Finite Group Databasebeta

← #24913338

Subgroups — #24913338

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×#14581782C211yesmaximal, characteristic
2C2×Q8×Dic83C211yesmaximal, characteristic
3#19127643C212yesmaximal
4#19127641C211yesmaximal, characteristic
5#19127640C211yesmaximal, characteristic
6#19127634C212yesmaximal
7#19127620C211yesmaximal, characteristic
8#19127587C212yesmaximal
9#19127583C212yesmaximal
10#19127568C211yesmaximal, characteristic
11#395×C83C211yesmaximal, characteristic
12#14581782—24no—
13Q8×Dic83—24no—
14C2×C4⋊Dic83C2211yescharacteristic
15C2×C4⋊Dic83C2212yes—
16C2×C4⋊Dic83C2211yescharacteristic
17C2×Dic83⋊C4C2211yescharacteristic
18C2×Dic83⋊C4C2212yes—
19C2×Dic83⋊C4C2211yescharacteristic
20C2×Dic83⋊C4C2211yescharacteristic
21C2×Dic83⋊C4C2211yescharacteristic
22C2×C4×Dic83C2212yes—
23C2×C4×Dic83C2211yescharacteristic
24C83⋊#95C2212yes—
25C83⋊#95C2211yescharacteristic
26C83⋊#95C2212yes—
27C83⋊#95C2212yes—
28C83⋊#95C2212yes—
29C83⋊#95C2212yes—
30C83⋊#95C2212yes—
31C83⋊#95C2212yes—
32C22×Q8×C83C2211yescharacteristic
33C2×C4⋊C4×C83C2212yes—
34C2×C4⋊C4×C83C2211yescharacteristic
35#95×C83C2211yescharacteristic
36#95×C83C2212yes—
37C22×Dic83C2312yes—
38C22×Dic83C2312yes—
39C22×Dic83C2311yescharacteristic
40C22×Dic83C2311yescharacteristic
41C22×Dic83C2311yescharacteristic
42C22×Dic83C2311yescharacteristic
43C4⋊Dic83—22no—
44C4⋊Dic83—22no—
45C4⋊Dic83—24no—
46Dic83⋊C4—22no—
47Dic83⋊C4—24no—
48Dic83⋊C4—22no—
49Dic83⋊C4—22no—
50Dic83⋊C4—22no—
51C4×Dic83—24no—
52C4×Dic83D414yes—
53C2×Q8×C83—22no—
54C2×Q8×C83—24no—
55C22×C4×C83C2312yes—
56C22×C4×C83C2311yescharacteristic
57C22×C4×C83C2311yescharacteristic
58C22×C4×C83C2311yescharacteristic
59C22×C4×C83C2312yes—
60C4⋊C4×C83—22no—
61C4⋊C4×C83—24no—
62C23×C83C2411yescharacteristic
63Q8×C83—28no—
64C2×C4×C83—22no—
65C2×C4×C83—22no—
66C2×C4×C83—22no—
67C2×C4×C83—21no—
68C2×C4×C83—21no—
69C2×C4×C83—22no—
70C2×C4×C83—22no—
71C2×C4×C83—21no—
72C2×C4×C83—22no—
73C2×C4×C83—21no—
74C2×C4×C83—22no—
75C2×C4×C83C2×D412yes—
76C2×C4×C83#4114yes—
77C2×Dic83—21no—
78C2×Dic83—21no—
79C2×Dic83—22no—
80C2×Dic83—22no—
81C2×Dic83—21no—
82C2×Dic83—21no—
83C2×Dic83—22no—
84C2×Dic83—22no—
85C2×Dic83—21no—
86C2×Dic83—24no—
87C2×Dic83—21no—
88C2×Dic83—22no—
89C2×Dic83—22no—
90C2×Dic83C2×D412yes—
91C2×Dic83C2×D412yes—
92C22×C83C22×D411yescharacteristic
93C22×C83C2×#4112yes—
94C22×C832−1+411yescharacteristic
95C22×C832−1+411yescharacteristic
96C22×C832−1+412yes—
97C4×C83—22no—
98C4×C83—24no—
99C4×C83—41no—
100C4×C83—41no—
101C4×C83—42no—
102Dic83—22no—
103Dic83—22no—
104Dic83—41no—
105Dic83—41no—
106Dic83—42no—
107Dic83—42no—
108C2×C83#52511yescharacteristic
109C2×C83#53611yescharacteristic
110C2×C83#53611yescharacteristic
111C2×C83#54112yes—
112C2×C83#54112yes—
113#2634—831nomaximal, Sylow
114C83#263411yescharacteristic, complemented, Sylow
115C2×#125—831no—
116C2×C4×Q8—831no—
117#400—831no—
118#400—831no—
119#400—832no—
120#398—832no—
121#395—831no—
122#395D8311yescharacteristic
123#387—832no—
124#387—832no—
125#383—831no—
126C22×Q8C2×D8311yescharacteristic
127#125—1664no—
128C4×Q8—1664no—
129C2×C4⋊C4—832no—
130C2×C4⋊C4—831no—
131C2×C4⋊C4—831no—
132C2×C4⋊C4—831no—
133C2×C4⋊C4—831no—
134C2×C4⋊C4—831no—
135C2×C4⋊C4—831no—
136C2×C4⋊C4—832no—
137C2×C4⋊C4C2×D8311yescharacteristic
138C2×C4⋊C4C2×D8312yes—
139C2×C42—831no—
140C2×C42—832no—
141#95—832no—
142#95—831no—
143#95—832no—
144#95—832no—
145#95—832no—
146#95—832no—
147#95—832no—
148#95—832no—
149#95C2×D8311yescharacteristic
150#95C2×D8312yes—
151C2×Q8—22no—
152C2×Q8—24no—
153C22×C4—831no—
154C22×C4—831no—
155C22×C4—832no—
156C22×C4—832no—
157C22×C4—831no—
158C22×C4—831no—
159C22×C4C22×D8312yes—
160C22×C4C22×D8311yescharacteristic
161C22×C4C22×D8311yescharacteristic
162C22×C4C22×D8311yescharacteristic
163C22×C4C22×D8312yes—
164C4⋊C4—22no—
165C4⋊C4—24no—
166C4⋊C4—1664no—
167C4⋊C4—1662no—
168C4⋊C4—1662no—
169C4⋊C4—1662no—
170C4⋊C4—1662no—
171C4⋊C4—1662no—
172C4⋊C4—1662no—
173C4⋊C4—1664no—
174C42—834no—
175C42—1664no—
176C23C23×D8311yescharacteristic
177Q8—28no—
178C2×C4—22no—
179C2×C4—22no—
180C2×C4—22no—
181C2×C4—21no—
182C2×C4—21no—
183C2×C4—22no—
184C2×C4—22no—
185C2×C4—21no—
186C2×C4—22no—
187C2×C4—21no—
188C2×C4—22no—
189C2×C4—832no—
190C2×C4—832no—
191C2×C4—1662no—
192C2×C4—1661no—
193C2×C4—1661no—
194C2×C4—1662no—
195C2×C4—1662no—
196C2×C4—1661no—
197C2×C4—1661no—
198C2×C4—1664no—
199C2×C4—1662no—
200C2×C4—1662no—
201C2×C4—1661no—
202C2×C4—1661no—
203C2×C4—1662no—
204C2×C4D4×D8312yes—
205C2×C4#1305058914yes—
206C22C2×D4×D8311yescharacteristic
207C22C2×#1305058912yes—
208C22#1458183911yescharacteristic
209C22#1458184011yescharacteristic
210C22#1458184012yes—
211C4—22no—
212C4—24no—
213C4—41no—
214C4—41no—
215C4—42no—
216C4—3321no—
217C4—3321no—
218C4—3322no—
219C4—3322no—
220C4—1662no—
221C4—1662no—
222C2#1912820711yescharacteristic
223C2#1912827411yescharacteristic
224C2#1912827611yescharacteristic
225C2#1912831112yes—
226C2#1912831212yes—
subgroupG/H
center, FrattiniC23C23×D83
commutator, socle, prime radical, cosocleC23×C83C24
Fitting#395×C83C2
hypercenter#395D83
hypocenterC83#2634
LCSG ▷ C23×C83 ▷ C83
UCSC1 ◁ C23 ◁ #395

Complements

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

NH ≅ G/Ntype
114. C83#2634semidirect

Maximal subgroups

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

subgroupindex
C2×#145817822
C2×Q8×Dic832
#191276432
#191276412
#191276402
#191276342
#191276202
#191275872
#191275832
#191275682
#395×C832
#263483