Finite Group Databasebeta

← #24909157

Subgroups — #24909157

Order 10624.

230 conjugacy classes of subgroups; only the 65 normal subgroups are shown.

normal subgroups only

This group has 230 conjugacy classes of subgroups — too many to draw. Only its 65 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#19128272C211yesmaximal, characteristic
2#19127685C211yesmaximal, characteristic
3#19127499C214yesmaximal, complemented
4#413×C83C211yesmaximal, characteristic
5C22×Dic166C411yescharacteristic
6C2×#13050574—21no—
7#14581790C2212yes—
8#14581779C412yes—
9#14581773—21no—
10#14581773—21no—
11#14581771—21no—
12#14581771—21no—
13#14581751C411yescharacteristic
14#14581711C2212yes—
15#14581709—21no—
16C2×#41×C83C2211yescharacteristic
17C2×M16×C83—21no—
18#101×C83C2212yes—
19#100×C83—21no—
20C2×Dic166—21no—
21C2×Dic166—41no—
22C2×Dic166—41no—
23C2×Dic166C2×C412yes—
24C22×Dic83—21no—
25#13050574—22no—
26#13050574—41no—
27C2×C83⋊C8—41no—
28C4⋊Dic83—21no—
29Dic83⋊C4—22no—
30Dic83⋊C4—22no—
31C22⋊Dic83—22no—
32C22⋊Dic83—22no—
33C22⋊Dic83—21no—
34C4×Dic83C2×C412yes—
35#41×C83—41no—
36#41×C83—41no—
37C2×Q8×C83C2311yescharacteristic
38C2×D4×C83C2×C411yescharacteristic
39C2×D4×C83D411yescharacteristic
40C2×D4×C83D411yescharacteristic
41C22×C4×C83C2×C411yescharacteristic
42C22×C4×C83D411yescharacteristic
43C22×C4×C83D411yescharacteristic
44M16×C83—22no—
45M16×C83—41no—
46C2×C8×C83—41no—
47C23×C83C22⋊C411yescharacteristic
48C23×C83C22⋊C411yescharacteristic
49C23×C83C22⋊C411yescharacteristic
50Q8×C83—41no—
51D4×C83—41no—
52D4×C83—41no—
53D4×C83—41no—
54C2×C4×C83—21no—
55C2×C4×C83—21no—
56C2×C4×C83—21no—
57C2×C4×C83—21no—
58C2×C4×C83—21no—
59C2×C4×C83—21no—
60C2×C4×C83C22⋊C411yescharacteristic
61C2×C4×C83C22×C411yescharacteristic
62C2×C4×C83C2×D411yescharacteristic
63C2×C4×C83C2×D411yescharacteristic
64C2×Dic83—22no—
65C2×Dic83—22no—
66C2×Dic83—42no—
67Dic166—41no—
68Dic166—41no—
69Dic166—42no—
70C8×C83—42no—
71C83⋊C8—42no—
72C22×C83—21no—
73C22×C83—21no—
74C22×C83—21no—
75C22×C83—41no—
76C22×C83—41no—
77C22×C83—41no—
78C22×C83C2×C22⋊C411yescharacteristic
79C4×C83—21no—
80C4×C83—21no—
81C4×C83—21no—
82C4×C83#9911yescharacteristic
83C4×C83#9911yescharacteristic
84Dic83—42no—
85Dic83—42no—
86C2×C83—21no—
87C2×C83—41no—
88C2×C83—41no—
89C2×C83—41no—
90C2×C83C2×#9911yescharacteristic
91#2135—831nomaximal, Sylow
92C83#213511yescharacteristic, complemented, Sylow
93#536—831no—
94#413—831no—
95#413D8311yescharacteristic
96#356—834no—
97C2×#41C2×D8311yescharacteristic
98C22×Q8—831no—
99C2×M16—21no—
100C2×M16—1661no—
101C4⋊Q8—832no—
102#124—832no—
103#123—1661no—
104#123—1661no—
105C22⋊Q8—1661no—
106C22⋊Q8—1661no—
107#117—831no—
108#101—832no—
109#101C2×D8312yes—
110#100—21no—
111#100—1661no—
112#41—41no—
113#41—41no—
114C2×Q8—3321no—
115C2×Q8—3321no—
116C2×Q8—832no—
117C2×Q8—1661no—
118C2×Q8C22×D8311yescharacteristic
119C2×D4C4×D8311yescharacteristic
120C2×D4D33211yescharacteristic
121C2×D4C22⋊D8311yescharacteristic
122C22×C4—1661no—
123C22×C4C4×D8311yescharacteristic
124C22×C4D33211yescharacteristic
125C22×C4C22⋊D8311yescharacteristic
126M16—22no—
127M16—41no—
128M16—3321no—
129M16—1662no—
130C2×C8—41no—
131C2×C8—3321no—
132C4⋊C4—1661no—
133C4⋊C4—1662no—
134C4⋊C4—1662no—
135C22⋊C4—1661no—
136C22⋊C4—1662no—
137C22⋊C4—1662no—
138C42—832no—
139C23(C2×D83)⋊C411yescharacteristic
140C23(C2×D83)⋊C411yescharacteristic
141C23(C2×D83)⋊C411yescharacteristic
142Q8—41no—
143Q8—3322no—
144Q8—3321no—
145Q8—3321no—
146D4—41no—
147D4—41no—
148D4—41no—
149C2×C4—21no—
150C2×C4—21no—
151C2×C4—21no—
152C2×C4—21no—
153C2×C4—21no—
154C2×C4—21no—
155C2×C4—3322no—
156C2×C4—1662no—
157C2×C4—1662no—
158C2×C4(C2×D83)⋊C411yescharacteristic
159C2×C4C2×C4×D8311yescharacteristic
160C2×C4C2×C22⋊D8311yescharacteristic
161C2×C4C2×D33211yescharacteristic
162C8—42no—
163C8—3322no—
164C22—21no—
165C22—21no—
166C22—21no—
167C22—41no—
168C22—41no—
169C22—41no—
170C22C2×(C2×D83)⋊C411yescharacteristic
171C4—21no—
172C4—21no—
173C4—21no—
174C4—3322no—
175C4—3322no—
176C4#1458170611yescharacteristic
177C4#1458170611yescharacteristic
178C2—21no—
179C2—41no—
180C2—41no—
181C2—41no—
182C2C2×#1458170611yescharacteristic
subgroupG/H
centerC2C2×#14581706
commutatorC2×C4×C83C22×C4
FrattiniC2×Q8C22×D83
Fitting#413×C83C2
socleC2×C83C2×#99
prime radicalC2×#41×C83C22
cosocleC2×Q8×C83C23
hypercenter#413D83
hypocenterC83#2135
LCSG ▷ C2×C4×C83 ▷ C22×C83 ▷ C2×C83 ▷ C83
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×#41 ◁ #413

Complements

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

NH ≅ G/Ntype
3. #19127499C2semidirect
92. C83#2135semidirect

Maximal subgroups

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

subgroupindex
#191282722
#191276852
#191274992
#413×C832
#213583