Finite Group Databasebeta

← C2×#24910764 #35570704

Subgroups — C2×#24910764 #35570704

Order 21248.

2294 conjugacy classes of subgroups.

The subgroup lattice has 700 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#24910764C2116yesmaximal, direct product factor
2C2×C83⋊#401C211yesmaximal, characteristic, complemented
3C2×#19127643C211yesmaximal, characteristic, complemented
4C2×#19127640C211yesmaximal, characteristic, complemented
5C2×#19127639C211yesmaximal, characteristic, complemented
6C2×#19127630C211yesmaximal, characteristic
7C2×#19127628C211yesmaximal, characteristic
8C2×#19127627C211yesmaximal, characteristic
9C2×#19127623C211yesmaximal, characteristic
10C2×C4×Dic83⋊C4C211yesmaximal, characteristic, complemented
11C2×C4×C4⋊Dic83C211yesmaximal, characteristic, complemented
12C2×C4×(C2×D83)⋊C4C211yesmaximal, characteristic
13C2×C4×(C2×D83)⋊C4C211yesmaximal, characteristic
14C2×C4×(C2×D83)⋊C4C211yesmaximal, characteristic
15C2×#19127547C211yesmaximal, characteristic, complemented
16C2×C4×C4⋊C4×C83C211yesmaximal, characteristic, complemented
17C23×C4×D83C2211yescharacteristic
18C22×C4⋊Dic83C2211yescharacteristic
19C22×C4⋊Dic83C2211yescharacteristic
20C22×Dic83⋊C4C2211yescharacteristic
21C22×Dic83⋊C4C2211yescharacteristic
22C22×(C2×D83)⋊C4C2211yescharacteristic
23C22×(C2×D83)⋊C4C2211yescharacteristic
24C22×(C2×D83)⋊C4C2211yescharacteristic
25C22×(C2×D83)⋊C4C2211yescharacteristic
26C22×(C2×D83)⋊C4C2211yescharacteristic
27C22×(C2×D83)⋊C4C2211yescharacteristic
28C22×C4×Dic83C2211yescharacteristic
29C22×C4×Dic83C2211yescharacteristic
30C22×C4×Dic83C2211yescharacteristic
31C83⋊#401C2218yescomplemented
32#19127643C2218yescomplemented
33#19127640C2218yescomplemented
34#19127639C2218yescomplemented
35#19127630C2218yes—
36#19127628C2218yes—
37#19127627C2218yes—
38#19127623C2218yes—
39C4×Dic83⋊C4C2218yescomplemented
40C4×C4⋊Dic83C2218yescomplemented
41C4×(C2×D83)⋊C4C2218yes—
42C4×(C2×D83)⋊C4C2218yes—
43C4×(C2×D83)⋊C4C2218yes—
44#19127547C2218yescomplemented
45C2×C83⋊#95C2211yescharacteristic
46C2×C83⋊#95C2211yescharacteristic
47C2×C83⋊#95C2211yescharacteristic
48C2×C83⋊#95C2211yescharacteristic
49C2×C83⋊#95C2211yescharacteristic
50C2×C83⋊#95C2211yescharacteristic
51C2×C83⋊#95C2211yescharacteristic
52C2×C83⋊#95C2211yescharacteristic
53C2×C83⋊#95C2211yescharacteristic
54C2×C83⋊#95C2211yescharacteristic
55C2×C83⋊#95C2211yescharacteristic
56C2×C83⋊#95C2211yescharacteristic
57C2×C83⋊#95C2211yescharacteristic
58C2×C83⋊#95C2211yescharacteristic
59C22×C4⋊C4×C83C2211yescharacteristic
60C22×C4⋊C4×C83C2211yescharacteristic
61C22×C42×C83C2211yescharacteristic
62C22×C42×C83C2211yescharacteristic
63C22×C42×C83C2211yescharacteristic
64C4×C4⋊C4×C83C2218yescomplemented
65C2×#95×C83C2211yescharacteristic
66C2×#95×C83C2211yescharacteristic
67C24×D83C2311yescharacteristic
68C23×Dic83C2311yescharacteristic
69C23×Dic83C2311yescharacteristic
70C23×Dic83C2311yescharacteristic
71C23×Dic83C2311yescharacteristic
72C23×Dic83C2311yescharacteristic
73C23×Dic83C2311yescharacteristic
74C23×Dic83C2311yescharacteristic
75C22×C4×D83—24no—
76C22×C4×D83—24no—
77C22×C4×D83—24no—
78C22×C4×D83C2314yes—
79C2×C4⋊Dic83—24no—
80C2×C4⋊Dic83—24no—
81C2×C4⋊Dic83C2314yes—
82C2×C4⋊Dic83C2314yes—
83C2×Dic83⋊C4—24no—
84C2×Dic83⋊C4—24no—
85C2×Dic83⋊C4C2314yes—
86C2×Dic83⋊C4C2314yes—
87C2×(C2×D83)⋊C4—24no—
88C2×(C2×D83)⋊C4—24no—
89C2×(C2×D83)⋊C4—24no—
90C2×(C2×D83)⋊C4—24no—
91C2×(C2×D83)⋊C4—24no—
92C2×(C2×D83)⋊C4—24no—
93C2×(C2×D83)⋊C4C2314yes—
94C2×(C2×D83)⋊C4C2314yes—
95C2×(C2×D83)⋊C4C2314yes—
96C2×(C2×D83)⋊C4C2314yes—
97C2×(C2×D83)⋊C4C2314yes—
98C2×(C2×D83)⋊C4C2314yes—
99C2×C4×Dic83—24no—
100C2×C4×Dic83—24no—
101C2×C4×Dic83—24no—
102C2×C4×Dic83C2314yes—
103C2×C4×Dic83C2314yes—
104C2×C4×Dic83C2314yes—
105C83⋊#95C2314yes—
106C83⋊#95C2314yes—
107C83⋊#95C2314yes—
108C83⋊#95C2314yes—
109C83⋊#95C2314yes—
110C83⋊#95C2314yes—
111C83⋊#95C2314yes—
112C83⋊#95C2314yes—
113C83⋊#95C2314yes—
114C83⋊#95C2314yes—
115C83⋊#95C2314yes—
116C83⋊#95C2314yes—
117C83⋊#95C2314yes—
118C83⋊#95C2314yes—
119C23×C4×C83C2311yescharacteristic
120C23×C4×C83C2311yescharacteristic
121C23×C4×C83C2311yescharacteristic
122C23×C4×C83C2311yescharacteristic
123C23×C4×C83C2311yescharacteristic
124C23×C4×C83C2311yescharacteristic
125C23×C4×C83C2311yescharacteristic
126C2×C4⋊C4×C83—24no—
127C2×C4⋊C4×C83—24no—
128C2×C4⋊C4×C83C2314yes—
129C2×C4⋊C4×C83C2314yes—
130C2×C42×C83—24no—
131C2×C42×C83—24no—
132C2×C42×C83—24no—
133C2×C42×C83C2314yes—
134C2×C42×C83C2314yes—
135C2×C42×C83C2314yes—
136#95×C83C2314yes—
137#95×C83C2314yes—
138C23×D83—22no—
139C23×D83—22no—
140C23×D83—22no—
141C23×D83—22no—
142C23×D83—22no—
143C23×D83—22no—
144C23×D83#4114yes—
145C23×D83C2412yes—
146C22×Dic83—22no—
147C22×Dic83—22no—
148C22×Dic83—22no—
149C22×Dic83—22no—
150C22×Dic83—22no—
151C22×Dic83—22no—
152C22×Dic83—22no—
153C22×Dic83—22no—
154C22×Dic83—22no—
155C22×Dic83—22no—
156C22×Dic83—22no—
157C22×Dic83—22no—
158C22×Dic83—22no—
159C22×Dic83—22no—
160C22×Dic83—22no—
161C22×Dic83—22no—
162C22×Dic83—22no—
163C22×Dic83—22no—
164C22×Dic83—22no—
165C22×Dic83—22no—
166C22×Dic83#4114yes—
167C22×Dic83C2412yes—
168C22×Dic83C2412yes—
169C22×Dic83C2412yes—
170C22×Dic83C2412yes—
171C22×Dic83C2412yes—
172C22×Dic83C2412yes—
173C22×Dic83C2412yes—
174C2×C4×D83—28no—
175C2×C4×D83—28no—
176C2×C4×D83—28no—
177C2×C4×D83—416no—
178C4⋊Dic83—28no—
179C4⋊Dic83—28no—
180Dic83⋊C4—28no—
181Dic83⋊C4—28no—
182(C2×D83)⋊C4—28no—
183(C2×D83)⋊C4—28no—
184(C2×D83)⋊C4—28no—
185(C2×D83)⋊C4—28no—
186(C2×D83)⋊C4—28no—
187(C2×D83)⋊C4—28no—
188C4×Dic83—28no—
189C4×Dic83—28no—
190C4×Dic83—28no—
191C24×C83C2411yescharacteristic
192C22×C4×C83—22no—
193C22×C4×C83—22no—
194C22×C4×C83—22no—
195C22×C4×C83—22no—
196C22×C4×C83—22no—
197C22×C4×C83—22no—
198C22×C4×C83—22no—
199C22×C4×C83—22no—
200C22×C4×C83—22no—
201C22×C4×C83—22no—
202C22×C4×C83—22no—
203C22×C4×C83—22no—
204C22×C4×C83—22no—
205C22×C4×C83—22no—
206C22×C4×C83—22no—
207C22×C4×C83—22no—
208C22×C4×C83#4114yes—
209C22×C4×C83#4114yes—
210C22×C4×C83#4114yes—
211C22×C4×C83#4114yes—
212C22×C4×C83#4114yes—
213C22×C4×C83C2412yes—
214C22×C4×C83C2412yes—
215C22×C4×C83C2412yes—
216C22×C4×C83C2412yes—
217C22×C4×C83C2412yes—
218C22×C4×C83C2412yes—
219C22×C4×C83C2412yes—
220C4⋊C4×C83—28no—
221C4⋊C4×C83—28no—
222C42×C83—28no—
223C42×C83—28no—
224C42×C83—28no—
225C23×C83C2×#4112yes—
226C23×C83C2×#4112yes—
227C23×C83C2×#4112yes—
228C23×C83C2×#4112yes—
229C23×C83C2×#4112yes—
230C23×C83C2×#4112yes—
231C23×C83C2×#4112yes—
232C23×C83C2511yescharacteristic
233C22×D83—28no—
234C22×D83—28no—
235C22×D83—28no—
236C22×D83—22no—
237C22×D83—22no—
238C22×D83—22no—
239C22×D83—22no—
240C22×D83—22no—
241C22×D83—22no—
242C22×D83—44no—
243C22×D83—44no—
244C22×D83—44no—
245C22×D83—44no—
246C22×D83C2×#4114yes—
247C2×C4×C83—28no—
248C2×C4×C83—28no—
249C2×C4×C83—22no—
250C2×C4×C83—22no—
251C2×C4×C83—22no—
252C2×C4×C83—22no—
253C2×C4×C83—22no—
254C2×C4×C83—22no—
255C2×C4×C83—22no—
256C2×C4×C83—22no—
257C2×C4×C83—22no—
258C2×C4×C83—22no—
259C2×C4×C83—22no—
260C2×C4×C83—22no—
261C2×C4×C83—22no—
262C2×C4×C83—22no—
263C2×C4×C83—22no—
264C2×C4×C83—22no—
265C2×C4×C83—44no—
266C2×C4×C83—44no—
267C2×C4×C83—44no—
268C2×C4×C83—44no—
269C2×C4×C83#126116yes—
270C2×C4×C83C2×#4114yes—
271C2×C4×C83C2×#4114yes—
272C2×C4×C83C2×#4114yes—
273C2×C4×C83C2×#4114yes—
274C2×C4×C83C2×#4114yes—
275C2×Dic83—28no—
276C2×Dic83—22no—
277C2×Dic83—22no—
278C2×Dic83—22no—
279C2×Dic83—22no—
280C2×Dic83—22no—
281C2×Dic83—22no—
282C2×Dic83—22no—
283C2×Dic83—22no—
284C2×Dic83—22no—
285C2×Dic83—22no—
286C2×Dic83—22no—
287C2×Dic83—22no—
288C2×Dic83—22no—
289C2×Dic83—22no—
290C2×Dic83—22no—
291C2×Dic83—22no—
292C2×Dic83—22no—
293C2×Dic83—22no—
294C2×Dic83—22no—
295C2×Dic83—22no—
296C2×Dic83—44no—
297C2×Dic83—44no—
298C2×Dic83—44no—
299C2×Dic83—44no—
300C2×Dic83—44no—
301C2×Dic83—44no—
302C2×Dic83C2×#4114yes—
303C4×D83—416no—
304C22×C83C2×#12614yes—
305C22×C83#52914yes—
306C22×C83#52914yes—
307C22×C83#52914yes—
308C22×C83#52914yes—
309C22×C83#52914yes—
310C22×C83#52914yes—
311C22×C83C22×#4111yescharacteristic
312C22×C83C22×#4111yescharacteristic
313C22×C83C22×#4111yescharacteristic
314C22×C83C22×#4111yescharacteristic
315C22×C83C22×#4111yescharacteristic
316C22×C83C22×#4111yescharacteristic
317C22×C83C22×#4111yescharacteristic
318C2×D83—24no—
319C2×D83—24no—
320C2×D83—24no—
321C2×D83—416no—
322C2×D83—42no—
323C2×D83—42no—
324C2×D83—42no—
325C2×D83—42no—
326C4×C83—24no—
327C4×C83—24no—
328C4×C83—42no—
329C4×C83—42no—
330C4×C83—42no—
331C4×C83—42no—
332C4×C83C2×#12618yes—
333Dic83—24no—
334Dic83—42no—
335Dic83—42no—
336Dic83—42no—
337Dic83—42no—
338Dic83—42no—
339Dic83—42no—
340C2×#2401—831nomaximal, Sylow
341C2×C83#240118yescomplemented
342C2×C83C22×#12611yescharacteristic
343C2×C83C2×#52911yescharacteristic
344C2×C83C2×#52911yescharacteristic
345C2×C83C2×#52911yescharacteristic
346C2×C83C2×#52911yescharacteristic
347C2×C83C2×#52911yescharacteristic
348C2×C83C2×#52911yescharacteristic
349D83—44no—
350#2401—8316no—
351C2×#401—831no—
352C2×#400—831no—
353C2×#400—831no—
354C2×#400—831no—
355C2×#397—831no—
356C2×#397—831no—
357C2×#397—831no—
358C2×#396—831no—
359C2×C4×C4⋊C4—831no—
360C2×C4×C4⋊C4—831no—
361C2×C4×C4⋊C4D8311yescharacteristic, complemented
362C2×C4×C22⋊C4—831no—
363C2×C4×C22⋊C4—831no—
364C2×C4×C22⋊C4—831no—
365C2×#376—831no—
366C83C2×#240111yescharacteristic, complemented, Sylow
367C24×C4—831no—
368C22×C4⋊C4—831no—
369C22×C4⋊C4—831no—
370C22×C4⋊C4—831no—
371C22×C4⋊C4—831no—
372C22×C4⋊C4C2×D8311yescharacteristic
373C22×C4⋊C4C2×D8311yescharacteristic
374C22×C22⋊C4—831no—
375C22×C22⋊C4—831no—
376C22×C22⋊C4—831no—
377C22×C22⋊C4—831no—
378C22×C22⋊C4—831no—
379C22×C22⋊C4—831no—
380C22×C42—831no—
381C22×C42—831no—
382C22×C42—831no—
383C22×C42C2×D8311yescharacteristic
384C22×C42C2×D8311yescharacteristic
385C22×C42C2×D8311yescharacteristic
386#401—838no—
387#400—838no—
388#400—838no—
389#400—838no—
390#397—838no—
391#397—838no—
392#397—838no—
393#396—838no—
394C4×C4⋊C4—838no—
395C4×C4⋊C4—838no—
396C4×C4⋊C4C2×D8318yescomplemented
397C4×C22⋊C4—838no—
398C4×C22⋊C4—838no—
399C4×C22⋊C4—838no—
400#376—838no—
401C2×#95—831no—
402C2×#95—831no—
403C2×#95—831no—
404C2×#95—831no—
405C2×#95—831no—
406C2×#95—831no—
407C2×#95—831no—
408C2×#95—831no—
409C2×#95—831no—
410C2×#95—831no—
411C2×#95—831no—
412C2×#95—831no—
413C2×#95—831no—
414C2×#95—831no—
415C2×#95C2×D8311yescharacteristic
416C2×#95C2×D8311yescharacteristic
417C25—831no—
418C23×C4—831no—
419C23×C4—831no—
420C23×C4—831no—
421C23×C4—831no—
422C23×C4—831no—
423C23×C4—831no—
424C23×C4—831no—
425C23×C4—834no—
426C23×C4—1664no—
427C23×C4—1664no—
428C23×C4—1664no—
429C23×C4C22×D8311yescharacteristic
430C23×C4C22×D8311yescharacteristic
431C23×C4C22×D8311yescharacteristic
432C23×C4C22×D8311yescharacteristic
433C23×C4C22×D8311yescharacteristic
434C23×C4C22×D8311yescharacteristic
435C23×C4C22×D8311yescharacteristic
436C2×C4⋊C4—24no—
437C2×C4⋊C4—24no—
438C2×C4⋊C4—834no—
439C2×C4⋊C4—834no—
440C2×C4⋊C4—834no—
441C2×C4⋊C4—834no—
442C2×C4⋊C4—1664no—
443C2×C4⋊C4—1664no—
444C2×C4⋊C4—1664no—
445C2×C4⋊C4—1664no—
446C2×C4⋊C4C22×D8314yes—
447C2×C4⋊C4C22×D8314yes—
448C2×C22⋊C4—834no—
449C2×C22⋊C4—834no—
450C2×C22⋊C4—834no—
451C2×C22⋊C4—834no—
452C2×C22⋊C4—834no—
453C2×C22⋊C4—834no—
454C2×C22⋊C4—1664no—
455C2×C22⋊C4—1664no—
456C2×C22⋊C4—1664no—
457C2×C22⋊C4—1664no—
458C2×C22⋊C4—1664no—
459C2×C22⋊C4—1664no—
460C2×C42—24no—
461C2×C42—24no—
462C2×C42—24no—
463C2×C42—834no—
464C2×C42—834no—
465C2×C42—834no—
466C2×C42—1664no—
467C2×C42—1664no—
468C2×C42—1664no—
469C2×C42C22×D8314yes—
470C2×C42C22×D8314yes—
471C2×C42C22×D8314yes—
472#95—834no—
473#95—834no—
474#95—834no—
475#95—834no—
476#95—834no—
477#95—834no—
478#95—834no—
479#95—834no—
480#95—834no—
481#95—834no—
482#95—834no—
483#95—834no—
484#95—834no—
485#95—834no—
486#95C22×D8314yes—
487#95C22×D8314yes—
488C24—834no—
489C24—832no—
490C24—1662no—
491C24—1662no—
492C24—1662no—
493C24—1662no—
494C24—1662no—
495C24—1662no—
496C24C23×D8311yescharacteristic
497C22×C4—22no—
498C22×C4—22no—
499C22×C4—22no—
500C22×C4—22no—
501C22×C4—22no—
502C22×C4—22no—
503C22×C4—22no—
504C22×C4—22no—
505C22×C4—22no—
506C22×C4—22no—
507C22×C4—22no—
508C22×C4—22no—
509C22×C4—22no—
510C22×C4—22no—
511C22×C4—22no—
512C22×C4—22no—
513C22×C4—33216no—
514C22×C4—834no—
515C22×C4—832no—
516C22×C4—832no—
517C22×C4—832no—
518C22×C4—832no—
519C22×C4—832no—
520C22×C4—832no—
521C22×C4—832no—
522C22×C4—1662no—
523C22×C4—1662no—
524C22×C4—1662no—
525C22×C4—1662no—
526C22×C4—1662no—
527C22×C4—1662no—
528C22×C4—1662no—
529C22×C4—1662no—
530C22×C4—1662no—
531C22×C4—1662no—
532C22×C4—1662no—
533C22×C4—1662no—
534C22×C4—1662no—
535C22×C4—1662no—
536C22×C4—1662no—
537C22×C4—1662no—
538C22×C4—1662no—
539C22×C4—1662no—
540C22×C4—1668no—
541C22×C4—1668no—
542C22×C4—1668no—
543C22×C4—1662no—
544C22×C4—1662no—
545C22×C4#1305058914yes—
546C22×C4#1305059014yes—
547C22×C4#1305059014yes—
548C22×C4#1305059014yes—
549C22×C4#1305059114yes—
550C22×C4C23×D8312yes—
551C22×C4C23×D8312yes—
552C22×C4C23×D8312yes—
553C22×C4C23×D8312yes—
554C22×C4C23×D8312yes—
555C22×C4C23×D8312yes—
556C22×C4C23×D8312yes—
557C4⋊C4—28no—
558C4⋊C4—28no—
559C4⋊C4—1668no—
560C4⋊C4—1668no—
561C4⋊C4—1668no—
562C4⋊C4—1668no—
563C22⋊C4—1668no—
564C22⋊C4—1668no—
565C22⋊C4—1668no—
566C22⋊C4—1668no—
567C22⋊C4—1668no—
568C22⋊C4—1668no—
569C42—28no—
570C42—28no—
571C42—28no—
572C42—1668no—
573C42—1668no—
574C42—1668no—
575C23—3324no—
576C23—3324no—
577C23—3324no—
578C23—3324no—
579C23—834no—
580C23—1668no—
581C23—1668no—
582C23—1668no—
583C23—1662no—
584C23—1662no—
585C23—1662no—
586C23—1662no—
587C23—1662no—
588C23—1662no—
589C23#41×D8312yes—
590C23#41×D8312yes—
591C23C2×#1305058912yes—
592C23C2×#1305059012yes—
593C23C2×#1305059012yes—
594C23C2×#1305059012yes—
595C23C2×#1305059112yes—
596C23C24×D8311yescharacteristic
597C2×C4—28no—
598C2×C4—28no—
599C2×C4—22no—
600C2×C4—22no—
601C2×C4—22no—
602C2×C4—22no—
603C2×C4—22no—
604C2×C4—22no—
605C2×C4—22no—
606C2×C4—22no—
607C2×C4—22no—
608C2×C4—22no—
609C2×C4—22no—
610C2×C4—22no—
611C2×C4—22no—
612C2×C4—22no—
613C2×C4—22no—
614C2×C4—22no—
615C2×C4—44no—
616C2×C4—44no—
617C2×C4—44no—
618C2×C4—44no—
619C2×C4—3324no—
620C2×C4—3324no—
621C2×C4—3324no—
622C2×C4—3324no—
623C2×C4—3324no—
624C2×C4—3324no—
625C2×C4—33216no—
626C2×C4—834no—
627C2×C4—1662no—
628C2×C4—1662no—
629C2×C4—1662no—
630C2×C4—1662no—
631C2×C4—1662no—
632C2×C4—1662no—
633C2×C4—1662no—
634C2×C4—1662no—
635C2×C4—1662no—
636C2×C4—1662no—
637C2×C4—1662no—
638C2×C4—1662no—
639C2×C4—1662no—
640C2×C4—1662no—
641C2×C4—1662no—
642C2×C4—1662no—
643C2×C4—1662no—
644C2×C4—1662no—
645C2×C4—1668no—
646C2×C4—1662no—
647C2×C4—1662no—
648C2×C4#14581787116yes—
649C2×C4C2×#1305058914yes—
650C2×C4C2×#1305059014yes—
651C2×C4C2×#1305059014yes—
652C2×C4C2×#1305059014yes—
653C2×C4C2×#1305059114yes—
654C22—3322no—
655C22—3322no—
656C22—3322no—
657C22—3322no—
658C22—33216no—
659C22—1664no—
660C22—1664no—
661C22—1664no—
662C22C2×#1458178714yes—
663C22#1912822914yes—
664C22#1912823114yes—
665C22#1912823314yes—
666C22#1912823514yes—
667C22#1912823814yes—
668C22#1912823814yes—
669C22C2×#41×D8311yescharacteristic
670C22C2×#41×D8311yescharacteristic
671C22C22×#1305058911yescharacteristic
672C22C22×#1305059011yescharacteristic
673C22C22×#1305059011yescharacteristic
674C22C22×#1305059011yescharacteristic
675C22C22×#1305059111yescharacteristic
676C4—24no—
677C4—24no—
678C4—42no—
679C4—42no—
680C4—42no—
681C4—42no—
682C4—3322no—
683C4—3322no—
684C4—3322no—
685C4—3322no—
686C4—3322no—
687C4—3322no—
688C4—1664no—
689C4C2×#1458178718yes—
690C2—3324no—
691C2#2491076418yesdirect product factor
692C2C22×#1458178711yescharacteristic
693C2C2×#1912822911yescharacteristic
694C2C2×#1912823111yescharacteristic
695C2C2×#1912823311yescharacteristic
696C2C2×#1912823511yescharacteristic
697C2C2×#1912823811yescharacteristic
698C2C2×#1912823811yescharacteristic
subgroupG/H
centerC23×C4C22×D83
commutator, cosocleC23×C83C25
FrattiniC23C24×D83
FittingC2×C4×C4⋊C4×C83C2
socleC24×C83C24
prime radicalC24×D83C23
hypercenterC2×C4×C4⋊C4D83
hypocenterC83C2×#2401
LCSG ▷ C23×C83 ▷ C83
UCSC1 ◁ C23×C4 ◁ C2×C4×C4⋊C4

Complements

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

NH ≅ G/Ntype
1. #24910764C2direct (N × H)
2. C2×C83⋊#401C2semidirect
3. C2×#19127643C2semidirect
4. C2×#19127640C2semidirect
5. C2×#19127639C2semidirect
10. C2×C4×Dic83⋊C4C2semidirect
11. C2×C4×C4⋊Dic83C2semidirect
15. C2×#19127547C2semidirect
16. C2×C4×C4⋊C4×C83C2semidirect
31. C83⋊#401C22semidirect
32. #19127643C22semidirect
33. #19127640C22semidirect
34. #19127639C22semidirect
39. C4×Dic83⋊C4C22semidirect
40. C4×C4⋊Dic83C22semidirect
44. #19127547C22semidirect
64. C4×C4⋊C4×C83C22semidirect
341. C2×C83#2401semidirect
361. C2×C4×C4⋊C4D83semidirect
366. C83C2×#2401semidirect
396. C4×C4⋊C4C2×D83semidirect
691. C2#24910764direct (N × H)

Maximal subgroups

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

subgroupindex
#249107642
C2×C83⋊#4012
C2×#191276432
C2×#191276402
C2×#191276392
C2×#191276302
C2×#191276282
C2×#191276272
C2×#191276232
C2×C4×Dic83⋊C42
C2×C4×C4⋊Dic832
C2×C4×(C2×D83)⋊C42
C2×#191275472
C2×C4×C4⋊C4×C832
C2×#240183