Finite Group Databasebeta

← #24905946

Subgroups — #24905946

Order 10624.

238 conjugacy classes of subgroups; only the 63 normal subgroups are shown.

normal subgroups only

This group has 238 conjugacy classes of subgroups — too many to draw. Only its 63 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#19128232C211yesmaximal, characteristic
2#19127751C211yesmaximal, characteristic, complemented
3#19127546C211yesmaximal, characteristic, complemented
4#19127439C211yesmaximal, characteristic, complemented
5#19127437C211yesmaximal, characteristic, complemented
6#19127435C211yesmaximal, characteristic
7#327×C83C211yesmaximal, characteristic
8#14581785—21no—
9#14581783C411yescharacteristic, complemented
10#14581779C411yescharacteristic, complemented
11#14581773—21no—
12#14581771C2211yescharacteristic
13#14581757C411yescharacteristic, complemented
14D4×Dic83—21no—
15D4×Dic83C411yescharacteristic, complemented
16#14581748—21no—
17C2×C4×Dic83—21no—
18C2×C4×Dic83C2211yescharacteristic
19Dic83⋊C8—21no—
20C22⋊(C83⋊C8)C2211yescharacteristic
21C8×Dic83—21no—
22C83⋊#95—21no—
23C83⋊#95C2211yescharacteristic
24#121×C83C2211yescharacteristic
25C22⋊C8×C83C2211yescharacteristic
26#95×C83C2211yescharacteristic
27C2×Dic166C2×C411yescharacteristic
28C22×Dic83—21no—
29C22×Dic83—21no—
30C22×Dic83D411yescharacteristic
31C22×Dic83D411yescharacteristic
32C2×C83⋊C8—21no—
33C4⋊Dic83—21no—
34C4⋊Dic83C2×C411yescharacteristic
35Dic83⋊C4—21no—
36Dic83⋊C4—21no—
37Dic83⋊C4—21no—
38C22⋊Dic83—21no—
39C22⋊Dic83—21no—
40C22⋊Dic83—21no—
41C22⋊Dic83—21no—
42C4×Dic83—24no—
43C4×Dic83—21no—
44C4×Dic83C2×C411yescharacteristic
45C4×Dic83C2×C411yescharacteristic
46C4×Dic83D411yescharacteristic
47C4×Dic83D411yescharacteristic
48C2×D4×C83—21no—
49C2×D4×C83C2×C411yescharacteristic
50C22×C4×C83—21no—
51C22×C4×C83C2311yescharacteristic
52C2×C8×C83—21no—
53C4⋊C4×C83C2×C411yescharacteristic
54C22⋊C4×C83—21no—
55C23×C83—21no—
56C23×C83C2×D411yescharacteristic
57D4×C83—41no—
58D4×C83—41no—
59D4×C83—41no—
60C2×C4×C83—22no—
61C2×C4×C83—21no—
62C2×C4×C83—41no—
63C2×C4×C83—41no—
64C2×C4×C83—41no—
65C2×C4×C83C22×C411yescharacteristic
66C2×C4×C83C2×D411yescharacteristic
67C2×Dic83—21no—
68C2×Dic83—21no—
69C2×Dic83—22no—
70C2×Dic83—22no—
71C2×Dic83—21no—
72C2×Dic83—21no—
73C2×Dic83—41no—
74C2×Dic83—41no—
75C2×Dic83—42no—
76C2×Dic83C22⋊C411yescharacteristic
77C2×Dic83C22⋊C411yescharacteristic
78C2×Dic83C22⋊C411yescharacteristic
79C2×Dic83C22⋊C411yescharacteristic
80Dic166—41no—
81C8×C83—41no—
82C83⋊C8—41no—
83C22×C83—21no—
84C22×C83—21no—
85C22×C83—41no—
86C22×C83—41no—
87C22×C83—41no—
88C22×C83C2×C22⋊C411yescharacteristic
89C22×C83#13511yescharacteristic
90C22×C83#13511yescharacteristic
91C4×C83—21no—
92C4×C83—21no—
93C4×C83—42no—
94C4×C83—41no—
95Dic83—21no—
96Dic83—21no—
97Dic83—21no—
98Dic83—42no—
99Dic83—41no—
100Dic83—41no—
101Dic83#10412yes—
102C2×C83—21no—
103C2×C83—21no—
104C2×C83—81no—
105C2×C83#41011yescharacteristic
106C2×C83#41611yescharacteristic
107C2×C83C2×#10411yescharacteristic
108#1500—831nomaximal, Sylow
109C83#150011yescharacteristic, complemented, Sylow
110#529—831no—
111#431—831no—
112#376—831no—
113#328—831no—
114#328—831no—
115#327—831no—
116#327D8311yescharacteristic
117#126—1661no—
118#125—831no—
119#124—831no—
120#123—1661no—
121C22⋊Q8—831no—
122#121C2×D8311yescharacteristic
123C4×Q8—831no—
124C4×D4—831no—
125C4×D4—1661no—
126#117—1661no—
127C2×C42—831no—
128C2×C42—1661no—
129C4⋊C8—1661no—
130C22⋊C8—831no—
131C22⋊C8C2×D8311yescharacteristic
132C4×C8—1661no—
133#95—831no—
134#95—1661no—
135#95C2×D8311yescharacteristic
136C2×Q8—831no—
137C2×D4—21no—
138C2×D4C4×D8311yescharacteristic
139C22×C4—21no—
140C22×C4—831no—
141C22×C4—831no—
142C22×C4—1661no—
143C22×C4—1661no—
144C22×C4C22×D8311yescharacteristic
145C2×C8—21no—
146C2×C8—1661no—
147C4⋊C4—831no—
148C4⋊C4—1661no—
149C4⋊C4—1661no—
150C4⋊C4—1661no—
151C4⋊C4—1661no—
152C4⋊C4C4×D8311yescharacteristic
153C22⋊C4—21no—
154C22⋊C4—1661no—
155C22⋊C4—1661no—
156C22⋊C4—1661no—
157C22⋊C4—1661no—
158C42—831no—
159C42—831no—
160C42—831no—
161C42—831no—
162C42—1661no—
163C42—1664no—
164C23—21no—
165C23D4×D8311yescharacteristic
166Q8—3321no—
167D4—41no—
168D4—41no—
169D4—41no—
170C2×C4—22no—
171C2×C4—21no—
172C2×C4—41no—
173C2×C4—41no—
174C2×C4—41no—
175C2×C4—3321no—
176C2×C4—3321no—
177C2×C4—3322no—
178C2×C4—831no—
179C2×C4—831no—
180C2×C4—831no—
181C2×C4—831no—
182C2×C4—1662no—
183C2×C4—1661no—
184C2×C4—1661no—
185C2×C4—1662no—
186C2×C4—1661no—
187C2×C4—1661no—
188C2×C4C2×C4×D8311yescharacteristic
189C2×C4D4×D8311yescharacteristic
190C8—41no—
191C8—3321no—
192C22—21no—
193C22—21no—
194C22—41no—
195C22—41no—
196C22—41no—
197C22C22⋊C4×D8311yescharacteristic
198C22#1458181111yescharacteristic
199C22#1458181311yescharacteristic
200C4—21no—
201C4—21no—
202C4—42no—
203C4—41no—
204C4—3322no—
205C4—3321no—
206C4—3321no—
207C4—832no—
208C4—1661no—
209C4—1661no—
210C4—1661no—
211C2—21no—
212C2—21no—
213C2—81no—
214C2#1912767311yescharacteristic
215C2#1912769411yescharacteristic
216C2#104×D8311yescharacteristic
subgroupG/H
centerC22C22⋊C4×D83
commutatorC2×C4×C83C22×C4
FrattiniC22×C4C22×D83
Fitting#327×C83C2
socleC22×C83C2×C22⋊C4
prime radical#121×C83C22
cosocleC22×C4×C83C23
hypercenter#327D83
hypocenterC83#1500
LCSG ▷ C2×C4×C83 ▷ C22×C83 ▷ C83
UCSC1 ◁ C22 ◁ C22×C4 ◁ #327

Complements

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

NH ≅ G/Ntype
2. #19127751C2semidirect
3. #19127546C2semidirect
4. #19127439C2semidirect
5. #19127437C2semidirect
9. #14581783C4semidirect
10. #14581779C4semidirect
13. #14581757C4semidirect
15. D4×Dic83C4semidirect
109. C83#1500semidirect