Finite Group Databasebeta

← #35319064

Subgroups — #35319064

Order 21248.

284 conjugacy classes of subgroups; only the 87 normal subgroups are shown.

normal subgroups only

This group has 284 conjugacy classes of subgroups — too many to draw. Only its 87 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#24909745C211yesmaximal, characteristic, complemented
2#24909690C211yesmaximal, characteristic, complemented
3#24909686C211yesmaximal, characteristic
4#24907057C211yesmaximal, characteristic, complemented
5#24907052C211yesmaximal, characteristic
6C16×C83⋊C8C211yesmaximal, characteristic, complemented
7C83×#2248C211yesmaximal, characteristic
8#19128106C2211yescharacteristic
9#19128106C2211yescharacteristic
10#19128097—21no—
11#19128073—21no—
12#19128053—21no—
13#19128047—21no—
14#19127529—22no—
15#19127505—22no—
16#19127502—22no—
17C4×C83⋊C16C2211yescharacteristic
18C8×C83⋊C8C2211yescharacteristic
19C2×SD32×C83—22no—
20#494×C83C2211yescharacteristic
21#493×C83C2211yescharacteristic
22C4×C16×C83C2211yescharacteristic
23C2×#13050578—42no—
24#14581792—21no—
25#14581792—21no—
26C2×C83⋊C16D412yes—
27#14581726—21no—
28#14581726—21no—
29#14581726—21no—
30#14581726—21no—
31#14581723—42no—
32#14581715—42no—
33#14581713—42no—
34C4×C83⋊C8D411yescharacteristic
35C4×C83⋊C8D411yescharacteristic
36C2×Q16×C83—21no—
37C2×Q16×C83—21no—
38C2×D8×C83—21no—
39C2×D8×C83—21no—
40C4⋊Q8×C83—21no—
41#127×C83—21no—
42SD32×C83—44no—
43C2×C16×C83D412yes—
44C4×C8×C83C2311yescharacteristic
45C2×Dic166—41no—
46C2×Dic166—41no—
47#13050578—84no—
48C2×C83⋊C8D812yes—
49C2×C83⋊C8D812yes—
50C4⋊Dic83—41no—
51C4⋊Dic83—41no—
52C4⋊Dic83—41no—
53C4⋊Dic83—41no—
54C83⋊C16—22no—
55C2×Q8×C83—41no—
56C2×D4×C83—41no—
57C2×D4×C83—41no—
58C2×D4×C83—41no—
59Q16×C83—42no—
60Q16×C83—42no—
61D8×C83—42no—
62D8×C83—42no—
63C2×C8×C83C2×D411yescharacteristic
64C2×C8×C83C2×D411yescharacteristic
65C4⋊C4×C83—41no—
66C4⋊C4×C83—41no—
67C42×C83C2×D411yescharacteristic
68C16×C83SD1614yescomplemented
69C23×C83—81no—
70Q8×C83—81no—
71Q8×C83—81no—
72D4×C83—81no—
73D4×C83—81no—
74D4×C83—82no—
75D4×C83—82no—
76C2×C4×C83—81no—
77C2×C4×C83#12711yescharacteristic
78C2×C4×C83C2×D811yescharacteristic
79C2×C4×C83C2×D811yescharacteristic
80C2×Dic83—81no—
81C2×Dic83—81no—
82Dic166—82no—
83Dic166—82no—
84C8×C83C2×SD1612yes—
85C8×C83#13512yes—
86C83⋊C8—22no—
87C83⋊C8SD3214yescomplemented
88C22×C83—161no—
89C22×C83—161no—
90C22×C83—161no—
91C22×C83#49311yescharacteristic
92C4×C83—161no—
93C4×C83#49211yescharacteristic
94C4×C83#49511yescharacteristic
95C4×C83C2×SD3212yes—
96C4×C83#50812yes—
97Dic83—161no—
98Dic83—161no—
99#12505—831nomaximal, Sylow
100C2×C83—321no—
101C2×C83#170611yescharacteristic
102C2×C83#224811yescharacteristic
103C2×C83#224911yescharacteristic
104#2254—831no—
105#2248D8311yescharacteristic
106#2241—831no—
107#2240—831no—
108#1707—831no—
109#1706—831no—
110C8×C16—831no—
111C83#1250511yescharacteristic, complemented, Sylow
112C2×SD32—22no—
113#500—831no—
114#500—831no—
115#498—1661no—
116#494C2×D8311yescharacteristic
117#493C2×D8311yescharacteristic
118#492—1661no—
119#487—1661no—
120#486—1661no—
121#367—1662no—
122#358—1662no—
123#357—1662no—
124C4×C16—831no—
125C4×C16C2×D8311yescharacteristic
126C82—831no—
127C2×Q16—21no—
128C2×Q16—21no—
129C2×SD16—3322no—
130C2×D8—21no—
131C2×D8—21no—
132C4⋊Q8—21no—
133C4⋊Q8—1661no—
134C4⋊Q8—1661no—
135#127—21no—
136SD32—44no—
137C2×C16—832no—
138C2×C16C22⋊D8312yes—
139#107—1661no—
140#107—1661no—
141#107—1661no—
142#107—1661no—
143#106—3322no—
144#103—3322no—
145#102—3322no—
146C4×C8—831no—
147C4×C8—831no—
148C4×C8C22×D8311yescharacteristic
149C2×Q8—41no—
150C2×Q8—3321no—
151C2×Q8—3321no—
152C2×D4—41no—
153C2×D4—41no—
154C2×D4—41no—
155Q16—42no—
156Q16—42no—
157SD16—6644no—
158D8—42no—
159D8—42no—
160C2×C8—832no—
161C2×C8—832no—
162C2×C8D4×D8311yescharacteristic
163C2×C8C2×C22⋊D8311yescharacteristic
164C4⋊C4—41no—
165C4⋊C4—41no—
166C4⋊C4—3321no—
167C4⋊C4—3321no—
168C4⋊C4—3321no—
169C4⋊C4—3321no—
170C42D4×D8311yescharacteristic
171C16—1662no—
172C16#1305057814yescomplemented
173C23—81no—
174Q8—81no—
175Q8—81no—
176Q8—6642no—
177Q8—6642no—
178D4—81no—
179D4—81no—
180D4—82no—
181D4—82no—
182C2×C4—81no—
183C2×C4—6641no—
184C2×C4—6641no—
185C2×C4#1458178811yescharacteristic
186C2×C4D8×D8311yescharacteristic
187C2×C4D8×D8311yescharacteristic
188C8—834no—
189C8—1662no—
190C8C2×#1305057812yes—
191C8#1458181112yes—
192C22—161no—
193C22—161no—
194C22—161no—
195C22#1912807611yescharacteristic
196C4—161no—
197C4—13281no—
198C4—13281no—
199C4#1912807311yescharacteristic
200C4#1912808411yescharacteristic
201C4SD32×D8312yes—
202C4#1912813212yes—
203C2—321no—
204C2#2490705211yescharacteristic
205C2#2490971711yescharacteristic
206C2#2490972311yescharacteristic
subgroupG/H
centerC22#19128076
commutator, cosocleC4×C8×C83C23
FrattiniC4×C8C22×D83
FittingC83×#2248C2
socleC22×C83#493
prime radical#493×C83C22
hypercenter#2248D83
hypocenterC83#12505
LCSG ▷ C4×C8×C83 ▷ C2×C4×C83 ▷ C2×C83 ▷ C83
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8 ◁ #2248

Complements

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

NH ≅ G/Ntype
1. #24909745C2semidirect
2. #24909690C2semidirect
4. #24907057C2semidirect
6. C16×C83⋊C8C2semidirect
68. C16×C83SD16semidirect
87. C83⋊C8SD32semidirect
111. C83#12505semidirect
172. C16#13050578semidirect

Maximal subgroups

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

subgroupindex
#249097452
#249096902
#249096862
#249070572
#249070522
C16×C83⋊C82
C83×#22482
#1250583