Finite Group Databasebeta

← #35406755

Subgroups — #35406755

Order 21248.

1226 conjugacy classes of subgroups.

The subgroup lattice has 790 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#19127726C211yesmaximal, characteristic, complemented
2C2×#19127663C211yesmaximal, characteristic
3C2×C22⋊C8×D83C211yesmaximal, characteristic
4C2×#19127658C211yesmaximal, characteristic, complemented
5#24909844C211yesmaximal, characteristic
6#24908079C211yesmaximal, characteristic, complemented
7#24908076C211yesmaximal, characteristic, complemented
8#24908075C211yesmaximal, characteristic, complemented
9#24908071C211yesmaximal, characteristic, complemented
10#24908070C211yesmaximal, characteristic, complemented
11#24908067C211yesmaximal, characteristic, complemented
12#24908066C211yesmaximal, characteristic, complemented
13#24907158C211yesmaximal, characteristic, complemented
14#24907158C211yesmaximal, characteristic, complemented
15C83×#1924C211yesmaximal, characteristic, complemented
16C23×C4×D83C2211yescharacteristic
17C22×#13050573C2211yescharacteristic
18C22×#13050573C2211yescharacteristic
19C22×C8×D83C2211yescharacteristic
20C22×C8×D83C2211yescharacteristic
21C2×#14581749C2211yescharacteristic
22C2×#14581749C2211yescharacteristic
23#19127726—24no—
24C2×C4⋊(C83⋊C8)C2211yescharacteristic, complemented
25C2×Dic83⋊C8C2211yescharacteristic, complemented
26C2×Dic83⋊C8C2211yescharacteristic, complemented
27#19127663—24no—
28C2×C22⋊(C83⋊C8)C2211yescharacteristic
29C2×C22⋊(C83⋊C8)C2211yescharacteristic
30C2×(C2×D83)⋊C8C2211yescharacteristic
31C2×(C2×D83)⋊C8C2211yescharacteristic
32C2×(C2×D83)⋊C8C2211yescharacteristic
33C2×(C2×D83)⋊C8C2211yescharacteristic
34C22⋊C8×D83—24no—
35#19127658—24no—
36C2×#14581702C2211yescharacteristic, complemented
37C2×C4×C83⋊C8C2211yescharacteristic, complemented
38C2×C8×Dic83C2211yescharacteristic, complemented
39#19127563C411yescharacteristic
40#19127563C411yescharacteristic
41#19127560C411yescharacteristic
42#19127560C411yescharacteristic
43#19127559C411yescharacteristic
44#19127559C411yescharacteristic
45#19127556C411yescharacteristic
46#19127556C411yescharacteristic
47C4×(C2×D83)⋊C4C2211yescharacteristic
48C4×(C2×D83)⋊C4C2211yescharacteristic
49C4×C22⋊Dic83C2211yescharacteristic
50#19127456C2211yescharacteristic, complemented
51#19127456C2211yescharacteristic, complemented
52#19127455C2211yescharacteristic, complemented
53#19127455C2211yescharacteristic, complemented
54#19127455C2211yescharacteristic, complemented
55#19127455C2211yescharacteristic, complemented
56C2×C4⋊C8×C83C2211yescharacteristic, complemented
57C2×C22⋊C8×C83C2211yescharacteristic
58C2×C22⋊C8×C83C2211yescharacteristic
59C2×#97×C83C2211yescharacteristic, complemented
60C4×C22⋊C4×C83C2211yescharacteristic
61#336×C83C2211yescharacteristic, complemented
62#336×C83C2211yescharacteristic, complemented
63C24×D83C2×C411yescharacteristic
64C23×Dic83C2×C411yescharacteristic
65C22×C4×D83—22no—
66C22×C4×D83—22no—
67C22×C4×D83—22no—
68C22×C4×D83—22no—
69C22×C4×D83—22no—
70C22×C4×D83—22no—
71C22×C4×D83C2×C411yescharacteristic
72C22×C4×D83C2×C411yescharacteristic
73C22×C4×D83C2311yescharacteristic
74C22×C4×D83C2311yescharacteristic
75C2×#13050573—22no—
76C2×#13050573—22no—
77C2×#13050573—22no—
78C2×#13050573—22no—
79C2×#13050573—22no—
80C2×#13050573D414yes—
81C22×C83⋊C8C2311yescharacteristic
82C22×C83⋊C8C2311yescharacteristic
83C22×C83⋊C8C2311yescharacteristic
84C22×C83⋊C8C2311yescharacteristic
85C2×C8×D83—22no—
86C2×C8×D83—22no—
87C2×C8×D83—22no—
88C2×C8×D83—22no—
89C2×C8×D83—22no—
90C2×C8×D83D414yes—
91#14581749—22no—
92#14581749—22no—
93#14581749—22no—
94#14581749—22no—
95C2×Dic83⋊C4C2×C411yescharacteristic
96C2×Dic83⋊C4C2×C411yescharacteristic
97C2×Dic83⋊C4C2×C411yescharacteristic
98C2×Dic83⋊C4C2×C411yescharacteristic
99C2×C22⋊Dic83C2×C411yescharacteristic
100C2×C22⋊Dic83C2×C411yescharacteristic
101C2×(C2×D83)⋊C4C2×C411yescharacteristic
102C2×(C2×D83)⋊C4C2×C411yescharacteristic
103C2×(C2×D83)⋊C4C2×C411yescharacteristic
104C2×(C2×D83)⋊C4C2×C411yescharacteristic
105C2×(C2×D83)⋊C4C2×C411yescharacteristic
106C2×(C2×D83)⋊C4C2×C411yescharacteristic
107C2×(C2×D83)⋊C4C2×C411yescharacteristic
108C2×(C2×D83)⋊C4C2×C411yescharacteristic
109C2×C4×Dic83C2311yescharacteristic
110C2×C4×Dic83C2311yescharacteristic
111C4⋊(C83⋊C8)—22no—
112Dic83⋊C8—22no—
113Dic83⋊C8—22no—
114C22⋊(C83⋊C8)—22no—
115C22⋊(C83⋊C8)—22no—
116(C2×D83)⋊C8—22no—
117(C2×D83)⋊C8—22no—
118(C2×D83)⋊C8—22no—
119(C2×D83)⋊C8—22no—
120#14581702—22no—
121C4×C83⋊C8—22no—
122C8×Dic83—22no—
123C83⋊#95C2×C411yescharacteristic
124C83⋊#95C2×C411yescharacteristic
125C83⋊#95C2×C411yescharacteristic
126C83⋊#95C2×C411yescharacteristic
127C83⋊#95C2×C411yescharacteristic
128C83⋊#95C2×C411yescharacteristic
129C23×C4×C83C2311yescharacteristic
130C22×C8×C83C2311yescharacteristic
131C22×C8×C83C2311yescharacteristic
132C22×C8×C83C2311yescharacteristic
133C22×C8×C83C2311yescharacteristic
134C2×C22⋊C4×C83C2×C411yescharacteristic
135C2×C22⋊C4×C83C2×C411yescharacteristic
136C2×C42×C83C2311yescharacteristic
137C2×C42×C83C2311yescharacteristic
138C4⋊C8×C83—22no—
139C22⋊C8×C83—22no—
140C22⋊C8×C83—22no—
141#97×C83—22no—
142#95×C83C2×C411yescharacteristic
143#95×C83C2×C411yescharacteristic
144C23×D83—22no—
145C23×D83—22no—
146C23×D83—22no—
147C23×D83—22no—
148C23×D83—22no—
149C23×D83—41no—
150C23×D83—41no—
151C23×D83C22×C411yescharacteristic
152C23×D83C22×C411yescharacteristic
153C22×Dic83—22no—
154C22×Dic83—22no—
155C22×Dic83—22no—
156C22×Dic83C22×C411yescharacteristic
157C22×Dic83C22×C411yescharacteristic
158C22×Dic83C22×C411yescharacteristic
159C22×Dic83C22×C411yescharacteristic
160C22×Dic83C22×C411yescharacteristic
161C22×Dic83C22×C411yescharacteristic
162C2×C4×D83—22no—
163C2×C4×D83—22no—
164C2×C4×D83—22no—
165C2×C4×D83—21no—
166C2×C4×D83—21no—
167C2×C4×D83—21no—
168C2×C4×D83—21no—
169C2×C4×D83—21no—
170C2×C4×D83—21no—
171C2×C4×D83—22no—
172C2×C4×D83—22no—
173C2×C4×D83—22no—
174C2×C4×D83—44no—
175C2×C4×D83—44no—
176C2×C4×D83—44no—
177C2×C4×D83—44no—
178C2×C4×D83C2×D412yes—
179C2×C4×D83C2×D412yes—
180C2×C4×D83#4112yes—
181C2×C4×D83#4112yes—
182C2×C4×D83#4112yes—
183C2×C4×D83#4112yes—
184#13050573—28no—
185#13050573—44no—
186C2×C83⋊C8—21no—
187C2×C83⋊C8—21no—
188C2×C83⋊C8—21no—
189C2×C83⋊C8—21no—
190C2×C83⋊C8—21no—
191C2×C83⋊C8—21no—
192C2×C83⋊C8—21no—
193C2×C83⋊C8—21no—
194C2×C83⋊C8—21no—
195C2×C83⋊C8—21no—
196C2×C83⋊C8C2×D412yes—
197C2×C83⋊C8C2×D412yes—
198C8×D83—28no—
199C8×D83—44no—
200Dic83⋊C4—22no—
201Dic83⋊C4—22no—
202Dic83⋊C4—22no—
203Dic83⋊C4—22no—
204C22⋊Dic83—22no—
205C22⋊Dic83—41no—
206(C2×D83)⋊C4—22no—
207(C2×D83)⋊C4—22no—
208(C2×D83)⋊C4—22no—
209(C2×D83)⋊C4—22no—
210(C2×D83)⋊C4—22no—
211(C2×D83)⋊C4—22no—
212(C2×D83)⋊C4—41no—
213(C2×D83)⋊C4—41no—
214C4×Dic83—21no—
215C4×Dic83—21no—
216C4×Dic83—21no—
217C4×Dic83—21no—
218C24×C83C22×C411yescharacteristic
219C22×C4×C83—21no—
220C22×C4×C83—21no—
221C22×C4×C83—21no—
222C22×C4×C83—21no—
223C22×C4×C83—21no—
224C22×C4×C83—21no—
225C22×C4×C83C22×C411yescharacteristic
226C22×C4×C83C22×C411yescharacteristic
227C22×C4×C83C22×C411yescharacteristic
228C22×C4×C83C22×C411yescharacteristic
229C22×C4×C83C22×C411yescharacteristic
230C22×C4×C83C2411yescharacteristic
231C2×C8×C83—21no—
232C2×C8×C83—21no—
233C2×C8×C83—21no—
234C2×C8×C83—21no—
235C2×C8×C83—21no—
236C2×C8×C83—21no—
237C2×C8×C83—21no—
238C2×C8×C83—21no—
239C2×C8×C83—21no—
240C2×C8×C83—21no—
241C2×C8×C83C2×D412yes—
242C2×C8×C83C2×D412yes—
243C22⋊C4×C83—22no—
244C22⋊C4×C83—41no—
245C42×C83—21no—
246C42×C83—21no—
247C42×C83—21no—
248C42×C83—21no—
249C23×C83—21no—
250C23×C83—21no—
251C23×C83—21no—
252C23×C83—21no—
253C23×C83—21no—
254C23×C83—21no—
255C23×C83#13112yes—
256C23×C83C23×C411yescharacteristic
257C22×D83—21no—
258C22×D83—21no—
259C22×D83—21no—
260C22×D83—21no—
261C22×D83—28no—
262C22×D83—21no—
263C22×D83—21no—
264C22×D83—21no—
265C22×D83—21no—
266C22×D83—21no—
267C22×D83—21no—
268C22×D83—44no—
269C22×D83—44no—
270C22×D83—44no—
271C22×D83—44no—
272C22×D83—44no—
273C22×D83—44no—
274C22×D83#11712yes—
275C22×D83C4×D412yes—
276C22×D83C4×D412yes—
277C22×D83#13112yes—
278C2×C4×C83—21no—
279C2×C4×C83—21no—
280C2×C4×C83—21no—
281C2×C4×C83—21no—
282C2×C4×C83—21no—
283C2×C4×C83—21no—
284C2×C4×C83—21no—
285C2×C4×C83—21no—
286C2×C4×C83—21no—
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—41no—
294C2×C4×C83—41no—
295C2×C4×C83—41no—
296C2×C4×C83—41no—
297C2×C4×C83C22×D411yescharacteristic
298C2×C4×C83C22×D411yescharacteristic
299C2×C4×C83C2×#4111yescharacteristic
300C2×C4×C83C2×#4111yescharacteristic
301C2×C4×C83C2×#4111yescharacteristic
302C2×C4×C83C2×#4111yescharacteristic
303C2×Dic83—21no—
304C2×Dic83—21no—
305C2×Dic83—21no—
306C2×Dic83—21no—
307C2×Dic83—21no—
308C2×Dic83—21no—
309C2×Dic83—21no—
310C2×Dic83—21no—
311C2×Dic83—21no—
312C2×Dic83—21no—
313C2×Dic83—21no—
314C2×Dic83—21no—
315C2×Dic83—21no—
316C2×Dic83—21no—
317C2×Dic83—21no—
318C2×Dic83—44no—
319C2×Dic83#11712yes—
320C2×Dic83C4×D412yes—
321C2×Dic83C4×D412yes—
322C4×D83—44no—
323C4×D83—41no—
324C4×D83—41no—
325C4×D83—41no—
326C4×D83—41no—
327C4×D83—44no—
328C4×D83#12114yes—
329C4×D83#12314yes—
330C4×D83#12414yes—
331C4×D83#12614yes—
332C8×C83—22no—
333C8×C83—22no—
334C8×C83—41no—
335C8×C83—41no—
336C83⋊C8—22no—
337C83⋊C8—22no—
338C83⋊C8—41no—
339C83⋊C8—41no—
340C22×C83—22no—
341C22×C83—22no—
342C22×C83—22no—
343C22×C83—41no—
344C22×C83—41no—
345C22×C83—41no—
346C22×C83—41no—
347C22×C83C2×#11711yescharacteristic
348C22×C83C2×C4×D411yescharacteristic
349C22×C83C2×C4×D411yescharacteristic
350C22×C83C2×#13111yescharacteristic
351C22×C83C2×#13111yescharacteristic
352C22×C83#56811yescharacteristic
353C22×C83#56811yescharacteristic
354C2×D83—22no—
355C2×D83—22no—
356C2×D83—22no—
357C2×D83—22no—
358C2×D83—22no—
359C2×D83—22no—
360C2×D83—22no—
361C2×D83—22no—
362C2×D83—22no—
363C2×D83—416no—
364C2×D83—41no—
365C2×D83—41no—
366C2×D83—41no—
367C2×D83—41no—
368C2×D83#38814yes—
369C4×C83—41no—
370C4×C83—41no—
371C4×C83—41no—
372C4×C83—41no—
373C4×C83—41no—
374C4×C83C2×#12111yescharacteristic
375C4×C83C2×#12311yescharacteristic
376C4×C83C2×#12411yescharacteristic
377C4×C83C2×#12611yescharacteristic
378Dic83—41no—
379Dic83—41no—
380Dic83—41no—
381Dic83—41no—
382Dic83—41no—
383Dic83#38814yes—
384#21053—831nomaximal, Sylow
385C2×C83—42no—
386C2×C83C2×#38811yescharacteristic
387C2×C83#292411yescharacteristic
388C2×C83#292411yescharacteristic
389C2×C83#292911yescharacteristic
390C2×C83#293011yescharacteristic
391C2×C83#293311yescharacteristic
392C2×C83#293311yescharacteristic
393D83—24no—
394D83—42no—
395C2×#424—831no—
396C2×#407—831no—
397C22×C22⋊C8—831no—
398C2×#405—831no—
399#2280—831no—
400#1924—831no—
401#1924—831no—
402#1924—831no—
403#1924D8311yescharacteristic, complemented
404#1923—831no—
405#1923—831no—
406#1923—831no—
407#1923—831no—
408#1729—831no—
409#1729—831no—
410C83#2105311yescharacteristic, complemented, Sylow
411C24×C4—831no—
412C22×M16—831no—
413C22×M16—831no—
414C23×C8—831no—
415C23×C8—831no—
416C2×#117—831no—
417C2×#117—831no—
418#424—1664no—
419C2×C4⋊C8—831no—
420C2×C4⋊C8—831no—
421C2×C4⋊C8—831no—
422C2×C4⋊C8C2×D8311yescharacteristic, complemented
423#407—1664no—
424C2×C22⋊C8—831no—
425C2×C22⋊C8—831no—
426C2×C22⋊C8—831no—
427C2×C22⋊C8—831no—
428C2×C22⋊C8—831no—
429C2×C22⋊C8—831no—
430C2×C22⋊C8—1664no—
431C2×C22⋊C8C2×D8311yescharacteristic
432C2×C22⋊C8C2×D8311yescharacteristic
433#405—1664no—
434C2×#97—831no—
435C2×#97C2×D8311yescharacteristic, complemented
436C2×C4×C8—831no—
437C2×C4×C8—831no—
438#381—831no—
439#381—831no—
440#380—831no—
441#380—831no—
442#380—831no—
443#380—831no—
444#379—831no—
445#379—831no—
446C4×C22⋊C4—831no—
447C4×C22⋊C4—831no—
448C4×C22⋊C4—831no—
449C4×C22⋊C4C2×D8311yescharacteristic
450#336—831no—
451#336—831no—
452#336—831no—
453#336—831no—
454#336—831no—
455#336—831no—
456#336C2×D8311yescharacteristic, complemented
457#336C2×D8311yescharacteristic, complemented
458C25—831no—
459C23×C4—831no—
460C23×C4—831no—
461C23×C4—831no—
462C23×C4—831no—
463C23×C4—831no—
464C23×C4—1662no—
465C23×C4—1662no—
466C23×C4—1662no—
467C23×C4—1662no—
468C23×C4—1662no—
469C23×C4—1662no—
470C23×C4C22×D8311yescharacteristic
471C2×M16—834no—
472C2×M16—1662no—
473C2×M16—1662no—
474C2×M16—1662no—
475C2×M16—1662no—
476C2×M16—1662no—
477C22×C8—831no—
478C22×C8—831no—
479C22×C8—834no—
480C22×C8—831no—
481C22×C8—831no—
482C22×C8—1662no—
483C22×C8—1662no—
484C22×C8—1662no—
485C22×C8—1662no—
486C22×C8—1662no—
487C22×C8C22×D8311yescharacteristic
488C22×C8C22×D8311yescharacteristic
489C22×C8C22×D8311yescharacteristic
490C22×C8C22×D8311yescharacteristic
491#117—1662no—
492#117—1662no—
493#117—1662no—
494#117—1662no—
495C2×C4⋊C4—831no—
496C2×C4⋊C4—831no—
497C2×C4⋊C4—831no—
498C2×C4⋊C4—831no—
499C2×C22⋊C4—831no—
500C2×C22⋊C4—831no—
501C2×C22⋊C4—831no—
502C2×C22⋊C4—831no—
503C2×C22⋊C4—831no—
504C2×C22⋊C4—831no—
505C2×C22⋊C4—831no—
506C2×C22⋊C4—831no—
507C2×C22⋊C4—831no—
508C2×C22⋊C4—831no—
509C2×C22⋊C4C4×D8311yescharacteristic
510C2×C22⋊C4C4×D8311yescharacteristic
511C2×C42—831no—
512C2×C42—831no—
513C2×C42C22×D8311yescharacteristic
514C2×C42C22×D8311yescharacteristic
515C4⋊C8—22no—
516C4⋊C8—1662no—
517C4⋊C8—1662no—
518C4⋊C8—1662no—
519C22⋊C8—22no—
520C22⋊C8—22no—
521C22⋊C8—1662no—
522C22⋊C8—1662no—
523C22⋊C8—1662no—
524C22⋊C8—1662no—
525C22⋊C8—1662no—
526C22⋊C8—1662no—
527#97—22no—
528#97—1662no—
529C4×C8—1662no—
530C4×C8—1662no—
531#95—831no—
532#95—831no—
533#95—831no—
534#95—831no—
535#95—831no—
536#95—831no—
537#95C4×D8311yescharacteristic
538#95C4×D8311yescharacteristic
539C24—3321no—
540C24—3321no—
541C24—831no—
542C24—831no—
543C24—1662no—
544C24—1662no—
545C24—1662no—
546C24—1662no—
547C24—1662no—
548C24C2×C4×D8311yescharacteristic
549C22×C4—21no—
550C22×C4—21no—
551C22×C4—21no—
552C22×C4—21no—
553C22×C4—21no—
554C22×C4—21no—
555C22×C4—3324no—
556C22×C4—3324no—
557C22×C4—3324no—
558C22×C4—3324no—
559C22×C4—831no—
560C22×C4—832no—
561C22×C4—832no—
562C22×C4—832no—
563C22×C4—832no—
564C22×C4—832no—
565C22×C4—832no—
566C22×C4—831no—
567C22×C4—831no—
568C22×C4—831no—
569C22×C4—831no—
570C22×C4—831no—
571C22×C4—1662no—
572C22×C4—1662no—
573C22×C4—1662no—
574C22×C4—1662no—
575C22×C4—1662no—
576C22×C4—1662no—
577C22×C4—1662no—
578C22×C4—1662no—
579C22×C4—1662no—
580C22×C4—1661no—
581C22×C4—1661no—
582C22×C4—1661no—
583C22×C4—1661no—
584C22×C4—1661no—
585C22×C4—1661no—
586C22×C4C2×C4×D8311yescharacteristic
587C22×C4C2×C4×D8311yescharacteristic
588C22×C4C2×C4×D8311yescharacteristic
589C22×C4C2×C4×D8311yescharacteristic
590C22×C4C2×C4×D8311yescharacteristic
591C22×C4C23×D8311yescharacteristic
592M16—3324no—
593M16—1668no—
594C2×C8—21no—
595C2×C8—21no—
596C2×C8—21no—
597C2×C8—21no—
598C2×C8—21no—
599C2×C8—21no—
600C2×C8—21no—
601C2×C8—21no—
602C2×C8—21no—
603C2×C8—21no—
604C2×C8—3324no—
605C2×C8—832no—
606C2×C8—832no—
607C2×C8—1668no—
608C2×C8—1661no—
609C2×C8—1661no—
610C2×C8—1661no—
611C2×C8—1661no—
612C2×C8—1661no—
613C2×C8—1661no—
614C2×C8—1661no—
615C2×C8—1661no—
616C2×C8—1661no—
617C2×C8—1661no—
618C2×C8D4×D8312yes—
619C2×C8D4×D8312yes—
620C4⋊C4—1662no—
621C4⋊C4—1662no—
622C4⋊C4—1662no—
623C4⋊C4—1662no—
624C22⋊C4—22no—
625C22⋊C4—41no—
626C22⋊C4—3321no—
627C22⋊C4—3321no—
628C22⋊C4—3321no—
629C22⋊C4—1662no—
630C22⋊C4—1662no—
631C22⋊C4—1662no—
632C22⋊C4—1662no—
633C22⋊C4—1662no—
634C22⋊C4—1662no—
635C22⋊C4—1662no—
636C42—21no—
637C42—21no—
638C42—21no—
639C42—21no—
640C42—1661no—
641C42—1661no—
642C42—1661no—
643C42—1661no—
644C23—21no—
645C23—21no—
646C23—21no—
647C23—21no—
648C23—21no—
649C23—21no—
650C23—3324no—
651C23—3324no—
652C23—3324no—
653C23—3324no—
654C23—3324no—
655C23—3324no—
656C23—832no—
657C23—832no—
658C23—832no—
659C23—832no—
660C23—1668no—
661C23—1661no—
662C23—1661no—
663C23—1661no—
664C23—1661no—
665C23—1661no—
666C23—1661no—
667C23—1661no—
668C23—1661no—
669C23—1661no—
670C23—1661no—
671C23#1458180012yes—
672C23C22×C4×D8311yescharacteristic
673C2×C4—21no—
674C2×C4—21no—
675C2×C4—21no—
676C2×C4—21no—
677C2×C4—21no—
678C2×C4—21no—
679C2×C4—21no—
680C2×C4—21no—
681C2×C4—21no—
682C2×C4—21no—
683C2×C4—21no—
684C2×C4—21no—
685C2×C4—21no—
686C2×C4—21no—
687C2×C4—21no—
688C2×C4—41no—
689C2×C4—41no—
690C2×C4—41no—
691C2×C4—41no—
692C2×C4—3324no—
693C2×C4—3324no—
694C2×C4—3324no—
695C2×C4—3321no—
696C2×C4—3321no—
697C2×C4—3321no—
698C2×C4—3321no—
699C2×C4—832no—
700C2×C4—832no—
701C2×C4—832no—
702C2×C4—834no—
703C2×C4—834no—
704C2×C4—834no—
705C2×C4—834no—
706C2×C4—1661no—
707C2×C4—1661no—
708C2×C4—1661no—
709C2×C4—1661no—
710C2×C4—1661no—
711C2×C4—1661no—
712C2×C4—1661no—
713C2×C4—1661no—
714C2×C4—1661no—
715C2×C4—1661no—
716C2×C4—1661no—
717C2×C4—1661no—
718C2×C4—1661no—
719C2×C4—1661no—
720C2×C4—1661no—
721C2×C4C2×D4×D8311yescharacteristic
722C2×C4C2×D4×D8311yescharacteristic
723C2×C4#41×D8311yescharacteristic
724C2×C4#41×D8311yescharacteristic
725C2×C4#41×D8311yescharacteristic
726C2×C4#41×D8311yescharacteristic
727C8—22no—
728C8—22no—
729C8—41no—
730C8—41no—
731C8—3321no—
732C8—3321no—
733C8—1662no—
734C8—1662no—
735C22—22no—
736C22—22no—
737C22—22no—
738C22—41no—
739C22—41no—
740C22—41no—
741C22—41no—
742C22—33216no—
743C22—3321no—
744C22—3321no—
745C22—3321no—
746C22—3321no—
747C22—834no—
748C22—1662no—
749C22—1662no—
750C22—1662no—
751C22—1662no—
752C22—1662no—
753C22—1662no—
754C22—1662no—
755C22—1662no—
756C22—1662no—
757C22#117×D8311yescharacteristic
758C22C4×D4×D8311yescharacteristic
759C22C4×D4×D8311yescharacteristic
760C22#131×D8311yescharacteristic
761C22C2×#1458180011yescharacteristic
762C22#1912846611yescharacteristic
763C22#1912846711yescharacteristic
764C4—41no—
765C4—41no—
766C4—41no—
767C4—41no—
768C4—41no—
769C4—3321no—
770C4—3321no—
771C4—3321no—
772C4—3321no—
773C4—3321no—
774C4—834no—
775C4#121×D8311yescharacteristic
776C4#123×D8311yescharacteristic
777C4#124×D8311yescharacteristic
778C4#126×D8311yescharacteristic
779C2—42no—
780C2—3322no—
781C2—1664no—
782C2#388×D8311yescharacteristic
783C2#2491611911yescharacteristic
784C2#2491612211yescharacteristic
785C2#2491615411yescharacteristic
786C2#2491616111yescharacteristic
787C2#2491618911yescharacteristic
788C2#2491619211yescharacteristic
subgroupG/H
center, FrattiniC22×C4C23×D83
commutator, socleC23×C83C23×C4
FittingC83×#1924C2
prime radicalC24×D83C2×C4
cosocleC22×C4×C83C24
hypercenter#1924D83
hypocenterC83#21053
LCSG ▷ C23×C83 ▷ C83
UCSC1 ◁ C22×C4 ◁ #1924

Complements

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

NH ≅ G/Ntype
1. C2×#19127726C2semidirect
4. C2×#19127658C2semidirect
6. #24908079C2semidirect
7. #24908076C2semidirect
8. #24908075C2semidirect
9. #24908071C2semidirect
10. #24908070C2semidirect
11. #24908067C2semidirect
12. #24908066C2semidirect
13. #24907158C2semidirect
14. #24907158C2semidirect
15. C83×#1924C2semidirect
24. C2×C4⋊(C83⋊C8)C22semidirect
25. C2×Dic83⋊C8C22semidirect
26. C2×Dic83⋊C8C22semidirect
36. C2×#14581702C22semidirect
37. C2×C4×C83⋊C8C22semidirect
38. C2×C8×Dic83C22semidirect
50. #19127456C22semidirect
51. #19127456C22semidirect
52. #19127455C22semidirect
53. #19127455C22semidirect
54. #19127455C22semidirect
55. #19127455C22semidirect
56. C2×C4⋊C8×C83C22semidirect
59. C2×#97×C83C22semidirect
61. #336×C83C22semidirect
62. #336×C83C22semidirect
403. #1924D83semidirect
410. C83#21053semidirect
422. C2×C4⋊C8C2×D83semidirect
435. C2×#97C2×D83semidirect
456. #336C2×D83semidirect
457. #336C2×D83semidirect

Maximal subgroups

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

subgroupindex
C2×#191277262
C2×#191276632
C2×C22⋊C8×D832
C2×#191276582
#249098442
#249080792
#249080762
#249080752
#249080712
#249080702
#249080672
#249080662
#249071582
C83×#19242
#2105383