Finite Group Databasebeta

← #35315913

Subgroups — #35315913

Order 21248.

308 conjugacy classes of subgroups; only the 85 normal subgroups are shown.

normal subgroups only

This group has 308 conjugacy classes of subgroups — too many to draw. Only its 85 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#24918047C211yesmaximal, characteristic
2#24909217C211yesmaximal, characteristic
3#24906220C211yesmaximal, characteristic
4#24905519C211yesmaximal, characteristic, complemented
5#24905517C211yesmaximal, characteristic, complemented
6#24905512C211yesmaximal, characteristic, complemented
7C83×#1362C211yesmaximal, characteristic, complemented
8#19128256—21no—
9C2×#14581731—21no—
10#19128106C2211yescharacteristic
11#19128051—21no—
12#19127939—21no—
13#19127939C412yes—
14Q16×Dic83—21no—
15Q16×Dic83C412yes—
16#19127723—21no—
17C4×C8×D83C2211yescharacteristic
18C4⋊(C83⋊C16)C2211yescharacteristic
19Dic83⋊C16—21no—
20#19127454C2211yescharacteristic
21#19127453—21no—
22#494×C83C2211yescharacteristic
23C4⋊C16×C83C2211yescharacteristic
24#335×C83C2211yescharacteristic
25C2×#13050573—41no—
26C2×C8×D83C2×C411yescharacteristic
27C2×C8×D83D411yescharacteristic
28#14581792—21no—
29#14581783—41no—
30#14581772—41no—
31#14581768—22no—
32Q8×Dic83—22no—
33#14581757—41no—
34#14581750—41no—
35C42×D83D411yescharacteristic
36#14581731—42no—
37C2×C83⋊C16—21no—
38#14581726—21no—
39#14581726C2×C412yes—
40C4⋊(C83⋊C8)—21no—
41Dic83⋊C8—41no—
42#14581716—22no—
43#14581716—22no—
44C4×C83⋊C8D411yescharacteristic
45C8×Dic83C2×C411yescharacteristic
46C8×Dic83D411yescharacteristic
47C2×Q16×C83—21no—
48C2×Q16×C83C2×C412yes—
49C4⋊Q8×C83—21no—
50C2×C16×C83—21no—
51C4⋊C8×C83—21no—
52C4×C8×C83C2311yescharacteristic
53C2×Dic166—41no—
54C2×C4×D83C22⋊C411yescharacteristic
55C2×C4×D83D811yescharacteristic
56C2×C4×D83SD1611yescharacteristic
57#13050573—82no—
58C2×C83⋊C8—41no—
59C2×C83⋊C8C22⋊C411yescharacteristic
60C2×C83⋊C8C22⋊C411yescharacteristic
61C8×D83—21no—
62C8×D83—21no—
63C8×D83—41no—
64C4⋊Dic83—22no—
65C4⋊Dic83—41no—
66C4⋊Dic83—42no—
67Dic83⋊C4—42no—
68(C2×D83)⋊C4—42no—
69C4×Dic83—42no—
70C4×Dic83C22⋊C411yescharacteristic
71C4×Dic83D811yescharacteristic
72C4×Dic83SD1611yescharacteristic
73C83⋊C16—41no—
74C2×Q8×C83—22no—
75Q16×C83—42no—
76Q16×C83—41no—
77Q16×C83—41no—
78C2×C8×C83—41no—
79C2×C8×C83C22×C411yescharacteristic
80C2×C8×C83C2×D411yescharacteristic
81C4⋊C4×C83—41no—
82C4⋊C4×C83—41no—
83C42×C83C2×D411yescharacteristic
84C16×C83—41no—
85C22×D83#10211yescharacteristic
86Q8×C83—42no—
87Q8×C83—42no—
88C2×C4×C83—42no—
89C2×C4×C83C2×C22⋊C411yescharacteristic
90C2×C4×C83C2×D811yescharacteristic
91C2×C4×C83C2×SD1611yescharacteristic
92C2×Dic83—42no—
93C2×Dic83#10211yescharacteristic
94C2×Dic83#10211yescharacteristic
95C2×Dic83#10211yescharacteristic
96C4×D83—21no—
97C4×D83—21no—
98C4×D83—21no—
99C4×D83—21no—
100C4×D83—22no—
101Dic166—81no—
102Dic166—81no—
103C8×C83—21no—
104C8×C83—81no—
105C8×C83AGL(1,ℤ/8)11yescharacteristic
106C8×C83#13711yescharacteristic
107C83⋊C8—21no—
108C83⋊C8—21no—
109C83⋊C8—81no—
110C22×C83C2×#10211yescharacteristic
111C2×D83—21no—
112C2×D83—21no—
113C2×D83—21no—
114C4×C83—21no—
115C4×C83—82no—
116C4×C83#41311yescharacteristic
117C4×C83#41711yescharacteristic
118C4×C83#50911yescharacteristic
119C4×C83#51011yescharacteristic
120Dic83—21no—
121Dic83—21no—
122Dic83—82no—
123Dic83#36212yes—
124#11988—831nomaximal, Sylow
125C2×C83#154711yescharacteristic
126C2×C83#213911yescharacteristic
127C2×C83C2×#36211yescharacteristic
128D83—41no—
129#3170—831no—
130#2150—831no—
131#1567—831no—
132#1364—831no—
133#1364—831no—
134#1362—831no—
135#1362D8311yescharacteristic, complemented
136C83#1198811yescharacteristic, complemented, Sylow
137#533—1661no—
138C2×M32—1661no—
139#500—831no—
140#494C2×D8311yescharacteristic
141#487—1661no—
142#467—832no—
143#467—1661no—
144C4×Q16—832no—
145C4×Q16—1661no—
146#423—1661no—
147C2×C4×C8—831no—
148C4⋊C16—831no—
149C4⋊C16—1661no—
150C4⋊C16C2×D8311yescharacteristic
151#335—831no—
152#335—1661no—
153#335C2×D8311yescharacteristic
154C2×Q16—21no—
155C2×Q16C4×D8312yes—
156C2×M16—3321no—
157C22×C8—831no—
158C22×C8—831no—
159C4⋊Q8—21no—
160C4⋊Q8—1661no—
161#125—3321no—
162C22⋊Q8—3321no—
163C22⋊Q8—1662no—
164C4×Q8—3321no—
165C4×Q8—1662no—
166#117—3321no—
167C2×C42—831no—
168M32—3322no—
169C2×C16—21no—
170C2×C16—1661no—
171#107—832no—
172#107—1661no—
173C4⋊C8—21no—
174C4⋊C8—3321no—
175C4⋊C8—1661no—
176#103—1662no—
177#103—1662no—
178C4×C8—831no—
179C4×C8—831no—
180C4×C8—831no—
181C4×C8C22×D8311yescharacteristic
182C2×Q8—22no—
183C2×Q8—3321no—
184C22×C4—831no—
185C22×C4—831no—
186C22×C4—831no—
187Q16—42no—
188Q16—41no—
189Q16—41no—
190M16—6642no—
191C2×C8—41no—
192C2×C8—3321no—
193C2×C8—3321no—
194C2×C8—831no—
195C2×C8—831no—
196C2×C8—1661no—
197C2×C8—1661no—
198C2×C8C2×C4×D8311yescharacteristic
199C2×C8D4×D8311yescharacteristic
200C4⋊C4—41no—
201C4⋊C4—41no—
202C4⋊C4—3322no—
203C4⋊C4—3322no—
204C4⋊C4—3321no—
205C4⋊C4—1662no—
206C22⋊C4—3322no—
207C42—3322no—
208C42—831no—
209C42—831no—
210C42—831no—
211C42D4×D8311yescharacteristic
212C16—41no—
213C16—3321no—
214C23—831no—
215Q8—42no—
216Q8—42no—
217Q8—6641no—
218Q8—6641no—
219C2×C4—42no—
220C2×C4—3322no—
221C2×C4—831no—
222C2×C4—831no—
223C2×C4—831no—
224C2×C4—1662no—
225C2×C4—1661no—
226C2×C4—1661no—
227C2×C4—1661no—
228C2×C4—1661no—
229C2×C4C22⋊C4×D8311yescharacteristic
230C2×C4D8×D8311yescharacteristic
231C2×C4SD16×D8311yescharacteristic
232C8—21no—
233C8—81no—
234C8—6641no—
235C8—1661no—
236C8—1661no—
237C8#1458181611yescharacteristic
238C8#1458182111yescharacteristic
239C22—1661no—
240C22—1661no—
241C22—1661no—
242C22#102×D8311yescharacteristic
243C4—21no—
244C4—82no—
245C4—832no—
246C4—6642no—
247C4—1661no—
248C4—1661no—
249C4#1912768211yescharacteristic
250C4#1912769911yescharacteristic
251C4#1912813811yescharacteristic
252C4#1912814311yescharacteristic
253C2—3321no—
254C2#2490613711yescharacteristic
255C2#2490917411yescharacteristic
256C2#362×D8311yescharacteristic
subgroupG/H
centerC22#102×D83
commutatorC2×C8×C83C22×C4
FrattiniC4×C8C22×D83
FittingC83×#1362C2
socleC22×C83C2×#102
prime radicalC22×D83#102
cosocleC4×C8×C83C23
hypercenter#1362D83
hypocenterC83#11988
LCSG ▷ C2×C8×C83 ▷ C2×C4×C83 ▷ C2×C83 ▷ C83
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8 ◁ #1362

Complements

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

NH ≅ G/Ntype
4. #24905519C2semidirect
5. #24905517C2semidirect
6. #24905512C2semidirect
7. C83×#1362C2semidirect
135. #1362D83semidirect
136. C83#11988semidirect

Maximal subgroups

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

subgroupindex
#249180472
#249092172
#249062202
#249055192
#249055172
#249055122
C83×#13622
#1198883