Finite Group Databasebeta

← C2×#24910213 #35563255

Subgroups — C2×#24910213 #35563255

Order 21248.

2678 conjugacy classes of subgroups.

The subgroup lattice has 724 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#14581769C211yesmaximal, characteristic
2#24910213C2116yesmaximal, direct product factor
3C2×#19127607C211yesmaximal, characteristic, complemented
4C2×#19127605C211yesmaximal, characteristic, complemented
5C2×#19127594C211yesmaximal, characteristic
6C2×#19127589C211yesmaximal, characteristic
7C2×#19127589C211yesmaximal, characteristic
8C2×#19127588C211yesmaximal, characteristic, complemented
9C2×#19127586C211yesmaximal, characteristic, complemented
10C2×#19127583C211yesmaximal, characteristic, complemented
11C2×#19127582C211yesmaximal, characteristic, complemented
12C2×#19127562C211yesmaximal, characteristic
13C2×C4⋊C4×Dic83C211yesmaximal, characteristic, complemented
14C2×C4×Dic83⋊C4C211yesmaximal, characteristic, complemented
15C2×C22⋊C4×Dic83C211yesmaximal, characteristic
16C2×#388×C83C211yesmaximal, characteristic
17C23×Dic166C2211yescharacteristic
18C24×Dic83C2211yescharacteristic
19C2×#14581769C4116yescomplemented
20C2×#14581769C2218yes—
21C22×C4⋊Dic83C2211yescharacteristic
22C22×C4⋊Dic83C2211yescharacteristic
23C22×Dic83⋊C4C2211yescharacteristic
24C22×Dic83⋊C4C2211yescharacteristic
25C22×Dic83⋊C4C2211yescharacteristic
26C22×Dic83⋊C4C2211yescharacteristic
27C22×C22⋊Dic83C2211yescharacteristic
28C22×C22⋊Dic83C2211yescharacteristic
29C22×C22⋊Dic83C2211yescharacteristic
30C22×C4×Dic83C2211yescharacteristic
31C22×C4×Dic83C2211yescharacteristic
32C22×C4×Dic83C2211yescharacteristic
33C22×C4×Dic83C2211yescharacteristic
34C22×C4×Dic83C2211yescharacteristic
35#19127607C2218yescomplemented
36#19127605C2218yescomplemented
37#19127594C2218yes—
38#19127589C2218yes—
39#19127589C2218yes—
40#19127588C2218yescomplemented
41#19127586C2218yescomplemented
42#19127583C2218yescomplemented
43#19127582C2218yescomplemented
44#19127562C2218yes—
45C4⋊C4×Dic83C2218yescomplemented
46C4×Dic83⋊C4C2218yescomplemented
47C22⋊C4×Dic83C2218yes—
48C2×C83⋊#95C2211yescharacteristic
49C2×C83⋊#95C2211yescharacteristic
50C2×C83⋊#95C2211yescharacteristic
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
60C22×C4⋊C4×C83C2211yescharacteristic
61C22×C22⋊C4×C83C2211yescharacteristic
62C22×C22⋊C4×C83C2211yescharacteristic
63C22×C22⋊C4×C83C2211yescharacteristic
64C22×C42×C83C2211yescharacteristic
65#388×C83C2218yes—
66C2×#95×C83C2211yescharacteristic
67C2×#95×C83C2211yescharacteristic
68C22×Dic166—42no—
69C22×Dic166—42no—
70C22×Dic166C2×C418yes—
71C22×Dic166C2314yes—
72C23×Dic83—42no—
73C23×Dic83—42no—
74C23×Dic83C2×C418yes—
75C23×Dic83C2311yescharacteristic
76C23×Dic83C2311yescharacteristic
77C23×Dic83C2311yescharacteristic
78C23×Dic83C2311yescharacteristic
79C23×Dic83C2311yescharacteristic
80C23×Dic83C2311yescharacteristic
81C23×Dic83C2311yescharacteristic
82C23×Dic83C2311yescharacteristic
83C23×Dic83C2314yes—
84#14581769C2×C4164yescomplemented
85C2×C4⋊Dic83—42no—
86C2×C4⋊Dic83C2×C418yes—
87C2×C4⋊Dic83C2314yes—
88C2×C4⋊Dic83C2314yes—
89C2×Dic83⋊C4—24no—
90C2×Dic83⋊C4—42no—
91C2×Dic83⋊C4C2×C418yes—
92C2×Dic83⋊C4C2×C418yes—
93C2×Dic83⋊C4C2314yes—
94C2×Dic83⋊C4C2314yes—
95C2×Dic83⋊C4C2314yes—
96C2×Dic83⋊C4C2314yes—
97C2×C22⋊Dic83—24no—
98C2×C22⋊Dic83—42no—
99C2×C22⋊Dic83C2×C418yes—
100C2×C22⋊Dic83C2314yes—
101C2×C22⋊Dic83C2314yes—
102C2×C22⋊Dic83C2314yes—
103C2×C4×Dic83—24no—
104C2×C4×Dic83—24no—
105C2×C4×Dic83—42no—
106C2×C4×Dic83—42no—
107C2×C4×Dic83—42no—
108C2×C4×Dic83C2314yes—
109C2×C4×Dic83C2314yes—
110C2×C4×Dic83C2314yes—
111C2×C4×Dic83C2314yes—
112C2×C4×Dic83C2314yes—
113C83⋊#95C2314yes—
114C83⋊#95C2314yes—
115C83⋊#95C2314yes—
116C83⋊#95C2314yes—
117C83⋊#95C2314yes—
118C83⋊#95C2314yes—
119C83⋊#95C2314yes—
120C83⋊#95C2314yes—
121C83⋊#95C2314yes—
122C83⋊#95C2314yes—
123C83⋊#95C2314yes—
124C83⋊#95C2314yes—
125C25×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×C83C2314yes—
134C2×C22⋊C4×C83—24no—
135C2×C22⋊C4×C83—42no—
136C2×C22⋊C4×C83C2×C418yes—
137C2×C22⋊C4×C83C2314yes—
138C2×C22⋊C4×C83C2314yes—
139C2×C22⋊C4×C83C2314yes—
140C2×C42×C83—42no—
141C2×C42×C83C2314yes—
142#95×C83C2314yes—
143#95×C83C2314yes—
144C2×Dic166—416no—
145C2×Dic166—44no—
146C2×Dic166—44no—
147C2×Dic166C22×C4116yes—
148C22×Dic83—22no—
149C22×Dic83—22no—
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—416no—
168C22×Dic83—44no—
169C22×Dic83—44no—
170C22×Dic83C22×C414yes—
171C22×Dic83C22×C414yes—
172C22×Dic83C22×C414yes—
173C22×Dic83C22×C414yes—
174C22×Dic83C22×C4116yes—
175C22×Dic83#4114yes—
176C22×Dic83C2412yes—
177C22×Dic83C2412yes—
178C22×Dic83C2412yes—
179C22×Dic83C2412yes—
180C22×Dic83C2412yes—
181C22×Dic83C2412yes—
182C22×Dic83C2412yes—
183C22×Dic83C2412yes—
184C4⋊Dic83—44no—
185C4⋊Dic83C22×C4116yes—
186Dic83⋊C4—28no—
187Dic83⋊C4—44no—
188Dic83⋊C4C22×C4116yes—
189Dic83⋊C4C22×C4116yes—
190C22⋊Dic83—28no—
191C22⋊Dic83—44no—
192C22⋊Dic83C22×C4116yes—
193C4×Dic83—28no—
194C4×Dic83—28no—
195C4×Dic83—44no—
196C4×Dic83—44no—
197C4×Dic83—44no—
198C24×C83—22no—
199C24×C83—22no—
200C24×C83—22no—
201C24×C83—22no—
202C24×C83—22no—
203C24×C83—22no—
204C24×C83C22×C414yes—
205C24×C83C2412yes—
206C24×C83C2411yescharacteristic
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×C83C22×C414yes—
223C22×C4×C83C22×C414yes—
224C22×C4×C83#4114yes—
225C22×C4×C83C2412yes—
226C22×C4×C83C2412yes—
227C22×C4×C83C2412yes—
228C22×C4×C83C2412yes—
229C22×C4×C83C2412yes—
230C22×C4×C83C2412yes—
231C4⋊C4×C83—28no—
232C22⋊C4×C83—28no—
233C22⋊C4×C83—44no—
234C22⋊C4×C83C22×C4116yes—
235C42×C83—44no—
236C23×C83—28no—
237C23×C83—28no—
238C23×C83—28no—
239C23×C83—22no—
240C23×C83—22no—
241C23×C83—22no—
242C23×C83—22no—
243C23×C83—22no—
244C23×C83—22no—
245C23×C83—44no—
246C23×C83—44no—
247C23×C83—44no—
248C23×C83—44no—
249C23×C83C23×C414yes—
250C23×C83C23×C412yes—
251C23×C83C2×#4112yes—
252C23×C83C2×#4112yes—
253C23×C83H(5,𝔽2)12yes—
254C23×C83H(5,𝔽2)12yes—
255C23×C832−1+412yes—
256C23×C832−1+412yes—
257C23×C83C2511yescharacteristic
258C2×C4×C83—28no—
259C2×C4×C83—28no—
260C2×C4×C83—28no—
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×C83C23×C414yes—
280C2×C4×C83C23×C414yes—
281C2×C4×C83C2×#4114yes—
282C2×Dic83—28no—
283C2×Dic83—28no—
284C2×Dic83—28no—
285C2×Dic83—28no—
286C2×Dic83—28no—
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—22no—
305C2×Dic83—22no—
306C2×Dic83—416no—
307C2×Dic83—44no—
308C2×Dic83—44no—
309C2×Dic83—44no—
310C2×Dic83C23×C414yes—
311C2×Dic83C23×C414yes—
312C2×Dic83C23×C414yes—
313C2×Dic83C23×C414yes—
314C2×Dic83C2×#4114yes—
315Dic166—416no—
316C22×C83—24no—
317C22×C83—24no—
318C22×C83—24no—
319C22×C83—416no—
320C22×C83—42no—
321C22×C83—42no—
322C22×C83—42no—
323C22×C83—42no—
324C22×C83C4×#4114yes—
325C22×C83#51814yes—
326C22×C83#51914yes—
327C22×C83#53914yes—
328C22×C83#53914yes—
329C22×C83#54214yes—
330C22×C83#54214yes—
331C22×C83C24×C411yescharacteristic
332C22×C83C22×#4111yescharacteristic
333C22×C83C22×#4111yescharacteristic
334C22×C83C2×H(5,𝔽2)11yescharacteristic
335C22×C83C2×H(5,𝔽2)11yescharacteristic
336C22×C83C2×2−1+411yescharacteristic
337C22×C83C2×2−1+411yescharacteristic
338C4×C83—24no—
339C4×C83—24no—
340C4×C83—24no—
341C4×C83—42no—
342C4×C83—42no—
343C4×C83—42no—
344Dic83—24no—
345Dic83—24no—
346Dic83—24no—
347Dic83—24no—
348Dic83—24no—
349Dic83—42no—
350Dic83—42no—
351Dic83—42no—
352C2×#2332—831nomaximal, Sylow
353C2×C83—44no—
354C2×C83#233218yescomplemented
355C2×C83C2×C4×#4111yescharacteristic
356C2×C83C2×#51811yescharacteristic
357C2×C83C2×#51911yescharacteristic
358C2×C83C2×#53911yescharacteristic
359C2×C83C2×#53911yescharacteristic
360C2×C83C2×#54211yescharacteristic
361C2×C83C2×#54211yescharacteristic
362C22×C22⋊Q8—831no—
363#2332—8316no—
364C2×#391—831no—
365C2×#391—831no—
366C2×#388—831no—
367C2×#388—831no—
368C2×#388—831no—
369C2×#388D8311yescharacteristic
370C2×#387—831no—
371C2×#387—831no—
372C2×#387—831no—
373C2×#387—831no—
374C2×#381—831no—
375C2×C4×C4⋊C4—831no—
376C2×C4×C4⋊C4—831no—
377C2×C4×C22⋊C4—831no—
378C83C2×#233211yescharacteristic, complemented, Sylow
379C23×Q8—831no—
380C24×C4—831no—
381C2×C22⋊Q8—8316no—
382C2×C22⋊Q8—838no—
383C22×C4⋊C4—831no—
384C22×C4⋊C4—831no—
385C22×C4⋊C4—831no—
386C22×C4⋊C4—831no—
387C22×C4⋊C4—831no—
388C22×C4⋊C4—831no—
389C22×C4⋊C4C2×D8311yescharacteristic
390C22×C22⋊C4—831no—
391C22×C22⋊C4—831no—
392C22×C22⋊C4—831no—
393C22×C22⋊C4C2×D8311yescharacteristic
394C22×C22⋊C4C2×D8311yescharacteristic
395C22×C22⋊C4C2×D8311yescharacteristic
396C22×C42—831no—
397C22×C42—831no—
398C22×C42—831no—
399C22×C42—831no—
400C22×C42—831no—
401C22×C42C2×D8311yescharacteristic
402#391—838no—
403#391—838no—
404#388—838no—
405#388—838no—
406#388—838no—
407#388C2×D8318yes—
408#387—838no—
409#387—838no—
410#387—838no—
411#387—838no—
412#381—838no—
413C4×C4⋊C4—838no—
414C4×C4⋊C4—838no—
415C4×C22⋊C4—838no—
416C2×#95—831no—
417C2×#95—831no—
418C2×#95—831no—
419C2×#95—831no—
420C2×#95—831no—
421C2×#95—831no—
422C2×#95—831no—
423C2×#95—831no—
424C2×#95—831no—
425C2×#95—831no—
426C2×#95—831no—
427C2×#95—831no—
428C2×#95C2×D8311yescharacteristic
429C2×#95C2×D8311yescharacteristic
430C25C22×D8311yescharacteristic
431C22×Q8—3322no—
432C22×Q8—3322no—
433C22×Q8—838no—
434C22×Q8—834no—
435C23×C4—3322no—
436C23×C4—3322no—
437C23×C4—838no—
438C23×C4—834no—
439C23×C4—831no—
440C23×C4—831no—
441C23×C4—831no—
442C23×C4—831no—
443C23×C4—831no—
444C23×C4—831no—
445C23×C4—831no—
446C23×C4—831no—
447C23×C4C22×D8311yescharacteristic
448C23×C4C22×D8311yescharacteristic
449C23×C4C22×D8311yescharacteristic
450C23×C4C22×D8311yescharacteristic
451C23×C4C22×D8311yescharacteristic
452C23×C4C22×D8311yescharacteristic
453C22⋊Q8—8364no—
454C2×C4⋊C4—24no—
455C2×C4⋊C4—3322no—
456C2×C4⋊C4—3322no—
457C2×C4⋊C4—834no—
458C2×C4⋊C4—834no—
459C2×C4⋊C4—838no—
460C2×C4⋊C4—838no—
461C2×C4⋊C4—838no—
462C2×C4⋊C4—834no—
463C2×C4⋊C4—834no—
464C2×C4⋊C4—834no—
465C2×C4⋊C4—834no—
466C2×C4⋊C4—1664no—
467C2×C4⋊C4C22×D8314yes—
468C2×C22⋊C4—24no—
469C2×C22⋊C4—42no—
470C2×C22⋊C4—3322no—
471C2×C22⋊C4—834no—
472C2×C22⋊C4—838no—
473C2×C22⋊C4—834no—
474C2×C22⋊C4—834no—
475C2×C22⋊C4—1664no—
476C2×C22⋊C4C4×D8318yes—
477C2×C22⋊C4C22×D8314yes—
478C2×C22⋊C4C22×D8314yes—
479C2×C22⋊C4C22×D8314yes—
480C2×C42—42no—
481C2×C42—3322no—
482C2×C42—3322no—
483C2×C42—3322no—
484C2×C42—834no—
485C2×C42—834no—
486C2×C42—834no—
487C2×C42—834no—
488C2×C42—834no—
489C2×C42—1664no—
490C2×C42—1664no—
491C2×C42C22×D8314yes—
492#95—834no—
493#95—834no—
494#95—834no—
495#95—834no—
496#95—834no—
497#95—834no—
498#95—834no—
499#95—834no—
500#95—834no—
501#95—834no—
502#95—834no—
503#95—834no—
504#95C22×D8314yes—
505#95C22×D8314yes—
506C24—22no—
507C24—22no—
508C24—22no—
509C24—22no—
510C24—22no—
511C24—22no—
512C24C2×C4×D8314yes—
513C24C23×D8312yes—
514C24C23×D8311yescharacteristic
515C2×Q8—33216no—
516C2×Q8—3324no—
517C2×Q8—3324no—
518C2×Q8—8316no—
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—22no—
529C22×C4—22no—
530C22×C4—22no—
531C22×C4—22no—
532C22×C4—22no—
533C22×C4—22no—
534C22×C4—33216no—
535C22×C4—3324no—
536C22×C4—3324no—
537C22×C4—8316no—
538C22×C4—834no—
539C22×C4—834no—
540C22×C4—834no—
541C22×C4—834no—
542C22×C4—834no—
543C22×C4—832no—
544C22×C4—832no—
545C22×C4—832no—
546C22×C4—832no—
547C22×C4—832no—
548C22×C4—832no—
549C22×C4—832no—
550C22×C4—832no—
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×C4—1662no—
561C22×C4—1662no—
562C22×C4—1662no—
563C22×C4—1662no—
564C22×C4—1662no—
565C22×C4—1662no—
566C22×C4—1662no—
567C22×C4—1662no—
568C22×C4—1662no—
569C22×C4—1662no—
570C22×C4C2×C4×D8314yes—
571C22×C4C2×C4×D8314yes—
572C22×C4#1305058914yes—
573C22×C4C23×D8312yes—
574C22×C4C23×D8312yes—
575C22×C4C23×D8312yes—
576C22×C4C23×D8312yes—
577C22×C4C23×D8312yes—
578C22×C4C23×D8312yes—
579C4⋊C4—28no—
580C4⋊C4—3324no—
581C4⋊C4—3324no—
582C4⋊C4—8316no—
583C4⋊C4—8316no—
584C4⋊C4—8316no—
585C4⋊C4—1668no—
586C22⋊C4—28no—
587C22⋊C4—44no—
588C22⋊C4—3324no—
589C22⋊C4—8316no—
590C22⋊C4—1668no—
591C22⋊C4C2×C4×D83116yes—
592C42—44no—
593C42—3324no—
594C42—3324no—
595C42—3324no—
596C42—1668no—
597C42—1668no—
598C23—28no—
599C23—28no—
600C23—28no—
601C23—22no—
602C23—22no—
603C23—22no—
604C23—22no—
605C23—22no—
606C23—22no—
607C23—44no—
608C23—44no—
609C23—44no—
610C23—44no—
611C23C22×C4×D8314yes—
612C23C22×C4×D8312yes—
613C23#41×D8312yes—
614C23C2×#1305058912yes—
615C23#1458183712yes—
616C23#1458183812yes—
617C23#1458183912yes—
618C23#1458183912yes—
619C23C24×D8311yescharacteristic
620Q8—33216no—
621C2×C4—28no—
622C2×C4—28no—
623C2×C4—22no—
624C2×C4—22no—
625C2×C4—22no—
626C2×C4—22no—
627C2×C4—22no—
628C2×C4—22no—
629C2×C4—28no—
630C2×C4—22no—
631C2×C4—22no—
632C2×C4—22no—
633C2×C4—22no—
634C2×C4—22no—
635C2×C4—22no—
636C2×C4—22no—
637C2×C4—22no—
638C2×C4—22no—
639C2×C4—44no—
640C2×C4—44no—
641C2×C4—44no—
642C2×C4—3324no—
643C2×C4—3324no—
644C2×C4—3324no—
645C2×C4—33216no—
646C2×C4—834no—
647C2×C4—834no—
648C2×C4—834no—
649C2×C4—834no—
650C2×C4—834no—
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—1668no—
661C2×C4—1668no—
662C2×C4—1668no—
663C2×C4—1668no—
664C2×C4—1662no—
665C2×C4—1662no—
666C2×C4—1662no—
667C2×C4—1662no—
668C2×C4—1662no—
669C2×C4—1662no—
670C2×C4—1662no—
671C2×C4—1662no—
672C2×C4—1662no—
673C2×C4—1662no—
674C2×C4—1668no—
675C2×C4C22×C4×D8314yes—
676C2×C4C22×C4×D8314yes—
677C2×C4C2×#1305058914yes—
678C22—24no—
679C22—24no—
680C22—24no—
681C22—42no—
682C22—42no—
683C22—416no—
684C22—42no—
685C22—42no—
686C22C4×#1305058914yes—
687C22#1912817314yes—
688C22#1912817814yes—
689C22#1912829414yes—
690C22#1912829614yes—
691C22#1912831714yes—
692C22#1912832014yes—
693C22C23×C4×D8311yescharacteristic
694C22C2×#41×D8311yescharacteristic
695C22C22×#1305058911yescharacteristic
696C22C2×#1458183711yescharacteristic
697C22C2×#1458183811yescharacteristic
698C22C2×#1458183911yescharacteristic
699C22C2×#1458183911yescharacteristic
700C4—24no—
701C4—24no—
702C4—24no—
703C4—42no—
704C4—42no—
705C4—42no—
706C4—3322no—
707C4—3322no—
708C4—3322no—
709C4—1664no—
710C4—1664no—
711C4—1664no—
712C4—1664no—
713C4—1664no—
714C2—44no—
715C2#2491021318yesdirect product factor
716C2C2×C4×#1305058911yescharacteristic
717C2C2×#1912817311yescharacteristic
718C2C2×#1912817811yescharacteristic
719C2C2×#1912829411yescharacteristic
720C2C2×#1912829611yescharacteristic
721C2C2×#1912831711yescharacteristic
722C2C2×#1912832011yescharacteristic
subgroupG/H
centerC24C23×D83
commutatorC22×C83C24×C4
FrattiniC23C24×D83
FittingC2×#388×C83C2
socleC24×C83C24
prime radicalC25×C83C23
cosocleC23×C83C25
hypercenterC2×#388D83
hypocenterC83C2×#2332
LCSG ▷ C22×C83 ▷ C83
UCSC1 ◁ C24 ◁ C2×#388

Complements

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

NH ≅ G/Ntype
2. #24910213C2direct (N × H)
3. C2×#19127607C2semidirect
4. C2×#19127605C2semidirect
8. C2×#19127588C2semidirect
9. C2×#19127586C2semidirect
10. C2×#19127583C2semidirect
11. C2×#19127582C2semidirect
13. C2×C4⋊C4×Dic83C2semidirect
14. C2×C4×Dic83⋊C4C2semidirect
19. C2×#14581769C4semidirect
35. #19127607C22semidirect
36. #19127605C22semidirect
40. #19127588C22semidirect
41. #19127586C22semidirect
42. #19127583C22semidirect
43. #19127582C22semidirect
45. C4⋊C4×Dic83C22semidirect
46. C4×Dic83⋊C4C22semidirect
84. #14581769C2×C4semidirect
354. C2×C83#2332semidirect
378. C83C2×#2332semidirect
715. C2#24910213direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#145817692
#249102132
C2×#191276072
C2×#191276052
C2×#191275942
C2×#191275892
C2×#191275882
C2×#191275862
C2×#191275832
C2×#191275822
C2×#191275622
C2×C4⋊C4×Dic832
C2×C4×Dic83⋊C42
C2×C22⋊C4×Dic832
C2×#388×C832
C2×#233283