Finite Group Databasebeta

← C2×#24912483 #35575588

Subgroups — C2×#24912483 #35575588

Order 21248.

2574 conjugacy classes of subgroups.

The subgroup lattice has 692 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#14581791C211yesmaximal, characteristic
2C22×#14581782C211yesmaximal, characteristic
3#24912483C2116yesmaximal, direct product factor
4C2×#19127634C211yesmaximal, characteristic
5C2×#19127631C211yesmaximal, characteristic
6C2×#19127621C211yesmaximal, characteristic
7C2×#19127621C211yesmaximal, characteristic
8C2×#19127607C211yesmaximal, characteristic
9C2×#19127605C211yesmaximal, characteristic
10C2×#19127598C211yesmaximal, characteristic
11C2×#19127596C211yesmaximal, characteristic
12C2×#19127596C211yesmaximal, characteristic
13C2×#19127565C211yesmaximal, characteristic
14C2×C4×Dic83⋊C4C211yesmaximal, characteristic
15C2×#19127552C211yesmaximal, characteristic
16C2×#389×C83C211yesmaximal, characteristic
17C23×Dic166C2211yescharacteristic
18C23×Dic166C2211yescharacteristic
19C2×#14581791—28no—
20C2×#14581791C2218yes—
21C2×#14581782—28no—
22C2×#14581782C2218yes—
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×C4×Dic83C2211yescharacteristic
36C22×C4×Dic83C2211yescharacteristic
37C22×C4×Dic83C2211yescharacteristic
38C22×C4×Dic83C2211yescharacteristic
39#19127634C2218yes—
40#19127631C2218yes—
41#19127621C2218yes—
42#19127621C2218yes—
43#19127607C2218yes—
44#19127605C2218yes—
45#19127598C2218yes—
46#19127596C2218yes—
47#19127596C2218yes—
48#19127565C2218yes—
49C4×Dic83⋊C4C2218yes—
50#19127552C2218yes—
51C2×C83⋊#95C2211yescharacteristic
52C2×C83⋊#95C2211yescharacteristic
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×Dic166—24no—
73C22×Dic166—42no—
74C22×Dic166—42no—
75C22×Dic166C2314yes—
76C22×Dic166C2314yes—
77C23×Dic83C2311yescharacteristic
78C23×Dic83C2311yescharacteristic
79C23×Dic83C2311yescharacteristic
80C23×Dic83C2311yescharacteristic
81C23×Dic83C2311yescharacteristic
82C23×Dic83C2311yescharacteristic
83C23×Dic83C2311yescharacteristic
84C23×Dic83C2311yescharacteristic
85#14581791—232no—
86#14581782—232no—
87C2×C4⋊Dic83—24no—
88C2×C4⋊Dic83—24no—
89C2×C4⋊Dic83C2314yes—
90C2×C4⋊Dic83C2314yes—
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—24no—
98C2×Dic83⋊C4—42no—
99C2×Dic83⋊C4D418yes—
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×C4×Dic83—24no—
112C2×C4×Dic83—24no—
113C2×C4×Dic83—42no—
114C2×C4×Dic83Q818yescomplemented
115C2×C4×Dic83C2314yes—
116C2×C4×Dic83C2314yes—
117C2×C4×Dic83C2314yes—
118C2×C4×Dic83C2314yes—
119C83⋊#95C2314yes—
120C83⋊#95C2314yes—
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—28no—
149C2×Dic166—28no—
150C2×Dic166—28no—
151C2×Dic166—28no—
152C2×Dic166—44no—
153C2×Dic166—44no—
154C2×Dic166—416no—
155C2×Dic166—416no—
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×Dic83—22no—
170C22×Dic83—22no—
171C22×Dic83—22no—
172C22×Dic83—22no—
173C22×Dic83C2×D414yes—
174C22×Dic83C2×D414yes—
175C22×Dic83C2×Q814yes—
176C22×Dic83C2×Q814yes—
177C22×Dic83C2×Q814yes—
178C22×Dic83C2×Q814yes—
179C22×Dic83#4114yes—
180C22×Dic83C2412yes—
181C22×Dic83C2412yes—
182C22×Dic83C2412yes—
183C22×Dic83C2412yes—
184C22×Dic83C2412yes—
185C22×Dic83C2412yes—
186C22×Dic83C2412yes—
187C22×Dic83C2412yes—
188C4⋊Dic83—28no—
189C4⋊Dic83—28no—
190Dic83⋊C4—28no—
191Dic83⋊C4—28no—
192Dic83⋊C4—28no—
193Dic83⋊C4—28no—
194Dic83⋊C4—28no—
195Dic83⋊C4—28no—
196Dic83⋊C4—28no—
197Dic83⋊C4—44no—
198Dic83⋊C4C2×D4116yes—
199Dic83⋊C4C2×Q8116yescomplemented
200C4×Dic83—28no—
201C4×Dic83—28no—
202C4×Dic83—44no—
203C4×Dic83C2×Q8116yescomplemented
204C24×C83C2411yescharacteristic
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×C83—22no—
222C22×C4×C83C2×D414yes—
223C22×C4×C83C2×Q814yes—
224C22×C4×C83C2×Q814yes—
225C22×C4×C83#4114yes—
226C22×C4×C83C2412yes—
227C22×C4×C83C2412yes—
228C22×C4×C83C2412yes—
229C22×C4×C83C2412yes—
230C22×C4×C83C2412yes—
231C22×C4×C83C2412yes—
232C22×C4×C83C2412yes—
233C4⋊C4×C83—28no—
234C4⋊C4×C83—28no—
235C4⋊C4×C83—28no—
236C4⋊C4×C83—44no—
237C42×C83—44no—
238C23×C83C22×D412yes—
239C23×C83C22×Q812yes—
240C23×C83C22×Q812yes—
241C23×C83C2×#4112yes—
242C23×C83C2×#4112yes—
243C23×C83H(5,𝔽2)12yes—
244C23×C832−1+412yes—
245C23×C83C2511yescharacteristic
246C2×C4×C83—28no—
247C2×C4×C83—28no—
248C2×C4×C83—28no—
249C2×C4×C83—28no—
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—22no—
267C2×C4×C83—44no—
268C2×C4×C83—44no—
269C2×C4×C83—44no—
270C2×C4×C83C22×D414yes—
271C2×C4×C83C22×Q814yes—
272C2×C4×C83C22×Q814yes—
273C2×C4×C83C2×#4114yes—
274C2×Dic83—28no—
275C2×Dic83—28no—
276C2×Dic83—28no—
277C2×Dic83—28no—
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—44no—
296C2×Dic83—44no—
297C2×Dic83—44no—
298C2×Dic83C4⋊Q8116yes—
299C2×Dic83C22×D414yes—
300C2×Dic83C22×D414yes—
301C2×Dic83C22×Q814yes—
302C2×Dic83C22×Q814yes—
303C2×Dic83C22×Q814yes—
304C2×Dic83C22×Q814yes—
305C2×Dic83C2×#4114yes—
306Dic166—416no—
307Dic166—416no—
308C22×C83C2×C4⋊Q814yes—
309C22×C83#53314yes—
310C22×C83#54414yes—
311C22×C83#54614yes—
312C22×C83#54814yes—
313C22×C83#55414yes—
314C22×C83#55714yes—
315C22×C83C23×D411yescharacteristic
316C22×C83C23×Q811yescharacteristic
317C22×C83C23×Q811yescharacteristic
318C22×C83C22×#4111yescharacteristic
319C22×C83C22×#4111yescharacteristic
320C22×C83C2×H(5,𝔽2)11yescharacteristic
321C22×C83C2×2−1+411yescharacteristic
322C4×C83—24no—
323C4×C83—24no—
324C4×C83—24no—
325C4×C83—24no—
326C4×C83—42no—
327C4×C83—42no—
328C4×C83—42no—
329Dic83—24no—
330Dic83—24no—
331Dic83—24no—
332Dic83—24no—
333Dic83—42no—
334Dic83—42no—
335Dic83—42no—
336Dic83C2×C4⋊Q818yes—
337C2×#2550—831nomaximal, Sylow
338C2×C83#255018yescomplemented
339C2×C83C22×C4⋊Q811yescharacteristic
340C2×C83C2×#53311yescharacteristic
341C2×C83C2×#54411yescharacteristic
342C2×C83C2×#54611yescharacteristic
343C2×C83C2×#54811yescharacteristic
344C2×C83C2×#55411yescharacteristic
345C2×C83C2×#55711yescharacteristic
346C22×C4⋊Q8—831no—
347C22×#125—831no—
348#2550—8316no—
349C2×#398—831no—
350C2×#398—831no—
351C2×#395—831no—
352C2×#395—831no—
353C2×#391—831no—
354C2×#391—831no—
355C2×#389—831no—
356C2×#389—831no—
357C2×#389—831no—
358C2×#389D8311yescharacteristic
359C2×#382—831no—
360C2×C4×C4⋊C4—831no—
361C2×C4×C4⋊C4—831no—
362C83C2×#255011yescharacteristic, complemented, Sylow
363C23×Q8—831no—
364C23×Q8—831no—
365C2×C4⋊Q8—838no—
366C2×C4⋊Q8—1668no—
367C2×#125—838no—
368C2×#125—1668no—
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#391—838no—
395#391—838no—
396#389—838no—
397#389—838no—
398#389—838no—
399#389C2×D8318yes—
400#382—838no—
401C4×C4⋊C4—838no—
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×#95—831no—
412C2×#95—831no—
413C2×#95C2×D8311yescharacteristic
414C2×#95C2×D8311yescharacteristic
415C22×Q8—3322no—
416C22×Q8—3322no—
417C22×Q8—834no—
418C22×Q8—834no—
419C22×Q8—1664no—
420C22×Q8—1664no—
421C22×Q8—1664no—
422C22×Q8—1664no—
423C23×C4—831no—
424C23×C4—831no—
425C23×C4—831no—
426C23×C4—831no—
427C23×C4—831no—
428C23×C4—831no—
429C23×C4—831no—
430C23×C4—831no—
431C23×C4C22×D8311yescharacteristic
432C23×C4C22×D8311yescharacteristic
433C23×C4C22×D8311yescharacteristic
434C23×C4C22×D8311yescharacteristic
435C23×C4C22×D8311yescharacteristic
436C23×C4C22×D8311yescharacteristic
437C23×C4C22×D8311yescharacteristic
438C4⋊Q8—16632no—
439#125—16632no—
440C2×C4⋊C4—24no—
441C2×C4⋊C4—24no—
442C2×C4⋊C4—24no—
443C2×C4⋊C4—42no—
444C2×C4⋊C4—3322no—
445C2×C4⋊C4—834no—
446C2×C4⋊C4—838no—
447C2×C4⋊C4—838no—
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—834no—
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#95—834no—
491#95—834no—
492#95C22×D8314yes—
493#95C22×D8314yes—
494C24C23×D8311yescharacteristic
495C2×Q8—33216no—
496C2×Q8—3324no—
497C2×Q8—3324no—
498C2×Q8—33216no—
499C2×Q8—1668no—
500C2×Q8—1668no—
501C2×Q8—1668no—
502C2×Q8—1668no—
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—22no—
515C22×C4—22no—
516C22×C4—22no—
517C22×C4—22no—
518C22×C4—22no—
519C22×C4—22no—
520C22×C4—834no—
521C22×C4—834no—
522C22×C4—834no—
523C22×C4—832no—
524C22×C4—834no—
525C22×C4—834no—
526C22×C4—834no—
527C22×C4—834no—
528C22×C4—832no—
529C22×C4—832no—
530C22×C4—832no—
531C22×C4—832no—
532C22×C4—832no—
533C22×C4—832no—
534C22×C4—832no—
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×C4—1662no—
547C22×C4—1662no—
548C22×C4—1662no—
549C22×C4—1662no—
550C22×C4—1662no—
551C22×C4—1662no—
552C22×C4D4×D8314yes—
553C22×C4Q8×D8314yes—
554C22×C4Q8×D8314yes—
555C22×C4#1305059014yes—
556C22×C4C23×D8312yes—
557C22×C4C23×D8312yes—
558C22×C4C23×D8312yes—
559C22×C4C23×D8312yes—
560C22×C4C23×D8312yes—
561C22×C4C23×D8312yes—
562C22×C4C23×D8312yes—
563C4⋊C4—28no—
564C4⋊C4—28no—
565C4⋊C4—28no—
566C4⋊C4—44no—
567C4⋊C4—3324no—
568C4⋊C4—8316no—
569C4⋊C4—8316no—
570C4⋊C4—1668no—
571C4⋊C4—1668no—
572C4⋊C4—1668no—
573C4⋊C4—1668no—
574C4⋊C4—1668no—
575C4⋊C4—1668no—
576C4⋊C4—1668no—
577C4⋊C4—1668no—
578C4⋊C4—1668no—
579C42—44no—
580C42—3324no—
581C42—8316no—
582C42—1668no—
583C42—1668no—
584C23C2×D4×D8312yes—
585C23C2×Q8×D8312yes—
586C23C2×Q8×D8312yes—
587C23#41×D8312yes—
588C23C2×#1305059012yes—
589C23#1458183712yes—
590C23#1458183912yes—
591C23C24×D8311yescharacteristic
592Q8—33216no—
593Q8—33216no—
594C2×C4—28no—
595C2×C4—28no—
596C2×C4—28no—
597C2×C4—28no—
598C2×C4—22no—
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—3324no—
619C2×C4—3324no—
620C2×C4—3324no—
621C2×C4—8316no—
622C2×C4—834no—
623C2×C4—834no—
624C2×C4—834no—
625C2×C4—834no—
626C2×C4—834no—
627C2×C4—834no—
628C2×C4—834no—
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—1668no—
639C2×C4—1668no—
640C2×C4—1668no—
641C2×C4—1668no—
642C2×C4—1662no—
643C2×C4—1662no—
644C2×C4—1662no—
645C2×C4—1662no—
646C2×C4—1662no—
647C2×C4—1662no—
648C2×C4—1662no—
649C2×C4—1662no—
650C2×C4C2×D4×D8314yes—
651C2×C4C2×Q8×D8314yes—
652C2×C4C2×Q8×D8314yes—
653C2×C4C2×#1305059014yes—
654C22C4⋊Q8×D8314yes—
655C22#1912825514yes—
656C22#1912833014yes—
657C22#1912834014yes—
658C22#1912836014yes—
659C22#1912840614yes—
660C22#1912842814yes—
661C22C22×D4×D8311yescharacteristic
662C22C22×Q8×D8311yescharacteristic
663C22C22×Q8×D8311yescharacteristic
664C22C2×#41×D8311yescharacteristic
665C22C22×#1305059011yescharacteristic
666C22C2×#1458183711yescharacteristic
667C22C2×#1458183911yescharacteristic
668C4—24no—
669C4—24no—
670C4—24no—
671C4—24no—
672C4—42no—
673C4—42no—
674C4—42no—
675C4—3322no—
676C4—3322no—
677C4—3322no—
678C4—838no—
679C4—1664no—
680C4—1664no—
681C4—1664no—
682C4—1664no—
683C2#2491248318yesdirect product factor
684C2C2×C4⋊Q8×D8311yescharacteristic
685C2C2×#1912825511yescharacteristic
686C2C2×#1912833011yescharacteristic
687C2C2×#1912834011yescharacteristic
688C2C2×#1912836011yescharacteristic
689C2C2×#1912840611yescharacteristic
690C2C2×#1912842811yescharacteristic
subgroupG/H
centerC24C23×D83
commutator, cosocleC23×C83C25
FrattiniC23C24×D83
FittingC2×#389×C83C2
socle, prime radicalC24×C83C24
hypercenterC2×#389D83
hypocenterC83C2×#2550
LCSG ▷ C23×C83 ▷ C83
UCSC1 ◁ C24 ◁ C2×#389

Complements

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

NH ≅ G/Ntype
3. #24912483C2direct (N × H)
100. C2×Dic83⋊C4Q8semidirect
114. C2×C4×Dic83Q8semidirect
199. Dic83⋊C4C2×Q8semidirect
203. C4×Dic83C2×Q8semidirect
338. C2×C83#2550semidirect
362. C83C2×#2550semidirect
683. C2#24912483direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#145817912
C22×#145817822
#249124832
C2×#191276342
C2×#191276312
C2×#191276212
C2×#191276072
C2×#191276052
C2×#191275982
C2×#191275962
C2×#191275652
C2×C4×Dic83⋊C42
C2×#191275522
C2×#389×C832
C2×#255083