Finite Group Databasebeta

← #35420494

Subgroups — #35420494

Order 21248.

1162 conjugacy classes of subgroups.

The subgroup lattice has 804 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#19127779C211yesmaximal, characteristic, complemented
2C2×#19127773C211yesmaximal, characteristic, complemented
3#24908404C211yesmaximal, characteristic, complemented
4#24908400C211yesmaximal, characteristic, complemented
5#24907761C211yesmaximal, characteristic, complemented
6#24907761C211yesmaximal, characteristic, complemented
7#24907761C211yesmaximal, characteristic, complemented
8#24907756C211yesmaximal, characteristic, complemented
9#24907534C211yesmaximal, characteristic, complemented
10#24907531C211yesmaximal, characteristic, complemented
11#24907447C211yesmaximal, characteristic, complemented
12#24907229C211yesmaximal, characteristic, complemented
13#24907160C211yesmaximal, characteristic, complemented
14#24907157C211yesmaximal, characteristic, complemented
15C2×#529×C83C211yesmaximal, characteristic
16C22×#13050574C2211yescharacteristic
17C22×#13050574C2211yescharacteristic
18C22×#13050574C2211yescharacteristic
19C23×C83⋊C8C2211yescharacteristic
20#19127779—24no—
21#19127773—24no—
22C2×C4⋊(C83⋊C8)C2211yescharacteristic
23C2×C4⋊(C83⋊C8)C2211yescharacteristic
24C2×C22⋊(C83⋊C8)C2211yescharacteristic
25C2×C22⋊(C83⋊C8)C2211yescharacteristic
26C2×C22⋊(C83⋊C8)C2211yescharacteristic
27C2×C22⋊(C83⋊C8)C2211yescharacteristic
28C2×C22⋊(C83⋊C8)C2211yescharacteristic
29C2×C22⋊(C83⋊C8)C2211yescharacteristic
30C2×C22⋊(C83⋊C8)C2211yescharacteristic
31C2×C22⋊(C83⋊C8)C2211yescharacteristic
32C2×#14581703C2211yescharacteristic
33C2×C4×C83⋊C8C2211yescharacteristic
34#19127456C2211yescharacteristic
35#19127456C2211yescharacteristic
36#19127456C2211yescharacteristic
37#19127456C2211yescharacteristic
38#19127456C2211yescharacteristic
39#19127456C2211yescharacteristic
40#19127456C2211yescharacteristic
41#19127456C2211yescharacteristic
42#19127456C2211yescharacteristic
43#19127456C2211yescharacteristic
44#19127456C2211yescharacteristic
45#19127456C2211yescharacteristic
46#529×C83—24no—
47#529×C83—24no—
48C2×#126×C83C411yescharacteristic
49C2×#126×C83C411yescharacteristic
50C2×#125×C83C411yescharacteristic
51C2×#124×C83C411yescharacteristic
52C2×#123×C83C411yescharacteristic
53C2×#123×C83C411yescharacteristic
54C2×C22⋊Q8×C83C411yescharacteristic
55C2×#121×C83C411yescharacteristic
56C2×C4×Q8×C83C2211yescharacteristic
57C2×C4×D4×C83C2211yescharacteristic
58C2×C4×D4×C83C2211yescharacteristic
59C2×C4×D4×C83C2211yescharacteristic
60C2×#117×C83C2211yescharacteristic
61C2×#117×C83C2211yescharacteristic
62C22×C42×C83C2211yescharacteristic
63C2×#13050574—22no—
64C2×#13050574—22no—
65C2×#13050574—22no—
66C2×#13050574—22no—
67C2×#13050574—22no—
68C2×#13050574—22no—
69C2×#13050574—41no—
70C2×#13050574—41no—
71C2×#13050574—41no—
72C22×C83⋊C8—22no—
73C22×C83⋊C8—22no—
74C22×C83⋊C8—41no—
75C22×C83⋊C8C2311yescharacteristic
76C22×C83⋊C8C2311yescharacteristic
77C22×C83⋊C8C2311yescharacteristic
78C22×C83⋊C8C2311yescharacteristic
79C22×C83⋊C8C2311yescharacteristic
80C22×C83⋊C8C2311yescharacteristic
81C22×C83⋊C8C2311yescharacteristic
82C22×C83⋊C8C2311yescharacteristic
83C4⋊(C83⋊C8)—22no—
84C4⋊(C83⋊C8)—22no—
85C22⋊(C83⋊C8)—22no—
86C22⋊(C83⋊C8)—22no—
87C22⋊(C83⋊C8)—22no—
88C22⋊(C83⋊C8)—22no—
89C22⋊(C83⋊C8)—22no—
90C22⋊(C83⋊C8)—22no—
91C22⋊(C83⋊C8)—41no—
92C22⋊(C83⋊C8)—41no—
93#14581703—22no—
94C4×C83⋊C8—22no—
95C22×Q8×C83C2×C411yescharacteristic
96C22×D4×C83C2×C411yescharacteristic
97C22×D4×C83C2×C411yescharacteristic
98C22×D4×C83C2×C411yescharacteristic
99C23×C4×C83C2×C411yescharacteristic
100C23×C4×C83C2×C411yescharacteristic
101C23×C4×C83C2311yescharacteristic
102C23×C4×C83C2311yescharacteristic
103C23×C4×C83C2311yescharacteristic
104#126×C83—24no—
105#126×C83—24no—
106#125×C83—24no—
107#124×C83—24no—
108#123×C83—24no—
109#123×C83—24no—
110C22⋊Q8×C83—24no—
111#121×C83—24no—
112C4×Q8×C83—22no—
113C4×Q8×C83—22no—
114C4×D4×C83—22no—
115C4×D4×C83—22no—
116C4×D4×C83—22no—
117C4×D4×C83—22no—
118C4×D4×C83D414yes—
119C4×D4×C83D414yes—
120#117×C83—22no—
121#117×C83—22no—
122#117×C83—22no—
123#117×C83—22no—
124C2×C4⋊C4×C83C2×C411yescharacteristic
125C2×C4⋊C4×C83C2×C411yescharacteristic
126C2×C4⋊C4×C83C2×C411yescharacteristic
127C2×C4⋊C4×C83C2×C411yescharacteristic
128C2×C4⋊C4×C83C2×C411yescharacteristic
129C2×C4⋊C4×C83C2×C411yescharacteristic
130C2×C4⋊C4×C83C2×C411yescharacteristic
131C2×C4⋊C4×C83C2×C411yescharacteristic
132C2×C4⋊C4×C83C2×C411yescharacteristic
133C2×C4⋊C4×C83C2×C411yescharacteristic
134C2×C22⋊C4×C83C2×C411yescharacteristic
135C2×C22⋊C4×C83C2×C411yescharacteristic
136C2×C22⋊C4×C83C2×C411yescharacteristic
137C2×C22⋊C4×C83C2×C411yescharacteristic
138C2×C22⋊C4×C83C2×C411yescharacteristic
139C2×C22⋊C4×C83C2×C411yescharacteristic
140C2×C22⋊C4×C83C2×C411yescharacteristic
141C2×C22⋊C4×C83C2×C411yescharacteristic
142C2×C22⋊C4×C83C2×C411yescharacteristic
143C2×C22⋊C4×C83C2×C411yescharacteristic
144C2×C42×C83—22no—
145C2×C42×C83—22no—
146C2×C42×C83C2×C411yescharacteristic
147C2×C42×C83C2×C411yescharacteristic
148C2×C42×C83C2311yescharacteristic
149C2×C42×C83C2311yescharacteristic
150C2×C42×C83C2311yescharacteristic
151C2×C42×C83C2311yescharacteristic
152#13050574—44no—
153#13050574—44no—
154#13050574—44no—
155C2×C83⋊C8—21no—
156C2×C83⋊C8—21no—
157C2×C83⋊C8—21no—
158C2×C83⋊C8—21no—
159C2×C83⋊C8—21no—
160C2×C83⋊C8—21no—
161C2×C83⋊C8—21no—
162C2×C83⋊C8—21no—
163C2×C83⋊C8—21no—
164C2×C83⋊C8—21no—
165C2×C83⋊C8—21no—
166C2×C83⋊C8—21no—
167C2×C83⋊C8—21no—
168C2×C83⋊C8—21no—
169C2×C83⋊C8—21no—
170C2×C83⋊C8—21no—
171C2×C83⋊C8—21no—
172C2×C83⋊C8—21no—
173C2×C83⋊C8—21no—
174C2×C83⋊C8—21no—
175C2×C83⋊C8—21no—
176C2×C83⋊C8—21no—
177C2×C83⋊C8—44no—
178C2×C83⋊C8#4112yes—
179C2×C83⋊C8#4112yes—
180C24×C83C22×C411yescharacteristic
181C24×C83C22×C411yescharacteristic
182C24×C83C22×C411yescharacteristic
183C2×Q8×C83—22no—
184C2×Q8×C83—22no—
185C2×Q8×C83—41no—
186C2×D4×C83—22no—
187C2×D4×C83—22no—
188C2×D4×C83—22no—
189C2×D4×C83—41no—
190C2×D4×C83—41no—
191C2×D4×C83—41no—
192C2×D4×C83—41no—
193C2×D4×C83—41no—
194C2×D4×C83C22⋊C414yes—
195C22×C4×C83—21no—
196C22×C4×C83—21no—
197C22×C4×C83—21no—
198C22×C4×C83—21no—
199C22×C4×C83—21no—
200C22×C4×C83—21no—
201C22×C4×C83—21no—
202C22×C4×C83—21no—
203C22×C4×C83—22no—
204C22×C4×C83—22no—
205C22×C4×C83—22no—
206C22×C4×C83—21no—
207C22×C4×C83—21no—
208C22×C4×C83—21no—
209C22×C4×C83—21no—
210C22×C4×C83—21no—
211C22×C4×C83—21no—
212C22×C4×C83—41no—
213C22×C4×C83—41no—
214C22×C4×C83—41no—
215C22×C4×C83C22×C411yescharacteristic
216C22×C4×C83C22×C411yescharacteristic
217C22×C4×C83C22×C411yescharacteristic
218C22×C4×C83C22×C411yescharacteristic
219C22×C4×C83C22×C411yescharacteristic
220C22×C4×C83C22×C411yescharacteristic
221C22×C4×C83C22×C411yescharacteristic
222C22×C4×C83C22×C411yescharacteristic
223C22×C4×C83C22×C411yescharacteristic
224C22×C4×C83C22×C411yescharacteristic
225C22×C4×C83C22×C411yescharacteristic
226C22×C4×C83C2×D412yes—
227C22×C4×C83C2×D412yes—
228C22×C4×C83C2×D412yes—
229C22×C4×C83C2×D412yes—
230C22×C4×C83C2411yescharacteristic
231C4⋊C4×C83—22no—
232C4⋊C4×C83—22no—
233C4⋊C4×C83—22no—
234C4⋊C4×C83—22no—
235C4⋊C4×C83—22no—
236C4⋊C4×C83—22no—
237C4⋊C4×C83—22no—
238C4⋊C4×C83—22no—
239C4⋊C4×C83—22no—
240C4⋊C4×C83C22⋊C414yes—
241C22⋊C4×C83—22no—
242C22⋊C4×C83—22no—
243C22⋊C4×C83—22no—
244C22⋊C4×C83—22no—
245C22⋊C4×C83—22no—
246C22⋊C4×C83—22no—
247C22⋊C4×C83—22no—
248C22⋊C4×C83—22no—
249C22⋊C4×C83C22⋊C414yes—
250C22⋊C4×C83C22⋊C414yes—
251C42×C83—22no—
252C42×C83—22no—
253C42×C83—21no—
254C42×C83—21no—
255C42×C83—21no—
256C42×C83—21no—
257C42×C83—21no—
258C42×C83—21no—
259C42×C83C2×D412yes—
260C42×C83C2×D412yes—
261C23×C83—21no—
262C23×C83—21no—
263C23×C83—21no—
264C23×C83—21no—
265C23×C83—21no—
266C23×C83—21no—
267C23×C83—21no—
268C23×C83—21no—
269C23×C83—21no—
270C23×C83—21no—
271C23×C83—21no—
272C23×C83—21no—
273C23×C83—21no—
274C23×C83—21no—
275C23×C83—21no—
276C23×C83—21no—
277C23×C83—21no—
278C23×C83—21no—
279C23×C83—21no—
280C23×C83C2×C22⋊C412yes—
281C23×C83C2×C22⋊C412yes—
282C23×C83C23×C411yescharacteristic
283Q8×C83—44no—
284D4×C83—44no—
285D4×C83—44no—
286D4×C83—44no—
287C2×C4×C83—21no—
288C2×C4×C83—21no—
289C2×C4×C83—21no—
290C2×C4×C83—21no—
291C2×C4×C83—21no—
292C2×C4×C83—21no—
293C2×C4×C83—21no—
294C2×C4×C83—21no—
295C2×C4×C83—21no—
296C2×C4×C83—21no—
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—21no—
306C2×C4×C83—21no—
307C2×C4×C83—21no—
308C2×C4×C83—21no—
309C2×C4×C83—21no—
310C2×C4×C83—21no—
311C2×C4×C83—21no—
312C2×C4×C83—21no—
313C2×C4×C83—21no—
314C2×C4×C83—21no—
315C2×C4×C83—21no—
316C2×C4×C83—21no—
317C2×C4×C83—21no—
318C2×C4×C83—21no—
319C2×C4×C83—21no—
320C2×C4×C83—21no—
321C2×C4×C83—21no—
322C2×C4×C83—21no—
323C2×C4×C83—44no—
324C2×C4×C83—44no—
325C2×C4×C83—41no—
326C2×C4×C83—41no—
327C2×C4×C83—41no—
328C2×C4×C83—41no—
329C2×C4×C83C2×C22⋊C412yes—
330C2×C4×C83C2×C22⋊C412yes—
331C2×C4×C83C2×C22⋊C412yes—
332C2×C4×C83C2×C22⋊C412yes—
333C2×C4×C83#13112yes—
334C2×C4×C83C22×D411yescharacteristic
335C2×C4×C83C22×D411yescharacteristic
336C2×C4×C83C2×#4111yescharacteristic
337C2×C4×C83C2×#4111yescharacteristic
338C2×C4×C83H(5,𝔽2)11yescharacteristic
339C2×C4×C832−1+411yescharacteristic
340C83⋊C8—22no—
341C83⋊C8—22no—
342C83⋊C8—41no—
343C83⋊C8—41no—
344C83⋊C8—41no—
345C83⋊C8—41no—
346C83⋊C8—41no—
347C83⋊C8—41no—
348C22×C83—22no—
349C22×C83—22no—
350C22×C83—22no—
351C22×C83—22no—
352C22×C83—22no—
353C22×C83—22no—
354C22×C83—41no—
355C22×C83—41no—
356C22×C83—41no—
357C22×C83—41no—
358C22×C83—41no—
359C22×C83—41no—
360C22×C83—41no—
361C22×C83—41no—
362C22×C83—41no—
363C22×C83—41no—
364C22×C83—41no—
365C22×C83—41no—
366C22×C83—41no—
367C22×C83—41no—
368C22×C83—41no—
369C22×C83C22×C22⋊C411yescharacteristic
370C22×C83C4×#4111yescharacteristic
371C22×C83#52011yescharacteristic
372C22×C83C2×#13111yescharacteristic
373C22×C83#56811yescharacteristic
374C22×C83#56811yescharacteristic
375C22×C83#56811yescharacteristic
376C4×C83—22no—
377C4×C83—22no—
378C4×C83—22no—
379C4×C83—22no—
380C4×C83—22no—
381C4×C83—41no—
382C4×C83—41no—
383C4×C83—41no—
384C4×C83—41no—
385C4×C83—41no—
386C4×C83—41no—
387C4×C83#54611yescharacteristic
388C4×C83#54611yescharacteristic
389C4×C83#54711yescharacteristic
390C4×C83#54711yescharacteristic
391#22472—831nomaximal, Sylow
392C2×C83—42no—
393C2×C83—42no—
394C2×C83—81no—
395C2×C83#233911yescharacteristic
396C2×C83#287911yescharacteristic
397C2×C83#288011yescharacteristic
398C2×C83#296711yescharacteristic
399C2×C83#296911yescharacteristic
400C2×C83#299311yescharacteristic
401C2×C83#299511yescharacteristic
402C2×#529D8311yescharacteristic
403C2×#436—831no—
404C2×#435—831no—
405#1985—831no—
406#1984—831no—
407#1870—831no—
408#1870—831no—
409#1870—831no—
410#1869—831no—
411#1818—831no—
412#1817—831no—
413#1798—831no—
414#1750—831no—
415#1729—831no—
416#1728—831no—
417C83#2247211yescharacteristic, complemented, Sylow
418C22×M16—831no—
419C22×M16—831no—
420C22×M16—831no—
421C23×C8—831no—
422#529—24no—
423#529—24no—
424C2×#126Dic8311yescharacteristic
425C2×#126Dic8311yescharacteristic
426C2×#125Dic8311yescharacteristic
427C2×#124Dic8311yescharacteristic
428C2×#123Dic8311yescharacteristic
429C2×#123Dic8311yescharacteristic
430C2×C22⋊Q8Dic8311yescharacteristic
431C2×#121Dic8311yescharacteristic
432C2×C4×Q8C2×D8311yescharacteristic
433C2×C4×D4C2×D8311yescharacteristic
434C2×C4×D4C2×D8311yescharacteristic
435C2×C4×D4C2×D8311yescharacteristic
436C2×#117C2×D8311yescharacteristic
437C2×#117C2×D8311yescharacteristic
438C22×C42C2×D8311yescharacteristic
439#436—1664no—
440#435—1664no—
441C2×C4⋊C8—831no—
442C2×C4⋊C8—831no—
443C2×C22⋊C8—831no—
444C2×C22⋊C8—831no—
445C2×C22⋊C8—831no—
446C2×C22⋊C8—831no—
447C2×C22⋊C8—831no—
448C2×C22⋊C8—831no—
449C2×C22⋊C8—831no—
450C2×C22⋊C8—831no—
451C2×#97—831no—
452C2×C4×C8—831no—
453#336—831no—
454#336—831no—
455#336—831no—
456#336—831no—
457#336—831no—
458#336—831no—
459#336—831no—
460#336—831no—
461#336—831no—
462#336—831no—
463#336—831no—
464#336—831no—
465C22×Q8C2×Dic8311yescharacteristic
466C22×D4C2×Dic8311yescharacteristic
467C22×D4C2×Dic8311yescharacteristic
468C22×D4C2×Dic8311yescharacteristic
469C23×C4C2×Dic8311yescharacteristic
470C23×C4C2×Dic8311yescharacteristic
471C23×C4C22×D8311yescharacteristic
472C23×C4C22×D8311yescharacteristic
473C23×C4C22×D8311yescharacteristic
474C2×M16—3321no—
475C2×M16—3321no—
476C2×M16—3321no—
477C2×M16—1662no—
478C2×M16—1662no—
479C2×M16—1662no—
480C2×M16—1662no—
481C2×M16—1662no—
482C2×M16—1662no—
483C22×C8—3321no—
484C22×C8—831no—
485C22×C8—831no—
486C22×C8—831no—
487C22×C8—831no—
488C22×C8—831no—
489C22×C8—831no—
490C22×C8—831no—
491C22×C8—831no—
492C22×C8—1662no—
493C22×C8—1662no—
494#126—24no—
495#126—24no—
496#125—24no—
497#124—24no—
498#123—24no—
499#123—24no—
500C22⋊Q8—24no—
501#121—24no—
502C4×Q8—22no—
503C4×Q8—22no—
504C4×D4—22no—
505C4×D4—22no—
506C4×D4—22no—
507C4×D4—22no—
508C4×D4C22⋊D8314yes—
509C4×D4C22⋊D8314yes—
510#117—22no—
511#117—22no—
512#117—22no—
513#117—22no—
514C2×C4⋊C4C2×Dic8311yescharacteristic
515C2×C4⋊C4C2×Dic8311yescharacteristic
516C2×C4⋊C4C2×Dic8311yescharacteristic
517C2×C4⋊C4C2×Dic8311yescharacteristic
518C2×C4⋊C4C2×Dic8311yescharacteristic
519C2×C4⋊C4C2×Dic8311yescharacteristic
520C2×C4⋊C4C2×Dic8311yescharacteristic
521C2×C4⋊C4C2×Dic8311yescharacteristic
522C2×C4⋊C4C2×Dic8311yescharacteristic
523C2×C4⋊C4C2×Dic8311yescharacteristic
524C2×C22⋊C4C2×Dic8311yescharacteristic
525C2×C22⋊C4C2×Dic8311yescharacteristic
526C2×C22⋊C4C2×Dic8311yescharacteristic
527C2×C22⋊C4C2×Dic8311yescharacteristic
528C2×C22⋊C4C2×Dic8311yescharacteristic
529C2×C22⋊C4C2×Dic8311yescharacteristic
530C2×C22⋊C4C2×Dic8311yescharacteristic
531C2×C22⋊C4C2×Dic8311yescharacteristic
532C2×C22⋊C4C2×Dic8311yescharacteristic
533C2×C22⋊C4C2×Dic8311yescharacteristic
534C2×C42—22no—
535C2×C42—22no—
536C2×C42C2×Dic8311yescharacteristic
537C2×C42C2×Dic8311yescharacteristic
538C2×C42C22×D8311yescharacteristic
539C2×C42C22×D8311yescharacteristic
540C2×C42C22×D8311yescharacteristic
541C2×C42C22×D8311yescharacteristic
542C4⋊C8—1662no—
543C4⋊C8—1662no—
544C22⋊C8—3321no—
545C22⋊C8—3321no—
546C22⋊C8—1662no—
547C22⋊C8—1662no—
548C22⋊C8—1662no—
549C22⋊C8—1662no—
550C22⋊C8—1662no—
551C22⋊C8—1662no—
552#97—1662no—
553C4×C8—1662no—
554C24C22×Dic8311yescharacteristic
555C24C22×Dic8311yescharacteristic
556C24C22×Dic8311yescharacteristic
557C2×Q8—22no—
558C2×Q8—22no—
559C2×Q8—41no—
560C2×D4—22no—
561C2×D4—22no—
562C2×D4—22no—
563C2×D4—41no—
564C2×D4—41no—
565C2×D4—41no—
566C2×D4—41no—
567C2×D4—41no—
568C2×D4C22⋊Dic8314yes—
569C22×C4—21no—
570C22×C4—21no—
571C22×C4—21no—
572C22×C4—21no—
573C22×C4—21no—
574C22×C4—21no—
575C22×C4—21no—
576C22×C4—21no—
577C22×C4—22no—
578C22×C4—22no—
579C22×C4—22no—
580C22×C4—21no—
581C22×C4—21no—
582C22×C4—21no—
583C22×C4—21no—
584C22×C4—21no—
585C22×C4—21no—
586C22×C4—41no—
587C22×C4—41no—
588C22×C4—41no—
589C22×C4C22×Dic8311yescharacteristic
590C22×C4C22×Dic8311yescharacteristic
591C22×C4C22×Dic8311yescharacteristic
592C22×C4C22×Dic8311yescharacteristic
593C22×C4C22×Dic8311yescharacteristic
594C22×C4C22×Dic8311yescharacteristic
595C22×C4C22×Dic8311yescharacteristic
596C22×C4C22×Dic8311yescharacteristic
597C22×C4C22×Dic8311yescharacteristic
598C22×C4C22×Dic8311yescharacteristic
599C22×C4C22×Dic8311yescharacteristic
600C22×C4C2×C22⋊D8312yes—
601C22×C4C2×C22⋊D8312yes—
602C22×C4C2×C22⋊D8312yes—
603C22×C4C2×C22⋊D8312yes—
604C22×C4C23×D8311yescharacteristic
605M16—3324no—
606M16—3324no—
607M16—3324no—
608C2×C8—3324no—
609C2×C8—832no—
610C2×C8—832no—
611C2×C8—1661no—
612C2×C8—1661no—
613C2×C8—1661no—
614C2×C8—1661no—
615C2×C8—1661no—
616C2×C8—1661no—
617C2×C8—1661no—
618C2×C8—1661no—
619C2×C8—1661no—
620C2×C8—1661no—
621C2×C8—1661no—
622C2×C8—1661no—
623C2×C8—1661no—
624C2×C8—1661no—
625C2×C8—1661no—
626C2×C8—1661no—
627C2×C8—1661no—
628C2×C8—1661no—
629C2×C8—1661no—
630C2×C8—1661no—
631C2×C8—1661no—
632C2×C8—1661no—
633C4⋊C4—22no—
634C4⋊C4—22no—
635C4⋊C4—22no—
636C4⋊C4—22no—
637C4⋊C4—22no—
638C4⋊C4—22no—
639C4⋊C4—22no—
640C4⋊C4—22no—
641C4⋊C4—22no—
642C4⋊C4C22⋊Dic8314yes—
643C22⋊C4—22no—
644C22⋊C4—22no—
645C22⋊C4—22no—
646C22⋊C4—22no—
647C22⋊C4—22no—
648C22⋊C4—22no—
649C22⋊C4—22no—
650C22⋊C4—22no—
651C22⋊C4C22⋊Dic8314yes—
652C22⋊C4C22⋊Dic8314yes—
653C42—21no—
654C42—21no—
655C42—21no—
656C42—21no—
657C42—21no—
658C42—21no—
659C42—22no—
660C42—22no—
661C42C2×C22⋊D8312yes—
662C42C2×C22⋊D8312yes—
663C23—21no—
664C23—21no—
665C23—21no—
666C23—21no—
667C23—21no—
668C23—21no—
669C23—21no—
670C23—21no—
671C23—21no—
672C23—21no—
673C23—21no—
674C23—21no—
675C23—21no—
676C23—21no—
677C23—21no—
678C23—21no—
679C23—21no—
680C23—21no—
681C23—21no—
682C23C2×C22⋊Dic8312yes—
683C23C2×C22⋊Dic8312yes—
684C23C23×Dic8311yescharacteristic
685Q8—44no—
686D4—44no—
687D4—44no—
688D4—44no—
689C2×C4—21no—
690C2×C4—21no—
691C2×C4—21no—
692C2×C4—21no—
693C2×C4—21no—
694C2×C4—21no—
695C2×C4—21no—
696C2×C4—21no—
697C2×C4—21no—
698C2×C4—21no—
699C2×C4—22no—
700C2×C4—22no—
701C2×C4—22no—
702C2×C4—22no—
703C2×C4—22no—
704C2×C4—22no—
705C2×C4—22no—
706C2×C4—22no—
707C2×C4—21no—
708C2×C4—21no—
709C2×C4—21no—
710C2×C4—21no—
711C2×C4—21no—
712C2×C4—21no—
713C2×C4—21no—
714C2×C4—21no—
715C2×C4—21no—
716C2×C4—21no—
717C2×C4—21no—
718C2×C4—21no—
719C2×C4—21no—
720C2×C4—21no—
721C2×C4—21no—
722C2×C4—21no—
723C2×C4—21no—
724C2×C4—21no—
725C2×C4—44no—
726C2×C4—44no—
727C2×C4—41no—
728C2×C4—41no—
729C2×C4—41no—
730C2×C4—41no—
731C2×C4C2×C22⋊Dic8312yes—
732C2×C4C2×C22⋊Dic8312yes—
733C2×C4C2×C22⋊Dic8312yes—
734C2×C4C2×C22⋊Dic8312yes—
735C2×C4#1458179912yes—
736C2×C4C22×C22⋊D8311yescharacteristic
737C2×C4C22×C22⋊D8311yescharacteristic
738C2×C4#41×D8311yescharacteristic
739C2×C4#41×D8311yescharacteristic
740C2×C4#1458183811yescharacteristic
741C2×C4#1458183911yescharacteristic
742C8—3321no—
743C8—3321no—
744C8—3321no—
745C8—3321no—
746C8—3321no—
747C8—3321no—
748C8—1662no—
749C8—1662no—
750C22—22no—
751C22—22no—
752C22—22no—
753C22—22no—
754C22—22no—
755C22—22no—
756C22—41no—
757C22—41no—
758C22—41no—
759C22—41no—
760C22—41no—
761C22—41no—
762C22—41no—
763C22—41no—
764C22—41no—
765C22—41no—
766C22—41no—
767C22—41no—
768C22—41no—
769C22—41no—
770C22—41no—
771C22C22×C22⋊Dic8311yescharacteristic
772C22#41×Dic8311yescharacteristic
773C22#1912818411yescharacteristic
774C22C2×#1458179911yescharacteristic
775C22#1912846811yescharacteristic
776C22#1912846811yescharacteristic
777C22#1912846811yescharacteristic
778C4—22no—
779C4—22no—
780C4—22no—
781C4—22no—
782C4—22no—
783C4—41no—
784C4—41no—
785C4—41no—
786C4—41no—
787C4—41no—
788C4—41no—
789C4#1912833911yescharacteristic
790C4#1912833911yescharacteristic
791C4#1912835011yescharacteristic
792C4#1912835011yescharacteristic
793C2—42no—
794C2—42no—
795C2—81no—
796C2#2491029311yescharacteristic
797C2#2491590811yescharacteristic
798C2#2491591211yescharacteristic
799C2#2491645011yescharacteristic
800C2#2491646811yescharacteristic
801C2#2491661211yescharacteristic
802C2#2491663311yescharacteristic
subgroupG/H
center, FrattiniC22×C4C23×D83
commutator, socleC23×C83C23×C4
FittingC2×#529×C83C2
prime radicalC2×#121×C83C4
cosocleC22×C4×C83C24
hypercenterC2×#529D83
hypocenterC83#22472
LCSG ▷ C23×C83 ▷ C83
UCSC1 ◁ C22×C4 ◁ C2×#529

Complements

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

NH ≅ G/Ntype
1. C2×#19127779C2semidirect
2. C2×#19127773C2semidirect
3. #24908404C2semidirect
4. #24908400C2semidirect
5. #24907761C2semidirect
6. #24907761C2semidirect
7. #24907761C2semidirect
8. #24907756C2semidirect
9. #24907534C2semidirect
10. #24907531C2semidirect
11. #24907447C2semidirect
12. #24907229C2semidirect
13. #24907160C2semidirect
14. #24907157C2semidirect
417. C83#22472semidirect

Maximal subgroups

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

subgroupindex
C2×#191277792
C2×#191277732
#249084042
#249084002
#249077612
#249077562
#249075342
#249075312
#249074472
#249072292
#249071602
#249071572
C2×#529×C832
#2247283