Finite Group Databasebeta

← #35410570

Subgroups — #35410570

Order 21248.

1044 conjugacy classes of subgroups.

The subgroup lattice has 758 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#19127776C211yesmaximal, characteristic, complemented
2C2×#19127773C211yesmaximal, characteristic, complemented
3C2×#19127769C211yesmaximal, characteristic, complemented
4C2×#19127656C211yesmaximal, characteristic, complemented
5#24910705C211yesmaximal, characteristic
6#24908255C211yesmaximal, characteristic, complemented
7#24908180C211yesmaximal, characteristic, complemented
8#24908077C211yesmaximal, characteristic, complemented
9#24908073C211yesmaximal, characteristic, complemented
10#24907755C211yesmaximal, characteristic, complemented
11#24907445C211yesmaximal, characteristic, complemented
12#24907336C211yesmaximal, characteristic, complemented
13#24907245C211yesmaximal, characteristic, complemented
14#24907237C211yesmaximal, characteristic, complemented
15C83×#1869C211yesmaximal, characteristic, complemented
16C22×#13050574C2211yescharacteristic
17C22×#13050573C2211yescharacteristic
18C23×C83⋊C8C2211yescharacteristic
19C2×C4×C22⋊D83C2211yescharacteristic
20C2×C4×C22⋊D83C2211yescharacteristic
21C2×#14581751C2211yescharacteristic
22#19127776—24no—
23#19127773—24no—
24#19127769—24no—
25C2×C4⋊(C83⋊C8)C2211yescharacteristic
26C2×Dic83⋊C8C2211yescharacteristic
27C2×Dic83⋊C8C2211yescharacteristic
28C2×Dic83⋊C8C2211yescharacteristic
29C2×C22⋊(C83⋊C8)C2211yescharacteristic
30C2×C22⋊(C83⋊C8)C2211yescharacteristic
31C2×(C2×D83)⋊C8C2211yescharacteristic
32C2×(C2×D83)⋊C8C2211yescharacteristic
33C2×(C2×D83)⋊C8C2211yescharacteristic
34#19127656—24no—
35C2×#14581703C2211yescharacteristic
36C2×#14581702C2211yescharacteristic
37C2×#14581702C2211yescharacteristic
38C2×C8×Dic83C2211yescharacteristic
39C2×C8×Dic83C2211yescharacteristic
40C2×C8×Dic83C2211yescharacteristic
41#19127634C411yescharacteristic
42#19127629C411yescharacteristic
43#19127624C411yescharacteristic
44#19127623C411yescharacteristic
45#19127617C411yescharacteristic
46#19127616C411yescharacteristic
47#19127615C411yescharacteristic
48#19127609C411yescharacteristic
49C4×Dic83⋊C4C2211yescharacteristic
50C4×(C2×D83)⋊C4C2211yescharacteristic
51C4×C22⋊Dic83C2211yescharacteristic
52#19127455C2211yescharacteristic
53#19127455C2211yescharacteristic
54#19127455C2211yescharacteristic
55#19127455C2211yescharacteristic
56C23×C8×C83C2211yescharacteristic
57C2×C4×D4×C83C2211yescharacteristic
58C2×C22⋊C8×C83C2211yescharacteristic
59C2×C22⋊C8×C83C2211yescharacteristic
60C2×C22⋊C8×C83C2211yescharacteristic
61#336×C83C2211yescharacteristic
62#336×C83C2211yescharacteristic
63C22×C22⋊D83C2×C411yescharacteristic
64C22×C22⋊D83C2×C411yescharacteristic
65C22×C4×D83C2311yescharacteristic
66C2×#13050574—22no—
67C2×#13050574—22no—
68C2×#13050574D414yescomplemented
69C2×#13050573—22no—
70C2×#13050573—22no—
71C2×#13050573—22no—
72C22×C83⋊C8—22no—
73C22×C83⋊C8—22no—
74C22×C83⋊C8—22no—
75C22×C83⋊C8C2311yescharacteristic
76C22×C83⋊C8C2311yescharacteristic
77C22×C83⋊C8C2311yescharacteristic
78C22×C83⋊C8C2311yescharacteristic
79C4×C22⋊D83—22no—
80C4×C22⋊D83—22no—
81C4×C22⋊D83—22no—
82C4×C22⋊D83—22no—
83#14581751—22no—
84#14581751—22no—
85C2×C4⋊Dic83C2×C411yescharacteristic
86C2×C4⋊Dic83C2×C411yescharacteristic
87C2×Dic83⋊C4C2×C411yescharacteristic
88C2×Dic83⋊C4C2×C411yescharacteristic
89C2×Dic83⋊C4C2×C411yescharacteristic
90C2×Dic83⋊C4C2×C411yescharacteristic
91C2×C22⋊Dic83C2×C411yescharacteristic
92C2×C22⋊Dic83C2×C411yescharacteristic
93C2×C22⋊Dic83C2×C411yescharacteristic
94C2×C22⋊Dic83C2×C411yescharacteristic
95C2×C22⋊Dic83C2×C411yescharacteristic
96C2×C22⋊Dic83C2×C411yescharacteristic
97C2×(C2×D83)⋊C4C2×C411yescharacteristic
98C2×(C2×D83)⋊C4C2×C411yescharacteristic
99C2×(C2×D83)⋊C4C2×C411yescharacteristic
100C2×(C2×D83)⋊C4C2×C411yescharacteristic
101C2×C4×Dic83C2311yescharacteristic
102C2×C4×Dic83C2311yescharacteristic
103C2×C4×Dic83C2311yescharacteristic
104C4⋊(C83⋊C8)—22no—
105Dic83⋊C8—22no—
106Dic83⋊C8—22no—
107Dic83⋊C8—22no—
108C22⋊(C83⋊C8)—22no—
109C22⋊(C83⋊C8)—22no—
110(C2×D83)⋊C8—22no—
111(C2×D83)⋊C8—22no—
112(C2×D83)⋊C8—22no—
113#14581703—22no—
114#14581702—22no—
115#14581702D414yescomplemented
116C8×Dic83—22no—
117C8×Dic83—22no—
118C8×Dic83—22no—
119C83⋊#95C2×C411yescharacteristic
120C83⋊#95C2×C411yescharacteristic
121C83⋊#95C2×C411yescharacteristic
122C83⋊#95C2×C411yescharacteristic
123C83⋊#95C2×C411yescharacteristic
124C83⋊#95C2×C411yescharacteristic
125C22×D4×C83C2×C411yescharacteristic
126C23×C4×C83C2311yescharacteristic
127C23×C4×C83C2311yescharacteristic
128C22×C8×C83—22no—
129C22×C8×C83—22no—
130C22×C8×C83—22no—
131C22×C8×C83C2311yescharacteristic
132C22×C8×C83C2311yescharacteristic
133C22×C8×C83C2311yescharacteristic
134C22×C8×C83C2311yescharacteristic
135C4×D4×C83—22no—
136C4×D4×C83—22no—
137C2×C4⋊C4×C83C2×C411yescharacteristic
138C2×C22⋊C4×C83C2×C411yescharacteristic
139C2×C22⋊C4×C83C2×C411yescharacteristic
140C2×C42×C83C2311yescharacteristic
141C22⋊C8×C83—22no—
142C22⋊C8×C83—22no—
143C22⋊C8×C83—22no—
144C23×D83C22×C411yescharacteristic
145C2×C22⋊D83—22no—
146C2×C22⋊D83—22no—
147C2×C22⋊D83—22no—
148C2×C22⋊D83—22no—
149C2×C22⋊D83—41no—
150C2×C22⋊D83—41no—
151C22×Dic83C22×C411yescharacteristic
152C22×Dic83C22×C411yescharacteristic
153C22×Dic83C22×C411yescharacteristic
154C22×Dic83C22×C411yescharacteristic
155C22×Dic83C22×C411yescharacteristic
156C22×Dic83C22×C411yescharacteristic
157C22×Dic83C22×C411yescharacteristic
158C2×C4×D83—21no—
159C2×C4×D83—21no—
160C2×C4×D83—21no—
161C2×C4×D83—21no—
162C2×C4×D83—21no—
163C2×C4×D83—21no—
164#13050574—28no—
165#13050573—44no—
166C2×C83⋊C8—21no—
167C2×C83⋊C8—21no—
168C2×C83⋊C8—21no—
169C2×C83⋊C8—21no—
170C2×C83⋊C8—21no—
171C2×C83⋊C8—21no—
172C2×C83⋊C8—21no—
173C2×C83⋊C8—21no—
174C2×C83⋊C8—44no—
175C2×C83⋊C8C2×D412yes—
176C2×C83⋊C8C2×D412yes—
177C2×C83⋊C8C2×D412yes—
178C2×C83⋊C8#4112yes—
179C4⋊Dic83—22no—
180C4⋊Dic83—22no—
181Dic83⋊C4—22no—
182Dic83⋊C4—22no—
183Dic83⋊C4—22no—
184Dic83⋊C4—41no—
185C22⋊Dic83—22no—
186C22⋊Dic83—22no—
187C22⋊Dic83—22no—
188C22⋊Dic83—22no—
189C22⋊Dic83—22no—
190C22⋊Dic83—22no—
191(C2×D83)⋊C4—22no—
192(C2×D83)⋊C4—22no—
193(C2×D83)⋊C4—41no—
194(C2×D83)⋊C4—41no—
195C4×Dic83—21no—
196C4×Dic83—21no—
197C4×Dic83—21no—
198C4×Dic83—21no—
199C4×Dic83C2×D412yes—
200C4×Dic83#4112yes—
201C24×C83C22×C411yescharacteristic
202C24×C83C22×C411yescharacteristic
203C2×D4×C83—22no—
204C2×D4×C83—22no—
205C2×D4×C83—41no—
206C22×C4×C83—21no—
207C22×C4×C83—21no—
208C22×C4×C83—21no—
209C22×C4×C83—21no—
210C22×C4×C83—21no—
211C22×C4×C83—21no—
212C22×C4×C83—21no—
213C22×C4×C83—21no—
214C22×C4×C83—21no—
215C22×C4×C83—21no—
216C22×C4×C83C22×C411yescharacteristic
217C22×C4×C83C22×C411yescharacteristic
218C22×C4×C83C22×C411yescharacteristic
219C22×C4×C83C22×C411yescharacteristic
220C22×C4×C83C2×D412yes—
221C22×C4×C83#4112yes—
222C22×C4×C83C2411yescharacteristic
223C2×C8×C83—28no—
224C2×C8×C83—21no—
225C2×C8×C83—21no—
226C2×C8×C83—21no—
227C2×C8×C83—21no—
228C2×C8×C83—21no—
229C2×C8×C83—21no—
230C2×C8×C83—21no—
231C2×C8×C83—21no—
232C2×C8×C83—21no—
233C2×C8×C83—21no—
234C2×C8×C83C2×D412yes—
235C2×C8×C83#4112yes—
236C4⋊C4×C83—22no—
237C22⋊C4×C83—22no—
238C22⋊C4×C83—22no—
239C42×C83—21no—
240C42×C83—21no—
241C23×C83—21no—
242C23×C83—21no—
243C23×C83—21no—
244C23×C83—21no—
245C23×C83—21no—
246C23×C83—21no—
247C23×C83—21no—
248C23×C83—21no—
249C23×C83—21no—
250C23×C83—21no—
251C23×C83—21no—
252C23×C83—21no—
253C23×C83C4×D412yes—
254C23×C83#13112yes—
255C23×C83C23×C411yescharacteristic
256C22×D83—21no—
257C22×D83—21no—
258C22×D83—21no—
259C22×D83—21no—
260C22×D83—21no—
261C22×D83—21no—
262C22×D83—21no—
263D4×C83—44no—
264C2×C4×C83—21no—
265C2×C4×C83—21no—
266C2×C4×C83—22no—
267C2×C4×C83—22no—
268C2×C4×C83—22no—
269C2×C4×C83—22no—
270C2×C4×C83—21no—
271C2×C4×C83—21no—
272C2×C4×C83—21no—
273C2×C4×C83—21no—
274C2×C4×C83—21no—
275C2×C4×C83—21no—
276C2×C4×C83—21no—
277C2×C4×C83—21no—
278C2×C4×C83—21no—
279C2×C4×C83—41no—
280C2×C4×C83—41no—
281C2×C4×C83—41no—
282C2×C4×C83—41no—
283C2×C4×C83C4×D412yes—
284C2×C4×C83C22×D411yescharacteristic
285C2×C4×C83C22×D411yescharacteristic
286C2×C4×C83C2×#4111yescharacteristic
287C2×C4×C83C2×#4111yescharacteristic
288C2×C4×C83C2×#4111yescharacteristic
289C2×C4×C83C2×#4111yescharacteristic
290C22⋊D83—44no—
291C22⋊D83—44no—
292C2×Dic83—21no—
293C2×Dic83—21no—
294C2×Dic83—21no—
295C2×Dic83—21no—
296C2×Dic83—21no—
297C2×Dic83—21no—
298C2×Dic83—21no—
299C2×Dic83—21no—
300C2×Dic83—21no—
301C2×Dic83—21no—
302C2×Dic83—21no—
303C2×Dic83—21no—
304C2×Dic83—21no—
305C2×Dic83—21no—
306C2×Dic83—21no—
307C2×Dic83—21no—
308C2×Dic83—21no—
309C2×Dic83—21no—
310C2×Dic83C4×D412yes—
311C2×Dic83C4×D412yes—
312C2×Dic83#13112yes—
313C4×D83—41no—
314C4×D83—41no—
315C4×D83—41no—
316C4×D83—41no—
317C8×C83—22no—
318C8×C83—22no—
319C8×C83—41no—
320C8×C83—41no—
321C83⋊C8—22no—
322C83⋊C8—41no—
323C83⋊C8—41no—
324C83⋊C8#12114yes—
325C22×C83—22no—
326C22×C83—22no—
327C22×C83—22no—
328C22×C83—22no—
329C22×C83—22no—
330C22×C83—22no—
331C22×C83—41no—
332C22×C83—41no—
333C22×C83—41no—
334C22×C83—41no—
335C22×C83—41no—
336C22×C83—41no—
337C22×C83—41no—
338C22×C83—41no—
339C22×C83C2×C4×D411yescharacteristic
340C22×C83C2×C4×D411yescharacteristic
341C22×C83C4×#4111yescharacteristic
342C22×C83C2×#13111yescharacteristic
343C22×C83C2×#13111yescharacteristic
344C22×C83#56811yescharacteristic
345C22×C83#56811yescharacteristic
346C2×D83—41no—
347C2×D83—41no—
348C2×D83—41no—
349C2×D83—41no—
350C2×D83—41no—
351C2×D83—41no—
352C2×D83—41no—
353C4×C83—22no—
354C4×C83—41no—
355C4×C83—41no—
356C4×C83—41no—
357C4×C83C2×#12111yescharacteristic
358C4×C83#52511yescharacteristic
359C4×C83#52911yescharacteristic
360C4×C83#53211yescharacteristic
361Dic83—22no—
362Dic83—22no—
363Dic83—22no—
364Dic83—41no—
365Dic83—41no—
366Dic83—41no—
367Dic83—41no—
368#21496—831nomaximal, Sylow
369C2×C83—42no—
370C2×C83—42no—
371C2×C83C4×#12111yescharacteristic
372C2×C83#293311yescharacteristic
373C2×C83#293311yescharacteristic
374C2×C83#293311yescharacteristic
375C2×C83#293511yescharacteristic
376C2×C83#296611yescharacteristic
377C2×C83#296711yescharacteristic
378D83—81no—
379C2×#436—831no—
380C2×#435—831no—
381C2×#435—831no—
382C2×#405—831no—
383#2392—831no—
384#1954—831no—
385#1939—831no—
386#1924—831no—
387#1924—831no—
388#1869—831no—
389#1869D8311yescharacteristic, complemented
390#1798—831no—
391#1771—831no—
392#1753—831no—
393C8×C22⋊C4—831no—
394C83#2149611yescharacteristic, complemented, Sylow
395C22×M16—831no—
396C22×M16—831no—
397C23×C8—831no—
398C23×C8C2×D8311yescharacteristic
399C2×C4×D4—831no—
400C2×C4×D4—831no—
401C2×C4×D4C2×D8311yescharacteristic
402C2×#117—831no—
403#436—1664no—
404#435—1664no—
405#435—1664no—
406C2×C4⋊C8—831no—
407C2×C4⋊C8—831no—
408C2×C4⋊C8—831no—
409C2×C4⋊C8—831no—
410C2×C22⋊C8—831no—
411C2×C22⋊C8—831no—
412C2×C22⋊C8—831no—
413C2×C22⋊C8—831no—
414C2×C22⋊C8—831no—
415C2×C22⋊C8C2×D8311yescharacteristic
416C2×C22⋊C8C2×D8311yescharacteristic
417C2×C22⋊C8C2×D8311yescharacteristic
418#405—1664no—
419C2×#97—831no—
420C2×#97—831no—
421C2×#97—831no—
422C2×C4×C8—831no—
423C2×C4×C8—831no—
424C2×C4×C8—831no—
425#398—831no—
426#397—831no—
427#396—831no—
428#396—831no—
429#394—831no—
430#394—831no—
431#394—831no—
432#392—831no—
433C4×C4⋊C4—831no—
434C4×C22⋊C4—831no—
435C4×C22⋊C4—831no—
436#336—831no—
437#336—831no—
438#336—831no—
439#336—831no—
440#336C2×D8311yescharacteristic
441#336C2×D8311yescharacteristic
442C22×D4—831no—
443C22×D4—831no—
444C22×D4C4×D8311yescharacteristic
445C23×C4—831no—
446C23×C4C22×D8311yescharacteristic
447C23×C4C22×D8311yescharacteristic
448C2×M16—834no—
449C2×M16—1662no—
450C2×M16—1662no—
451C2×M16—1662no—
452C2×M16—1662no—
453C2×M16—1662no—
454C22×C8—22no—
455C22×C8—22no—
456C22×C8—22no—
457C22×C8—831no—
458C22×C8—831no—
459C22×C8—831no—
460C22×C8—831no—
461C22×C8—1662no—
462C22×C8—1662no—
463C22×C8—1662no—
464C22×C8C22×D8311yescharacteristic
465C22×C8C22×D8311yescharacteristic
466C22×C8C22×D8311yescharacteristic
467C22×C8C22×D8311yescharacteristic
468C4×D4—22no—
469C4×D4—22no—
470C4×D4—1662no—
471C4×D4—1662no—
472C4×D4—1662no—
473C4×D4—1662no—
474#117—1662no—
475#117—1662no—
476C2×C4⋊C4—831no—
477C2×C4⋊C4—831no—
478C2×C4⋊C4—831no—
479C2×C4⋊C4—831no—
480C2×C4⋊C4—831no—
481C2×C4⋊C4—831no—
482C2×C4⋊C4C4×D8311yescharacteristic
483C2×C22⋊C4—831no—
484C2×C22⋊C4—831no—
485C2×C22⋊C4—831no—
486C2×C22⋊C4—831no—
487C2×C22⋊C4—831no—
488C2×C22⋊C4—831no—
489C2×C22⋊C4—831no—
490C2×C22⋊C4—831no—
491C2×C22⋊C4—831no—
492C2×C22⋊C4—831no—
493C2×C22⋊C4C4×D8311yescharacteristic
494C2×C22⋊C4C4×D8311yescharacteristic
495C2×C42—831no—
496C2×C42—831no—
497C2×C42—831no—
498C2×C42C22×D8311yescharacteristic
499C4⋊C8—1662no—
500C4⋊C8—1662no—
501C4⋊C8—1662no—
502C4⋊C8—1662no—
503C22⋊C8—22no—
504C22⋊C8—22no—
505C22⋊C8—22no—
506C22⋊C8—1662no—
507C22⋊C8—1662no—
508C22⋊C8—1662no—
509C22⋊C8—1662no—
510C22⋊C8—1662no—
511#97—834no—
512#97—1662no—
513#97—1662no—
514C4×C8—1662no—
515C4×C8—1662no—
516C4×C8—1662no—
517#95—831no—
518#95—831no—
519#95—831no—
520#95—831no—
521#95—831no—
522#95—831no—
523C24—831no—
524C24C2×C4×D8311yescharacteristic
525C24C2×C4×D8311yescharacteristic
526C2×D4—22no—
527C2×D4—22no—
528C2×D4—41no—
529C2×D4—3321no—
530C2×D4—3321no—
531C2×D4—1662no—
532C2×D4—1662no—
533C2×D4—1662no—
534C2×D4—1662no—
535C22×C4—21no—
536C22×C4—21no—
537C22×C4—21no—
538C22×C4—21no—
539C22×C4—21no—
540C22×C4—21no—
541C22×C4—21no—
542C22×C4—21no—
543C22×C4—21no—
544C22×C4—21no—
545C22×C4—831no—
546C22×C4—831no—
547C22×C4—831no—
548C22×C4—831no—
549C22×C4—831no—
550C22×C4—831no—
551C22×C4—831no—
552C22×C4—1661no—
553C22×C4—1661no—
554C22×C4—1661no—
555C22×C4—1661no—
556C22×C4—1661no—
557C22×C4—1661no—
558C22×C4C2×C4×D8311yescharacteristic
559C22×C4C2×C4×D8311yescharacteristic
560C22×C4C2×C4×D8311yescharacteristic
561C22×C4C2×C4×D8311yescharacteristic
562C22×C4D4×D8312yes—
563C22×C4#1305058912yes—
564C22×C4C23×D8311yescharacteristic
565M16—3324no—
566M16—1668no—
567C2×C8—28no—
568C2×C8—21no—
569C2×C8—21no—
570C2×C8—21no—
571C2×C8—21no—
572C2×C8—21no—
573C2×C8—21no—
574C2×C8—21no—
575C2×C8—21no—
576C2×C8—21no—
577C2×C8—21no—
578C2×C8—3324no—
579C2×C8—832no—
580C2×C8—832no—
581C2×C8—832no—
582C2×C8—832no—
583C2×C8—1661no—
584C2×C8—1661no—
585C2×C8—1661no—
586C2×C8—1661no—
587C2×C8—1661no—
588C2×C8—1661no—
589C2×C8—1661no—
590C2×C8—1661no—
591C2×C8D4×D8312yes—
592C2×C8#1305058912yes—
593C4⋊C4—22no—
594C4⋊C4—3321no—
595C4⋊C4—1662no—
596C4⋊C4—1662no—
597C4⋊C4—1662no—
598C4⋊C4—1662no—
599C4⋊C4—1662no—
600C22⋊C4—22no—
601C22⋊C4—22no—
602C22⋊C4—3321no—
603C22⋊C4—3321no—
604C22⋊C4—1662no—
605C22⋊C4—1662no—
606C22⋊C4—1662no—
607C22⋊C4—1662no—
608C22⋊C4—1662no—
609C22⋊C4—1662no—
610C22⋊C4—1662no—
611C22⋊C4—1662no—
612C42—21no—
613C42—21no—
614C42—832no—
615C42—832no—
616C42—1661no—
617C42—1661no—
618C42—1661no—
619C42—1661no—
620C23—21no—
621C23—21no—
622C23—21no—
623C23—21no—
624C23—21no—
625C23—21no—
626C23—21no—
627C23—21no—
628C23—21no—
629C23—21no—
630C23—21no—
631C23—21no—
632C23—1661no—
633C23—1661no—
634C23—1661no—
635C23—1661no—
636C23—1661no—
637C23—1661no—
638C23—1661no—
639C23(C22⋊D83)⋊C412yes—
640C23#1458179812yes—
641C23C22×C4×D8311yescharacteristic
642D4—44no—
643D4—3324no—
644D4—3324no—
645C2×C4—21no—
646C2×C4—21no—
647C2×C4—22no—
648C2×C4—22no—
649C2×C4—22no—
650C2×C4—22no—
651C2×C4—21no—
652C2×C4—21no—
653C2×C4—21no—
654C2×C4—21no—
655C2×C4—21no—
656C2×C4—21no—
657C2×C4—21no—
658C2×C4—21no—
659C2×C4—21no—
660C2×C4—41no—
661C2×C4—41no—
662C2×C4—41no—
663C2×C4—41no—
664C2×C4—3321no—
665C2×C4—3321no—
666C2×C4—3321no—
667C2×C4—3321no—
668C2×C4—832no—
669C2×C4—832no—
670C2×C4—832no—
671C2×C4—1661no—
672C2×C4—1661no—
673C2×C4—1661no—
674C2×C4—1661no—
675C2×C4—1661no—
676C2×C4—1661no—
677C2×C4—1661no—
678C2×C4—1661no—
679C2×C4—1661no—
680C2×C4—1661no—
681C2×C4—1661no—
682C2×C4—1661no—
683C2×C4—1661no—
684C2×C4—1661no—
685C2×C4—1661no—
686C2×C4—1661no—
687C2×C4—1661no—
688C2×C4—1661no—
689C2×C4(C22⋊D83)⋊C412yes—
690C2×C4C2×D4×D8311yescharacteristic
691C2×C4C2×D4×D8311yescharacteristic
692C2×C4#41×D8311yescharacteristic
693C2×C4#41×D8311yescharacteristic
694C2×C4C2×#1305058911yescharacteristic
695C2×C4C2×#1305058911yescharacteristic
696C8—22no—
697C8—22no—
698C8—41no—
699C8—41no—
700C8—3321no—
701C8—3321no—
702C8—834no—
703C8—1662no—
704C22—22no—
705C22—22no—
706C22—22no—
707C22—22no—
708C22—22no—
709C22—22no—
710C22—41no—
711C22—41no—
712C22—41no—
713C22—41no—
714C22—41no—
715C22—41no—
716C22—41no—
717C22—41no—
718C22—3321no—
719C22—3321no—
720C22—3321no—
721C22—3321no—
722C22—3321no—
723C22—3321no—
724C22—3321no—
725C22C4×D4×D8311yescharacteristic
726C22C2×(C22⋊D83)⋊C411yescharacteristic
727C22C4×#1305058911yescharacteristic
728C22#131×D8311yescharacteristic
729C22C2×#1458179811yescharacteristic
730C22#1912846611yescharacteristic
731C22#1912846711yescharacteristic
732C4—22no—
733C4—41no—
734C4—41no—
735C4—41no—
736C4—3321no—
737C4—3321no—
738C4—3321no—
739C4—3321no—
740C4—1662no—
741C4—1662no—
742C4—1662no—
743C4#121×D8311yescharacteristic
744C4#1912820711yescharacteristic
745C4#1912822811yescharacteristic
746C4#1912824611yescharacteristic
747C2—42no—
748C2—42no—
749C2—6641no—
750C2#2490997311yescharacteristic
751C2#2491618311yescharacteristic
752C2#2491618411yescharacteristic
753C2#2491619311yescharacteristic
754C2#2491620411yescharacteristic
755C2#2491643111yescharacteristic
756C2#2491644511yescharacteristic
subgroupG/H
center, FrattiniC22×C4C23×D83
commutator, socleC23×C83C23×C4
FittingC83×#1869C2
prime radical#19127609C4
cosocleC22×C4×C83C24
hypercenter#1869D83
hypocenterC83#21496
LCSG ▷ C23×C83 ▷ C83
UCSC1 ◁ C22×C4 ◁ #1869

Complements

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

NH ≅ G/Ntype
1. C2×#19127776C2semidirect
2. C2×#19127773C2semidirect
3. C2×#19127769C2semidirect
4. C2×#19127656C2semidirect
6. #24908255C2semidirect
7. #24908180C2semidirect
8. #24908077C2semidirect
9. #24908073C2semidirect
10. #24907755C2semidirect
11. #24907445C2semidirect
12. #24907336C2semidirect
13. #24907245C2semidirect
14. #24907237C2semidirect
15. C83×#1869C2semidirect
68. C2×#13050574D4semidirect
115. #14581702D4semidirect
389. #1869D83semidirect
394. C83#21496semidirect

Maximal subgroups

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

subgroupindex
C2×#191277762
C2×#191277732
C2×#191277692
C2×#191276562
#249107052
#249082552
#249081802
#249080772
#249080732
#249077552
#249074452
#249073362
#249072452
#249072372
C83×#18692
#2149683