Finite Group Databasebeta

← #24915413

Subgroups — #24915413

Order 10624.

368 conjugacy classes of subgroups; only the 133 normal subgroups are shown.

normal subgroups only

This group has 368 conjugacy classes of subgroups — too many to draw. Only its 133 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#19127643C212yesmaximal
2#19127639C212yesmaximal
3#19127621C212yesmaximal
4#19127607C211yesmaximal, characteristic
5#19127599C211yesmaximal, characteristic
6#19127596C212yesmaximal
7#19127587C212yesmaximal
8#19127586C212yesmaximal
9#389×C83C211yesmaximal, characteristic
10C22×Dic166C2211yescharacteristic
11C2×C4⋊Dic83C2211yescharacteristic
12C2×C4⋊Dic83C2211yescharacteristic
13C2×C4⋊Dic83C2211yescharacteristic
14C2×Dic83⋊C4C2212yes—
15C2×Dic83⋊C4C2212yes—
16C2×Dic83⋊C4C2212yes—
17C2×C4×Dic83C2212yes—
18C83⋊#95C2212yes—
19C83⋊#95C2212yes—
20C83⋊#95C2212yes—
21C83⋊#95C2212yes—
22C83⋊#95C2212yes—
23C83⋊#95C2212yes—
24C83⋊#95C2212yes—
25C83⋊#95C2212yes—
26C2×C4⋊C4×C83C2212yes—
27C2×C4⋊C4×C83C2211yescharacteristic
28C2×C4⋊C4×C83C2211yescharacteristic
29C2×C42×C83C2211yescharacteristic
30#95×C83C2212yes—
31C2×Dic166—22no—
32C2×Dic166—41no—
33C2×Dic166—41no—
34C22×Dic83C2312yes—
35C22×Dic83C2312yes—
36C22×Dic83C2312yes—
37C22×Dic83C2312yes—
38C4⋊Dic83—41no—
39C4⋊Dic83—41no—
40C4⋊Dic83Q814yescomplemented
41Dic83⋊C4—24no—
42Dic83⋊C4—42no—
43Dic83⋊C4—42no—
44C4×Dic83—42no—
45C22×C4×C83C2312yes—
46C22×C4×C83C2312yes—
47C22×C4×C83C2311yescharacteristic
48C22×C4×C83C2311yescharacteristic
49C22×C4×C83C2311yescharacteristic
50C4⋊C4×C83—24no—
51C4⋊C4×C83—22no—
52C4⋊C4×C83—41no—
53C42×C83—41no—
54C23×C83C2411yescharacteristic
55C2×C4×C83—21no—
56C2×C4×C83—21no—
57C2×C4×C83—21no—
58C2×C4×C83—21no—
59C2×C4×C83—21no—
60C2×C4×C83—21no—
61C2×C4×C83—22no—
62C2×C4×C83—22no—
63C2×C4×C83—22no—
64C2×C4×C83—22no—
65C2×C4×C83—22no—
66C2×C4×C83—22no—
67C2×C4×C83C2×Q812yes—
68C2×C4×C83#4112yes—
69C2×C4×C83#4112yes—
70C2×Dic83—22no—
71C2×Dic83—22no—
72C2×Dic83—22no—
73C2×Dic83—22no—
74C2×Dic83—22no—
75C2×Dic83—22no—
76C2×Dic83—22no—
77C2×Dic83—22no—
78C2×Dic83—22no—
79C2×Dic83—22no—
80C2×Dic83—22no—
81C2×Dic83C2×Q814yes—
82Dic166—44no—
83C22×C83C22×Q811yescharacteristic
84C22×C83C2×#4111yescharacteristic
85C22×C83C2×#4111yescharacteristic
86C22×C83H(5,𝔽2)11yescharacteristic
87C22×C83H(5,𝔽2)11yescharacteristic
88C22×C832−1+411yescharacteristic
89C22×C832−1+411yescharacteristic
90C4×C83—22no—
91C4×C83—22no—
92C4×C83—22no—
93C4×C83—42no—
94C4×C83—42no—
95Dic83—24no—
96Dic83—42no—
97Dic83—42no—
98Dic83—42no—
99C2×C83#53811yescharacteristic
100C2×C83#53911yescharacteristic
101C2×C83#54411yescharacteristic
102C2×C83#55411yescharacteristic
103C2×C83#55611yescharacteristic
104C2×C83#55711yescharacteristic
105C2×C83#56311yescharacteristic
106#2805—831nomaximal, Sylow
107C83#280511yescharacteristic, complemented, Sylow
108#400—832no—
109#400—832no—
110#395—832no—
111#391—831no—
112#389—832no—
113#389—831no—
114#389D8311yescharacteristic
115#387—832no—
116#387—832no—
117C22×Q8—831no—
118C2×C4⋊C4—831no—
119C2×C4⋊C4—832no—
120C2×C4⋊C4—832no—
121C2×C4⋊C4—831no—
122C2×C4⋊C4—831no—
123C2×C4⋊C4—832no—
124C2×C4⋊C4C2×D8312yes—
125C2×C4⋊C4C2×D8311yescharacteristic
126C2×C4⋊C4C2×D8311yescharacteristic
127C2×C42—832no—
128C2×C42C2×D8311yescharacteristic
129#95—832no—
130#95—832no—
131#95—832no—
132#95—832no—
133#95—832no—
134#95—832no—
135#95—832no—
136#95—832no—
137#95C2×D8312yes—
138C2×Q8—3321no—
139C2×Q8—3321no—
140C2×Q8—1662no—
141C22×C4—832no—
142C22×C4—832no—
143C22×C4—832no—
144C22×C4—832no—
145C22×C4C22×D8312yes—
146C22×C4C22×D8312yes—
147C22×C4C22×D8311yescharacteristic
148C22×C4C22×D8311yescharacteristic
149C22×C4C22×D8311yescharacteristic
150C4⋊C4—24no—
151C4⋊C4—22no—
152C4⋊C4—41no—
153C4⋊C4—3322no—
154C4⋊C4—3322no—
155C4⋊C4—3321no—
156C4⋊C4—3321no—
157C4⋊C4—834no—
158C4⋊C4—1664no—
159C42—41no—
160C42—3322no—
161C23C23×D8311yescharacteristic
162Q8—3324no—
163C2×C4—21no—
164C2×C4—21no—
165C2×C4—21no—
166C2×C4—21no—
167C2×C4—21no—
168C2×C4—21no—
169C2×C4—22no—
170C2×C4—22no—
171C2×C4—22no—
172C2×C4—22no—
173C2×C4—22no—
174C2×C4—22no—
175C2×C4—834no—
176C2×C4—1662no—
177C2×C4—1662no—
178C2×C4—1662no—
179C2×C4—1662no—
180C2×C4—1662no—
181C2×C4—1662no—
182C2×C4—1662no—
183C2×C4—1662no—
184C2×C4—1662no—
185C2×C4—1662no—
186C2×C4—1662no—
187C2×C4Q8×D8312yes—
188C2×C4#1305058912yes—
189C2×C4#1305059012yes—
190C22C2×Q8×D8311yescharacteristic
191C22C2×#1305058911yescharacteristic
192C22C2×#1305059011yescharacteristic
193C22#1458183711yescharacteristic
194C22#1458183811yescharacteristic
195C22#1458183911yescharacteristic
196C22#1458184011yescharacteristic
197C4—22no—
198C4—22no—
199C4—22no—
200C4—42no—
201C4—42no—
202C4—3322no—
203C4—3322no—
204C4—3322no—
205C4—1664no—
206C2#1912828811yescharacteristic
207C2#1912829811yescharacteristic
208C2#1912833011yescharacteristic
209C2#1912841111yescharacteristic
210C2#1912842111yescharacteristic
211C2#1912842611yescharacteristic
212C2#1912845511yescharacteristic
subgroupG/H
center, FrattiniC23C23×D83
commutator, socle, prime radical, cosocleC23×C83C24
Fitting#389×C83C2
hypercenter#389D83
hypocenterC83#2805
LCSG ▷ C23×C83 ▷ C83
UCSC1 ◁ C23 ◁ #389

Complements

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

NH ≅ G/Ntype
40. C4⋊Dic83Q8semidirect
107. C83#2805semidirect

Maximal subgroups

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

subgroupindex
#191276432
#191276392
#191276212
#191276072
#191275992
#191275962
#191275872
#191275862
#389×C832
#280583