Finite Group Databasebeta

← #35313839

Subgroups — #35313839

Order 21248.

284 conjugacy classes of subgroups; only the 69 normal subgroups are shown.

normal subgroups only

This group has 284 conjugacy classes of subgroups — too many to draw. Only its 69 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#24916100C211yesmaximal, characteristic
2#24909272C212yesmaximal, complemented
3#24905414C211yesmaximal, characteristic, complemented
4#24905398C212yesmaximal
5C83×#1327C211yesmaximal, characteristic, complemented
6C2×#14581749C411yescharacteristic
7#19127761—22no—
8#19127761—22no—
9#19127725C411yescharacteristic
10#19127664C411yescharacteristic
11#19127664C2211yescharacteristic
12M16×Dic83C411yescharacteristic
13M16×Dic83C2211yescharacteristic
14#19127521—22no—
15#19127483C2212yes—
16#19127478—22no—
17#423×C83C2211yescharacteristic
18#349×C83C2212yes—
19C22×C4×D83C2×C411yescharacteristic
20C2×#13050574C2×C411yescharacteristic
21C2×#13050574C2×C411yescharacteristic
22#14581749—21no—
23#14581749—21no—
24#14581749—22no—
25C2×Dic83⋊C4—21no—
26C2×(C2×D83)⋊C4—21no—
27C2×C4×Dic83C2×C411yescharacteristic
28#14581732—22no—
29C4⋊(C83⋊C8)—22no—
30(C2×D83)⋊C8—22no—
31(C2×D83)⋊C8—22no—
32#14581702—21no—
33#14581702D412yes—
34C8×Dic83—21no—
35C8×Dic83D412yes—
36C2×M16×C83C2×C411yescharacteristic
37C2×M16×C83C2311yescharacteristic
38C2×C42×C83C2×C411yescharacteristic
39M32×C83—22no—
40C4⋊C8×C83—22no—
41C23×D83M1611yescharacteristic
42C22×Dic83—21no—
43C22×Dic83M1611yescharacteristic
44C2×C4×D83—21no—
45C2×C4×D83—21no—
46C2×C4×D83—41no—
47C2×C4×D83—41no—
48#13050574—41no—
49#13050574—41no—
50C2×C83⋊C8—21no—
51C2×C83⋊C8C22⋊C412yes—
52Dic83⋊C4—22no—
53Dic83⋊C4—22no—
54(C2×D83)⋊C4—22no—
55(C2×D83)⋊C4—22no—
56C4×Dic83—21no—
57C4×Dic83C22⋊C411yescharacteristic
58C4×Dic83C22⋊C411yescharacteristic
59C83⋊C16—42no—
60C22×C4×C83—21no—
61C22×C4×C83C22×C411yescharacteristic
62M16×C83—41no—
63M16×C83—41no—
64C2×C8×C83—21no—
65C2×C8×C83C2×D412yes—
66C42×C83—21no—
67C42×C83M1612yes—
68C16×C83—42no—
69C23×C83C2×M1611yescharacteristic
70C22×D83—21no—
71C22×D83—41no—
72C22×D83—81no—
73C2×C4×C83—21no—
74C2×C4×C83—21no—
75C2×C4×C83—22no—
76C2×C4×C83—81no—
77C2×C4×C83C2×C22⋊C411yescharacteristic
78C2×C4×C83C2×M1611yescharacteristic
79C2×Dic83—21no—
80C2×Dic83—21no—
81C2×Dic83—21no—
82C2×Dic83—41no—
83C2×Dic83—81no—
84C4×D83—42no—
85C4×D83—41no—
86C4×D83—41no—
87C8×C83—22no—
88C8×C83—41no—
89C83⋊C8—22no—
90C83⋊C8—41no—
91C22×C83—21no—
92C22×C83—41no—
93C22×C83#40711yescharacteristic
94C2×D83—42no—
95C2×D83—41no—
96C2×D83—82no—
97C4×C83—21no—
98C4×C83—42no—
99C4×C83#41011yescharacteristic
100C4×C83#41311yescharacteristic
101Dic83—41no—
102Dic83—41no—
103Dic83—41no—
104#11522—831nomaximal, Sylow
105C2×C83—21no—
106C2×C83—41no—
107C2×C83#146411yescharacteristic
108D83—81no—
109#2921—831no—
110#2165—832no—
111#1327—831no—
112#1327D8311yescharacteristic, complemented
113#1320—832no—
114C83#1152211yescharacteristic, complemented, Sylow
115C2×#117—831no—
116#433—1662no—
117#433—1662no—
118#423—831no—
119#423C2×D8311yescharacteristic
120#407—831no—
121#407—831no—
122C4×M16—831no—
123C4×M16—831no—
124#364—1662no—
125#349—832no—
126#349C2×D8312yes—
127#347—1662no—
128C23×C4—831no—
129C2×M16—831no—
130C2×M16—831no—
131C2×M16C4×D8311yescharacteristic
132C2×M16C22×D8311yescharacteristic
133#117—1661no—
134#117—1661no—
135#117—1662no—
136C2×C4⋊C4—1661no—
137C2×C22⋊C4—1661no—
138C2×C42—831no—
139C2×C42C4×D8311yescharacteristic
140M32—22no—
141M32—1662no—
142C4⋊C8—22no—
143C4⋊C8—1662no—
144C22⋊C8—1662no—
145C22⋊C8—1662no—
146#97—832no—
147#97—1661no—
148C4×C8—832no—
149C4×C8—1661no—
150C24—831no—
151C22×C4—21no—
152C22×C4—3321no—
153C22×C4—3321no—
154C22×C4—831no—
155C22×C4—1661no—
156C22×C4—1661no—
157C22×C4—1661no—
158C22×C4C2×C4×D8311yescharacteristic
159M16—41no—
160M16—41no—
161M16—3321no—
162M16—3321no—
163C2×C8—21no—
164C2×C8—832no—
165C2×C8—1661no—
166C2×C8D4×D8312yes—
167C4⋊C4—1662no—
168C4⋊C4—1662no—
169C22⋊C4—1662no—
170C22⋊C4—1662no—
171C42—21no—
172C42—831no—
173C42—831no—
174C42—1661no—
175C42#1305057312yes—
176C16—42no—
177C16—3322no—
178C23—3321no—
179C23—6641no—
180C23—1661no—
181C23M16×D8311yescharacteristic
182C2×C4—21no—
183C2×C4—21no—
184C2×C4—22no—
185C2×C4—81no—
186C2×C4—3322no—
187C2×C4—3321no—
188C2×C4—3321no—
189C2×C4—3321no—
190C2×C4—6641no—
191C2×C4—1661no—
192C2×C4—1661no—
193C2×C4—1661no—
194C2×C4C22⋊C4×D8311yescharacteristic
195C2×C4C2×#1305057311yescharacteristic
196C8—22no—
197C8—41no—
198C8—3321no—
199C8—1662no—
200C22—21no—
201C22—41no—
202C22—3322no—
203C22—3321no—
204C22—6642no—
205C22#1912766311yescharacteristic
206C4—21no—
207C4—42no—
208C4—3321no—
209C4—3321no—
210C4—3321no—
211C4#1912767311yescharacteristic
212C4#1912768411yescharacteristic
213C2—21no—
214C2—41no—
215C2—6641no—
216C2#2490579611yescharacteristic
subgroupG/H
centerC4#19127673
commutatorC22×C4×C83C22×C4
FrattiniC2×M16C22×D83
FittingC83×#1327C2
socleC2×C83#1464
prime radicalC23×D83M16
cosocleC2×M16×C83C23
hypercenter#1327D83
hypocenterC83#11522
LCSG ▷ C22×C4×C83 ▷ C22×C83 ▷ C2×C83 ▷ C83
UCSC1 ◁ C4 ◁ C2×C4 ◁ C2×M16 ◁ #1327

Complements

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

NH ≅ G/Ntype
2. #24909272C2semidirect
3. #24905414C2semidirect
5. C83×#1327C2semidirect
112. #1327D83semidirect
114. C83#11522semidirect

Maximal subgroups

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

subgroupindex
#249161002
#249092722
#249054142
#249053982
C83×#13272
#1152283