Finite Group Databasebeta

← #35292201

Subgroups — #35292201

Order 21248.

266 conjugacy classes of subgroups; only the 59 normal subgroups are shown.

normal subgroups only

This group has 266 conjugacy classes of subgroups — too many to draw. Only its 59 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#24909148C211yesmaximal, characteristic
2#24908296C211yesmaximal, characteristic
3C83×#2132C211yesmaximal, characteristic
4#19127725C411yescharacteristic
5C2×#14581719—21no—
6C2×#14581719—21no—
7#19127685—21no—
8#19127547C411yescharacteristic
9#19127500—21no—
10#19127498C412yescomplemented
11#532×C83C2211yescharacteristic
12#413×C83—21no—
13#356×C83—21no—
14#355×C83C412yescomplemented
15C2×#13050574—21no—
16C2×#13050574—41no—
17C2×C4×Dic83—21no—
18C4⋊(C83⋊C8)—41no—
19#14581719—42no—
20#14581719—42no—
21#14581711—22no—
22#14581709—41no—
23C83⋊#95—41no—
24C2×#41×C83D411yescharacteristic
25C2×#41×C83D411yescharacteristic
26C2×M16×C83—41no—
27C4⋊Q8×C83D411yescharacteristic
28#127×C83Q811yescharacteristic
29#124×C83C2×C411yescharacteristic
30#124×C83C2×C411yescharacteristic
31#121×C83—41no—
32C4×D4×C83—41no—
33C2×C42×C83C2×C411yescharacteristic
34#101×C83—22no—
35#100×C83—41no—
36C22×Dic83—41no—
37#13050574—41no—
38#13050574—41no—
39#13050574—42no—
40#13050574—81no—
41C2×C83⋊C8—41no—
42C2×C83⋊C8—81no—
43C4×Dic83—22no—
44C4×Dic83—41no—
45#41×C83—41no—
46#41×C83—41no—
47#41×C83—41no—
48#41×C83—41no—
49C2×Q8×C83C22⋊C411yescharacteristic
50C2×Q8×C83C22⋊C411yescharacteristic
51C2×D4×C83—21no—
52C2×D4×C83—21no—
53C2×D4×C83—41no—
54C2×D4×C83C4⋊C411yescharacteristic
55C2×D4×C83C4⋊C411yescharacteristic
56C22×C4×C83—21no—
57C22×C4×C83—21no—
58C22×C4×C83—21no—
59C22×C4×C83C22⋊C411yescharacteristic
60M16×C83—42no—
61M16×C83—81no—
62C2×C8×C83—81no—
63C4⋊C4×C83—41no—
64C22⋊C4×C83—41no—
65C22⋊C4×C83—41no—
66C42×C83—21no—
67C42×C83C4211yescharacteristic
68C42×C83C4⋊C411yescharacteristic
69C23×C83—21no—
70C23×C83—21no—
71C23×C83#9911yescharacteristic
72Q8×C83—41no—
73Q8×C83—41no—
74D4×C83—41no—
75D4×C83—41no—
76D4×C83—81no—
77D4×C83—81no—
78D4×C83—82no—
79C2×C4×C83—21no—
80C2×C4×C83—21no—
81C2×C4×C83—21no—
82C2×C4×C83—21no—
83C2×C4×C83—21no—
84C2×C4×C83—21no—
85C2×C4×C83—41no—
86C2×C4×C83—41no—
87C2×C4×C83—41no—
88C2×C4×C83—41no—
89C2×C4×C83—81no—
90C2×C4×C83#9511yescharacteristic
91C2×C4×C83#9911yescharacteristic
92C2×Dic83—42no—
93C2×Dic83—82no—
94C8×C83—82no—
95C83⋊C8—82no—
96C83⋊C8—81no—
97C22×C83—21no—
98C22×C83—41no—
99C22×C83—41no—
100C22×C83—41no—
101C22×C83—81no—
102C22×C83—81no—
103C22×C83#34211yescharacteristic
104C4×C83—21no—
105C4×C83—41no—
106C4×C83—41no—
107C4×C83—41no—
108C4×C83—41no—
109C4×C83#35311yescharacteristic
110C4×C83#35411yescharacteristic
111Dic83—82no—
112#7507—831nomaximal, Sylow
113C2×C83—21no—
114C2×C83—41no—
115C2×C83—81no—
116C2×C83—81no—
117C2×C83#139311yescharacteristic
118#2132—831no—
119#2132D8311yescharacteristic
120#1963—831no—
121C83#750711yescharacteristic, complemented, Sylow
122#532C2×D8311yescharacteristic
123#423—831no—
124C2×#104—1661no—
125C2×#104—1661no—
126#413—21no—
127#413—1661no—
128#376—831no—
129#356—21no—
130#356—1661no—
131#355—832no—
132#355Dic8312yescomplemented
133C2×#41D33211yescharacteristic
134C2×#41C22⋊D8311yescharacteristic
135C2×M16—41no—
136C2×M16—3321no—
137C2×M16—1661no—
138C4⋊Q8C22⋊D8311yescharacteristic
139#127Dic16611yescharacteristic
140#124C4×D8311yescharacteristic
141#124C2×Dic8311yescharacteristic
142#121—41no—
143C4×D4—41no—
144C2×C42—1661no—
145C2×C42C4×D8311yescharacteristic
146C4⋊C8—3321no—
147#104—3322no—
148#104—3322no—
149#101—22no—
150#101—1662no—
151#100—41no—
152#100—3321no—
153#95—3321no—
154#41—41no—
155#41—41no—
156#41—41no—
157#41—41no—
158C2×Q8(C2×D83)⋊C411yescharacteristic
159C2×Q8C22⋊Dic8311yescharacteristic
160C2×D4—21no—
161C2×D4—21no—
162C2×D4—41no—
163C2×D4Dic83⋊C411yescharacteristic
164C2×D4C4⋊Dic8311yescharacteristic
165C22×C4—21no—
166C22×C4—21no—
167C22×C4—21no—
168C22×C4—3321no—
169C22×C4(C2×D83)⋊C411yescharacteristic
170M16—42no—
171M16—81no—
172M16—3322no—
173M16—3321no—
174M16—3321no—
175M16—6641no—
176C2×C8—81no—
177C2×C8—3321no—
178C2×C8—6641no—
179C4⋊C4—41no—
180C22⋊C4—41no—
181C22⋊C4—41no—
182C42—21no—
183C42—3321no—
184C42—1662no—
185C42C4×Dic8311yescharacteristic
186C42Dic83⋊C411yescharacteristic
187C23—21no—
188C23—21no—
189C23#1458170611yescharacteristic
190Q8—41no—
191Q8—41no—
192D4—41no—
193D4—41no—
194D4—81no—
195D4—81no—
196D4—82no—
197C2×C4—21no—
198C2×C4—21no—
199C2×C4—21no—
200C2×C4—21no—
201C2×C4—21no—
202C2×C4—21no—
203C2×C4—41no—
204C2×C4—41no—
205C2×C4—41no—
206C2×C4—41no—
207C2×C4—81no—
208C2×C4—3322no—
209C2×C4—6642no—
210C2×C4C83⋊#9511yescharacteristic
211C2×C4#1458170611yescharacteristic
212C8—82no—
213C8—6642no—
214C8—6641no—
215C22—21no—
216C22—41no—
217C22—41no—
218C22—41no—
219C22—81no—
220C22—81no—
221C22#1912746711yescharacteristic
222C4—21no—
223C4—41no—
224C4—41no—
225C4—41no—
226C4—41no—
227C4—6642no—
228C4#1912749311yescharacteristic
229C4#1912749511yescharacteristic
230C2—21no—
231C2—41no—
232C2—81no—
233C2—81no—
234C2#2490558711yescharacteristic
subgroupG/H
centerC4#19127493
commutatorC42×C83C42
Frattini#532C2×D83
FittingC83×#2132C2
socleC2×C83#1393
prime radical, cosocle#532×C83C22
hypercenter#2132D83
hypocenterC83#7507
LCSG ▷ C42×C83 ▷ C2×C4×C83 ▷ C22×C83 ▷ C2×C83 ▷ C83
UCSC1 ◁ C4 ◁ C2×C4 ◁ C22×C4 ◁ #532 ◁ #2132

Complements

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

NH ≅ G/Ntype
10. #19127498C4semidirect
14. #355×C83C4semidirect
121. C83#7507semidirect
132. #355Dic83semidirect

Maximal subgroups

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

subgroupindex
#249091482
#249082962
C83×#21322
#750783