Finite Group Databasebeta

← C2×#24921156 #36312455

Subgroups — C2×#24921156 #36312455

Order 21248.

7390 conjugacy classes of subgroups.

The subgroup lattice has 760 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#24921156C2132yesmaximal, direct product factor
2C2×#19128391C214yesmaximal, complemented
3C2×#19128384C214yesmaximal, complemented
4C2×#19128380C214yesmaximal, complemented
5C2×#19128377C214yesmaximal, complemented
6C2×#19128327C211yesmaximal, characteristic, complemented
7C2×#19128293C214yesmaximal, complemented
8C2×#19128260C211yesmaximal, characteristic
9C2×#19128231C214yesmaximal, complemented
10C22×#14581776C211yesmaximal, characteristic, complemented
11C22×#14581773C211yesmaximal, characteristic, complemented
12C2×#19128174C211yesmaximal, characteristic, complemented
13C22×#14581748C211yesmaximal, characteristic, complemented
14C2×#518×C83C211yesmaximal, characteristic, complemented
15C23×C22⋊D83C2211yescharacteristic
16C24×Dic83C2211yescharacteristic
17#19128391C22164yescomplemented
18#19128384C22164yescomplemented
19#19128380C22164yescomplemented
20#19128377C22164yescomplemented
21#19128327C22116yescomplemented
22#19128293C22164yescomplemented
23#19128260C22116yes—
24#19128231C22164yescomplemented
25C2×#14581787C2214yescomplemented
26C2×#14581786C2214yescomplemented
27C2×#14581785C2214yescomplemented
28C2×#14581785C2214yescomplemented
29C2×#14581784C2214yescomplemented
30C2×#14581782C2214yescomplemented
31C2×#14581782C2214yescomplemented
32C2×#14581778C2214yescomplemented
33C2×#14581776C2214yes—
34C2×#14581776C22116yescomplemented
35C2×#14581776C2212yescomplemented
36C2×#14581776C2212yescomplemented
37C2×#14581775C2212yes—
38C2×#14581775C2214yescomplemented
39C2×#14581774C2214yescomplemented
40C2×#14581773C2214yes—
41C2×#14581773C2212yes—
42C2×#14581773C22116yescomplemented
43C2×#14581773C2212yescomplemented
44C2×#14581773C2212yescomplemented
45C2×#14581771C2214yescomplemented
46C2×#14581771C2214yescomplemented
47C2×#14581770C2214yescomplemented
48C2×#14581769C2214yescomplemented
49C2×#14581769C2214yescomplemented
50C2×#14581764C2214yes—
51C2×#14581761C2212yes—
52C2×#14581760C2212yes—
53#19128174C22116yescomplemented
54C2×C4×Dic166C2214yescomplemented
55C2×C4×C22⋊D83C2214yescomplemented
56C2×C4×C22⋊D83C2214yescomplemented
57C2×(C22⋊D83)⋊C4C2214yes—
58C2×#14581751C2214yescomplemented
59C2×#14581749C2214yescomplemented
60C2×#14581748C2214yescomplemented
61C2×#14581748C2214yescomplemented
62C2×#14581748C2212yescomplemented
63C2×#14581748C22116yescomplemented
64C22×C4⋊Dic83C2212yescomplemented
65C22×Dic83⋊C4C2212yescomplemented
66C22×Dic83⋊C4C2212yescomplemented
67C22×C22⋊Dic83C2211yescharacteristic
68C22×C22⋊Dic83C2211yescharacteristic
69C22×C22⋊Dic83C2212yescomplemented
70C22×(C2×D83)⋊C4C2212yescomplemented
71C2×C22⋊C4×D83C2212yescomplemented
72C22×C4×Dic83C2212yescomplemented
73C23×D4×C83C2211yescharacteristic
74#518×C83C22116yescomplemented
75C2×C4×D4×C83C2214yes—
76C2×C4×D4×C83C2214yescomplemented
77C2×#117×C83C2212yescomplemented
78C22×C22⋊C4×C83C2211yescharacteristic
79C22×C22⋊C4×C83C2211yescharacteristic
80C22×C22⋊C4×C83C2212yescomplemented
81C24×D83C2311yescharacteristic
82C22×Dic166C2314yes—
83C22×C22⋊D83—28no—
84C22×C22⋊D83C2312yes—
85C22×C22⋊D83C2312yes—
86C22×C22⋊D83C2318yes—
87C22×C22⋊D83C2314yes—
88C23×Dic83—28no—
89C23×Dic83C2311yescharacteristic
90C23×Dic83C2312yes—
91C23×Dic83C2312yes—
92C23×Dic83C2311yescharacteristic
93C23×Dic83C2311yescharacteristic
94C23×Dic83C2318yes—
95C23×Dic83C2312yes—
96C23×Dic83C2312yes—
97C22×C4×D83C2314yes—
98#14581787C23132yescomplemented
99#14581786C23132yescomplemented
100#14581785C23132yescomplemented
101#14581785C23132yescomplemented
102#14581784C23132yescomplemented
103#14581782C23132yescomplemented
104#14581782C23132yescomplemented
105#14581778C23132yescomplemented
106#14581776C23132yes—
107#14581776C23116yescomplemented
108#14581776C23116yescomplemented
109#14581775C23116yes—
110#14581775C23132yescomplemented
111#14581774C23132yescomplemented
112#14581773C23132yes—
113#14581773C23116yes—
114#14581773C23116yescomplemented
115#14581773C23116yescomplemented
116#14581771C23132yescomplemented
117#14581771C23132yescomplemented
118#14581770C23132yescomplemented
119#14581769C23132yescomplemented
120#14581769C23132yescomplemented
121#14581764C23132yes—
122#14581761C23116yes—
123#14581760C23116yes—
124C4×Dic166C23132yescomplemented
125C4×C22⋊D83C23132yescomplemented
126C4×C22⋊D83C23132yescomplemented
127(C22⋊D83)⋊C4C23132yes—
128#14581751C23132yescomplemented
129#14581749C23132yescomplemented
130#14581748C23132yescomplemented
131#14581748C23132yescomplemented
132#14581748C23116yescomplemented
133C2×C4⋊Dic83C2314yes—
134C2×C4⋊Dic83C2314yes—
135C2×C4⋊Dic83C2314yes—
136C2×C4⋊Dic83C23116yescomplemented
137C2×Dic83⋊C4C2314yes—
138C2×Dic83⋊C4C2314yes—
139C2×Dic83⋊C4C2314yes—
140C2×Dic83⋊C4C2314yes—
141C2×Dic83⋊C4C2314yes—
142C2×Dic83⋊C4C2314yes—
143C2×Dic83⋊C4C2314yes—
144C2×Dic83⋊C4C2314yes—
145C2×Dic83⋊C4C23116yescomplemented
146C2×Dic83⋊C4C23116yescomplemented
147C2×C22⋊Dic83C2318yes—
148C2×C22⋊Dic83C2318yes—
149C2×C22⋊Dic83C2312yes—
150C2×C22⋊Dic83C2312yes—
151C2×C22⋊Dic83C2312yes—
152C2×C22⋊Dic83C2312yes—
153C2×C22⋊Dic83C2314yes—
154C2×C22⋊Dic83C2314yes—
155C2×C22⋊Dic83C2314yes—
156C2×C22⋊Dic83C23116yescomplemented
157C2×(C2×D83)⋊C4C2314yes—
158C2×(C2×D83)⋊C4C2314yes—
159C2×(C2×D83)⋊C4C2314yes—
160C2×(C2×D83)⋊C4C2314yes—
161C2×(C2×D83)⋊C4C23116yescomplemented
162C22⋊C4×D83C23116yescomplemented
163C2×C4×Dic83C2314yes—
164C2×C4×Dic83C2314yes—
165C2×C4×Dic83C2314yes—
166C2×C4×Dic83C23116yescomplemented
167C25×C83C2311yescharacteristic
168C25×C83C2311yescharacteristic
169C22×D4×C83—28no—
170C22×D4×C83C2312yes—
171C22×D4×C83C2312yes—
172C22×D4×C83C2318yes—
173C23×C4×C83C2311yescharacteristic
174C23×C4×C83C2312yes—
175C23×C4×C83C2312yes—
176C23×C4×C83C2314yes—
177C4×D4×C83C23132yes—
178C4×D4×C83C23132yescomplemented
179#117×C83C23116yescomplemented
180C2×C4⋊C4×C83C2314yes—
181C2×C22⋊C4×C83C2318yes—
182C2×C22⋊C4×C83C2312yes—
183C2×C22⋊C4×C83C2312yes—
184C2×C22⋊C4×C83C2312yes—
185C2×C22⋊C4×C83C2312yes—
186C2×C22⋊C4×C83C2318yes—
187C2×C22⋊C4×C83C2314yes—
188C2×C22⋊C4×C83C23116yescomplemented
189C2×C42×C83C2314yes—
190C23×D83—24no—
191C23×D83—44no—
192C23×D83C2412yes—
193C23×D83C2414yes—
194C2×Dic166—48no—
195C2×Dic166C24116yes—
196C2×C22⋊D83—28no—
197C2×C22⋊D83—28no—
198C2×C22⋊D83—232no—
199C2×C22⋊D83—48no—
200C2×C22⋊D83C2418yes—
201C2×C22⋊D83C2418yes—
202C2×C22⋊D83C24116yes—
203C22×Dic83—28no—
204C22×Dic83—28no—
205C22×Dic83—24no—
206C22×Dic83—24no—
207C22×Dic83—232no—
208C22×Dic83—24no—
209C22×Dic83—44no—
210C22×Dic83—44no—
211C22×Dic83C2418yes—
212C22×Dic83C2414yes—
213C22×Dic83C2414yes—
214C22×Dic83C2414yes—
215C22×Dic83C2418yes—
216C22×Dic83C2414yes—
217C22×Dic83C2412yes—
218C22×Dic83C2412yes—
219C22×Dic83C2412yes—
220C22×Dic83C2414yes—
221C22×Dic83C2418yes—
222C22×Dic83C2418yes—
223C2×C4×D83—48no—
224C2×C4×D83C24116yes—
225C4⋊Dic83C24116yes—
226C4⋊Dic83C24116yes—
227C4⋊Dic83C24116yes—
228Dic83⋊C4C24116yes—
229Dic83⋊C4C24116yes—
230Dic83⋊C4C24116yes—
231Dic83⋊C4C24116yes—
232Dic83⋊C4C24116yes—
233Dic83⋊C4C24116yes—
234Dic83⋊C4C24116yes—
235Dic83⋊C4C24116yes—
236C22⋊Dic83C2418yes—
237C22⋊Dic83C24116yes—
238C22⋊Dic83C2418yes—
239C22⋊Dic83C2418yes—
240C22⋊Dic83C2418yes—
241C22⋊Dic83C24116yes—
242C22⋊Dic83C24116yes—
243(C2×D83)⋊C4C24116yes—
244(C2×D83)⋊C4C24116yes—
245(C2×D83)⋊C4C24116yes—
246(C2×D83)⋊C4C24116yes—
247C4×Dic83C24116yes—
248C4×Dic83C24116yes—
249C4×Dic83C24116yes—
250C24×C83—24no—
251C24×C83—44no—
252C24×C83—44no—
253C24×C83#4118yes—
254C24×C83C2412yes—
255C24×C83C2411yescharacteristic
256C24×C83C2411yescharacteristic
257C24×C83C2411yescharacteristic
258C24×C83C2414yes—
259C24×C83C2414yes—
260C2×D4×C83—28no—
261C2×D4×C83—28no—
262C2×D4×C83—232no—
263C2×D4×C83C2418yes—
264C2×D4×C83C2418yes—
265C22×C4×C83—24no—
266C22×C4×C83—44no—
267C22×C4×C83—48no—
268C22×C4×C83—44no—
269C22×C4×C83C2414yes—
270C22×C4×C83C2414yes—
271C22×C4×C83C2414yes—
272C22×C4×C83C2412yes—
273C22×C4×C83C2418yes—
274C22×C4×C83C24116yes—
275C22×C4×C83C2418yes—
276C4⋊C4×C83C24116yes—
277C22⋊C4×C83C2418yes—
278C22⋊C4×C83C2418yes—
279C22⋊C4×C83C24116yes—
280C22⋊C4×C83C2418yes—
281C22⋊C4×C83C2418yes—
282C42×C83C24116yes—
283C23×C83—24no—
284C23×C83—24no—
285C23×C83—24no—
286C23×C83—24no—
287C23×C83—28no—
288C23×C83—28no—
289C23×C83—416no—
290C23×C83—48no—
291C23×C83—48no—
292C23×C83—88no—
293C23×C83C2×#4114yes—
294C23×C83C2×#4114yes—
295C23×C83C2×#4114yes—
296C23×C83C2×#41116yes—
297C23×C83C2514yes—
298C23×C83C2512yes—
299C23×C83C2512yes—
300C23×C83C2512yes—
301C23×C83C2511yescharacteristic
302C22×D83—24no—
303C22×D83—28no—
304C22×D83—28no—
305C22×D83—48no—
306C22×D83—88no—
307C22×D83C2514yes—
308D4×C83—216no—
309D4×C83—216no—
310C2×C4×C83—28no—
311C2×C4×C83—24no—
312C2×C4×C83—28no—
313C2×C4×C83—28no—
314C2×C4×C83—48no—
315C2×C4×C83—416no—
316C2×C4×C83—48no—
317C2×C4×C83C2514yes—
318C2×C4×C83C2518yes—
319C2×C4×C83C2518yes—
320C22⋊D83—216no—
321C22⋊D83—216no—
322C22⋊D83—416no—
323C2×Dic83—216no—
324C2×Dic83—216no—
325C2×Dic83—28no—
326C2×Dic83—28no—
327C2×Dic83—24no—
328C2×Dic83—24no—
329C2×Dic83—28no—
330C2×Dic83—24no—
331C2×Dic83—28no—
332C2×Dic83—28no—
333C2×Dic83—48no—
334C2×Dic83—48no—
335C2×Dic83C2514yes—
336C2×Dic83C2518yes—
337C2×Dic83C2514yes—
338C2×Dic83C2518yes—
339C2×Dic83C2514yes—
340C4×D83—416no—
341Dic166—416no—
342C22×C83—24no—
343C22×C83—24no—
344C22×C83—24no—
345C22×C83—28no—
346C22×C83—28no—
347C22×C83—28no—
348C22×C83—24no—
349C22×C83—28no—
350C22×C83—416no—
351C22×C83—48no—
352C22×C83—88no—
353C22×C83C22×#4114yes—
354C22×C83C22×#4114yes—
355C22×C83C22×#4114yes—
356C22×C83C22×#4112yes—
357C22×C83#58514yes—
358C22×C83C2611yescharacteristic
359C2×D83—24no—
360C2×D83—28no—
361C2×D83—48no—
362C2×D83—88no—
363C4×C83—24no—
364C4×C83—28no—
365C4×C83—28no—
366Dic83—24no—
367Dic83—24no—
368Dic83—24no—
369Dic83—28no—
370Dic83—28no—
371C2×#3491—831nomaximal, Sylow
372C2×C83—24no—
373C2×C83—24no—
374C2×C83—24no—
375C2×C83—44no—
376C2×C83#349114yescomplemented
377C2×C83C23×#4111yescharacteristic
378C2×C83C2×#58512yes—
379D83—44no—
380#3491—8332no—
381C2×#552—834no—
382C2×#552—834no—
383C2×#551—834no—
384C2×#551—834no—
385C2×#543—831no—
386C2×#539—834no—
387C2×#534—831no—
388C2×#529—834no—
389C22×#123—831no—
390C22×#123—831no—
391C2×#518—831no—
392C2×#518D8311yescharacteristic, complemented
393C22×#117—831no—
394C83C2×#349111yescharacteristic, complemented, Sylow
395C23×D4—831no—
396C23×D4C2×D8311yescharacteristic
397C24×C4—831no—
398#552—8364no—
399#552—8364no—
400#551—8364no—
401#551—8364no—
402#543—8316no—
403#539—8364no—
404#534—8316no—
405#529—8364no—
406C2×#126—834no—
407C2×#126—834no—
408C2×#126—834no—
409C2×#126—834no—
410C2×#125—834no—
411C2×#125—834no—
412C2×#125—834no—
413C2×#124—834no—
414C2×#123—832no—
415C2×#123—832no—
416C2×#123—834no—
417C2×#123—8316no—
418C2×#123—832no—
419C2×#123—832no—
420C2×#123—834no—
421C2×#123—832no—
422C2×#123—832no—
423C2×#123—834no—
424C2×#123—8316no—
425C2×#123—834no—
426C2×C22⋊Q8—834no—
427C2×C22⋊Q8—834no—
428C2×C22⋊Q8—834no—
429C2×C22⋊Q8—834no—
430C2×C22⋊Q8—834no—
431C2×#121—834no—
432C2×#120—832no—
433C2×#120—832no—
434#518—8316no—
435#518C2×D83116yescomplemented
436C2×C4×Q8—834no—
437C2×C4×D4—834no—
438C2×C4×D4—834no—
439C2×C4×D4—834no—
440C2×C4×D4C2×D8314yes—
441C2×C4×D4C2×D8314yescomplemented
442C2×#117—834no—
443C2×#117—834no—
444C2×#117—834no—
445C2×#117—8316no—
446C2×#117—832no—
447C2×#117—834no—
448C2×#117C2×D8312yescomplemented
449C22×C4⋊C4—832no—
450C22×C4⋊C4—832no—
451C22×C4⋊C4—832no—
452C22×C22⋊C4—831no—
453C22×C22⋊C4—831no—
454C22×C22⋊C4—832no—
455C22×C22⋊C4—832no—
456C22×C22⋊C4—832no—
457C22×C22⋊C4C2×D8311yescharacteristic
458C22×C22⋊C4C2×D8311yescharacteristic
459C22×C22⋊C4C2×D8312yescomplemented
460C22×C42—832no—
461C25—831no—
462C25C22×D8311yescharacteristic
463C25C22×D8311yescharacteristic
464C22×Q8—834no—
465C22×D4—28no—
466C22×D4—834no—
467C22×D4—832no—
468C22×D4—832no—
469C22×D4—838no—
470C22×D4—1668no—
471C22×D4C22×D8312yes—
472C22×D4C22×D8312yes—
473C22×D4C22×D8318yes—
474C23×C4—832no—
475C23×C4—832no—
476C23×C4—834no—
477C23×C4—832no—
478C23×C4—832no—
479C23×C4—831no—
480C23×C4—831no—
481C23×C4—838no—
482C23×C4—831no—
483C23×C4—1668no—
484C23×C4C22×D8311yescharacteristic
485C23×C4C22×D8312yes—
486C23×C4C22×D8312yes—
487C23×C4C22×D8314yes—
488#126—8332no—
489#126—8332no—
490#126—8332no—
491#126—8332no—
492#125—8332no—
493#125—8332no—
494#125—8332no—
495#124—8332no—
496#123—8332no—
497#123—8316no—
498#123—8316no—
499#123—8316no—
500#123—8316no—
501#123—8332no—
502#123—8332no—
503#123—8316no—
504#123—8316no—
505#123—8332no—
506C22⋊Q8—8332no—
507C22⋊Q8—8332no—
508C22⋊Q8—8332no—
509C22⋊Q8—8332no—
510C22⋊Q8—8332no—
511#121—8332no—
512#120—8316no—
513#120—8316no—
514C4×Q8—8332no—
515C4×D4—8332no—
516C4×D4—8332no—
517C4×D4—8332no—
518C4×D4C22×D83132yes—
519C4×D4C22×D83132yescomplemented
520#117—8332no—
521#117—8332no—
522#117—8332no—
523#117—8316no—
524#117—8332no—
525#117C22×D83116yescomplemented
526C2×C4⋊C4—834no—
527C2×C4⋊C4—834no—
528C2×C4⋊C4—8316no—
529C2×C4⋊C4—834no—
530C2×C4⋊C4—834no—
531C2×C4⋊C4—834no—
532C2×C4⋊C4—834no—
533C2×C4⋊C4—8316no—
534C2×C4⋊C4—8316no—
535C2×C4⋊C4—834no—
536C2×C4⋊C4—834no—
537C2×C4⋊C4—834no—
538C2×C4⋊C4—834no—
539C2×C4⋊C4—834no—
540C2×C4⋊C4C22×D8314yes—
541C2×C22⋊C4—832no—
542C2×C22⋊C4—832no—
543C2×C22⋊C4—832no—
544C2×C22⋊C4—838no—
545C2×C22⋊C4—834no—
546C2×C22⋊C4—832no—
547C2×C22⋊C4—838no—
548C2×C22⋊C4—834no—
549C2×C22⋊C4—8316no—
550C2×C22⋊C4—834no—
551C2×C22⋊C4—834no—
552C2×C22⋊C4—834no—
553C2×C22⋊C4—834no—
554C2×C22⋊C4—8316no—
555C2×C22⋊C4—834no—
556C2×C22⋊C4—8316no—
557C2×C22⋊C4C22×D8312yes—
558C2×C22⋊C4C22×D8312yes—
559C2×C22⋊C4C22×D8312yes—
560C2×C22⋊C4C22×D8318yes—
561C2×C22⋊C4C22×D8312yes—
562C2×C22⋊C4C22×D8318yes—
563C2×C22⋊C4C22×D8314yes—
564C2×C22⋊C4C22×D83116yescomplemented
565C2×C42—834no—
566C2×C42—834no—
567C2×C42—834no—
568C2×C42—8316no—
569C2×C42C22×D8314yes—
570C24—24no—
571C24—44no—
572C24—44no—
573C24—3324no—
574C24—834no—
575C24—832no—
576C24—1664no—
577C24#1305059018yes—
578C24C23×D8312yes—
579C24C23×D8311yescharacteristic
580C24C23×D8311yescharacteristic
581C24C23×D8311yescharacteristic
582C24C23×D8314yes—
583C24C23×D8314yes—
584C2×Q8—3328no—
585C2×Q8—8316no—
586C2×D4—28no—
587C2×D4—28no—
588C2×D4—232no—
589C2×D4—3328no—
590C2×D4—8316no—
591C2×D4—838no—
592C2×D4—838no—
593C2×D4—1668no—
594C2×D4—1668no—
595C2×D4—16632no—
596C2×D4C23×D8318yes—
597C2×D4C23×D8318yes—
598C22×C4—24no—
599C22×C4—44no—
600C22×C4—48no—
601C22×C4—44no—
602C22×C4—3328no—
603C22×C4—3324no—
604C22×C4—3324no—
605C22×C4—838no—
606C22×C4—838no—
607C22×C4—8316no—
608C22×C4—834no—
609C22×C4—838no—
610C22×C4—838no—
611C22×C4—834no—
612C22×C4—834no—
613C22×C4—832no—
614C22×C4—834no—
615C22×C4—832no—
616C22×C4—834no—
617C22×C4—832no—
618C22×C4—1668no—
619C22×C4—1668no—
620C22×C4—1664no—
621C22×C4—1664no—
622C22×C4—16632no—
623C22×C4—1664no—
624C22×C4C23×D8314yes—
625C22×C4C23×D8314yes—
626C22×C4C23×D8312yes—
627C22×C4C23×D8314yes—
628C22×C4C23×D8318yes—
629C22×C4C23×D8318yes—
630C22×C4C23×D83116yes—
631C4⋊C4—8316no—
632C4⋊C4—8316no—
633C4⋊C4—8316no—
634C4⋊C4—8316no—
635C4⋊C4—8316no—
636C4⋊C4—8316no—
637C4⋊C4—8316no—
638C4⋊C4—8316no—
639C4⋊C4—8316no—
640C4⋊C4—8316no—
641C4⋊C4—8316no—
642C4⋊C4C23×D83116yes—
643C22⋊C4—838no—
644C22⋊C4—838no—
645C22⋊C4—838no—
646C22⋊C4—8316no—
647C22⋊C4—838no—
648C22⋊C4—8316no—
649C22⋊C4—8316no—
650C22⋊C4—8316no—
651C22⋊C4—8316no—
652C22⋊C4—8316no—
653C22⋊C4—8316no—
654C22⋊C4C23×D8318yes—
655C22⋊C4C23×D8318yes—
656C22⋊C4C23×D8318yes—
657C22⋊C4C23×D8318yes—
658C22⋊C4C23×D83116yes—
659C42—8316no—
660C42—8316no—
661C42—8316no—
662C42C23×D83116yes—
663C23—24no—
664C23—24no—
665C23—24no—
666C23—24no—
667C23—28no—
668C23—28no—
669C23—416no—
670C23—48no—
671C23—48no—
672C23—88no—
673C23—3328no—
674C23—834no—
675C23—6648no—
676C23—1664no—
677C23—1668no—
678C23—1668no—
679C23C2×#1305059014yes—
680C23C2×#1305059014yes—
681C23C2×#1305059014yes—
682C23C2×#13050590116yes—
683C23C24×D8314yes—
684C23C24×D8312yes—
685C23C24×D8312yes—
686C23C24×D8312yes—
687C23C24×D8311yescharacteristic
688Q8—33216no—
689D4—216no—
690D4—216no—
691D4—33216no—
692D4—16616no—
693D4—16616no—
694C2×C4—28no—
695C2×C4—24no—
696C2×C4—28no—
697C2×C4—28no—
698C2×C4—48no—
699C2×C4—416no—
700C2×C4—48no—
701C2×C4—33216no—
702C2×C4—3328no—
703C2×C4—3328no—
704C2×C4—834no—
705C2×C4—838no—
706C2×C4—834no—
707C2×C4—838no—
708C2×C4—834no—
709C2×C4—16616no—
710C2×C4—16616no—
711C2×C4—1668no—
712C2×C4—1668no—
713C2×C4—1664no—
714C2×C4—1664no—
715C2×C4—1668no—
716C2×C4—1664no—
717C2×C4—1668no—
718C2×C4—1668no—
719C2×C4C24×D8318yes—
720C2×C4C24×D8314yes—
721C2×C4C24×D8318yes—
722C22—28no—
723C22—28no—
724C22—28no—
725C22—24no—
726C22—24no—
727C22—24no—
728C22—24no—
729C22—28no—
730C22—416no—
731C22—48no—
732C22—88no—
733C22—3328no—
734C22—6648no—
735C22—1664no—
736C22—1668no—
737C22C22×#1305059014yes—
738C22C22×#1305059014yes—
739C22C22×#1305059014yes—
740C22C22×#1305059012yes—
741C22#1912853614yes—
742C22C25×D8311yescharacteristic
743C4—24no—
744C4—28no—
745C4—28no—
746C4—1664no—
747C4—1664no—
748C4—1664no—
749C4—1668no—
750C4—1668no—
751C2—24no—
752C2—24no—
753C2—24no—
754C2—44no—
755C2—3324no—
756C2#2492115614yesdirect product factor
757C2C23×#1305059011yescharacteristic
758C2C2×#1912853612yes—
subgroupG/H
centerC23C24×D83
commutator, cosocleC22×C83C26
FrattiniC22C25×D83
FittingC2×#518×C83C2
socleC23×C83C25
prime radicalC2×#19128260C2
hypercenterC2×#518D83
hypocenterC83C2×#3491
LCSG ▷ C22×C83 ▷ C83
UCSC1 ◁ C23 ◁ C2×#518

Complements

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

NH ≅ G/Ntype
1. #24921156C2direct (N × H)
2. C2×#19128391C2semidirect
3. C2×#19128384C2semidirect
4. C2×#19128380C2semidirect
5. C2×#19128377C2semidirect
6. C2×#19128327C2semidirect
7. C2×#19128293C2semidirect
9. C2×#19128231C2semidirect
10. C22×#14581776C2semidirect
11. C22×#14581773C2semidirect
12. C2×#19128174C2semidirect
13. C22×#14581748C2semidirect
14. C2×#518×C83C2semidirect
17. #19128391C22semidirect
18. #19128384C22semidirect
19. #19128380C22semidirect
20. #19128377C22semidirect
21. #19128327C22semidirect
22. #19128293C22semidirect
24. #19128231C22semidirect
25. C2×#14581787C22semidirect
26. C2×#14581786C22semidirect
27. C2×#14581785C22semidirect
28. C2×#14581785C22semidirect
29. C2×#14581784C22semidirect
30. C2×#14581782C22semidirect
31. C2×#14581782C22semidirect
32. C2×#14581778C22semidirect
34. C2×#14581776C22semidirect
35. C2×#14581776C22semidirect
36. C2×#14581776C22semidirect
38. C2×#14581775C22semidirect
39. C2×#14581774C22semidirect
42. C2×#14581773C22semidirect
43. C2×#14581773C22semidirect
44. C2×#14581773C22semidirect
45. C2×#14581771C22semidirect
46. C2×#14581771C22semidirect
47. C2×#14581770C22semidirect
48. C2×#14581769C22semidirect
49. C2×#14581769C22semidirect
53. #19128174C22semidirect
54. C2×C4×Dic166C22semidirect
55. C2×C4×C22⋊D83C22semidirect
56. C2×C4×C22⋊D83C22semidirect
58. C2×#14581751C22semidirect
59. C2×#14581749C22semidirect
60. C2×#14581748C22semidirect
61. C2×#14581748C22semidirect
62. C2×#14581748C22semidirect
63. C2×#14581748C22semidirect
64. C22×C4⋊Dic83C22semidirect
65. C22×Dic83⋊C4C22semidirect
66. C22×Dic83⋊C4C22semidirect
69. C22×C22⋊Dic83C22semidirect
70. C22×(C2×D83)⋊C4C22semidirect
71. C2×C22⋊C4×D83C22semidirect
72. C22×C4×Dic83C22semidirect
74. #518×C83C22semidirect
76. C2×C4×D4×C83C22semidirect
77. C2×#117×C83C22semidirect
80. C22×C22⋊C4×C83C22semidirect
98. #14581787C23semidirect
99. #14581786C23semidirect
100. #14581785C23semidirect
101. #14581785C23semidirect
102. #14581784C23semidirect
103. #14581782C23semidirect
104. #14581782C23semidirect
105. #14581778C23semidirect
107. #14581776C23semidirect
108. #14581776C23semidirect
110. #14581775C23semidirect
111. #14581774C23semidirect
114. #14581773C23semidirect
115. #14581773C23semidirect
116. #14581771C23semidirect
117. #14581771C23semidirect
118. #14581770C23semidirect
119. #14581769C23semidirect
120. #14581769C23semidirect
124. C4×Dic166C23semidirect
125. C4×C22⋊D83C23semidirect
126. C4×C22⋊D83C23semidirect
128. #14581751C23semidirect
129. #14581749C23semidirect
130. #14581748C23semidirect
131. #14581748C23semidirect
132. #14581748C23semidirect
136. C2×C4⋊Dic83C23semidirect
145. C2×Dic83⋊C4C23semidirect
146. C2×Dic83⋊C4C23semidirect
156. C2×C22⋊Dic83C23semidirect
161. C2×(C2×D83)⋊C4C23semidirect
162. C22⋊C4×D83C23semidirect
166. C2×C4×Dic83C23semidirect
178. C4×D4×C83C23semidirect
179. #117×C83C23semidirect
188. C2×C22⋊C4×C83C23semidirect
376. C2×C83#3491semidirect
392. C2×#518D83semidirect
394. C83C2×#3491semidirect
435. #518C2×D83semidirect
441. C2×C4×D4C2×D83semidirect
448. C2×#117C2×D83semidirect
459. C22×C22⋊C4C2×D83semidirect
519. C4×D4C22×D83semidirect
525. #117C22×D83semidirect
564. C2×C22⋊C4C22×D83semidirect
756. C2#24921156direct (N × H)

Maximal subgroups

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

subgroupindex
#249211562
C2×#191283912
C2×#191283842
C2×#191283802
C2×#191283772
C2×#191283272
C2×#191282932
C2×#191282602
C2×#191282312
C22×#145817762
C22×#145817732
C2×#191281742
C22×#145817482
C2×#518×C832
C2×#349183