Finite Group Databasebeta

← #35311322

Subgroups — #35311322

Order 21248.

1262 conjugacy classes of subgroups.

The subgroup lattice has 882 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×Dic83⋊C8C211yesmaximal, characteristic, complemented
2C22×(C2×D83)⋊C8C211yesmaximal, characteristic
3C22×(C2×D83)⋊C8C211yesmaximal, characteristic
4C2×C4×(C2×D83)⋊C4C211yesmaximal, characteristic
5C2×#19127456C211yesmaximal, characteristic, complemented
6C2×#19127455C211yesmaximal, characteristic, complemented
7C2×#336×C83C211yesmaximal, characteristic, complemented
8C23×C4×D83C2211yescharacteristic
9C23×C83⋊C8C2211yescharacteristic
10C23×C83⋊C8C2211yescharacteristic
11C22×(C2×D83)⋊C4C411yescharacteristic
12C22×(C2×D83)⋊C4C411yescharacteristic
13C22×C4×Dic83C2211yescharacteristic
14C2×Dic83⋊C8—22no—
15C2×Dic83⋊C8—22no—
16C2×Dic83⋊C8—22no—
17C2×(C2×D83)⋊C8—22no—
18C2×(C2×D83)⋊C8—22no—
19C2×(C2×D83)⋊C8—22no—
20C2×(C2×D83)⋊C8—22no—
21C2×(C2×D83)⋊C8—22no—
22C2×(C2×D83)⋊C8—22no—
23C4×(C2×D83)⋊C4—22no—
24C4×(C2×D83)⋊C4—22no—
25C2×C83⋊#95C411yescharacteristic
26C2×C83⋊#95C411yescharacteristic
27#19127456—22no—
28#19127455—22no—
29C23×C8×C83C2211yescharacteristic
30C23×C8×C83C2211yescharacteristic
31C22×C42×C83C2211yescharacteristic
32#336×C83—22no—
33C24×D83C2×C411yescharacteristic
34C23×Dic83C2×C411yescharacteristic
35C23×Dic83C2×C411yescharacteristic
36C23×Dic83C2×C411yescharacteristic
37C22×C4×D83—21no—
38C22×C4×D83—21no—
39C22×C4×D83—21no—
40C22×C4×D83—21no—
41C22×C4×D83—21no—
42C22×C4×D83—21no—
43C22×C4×D83—21no—
44C22×C4×D83—21no—
45C22×C4×D83—21no—
46C22×C4×D83—21no—
47C22×C4×D83—21no—
48C22×C4×D83—21no—
49C22×C4×D83D412yes—
50C22×C4×D83Q812yes—
51C22×C83⋊C8—21no—
52C22×C83⋊C8—21no—
53C22×C83⋊C8—21no—
54C22×C83⋊C8—21no—
55C22×C83⋊C8—21no—
56C22×C83⋊C8—21no—
57C22×C83⋊C8—21no—
58C22×C83⋊C8—21no—
59C22×C83⋊C8—21no—
60C22×C83⋊C8—21no—
61C22×C83⋊C8—21no—
62C22×C83⋊C8—21no—
63C22×C83⋊C8D412yes—
64C22×C83⋊C8D412yes—
65C2×(C2×D83)⋊C4—22no—
66C2×(C2×D83)⋊C4—22no—
67C2×(C2×D83)⋊C4—22no—
68C2×(C2×D83)⋊C4—22no—
69C2×(C2×D83)⋊C4—22no—
70C2×(C2×D83)⋊C4C814yescomplemented
71C2×C4×Dic83—21no—
72C2×C4×Dic83—21no—
73C2×C4×Dic83—21no—
74C2×C4×Dic83—21no—
75C2×C4×Dic83D412yes—
76C2×C4×Dic83D412yes—
77Dic83⋊C8—28no—
78(C2×D83)⋊C8—28no—
79(C2×D83)⋊C8—28no—
80C83⋊#95—22no—
81C83⋊#95—22no—
82C23×C4×C83C2×C411yescharacteristic
83C23×C4×C83C2×C411yescharacteristic
84C23×C4×C83C2311yescharacteristic
85C22×C8×C83—21no—
86C22×C8×C83—21no—
87C22×C8×C83—21no—
88C22×C8×C83—21no—
89C22×C8×C83—21no—
90C22×C8×C83—21no—
91C22×C8×C83—21no—
92C22×C8×C83—21no—
93C22×C8×C83—21no—
94C22×C8×C83—21no—
95C22×C8×C83—21no—
96C22×C8×C83—21no—
97C22×C8×C83D412yes—
98C22×C8×C83D412yes—
99C2×C42×C83—21no—
100C2×C42×C83—21no—
101C2×C42×C83—21no—
102C2×C42×C83—21no—
103C2×C42×C83—21no—
104C2×C42×C83—21no—
105C23×D83—21no—
106C23×D83—21no—
107C23×D83—21no—
108C23×D83—21no—
109C23×D83—21no—
110C23×D83—21no—
111C23×D83—21no—
112C23×D83—21no—
113C23×D83—21no—
114C23×D83—21no—
115C23×D83—21no—
116C23×D83—21no—
117C23×D83C4⋊C412yes—
118C23×D83C2×C812yes—
119C23×D83M1612yes—
120C22×Dic83—21no—
121C22×Dic83—21no—
122C22×Dic83—21no—
123C22×Dic83—21no—
124C22×Dic83—21no—
125C22×Dic83—21no—
126C22×Dic83—21no—
127C22×Dic83—21no—
128C22×Dic83—21no—
129C22×Dic83—21no—
130C22×Dic83—21no—
131C22×Dic83—21no—
132C22×Dic83—21no—
133C22×Dic83—21no—
134C22×Dic83—21no—
135C22×Dic83—21no—
136C22×Dic83C22⋊C412yes—
137C22×Dic83C22⋊C412yes—
138C22×Dic83C4⋊C412yes—
139C22×Dic83C2×C812yes—
140C22×Dic83M1612yes—
141C2×C4×D83—22no—
142C2×C4×D83—22no—
143C2×C4×D83—22no—
144C2×C4×D83—22no—
145C2×C4×D83—22no—
146C2×C4×D83—22no—
147C2×C4×D83—22no—
148C2×C4×D83—22no—
149C2×C4×D83—22no—
150C2×C4×D83—22no—
151C2×C4×D83—22no—
152C2×C4×D83—22no—
153C2×C4×D83—41no—
154C2×C4×D83—41no—
155C2×C4×D83—41no—
156C2×C4×D83—41no—
157C2×C4×D83—41no—
158C2×C4×D83—41no—
159C2×C4×D83—41no—
160C2×C4×D83—41no—
161C2×C4×D83—41no—
162C2×C4×D83—41no—
163C2×C4×D83—41no—
164C2×C4×D83—41no—
165C2×C4×D83—41no—
166C2×C4×D83—41no—
167C2×C4×D83—41no—
168C2×C4×D83—41no—
169C2×C83⋊C8—22no—
170C2×C83⋊C8—22no—
171C2×C83⋊C8—22no—
172C2×C83⋊C8—22no—
173C2×C83⋊C8—22no—
174C2×C83⋊C8—22no—
175C2×C83⋊C8—41no—
176C2×C83⋊C8—41no—
177C2×C83⋊C8—41no—
178C2×C83⋊C8—41no—
179C2×C83⋊C8—41no—
180C2×C83⋊C8—41no—
181C2×C83⋊C8—41no—
182C2×C83⋊C8—41no—
183(C2×D83)⋊C4—28no—
184(C2×D83)⋊C4—28no—
185C4×Dic83—22no—
186C4×Dic83—22no—
187C4×Dic83—22no—
188C4×Dic83—22no—
189C24×C83C22×C411yescharacteristic
190C22×C4×C83—21no—
191C22×C4×C83—21no—
192C22×C4×C83—21no—
193C22×C4×C83—21no—
194C22×C4×C83—21no—
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×C83C2×C812yes—
203C22×C4×C83M1612yes—
204C22×C4×C83C2×D411yescharacteristic
205C22×C4×C83C2×D411yescharacteristic
206C22×C4×C83C2×D411yescharacteristic
207C22×C4×C83C2×D411yescharacteristic
208C22×C4×C83C2×D411yescharacteristic
209C22×C4×C83C2×D411yescharacteristic
210C22×C4×C83C2×D411yescharacteristic
211C22×C4×C83C2×Q811yescharacteristic
212C22×C4×C83#4111yescharacteristic
213C22×C4×C83#4111yescharacteristic
214C22×C4×C83#4111yescharacteristic
215C22×C4×C83#4111yescharacteristic
216C22×C4×C83#4111yescharacteristic
217C22×C4×C83#4111yescharacteristic
218C2×C8×C83—22no—
219C2×C8×C83—22no—
220C2×C8×C83—22no—
221C2×C8×C83—22no—
222C2×C8×C83—22no—
223C2×C8×C83—22no—
224C2×C8×C83—41no—
225C2×C8×C83—41no—
226C2×C8×C83—41no—
227C2×C8×C83—41no—
228C2×C8×C83—41no—
229C2×C8×C83—41no—
230C2×C8×C83—41no—
231C2×C8×C83—41no—
232C42×C83—41no—
233C42×C83—41no—
234C42×C83—41no—
235C42×C83—41no—
236C23×C83C2×C22⋊C411yescharacteristic
237C23×C83C2×C4⋊C411yescharacteristic
238C23×C83#11711yescharacteristic
239C23×C83C4×D411yescharacteristic
240C23×C83C4×D411yescharacteristic
241C23×C83C4×D411yescharacteristic
242C23×C83C4×D411yescharacteristic
243C23×C83C22×C811yescharacteristic
244C23×C83C2×M1611yescharacteristic
245C23×C83C2×M1611yescharacteristic
246C23×C83C2×M1611yescharacteristic
247C23×C83#13111yescharacteristic
248C23×C83#13111yescharacteristic
249C23×C83#13111yescharacteristic
250C23×C83#13111yescharacteristic
251C22×D83—22no—
252C22×D83—22no—
253C22×D83—22no—
254C22×D83—22no—
255C22×D83—22no—
256C22×D83—22no—
257C22×D83—22no—
258C22×D83—22no—
259C22×D83—22no—
260C22×D83—22no—
261C22×D83—22no—
262C22×D83—22no—
263C22×D83—22no—
264C22×D83—22no—
265C22×D83—22no—
266C22×D83—22no—
267C22×D83—22no—
268C22×D83—22no—
269C22×D83—41no—
270C22×D83—41no—
271C22×D83—41no—
272C22×D83—41no—
273C22×D83—41no—
274C22×D83—41no—
275C22×D83—41no—
276C22×D83—41no—
277C22×D83—41no—
278C22×D83—41no—
279C22×D83—41no—
280C22×D83—41no—
281C22×D83—41no—
282C22×D83—41no—
283C22×D83—41no—
284C22×D83—41no—
285C22×D83C4⋊C814yescomplemented
286C2×C4×C83—22no—
287C2×C4×C83—22no—
288C2×C4×C83—22no—
289C2×C4×C83—22no—
290C2×C4×C83—22no—
291C2×C4×C83—22no—
292C2×C4×C83—41no—
293C2×C4×C83—41no—
294C2×C4×C83—41no—
295C2×C4×C83—41no—
296C2×C4×C83—41no—
297C2×C4×C83—41no—
298C2×C4×C83—41no—
299C2×C4×C83—41no—
300C2×C4×C83#12011yescharacteristic
301C2×C4×C83#12011yescharacteristic
302C2×C4×C83#12011yescharacteristic
303C2×C4×C83#12111yescharacteristic
304C2×C4×C83#12111yescharacteristic
305C2×C4×C83#12111yescharacteristic
306C2×C4×C83#12111yescharacteristic
307C2×C4×C83#12111yescharacteristic
308C2×C4×C83#12111yescharacteristic
309C2×C4×C83#12111yescharacteristic
310C2×C4×C83#12111yescharacteristic
311C2×C4×C83C22⋊Q811yescharacteristic
312C2×C4×C83C22⋊Q811yescharacteristic
313C2×C4×C83C22⋊Q811yescharacteristic
314C2×C4×C83C22⋊Q811yescharacteristic
315C2×C4×C83C22⋊Q811yescharacteristic
316C2×C4×C83C22⋊Q811yescharacteristic
317C2×C4×C83#12311yescharacteristic
318C2×C4×C83#12311yescharacteristic
319C2×C4×C83#12311yescharacteristic
320C2×C4×C83#12311yescharacteristic
321C2×C4×C83#12311yescharacteristic
322C2×C4×C83#12411yescharacteristic
323C2×C4×C83#12411yescharacteristic
324C2×C4×C83#12411yescharacteristic
325C2×C4×C83#12611yescharacteristic
326C2×C4×C83#12611yescharacteristic
327C2×C4×C83#12711yescharacteristic
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—22no—
339C2×Dic83—22no—
340C2×Dic83—41no—
341C2×Dic83—41no—
342C2×Dic83—41no—
343C2×Dic83—41no—
344C2×Dic83—41no—
345C2×Dic83—41no—
346C2×Dic83—41no—
347C2×Dic83—41no—
348C2×Dic83C22⋊C814yescomplemented
349C4×D83—42no—
350C4×D83—42no—
351C4×D83—42no—
352C4×D83—42no—
353C4×D83—42no—
354C4×D83—42no—
355C4×D83—42no—
356C4×D83—42no—
357C8×C83—42no—
358C8×C83—42no—
359C83⋊C8—42no—
360C83⋊C8—42no—
361C22×C83#38011yescharacteristic
362C22×C83#38511yescharacteristic
363C22×C83#38511yescharacteristic
364C22×C83#38611yescharacteristic
365C22×C83#38811yescharacteristic
366C22×C83#38811yescharacteristic
367C22×C83#39011yescharacteristic
368C22×C83C2×C22⋊C811yescharacteristic
369C22×C83#40711yescharacteristic
370C22×C83#40811yescharacteristic
371C22×C83#40811yescharacteristic
372C22×C83C2×C4⋊C811yescharacteristic
373C22×C83#42311yescharacteristic
374C22×C83#42411yescharacteristic
375C22×C83#42411yescharacteristic
376C22×C83#43111yescharacteristic
377C22×C83#43211yescharacteristic
378C22×C83#43311yescharacteristic
379C22×C83#43311yescharacteristic
380C22×C83C8×D411yescharacteristic
381C22×C83C8×D411yescharacteristic
382C22×C83C8×D411yescharacteristic
383C22×C83C8×D411yescharacteristic
384C22×C83#43511yescharacteristic
385C22×C83#43511yescharacteristic
386C22×C83#43511yescharacteristic
387C22×C83#43511yescharacteristic
388C22×C83#43511yescharacteristic
389C22×C83#43511yescharacteristic
390C22×C83#43511yescharacteristic
391C22×C83#43511yescharacteristic
392C22×C83#43611yescharacteristic
393C22×C83#43611yescharacteristic
394C22×C83#43611yescharacteristic
395C22×C83#43611yescharacteristic
396C2×D83—24no—
397C2×D83—24no—
398C2×D83—24no—
399C2×D83—42no—
400C2×D83—42no—
401C2×D83—42no—
402C2×D83—42no—
403C2×D83—42no—
404C2×D83—42no—
405C2×D83—42no—
406C2×D83—42no—
407C2×D83—42no—
408C2×D83—42no—
409C2×D83—42no—
410C2×D83—42no—
411C4×C83—42no—
412C4×C83—42no—
413C4×C83#39211yescharacteristic
414C4×C83#39311yescharacteristic
415C4×C83#39411yescharacteristic
416C4×C83#39411yescharacteristic
417C4×C83#39611yescharacteristic
418C4×C83#39611yescharacteristic
419C4×C83#39711yescharacteristic
420C4×C83#39911yescharacteristic
421Dic83—24no—
422Dic83—42no—
423Dic83—42no—
424#11042—831nomaximal, Sylow
425C2×C83#143911yescharacteristic
426C2×C83#179711yescharacteristic
427C2×C83#179811yescharacteristic
428C2×C83#185011yescharacteristic
429C2×C83#185011yescharacteristic
430C2×C83#185111yescharacteristic
431C2×C83#185111yescharacteristic
432C2×C83#186911yescharacteristic
433C2×C83#187011yescharacteristic
434C2×C83#192311yescharacteristic
435C2×C83#192311yescharacteristic
436C2×C83#192411yescharacteristic
437C2×C83#192411yescharacteristic
438C2×C83#195411yescharacteristic
439C2×C83#195511yescharacteristic
440D83—44no—
441C22×C4⋊C8—831no—
442C22×C22⋊C8—831no—
443C22×C22⋊C8—831no—
444C2×C4×C22⋊C4—831no—
445C2×#336—831no—
446C2×#336—831no—
447C2×#336D8311yescharacteristic, complemented
448C83#1104211yescharacteristic, complemented, Sylow
449C24×C4—831no—
450C23×C8—831no—
451C23×C8—831no—
452C23×C8C2×D8311yescharacteristic
453C23×C8C2×D8311yescharacteristic
454C22×C22⋊C4—831no—
455C22×C22⋊C4—831no—
456C22×C42—831no—
457C22×C42C2×D8311yescharacteristic
458C2×C4⋊C8—1662no—
459C2×C4⋊C8—1662no—
460C2×C4⋊C8—1662no—
461C2×C22⋊C8—1662no—
462C2×C22⋊C8—1662no—
463C2×C22⋊C8—1662no—
464C2×C22⋊C8—1662no—
465C2×C22⋊C8—1662no—
466C2×C22⋊C8—1662no—
467C4×C22⋊C4—1662no—
468C4×C22⋊C4—1662no—
469C2×#95—831no—
470C2×#95—831no—
471#336—22no—
472#336—1662no—
473#336—1662no—
474C25—831no—
475C23×C4—831no—
476C23×C4—831no—
477C23×C4—831no—
478C23×C4—832no—
479C23×C4—832no—
480C23×C4—1661no—
481C23×C4—1661no—
482C23×C4—1661no—
483C23×C4—1661no—
484C23×C4—1661no—
485C23×C4—1661no—
486C23×C4—1661no—
487C23×C4—1661no—
488C23×C4—1661no—
489C23×C4—1661no—
490C23×C4—1661no—
491C23×C4—1661no—
492C23×C4C4×D8311yescharacteristic
493C23×C4C4×D8311yescharacteristic
494C23×C4C22×D8311yescharacteristic
495C22×C8—21no—
496C22×C8—21no—
497C22×C8—21no—
498C22×C8—21no—
499C22×C8—21no—
500C22×C8—21no—
501C22×C8—21no—
502C22×C8—21no—
503C22×C8—21no—
504C22×C8—21no—
505C22×C8—21no—
506C22×C8—21no—
507C22×C8—832no—
508C22×C8—832no—
509C22×C8—1661no—
510C22×C8—1661no—
511C22×C8—1661no—
512C22×C8—1661no—
513C22×C8—1661no—
514C22×C8—1661no—
515C22×C8—1661no—
516C22×C8—1661no—
517C22×C8—1661no—
518C22×C8—1661no—
519C22×C8—1661no—
520C22×C8—1661no—
521C22×C8D33212yes—
522C22×C8C22⋊D8312yes—
523C2×C22⋊C4—834no—
524C2×C22⋊C4—1662no—
525C2×C22⋊C4—1662no—
526C2×C22⋊C4—1662no—
527C2×C22⋊C4—1662no—
528C2×C22⋊C4—1662no—
529C2×C42—21no—
530C2×C42—21no—
531C2×C42—21no—
532C2×C42—21no—
533C2×C42—21no—
534C2×C42—21no—
535C2×C42—832no—
536C2×C42—832no—
537C2×C42—1661no—
538C2×C42—1661no—
539C2×C42—1661no—
540C2×C42—1661no—
541C4⋊C8—1668no—
542C22⋊C8—1668no—
543C22⋊C8—1668no—
544#95—1662no—
545#95—1662no—
546C24—832no—
547C24—832no—
548C24—832no—
549C24—1661no—
550C24—1661no—
551C24—1661no—
552C24—1661no—
553C24—1661no—
554C24—1661no—
555C24—1661no—
556C24—1661no—
557C24—1661no—
558C24—1661no—
559C24—1661no—
560C24—1661no—
561C24C2×C4×D8311yescharacteristic
562C22×C4—21no—
563C22×C4—21no—
564C22×C4—21no—
565C22×C4—21no—
566C22×C4—21no—
567C22×C4—21no—
568C22×C4—21no—
569C22×C4—21no—
570C22×C4—21no—
571C22×C4—21no—
572C22×C4—21no—
573C22×C4—21no—
574C22×C4—3321no—
575C22×C4—3321no—
576C22×C4—3321no—
577C22×C4—3321no—
578C22×C4—3321no—
579C22×C4—3321no—
580C22×C4—3321no—
581C22×C4—3321no—
582C22×C4—3321no—
583C22×C4—3321no—
584C22×C4—3321no—
585C22×C4—3321no—
586C22×C4—3321no—
587C22×C4—3321no—
588C22×C4—3321no—
589C22×C4—3321no—
590C22×C4—832no—
591C22×C4—832no—
592C22×C4—832no—
593C22×C4—832no—
594C22×C4—832no—
595C22×C4—1661no—
596C22×C4—1661no—
597C22×C4—1661no—
598C22×C4—1661no—
599C22×C4—1661no—
600C22×C4—1661no—
601C22×C4—1661no—
602C22×C4—1661no—
603C22×C4—1661no—
604C22×C4—1661no—
605C22×C4—1661no—
606C22×C4—1661no—
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—1661no—
620C22×C4—1661no—
621C22×C4—1661no—
622C22×C4—1661no—
623C22×C4C8×D8312yes—
624C22×C4#1305057312yes—
625C22×C4D4×D8311yescharacteristic
626C22×C4D4×D8311yescharacteristic
627C22×C4D4×D8311yescharacteristic
628C22×C4D4×D8311yescharacteristic
629C22×C4D4×D8311yescharacteristic
630C22×C4C2×C22⋊D8311yescharacteristic
631C22×C4C2×D33211yescharacteristic
632C22×C4Q8×D8311yescharacteristic
633C22×C4#1305058911yescharacteristic
634C22×C4#1305059011yescharacteristic
635C22×C4#1305059011yescharacteristic
636C22×C4#1305059011yescharacteristic
637C22×C4#1305059011yescharacteristic
638C22×C4#1305059111yescharacteristic
639C2×C8—22no—
640C2×C8—22no—
641C2×C8—22no—
642C2×C8—22no—
643C2×C8—22no—
644C2×C8—22no—
645C2×C8—41no—
646C2×C8—41no—
647C2×C8—41no—
648C2×C8—41no—
649C2×C8—41no—
650C2×C8—41no—
651C2×C8—41no—
652C2×C8—41no—
653C2×C8—3321no—
654C2×C8—3321no—
655C2×C8—3321no—
656C2×C8—3321no—
657C2×C8—3321no—
658C2×C8—3321no—
659C2×C8—3321no—
660C2×C8—3321no—
661C2×C8—1662no—
662C2×C8—1662no—
663C2×C8—1662no—
664C2×C8—1662no—
665C2×C8—1662no—
666C2×C8—1662no—
667C22⋊C4—1668no—
668C22⋊C4—1668no—
669C42—41no—
670C42—41no—
671C42—41no—
672C42—41no—
673C42—1662no—
674C42—1662no—
675C42—1662no—
676C42—1662no—
677C23—3321no—
678C23—3321no—
679C23—3321no—
680C23—3321no—
681C23—3321no—
682C23—3321no—
683C23—3321no—
684C23—3321no—
685C23—3321no—
686C23—3321no—
687C23—3321no—
688C23—3321no—
689C23—3321no—
690C23—3321no—
691C23—3321no—
692C23—3321no—
693C23—834no—
694C23—1662no—
695C23—1662no—
696C23—1662no—
697C23—1662no—
698C23—1662no—
699C23—1662no—
700C23—1662no—
701C23—1662no—
702C23—1662no—
703C23—1662no—
704C23—1662no—
705C23—1662no—
706C23—1662no—
707C23—1662no—
708C23—1662no—
709C23—1662no—
710C23—1662no—
711C23—1662no—
712C23C22⋊C4×D8311yescharacteristic
713C23C4⋊C4×D8311yescharacteristic
714C23#1458174911yescharacteristic
715C23(C22⋊D83)⋊C411yescharacteristic
716C23C4×C22⋊D8311yescharacteristic
717C23#1458175411yescharacteristic
718C23C4×D33211yescharacteristic
719C23C2×C8×D8311yescharacteristic
720C23M16×D8311yescharacteristic
721C23M16×D8311yescharacteristic
722C23C2×#1305057311yescharacteristic
723C23#1458179811yescharacteristic
724C23#1458179811yescharacteristic
725C23#1458180011yescharacteristic
726C23#1458180011yescharacteristic
727C2×C4—22no—
728C2×C4—22no—
729C2×C4—22no—
730C2×C4—22no—
731C2×C4—22no—
732C2×C4—22no—
733C2×C4—41no—
734C2×C4—41no—
735C2×C4—41no—
736C2×C4—41no—
737C2×C4—41no—
738C2×C4—41no—
739C2×C4—41no—
740C2×C4—41no—
741C2×C4—3321no—
742C2×C4—3321no—
743C2×C4—3321no—
744C2×C4—3321no—
745C2×C4—3321no—
746C2×C4—3321no—
747C2×C4—3321no—
748C2×C4—3321no—
749C2×C4—3322no—
750C2×C4—3322no—
751C2×C4—3322no—
752C2×C4—3322no—
753C2×C4—3322no—
754C2×C4—3322no—
755C2×C4—3322no—
756C2×C4—3322no—
757C2×C4—834no—
758C2×C4—1662no—
759C2×C4—1662no—
760C2×C4—1662no—
761C2×C4—1662no—
762C2×C4—1662no—
763C2×C4—1662no—
764C2×C4—1662no—
765C2×C4—1662no—
766C2×C4—1662no—
767C2×C4—1662no—
768C2×C4—1662no—
769C2×C4—1662no—
770C2×C4#1458176011yescharacteristic
771C2×C4#1458176211yescharacteristic
772C2×C4#1458176211yescharacteristic
773C2×C4#1458176411yescharacteristic
774C2×C4#1458176511yescharacteristic
775C2×C4#1458176511yescharacteristic
776C2×C4#1458176511yescharacteristic
777C2×C4#1458176511yescharacteristic
778C2×C4#1458176511yescharacteristic
779C2×C4#1458176611yescharacteristic
780C2×C4#1458176711yescharacteristic
781C2×C4#1458176811yescharacteristic
782C2×C4#1458177011yescharacteristic
783C2×C4#1458177011yescharacteristic
784C2×C4#1458177011yescharacteristic
785C2×C4#1458177011yescharacteristic
786C2×C4#1458177211yescharacteristic
787C2×C4#1458177411yescharacteristic
788C2×C4#1458177511yescharacteristic
789C2×C4#1458177711yescharacteristic
790C2×C4#1458177711yescharacteristic
791C2×C4#1458177711yescharacteristic
792C2×C4#1458177811yescharacteristic
793C2×C4#1458177811yescharacteristic
794C2×C4#1458178011yescharacteristic
795C2×C4#1458178611yescharacteristic
796C2×C4#1458178711yescharacteristic
797C2×C4#1458178811yescharacteristic
798C8—42no—
799C8—42no—
800C8—3322no—
801C8—3322no—
802C22—3322no—
803C22—3322no—
804C22—3322no—
805C22—3322no—
806C22—3322no—
807C22—3322no—
808C22—3322no—
809C22—3322no—
810C22—3322no—
811C22—3322no—
812C22—3322no—
813C22—3322no—
814C22—1664no—
815C22—1664no—
816C22—1664no—
817C22#1912756011yescharacteristic
818C22#1912757211yescharacteristic
819C22#1912757511yescharacteristic
820C22#1912757911yescharacteristic
821C22#1912759011yescharacteristic
822C22#1912759211yescharacteristic
823C22#1912760111yescharacteristic
824C22C22⋊C8×D8311yescharacteristic
825C22#1912766311yescharacteristic
826C22#1912766611yescharacteristic
827C22#1912766611yescharacteristic
828C22C4⋊C8×D8311yescharacteristic
829C22#1912772311yescharacteristic
830C22#1912772611yescharacteristic
831C22#1912772611yescharacteristic
832C22#1912775211yescharacteristic
833C22#1912775611yescharacteristic
834C22#1912776011yescharacteristic
835C22#1912776311yescharacteristic
836C22(C22⋊D83)⋊C811yescharacteristic
837C22C8×C22⋊D8311yescharacteristic
838C22#1912776611yescharacteristic
839C22C8×D33211yescharacteristic
840C22#1912776911yescharacteristic
841C22#1912777011yescharacteristic
842C22#1912777111yescharacteristic
843C22#1912777111yescharacteristic
844C22#1912777211yescharacteristic
845C22#1912777411yescharacteristic
846C22#1912777411yescharacteristic
847C22#1912777511yescharacteristic
848C22#1912777611yescharacteristic
849C22#1912777711yescharacteristic
850C22#1912777811yescharacteristic
851C22#1912778011yescharacteristic
852C4—42no—
853C4—42no—
854C4—3322no—
855C4—3322no—
856C4—1664no—
857C4#1912761011yescharacteristic
858C4#1912761411yescharacteristic
859C4#1912761611yescharacteristic
860C4#1912761911yescharacteristic
861C4#1912762311yescharacteristic
862C4#1912762511yescharacteristic
863C4#1912763011yescharacteristic
864C4#1912763611yescharacteristic
865C2—3324no—
866C2#2490570711yescharacteristic
867C2#2490744211yescharacteristic
868C2#2490744611yescharacteristic
869C2#2490763911yescharacteristic
870C2#2490764211yescharacteristic
871C2#2490764411yescharacteristic
872C2#2490764711yescharacteristic
873C2#2490775411yescharacteristic
874C2#2490775911yescharacteristic
875C2#2490806711yescharacteristic
876C2#2490806911yescharacteristic
877C2#2490807411yescharacteristic
878C2#2490807611yescharacteristic
879C2#2490825511yescharacteristic
880C2#2490825911yescharacteristic
subgroupG/H
center, FrattiniC23×C4C22×D83
commutatorC23×C83C22×C8
FittingC2×#336×C83C2
socleC24×C83C22×C4
prime radicalC24×D83C2×C4
cosocleC23×C4×C83C23
hypercenterC2×#336D83
hypocenterC83#11042
LCSG ▷ C23×C83 ▷ C83
UCSC1 ◁ C23×C4 ◁ C2×#336

Complements

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

NH ≅ G/Ntype
1. C22×Dic83⋊C8C2semidirect
5. C2×#19127456C2semidirect
6. C2×#19127455C2semidirect
7. C2×#336×C83C2semidirect
70. C2×(C2×D83)⋊C4C8semidirect
285. C22×D83C4⋊C8semidirect
348. C2×Dic83C22⋊C8semidirect
447. C2×#336D83semidirect
448. C83#11042semidirect

Maximal subgroups

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

subgroupindex
C22×Dic83⋊C82
C22×(C2×D83)⋊C82
C2×C4×(C2×D83)⋊C42
C2×#191274562
C2×#191274552
C2×#336×C832
#1104283