Finite Group Databasebeta

← #35303757

Subgroups — #35303757

Order 21248.

428 conjugacy classes of subgroups.

The subgroup lattice has 378 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C8×C4⋊Dic83C211yesmaximal, characteristic, complemented
2#24906211C211yesmaximal, characteristic, complemented
3#24905962C211yesmaximal, characteristic, complemented
4#24905958C211yesmaximal, characteristic
5#24905866C211yesmaximal, characteristic, complemented
6#24905862C211yesmaximal, characteristic
7C83×#3131C211yesmaximal, characteristic
8#19127754C2211yescharacteristic
9#19127754C2211yescharacteristic
10C2×C4⋊(C83⋊C8)C2211yescharacteristic
11C2×C8×Dic83—21no—
12C4×C4⋊Dic83C2211yescharacteristic
13#19127455—21no—
14#19127454—21no—
15#19127452—21no—
16#19127438—22no—
17#19127435—22no—
18Q8⋊(C83⋊C8)—22no—
19D4⋊(C83⋊C8)—22no—
20#533×C83C2211yescharacteristic
21#532×C83C2211yescharacteristic
22#488×C83—21no—
23#488×C83—21no—
24#487×C83C411yescharacteristic, complemented
25#487×C83C411yescharacteristic, complemented
26#486×C83C411yescharacteristic, complemented
27#486×C83C411yescharacteristic, complemented
28#416×C83—21no—
29#416×C83—21no—
30C2×C4×C8×C83C2211yescharacteristic
31C22×C83⋊C8—21no—
32C2×C4⋊Dic83—21no—
33C2×C4×Dic83—21no—
34C4⋊(C83⋊C8)—21no—
35C4⋊(C83⋊C8)—21no—
36C4⋊(C83⋊C8)—21no—
37C4⋊(C83⋊C8)D412yes—
38C22⋊(C83⋊C8)—21no—
39C22⋊(C83⋊C8)—21no—
40C4×C83⋊C8—21no—
41C4×C83⋊C8—21no—
42C8×Dic83—42no—
43C83⋊#95D412yes—
44C2×#41×C83—21no—
45C22×C8×C83D411yescharacteristic
46C22×C8×C83D411yescharacteristic
47C4⋊Q8×C83C2×C411yescharacteristic
48C4⋊Q8×C83C2×C411yescharacteristic
49C4⋊Q8×C83C2×C411yescharacteristic
50#127×C83C2×C411yescharacteristic
51#125×C83—21no—
52#124×C83—21no—
53C22⋊Q8×C83—21no—
54C22⋊Q8×C83—21no—
55#121×C83—21no—
56#121×C83—21no—
57C4×Q8×C83—21no—
58C4×Q8×C83—21no—
59C4×D4×C83—21no—
60C4×D4×C83—21no—
61#117×C83—21no—
62C2×C42×C83C2311yescharacteristic
63#103×C83—21no—
64#103×C83—21no—
65#103×C83—21no—
66#103×C83—21no—
67#102×C83—21no—
68#102×C83—21no—
69#102×C83—21no—
70#102×C83—21no—
71C4×C8×C83C2×C411yescharacteristic
72C4×C8×C83C2×C411yescharacteristic
73C4×C8×C83D411yescharacteristic
74C4×C8×C83D411yescharacteristic
75C22×Dic83—22no—
76C2×C83⋊C8—22no—
77C2×C83⋊C8—41no—
78C2×C83⋊C8—41no—
79C2×C83⋊C8—41no—
80C2×C83⋊C8—41no—
81C4⋊Dic83—24no—
82C4×Dic83—41no—
83C4×Dic83—41no—
84#41×C83—41no—
85#41×C83—41no—
86#41×C83—41no—
87#41×C83—41no—
88C2×Q8×C83—21no—
89C2×Q8×C83—21no—
90C2×Q8×C83—21no—
91C2×D4×C83—21no—
92C2×D4×C83—21no—
93C2×D4×C83—21no—
94C2×D4×C83—41no—
95C22×C4×C83—41no—
96C22×C4×C83C2×D411yescharacteristic
97C22×C4×C83C2×D411yescharacteristic
98C22×C4×C83#4111yescharacteristic
99C2×C8×C83—21no—
100C2×C8×C83—21no—
101C2×C8×C83—21no—
102C2×C8×C83—21no—
103C2×C8×C83C22⋊C411yescharacteristic
104C2×C8×C83C22⋊C411yescharacteristic
105C2×C8×C83C22⋊C411yescharacteristic
106C2×C8×C83C22⋊C411yescharacteristic
107C4⋊C4×C83—21no—
108C4⋊C4×C83—21no—
109C4⋊C4×C83—21no—
110C4⋊C4×C83—21no—
111C4⋊C4×C83—21no—
112C4⋊C4×C83—21no—
113C4⋊C4×C83—41no—
114C4⋊C4×C83—41no—
115C22⋊C4×C83—41no—
116C22⋊C4×C83—41no—
117C22⋊C4×C83—41no—
118C42×C83—41no—
119C42×C83C22×C411yescharacteristic
120C42×C83C2×D411yescharacteristic
121C42×C83C2×D411yescharacteristic
122C42×C83#4111yescharacteristic
123C23×C83—41no—
124C23×C83#12111yescharacteristic
125Q8×C83—41no—
126Q8×C83—41no—
127Q8×C83—42no—
128Q8×C83—81no—
129D4×C83—41no—
130D4×C83—41no—
131D4×C83—42no—
132D4×C83—81no—
133D4×C83—81no—
134D4×C83—81no—
135C2×C4×C83—22no—
136C2×C4×C83—41no—
137C2×C4×C83—41no—
138C2×C4×C83—41no—
139C2×C4×C83—41no—
140C2×C4×C83—81no—
141C2×C4×C83—81no—
142C2×C4×C83C2×C22⋊C411yescharacteristic
143C2×C4×C83C4×D411yescharacteristic
144C2×C4×C83C4×D411yescharacteristic
145C2×C4×C83#12111yescharacteristic
146C2×C4×C83#12411yescharacteristic
147C2×C4×C83#12711yescharacteristic
148C2×C4×C83#13511yescharacteristic
149C2×C4×C83#13511yescharacteristic
150C2×C4×C83AGL(1,ℤ/8)11yescharacteristic
151C2×C4×C83#13711yescharacteristic
152C2×Dic83—24no—
153C2×Dic83—42no—
154C2×Dic83—42no—
155C8×C83—21no—
156C8×C83—21no—
157C8×C83—21no—
158C8×C83—21no—
159C83⋊C8—42no—
160C83⋊C8—81no—
161C83⋊C8—81no—
162C22×C83—21no—
163C22×C83—21no—
164C22×C83—81no—
165C22×C83—81no—
166C22×C83—81no—
167C22×C83#39011yescharacteristic
168C22×C83#46311yescharacteristic
169C22×C83#46411yescharacteristic
170C4×C83—21no—
171C4×C83—21no—
172C4×C83—21no—
173C4×C83—81no—
174C4×C83—81no—
175C4×C83—81no—
176C4×C83#41611yescharacteristic
177C4×C83#41711yescharacteristic
178C4×C83#44312yes—
179C4×C83#46311yescharacteristic
180C4×C83#46411yescharacteristic
181Dic83—44no—
182#9751—831nomaximal, Sylow
183C2×C83—21no—
184C2×C83—21no—
185C2×C83—161no—
186C2×C83#197411yescharacteristic
187C2×C83#197611yescharacteristic
188C2×C83#198311yescharacteristic
189#3131D8311yescharacteristic
190C8×C4⋊C4—831no—
191#1564—831no—
192#1503—831no—
193#1502—831no—
194#1481—831no—
195#1480—831no—
196C83#975111yescharacteristic, complemented, Sylow
197#533C2×D8311yescharacteristic
198#532C2×D8311yescharacteristic
199#488—21no—
200#488—21no—
201#487Dic8311yescharacteristic, complemented
202#487Dic8311yescharacteristic, complemented
203#486Dic8311yescharacteristic, complemented
204#486Dic8311yescharacteristic, complemented
205#431—831no—
206#431—831no—
207C2×C4⋊C8—831no—
208#416—21no—
209#416—21no—
210C2×C4×C8—1661no—
211C2×C4×C8C2×D8311yescharacteristic
212C4×C4⋊C4—831no—
213#336—1661no—
214#335—1661no—
215#334—1661no—
216#328—1662no—
217#327—1662no—
218Q8⋊C8—1662no—
219D4⋊C8—1662no—
220C2×#41—21no—
221C22×C8—1661no—
222C22×C8C22⋊D8311yescharacteristic
223C22×C8C22⋊D8311yescharacteristic
224C4⋊Q8C2×Dic8311yescharacteristic
225C4⋊Q8C2×Dic8311yescharacteristic
226C4⋊Q8C2×Dic8311yescharacteristic
227#127C2×Dic8311yescharacteristic
228#125—21no—
229#124—21no—
230C22⋊Q8—21no—
231C22⋊Q8—21no—
232#121—21no—
233#121—21no—
234C4×Q8—21no—
235C4×Q8—21no—
236C4×D4—21no—
237C4×D4—21no—
238#117—21no—
239C2×C4⋊C4—1661no—
240C2×C42—1661no—
241C2×C42C22×D8311yescharacteristic
242C4⋊C8—832no—
243C4⋊C8—1661no—
244C4⋊C8—1661no—
245C4⋊C8—1661no—
246#103—21no—
247#103—21no—
248#103—21no—
249#103—21no—
250#102—21no—
251#102—21no—
252#102—21no—
253#102—21no—
254C22⋊C8—1661no—
255C22⋊C8—1661no—
256C4×C8—3322no—
257C4×C8—1661no—
258C4×C8—1661no—
259C4×C8C2×Dic8311yescharacteristic
260C4×C8C2×Dic8311yescharacteristic
261C4×C8C22⋊D8311yescharacteristic
262C4×C8C22⋊D8311yescharacteristic
263#95—832no—
264#41—41no—
265#41—41no—
266#41—41no—
267#41—41no—
268C2×Q8—21no—
269C2×Q8—21no—
270C2×Q8—21no—
271C2×D4—21no—
272C2×D4—21no—
273C2×D4—21no—
274C2×D4—41no—
275C22×C4—41no—
276C22×C4—1662no—
277C22×C4D4×D8311yescharacteristic
278C22×C4C2×C22⋊D8311yescharacteristic
279C22×C4#1305058911yescharacteristic
280C2×C8—21no—
281C2×C8—21no—
282C2×C8—21no—
283C2×C8—21no—
284C2×C8—3321no—
285C2×C8—3321no—
286C2×C8—3321no—
287C2×C8—3321no—
288C2×C8—1662no—
289C2×C8C22⋊Dic8311yescharacteristic
290C2×C8C22⋊Dic8311yescharacteristic
291C2×C8C22⋊Dic8311yescharacteristic
292C2×C8C22⋊Dic8311yescharacteristic
293C4⋊C4—21no—
294C4⋊C4—21no—
295C4⋊C4—21no—
296C4⋊C4—21no—
297C4⋊C4—21no—
298C4⋊C4—21no—
299C4⋊C4—41no—
300C4⋊C4—41no—
301C4⋊C4—1664no—
302C22⋊C4—41no—
303C22⋊C4—41no—
304C22⋊C4—41no—
305C42—41no—
306C42—3321no—
307C42—3321no—
308C42C22×Dic8311yescharacteristic
309C42D4×D8311yescharacteristic
310C42C2×C22⋊D8311yescharacteristic
311C42#1305058911yescharacteristic
312C23—41no—
313C23#1458176311yescharacteristic
314Q8—42no—
315Q8—41no—
316Q8—41no—
317Q8—81no—
318D4—42no—
319D4—41no—
320D4—41no—
321D4—81no—
322D4—81no—
323D4—81no—
324C2×C4—22no—
325C2×C4—41no—
326C2×C4—41no—
327C2×C4—41no—
328C2×C4—41no—
329C2×C4—81no—
330C2×C4—81no—
331C2×C4—3322no—
332C2×C4—3322no—
333C2×C4—1664no—
334C2×C4C2×C22⋊Dic8311yescharacteristic
335C2×C4D4×Dic8311yescharacteristic
336C2×C4D4×Dic8311yescharacteristic
337C2×C4#1458176311yescharacteristic
338C2×C4#1458177911yescharacteristic
339C2×C4#1458178811yescharacteristic
340C2×C4#1458181211yescharacteristic
341C2×C4#1458181211yescharacteristic
342C2×C4#1458181711yescharacteristic
343C2×C4#1458182211yescharacteristic
344C8—21no—
345C8—21no—
346C8—21no—
347C8—21no—
348C8—3322no—
349C8—6641no—
350C8—6641no—
351C22—21no—
352C22—21no—
353C22—81no—
354C22—81no—
355C22—81no—
356C22#1912760411yescharacteristic
357C22#1912791311yescharacteristic
358C22#1912792011yescharacteristic
359C4—21no—
360C4—21no—
361C4—21no—
362C4—81no—
363C4—81no—
364C4—81no—
365C4—3324no—
366C4#1912769711yescharacteristic
367C4#1912770211yescharacteristic
368C4#1912781812yes—
369C4#1912791311yescharacteristic
370C4#1912792011yescharacteristic
371C2—21no—
372C2—21no—
373C2—161no—
374C2#2490835211yescharacteristic
375C2#2490836211yescharacteristic
376C2#2490839611yescharacteristic
subgroupG/H
centerC2×C4#14581763
commutatorC42×C83C22×C4
FrattiniC2×C42C22×D83
FittingC83×#3131C2
socleC22×C83#390
prime radical#532×C83C22
cosocleC2×C42×C83C23
hypercenter#3131D83
hypocenterC83#9751
LCSG ▷ C42×C83 ▷ C22×C83 ▷ C83
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #3131

Complements

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

NH ≅ G/Ntype
1. C8×C4⋊Dic83C2semidirect
2. #24906211C2semidirect
3. #24905962C2semidirect
5. #24905866C2semidirect
24. #487×C83C4semidirect
25. #487×C83C4semidirect
26. #486×C83C4semidirect
27. #486×C83C4semidirect
196. C83#9751semidirect
201. #487Dic83semidirect
202. #487Dic83semidirect
203. #486Dic83semidirect
204. #486Dic83semidirect

Maximal subgroups

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

subgroupindex
C8×C4⋊Dic832
#249062112
#249059622
#249059582
#249058662
#249058622
C83×#31312
#975183