Finite Group Databasebeta

← #35565349

Subgroups — #35565349

Order 21248.

3106 conjugacy classes of subgroups.

The subgroup lattice has 796 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#19128182C211yesmaximal, characteristic
2C2×#19128182C211yesmaximal, characteristic
3C2×C4×#13050590C211yesmaximal, characteristic
4#24910382C212yesmaximal, complemented
5#24910377C212yesmaximal, complemented
6#24910372C212yesmaximal, complemented
7#24910370C214yesmaximal, complemented
8#24910364C212yesmaximal, complemented
9C4⋊C4×C22⋊D83C214yesmaximal, complemented
10#24910087C211yesmaximal, characteristic, complemented
11#24910085C212yesmaximal, complemented
12#24910081C211yesmaximal, characteristic, complemented
13#24910078C212yesmaximal, complemented
14#24909946C211yesmaximal, characteristic, complemented
15#24909944C212yesmaximal, complemented
16#389×D83C212yesmaximal, complemented
17C2×#389×C83C211yesmaximal, characteristic, complemented
18C22×#13050590C2211yescharacteristic
19#19128182—28no—
20#19128182C4116yescomplemented
21C4×#13050590—28no—
22C2×C4×Dic166C2211yescharacteristic
23C2×C4×Dic166C2211yescharacteristic
24C2×#14581757C2212yes—
25C2×#14581757C2212yes—
26C2×C4×D332C2211yescharacteristic
27C2×C4×D332C2211yescharacteristic
28C2×#14581754C2212yes—
29C2×#14581754C2212yes—
30C2×C4×C22⋊D83C2212yes—
31C2×C4×C22⋊D83C2214yes—
32C2×C4×C22⋊D83C2212yes—
33C2×C4×C22⋊D83C2214yes—
34C2×#14581751C2211yescharacteristic
35C2×#14581751C2211yescharacteristic
36C2×#14581751C2211yescharacteristic
37C2×#14581750C2212yes—
38C2×#14581750C2212yes—
39C2×#14581749C2212yes—
40C2×C4⋊C4×D83C2212yes—
41C2×C4⋊C4×D83C2214yes—
42C2×C4⋊C4×D83C2212yes—
43C2×C42×D83C2212yes—
44#19127600C2212yes—
45#19127600C2212yes—
46#19127600C2212yes—
47#19127600C2212yes—
48#19127599C2211yescharacteristic
49#19127599C2211yescharacteristic
50#19127599C2211yescharacteristic
51#19127599C2211yescharacteristic
52#19127598C2214yes—
53#19127598C2214yes—
54#19127597C2212yes—
55#19127597C2212yes—
56#19127596C2214yes—
57#19127596C2214yes—
58#19127575C2214yes—
59#19127575C2214yes—
60#19127574C2214yes—
61#19127574C2212yes—
62#19127574C2212yes—
63#19127572C2214yes—
64#19127572C2214yes—
65#19127570C2214yes—
66#19127570C2212yes—
67#19127566C2212yes—
68#19127565C2214yes—
69#19127561C2214yes—
70#19127560C2214yes—
71#19127558C2214yes—
72C4⋊C4×Dic83C2214yes—
73C4×Dic83⋊C4C2212yes—
74C4×Dic83⋊C4C2212yes—
75#19127552C2214yes—
76#95×D83C2214yes—
77C22×C4⋊C4×C83C2211yescharacteristic
78C22×C4⋊C4×C83C2212yes—
79C22×C4⋊C4×C83C2211yescharacteristic
80C22×C42×C83C2211yescharacteristic
81#389×C83C2212yes—
82#389×C83C2212yes—
83#389×C83C2212yes—
84#389×C83C2212yes—
85C2×#95×C83C2212yes—
86C2×#13050590C2×C418yes—
87C2×#13050590D418yes—
88C2×#13050590Q818yes—
89C22×Dic166C2311yescharacteristic
90C22×D332C2311yescharacteristic
91C22×C22⋊D83C2312yes—
92C22×C4×D83C2312yes—
93C22×C4×D83C2312yes—
94C22×C4×D83C2314yes—
95C22×C4×D83C2314yes—
96C22×C4×D83C2312yes—
97C4×Dic166—24no—
98C4×Dic166—24no—
99#14581757—28no—
100#14581757C2×C4116yescomplemented
101C4×D332—24no—
102C4×D332—24no—
103#14581754—28no—
104#14581754C2×C4116yescomplemented
105C4×C22⋊D83—28no—
106C4×C22⋊D83—28no—
107C4×C22⋊D83—216no—
108C4×C22⋊D83C2×C4132yescomplemented
109#14581751—24no—
110#14581751—24no—
111#14581751C2×C418yescomplemented
112#14581750—28no—
113#14581750C2×C4116yescomplemented
114#14581749—28no—
115C2×C4⋊Dic83C2311yescharacteristic
116C2×C4⋊Dic83C2311yescharacteristic
117C2×C4⋊Dic83C2311yescharacteristic
118C2×C4⋊Dic83C2311yescharacteristic
119C2×C4⋊Dic83C2314yes—
120C2×C4⋊Dic83C2314yes—
121C2×C4⋊Dic83C2311yescharacteristic
122C2×C4⋊Dic83C2311yescharacteristic
123C2×Dic83⋊C4C2312yes—
124C2×Dic83⋊C4C2312yes—
125C2×Dic83⋊C4C2312yes—
126C2×Dic83⋊C4C2314yes—
127C2×Dic83⋊C4C2312yes—
128C2×Dic83⋊C4C2314yes—
129C2×Dic83⋊C4C2312yes—
130C2×Dic83⋊C4C2312yes—
131C2×Dic83⋊C4C2314yes—
132C2×Dic83⋊C4C2314yes—
133C4⋊C4×D83—28no—
134C4⋊C4×D83—48no—
135C4⋊C4×D83C2×C4116yescomplemented
136C2×C22⋊Dic83C2312yes—
137C2×C22⋊Dic83C2312yes—
138C2×C22⋊Dic83C2312yes—
139C2×(C2×D83)⋊C4C2312yes—
140C2×(C2×D83)⋊C4C2314yes—
141C2×(C2×D83)⋊C4C2312yes—
142C2×(C2×D83)⋊C4C2314yes—
143C2×C4×Dic83C2312yes—
144C2×C4×Dic83C2314yes—
145C2×C4×Dic83C2312yes—
146C2×C4×Dic83C2312yes—
147C2×C4×Dic83C2312yes—
148C2×C4×Dic83C2314yes—
149C2×C4×Dic83C2312yes—
150C42×D83—28no—
151C83⋊#95C2314yes—
152C83⋊#95C2312yes—
153C83⋊#95C2312yes—
154C83⋊#95C2312yes—
155C83⋊#95C2312yes—
156C83⋊#95C2314yes—
157C83⋊#95C2314yes—
158C83⋊#95C2314yes—
159C23×C4×C83C2311yescharacteristic
160C23×C4×C83C2311yescharacteristic
161C23×C4×C83C2312yes—
162C23×C4×C83C2312yes—
163C23×C4×C83C2311yescharacteristic
164C2×C4⋊C4×C83—24no—
165C2×C4⋊C4×C83—44no—
166C2×C4⋊C4×C83C2×C418yescomplemented
167C2×C4⋊C4×C83C2314yes—
168C2×C4⋊C4×C83C2312yes—
169C2×C4⋊C4×C83C2312yes—
170C2×C4⋊C4×C83C2314yes—
171C2×C4⋊C4×C83C2312yes—
172C2×C4⋊C4×C83C2312yes—
173C2×C42×C83—24no—
174C2×C42×C83C2311yescharacteristic
175C2×C42×C83C2311yescharacteristic
176C2×C42×C83C2311yescharacteristic
177C2×C42×C83C2311yescharacteristic
178#95×C83C2314yes—
179#95×C83C2314yes—
180C23×D83C2412yes—
181#13050590C4⋊C4164yescomplemented
182C2×Dic166C22×C414yes—
183C2×Dic166C2×D414yes—
184C2×Dic166C2×Q814yes—
185C2×D332C22×C414yes—
186C2×D332C2×D414yes—
187C2×D332C2×Q814yes—
188C2×C22⋊D83C22×C418yes—
189C2×C22⋊D83C2×D418yes—
190C2×C22⋊D83C2×Q818yes—
191C22×Dic83C2412yes—
192C22×Dic83C2412yes—
193C22×Dic83C2412yes—
194C22×Dic83C2412yes—
195C22×Dic83C2412yes—
196C22×Dic83C2412yes—
197C22×Dic83C2412yes—
198C2×C4×D83—24no—
199C2×C4×D83—24no—
200C2×C4×D83—24no—
201C2×C4×D83—24no—
202C2×C4×D83—28no—
203C2×C4×D83—44no—
204C2×C4×D83—42no—
205C2×C4×D83—42no—
206C2×C4×D83—44no—
207C2×C4×D83—44no—
208C2×C4×D83—44no—
209C2×C4×D83C22×C4116yes—
210C2×C4×D83C22×C418yes—
211C2×C4×D83C2×D418yes—
212C2×C4×D83C2×Q818yes—
213C4⋊Dic83—22no—
214C4⋊Dic83—22no—
215C4⋊Dic83—22no—
216C4⋊Dic83—22no—
217C4⋊Dic83—44no—
218C4⋊Dic83—44no—
219C4⋊Dic83C22×C414yes—
220C4⋊Dic83C22×C414yes—
221Dic83⋊C4—24no—
222Dic83⋊C4—24no—
223Dic83⋊C4—28no—
224Dic83⋊C4—24no—
225Dic83⋊C4—24no—
226Dic83⋊C4—44no—
227Dic83⋊C4—44no—
228Dic83⋊C4—42no—
229Dic83⋊C4—42no—
230Dic83⋊C4C22×C4116yes—
231C22⋊Dic83—24no—
232C22⋊Dic83—24no—
233C22⋊Dic83C22×C418yes—
234(C2×D83)⋊C4—24no—
235(C2×D83)⋊C4—24no—
236(C2×D83)⋊C4—28no—
237(C2×D83)⋊C4C22×C4116yes—
238C4×Dic83—24no—
239C4×Dic83—24no—
240C4×Dic83—24no—
241C4×Dic83—24no—
242C4×Dic83—28no—
243C4×Dic83C22×C4116yes—
244C4×Dic83C22×C418yes—
245C24×C83C2411yescharacteristic
246C22×C4×C83—22no—
247C22×C4×C83—22no—
248C22×C4×C83—24no—
249C22×C4×C83—22no—
250C22×C4×C83—22no—
251C22×C4×C83—42no—
252C22×C4×C83—42no—
253C22×C4×C83—41no—
254C22×C4×C83—41no—
255C22×C4×C83—42no—
256C22×C4×C83—42no—
257C22×C4×C83C22×C418yes—
258C22×C4×C83C22×C414yes—
259C22×C4×C83C2×D414yes—
260C22×C4×C83C2×Q814yes—
261C22×C4×C83C2414yes—
262C22×C4×C83C2411yescharacteristic
263C22×C4×C83C2411yescharacteristic
264C22×C4×C83C2414yes—
265C22×C4×C83C2411yescharacteristic
266C22×C4×C83C2411yescharacteristic
267C22×C4×C83C2411yescharacteristic
268C22×C4×C83C2411yescharacteristic
269C4⋊C4×C83—24no—
270C4⋊C4×C83—24no—
271C4⋊C4×C83—28no—
272C4⋊C4×C83—44no—
273C4⋊C4×C83C22×C418yes—
274C4⋊C4×C83C22×C418yes—
275C42×C83—22no—
276C42×C83—22no—
277C42×C83—22no—
278C42×C83—22no—
279C23×C83—21no—
280C23×C83—21no—
281C23×C83—21no—
282C23×C83—21no—
283C23×C83C23×C412yes—
284C23×C83C22×D412yes—
285C23×C83C22×Q812yes—
286C23×C83C2511yescharacteristic
287C22×D83—22no—
288C22×D83—22no—
289C22×D83—22no—
290C22×D83—22no—
291C22×D83C23×C414yes—
292C22×D83C22×D414yes—
293C22×D83C22×Q814yes—
294C2×C4×C83—21no—
295C2×C4×C83—21no—
296C2×C4×C83—24no—
297C2×C4×C83—24no—
298C2×C4×C83—21no—
299C2×C4×C83—21no—
300C2×C4×C83—21no—
301C2×C4×C83—21no—
302C2×C4×C83—24no—
303C2×C4×C83—24no—
304C2×C4×C83—21no—
305C2×C4×C83—21no—
306C2×C4×C83—21no—
307C2×C4×C83—21no—
308C2×C4×C83—24no—
309C2×C4×C83—48no—
310C2×C4×C83—44no—
311C2×C4×C83—44no—
312C2×C4×C83—84no—
313C2×C4×C83C2×C4⋊C4116yescomplemented
314C2×C4×C83C23×C418yes—
315C2×C4×C83C23×C412yes—
316C2×C4×C83C23×C412yes—
317C2×C4×C83C22×D412yes—
318C2×C4×C83C22×D412yes—
319C2×C4×C83C22×Q812yes—
320C2×C4×C83C22×Q812yes—
321C2×C4×C83H(5,𝔽2)12yes—
322C2×C4×C832−1+412yes—
323C22⋊D83C2×C4⋊C4132yescomplemented
324C2×Dic83—22no—
325C2×Dic83—22no—
326C2×Dic83—22no—
327C2×Dic83—22no—
328C2×Dic83—22no—
329C2×Dic83—22no—
330C2×Dic83—22no—
331C2×Dic83—22no—
332C2×Dic83—22no—
333C2×Dic83—22no—
334C2×Dic83—22no—
335C2×Dic83—22no—
336C2×Dic83—22no—
337C2×Dic83—22no—
338C2×Dic83—22no—
339C2×Dic83—22no—
340C2×Dic83C23×C414yes—
341C2×Dic83C23×C414yes—
342C2×Dic83C23×C414yes—
343C2×Dic83C22×D414yes—
344C2×Dic83C22×Q814yes—
345D332C2×C4⋊C4116yescomplemented
346C4×D83—416no—
347C4×D83—48no—
348C4×D83—48no—
349C4×D83—88no—
350C4×D83C2×C4⋊C4132yescomplemented
351Dic166C2×C4⋊C4116yescomplemented
352C22×C83—22no—
353C22×C83—22no—
354C22×C83—22no—
355C22×C83—22no—
356C22×C83—22no—
357C22×C83—22no—
358C22×C83C22×C4⋊C414yes—
359C22×C83C24×C411yescharacteristic
360C22×C83C23×D411yescharacteristic
361C22×C83C23×Q811yescharacteristic
362C22×C83C2×H(5,𝔽2)11yescharacteristic
363C22×C83C2×2−1+411yescharacteristic
364C22×C83#58511yescharacteristic
365C22×C83#58511yescharacteristic
366C2×D83—24no—
367C2×D83—24no—
368C2×D83—24no—
369C2×D83—24no—
370C2×D83—24no—
371C2×D83—24no—
372C2×D83C22×C4⋊C418yes—
373C4×C83—28no—
374C4×C83—22no—
375C4×C83—22no—
376C4×C83—44no—
377C4×C83—41no—
378C4×C83—41no—
379C4×C83C22×C4⋊C414yes—
380C4×C83C22×C4⋊C414yes—
381Dic83—24no—
382Dic83—24no—
383Dic83—42no—
384Dic83—42no—
385Dic83—42no—
386Dic83—42no—
387Dic83C22×C4⋊C418yes—
388#34250—831nomaximal, Sylow
389C2×C83—24no—
390C2×C83C23×C4⋊C411yescharacteristic
391C2×C83C4×H(5,𝔽2)11yescharacteristic
392C2×C83C4×2−1+411yescharacteristic
393C2×C83#348811yescharacteristic
394C2×C83#348911yescharacteristic
395C2×C83#350311yescharacteristic
396C2×C83#350411yescharacteristic
397D83—28no—
398C2×#520—831no—
399C2×#520—831no—
400C2×C4×#41—831no—
401#2351—832no—
402Q8×C4⋊C4—832no—
403#2349—832no—
404#2349—834no—
405D4×C4⋊C4—832no—
406D4×C4⋊C4—834no—
407#2317—832no—
408#2317—831no—
409#2316—832no—
410#2316—831no—
411#2296—831no—
412#2296—832no—
413C2×#389—832no—
414C2×#389D8311yescharacteristic, complemented
415C83#3425011yescharacteristic, complemented, Sylow
416C22×#41—831no—
417#520—8316no—
418#520—1668no—
419C4×#41—1668no—
420C2×C4×Q8—832no—
421C2×C4×Q8—832no—
422C2×C4×Q8—831no—
423C2×C4×Q8—831no—
424C2×C4×D4—834no—
425C2×C4×D4—832no—
426C2×C4×D4—834no—
427C2×C4×D4—832no—
428C2×C4×D4—832no—
429C2×C4×D4—832no—
430C2×C4×D4—831no—
431C2×C4×D4—831no—
432C2×#117—831no—
433C2×#117—831no—
434C2×#117—831no—
435C2×#117—832no—
436C2×#117—832no—
437C2×#117—832no—
438C22×C4⋊C4—834no—
439C22×C4⋊C4—832no—
440C22×C4⋊C4—832no—
441C22×C4⋊C4C2×D8311yescharacteristic
442C22×C4⋊C4C2×D8312yes—
443C22×C4⋊C4C2×D8311yescharacteristic
444C22×C42—832no—
445C22×C42C2×D8311yescharacteristic
446#389—832no—
447#389—832no—
448#389—832no—
449#389—834no—
450#389—832no—
451#389—832no—
452#389—832no—
453#389—834no—
454#389—831no—
455#389—831no—
456#389—831no—
457#389—831no—
458#389—834no—
459#389—834no—
460#389C2×D8312yes—
461#389C2×D8312yes—
462#389C2×D8312yes—
463#389C2×D8312yes—
464#385—834no—
465#385—832no—
466#385—832no—
467#385—834no—
468#385—834no—
469#385—834no—
470#385—834no—
471#384—832no—
472#384—834no—
473#382—832no—
474#382—834no—
475#380—834no—
476#380—834no—
477#380—834no—
478C4×C4⋊C4—834no—
479C4×C4⋊C4—832no—
480C4×C4⋊C4—832no—
481C4×C4⋊C4—834no—
482C2×#95—834no—
483C2×#95C2×D8312yes—
484C2×#41—838no—
485C2×#41—838no—
486C2×#41—838no—
487C22×Q8—831no—
488C22×D4—832no—
489C22×D4—831no—
490C23×C4—834no—
491C23×C4—834no—
492C23×C4—832no—
493C23×C4—832no—
494C23×C4—832no—
495C23×C4C22×D8311yescharacteristic
496C23×C4C22×D8311yescharacteristic
497C23×C4C22×D8312yes—
498C23×C4C22×D8312yes—
499C23×C4C22×D8311yescharacteristic
500C4×Q8—8316no—
501C4×Q8—1664no—
502C4×Q8—1664no—
503C4×Q8—1668no—
504C4×D4—8332no—
505C4×D4—8316no—
506C4×D4—1664no—
507C4×D4—1664no—
508C4×D4—1668no—
509C4×D4—1668no—
510C4×D4—1668no—
511C4×D4—16616no—
512#117—838no—
513#117—8316no—
514#117—1668no—
515#117—1668no—
516#117—1664no—
517#117—1664no—
518C2×C4⋊C4—24no—
519C2×C4⋊C4—44no—
520C2×C4⋊C4—3328no—
521C2×C4⋊C4—834no—
522C2×C4⋊C4—834no—
523C2×C4⋊C4—832no—
524C2×C4⋊C4—834no—
525C2×C4⋊C4—832no—
526C2×C4⋊C4—834no—
527C2×C4⋊C4—831no—
528C2×C4⋊C4—834no—
529C2×C4⋊C4—831no—
530C2×C4⋊C4—8316no—
531C2×C4⋊C4—831no—
532C2×C4⋊C4—832no—
533C2×C4⋊C4—834no—
534C2×C4⋊C4—831no—
535C2×C4⋊C4—832no—
536C2×C4⋊C4—831no—
537C2×C4⋊C4—832no—
538C2×C4⋊C4—831no—
539C2×C4⋊C4—832no—
540C2×C4⋊C4—1668no—
541C2×C4⋊C4C4×D8318yescomplemented
542C2×C4⋊C4C22×D8312yes—
543C2×C4⋊C4C22×D8314yes—
544C2×C4⋊C4C22×D8312yes—
545C2×C4⋊C4C22×D8314yes—
546C2×C4⋊C4C22×D8312yes—
547C2×C4⋊C4C22×D8312yes—
548C2×C22⋊C4—832no—
549C2×C22⋊C4—834no—
550C2×C22⋊C4—832no—
551C2×C22⋊C4—832no—
552C2×C22⋊C4—832no—
553C2×C22⋊C4—834no—
554C2×C22⋊C4—832no—
555C2×C42—24no—
556C2×C42—834no—
557C2×C42—832no—
558C2×C42—832no—
559C2×C42—834no—
560C2×C42—832no—
561C2×C42—832no—
562C2×C42—832no—
563C2×C42—1668no—
564C2×C42C22×D8311yescharacteristic
565C2×C42C22×D8311yescharacteristic
566C2×C42C22×D8311yescharacteristic
567C2×C42C22×D8311yescharacteristic
568#95—832no—
569#95—834no—
570#95—834no—
571#95—832no—
572#95—832no—
573#95—834no—
574#95—834no—
575#95—832no—
576#95C22×D8314yes—
577#95C22×D8314yes—
578C24—832no—
579C24C23×D8311yescharacteristic
580#41—8364no—
581C2×Q8—834no—
582C2×Q8—834no—
583C2×Q8—834no—
584C2×D4—838no—
585C2×D4—838no—
586C2×D4—838no—
587C2×D4—834no—
588C2×D4—834no—
589C2×D4—834no—
590C22×C4—22no—
591C22×C4—22no—
592C22×C4—24no—
593C22×C4—22no—
594C22×C4—22no—
595C22×C4—42no—
596C22×C4—42no—
597C22×C4—41no—
598C22×C4—41no—
599C22×C4—42no—
600C22×C4—42no—
601C22×C4—3324no—
602C22×C4—3324no—
603C22×C4—3322no—
604C22×C4—3322no—
605C22×C4—3324no—
606C22×C4—3324no—
607C22×C4—8316no—
608C22×C4—832no—
609C22×C4—838no—
610C22×C4—838no—
611C22×C4—838no—
612C22×C4—832no—
613C22×C4—832no—
614C22×C4—832no—
615C22×C4—832no—
616C22×C4—832no—
617C22×C4—832no—
618C22×C4—1664no—
619C22×C4—1664no—
620C22×C4—1668no—
621C22×C4—1664no—
622C22×C4—1664no—
623C22×C4C2×C4×D8318yes—
624C22×C4C2×C4×D8314yes—
625C22×C4D4×D8314yes—
626C22×C4Q8×D8314yes—
627C22×C4C23×D8311yescharacteristic
628C22×C4C23×D8314yes—
629C22×C4C23×D8311yescharacteristic
630C22×C4C23×D8314yes—
631C22×C4C23×D8311yescharacteristic
632C22×C4C23×D8311yescharacteristic
633C22×C4C23×D8311yescharacteristic
634C22×C4C23×D8311yescharacteristic
635C4⋊C4—24no—
636C4⋊C4—24no—
637C4⋊C4—28no—
638C4⋊C4—44no—
639C4⋊C4—3324no—
640C4⋊C4—3324no—
641C4⋊C4—3322no—
642C4⋊C4—3322no—
643C4⋊C4—3324no—
644C4⋊C4—3324no—
645C4⋊C4—834no—
646C4⋊C4—8316no—
647C4⋊C4—834no—
648C4⋊C4—1668no—
649C4⋊C4—1664no—
650C4⋊C4—1664no—
651C4⋊C4—1662no—
652C4⋊C4—1662no—
653C4⋊C4—1662no—
654C4⋊C4—1662no—
655C4⋊C4—1664no—
656C4⋊C4—1664no—
657C4⋊C4C2×C4×D8318yes—
658C4⋊C4C2×C4×D8318yes—
659C22⋊C4—838no—
660C22⋊C4—8316no—
661C22⋊C4—1664no—
662C22⋊C4—1664no—
663C22⋊C4—1668no—
664C22⋊C4—1664no—
665C22⋊C4—1664no—
666C42—22no—
667C42—22no—
668C42—22no—
669C42—22no—
670C42—8316no—
671C42—838no—
672C42—1664no—
673C42—1664no—
674C42—1668no—
675C42—1664no—
676C42—1664no—
677C23—21no—
678C23—21no—
679C23—21no—
680C23—21no—
681C23—834no—
682C23—834no—
683C23—834no—
684C23—1662no—
685C23—1662no—
686C23—1662no—
687C23—1662no—
688C23C22×C4×D8312yes—
689C23C2×D4×D8312yes—
690C23C2×Q8×D8312yes—
691C23C24×D8311yescharacteristic
692Q8—8316no—
693D4—8332no—
694D4—8316no—
695C2×C4—21no—
696C2×C4—21no—
697C2×C4—24no—
698C2×C4—24no—
699C2×C4—21no—
700C2×C4—21no—
701C2×C4—21no—
702C2×C4—21no—
703C2×C4—24no—
704C2×C4—24no—
705C2×C4—21no—
706C2×C4—21no—
707C2×C4—21no—
708C2×C4—21no—
709C2×C4—24no—
710C2×C4—48no—
711C2×C4—44no—
712C2×C4—44no—
713C2×C4—84no—
714C2×C4—3328no—
715C2×C4—3328no—
716C2×C4—33216no—
717C2×C4—834no—
718C2×C4—834no—
719C2×C4—834no—
720C2×C4—8332no—
721C2×C4—834no—
722C2×C4—834no—
723C2×C4—6648no—
724C2×C4—1662no—
725C2×C4—1662no—
726C2×C4—1662no—
727C2×C4—1662no—
728C2×C4—1662no—
729C2×C4—1662no—
730C2×C4—1662no—
731C2×C4—1662no—
732C2×C4—1662no—
733C2×C4—1662no—
734C2×C4—1662no—
735C2×C4—1662no—
736C2×C4—1662no—
737C2×C4—1662no—
738C2×C4—1662no—
739C2×C4—1662no—
740C2×C4C4⋊C4×D83116yescomplemented
741C2×C4C22×C4×D8318yes—
742C2×C4C22×C4×D8312yes—
743C2×C4C22×C4×D8312yes—
744C2×C4C2×D4×D8312yes—
745C2×C4C2×D4×D8312yes—
746C2×C4C2×Q8×D8312yes—
747C2×C4C2×Q8×D8312yes—
748C2×C4#1458183712yes—
749C2×C4#1458184012yes—
750C22—22no—
751C22—22no—
752C22—22no—
753C22—22no—
754C22—22no—
755C22—22no—
756C22—838no—
757C22—1664no—
758C22—1664no—
759C22—1664no—
760C22—1664no—
761C22—1664no—
762C22—1664no—
763C22C2×C4⋊C4×D8314yes—
764C22C23×C4×D8311yescharacteristic
765C22C22×D4×D8311yescharacteristic
766C22C22×Q8×D8311yescharacteristic
767C22C2×#1458183711yescharacteristic
768C22C2×#1458184011yescharacteristic
769C22#1912853711yescharacteristic
770C22#1912853711yescharacteristic
771C4—22no—
772C4—22no—
773C4—28no—
774C4—41no—
775C4—44no—
776C4—41no—
777C4—3322no—
778C4—3322no—
779C4—3322no—
780C4—3322no—
781C4—838no—
782C4—1664no—
783C4—1664no—
784C4C2×C4⋊C4×D8314yes—
785C4C2×C4⋊C4×D8314yes—
786C2—24no—
787C2—1668no—
788C2C22×C4⋊C4×D8311yescharacteristic
789C2C4×#1458183711yescharacteristic
790C2C4×#1458184011yescharacteristic
791C2#2492112811yescharacteristic
792C2#2492113911yescharacteristic
793C2#2492127911yescharacteristic
794C2#2492128711yescharacteristic
subgroupG/H
center, FrattiniC23C24×D83
commutatorC22×C83C24×C4
FittingC2×#389×C83C2
socle, cosocleC23×C83C25
prime radicalC22×#13050590C22
hypercenterC2×#389D83
hypocenterC83#34250
LCSG ▷ C22×C83 ▷ C83
UCSC1 ◁ C23 ◁ C2×#389

Complements

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

NH ≅ G/Ntype
4. #24910382C2semidirect
5. #24910377C2semidirect
6. #24910372C2semidirect
7. #24910370C2semidirect
8. #24910364C2semidirect
9. C4⋊C4×C22⋊D83C2semidirect
10. #24910087C2semidirect
11. #24910085C2semidirect
12. #24910081C2semidirect
13. #24910078C2semidirect
14. #24909946C2semidirect
15. #24909944C2semidirect
16. #389×D83C2semidirect
17. C2×#389×C83C2semidirect
20. #19128182C4semidirect
100. #14581757C2×C4semidirect
104. #14581754C2×C4semidirect
108. C4×C22⋊D83C2×C4semidirect
111. #14581751C2×C4semidirect
113. #14581750C2×C4semidirect
135. C4⋊C4×D83C2×C4semidirect
166. C2×C4⋊C4×C83C2×C4semidirect
181. #13050590C4⋊C4semidirect
313. C2×C4×C83C2×C4⋊C4semidirect
323. C22⋊D83C2×C4⋊C4semidirect
345. D332C2×C4⋊C4semidirect
350. C4×D83C2×C4⋊C4semidirect
351. Dic166C2×C4⋊C4semidirect
414. C2×#389D83semidirect
415. C83#34250semidirect
541. C2×C4⋊C4C4×D83semidirect
740. C2×C4C4⋊C4×D83semidirect

Maximal subgroups

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

subgroupindex
C2×#191281822
C2×C4×#130505902
#249103822
#249103772
#249103722
#249103702
#249103642
C4⋊C4×C22⋊D832
#249100872
#249100852
#249100812
#249100782
#249099462
#249099442
#389×D832
C2×#389×C832
#3425083