Finite Group Databasebeta

← C2×#24910250 #35563295

Subgroups — C2×#24910250 #35563295

Order 21248.

2982 conjugacy classes of subgroups.

The subgroup lattice has 796 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#14581773C211yesmaximal, characteristic
2#24910250C2116yesmaximal, direct product factor
3C2×#19127596C211yesmaximal, characteristic, complemented
4C2×#19127595C211yesmaximal, characteristic, complemented
5C2×#19127589C211yesmaximal, characteristic, complemented
6C2×#19127589C211yesmaximal, characteristic, complemented
7C2×#19127589C211yesmaximal, characteristic, complemented
8C2×#19127585C211yesmaximal, characteristic, complemented
9C2×#19127582C211yesmaximal, characteristic, complemented
10C2×#19127581C211yesmaximal, characteristic
11C2×#19127573C211yesmaximal, characteristic, complemented
12C2×#19127559C211yesmaximal, characteristic, complemented
13C2×C4×Dic83⋊C4C211yesmaximal, characteristic, complemented
14C2×C22⋊C4×Dic83C211yesmaximal, characteristic, complemented
15C2×C22⋊C4×Dic83C211yesmaximal, characteristic, complemented
16C2×#390×C83C211yesmaximal, characteristic
17C24×Dic83C2211yescharacteristic
18C24×Dic83C2211yescharacteristic
19C2×#14581773C4116yescomplemented
20C2×#14581773C2218yes—
21C22×Dic83⋊C4C2211yescharacteristic
22C22×Dic83⋊C4C2211yescharacteristic
23C22×Dic83⋊C4C2211yescharacteristic
24C22×Dic83⋊C4C2211yescharacteristic
25C22×Dic83⋊C4C2211yescharacteristic
26C22×Dic83⋊C4C2211yescharacteristic
27C22×C22⋊Dic83C2211yescharacteristic
28C22×C22⋊Dic83C2211yescharacteristic
29C22×C22⋊Dic83C2211yescharacteristic
30C22×C22⋊Dic83C2211yescharacteristic
31C22×C22⋊Dic83C2211yescharacteristic
32C22×C22⋊Dic83C2211yescharacteristic
33C22×C4×Dic83C2211yescharacteristic
34C22×C4×Dic83C2211yescharacteristic
35C22×C4×Dic83C2211yescharacteristic
36C22×C4×Dic83C2211yescharacteristic
37#19127596C2218yescomplemented
38#19127595C2218yescomplemented
39#19127589C2218yescomplemented
40#19127589C2218yescomplemented
41#19127589C2218yescomplemented
42#19127585C2218yescomplemented
43#19127582C2218yescomplemented
44#19127581C2218yes—
45#19127573C2218yescomplemented
46#19127559C2218yescomplemented
47C4×Dic83⋊C4C2218yescomplemented
48C22⋊C4×Dic83C2218yescomplemented
49C22⋊C4×Dic83C2218yescomplemented
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
60C23×D4×C83C2211yescharacteristic
61C22×C4⋊C4×C83C2211yescharacteristic
62C22×C22⋊C4×C83C2211yescharacteristic
63C22×C22⋊C4×C83C2211yescharacteristic
64C22×C22⋊C4×C83C2211yescharacteristic
65C22×C22⋊C4×C83C2211yescharacteristic
66C22×C42×C83C2211yescharacteristic
67#390×C83C2218yes—
68C23×Dic83—24no—
69C23×Dic83—42no—
70C23×Dic83—42no—
71C23×Dic83—42no—
72C23×Dic83—42no—
73C23×Dic83C2×C418yescomplemented
74C23×Dic83C2311yescharacteristic
75C23×Dic83C2311yescharacteristic
76C23×Dic83C2311yescharacteristic
77C23×Dic83C2311yescharacteristic
78C23×Dic83C2311yescharacteristic
79C23×Dic83C2311yescharacteristic
80C23×Dic83C2311yescharacteristic
81C23×Dic83C2311yescharacteristic
82C23×Dic83C2314yes—
83C23×Dic83C2314yes—
84#14581773C2×C4164yescomplemented
85C2×Dic83⋊C4—24no—
86C2×Dic83⋊C4—42no—
87C2×Dic83⋊C4—42no—
88C2×Dic83⋊C4—42no—
89C2×Dic83⋊C4C2×C418yescomplemented
90C2×Dic83⋊C4C2×C418yescomplemented
91C2×Dic83⋊C4C2314yes—
92C2×Dic83⋊C4C2314yes—
93C2×Dic83⋊C4C2314yes—
94C2×Dic83⋊C4C2314yes—
95C2×Dic83⋊C4C2314yes—
96C2×Dic83⋊C4C2314yes—
97C2×C22⋊Dic83—24no—
98C2×C22⋊Dic83—42no—
99C2×C22⋊Dic83—42no—
100C2×C22⋊Dic83C2×C418yes—
101C2×C22⋊Dic83C2×C418yes—
102C2×C22⋊Dic83C2×C418yescomplemented
103C2×C22⋊Dic83C2314yes—
104C2×C22⋊Dic83C2314yes—
105C2×C22⋊Dic83C2314yes—
106C2×C22⋊Dic83C2314yes—
107C2×C22⋊Dic83C2314yes—
108C2×C22⋊Dic83C2314yes—
109C2×C4×Dic83—24no—
110C2×C4×Dic83—42no—
111C2×C4×Dic83—42no—
112C2×C4×Dic83—42no—
113C2×C4×Dic83C2314yes—
114C2×C4×Dic83C2314yes—
115C2×C4×Dic83C2314yes—
116C2×C4×Dic83C2314yes—
117C83⋊#95C2314yes—
118C83⋊#95C2314yes—
119C83⋊#95C2314yes—
120C83⋊#95C2314yes—
121C83⋊#95C2314yes—
122C83⋊#95C2314yes—
123C83⋊#95C2314yes—
124C83⋊#95C2314yes—
125C83⋊#95C2314yes—
126C83⋊#95C2314yes—
127C25×C83C2311yescharacteristic
128C25×C83C2311yescharacteristic
129C22×D4×C83—42no—
130C22×D4×C83—42no—
131C22×D4×C83C2×C418yes—
132C22×D4×C83C2314yes—
133C23×C4×C83C2311yescharacteristic
134C23×C4×C83C2311yescharacteristic
135C23×C4×C83C2311yescharacteristic
136C23×C4×C83C2311yescharacteristic
137C23×C4×C83C2311yescharacteristic
138C2×C4⋊C4×C83—42no—
139C2×C4⋊C4×C83C2314yes—
140C2×C22⋊C4×C83—24no—
141C2×C22⋊C4×C83—24no—
142C2×C22⋊C4×C83—42no—
143C2×C22⋊C4×C83—42no—
144C2×C22⋊C4×C83C2314yes—
145C2×C22⋊C4×C83C2314yes—
146C2×C22⋊C4×C83C2314yes—
147C2×C22⋊C4×C83C2314yes—
148C2×C42×C83—42no—
149C2×C42×C83C2314yes—
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×Dic83—28no—
170C22×Dic83—416no—
171C22×Dic83—44no—
172C22×Dic83—44no—
173C22×Dic83—44no—
174C22×Dic83—44no—
175C22×Dic83—416no—
176C22×Dic83C22×C414yes—
177C22×Dic83C22×C414yes—
178C22×Dic83C22×C414yes—
179C22×Dic83C22×C414yes—
180C22×Dic83C22×C4116yescomplemented
181C22×Dic83#4114yes—
182C22×Dic83C2412yes—
183C22×Dic83C2412yes—
184C22×Dic83C2412yes—
185C22×Dic83C2412yes—
186C22×Dic83C2412yes—
187C22×Dic83C2412yes—
188C22×Dic83C2412yes—
189C22×Dic83C2412yes—
190Dic83⋊C4—28no—
191Dic83⋊C4—44no—
192Dic83⋊C4—44no—
193Dic83⋊C4—44no—
194Dic83⋊C4C22×C4116yescomplemented
195Dic83⋊C4C22×C4116yescomplemented
196C22⋊Dic83—28no—
197C22⋊Dic83—44no—
198C22⋊Dic83—44no—
199C22⋊Dic83C22×C4116yes—
200C22⋊Dic83C22×C4116yes—
201C22⋊Dic83C22×C4116yescomplemented
202C4×Dic83—28no—
203C4×Dic83—44no—
204C4×Dic83—44no—
205C4×Dic83—44no—
206C24×C83—22no—
207C24×C83—22no—
208C24×C83—22no—
209C24×C83—22no—
210C24×C83—22no—
211C24×C83—22no—
212C24×C83—22no—
213C24×C83—22no—
214C24×C83—22no—
215C24×C83—22no—
216C24×C83—22no—
217C24×C83—22no—
218C24×C83C22×C414yes—
219C24×C83C22×C414yes—
220C24×C83C2412yes—
221C24×C83C2412yes—
222C24×C83C2411yescharacteristic
223C2×D4×C83—416no—
224C2×D4×C83—44no—
225C2×D4×C83—44no—
226C2×D4×C83C22×C4116yes—
227C22×C4×C83—22no—
228C22×C4×C83—22no—
229C22×C4×C83—22no—
230C22×C4×C83—22no—
231C22×C4×C83—22no—
232C22×C4×C83—22no—
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×C83—22no—
240C22×C4×C83C22×C414yes—
241C22×C4×C83#4114yes—
242C22×C4×C83C2412yes—
243C22×C4×C83C2412yes—
244C22×C4×C83C2412yes—
245C22×C4×C83C2412yes—
246C22×C4×C83C2412yes—
247C4⋊C4×C83—44no—
248C22⋊C4×C83—28no—
249C22⋊C4×C83—28no—
250C22⋊C4×C83—44no—
251C22⋊C4×C83—44no—
252C42×C83—44no—
253C23×C83—28no—
254C23×C83—28no—
255C23×C83—28no—
256C23×C83—28no—
257C23×C83—28no—
258C23×C83—28no—
259C23×C83—22no—
260C23×C83—22no—
261C23×C83—22no—
262C23×C83—22no—
263C23×C83—22no—
264C23×C83—22no—
265C23×C83—22no—
266C23×C83—22no—
267C23×C83—22no—
268C23×C83—22no—
269C23×C83—22no—
270C23×C83—22no—
271C23×C83—44no—
272C23×C83—44no—
273C23×C83—44no—
274C23×C83—44no—
275C23×C83—44no—
276C23×C83—44no—
277C23×C83—44no—
278C23×C83—44no—
279C23×C83C23×C414yes—
280C23×C83C23×C414yes—
281C23×C83C23×C412yes—
282C23×C83C2×#4112yes—
283C23×C83C2×#4112yes—
284C23×C83H(5,𝔽2)12yes—
285C23×C83H(5,𝔽2)12yes—
286C23×C83H(5,𝔽2)12yes—
287C23×C832−1+412yes—
288C23×C83C2511yescharacteristic
289D4×C83—416no—
290C2×C4×C83—28no—
291C2×C4×C83—28no—
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—22no—
300C2×C4×C83—22no—
301C2×C4×C83—22no—
302C2×C4×C83—22no—
303C2×C4×C83—22no—
304C2×C4×C83—22no—
305C2×C4×C83—44no—
306C2×C4×C83—44no—
307C2×C4×C83—44no—
308C2×C4×C83C23×C414yes—
309C2×C4×C83C2×#4114yes—
310C2×Dic83—28no—
311C2×Dic83—28no—
312C2×Dic83—28no—
313C2×Dic83—28no—
314C2×Dic83—28no—
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—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—416no—
335C2×Dic83—416no—
336C2×Dic83—44no—
337C2×Dic83—44no—
338C2×Dic83—44no—
339C2×Dic83C23×C414yes—
340C2×Dic83C23×C414yes—
341C2×Dic83C23×C414yes—
342C2×Dic83C23×C414yes—
343C2×Dic83C2×#4114yes—
344C22×C83—24no—
345C22×C83—24no—
346C22×C83—24no—
347C22×C83—24no—
348C22×C83—24no—
349C22×C83—24no—
350C22×C83—416no—
351C22×C83—416no—
352C22×C83—42no—
353C22×C83—42no—
354C22×C83—42no—
355C22×C83—42no—
356C22×C83—42no—
357C22×C83—42no—
358C22×C83—42no—
359C22×C83—42no—
360C22×C83C4×#4114yes—
361C22×C83#51814yes—
362C22×C83#52014yes—
363C22×C83#53814yes—
364C22×C83#53914yes—
365C22×C83#54014yes—
366C22×C83#54214yes—
367C22×C83C24×C411yescharacteristic
368C22×C83C22×#4111yescharacteristic
369C22×C83C22×#4111yescharacteristic
370C22×C83C2×H(5,𝔽2)11yescharacteristic
371C22×C83C2×H(5,𝔽2)11yescharacteristic
372C22×C83C2×H(5,𝔽2)11yescharacteristic
373C22×C83C2×2−1+411yescharacteristic
374C4×C83—24no—
375C4×C83—24no—
376C4×C83—42no—
377C4×C83—42no—
378C4×C83—42no—
379Dic83—24no—
380Dic83—24no—
381Dic83—24no—
382Dic83—24no—
383Dic83—24no—
384Dic83—42no—
385Dic83—42no—
386Dic83—42no—
387C2×#2335—831nomaximal, Sylow
388C2×C83—44no—
389C2×C83—44no—
390C2×C83#233518yescomplemented
391C2×C83C2×C4×#4111yescharacteristic
392C2×C83C2×#51811yescharacteristic
393C2×C83C2×#52011yescharacteristic
394C2×C83C2×#53811yescharacteristic
395C2×C83C2×#53911yescharacteristic
396C2×C83C2×#54011yescharacteristic
397C2×C83C2×#54211yescharacteristic
398C22×#123—831no—
399#2335—8316no—
400C2×#390D8311yescharacteristic
401C2×#389—831no—
402C2×#388—831no—
403C2×#388—831no—
404C2×#388—831no—
405C2×#388—831no—
406C2×#387—831no—
407C2×#387—831no—
408C2×#386—831no—
409C2×#385—831no—
410C2×#380—831no—
411C2×C4×C4⋊C4—831no—
412C2×C4×C22⋊C4—831no—
413C2×C4×C22⋊C4—831no—
414C83C2×#233511yescharacteristic, complemented, Sylow
415C23×D4C2×D8311yescharacteristic
416C24×C4—831no—
417C24×C4—831no—
418C2×#123—8316no—
419C2×#123—838no—
420C22×C4⋊C4—831no—
421C22×C4⋊C4—831no—
422C22×C4⋊C4—831no—
423C22×C4⋊C4—831no—
424C22×C4⋊C4—831no—
425C22×C4⋊C4—831no—
426C22×C4⋊C4C2×D8311yescharacteristic
427C22×C22⋊C4—831no—
428C22×C22⋊C4—831no—
429C22×C22⋊C4—831no—
430C22×C22⋊C4—831no—
431C22×C22⋊C4—831no—
432C22×C22⋊C4—831no—
433C22×C22⋊C4C2×D8311yescharacteristic
434C22×C22⋊C4C2×D8311yescharacteristic
435C22×C22⋊C4C2×D8311yescharacteristic
436C22×C22⋊C4C2×D8311yescharacteristic
437C22×C42—831no—
438C22×C42—831no—
439C22×C42—831no—
440C22×C42—831no—
441C22×C42C2×D8311yescharacteristic
442#390C2×D8318yes—
443#389—838no—
444#388—838no—
445#388—838no—
446#388—838no—
447#388—838no—
448#387—838no—
449#387—838no—
450#386—838no—
451#385—838no—
452#380—838no—
453C4×C4⋊C4—838no—
454C4×C22⋊C4—838no—
455C4×C22⋊C4—838no—
456C2×#95—831no—
457C2×#95—831no—
458C2×#95—831no—
459C2×#95—831no—
460C2×#95—831no—
461C2×#95—831no—
462C2×#95—831no—
463C2×#95—831no—
464C2×#95—831no—
465C2×#95—831no—
466C25C22×D8311yescharacteristic
467C25C22×D8311yescharacteristic
468C22×D4—42no—
469C22×D4—42no—
470C22×D4C4×D8318yes—
471C22×D4C22×D8314yes—
472C23×C4—3322no—
473C23×C4—3322no—
474C23×C4—3322no—
475C23×C4—3322no—
476C23×C4—838no—
477C23×C4—834no—
478C23×C4—834no—
479C23×C4—831no—
480C23×C4—831no—
481C23×C4—831no—
482C23×C4—831no—
483C23×C4—831no—
484C23×C4—831no—
485C23×C4—831no—
486C23×C4—831no—
487C23×C4—1664no—
488C23×C4C22×D8311yescharacteristic
489C23×C4C22×D8311yescharacteristic
490C23×C4C22×D8311yescharacteristic
491C23×C4C22×D8311yescharacteristic
492C23×C4C22×D8311yescharacteristic
493#123—8364no—
494C2×C4⋊C4—42no—
495C2×C4⋊C4—3322no—
496C2×C4⋊C4—3322no—
497C2×C4⋊C4—3322no—
498C2×C4⋊C4—834no—
499C2×C4⋊C4—834no—
500C2×C4⋊C4—834no—
501C2×C4⋊C4—838no—
502C2×C4⋊C4—838no—
503C2×C4⋊C4—834no—
504C2×C4⋊C4—834no—
505C2×C4⋊C4—834no—
506C2×C4⋊C4—1664no—
507C2×C4⋊C4C22×D8314yes—
508C2×C22⋊C4—24no—
509C2×C22⋊C4—24no—
510C2×C22⋊C4—42no—
511C2×C22⋊C4—42no—
512C2×C22⋊C4—3322no—
513C2×C22⋊C4—3322no—
514C2×C22⋊C4—834no—
515C2×C22⋊C4—834no—
516C2×C22⋊C4—838no—
517C2×C22⋊C4—838no—
518C2×C22⋊C4—838no—
519C2×C22⋊C4—834no—
520C2×C22⋊C4—834no—
521C2×C22⋊C4—834no—
522C2×C22⋊C4—834no—
523C2×C22⋊C4—1664no—
524C2×C22⋊C4C22×D8314yes—
525C2×C22⋊C4C22×D8314yes—
526C2×C22⋊C4C22×D8314yes—
527C2×C22⋊C4C22×D8314yes—
528C2×C42—42no—
529C2×C42—3322no—
530C2×C42—3322no—
531C2×C42—3322no—
532C2×C42—834no—
533C2×C42—834no—
534C2×C42—834no—
535C2×C42—834no—
536C2×C42—1664no—
537C2×C42C22×D8314yes—
538#95—834no—
539#95—834no—
540#95—834no—
541#95—834no—
542#95—834no—
543#95—834no—
544#95—834no—
545#95—834no—
546#95—834no—
547#95—834no—
548C24—22no—
549C24—22no—
550C24—22no—
551C24—22no—
552C24—22no—
553C24—22no—
554C24—22no—
555C24—22no—
556C24—22no—
557C24—22no—
558C24—22no—
559C24—22no—
560C24C2×C4×D8314yes—
561C24C2×C4×D8314yes—
562C24C23×D8312yes—
563C24C23×D8312yes—
564C24C23×D8311yescharacteristic
565C2×D4—416no—
566C2×D4—44no—
567C2×D4—44no—
568C2×D4C2×C4×D83116yes—
569C22×C4—22no—
570C22×C4—22no—
571C22×C4—22no—
572C22×C4—22no—
573C22×C4—22no—
574C22×C4—22no—
575C22×C4—22no—
576C22×C4—22no—
577C22×C4—22no—
578C22×C4—22no—
579C22×C4—22no—
580C22×C4—22no—
581C22×C4—22no—
582C22×C4—33216no—
583C22×C4—3324no—
584C22×C4—3324no—
585C22×C4—33216no—
586C22×C4—3324no—
587C22×C4—3324no—
588C22×C4—8316no—
589C22×C4—834no—
590C22×C4—834no—
591C22×C4—834no—
592C22×C4—834no—
593C22×C4—834no—
594C22×C4—832no—
595C22×C4—832no—
596C22×C4—832no—
597C22×C4—832no—
598C22×C4—832no—
599C22×C4—832no—
600C22×C4—832no—
601C22×C4—832no—
602C22×C4—1668no—
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×C4C2×C4×D8314yes—
623C22×C4#1305058914yes—
624C22×C4C23×D8312yes—
625C22×C4C23×D8312yes—
626C22×C4C23×D8312yes—
627C22×C4C23×D8312yes—
628C22×C4C23×D8312yes—
629C4⋊C4—44no—
630C4⋊C4—3324no—
631C4⋊C4—3324no—
632C4⋊C4—3324no—
633C4⋊C4—8316no—
634C4⋊C4—8316no—
635C4⋊C4—1668no—
636C22⋊C4—28no—
637C22⋊C4—28no—
638C22⋊C4—44no—
639C22⋊C4—44no—
640C22⋊C4—3324no—
641C22⋊C4—3324no—
642C22⋊C4—8316no—
643C22⋊C4—8316no—
644C22⋊C4—8316no—
645C22⋊C4—1668no—
646C42—44no—
647C42—3324no—
648C42—3324no—
649C42—3324no—
650C42—1668no—
651C23—28no—
652C23—28no—
653C23—28no—
654C23—28no—
655C23—28no—
656C23—28no—
657C23—22no—
658C23—22no—
659C23—22no—
660C23—22no—
661C23—22no—
662C23—22no—
663C23—22no—
664C23—22no—
665C23—22no—
666C23—22no—
667C23—22no—
668C23—22no—
669C23—44no—
670C23—44no—
671C23—44no—
672C23—44no—
673C23—44no—
674C23—44no—
675C23—44no—
676C23—44no—
677C23C22×C4×D8314yes—
678C23C22×C4×D8314yes—
679C23C22×C4×D8312yes—
680C23#41×D8312yes—
681C23C2×#1305058912yes—
682C23#1458183712yes—
683C23#1458183712yes—
684C23#1458183712yes—
685C23#1458183912yes—
686C23C24×D8311yescharacteristic
687D4—416no—
688C2×C4—28no—
689C2×C4—22no—
690C2×C4—22no—
691C2×C4—22no—
692C2×C4—22no—
693C2×C4—28no—
694C2×C4—22no—
695C2×C4—22no—
696C2×C4—22no—
697C2×C4—22no—
698C2×C4—22no—
699C2×C4—22no—
700C2×C4—22no—
701C2×C4—22no—
702C2×C4—22no—
703C2×C4—44no—
704C2×C4—44no—
705C2×C4—44no—
706C2×C4—3324no—
707C2×C4—3324no—
708C2×C4—3324no—
709C2×C4—33216no—
710C2×C4—33216no—
711C2×C4—834no—
712C2×C4—834no—
713C2×C4—834no—
714C2×C4—834no—
715C2×C4—834no—
716C2×C4—1662no—
717C2×C4—1662no—
718C2×C4—1662no—
719C2×C4—1662no—
720C2×C4—1662no—
721C2×C4—1662no—
722C2×C4—1662no—
723C2×C4—1662no—
724C2×C4—1662no—
725C2×C4—1668no—
726C2×C4—1668no—
727C2×C4—1668no—
728C2×C4—1668no—
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×C4C22×C4×D8314yes—
741C2×C4C2×#1305058914yes—
742C22—24no—
743C22—24no—
744C22—24no—
745C22—24no—
746C22—24no—
747C22—24no—
748C22—42no—
749C22—42no—
750C22—416no—
751C22—416no—
752C22—42no—
753C22—42no—
754C22—42no—
755C22—42no—
756C22—42no—
757C22—42no—
758C22C4×#1305058914yes—
759C22#1912817414yes—
760C22#1912818014yes—
761C22#1912828314yes—
762C22#1912829614yes—
763C22#1912830514yes—
764C22#1912831514yes—
765C22C23×C4×D8311yescharacteristic
766C22C2×#41×D8311yescharacteristic
767C22C22×#1305058911yescharacteristic
768C22C2×#1458183711yescharacteristic
769C22C2×#1458183711yescharacteristic
770C22C2×#1458183711yescharacteristic
771C22C2×#1458183911yescharacteristic
772C4—24no—
773C4—24no—
774C4—42no—
775C4—42no—
776C4—42no—
777C4—3322no—
778C4—3322no—
779C4—3322no—
780C4—1664no—
781C4—1664no—
782C4—1664no—
783C4—1664no—
784C4—1664no—
785C2—44no—
786C2—44no—
787C2#2491025018yesdirect product factor
788C2C2×C4×#1305058911yescharacteristic
789C2C2×#1912817411yescharacteristic
790C2C2×#1912818011yescharacteristic
791C2C2×#1912828311yescharacteristic
792C2C2×#1912829611yescharacteristic
793C2C2×#1912830511yescharacteristic
794C2C2×#1912831511yescharacteristic
subgroupG/H
centerC24C23×D83
commutatorC22×C83C24×C4
FrattiniC23C24×D83
FittingC2×#390×C83C2
socleC24×C83C24
prime radicalC23×D4×C83C22
cosocleC23×C83C25
hypercenterC2×#390D83
hypocenterC83C2×#2335
LCSG ▷ C22×C83 ▷ C83
UCSC1 ◁ C24 ◁ C2×#390

Complements

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

NH ≅ G/Ntype
2. #24910250C2direct (N × H)
3. C2×#19127596C2semidirect
4. C2×#19127595C2semidirect
5. C2×#19127589C2semidirect
6. C2×#19127589C2semidirect
7. C2×#19127589C2semidirect
8. C2×#19127585C2semidirect
9. C2×#19127582C2semidirect
11. C2×#19127573C2semidirect
12. C2×#19127559C2semidirect
13. C2×C4×Dic83⋊C4C2semidirect
14. C2×C22⋊C4×Dic83C2semidirect
15. C2×C22⋊C4×Dic83C2semidirect
19. C2×#14581773C4semidirect
37. #19127596C22semidirect
38. #19127595C22semidirect
39. #19127589C22semidirect
40. #19127589C22semidirect
41. #19127589C22semidirect
42. #19127585C22semidirect
43. #19127582C22semidirect
45. #19127573C22semidirect
46. #19127559C22semidirect
47. C4×Dic83⋊C4C22semidirect
48. C22⋊C4×Dic83C22semidirect
49. C22⋊C4×Dic83C22semidirect
73. C23×Dic83C2×C4semidirect
84. #14581773C2×C4semidirect
89. C2×Dic83⋊C4C2×C4semidirect
90. C2×Dic83⋊C4C2×C4semidirect
102. C2×C22⋊Dic83C2×C4semidirect
180. C22×Dic83C22×C4semidirect
194. Dic83⋊C4C22×C4semidirect
195. Dic83⋊C4C22×C4semidirect
201. C22⋊Dic83C22×C4semidirect
390. C2×C83#2335semidirect
414. C83C2×#2335semidirect
787. C2#24910250direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#145817732
#249102502
C2×#191275962
C2×#191275952
C2×#191275892
C2×#191275852
C2×#191275822
C2×#191275812
C2×#191275732
C2×#191275592
C2×C4×Dic83⋊C42
C2×C22⋊C4×Dic832
C2×#390×C832
C2×#233583