Finite Group Databasebeta

← #35313618

Subgroups — #35313618

Order 21248.

306 conjugacy classes of subgroups; only the 85 normal subgroups are shown.

normal subgroups only

This group has 306 conjugacy classes of subgroups — too many to draw. Only its 85 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#24916106C211yesmaximal, characteristic
2#24909263C212yesmaximal, complemented
3#24905405C211yesmaximal, characteristic, complemented
4#24905388C212yesmaximal
5C83×#1323C211yesmaximal, characteristic, complemented
6#19128169C411yescharacteristic
7#19127761—22no—
8#19127753—22no—
9#19127728C411yescharacteristic
10#19127669C411yescharacteristic
11#19127667C2211yescharacteristic
12M16×Dic83C411yescharacteristic
13C2×C8×Dic83C2211yescharacteristic
14Dic83⋊C16—22no—
15C22⋊(C83⋊C16)C2212yes—
16#19127476—22no—
17#424×C83C2211yescharacteristic
18C22⋊C16×C83C2212yes—
19C2×#13050590C2×C411yescharacteristic
20C2×#13050574C2×C411yescharacteristic
21C22×C83⋊C8C2×C411yescharacteristic
22#14581757C812yes—
23#14581754C812yes—
24(C22⋊D83)⋊C4—22no—
25#14581749—21no—
26C2×C4×Dic83C2×C411yescharacteristic
27C42×D83—21no—
28C2×C83⋊C16—22no—
29C4⋊(C83⋊C8)—22no—
30(C2×D83)⋊C8—22no—
31(C2×D83)⋊C8—22no—
32#14581702—21no—
33C8×Dic83—21no—
34C8×Dic83D412yes—
35C8×Dic83D412yes—
36C2×M16×C83C2×C411yescharacteristic
37C22×C8×C83C2311yescharacteristic
38#117×C83C2×C411yescharacteristic
39C2×C16×C83—22no—
40C4⋊C8×C83—22no—
41#13050590—41no—
42#13050590—41no—
43C2×Dic166C2×C811yescharacteristic
44C2×D332C2×C811yescharacteristic
45C2×C22⋊D83—21no—
46C22×Dic83M1612yes—
47C2×C4×D83—21no—
48C2×C4×D83—22no—
49#13050574—41no—
50C2×C83⋊C8—21no—
51C2×C83⋊C8—41no—
52C2×C83⋊C8C22⋊C412yes—
53Dic83⋊C4—22no—
54(C2×D83)⋊C4—22no—
55C4×Dic83—22no—
56C4×Dic83C22⋊C411yescharacteristic
57C4×Dic83C22⋊C411yescharacteristic
58C4×Dic83C2×C812yes—
59C83⋊C16—42no—
60C22×C4×C83C22×C411yescharacteristic
61M16×C83—41no—
62C2×C8×C83—21no—
63C2×C8×C83—41no—
64C2×C8×C83C2×D412yes—
65C4⋊C4×C83C2×C812yes—
66C22⋊C4×C83—21no—
67C42×C83—21no—
68C16×C83—42no—
69C23×C83C2×M1611yescharacteristic
70C22×D83—21no—
71C2×C4×C83—21no—
72C2×C4×C83—21no—
73C2×C4×C83—22no—
74C2×C4×C83C2×C22⋊C411yescharacteristic
75C2×C4×C83C22×C811yescharacteristic
76C22⋊D83—42no—
77C2×Dic83—21no—
78C2×Dic83—42no—
79C2×Dic83C22⋊C812yes—
80C2×Dic83C22⋊C812yes—
81D332—41no—
82C4×D83—44no—
83C4×D83—41no—
84C4×D83—41no—
85Dic166—41no—
86C8×C83—22no—
87C8×C83—41no—
88C83⋊C8—22no—
89C83⋊C8—41no—
90C22×C83—22no—
91C22×C83—21no—
92C22×C83C2×C22⋊C811yescharacteristic
93C2×D83—42no—
94C2×D83—41no—
95C4×C83—21no—
96C4×C83—42no—
97C4×C83#41011yescharacteristic
98C4×C83#41311yescharacteristic
99Dic83—22no—
100Dic83—22no—
101Dic83—41no—
102#11463—831nomaximal, Sylow
103C2×C83—41no—
104C2×C83#145811yescharacteristic
105C2×C83#211712yes—
106D83—81no—
107#2922—831no—
108#2163—832no—
109#1323—831no—
110#1323D8311yescharacteristic, complemented
111#1315—832no—
112C83#1146311yescharacteristic, complemented, Sylow
113C4×#41—831no—
114#433—1662no—
115#431—1662no—
116#424—831no—
117#424C2×D8311yescharacteristic
118#408—831no—
119#408—831no—
120C4×M16—831no—
121C2×C4×C8—831no—
122C4⋊C16—1662no—
123C22⋊C16—832no—
124C22⋊C16C2×D8312yes—
125#346—1662no—
126C2×#41—831no—
127C2×M16—831no—
128C2×M16C4×D8311yescharacteristic
129C22×C8—831no—
130C22×C8C22×D8311yescharacteristic
131C4×Q8—832no—
132C4×D4—832no—
133C4×D4—1662no—
134#117—1661no—
135#117C4×D8311yescharacteristic
136C2×C42—831no—
137C2×C42—1661no—
138C2×C16—22no—
139C2×C16—1662no—
140C4⋊C8—22no—
141C4⋊C8—1662no—
142C22⋊C8—1662no—
143C22⋊C8—1662no—
144#97—1661no—
145C4×C8—832no—
146C4×C8—832no—
147C4×C8—1661no—
148#41—3321no—
149#41—3321no—
150C2×Q8—831no—
151C2×D4—831no—
152C2×D4—1661no—
153C22×C4—832no—
154C22×C4—1662no—
155C22×C4—1661no—
156C22×C4C2×C4×D8311yescharacteristic
157M16—41no—
158M16—3321no—
159C2×C8—21no—
160C2×C8—41no—
161C2×C8—3321no—
162C2×C8—832no—
163C2×C8—1661no—
164C2×C8D4×D8312yes—
165C4⋊C4—1662no—
166C4⋊C4C8×D8312yes—
167C22⋊C4—21no—
168C22⋊C4—1662no—
169C42—21no—
170C42—832no—
171C42—831no—
172C42—831no—
173C42—1662no—
174C16—42no—
175C16—3322no—
176C23—1661no—
177C23M16×D8311yescharacteristic
178Q8—3321no—
179D4—3321no—
180D4—3322no—
181C2×C4—21no—
182C2×C4—21no—
183C2×C4—22no—
184C2×C4—3324no—
185C2×C4—3321no—
186C2×C4—3321no—
187C2×C4—3322no—
188C2×C4—832no—
189C2×C4—832no—
190C2×C4—1661no—
191C2×C4C22⋊C4×D8311yescharacteristic
192C2×C4C2×C8×D8311yescharacteristic
193C8—22no—
194C8—41no—
195C8—3321no—
196C8—1662no—
197C22—22no—
198C22—21no—
199C22—3322no—
200C22—3321no—
201C22C22⋊C8×D8311yescharacteristic
202C4—21no—
203C4—42no—
204C4—3321no—
205C4—1662no—
206C4—1662no—
207C4#1912767311yescharacteristic
208C4#1912768411yescharacteristic
209C2—41no—
210C2—6641no—
211C2#2490577611yescharacteristic
212C2#2490908912yes—
subgroupG/H
centerC2×C4C22⋊C4×D83
commutatorC2×C4×C83C22×C8
FrattiniC22×C8C22×D83
FittingC83×#1323C2
socleC22×C83C2×C22⋊C8
prime radicalC2×#13050590C2×C4
cosocleC22×C8×C83C23
hypercenter#1323D83
hypocenterC83#11463
LCSG ▷ C2×C4×C83 ▷ C22×C83 ▷ C83
UCSC1 ◁ C2×C4 ◁ C22×C8 ◁ #1323

Complements

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

NH ≅ G/Ntype
2. #24909263C2semidirect
3. #24905405C2semidirect
5. C83×#1323C2semidirect
110. #1323D83semidirect
112. C83#11463semidirect

Maximal subgroups

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

subgroupindex
#249161062
#249092632
#249054052
#249053882
C83×#13232
#1146383