Finite Group Databasebeta

← #35325251

Subgroups — #35325251

Order 21248.

210 conjugacy classes of subgroups; only the 55 normal subgroups are shown.

normal subgroups only

This group has 210 conjugacy classes of subgroups — too many to draw. Only its 55 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×#19127536C211yesmaximal, characteristic, complemented
2C2×#19127534C211yesmaximal, characteristic, complemented
3#24909550C211yesmaximal, characteristic, complemented
4#24909546C211yesmaximal, characteristic, complemented
5#24905664C211yesmaximal, characteristic, complemented
6#24905642C211yesmaximal, characteristic, complemented
7C83×#1415C211yesmaximal, characteristic, complemented
8C2×D1328C2211yescharacteristic
9C2×C16×D83C2211yescharacteristic
10#19127938—21no—
11#19127934—21no—
12#19127536—22no—
13#19127534—22no—
14C2×C83⋊C32C2211yescharacteristic
15#19127527C2211yescharacteristic
16#19127502—21no—
17#19127501—21no—
18C2×D16×C83C2211yescharacteristic
19C2×C32×C83C2211yescharacteristic
20#366×C83C2211yescharacteristic
21C2×D664—21no—
22C2×C8×D83D411yescharacteristic
23#14581767—41no—
24#14581763—41no—
25D1328—21no—
26D1328—21no—
27C2×C83⋊C16D411yescharacteristic
28C16×D83—21no—
29C16×D83—21no—
30#14581726—21no—
31#14581713—41no—
32#14581712—41no—
33C83⋊C32D412yescomplemented
34C2×D8×C83—21no—
35D16×C83—21no—
36D16×C83—21no—
37C2×C16×C83C2311yescharacteristic
38#107×C83—21no—
39C32×C83—21no—
40C2×D332—41no—
41C2×D332—81no—
42C2×C22⋊D83—81no—
43C2×C4×D83D811yescharacteristic
44D664—41no—
45D664—41no—
46C2×C83⋊C8D811yescharacteristic
47C8×D83—21no—
48C8×D83—21no—
49C4⋊Dic83—41no—
50C22⋊Dic83—81no—
51(C2×D83)⋊C4—81no—
52C83⋊C16—21no—
53C2×D4×C83—41no—
54D8×C83—41no—
55D8×C83—41no—
56C2×C8×C83C2×D411yescharacteristic
57C4⋊C4×C83—41no—
58C16×C83C2×D411yescharacteristic
59C16×C83#4111yescharacteristic
60C23×C83—81no—
61C22×D83—81no—
62C22×D83D1611yescharacteristic
63D4×C83—81no—
64D4×C83—81no—
65C2×C4×C83—81no—
66C2×C4×C83C2×D811yescharacteristic
67C22⋊D83—162no—
68C2×Dic83—81no—
69C2×Dic83D1611yescharacteristic
70D332—81no—
71D332—81no—
72D332—162no—
73C4×D83—21no—
74C4×D83—21no—
75C8×C83#12111yescharacteristic
76C8×C83#13511yescharacteristic
77C83⋊C8—21no—
78C22×C83—161no—
79C22×C83—161no—
80C22×C83—161no—
81C22×C83C2×D1611yescharacteristic
82C2×D83—21no—
83C2×D83—21no—
84C2×D83—21no—
85C2×D83—161no—
86C2×D83—161no—
87C2×D83—161no—
88C4×C83—161no—
89C4×C83#46611yescharacteristic
90C4×C83#50811yescharacteristic
91Dic83—21no—
92Dic83—161no—
93#13697—831nomaximal, Sylow
94C2×C83—321no—
95C2×C83#221511yescharacteristic
96C2×C83#226311yescharacteristic
97C2×C83#226311yescharacteristic
98D83—41no—
99D83—321no—
100C2×D32—831no—
101C2×M64—831no—
102#2215—831no—
103#2215—831no—
104#1424—831no—
105#1415—831no—
106#1415D8311yescharacteristic, complemented
107C83#1369711yescharacteristic, complemented, Sylow
108C2×D16—831no—
109C2×D16C2×D8311yescharacteristic
110C22×C16—831no—
111#466—1661no—
112#466—1661no—
113D32—1662no—
114M64—1662no—
115C2×C32—831no—
116C2×C32C2×D8311yescharacteristic
117#366—831no—
118#366C2×D8311yescharacteristic
119#357—1661no—
120#357—1661no—
121C2×D8—21no—
122C2×D8—1661no—
123C22×C8—831no—
124#121—3321no—
125#121—3321no—
126D16—21no—
127D16—21no—
128D16—1661no—
129D16—1661no—
130C2×C16—831no—
131C2×C16—1661no—
132C2×C16—1661no—
133C2×C16C22×D8311yescharacteristic
134#107—21no—
135#107—1661no—
136#102—3321no—
137#102—3321no—
138C32—21no—
139C32—832no—
140C2×D4—41no—
141C2×D4—3321no—
142C2×D4—6641no—
143C2×D4—6641no—
144C22×C4—831no—
145D8—41no—
146D8—41no—
147D8—3321no—
148D8—3321no—
149C2×C8—831no—
150C2×C8—1661no—
151C2×C8—1661no—
152C2×C8D4×D8311yescharacteristic
153C4⋊C4—41no—
154C4⋊C4—3321no—
155C22⋊C4—6641no—
156C22⋊C4—6641no—
157C16—1661no—
158C16D4×D8311yescharacteristic
159C16#1305059011yescharacteristic
160C23—81no—
161C23—831no—
162C23—6641no—
163D4—81no—
164D4—81no—
165D4—13282no—
166D4—13282no—
167D4—6641no—
168D4—6641no—
169C2×C4—81no—
170C2×C4—831no—
171C2×C4—6641no—
172C2×C4—1661no—
173C2×C4—1661no—
174C2×C4D8×D8311yescharacteristic
175C8—1661no—
176C8#1458176511yescharacteristic
177C8#1458181311yescharacteristic
178C22—161no—
179C22—161no—
180C22—161no—
181C22—13281no—
182C22—13281no—
183C22—13281no—
184C22—1661no—
185C22—1661no—
186C22—1661no—
187C22D16×D8311yescharacteristic
188C4—161no—
189C4—13281no—
190C4—1661no—
191C4#1912793611yescharacteristic
192C4#1912813211yescharacteristic
193C2—321no—
194C2—3321no—
195C2—26561no—
196C2#2490954811yescharacteristic
197C2#2490977411yescharacteristic
198C2#2490977711yescharacteristic
subgroupG/H
centerC22D16×D83
commutator, cosocleC2×C16×C83C23
FrattiniC2×C16C22×D83
FittingC83×#1415C2
socleC22×C83C2×D16
hypercenter#1415D83
hypocenterC83#13697
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×#19127536C2semidirect
2. C2×#19127534C2semidirect
3. #24909550C2semidirect
4. #24909546C2semidirect
5. #24905664C2semidirect
6. #24905642C2semidirect
7. C83×#1415C2semidirect
33. C83⋊C32D4semidirect
106. #1415D83semidirect
107. C83#13697semidirect

Maximal subgroups

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

subgroupindex
C2×#191275362
C2×#191275342
#249095502
#249095462
#249056642
#249056422
C83×#14152
#1369783