Finite Group Databasebeta

← #35316331

Subgroups — #35316331

Order 21248.

226 conjugacy classes of subgroups; only the 75 normal subgroups are shown.

normal subgroups only

This group has 226 conjugacy classes of subgroups — too many to draw. Only its 75 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
1C4×#14581736C211yesmaximal, characteristic
2#24906359C211yesmaximal, characteristic, complemented
3D8×C83⋊C8C211yesmaximal, characteristic
4#24905534C211yesmaximal, characteristic, complemented
5#24905428C211yesmaximal, characteristic, complemented
6#24905382C211yesmaximal, characteristic, complemented
7C83×#1331C211yesmaximal, characteristic
8C2×#14581736C411yescharacteristic
9#19127828—21no—
10C4×Dic332C2211yescharacteristic
11D4×C83⋊C8—21no—
12#19127528C411yescharacteristic
13#19127504C411yescharacteristic
14#19127502C411yescharacteristic
15C4×C83⋊C16C2211yescharacteristic
16#19127454C2211yescharacteristic
17#19127431—21no—
18D4⋊(C83⋊C8)—21no—
19C8×C83⋊C8C2211yescharacteristic
20C4×D8×C83C2211yescharacteristic
21C4×C16×C83C2211yescharacteristic
22#335×C83C2211yescharacteristic
23C2×Dic332C2×C411yescharacteristic
24C22×C83⋊C8—41no—
25C4×Dic166—21no—
26#14581736—22no—
27C2×C83⋊C16C2×C411yescharacteristic
28C2×C83⋊C16C2×C411yescharacteristic
29#14581726C2×C411yescharacteristic
30C4⋊(C83⋊C8)—21no—
31Dic83⋊C8—41no—
32#14581717—21no—
33C22⋊(C83⋊C8)—41no—
34#14581702—41no—
35C4×C83⋊C8D411yescharacteristic
36C4×C83⋊C8D411yescharacteristic
37C2×D8×C83C2×C411yescharacteristic
38C4×D4×C83—21no—
39C2×C16×C83—21no—
40#107×C83C2×C411yescharacteristic
41C4⋊C8×C83—21no—
42#102×C83—21no—
43C4×C8×C83C2311yescharacteristic
44C2×Dic166—21no—
45Dic332—21no—
46Dic332—21no—
47C2×C83⋊C8—21no—
48C2×C83⋊C8—41no—
49C2×C83⋊C8—82no—
50C2×C83⋊C8D811yescharacteristic
51C2×C83⋊C8D811yescharacteristic
52C4⋊Dic83—21no—
53Dic83⋊C4—41no—
54C4×Dic83—41no—
55C83⋊C16—21no—
56C83⋊C16—21no—
57C2×D4×C83—21no—
58C22×C4×C83—41no—
59D8×C83—21no—
60D8×C83M1612yes—
61C2×C8×C83—41no—
62C2×C8×C83C22×C411yescharacteristic
63C2×C8×C83#4111yescharacteristic
64C4⋊C4×C83—21no—
65C22⋊C4×C83—41no—
66C42×C83C2×D411yescharacteristic
67C16×C83—41no—
68C23×C83—41no—
69D4×C83—22no—
70D4×C83—41no—
71C2×C4×C83—41no—
72C2×C4×C83—81no—
73C2×C4×C83—81no—
74C2×C4×C83C4×D411yescharacteristic
75C2×C4×C83C2×D811yescharacteristic
76C2×C4×C83#13511yescharacteristic
77C2×Dic83—41no—
78C2×Dic83—41no—
79Dic166—41no—
80Dic166—41no—
81C8×C83—21no—
82C8×C83—81no—
83C8×C83C2×M1611yescharacteristic
84C8×C83#13111yescharacteristic
85C83⋊C8—22no—
86C83⋊C8—21no—
87C83⋊C8—21no—
88C83⋊C8—81no—
89C22×C83—42no—
90C22×C83—81no—
91C22×C83—81no—
92C22×C83C4×D811yescharacteristic
93C4×C83—21no—
94C4×C83—81no—
95C4×C83#43511yescharacteristic
96C4×C83#44411yescharacteristic
97C4×C83#50911yescharacteristic
98C4×C83#51011yescharacteristic
99Dic83—81no—
100Dic83—81no—
101#12074—831nomaximal, Sylow
102C2×C83—82no—
103C2×C83#158111yescharacteristic
104C2×C83#217511yescharacteristic
105C2×C83#217811yescharacteristic
106C4×SD32—831no—
107#1591—831no—
108C8×D8—831no—
109#1371—831no—
110#1332—831no—
111#1331D8311yescharacteristic
112#1312—831no—
113C83#1207411yescharacteristic, complemented, Sylow
114C2×SD32—831no—
115#446—1661no—
116C4×Q16—831no—
117C4×D8C2×D8311yescharacteristic
118C8×D4—1661no—
119#367—831no—
120#358—831no—
121#357—831no—
122C4×C16—831no—
123C4×C16C2×D8311yescharacteristic
124#335—831no—
125#335C2×D8311yescharacteristic
126Q8⋊C8—1661no—
127D4⋊C8—1661no—
128C82—831no—
129C2×Q16—831no—
130C2×D8C4×D8311yescharacteristic
131C22×C8—3321no—
132C4×Q8—1661no—
133C4×D4—21no—
134SD32—1662no—
135C2×C16—21no—
136C2×C16—831no—
137C2×C16—831no—
138#107—831no—
139#107C4×D8311yescharacteristic
140C4⋊C8—21no—
141C4⋊C8—3321no—
142C4⋊C8—1661no—
143#103—1661no—
144#102—21no—
145C22⋊C8—3321no—
146#97—3321no—
147C4×C8—831no—
148C4×C8—831no—
149C4×C8C22×D8311yescharacteristic
150C2×Q8—1661no—
151C2×D4—21no—
152C22×C4—41no—
153Q16—1661no—
154Q16—1661no—
155D8—21no—
156D8#1305057312yes—
157C2×C8—41no—
158C2×C8—3321no—
159C2×C8—831no—
160C2×C8—831no—
161C2×C8—6642no—
162C2×C8—1661no—
163C2×C8C2×C4×D8311yescharacteristic
164C2×C8#1305058911yescharacteristic
165C4⋊C4—21no—
166C4⋊C4—3321no—
167C4⋊C4—1661no—
168C22⋊C4—41no—
169C42—3321no—
170C42D4×D8311yescharacteristic
171C16—41no—
172C16—1661no—
173C16—1661no—
174C23—41no—
175Q8—3321no—
176Q8—3321no—
177D4—22no—
178D4—41no—
179C2×C4—41no—
180C2×C4—81no—
181C2×C4—81no—
182C2×C4—3321no—
183C2×C4—3321no—
184C2×C4(C22⋊D83)⋊C411yescharacteristic
185C2×C4D8×D8311yescharacteristic
186C2×C4#1458181311yescharacteristic
187C8—21no—
188C8—81no—
189C8—6641no—
190C8—1662no—
191C8—1661no—
192C8—1661no—
193C8C2×#1305057311yescharacteristic
194C8#1458180011yescharacteristic
195C22—42no—
196C22—81no—
197C22—81no—
198C22#1912778111yescharacteristic
199C4—21no—
200C4—81no—
201C4—6641no—
202C4—6641no—
203C4#1912776911yescharacteristic
204C4#1912782011yescharacteristic
205C4#1912813511yescharacteristic
206C4#1912814011yescharacteristic
207C2—82no—
208C2#2490628911yescharacteristic
209C2#2490932411yescharacteristic
210C2#2490934111yescharacteristic
subgroupG/H
centerC2×C4D8×D83
commutatorC2×C8×C83C22×C4
FrattiniC4×C8C22×D83
FittingC83×#1331C2
socleC22×C83C4×D8
prime radicalC2×D8×C83C2×C4
cosocleC4×C8×C83C23
hypercenter#1331D83
hypocenterC83#12074
LCSG ▷ C2×C8×C83 ▷ C4×C83 ▷ C2×C83 ▷ C83
UCSC1 ◁ C2×C4 ◁ C42 ◁ C4×C8 ◁ #1331

Complements

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

NH ≅ G/Ntype
2. #24906359C2semidirect
4. #24905534C2semidirect
5. #24905428C2semidirect
6. #24905382C2semidirect
113. C83#12074semidirect

Maximal subgroups

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

subgroupindex
C4×#145817362
#249063592
D8×C83⋊C82
#249055342
#249054282
#249053822
C83×#13312
#1207483