Finite Group Databasebeta

← C2×#24913135 #35575239

Subgroups — C2×#24913135 #35575239

Order 21248.

3070 conjugacy classes of subgroups.

The subgroup lattice has 800 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#14581749C211yesmaximal, characteristic, complemented
2#24913135C2116yesmaximal, direct product factor
3C2×#19127634C211yesmaximal, characteristic, complemented
4C2×#19127624C211yesmaximal, characteristic, complemented
5C2×#19127623C211yesmaximal, characteristic, complemented
6C2×#19127617C211yesmaximal, characteristic
7C2×#19127592C211yesmaximal, characteristic, complemented
8C2×#19127589C211yesmaximal, characteristic, complemented
9C2×#19127585C211yesmaximal, characteristic, complemented
10C2×#19127582C211yesmaximal, characteristic, complemented
11C2×#19127580C211yesmaximal, characteristic
12C2×#19127577C211yesmaximal, characteristic
13C2×#19127574C211yesmaximal, characteristic, complemented
14C2×#19127572C211yesmaximal, characteristic, complemented
15C2×#19127567C211yesmaximal, characteristic, complemented
16C22×#117×C83C211yesmaximal, characteristic, complemented
17C23×C22⋊D83C2211yescharacteristic
18C23×C4×D83C2211yescharacteristic
19C2×#14581749—28no—
20C2×#14581749C2218yescomplemented
21C22×C4⋊Dic83C2211yescharacteristic
22C22×C4⋊Dic83C2211yescharacteristic
23C22×Dic83⋊C4C2211yescharacteristic
24C22×Dic83⋊C4C2211yescharacteristic
25C22×Dic83⋊C4C2211yescharacteristic
26C22×Dic83⋊C4C2211yescharacteristic
27C22×Dic83⋊C4C2211yescharacteristic
28C22×C22⋊Dic83C2211yescharacteristic
29C22×C22⋊Dic83C2211yescharacteristic
30C22×C22⋊Dic83C2211yescharacteristic
31C22×(C2×D83)⋊C4C2211yescharacteristic
32C22×(C2×D83)⋊C4C2211yescharacteristic
33C22×(C2×D83)⋊C4C2211yescharacteristic
34C22×(C2×D83)⋊C4C2211yescharacteristic
35C22×(C2×D83)⋊C4C2211yescharacteristic
36C22×C4×Dic83C2211yescharacteristic
37#19127634C2218yescomplemented
38#19127624C2218yescomplemented
39#19127623C2218yescomplemented
40#19127617C2218yes—
41#19127592C2218yescomplemented
42#19127589C2218yescomplemented
43#19127585C2218yescomplemented
44#19127582C2218yescomplemented
45#19127580C2218yes—
46#19127577C2218yes—
47#19127574C2218yescomplemented
48#19127572C2218yescomplemented
49#19127567C2218yescomplemented
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
60C24×C4×C83C2211yescharacteristic
61C2×#117×C83—28no—
62C2×#117×C83C2218yescomplemented
63C22×C4⋊C4×C83C2211yescharacteristic
64C22×C4⋊C4×C83C2211yescharacteristic
65C22×C22⋊C4×C83C2211yescharacteristic
66C22×C22⋊C4×C83C2211yescharacteristic
67C22×C42×C83C2211yescharacteristic
68C22×C42×C83C2211yescharacteristic
69C24×D83C2311yescharacteristic
70C22×C22⋊D83—24no—
71C22×C22⋊D83—24no—
72C22×C22⋊D83—42no—
73C22×C22⋊D83C2314yes—
74C23×Dic83C2311yescharacteristic
75C23×Dic83C2311yescharacteristic
76C23×Dic83C2311yescharacteristic
77C23×Dic83C2311yescharacteristic
78C23×Dic83C2311yescharacteristic
79C23×Dic83C2311yescharacteristic
80C23×Dic83C2311yescharacteristic
81C22×C4×D83—24no—
82C22×C4×D83—24no—
83C22×C4×D83—24no—
84C22×C4×D83C2314yes—
85#14581749—232no—
86C2×C4⋊Dic83—42no—
87C2×C4⋊Dic83—42no—
88C2×C4⋊Dic83C2314yes—
89C2×C4⋊Dic83C2314yes—
90C2×Dic83⋊C4—24no—
91C2×Dic83⋊C4—24no—
92C2×Dic83⋊C4—24no—
93C2×Dic83⋊C4—24no—
94C2×Dic83⋊C4—42no—
95C2×Dic83⋊C4C2314yes—
96C2×Dic83⋊C4C2314yes—
97C2×Dic83⋊C4C2314yes—
98C2×Dic83⋊C4C2314yes—
99C2×Dic83⋊C4C2314yes—
100C2×C22⋊Dic83—24no—
101C2×C22⋊Dic83—24no—
102C2×C22⋊Dic83—42no—
103C2×C22⋊Dic83C2314yes—
104C2×C22⋊Dic83C2314yes—
105C2×C22⋊Dic83C2314yes—
106C2×(C2×D83)⋊C4—24no—
107C2×(C2×D83)⋊C4—24no—
108C2×(C2×D83)⋊C4—24no—
109C2×(C2×D83)⋊C4—24no—
110C2×(C2×D83)⋊C4—42no—
111C2×(C2×D83)⋊C4C2314yes—
112C2×(C2×D83)⋊C4C2314yes—
113C2×(C2×D83)⋊C4C2314yes—
114C2×(C2×D83)⋊C4C2314yes—
115C2×(C2×D83)⋊C4C2314yes—
116C2×C4×Dic83—24no—
117C2×C4×Dic83C2314yes—
118C83⋊#95C2314yes—
119C83⋊#95C2314yes—
120C83⋊#95C2314yes—
121C83⋊#95C2314yes—
122C83⋊#95C2314yes—
123C83⋊#95C2314yes—
124C83⋊#95C2314yes—
125C83⋊#95C2314yes—
126C83⋊#95C2314yes—
127C83⋊#95C2314yes—
128C25×C83C2311yescharacteristic
129C23×C4×C83—24no—
130C23×C4×C83—24no—
131C23×C4×C83—24no—
132C23×C4×C83C2314yes—
133C23×C4×C83C2311yescharacteristic
134C23×C4×C83C2311yescharacteristic
135C23×C4×C83C2311yescharacteristic
136C23×C4×C83C2311yescharacteristic
137C23×C4×C83C2311yescharacteristic
138C23×C4×C83C2311yescharacteristic
139#117×C83—232no—
140C2×C4⋊C4×C83—24no—
141C2×C4⋊C4×C83—24no—
142C2×C4⋊C4×C83C2314yes—
143C2×C4⋊C4×C83C2314yes—
144C2×C22⋊C4×C83—24no—
145C2×C22⋊C4×C83—24no—
146C2×C22⋊C4×C83C2314yes—
147C2×C22⋊C4×C83C2314yes—
148C2×C42×C83—24no—
149C2×C42×C83D418yescomplemented
150C2×C42×C83C2314yes—
151C2×C42×C83C2314yes—
152C23×D83—22no—
153C23×D83—22no—
154C23×D83—22no—
155C23×D83—22no—
156C23×D83—22no—
157C23×D83—22no—
158C23×D83#4114yes—
159C23×D83C2412yes—
160C2×C22⋊D83—28no—
161C2×C22⋊D83—28no—
162C2×C22⋊D83—44no—
163C2×C22⋊D83—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—22no—
182C22×Dic83—22no—
183C22×Dic83—22no—
184C22×Dic83#4114yes—
185C22×Dic83C2412yes—
186C22×Dic83C2412yes—
187C22×Dic83C2412yes—
188C22×Dic83C2412yes—
189C22×Dic83C2412yes—
190C22×Dic83C2412yes—
191C22×Dic83C2412yes—
192C2×C4×D83—232no—
193C2×C4×D83—28no—
194C2×C4×D83—28no—
195C2×C4×D83—28no—
196C4⋊Dic83—44no—
197C4⋊Dic83—44no—
198Dic83⋊C4—28no—
199Dic83⋊C4—28no—
200Dic83⋊C4—28no—
201Dic83⋊C4—28no—
202Dic83⋊C4—44no—
203C22⋊Dic83—28no—
204C22⋊Dic83—28no—
205C22⋊Dic83—44no—
206(C2×D83)⋊C4—28no—
207(C2×D83)⋊C4—28no—
208(C2×D83)⋊C4—28no—
209(C2×D83)⋊C4—28no—
210(C2×D83)⋊C4—44no—
211C4×Dic83—28no—
212C24×C83—22no—
213C24×C83—22no—
214C24×C83—22no—
215C24×C83—22no—
216C24×C83—22no—
217C24×C83—22no—
218C24×C83#4114yes—
219C24×C83C2412yes—
220C24×C83C2411yescharacteristic
221C22×C4×C83—232no—
222C22×C4×C83—22no—
223C22×C4×C83—22no—
224C22×C4×C83—22no—
225C22×C4×C83—28no—
226C22×C4×C83—22no—
227C22×C4×C83—22no—
228C22×C4×C83—22no—
229C22×C4×C83—22no—
230C22×C4×C83—22no—
231C22×C4×C83—28no—
232C22×C4×C83—28no—
233C22×C4×C83—22no—
234C22×C4×C83—22no—
235C22×C4×C83—22no—
236C22×C4×C83—22no—
237C22×C4×C83—22no—
238C22×C4×C83—22no—
239C22×C4×C83C2×D414yes—
240C22×C4×C83C2×D414yes—
241C22×C4×C83C2×D414yes—
242C22×C4×C83#4114yes—
243C22×C4×C83C2412yes—
244C22×C4×C83C2412yes—
245C22×C4×C83C2412yes—
246C22×C4×C83C2412yes—
247C22×C4×C83C2412yes—
248C22×C4×C83C2412yes—
249C4⋊C4×C83—28no—
250C4⋊C4×C83—28no—
251C22⋊C4×C83—28no—
252C22⋊C4×C83—28no—
253C42×C83—28no—
254C42×C83C2×D4116yescomplemented
255C23×C83—28no—
256C23×C83—28no—
257C23×C83—28no—
258C23×C83—22no—
259C23×C83—22no—
260C23×C83—22no—
261C23×C83—22no—
262C23×C83—22no—
263C23×C83—22no—
264C23×C83—44no—
265C23×C83—44no—
266C23×C83—44no—
267C23×C83—44no—
268C23×C83C22×D412yes—
269C23×C83C2×#4112yes—
270C23×C83C2×#4112yes—
271C23×C83C2×#4114yes—
272C23×C83C2×#4112yes—
273C23×C83C2×#4112yes—
274C23×C83H(5,𝔽2)12yes—
275C23×C832−1+412yes—
276C23×C83C2511yescharacteristic
277C22×D83—28no—
278C22×D83—28no—
279C22×D83—28no—
280C22×D83—22no—
281C22×D83—22no—
282C22×D83—22no—
283C22×D83—22no—
284C22×D83—22no—
285C22×D83—22no—
286C22×D83—44no—
287C22×D83—44no—
288C22×D83—44no—
289C22×D83—44no—
290C22×D83C2×#4114yes—
291C2×C4×C83—232no—
292C2×C4×C83—28no—
293C2×C4×C83—28no—
294C2×C4×C83—28no—
295C2×C4×C83—28no—
296C2×C4×C83—22no—
297C2×C4×C83—22no—
298C2×C4×C83—22no—
299C2×C4×C83—22no—
300C2×C4×C83—22no—
301C2×C4×C83—22no—
302C2×C4×C83—22no—
303C2×C4×C83—22no—
304C2×C4×C83—22no—
305C2×C4×C83—22no—
306C2×C4×C83—22no—
307C2×C4×C83—22no—
308C2×C4×C83—22no—
309C2×C4×C83—22no—
310C2×C4×C83—44no—
311C2×C4×C83—44no—
312C2×C4×C83C22×D414yes—
313C2×C4×C83C22×D414yes—
314C2×C4×C83C22×D414yes—
315C2×C4×C83C2×#4114yes—
316C22⋊D83—416no—
317C2×Dic83—28no—
318C2×Dic83—22no—
319C2×Dic83—22no—
320C2×Dic83—22no—
321C2×Dic83—22no—
322C2×Dic83—22no—
323C2×Dic83—22no—
324C2×Dic83—22no—
325C2×Dic83—22no—
326C2×Dic83—22no—
327C2×Dic83—22no—
328C2×Dic83—22no—
329C2×Dic83—22no—
330C2×Dic83—22no—
331C2×Dic83—22no—
332C2×Dic83—22no—
333C2×Dic83—22no—
334C2×Dic83—22no—
335C2×Dic83—22no—
336C2×Dic83—22no—
337C2×Dic83—22no—
338C2×Dic83—44no—
339C2×Dic83—44no—
340C2×Dic83—44no—
341C2×Dic83—44no—
342C2×Dic83—44no—
343C2×Dic83—44no—
344C2×Dic83C2×#4114yes—
345C4×D83—232no—
346C22×C83—24no—
347C22×C83—24no—
348C22×C83—24no—
349C22×C83—416no—
350C22×C83—42no—
351C22×C83—42no—
352C22×C83—42no—
353C22×C83—42no—
354C22×C83#52514yes—
355C22×C83#52514yes—
356C22×C83#53714yes—
357C22×C83#55114yes—
358C22×C83#55214yes—
359C22×C83#55214yes—
360C22×C83#55514yes—
361C22×C83C23×D411yescharacteristic
362C22×C83C22×#4111yescharacteristic
363C22×C83C22×#4111yescharacteristic
364C22×C83C22×#4111yescharacteristic
365C22×C83C22×#4111yescharacteristic
366C22×C83C2×H(5,𝔽2)11yescharacteristic
367C22×C83C2×2−1+411yescharacteristic
368C2×D83—24no—
369C2×D83—24no—
370C2×D83—24no—
371C2×D83—416no—
372C2×D83—42no—
373C2×D83—42no—
374C2×D83—42no—
375C2×D83—42no—
376C4×C83—24no—
377C4×C83—24no—
378C4×C83—24no—
379C4×C83—24no—
380C4×C83—42no—
381C4×C83—42no—
382Dic83—24no—
383Dic83—42no—
384Dic83—42no—
385Dic83—42no—
386Dic83—42no—
387Dic83—42no—
388Dic83—42no—
389C2×#2609—831nomaximal, Sylow
390C2×C83—44no—
391C2×C83#260918yescomplemented
392C2×C83C2×#52511yescharacteristic
393C2×C83C2×#52511yescharacteristic
394C2×C83C2×#53711yescharacteristic
395C2×C83C2×#55111yescharacteristic
396C2×C83C2×#55211yescharacteristic
397C2×C83C2×#55211yescharacteristic
398C2×C83C2×#55511yescharacteristic
399D83—44no—
400C22×#117—831no—
401C22×#117D8311yescharacteristic, complemented
402#2609—8316no—
403C2×#398—831no—
404C2×#396—831no—
405C2×#396—831no—
406C2×#394—831no—
407C2×#388—831no—
408C2×#388—831no—
409C2×#387—831no—
410C2×#387—831no—
411C2×#386—831no—
412C2×#386—831no—
413C2×#385—831no—
414C2×#385—831no—
415C2×#382—831no—
416C83C2×#260911yescharacteristic, complemented, Sylow
417C23×D4—831no—
418C24×C4—831no—
419C24×C4C2×D8311yescharacteristic
420C2×#117—28no—
421C2×#117—838no—
422C2×#117—1668no—
423C2×#117C2×D8318yescomplemented
424C22×C4⋊C4—831no—
425C22×C4⋊C4—831no—
426C22×C4⋊C4—831no—
427C22×C4⋊C4—831no—
428C22×C4⋊C4—831no—
429C22×C4⋊C4—831no—
430C22×C4⋊C4—831no—
431C22×C4⋊C4C2×D8311yescharacteristic
432C22×C4⋊C4C2×D8311yescharacteristic
433C22×C22⋊C4—831no—
434C22×C22⋊C4—831no—
435C22×C22⋊C4—831no—
436C22×C22⋊C4—831no—
437C22×C22⋊C4—831no—
438C22×C22⋊C4—831no—
439C22×C22⋊C4—831no—
440C22×C22⋊C4—831no—
441C22×C22⋊C4C2×D8311yescharacteristic
442C22×C22⋊C4C2×D8311yescharacteristic
443C22×C42—831no—
444C22×C42C2×D8311yescharacteristic
445C22×C42C2×D8311yescharacteristic
446#398—838no—
447#396—838no—
448#396—838no—
449#394—838no—
450#388—838no—
451#388—838no—
452#387—838no—
453#387—838no—
454#386—838no—
455#386—838no—
456#385—838no—
457#385—838no—
458#382—838no—
459C2×#95—831no—
460C2×#95—831no—
461C2×#95—831no—
462C2×#95—831no—
463C2×#95—831no—
464C2×#95—831no—
465C2×#95—831no—
466C2×#95—831no—
467C2×#95—831no—
468C2×#95—831no—
469C25—831no—
470C25C22×D8311yescharacteristic
471C22×D4—3322no—
472C22×D4—834no—
473C22×D4—1664no—
474C22×D4—1664no—
475C23×C4—24no—
476C23×C4—24no—
477C23×C4—24no—
478C23×C4—831no—
479C23×C4—831no—
480C23×C4—831no—
481C23×C4—831no—
482C23×C4—831no—
483C23×C4—831no—
484C23×C4—831no—
485C23×C4—834no—
486C23×C4—1664no—
487C23×C4—1664no—
488C23×C4—1664no—
489C23×C4C22×D8314yes—
490C23×C4C22×D8311yescharacteristic
491C23×C4C22×D8311yescharacteristic
492C23×C4C22×D8311yescharacteristic
493C23×C4C22×D8311yescharacteristic
494C23×C4C22×D8311yescharacteristic
495C23×C4C22×D8311yescharacteristic
496#117—232no—
497#117—16632no—
498C2×C4⋊C4—24no—
499C2×C4⋊C4—24no—
500C2×C4⋊C4—3322no—
501C2×C4⋊C4—3322no—
502C2×C4⋊C4—3322no—
503C2×C4⋊C4—834no—
504C2×C4⋊C4—834no—
505C2×C4⋊C4—834no—
506C2×C4⋊C4—834no—
507C2×C4⋊C4—834no—
508C2×C4⋊C4—834no—
509C2×C4⋊C4—834no—
510C2×C4⋊C4—1664no—
511C2×C4⋊C4—1664no—
512C2×C4⋊C4—1664no—
513C2×C4⋊C4—1664no—
514C2×C4⋊C4C22×D8314yes—
515C2×C4⋊C4C22×D8314yes—
516C2×C22⋊C4—24no—
517C2×C22⋊C4—24no—
518C2×C22⋊C4—3322no—
519C2×C22⋊C4—3322no—
520C2×C22⋊C4—834no—
521C2×C22⋊C4—834no—
522C2×C22⋊C4—834no—
523C2×C22⋊C4—834no—
524C2×C22⋊C4—834no—
525C2×C22⋊C4—834no—
526C2×C22⋊C4—834no—
527C2×C22⋊C4—834no—
528C2×C22⋊C4—1664no—
529C2×C22⋊C4—1664no—
530C2×C22⋊C4—1664no—
531C2×C22⋊C4—1664no—
532C2×C22⋊C4—1664no—
533C2×C22⋊C4—1664no—
534C2×C22⋊C4C22×D8314yes—
535C2×C22⋊C4C22×D8314yes—
536C2×C42—24no—
537C2×C42—834no—
538C2×C42—1664no—
539C2×C42C22⋊D8318yescomplemented
540C2×C42C22×D8314yes—
541C2×C42C22×D8314yes—
542#95—834no—
543#95—834no—
544#95—834no—
545#95—834no—
546#95—834no—
547#95—834no—
548#95—834no—
549#95—834no—
550#95—834no—
551#95—834no—
552C24—22no—
553C24—22no—
554C24—22no—
555C24—22no—
556C24—22no—
557C24—22no—
558C24—834no—
559C24—832no—
560C24—1662no—
561C24—1662no—
562C24—1662no—
563C24—1662no—
564C24—1662no—
565C24—1662no—
566C24#1305059014yes—
567C24C23×D8312yes—
568C24C23×D8311yescharacteristic
569C2×D4—33216no—
570C2×D4—3324no—
571C2×D4—1668no—
572C2×D4—1668no—
573C22×C4—232no—
574C22×C4—22no—
575C22×C4—22no—
576C22×C4—22no—
577C22×C4—28no—
578C22×C4—22no—
579C22×C4—22no—
580C22×C4—22no—
581C22×C4—22no—
582C22×C4—22no—
583C22×C4—28no—
584C22×C4—28no—
585C22×C4—22no—
586C22×C4—22no—
587C22×C4—22no—
588C22×C4—22no—
589C22×C4—22no—
590C22×C4—22no—
591C22×C4—834no—
592C22×C4—832no—
593C22×C4—832no—
594C22×C4—832no—
595C22×C4—832no—
596C22×C4—832no—
597C22×C4—832no—
598C22×C4—832no—
599C22×C4—1668no—
600C22×C4—1668no—
601C22×C4—16632no—
602C22×C4—1662no—
603C22×C4—1662no—
604C22×C4—1662no—
605C22×C4—1662no—
606C22×C4—1662no—
607C22×C4—1662no—
608C22×C4—1662no—
609C22×C4—1662no—
610C22×C4—1662no—
611C22×C4—1662no—
612C22×C4—1662no—
613C22×C4—1662no—
614C22×C4—1662no—
615C22×C4—1662no—
616C22×C4—1662no—
617C22×C4—1662no—
618C22×C4—1662no—
619C22×C4—1662no—
620C22×C4—1662no—
621C22×C4—1662no—
622C22×C4—1668no—
623C22×C4C2×C22⋊D8314yes—
624C22×C4C2×C22⋊D8314yes—
625C22×C4C2×C22⋊D8314yes—
626C22×C4#1305059014yes—
627C22×C4C23×D8312yes—
628C22×C4C23×D8312yes—
629C22×C4C23×D8312yes—
630C22×C4C23×D8312yes—
631C22×C4C23×D8312yes—
632C22×C4C23×D8312yes—
633C4⋊C4—28no—
634C4⋊C4—28no—
635C4⋊C4—3324no—
636C4⋊C4—3324no—
637C4⋊C4—3324no—
638C4⋊C4—1668no—
639C4⋊C4—1668no—
640C4⋊C4—1668no—
641C4⋊C4—1668no—
642C22⋊C4—28no—
643C22⋊C4—28no—
644C22⋊C4—3324no—
645C22⋊C4—3324no—
646C22⋊C4—1668no—
647C22⋊C4—1668no—
648C22⋊C4—1668no—
649C22⋊C4—1668no—
650C22⋊C4—1668no—
651C22⋊C4—1668no—
652C42—28no—
653C42—1668no—
654C42C2×C22⋊D83116yescomplemented
655C23—28no—
656C23—28no—
657C23—28no—
658C23—22no—
659C23—22no—
660C23—22no—
661C23—22no—
662C23—22no—
663C23—22no—
664C23—44no—
665C23—44no—
666C23—44no—
667C23—44no—
668C23—3324no—
669C23—3324no—
670C23—3324no—
671C23—3324no—
672C23—834no—
673C23—1668no—
674C23—1668no—
675C23—1668no—
676C23—1662no—
677C23—1662no—
678C23—1662no—
679C23—1662no—
680C23—1662no—
681C23—1662no—
682C23C22×C22⋊D8312yes—
683C23#41×D8312yes—
684C23#41×D8312yes—
685C23C2×#1305059014yes—
686C23C2×#1305059012yes—
687C23C2×#1305059012yes—
688C23#1458183812yes—
689C23#1458183912yes—
690C23C24×D8311yescharacteristic
691D4—33216no—
692C2×C4—232no—
693C2×C4—28no—
694C2×C4—28no—
695C2×C4—28no—
696C2×C4—22no—
697C2×C4—22no—
698C2×C4—22no—
699C2×C4—22no—
700C2×C4—22no—
701C2×C4—22no—
702C2×C4—22no—
703C2×C4—22no—
704C2×C4—28no—
705C2×C4—22no—
706C2×C4—22no—
707C2×C4—22no—
708C2×C4—22no—
709C2×C4—22no—
710C2×C4—22no—
711C2×C4—44no—
712C2×C4—44no—
713C2×C4—3324no—
714C2×C4—3324no—
715C2×C4—3324no—
716C2×C4—3324no—
717C2×C4—3324no—
718C2×C4—3324no—
719C2×C4—834no—
720C2×C4—16632no—
721C2×C4—1662no—
722C2×C4—1662no—
723C2×C4—1662no—
724C2×C4—1662no—
725C2×C4—1662no—
726C2×C4—1662no—
727C2×C4—1662no—
728C2×C4—1662no—
729C2×C4—1662no—
730C2×C4—1662no—
731C2×C4—1662no—
732C2×C4—1662no—
733C2×C4—1662no—
734C2×C4—1662no—
735C2×C4—1662no—
736C2×C4—1662no—
737C2×C4—1662no—
738C2×C4—1662no—
739C2×C4—1668no—
740C2×C4—1662no—
741C2×C4—1662no—
742C2×C4C22×C22⋊D8314yes—
743C2×C4C22×C22⋊D8314yes—
744C2×C4C22×C22⋊D8314yes—
745C2×C4C2×#1305059014yes—
746C22—24no—
747C22—24no—
748C22—24no—
749C22—42no—
750C22—42no—
751C22—42no—
752C22—42no—
753C22—416no—
754C22—3322no—
755C22—3322no—
756C22—3322no—
757C22—3322no—
758C22—33216no—
759C22—1664no—
760C22—1664no—
761C22—1664no—
762C22#1912820814yes—
763C22#1912821214yes—
764C22#1912827914yes—
765C22#1912837514yes—
766C22#1912838414yes—
767C22#1912839014yes—
768C22#1912841414yes—
769C22C23×C22⋊D8311yescharacteristic
770C22C2×#41×D8311yescharacteristic
771C22C2×#41×D8311yescharacteristic
772C22C22×#1305059011yescharacteristic
773C22C22×#1305059011yescharacteristic
774C22C2×#1458183811yescharacteristic
775C22C2×#1458183911yescharacteristic
776C4—24no—
777C4—24no—
778C4—24no—
779C4—24no—
780C4—42no—
781C4—42no—
782C4—3322no—
783C4—3322no—
784C4—3322no—
785C4—3322no—
786C4—3322no—
787C4—3322no—
788C4—1664no—
789C2—44no—
790C2—3324no—
791C2#2491313518yesdirect product factor
792C2C2×#1912820811yescharacteristic
793C2C2×#1912821211yescharacteristic
794C2C2×#1912827911yescharacteristic
795C2C2×#1912837511yescharacteristic
796C2C2×#1912838411yescharacteristic
797C2C2×#1912839011yescharacteristic
798C2C2×#1912841411yescharacteristic
subgroupG/H
centerC24C23×D83
commutator, cosocleC23×C83C25
FrattiniC23C24×D83
FittingC22×#117×C83C2
socleC24×C83C24
prime radicalC23×C22⋊D83C22
hypercenterC22×#117D83
hypocenterC83C2×#2609
LCSG ▷ C23×C83 ▷ C83
UCSC1 ◁ C24 ◁ C22×#117

Complements

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

NH ≅ G/Ntype
1. C22×#14581749C2semidirect
2. #24913135C2direct (N × H)
3. C2×#19127634C2semidirect
4. C2×#19127624C2semidirect
5. C2×#19127623C2semidirect
7. C2×#19127592C2semidirect
8. C2×#19127589C2semidirect
9. C2×#19127585C2semidirect
10. C2×#19127582C2semidirect
13. C2×#19127574C2semidirect
14. C2×#19127572C2semidirect
15. C2×#19127567C2semidirect
16. C22×#117×C83C2semidirect
20. C2×#14581749C22semidirect
37. #19127634C22semidirect
38. #19127624C22semidirect
39. #19127623C22semidirect
41. #19127592C22semidirect
42. #19127589C22semidirect
43. #19127585C22semidirect
44. #19127582C22semidirect
47. #19127574C22semidirect
48. #19127572C22semidirect
49. #19127567C22semidirect
62. C2×#117×C83C22semidirect
149. C2×C42×C83D4semidirect
254. C42×C83C2×D4semidirect
391. C2×C83#2609semidirect
401. C22×#117D83semidirect
416. C83C2×#2609semidirect
423. C2×#117C2×D83semidirect
539. C2×C42C22⋊D83semidirect
654. C42C2×C22⋊D83semidirect
791. C2#24913135direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#145817492
#249131352
C2×#191276342
C2×#191276242
C2×#191276232
C2×#191276172
C2×#191275922
C2×#191275892
C2×#191275852
C2×#191275822
C2×#191275802
C2×#191275772
C2×#191275742
C2×#191275722
C2×#191275672
C22×#117×C832
C2×#260983