Finite Group Databasebeta

← #16817977

Subgroups — #16817977

Order 3712.

238 conjugacy classes of subgroups; only the 63 normal subgroups are shown.

normal subgroups only

This group has 238 conjugacy classes of subgroups — too many to draw. Only its 63 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#14271699C211yesmaximal, characteristic
2#14271213C211yesmaximal, characteristic, complemented
3#14271008C211yesmaximal, characteristic, complemented
4#14270900C211yesmaximal, characteristic, complemented
5#14270898C211yesmaximal, characteristic
6#14270896C211yesmaximal, characteristic
7C29×#328C211yesmaximal, characteristic, complemented
8C29×C22⋊Q8C2211yescharacteristic
9#11745309C411yescharacteristic, complemented
10Q8×Dic29C411yescharacteristic, complemented
11#11745292C2211yescharacteristic
12C2×C4×Dic29—21no—
13C2×C4×Dic29C2211yescharacteristic
14#11745260—21no—
15#11745255C411yescharacteristic, complemented
16#11745254—21no—
17#11745252C411yescharacteristic, complemented
18#11745248—21no—
19#11745243—21no—
20C29×C22⋊C8C2211yescharacteristic
21C29×#95C2211yescharacteristic
22#11745179—21no—
23#11745179C2211yescharacteristic
24C22⋊#6597C2211yescharacteristic
25#11745162—21no—
26C8×Dic29—21no—
27C2×Q8×C29C2×C411yescharacteristic
28C22×C4×C29—21no—
29C22×C4×C29C2311yescharacteristic
30C2×C22⋊D29—21no—
31C22×Dic29—21no—
32C22×Dic29D411yescharacteristic
33C22×Dic29D411yescharacteristic
34C2×D116C2×C411yescharacteristic
35C2×C4×D29—21no—
36C2×C8×C29—21no—
37C4⋊C4×C29—21no—
38C4⋊C4×C29C2×C411yescharacteristic
39C22⋊C4×C29—21no—
40#90781—21no—
41#90781—21no—
42#90781—21no—
43#90781—21no—
44C4⋊Dic29—21no—
45C4⋊Dic29—21no—
46C4⋊Dic29C2×C411yescharacteristic
47#90779—21no—
48C4×Dic29—24no—
49C4×Dic29—21no—
50C4×Dic29C2×C411yescharacteristic
51C4×Dic29C2×C411yescharacteristic
52C4×Dic29D411yescharacteristic
53C4×Dic29D411yescharacteristic
54C2×#6597—21no—
55C23×C29C2×D411yescharacteristic
56C22×D29—21no—
57Q8×C29—41no—
58C2×C4×C29—22no—
59C2×C4×C29—21no—
60C2×C4×C29—21no—
61C2×C4×C29—41no—
62C2×C4×C29—41no—
63C2×C4×C29—41no—
64C2×C4×C29C22×C411yescharacteristic
65C2×C4×C29C2×D411yescharacteristic
66C22⋊D29—41no—
67C22⋊D29—41no—
68C2×Dic29—21no—
69C2×Dic29—21no—
70C2×Dic29—22no—
71C2×Dic29—22no—
72C2×Dic29—21no—
73C2×Dic29—41no—
74C2×Dic29—41no—
75C2×Dic29C22⋊C411yescharacteristic
76C2×Dic29C22⋊C411yescharacteristic
77C2×Dic29C22⋊C411yescharacteristic
78C2×Dic29C22⋊C411yescharacteristic
79D116—41no—
80C4×D29—42no—
81C8×C29—41no—
82#6597—41no—
83#1500—291nomaximal, Sylow
84C22×C29—21no—
85C22×C29—21no—
86C22×C29C2×C22⋊C411yescharacteristic
87C22×C29#13511yescharacteristic
88C22×C29#13511yescharacteristic
89C2×D29—41no—
90C2×D29—41no—
91C2×D29—41no—
92C4×C29—21no—
93C4×C29—21no—
94C4×C29—42no—
95C4×C29—41no—
96C4×C29—41no—
97Dic29—21no—
98Dic29—21no—
99Dic29—21no—
100Dic29—42no—
101Dic29—41no—
102Dic29#10412yes—
103#529—291no—
104#431—291no—
105#376—291no—
106#328—291no—
107#328D2911yescharacteristic, complemented
108#327—291no—
109#327—291no—
110C2×C29—21no—
111C2×C29—21no—
112C2×C29#41011yescharacteristic
113C2×C29#41611yescharacteristic
114C2×C29C2×#10411yescharacteristic
115D29—81no—
116#126—581no—
117#125—291no—
118#124—291no—
119#123—581no—
120C22⋊Q8C2×D2911yescharacteristic
121#121—291no—
122C4×Q8—291no—
123C4×D4—291no—
124C4×D4—581no—
125#117—581no—
126C2×C42—291no—
127C2×C42—581no—
128C4⋊C8—581no—
129C22⋊C8—291no—
130C22⋊C8C2×D2911yescharacteristic
131C4×C8—581no—
132#95—291no—
133#95—581no—
134#95C2×D2911yescharacteristic
135C29#150011yescharacteristic, complemented, Sylow
136C2×Q8C4×D2911yescharacteristic
137C2×D4—291no—
138C2×D4—581no—
139C22×C4—21no—
140C22×C4—291no—
141C22×C4—291no—
142C22×C4—581no—
143C22×C4—581no—
144C22×C4C22×D2911yescharacteristic
145C2×C8—21no—
146C2×C8—581no—
147C4⋊C4—21no—
148C4⋊C4—291no—
149C4⋊C4—581no—
150C4⋊C4—581no—
151C4⋊C4—581no—
152C4⋊C4C4×D2911yescharacteristic
153C22⋊C4—21no—
154C22⋊C4—581no—
155C22⋊C4—581no—
156C22⋊C4—581no—
157C22⋊C4—581no—
158C42—291no—
159C42—291no—
160C42—291no—
161C42—291no—
162C42—581no—
163C42—584no—
164C23—581no—
165C23D4×D2911yescharacteristic
166Q8—41no—
167D4—1161no—
168D4—1161no—
169D4—1161no—
170C2×C4—22no—
171C2×C4—21no—
172C2×C4—21no—
173C2×C4—41no—
174C2×C4—41no—
175C2×C4—41no—
176C2×C4—291no—
177C2×C4—291no—
178C2×C4—291no—
179C2×C4—291no—
180C2×C4—582no—
181C2×C4—581no—
182C2×C4—581no—
183C2×C4—582no—
184C2×C4—581no—
185C2×C4—1162no—
186C2×C4—1161no—
187C2×C4—1161no—
188C2×C4C2×C4×D2911yescharacteristic
189C2×C4D4×D2911yescharacteristic
190C8—41no—
191C8—1161no—
192C22—21no—
193C22—21no—
194C22—1161no—
195C22—1161no—
196C22—1161no—
197C22C22⋊C4×D2911yescharacteristic
198C22#1174527811yescharacteristic
199C22#1174528111yescharacteristic
200C4—21no—
201C4—21no—
202C4—42no—
203C4—41no—
204C4—41no—
205C4—292no—
206C4—581no—
207C4—581no—
208C4—581no—
209C4—1162no—
210C4—1161no—
211C2—21no—
212C2—21no—
213C2—2321no—
214C2#1427113511yescharacteristic
215C2#1427115811yescharacteristic
216C2#104×D2911yescharacteristic
subgroupG/H
centerC22C22⋊C4×D29
commutatorC2×C4×C29C22×C4
FrattiniC22×C4C22×D29
FittingC29×#328C2
socleC22×C29C2×C22⋊C4
prime radical#11745292C22
cosocleC22×C4×C29C23
hypercenter#328D29
hypocenterC29#1500
LCSG ▷ C2×C4×C29 ▷ C22×C29 ▷ C29
UCSC1 ◁ C22 ◁ C22×C4 ◁ #328

Complements

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

NH ≅ G/Ntype
2. #14271213C2semidirect
3. #14271008C2semidirect
4. #14270900C2semidirect
7. C29×#328C2semidirect
9. #11745309C4semidirect
10. Q8×Dic29C4semidirect
15. #11745255C4semidirect
17. #11745252C4semidirect
107. #328D29semidirect
135. C29#1500semidirect

Maximal subgroups

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

subgroupindex
#142716992
#142712132
#142710082
#142709002
#142708982
#142708962
C29×#3282
#150029