Finite Group Databasebeta

← #24913345

Subgroups — #24913345

Order 10624.

416 conjugacy classes of subgroups; only the 131 normal subgroups are shown.

normal subgroups only

This group has 416 conjugacy classes of subgroups — too many to draw. Only its 131 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×#14581783C211yesmaximal, characteristic
2C2×#14581757C211yesmaximal, characteristic
3#19127643C212yesmaximal
4#19127639C211yesmaximal, characteristic
5#19127633C211yesmaximal, characteristic
6#19127631C211yesmaximal, characteristic
7#19127622C212yesmaximal
8#19127584C212yesmaximal
9#19127583C212yesmaximal
10#19127568C211yesmaximal, characteristic
11#400×C83C211yesmaximal, characteristic
12C22×Dic166C2211yescharacteristic
13#14581783—24no—
14#14581757—24no—
15C2×C4⋊Dic83C2212yes—
16C2×C4⋊Dic83C2212yes—
17C2×C4⋊Dic83C2211yescharacteristic
18C2×Dic83⋊C4C2212yes—
19C2×Dic83⋊C4C2212yes—
20C2×Dic83⋊C4C2211yescharacteristic
21C2×Dic83⋊C4C2211yescharacteristic
22C2×C4×Dic83C2211yescharacteristic
23C2×C4×Dic83C2211yescharacteristic
24C2×C4×Dic83C2211yescharacteristic
25C83⋊#95C2212yes—
26C83⋊#95C2212yes—
27C83⋊#95C2211yescharacteristic
28C83⋊#95C2212yes—
29C83⋊#95C2212yes—
30C83⋊#95C2212yes—
31C83⋊#95C2212yes—
32C2×C4⋊C4×C83C2211yescharacteristic
33C2×C4⋊C4×C83C2211yescharacteristic
34#95×C83C2211yescharacteristic
35#95×C83C2212yes—
36#95×C83C2212yes—
37C2×Dic166—22no—
38C2×Dic166—22no—
39C2×Dic166—22no—
40C22×Dic83C2312yes—
41C22×Dic83C2311yescharacteristic
42C22×Dic83C2312yes—
43C22×Dic83C2311yescharacteristic
44C22×Dic83C2311yescharacteristic
45C22×Dic83C2311yescharacteristic
46C4⋊Dic83—22no—
47C4⋊Dic83—24no—
48C4⋊Dic83—24no—
49Dic83⋊C4—22no—
50Dic83⋊C4—24no—
51Dic83⋊C4—24no—
52Dic83⋊C4—22no—
53C4×Dic83—22no—
54C4×Dic83—22no—
55C4×Dic83D414yes—
56C22×C4×C83C2312yes—
57C22×C4×C83C2311yescharacteristic
58C22×C4×C83C2312yes—
59C22×C4×C83C2311yescharacteristic
60C22×C4×C83C2311yescharacteristic
61C4⋊C4×C83—22no—
62C4⋊C4×C83—22no—
63C23×C83C2411yescharacteristic
64C2×C4×C83—21no—
65C2×C4×C83—21no—
66C2×C4×C83—22no—
67C2×C4×C83—21no—
68C2×C4×C83—22no—
69C2×C4×C83—22no—
70C2×C4×C83—22no—
71C2×C4×C83—24no—
72C2×C4×C83—22no—
73C2×C4×C83—22no—
74C2×C4×C83C2×D412yes—
75C2×C4×C83#4112yes—
76C2×Dic83—21no—
77C2×Dic83—21no—
78C2×Dic83—21no—
79C2×Dic83—21no—
80C2×Dic83—22no—
81C2×Dic83—21no—
82C2×Dic83—22no—
83C2×Dic83—22no—
84C2×Dic83—22no—
85C2×Dic83—22no—
86C2×Dic83—22no—
87C2×Dic83—22no—
88C2×Dic83—22no—
89C2×Dic83C2×D412yes—
90C2×Dic83C2×D412yes—
91C2×Dic83#4112yes—
92Dic166—28no—
93C22×C83C22×D411yescharacteristic
94C22×C83C2×#4111yescharacteristic
95C22×C83C2×#4111yescharacteristic
96C22×C832−1+412yes—
97C22×C832−1+412yes—
98C4×C83—22no—
99C4×C83—22no—
100C4×C83—42no—
101C4×C83—41no—
102C4×C83—42no—
103Dic83—22no—
104Dic83—22no—
105Dic83—22no—
106Dic83—42no—
107Dic83—41no—
108Dic83—42no—
109C2×C83#52511yescharacteristic
110C2×C83#53611yescharacteristic
111C2×C83#53611yescharacteristic
112C2×C83#54112yes—
113C2×C83#54112yes—
114#2634—831nomaximal, Sylow
115C83#263411yescharacteristic, complemented, Sylow
116C2×#125—831no—
117C2×C4×Q8—831no—
118#400—831no—
119#400—832no—
120#400D8311yescharacteristic
121#398—831no—
122#398—831no—
123#395—832no—
124#387—832no—
125#387—832no—
126#383—831no—
127C22×Q8—831no—
128#125—1664no—
129C4×Q8—1664no—
130C2×C4⋊C4—831no—
131C2×C4⋊C4—831no—
132C2×C4⋊C4—832no—
133C2×C4⋊C4—832no—
134C2×C4⋊C4—831no—
135C2×C4⋊C4—832no—
136C2×C4⋊C4—832no—
137C2×C4⋊C4C2×D8311yescharacteristic
138C2×C4⋊C4C2×D8311yescharacteristic
139C2×C42—831no—
140C2×C42—831no—
141C2×C42—831no—
142#95—832no—
143#95—832no—
144#95—831no—
145#95—832no—
146#95—832no—
147#95—832no—
148#95—832no—
149#95C2×D8311yescharacteristic
150#95C2×D8312yes—
151#95C2×D8312yes—
152C2×Q8—1662no—
153C2×Q8—1662no—
154C2×Q8—1662no—
155C22×C4—831no—
156C22×C4—831no—
157C22×C4—831no—
158C22×C4—832no—
159C22×C4—831no—
160C22×C4—832no—
161C22×C4C22×D8312yes—
162C22×C4C22×D8311yescharacteristic
163C22×C4C22×D8312yes—
164C22×C4C22×D8311yescharacteristic
165C22×C4C22×D8311yescharacteristic
166C4⋊C4—22no—
167C4⋊C4—22no—
168C4⋊C4—1662no—
169C4⋊C4—1664no—
170C4⋊C4—1664no—
171C4⋊C4—1664no—
172C4⋊C4—1662no—
173C4⋊C4—1662no—
174C4⋊C4—1664no—
175C42—834no—
176C42—1662no—
177C42—1662no—
178C23C23×D8311yescharacteristic
179Q8—1668no—
180C2×C4—21no—
181C2×C4—21no—
182C2×C4—22no—
183C2×C4—21no—
184C2×C4—22no—
185C2×C4—22no—
186C2×C4—24no—
187C2×C4—22no—
188C2×C4—22no—
189C2×C4—22no—
190C2×C4—832no—
191C2×C4—832no—
192C2×C4—832no—
193C2×C4—1661no—
194C2×C4—1662no—
195C2×C4—1662no—
196C2×C4—1662no—
197C2×C4—1662no—
198C2×C4—1662no—
199C2×C4—1662no—
200C2×C4—1662no—
201C2×C4—1661no—
202C2×C4—1661no—
203C2×C4—1661no—
204C2×C4—1661no—
205C2×C4—1662no—
206C2×C4D4×D8312yes—
207C2×C4#1305059112yes—
208C22C2×D4×D8311yescharacteristic
209C22#41×D8311yescharacteristic
210C22C2×#1305059111yescharacteristic
211C22#1458183912yes—
212C22#1458183912yes—
213C4—22no—
214C4—22no—
215C4—42no—
216C4—41no—
217C4—42no—
218C4—3322no—
219C4—3321no—
220C4—3322no—
221C4—1662no—
222C4—1662no—
223C4—1662no—
224C2#1912821411yescharacteristic
225C2#1912827111yescharacteristic
226C2#1912827311yescharacteristic
227C2#1912830812yes—
228C2#1912831412yes—
subgroupG/H
center, FrattiniC23C23×D83
commutator, socle, prime radical, cosocleC23×C83C24
Fitting#400×C83C2
hypercenter#400D83
hypocenterC83#2634
LCSG ▷ C23×C83 ▷ C83
UCSC1 ◁ C23 ◁ #400

Complements

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

NH ≅ G/Ntype
115. C83#2634semidirect

Maximal subgroups

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

subgroupindex
C2×#145817832
C2×#145817572
#191276432
#191276392
#191276332
#191276312
#191276222
#191275842
#191275832
#191275682
#400×C832
#263483