Finite Group Databasebeta

← #24912674

Subgroups — #24912674

Order 10624.

468 conjugacy classes of subgroups; only the 151 normal subgroups are shown.

normal subgroups only

This group has 468 conjugacy classes of subgroups — too many to draw. Only its 151 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×#14581757C211yesmaximal, characteristic
3#19127641C211yesmaximal, characteristic
4#19127640C211yesmaximal, characteristic
5#19127639C211yesmaximal, characteristic
6#19127605C212yesmaximal
7#19127605C212yesmaximal
8#19127605C212yesmaximal
9#19127565C212yesmaximal
10#19127552C211yesmaximal, characteristic
11#400×C83C211yesmaximal, characteristic
12C22×Dic166C2212yes—
13C22×Dic166C2211yescharacteristic
14#14581791—24no—
15#14581757—24no—
16C2×C4⋊Dic83C2211yescharacteristic
17C2×Dic83⋊C4C2212yes—
18C2×Dic83⋊C4C2211yescharacteristic
19C2×Dic83⋊C4C2212yes—
20C2×Dic83⋊C4C2211yescharacteristic
21C2×C4×Dic83C2212yes—
22C2×C4×Dic83C2211yescharacteristic
23C2×C4×Dic83C2211yescharacteristic
24C2×C4×Dic83C2211yescharacteristic
25C83⋊#95C2211yescharacteristic
26C83⋊#95C2212yes—
27C83⋊#95C2212yes—
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—24no—
40C2×Dic166—28no—
41C2×Dic166Q814yescomplemented
42C22×Dic83C2312yes—
43C22×Dic83C2312yes—
44C22×Dic83C2311yescharacteristic
45C22×Dic83C2311yescharacteristic
46C22×Dic83C2311yescharacteristic
47C22×Dic83C2311yescharacteristic
48C4⋊Dic83—22no—
49Dic83⋊C4—22no—
50Dic83⋊C4—24no—
51Dic83⋊C4—22no—
52Dic83⋊C4—24no—
53C4×Dic83—22no—
54C4×Dic83—22no—
55C4×Dic83—24no—
56C4×Dic83D414yes—
57C22×C4×C83C2312yes—
58C22×C4×C83C2312yes—
59C22×C4×C83C2311yescharacteristic
60C22×C4×C83C2311yescharacteristic
61C22×C4×C83C2311yescharacteristic
62C4⋊C4×C83—22no—
63C4⋊C4×C83—22no—
64C23×C83C2411yescharacteristic
65C2×C4×C83—21no—
66C2×C4×C83—21no—
67C2×C4×C83—22no—
68C2×C4×C83—21no—
69C2×C4×C83—22no—
70C2×C4×C83—22no—
71C2×C4×C83—22no—
72C2×C4×C83—24no—
73C2×C4×C83—22no—
74C2×C4×C83—22no—
75C2×C4×C83C2×D412yes—
76C2×C4×C83C2×Q812yes—
77C2×Dic83—21no—
78C2×Dic83—21no—
79C2×Dic83—21no—
80C2×Dic83—22no—
81C2×Dic83—22no—
82C2×Dic83—22no—
83C2×Dic83—24no—
84C2×Dic83—22no—
85C2×Dic83—22no—
86C2×Dic83C2×D412yes—
87C2×Dic83C2×D412yes—
88C2×Dic83C2×Q812yes—
89C2×Dic83C2×Q812yes—
90C2×Dic83#4112yes—
91C2×Dic83#4114yes—
92Dic166—28no—
93Dic166—48no—
94C22×C83C22×D411yescharacteristic
95C22×C83C22×Q811yescharacteristic
96C22×C83C2×#4111yescharacteristic
97C22×C83C2×#4112yes—
98C22×C832−1+412yes—
99C4×C83—22no—
100C4×C83—22no—
101C4×C83—42no—
102C4×C83—41no—
103C4×C83—42no—
104Dic83—22no—
105Dic83—42no—
106Dic83—41no—
107Dic83—42no—
108Dic83C22⋊Q814yes—
109Dic83#12414yes—
110C2×C83C2×C22⋊Q811yescharacteristic
111C2×C83C2×#12411yescharacteristic
112C2×C83#53611yescharacteristic
113C2×C83#55612yes—
114C2×C83#55712yes—
115#2568—831nomaximal, Sylow
116C83#256811yescharacteristic, complemented, Sylow
117C2×C4⋊Q8—831no—
118C2×C4×Q8—831no—
119#400—831no—
120#400—831no—
121#400—831no—
122#400D8311yescharacteristic
123#391—832no—
124#391—832no—
125#391—832no—
126#382—832no—
127C4×C4⋊C4—831no—
128C22×Q8—831no—
129C22×Q8—832no—
130C4⋊Q8—1664no—
131C4×Q8—1664no—
132C2×C4⋊C4—831no—
133C2×C4⋊C4—831no—
134C2×C4⋊C4—832no—
135C2×C4⋊C4—831no—
136C2×C4⋊C4—832no—
137C2×C4⋊C4C2×D8311yescharacteristic
138C2×C4⋊C4C2×D8311yescharacteristic
139C2×C42—831no—
140C2×C42—831no—
141C2×C42—831no—
142C2×C42—832no—
143#95—831no—
144#95—832no—
145#95—832no—
146#95—832no—
147#95—832no—
148#95—832no—
149#95—832no—
150#95C2×D8311yescharacteristic
151#95C2×D8312yes—
152#95C2×D8312yes—
153C2×Q8—834no—
154C2×Q8—1664no—
155C2×Q8—1668no—
156C2×Q8—1662no—
157C2×Q8—1662no—
158C22×C4—831no—
159C22×C4—831no—
160C22×C4—831no—
161C22×C4—832no—
162C22×C4—831no—
163C22×C4—832no—
164C22×C4C22×D8312yes—
165C22×C4C22×D8311yescharacteristic
166C22×C4C22×D8312yes—
167C22×C4C22×D8311yescharacteristic
168C22×C4C22×D8311yescharacteristic
169C4⋊C4—22no—
170C4⋊C4—22no—
171C4⋊C4—1662no—
172C4⋊C4—1664no—
173C4⋊C4—1664no—
174C4⋊C4—1662no—
175C4⋊C4—1662no—
176C42—834no—
177C42—1662no—
178C42—1662no—
179C42—1664no—
180C23C23×D8311yescharacteristic
181Q8—3328no—
182Q8—1668no—
183C2×C4—21no—
184C2×C4—21no—
185C2×C4—22no—
186C2×C4—21no—
187C2×C4—22no—
188C2×C4—22no—
189C2×C4—22no—
190C2×C4—24no—
191C2×C4—22no—
192C2×C4—22no—
193C2×C4—832no—
194C2×C4—832no—
195C2×C4—832no—
196C2×C4—832no—
197C2×C4—834no—
198C2×C4—832no—
199C2×C4—1661no—
200C2×C4—1662no—
201C2×C4—1662no—
202C2×C4—1662no—
203C2×C4—1664no—
204C2×C4—1662no—
205C2×C4—1662no—
206C2×C4—1661no—
207C2×C4—1661no—
208C2×C4D4×D8312yes—
209C2×C4Q8×D8312yes—
210C22C2×D4×D8311yescharacteristic
211C22C2×Q8×D8311yescharacteristic
212C22#41×D8311yescharacteristic
213C22#41×D8312yes—
214C22#1458183912yes—
215C4—22no—
216C4—22no—
217C4—42no—
218C4—42no—
219C4—41no—
220C4—3322no—
221C4—3322no—
222C4—3321no—
223C4—834no—
224C4—834no—
225C4—1662no—
226C2C22⋊Q8×D8311yescharacteristic
227C2#124×D8311yescharacteristic
228C2#1912827311yescharacteristic
229C2#1912841812yes—
230C2#1912842812yes—
subgroupG/H
center, FrattiniC23C23×D83
commutator, socle, prime radical, cosocleC23×C83C24
Fitting#400×C83C2
hypercenter#400D83
hypocenterC83#2568
LCSG ▷ C23×C83 ▷ C83
UCSC1 ◁ C23 ◁ #400

Complements

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

NH ≅ G/Ntype
41. C2×Dic166Q8semidirect
116. C83#2568semidirect

Maximal subgroups

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

subgroupindex
C2×#145817912
C2×#145817572
#191276412
#191276402
#191276392
#191276052
#191275652
#191275522
#400×C832
#256883