Finite Group Databasebeta

← #35328220

Subgroups — #35328220

Order 21248.

1838 conjugacy classes of subgroups.

The subgroup lattice has 704 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#19127608C212yesmaximal
2C2×#19127600C211yesmaximal, characteristic
3C2×C4⋊C4×Dic83C211yesmaximal, characteristic
4#24905734C212yesmaximal
5#24905716C212yesmaximal
6#24905695C212yesmaximal
7#24905693C211yesmaximal, characteristic
8#24905692C211yesmaximal, characteristic
9#24905692C211yesmaximal, characteristic
10C4×C83⋊#95C211yesmaximal, characteristic
11C22×C4⋊Q8×C83C211yesmaximal, characteristic
12C22×C4⋊Dic83C2211yescharacteristic
13C22×C4⋊Dic83C2212yes—
14C22×C4⋊Dic83C2211yescharacteristic
15C22×C4×Dic83C2211yescharacteristic
16C22×C4×Dic83C2212yes—
17C22×C4×Dic83C2211yescharacteristic
18#19127608—28no—
19#19127600—24no—
20C4⋊C4×Dic83—24no—
21C2×C83⋊#95C2211yescharacteristic
22C2×C83⋊#95C2212yes—
23C2×C83⋊#95C2212yes—
24C2×C83⋊#95C2212yes—
25C2×C83⋊#95C2212yes—
26C2×C83⋊#95C2212yes—
27C2×C83⋊#95C2211yescharacteristic
28C2×C83⋊#95C2212yes—
29C2×C83⋊#95C2212yes—
30C2×C83⋊#95C2212yes—
31C2×C83⋊#95C2211yescharacteristic
32C2×C83⋊#95C2211yescharacteristic
33C23×Q8×C83C2212yes—
34C2×C4⋊Q8×C83—24no—
35C2×C4⋊Q8×C83—24no—
36C2×C4⋊Q8×C83C418yescomplemented
37C22×C4⋊C4×C83C2211yescharacteristic
38C22×C4⋊C4×C83C2212yes—
39C22×C4⋊C4×C83C2211yescharacteristic
40C22×C42×C83C2211yescharacteristic
41C23×Dic83C2312yes—
42C23×Dic83C2311yescharacteristic
43C23×Dic83C2312yes—
44C23×Dic83C2311yescharacteristic
45C23×Dic83C2311yescharacteristic
46C23×Dic83C2311yescharacteristic
47C2×C4⋊Dic83—24no—
48C2×C4⋊Dic83—22no—
49C2×C4⋊Dic83—24no—
50C2×C4⋊Dic83—22no—
51C2×C4⋊Dic83—22no—
52C2×C4⋊Dic83—22no—
53C2×C4⋊Dic83—22no—
54C2×C4⋊Dic83—42no—
55C2×C4⋊Dic83Q814yescomplemented
56C2×C4×Dic83—24no—
57C2×C4×Dic83—22no—
58C2×C4×Dic83—24no—
59C2×C4×Dic83—22no—
60C2×C4×Dic83—22no—
61C2×C4×Dic83—22no—
62C2×C4×Dic83—22no—
63C2×C4×Dic83—42no—
64C2×C4×Dic83Q814yescomplemented
65C83⋊#95—24no—
66C83⋊#95—24no—
67C83⋊#95—24no—
68C83⋊#95—24no—
69C83⋊#95—24no—
70C83⋊#95—22no—
71C83⋊#95—22no—
72C83⋊#95—24no—
73C83⋊#95—42no—
74C83⋊#95—42no—
75C83⋊#95D414yes—
76C83⋊#95Q814yescomplemented
77C22×Q8×C83—24no—
78C22×Q8×C83—24no—
79C22×Q8×C83—24no—
80C22×Q8×C83—24no—
81C22×Q8×C83—42no—
82C22×Q8×C83—42no—
83C22×Q8×C83C2×C418yes—
84C23×C4×C83C2312yes—
85C23×C4×C83C2312yes—
86C23×C4×C83C2311yescharacteristic
87C23×C4×C83C2311yescharacteristic
88C23×C4×C83C2311yescharacteristic
89C4⋊Q8×C83—232no—
90C2×C4⋊C4×C83—24no—
91C2×C4⋊C4×C83—24no—
92C2×C4⋊C4×C83—22no—
93C2×C4⋊C4×C83—22no—
94C2×C4⋊C4×C83C2×C414yes—
95C2×C4⋊C4×C83C2×C418yes—
96C2×C4⋊C4×C83C2×C414yes—
97C2×C4⋊C4×C83D414yes—
98C2×C4⋊C4×C83D414yes—
99C2×C42×C83—22no—
100C2×C42×C83—22no—
101C2×C42×C83C2×C414yes—
102C22×Dic83—21no—
103C22×Dic83—21no—
104C22×Dic83—21no—
105C22×Dic83—21no—
106C22×Dic83—22no—
107C22×Dic83—21no—
108C22×Dic83—21no—
109C22×Dic83—22no—
110C22×Dic83—21no—
111C22×Dic83—21no—
112C22×Dic83—21no—
113C22×Dic83—21no—
114C22×Dic83—21no—
115C22×Dic83—22no—
116C22×Dic83—21no—
117C22×Dic83—21no—
118C22×Dic83—21no—
119C22×Dic83—21no—
120C22×Dic83—21no—
121C22×Dic83—22no—
122C22×Dic83—21no—
123C22×Dic83—21no—
124C22×Dic83—22no—
125C22×Dic83—21no—
126C22×Dic83—21no—
127C22×Dic83—21no—
128C22×Dic83—22no—
129C22×Dic83—21no—
130C22×Dic83—22no—
131C22×Dic83—22no—
132C22×Dic83—22no—
133C22×Dic83—22no—
134C22×Dic83—22no—
135C22×Dic83—22no—
136C22×Dic83—22no—
137C22×Dic83C2×D412yes—
138C22×Dic83C2×D412yes—
139C22×Dic83C2×Q812yes—
140C22×Dic83C2×Q812yes—
141C22×Dic83C2×Q814yes—
142C22×Dic83C2×Q812yes—
143C22×Dic83C2×Q812yes—
144C4⋊Dic83—28no—
145C4⋊Dic83—48no—
146C4⋊Dic83—44no—
147C4×Dic83—28no—
148C4×Dic83—48no—
149C4×Dic83—44no—
150C24×C83C2411yescharacteristic
151C2×Q8×C83—216no—
152C2×Q8×C83—216no—
153C2×Q8×C83—48no—
154C2×Q8×C83—48no—
155C2×Q8×C83—48no—
156C2×Q8×C83—48no—
157C2×Q8×C83—48no—
158C22×C4×C83—21no—
159C22×C4×C83—21no—
160C22×C4×C83—21no—
161C22×C4×C83—21no—
162C22×C4×C83—22no—
163C22×C4×C83—22no—
164C22×C4×C83—21no—
165C22×C4×C83—21no—
166C22×C4×C83—22no—
167C22×C4×C83—22no—
168C22×C4×C83—21no—
169C22×C4×C83—21no—
170C22×C4×C83—22no—
171C22×C4×C83—22no—
172C22×C4×C83—22no—
173C22×C4×C83—22no—
174C22×C4×C83—22no—
175C22×C4×C83—22no—
176C22×C4×C83C22×C414yes—
177C22×C4×C83C22×C414yes—
178C22×C4×C83C22×C412yes—
179C22×C4×C83C22×C412yes—
180C22×C4×C83C22×C412yes—
181C22×C4×C83C2×D412yes—
182C22×C4×C83C2×D414yes—
183C22×C4×C83C2×D414yes—
184C22×C4×C83C2×D412yes—
185C22×C4×C83C2×D412yes—
186C22×C4×C83C2×Q812yes—
187C22×C4×C83C2×Q812yes—
188C22×C4×C83C2×Q812yes—
189C22×C4×C83#4112yes—
190C22×C4×C83#4112yes—
191C22×C4×C83#4112yes—
192C22×C4×C83#4112yes—
193C4⋊C4×C83—216no—
194C4⋊C4×C83—28no—
195C4⋊C4×C83C22⋊C4116yes—
196C42×C83—28no—
197C23×C83C23×C411yescharacteristic
198C23×C83C22×D411yescharacteristic
199C23×C83C22×D411yescharacteristic
200C23×C83C22×D411yescharacteristic
201C23×C83C22×Q811yescharacteristic
202C23×C83C22×Q811yescharacteristic
203C23×C83C22×Q811yescharacteristic
204C23×C83C2×#4111yescharacteristic
205C23×C83C2×#4111yescharacteristic
206C23×C83C2×#4111yescharacteristic
207C23×C83C2×#4111yescharacteristic
208C23×C83H(5,𝔽2)11yescharacteristic
209C23×C83H(5,𝔽2)11yescharacteristic
210C23×C832−1+411yescharacteristic
211C23×C832−1+411yescharacteristic
212Q8×C83—432no—
213C2×C4×C83—22no—
214C2×C4×C83—22no—
215C2×C4×C83—24no—
216C2×C4×C83—24no—
217C2×C4×C83—22no—
218C2×C4×C83—22no—
219C2×C4×C83—22no—
220C2×C4×C83—22no—
221C2×C4×C83—24no—
222C2×C4×C83—24no—
223C2×C4×C83—24no—
224C2×C4×C83—24no—
225C2×C4×C83—22no—
226C2×C4×C83—22no—
227C2×C4×C83—22no—
228C2×C4×C83—22no—
229C2×C4×C83—22no—
230C2×C4×C83—22no—
231C2×C4×C83—24no—
232C2×C4×C83—24no—
233C2×C4×C83—24no—
234C2×C4×C83—42no—
235C2×C4×C83—42no—
236C2×C4×C83—42no—
237C2×C4×C83—42no—
238C2×C4×C83C2×C22⋊C418yes—
239C2×C4×C83C2×C22⋊C414yes—
240C2×C4×C83C4×D414yes—
241C2×C4×C83C4×Q814yes—
242C2×C4×C83C4×Q814yes—
243C2×C4×C83C4×Q814yes—
244C2×C4×C83C22⋊Q814yes—
245C2×C4×C83C22⋊Q814yes—
246C2×C4×C83#12414yes—
247C2×C4×C83C4⋊Q814yes—
248C2×Dic83—22no—
249C2×Dic83—22no—
250C2×Dic83—22no—
251C2×Dic83—22no—
252C2×Dic83—22no—
253C2×Dic83—22no—
254C2×Dic83—22no—
255C2×Dic83—24no—
256C2×Dic83—22no—
257C2×Dic83—22no—
258C2×Dic83—22no—
259C2×Dic83—22no—
260C2×Dic83—22no—
261C2×Dic83—22no—
262C2×Dic83—22no—
263C2×Dic83—24no—
264C2×Dic83—24no—
265C2×Dic83—22no—
266C2×Dic83—41no—
267C2×Dic83—41no—
268C2×Dic83—42no—
269C2×Dic83—42no—
270C2×Dic83—41no—
271C2×Dic83—41no—
272C2×Dic83—42no—
273C2×Dic83—41no—
274C2×Dic83—41no—
275C2×Dic83—41no—
276C2×Dic83—42no—
277C2×Dic83—41no—
278C2×Dic83—41no—
279C2×Dic83—41no—
280C2×Dic83—41no—
281C2×Dic83—41no—
282C2×Dic83—42no—
283C2×Dic83—42no—
284C2×Dic83—42no—
285C2×Dic83—42no—
286C2×Dic83—42no—
287C2×Dic83—42no—
288C2×Dic83—42no—
289C2×Dic83C4⋊Q814yescomplemented
290C22×C83C22×C22⋊C411yescharacteristic
291C22×C83C2×C4×D411yescharacteristic
292C22×C83C2×C4×Q811yescharacteristic
293C22×C83C2×C4×Q811yescharacteristic
294C22×C83C2×C4×Q811yescharacteristic
295C22×C83#51811yescharacteristic
296C22×C83#51911yescharacteristic
297C22×C83C2×C22⋊Q811yescharacteristic
298C22×C83C2×C22⋊Q811yescharacteristic
299C22×C83C2×#12411yescharacteristic
300C22×C83C2×C4⋊Q811yescharacteristic
301C22×C83C2×C4⋊Q811yescharacteristic
302C22×C83#53211yescharacteristic
303C22×C83#53311yescharacteristic
304C22×C83#53311yescharacteristic
305C22×C83#54211yescharacteristic
306C22×C83#54211yescharacteristic
307C22×C83#54411yescharacteristic
308C22×C83#54411yescharacteristic
309C22×C83D4211yescharacteristic
310C22×C83D4211yescharacteristic
311C22×C83#54611yescharacteristic
312C22×C83#54611yescharacteristic
313C22×C83#54711yescharacteristic
314C22×C83#54811yescharacteristic
315C22×C83#54811yescharacteristic
316C22×C83D4×Q811yescharacteristic
317C22×C83D4×Q811yescharacteristic
318C22×C83D4×Q811yescharacteristic
319C22×C83#55411yescharacteristic
320C22×C83#55411yescharacteristic
321C22×C83#55511yescharacteristic
322C22×C83#55611yescharacteristic
323C22×C83#55711yescharacteristic
324C22×C83Q8211yescharacteristic
325C4×C83—28no—
326C4×C83—24no—
327C4×C83—24no—
328C4×C83—44no—
329C4×C83#39118yescomplemented
330Dic83—24no—
331Dic83—42no—
332Dic83—44no—
333Dic83—42no—
334Dic83—42no—
335Dic83—82no—
336#14053—831nomaximal, Sylow
337C2×C83C2×#39111yescharacteristic
338C2×C83C4×C4⋊Q811yescharacteristic
339C2×C83#233111yescharacteristic
340C2×C83D4×C22⋊C411yescharacteristic
341C2×C83Q8×C22⋊C411yescharacteristic
342C2×C83#236511yescharacteristic
343C2×C83#236911yescharacteristic
344C2×C83#243911yescharacteristic
345C2×C83#244011yescharacteristic
346C2×C83#245111yescharacteristic
347C2×C83#245211yescharacteristic
348C2×C83#249111yescharacteristic
349C2×C83#249211yescharacteristic
350C2×C83#255011yescharacteristic
351C2×C83#255111yescharacteristic
352C22×C4⋊Q8D8311yescharacteristic
353C2×#391—832no—
354C2×#389—831no—
355C2×C4×C4⋊C4—831no—
356#1446—832no—
357#1441—832no—
358#1436—832no—
359C4⋊#95—831no—
360C4⋊#95—831no—
361C4⋊#95—831no—
362C4×#95—831no—
363C83#1405311yescharacteristic, complemented, Sylow
364C23×Q8C2×D8312yes—
365C2×C4⋊Q8—24no—
366C2×C4⋊Q8—24no—
367C2×C4⋊Q8Dic8318yescomplemented
368C22×C4⋊C4—832no—
369C22×C4⋊C4—831no—
370C22×C4⋊C4—831no—
371C22×C4⋊C4C2×D8311yescharacteristic
372C22×C4⋊C4C2×D8312yes—
373C22×C4⋊C4C2×D8311yescharacteristic
374C22×C42—832no—
375C22×C42—831no—
376C22×C42—831no—
377C22×C42C2×D8311yescharacteristic
378#391—1668no—
379#389—1664no—
380C4×C4⋊C4—1664no—
381C2×#95—832no—
382C2×#95—832no—
383C2×#95—831no—
384C2×#95—831no—
385C2×#95—831no—
386C2×#95—831no—
387C2×#95—832no—
388C2×#95—832no—
389C2×#95—832no—
390C2×#95—832no—
391C2×#95—832no—
392C2×#95—832no—
393C22×Q8—24no—
394C22×Q8—24no—
395C22×Q8—24no—
396C22×Q8—24no—
397C22×Q8—42no—
398C22×Q8—42no—
399C22×Q8C2×Dic8318yes—
400C23×C4—831no—
401C23×C4—831no—
402C23×C4—832no—
403C23×C4—831no—
404C23×C4—831no—
405C23×C4—832no—
406C23×C4C22×D8312yes—
407C23×C4C22×D8311yescharacteristic
408C23×C4C22×D8312yes—
409C23×C4C22×D8311yescharacteristic
410C23×C4C22×D8311yescharacteristic
411C4⋊Q8—232no—
412C2×C4⋊C4—24no—
413C2×C4⋊C4—24no—
414C2×C4⋊C4—22no—
415C2×C4⋊C4—22no—
416C2×C4⋊C4—3322no—
417C2×C4⋊C4—834no—
418C2×C4⋊C4—1664no—
419C2×C4⋊C4—1664no—
420C2×C4⋊C4—1662no—
421C2×C4⋊C4—1662no—
422C2×C4⋊C4—1662no—
423C2×C4⋊C4—1662no—
424C2×C4⋊C4—1662no—
425C2×C4⋊C4C2×Dic8314yes—
426C2×C4⋊C4C2×Dic8318yes—
427C2×C4⋊C4C2×Dic8314yes—
428C2×C4⋊C4C22⋊D8314yes—
429C2×C4⋊C4C22⋊D8314yes—
430C2×C42—22no—
431C2×C42—22no—
432C2×C42—3322no—
433C2×C42—834no—
434C2×C42—1664no—
435C2×C42—1664no—
436C2×C42—1662no—
437C2×C42—1662no—
438C2×C42—1662no—
439C2×C42—1662no—
440C2×C42—1662no—
441C2×C42C2×Dic8314yes—
442#95—3322no—
443#95—3322no—
444#95—834no—
445#95—834no—
446#95—1664no—
447#95—1664no—
448#95—1664no—
449#95—1664no—
450#95—1664no—
451#95—1662no—
452#95—1664no—
453#95—1662no—
454C24C23×D8311yescharacteristic
455C2×Q8—216no—
456C2×Q8—216no—
457C2×Q8—48no—
458C2×Q8—48no—
459C2×Q8—48no—
460C2×Q8—48no—
461C2×Q8—48no—
462C22×C4—22no—
463C22×C4—21no—
464C22×C4—21no—
465C22×C4—21no—
466C22×C4—21no—
467C22×C4—22no—
468C22×C4—22no—
469C22×C4—22no—
470C22×C4—21no—
471C22×C4—21no—
472C22×C4—21no—
473C22×C4—21no—
474C22×C4—22no—
475C22×C4—22no—
476C22×C4—22no—
477C22×C4—22no—
478C22×C4—22no—
479C22×C4—22no—
480C22×C4—832no—
481C22×C4—832no—
482C22×C4—832no—
483C22×C4—832no—
484C22×C4—832no—
485C22×C4—832no—
486C22×C4—834no—
487C22×C4—1662no—
488C22×C4—1662no—
489C22×C4—1662no—
490C22×C4—1662no—
491C22×C4—1662no—
492C22×C4—1662no—
493C22×C4—1662no—
494C22×C4—1662no—
495C22×C4—1661no—
496C22×C4—1661no—
497C22×C4—1662no—
498C22×C4—1661no—
499C22×C4—1661no—
500C22×C4—1661no—
501C22×C4—1661no—
502C22×C4—1661no—
503C22×C4—1662no—
504C22×C4—1661no—
505C22×C4—1661no—
506C22×C4—1661no—
507C22×C4—1661no—
508C22×C4—1661no—
509C22×C4—1662no—
510C22×C4—1661no—
511C22×C4—1661no—
512C22×C4—1662no—
513C22×C4—1661no—
514C22×C4—1661no—
515C22×C4—1662no—
516C22×C4—1661no—
517C22×C4—1661no—
518C22×C4—1661no—
519C22×C4—1661no—
520C22×C4—1661no—
521C22×C4—1661no—
522C22×C4C22×Dic8314yes—
523C22×C4C22×Dic8314yes—
524C22×C4C22×Dic8312yes—
525C22×C4C22×Dic8312yes—
526C22×C4C22×Dic8312yes—
527C22×C4D4×D8312yes—
528C22×C4C2×C22⋊D8314yes—
529C22×C4C2×C22⋊D8314yes—
530C22×C4C2×C22⋊D8312yes—
531C22×C4C2×C22⋊D8312yes—
532C22×C4Q8×D8312yes—
533C22×C4Q8×D8312yes—
534C22×C4Q8×D8312yes—
535C22×C4#1305058912yes—
536C22×C4#1305059112yes—
537C22×C4#1305059112yes—
538C22×C4#1305059112yes—
539C4⋊C4—216no—
540C4⋊C4—28no—
541C4⋊C4—3328no—
542C4⋊C4—3324no—
543C4⋊C4—1668no—
544C4⋊C4C22⋊Dic83116yes—
545C42—28no—
546C42—3328no—
547C42—3324no—
548C42—1668no—
549C23C23×Dic8311yescharacteristic
550C23C2×D4×D8311yescharacteristic
551C23C22×C22⋊D8311yescharacteristic
552C23C22×C22⋊D8311yescharacteristic
553C23C2×Q8×D8311yescharacteristic
554C23C2×Q8×D8311yescharacteristic
555C23C2×Q8×D8311yescharacteristic
556C23C2×#1305058911yescharacteristic
557C23C2×#1305059111yescharacteristic
558C23C2×#1305059111yescharacteristic
559C23C2×#1305059111yescharacteristic
560C23#1458183711yescharacteristic
561C23#1458183711yescharacteristic
562C23#1458184011yescharacteristic
563C23#1458184011yescharacteristic
564Q8—432no—
565C2×C4—24no—
566C2×C4—24no—
567C2×C4—22no—
568C2×C4—22no—
569C2×C4—24no—
570C2×C4—24no—
571C2×C4—22no—
572C2×C4—22no—
573C2×C4—22no—
574C2×C4—22no—
575C2×C4—22no—
576C2×C4—22no—
577C2×C4—22no—
578C2×C4—22no—
579C2×C4—24no—
580C2×C4—22no—
581C2×C4—24no—
582C2×C4—22no—
583C2×C4—24no—
584C2×C4—24no—
585C2×C4—24no—
586C2×C4—42no—
587C2×C4—42no—
588C2×C4—42no—
589C2×C4—42no—
590C2×C4—3322no—
591C2×C4—3321no—
592C2×C4—3321no—
593C2×C4—3322no—
594C2×C4—3321no—
595C2×C4—3321no—
596C2×C4—3321no—
597C2×C4—3322no—
598C2×C4—3321no—
599C2×C4—3321no—
600C2×C4—3321no—
601C2×C4—3321no—
602C2×C4—3321no—
603C2×C4—3321no—
604C2×C4—3321no—
605C2×C4—3322no—
606C2×C4—3322no—
607C2×C4—3322no—
608C2×C4—3322no—
609C2×C4—3322no—
610C2×C4—3322no—
611C2×C4—3322no—
612C2×C4—3322no—
613C2×C4—834no—
614C2×C4—1662no—
615C2×C4—1662no—
616C2×C4—1662no—
617C2×C4—1662no—
618C2×C4—1664no—
619C2×C4—1664no—
620C2×C4—1662no—
621C2×C4—1662no—
622C2×C4—1664no—
623C2×C4—1662no—
624C2×C4—1662no—
625C2×C4—1662no—
626C2×C4—1662no—
627C2×C4—1662no—
628C2×C4—1662no—
629C2×C4—1662no—
630C2×C4—1662no—
631C2×C4—1662no—
632C2×C4C2×C22⋊Dic8318yes—
633C2×C4C2×C22⋊Dic8314yes—
634C2×C4D4×Dic8314yes—
635C2×C4Q8×Dic8314yes—
636C2×C4Q8×Dic8314yes—
637C2×C4Q8×Dic8314yes—
638C2×C4#1458176814yes—
639C2×C4#1458176814yes—
640C2×C4#1458178114yes—
641C2×C4#1458179014yes—
642C22C22×C22⋊Dic8311yescharacteristic
643C22C2×D4×Dic8311yescharacteristic
644C22C2×Q8×Dic8311yescharacteristic
645C22C2×Q8×Dic8311yescharacteristic
646C22C2×Q8×Dic8311yescharacteristic
647C22#1912817611yescharacteristic
648C22#1912817911yescharacteristic
649C22C2×#1458176811yescharacteristic
650C22C2×#1458176811yescharacteristic
651C22C2×#1458178111yescharacteristic
652C22C4⋊Q8×D8311yescharacteristic
653C22C2×#1458179011yescharacteristic
654C22#1912825211yescharacteristic
655C22#1912825611yescharacteristic
656C22#1912825611yescharacteristic
657C22#1912832511yescharacteristic
658C22#1912832511yescharacteristic
659C22#1912832811yescharacteristic
660C22#1912832811yescharacteristic
661C22D4×C22⋊D8311yescharacteristic
662C22D4×C22⋊D8311yescharacteristic
663C22#1912834511yescharacteristic
664C22#1912834511yescharacteristic
665C22#1912835411yescharacteristic
666C22#1912836211yescharacteristic
667C22#1912836211yescharacteristic
668C22Q8×C22⋊D8311yescharacteristic
669C22Q8×C22⋊D8311yescharacteristic
670C22#1912836611yescharacteristic
671C22#1912841211yescharacteristic
672C22#1912841211yescharacteristic
673C22#1912841711yescharacteristic
674C22#1912842511yescharacteristic
675C22#1912842611yescharacteristic
676C22#1912843111yescharacteristic
677C4—28no—
678C4—24no—
679C4—24no—
680C4—44no—
681C4—3322no—
682C4—3324no—
683C4—3322no—
684C4—3322no—
685C4—6642no—
686C4—1664no—
687C4#1912760818yescomplemented
688C2C2×#1912760811yescharacteristic
689C2C4⋊Q8×Dic8311yescharacteristic
690C2#2491021211yescharacteristic
691C2D4×C22⋊Dic8311yescharacteristic
692C2Q8×C22⋊Dic8311yescharacteristic
693C2#2491052311yescharacteristic
694C2#2491055311yescharacteristic
695C2#2491115011yescharacteristic
696C2#2491116111yescharacteristic
697C2#2491129811yescharacteristic
698C2#2491130911yescharacteristic
699C2#2491182911yescharacteristic
700C2#2491184011yescharacteristic
701C2#2491248011yescharacteristic
702C2#2491249011yescharacteristic
subgroupG/H
center, FrattiniC24C23×D83
commutatorC23×C83C23×C4
FittingC22×C4⋊Q8×C83C2
socle, prime radical, cosocleC24×C83C24
hypercenterC22×C4⋊Q8D83
hypocenterC83#14053
LCSG ▷ C23×C83 ▷ C83
UCSC1 ◁ C24 ◁ C22×C4⋊Q8

Complements

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

NH ≅ G/Ntype
36. C2×C4⋊Q8×C83C4semidirect
55. C2×C4⋊Dic83Q8semidirect
64. C2×C4×Dic83Q8semidirect
76. C83⋊#95Q8semidirect
289. C2×Dic83C4⋊Q8semidirect
329. C4×C83#391semidirect
363. C83#14053semidirect
367. C2×C4⋊Q8Dic83semidirect
687. C4#19127608semidirect

Maximal subgroups

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

subgroupindex
C2×#191276082
C2×#191276002
C2×C4⋊C4×Dic832
#249057342
#249057162
#249056952
#249056932
#249056922
C4×C83⋊#952
C22×C4⋊Q8×C832
#1405383