Finite Group Databasebeta

← #24913410

Subgroups — #24913410

Order 10624.

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

normal subgroups only

This group has 416 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
1C2×#14581791C211yesmaximal, characteristic
2C2×#14581782C211yesmaximal, characteristic
3#19127643C212yesmaximal
4#19127642C212yesmaximal
5#19127641C211yesmaximal, characteristic
6#19127640C211yesmaximal, characteristic
7#19127639C211yesmaximal, characteristic
8#19127605C212yesmaximal
9#19127605C212yesmaximal
10#19127546C211yesmaximal, characteristic
11#400×C83C211yesmaximal, characteristic
12C22×Dic166C2212yes—
13#14581791—24no—
14#14581782—24no—
15C2×C4⋊Dic83C2211yescharacteristic
16C2×C4⋊Dic83C2211yescharacteristic
17C2×Dic83⋊C4C2211yescharacteristic
18C2×Dic83⋊C4C2211yescharacteristic
19C2×Dic83⋊C4C2211yescharacteristic
20C2×Dic83⋊C4C2211yescharacteristic
21C2×Dic83⋊C4C2212yes—
22C2×C4×Dic83C2212yes—
23C2×C4×Dic83C2211yescharacteristic
24C83⋊#95C2212yes—
25C83⋊#95C2212yes—
26C83⋊#95C2212yes—
27C83⋊#95C2212yes—
28C83⋊#95C2212yes—
29C83⋊#95C2212yes—
30C83⋊#95C2211yescharacteristic
31C83⋊#95C2212yes—
32C2×C4⋊C4×C83C2211yescharacteristic
33C2×C4⋊C4×C83C2211yescharacteristic
34#95×C83C2212yes—
35#95×C83C2212yes—
36#95×C83C2211yescharacteristic
37C2×Dic166—24no—
38C2×Dic166—28no—
39C22×Dic83C2312yes—
40C22×Dic83C2312yes—
41C22×Dic83C2311yescharacteristic
42C22×Dic83C2311yescharacteristic
43C22×Dic83C2311yescharacteristic
44C22×Dic83C2311yescharacteristic
45C4⋊Dic83—22no—
46C4⋊Dic83—22no—
47Dic83⋊C4—22no—
48Dic83⋊C4—22no—
49Dic83⋊C4—22no—
50Dic83⋊C4—22no—
51Dic83⋊C4—24no—
52C4×Dic83—24no—
53C4×Dic83D414yes—
54C22×C4×C83C2312yes—
55C22×C4×C83C2312yes—
56C22×C4×C83C2311yescharacteristic
57C22×C4×C83C2311yescharacteristic
58C22×C4×C83C2311yescharacteristic
59C4⋊C4×C83—22no—
60C4⋊C4×C83—22no—
61C23×C83C2411yescharacteristic
62C2×C4×C83—22no—
63C2×C4×C83—21no—
64C2×C4×C83—21no—
65C2×C4×C83—22no—
66C2×C4×C83—22no—
67C2×C4×C83—24no—
68C2×C4×C83—21no—
69C2×C4×C83—22no—
70C2×C4×C83—22no—
71C2×C4×C83—22no—
72C2×C4×C83—21no—
73C2×C4×C83C2×D412yes—
74C2×Dic83—21no—
75C2×Dic83—21no—
76C2×Dic83—21no—
77C2×Dic83—21no—
78C2×Dic83—22no—
79C2×Dic83—22no—
80C2×Dic83—24no—
81C2×Dic83—22no—
82C2×Dic83—21no—
83C2×Dic83—22no—
84C2×Dic83—21no—
85C2×Dic83—22no—
86C2×Dic83C2×D412yes—
87C2×Dic83C2×D412yes—
88C2×Dic83#4114yes—
89Dic166—48no—
90C22×C83C22×D411yescharacteristic
91C22×C83C2×#4112yes—
92C22×C832−1+412yes—
93C22×C832−1+411yescharacteristic
94C22×C832−1+411yescharacteristic
95C4×C83—22no—
96C4×C83—42no—
97C4×C83—41no—
98C4×C83—41no—
99C4×C83—42no—
100Dic83—22no—
101Dic83—42no—
102Dic83—41no—
103Dic83—41no—
104Dic83—42no—
105Dic83#12414yes—
106C2×C83C2×#12411yescharacteristic
107C2×C83#53611yescharacteristic
108C2×C83#53611yescharacteristic
109C2×C83#54112yes—
110C2×C83#54112yes—
111#2642—831nomaximal, Sylow
112C83#264211yescharacteristic, complemented, Sylow
113C2×C4⋊Q8—831no—
114C2×#125—831no—
115#400—831no—
116#400—831no—
117#400—831no—
118#400—832no—
119#400—832no—
120#400D8311yescharacteristic
121#391—832no—
122#391—832no—
123#376—831no—
124C22×Q8—832no—
125C4⋊Q8—1664no—
126#125—1664no—
127C2×C4⋊C4—831no—
128C2×C4⋊C4—831no—
129C2×C4⋊C4—831no—
130C2×C4⋊C4—831no—
131C2×C4⋊C4—831no—
132C2×C4⋊C4—832no—
133C2×C4⋊C4—831no—
134C2×C4⋊C4C2×D8311yescharacteristic
135C2×C4⋊C4C2×D8311yescharacteristic
136C2×C42—831no—
137C2×C42—832no—
138#95—832no—
139#95—831no—
140#95—832no—
141#95—832no—
142#95—832no—
143#95—832no—
144#95—832no—
145#95—832no—
146#95C2×D8311yescharacteristic
147#95C2×D8312yes—
148#95C2×D8312yes—
149C2×Q8—1664no—
150C2×Q8—1668no—
151C22×C4—831no—
152C22×C4—831no—
153C22×C4—832no—
154C22×C4—831no—
155C22×C4—831no—
156C22×C4—832no—
157C22×C4C22×D8312yes—
158C22×C4C22×D8311yescharacteristic
159C22×C4C22×D8311yescharacteristic
160C22×C4C22×D8312yes—
161C22×C4C22×D8311yescharacteristic
162C4⋊C4—22no—
163C4⋊C4—22no—
164C4⋊C4—1662no—
165C4⋊C4—1662no—
166C4⋊C4—1662no—
167C4⋊C4—1662no—
168C4⋊C4—1664no—
169C4⋊C4—1662no—
170C4⋊C4—1662no—
171C42—834no—
172C42—1664no—
173C23C23×D8311yescharacteristic
174Q8—3328no—
175C2×C4—22no—
176C2×C4—21no—
177C2×C4—21no—
178C2×C4—22no—
179C2×C4—22no—
180C2×C4—24no—
181C2×C4—22no—
182C2×C4—21no—
183C2×C4—22no—
184C2×C4—22no—
185C2×C4—21no—
186C2×C4—832no—
187C2×C4—834no—
188C2×C4—832no—
189C2×C4—1661no—
190C2×C4—1661no—
191C2×C4—1662no—
192C2×C4—1662no—
193C2×C4—1664no—
194C2×C4—1662no—
195C2×C4—1661no—
196C2×C4—1662no—
197C2×C4—1661no—
198C2×C4—1662no—
199C2×C4—1661no—
200C2×C4—1661no—
201C2×C4D4×D8312yes—
202C22C2×D4×D8311yescharacteristic
203C22#41×D8312yes—
204C22#1458183912yes—
205C22#1458183911yescharacteristic
206C22#1458184011yescharacteristic
207C4—22no—
208C4—42no—
209C4—41no—
210C4—41no—
211C4—42no—
212C4—3322no—
213C4—3321no—
214C4—3321no—
215C4—3322no—
216C4—834no—
217C4—1662no—
218C2#124×D8311yescharacteristic
219C2#1912827311yescharacteristic
220C2#1912827411yescharacteristic
221C2#1912830812yes—
222C2#1912831012yes—
subgroupG/H
center, FrattiniC23C23×D83
commutator, socle, prime radical, cosocleC23×C83C24
Fitting#400×C83C2
hypercenter#400D83
hypocenterC83#2642
LCSG ▷ C23×C83 ▷ C83
UCSC1 ◁ C23 ◁ #400

Complements

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

NH ≅ G/Ntype
112. C83#2642semidirect

Maximal subgroups

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

subgroupindex
C2×#145817912
C2×#145817822
#191276432
#191276422
#191276412
#191276402
#191276392
#191276052
#191275462
#400×C832
#264283