Finite Group Databasebeta

← #35425296

Subgroups — #35425296

Order 21248.

980 conjugacy classes of subgroups.

The subgroup lattice has 688 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C8×D332C211yesmaximal, characteristic
2C2×#19127752C211yesmaximal, characteristic, complemented
3C4×#14581777C211yesmaximal, characteristic
4#24908180C211yesmaximal, characteristic, complemented
5#24908069C211yesmaximal, characteristic, complemented
6#24908069C211yesmaximal, characteristic, complemented
7#24908022C211yesmaximal, characteristic, complemented
8#24908020C211yesmaximal, characteristic, complemented
9#24907754C211yesmaximal, characteristic
10#24907639C211yesmaximal, characteristic, complemented
11#24907639C211yesmaximal, characteristic, complemented
12C8×(C2×D83)⋊C4C211yesmaximal, characteristic, complemented
13#24907233C211yesmaximal, characteristic, complemented
14#336×D83C211yesmaximal, characteristic, complemented
15C8×C4⋊C4×C83C211yesmaximal, characteristic, complemented
16C22×C8×D83C2211yescharacteristic
17C22×C8×D83C2211yescharacteristic
18C22×C8×D83C2211yescharacteristic
19C2×#14581777C411yescharacteristic
20C2×C4×D332C2211yescharacteristic
21C2×C42×D83C2211yescharacteristic
22C8×D332—24no—
23#19127752—24no—
24C2×C4⋊(C83⋊C8)C2211yescharacteristic
25C2×Dic83⋊C8C2211yescharacteristic
26C2×Dic83⋊C8C2211yescharacteristic
27C2×Dic83⋊C8C2211yescharacteristic
28C2×(C2×D83)⋊C8C2211yescharacteristic
29C2×(C2×D83)⋊C8C2211yescharacteristic
30C2×(C2×D83)⋊C8C2211yescharacteristic
31C2×(C2×D83)⋊C8C2211yescharacteristic
32C2×(C2×D83)⋊C8C2211yescharacteristic
33C2×C4×C83⋊C8C2211yescharacteristic
34C2×C8×Dic83C2211yescharacteristic
35#19127591C411yescharacteristic
36#19127590C411yescharacteristic
37#19127588C411yescharacteristic
38#19127587C411yescharacteristic
39#19127579C411yescharacteristic
40#19127572C411yescharacteristic
41#19127563C411yescharacteristic
42C4×Dic83⋊C4C2211yescharacteristic
43C4×(C2×D83)⋊C4C2211yescharacteristic
44C4×(C2×D83)⋊C4C2211yescharacteristic
45C4×(C2×D83)⋊C4C2211yescharacteristic
46#19127456C2211yescharacteristic
47#19127456C2211yescharacteristic
48#19127456C2211yescharacteristic
49#19127456C2211yescharacteristic
50#19127455C2211yescharacteristic
51#19127455C2211yescharacteristic
52#19127455C2211yescharacteristic
53#19127455C2211yescharacteristic
54C2×C4⋊C8×C83C2211yescharacteristic
55C2×C4×C8×C83C2211yescharacteristic
56C2×C4×C8×C83C2211yescharacteristic
57C2×C4×C8×C83C2211yescharacteristic
58C4×C4⋊C4×C83C2211yescharacteristic
59#336×C83C2211yescharacteristic
60#336×C83C2211yescharacteristic
61C22×D332C2×C411yescharacteristic
62C22×C4×D83C2×C411yescharacteristic
63C22×C4×D83C2×C411yescharacteristic
64C22×C4×D83C2311yescharacteristic
65C22×C4×D83C2311yescharacteristic
66C22×C83⋊C8C2311yescharacteristic
67C22×C83⋊C8C2311yescharacteristic
68C22×C83⋊C8C2311yescharacteristic
69C22×C83⋊C8C2311yescharacteristic
70C2×C8×D83—22no—
71C2×C8×D83—22no—
72C2×C8×D83—22no—
73C2×C8×D83—22no—
74C2×C8×D83—22no—
75C2×C8×D83—22no—
76C2×C8×D83—41no—
77C2×C8×D83—41no—
78C2×C8×D83—41no—
79#14581777C818yescomplemented
80C4×D332—22no—
81C4×D332—22no—
82C2×C4⋊Dic83C2×C411yescharacteristic
83C2×Dic83⋊C4C2×C411yescharacteristic
84C2×Dic83⋊C4C2×C411yescharacteristic
85C2×(C2×D83)⋊C4C2×C411yescharacteristic
86C2×(C2×D83)⋊C4C2×C411yescharacteristic
87C2×(C2×D83)⋊C4C2×C411yescharacteristic
88C2×(C2×D83)⋊C4C2×C411yescharacteristic
89C2×(C2×D83)⋊C4C2×C411yescharacteristic
90C2×(C2×D83)⋊C4C2×C411yescharacteristic
91C2×(C2×D83)⋊C4C2×C411yescharacteristic
92C2×(C2×D83)⋊C4C2×C411yescharacteristic
93C2×C4×Dic83C2×C411yescharacteristic
94C2×C4×Dic83C2×C411yescharacteristic
95C2×C4×Dic83C2311yescharacteristic
96C2×C4×Dic83C2311yescharacteristic
97C42×D83—22no—
98C42×D83—22no—
99C4⋊(C83⋊C8)—22no—
100Dic83⋊C8—22no—
101Dic83⋊C8—22no—
102Dic83⋊C8—41no—
103(C2×D83)⋊C8—22no—
104(C2×D83)⋊C8—22no—
105(C2×D83)⋊C8—22no—
106(C2×D83)⋊C8—41no—
107(C2×D83)⋊C8D414yes—
108C4×C83⋊C8—22no—
109C8×Dic83—41no—
110C83⋊#95C2×C411yescharacteristic
111C83⋊#95C2×C411yescharacteristic
112C83⋊#95C2×C411yescharacteristic
113C83⋊#95C2×C411yescharacteristic
114C83⋊#95C2×C411yescharacteristic
115C83⋊#95C2×C411yescharacteristic
116C83⋊#95C2×C411yescharacteristic
117C83⋊#95C2×C411yescharacteristic
118C22×C8×C83C2311yescharacteristic
119C22×C8×C83C2311yescharacteristic
120C22×C8×C83C2311yescharacteristic
121C22×C8×C83C2311yescharacteristic
122C2×C4⋊C4×C83C2×C411yescharacteristic
123C2×C4⋊C4×C83C2×C411yescharacteristic
124C2×C42×C83C2311yescharacteristic
125C2×C42×C83C2311yescharacteristic
126C2×C42×C83C2311yescharacteristic
127C4⋊C8×C83—22no—
128C4×C8×C83—22no—
129C4×C8×C83—22no—
130C4×C8×C83—22no—
131#95×C83C2×C411yescharacteristic
132#95×C83C2×C411yescharacteristic
133C23×D83C22×C411yescharacteristic
134C23×D83C22×C411yescharacteristic
135C2×D332—22no—
136C2×D332—22no—
137C2×D332C2×C814yes—
138C22×Dic83C22×C411yescharacteristic
139C22×Dic83C22×C411yescharacteristic
140C22×Dic83C22×C411yescharacteristic
141C22×Dic83C22×C411yescharacteristic
142C22×Dic83C22×C411yescharacteristic
143C22×Dic83C22×C411yescharacteristic
144C2×C4×D83—22no—
145C2×C4×D83—22no—
146C2×C4×D83—21no—
147C2×C4×D83—21no—
148C2×C4×D83—21no—
149C2×C4×D83—21no—
150C2×C4×D83—22no—
151C2×C4×D83—22no—
152C2×C4×D83—21no—
153C2×C4×D83—21no—
154C2×C4×D83—21no—
155C2×C4×D83—21no—
156C2×C4×D83—21no—
157C2×C4×D83—21no—
158C2×C4×D83—41no—
159C2×C4×D83C2×C814yescomplemented
160C2×C4×D83C2×D412yes—
161C2×C4×D83#4112yes—
162C2×C83⋊C8—21no—
163C2×C83⋊C8—21no—
164C2×C83⋊C8—21no—
165C2×C83⋊C8—21no—
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⋊C8C2×D412yes—
174C8×D83—44no—
175C8×D83—44no—
176C8×D83—44no—
177C4⋊Dic83—22no—
178Dic83⋊C4—41no—
179Dic83⋊C4C2×C814yescomplemented
180(C2×D83)⋊C4—22no—
181(C2×D83)⋊C4—22no—
182(C2×D83)⋊C4—22no—
183(C2×D83)⋊C4—22no—
184(C2×D83)⋊C4—41no—
185(C2×D83)⋊C4C2×C814yescomplemented
186(C2×D83)⋊C4C2×C814yescomplemented
187(C2×D83)⋊C4C2×C814yescomplemented
188C4×Dic83—21no—
189C4×Dic83—21no—
190C4×Dic83—21no—
191C4×Dic83—21no—
192C4×Dic83—22no—
193C4×Dic83—22no—
194C22×C4×C83C22×C411yescharacteristic
195C22×C4×C83C22×C411yescharacteristic
196C22×C4×C83C22×C411yescharacteristic
197C22×C4×C83C22×C411yescharacteristic
198C22×C4×C83C22×C411yescharacteristic
199C22×C4×C83C22×C411yescharacteristic
200C22×C4×C83C2411yescharacteristic
201C2×C8×C83—21no—
202C2×C8×C83—21no—
203C2×C8×C83—21no—
204C2×C8×C83—21no—
205C2×C8×C83—21no—
206C2×C8×C83—21no—
207C2×C8×C83—21no—
208C2×C8×C83—21no—
209C2×C8×C83—21no—
210C2×C8×C83C2×D412yes—
211C2×C8×C83#4112yes—
212C2×C8×C83#4112yes—
213C4⋊C4×C83—22no—
214C4⋊C4×C83C2×C814yescomplemented
215C42×C83—21no—
216C42×C83—21no—
217C42×C83—21no—
218C42×C83—21no—
219C42×C83—21no—
220C42×C83—21no—
221C23×C83C23×C411yescharacteristic
222C22×D83—21no—
223C22×D83—21no—
224C22×D83—21no—
225C22×D83—21no—
226C22×D83—21no—
227C22×D83—21no—
228C22×D83—21no—
229C22×D83—21no—
230C22×D83—21no—
231C22×D83—21no—
232C22×D83C4×D412yes—
233C22×D83C22×C812yes—
234C22×D83C22×C812yes—
235C22×D83#13112yes—
236C2×C4×C83—21no—
237C2×C4×C83—21no—
238C2×C4×C83—21no—
239C2×C4×C83—21no—
240C2×C4×C83—21no—
241C2×C4×C83—21no—
242C2×C4×C83—21no—
243C2×C4×C83—21no—
244C2×C4×C83—21no—
245C2×C4×C83—21no—
246C2×C4×C83—21no—
247C2×C4×C83—21no—
248C2×C4×C83—21no—
249C2×C4×C83—21no—
250C2×C4×C83C22×C812yes—
251C2×C4×C83C22×C812yes—
252C2×C4×C83C22×C812yes—
253C2×C4×C83#13112yes—
254C2×C4×C83C22×D411yescharacteristic
255C2×C4×C83C2×#4111yescharacteristic
256C2×C4×C83C2×#4111yescharacteristic
257C2×C4×C83C2×#4111yescharacteristic
258C2×C4×C83H(5,𝔽2)11yescharacteristic
259C2×C4×C832−1+411yescharacteristic
260C2×Dic83—21no—
261C2×Dic83—21no—
262C2×Dic83—21no—
263C2×Dic83—21no—
264C2×Dic83—21no—
265C2×Dic83—21no—
266C2×Dic83—21no—
267C2×Dic83—21no—
268C2×Dic83—21no—
269C2×Dic83—21no—
270C2×Dic83—21no—
271C2×Dic83—21no—
272C2×Dic83—21no—
273C2×Dic83—21no—
274C2×Dic83—21no—
275C2×Dic83C4×D412yes—
276C2×Dic83C22×C812yes—
277C2×Dic83C22×C812yes—
278D332—28no—
279C4×D83—28no—
280C4×D83—22no—
281C4×D83—22no—
282C4×D83—22no—
283C4×D83—22no—
284C4×D83—44no—
285C4×D83—41no—
286C4×D83—41no—
287C4×D83—41no—
288C4×D83—41no—
289C8×C83—22no—
290C8×C83—22no—
291C8×C83—22no—
292C8×C83—41no—
293C83⋊C8—22no—
294C83⋊C8—41no—
295C83⋊C8—41no—
296C83⋊C8—41no—
297C22×C83C2×C4×D411yescharacteristic
298C22×C83C4×#4111yescharacteristic
299C22×C83#52011yescharacteristic
300C22×C83C23×C811yescharacteristic
301C22×C83C2×#13111yescharacteristic
302C22×C83C2×#13111yescharacteristic
303C22×C83#56811yescharacteristic
304C2×D83—22no—
305C2×D83—22no—
306C2×D83—22no—
307C2×D83—22no—
308C2×D83—22no—
309C2×D83—22no—
310C2×D83—22no—
311C2×D83—22no—
312C2×D83—22no—
313C2×D83—41no—
314C2×D83—41no—
315C2×D83—41no—
316C2×D83—41no—
317C2×D83C8×D414yes—
318C4×C83—22no—
319C4×C83—22no—
320C4×C83—22no—
321C4×C83—22no—
322C4×C83—41no—
323C4×C83—41no—
324C4×C83#54611yescharacteristic
325C4×C83#54711yescharacteristic
326C4×C83#55111yescharacteristic
327C4×C83#55211yescharacteristic
328Dic83—22no—
329Dic83—22no—
330Dic83—22no—
331Dic83—41no—
332Dic83—41no—
333Dic83—41no—
334#22900—831nomaximal, Sylow
335C2×C83#235911yescharacteristic
336C2×C83C2×C8×D411yescharacteristic
337C2×C83#293311yescharacteristic
338C2×C83C8×#4111yescharacteristic
339C2×C83#296811yescharacteristic
340C2×C83#298811yescharacteristic
341C2×C83#299411yescharacteristic
342D83—24no—
343D83—42no—
344C2×C8×D4—831no—
345C2×#431—831no—
346C4×#123—831no—
347#1939—831no—
348#1923—831no—
349#1923—831no—
350#1916—831no—
351#1916—831no—
352#1869—831no—
353#1850—831no—
354#1850—831no—
355C8×C4⋊C4D8311yescharacteristic, complemented
356C8×C22⋊C4—831no—
357C8×C22⋊C4—831no—
358C2×#336—831no—
359C83#2290011yescharacteristic, complemented, Sylow
360C23×C8—831no—
361C23×C8—831no—
362C23×C8—831no—
363C2×#123—831no—
364C2×C4×D4—831no—
365C22×C42—831no—
366C8×D4—1664no—
367#431—1664no—
368C2×C4⋊C8—831no—
369C2×C4⋊C8—831no—
370C2×C4⋊C8—831no—
371C2×C4⋊C8—831no—
372C2×C4⋊C8C2×D8311yescharacteristic
373C2×C22⋊C8—831no—
374C2×C22⋊C8—831no—
375C2×C22⋊C8—831no—
376C2×C22⋊C8—831no—
377C2×C22⋊C8—831no—
378C2×C4×C8—831no—
379C2×C4×C8—831no—
380C2×C4×C8C2×D8311yescharacteristic
381C2×C4×C8C2×D8311yescharacteristic
382C2×C4×C8C2×D8311yescharacteristic
383#388—831no—
384#388—831no—
385#387—831no—
386#387—831no—
387#386—831no—
388#385—831no—
389#381—831no—
390C4×C4⋊C4—831no—
391C4×C4⋊C4C2×D8311yescharacteristic
392C4×C22⋊C4—831no—
393C4×C22⋊C4—831no—
394C4×C22⋊C4—831no—
395#336—831no—
396#336—831no—
397#336—831no—
398#336—831no—
399#336—831no—
400#336—831no—
401#336—831no—
402#336—831no—
403#336C2×D8311yescharacteristic
404#336C2×D8311yescharacteristic
405C22×D4—831no—
406C23×C4—831no—
407C23×C4—831no—
408C23×C4—831no—
409C23×C4—831no—
410C22×C8—3321no—
411C22×C8—3321no—
412C22×C8—3321no—
413C22×C8—831no—
414C22×C8—831no—
415C22×C8—831no—
416C22×C8—831no—
417C22×C8—1662no—
418C22×C8—1662no—
419C22×C8—1662no—
420C22×C8—1662no—
421C22×C8—1662no—
422C22×C8—1662no—
423C22×C8C22×D8311yescharacteristic
424C22×C8C22×D8311yescharacteristic
425C22×C8C22×D8311yescharacteristic
426C22×C8C22×D8311yescharacteristic
427#123—838no—
428C4×D4—1662no—
429C4×D4—1662no—
430C2×C4⋊C4—831no—
431C2×C4⋊C4—831no—
432C2×C4⋊C4—831no—
433C2×C4⋊C4C4×D8311yescharacteristic
434C2×C4⋊C4C4×D8311yescharacteristic
435C2×C22⋊C4—831no—
436C2×C22⋊C4—831no—
437C2×C22⋊C4—831no—
438C2×C22⋊C4—831no—
439C2×C22⋊C4—831no—
440C2×C22⋊C4—831no—
441C2×C22⋊C4—831no—
442C2×C22⋊C4—831no—
443C2×C42—831no—
444C2×C42—831no—
445C2×C42—831no—
446C2×C42—831no—
447C2×C42—1662no—
448C2×C42—1662no—
449C2×C42C22×D8311yescharacteristic
450C2×C42C22×D8311yescharacteristic
451C2×C42C22×D8311yescharacteristic
452C4⋊C8—22no—
453C4⋊C8—3321no—
454C4⋊C8—1662no—
455C4⋊C8—1662no—
456C4⋊C8—1662no—
457C22⋊C8—3321no—
458C22⋊C8—834no—
459C22⋊C8—1662no—
460C22⋊C8—1662no—
461C22⋊C8—1662no—
462C4×C8—22no—
463C4×C8—22no—
464C4×C8—22no—
465C4×C8—3321no—
466C4×C8—1662no—
467#95—831no—
468#95—831no—
469#95—831no—
470#95—831no—
471#95—831no—
472#95—831no—
473#95—831no—
474#95—831no—
475#95C4×D8311yescharacteristic
476#95C4×D8311yescharacteristic
477C24—831no—
478C24—831no—
479C2×D4—834no—
480C2×D4—1662no—
481C2×D4—1662no—
482C22×C4—3321no—
483C22×C4—831no—
484C22×C4—831no—
485C22×C4—831no—
486C22×C4—834no—
487C22×C4—832no—
488C22×C4—832no—
489C22×C4—831no—
490C22×C4—831no—
491C22×C4—831no—
492C22×C4—1662no—
493C22×C4—1662no—
494C22×C4—1662no—
495C22×C4—1662no—
496C22×C4—1661no—
497C22×C4—1661no—
498C22×C4—1661no—
499C22×C4—1661no—
500C22×C4—1661no—
501C22×C4—1661no—
502C22×C4—1661no—
503C22×C4—1661no—
504C22×C4—1661no—
505C22×C4—1661no—
506C22×C4C2×C4×D8311yescharacteristic
507C22×C4C2×C4×D8311yescharacteristic
508C22×C4C2×C4×D8311yescharacteristic
509C22×C4C2×C4×D8311yescharacteristic
510C22×C4C2×C4×D8311yescharacteristic
511C22×C4C2×C4×D8311yescharacteristic
512C22×C4C23×D8311yescharacteristic
513C2×C8—21no—
514C2×C8—21no—
515C2×C8—21no—
516C2×C8—21no—
517C2×C8—21no—
518C2×C8—21no—
519C2×C8—21no—
520C2×C8—21no—
521C2×C8—21no—
522C2×C8—3324no—
523C2×C8—3324no—
524C2×C8—3324no—
525C2×C8—832no—
526C2×C8—1661no—
527C2×C8—1661no—
528C2×C8—1661no—
529C2×C8—1661no—
530C2×C8—1661no—
531C2×C8—1661no—
532C2×C8—1661no—
533C2×C8—1661no—
534C2×C8—1661no—
535C2×C8—1661no—
536C2×C8—1661no—
537C2×C8D4×D8312yes—
538C2×C8#1305059012yes—
539C2×C8#1305059012yes—
540C4⋊C4—22no—
541C4⋊C4—3321no—
542C4⋊C4—834no—
543C4⋊C4—1662no—
544C4⋊C4C8×D8314yescomplemented
545C22⋊C4—3321no—
546C22⋊C4—834no—
547C22⋊C4—834no—
548C22⋊C4—834no—
549C22⋊C4—1662no—
550C22⋊C4—1662no—
551C22⋊C4—1662no—
552C22⋊C4—1662no—
553C42—21no—
554C42—21no—
555C42—21no—
556C42—21no—
557C42—21no—
558C42—21no—
559C42—1662no—
560C42—1662no—
561C42—1661no—
562C42—1661no—
563C42—1661no—
564C42—1661no—
565C23—832no—
566C23—832no—
567C23—832no—
568C23—832no—
569C23—1661no—
570C23—1661no—
571C23—1661no—
572C23—1661no—
573C23—1661no—
574C23—1661no—
575C23—1661no—
576C23—1661no—
577C23—1661no—
578C23—1661no—
579C23C22×C4×D8311yescharacteristic
580D4—1668no—
581C2×C4—21no—
582C2×C4—21no—
583C2×C4—21no—
584C2×C4—21no—
585C2×C4—21no—
586C2×C4—21no—
587C2×C4—21no—
588C2×C4—21no—
589C2×C4—21no—
590C2×C4—21no—
591C2×C4—21no—
592C2×C4—21no—
593C2×C4—21no—
594C2×C4—21no—
595C2×C4—3324no—
596C2×C4—3321no—
597C2×C4—3321no—
598C2×C4—3321no—
599C2×C4—3321no—
600C2×C4—832no—
601C2×C4—832no—
602C2×C4—832no—
603C2×C4—1668no—
604C2×C4—1661no—
605C2×C4—1661no—
606C2×C4—1661no—
607C2×C4—1661no—
608C2×C4—1661no—
609C2×C4—1661no—
610C2×C4—1661no—
611C2×C4—1661no—
612C2×C4—1661no—
613C2×C4—1661no—
614C2×C4—1661no—
615C2×C4—1661no—
616C2×C4—1661no—
617C2×C4—1661no—
618C2×C4—1661no—
619C2×C4—1662no—
620C2×C4—1662no—
621C2×C4—1662no—
622C2×C4—1662no—
623C2×C4C2×C8×D8312yes—
624C2×C4C2×C8×D8312yes—
625C2×C4C2×C8×D8312yes—
626C2×C4#1458179812yes—
627C2×C4C2×D4×D8311yescharacteristic
628C2×C4#41×D8311yescharacteristic
629C2×C4C2×#1305059011yescharacteristic
630C2×C4C2×#1305059011yescharacteristic
631C2×C4#1458183811yescharacteristic
632C2×C4#1458184011yescharacteristic
633C8—22no—
634C8—22no—
635C8—22no—
636C8—41no—
637C8—3321no—
638C8—3321no—
639C8—3321no—
640C8—1662no—
641C22—3321no—
642C22—3321no—
643C22—3321no—
644C22—3321no—
645C22—834no—
646C22—1662no—
647C22—1662no—
648C22—1662no—
649C22—1662no—
650C22—1662no—
651C22—1662no—
652C22—1662no—
653C22—1662no—
654C22—1662no—
655C22C4×D4×D8311yescharacteristic
656C22C4×#1305059011yescharacteristic
657C22#1912818311yescharacteristic
658C22C22×C8×D8311yescharacteristic
659C22#131×D8311yescharacteristic
660C22C2×#1458179811yescharacteristic
661C22#1912846611yescharacteristic
662C4—22no—
663C4—22no—
664C4—22no—
665C4—22no—
666C4—41no—
667C4—41no—
668C4—3321no—
669C4—3321no—
670C4—3321no—
671C4—1662no—
672C4—1662no—
673C4—1662no—
674C4#1912834711yescharacteristic
675C4#1912835211yescharacteristic
676C4#1912837511yescharacteristic
677C4#1912839211yescharacteristic
678C2—3322no—
679C2—1664no—
680C2#2491046011yescharacteristic
681C2C8×D4×D8311yescharacteristic
682C2#2491618311yescharacteristic
683C2C8×#1305059011yescharacteristic
684C2#2491645311yescharacteristic
685C2#2491657311yescharacteristic
686C2#2491662211yescharacteristic
subgroupG/H
center, FrattiniC22×C4C23×D83
commutatorC22×C83C23×C8
FittingC8×C4⋊C4×C83C2
socleC23×C83C23×C4
prime radicalC22×D332C2×C4
cosocleC22×C4×C83C24
hypercenterC8×C4⋊C4D83
hypocenterC83#22900
LCSG ▷ C22×C83 ▷ C83
UCSC1 ◁ C22×C4 ◁ C8×C4⋊C4

Complements

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

NH ≅ G/Ntype
2. C2×#19127752C2semidirect
4. #24908180C2semidirect
5. #24908069C2semidirect
6. #24908069C2semidirect
7. #24908022C2semidirect
8. #24908020C2semidirect
10. #24907639C2semidirect
11. #24907639C2semidirect
12. C8×(C2×D83)⋊C4C2semidirect
13. #24907233C2semidirect
14. #336×D83C2semidirect
15. C8×C4⋊C4×C83C2semidirect
79. #14581777C8semidirect
159. C2×C4×D83C2×C8semidirect
179. Dic83⋊C4C2×C8semidirect
185. (C2×D83)⋊C4C2×C8semidirect
186. (C2×D83)⋊C4C2×C8semidirect
187. (C2×D83)⋊C4C2×C8semidirect
214. C4⋊C4×C83C2×C8semidirect
355. C8×C4⋊C4D83semidirect
359. C83#22900semidirect
544. C4⋊C4C8×D83semidirect

Maximal subgroups

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

subgroupindex
C2×C8×D3322
C2×#191277522
C4×#145817772
#249081802
#249080692
#249080222
#249080202
#249077542
#249076392
C8×(C2×D83)⋊C42
#249072332
#336×D832
C8×C4⋊C4×C832
#2290083