Finite Group Databasebeta

← C2×#24913464 #35570909

Subgroups — C2×#24913464 #35570909

Order 21248.

2330 conjugacy classes of subgroups.

The subgroup lattice has 772 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#24913464C2116yesmaximal, direct product factor
2C2×#19127642C211yesmaximal, characteristic, complemented
3C2×#19127642C211yesmaximal, characteristic, complemented
4C2×#19127636C211yesmaximal, characteristic, complemented
5C2×#19127630C211yesmaximal, characteristic, complemented
6C2×#19127628C211yesmaximal, characteristic, complemented
7C2×#19127623C211yesmaximal, characteristic, complemented
8C2×#19127619C211yesmaximal, characteristic
9C2×#19127619C211yesmaximal, characteristic
10C2×#19127598C211yesmaximal, characteristic, complemented
11C2×#19127592C211yesmaximal, characteristic, complemented
12C2×#19127591C211yesmaximal, characteristic, complemented
13C2×#19127579C211yesmaximal, characteristic
14C2×#19127572C211yesmaximal, characteristic, complemented
15C2×C4×(C2×D83)⋊C4C211yesmaximal, characteristic, complemented
16C2×#387×C83C211yesmaximal, characteristic, complemented
17C23×D332C2211yescharacteristic
18C23×C4×D83C2211yescharacteristic
19C22×C4⋊Dic83C2211yescharacteristic
20C22×Dic83⋊C4C2211yescharacteristic
21C22×Dic83⋊C4C2211yescharacteristic
22C22×Dic83⋊C4C2211yescharacteristic
23C22×Dic83⋊C4C2211yescharacteristic
24C22×Dic83⋊C4C2211yescharacteristic
25C22×(C2×D83)⋊C4C2211yescharacteristic
26C22×(C2×D83)⋊C4C2211yescharacteristic
27C22×(C2×D83)⋊C4C2211yescharacteristic
28C22×(C2×D83)⋊C4C2211yescharacteristic
29C22×(C2×D83)⋊C4C2211yescharacteristic
30C22×(C2×D83)⋊C4C2211yescharacteristic
31C22×(C2×D83)⋊C4C2211yescharacteristic
32C22×(C2×D83)⋊C4C2211yescharacteristic
33C22×(C2×D83)⋊C4C2211yescharacteristic
34C22×(C2×D83)⋊C4C2211yescharacteristic
35C22×(C2×D83)⋊C4C2211yescharacteristic
36C22×C4×Dic83C2211yescharacteristic
37#19127642C2218yescomplemented
38#19127642C2218yescomplemented
39#19127636C2218yescomplemented
40#19127630C2218yescomplemented
41#19127628C2218yescomplemented
42#19127623C2218yescomplemented
43#19127619C2218yes—
44#19127619C2218yes—
45#19127598C2218yescomplemented
46#19127592C2218yescomplemented
47#19127591C2218yescomplemented
48#19127579C2218yes—
49#19127572C2218yescomplemented
50C4×(C2×D83)⋊C4C2218yescomplemented
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
62#387×C83C2218yescomplemented
63C2×#95×C83C2211yescharacteristic
64C2×#95×C83C2211yescharacteristic
65C2×#95×C83C2211yescharacteristic
66C2×#95×C83C2211yescharacteristic
67C24×D83C2311yescharacteristic
68C24×D83C2311yescharacteristic
69C22×D332—24no—
70C22×D332—42no—
71C22×D332—42no—
72C22×D332C2314yes—
73C23×Dic83C2311yescharacteristic
74C23×Dic83C2311yescharacteristic
75C23×Dic83C2311yescharacteristic
76C23×Dic83C2311yescharacteristic
77C23×Dic83C2311yescharacteristic
78C23×Dic83C2311yescharacteristic
79C22×C4×D83—24no—
80C22×C4×D83—42no—
81C22×C4×D83—42no—
82C22×C4×D83C2314yes—
83C2×C4⋊Dic83—42no—
84C2×C4⋊Dic83C2314yes—
85C2×Dic83⋊C4—24no—
86C2×Dic83⋊C4—42no—
87C2×Dic83⋊C4—42no—
88C2×Dic83⋊C4—42no—
89C2×Dic83⋊C4—42no—
90C2×Dic83⋊C4C2314yes—
91C2×Dic83⋊C4C2314yes—
92C2×Dic83⋊C4C2314yes—
93C2×Dic83⋊C4C2314yes—
94C2×Dic83⋊C4C2314yes—
95C2×(C2×D83)⋊C4—24no—
96C2×(C2×D83)⋊C4—24no—
97C2×(C2×D83)⋊C4—24no—
98C2×(C2×D83)⋊C4—24no—
99C2×(C2×D83)⋊C4—24no—
100C2×(C2×D83)⋊C4—42no—
101C2×(C2×D83)⋊C4—42no—
102C2×(C2×D83)⋊C4—42no—
103C2×(C2×D83)⋊C4—42no—
104C2×(C2×D83)⋊C4—42no—
105C2×(C2×D83)⋊C4—42no—
106C2×(C2×D83)⋊C4C2314yes—
107C2×(C2×D83)⋊C4C2314yes—
108C2×(C2×D83)⋊C4C2314yes—
109C2×(C2×D83)⋊C4C2314yes—
110C2×(C2×D83)⋊C4C2314yes—
111C2×(C2×D83)⋊C4C2314yes—
112C2×(C2×D83)⋊C4C2314yes—
113C2×(C2×D83)⋊C4C2314yes—
114C2×(C2×D83)⋊C4C2314yes—
115C2×(C2×D83)⋊C4C2314yes—
116C2×(C2×D83)⋊C4C2314yes—
117C2×C4×Dic83—42no—
118C2×C4×Dic83C2314yes—
119C83⋊#95C2314yes—
120C83⋊#95C2314yes—
121C83⋊#95C2314yes—
122C83⋊#95C2314yes—
123C83⋊#95C2314yes—
124C83⋊#95C2314yes—
125C83⋊#95C2314yes—
126C83⋊#95C2314yes—
127C23×C4×C83C2311yescharacteristic
128C23×C4×C83C2311yescharacteristic
129C23×C4×C83C2311yescharacteristic
130C23×C4×C83C2311yescharacteristic
131C23×C4×C83C2311yescharacteristic
132C23×C4×C83C2311yescharacteristic
133C23×C4×C83C2311yescharacteristic
134C2×C4⋊C4×C83—24no—
135C2×C4⋊C4×C83—42no—
136C2×C4⋊C4×C83C2314yes—
137C2×C4⋊C4×C83C2314yes—
138C2×C42×C83—42no—
139C2×C42×C83C2314yes—
140#95×C83C2314yes—
141#95×C83C2314yes—
142#95×C83C2314yes—
143#95×C83C2314yes—
144C23×D83—22no—
145C23×D83—22no—
146C23×D83—22no—
147C23×D83—22no—
148C23×D83—22no—
149C23×D83—22no—
150C23×D83—22no—
151C23×D83—22no—
152C23×D83—22no—
153C23×D83—22no—
154C23×D83—22no—
155C23×D83—22no—
156C23×D83—22no—
157C23×D83#4114yes—
158C23×D83C2412yes—
159C23×D83C2412yes—
160C2×D332—28no—
161C2×D332—44no—
162C2×D332—44no—
163C2×D332—416no—
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×Dic83—22no—
174C22×Dic83—22no—
175C22×Dic83—22no—
176C22×Dic83—22no—
177C22×Dic83—22no—
178C22×Dic83—22no—
179C22×Dic83—22no—
180C22×Dic83—22no—
181C22×Dic83#4114yes—
182C22×Dic83C2412yes—
183C22×Dic83C2412yes—
184C22×Dic83C2412yes—
185C22×Dic83C2412yes—
186C22×Dic83C2412yes—
187C22×Dic83C2412yes—
188C2×C4×D83—28no—
189C2×C4×D83—44no—
190C2×C4×D83—44no—
191C2×C4×D83—416no—
192C4⋊Dic83—44no—
193Dic83⋊C4—28no—
194Dic83⋊C4—44no—
195Dic83⋊C4—44no—
196Dic83⋊C4—44no—
197Dic83⋊C4—44no—
198(C2×D83)⋊C4—28no—
199(C2×D83)⋊C4—28no—
200(C2×D83)⋊C4—28no—
201(C2×D83)⋊C4—28no—
202(C2×D83)⋊C4—28no—
203(C2×D83)⋊C4—44no—
204(C2×D83)⋊C4—44no—
205(C2×D83)⋊C4—44no—
206(C2×D83)⋊C4—44no—
207(C2×D83)⋊C4—44no—
208(C2×D83)⋊C4—44no—
209C4×Dic83—44no—
210C24×C83C2411yescharacteristic
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×C83—22no—
223C22×C4×C83—22no—
224C22×C4×C83—22no—
225C22×C4×C83—22no—
226C22×C4×C83—22no—
227C22×C4×C83—22no—
228C22×C4×C83—22no—
229C22×C4×C83—22no—
230C22×C4×C83—22no—
231C22×C4×C83#4114yes—
232C22×C4×C83C2412yes—
233C22×C4×C83C2412yes—
234C22×C4×C83C2412yes—
235C22×C4×C83C2412yes—
236C22×C4×C83C2412yes—
237C22×C4×C83C2412yes—
238C22×C4×C83C2412yes—
239C4⋊C4×C83—28no—
240C4⋊C4×C83—44no—
241C42×C83—44no—
242C23×C83C2×#4112yes—
243C23×C83C2×#4112yes—
244C23×C83C2×#4112yes—
245C23×C83H(5,𝔽2)12yes—
246C23×C83H(5,𝔽2)12yes—
247C23×C83H(5,𝔽2)12yes—
248C23×C832−1+412yes—
249C23×C83C2511yescharacteristic
250C22×D83—28no—
251C22×D83—28no—
252C22×D83—28no—
253C22×D83—22no—
254C22×D83—22no—
255C22×D83—22no—
256C22×D83—22no—
257C22×D83—22no—
258C22×D83—22no—
259C22×D83—22no—
260C22×D83—22no—
261C22×D83—22no—
262C22×D83—22no—
263C22×D83—22no—
264C22×D83—22no—
265C22×D83—22no—
266C22×D83—44no—
267C22×D83—44no—
268C22×D83—44no—
269C22×D83—44no—
270C22×D83—44no—
271C22×D83—44no—
272C22×D83—44no—
273C22×D83—44no—
274C22×D83—44no—
275C22×D83—44no—
276C22×D83—44no—
277C22×D83C2×#4114yes—
278C2×C4×C83—28no—
279C2×C4×C83—22no—
280C2×C4×C83—22no—
281C2×C4×C83—22no—
282C2×C4×C83—22no—
283C2×C4×C83—22no—
284C2×C4×C83—22no—
285C2×C4×C83—22no—
286C2×C4×C83—22no—
287C2×C4×C83—22no—
288C2×C4×C83—22no—
289C2×C4×C83—22no—
290C2×C4×C83—22no—
291C2×C4×C83—22no—
292C2×C4×C83—22no—
293C2×C4×C83—22no—
294C2×C4×C83—22no—
295C2×C4×C83—22no—
296C2×C4×C83—22no—
297C2×C4×C83—22no—
298C2×C4×C83—22no—
299C2×C4×C83—44no—
300C2×C4×C83—44no—
301C2×C4×C83—44no—
302C2×C4×C83—44no—
303C2×C4×C83—44no—
304C2×C4×C83—44no—
305C2×C4×C83C2×#4114yes—
306C2×Dic83—28no—
307C2×Dic83—22no—
308C2×Dic83—22no—
309C2×Dic83—22no—
310C2×Dic83—22no—
311C2×Dic83—22no—
312C2×Dic83—22no—
313C2×Dic83—22no—
314C2×Dic83—22no—
315C2×Dic83—22no—
316C2×Dic83—22no—
317C2×Dic83—22no—
318C2×Dic83—22no—
319C2×Dic83—22no—
320C2×Dic83—22no—
321C2×Dic83—22no—
322C2×Dic83—22no—
323C2×Dic83—22no—
324C2×Dic83—44no—
325C2×Dic83—44no—
326C2×Dic83—44no—
327C2×Dic83—44no—
328C2×Dic83—44no—
329C2×Dic83C2×#4114yes—
330D332—416no—
331C4×D83—416no—
332C22×C83#52914yes—
333C22×C83#53814yes—
334C22×C83#53814yes—
335C22×C83#53914yes—
336C22×C83#53914yes—
337C22×C83#54014yes—
338C22×C83#54214yes—
339C22×C83C22×#4111yescharacteristic
340C22×C83C22×#4111yescharacteristic
341C22×C83C22×#4111yescharacteristic
342C22×C83C2×H(5,𝔽2)11yescharacteristic
343C22×C83C2×H(5,𝔽2)11yescharacteristic
344C22×C83C2×H(5,𝔽2)11yescharacteristic
345C22×C83C2×2−1+411yescharacteristic
346C2×D83—24no—
347C2×D83—24no—
348C2×D83—24no—
349C2×D83—416no—
350C2×D83—42no—
351C2×D83—42no—
352C2×D83—42no—
353C2×D83—42no—
354C2×D83—42no—
355C2×D83—42no—
356C2×D83—42no—
357C2×D83—42no—
358C2×D83—42no—
359C2×D83—42no—
360C2×D83—42no—
361C2×D83—88no—
362C4×C83—24no—
363C4×C83—42no—
364C4×C83—42no—
365C4×C83—42no—
366C4×C83—42no—
367C4×C83—42no—
368C4×C83—42no—
369Dic83—24no—
370Dic83—42no—
371Dic83—42no—
372Dic83—42no—
373Dic83—42no—
374Dic83—42no—
375C2×#2649—831nomaximal, Sylow
376C2×C83#264918yescomplemented
377C2×C83C2×#52911yescharacteristic
378C2×C83C2×#53811yescharacteristic
379C2×C83C2×#53811yescharacteristic
380C2×C83C2×#53911yescharacteristic
381C2×C83C2×#53911yescharacteristic
382C2×C83C2×#54011yescharacteristic
383C2×C83C2×#54211yescharacteristic
384D83—44no—
385D83—82no—
386#2649—8316no—
387C2×#400—831no—
388C2×#400—831no—
389C2×#399—831no—
390C2×#397—831no—
391C2×#397—831no—
392C2×#396—831no—
393C2×#394—831no—
394C2×#394—831no—
395C2×#389—831no—
396C2×#388—831no—
397C2×#388—831no—
398C2×#387D8311yescharacteristic, complemented
399C2×#386—831no—
400C2×#385—831no—
401C2×C4×C22⋊C4—831no—
402C83C2×#264911yescharacteristic, complemented, Sylow
403C23×D4—831no—
404C24×C4—831no—
405C22×C4⋊C4—831no—
406C22×C4⋊C4—831no—
407C22×C4⋊C4—831no—
408C22×C4⋊C4—831no—
409C22×C4⋊C4—831no—
410C22×C4⋊C4—831no—
411C22×C4⋊C4C2×D8311yescharacteristic
412C22×C4⋊C4C2×D8311yescharacteristic
413C22×C22⋊C4—831no—
414C22×C22⋊C4—831no—
415C22×C22⋊C4—831no—
416C22×C22⋊C4—831no—
417C22×C22⋊C4—831no—
418C22×C22⋊C4—831no—
419C22×C22⋊C4—831no—
420C22×C22⋊C4—831no—
421C22×C22⋊C4—831no—
422C22×C22⋊C4—831no—
423C22×C22⋊C4—831no—
424C22×C42—831no—
425C22×C42C2×D8311yescharacteristic
426#400—838no—
427#400—838no—
428#399—838no—
429#397—838no—
430#397—838no—
431#396—838no—
432#394—838no—
433#394—838no—
434#389—838no—
435#388—838no—
436#388—838no—
437#387C2×D8318yescomplemented
438#386—838no—
439#385—838no—
440C4×C22⋊C4—838no—
441C2×#95—831no—
442C2×#95—831no—
443C2×#95—831no—
444C2×#95—831no—
445C2×#95—831no—
446C2×#95—831no—
447C2×#95—831no—
448C2×#95—831no—
449C2×#95C2×D8311yescharacteristic
450C2×#95C2×D8311yescharacteristic
451C2×#95C2×D8311yescharacteristic
452C2×#95C2×D8311yescharacteristic
453C25—831no—
454C25—831no—
455C22×D4—3322no—
456C22×D4—3322no—
457C22×D4—834no—
458C22×D4—1664no—
459C23×C4—3322no—
460C23×C4—3322no—
461C23×C4—834no—
462C23×C4—831no—
463C23×C4—831no—
464C23×C4—831no—
465C23×C4—831no—
466C23×C4—831no—
467C23×C4—831no—
468C23×C4—1664no—
469C23×C4C22×D8311yescharacteristic
470C23×C4C22×D8311yescharacteristic
471C23×C4C22×D8311yescharacteristic
472C23×C4C22×D8311yescharacteristic
473C23×C4C22×D8311yescharacteristic
474C23×C4C22×D8311yescharacteristic
475C23×C4C22×D8311yescharacteristic
476C2×C4⋊C4—24no—
477C2×C4⋊C4—42no—
478C2×C4⋊C4—3322no—
479C2×C4⋊C4—3322no—
480C2×C4⋊C4—3322no—
481C2×C4⋊C4—3322no—
482C2×C4⋊C4—3322no—
483C2×C4⋊C4—834no—
484C2×C4⋊C4—834no—
485C2×C4⋊C4—834no—
486C2×C4⋊C4—834no—
487C2×C4⋊C4—834no—
488C2×C4⋊C4—834no—
489C2×C4⋊C4—1664no—
490C2×C4⋊C4C22×D8314yes—
491C2×C4⋊C4C22×D8314yes—
492C2×C22⋊C4—3322no—
493C2×C22⋊C4—3322no—
494C2×C22⋊C4—3322no—
495C2×C22⋊C4—3322no—
496C2×C22⋊C4—3322no—
497C2×C22⋊C4—3322no—
498C2×C22⋊C4—834no—
499C2×C22⋊C4—834no—
500C2×C22⋊C4—834no—
501C2×C22⋊C4—834no—
502C2×C22⋊C4—834no—
503C2×C22⋊C4—834no—
504C2×C22⋊C4—834no—
505C2×C22⋊C4—834no—
506C2×C22⋊C4—834no—
507C2×C22⋊C4—834no—
508C2×C22⋊C4—834no—
509C2×C22⋊C4—1664no—
510C2×C22⋊C4—1664no—
511C2×C22⋊C4—1664no—
512C2×C22⋊C4—1664no—
513C2×C22⋊C4—1664no—
514C2×C42—42no—
515C2×C42—3322no—
516C2×C42—834no—
517C2×C42C22×D8314yes—
518#95—834no—
519#95—834no—
520#95—834no—
521#95—834no—
522#95—834no—
523#95—834no—
524#95—834no—
525#95—834no—
526#95C22×D8314yes—
527#95C22×D8314yes—
528#95C22×D8314yes—
529#95C22×D8314yes—
530C24—834no—
531C24—832no—
532C24—832no—
533C24—1662no—
534C24—1662no—
535C24—1662no—
536C24—1662no—
537C24—1662no—
538C24—1662no—
539C24—1662no—
540C24—1662no—
541C24—1662no—
542C24—1662no—
543C24—1662no—
544C24—1662no—
545C24—1662no—
546C24C23×D8311yescharacteristic
547C2×D4—3324no—
548C2×D4—3324no—
549C2×D4—33216no—
550C2×D4—1668no—
551C22×C4—22no—
552C22×C4—22no—
553C22×C4—22no—
554C22×C4—22no—
555C22×C4—22no—
556C22×C4—22no—
557C22×C4—22no—
558C22×C4—22no—
559C22×C4—22no—
560C22×C4—22no—
561C22×C4—22no—
562C22×C4—22no—
563C22×C4—22no—
564C22×C4—22no—
565C22×C4—22no—
566C22×C4—22no—
567C22×C4—22no—
568C22×C4—22no—
569C22×C4—22no—
570C22×C4—22no—
571C22×C4—33216no—
572C22×C4—3324no—
573C22×C4—3324no—
574C22×C4—834no—
575C22×C4—832no—
576C22×C4—832no—
577C22×C4—832no—
578C22×C4—832no—
579C22×C4—832no—
580C22×C4—832no—
581C22×C4—1662no—
582C22×C4—1662no—
583C22×C4—1662no—
584C22×C4—1662no—
585C22×C4—1662no—
586C22×C4—1662no—
587C22×C4—1662no—
588C22×C4—1662no—
589C22×C4—1662no—
590C22×C4—1662no—
591C22×C4—1662no—
592C22×C4—1662no—
593C22×C4—1662no—
594C22×C4—1662no—
595C22×C4—1662no—
596C22×C4—1668no—
597C22×C4—1662no—
598C22×C4—1662no—
599C22×C4#1305059014yes—
600C22×C4C23×D8312yes—
601C22×C4C23×D8312yes—
602C22×C4C23×D8312yes—
603C22×C4C23×D8312yes—
604C22×C4C23×D8312yes—
605C22×C4C23×D8312yes—
606C22×C4C23×D8312yes—
607C4⋊C4—28no—
608C4⋊C4—44no—
609C4⋊C4—3324no—
610C4⋊C4—3324no—
611C4⋊C4—3324no—
612C4⋊C4—3324no—
613C4⋊C4—3324no—
614C4⋊C4—1668no—
615C22⋊C4—3324no—
616C22⋊C4—3324no—
617C22⋊C4—3324no—
618C22⋊C4—3324no—
619C22⋊C4—3324no—
620C22⋊C4—3324no—
621C22⋊C4—1668no—
622C22⋊C4—1668no—
623C22⋊C4—1668no—
624C22⋊C4—1668no—
625C22⋊C4—1668no—
626C42—44no—
627C42—3324no—
628C23—3324no—
629C23—3324no—
630C23—3324no—
631C23—3324no—
632C23—3324no—
633C23—3324no—
634C23—3324no—
635C23—3324no—
636C23—3324no—
637C23—3324no—
638C23—3324no—
639C23—834no—
640C23—1662no—
641C23—1662no—
642C23—1662no—
643C23—1662no—
644C23—1662no—
645C23—1662no—
646C23—1662no—
647C23—1668no—
648C23—1662no—
649C23—1662no—
650C23—1662no—
651C23—1662no—
652C23—1662no—
653C23—1662no—
654C23—1668no—
655C23—1668no—
656C23#41×D8312yes—
657C23#41×D8312yes—
658C23C2×#1305059012yes—
659C23#1458183712yes—
660C23#1458183812yes—
661C23#1458183812yes—
662C23#1458184012yes—
663C23C24×D8311yescharacteristic
664D4—33216no—
665C2×C4—22no—
666C2×C4—22no—
667C2×C4—28no—
668C2×C4—22no—
669C2×C4—22no—
670C2×C4—22no—
671C2×C4—22no—
672C2×C4—22no—
673C2×C4—22no—
674C2×C4—22no—
675C2×C4—22no—
676C2×C4—22no—
677C2×C4—22no—
678C2×C4—22no—
679C2×C4—22no—
680C2×C4—22no—
681C2×C4—22no—
682C2×C4—22no—
683C2×C4—22no—
684C2×C4—22no—
685C2×C4—22no—
686C2×C4—44no—
687C2×C4—44no—
688C2×C4—44no—
689C2×C4—44no—
690C2×C4—44no—
691C2×C4—44no—
692C2×C4—33216no—
693C2×C4—3324no—
694C2×C4—3324no—
695C2×C4—3324no—
696C2×C4—3324no—
697C2×C4—3324no—
698C2×C4—834no—
699C2×C4—1662no—
700C2×C4—1662no—
701C2×C4—1662no—
702C2×C4—1662no—
703C2×C4—1662no—
704C2×C4—1662no—
705C2×C4—1662no—
706C2×C4—1662no—
707C2×C4—1662no—
708C2×C4—1662no—
709C2×C4—1662no—
710C2×C4—1662no—
711C2×C4—1662no—
712C2×C4—1662no—
713C2×C4—1662no—
714C2×C4—1662no—
715C2×C4—1662no—
716C2×C4—1668no—
717C2×C4C2×#1305059014yes—
718C22—3322no—
719C22—33216no—
720C22—3322no—
721C22—3322no—
722C22—3322no—
723C22—3322no—
724C22—3322no—
725C22—3322no—
726C22—3322no—
727C22—3322no—
728C22—3322no—
729C22—3322no—
730C22—6648no—
731C22—1664no—
732C22—1664no—
733C22—1664no—
734C22#1912822914yes—
735C22#1912828414yes—
736C22#1912829014yes—
737C22#1912829714yes—
738C22#1912829914yes—
739C22#1912830314yes—
740C22#1912832314yes—
741C22C2×#41×D8311yescharacteristic
742C22C2×#41×D8311yescharacteristic
743C22C22×#1305059011yescharacteristic
744C22C2×#1458183711yescharacteristic
745C22C2×#1458183811yescharacteristic
746C22C2×#1458183811yescharacteristic
747C22C2×#1458184011yescharacteristic
748C4—24no—
749C4—42no—
750C4—42no—
751C4—42no—
752C4—42no—
753C4—42no—
754C4—42no—
755C4—3322no—
756C4—3322no—
757C4—3322no—
758C4—3322no—
759C4—3322no—
760C4—1664no—
761C2—3324no—
762C2—6642no—
763C2#2491346418yesdirect product factor
764C2C2×#1912822911yescharacteristic
765C2C2×#1912828411yescharacteristic
766C2C2×#1912829011yescharacteristic
767C2C2×#1912829711yescharacteristic
768C2C2×#1912829911yescharacteristic
769C2C2×#1912830311yescharacteristic
770C2C2×#1912832311yescharacteristic
subgroupG/H
centerC24C23×D83
commutator, cosocleC23×C83C25
FrattiniC23C24×D83
FittingC2×#387×C83C2
socleC24×C83C24
prime radicalC23×D332C22
hypercenterC2×#387D83
hypocenterC83C2×#2649
LCSG ▷ C23×C83 ▷ C83
UCSC1 ◁ C24 ◁ C2×#387

Complements

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

NH ≅ G/Ntype
1. #24913464C2direct (N × H)
2. C2×#19127642C2semidirect
3. C2×#19127642C2semidirect
4. C2×#19127636C2semidirect
5. C2×#19127630C2semidirect
6. C2×#19127628C2semidirect
7. C2×#19127623C2semidirect
10. C2×#19127598C2semidirect
11. C2×#19127592C2semidirect
12. C2×#19127591C2semidirect
14. C2×#19127572C2semidirect
15. C2×C4×(C2×D83)⋊C4C2semidirect
16. C2×#387×C83C2semidirect
37. #19127642C22semidirect
38. #19127642C22semidirect
39. #19127636C22semidirect
40. #19127630C22semidirect
41. #19127628C22semidirect
42. #19127623C22semidirect
45. #19127598C22semidirect
46. #19127592C22semidirect
47. #19127591C22semidirect
49. #19127572C22semidirect
50. C4×(C2×D83)⋊C4C22semidirect
62. #387×C83C22semidirect
376. C2×C83#2649semidirect
398. C2×#387D83semidirect
402. C83C2×#2649semidirect
437. #387C2×D83semidirect
763. C2#24913464direct (N × H)

Maximal subgroups

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

subgroupindex
#249134642
C2×#191276422
C2×#191276362
C2×#191276302
C2×#191276282
C2×#191276232
C2×#191276192
C2×#191275982
C2×#191275922
C2×#191275912
C2×#191275792
C2×#191275722
C2×C4×(C2×D83)⋊C42
C2×#387×C832
C2×#264983