Finite Group Databasebeta

← #35325049

Subgroups — #35325049

Order 21248.

294 conjugacy classes of subgroups; only the 61 normal subgroups are shown.

normal subgroups only

This group has 294 conjugacy classes of subgroups — too many to draw. Only its 61 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×Q32×D83C211yesmaximal, characteristic, complemented
2C2×#19127540C211yesmaximal, characteristic, complemented
3C2×#19127538C211yesmaximal, characteristic, complemented
4#24909550C211yesmaximal, characteristic
5#24905643C211yesmaximal, characteristic, complemented
6(C2×D83)⋊C32C211yesmaximal, characteristic, complemented
7C83×#1416C211yesmaximal, characteristic, complemented
8C2×Q16×D83—21no—
9C2×Dic664C2211yescharacteristic
10C2×#14581738—21no—
11Q32×D83—22no—
12Q32×D83—22no—
13C2×D1328C2211yescharacteristic
14C2×C16×D83C2211yescharacteristic
15#19127938—21no—
16#19127540—22no—
17#19127538—22no—
18C2×C83⋊C32C2211yescharacteristic
19#19127501—21no—
20C2×Q32×C83C2211yescharacteristic
21C2×C32×C83C2211yescharacteristic
22#366×C83C2211yescharacteristic
23C2×Q8×D83—41no—
24C2×Dic332—21no—
25C2×#13050580—41no—
26Q16×D83—24no—
27Q16×D83—42no—
28C2×D664—21no—
29C2×C8×D83D411yescharacteristic
30#14581767—41no—
31Dic664—21no—
32Dic664D412yescomplemented
33#14581738—24no—
34D1328—21no—
35D1328—21no—
36C2×C83⋊C16D411yescharacteristic
37C16×D83—21no—
38C16×D83—21no—
39#14581712—41no—
40C83⋊C32—21no—
41C2×Q16×C83—21no—
42Q32×C83—21no—
43Q32×C83D412yescomplemented
44C2×C16×C83C2311yescharacteristic
45#107×C83—21no—
46C32×C83—21no—
47C2×Dic166—41no—
48C2×Dic166—81no—
49Q8×D83—44no—
50Q8×D83—82no—
51C2×D332—41no—
52C2×D332—81no—
53C2×C4×D83—81no—
54C2×C4×D83D811yescharacteristic
55Dic332—22no—
56Dic332—41no—
57#13050580—44no—
58D664—41no—
59D664—41no—
60C2×C83⋊C8D811yescharacteristic
61C8×D83—21no—
62C8×D83—21no—
63(C2×D83)⋊C4—81no—
64C83⋊C16—21no—
65C2×Q8×C83—41no—
66Q16×C83—22no—
67Q16×C83—41no—
68C2×C8×C83C2×D411yescharacteristic
69C4⋊C4×C83—41no—
70C16×C83C2×D411yescharacteristic
71C16×C83C2×D411yescharacteristic
72C22×D83—81no—
73C22×D83D1611yescharacteristic
74Q8×C83—42no—
75Q8×C83—81no—
76C2×C4×C83—81no—
77C2×C4×C83—81no—
78C2×C4×C83C2×D811yescharacteristic
79C2×Dic83—81no—
80C2×Dic83D1611yescharacteristic
81D332—81no—
82D332—81no—
83D332—162no—
84C4×D83—21no—
85C4×D83—21no—
86C4×D83—84no—
87Dic166—42no—
88Dic166—84no—
89Dic166—81no—
90C8×C83#12011yescharacteristic
91C8×C83AGL(1,ℤ/8)11yescharacteristic
92C83⋊C8—21no—
93C22×C83C2×D1611yescharacteristic
94C2×D83—21no—
95C2×D83—21no—
96C2×D83—161no—
97C2×D83—161no—
98C2×D83—161no—
99C2×D83SD6412yescomplemented
100C4×C83—82no—
101C4×C83—161no—
102C4×C83#44711yescharacteristic
103C4×C83#50911yescharacteristic
104Dic83—21no—
105Dic83—82no—
106#13662—831nomaximal, Sylow
107C2×C83#218411yescharacteristic
108C2×C83C2×SD6411yescharacteristic
109C2×C83#226411yescharacteristic
110D83—22no—
111D83—321no—
112C22×Q32—831no—
113C2×SD64—831no—
114C2×SD64—831no—
115#2215—831no—
116#1416—831no—
117#1416D8311yescharacteristic, complemented
118C22⋊C32—831no—
119C83#1366211yescharacteristic, complemented, Sylow
120C22×Q16—1661no—
121C2×Q32—831no—
122C2×Q32—1661no—
123C2×Q32—1662no—
124C2×Q32—1662no—
125C2×Q32C2×D8311yescharacteristic
126C2×D16—831no—
127C22×C16—831no—
128#466—1661no—
129SD64—1662no—
130SD64—1662no—
131C2×C32—831no—
132C2×C32C2×D8311yescharacteristic
133#366C2×D8311yescharacteristic
134#357—1661no—
135C22×Q8—3321no—
136C2×Q16—21no—
137C2×Q16—3321no—
138C2×Q16—3322no—
139C2×Q16—1664no—
140C2×Q16—1661no—
141C2×D8—1661no—
142C22×C8—831no—
143#121—3321no—
144Q32—21no—
145Q32—832no—
146Q32—1664no—
147Q32—1661no—
148Q32D33212yescomplemented
149D16—1661no—
150D16—1661no—
151C2×C16—831no—
152C2×C16—1661no—
153C2×C16—1661no—
154C2×C16C22×D8311yescharacteristic
155#107—21no—
156#102—3321no—
157C32—21no—
158C32—1661no—
159C2×Q8—41no—
160C2×Q8—3324no—
161C2×Q8—3321no—
162C2×Q8—6641no—
163C2×Q8—6642no—
164C2×D4—3321no—
165C2×D4—6641no—
166C22×C4—831no—
167C22×C4—6641no—
168Q16—22no—
169Q16—41no—
170Q16—3324no—
171Q16—3321no—
172Q16—1662no—
173D8—3321no—
174D8—3321no—
175C2×C8—831no—
176C2×C8—1661no—
177C2×C8—1661no—
178C2×C8D4×D8311yescharacteristic
179C4⋊C4—41no—
180C22⋊C4—6641no—
181C16—1661no—
182C16D4×D8311yescharacteristic
183C16C2×D33211yescharacteristic
184C23—831no—
185C23—6641no—
186Q8—42no—
187Q8—81no—
188Q8—3322no—
189Q8—6644no—
190Q8—6641no—
191D4—13282no—
192D4—6641no—
193D4—6641no—
194C2×C4—81no—
195C2×C4—81no—
196C2×C4—831no—
197C2×C4—6644no—
198C2×C4—6641no—
199C2×C4—1661no—
200C2×C4—1661no—
201C2×C4D8×D8311yescharacteristic
202C8—1661no—
203C8#1458176211yescharacteristic
204C8#1458181911yescharacteristic
205C22—13281no—
206C22—13281no—
207C22—13281no—
208C22—832no—
209C22—1661no—
210C22—1661no—
211C22D16×D8311yescharacteristic
212C4—82no—
213C4—161no—
214C4—6642no—
215C4—1661no—
216C4#1912783611yescharacteristic
217C4#1912813811yescharacteristic
218C2—26561no—
219C2—1662no—
220C2#2490937611yescharacteristic
221C2SD64×D8311yescharacteristic
222C2#2490978211yescharacteristic
subgroupG/H
centerC22D16×D83
commutator, cosocleC2×C16×C83C23
FrattiniC2×C16C22×D83
FittingC83×#1416C2
socleC22×C83C2×D16
prime radical#24909550C2
hypercenter#1416D83
hypocenterC83#13662
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×Q32×D83C2semidirect
2. C2×#19127540C2semidirect
3. C2×#19127538C2semidirect
5. #24905643C2semidirect
6. (C2×D83)⋊C32C2semidirect
7. C83×#1416C2semidirect
32. Dic664D4semidirect
43. Q32×C83D4semidirect
99. C2×D83SD64semidirect
117. #1416D83semidirect
119. C83#13662semidirect
148. Q32D332semidirect

Maximal subgroups

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

subgroupindex
C2×Q32×D832
C2×#191275402
C2×#191275382
#249095502
#249056432
(C2×D83)⋊C322
C83×#14162
#1366283