Finite Group Databasebeta

← #16835755

Subgroups — #16835755

Order 3712.

234 conjugacy classes of subgroups; only the 52 normal subgroups are shown.

normal subgroups only

This group has 234 conjugacy classes of subgroups — too many to draw. Only its 52 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#14272150C211yesmaximal, characteristic
2#14272143C211yesmaximal, characteristic
3#14272066C212yesmaximal, complemented
4#14272065C212yesmaximal, complemented
5#14271735C211yesmaximal, characteristic
6C2×#90807C2211yescharacteristic
7C22×Dic58C411yescharacteristic, complemented
8C2×#90800—21no—
9#11745345—21no—
10C29×#123C411yescharacteristic, complemented
11#11745297C411yescharacteristic, complemented
12#11745291C2211yescharacteristic
13#11745258—21no—
14#11745250—21no—
15#11745248C2211yescharacteristic
16#11745247—21no—
17#11745240—21no—
18#11745239C411yescharacteristic, complemented
19#11745229C2212yes—
20#11745227—21no—
21#11745227C2212yes—
22#11745221—21no—
23C2×D4×C29C2×C411yescharacteristic
24C22×C4×C29C2×C411yescharacteristic
25C2×C22⋊D29D411yescharacteristic
26C2×C22⋊D29C2311yescharacteristic
27C22×Dic29C2×C411yescharacteristic
28C22×Dic29C2×C411yescharacteristic
29C22×Dic29D411yescharacteristic
30#90807—41no—
31#90807—41no—
32C2×C4×D29D411yescharacteristic
33C2×Dic58—21no—
34C2×Dic58—21no—
35C2×Dic58—41no—
36C2×Dic58—41no—
37C2×Dic58D411yescharacteristic
38C22⋊#1181—22no—
39#90800—22no—
40#90800—41no—
41C2×#6599—41no—
42C4⋊#1181—41no—
43C4×#1181—41no—
44C4⋊C4×C29—21no—
45C22⋊C4×C29—21no—
46C22⋊C4×C29C2×C411yescharacteristic
47C22⋊Dic29—21no—
48C22⋊Dic29C2×C411yescharacteristic
49#90781—21no—
50#90781—21no—
51C4⋊Dic29—21no—
52#90779—21no—
53#90779—21no—
54#90779—21no—
55C4×Dic29—21no—
56C23×C29C22⋊C411yescharacteristic
57C23×C29C22×C411yescharacteristic
58C22×D29C2×D411yescharacteristic
59C2×#1181—42no—
60D4×C29—41no—
61C2×C4×C29—21no—
62C2×C4×C29—21no—
63C2×C4×C29—41no—
64C2×C4×C29C22⋊C411yescharacteristic
65C22⋊D29—41no—
66C22⋊D29—41no—
67C2×Dic29—21no—
68C2×Dic29—21no—
69C2×Dic29—21no—
70C2×Dic29—21no—
71C2×Dic29—21no—
72C2×Dic29—21no—
73C2×Dic29—41no—
74C2×Dic29C22⋊C411yescharacteristic
75C2×Dic29C22⋊C411yescharacteristic
76C2×Dic29C2×D411yescharacteristic
77C4×D29—21no—
78C4×D29—21no—
79Dic58—41no—
80Dic58—42no—
81Dic58—41no—
82Dic58—41no—
83#6599—42no—
84#2123—291nomaximal, Sylow
85C22×C29—21no—
86C22×C29—21no—
87C22×C29—41no—
88C22×C29—41no—
89C22×C29C2×C22⋊C411yescharacteristic
90C2×D29—21no—
91C2×D29—41no—
92#1181—82no—
93C4×C29—21no—
94C4×C29—41no—
95C4×C29—41no—
96Dic29—21no—
97Dic29—21no—
98Dic29—41no—
99Dic29—41no—
100Dic29#9911yescharacteristic
101Dic29#9911yescharacteristic
102#536—291no—
103#413—291no—
104#410—291no—
105#352—292no—
106#352—292no—
107C2×C29—21no—
108C2×C29—41no—
109C2×C29—41no—
110C2×C29C2×#9911yescharacteristic
111D29—41no—
112C2×#41—291no—
113C22×Q8—291no—
114C2×M16—581no—
115C4⋊Q8—581no—
116#124—581no—
117#123—291no—
118#123—291no—
119#123—291no—
120#123#118111yescharacteristic, complemented
121C22⋊Q8—581no—
122C22⋊Q8—581no—
123#117—291no—
124#117—581no—
125#101—581no—
126#100—292no—
127#99—292no—
128#99—581no—
129C29#212311yescharacteristic, complemented, Sylow
130#41—1161no—
131#41—1161no—
132C2×Q8—291no—
133C2×Q8—581no—
134C2×Q8—581no—
135C2×Q8—1161no—
136C2×Q8—1161no—
137C2×D4—291no—
138C2×D4—291no—
139C2×D4C2×#118111yescharacteristic
140C22×C4—291no—
141C22×C4—291no—
142C22×C4—291no—
143C22×C4—291no—
144C22×C4C2×#118111yescharacteristic
145M16—582no—
146M16—1161no—
147C2×C8—1161no—
148C4⋊C4—21no—
149C4⋊C4—581no—
150C4⋊C4—581no—
151C4⋊C4—581no—
152C4⋊C4—581no—
153C4⋊C4—1161no—
154C22⋊C4—21no—
155C22⋊C4—291no—
156C22⋊C4—581no—
157C22⋊C4—581no—
158C22⋊C4—581no—
159C22⋊C4—582no—
160C22⋊C4C2×#118111yescharacteristic
161C42—581no—
162C42—1161no—
163C23—291no—
164C23C22⋊#118111yescharacteristic
165C23C22×#118111yescharacteristic
166Q8—1161no—
167Q8—1161no—
168Q8—1161no—
169Q8—1162no—
170D4—41no—
171D4—1161no—
172D4—1161no—
173C2×C4—21no—
174C2×C4—21no—
175C2×C4—41no—
176C2×C4—291no—
177C2×C4—291no—
178C2×C4—291no—
179C2×C4—581no—
180C2×C4—581no—
181C2×C4—581no—
182C2×C4—581no—
183C2×C4—581no—
184C2×C4—581no—
185C2×C4—581no—
186C2×C4—581no—
187C2×C4—1161no—
188C2×C4—1162no—
189C2×C4C22⋊#118111yescharacteristic
190C8—1162no—
191C22—21no—
192C22—21no—
193C22—41no—
194C22—41no—
195C22—581no—
196C22—1161no—
197C22C2×C22⋊#118111yescharacteristic
198C4—21no—
199C4—41no—
200C4—41no—
201C4—291no—
202C4—291no—
203C4—581no—
204C4—581no—
205C4—1161no—
206C4—1161no—
207C4—2322no—
208C2—21no—
209C2—41no—
210C2—41no—
211C2—1161no—
212C2D29⋊#9911yescharacteristic
subgroupG/H
centerC2D29⋊#99
commutatorC23×C29C22×C4
FrattiniC23C22×#1181
FittingC29×#123C4
socleC2×C29C2×#99
prime radicalC2×#90807C22
cosocleC2×C22⋊D29C23
hypercenter#123#1181
hypocenterC29#2123
LCSG ▷ C23×C29 ▷ C22×C29 ▷ C2×C29 ▷ C29
UCSC1 ◁ C2 ◁ C22 ◁ C2×D4 ◁ #123

Complements

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

NH ≅ G/Ntype
3. #14272066C2semidirect
4. #14272065C2semidirect
7. C22×Dic58C4semidirect
10. C29×#123C4semidirect
11. #11745297C4semidirect
18. #11745239C4semidirect
120. #123#1181semidirect
129. C29#2123semidirect

Maximal subgroups

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

subgroupindex
#142721502
#142721432
#142720662
#142720652
#142717352
#212329