Finite Group Databasebeta

← C2×#24913663 #35571007

Subgroups — C2×#24913663 #35571007

Order 21248.

2158 conjugacy classes of subgroups.

The subgroup lattice has 716 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#24913663C2116yesmaximal, direct product factor
2C2×#19127638C211yesmaximal, characteristic
3C2×#19127636C211yesmaximal, characteristic
4C2×#19127635C211yesmaximal, characteristic, complemented
5C2×#19127635C211yesmaximal, characteristic, complemented
6C2×#19127634C211yesmaximal, characteristic, complemented
7C2×#19127631C211yesmaximal, characteristic, complemented
8C2×#19127625C211yesmaximal, characteristic
9C2×#19127623C211yesmaximal, characteristic
10C2×#19127599C211yesmaximal, characteristic, complemented
11C2×#19127598C211yesmaximal, characteristic, complemented
12C2×#19127588C211yesmaximal, characteristic, complemented
13C2×#19127563C211yesmaximal, characteristic
14C2×#19127560C211yesmaximal, characteristic
15C2×C4×(C2×D83)⋊C4C211yesmaximal, characteristic
16C2×#387×C83C211yesmaximal, characteristic, complemented
17C23×C4×D83C2211yescharacteristic
18C22×C4⋊Dic83C2211yescharacteristic
19C22×C4⋊Dic83C2211yescharacteristic
20C22×C4⋊Dic83C2211yescharacteristic
21C22×C4⋊Dic83C2211yescharacteristic
22C22×Dic83⋊C4C2211yescharacteristic
23C22×Dic83⋊C4C2211yescharacteristic
24C22×Dic83⋊C4C2211yescharacteristic
25C22×Dic83⋊C4C2211yescharacteristic
26C22×Dic83⋊C4C2211yescharacteristic
27C22×Dic83⋊C4C2211yescharacteristic
28C22×Dic83⋊C4C2211yescharacteristic
29C22×Dic83⋊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#19127638C2218yes—
38#19127636C2218yes—
39#19127635C2218yescomplemented
40#19127635C2218yescomplemented
41#19127634C2218yescomplemented
42#19127631C2218yescomplemented
43#19127625C2218yes—
44#19127623C2218yes—
45#19127599C2218yescomplemented
46#19127598C2218yescomplemented
47#19127588C2218yescomplemented
48#19127563C2218yes—
49#19127560C2218yes—
50C4×(C2×D83)⋊C4C2218yes—
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
68C23×Dic83C2311yescharacteristic
69C23×Dic83C2311yescharacteristic
70C23×Dic83C2311yescharacteristic
71C23×Dic83C2311yescharacteristic
72C23×Dic83C2311yescharacteristic
73C23×Dic83C2311yescharacteristic
74C23×Dic83C2311yescharacteristic
75C22×C4×D83—42no—
76C22×C4×D83—42no—
77C22×C4×D83Q818yes—
78C22×C4×D83C2314yes—
79C2×C4⋊Dic83—24no—
80C2×C4⋊Dic83—42no—
81C2×C4⋊Dic83—42no—
82C2×C4⋊Dic83—42no—
83C2×C4⋊Dic83C2314yes—
84C2×C4⋊Dic83C2314yes—
85C2×C4⋊Dic83C2314yes—
86C2×C4⋊Dic83C2314yes—
87C2×Dic83⋊C4—24no—
88C2×Dic83⋊C4—24no—
89C2×Dic83⋊C4—42no—
90C2×Dic83⋊C4—42no—
91C2×Dic83⋊C4—42no—
92C2×Dic83⋊C4—42no—
93C2×Dic83⋊C4—42no—
94C2×Dic83⋊C4—42no—
95C2×Dic83⋊C4C2314yes—
96C2×Dic83⋊C4C2314yes—
97C2×Dic83⋊C4C2314yes—
98C2×Dic83⋊C4C2314yes—
99C2×Dic83⋊C4C2314yes—
100C2×Dic83⋊C4C2314yes—
101C2×Dic83⋊C4C2314yes—
102C2×Dic83⋊C4C2314yes—
103C2×(C2×D83)⋊C4—24no—
104C2×(C2×D83)⋊C4—24no—
105C2×(C2×D83)⋊C4—42no—
106C2×(C2×D83)⋊C4—42no—
107C2×(C2×D83)⋊C4—42no—
108C2×(C2×D83)⋊C4—42no—
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×C4×Dic83—42no—
116C2×C4×Dic83C2314yes—
117C83⋊#95C2314yes—
118C83⋊#95C2314yes—
119C83⋊#95C2314yes—
120C83⋊#95C2314yes—
121C83⋊#95C2314yes—
122C83⋊#95C2314yes—
123C83⋊#95C2314yes—
124C83⋊#95C2314yes—
125C23×C4×C83C2311yescharacteristic
126C23×C4×C83C2311yescharacteristic
127C23×C4×C83C2311yescharacteristic
128C23×C4×C83C2311yescharacteristic
129C23×C4×C83C2311yescharacteristic
130C23×C4×C83C2311yescharacteristic
131C23×C4×C83C2311yescharacteristic
132C2×C4⋊C4×C83—24no—
133C2×C4⋊C4×C83—42no—
134C2×C4⋊C4×C83C2314yes—
135C2×C4⋊C4×C83C2314yes—
136C2×C42×C83—42no—
137C2×C42×C83C2314yes—
138#95×C83C2314yes—
139#95×C83C2314yes—
140#95×C83C2314yes—
141#95×C83C2314yes—
142C23×D83—22no—
143C23×D83—22no—
144C23×D83—22no—
145C23×D83—22no—
146C23×D83—22no—
147C23×D83—22no—
148C23×D83C2×Q814yes—
149C23×D83C2412yes—
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—22no—
167C22×Dic83—22no—
168C22×Dic83—22no—
169C22×Dic83C2×Q814yes—
170C22×Dic83#4114yes—
171C22×Dic83C2412yes—
172C22×Dic83C2412yes—
173C22×Dic83C2412yes—
174C22×Dic83C2412yes—
175C22×Dic83C2412yes—
176C22×Dic83C2412yes—
177C22×Dic83C2412yes—
178C2×C4×D83—416no—
179C2×C4×D83—44no—
180C2×C4×D83—44no—
181C2×C4×D83C2×Q8116yes—
182C4⋊Dic83—28no—
183C4⋊Dic83—44no—
184C4⋊Dic83—44no—
185C4⋊Dic83—44no—
186Dic83⋊C4—28no—
187Dic83⋊C4—28no—
188Dic83⋊C4—44no—
189Dic83⋊C4—44no—
190Dic83⋊C4—44no—
191Dic83⋊C4—44no—
192Dic83⋊C4—44no—
193Dic83⋊C4—44no—
194(C2×D83)⋊C4—28no—
195(C2×D83)⋊C4—28no—
196(C2×D83)⋊C4—44no—
197(C2×D83)⋊C4—44no—
198(C2×D83)⋊C4—44no—
199(C2×D83)⋊C4—44no—
200C4×Dic83—44no—
201C24×C83C2411yescharacteristic
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—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×Q814yes—
222C22×C4×C83#4114yes—
223C22×C4×C83C2412yes—
224C22×C4×C83C2412yes—
225C22×C4×C83C2412yes—
226C22×C4×C83C2412yes—
227C22×C4×C83C2412yes—
228C22×C4×C83C2412yes—
229C22×C4×C83C2412yes—
230C4⋊C4×C83—28no—
231C4⋊C4×C83—44no—
232C42×C83—44no—
233C23×C83C22×Q812yes—
234C23×C83C2×#4112yes—
235C23×C83C2×#4112yes—
236C23×C83H(5,𝔽2)12yes—
237C23×C83H(5,𝔽2)12yes—
238C23×C83H(5,𝔽2)12yes—
239C23×C832−1+412yes—
240C23×C83C2511yescharacteristic
241C22×D83—28no—
242C22×D83—28no—
243C22×D83—28no—
244C22×D83—22no—
245C22×D83—22no—
246C22×D83—22no—
247C22×D83—22no—
248C22×D83—22no—
249C22×D83—22no—
250C22×D83—44no—
251C22×D83—44no—
252C22×D83—44no—
253C22×D83—44no—
254C22×D83C22×Q814yes—
255C2×C4×C83—28no—
256C2×C4×C83—28no—
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—22no—
268C2×C4×C83—22no—
269C2×C4×C83—22no—
270C2×C4×C83—22no—
271C2×C4×C83—22no—
272C2×C4×C83—22no—
273C2×C4×C83—22no—
274C2×C4×C83—22no—
275C2×C4×C83—22no—
276C2×C4×C83—44no—
277C2×C4×C83—44no—
278C2×C4×C83—44no—
279C2×C4×C83—44no—
280C2×C4×C83—44no—
281C2×C4×C83C22×Q814yes—
282C2×C4×C83C2×#4114yes—
283C2×Dic83—28no—
284C2×Dic83—28no—
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—22no—
297C2×Dic83—22no—
298C2×Dic83—22no—
299C2×Dic83—22no—
300C2×Dic83—22no—
301C2×Dic83—22no—
302C2×Dic83—22no—
303C2×Dic83—22no—
304C2×Dic83—44no—
305C2×Dic83—44no—
306C2×Dic83—44no—
307C2×Dic83—44no—
308C2×Dic83—44no—
309C2×Dic83C22×Q814yes—
310C2×Dic83C2×#4114yes—
311C4×D83—416no—
312C22×C83#53314yes—
313C22×C83#53914yes—
314C22×C83#53914yes—
315C22×C83#54014yes—
316C22×C83#54014yes—
317C22×C83#54314yes—
318C22×C83#54414yes—
319C22×C83C23×Q811yescharacteristic
320C22×C83C22×#4111yescharacteristic
321C22×C83C22×#4111yescharacteristic
322C22×C83C2×H(5,𝔽2)11yescharacteristic
323C22×C83C2×H(5,𝔽2)11yescharacteristic
324C22×C83C2×H(5,𝔽2)11yescharacteristic
325C22×C83C2×2−1+411yescharacteristic
326C2×D83—24no—
327C2×D83—24no—
328C2×D83—24no—
329C2×D83—416no—
330C2×D83—42no—
331C2×D83—42no—
332C2×D83—42no—
333C2×D83—42no—
334C4×C83—24no—
335C4×C83—24no—
336C4×C83—42no—
337C4×C83—42no—
338C4×C83—42no—
339C4×C83—42no—
340C4×C83—42no—
341Dic83—24no—
342Dic83—24no—
343Dic83—42no—
344Dic83—42no—
345Dic83—42no—
346Dic83—42no—
347Dic83—42no—
348C2×#2667—831nomaximal, Sylow
349C2×C83#266718yescomplemented
350C2×C83C2×#53311yescharacteristic
351C2×C83C2×#53911yescharacteristic
352C2×C83C2×#53911yescharacteristic
353C2×C83C2×#54011yescharacteristic
354C2×C83C2×#54011yescharacteristic
355C2×C83C2×#54311yescharacteristic
356C2×C83C2×#54411yescharacteristic
357D83—44no—
358#2667—8316no—
359C2×#399—831no—
360C2×#399—831no—
361C2×#398—831no—
362C2×#398—831no—
363C2×#398—831no—
364C2×#398—831no—
365C2×#396—831no—
366C2×#396—831no—
367C2×#389—831no—
368C2×#389—831no—
369C2×#387—831no—
370C2×#387D8311yescharacteristic, complemented
371C2×#381—831no—
372C2×#380—831no—
373C2×C4×C22⋊C4—831no—
374C83C2×#266711yescharacteristic, complemented, Sylow
375C24×C4—831no—
376C22×C4⋊C4—831no—
377C22×C4⋊C4—831no—
378C22×C4⋊C4—831no—
379C22×C4⋊C4—831no—
380C22×C4⋊C4—831no—
381C22×C4⋊C4—831no—
382C22×C4⋊C4—831no—
383C22×C4⋊C4—831no—
384C22×C4⋊C4—831no—
385C22×C4⋊C4—831no—
386C22×C4⋊C4—831no—
387C22×C4⋊C4—831no—
388C22×C4⋊C4C2×D8311yescharacteristic
389C22×C4⋊C4C2×D8311yescharacteristic
390C22×C22⋊C4—831no—
391C22×C22⋊C4—831no—
392C22×C22⋊C4—831no—
393C22×C22⋊C4—831no—
394C22×C22⋊C4—831no—
395C22×C22⋊C4—831no—
396C22×C42—831no—
397C22×C42C2×D8311yescharacteristic
398#399—838no—
399#399—838no—
400#398—838no—
401#398—838no—
402#398—838no—
403#398—838no—
404#396—838no—
405#396—838no—
406#389—838no—
407#389—838no—
408#387—838no—
409#387C2×D8318yescomplemented
410#381—838no—
411#380—838no—
412C4×C22⋊C4—838no—
413C2×#95—831no—
414C2×#95—831no—
415C2×#95—831no—
416C2×#95—831no—
417C2×#95—831no—
418C2×#95—831no—
419C2×#95—831no—
420C2×#95—831no—
421C2×#95C2×D8311yescharacteristic
422C2×#95C2×D8311yescharacteristic
423C2×#95C2×D8311yescharacteristic
424C2×#95C2×D8311yescharacteristic
425C25—831no—
426C23×C4—3322no—
427C23×C4—3322no—
428C23×C4—838no—
429C23×C4—834no—
430C23×C4—831no—
431C23×C4—831no—
432C23×C4—831no—
433C23×C4—831no—
434C23×C4—831no—
435C23×C4—831no—
436C23×C4—831no—
437C23×C4C22×D8311yescharacteristic
438C23×C4C22×D8311yescharacteristic
439C23×C4C22×D8311yescharacteristic
440C23×C4C22×D8311yescharacteristic
441C23×C4C22×D8311yescharacteristic
442C23×C4C22×D8311yescharacteristic
443C23×C4C22×D8311yescharacteristic
444C2×C4⋊C4—24no—
445C2×C4⋊C4—42no—
446C2×C4⋊C4—3322no—
447C2×C4⋊C4—3322no—
448C2×C4⋊C4—3322no—
449C2×C4⋊C4—3322no—
450C2×C4⋊C4—3322no—
451C2×C4⋊C4—3322no—
452C2×C4⋊C4—3322no—
453C2×C4⋊C4—3322no—
454C2×C4⋊C4—3322no—
455C2×C4⋊C4—834no—
456C2×C4⋊C4—834no—
457C2×C4⋊C4—834no—
458C2×C4⋊C4—834no—
459C2×C4⋊C4—834no—
460C2×C4⋊C4—834no—
461C2×C4⋊C4—834no—
462C2×C4⋊C4—834no—
463C2×C4⋊C4—834no—
464C2×C4⋊C4—834no—
465C2×C4⋊C4—834no—
466C2×C4⋊C4—834no—
467C2×C4⋊C4—1664no—
468C2×C4⋊C4—1664no—
469C2×C4⋊C4—1664no—
470C2×C4⋊C4C22×D8314yes—
471C2×C4⋊C4C22×D8314yes—
472C2×C22⋊C4—3322no—
473C2×C22⋊C4—3322no—
474C2×C22⋊C4—3322no—
475C2×C22⋊C4—3322no—
476C2×C22⋊C4—834no—
477C2×C22⋊C4—834no—
478C2×C22⋊C4—834no—
479C2×C22⋊C4—834no—
480C2×C22⋊C4—834no—
481C2×C22⋊C4—834no—
482C2×C22⋊C4—1664no—
483C2×C22⋊C4—1664no—
484C2×C42—42no—
485C2×C42—3322no—
486C2×C42—834no—
487C2×C42C22×D8314yes—
488#95—834no—
489#95—834no—
490#95—834no—
491#95—834no—
492#95—834no—
493#95—834no—
494#95—834no—
495#95—834no—
496#95C22×D8314yes—
497#95C22×D8314yes—
498#95C22×D8314yes—
499#95C22×D8314yes—
500C24—834no—
501C24—832no—
502C24—1662no—
503C24—1662no—
504C24—1662no—
505C24—1662no—
506C24—1662no—
507C24—1662no—
508C24C23×D8311yescharacteristic
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—22no—
521C22×C4—22no—
522C22×C4—22no—
523C22×C4—22no—
524C22×C4—22no—
525C22×C4—22no—
526C22×C4—22no—
527C22×C4—22no—
528C22×C4—33216no—
529C22×C4—3324no—
530C22×C4—3324no—
531C22×C4—8316no—
532C22×C4—834no—
533C22×C4—834no—
534C22×C4—832no—
535C22×C4—832no—
536C22×C4—832no—
537C22×C4—832no—
538C22×C4—832no—
539C22×C4—832no—
540C22×C4—832no—
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×C4—1662no—
553C22×C4—1662no—
554C22×C4—1662no—
555C22×C4—1662no—
556C22×C4—1662no—
557C22×C4—1662no—
558C22×C4—1662no—
559C22×C4—1662no—
560C22×C4Q8×D8314yes—
561C22×C4#1305059014yes—
562C22×C4C23×D8312yes—
563C22×C4C23×D8312yes—
564C22×C4C23×D8312yes—
565C22×C4C23×D8312yes—
566C22×C4C23×D8312yes—
567C22×C4C23×D8312yes—
568C22×C4C23×D8312yes—
569C4⋊C4—28no—
570C4⋊C4—44no—
571C4⋊C4—3324no—
572C4⋊C4—3324no—
573C4⋊C4—3324no—
574C4⋊C4—3324no—
575C4⋊C4—3324no—
576C4⋊C4—3324no—
577C4⋊C4—3324no—
578C4⋊C4—3324no—
579C4⋊C4—3324no—
580C4⋊C4—1668no—
581C4⋊C4—1668no—
582C4⋊C4—1668no—
583C22⋊C4—3324no—
584C22⋊C4—3324no—
585C22⋊C4—3324no—
586C22⋊C4—3324no—
587C22⋊C4—1668no—
588C22⋊C4—1668no—
589C42—44no—
590C42—3324no—
591C23—3324no—
592C23—3324no—
593C23—3324no—
594C23—3324no—
595C23—834no—
596C23—1668no—
597C23—1668no—
598C23—1668no—
599C23—1662no—
600C23—1662no—
601C23—1662no—
602C23—1662no—
603C23—1662no—
604C23—1662no—
605C23C2×Q8×D8312yes—
606C23#41×D8312yes—
607C23C2×#1305059012yes—
608C23#1458183712yes—
609C23#1458183812yes—
610C23#1458183812yes—
611C23#1458183912yes—
612C23C24×D8311yescharacteristic
613C2×C4—28no—
614C2×C4—22no—
615C2×C4—22no—
616C2×C4—22no—
617C2×C4—22no—
618C2×C4—28no—
619C2×C4—22no—
620C2×C4—22no—
621C2×C4—22no—
622C2×C4—22no—
623C2×C4—22no—
624C2×C4—22no—
625C2×C4—22no—
626C2×C4—22no—
627C2×C4—22no—
628C2×C4—22no—
629C2×C4—22no—
630C2×C4—22no—
631C2×C4—22no—
632C2×C4—22no—
633C2×C4—22no—
634C2×C4—44no—
635C2×C4—44no—
636C2×C4—44no—
637C2×C4—44no—
638C2×C4—44no—
639C2×C4—33216no—
640C2×C4—3324no—
641C2×C4—3324no—
642C2×C4—3324no—
643C2×C4—3324no—
644C2×C4—3324no—
645C2×C4—834no—
646C2×C4—834no—
647C2×C4—1662no—
648C2×C4—1662no—
649C2×C4—1662no—
650C2×C4—1662no—
651C2×C4—1662no—
652C2×C4—1662no—
653C2×C4—1662no—
654C2×C4—1662no—
655C2×C4—1662no—
656C2×C4—1662no—
657C2×C4—1662no—
658C2×C4—1662no—
659C2×C4—1662no—
660C2×C4—1662no—
661C2×C4—1662no—
662C2×C4—1668no—
663C2×C4—1662no—
664C2×C4—1662no—
665C2×C4—1662no—
666C2×C4—1662no—
667C2×C4—1668no—
668C2×C4C2×Q8×D8314yes—
669C2×C4C2×#1305059014yes—
670C22—3322no—
671C22—3322no—
672C22—3322no—
673C22—3322no—
674C22—33216no—
675C22—1664no—
676C22—1664no—
677C22—1664no—
678C22#1912825514yes—
679C22#1912829214yes—
680C22#1912829314yes—
681C22#1912830314yes—
682C22#1912830614yes—
683C22#1912832614yes—
684C22#1912833114yes—
685C22C22×Q8×D8311yescharacteristic
686C22C2×#41×D8311yescharacteristic
687C22C22×#1305059011yescharacteristic
688C22C2×#1458183711yescharacteristic
689C22C2×#1458183811yescharacteristic
690C22C2×#1458183811yescharacteristic
691C22C2×#1458183911yescharacteristic
692C4—24no—
693C4—24no—
694C4—42no—
695C4—42no—
696C4—42no—
697C4—42no—
698C4—42no—
699C4—3322no—
700C4—3322no—
701C4—3322no—
702C4—3322no—
703C4—3322no—
704C4—1664no—
705C4—1664no—
706C2—3324no—
707C2#2491366318yesdirect product factor
708C2C2×#1912825511yescharacteristic
709C2C2×#1912829211yescharacteristic
710C2C2×#1912829311yescharacteristic
711C2C2×#1912830311yescharacteristic
712C2C2×#1912830611yescharacteristic
713C2C2×#1912832611yescharacteristic
714C2C2×#1912833111yescharacteristic
subgroupG/H
centerC24C23×D83
commutator, cosocleC23×C83C25
FrattiniC23C24×D83
FittingC2×#387×C83C2
socleC24×C83C24
prime radicalC24×D83C23
hypercenterC2×#387D83
hypocenterC83C2×#2667
LCSG ▷ C23×C83 ▷ C83
UCSC1 ◁ C24 ◁ C2×#387

Complements

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

NH ≅ G/Ntype
1. #24913663C2direct (N × H)
4. C2×#19127635C2semidirect
5. C2×#19127635C2semidirect
6. C2×#19127634C2semidirect
7. C2×#19127631C2semidirect
10. C2×#19127599C2semidirect
11. C2×#19127598C2semidirect
12. C2×#19127588C2semidirect
16. C2×#387×C83C2semidirect
39. #19127635C22semidirect
40. #19127635C22semidirect
41. #19127634C22semidirect
42. #19127631C22semidirect
45. #19127599C22semidirect
46. #19127598C22semidirect
47. #19127588C22semidirect
62. #387×C83C22semidirect
349. C2×C83#2667semidirect
370. C2×#387D83semidirect
374. C83C2×#2667semidirect
409. #387C2×D83semidirect
707. C2#24913663direct (N × H)

Maximal subgroups

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

subgroupindex
#249136632
C2×#191276382
C2×#191276362
C2×#191276352
C2×#191276342
C2×#191276312
C2×#191276252
C2×#191276232
C2×#191275992
C2×#191275982
C2×#191275882
C2×#191275632
C2×#191275602
C2×C4×(C2×D83)⋊C42
C2×#387×C832
C2×#266783