Finite Group Databasebeta

← #35327801

Subgroups — #35327801

Order 21248.

2474 conjugacy classes of subgroups.

The subgroup lattice has 862 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C4×D332C211yesmaximal, characteristic
2C2×#19127603C211yesmaximal, characteristic
3C2×#19127603C211yesmaximal, characteristic
4C2×#19127599C211yesmaximal, characteristic, complemented
5C2×#19127572C212yesmaximal, complemented
6#24905707C212yesmaximal, complemented
7#24905705C212yesmaximal, complemented
8#24905693C211yesmaximal, characteristic, complemented
9#24905693C211yesmaximal, characteristic, complemented
10(C2×D83)⋊#95C212yesmaximal, complemented
11C2×C4×C4⋊C4×C83C211yesmaximal, characteristic, complemented
12C23×D332C2211yescharacteristic
13C23×C4×D83C2212yes—
14C2×C4×D332—24no—
15C2×C4×D332—24no—
16C2×C4×D332—24no—
17C22×C4⋊Dic83C2211yescharacteristic
18C22×C4⋊Dic83C2211yescharacteristic
19C22×C4⋊Dic83C2211yescharacteristic
20C22×Dic83⋊C4C2212yes—
21C22×(C2×D83)⋊C4C2212yes—
22C22×(C2×D83)⋊C4C2212yes—
23C22×(C2×D83)⋊C4C2212yes—
24C22×(C2×D83)⋊C4C2212yes—
25C22×(C2×D83)⋊C4C2212yes—
26#19127603—24no—
27#19127603C418yescomplemented
28#19127599—24no—
29#19127572—28no—
30C2×C83⋊#95C2212yes—
31C2×C83⋊#95C2212yes—
32C2×C83⋊#95C2212yes—
33C2×C83⋊#95C2212yes—
34C2×C83⋊#95C2212yes—
35C22×C4⋊C4×C83C2211yescharacteristic
36C22×C4⋊C4×C83C2211yescharacteristic
37C22×C42×C83C2211yescharacteristic
38C22×C42×C83C2211yescharacteristic
39C22×C42×C83C2211yescharacteristic
40C4×C4⋊C4×C83—24no—
41C2×#95×C83C2211yescharacteristic
42C2×#95×C83C2211yescharacteristic
43C24×D83C2312yes—
44C22×D332—22no—
45C22×D332—22no—
46C22×D332—22no—
47C22×D332—22no—
48C22×D332C2×C414yes—
49C22×D332D414yes—
50C22×D332Q814yes—
51C23×Dic83C2312yes—
52C23×Dic83C2312yes—
53C23×Dic83C2312yes—
54C22×C4×D83—24no—
55C22×C4×D83—24no—
56C22×C4×D83—24no—
57C22×C4×D83—24no—
58C22×C4×D83—24no—
59C22×C4×D83—42no—
60C22×C4×D83—42no—
61C4×D332—232no—
62C2×C4⋊Dic83—22no—
63C2×C4⋊Dic83—22no—
64C2×C4⋊Dic83—22no—
65C2×C4⋊Dic83—22no—
66C2×C4⋊Dic83—22no—
67C2×C4⋊Dic83—22no—
68C2×C4⋊Dic83—22no—
69C2×C4⋊Dic83C2×C414yescomplemented
70C2×C4⋊Dic83D414yes—
71C2×Dic83⋊C4—24no—
72C2×Dic83⋊C4—24no—
73C2×Dic83⋊C4—42no—
74C2×(C2×D83)⋊C4—24no—
75C2×(C2×D83)⋊C4—24no—
76C2×(C2×D83)⋊C4—24no—
77C2×(C2×D83)⋊C4—24no—
78C2×(C2×D83)⋊C4—24no—
79C2×(C2×D83)⋊C4—24no—
80C2×(C2×D83)⋊C4—24no—
81C2×(C2×D83)⋊C4—24no—
82C2×(C2×D83)⋊C4—24no—
83C2×(C2×D83)⋊C4—42no—
84C2×(C2×D83)⋊C4—42no—
85C2×(C2×D83)⋊C4—42no—
86C2×(C2×D83)⋊C4—42no—
87C2×(C2×D83)⋊C4C2×C418yescomplemented
88C2×(C2×D83)⋊C4C2×C418yescomplemented
89C83⋊#95—24no—
90C83⋊#95—24no—
91C83⋊#95—24no—
92C83⋊#95—42no—
93C83⋊#95—42no—
94C23×C4×C83C2311yescharacteristic
95C23×C4×C83C2311yescharacteristic
96C23×C4×C83C2311yescharacteristic
97C23×C4×C83C2311yescharacteristic
98C23×C4×C83C2311yescharacteristic
99C23×C4×C83C2311yescharacteristic
100C23×C4×C83C2311yescharacteristic
101C2×C4⋊C4×C83—22no—
102C2×C4⋊C4×C83—22no—
103C2×C4⋊C4×C83—22no—
104C2×C4⋊C4×C83—22no—
105C2×C4⋊C4×C83—22no—
106C2×C4⋊C4×C83D414yescomplemented
107C2×C42×C83—22no—
108C2×C42×C83—22no—
109C2×C42×C83—22no—
110C2×C42×C83—22no—
111C2×C42×C83—22no—
112C2×C42×C83—22no—
113C2×C42×C83—22no—
114C2×C42×C83C2×C414yescomplemented
115C2×C42×C83D414yes—
116#95×C83—22no—
117#95×C83—22no—
118C23×D83—22no—
119C23×D83—22no—
120C23×D83—22no—
121C23×D83—22no—
122C23×D83—22no—
123C23×D83—22no—
124C23×D83—22no—
125C23×D83—22no—
126C23×D83—22no—
127C23×D83—22no—
128C23×D83—22no—
129C23×D83—22no—
130C23×D83C22×C414yes—
131C23×D83C2×D414yes—
132C23×D83C2×Q814yes—
133C2×D332—28no—
134C2×D332—28no—
135C2×D332—28no—
136C2×D332—28no—
137C2×D332—28no—
138C2×D332—28no—
139C2×D332C4⋊C4116yescomplemented
140C22×Dic83—22no—
141C22×Dic83—22no—
142C22×Dic83—22no—
143C22×Dic83—22no—
144C22×Dic83—22no—
145C22×Dic83—22no—
146C22×Dic83—22no—
147C22×Dic83—22no—
148C22×Dic83—22no—
149C22×Dic83—22no—
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×Dic83C22×C414yes—
160C22×Dic83C2×D414yes—
161C2×C4×D83—216no—
162C2×C4×D83—48no—
163C2×C4×D83—48no—
164C2×C4×D83—48no—
165C2×C4×D83—48no—
166C2×C4×D83—48no—
167C2×C4×D83—48no—
168C4⋊Dic83—28no—
169C4⋊Dic83—28no—
170C4⋊Dic83—44no—
171Dic83⋊C4—48no—
172(C2×D83)⋊C4—216no—
173(C2×D83)⋊C4—216no—
174(C2×D83)⋊C4—48no—
175(C2×D83)⋊C4—48no—
176(C2×D83)⋊C4—48no—
177C24×C83C2411yescharacteristic
178C22×C4×C83—21no—
179C22×C4×C83—21no—
180C22×C4×C83—21no—
181C22×C4×C83—21no—
182C22×C4×C83—21no—
183C22×C4×C83—21no—
184C22×C4×C83—21no—
185C22×C4×C83—21no—
186C22×C4×C83—21no—
187C22×C4×C83—21no—
188C22×C4×C83—21no—
189C22×C4×C83—21no—
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×C83—21no—
203C22×C4×C83—21no—
204C22×C4×C83—21no—
205C22×C4×C83—21no—
206C22×C4×C83—21no—
207C22×C4×C83—21no—
208C22×C4×C83—21no—
209C22×C4×C83—21no—
210C22×C4×C83C22×C412yes—
211C22×C4×C83C22×C412yes—
212C22×C4×C83C22×C412yes—
213C22×C4×C83C2×D412yes—
214C22×C4×C83C2×D412yes—
215C22×C4×C83C2×D412yes—
216C22×C4×C83C2×D412yes—
217C22×C4×C83C2×D412yes—
218C22×C4×C83C2×D412yes—
219C22×C4×C83C2×D412yes—
220C22×C4×C83C2×D412yes—
221C22×C4×C83C2×Q812yes—
222C22×C4×C83#4112yes—
223C22×C4×C83#4112yes—
224C22×C4×C83#4112yes—
225C22×C4×C83#4112yes—
226C22×C4×C83#4112yes—
227C4⋊C4×C83—28no—
228C4⋊C4×C83—28no—
229C42×C83—28no—
230C42×C83—28no—
231C42×C83—44no—
232C23×C83C23×C411yescharacteristic
233C23×C83C22×D411yescharacteristic
234C23×C83C22×D411yescharacteristic
235C23×C83C22×D411yescharacteristic
236C23×C83C22×D411yescharacteristic
237C23×C83C22×Q811yescharacteristic
238C23×C83C2×#4111yescharacteristic
239C23×C83C2×#4111yescharacteristic
240C23×C83C2×#4111yescharacteristic
241C23×C83C2×#4111yescharacteristic
242C23×C83C2×#4111yescharacteristic
243C23×C83H(5,𝔽2)11yescharacteristic
244C23×C83H(5,𝔽2)11yescharacteristic
245C23×C83H(5,𝔽2)11yescharacteristic
246C23×C832−1+411yescharacteristic
247C22×D83—24no—
248C22×D83—24no—
249C22×D83—24no—
250C22×D83—24no—
251C22×D83—24no—
252C22×D83—24no—
253C22×D83—24no—
254C22×D83—24no—
255C22×D83—24no—
256C22×D83—24no—
257C22×D83—24no—
258C22×D83—24no—
259C22×D83—24no—
260C22×D83—24no—
261C22×D83—24no—
262C22×D83—24no—
263C22×D83—24no—
264C22×D83—24no—
265C22×D83—42no—
266C22×D83—42no—
267C22×D83—42no—
268C22×D83—42no—
269C22×D83—42no—
270C22×D83—42no—
271C22×D83—42no—
272C22×D83—42no—
273C22×D83—42no—
274C22×D83—42no—
275C22×D83—42no—
276C22×D83—42no—
277C22×D83—42no—
278C22×D83—42no—
279C22×D83—42no—
280C22×D83—42no—
281C22×D83C2×C4⋊C418yes—
282C2×C4×C83—22no—
283C2×C4×C83—22no—
284C2×C4×C83—22no—
285C2×C4×C83—22no—
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—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—22no—
306C2×C4×C83—41no—
307C2×C4×C83—41no—
308C2×C4×C83—41no—
309C2×C4×C83—41no—
310C2×C4×C83—41no—
311C2×C4×C83—41no—
312C2×C4×C83—41no—
313C2×C4×C83—41no—
314C2×C4×C83—41no—
315C2×C4×C83—41no—
316C2×C4×C83—41no—
317C2×C4×C83—41no—
318C2×C4×C83—41no—
319C2×C4×C83—41no—
320C2×C4×C83—41no—
321C2×C4×C83—41no—
322C2×C4×C83C2×C4⋊C414yes—
323C2×C4×C83C4×D414yes—
324C2×C4×C83C4×D414yes—
325C2×C4×C83C4×D414yescomplemented
326C2×C4×C83#12014yes—
327C2×C4×C83#12114yes—
328C2×C4×C83C22⋊Q814yes—
329C2×C4×C83C22⋊Q814yes—
330C2×C4×C83#12314yes—
331C2×Dic83—24no—
332C2×Dic83—24no—
333C2×Dic83—24no—
334C2×Dic83—24no—
335C2×Dic83—24no—
336C2×Dic83—24no—
337C2×Dic83—42no—
338C2×Dic83—42no—
339C2×Dic83—42no—
340C2×Dic83—42no—
341C2×Dic83—42no—
342C2×Dic83—42no—
343C2×Dic83—42no—
344C2×Dic83—42no—
345C2×Dic83—42no—
346C2×Dic83—42no—
347C2×Dic83—42no—
348C2×Dic83—42no—
349C2×Dic83—42no—
350C2×Dic83—42no—
351C2×Dic83—42no—
352D332—232no—
353C4×D83—432no—
354C22×C83C22×C4⋊C411yescharacteristic
355C22×C83C2×C4×D411yescharacteristic
356C22×C83C2×C4×D411yescharacteristic
357C22×C83C2×C4×D411yescharacteristic
358C22×C83C4×#4111yescharacteristic
359C22×C83#51811yescharacteristic
360C22×C83#52011yescharacteristic
361C22×C83C2×#12011yescharacteristic
362C22×C83C2×#12111yescharacteristic
363C22×C83C2×C22⋊Q811yescharacteristic
364C22×C83C2×C22⋊Q811yescharacteristic
365C22×C83C2×#12311yescharacteristic
366C22×C83#52511yescharacteristic
367C22×C83#52911yescharacteristic
368C22×C83#53211yescharacteristic
369C22×C83#53511yescharacteristic
370C22×C83#53711yescharacteristic
371C22×C83#54011yescharacteristic
372C22×C83#54211yescharacteristic
373C22×C83D4211yescharacteristic
374C22×C83D4211yescharacteristic
375C22×C83#54611yescharacteristic
376C22×C83#54611yescharacteristic
377C22×C83#54611yescharacteristic
378C22×C83#54711yescharacteristic
379C22×C83#54811yescharacteristic
380C22×C83D4×Q811yescharacteristic
381C22×C83#55011yescharacteristic
382C22×C83#55011yescharacteristic
383C22×C83#55411yescharacteristic
384C22×C83#55411yescharacteristic
385C22×C83#55411yescharacteristic
386C22×C83#55611yescharacteristic
387C22×C83#55911yescharacteristic
388C22×C83#55911yescharacteristic
389C2×D83—28no—
390C2×D83—28no—
391C2×D83—28no—
392C2×D83—44no—
393C2×D83—44no—
394C2×D83—44no—
395C2×D83—44no—
396C2×D83—44no—
397C2×D83—44no—
398C2×D83—44no—
399C2×D83—44no—
400C2×D83—44no—
401C2×D83—44no—
402C2×D83—44no—
403C2×D83—44no—
404C4×C83—24no—
405C4×C83—24no—
406C4×C83—42no—
407C4×C83—42no—
408C4×C83—42no—
409C4×C83—42no—
410C4×C83#38518yescomplemented
411Dic83—44no—
412Dic83—44no—
413Dic83—82no—
414#14018—831nomaximal, Sylow
415C2×C83C2×#38511yescharacteristic
416C2×C83C4×#12111yescharacteristic
417C2×C83#232411yescharacteristic
418C2×C83D4×C4⋊C411yescharacteristic
419C2×C83#234911yescharacteristic
420C2×C83#236611yescharacteristic
421C2×C83#236711yescharacteristic
422C2×C83#240711yescharacteristic
423C2×C83#240811yescharacteristic
424C2×C83#244511yescharacteristic
425C2×C83#244711yescharacteristic
426C2×C83#245211yescharacteristic
427C2×C83#245411yescharacteristic
428C2×C83#253811yescharacteristic
429C2×C83#258011yescharacteristic
430D83—48no—
431C22×C4×D4—831no—
432C2×#390—831no—
433C2×#390—831no—
434C2×#389—831no—
435C2×#385—832no—
436C2×C4×C4⋊C4D8311yescharacteristic, complemented
437#1439—832no—
438#1439—832no—
439C4⋊#95—831no—
440C4⋊#95—831no—
441C22⋊#95—832no—
442C83#1401811yescharacteristic, complemented, Sylow
443C23×D4—831no—
444C24×C4—832no—
445C2×C4×D4—1664no—
446C2×C4×D4—1664no—
447C2×C4×D4—1664no—
448C22×C4⋊C4—832no—
449C22×C4⋊C4—831no—
450C22×C4⋊C4—831no—
451C22×C4⋊C4—831no—
452C22×C4⋊C4C2×D8311yescharacteristic
453C22×C4⋊C4C2×D8311yescharacteristic
454C22×C22⋊C4—832no—
455C22×C22⋊C4—832no—
456C22×C22⋊C4—832no—
457C22×C22⋊C4—832no—
458C22×C22⋊C4—832no—
459C22×C42C2×D8311yescharacteristic
460C22×C42C2×D8311yescharacteristic
461C22×C42C2×D8311yescharacteristic
462#390—838no—
463#390—1664no—
464#389—1664no—
465#385—1668no—
466C4×C4⋊C4—24no—
467C2×#95—832no—
468C2×#95—832no—
469C2×#95—832no—
470C2×#95—832no—
471C2×#95—832no—
472C2×#95C2×D8311yescharacteristic
473C2×#95C2×D8311yescharacteristic
474C25—832no—
475C22×D4—834no—
476C22×D4—834no—
477C22×D4—834no—
478C22×D4—1662no—
479C22×D4—1662no—
480C22×D4—1662no—
481C22×D4—1662no—
482C23×C4—3322no—
483C23×C4—3322no—
484C23×C4—832no—
485C23×C4—832no—
486C23×C4—832no—
487C23×C4—1664no—
488C23×C4—1664no—
489C23×C4—1664no—
490C23×C4—1664no—
491C23×C4—1664no—
492C23×C4C22×D8311yescharacteristic
493C23×C4C22×D8311yescharacteristic
494C23×C4C22×D8311yescharacteristic
495C23×C4C22×D8311yescharacteristic
496C23×C4C22×D8311yescharacteristic
497C23×C4C22×D8311yescharacteristic
498C23×C4C22×D8311yescharacteristic
499C4×D4—16632no—
500C2×C4⋊C4—22no—
501C2×C4⋊C4—22no—
502C2×C4⋊C4—22no—
503C2×C4⋊C4—22no—
504C2×C4⋊C4—22no—
505C2×C4⋊C4—3322no—
506C2×C4⋊C4—834no—
507C2×C4⋊C4—834no—
508C2×C4⋊C4—1664no—
509C2×C4⋊C4—1662no—
510C2×C4⋊C4—1664no—
511C2×C4⋊C4—1662no—
512C2×C4⋊C4—1662no—
513C2×C4⋊C4—1662no—
514C2×C4⋊C4—1662no—
515C2×C4⋊C4—1662no—
516C2×C4⋊C4—1662no—
517C2×C4⋊C4D33214yescomplemented
518C2×C22⋊C4—3322no—
519C2×C22⋊C4—3322no—
520C2×C22⋊C4—3322no—
521C2×C22⋊C4—3322no—
522C2×C22⋊C4—838no—
523C2×C22⋊C4—838no—
524C2×C22⋊C4—1664no—
525C2×C22⋊C4—1664no—
526C2×C22⋊C4—1664no—
527C2×C22⋊C4—1664no—
528C2×C22⋊C4—1664no—
529C2×C22⋊C4—1664no—
530C2×C22⋊C4—1664no—
531C2×C22⋊C4—1664no—
532C2×C22⋊C4—1664no—
533C2×C42—22no—
534C2×C42—22no—
535C2×C42—22no—
536C2×C42—22no—
537C2×C42—22no—
538C2×C42—22no—
539C2×C42—22no—
540C2×C42C4×D8314yescomplemented
541C2×C42C22⋊D8314yes—
542#95—22no—
543#95—22no—
544#95—3322no—
545#95—3322no—
546#95—1664no—
547#95—1664no—
548#95—1664no—
549C24—834no—
550C24—834no—
551C24—834no—
552C24—1662no—
553C24—1662no—
554C24—1662no—
555C24—1662no—
556C24—1662no—
557C24—1662no—
558C24—1662no—
559C24—1662no—
560C24—1662no—
561C24—1662no—
562C24—1662no—
563C24—1662no—
564C24C23×D8311yescharacteristic
565C2×D4—8316no—
566C2×D4—1668no—
567C2×D4—1668no—
568C2×D4—1668no—
569C2×D4—1668no—
570C2×D4—1668no—
571C2×D4—1668no—
572C22×C4—21no—
573C22×C4—21no—
574C22×C4—21no—
575C22×C4—21no—
576C22×C4—21no—
577C22×C4—21no—
578C22×C4—21no—
579C22×C4—21no—
580C22×C4—21no—
581C22×C4—21no—
582C22×C4—21no—
583C22×C4—21no—
584C22×C4—21no—
585C22×C4—21no—
586C22×C4—21no—
587C22×C4—21no—
588C22×C4—21no—
589C22×C4—21no—
590C22×C4—21no—
591C22×C4—21no—
592C22×C4—21no—
593C22×C4—21no—
594C22×C4—21no—
595C22×C4—21no—
596C22×C4—21no—
597C22×C4—21no—
598C22×C4—21no—
599C22×C4—21no—
600C22×C4—21no—
601C22×C4—21no—
602C22×C4—21no—
603C22×C4—21no—
604C22×C4—3328no—
605C22×C4—3328no—
606C22×C4—3328no—
607C22×C4—3328no—
608C22×C4—3328no—
609C22×C4—3328no—
610C22×C4—834no—
611C22×C4—834no—
612C22×C4—16616no—
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—1662no—
623C22×C4—1662no—
624C22×C4—1662no—
625C22×C4—1662no—
626C22×C4—1662no—
627C22×C4—1662no—
628C22×C4—1662no—
629C22×C4—1662no—
630C22×C4—1662no—
631C22×C4—1662no—
632C22×C4C2×C4×D8312yes—
633C22×C4C2×C4×D8312yes—
634C22×C4C2×C4×D8312yes—
635C22×C4D4×D8312yes—
636C22×C4D4×D8312yes—
637C22×C4C2×C22⋊D8312yes—
638C22×C4C2×C22⋊D8312yes—
639C22×C4C2×C22⋊D8312yes—
640C22×C4C2×D33212yes—
641C22×C4C2×D33212yes—
642C22×C4C2×D33212yes—
643C22×C4Q8×D8312yes—
644C22×C4#1305059012yes—
645C22×C4#1305059012yes—
646C22×C4#1305059012yes—
647C22×C4#1305059012yes—
648C22×C4#1305059112yes—
649C4⋊C4—28no—
650C4⋊C4—28no—
651C4⋊C4—3328no—
652C4⋊C4—3324no—
653C4⋊C4—1668no—
654C4⋊C4—1668no—
655C22⋊C4—3328no—
656C22⋊C4—3328no—
657C22⋊C4—3328no—
658C22⋊C4—16616no—
659C22⋊C4—16616no—
660C42—28no—
661C42—28no—
662C42—44no—
663C23—3322no—
664C23—3322no—
665C23—3322no—
666C23—3322no—
667C23—3322no—
668C23—3322no—
669C23—3322no—
670C23—3322no—
671C23—3322no—
672C23—3322no—
673C23—3322no—
674C23—3322no—
675C23—3322no—
676C23—3322no—
677C23—3322no—
678C23—3322no—
679C23—838no—
680C23—1664no—
681C23—1664no—
682C23—1664no—
683C23—1664no—
684C23—1664no—
685C23—1664no—
686C23—1664no—
687C23—1664no—
688C23—1664no—
689C23—1664no—
690C23—1664no—
691C23—1664no—
692C23—1664no—
693C23—1664no—
694C23—1664no—
695C23—1664no—
696C23—1664no—
697C23—1664no—
698C23C22×C4×D8311yescharacteristic
699C23C2×D4×D8311yescharacteristic
700C23C2×D4×D8311yescharacteristic
701C23C22×C22⋊D8311yescharacteristic
702C23C22×D33211yescharacteristic
703C23C2×Q8×D8311yescharacteristic
704C23C2×#1305059011yescharacteristic
705C23C2×#1305059011yescharacteristic
706C23C2×#1305059011yescharacteristic
707C23C2×#1305059011yescharacteristic
708C23C2×#1305059111yescharacteristic
709C23#1458183811yescharacteristic
710C23#1458183811yescharacteristic
711C23#1458183811yescharacteristic
712C23#1458183911yescharacteristic
713D4—16632no—
714C2×C4—22no—
715C2×C4—22no—
716C2×C4—22no—
717C2×C4—22no—
718C2×C4—22no—
719C2×C4—22no—
720C2×C4—22no—
721C2×C4—22no—
722C2×C4—22no—
723C2×C4—22no—
724C2×C4—22no—
725C2×C4—22no—
726C2×C4—22no—
727C2×C4—22no—
728C2×C4—22no—
729C2×C4—22no—
730C2×C4—22no—
731C2×C4—22no—
732C2×C4—22no—
733C2×C4—22no—
734C2×C4—22no—
735C2×C4—22no—
736C2×C4—22no—
737C2×C4—22no—
738C2×C4—41no—
739C2×C4—41no—
740C2×C4—41no—
741C2×C4—41no—
742C2×C4—41no—
743C2×C4—41no—
744C2×C4—41no—
745C2×C4—41no—
746C2×C4—41no—
747C2×C4—41no—
748C2×C4—41no—
749C2×C4—41no—
750C2×C4—41no—
751C2×C4—41no—
752C2×C4—41no—
753C2×C4—41no—
754C2×C4—33232no—
755C2×C4—3322no—
756C2×C4—3322no—
757C2×C4—3322no—
758C2×C4—3322no—
759C2×C4—3322no—
760C2×C4—3322no—
761C2×C4—3322no—
762C2×C4—3322no—
763C2×C4—3322no—
764C2×C4—3322no—
765C2×C4—3322no—
766C2×C4—3322no—
767C2×C4—3322no—
768C2×C4—3322no—
769C2×C4—3322no—
770C2×C4—1664no—
771C2×C4—1664no—
772C2×C4—1664no—
773C2×C4—1664no—
774C2×C4—1664no—
775C2×C4—1664no—
776C2×C4C4⋊C4×D8314yes—
777C2×C4C4×C22⋊D8314yes—
778C2×C4#1458175414yes—
779C2×C4C4×D33214yescomplemented
780C2×C4#1458176014yes—
781C2×C4#1458176614yes—
782C2×C4#1458176814yes—
783C2×C4#1458177014yes—
784C2×C4#1458177714yes—
785C22—3324no—
786C22—3324no—
787C22—3324no—
788C22—3324no—
789C22—3324no—
790C22—3324no—
791C22—3324no—
792C22—3324no—
793C22—3324no—
794C22—3324no—
795C22—3324no—
796C22—3324no—
797C22—1668no—
798C22—1668no—
799C22—1668no—
800C22C2×C4⋊C4×D8311yescharacteristic
801C22C2×C4×C22⋊D8311yescharacteristic
802C22C2×#1458175411yescharacteristic
803C22C2×C4×D33211yescharacteristic
804C22C4×#1305059011yescharacteristic
805C22#1912817511yescharacteristic
806C22#1912818111yescharacteristic
807C22C2×#1458176011yescharacteristic
808C22C2×#1458176611yescharacteristic
809C22C2×#1458176811yescharacteristic
810C22C2×#1458177011yescharacteristic
811C22C2×#1458177711yescharacteristic
812C22#1912821211yescharacteristic
813C22#1912823511yescharacteristic
814C22#1912825111yescharacteristic
815C22#1912826511yescharacteristic
816C22#1912827911yescharacteristic
817C22#1912830611yescharacteristic
818C22#1912832211yescharacteristic
819C22D4×D33211yescharacteristic
820C22D4×D33211yescharacteristic
821C22#1912834711yescharacteristic
822C22#1912834711yescharacteristic
823C22#1912834711yescharacteristic
824C22#1912835611yescharacteristic
825C22#1912836011yescharacteristic
826C22Q8×D33211yescharacteristic
827C22#1912837211yescharacteristic
828C22#1912837311yescharacteristic
829C22#1912841111yescharacteristic
830C22#1912841111yescharacteristic
831C22#1912841111yescharacteristic
832C22#1912842411yescharacteristic
833C22#1912843611yescharacteristic
834C22#1912843611yescharacteristic
835C4—24no—
836C4—24no—
837C4—42no—
838C4—42no—
839C4—42no—
840C4—42no—
841C4—3324no—
842C4—3324no—
843C4—6642no—
844C4#1912757218yescomplemented
845C2—3328no—
846C2C2×#1912757211yescharacteristic
847C2C4×#1458176611yescharacteristic
848C2#2491015611yescharacteristic
849C2C4⋊C4×D33211yescharacteristic
850C2#2491037411yescharacteristic
851C2#2491052711yescharacteristic
852C2#2491053211yescharacteristic
853C2#2491080811yescharacteristic
854C2#2491081911yescharacteristic
855C2#2491122811yescharacteristic
856C2#2491125011yescharacteristic
857C2#2491131311yescharacteristic
858C2#2491133511yescharacteristic
859C2#2491238111yescharacteristic
860C2#2491282111yescharacteristic
subgroupG/H
center, FrattiniC24C23×D83
commutatorC23×C83C23×C4
FittingC2×C4×C4⋊C4×C83C2
socle, cosocleC24×C83C24
prime radicalC23×D332C22
hypercenterC2×C4×C4⋊C4D83
hypocenterC83#14018
LCSG ▷ C23×C83 ▷ C83
UCSC1 ◁ C24 ◁ C2×C4×C4⋊C4

Complements

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

NH ≅ G/Ntype
4. C2×#19127599C2semidirect
5. C2×#19127572C2semidirect
6. #24905707C2semidirect
7. #24905705C2semidirect
8. #24905693C2semidirect
9. #24905693C2semidirect
10. (C2×D83)⋊#95C2semidirect
11. C2×C4×C4⋊C4×C83C2semidirect
27. #19127603C4semidirect
69. C2×C4⋊Dic83C2×C4semidirect
87. C2×(C2×D83)⋊C4C2×C4semidirect
88. C2×(C2×D83)⋊C4C2×C4semidirect
106. C2×C4⋊C4×C83D4semidirect
114. C2×C42×C83C2×C4semidirect
139. C2×D332C4⋊C4semidirect
325. C2×C4×C83C4×D4semidirect
410. C4×C83#385semidirect
436. C2×C4×C4⋊C4D83semidirect
442. C83#14018semidirect
517. C2×C4⋊C4D332semidirect
540. C2×C42C4×D83semidirect
779. C2×C4C4×D332semidirect
844. C4#19127572semidirect

Maximal subgroups

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

subgroupindex
C22×C4×D3322
C2×#191276032
C2×#191275992
C2×#191275722
#249057072
#249057052
#249056932
(C2×D83)⋊#952
C2×C4×C4⋊C4×C832
#1401883