Finite Group Databasebeta

← #35317691

Subgroups — #35317691

Order 21248.

310 conjugacy classes of subgroups; only the 67 normal subgroups are shown.

normal subgroups only

This group has 310 conjugacy classes of subgroups — too many to draw. Only its 67 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#24918808C211yesmaximal, characteristic
2#24909666C212yesmaximal
3#24908956C211yesmaximal, characteristic
4#24905476C212yesmaximal
5C83×#1322C211yesmaximal, characteristic
6#19128258—21no—
7#19127997—22no—
8#19127942—21no—
9#19127942C2212yes—
10#19127912—22no—
11C2×#14581726C2211yescharacteristic
12#19127599—21no—
13#19127527—22no—
14#19127506—22no—
15#19127464—21no—
16#19127464C2211yescharacteristic
17C2×C4⋊C8×C83C2211yescharacteristic
18C22⋊C16×C83C2212yes—
19C2×Dic332—21no—
20C2×Dic332D412yes—
21#14581792—21no—
22#14581792—21no—
23#14581784—41no—
24#14581771—22no—
25#14581771—41no—
26C4×Dic166—22no—
27C4×Dic166—41no—
28#14581751—41no—
29C2×C4⋊Dic83—21no—
30C2×C4⋊Dic83—21no—
31C2×Dic83⋊C4—41no—
32#14581726—21no—
33#14581726—22no—
34#14581726D412yes—
35#14581717—22no—
36#14581717—22no—
37C83⋊#95—41no—
38C22×C8×C83D411yescharacteristic
39C22×C8×C83C2311yescharacteristic
40C2×C42×C83D411yescharacteristic
41C2×C16×C83—22no—
42C4⋊C8×C83—22no—
43C2×Dic166—22no—
44C2×Dic166—41no—
45C22×Dic83—41no—
46C22×Dic83—41no—
47Dic332—42no—
48Dic332—81no—
49C4⋊Dic83—22no—
50C4⋊Dic83—22no—
51C4⋊Dic83—41no—
52C4⋊Dic83—41no—
53C4⋊Dic83—41no—
54C4⋊Dic83—41no—
55C4⋊Dic83—41no—
56C4⋊Dic83—41no—
57Dic83⋊C4—42no—
58Dic83⋊C4—42no—
59Dic83⋊C4—82no—
60C22⋊Dic83—42no—
61C4×Dic83—42no—
62C22×C4×C83D811yescharacteristic
63C22×C4×C83D811yescharacteristic
64C22×C4×C83C2×D411yescharacteristic
65C2×C8×C83—21no—
66C2×C8×C83—41no—
67C2×C8×C83—41no—
68C2×C8×C83C2×D412yes—
69C42×C83—21no—
70C42×C83—21no—
71C16×C83—42no—
72C23×C83C2×D811yescharacteristic
73C2×C4×C83—21no—
74C2×C4×C83—21no—
75C2×C4×C83—21no—
76C2×C4×C83—21no—
77C2×C4×C83—21no—
78C2×C4×C83—41no—
79C2×C4×C83Q3212yes—
80C2×C4×C83#12011yescharacteristic
81C2×C4×C83AGL(1,ℤ/8)11yescharacteristic
82C2×Dic83—42no—
83C2×Dic83—42no—
84C2×Dic83—42no—
85C2×Dic83—81no—
86C2×Dic83—81no—
87C2×Dic83—81no—
88C2×Dic83—81no—
89C2×Dic83—81no—
90Dic166—42no—
91Dic166—42no—
92Dic166—82no—
93C8×C83—22no—
94C8×C83—41no—
95C22×C83—21no—
96C22×C83—21no—
97C22×C83#44711yescharacteristic
98C22×C83C2×Q3211yescharacteristic
99C22×C83#51011yescharacteristic
100C4×C83—21no—
101C4×C83—22no—
102C4×C83—41no—
103C4×C83#45611yescharacteristic
104C4×C83#45811yescharacteristic
105Dic83—82no—
106Dic83—82no—
107Dic83—82no—
108Dic83—161no—
109#12292—831nomaximal, Sylow
110C2×C83—21no—
111C2×C83—21no—
112C2×C83#161011yescharacteristic
113C2×C83#218811yescharacteristic
114C2×C83#219011yescharacteristic
115#3249—831no—
116#2236—832no—
117#2087—831no—
118#1348—832no—
119#1322D8311yescharacteristic
120C83#1229211yescharacteristic, complemented, Sylow
121#533—1661no—
122#477—1662no—
123#467—832no—
124#467—1661no—
125#462—1662no—
126C2×#107—831no—
127C2×C4⋊C8C2×D8311yescharacteristic
128#389—1661no—
129#366—1662no—
130#358—1662no—
131C22⋊C16C2×D8312yes—
132#340—831no—
133#340—1661no—
134C2×Q16—832no—
135C2×Q16—1661no—
136C22×C8D33211yescharacteristic
137C22×C8C22×D8311yescharacteristic
138C4⋊Q8—1661no—
139C4⋊Q8—1661no—
140#125—3321no—
141C22⋊Q8—3321no—
142C22⋊Q8—1662no—
143C4×Q8—3321no—
144C4×Q8—1662no—
145#117—3321no—
146C2×C4⋊C4—3321no—
147C2×C4⋊C4—1661no—
148C2×C4⋊C4—1661no—
149C2×C42D33211yescharacteristic
150C2×C16—22no—
151#107—832no—
152#107—1662no—
153#107—1661no—
154C4⋊C8—22no—
155#103—1662no—
156#103—1662no—
157#95—3321no—
158C2×Q8—3321no—
159C2×Q8—1662no—
160C22×C4—3321no—
161C22×C4—3321no—
162C22×C4D66411yescharacteristic
163C22×C4D66411yescharacteristic
164C22×C4C2×D33211yescharacteristic
165Q16—3322no—
166Q16—6641no—
167C2×C8—21no—
168C2×C8—41no—
169C2×C8—41no—
170C2×C8D4×D8312yes—
171C4⋊C4—3321no—
172C4⋊C4—3321no—
173C4⋊C4—3321no—
174C4⋊C4—3321no—
175C4⋊C4—3322no—
176C4⋊C4—3322no—
177C4⋊C4—3321no—
178C4⋊C4—3321no—
179C4⋊C4—6642no—
180C4⋊C4—1662no—
181C4⋊C4—1662no—
182C22⋊C4—3322no—
183C42—21no—
184C42—21no—
185C42—3322no—
186C16—42no—
187C23C2×D66411yescharacteristic
188Q8—3322no—
189Q8—3322no—
190Q8—6642no—
191C2×C4—21no—
192C2×C4—21no—
193C2×C4—21no—
194C2×C4—21no—
195C2×C4—21no—
196C2×C4—41no—
197C2×C4—3322no—
198C2×C4—3322no—
199C2×C4—3322no—
200C2×C4—6641no—
201C2×C4—6641no—
202C2×C4—6641no—
203C2×C4—6641no—
204C2×C4—6641no—
205C2×C4Dic66412yes—
206C2×C4#1458176211yescharacteristic
207C2×C4#1458182011yescharacteristic
208C8—22no—
209C8—41no—
210C22—21no—
211C22—21no—
212C22#1912783711yescharacteristic
213C22C2×Dic66411yescharacteristic
214C22#1912814411yescharacteristic
215C4—22no—
216C4—21no—
217C4—41no—
218C4—13281no—
219C4—6642no—
220C4—6642no—
221C4—6642no—
222C4#1912788611yescharacteristic
223C4#1912789211yescharacteristic
224C2—21no—
225C2—21no—
226C2#2490646811yescharacteristic
227C2#2490939911yescharacteristic
228C2#2490941111yescharacteristic
subgroupG/H
centerC22#19127837
commutator, cosocleC22×C8×C83C23
FrattiniC22×C8C22×D83
FittingC83×#1322C2
socleC22×C83#447
prime radicalC23×C83C2×D8
hypercenter#1322D83
hypocenterC83#12292
LCSG ▷ C22×C8×C83 ▷ C2×C4×C83 ▷ C2×C83 ▷ C83
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4⋊C8 ◁ #1322

Complements

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

NH ≅ G/Ntype
120. C83#12292semidirect

Maximal subgroups

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

subgroupindex
#249188082
#249096662
#249089562
#249054762
C83×#13222
#1229283