Finite Group Databasebeta

← C2×#24910738 #35570663

Subgroups — C2×#24910738 #35570663

Order 21248.

2966 conjugacy classes of subgroups.

The subgroup lattice has 744 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#14581757C211yesmaximal, characteristic, complemented
2C22×#14581748C211yesmaximal, characteristic
3#24910738C2116yesmaximal, direct product factor
4C2×#19127642C211yesmaximal, characteristic, complemented
5C2×#19127637C211yesmaximal, characteristic
6C2×#19127634C211yesmaximal, characteristic, complemented
7C2×#19127631C211yesmaximal, characteristic, complemented
8C2×#19127624C211yesmaximal, characteristic
9C2×#19127621C211yesmaximal, characteristic, complemented
10C2×#19127613C211yesmaximal, characteristic
11C2×C4⋊C4×Dic83C211yesmaximal, characteristic, complemented
12C2×C4⋊C4×Dic83C211yesmaximal, characteristic, complemented
13C2×#19127552C211yesmaximal, characteristic, complemented
14C2×C22⋊C4×Dic83C211yesmaximal, characteristic
15C2×C22⋊C4×Dic83C211yesmaximal, characteristic
16C2×#396×C83C211yesmaximal, characteristic
17C23×Dic166C2211yescharacteristic
18C24×Dic83C2211yescharacteristic
19C2×#14581757—28no—
20C2×#14581757C2218yescomplemented
21C2×#14581748—28no—
22C2×#14581748C2218yes—
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×C22⋊Dic83C2211yescharacteristic
32C22×C22⋊Dic83C2211yescharacteristic
33C22×C22⋊Dic83C2211yescharacteristic
34C22×C4×Dic83C2211yescharacteristic
35C22×C4×Dic83C2211yescharacteristic
36C22×C4×Dic83C2211yescharacteristic
37C22×C4×Dic83C2211yescharacteristic
38C22×C4×Dic83C2211yescharacteristic
39C22×C4×Dic83C2211yescharacteristic
40#19127642C2218yescomplemented
41#19127637C2218yes—
42#19127634C2218yescomplemented
43#19127631C2218yescomplemented
44#19127624C2218yes—
45#19127621C2218yescomplemented
46#19127613C2218yes—
47C4⋊C4×Dic83C2218yescomplemented
48C4⋊C4×Dic83C2218yescomplemented
49#19127552C2218yescomplemented
50C22⋊C4×Dic83C2218yes—
51C22⋊C4×Dic83C2218yes—
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×C22⋊C4×C83C2211yescharacteristic
65C22×C22⋊C4×C83C2211yescharacteristic
66C22×C22⋊C4×C83C2211yescharacteristic
67#396×C83C2218yes—
68C2×#95×C83C2211yescharacteristic
69C22×Dic166—24no—
70C22×Dic166—24no—
71C22×Dic166—24no—
72C22×Dic166C2314yes—
73C23×Dic83—24no—
74C23×Dic83—24no—
75C23×Dic83Q818yescomplemented
76C23×Dic83C2311yescharacteristic
77C23×Dic83C2311yescharacteristic
78C23×Dic83C2311yescharacteristic
79C23×Dic83C2311yescharacteristic
80C23×Dic83C2311yescharacteristic
81C23×Dic83C2314yes—
82C23×Dic83C2311yescharacteristic
83C23×Dic83C2311yescharacteristic
84C23×Dic83C2311yescharacteristic
85#14581757—232no—
86#14581748—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⋊C4C2314yes—
98C2×Dic83⋊C4C2314yes—
99C2×Dic83⋊C4C2314yes—
100C2×Dic83⋊C4C2314yes—
101C2×Dic83⋊C4C2314yes—
102C2×Dic83⋊C4C2314yes—
103C2×C22⋊Dic83—24no—
104C2×C22⋊Dic83—24no—
105C2×C22⋊Dic83—24no—
106C2×C22⋊Dic83C2314yes—
107C2×C22⋊Dic83C2314yes—
108C2×C22⋊Dic83C2314yes—
109C2×C4×Dic83—24no—
110C2×C4×Dic83—24no—
111C2×C4×Dic83—24no—
112C2×C4×Dic83—24no—
113C2×C4×Dic83—24no—
114C2×C4×Dic83D418yes—
115C2×C4×Dic83C2314yes—
116C2×C4×Dic83C2314yes—
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—
129C83⋊#95C2314yes—
130C25×C83C2311yescharacteristic
131C23×C4×C83C2311yescharacteristic
132C23×C4×C83C2311yescharacteristic
133C23×C4×C83C2311yescharacteristic
134C23×C4×C83C2311yescharacteristic
135C23×C4×C83C2311yescharacteristic
136C23×C4×C83C2311yescharacteristic
137C2×C4⋊C4×C83—24no—
138C2×C4⋊C4×C83—24no—
139C2×C4⋊C4×C83—24no—
140C2×C4⋊C4×C83C2314yes—
141C2×C4⋊C4×C83C2314yes—
142C2×C4⋊C4×C83C2314yes—
143C2×C22⋊C4×C83—24no—
144C2×C22⋊C4×C83—24no—
145C2×C22⋊C4×C83—24no—
146C2×C22⋊C4×C83C2314yes—
147C2×C22⋊C4×C83C2314yes—
148C2×C22⋊C4×C83C2314yes—
149#95×C83C2314yes—
150C2×Dic166—232no—
151C2×Dic166—28no—
152C2×Dic166—28no—
153C2×Dic166—28no—
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—232no—
163C22×Dic83—28no—
164C22×Dic83—28no—
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×Dic83C2×D414yes—
175C22×Dic83C2×D414yes—
176C22×Dic83C2×Q814yes—
177C22×Dic83C2×Q814yes—
178C22×Dic83C2×Q8116yescomplemented
179C22×Dic83#4114yes—
180C22×Dic83#4114yes—
181C22×Dic83#4114yes—
182C22×Dic83C2412yes—
183C22×Dic83C2412yes—
184C22×Dic83C2412yes—
185C22×Dic83C2412yes—
186C22×Dic83C2412yes—
187C22×Dic83C2412yes—
188C22×Dic83C2412yes—
189C22×Dic83C2412yes—
190C4⋊Dic83—28no—
191C4⋊Dic83—28no—
192Dic83⋊C4—28no—
193Dic83⋊C4—28no—
194Dic83⋊C4—28no—
195Dic83⋊C4—28no—
196Dic83⋊C4—28no—
197Dic83⋊C4—28no—
198C22⋊Dic83—28no—
199C22⋊Dic83—28no—
200C22⋊Dic83—28no—
201C4×Dic83—28no—
202C4×Dic83—28no—
203C4×Dic83—28no—
204C4×Dic83—28no—
205C4×Dic83—28no—
206C4×Dic83C2×D4116yes—
207C24×C83—22no—
208C24×C83—22no—
209C24×C83—22no—
210C24×C83—22no—
211C24×C83—22no—
212C24×C83—22no—
213C24×C83C2×Q814yes—
214C24×C83C2412yes—
215C24×C83C2411yescharacteristic
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×C83C2×D414yes—
232C22×C4×C83#4114yes—
233C22×C4×C83#4114yes—
234C22×C4×C83C2412yes—
235C22×C4×C83C2412yes—
236C22×C4×C83C2412yes—
237C22×C4×C83C2412yes—
238C22×C4×C83C2412yes—
239C22×C4×C83C2412yes—
240C4⋊C4×C83—28no—
241C4⋊C4×C83—28no—
242C4⋊C4×C83—28no—
243C22⋊C4×C83—28no—
244C22⋊C4×C83—28no—
245C22⋊C4×C83—28no—
246C23×C83—28no—
247C23×C83—28no—
248C23×C83—28no—
249C23×C83—22no—
250C23×C83—22no—
251C23×C83—22no—
252C23×C83—22no—
253C23×C83—22no—
254C23×C83—22no—
255C23×C83—44no—
256C23×C83—44no—
257C23×C83—44no—
258C23×C83—44no—
259C23×C83C22×D412yes—
260C23×C83C22×Q814yes—
261C23×C83C22×Q812yes—
262C23×C83C2×#4112yes—
263C23×C83C2×#4112yes—
264C23×C83C2×#4112yes—
265C23×C83C2×#4112yes—
266C23×C83C2×#4112yes—
267C23×C83C2511yescharacteristic
268C2×C4×C83—28no—
269C2×C4×C83—28no—
270C2×C4×C83—28no—
271C2×C4×C83—22no—
272C2×C4×C83—22no—
273C2×C4×C83—22no—
274C2×C4×C83—22no—
275C2×C4×C83—22no—
276C2×C4×C83—22no—
277C2×C4×C83—22no—
278C2×C4×C83—22no—
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—44no—
287C2×C4×C83—44no—
288C2×C4×C83—44no—
289C2×C4×C83C22×D414yes—
290C2×C4×C83C2×#4114yes—
291C2×C4×C83C2×#4114yes—
292C2×Dic83—28no—
293C2×Dic83—28no—
294C2×Dic83—28no—
295C2×Dic83—28no—
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—232no—
305C2×Dic83—22no—
306C2×Dic83—22no—
307C2×Dic83—22no—
308C2×Dic83—22no—
309C2×Dic83—22no—
310C2×Dic83—22no—
311C2×Dic83—22no—
312C2×Dic83—22no—
313C2×Dic83—22no—
314C2×Dic83—44no—
315C2×Dic83—44no—
316C2×Dic83—44no—
317C2×Dic83C22⋊Q8116yes—
318C2×Dic83C22×D414yes—
319C2×Dic83C22×D414yes—
320C2×Dic83C22×Q814yes—
321C2×Dic83C22×Q814yes—
322C2×Dic83C2×#4114yes—
323C2×Dic83C2×#4114yes—
324C2×Dic83C2×#4114yes—
325Dic166—232no—
326C22×C83—24no—
327C22×C83—24no—
328C22×C83—24no—
329C22×C83—416no—
330C22×C83—42no—
331C22×C83—42no—
332C22×C83—42no—
333C22×C83—42no—
334C22×C83C2×C22⋊Q814yes—
335C22×C83#52514yes—
336C22×C83#52914yes—
337C22×C83#52914yes—
338C22×C83#53214yes—
339C22×C83#53314yes—
340C22×C83#53314yes—
341C22×C83C23×D411yescharacteristic
342C22×C83C23×Q811yescharacteristic
343C22×C83C22×#4111yescharacteristic
344C22×C83C22×#4111yescharacteristic
345C22×C83C22×#4111yescharacteristic
346C22×C83C22×#4111yescharacteristic
347C22×C83C22×#4111yescharacteristic
348C4×C83—24no—
349C4×C83—24no—
350C4×C83—24no—
351C4×C83—42no—
352C4×C83—42no—
353C4×C83—42no—
354Dic83—24no—
355Dic83—24no—
356Dic83—24no—
357Dic83—24no—
358Dic83—42no—
359Dic83—42no—
360Dic83—42no—
361Dic83C2×C22⋊Q818yes—
362C2×#2396—831nomaximal, Sylow
363C2×C83—44no—
364C2×C83#239618yescomplemented
365C2×C83C22×C22⋊Q811yescharacteristic
366C2×C83C2×#52511yescharacteristic
367C2×C83C2×#52911yescharacteristic
368C2×C83C2×#52911yescharacteristic
369C2×C83C2×#53211yescharacteristic
370C2×C83C2×#53311yescharacteristic
371C2×C83C2×#53311yescharacteristic
372C22×C4×Q8—831no—
373C22×#117—831no—
374#2396—8316no—
375C2×#400—831no—
376C2×#399—831no—
377C2×#398—831no—
378C2×#398—831no—
379C2×#396—831no—
380C2×#396D8311yescharacteristic
381C2×#395—831no—
382C2×#393—831no—
383C2×C4×C4⋊C4—831no—
384C2×C4×C4⋊C4—831no—
385C2×C4×C4⋊C4—831no—
386C2×C4×C22⋊C4—831no—
387C2×C4×C22⋊C4—831no—
388C83C2×#239611yescharacteristic, complemented, Sylow
389C23×Q8—831no—
390C24×C4—831no—
391C2×C4×Q8—838no—
392C2×C4×Q8—1668no—
393C2×#117—838no—
394C2×#117—1668no—
395C22×C4⋊C4—831no—
396C22×C4⋊C4—831no—
397C22×C4⋊C4—831no—
398C22×C4⋊C4—831no—
399C22×C4⋊C4—831no—
400C22×C4⋊C4—831no—
401C22×C4⋊C4—831no—
402C22×C4⋊C4—831no—
403C22×C4⋊C4C2×D8311yescharacteristic
404C22×C4⋊C4C2×D8311yescharacteristic
405C22×C4⋊C4C2×D8311yescharacteristic
406C22×C22⋊C4—831no—
407C22×C22⋊C4—831no—
408C22×C22⋊C4—831no—
409C22×C22⋊C4C2×D8311yescharacteristic
410C22×C22⋊C4C2×D8311yescharacteristic
411C22×C22⋊C4C2×D8311yescharacteristic
412C22×C42—831no—
413C22×C42—831no—
414C22×C42—831no—
415C22×C42—831no—
416C22×C42—831no—
417C22×C42—831no—
418#400—838no—
419#399—838no—
420#398—838no—
421#398—838no—
422#396—838no—
423#396C2×D8318yes—
424#395—838no—
425#393—838no—
426C4×C4⋊C4—838no—
427C4×C4⋊C4—838no—
428C4×C4⋊C4—838no—
429C4×C22⋊C4—838no—
430C4×C22⋊C4—838no—
431C2×#95—831no—
432C2×#95—831no—
433C2×#95—831no—
434C2×#95—831no—
435C2×#95—831no—
436C2×#95—831no—
437C2×#95—831no—
438C2×#95—831no—
439C2×#95—831no—
440C2×#95C2×D8311yescharacteristic
441C25C22×D8311yescharacteristic
442C22×Q8—834no—
443C22×Q8—1664no—
444C22×Q8—1664no—
445C22×Q8—1664no—
446C23×C4—831no—
447C23×C4—838no—
448C23×C4—834no—
449C23×C4—831no—
450C23×C4—831no—
451C23×C4—831no—
452C23×C4—831no—
453C23×C4—831no—
454C23×C4—831no—
455C23×C4—831no—
456C23×C4—1664no—
457C23×C4—1664no—
458C23×C4C22×D8311yescharacteristic
459C23×C4C22×D8311yescharacteristic
460C23×C4C22×D8311yescharacteristic
461C23×C4C22×D8311yescharacteristic
462C23×C4C22×D8311yescharacteristic
463C23×C4C22×D8311yescharacteristic
464C4×Q8—16632no—
465#117—16632no—
466C2×C4⋊C4—24no—
467C2×C4⋊C4—24no—
468C2×C4⋊C4—24no—
469C2×C4⋊C4—834no—
470C2×C4⋊C4—834no—
471C2×C4⋊C4—834no—
472C2×C4⋊C4—834no—
473C2×C4⋊C4—834no—
474C2×C4⋊C4—834no—
475C2×C4⋊C4—834no—
476C2×C4⋊C4—834no—
477C2×C4⋊C4—1664no—
478C2×C4⋊C4—1664no—
479C2×C4⋊C4—1664no—
480C2×C4⋊C4—1664no—
481C2×C4⋊C4—1664no—
482C2×C4⋊C4—1664no—
483C2×C4⋊C4—1664no—
484C2×C4⋊C4—1664no—
485C2×C4⋊C4C22×D8314yes—
486C2×C4⋊C4C22×D8314yes—
487C2×C4⋊C4C22×D8314yes—
488C2×C22⋊C4—24no—
489C2×C22⋊C4—24no—
490C2×C22⋊C4—24no—
491C2×C22⋊C4—834no—
492C2×C22⋊C4—834no—
493C2×C22⋊C4—834no—
494C2×C22⋊C4—1664no—
495C2×C22⋊C4—1664no—
496C2×C22⋊C4—1664no—
497C2×C22⋊C4C22×D8314yes—
498C2×C22⋊C4C22×D8314yes—
499C2×C22⋊C4C22×D8314yes—
500C2×C42—838no—
501C2×C42—834no—
502C2×C42—834no—
503C2×C42—834no—
504C2×C42—834no—
505C2×C42—834no—
506C2×C42—834no—
507C2×C42—1664no—
508C2×C42—1664no—
509C2×C42—1664no—
510C2×C42—1664no—
511C2×C42—1664no—
512#95—834no—
513#95—834no—
514#95—834no—
515#95—834no—
516#95—834no—
517#95—834no—
518#95—834no—
519#95—834no—
520#95—834no—
521#95C22×D8314yes—
522C24—22no—
523C24—22no—
524C24—22no—
525C24—22no—
526C24—22no—
527C24—22no—
528C24Q8×D8314yes—
529C24C23×D8312yes—
530C24C23×D8311yescharacteristic
531C2×Q8—1668no—
532C2×Q8—1668no—
533C2×Q8—16632no—
534C2×Q8—1668no—
535C22×C4—22no—
536C22×C4—22no—
537C22×C4—22no—
538C22×C4—22no—
539C22×C4—22no—
540C22×C4—22no—
541C22×C4—22no—
542C22×C4—22no—
543C22×C4—22no—
544C22×C4—22no—
545C22×C4—22no—
546C22×C4—22no—
547C22×C4—22no—
548C22×C4—22no—
549C22×C4—22no—
550C22×C4—834no—
551C22×C4—834no—
552C22×C4—834no—
553C22×C4—832no—
554C22×C4—834no—
555C22×C4—834no—
556C22×C4—8316no—
557C22×C4—834no—
558C22×C4—834no—
559C22×C4—832no—
560C22×C4—832no—
561C22×C4—832no—
562C22×C4—832no—
563C22×C4—832no—
564C22×C4—832no—
565C22×C4—832no—
566C22×C4—1662no—
567C22×C4—1662no—
568C22×C4—1662no—
569C22×C4—1662no—
570C22×C4—1662no—
571C22×C4—1662no—
572C22×C4—1662no—
573C22×C4—1662no—
574C22×C4—1662no—
575C22×C4—1668no—
576C22×C4—16632no—
577C22×C4—1668no—
578C22×C4—1662no—
579C22×C4—1662no—
580C22×C4—1662no—
581C22×C4—1662no—
582C22×C4—1662no—
583C22×C4—1662no—
584C22×C4—1662no—
585C22×C4—1662no—
586C22×C4D4×D8314yes—
587C22×C4#1305058914yes—
588C22×C4#1305058914yes—
589C22×C4C23×D8312yes—
590C22×C4C23×D8312yes—
591C22×C4C23×D8312yes—
592C22×C4C23×D8312yes—
593C22×C4C23×D8312yes—
594C22×C4C23×D8312yes—
595C4⋊C4—28no—
596C4⋊C4—28no—
597C4⋊C4—28no—
598C4⋊C4—1668no—
599C4⋊C4—1668no—
600C4⋊C4—1668no—
601C4⋊C4—1668no—
602C4⋊C4—1668no—
603C4⋊C4—1668no—
604C4⋊C4—1668no—
605C4⋊C4—1668no—
606C22⋊C4—28no—
607C22⋊C4—28no—
608C22⋊C4—28no—
609C22⋊C4—1668no—
610C22⋊C4—1668no—
611C22⋊C4—1668no—
612C42—8316no—
613C42—1668no—
614C42—1668no—
615C42—1668no—
616C42—1668no—
617C42—1668no—
618C23—28no—
619C23—28no—
620C23—28no—
621C23—22no—
622C23—22no—
623C23—22no—
624C23—22no—
625C23—22no—
626C23—22no—
627C23—44no—
628C23—44no—
629C23—44no—
630C23—44no—
631C23C2×D4×D8312yes—
632C23C2×Q8×D8314yes—
633C23C2×Q8×D8312yes—
634C23#41×D8312yes—
635C23#41×D8312yes—
636C23#41×D8312yes—
637C23C2×#1305058912yes—
638C23C2×#1305058912yes—
639C23C24×D8311yescharacteristic
640Q8—16632no—
641C2×C4—28no—
642C2×C4—28no—
643C2×C4—28no—
644C2×C4—22no—
645C2×C4—22no—
646C2×C4—22no—
647C2×C4—22no—
648C2×C4—22no—
649C2×C4—22no—
650C2×C4—22no—
651C2×C4—22no—
652C2×C4—22no—
653C2×C4—22no—
654C2×C4—22no—
655C2×C4—22no—
656C2×C4—22no—
657C2×C4—22no—
658C2×C4—22no—
659C2×C4—44no—
660C2×C4—44no—
661C2×C4—44no—
662C2×C4—3324no—
663C2×C4—3324no—
664C2×C4—3324no—
665C2×C4—8316no—
666C2×C4—834no—
667C2×C4—834no—
668C2×C4—834no—
669C2×C4—834no—
670C2×C4—834no—
671C2×C4—834no—
672C2×C4—834no—
673C2×C4—1662no—
674C2×C4—1662no—
675C2×C4—1662no—
676C2×C4—1662no—
677C2×C4—1662no—
678C2×C4—1662no—
679C2×C4—1662no—
680C2×C4—1662no—
681C2×C4—1662no—
682C2×C4—16632no—
683C2×C4—1668no—
684C2×C4—1668no—
685C2×C4—1668no—
686C2×C4—1668no—
687C2×C4—1662no—
688C2×C4—1662no—
689C2×C4—1662no—
690C2×C4—1662no—
691C2×C4—1662no—
692C2×C4—1662no—
693C2×C4—1662no—
694C2×C4—1662no—
695C2×C4C2×D4×D8314yes—
696C2×C4C2×#1305058914yes—
697C2×C4C2×#1305058914yes—
698C22—24no—
699C22—24no—
700C22—24no—
701C22—42no—
702C22—416no—
703C22—42no—
704C22—42no—
705C22—42no—
706C22C22⋊Q8×D8314yes—
707C22#1912821114yes—
708C22#1912823214yes—
709C22#1912823414yes—
710C22#1912824614yes—
711C22#1912825314yes—
712C22#1912825314yes—
713C22C22×D4×D8311yescharacteristic
714C22C22×Q8×D8311yescharacteristic
715C22C2×#41×D8311yescharacteristic
716C22C2×#41×D8311yescharacteristic
717C22C2×#41×D8311yescharacteristic
718C22C22×#1305058911yescharacteristic
719C22C22×#1305058911yescharacteristic
720C4—24no—
721C4—24no—
722C4—24no—
723C4—42no—
724C4—42no—
725C4—42no—
726C4—3322no—
727C4—3322no—
728C4—3322no—
729C4—838no—
730C4—1664no—
731C4—1664no—
732C4—1664no—
733C4—1664no—
734C2—44no—
735C2#2491073818yesdirect product factor
736C2C2×C22⋊Q8×D8311yescharacteristic
737C2C2×#1912821111yescharacteristic
738C2C2×#1912823211yescharacteristic
739C2C2×#1912823411yescharacteristic
740C2C2×#1912824611yescharacteristic
741C2C2×#1912825311yescharacteristic
742C2C2×#1912825311yescharacteristic
subgroupG/H
centerC24C23×D83
commutator, cosocleC23×C83C25
FrattiniC23C24×D83
FittingC2×#396×C83C2
socleC24×C83C24
prime radicalC25×C83C23
hypercenterC2×#396D83
hypocenterC83C2×#2396
LCSG ▷ C23×C83 ▷ C83
UCSC1 ◁ C24 ◁ C2×#396

Complements

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

NH ≅ G/Ntype
1. C22×#14581757C2semidirect
3. #24910738C2direct (N × H)
4. C2×#19127642C2semidirect
6. C2×#19127634C2semidirect
7. C2×#19127631C2semidirect
9. C2×#19127621C2semidirect
11. C2×C4⋊C4×Dic83C2semidirect
12. C2×C4⋊C4×Dic83C2semidirect
13. C2×#19127552C2semidirect
20. C2×#14581757C22semidirect
40. #19127642C22semidirect
42. #19127634C22semidirect
43. #19127631C22semidirect
45. #19127621C22semidirect
47. C4⋊C4×Dic83C22semidirect
48. C4⋊C4×Dic83C22semidirect
49. #19127552C22semidirect
75. C23×Dic83Q8semidirect
178. C22×Dic83C2×Q8semidirect
364. C2×C83#2396semidirect
388. C83C2×#2396semidirect
735. C2#24910738direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#145817572
C22×#145817482
#249107382
C2×#191276422
C2×#191276372
C2×#191276342
C2×#191276312
C2×#191276242
C2×#191276212
C2×#191276132
C2×C4⋊C4×Dic832
C2×#191275522
C2×C22⋊C4×Dic832
C2×#396×C832
C2×#239683