Finite Group Databasebeta

← #35325188

Subgroups — #35325188

Order 21248.

220 conjugacy classes of subgroups; only the 57 normal subgroups are shown.

normal subgroups only

This group has 220 conjugacy classes of subgroups — too many to draw. Only its 57 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
1C2×#19127540C211yesmaximal, characteristic, complemented
2C2×#19127539C211yesmaximal, characteristic, complemented
3#24909711C211yesmaximal, characteristic
4#24909321C211yesmaximal, characteristic, complemented
5Dic83⋊C32C211yesmaximal, characteristic, complemented
6#24905640C211yesmaximal, characteristic, complemented
7C83×#1415C211yesmaximal, characteristic, complemented
8C2×Dic664C2211yescharacteristic
9C2×D1328C2211yescharacteristic
10C2×#14581733—21no—
11#19128076—21no—
12#19127795—21no—
13#19127540—22no—
14#19127539—22no—
15C2×C83⋊C32C2211yescharacteristic
16#19127504—21no—
17C16×Dic83C2211yescharacteristic
18C2×D16×C83C2211yescharacteristic
19C2×C32×C83C2211yescharacteristic
20#366×C83C2211yescharacteristic
21C2×Dic332—21no—
22C2×D664—21no—
23C2×#13050575—41no—
24#14581788—41no—
25#14581757—41no—
26Dic664—21no—
27Dic664D412yescomplemented
28D1328—21no—
29D1328—21no—
30#14581733—42no—
31C2×C83⋊C16D411yescharacteristic
32#14581715—41no—
33C8×Dic83D411yescharacteristic
34C83⋊C32—21no—
35C2×D8×C83—21no—
36D16×C83—21no—
37D16×C83—21no—
38C2×C16×C83C2311yescharacteristic
39#107×C83—21no—
40C32×C83—21no—
41C2×Dic166—41no—
42C2×D332—41no—
43C2×C22⋊D83—81no—
44C2×C22⋊D83—81no—
45Dic332—22no—
46Dic332—41no—
47D664—41no—
48D664—41no—
49#13050575—82no—
50C2×C83⋊C8D811yescharacteristic
51Dic83⋊C4—81no—
52C4×Dic83—81no—
53C4×Dic83D811yescharacteristic
54C83⋊C16—21no—
55C2×D4×C83—41no—
56D8×C83—41no—
57D8×C83—41no—
58C2×C8×C83C2×D411yescharacteristic
59C4⋊C4×C83—41no—
60C16×C83C2×D411yescharacteristic
61C16×C83#4111yescharacteristic
62C23×C83—81no—
63C22×D83—81no—
64D4×C83—81no—
65D4×C83—81no—
66C2×C4×C83—81no—
67C2×C4×C83C2×D811yescharacteristic
68C22⋊D83—162no—
69C22⋊D83—162no—
70C2×Dic83—81no—
71C2×Dic83D1611yescharacteristic
72C2×Dic83D1611yescharacteristic
73D332—81no—
74D332—81no—
75Dic166—42no—
76Dic166—81no—
77C8×C83#12111yescharacteristic
78C8×C83AGL(1,ℤ/8)11yescharacteristic
79C83⋊C8—21no—
80C22×C83—161no—
81C22×C83—161no—
82C22×C83—161no—
83C22×C83C2×D1611yescharacteristic
84C2×D83—161no—
85C2×D83—161no—
86C2×D83—161no—
87C4×C83—161no—
88C4×C83#45911yescharacteristic
89C4×C83#50911yescharacteristic
90Dic83—21no—
91Dic83—82no—
92Dic83SD6412yescomplemented
93#13686—831nomaximal, Sylow
94C2×C83—321no—
95C2×C83#220611yescharacteristic
96C2×C83C2×SD6411yescharacteristic
97C2×C83#226311yescharacteristic
98D83—321no—
99C2×SD64—831no—
100C2×SD64—831no—
101#2246—831no—
102C4×Q32—831no—
103C4⋊C32—831no—
104#1415—831no—
105#1415D8311yescharacteristic, complemented
106C83#1368611yescharacteristic, complemented, Sylow
107C2×Q32—831no—
108C2×D16—831no—
109C2×D16—1661no—
110C2×D16C2×D8311yescharacteristic
111#493—1661no—
112C4×Q16—1661no—
113SD64—1662no—
114SD64—1662no—
115C2×C32—831no—
116C2×C32C2×D8311yescharacteristic
117#366C2×D8311yescharacteristic
118#358—1661no—
119C4×C16—831no—
120C2×Q16—1661no—
121C2×D8—21no—
122C2×D8—3321no—
123C2×D8—1661no—
124#127—3321no—
125C4×Q8—3321no—
126Q32—832no—
127Q32—1661no—
128D16—21no—
129D16—21no—
130D16—3322no—
131D16—1661no—
132D16—1661no—
133C2×C16—831no—
134C2×C16C22×D8311yescharacteristic
135#107—21no—
136#103—3321no—
137C4×C8—831no—
138C32—21no—
139C32—1661no—
140C2×Q8—3321no—
141C2×D4—41no—
142C2×D4—3321no—
143C2×D4—6641no—
144C2×D4—6641no—
145Q16—3321no—
146Q16—1662no—
147D8—41no—
148D8—41no—
149D8—3321no—
150D8—3321no—
151D8—6642no—
152C2×C8—831no—
153C2×C8D4×D8311yescharacteristic
154C4⋊C4—41no—
155C4⋊C4—6641no—
156C42—831no—
157C42—6641no—
158C16—1661no—
159C16D4×D8311yescharacteristic
160C16#1305059011yescharacteristic
161C23—81no—
162C23—6641no—
163Q8—3322no—
164Q8—6641no—
165D4—81no—
166D4—81no—
167D4—13282no—
168D4—13282no—
169D4—6641no—
170D4—6641no—
171C2×C4—81no—
172C2×C4—831no—
173C2×C4—831no—
174C2×C4—6641no—
175C2×C4D8×D8311yescharacteristic
176C8—1661no—
177C8#1458176511yescharacteristic
178C8#1458181911yescharacteristic
179C22—161no—
180C22—161no—
181C22—161no—
182C22—13281no—
183C22—13281no—
184C22—13281no—
185C22D16×D8311yescharacteristic
186C4—161no—
187C4—832no—
188C4—6642no—
189C4—1661no—
190C4#1912789511yescharacteristic
191C4#1912813811yescharacteristic
192C2—321no—
193C2—26561no—
194C2#2490949711yescharacteristic
195C2SD64×D8311yescharacteristic
196C2#2490977411yescharacteristic
subgroupG/H
centerC22D16×D83
commutator, cosocleC2×C16×C83C23
FrattiniC2×C16C22×D83
FittingC83×#1415C2
socleC22×C83C2×D16
prime radical#24909711C2
hypercenter#1415D83
hypocenterC83#13686
LCSG ▷ C2×C16×C83 ▷ C8×C83 ▷ C4×C83 ▷ C2×C83 ▷ C83
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×C8 ◁ C2×C16 ◁ #1415

Complements

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

NH ≅ G/Ntype
1. C2×#19127540C2semidirect
2. C2×#19127539C2semidirect
4. #24909321C2semidirect
5. Dic83⋊C32C2semidirect
6. #24905640C2semidirect
7. C83×#1415C2semidirect
27. Dic664D4semidirect
92. Dic83SD64semidirect
105. #1415D83semidirect
106. C83#13686semidirect

Maximal subgroups

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

subgroupindex
C2×#191275402
C2×#191275392
#249097112
#249093212
Dic83⋊C322
#249056402
C83×#14152
#1368683