Finite Group Databasebeta

← #36275161

Subgroups — #36275161

Order 21248.

2342 conjugacy classes of subgroups.

The subgroup lattice has 1008 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#19128212C211yesmaximal, characteristic
2#24918293C214yesmaximal, complemented
3#24918284C212yesmaximal, complemented
4#24918265C212yesmaximal, complemented
5#24918244C214yesmaximal, complemented
6#24918235C212yesmaximal, complemented
7#24918216C212yesmaximal, complemented
8#24917407C212yesmaximal, complemented
9#24917386C212yesmaximal, complemented
10#24917089C214yesmaximal, complemented
11#24916721C212yesmaximal, complemented
12#24916697C212yesmaximal, complemented
13C2×#19127665C211yesmaximal, characteristic, complemented
14C22×C22⋊Q8×C83C211yesmaximal, characteristic, complemented
15C22×#13050590C2211yescharacteristic
16C2×#14581823C2214yescomplemented
17C22×#13050574C2212yescomplemented
18#19128212—21no—
19#19128212—21no—
20#19128212—21no—
21#19128212—21no—
22#19128212C2212yes—
23#19128212C2212yes—
24#19128212C2212yes—
25#19128212C2212yes—
26C2×#14581775—21no—
27C2×#14581771C2211yescharacteristic
28C2×#14581771C2211yescharacteristic
29C2×#14581766C2211yescharacteristic
30C2×#14581766C2211yescharacteristic
31C2×#14581761—21no—
32C2×C4×C22⋊D83—21no—
33C2×C4×C22⋊D83—21no—
34C2×#14581751C2211yescharacteristic
35#19128039C2218yescomplemented
36#19128036C2214yescomplemented
37#19128034C2214yescomplemented
38#19128031C2214yescomplemented
39#19128029C2214yescomplemented
40#19128019C2214yescomplemented
41#19128014C2214yescomplemented
42#19127957C2218yescomplemented
43#19127949C2218yescomplemented
44#19127940C2218yescomplemented
45#19127932C2218yescomplemented
46#19127861C2218yescomplemented
47#19127857C2214yescomplemented
48#19127857C2214yescomplemented
49#19127856C2214yescomplemented
50#19127851C2214yescomplemented
51#19127840C2214yescomplemented
52#19127840C2214yescomplemented
53#19127741C2214yescomplemented
54#19127710C2214yescomplemented
55#19127700C2214yescomplemented
56#19127665C2212yes—
57#19127665C2212yes—
58#19127665C2212yescomplemented
59#19127665C2212yescomplemented
60C2×C22⋊(C83⋊C8)C2212yes—
61C2×C22⋊(C83⋊C8)C2212yescomplemented
62C23×Q8×C83C2211yescharacteristic, complemented
63C24×C4×C83C2211yescharacteristic
64C2×C22⋊Q8×C83—21no—
65C2×C22⋊Q8×C83—21no—
66C2×C22⋊Q8×C83—21no—
67C2×C22⋊Q8×C83—21no—
68C2×C22⋊Q8×C83—21no—
69C2×C22⋊Q8×C83—21no—
70C2×C22⋊Q8×C83C2212yes—
71C2×C22⋊Q8×C83C2212yes—
72C2×C22⋊Q8×C83C2212yes—
73C2×C22⋊Q8×C83C2212yescomplemented
74C2×C22⋊Q8×C83C2212yescomplemented
75C2×C22⋊Q8×C83C2212yescomplemented
76C22×C4⋊C4×C83—21no—
77C22×C4⋊C4×C83C2211yescharacteristic, complemented
78C22×C22⋊C4×C83—21no—
79C2×#13050590—21no—
80C2×#13050590—21no—
81C2×#13050590—44no—
82C2×#13050590C2312yes—
83C2×#13050590C2312yes—
84C22×Dic166C2311yescharacteristic
85C22×D332C2311yescharacteristic
86C22×C22⋊D83—21no—
87C22×C22⋊D83—21no—
88C22×C22⋊D83—21no—
89C22×C4×D83—21no—
90#14581823—48no—
91C2×#13050580C2318yescomplemented
92C2×#13050577C2318yescomplemented
93C2×#13050574—44no—
94C2×#13050574C2314yes—
95C2×#13050574C2314yes—
96C22×C83⋊C8C2314yes—
97#14581775—22no—
98#14581775—22no—
99#14581775—22no—
100#14581775—22no—
101#14581771—21no—
102#14581771—21no—
103#14581771—21no—
104#14581771—21no—
105#14581771C2312yes—
106#14581771C2312yes—
107#14581771C2312yes—
108#14581771C2312yes—
109#14581766—21no—
110#14581766—21no—
111#14581766—21no—
112#14581766—21no—
113#14581766C2312yes—
114#14581766C2312yes—
115#14581766C2312yes—
116#14581766C2312yes—
117#14581761—22no—
118#14581761—22no—
119#14581761—22no—
120#14581761—22no—
121C4×C22⋊D83—22no—
122C4×C22⋊D83—22no—
123C4×C22⋊D83—22no—
124C4×C22⋊D83—22no—
125C4×C22⋊D83—22no—
126C4×C22⋊D83—22no—
127C4×C22⋊D83—22no—
128C4×C22⋊D83—22no—
129#14581751—21no—
130#14581751—21no—
131#14581751C2312yes—
132#14581751C2312yes—
133C2×C4⋊Dic83C2311yescharacteristic
134C2×C4⋊Dic83C2311yescharacteristic
135C2×Dic83⋊C4—21no—
136C2×Dic83⋊C4—21no—
137C2×C22⋊Dic83—21no—
138C2×C22⋊Dic83—21no—
139C2×C22⋊Dic83—21no—
140C2×(C2×D83)⋊C4—21no—
141C2×(C2×D83)⋊C4—21no—
142C2×C4×Dic83—21no—
143#14581725C2318yescomplemented
144#14581723C2318yescomplemented
145#14581716C2318yescomplemented
146#14581716C2318yescomplemented
147#14581715C2318yescomplemented
148#14581712C2318yescomplemented
149C22⋊(C83⋊C8)C2314yes—
150C22⋊(C83⋊C8)C2314yes—
151C22⋊(C83⋊C8)C2314yes—
152C22⋊(C83⋊C8)C2314yes—
153C25×C83D411yescharacteristic
154C22×Q8×C83—21no—
155C22×Q8×C83—21no—
156C22×Q8×C83—21no—
157C22×Q8×C83—44no—
158C22×Q8×C83C2312yes—
159C22×Q8×C83C2312yes—
160C22×Q8×C83C2312yes—
161C23×C4×C83—21no—
162C23×C4×C83—21no—
163C23×C4×C83—44no—
164C23×C4×C83D411yescharacteristic
165C23×C4×C83D411yescharacteristic
166C23×C4×C83D411yescharacteristic
167C23×C4×C83D411yescharacteristic
168C23×C4×C83D411yescharacteristic
169C23×C4×C83D411yescharacteristic
170C23×C4×C83D411yescharacteristic
171C23×C4×C83C2311yescharacteristic
172C23×C4×C83C2311yescharacteristic
173C23×C4×C83C2311yescharacteristic
174C23×C4×C83C2311yescharacteristic
175C23×C4×C83C2311yescharacteristic
176C23×C4×C83C2311yescharacteristic
177C23×C4×C83C2311yescharacteristic
178C22⋊Q8×C83—22no—
179C22⋊Q8×C83—22no—
180C22⋊Q8×C83—22no—
181C22⋊Q8×C83—22no—
182C22⋊Q8×C83—22no—
183C22⋊Q8×C83—22no—
184C22⋊Q8×C83—22no—
185C22⋊Q8×C83—22no—
186C22⋊Q8×C83—22no—
187C22⋊Q8×C83—22no—
188C22⋊Q8×C83—22no—
189C22⋊Q8×C83—22no—
190C22⋊Q8×C83C2314yes—
191C22⋊Q8×C83C2314yes—
192C22⋊Q8×C83C2314yes—
193C22⋊Q8×C83C2314yes—
194C2×C4⋊C4×C83—22no—
195C2×C4⋊C4×C83—22no—
196C2×C4⋊C4×C83—22no—
197C2×C4⋊C4×C83—22no—
198C2×C4⋊C4×C83—22no—
199C2×C4⋊C4×C83—22no—
200C2×C4⋊C4×C83—21no—
201C2×C4⋊C4×C83—21no—
202C2×C4⋊C4×C83—21no—
203C2×C4⋊C4×C83C2312yes—
204C2×C4⋊C4×C83C2312yes—
205C2×C4⋊C4×C83C2312yes—
206C2×C22⋊C4×C83—22no—
207C2×C22⋊C4×C83—22no—
208C2×C22⋊C4×C83—22no—
209C2×C22⋊C4×C83—22no—
210C2×C22⋊C4×C83—22no—
211C2×C22⋊C4×C83—22no—
212C23×D83—21no—
213#13050590—28no—
214#13050590—44no—
215#13050590—44no—
216#13050590—44no—
217C2×Dic166—21no—
218C2×Dic166—42no—
219C2×Dic166C2412yes—
220C2×D332—21no—
221C2×D332—42no—
222C2×D332C2412yes—
223C2×C22⋊D83—22no—
224C2×C22⋊D83—22no—
225C2×C22⋊D83—22no—
226C2×C22⋊D83—22no—
227C2×C22⋊D83—22no—
228C2×C22⋊D83—22no—
229C2×C22⋊D83—44no—
230C2×C22⋊D83—44no—
231C2×C22⋊D83—44no—
232C22×Dic83—21no—
233C22×Dic83—21no—
234C22×Dic83—21no—
235C2×C4×D83—22no—
236C2×C4×D83—22no—
237C2×C4×D83—44no—
238#13050580—48no—
239#13050577—48no—
240#13050574—28no—
241#13050574—44no—
242C2×C83⋊C8—44no—
243C2×C83⋊C8C2418yes—
244C4⋊Dic83—21no—
245C4⋊Dic83—21no—
246C4⋊Dic83C2412yes—
247C4⋊Dic83C2412yes—
248Dic83⋊C4—22no—
249Dic83⋊C4—22no—
250Dic83⋊C4—22no—
251Dic83⋊C4—22no—
252C22⋊Dic83—22no—
253C22⋊Dic83—22no—
254C22⋊Dic83—22no—
255C22⋊Dic83—22no—
256C22⋊Dic83—22no—
257C22⋊Dic83—22no—
258(C2×D83)⋊C4—22no—
259(C2×D83)⋊C4—22no—
260(C2×D83)⋊C4—22no—
261(C2×D83)⋊C4—22no—
262C4×Dic83—22no—
263C4×Dic83—22no—
264C24×C83—24no—
265C24×C83—42no—
266C24×C83—42no—
267C24×C83C2×D411yescharacteristic
268C24×C83C2×D411yescharacteristic
269C24×C83C2×D411yescharacteristic
270C24×C83C2×D411yescharacteristic
271C24×C83C2×D411yescharacteristic
272C24×C83C2×D411yescharacteristic
273C24×C83C2×D411yescharacteristic
274C2×Q8×C83—22no—
275C2×Q8×C83—22no—
276C2×Q8×C83—22no—
277C2×Q8×C83—28no—
278C2×Q8×C83—44no—
279C2×Q8×C83—44no—
280C2×Q8×C83—44no—
281C2×Q8×C83—44no—
282C2×Q8×C83—44no—
283C2×Q8×C83C2414yes—
284C22×C4×C83—24no—
285C22×C4×C83—24no—
286C22×C4×C83—24no—
287C22×C4×C83—22no—
288C22×C4×C83—22no—
289C22×C4×C83—22no—
290C22×C4×C83—22no—
291C22×C4×C83—22no—
292C22×C4×C83—22no—
293C22×C4×C83—42no—
294C22×C4×C83—42no—
295C22×C4×C83—42no—
296C22×C4×C83—42no—
297C22×C4×C83—42no—
298C22×C4×C83—42no—
299C22×C4×C83—42no—
300C22×C4×C83—42no—
301C22×C4×C83—42no—
302C22×C4×C83—42no—
303C22×C4×C83—42no—
304C22×C4×C83—44no—
305C22×C4×C83—44no—
306C22×C4×C83C2×D411yescharacteristic
307C22×C4×C83C2×D411yescharacteristic
308C22×C4×C83C2×D411yescharacteristic
309C22×C4×C83C2×D411yescharacteristic
310C22×C4×C83C2×D411yescharacteristic
311C22×C4×C83C2×D411yescharacteristic
312C22×C4×C83C2×D411yescharacteristic
313C22×C4×C83C2×D411yescharacteristic
314C22×C4×C83C2×D411yescharacteristic
315C22×C4×C83C2×D411yescharacteristic
316C22×C4×C83C2×D411yescharacteristic
317C22×C4×C83C2×D411yescharacteristic
318C22×C4×C83C2×D411yescharacteristic
319C22×C4×C83C2×D411yescharacteristic
320C22×C4×C83C2×D411yescharacteristic
321C22×C4×C83C2×D411yescharacteristic
322C22×C4×C83C2×D411yescharacteristic
323C22×C4×C83C2×D411yescharacteristic
324C22×C4×C83C2×D411yescharacteristic
325C22×C4×C83C2×D411yescharacteristic
326C22×C4×C83C2×D411yescharacteristic
327C22×C4×C83C2411yescharacteristic
328C22×C4×C83C2411yescharacteristic
329C22×C4×C83C2411yescharacteristic
330C22×C4×C83C2411yescharacteristic
331C22×C4×C83C2411yescharacteristic
332C22×C4×C83C2411yescharacteristic
333C22×C4×C83C2411yescharacteristic
334C4⋊C4×C83—24no—
335C4⋊C4×C83—24no—
336C4⋊C4×C83—24no—
337C4⋊C4×C83—24no—
338C4⋊C4×C83—22no—
339C4⋊C4×C83—22no—
340C4⋊C4×C83—22no—
341C4⋊C4×C83C2414yes—
342C22⋊C4×C83—24no—
343C22⋊C4×C83—24no—
344C22⋊C4×C83—24no—
345C22⋊C4×C83—24no—
346C23×C83—22no—
347C23×C83—22no—
348C23×C83—22no—
349C23×C83—22no—
350C23×C83—22no—
351C23×C83—22no—
352C23×C83—22no—
353C23×C83—22no—
354C23×C83—22no—
355C23×C83—22no—
356C23×C83—22no—
357C23×C83—22no—
358C23×C83—41no—
359C23×C83—41no—
360C23×C83—41no—
361C23×C83—41no—
362C23×C83—41no—
363C23×C83—41no—
364C23×C83—41no—
365C23×C83—41no—
366C23×C83—416no—
367C23×C83#13714yescomplemented
368C23×C83C22×D411yescharacteristic
369C23×C83C22×D411yescharacteristic
370C23×C83C22×D411yescharacteristic
371C23×C83C22×D411yescharacteristic
372C23×C83C22×D411yescharacteristic
373C23×C83C22×D411yescharacteristic
374C23×C83C22×D411yescharacteristic
375C22×D83—22no—
376C22×D83—42no—
377C22×D83—42no—
378C22×D83—42no—
379Q8×C83—28no—
380Q8×C83—44no—
381Q8×C83—44no—
382Q8×C83—44no—
383C2×C4×C83—22no—
384C2×C4×C83—22no—
385C2×C4×C83—22no—
386C2×C4×C83—22no—
387C2×C4×C83—22no—
388C2×C4×C83—22no—
389C2×C4×C83—22no—
390C2×C4×C83—22no—
391C2×C4×C83—22no—
392C2×C4×C83—22no—
393C2×C4×C83—22no—
394C2×C4×C83—22no—
395C2×C4×C83—22no—
396C2×C4×C83—22no—
397C2×C4×C83—22no—
398C2×C4×C83—24no—
399C2×C4×C83—24no—
400C2×C4×C83—41no—
401C2×C4×C83—41no—
402C2×C4×C83—41no—
403C2×C4×C83—41no—
404C2×C4×C83—41no—
405C2×C4×C83—41no—
406C2×C4×C83—41no—
407C2×C4×C83—41no—
408C2×C4×C83—41no—
409C2×C4×C83—41no—
410C2×C4×C83—41no—
411C2×C4×C83—41no—
412C2×C4×C83—44no—
413C2×C4×C83—44no—
414C2×C4×C83—44no—
415C2×C4×C83—44no—
416C2×C4×C83—44no—
417C2×C4×C83—44no—
418C2×C4×C83C22×D411yescharacteristic
419C2×C4×C83C22×D411yescharacteristic
420C2×C4×C83C22×D411yescharacteristic
421C2×C4×C83C22×D411yescharacteristic
422C2×C4×C83C22×D411yescharacteristic
423C2×C4×C83C22×D411yescharacteristic
424C2×C4×C83C22×D411yescharacteristic
425C2×C4×C83H(5,𝔽2)14yes—
426C2×C4×C83C2511yescharacteristic
427C22⋊D83—44no—
428C22⋊D83—44no—
429C22⋊D83—44no—
430C22⋊D83—44no—
431C22⋊D83—44no—
432C22⋊D83—44no—
433C2×Dic83—22no—
434C2×Dic83—22no—
435C2×Dic83—22no—
436C2×Dic83—42no—
437C2×Dic83—42no—
438C2×Dic83—42no—
439D332—24no—
440D332—42no—
441C4×D83—44no—
442C4×D83—44no—
443Dic166—24no—
444Dic166—42no—
445C83⋊C8—28no—
446C22×C83—28no—
447C22×C83—21no—
448C22×C83—21no—
449C22×C83—21no—
450C22×C83—21no—
451C22×C83—21no—
452C22×C83—21no—
453C22×C83—21no—
454C22×C83—21no—
455C22×C83—21no—
456C22×C83—21no—
457C22×C83—21no—
458C22×C83—21no—
459C22×C83—21no—
460C22×C83—21no—
461C22×C83—21no—
462C22×C83—21no—
463C22×C83—44no—
464C22×C83—44no—
465C22×C83—44no—
466C22×C83—44no—
467C22×C83—44no—
468C22×C83—44no—
469C22×C83#53412yes—
470C22×C83C2×#13712yes—
471C22×C83C2×#13712yes—
472C22×C83C2×#13712yes—
473C22×C83#57512yes—
474C22×C83C23×D411yescharacteristic
475C2×D83—42no—
476C2×D83—42no—
477C2×D83—42no—
478C2×D83—84no—
479C4×C83—21no—
480C4×C83—21no—
481C4×C83—21no—
482C4×C83—21no—
483C4×C83—21no—
484C4×C83—21no—
485C4×C83—44no—
486C4×C83—44no—
487C4×C83#53412yes—
488C4×C83C2×H(5,𝔽2)12yes—
489Dic83—42no—
490Dic83—42no—
491Dic83—42no—
492#60751—831nomaximal, Sylow
493C2×C83—22no—
494C2×C83—22no—
495C2×C83—22no—
496C2×C83—22no—
497C2×C83—22no—
498C2×C83—41no—
499C2×C83—41no—
500C2×C83C2×#53411yescharacteristic
501C2×C83C22×#13711yescharacteristic
502C2×C83C2×#57511yescharacteristic
503D83—82no—
504C2×#525—831no—
505C22×C22⋊Q8D8311yescharacteristic, complemented
506#3196—834no—
507#3195—832no—
508#3193—832no—
509#3190—834no—
510#3189—832no—
511#3187—832no—
512#3095—832no—
513#3092—832no—
514#3056—834no—
515#3007—832no—
516#3004—832no—
517C2×#407—831no—
518C83#6075111yescharacteristic, complemented, Sylow
519C22×#41—831no—
520C23×Q8C2×D8311yescharacteristic, complemented
521C24×C4C2×D8311yescharacteristic
522C2×#137—834no—
523C22×M16—832no—
524#525—832no—
525#525—832no—
526#525—832no—
527#525—832no—
528#525—1661no—
529#525—1661no—
530#525—1661no—
531#525—1661no—
532C2×#123—1661no—
533C2×C22⋊Q8—21no—
534C2×C22⋊Q8—21no—
535C2×C22⋊Q8—21no—
536C2×C22⋊Q8—21no—
537C2×C22⋊Q8—21no—
538C2×C22⋊Q8—21no—
539C2×C22⋊Q8—831no—
540C2×C22⋊Q8—831no—
541C2×C22⋊Q8C2×D8312yes—
542C2×C22⋊Q8C2×D8312yes—
543C2×C22⋊Q8C2×D8312yes—
544C2×C22⋊Q8C2×D8312yescomplemented
545C2×C22⋊Q8C2×D8312yescomplemented
546C2×C22⋊Q8C2×D8312yescomplemented
547C2×#121—831no—
548C2×#121—831no—
549C2×#120—1661no—
550C2×C4×D4—1661no—
551C2×C4×D4—1661no—
552C2×#117—831no—
553C22×C4⋊C4—21no—
554C22×C4⋊C4C2×D8311yescharacteristic, complemented
555C22×C22⋊C4—21no—
556#485—838no—
557#484—834no—
558#484—834no—
559#483—834no—
560#483—834no—
561#481—834no—
562#480—834no—
563#470—838no—
564#468—838no—
565#467—838no—
566#465—838no—
567#452—838no—
568#451—834no—
569#451—834no—
570#451—834no—
571#450—834no—
572#448—834no—
573#448—834no—
574#428—834no—
575#419—834no—
576#417—834no—
577#407—832no—
578#407—832no—
579#407—832no—
580#407—832no—
581C2×C22⋊C8—832no—
582C2×C22⋊C8—832no—
583C25C22⋊D8311yescharacteristic
584C2×#41—3324no—
585C2×#41—832no—
586C2×#41—832no—
587C2×#41—1661no—
588C2×#41—1661no—
589C22×Q8—21no—
590C22×Q8—21no—
591C22×Q8—21no—
592C22×Q8—44no—
593C22×Q8—831no—
594C22×Q8C22×D8312yes—
595C22×Q8C22×D8312yes—
596C22×Q8C22×D8312yes—
597C22×D4—831no—
598C22×D4—1661no—
599C22×D4—1661no—
600C22×D4—1661no—
601C23×C4—21no—
602C23×C4—21no—
603C23×C4—44no—
604C23×C4—1661no—
605C23×C4C22⋊D8311yescharacteristic
606C23×C4C22⋊D8311yescharacteristic
607C23×C4C22⋊D8311yescharacteristic
608C23×C4C22⋊D8311yescharacteristic
609C23×C4C22⋊D8311yescharacteristic
610C23×C4C22⋊D8311yescharacteristic
611C23×C4C22⋊D8311yescharacteristic
612C23×C4C22×D8311yescharacteristic
613C23×C4C22×D8311yescharacteristic
614C23×C4C22×D8311yescharacteristic
615C23×C4C22×D8311yescharacteristic
616C23×C4C22×D8311yescharacteristic
617C23×C4C22×D8311yescharacteristic
618C23×C4C22×D8311yescharacteristic
619#137—3328no—
620C2×Q16—838no—
621C2×SD16—838no—
622C2×M16—3324no—
623C2×M16—834no—
624C2×M16—834no—
625C22×C8—834no—
626#123—1662no—
627#123—1662no—
628#123—1662no—
629#123—1662no—
630C22⋊Q8—22no—
631C22⋊Q8—22no—
632C22⋊Q8—22no—
633C22⋊Q8—22no—
634C22⋊Q8—22no—
635C22⋊Q8—22no—
636C22⋊Q8—22no—
637C22⋊Q8—22no—
638C22⋊Q8—22no—
639C22⋊Q8—22no—
640C22⋊Q8—22no—
641C22⋊Q8—22no—
642C22⋊Q8—832no—
643C22⋊Q8—832no—
644C22⋊Q8—832no—
645C22⋊Q8—832no—
646C22⋊Q8—1661no—
647C22⋊Q8—1661no—
648C22⋊Q8—1661no—
649C22⋊Q8—1661no—
650C22⋊Q8C22×D8314yes—
651C22⋊Q8C22×D8314yes—
652C22⋊Q8C22×D8314yes—
653C22⋊Q8C22×D8314yes—
654#121—832no—
655#121—832no—
656#121—832no—
657#121—832no—
658#121—1661no—
659#121—1661no—
660#121—1661no—
661#121—1661no—
662#120—1662no—
663#120—1662no—
664#120—1662no—
665#120—1662no—
666C4×D4—1662no—
667C4×D4—1662no—
668C4×D4—1662no—
669C4×D4—1662no—
670C4×D4—1662no—
671C4×D4—1662no—
672C4×D4—1662no—
673C4×D4—1662no—
674#117—832no—
675#117—832no—
676#117—1661no—
677#117—1661no—
678C2×C4⋊C4—22no—
679C2×C4⋊C4—22no—
680C2×C4⋊C4—22no—
681C2×C4⋊C4—22no—
682C2×C4⋊C4—22no—
683C2×C4⋊C4—22no—
684C2×C4⋊C4—21no—
685C2×C4⋊C4—21no—
686C2×C4⋊C4—21no—
687C2×C4⋊C4—831no—
688C2×C4⋊C4—831no—
689C2×C4⋊C4—1661no—
690C2×C4⋊C4—1661no—
691C2×C4⋊C4C22×D8312yes—
692C2×C4⋊C4C22×D8312yes—
693C2×C4⋊C4C22×D8312yes—
694C2×C22⋊C4—22no—
695C2×C22⋊C4—22no—
696C2×C22⋊C4—22no—
697C2×C22⋊C4—22no—
698C2×C22⋊C4—22no—
699C2×C22⋊C4—22no—
700C2×C22⋊C4—1661no—
701C2×C22⋊C4—1661no—
702C2×C22⋊C4—1661no—
703C2×C22⋊C4—1661no—
704C2×C22⋊C4—1661no—
705C2×C42—1661no—
706#107—838no—
707#106—838no—
708#103—838no—
709#103—838no—
710#103—838no—
711#102—838no—
712C22⋊C8—834no—
713C22⋊C8—834no—
714C22⋊C8—834no—
715C22⋊C8—834no—
716C24—24no—
717C24—42no—
718C24—42no—
719C24—1661no—
720C24C2×C22⋊D8311yescharacteristic
721C24C2×C22⋊D8311yescharacteristic
722C24C2×C22⋊D8311yescharacteristic
723C24C2×C22⋊D8311yescharacteristic
724C24C2×C22⋊D8311yescharacteristic
725C24C2×C22⋊D8311yescharacteristic
726C24C2×C22⋊D8311yescharacteristic
727#41—3324no—
728#41—3324no—
729#41—3324no—
730#41—1668no—
731C2×Q8—22no—
732C2×Q8—22no—
733C2×Q8—22no—
734C2×Q8—28no—
735C2×Q8—44no—
736C2×Q8—44no—
737C2×Q8—44no—
738C2×Q8—44no—
739C2×Q8—44no—
740C2×Q8—3322no—
741C2×Q8—832no—
742C2×Q8—1661no—
743C2×Q8C23×D8314yes—
744C2×D4—3322no—
745C2×D4—3324no—
746C2×D4—3324no—
747C2×D4—3324no—
748C2×D4—832no—
749C2×D4—1662no—
750C2×D4—1662no—
751C2×D4—1662no—
752C2×D4—1662no—
753C2×D4—1662no—
754C2×D4—1662no—
755C2×D4—1661no—
756C22×C4—24no—
757C22×C4—24no—
758C22×C4—24no—
759C22×C4—22no—
760C22×C4—22no—
761C22×C4—22no—
762C22×C4—22no—
763C22×C4—22no—
764C22×C4—22no—
765C22×C4—42no—
766C22×C4—42no—
767C22×C4—42no—
768C22×C4—42no—
769C22×C4—42no—
770C22×C4—42no—
771C22×C4—42no—
772C22×C4—42no—
773C22×C4—42no—
774C22×C4—42no—
775C22×C4—42no—
776C22×C4—44no—
777C22×C4—44no—
778C22×C4—3324no—
779C22×C4—1661no—
780C22×C4—1661no—
781C22×C4—1661no—
782C22×C4—1662no—
783C22×C4—1662no—
784C22×C4C2×C22⋊D8311yescharacteristic
785C22×C4C2×C22⋊D8311yescharacteristic
786C22×C4C2×C22⋊D8311yescharacteristic
787C22×C4C2×C22⋊D8311yescharacteristic
788C22×C4C2×C22⋊D8311yescharacteristic
789C22×C4C2×C22⋊D8311yescharacteristic
790C22×C4C2×C22⋊D8311yescharacteristic
791C22×C4C2×C22⋊D8311yescharacteristic
792C22×C4C2×C22⋊D8311yescharacteristic
793C22×C4C2×C22⋊D8311yescharacteristic
794C22×C4C2×C22⋊D8311yescharacteristic
795C22×C4C2×C22⋊D8311yescharacteristic
796C22×C4C2×C22⋊D8311yescharacteristic
797C22×C4C2×C22⋊D8311yescharacteristic
798C22×C4C2×C22⋊D8311yescharacteristic
799C22×C4C2×C22⋊D8311yescharacteristic
800C22×C4C2×C22⋊D8311yescharacteristic
801C22×C4C2×C22⋊D8311yescharacteristic
802C22×C4C2×C22⋊D8311yescharacteristic
803C22×C4C2×C22⋊D8311yescharacteristic
804C22×C4C2×C22⋊D8311yescharacteristic
805C22×C4C23×D8311yescharacteristic
806C22×C4C23×D8311yescharacteristic
807C22×C4C23×D8311yescharacteristic
808C22×C4C23×D8311yescharacteristic
809C22×C4C23×D8311yescharacteristic
810C22×C4C23×D8311yescharacteristic
811C22×C4C23×D8311yescharacteristic
812Q16—3328no—
813SD16—3328no—
814M16—3324no—
815M16—1668no—
816C2×C8—3324no—
817C2×C8—838no—
818C4⋊C4—24no—
819C4⋊C4—24no—
820C4⋊C4—24no—
821C4⋊C4—24no—
822C4⋊C4—22no—
823C4⋊C4—22no—
824C4⋊C4—22no—
825C4⋊C4—832no—
826C4⋊C4—832no—
827C4⋊C4—1661no—
828C4⋊C4—1661no—
829C4⋊C4—1662no—
830C4⋊C4—1662no—
831C4⋊C4—1662no—
832C4⋊C4—1662no—
833C4⋊C4C23×D8314yes—
834C22⋊C4—24no—
835C22⋊C4—24no—
836C22⋊C4—24no—
837C22⋊C4—24no—
838C22⋊C4—1662no—
839C22⋊C4—1662no—
840C22⋊C4—1662no—
841C22⋊C4—1662no—
842C22⋊C4—1662no—
843C22⋊C4—1662no—
844C22⋊C4—1662no—
845C22⋊C4—1662no—
846C22⋊C4—1662no—
847C22⋊C4—1662no—
848C42—1662no—
849C42—1662no—
850C23—22no—
851C23—22no—
852C23—22no—
853C23—22no—
854C23—22no—
855C23—22no—
856C23—22no—
857C23—22no—
858C23—22no—
859C23—22no—
860C23—22no—
861C23—22no—
862C23—41no—
863C23—41no—
864C23—41no—
865C23—41no—
866C23—41no—
867C23—41no—
868C23—41no—
869C23—41no—
870C23—416no—
871C23—3322no—
872C23—3322no—
873C23—3322no—
874C23—1662no—
875C23#1458182314yescomplemented
876C23C22×C22⋊D8311yescharacteristic
877C23C22×C22⋊D8311yescharacteristic
878C23C22×C22⋊D8311yescharacteristic
879C23C22×C22⋊D8311yescharacteristic
880C23C22×C22⋊D8311yescharacteristic
881C23C22×C22⋊D8311yescharacteristic
882C23C22×C22⋊D8311yescharacteristic
883Q8—28no—
884Q8—44no—
885Q8—44no—
886Q8—44no—
887Q8—3322no—
888Q8—1664no—
889D4—3322no—
890D4—3324no—
891D4—3324no—
892D4—3324no—
893D4—3324no—
894D4—3324no—
895D4—3324no—
896D4—1664no—
897C2×C4—22no—
898C2×C4—22no—
899C2×C4—22no—
900C2×C4—22no—
901C2×C4—22no—
902C2×C4—22no—
903C2×C4—22no—
904C2×C4—22no—
905C2×C4—22no—
906C2×C4—22no—
907C2×C4—22no—
908C2×C4—22no—
909C2×C4—22no—
910C2×C4—22no—
911C2×C4—22no—
912C2×C4—24no—
913C2×C4—24no—
914C2×C4—41no—
915C2×C4—41no—
916C2×C4—41no—
917C2×C4—41no—
918C2×C4—41no—
919C2×C4—41no—
920C2×C4—41no—
921C2×C4—41no—
922C2×C4—41no—
923C2×C4—41no—
924C2×C4—41no—
925C2×C4—41no—
926C2×C4—44no—
927C2×C4—44no—
928C2×C4—44no—
929C2×C4—44no—
930C2×C4—44no—
931C2×C4—44no—
932C2×C4—3324no—
933C2×C4—3322no—
934C2×C4—3322no—
935C2×C4—3322no—
936C2×C4—3324no—
937C2×C4—1662no—
938C2×C4—1662no—
939C2×C4—1662no—
940C2×C4C22×C22⋊D8311yescharacteristic
941C2×C4C22×C22⋊D8311yescharacteristic
942C2×C4C22×C22⋊D8311yescharacteristic
943C2×C4C22×C22⋊D8311yescharacteristic
944C2×C4C22×C22⋊D8311yescharacteristic
945C2×C4C22×C22⋊D8311yescharacteristic
946C2×C4C22×C22⋊D8311yescharacteristic
947C2×C4#1458183714yes—
948C2×C4C24×D8311yescharacteristic
949C8—1668no—
950C22—28no—
951C22—21no—
952C22—21no—
953C22—21no—
954C22—21no—
955C22—21no—
956C22—21no—
957C22—21no—
958C22—21no—
959C22—21no—
960C22—21no—
961C22—21no—
962C22—21no—
963C22—21no—
964C22—21no—
965C22—21no—
966C22—21no—
967C22—44no—
968C22—44no—
969C22—44no—
970C22—44no—
971C22—44no—
972C22—44no—
973C22—3322no—
974C22—3322no—
975C22—3322no—
976C22—6644no—
977C22#1912826012yes—
978C22C2×#1458182312yes—
979C22C2×#1458182312yes—
980C22C2×#1458182312yes—
981C22#1912849912yes—
982C22C23×C22⋊D8311yescharacteristic
983C4—21no—
984C4—21no—
985C4—21no—
986C4—21no—
987C4—21no—
988C4—21no—
989C4—44no—
990C4—44no—
991C4—3322no—
992C4—3322no—
993C4—3322no—
994C4#1912826012yes—
995C4C2×#1458183712yes—
996C2—22no—
997C2—22no—
998C2—22no—
999C2—22no—
1000C2—22no—
1001C2—41no—
1002C2—41no—
1003C2—6642no—
1004C2C2×#1912826011yescharacteristic
1005C2C22×#1458182311yescharacteristic
1006C2C2×#1912849911yescharacteristic
subgroupG/H
centerC22C23×C22⋊D83
commutator, cosocleC2×C4×C83C25
FrattiniC2×C4C24×D83
FittingC22×C22⋊Q8×C83C2
socleC22×C83C23×D4
prime radicalC2×#19128212C2
hypercenterC22×C22⋊Q8D83
hypocenterC83#60751
LCSG ▷ C2×C4×C83 ▷ C2×C83 ▷ C83
UCSC1 ◁ C22 ◁ C24×C4 ◁ C22×C22⋊Q8

Complements

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

NH ≅ G/Ntype
2. #24918293C2semidirect
3. #24918284C2semidirect
4. #24918265C2semidirect
5. #24918244C2semidirect
6. #24918235C2semidirect
7. #24918216C2semidirect
8. #24917407C2semidirect
9. #24917386C2semidirect
10. #24917089C2semidirect
11. #24916721C2semidirect
12. #24916697C2semidirect
13. C2×#19127665C2semidirect
14. C22×C22⋊Q8×C83C2semidirect
16. C2×#14581823C22semidirect
17. C22×#13050574C22semidirect
35. #19128039C22semidirect
36. #19128036C22semidirect
37. #19128034C22semidirect
38. #19128031C22semidirect
39. #19128029C22semidirect
40. #19128019C22semidirect
41. #19128014C22semidirect
42. #19127957C22semidirect
43. #19127949C22semidirect
44. #19127940C22semidirect
45. #19127932C22semidirect
46. #19127861C22semidirect
47. #19127857C22semidirect
48. #19127857C22semidirect
49. #19127856C22semidirect
50. #19127851C22semidirect
51. #19127840C22semidirect
52. #19127840C22semidirect
53. #19127741C22semidirect
54. #19127710C22semidirect
55. #19127700C22semidirect
58. #19127665C22semidirect
59. #19127665C22semidirect
61. C2×C22⋊(C83⋊C8)C22semidirect
62. C23×Q8×C83C22semidirect
73. C2×C22⋊Q8×C83C22semidirect
74. C2×C22⋊Q8×C83C22semidirect
75. C2×C22⋊Q8×C83C22semidirect
77. C22×C4⋊C4×C83C22semidirect
91. C2×#13050580C23semidirect
92. C2×#13050577C23semidirect
143. #14581725C23semidirect
144. #14581723C23semidirect
145. #14581716C23semidirect
146. #14581716C23semidirect
147. #14581715C23semidirect
148. #14581712C23semidirect
367. C23×C83#137semidirect
505. C22×C22⋊Q8D83semidirect
518. C83#60751semidirect
520. C23×Q8C2×D83semidirect
544. C2×C22⋊Q8C2×D83semidirect
545. C2×C22⋊Q8C2×D83semidirect
546. C2×C22⋊Q8C2×D83semidirect
554. C22×C4⋊C4C2×D83semidirect
875. C23#14581823semidirect

Maximal subgroups

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

subgroupindex
C2×#191282122
#249182932
#249182842
#249182652
#249182442
#249182352
#249182162
#249174072
#249173862
#249170892
#249167212
#249166972
C2×#191276652
C22×C22⋊Q8×C832
#6075183