—
654C2×C4C2×(C2×D83)⋊C412yes—
655C2×C4C2×(C2×D83)⋊C412yes—
656C2×C4C2×(C2×D83)⋊C412yes—
657C2×C4C2×(C2×D83)⋊C412yes—
658C2×C4C2×(C2×D83)⋊C412yes—
659C2×C4C22×C4×D8311yescharacteristic
660C2×C4C22×C22⋊D8311yescharacteristic
661C2×C4#1458183811yescharacteristic
662C2×C4#1458183811yescharacteristic
663C2×C4#1458183911yescharacteristic
664C2×C4#1458183911yescharacteristic
665C8—41no—
666C8—41no—
667C8—41no—
668C8—41no—
669C22—22no—
670C22—22no—
671C22—22no—
672C22—41no—
673C22—41no—
674C22—41no—
675C22—41no—
676C22—3322no—
677C22—3322no—
678C22—3322no—
679C22—6641no—
680C22—6641no—
681C22—6641no—
682C22—6641no—
683C22C22×(C2×D83)⋊C411yescharacteristic
684C22#1912827011yescharacteristic
685C22#1912827711yescharacteristic
686C22#1912850611yescharacteristic
687C22#1912851311yescharacteristic
688C22#1912851311yescharacteristic
689C22#1912851811yescharacteristic
690C4—22no—
691C4—22no—
692C4—22no—
693C4—22no—
694C4—22no—
695C4—3322no—
696C4—3322no—
697C4—3322no—
698C4—6641no—
699C4—6641no—
700C4—6641no—
701C4—6641no—
702C4#1912818111yescharacteristic
703C4#1912818111yescharacteristic
704C4#1912827911yescharacteristic
705C4#1912827911yescharacteristic
706C2—42no—
707C2—6642no—
708C2#2491005111yescharacteristic
709C2#2491599011yescharacteristic
710C2#2491599711yescharacteristic
711C2#2491855911yescharacteristic
712C2#2491857411yescharacteristic
713C2#2491874811yescharacteristic
714C2#2491876311yescharacteristic
subgroupG/H
centerC23C22×D332
commutatorC2×C4×C83C23×C4
FrattiniC22×C4C23×D83
FittingC2×#433×C83C2
socleC23×C83C22×D4
prime radicalC2×#14581766C22
cosocleC22×C4×C83C24
hypercenterC2×#433D83
hypocenterC83#21871
LCSG ▷ C2×C4×C83 ▷ C2×C83 ▷ C83
UCSC1 ◁ C23 ◁ C2×#117 ◁ C2×#433

Complements

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

NH ≅ G/Ntype
2. #24910086C2semidirect
3. #24908436C2semidirect
4. #24908424C2semidirect
5. #24908279C2semidirect
6. #24908274C2semidirect
9. #24907773C2semidirect
10. #24907768C2semidirect
11. #24907479C2semidirect
12. #24907474C2semidirect
13. #24907469C2semidirect
14. #24907464C2semidirect
15. C2×#433×C83C2semidirect
17. #19128322C4semidirect
69. #14581792C2×C4semidirect
72. #14581780C2×C4semidirect
81. C4×Dic166C2×C4semidirect
83. C4×D332C2×C4semidirect
359. C2×#433D83semidirect
373. C83#21871semidirect

Maximal subgroups

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

subgroupindex
C2×#191283222
#249100862
#249084362
#249084242
#249082792
#249082742
#249077832
#249077782
#249077732
#249077682
#249074792
#249074742
#249074692
#249074642
C2×#433×C832
#2187183