Finite Group Databasebeta

← #16835498

Subgroups — #16835498

Order 3712.

324 conjugacy classes of subgroups; only the 68 normal subgroups are shown.

normal subgroups only

This group has 324 conjugacy classes of subgroups — too many to draw. Only its 68 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#14272231C211yesmaximal, characteristic
2#14272156C212yesmaximal
3D29⋊#101C211yesmaximal, characteristic
4#14272034C212yesmaximal
5C4⋊Q8×D29C211yesmaximal, characteristic
6C2×Q8×D29C2211yescharacteristic
7C2×Q8×D29C2211yescharacteristic
8Q8×#1181—24no—
9#11745345—22no—
10#11745345C2212yes—
11D29⋊M16C2212yes—
12C29×C4⋊Q8C411yescharacteristic, complemented
13#11745306C411yescharacteristic, complemented
14#11745306C411yescharacteristic, complemented
15C4⋊C4×D29—22no—
16#11745250—22no—
17C42×D29C2211yescharacteristic
18#11745231C411yescharacteristic, complemented
19#11745225—24no—
20#11745221—22no—
21C2×Q8×C29C2×C411yescharacteristic
22C2×Q8×C29C2×C411yescharacteristic
23Q8×D29—22no—
24Q8×D29—22no—
25Q8×D29—22no—
26Q8×D29—22no—
27C2×C4×D29—21no—
28C2×C4×D29—21no—
29C2×C4×D29D412yes—
30C2×C4×D29C2311yescharacteristic
31C2×Dic58—21no—
32C2×Dic58C2×C411yescharacteristic
33C2×Dic58C2×C411yescharacteristic
34C2×Dic58D412yes—
35C22⋊#1181—22no—
36#90800—22no—
37C4⋊#1181—24no—
38C4⋊#1181D414yes—
39C4×#1181—24no—
40C4×#1181—22no—
41#90796—22no—
42D29⋊C8—22no—
43C4⋊C4×C29—22no—
44C42×C29C2×C411yescharacteristic
45C4⋊Dic29—22no—
46#90779—22no—
47#90779—22no—
48C4×Dic29—21no—
49C4×Dic29C2×C411yescharacteristic
50C22×D29C2×D411yescharacteristic
51C2×#1181—24no—
52Q8×C29—22no—
53Q8×C29—22no—
54C2×C4×C29—21no—
55C2×C4×C29—21no—
56C2×C4×C29C22⋊C412yes—
57C2×C4×C29C22×C411yescharacteristic
58C2×Dic29—21no—
59C2×Dic29—21no—
60C2×Dic29C22⋊C412yes—
61C2×Dic29C2×D411yescharacteristic
62C4×D29—24no—
63C4×D29—22no—
64C4×D29—22no—
65C4×D29—41no—
66C4×D29—41no—
67C4×D29C2×D412yes—
68C4×D29#4112yes—
69Dic58—22no—
70Dic58—24no—
71Dic58—22no—
72Dic58—42no—
73#6599—42no—
74#1886—291nomaximal, Sylow
75C22×C29C2×C22⋊C411yescharacteristic
76C2×D29—22no—
77C2×D29#12011yescharacteristic
78C2×D29#12311yescharacteristic
79#1181—44no—
80C4×C29—22no—
81C4×C29—22no—
82C4×C29—41no—
83C4×C29C4×D412yes—
84Dic29—22no—
85Dic29—22no—
86Dic29—41no—
87Dic29#12112yes—
88C2×C4⋊Q8—291no—
89#519—291no—
90#419—292no—
91C2×#101—291no—
92#339—292no—
93C2×C29—21no—
94C2×C29#38611yescharacteristic
95D29—21no—
96D29#45612yes—
97C22×Q8—291no—
98C22×Q8—291no—
99C2×M16—292no—
100C4⋊Q8—291no—
101C4⋊Q8—291no—
102C4⋊Q8—291no—
103C4⋊Q8—582no—
104C4⋊Q8#118111yescharacteristic, complemented
105C4×Q8—584no—
106#117—292no—
107#117—582no—
108C2×C4⋊C4—582no—
109C2×C42—291no—
110#103—584no—
111#101—582no—
112C29#188611yescharacteristic, complemented, Sylow
113C2×Q8—292no—
114C2×Q8—291no—
115C2×Q8—291no—
116C2×Q8—581no—
117C2×Q8—582no—
118C2×Q8—582no—
119C2×Q8—582no—
120C2×Q8—582no—
121C2×Q8C2×#118111yescharacteristic
122C2×Q8C2×#118111yescharacteristic
123C22×C4—291no—
124C22×C4—292no—
125C22×C4—581no—
126C22×C4—581no—
127M16—582no—
128M16—582no—
129C2×C8—582no—
130C4⋊C4—22no—
131C4⋊C4—294no—
132C4⋊C4—582no—
133C4⋊C4—582no—
134C4⋊C4—584no—
135C4⋊C4—582no—
136C22⋊C4—582no—
137C42—291no—
138C42—581no—
139C42—582no—
140C42—584no—
141C42C2×#118111yescharacteristic
142C23—291no—
143Q8—22no—
144Q8—22no—
145Q8—584no—
146Q8—582no—
147Q8—582no—
148Q8—1162no—
149C2×C4—21no—
150C2×C4—21no—
151C2×C4—291no—
152C2×C4—292no—
153C2×C4—292no—
154C2×C4—292no—
155C2×C4—582no—
156C2×C4—582no—
157C2×C4—584no—
158C2×C4—581no—
159C2×C4—584no—
160C2×C4—581no—
161C2×C4—1161no—
162C2×C4—1161no—
163C2×C4C22⋊#118112yes—
164C2×C4C22×#118111yescharacteristic
165C8—1162no—
166C22—291no—
167C22—291no—
168C22—582no—
169C22C2×C22⋊#118111yescharacteristic
170C4—22no—
171C4—22no—
172C4—41no—
173C4—292no—
174C4—582no—
175C4—582no—
176C4—1164no—
177C4—1161no—
178C4D4×#118112yes—
179C2—21no—
180C2—292no—
181C2—581no—
182C2#1427211111yescharacteristic
subgroupG/H
centerC2#14272111
commutatorC2×C4×C29C22×C4
FrattiniC2×C4C22×#1181
FittingC29×C4⋊Q8C4
socleC2×C29#386
prime radicalC22×D29C2×D4
cosocleC2×C4×D29C23
hypercenterC4⋊Q8#1181
hypocenterC29#1886
LCSG ▷ C2×C4×C29 ▷ C2×C29 ▷ C29
UCSC1 ◁ C2 ◁ C2×C4 ◁ C4⋊Q8

Complements

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

NH ≅ G/Ntype
12. C29×C4⋊Q8C4semidirect
13. #11745306C4semidirect
14. #11745306C4semidirect
18. #11745231C4semidirect
104. C4⋊Q8#1181semidirect
112. C29#1886semidirect

Maximal subgroups

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

subgroupindex
#142722312
#142721562
D29⋊#1012
#142720342
C4⋊Q8×D292
#188629