Finite Group Databasebeta

← #35327303

Subgroups — #35327303

Order 21248.

2358 conjugacy classes of subgroups.

The subgroup lattice has 614 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#14581754C211yesmaximal, characteristic
2C2×#19127603C211yesmaximal, characteristic
3C2×#19127602C211yesmaximal, characteristic
4C2×#19127600C211yesmaximal, characteristic, complemented
5C2×#19127566C211yesmaximal, characteristic, complemented
6#24905709C214yesmaximal, complemented
7(C2×D83)⋊#95C214yesmaximal, complemented
8C4×C83⋊#95C211yesmaximal, characteristic, complemented
9C83×C4⋊#95C211yesmaximal, characteristic, complemented
10C23×D332C2211yescharacteristic
11C23×C4×D83C2212yes—
12C2×#14581754—24no—
13C2×#14581754—24no—
14C2×#14581754—24no—
15C22×C4⋊Dic83C2211yescharacteristic
16C22×C4⋊Dic83C2212yes—
17C22×(C2×D83)⋊C4C2212yes—
18C22×(C2×D83)⋊C4C2214yes—
19C22×(C2×D83)⋊C4C2214yes—
20C22×C4×Dic83C2211yescharacteristic
21C22×C4×Dic83C2211yescharacteristic
22#19127603—24no—
23#19127602C418yescomplemented
24#19127600—24no—
25#19127566—24no—
26C2×C83⋊#95C2214yes—
27C2×C83⋊#95C2212yes—
28C2×C83⋊#95C2212yes—
29C2×C83⋊#95C2212yes—
30C22×C4⋊C4×C83C2211yescharacteristic
31C22×C4⋊C4×C83C2211yescharacteristic
32C22×C42×C83C2211yescharacteristic
33C2×#95×C83C2214yes—
34C24×D83C2312yes—
35C22×D332—22no—
36C22×D332—22no—
37C22×D332—22no—
38C22×D332—22no—
39C22×D332C2×C414yes—
40C22×D332D414yes—
41C22×D332Q814yes—
42C23×Dic83C2312yes—
43C23×Dic83C2312yes—
44C23×Dic83C2311yescharacteristic
45C23×Dic83C2311yescharacteristic
46C22×C4×D83—24no—
47C22×C4×D83—24no—
48C22×C4×D83—28no—
49C22×C4×D83—24no—
50C22×C4×D83—44no—
51#14581754—232no—
52C2×C4⋊Dic83—24no—
53C2×C4⋊Dic83—22no—
54C2×C4⋊Dic83—22no—
55C2×C4⋊Dic83—22no—
56C2×C4⋊Dic83—44no—
57C2×(C2×D83)⋊C4—24no—
58C2×(C2×D83)⋊C4—24no—
59C2×(C2×D83)⋊C4—28no—
60C2×(C2×D83)⋊C4—24no—
61C2×(C2×D83)⋊C4—28no—
62C2×(C2×D83)⋊C4—44no—
63C2×(C2×D83)⋊C4—44no—
64C2×(C2×D83)⋊C4—44no—
65C2×(C2×D83)⋊C4C2×C4116yescomplemented
66C2×C4×Dic83—22no—
67C2×C4×Dic83—22no—
68C2×C4×Dic83—22no—
69C2×C4×Dic83—22no—
70C2×C4×Dic83C2×C414yescomplemented
71C2×C4×Dic83D414yes—
72C83⋊#95—24no—
73C83⋊#95—24no—
74C83⋊#95—28no—
75C83⋊#95—24no—
76C23×C4×C83C2312yes—
77C23×C4×C83C2312yes—
78C23×C4×C83C2312yes—
79C23×C4×C83C2311yescharacteristic
80C2×C4⋊C4×C83—22no—
81C2×C4⋊C4×C83—22no—
82C2×C4⋊C4×C83—22no—
83C2×C4⋊C4×C83—22no—
84C2×C4⋊C4×C83C2×C414yescomplemented
85C2×C4⋊C4×C83D414yes—
86C2×C42×C83—22no—
87C2×C42×C83—22no—
88C2×C42×C83—22no—
89#95×C83—44no—
90C23×D83—22no—
91C23×D83—22no—
92C23×D83—24no—
93C23×D83—22no—
94C23×D83—22no—
95C23×D83—24no—
96C23×D83—24no—
97C23×D83—24no—
98C23×D83C22×C414yes—
99C23×D83C2×D414yes—
100C23×D83C2×Q814yes—
101C2×D332—28no—
102C2×D332—28no—
103C2×D332—28no—
104C2×D332—28no—
105C2×D332—28no—
106C2×D332—28no—
107C2×D332C4⋊C4116yescomplemented
108C22×Dic83—21no—
109C22×Dic83—21no—
110C22×Dic83—22no—
111C22×Dic83—22no—
112C22×Dic83—21no—
113C22×Dic83—21no—
114C22×Dic83—22no—
115C22×Dic83—22no—
116C22×Dic83—22no—
117C22×Dic83—22no—
118C22×Dic83—22no—
119C22×Dic83—22no—
120C22×Dic83—22no—
121C22×Dic83—22no—
122C22×Dic83—22no—
123C22×Dic83—22no—
124C22×Dic83—24no—
125C22×Dic83—24no—
126C22×Dic83C22×C414yes—
127C22×Dic83C2×D412yes—
128C22×Dic83C2×D412yes—
129C22×Dic83#4114yes—
130C2×C4×D83—216no—
131C2×C4×D83—416no—
132C2×C4×D83—416no—
133C2×C4×D83—48no—
134C2×C4×D83—48no—
135C4⋊Dic83—48no—
136C4⋊Dic83—44no—
137(C2×D83)⋊C4—216no—
138(C2×D83)⋊C4—416no—
139(C2×D83)⋊C4—416no—
140C4×Dic83—28no—
141C4×Dic83—28no—
142C24×C83C2411yescharacteristic
143C22×C4×C83—22no—
144C22×C4×C83—22no—
145C22×C4×C83—22no—
146C22×C4×C83—22no—
147C22×C4×C83—24no—
148C22×C4×C83—22no—
149C22×C4×C83—22no—
150C22×C4×C83—22no—
151C22×C4×C83—22no—
152C22×C4×C83—24no—
153C22×C4×C83—22no—
154C22×C4×C83—24no—
155C22×C4×C83—22no—
156C22×C4×C83—24no—
157C22×C4×C83C22×C414yes—
158C22×C4×C83C22×C412yes—
159C22×C4×C83C2×D412yes—
160C22×C4×C83C2×D412yes—
161C22×C4×C83C2×D414yes—
162C22×C4×C83C2×D412yes—
163C22×C4×C83C2×Q812yes—
164C22×C4×C83#4112yes—
165C22×C4×C83#4112yes—
166C22×C4×C83#4114yes—
167C4⋊C4×C83—28no—
168C4⋊C4×C83—28no—
169C42×C83—44no—
170C23×C83C23×C411yescharacteristic
171C23×C83C22×D411yescharacteristic
172C23×C83C22×D411yescharacteristic
173C23×C83C22×D411yescharacteristic
174C23×C83C22×Q811yescharacteristic
175C23×C83C2×#4112yes—
176C23×C83C2×#4111yescharacteristic
177C23×C83C2×#4111yescharacteristic
178C23×C83C2×#4112yes—
179C23×C83H(5,𝔽2)12yes—
180C23×C83H(5,𝔽2)12yes—
181C22×D83—24no—
182C22×D83—24no—
183C22×D83—28no—
184C22×D83—28no—
185C22×D83—24no—
186C22×D83—24no—
187C22×D83—24no—
188C22×D83—24no—
189C22×D83—28no—
190C22×D83—28no—
191C22×D83—28no—
192C22×D83—28no—
193C22×D83—42no—
194C22×D83—44no—
195C22×D83—42no—
196C22×D83—42no—
197C22×D83—42no—
198C22×D83—44no—
199C22×D83—44no—
200C22×D83—44no—
201C22×D83—44no—
202C22×D83—44no—
203C22×D83C2×C4⋊C418yes—
204C2×C4×C83—24no—
205C2×C4×C83—28no—
206C2×C4×C83—24no—
207C2×C4×C83—24no—
208C2×C4×C83—28no—
209C2×C4×C83—24no—
210C2×C4×C83—24no—
211C2×C4×C83—42no—
212C2×C4×C83—42no—
213C2×C4×C83—42no—
214C2×C4×C83—42no—
215C2×C4×C83—42no—
216C2×C4×C83—44no—
217C2×C4×C83—42no—
218C2×C4×C83—42no—
219C2×C4×C83—44no—
220C2×C4×C83—42no—
221C2×C4×C83C2×C4⋊C414yes—
222C2×C4×C83C4×D414yes—
223C2×C4×C83C4×D414yes—
224C2×C4×C83#12014yes—
225C2×C4×C83C22⋊Q814yes—
226C2×C4×C83C22⋊Q814yes—
227C2×C4×C83#12314yes—
228C2×Dic83—22no—
229C2×Dic83—22no—
230C2×Dic83—24no—
231C2×Dic83—24no—
232C2×Dic83—24no—
233C2×Dic83—24no—
234C2×Dic83—24no—
235C2×Dic83—22no—
236C2×Dic83—22no—
237C2×Dic83—22no—
238C2×Dic83—42no—
239C2×Dic83—42no—
240C2×Dic83—42no—
241C2×Dic83—42no—
242C2×Dic83—42no—
243C2×Dic83—42no—
244C2×Dic83—42no—
245C2×Dic83—42no—
246C2×Dic83—42no—
247C2×Dic83—44no—
248C2×Dic83—44no—
249C2×Dic83#12414yes—
250D332—232no—
251C4×D83—432no—
252C22×C83C22×C4⋊C411yescharacteristic
253C22×C83C2×C4×D411yescharacteristic
254C22×C83C2×C4×D411yescharacteristic
255C22×C83C4×#4112yes—
256C22×C83#51812yes—
257C22×C83C2×#12011yescharacteristic
258C22×C83C2×C22⋊Q811yescharacteristic
259C22×C83C2×C22⋊Q811yescharacteristic
260C22×C83C2×#12311yescharacteristic
261C22×C83C2×#12411yescharacteristic
262C22×C83#52912yes—
263C22×C83#53211yescharacteristic
264C22×C83#53511yescharacteristic
265C22×C83#53511yescharacteristic
266C22×C83#54012yes—
267C22×C83#54612yes—
268C22×C83#54612yes—
269C22×C83#54612yes—
270C22×C83#55012yes—
271C22×C83#55312yes—
272C22×C83#55412yes—
273C22×C83#55412yes—
274C22×C83#55512yes—
275C2×D83—216no—
276C2×D83—28no—
277C2×D83—44no—
278C2×D83—44no—
279C2×D83—44no—
280C2×D83—48no—
281C2×D83—48no—
282C2×D83—44no—
283C2×D83—44no—
284C2×D83—48no—
285C2×D83—44no—
286C4×C83—44no—
287C4×C83—44no—
288C4×C83—44no—
289C4×C83#38518yes—
290Dic83—24no—
291Dic83—44no—
292Dic83—42no—
293Dic83—82no—
294#13979—831nomaximal, Sylow
295C2×C83C2×#38511yescharacteristic
296C2×C83C4×#12411yescharacteristic
297C2×C83#232811yescharacteristic
298C2×C83#234912yes—
299C2×C83#236312yes—
300C2×C83#242012yes—
301C2×C83#243111yescharacteristic
302C2×C83#243511yescharacteristic
303C2×C83#245412yes—
304C2×C83#256311yescharacteristic
305C2×C83#256611yescharacteristic
306D83—48no—
307C22×C4×D4—831no—
308C2×#390—831no—
309C2×#390—831no—
310C2×#389—831no—
311C2×#382—831no—
312#1439—834no—
313C4⋊#95D8311yescharacteristic, complemented
314C22⋊#95—834no—
315C4×#95—831no—
316C83#1397911yescharacteristic, complemented, Sylow
317C23×D4—831no—
318C24×C4—832no—
319C2×C4×D4—1664no—
320C2×C4×D4—1664no—
321C2×C4×D4—1664no—
322C22×C4⋊C4—832no—
323C22×C4⋊C4—831no—
324C22×C4⋊C4C2×D8311yescharacteristic
325C22×C4⋊C4C2×D8311yescharacteristic
326C22×C22⋊C4—834no—
327C22×C22⋊C4—834no—
328C22×C22⋊C4—832no—
329C22×C42—831no—
330C22×C42—831no—
331C22×C42C2×D8311yescharacteristic
332#390—838no—
333#390—1664no—
334#389—1664no—
335#382—1664no—
336C2×#95—832no—
337C2×#95—832no—
338C2×#95—832no—
339C2×#95—834no—
340C2×#95C2×D8314yes—
341C25—832no—
342C22×D4—834no—
343C22×D4—834no—
344C22×D4—834no—
345C22×D4—1662no—
346C22×D4—1662no—
347C22×D4—1662no—
348C22×D4—1662no—
349C23×C4—3324no—
350C23×C4—831no—
351C23×C4—831no—
352C23×C4—832no—
353C23×C4—832no—
354C23×C4—1668no—
355C23×C4—1664no—
356C23×C4—1664no—
357C23×C4—1664no—
358C23×C4C22×D8312yes—
359C23×C4C22×D8312yes—
360C23×C4C22×D8312yes—
361C23×C4C22×D8311yescharacteristic
362C4×D4—16632no—
363C2×C4⋊C4—22no—
364C2×C4⋊C4—22no—
365C2×C4⋊C4—22no—
366C2×C4⋊C4—22no—
367C2×C4⋊C4—3324no—
368C2×C4⋊C4—1664no—
369C2×C4⋊C4—1662no—
370C2×C4⋊C4—1662no—
371C2×C4⋊C4—1662no—
372C2×C4⋊C4C4×D8314yescomplemented
373C2×C4⋊C4D33214yes—
374C2×C22⋊C4—3324no—
375C2×C22⋊C4—3324no—
376C2×C22⋊C4—3324no—
377C2×C22⋊C4—8316no—
378C2×C22⋊C4—1668no—
379C2×C22⋊C4—1668no—
380C2×C22⋊C4—1664no—
381C2×C22⋊C4—1664no—
382C2×C22⋊C4—1664no—
383C2×C42—22no—
384C2×C42—22no—
385C2×C42—22no—
386C2×C42—834no—
387C2×C42—834no—
388C2×C42—1662no—
389C2×C42—1662no—
390C2×C42—1662no—
391C2×C42—1662no—
392#95—44no—
393#95—1664no—
394#95—1664no—
395#95—1668no—
396#95—1664no—
397C24—834no—
398C24—834no—
399C24—834no—
400C24—1662no—
401C24—1662no—
402C24—1664no—
403C24—1662no—
404C24—1662no—
405C24—1664no—
406C24—1664no—
407C24—1664no—
408C24C23×D8311yescharacteristic
409C2×D4—8316no—
410C2×D4—1668no—
411C2×D4—1668no—
412C2×D4—1668no—
413C2×D4—1668no—
414C2×D4—1668no—
415C2×D4—1668no—
416C22×C4—22no—
417C22×C4—22no—
418C22×C4—22no—
419C22×C4—22no—
420C22×C4—22no—
421C22×C4—24no—
422C22×C4—22no—
423C22×C4—22no—
424C22×C4—22no—
425C22×C4—22no—
426C22×C4—24no—
427C22×C4—24no—
428C22×C4—22no—
429C22×C4—24no—
430C22×C4—33216no—
431C22×C4—3328no—
432C22×C4—3328no—
433C22×C4—33216no—
434C22×C4—832no—
435C22×C4—834no—
436C22×C4—834no—
437C22×C4—832no—
438C22×C4—16616no—
439C22×C4—1662no—
440C22×C4—1662no—
441C22×C4—1662no—
442C22×C4—1664no—
443C22×C4—1664no—
444C22×C4—1661no—
445C22×C4—1662no—
446C22×C4—1661no—
447C22×C4—1662no—
448C22×C4—1662no—
449C22×C4—1662no—
450C22×C4—1662no—
451C22×C4—1662no—
452C22×C4—1662no—
453C22×C4—1662no—
454C22×C4—1661no—
455C22×C4—1661no—
456C22×C4—1662no—
457C22×C4C2×C4×D8314yes—
458C22×C4C2×C4×D8312yes—
459C22×C4D4×D8312yes—
460C22×C4D4×D8312yes—
461C22×C4C2×D33214yes—
462C22×C4C2×D33212yes—
463C22×C4Q8×D8312yes—
464C22×C4#1305058912yes—
465C22×C4#1305059012yes—
466C22×C4#1305059114yes—
467C4⋊C4—28no—
468C4⋊C4—28no—
469C4⋊C4—3328no—
470C4⋊C4—3324no—
471C22⋊C4—33216no—
472C22⋊C4—33216no—
473C22⋊C4—16616no—
474C42—44no—
475C42—1668no—
476C42—1668no—
477C23—3324no—
478C23—3324no—
479C23—3324no—
480C23—3324no—
481C23—3322no—
482C23—3324no—
483C23—3322no—
484C23—3322no—
485C23—3322no—
486C23—3324no—
487C23—838no—
488C23—1668no—
489C23—1668no—
490C23—1668no—
491C23—1668no—
492C23—1664no—
493C23—1664no—
494C23—1668no—
495C23—1668no—
496C23—1664no—
497C23—1664no—
498C23—1664no—
499C23—1664no—
500C23C22×C4×D8311yescharacteristic
501C23C2×D4×D8311yescharacteristic
502C23C2×D4×D8311yescharacteristic
503C23C22×D33211yescharacteristic
504C23C2×Q8×D8311yescharacteristic
505C23#41×D8312yes—
506C23C2×#1305058911yescharacteristic
507C23C2×#1305059011yescharacteristic
508C23C2×#1305059112yes—
509C23#1458183712yes—
510C23#1458183812yes—
511D4—16632no—
512C2×C4—24no—
513C2×C4—28no—
514C2×C4—24no—
515C2×C4—24no—
516C2×C4—28no—
517C2×C4—24no—
518C2×C4—24no—
519C2×C4—44no—
520C2×C4—42no—
521C2×C4—42no—
522C2×C4—42no—
523C2×C4—42no—
524C2×C4—42no—
525C2×C4—42no—
526C2×C4—42no—
527C2×C4—44no—
528C2×C4—42no—
529C2×C4—33232no—
530C2×C4—3322no—
531C2×C4—3322no—
532C2×C4—3322no—
533C2×C4—3322no—
534C2×C4—3322no—
535C2×C4—3322no—
536C2×C4—3324no—
537C2×C4—3324no—
538C2×C4—3322no—
539C2×C4—3322no—
540C2×C4—3322no—
541C2×C4—834no—
542C2×C4—1664no—
543C2×C4—1664no—
544C2×C4—1664no—
545C2×C4—1662no—
546C2×C4—1662no—
547C2×C4—1662no—
548C2×C4—1664no—
549C2×C4—1664no—
550C2×C4—1662no—
551C2×C4—1662no—
552C2×C4C4⋊C4×D8314yes—
553C2×C4(C22⋊D83)⋊C414yes—
554C2×C4C4×D33214yes—
555C2×C4#1458176214yes—
556C2×C4#1458177014yes—
557C2×C4#1458177214yes—
558C2×C4#1458177414yes—
559C22—3324no—
560C22—3324no—
561C22—3324no—
562C22—3328no—
563C22—3328no—
564C22—3324no—
565C22—3328no—
566C22—3324no—
567C22—3324no—
568C22—16616no—
569C22—1668no—
570C22C2×C4⋊C4×D8311yescharacteristic
571C22C2×(C22⋊D83)⋊C411yescharacteristic
572C22C2×C4×D33211yescharacteristic
573C22C4×#1305059112yes—
574C22#1912817312yes—
575C22C2×#1458176211yescharacteristic
576C22C2×#1458177011yescharacteristic
577C22C2×#1458177211yescharacteristic
578C22C2×#1458177411yescharacteristic
579C22#124×D8311yescharacteristic
580C22#1912823712yes—
581C22#1912825211yescharacteristic
582C22#1912826411yescharacteristic
583C22#1912826911yescharacteristic
584C22#1912830412yes—
585C22#1912834212yes—
586C22#1912834612yes—
587C22#1912834812yes—
588C22#1912837312yes—
589C22#1912839912yes—
590C22#1912840712yes—
591C22#1912841212yes—
592C22#1912841412yes—
593C4—44no—
594C4—44no—
595C4—44no—
596C4—3324no—
597C4—3322no—
598C4—6642no—
599C4—1664no—
600C4#1912757518yes—
601C2—3328no—
602C2C2×#1912757511yescharacteristic
603C2#2491000611yescharacteristic
604C2#2491018711yescharacteristic
605C2#2491037212yes—
606C2#2491050312yes—
607C2#2491095712yes—
608C2#2491108411yescharacteristic
609C2#2491111311yescharacteristic
610C2#2491133312yes—
611C2#2491263511yescharacteristic
612C2#2491266011yescharacteristic
subgroupG/H
center, FrattiniC24C23×D83
commutatorC23×C83C23×C4
FittingC83×C4⋊#95C2
socle, cosocleC24×C83C24
prime radicalC23×D332C22
hypercenterC4⋊#95D83
hypocenterC83#13979
LCSG ▷ C23×C83 ▷ C83
UCSC1 ◁ C24 ◁ C4⋊#95

Complements

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

NH ≅ G/Ntype
4. C2×#19127600C2semidirect
5. C2×#19127566C2semidirect
6. #24905709C2semidirect
7. (C2×D83)⋊#95C2semidirect
8. C4×C83⋊#95C2semidirect
9. C83×C4⋊#95C2semidirect
23. #19127602C4semidirect
65. C2×(C2×D83)⋊C4C2×C4semidirect
70. C2×C4×Dic83C2×C4semidirect
84. C2×C4⋊C4×C83C2×C4semidirect
107. C2×D332C4⋊C4semidirect
313. C4⋊#95D83semidirect
316. C83#13979semidirect
372. C2×C4⋊C4C4×D83semidirect

Maximal subgroups

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

subgroupindex
C22×#145817542
C2×#191276032
C2×#191276022
C2×#191276002
C2×#191275662
#249057092
(C2×D83)⋊#952
C4×C83⋊#952
C83×C4⋊#952
#1397983