Finite Group Databasebeta

← #16835654

Subgroups — #16835654

Order 3712.

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

normal subgroups only

This group has 276 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
1D29⋊#108C211yesmaximal, characteristic
2#14272156C212yesmaximal
3D29⋊#101C212yesmaximal
4#14272126C211yesmaximal, characteristic
5C2×Q16×D29C211yesmaximal, characteristic
6C2×Q8×D29C2212yes—
7#11745345C2211yescharacteristic
8D29⋊M16C2212yes—
9D29⋊M16C2211yescharacteristic
10C2×Q16×C29C411yescharacteristic, complemented
11C2×#90785C412yescomplemented
12Q16×D29—21no—
13Q16×D29—21no—
14Q16×D29—21no—
15Q16×D29—21no—
16C2×Dic116C411yescharacteristic, complemented
17C2×C8×D29C2211yescharacteristic
18#11745225—24no—
19#11745221—24no—
20#11745212—21no—
21#11745211—21no—
22#11745208—21no—
23C8×#1181—21no—
24C2×Q8×C29C2×C412yes—
25Q8×D29—22no—
26Q8×D29—22no—
27Q8×D29—22no—
28Q8×D29—22no—
29C2×C4×D29—22no—
30C2×C4×D29C2311yescharacteristic
31C2×Dic58—22no—
32C2×Dic58C2×C412yes—
33C22⋊#1181—21no—
34#90800—22no—
35#90800D412yes—
36C4⋊#1181D412yes—
37C4×#1181—21no—
38#90796—21no—
39#90796—22no—
40D29⋊C8—21no—
41D29⋊C8—22no—
42Q16×C29—21no—
43Q16×C29—21no—
44C2×C8×C29C2×C411yescharacteristic
45#90785—22no—
46#90785—22no—
47C2×#6597C2×C411yescharacteristic
48Dic116—21no—
49Dic116—21no—
50C8×D29D411yescharacteristic
51C8×D29D411yescharacteristic
52C8×D29D411yescharacteristic
53C8×D29D411yescharacteristic
54C22×D29#4111yescharacteristic
55C2×#1181—22no—
56Q8×C29—22no—
57Q8×C29—22no—
58C2×C4×C29—22no—
59C2×C4×C29C22×C411yescharacteristic
60C2×Dic29—22no—
61C2×Dic29C2×D411yescharacteristic
62C4×D29—42no—
63C4×D29—42no—
64C4×D29C2×D411yescharacteristic
65C4×D29C2×D411yescharacteristic
66C4×D29C2×D411yescharacteristic
67C4×D29#4111yescharacteristic
68Dic58—22no—
69Dic58—22no—
70Dic58—42no—
71Dic58—42no—
72#6599—22no—
73#6599—42no—
74C8×C29C22⋊C411yescharacteristic
75C8×C29C22⋊C411yescharacteristic
76#6597C22⋊C411yescharacteristic
77#6597C22⋊C411yescharacteristic
78#1979—291nomaximal, Sylow
79C22×C29C4×D411yescharacteristic
80C2×D29—22no—
81C2×D29#12111yescharacteristic
82C2×D29#12411yescharacteristic
83#1181—42no—
84C4×C29—42no—
85C4×C29C2×C22⋊C411yescharacteristic
86C4×C29C4×D411yescharacteristic
87Dic29—42no—
88Dic29#12111yescharacteristic
89Dic29#12711yescharacteristic
90C22×Q16—291no—
91C2×#108—291no—
92#419—292no—
93C2×#101—292no—
94#405—291no—
95C2×C29—21no—
96C2×C29#39011yescharacteristic
97D29—21no—
98D29#47312yes—
99C22×Q8—292no—
100C2×Q16—292no—
101C2×Q16—291no—
102C2×Q16—581no—
103C2×Q16—581no—
104C2×Q16—581no—
105C2×Q16—581no—
106C2×Q16#118111yescharacteristic, complemented
107C2×M16—291no—
108C2×M16—292no—
109C22×C8—291no—
110#117—291no—
111#108—581no—
112#108—581no—
113#103—584no—
114#101—584no—
115#97—581no—
116C4×C8—581no—
117C29#197911yescharacteristic, complemented, Sylow
118C2×Q8—292no—
119C2×Q8—582no—
120C2×Q8—582no—
121C2×Q8—582no—
122C2×Q8—582no—
123C2×Q8—582no—
124C2×Q8C2×#118112yes—
125C22×C4—291no—
126C22×C4—582no—
127Q16—21no—
128Q16—21no—
129Q16—582no—
130Q16—582no—
131Q16—581no—
132Q16—581no—
133M16—292no—
134M16—581no—
135M16—582no—
136M16—582no—
137C2×C8—291no—
138C2×C8—291no—
139C2×C8—291no—
140C2×C8—291no—
141C2×C8—291no—
142C2×C8—581no—
143C2×C8—582no—
144C2×C8C2×#118111yescharacteristic
145C4⋊C4—292no—
146C22⋊C4—581no—
147C42—581no—
148C23—291no—
149Q8—22no—
150Q8—22no—
151Q8—582no—
152Q8—582no—
153Q8—1162no—
154Q8—1162no—
155C2×C4—22no—
156C2×C4—291no—
157C2×C4—291no—
158C2×C4—291no—
159C2×C4—291no—
160C2×C4—291no—
161C2×C4—582no—
162C2×C4—582no—
163C2×C4—1162no—
164C2×C4—1162no—
165C2×C4C22×#118111yescharacteristic
166C8—291no—
167C8—291no—
168C8—582no—
169C8—1162no—
170C8C22⋊#118111yescharacteristic
171C8C22⋊#118111yescharacteristic
172C22—291no—
173C22—291no—
174C22—582no—
175C22D4×#118111yescharacteristic
176C4—42no—
177C4—291no—
178C4—291no—
179C4—1162no—
180C4—1162no—
181C4D4×#118111yescharacteristic
182C4C2×C22⋊#118111yescharacteristic
183C2—21no—
184C2—292no—
185C2—581no—
186C2#1427211511yescharacteristic
subgroupG/H
centerC2#14272115
commutatorC2×C4×C29C22×C4
FrattiniC2×C4C22×#1181
FittingC2×Q16×C29C4
socleC2×C29#390
prime radicalC22×D29#41
cosocleC2×C4×D29C23
hypercenterC2×Q16#1181
hypocenterC29#1979
LCSG ▷ C2×C4×C29 ▷ C2×C29 ▷ C29
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×Q16

Complements

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

NH ≅ G/Ntype
10. C2×Q16×C29C4semidirect
11. C2×#90785C4semidirect
16. C2×Dic116C4semidirect
106. C2×Q16#1181semidirect
117. C29#1979semidirect

Maximal subgroups

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

subgroupindex
D29⋊#1082
#142721562
D29⋊#1012
#142721262
C2×Q16×D292
#197929