Finite Group Databasebeta

← #16835351

Subgroups — #16835351

Order 3712.

312 conjugacy classes of subgroups; only the 92 normal subgroups are shown.

normal subgroups only

This group has 312 conjugacy classes of subgroups — too many to draw. Only its 92 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×#11745220C211yesmaximal, characteristic, complemented
2C2×C4⋊#6599C211yesmaximal, characteristic, complemented
3C2×#11745219C212yesmaximal
4#14272029C212yesmaximal, complemented
5C2×#11745254C211yesmaximal, characteristic
6C22×C4×D29C2211yescharacteristic
7C22×#6599C2212yes—
8C22×#6599C2212yes—
9C2×C4⋊C4×C29C411yescharacteristic
10C2×#90781C411yescharacteristic
11C2×#90781C411yescharacteristic
12C2×C4⋊Dic29C411yescharacteristic
13C2×C4×Dic29C2211yescharacteristic
14C2×C4×Dic29C2211yescharacteristic
15#11745254—22no—
16#11745254—22no—
17#11745220—22no—
18#11745219—24no—
19C4⋊#6599—22no—
20C23×D29C2×C411yescharacteristic
21C22×C4×C29C2×C411yescharacteristic
22C22×C4×C29C2×C411yescharacteristic
23C22×C4×C29C2×C411yescharacteristic
24C22×Dic29C2×C411yescharacteristic
25C22×Dic29C2×C411yescharacteristic
26C22×Dic29C2311yescharacteristic
27C2×C4×D29—21no—
28C2×C4×D29—21no—
29C2×C4×D29—21no—
30C2×C4×D29—21no—
31C2×C4×D29D412yes—
32C2×C4×D29Q812yes—
33C2×#6599—22no—
34C2×#6599—22no—
35C2×#6599—22no—
36C2×#6599—22no—
37C2×#6599—22no—
38C2×#6599—22no—
39C4⋊C4×C29—22no—
40#90781—22no—
41#90781—22no—
42C4⋊Dic29—22no—
43C4×Dic29—21no—
44C4×Dic29—21no—
45C4×Dic29D412yes—
46C4×Dic29D412yes—
47C23×C29C22×C411yescharacteristic
48C22×D29—21no—
49C22×D29—21no—
50C22×D29—22no—
51C22×D29—22no—
52C22×D29C4⋊C412yes—
53C2×C4×C29—21no—
54C2×C4×C29—21no—
55C2×C4×C29—22no—
56C2×C4×C29—21no—
57C2×C4×C29—22no—
58C2×C4×C29C22⋊C412yes—
59C2×C4×C29C4⋊C412yes—
60C2×Dic29—22no—
61C2×Dic29—21no—
62C2×Dic29—22no—
63C2×Dic29C22⋊C412yes—
64C2×Dic29C2×D411yescharacteristic
65C2×Dic29C2×D411yescharacteristic
66C2×Dic29C2×D411yescharacteristic
67C2×Dic29C2×Q811yescharacteristic
68C2×Dic29#4111yescharacteristic
69C2×Dic29#4111yescharacteristic
70C4×D29—22no—
71C4×D29—22no—
72C4×D29—22no—
73C4×D29—22no—
74#6599—42no—
75#6599—42no—
76#1798—291nomaximal, Sylow
77C22×C29C2×C22⋊C411yescharacteristic
78C22×C29C2×C4⋊C411yescharacteristic
79C22×C29#11711yescharacteristic
80C22×C29#13112yes—
81C22×C29#13112yes—
82C2×D29—22no—
83C2×D29—24no—
84C2×D29—41no—
85C2×D29—41no—
86C2×D29—42no—
87C4×C29—22no—
88C4×C29—22no—
89C4×C29—41no—
90Dic29—22no—
91Dic29—41no—
92Dic29#12111yescharacteristic
93Dic29#12111yescharacteristic
94Dic29C22⋊Q811yescharacteristic
95Dic29C22⋊Q811yescharacteristic
96C2×#117—291no—
97C2×C4⋊C8—291no—
98C2×C4⋊C8—291no—
99C2×C22⋊C8—292no—
100#336—292no—
101C2×C29#38011yescharacteristic
102C2×C29#40811yescharacteristic
103C2×C29#40811yescharacteristic
104C2×C29#42412yes—
105C2×C29#43312yes—
106D29—42no—
107C23×C4—291no—
108C22×C8—292no—
109C22×C8—292no—
110#117—582no—
111#117—582no—
112C2×C4⋊C4—291no—
113C2×C4⋊C4#118111yescharacteristic
114C2×C22⋊C4—291no—
115C2×C22⋊C4—291no—
116C2×C42—291no—
117C2×C42—291no—
118C4⋊C8—582no—
119C4⋊C8—582no—
120C22⋊C8—584no—
121C29#179811yescharacteristic, complemented, Sylow
122C24—291no—
123C22×C4—291no—
124C22×C4—291no—
125C22×C4—292no—
126C22×C4—292no—
127C22×C4—291no—
128C22×C4—581no—
129C22×C4—581no—
130C22×C4—581no—
131C22×C4—581no—
132C22×C4C2×#118111yescharacteristic
133C22×C4C2×#118111yescharacteristic
134C22×C4C2×#118111yescharacteristic
135C2×C8—582no—
136C2×C8—582no—
137C2×C8—582no—
138C2×C8—582no—
139C2×C8—582no—
140C2×C8—582no—
141C4⋊C4—22no—
142C4⋊C4—582no—
143C22⋊C4—582no—
144C22⋊C4—582no—
145C42—292no—
146C42—292no—
147C42—581no—
148C42—581no—
149C23—292no—
150C23—581no—
151C23—582no—
152C23—582no—
153C23—581no—
154C23C22×#118111yescharacteristic
155C2×C4—21no—
156C2×C4—22no—
157C2×C4—21no—
158C2×C4—22no—
159C2×C4—21no—
160C2×C4—291no—
161C2×C4—291no—
162C2×C4—291no—
163C2×C4—291no—
164C2×C4—291no—
165C2×C4—291no—
166C2×C4—292no—
167C2×C4—582no—
168C2×C4—582no—
169C2×C4—582no—
170C2×C4—582no—
171C2×C4—582no—
172C2×C4—582no—
173C2×C4—581no—
174C2×C4C4⋊#118112yes—
175C2×C4C22⋊#118112yes—
176C8—1162no—
177C8—1162no—
178C22—582no—
179C22—584no—
180C22—1161no—
181C22—1161no—
182C22—1162no—
183C22C2×C4⋊#118111yescharacteristic
184C22#1174534511yescharacteristic
185C22#1174534612yes—
186C22#1174534812yes—
187C22C2×C22⋊#118111yescharacteristic
188C4—22no—
189C4—22no—
190C4—41no—
191C4—291no—
192C4—291no—
193C4—291no—
194C4—291no—
195C4—582no—
196C4—1161no—
197C2—1162no—
198C2#1427210511yescharacteristic
199C2#1427213611yescharacteristic
200C2#1427213811yescharacteristic
201C2#1427217012yes—
202C2#1427218812yes—
subgroupG/H
center, FrattiniC23C22×#1181
commutator, socleC23×C29C22×C4
FittingC2×C4⋊C4×C29C4
prime radicalC23×D29C2×C4
cosocleC22×Dic29C23
hypercenterC2×C4⋊C4#1181
hypocenterC29#1798
LCSG ▷ C23×C29 ▷ C29
UCSC1 ◁ C23 ◁ C2×C4⋊C4

Complements

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

NH ≅ G/Ntype
1. C2×#11745220C2semidirect
2. C2×C4⋊#6599C2semidirect
4. #14272029C2semidirect
121. C29#1798semidirect

Maximal subgroups

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

subgroupindex
C2×#117452202
C2×C4⋊#65992
C2×#117452192
#142720292
C2×#117452542
#179829