Finite Group Databasebeta

← C2×#24912849 #35575636

Subgroups — C2×#24912849 #35575636

Order 21248.

2574 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
1C22×#14581782C211yesmaximal, characteristic
2C22×#14581757C211yesmaximal, characteristic
3#24912849C2116yesmaximal, direct product factor
4C2×#19127635C211yesmaximal, characteristic
5C2×#19127634C211yesmaximal, characteristic
6C2×#19127622C211yesmaximal, characteristic
7C2×#19127621C211yesmaximal, characteristic
8C2×#19127599C211yesmaximal, characteristic
9C2×#19127598C211yesmaximal, characteristic
10C2×#19127598C211yesmaximal, characteristic
11C2×#19127596C211yesmaximal, characteristic
12C2×#19127596C211yesmaximal, characteristic
13C2×#19127596C211yesmaximal, characteristic
14C2×#19127596C211yesmaximal, characteristic
15C2×C4×Dic83⋊C4C211yesmaximal, characteristic
16C2×#389×C83C211yesmaximal, characteristic
17C23×Dic166C2211yescharacteristic
18C2×#14581782—28no—
19C2×#14581782C2218yes—
20C2×#14581757—28no—
21C2×#14581757C2218yes—
22C22×C4⋊Dic83C2211yescharacteristic
23C22×C4⋊Dic83C2211yescharacteristic
24C22×C4⋊Dic83C2211yescharacteristic
25C22×Dic83⋊C4C2211yescharacteristic
26C22×Dic83⋊C4C2211yescharacteristic
27C22×Dic83⋊C4C2211yescharacteristic
28C22×Dic83⋊C4C2211yescharacteristic
29C22×Dic83⋊C4C2211yescharacteristic
30C22×Dic83⋊C4C2211yescharacteristic
31C22×Dic83⋊C4C2211yescharacteristic
32C22×Dic83⋊C4C2211yescharacteristic
33C22×Dic83⋊C4C2211yescharacteristic
34C22×Dic83⋊C4C2211yescharacteristic
35C22×Dic83⋊C4C2211yescharacteristic
36C22×Dic83⋊C4C2211yescharacteristic
37C22×C4×Dic83C2211yescharacteristic
38C22×C4×Dic83C2211yescharacteristic
39C22×C4×Dic83C2211yescharacteristic
40C22×C4×Dic83C2211yescharacteristic
41#19127635C2218yes—
42#19127634C2218yes—
43#19127622C2218yes—
44#19127621C2218yes—
45#19127599C2218yes—
46#19127598C2218yes—
47#19127598C2218yes—
48#19127596C2218yes—
49#19127596C2218yes—
50#19127596C2218yes—
51#19127596C2218yes—
52C4×Dic83⋊C4C2218yes—
53C2×C83⋊#95C2211yescharacteristic
54C2×C83⋊#95C2211yescharacteristic
55C2×C83⋊#95C2211yescharacteristic
56C2×C83⋊#95C2211yescharacteristic
57C2×C83⋊#95C2211yescharacteristic
58C2×C83⋊#95C2211yescharacteristic
59C2×C83⋊#95C2211yescharacteristic
60C2×C83⋊#95C2211yescharacteristic
61C22×C4⋊C4×C83C2211yescharacteristic
62C22×C4⋊C4×C83C2211yescharacteristic
63C22×C4⋊C4×C83C2211yescharacteristic
64C22×C4⋊C4×C83C2211yescharacteristic
65C22×C42×C83C2211yescharacteristic
66#389×C83C2218yes—
67C2×#95×C83C2211yescharacteristic
68C2×#95×C83C2211yescharacteristic
69C22×Dic166—24no—
70C22×Dic166—24no—
71C22×Dic166—24no—
72C22×Dic166C2314yes—
73C23×Dic83C2311yescharacteristic
74C23×Dic83C2311yescharacteristic
75C23×Dic83C2311yescharacteristic
76C23×Dic83C2311yescharacteristic
77C23×Dic83C2311yescharacteristic
78C23×Dic83C2311yescharacteristic
79C23×Dic83C2311yescharacteristic
80C23×Dic83C2311yescharacteristic
81#14581782—232no—
82#14581757—232no—
83C2×C4⋊Dic83—24no—
84C2×C4⋊Dic83—24no—
85C2×C4⋊Dic83—42no—
86C2×C4⋊Dic83C2314yes—
87C2×C4⋊Dic83C2314yes—
88C2×C4⋊Dic83C2314yes—
89C2×Dic83⋊C4—24no—
90C2×Dic83⋊C4—24no—
91C2×Dic83⋊C4—24no—
92C2×Dic83⋊C4—24no—
93C2×Dic83⋊C4—24no—
94C2×Dic83⋊C4—24no—
95C2×Dic83⋊C4—24no—
96C2×Dic83⋊C4—24no—
97C2×Dic83⋊C4—42no—
98C2×Dic83⋊C4—42no—
99C2×Dic83⋊C4Q818yescomplemented
100C2×Dic83⋊C4Q818yescomplemented
101C2×Dic83⋊C4C2314yes—
102C2×Dic83⋊C4C2314yes—
103C2×Dic83⋊C4C2314yes—
104C2×Dic83⋊C4C2314yes—
105C2×Dic83⋊C4C2314yes—
106C2×Dic83⋊C4C2314yes—
107C2×Dic83⋊C4C2314yes—
108C2×Dic83⋊C4C2314yes—
109C2×Dic83⋊C4C2314yes—
110C2×Dic83⋊C4C2314yes—
111C2×Dic83⋊C4C2314yes—
112C2×Dic83⋊C4C2314yes—
113C2×C4×Dic83—24no—
114C2×C4×Dic83—24no—
115C2×C4×Dic83—42no—
116C2×C4×Dic83D418yes—
117C2×C4×Dic83C2314yes—
118C2×C4×Dic83C2314yes—
119C2×C4×Dic83C2314yes—
120C2×C4×Dic83C2314yes—
121C83⋊#95C2314yes—
122C83⋊#95C2314yes—
123C83⋊#95C2314yes—
124C83⋊#95C2314yes—
125C83⋊#95C2314yes—
126C83⋊#95C2314yes—
127C83⋊#95C2314yes—
128C83⋊#95C2314yes—
129C23×C4×C83C2311yescharacteristic
130C23×C4×C83C2311yescharacteristic
131C23×C4×C83C2311yescharacteristic
132C23×C4×C83C2311yescharacteristic
133C23×C4×C83C2311yescharacteristic
134C23×C4×C83C2311yescharacteristic
135C23×C4×C83C2311yescharacteristic
136C2×C4⋊C4×C83—24no—
137C2×C4⋊C4×C83—24no—
138C2×C4⋊C4×C83—24no—
139C2×C4⋊C4×C83—42no—
140C2×C4⋊C4×C83C2314yes—
141C2×C4⋊C4×C83C2314yes—
142C2×C4⋊C4×C83C2314yes—
143C2×C4⋊C4×C83C2314yes—
144C2×C42×C83—42no—
145C2×C42×C83C2314yes—
146#95×C83C2314yes—
147#95×C83C2314yes—
148C2×Dic166—232no—
149C2×Dic166—28no—
150C2×Dic166—28no—
151C2×Dic166—28no—
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—22no—
167C22×Dic83—22no—
168C22×Dic83—22no—
169C22×Dic83C2×D414yes—
170C22×Dic83C2×D414yes—
171C22×Dic83C2×Q814yes—
172C22×Dic83C2×Q814yes—
173C22×Dic83C2×Q814yes—
174C22×Dic83C2×Q814yes—
175C22×Dic83#4114yes—
176C22×Dic83C2412yes—
177C22×Dic83C2412yes—
178C22×Dic83C2412yes—
179C22×Dic83C2412yes—
180C22×Dic83C2412yes—
181C22×Dic83C2412yes—
182C22×Dic83C2412yes—
183C22×Dic83C2412yes—
184C4⋊Dic83—28no—
185C4⋊Dic83—28no—
186C4⋊Dic83—44no—
187Dic83⋊C4—28no—
188Dic83⋊C4—28no—
189Dic83⋊C4—28no—
190Dic83⋊C4—28no—
191Dic83⋊C4—28no—
192Dic83⋊C4—28no—
193Dic83⋊C4—28no—
194Dic83⋊C4—28no—
195Dic83⋊C4—44no—
196Dic83⋊C4—44no—
197Dic83⋊C4C2×Q8116yescomplemented
198Dic83⋊C4C2×Q8116yescomplemented
199C4×Dic83—28no—
200C4×Dic83—28no—
201C4×Dic83—44no—
202C4×Dic83C2×D4116yes—
203C24×C83C2411yescharacteristic
204C22×C4×C83—22no—
205C22×C4×C83—22no—
206C22×C4×C83—22no—
207C22×C4×C83—22no—
208C22×C4×C83—22no—
209C22×C4×C83—22no—
210C22×C4×C83—22no—
211C22×C4×C83—22no—
212C22×C4×C83—22no—
213C22×C4×C83—22no—
214C22×C4×C83—22no—
215C22×C4×C83—22no—
216C22×C4×C83—22no—
217C22×C4×C83—22no—
218C22×C4×C83—22no—
219C22×C4×C83—22no—
220C22×C4×C83—22no—
221C22×C4×C83C2×D414yes—
222C22×C4×C83C2×Q814yes—
223C22×C4×C83C2×Q814yes—
224C22×C4×C83#4114yes—
225C22×C4×C83C2412yes—
226C22×C4×C83C2412yes—
227C22×C4×C83C2412yes—
228C22×C4×C83C2412yes—
229C22×C4×C83C2412yes—
230C22×C4×C83C2412yes—
231C22×C4×C83C2412yes—
232C4⋊C4×C83—28no—
233C4⋊C4×C83—28no—
234C4⋊C4×C83—28no—
235C4⋊C4×C83—44no—
236C42×C83—44no—
237C23×C83C22×D412yes—
238C23×C83C22×Q812yes—
239C23×C83C22×Q812yes—
240C23×C83C2×#4112yes—
241C23×C83C2×#4112yes—
242C23×C83H(5,𝔽2)12yes—
243C23×C832−1+412yes—
244C23×C83C2511yescharacteristic
245C2×C4×C83—28no—
246C2×C4×C83—28no—
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—22no—
266C2×C4×C83—44no—
267C2×C4×C83—44no—
268C2×C4×C83—44no—
269C2×C4×C83C22×D414yes—
270C2×C4×C83C22×Q814yes—
271C2×C4×C83C22×Q814yes—
272C2×C4×C83C2×#4114yes—
273C2×Dic83—28no—
274C2×Dic83—28no—
275C2×Dic83—28no—
276C2×Dic83—28no—
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—44no—
295C2×Dic83—44no—
296C2×Dic83—44no—
297C2×Dic83C4⋊Q8116yes—
298C2×Dic83C22×D414yes—
299C2×Dic83C22×D414yes—
300C2×Dic83C22×Q814yes—
301C2×Dic83C22×Q814yes—
302C2×Dic83C22×Q814yes—
303C2×Dic83C22×Q814yes—
304C2×Dic83C2×#4114yes—
305Dic166—232no—
306C22×C83#52514yes—
307C22×C83C2×C4⋊Q814yes—
308C22×C83#53714yes—
309C22×C83#55414yes—
310C22×C83#55414yes—
311C22×C83#55714yes—
312C22×C83#55714yes—
313C22×C83C23×D411yescharacteristic
314C22×C83C23×Q811yescharacteristic
315C22×C83C23×Q811yescharacteristic
316C22×C83C22×#4111yescharacteristic
317C22×C83C22×#4111yescharacteristic
318C22×C83C2×H(5,𝔽2)11yescharacteristic
319C22×C83C2×2−1+411yescharacteristic
320C4×C83—24no—
321C4×C83—24no—
322C4×C83—24no—
323C4×C83—24no—
324C4×C83—42no—
325C4×C83—42no—
326C4×C83—42no—
327Dic83—24no—
328Dic83—24no—
329Dic83—24no—
330Dic83—24no—
331Dic83—42no—
332Dic83—42no—
333Dic83—42no—
334Dic83C2×C4⋊Q818yes—
335C2×#2584—831nomaximal, Sylow
336C2×C83#258418yescomplemented
337C2×C83C2×#52511yescharacteristic
338C2×C83C22×C4⋊Q811yescharacteristic
339C2×C83C2×#53711yescharacteristic
340C2×C83C2×#55411yescharacteristic
341C2×C83C2×#55411yescharacteristic
342C2×C83C2×#55711yescharacteristic
343C2×C83C2×#55711yescharacteristic
344C22×#125—831no—
345C22×C4×Q8—831no—
346#2584—8316no—
347C2×#398—831no—
348C2×#398—831no—
349C2×#395—831no—
350C2×#395—831no—
351C2×#389—831no—
352C2×#389—831no—
353C2×#389—831no—
354C2×#389—831no—
355C2×#389—831no—
356C2×#389—831no—
357C2×#389—831no—
358C2×#389D8311yescharacteristic
359C2×C4×C4⋊C4—831no—
360C83C2×#258411yescharacteristic, complemented, Sylow
361C23×Q8—831no—
362C2×#125—838no—
363C2×#125—1668no—
364C2×C4×Q8—838no—
365C2×C4×Q8—1668no—
366C22×C4⋊C4—831no—
367C22×C4⋊C4—831no—
368C22×C4⋊C4—831no—
369C22×C4⋊C4—831no—
370C22×C4⋊C4—831no—
371C22×C4⋊C4—831no—
372C22×C4⋊C4—831no—
373C22×C4⋊C4—831no—
374C22×C4⋊C4—831no—
375C22×C4⋊C4—831no—
376C22×C4⋊C4—831no—
377C22×C4⋊C4—831no—
378C22×C4⋊C4—831no—
379C22×C4⋊C4—831no—
380C22×C4⋊C4—831no—
381C22×C4⋊C4C2×D8311yescharacteristic
382C22×C4⋊C4C2×D8311yescharacteristic
383C22×C4⋊C4C2×D8311yescharacteristic
384C22×C4⋊C4C2×D8311yescharacteristic
385C22×C42—831no—
386C22×C42—831no—
387C22×C42—831no—
388C22×C42—831no—
389C22×C42C2×D8311yescharacteristic
390#398—838no—
391#398—838no—
392#395—838no—
393#395—838no—
394#389—838no—
395#389—838no—
396#389—838no—
397#389—838no—
398#389—838no—
399#389—838no—
400#389—838no—
401#389C2×D8318yes—
402C4×C4⋊C4—838no—
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×#95C2×D8311yescharacteristic
412C2×#95C2×D8311yescharacteristic
413C22×Q8—834no—
414C22×Q8—1664no—
415C22×Q8—1664no—
416C22×Q8—1664no—
417C23×C4—831no—
418C23×C4—831no—
419C23×C4—831no—
420C23×C4—831no—
421C23×C4—831no—
422C23×C4—831no—
423C23×C4—831no—
424C23×C4—831no—
425C23×C4C22×D8311yescharacteristic
426C23×C4C22×D8311yescharacteristic
427C23×C4C22×D8311yescharacteristic
428C23×C4C22×D8311yescharacteristic
429C23×C4C22×D8311yescharacteristic
430C23×C4C22×D8311yescharacteristic
431C23×C4C22×D8311yescharacteristic
432#125—16632no—
433C4×Q8—16632no—
434C2×C4⋊C4—24no—
435C2×C4⋊C4—24no—
436C2×C4⋊C4—24no—
437C2×C4⋊C4—42no—
438C2×C4⋊C4—3322no—
439C2×C4⋊C4—3322no—
440C2×C4⋊C4—3322no—
441C2×C4⋊C4—834no—
442C2×C4⋊C4—834no—
443C2×C4⋊C4—834no—
444C2×C4⋊C4—838no—
445C2×C4⋊C4—838no—
446C2×C4⋊C4—834no—
447C2×C4⋊C4—834no—
448C2×C4⋊C4—834no—
449C2×C4⋊C4—834no—
450C2×C4⋊C4—834no—
451C2×C4⋊C4—834no—
452C2×C4⋊C4—834no—
453C2×C4⋊C4—834no—
454C2×C4⋊C4—834no—
455C2×C4⋊C4—834no—
456C2×C4⋊C4—834no—
457C2×C4⋊C4—834no—
458C2×C4⋊C4—1664no—
459C2×C4⋊C4—1664no—
460C2×C4⋊C4—1664no—
461C2×C4⋊C4—1664no—
462C2×C4⋊C4—1664no—
463C2×C4⋊C4—1664no—
464C2×C4⋊C4—1664no—
465C2×C4⋊C4—1664no—
466C2×C4⋊C4—1664no—
467C2×C4⋊C4—1664no—
468C2×C4⋊C4C22×D8314yes—
469C2×C4⋊C4C22×D8314yes—
470C2×C4⋊C4C22×D8314yes—
471C2×C4⋊C4C22×D8314yes—
472C2×C42—42no—
473C2×C42—3322no—
474C2×C42—834no—
475C2×C42—838no—
476C2×C42—834no—
477C2×C42—834no—
478C2×C42—834no—
479C2×C42—1664no—
480C2×C42—1664no—
481C2×C42C22×D8314yes—
482#95—834no—
483#95—834no—
484#95—834no—
485#95—834no—
486#95—834no—
487#95—834no—
488#95—834no—
489#95—834no—
490#95C22×D8314yes—
491#95C22×D8314yes—
492C24C23×D8311yescharacteristic
493C2×Q8—1668no—
494C2×Q8—1668no—
495C2×Q8—16632no—
496C2×Q8—1668no—
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—22no—
514C22×C4—834no—
515C22×C4—834no—
516C22×C4—834no—
517C22×C4—832no—
518C22×C4—834no—
519C22×C4—834no—
520C22×C4—834no—
521C22×C4—834no—
522C22×C4—832no—
523C22×C4—832no—
524C22×C4—832no—
525C22×C4—832no—
526C22×C4—832no—
527C22×C4—832no—
528C22×C4—832no—
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—1662no—
541C22×C4—1662no—
542C22×C4—1662no—
543C22×C4—1662no—
544C22×C4—1662no—
545C22×C4—1662no—
546C22×C4D4×D8314yes—
547C22×C4Q8×D8314yes—
548C22×C4Q8×D8314yes—
549C22×C4#1305059014yes—
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—28no—
560C4⋊C4—44no—
561C4⋊C4—3324no—
562C4⋊C4—3324no—
563C4⋊C4—3324no—
564C4⋊C4—8316no—
565C4⋊C4—8316no—
566C4⋊C4—1668no—
567C4⋊C4—1668no—
568C4⋊C4—1668no—
569C4⋊C4—1668no—
570C4⋊C4—1668no—
571C4⋊C4—1668no—
572C4⋊C4—1668no—
573C4⋊C4—1668no—
574C4⋊C4—1668no—
575C4⋊C4—1668no—
576C42—44no—
577C42—3324no—
578C42—8316no—
579C42—1668no—
580C42—1668no—
581C23C2×D4×D8312yes—
582C23C2×Q8×D8312yes—
583C23C2×Q8×D8312yes—
584C23#41×D8312yes—
585C23C2×#1305059012yes—
586C23#1458183712yes—
587C23#1458183912yes—
588C23C24×D8311yescharacteristic
589Q8—16632no—
590C2×C4—28no—
591C2×C4—28no—
592C2×C4—28no—
593C2×C4—22no—
594C2×C4—22no—
595C2×C4—22no—
596C2×C4—22no—
597C2×C4—22no—
598C2×C4—22no—
599C2×C4—22no—
600C2×C4—28no—
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—44no—
612C2×C4—44no—
613C2×C4—44no—
614C2×C4—3324no—
615C2×C4—3324no—
616C2×C4—3324no—
617C2×C4—8316no—
618C2×C4—834no—
619C2×C4—834no—
620C2×C4—834no—
621C2×C4—834no—
622C2×C4—834no—
623C2×C4—834no—
624C2×C4—834no—
625C2×C4—1662no—
626C2×C4—1662no—
627C2×C4—1662no—
628C2×C4—1662no—
629C2×C4—1662no—
630C2×C4—1662no—
631C2×C4—1662no—
632C2×C4—1662no—
633C2×C4—1662no—
634C2×C4—1668no—
635C2×C4—1668no—
636C2×C4—1668no—
637C2×C4—1668no—
638C2×C4—1662no—
639C2×C4—1662no—
640C2×C4—1662no—
641C2×C4—1662no—
642C2×C4—1662no—
643C2×C4—1662no—
644C2×C4—1662no—
645C2×C4—1662no—
646C2×C4C2×D4×D8314yes—
647C2×C4C2×Q8×D8314yes—
648C2×C4C2×Q8×D8314yes—
649C2×C4C2×#1305059014yes—
650C22#1912821014yes—
651C22C4⋊Q8×D8314yes—
652C22#1912827814yes—
653C22#1912840514yes—
654C22#1912840614yes—
655C22#1912842814yes—
656C22#1912842914yes—
657C22C22×D4×D8311yescharacteristic
658C22C22×Q8×D8311yescharacteristic
659C22C22×Q8×D8311yescharacteristic
660C22C2×#41×D8311yescharacteristic
661C22C22×#1305059011yescharacteristic
662C22C2×#1458183711yescharacteristic
663C22C2×#1458183911yescharacteristic
664C4—24no—
665C4—24no—
666C4—24no—
667C4—24no—
668C4—42no—
669C4—42no—
670C4—42no—
671C4—3322no—
672C4—3322no—
673C4—3322no—
674C4—838no—
675C4—1664no—
676C4—1664no—
677C4—1664no—
678C4—1664no—
679C2#2491284918yesdirect product factor
680C2C2×#1912821011yescharacteristic
681C2C2×C4⋊Q8×D8311yescharacteristic
682C2C2×#1912827811yescharacteristic
683C2C2×#1912840511yescharacteristic
684C2C2×#1912840611yescharacteristic
685C2C2×#1912842811yescharacteristic
686C2C2×#1912842911yescharacteristic
subgroupG/H
centerC24C23×D83
commutator, cosocleC23×C83C25
FrattiniC23C24×D83
FittingC2×#389×C83C2
socle, prime radicalC24×C83C24
hypercenterC2×#389D83
hypocenterC83C2×#2584
LCSG ▷ C23×C83 ▷ C83
UCSC1 ◁ C24 ◁ C2×#389

Complements

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

NH ≅ G/Ntype
3. #24912849C2direct (N × H)
99. C2×Dic83⋊C4Q8semidirect
100. C2×Dic83⋊C4Q8semidirect
197. Dic83⋊C4C2×Q8semidirect
198. Dic83⋊C4C2×Q8semidirect
336. C2×C83#2584semidirect
360. C83C2×#2584semidirect
679. C2#24912849direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#145817822
C22×#145817572
#249128492
C2×#191276352
C2×#191276342
C2×#191276222
C2×#191276212
C2×#191275992
C2×#191275982
C2×#191275962
C2×C4×Dic83⋊C42
C2×#389×C832
C2×#258483