Finite Group Databasebeta

← #35306696

Subgroups — #35306696

Order 21248.

466 conjugacy classes of subgroups; only the 105 normal subgroups are shown.

normal subgroups only

This group has 466 conjugacy classes of subgroups — too many to draw. Only its 105 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#24918604C212yesmaximal
2#24908283C211yesmaximal, characteristic
3#24906027C212yesmaximal
4#24905308C211yesmaximal, characteristic
5C83×#3162C211yesmaximal, characteristic
6C2×#14581792C2211yescharacteristic
7#19128097—22no—
8#19128051—22no—
9#19128029—24no—
10#19127986—24no—
11#19127754C2212yes—
12C2×#14581717—22no—
13#19127567C2211yescharacteristic
14#19127438—24no—
15#533×C83C2212yes—
16#501×C83—22no—
17#501×C83—22no—
18#427×C83—22no—
19C2×#97×C83C2211yescharacteristic
20C22×Dic166—21no—
21#14581792—22no—
22#14581792—21no—
23#14581792D412yes—
24C2×C4⋊Dic83—22no—
25C2×C4⋊Dic83—21no—
26#14581723—28no—
27C4⋊(C83⋊C8)—22no—
28#14581717—44no—
29#14581716—28no—
30C22⋊(C83⋊C8)D414yes—
31C4×C83⋊C8—22no—
32C83⋊#95—22no—
33C22×C8×C83D412yes—
34C4⋊Q8×C83D412yes—
35C4⋊Q8×C83D412yes—
36#125×C83—22no—
37C22⋊Q8×C83—22no—
38C22⋊Q8×C83—22no—
39C4×Q8×C83—22no—
40C4×Q8×C83—22no—
41#117×C83—22no—
42C2×C42×C83C2311yescharacteristic
43#107×C83—24no—
44#106×C83—22no—
45#106×C83—22no—
46#97×C83—22no—
47C2×Dic166—22no—
48C2×Dic166—42no—
49C2×Dic166—42no—
50C2×Dic166—41no—
51C22×Dic83—41no—
52C22×Dic83—41no—
53C2×C83⋊C8—24no—
54C4⋊Dic83—24no—
55C4⋊Dic83—42no—
56C4⋊Dic83—42no—
57C2×Q8×C83—22no—
58C2×Q8×C83—22no—
59C22×C4×C83C2×D412yes—
60C22×C4×C83C2×D411yescharacteristic
61C2×C8×C83—22no—
62C2×C8×C83—22no—
63C2×C8×C83SD1614yes—
64C4⋊C4×C83—22no—
65C4⋊C4×C83—22no—
66C4⋊C4×C83—22no—
67C4⋊C4×C83—22no—
68C4⋊C4×C83—42no—
69C4⋊C4×C83—42no—
70C22⋊C4×C83—42no—
71C42×C83—42no—
72C42×C83C2×D411yescharacteristic
73C42×C83C2×D412yes—
74C42×C83#4111yescharacteristic
75C23×C83#12711yescharacteristic
76Q8×C83—44no—
77Q8×C83—82no—
78C2×C4×C83—42no—
79C2×C4×C83—42no—
80C2×C4×C83—42no—
81C2×C4×C83#12012yes—
82C2×C4×C83#12011yescharacteristic
83C2×C4×C83#12111yescharacteristic
84C2×C4×C83#12112yes—
85C2×C4×C83C2×SD1612yes—
86C2×C4×C83#13712yes—
87C2×Dic83—42no—
88C2×Dic83—81no—
89C2×Dic83—81no—
90C2×Dic83—82no—
91C2×Dic83—81no—
92Dic166—44no—
93Dic166—82no—
94C8×C83—24no—
95C83⋊C8—44no—
96C22×C83—22no—
97C22×C83#39211yescharacteristic
98C22×C83#49211yescharacteristic
99C22×C83#49711yescharacteristic
100C4×C83—22no—
101C4×C83—22no—
102C4×C83—82no—
103C4×C83—82no—
104C4×C83#44812yes—
105C4×C83#46112yes—
106Dic83—82no—
107Dic83—161no—
108#10227—831nomaximal, Sylow
109C2×C83—21no—
110C2×C83—21no—
111C2×C83#200912yes—
112C2×C83#201311yescharacteristic
113#3229—832no—
114#3162D8311yescharacteristic
115#1960—831no—
116#1518—832no—
117#1281—831no—
118C83#1022711yescharacteristic, complemented, Sylow
119#533C2×D8312yes—
120C2×C4⋊Q8—831no—
121#501—22no—
122#501—22no—
123#498—1662no—
124#487—1662no—
125#483—1664no—
126#475—1664no—
127#431—832no—
128#427—22no—
129C2×#103—1662no—
130C2×#97C2×D8311yescharacteristic
131#382—831no—
132#328—1664no—
133C22×Q8—1661no—
134C22×C8C22⋊D8312yes—
135C4⋊Q8—832no—
136C4⋊Q8—1662no—
137C4⋊Q8—1661no—
138C4⋊Q8C22⋊D8312yes—
139C4⋊Q8C22⋊D8312yes—
140#125—22no—
141C22⋊Q8—22no—
142C22⋊Q8—22no—
143C4×Q8—22no—
144C4×Q8—22no—
145#117—22no—
146C2×C4⋊C4—1661no—
147C2×C4⋊C4—1662no—
148C2×C42C22×D8311yescharacteristic
149#107—24no—
150#106—22no—
151#106—22no—
152#106—1668no—
153C4⋊C8—1662no—
154#103—3324no—
155#103—1668no—
156C22⋊C8—834no—
157#97—22no—
158C4×C8—1662no—
159#95—1662no—
160C2×Q8—22no—
161C2×Q8—22no—
162C2×Q8—3321no—
163C2×Q8—3322no—
164C2×Q8—3322no—
165C2×Q8—1662no—
166C22×C4—3321no—
167C22×C4—3321no—
168C22×C4D4×D8312yes—
169C22×C4C2×C22⋊D8311yescharacteristic
170C2×C8—22no—
171C2×C8—22no—
172C2×C8—1664no—
173C2×C8#1305057714yes—
174C4⋊C4—22no—
175C4⋊C4—22no—
176C4⋊C4—22no—
177C4⋊C4—22no—
178C4⋊C4—42no—
179C4⋊C4—42no—
180C4⋊C4—3322no—
181C4⋊C4—3322no—
182C4⋊C4—1664no—
183C22⋊C4—42no—
184C42—42no—
185C42D4×D8311yescharacteristic
186C42C2×C22⋊D8312yes—
187C42#1305058911yescharacteristic
188C23#1458178811yescharacteristic
189Q8—44no—
190Q8—82no—
191Q8—3324no—
192Q8—6642no—
193C2×C4—42no—
194C2×C4—42no—
195C2×C4—42no—
196C2×C4—3322no—
197C2×C4—6642no—
198C2×C4—6641no—
199C2×C4—6641no—
200C2×C4—6641no—
201C2×C4#1458176012yes—
202C2×C4#1458176111yescharacteristic
203C2×C4#1458176311yescharacteristic
204C2×C4#1458176412yes—
205C2×C4C2×#1305057712yes—
206C2×C4#1458182312yes—
207C8—24no—
208C8—3324no—
209C22—22no—
210C22#1912760911yescharacteristic
211C22#1912807511yescharacteristic
212C22#1912809311yescharacteristic
213C4—22no—
214C4—22no—
215C4—82no—
216C4—82no—
217C4—13281no—
218C4—6642no—
219C4#1912784012yes—
220C4#1912790312yes—
221C2—21no—
222C2—21no—
223C2#2490852012yes—
224C2#2490854611yescharacteristic
subgroupG/H
centerC22#19127609
commutator, cosocleC2×C42×C83C23
FrattiniC2×C42C22×D83
FittingC83×#3162C2
socleC22×C83#392
prime radicalC23×C83#127
hypercenter#3162D83
hypocenterC83#10227
LCSG ▷ C2×C42×C83 ▷ C22×C83 ▷ C83
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3162

Complements

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

NH ≅ G/Ntype
118. C83#10227semidirect

Maximal subgroups

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

subgroupindex
#249186042
#249082832
#249060272
#249053082
C83×#31622
#1022783