Finite Group Databasebeta

← #35300496

Subgroups — #35300496

Order 21248.

532 conjugacy classes of subgroups.

The subgroup lattice has 460 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#41×C83⋊C8C211yesmaximal, characteristic, complemented
2#24907483C211yesmaximal, characteristic, complemented
3#24905958C211yesmaximal, characteristic, complemented
4#24905914C211yesmaximal, characteristic, complemented
5#24905360C211yesmaximal, characteristic, complemented
6#24905302C211yesmaximal, characteristic, complemented
7C83×#3035C211yesmaximal, characteristic
8Q8×C83⋊C8—21no—
9D4×C83⋊C8—22no—
10D4×C83⋊C8—21no—
11#19127754—21no—
12#19127754C2211yescharacteristic
13#19127725C2211yescharacteristic
14C2×#14581719—21no—
15C2×C4×C83⋊C8—21no—
16C2×C4×C83⋊C8C2211yescharacteristic
17C4×C4⋊Dic83C2211yescharacteristic
18#19127460—21no—
19#19127435—22no—
20D4⋊(C83⋊C8)—21no—
21D4⋊(C83⋊C8)—21no—
22C2×#135×C83—21no—
23#532×C83C2211yescharacteristic
24C4×#41×C83C2211yescharacteristic
25#464×C83—21no—
26#463×C83—21no—
27#462×C83C411yescharacteristic, complemented
28#461×C83C411yescharacteristic, complemented
29#460×C83C411yescharacteristic, complemented
30#459×C83C411yescharacteristic, complemented
31C2×C4⋊C8×C83C2211yescharacteristic
32#416×C83—21no—
33C2×#13050574—21no—
34C22×C83⋊C8—22no—
35C22×C83⋊C8—21no—
36C2×C4⋊Dic83—21no—
37C2×C4×Dic83—21no—
38C4⋊(C83⋊C8)—22no—
39C4⋊(C83⋊C8)—21no—
40C4⋊(C83⋊C8)—21no—
41C4⋊(C83⋊C8)—21no—
42#14581719—42no—
43C22⋊(C83⋊C8)—22no—
44C22⋊(C83⋊C8)D412yes—
45C4×C83⋊C8—22no—
46C4×C83⋊C8—21no—
47C4×C83⋊C8—21no—
48C4×C83⋊C8D411yescharacteristic
49C4×C83⋊C8D411yescharacteristic
50C83⋊#95—21no—
51C2×#41×C83—21no—
52C2×#41×C83D411yescharacteristic
53#135×C83—42no—
54#135×C83—42no—
55C2×Q16×C83—21no—
56C2×SD16×C83—21no—
57C2×SD16×C83—21no—
58C2×D8×C83—21no—
59C22×C8×C83—21no—
60C4⋊Q8×C83C2×C411yescharacteristic
61#127×C83C2×C411yescharacteristic
62#124×C83—21no—
63#121×C83—21no—
64#121×C83—21no—
65C4×Q8×C83C2×C411yescharacteristic
66C4×Q8×C83D411yescharacteristic
67C4×D4×C83—21no—
68C4×D4×C83—21no—
69C4×D4×C83—21no—
70C4×D4×C83—21no—
71C4×D4×C83C2×C411yescharacteristic
72C4×D4×C83D411yescharacteristic
73#117×C83—21no—
74#117×C83D411yescharacteristic
75C2×C42×C83—21no—
76C2×C42×C83C2311yescharacteristic
77C4⋊C8×C83—21no—
78C4⋊C8×C83C2×C411yescharacteristic
79C4⋊C8×C83C2×C411yescharacteristic
80#103×C83—21no—
81#103×C83—21no—
82#102×C83—21no—
83#102×C83—21no—
84C22×Dic83—41no—
85#13050574—41no—
86#13050574—41no—
87C2×C83⋊C8—21no—
88C2×C83⋊C8—22no—
89C2×C83⋊C8—21no—
90C2×C83⋊C8—42no—
91C2×C83⋊C8—44no—
92C2×C83⋊C8—41no—
93C4⋊Dic83—22no—
94C4⋊Dic83—41no—
95C4×Dic83—41no—
96C4×Dic83—41no—
97#41×C83—21no—
98#41×C83—21no—
99#41×C83—41no—
100#41×C83—41no—
101#41×C83—41no—
102#41×C83—41no—
103#41×C83D812yes—
104#41×C83SD1612yes—
105C2×Q8×C83—21no—
106C2×Q8×C83C22⋊C411yescharacteristic
107C2×D4×C83—21no—
108C2×D4×C83—21no—
109C2×D4×C83—21no—
110C2×D4×C83—21no—
111C2×D4×C83—41no—
112C2×D4×C83C22⋊C411yescharacteristic
113C22×C4×C83—21no—
114C22×C4×C83—21no—
115C22×C4×C83—21no—
116C22×C4×C83—41no—
117C22×C4×C83C2×D411yescharacteristic
118C22×C4×C83C2×D411yescharacteristic
119C22×C4×C83#4111yescharacteristic
120Q16×C83—42no—
121SD16×C83—42no—
122SD16×C83—42no—
123D8×C83—42no—
124C2×C8×C83—21no—
125C2×C8×C83—21no—
126C2×C8×C83—41no—
127C2×C8×C83—41no—
128C4⋊C4×C83—21no—
129C4⋊C4×C83—21no—
130C4⋊C4×C83—21no—
131C4⋊C4×C83—21no—
132C4⋊C4×C83C22⋊C411yescharacteristic
133C4⋊C4×C83C22⋊C411yescharacteristic
134C22⋊C4×C83—21no—
135C22⋊C4×C83—21no—
136C22⋊C4×C83—21no—
137C22⋊C4×C83—41no—
138C22⋊C4×C83—41no—
139C42×C83—21no—
140C42×C83—21no—
141C42×C83—21no—
142C42×C83C22×C411yescharacteristic
143C42×C83C2×D411yescharacteristic
144C42×C83C2×D411yescharacteristic
145C42×C83#4111yescharacteristic
146C23×C83—21no—
147C23×C83—41no—
148C23×C83#12111yescharacteristic
149Q8×C83—21no—
150Q8×C83—41no—
151Q8×C83—41no—
152Q8×C83#10212yes—
153D4×C83—22no—
154D4×C83—22no—
155D4×C83—21no—
156D4×C83—41no—
157D4×C83—41no—
158D4×C83—41no—
159D4×C83—41no—
160D4×C83—81no—
161D4×C83—81no—
162D4×C83—81no—
163D4×C83#10212yes—
164C2×C4×C83—21no—
165C2×C4×C83—21no—
166C2×C4×C83—21no—
167C2×C4×C83—22no—
168C2×C4×C83—22no—
169C2×C4×C83—21no—
170C2×C4×C83—21no—
171C2×C4×C83—41no—
172C2×C4×C83—42no—
173C2×C4×C83—41no—
174C2×C4×C83—41no—
175C2×C4×C83—41no—
176C2×C4×C83—81no—
177C2×C4×C83—81no—
178C2×C4×C83C2×C22⋊C411yescharacteristic
179C2×C4×C83C4×D411yescharacteristic
180C2×C4×C83C4×D411yescharacteristic
181C2×C4×C83#12011yescharacteristic
182C2×C4×C83#12111yescharacteristic
183C2×C4×C83#12311yescharacteristic
184C2×C4×C83C2×D811yescharacteristic
185C2×C4×C83C2×SD1611yescharacteristic
186C2×C4×C83#13511yescharacteristic
187C2×C4×C83#13511yescharacteristic
188C2×Dic83—42no—
189C2×Dic83—81no—
190C2×Dic83—81no—
191C8×C83—41no—
192C8×C83—41no—
193C83⋊C8—22no—
194C83⋊C8—42no—
195C83⋊C8—41no—
196C83⋊C8—81no—
197C22×C83—21no—
198C22×C83—21no—
199C22×C83—22no—
200C22×C83—41no—
201C22×C83—41no—
202C22×C83—81no—
203C22×C83—81no—
204C22×C83—81no—
205C22×C83#38611yescharacteristic
206C22×C83#46511yescharacteristic
207C22×C83#46611yescharacteristic
208C4×C83—21no—
209C4×C83—22no—
210C4×C83—21no—
211C4×C83—21no—
212C4×C83—41no—
213C4×C83—41no—
214C4×C83—81no—
215C4×C83C2×#10211yescharacteristic
216C4×C83#41611yescharacteristic
217C4×C83#44311yescharacteristic
218C4×C83#44411yescharacteristic
219C4×C83#46511yescharacteristic
220C4×C83#46611yescharacteristic
221Dic83—82no—
222#9208—831nomaximal, Sylow
223C2×C83—21no—
224C2×C83—21no—
225C2×C83—42no—
226C2×C83—161no—
227C2×C83#187611yescharacteristic
228C2×C83#189311yescharacteristic
229C2×C83#190611yescharacteristic
230#3035D8311yescharacteristic
231C8×#41—831no—
232#1806—831no—
233#1502—831no—
234#1492—831no—
235#1301—831no—
236#1279—831no—
237C83#920811yescharacteristic, complemented, Sylow
238C2×#135—21no—
239#532C2×D8311yescharacteristic
240C4×#41C2×D8311yescharacteristic
241#464—21no—
242#463—21no—
243#462Dic8311yescharacteristic, complemented
244#461Dic8311yescharacteristic, complemented
245#460Dic8311yescharacteristic, complemented
246#459Dic8311yescharacteristic, complemented
247C8×Q8—1661no—
248C8×D4—1662no—
249C8×D4—1661no—
250#431—831no—
251#431—1661no—
252#423—831no—
253C2×C4⋊C8C2×D8311yescharacteristic
254C2×#104—1661no—
255#416—21no—
256C2×C4×C8—831no—
257C2×C4×C8—1661no—
258C4×C4⋊C4—831no—
259#339—1661no—
260#327—1662no—
261D4⋊C8—1661no—
262D4⋊C8—1661no—
263C2×#41—21no—
264C2×#41C22⋊D8311yescharacteristic
265#135—42no—
266#135—42no—
267C2×Q16—21no—
268C2×SD16—21no—
269C2×SD16—21no—
270C2×D8—21no—
271C2×M16—1661no—
272C22×C8—21no—
273C22×C8—1662no—
274C22×C8—1661no—
275C4⋊Q8C2×Dic8311yescharacteristic
276#127C2×Dic8311yescharacteristic
277#124—21no—
278#121—21no—
279#121—21no—
280C4×Q8C2×Dic8311yescharacteristic
281C4×Q8C22⋊D8311yescharacteristic
282C4×D4—21no—
283C4×D4—21no—
284C4×D4—21no—
285C4×D4—21no—
286C4×D4C2×Dic8311yescharacteristic
287C4×D4C22⋊D8311yescharacteristic
288#117—21no—
289#117C22⋊D8311yescharacteristic
290C2×C4⋊C4—1661no—
291C2×C42—21no—
292C2×C42—1661no—
293C2×C42C22×D8311yescharacteristic
294C4⋊C8—21no—
295C4⋊C8—1662no—
296C4⋊C8—1661no—
297C4⋊C8—1661no—
298C4⋊C8—1661no—
299C4⋊C8C2×Dic8311yescharacteristic
300C4⋊C8C2×Dic8311yescharacteristic
301#104—3322no—
302#103—21no—
303#103—21no—
304#102—21no—
305#102—21no—
306C22⋊C8—832no—
307C22⋊C8—1662no—
308C4×C8—831no—
309C4×C8—831no—
310C4×C8—1662no—
311C4×C8—1661no—
312C4×C8—1661no—
313#95—1661no—
314#41—21no—
315#41—21no—
316#41—41no—
317#41—41no—
318#41—41no—
319#41—41no—
320#41#1305057512yes—
321#41#1305057812yes—
322C2×Q8—21no—
323C2×Q8C22⋊Dic8311yescharacteristic
324C2×D4—21no—
325C2×D4—21no—
326C2×D4—21no—
327C2×D4—21no—
328C2×D4—41no—
329C2×D4C22⋊Dic8311yescharacteristic
330C22×C4—21no—
331C22×C4—21no—
332C22×C4—21no—
333C22×C4—41no—
334C22×C4—3321no—
335C22×C4D4×D8311yescharacteristic
336C22×C4C2×C22⋊D8311yescharacteristic
337C22×C4#1305058911yescharacteristic
338Q16—42no—
339SD16—42no—
340SD16—42no—
341D8—42no—
342M16—3321no—
343M16—3321no—
344C2×C8—21no—
345C2×C8—21no—
346C2×C8—41no—
347C2×C8—41no—
348C2×C8—3322no—
349C2×C8—3324no—
350C2×C8—3321no—
351C2×C8—1661no—
352C2×C8—1662no—
353C2×C8—1661no—
354C4⋊C4—21no—
355C4⋊C4—21no—
356C4⋊C4—21no—
357C4⋊C4—21no—
358C4⋊C4—3321no—
359C4⋊C4—1662no—
360C4⋊C4C22⋊Dic8311yescharacteristic
361C4⋊C4C22⋊Dic8311yescharacteristic
362C22⋊C4—21no—
363C22⋊C4—21no—
364C22⋊C4—21no—
365C22⋊C4—41no—
366C22⋊C4—41no—
367C42—21no—
368C42—21no—
369C42—21no—
370C42—3321no—
371C42—3321no—
372C42C22×Dic8311yescharacteristic
373C42D4×D8311yescharacteristic
374C42C2×C22⋊D8311yescharacteristic
375C42#1305058911yescharacteristic
376C23—21no—
377C23—41no—
378C23#1458176411yescharacteristic
379Q8—21no—
380Q8—41no—
381Q8—41no—
382Q8#1458171312yes—
383D4—22no—
384D4—22no—
385D4—21no—
386D4—41no—
387D4—41no—
388D4—41no—
389D4—41no—
390D4—81no—
391D4—81no—
392D4—81no—
393D4#1458171312yes—
394C2×C4—21no—
395C2×C4—21no—
396C2×C4—21no—
397C2×C4—22no—
398C2×C4—22no—
399C2×C4—21no—
400C2×C4—21no—
401C2×C4—41no—
402C2×C4—42no—
403C2×C4—41no—
404C2×C4—41no—
405C2×C4—41no—
406C2×C4—81no—
407C2×C4—81no—
408C2×C4—3322no—
409C2×C4—6641no—
410C2×C4—6641no—
411C2×C4C2×C22⋊Dic8311yescharacteristic
412C2×C4D4×Dic8311yescharacteristic
413C2×C4D4×Dic8311yescharacteristic
414C2×C4#1458176011yescharacteristic
415C2×C4#1458176411yescharacteristic
416C2×C4#1458177311yescharacteristic
417C2×C4C2×#1305057511yescharacteristic
418C2×C4C2×#1305057811yescharacteristic
419C2×C4#1458181211yescharacteristic
420C2×C4#1458181211yescharacteristic
421C8—41no—
422C8—41no—
423C8—3321no—
424C8—3322no—
425C8—6641no—
426C8—1662no—
427C22—21no—
428C22—21no—
429C22—22no—
430C22—41no—
431C22—41no—
432C22—81no—
433C22—81no—
434C22—81no—
435C22#1912758111yescharacteristic
436C22#1912792811yescharacteristic
437C22#1912793511yescharacteristic
438C4—21no—
439C4—22no—
440C4—21no—
441C4—21no—
442C4—41no—
443C4—41no—
444C4—81no—
445C4—6642no—
446C4C2×#1458171311yescharacteristic
447C4#1912769711yescharacteristic
448C4#1912781811yescharacteristic
449C4#1912782311yescharacteristic
450C4#1912792811yescharacteristic
451C4#1912793511yescharacteristic
452C2—21no—
453C2—21no—
454C2—42no—
455C2—161no—
456C2#2490779211yescharacteristic
457C2#2490789211yescharacteristic
458C2#2490796611yescharacteristic
subgroupG/H
centerC2×C4#14581764
commutatorC42×C83C22×C4
FrattiniC2×C42C22×D83
Fitting, prime radicalC83×#3035C2
socleC22×C83#386
cosocleC2×C42×C83C23
hypercenter#3035D83
hypocenterC83#9208
LCSG ▷ C42×C83 ▷ C22×C83 ▷ C83
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #3035

Complements

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

NH ≅ G/Ntype
1. #41×C83⋊C8C2semidirect
2. #24907483C2semidirect
3. #24905958C2semidirect
4. #24905914C2semidirect
5. #24905360C2semidirect
6. #24905302C2semidirect
27. #462×C83C4semidirect
28. #461×C83C4semidirect
29. #460×C83C4semidirect
30. #459×C83C4semidirect
237. C83#9208semidirect
243. #462Dic83semidirect
244. #461Dic83semidirect
245. #460Dic83semidirect
246. #459Dic83semidirect

Maximal subgroups

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

subgroupindex
#41×C83⋊C82
#249074832
#249059582
#249059142
#249053602
#249053022
C83×#30352
#920883