Finite Group Databasebeta

← #35325265

Subgroups — #35325265

Order 21248.

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

normal subgroups only

This group has 200 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×#19127538C211yesmaximal, characteristic, complemented
2C2×#19127534C211yesmaximal, characteristic, complemented
3#24909551C211yesmaximal, characteristic, complemented
4#24909550C211yesmaximal, characteristic
5#24905662C211yesmaximal, characteristic, complemented
6#24905642C211yesmaximal, characteristic, complemented
7C83×#1416C211yesmaximal, characteristic, complemented
8C2×D1328C2211yescharacteristic
9C2×C16×D83C2211yescharacteristic
10#19127939—21no—
11#19127938—21no—
12#19127538—22no—
13#19127534—22no—
14C2×C83⋊C32C2211yescharacteristic
15#19127527C2211yescharacteristic
16#19127505—21no—
17#19127501—21no—
18C2×Q32×C83C2211yescharacteristic
19C2×C32×C83C2211yescharacteristic
20#366×C83C2211yescharacteristic
21C2×D664—21no—
22C2×C8×D83D411yescharacteristic
23#14581768—41no—
24#14581767—41no—
25D1328—21no—
26D1328—21no—
27C2×C83⋊C16D411yescharacteristic
28C16×D83—21no—
29C16×D83—21no—
30#14581726—21no—
31#14581716—41no—
32#14581712—41no—
33C83⋊C32D412yescomplemented
34C2×Q16×C83—21no—
35Q32×C83—21no—
36Q32×C83—21no—
37C2×C16×C83C2311yescharacteristic
38#107×C83—21no—
39C32×C83—21no—
40C2×D332—41no—
41C2×D332—81no—
42C2×C4×D83D811yescharacteristic
43D664—41no—
44D664—41no—
45C2×C83⋊C8D811yescharacteristic
46C8×D83—21no—
47C8×D83—21no—
48C4⋊Dic83—41no—
49Dic83⋊C4—81no—
50(C2×D83)⋊C4—81no—
51(C2×D83)⋊C4—81no—
52C83⋊C16—21no—
53C2×Q8×C83—41no—
54Q16×C83—41no—
55Q16×C83—41no—
56C2×C8×C83C2×D411yescharacteristic
57C4⋊C4×C83—41no—
58C16×C83C2×D411yescharacteristic
59C16×C83#4111yescharacteristic
60C22×D83—81no—
61C22×D83D1611yescharacteristic
62Q8×C83—81no—
63Q8×C83—81no—
64C2×C4×C83—81no—
65C2×C4×C83—81no—
66C2×C4×C83C2×D811yescharacteristic
67C2×Dic83—81no—
68C2×Dic83D1611yescharacteristic
69D332—81no—
70D332—81no—
71D332—162no—
72C4×D83—21no—
73C4×D83—21no—
74C8×C83#12111yescharacteristic
75C8×C83#13511yescharacteristic
76C83⋊C8—21no—
77C22×C83C2×D1611yescharacteristic
78C2×D83—21no—
79C2×D83—21no—
80C2×D83—21no—
81C2×D83—161no—
82C2×D83—161no—
83C2×D83—161no—
84C4×C83—161no—
85C4×C83—161no—
86C4×C83#46611yescharacteristic
87C4×C83#50811yescharacteristic
88Dic83—21no—
89Dic83—161no—
90#13699—831nomaximal, Sylow
91C2×C83#221511yescharacteristic
92C2×C83#226311yescharacteristic
93C2×C83#226411yescharacteristic
94D83—41no—
95D83—321no—
96C2×SD64—831no—
97C2×M64—831no—
98#2216—831no—
99#2215—831no—
100#1423—831no—
101#1416D8311yescharacteristic, complemented
102#1415—831no—
103C83#1369911yescharacteristic, complemented, Sylow
104C2×Q32C2×D8311yescharacteristic
105C2×D16—831no—
106C22×C16—831no—
107#467—1661no—
108#466—1661no—
109SD64—1662no—
110M64—1662no—
111C2×C32—831no—
112C2×C32C2×D8311yescharacteristic
113#366—831no—
114#366C2×D8311yescharacteristic
115#358—1661no—
116#357—1661no—
117C2×Q16—21no—
118C2×D8—1661no—
119C22×C8—831no—
120C22⋊Q8—3321no—
121#121—3321no—
122Q32—21no—
123Q32—21no—
124D16—1661no—
125D16—1661no—
126C2×C16—831no—
127C2×C16—1661no—
128C2×C16—1661no—
129C2×C16C22×D8311yescharacteristic
130#107—21no—
131#107—1661no—
132#103—3321no—
133#102—3321no—
134C32—21no—
135C32—832no—
136C2×Q8—41no—
137C2×D4—3321no—
138C2×D4—6641no—
139C22×C4—831no—
140Q16—41no—
141Q16—41no—
142D8—3321no—
143D8—3321no—
144C2×C8—831no—
145C2×C8—1661no—
146C2×C8—1661no—
147C2×C8D4×D8311yescharacteristic
148C4⋊C4—41no—
149C4⋊C4—3321no—
150C4⋊C4—6641no—
151C22⋊C4—6641no—
152C22⋊C4—6641no—
153C16—1661no—
154C16D4×D8311yescharacteristic
155C16#1305059011yescharacteristic
156C23—831no—
157C23—6641no—
158Q8—81no—
159Q8—81no—
160D4—13282no—
161D4—6641no—
162D4—6641no—
163C2×C4—81no—
164C2×C4—81no—
165C2×C4—831no—
166C2×C4—6641no—
167C2×C4—1661no—
168C2×C4—1661no—
169C2×C4D8×D8311yescharacteristic
170C8—1661no—
171C8#1458176511yescharacteristic
172C8#1458181311yescharacteristic
173C22—13281no—
174C22—13281no—
175C22—13281no—
176C22—1661no—
177C22—1661no—
178C22—1661no—
179C22D16×D8311yescharacteristic
180C4—161no—
181C4—161no—
182C4—13281no—
183C4—1661no—
184C4#1912793611yescharacteristic
185C4#1912813211yescharacteristic
186C2—3321no—
187C2—26561no—
188C2#2490954811yescharacteristic
189C2#2490977711yescharacteristic
190C2#2490978211yescharacteristic
subgroupG/H
centerC22D16×D83
commutator, cosocleC2×C16×C83C23
FrattiniC2×C16C22×D83
FittingC83×#1416C2
socleC22×C83C2×D16
prime radical#24909550C2
hypercenter#1416D83
hypocenterC83#13699
LCSG ▷ C2×C16×C83 ▷ C8×C83 ▷ C4×C83 ▷ C2×C83 ▷ C83
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×C8 ◁ C2×C16 ◁ #1416

Complements

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

NH ≅ G/Ntype
1. C2×#19127538C2semidirect
2. C2×#19127534C2semidirect
3. #24909551C2semidirect
5. #24905662C2semidirect
6. #24905642C2semidirect
7. C83×#1416C2semidirect
33. C83⋊C32D4semidirect
101. #1416D83semidirect
103. C83#13699semidirect

Maximal subgroups

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

subgroupindex
C2×#191275382
C2×#191275342
#249095512
#249095502
#249056622
#249056422
C83×#14162
#1369983