Finite Group Databasebeta

← #16818068

Subgroups — #16818068

Order 3712.

218 conjugacy classes of subgroups; only the 61 normal subgroups are shown.

normal subgroups only

This group has 218 conjugacy classes of subgroups — too many to draw. Only its 61 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#14271030C211yesmaximal, 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×Dic29C2211yescharacteristic
13#11745260—21no—
14#11745255C411yescharacteristic, complemented
15#11745254—21no—
16#11745252C411yescharacteristic, complemented
17#11745248—21no—
18#11745243—21no—
19C29×C22⋊C8C2211yescharacteristic
20C29×#95C2211yescharacteristic
21#11745179—21no—
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—21no—
49C4×Dic29C2×C411yescharacteristic
50C4×Dic29C2×C411yescharacteristic
51C4×Dic29D411yescharacteristic
52C4×Dic29D411yescharacteristic
53C2×#6597—21no—
54C23×C29C2×D411yescharacteristic
55C22×D29—21no—
56Q8×C29—41no—
57C2×C4×C29—21no—
58C2×C4×C29—21no—
59C2×C4×C29—41no—
60C2×C4×C29—41no—
61C2×C4×C29—41no—
62C2×C4×C29—41no—
63C2×C4×C29C22×C411yescharacteristic
64C2×C4×C29C2×D411yescharacteristic
65C22⋊D29—41no—
66C22⋊D29—41no—
67C2×Dic29—21no—
68C2×Dic29—21no—
69C2×Dic29—21no—
70C2×Dic29—41no—
71C2×Dic29—41no—
72C2×Dic29—41no—
73C2×Dic29—41no—
74C2×Dic29C22⋊C411yescharacteristic
75C2×Dic29C22⋊C411yescharacteristic
76C2×Dic29C22⋊C411yescharacteristic
77C2×Dic29C22⋊C411yescharacteristic
78D116—41no—
79C4×D29—42no—
80C8×C29—41no—
81#6597—41no—
82#1521—291nomaximal, Sylow
83C22×C29—21no—
84C22×C29—21no—
85C22×C29C2×C22⋊C411yescharacteristic
86C22×C29#13511yescharacteristic
87C22×C29#13511yescharacteristic
88C2×D29—41no—
89C2×D29—41no—
90C2×D29—41no—
91C4×C29—21no—
92C4×C29—21no—
93C4×C29—41no—
94C4×C29—41no—
95C4×C29—81no—
96Dic29—21no—
97Dic29—21no—
98Dic29—21no—
99Dic29—21no—
100Dic29—41no—
101Dic29—81no—
102#529—291no—
103#431—291no—
104#383—291no—
105#328—291no—
106#328D2911yescharacteristic, complemented
107#327—291no—
108#327—291no—
109C2×C29—21no—
110C2×C29—21no—
111C2×C29#41011yescharacteristic
112C2×C29#41611yescharacteristic
113C2×C29#42111yescharacteristic
114D29—81no—
115#126—581no—
116#125—291no—
117#124—291no—
118#123—581no—
119C22⋊Q8C2×D2911yescharacteristic
120#121—291no—
121C4×Q8—291no—
122C4×D4—291no—
123C4×D4—581no—
124#117—581no—
125C2×C42—291no—
126C4⋊C8—581no—
127C22⋊C8—291no—
128C22⋊C8C2×D2911yescharacteristic
129C4×C8—581no—
130#95—291no—
131#95—581no—
132#95—581no—
133#95C2×D2911yescharacteristic
134C29#152111yescharacteristic, complemented, Sylow
135C2×Q8C4×D2911yescharacteristic
136C2×D4—291no—
137C2×D4—581no—
138C22×C4—21no—
139C22×C4—291no—
140C22×C4—291no—
141C22×C4—581no—
142C22×C4—581no—
143C22×C4C22×D2911yescharacteristic
144C2×C8—21no—
145C2×C8—581no—
146C4⋊C4—21no—
147C4⋊C4—291no—
148C4⋊C4—581no—
149C4⋊C4—581no—
150C4⋊C4—581no—
151C4⋊C4C4×D2911yescharacteristic
152C22⋊C4—21no—
153C22⋊C4—581no—
154C22⋊C4—581no—
155C22⋊C4—581no—
156C22⋊C4—581no—
157C42—291no—
158C42—291no—
159C42—291no—
160C42—291no—
161C42—581no—
162C23—581no—
163C23D4×D2911yescharacteristic
164Q8—41no—
165D4—1161no—
166D4—1161no—
167D4—1161no—
168C2×C4—21no—
169C2×C4—21no—
170C2×C4—41no—
171C2×C4—41no—
172C2×C4—41no—
173C2×C4—41no—
174C2×C4—291no—
175C2×C4—291no—
176C2×C4—291no—
177C2×C4—291no—
178C2×C4—581no—
179C2×C4—581no—
180C2×C4—581no—
181C2×C4—1162no—
182C2×C4—1161no—
183C2×C4—1161no—
184C2×C4—1161no—
185C2×C4—1161no—
186C2×C4C2×C4×D2911yescharacteristic
187C2×C4D4×D2911yescharacteristic
188C8—41no—
189C8—1161no—
190C22—21no—
191C22—21no—
192C22—1161no—
193C22—1161no—
194C22—1161no—
195C22C22⋊C4×D2911yescharacteristic
196C22#1174527811yescharacteristic
197C22#1174528111yescharacteristic
198C4—21no—
199C4—21no—
200C4—41no—
201C4—41no—
202C4—81no—
203C4—581no—
204C4—581no—
205C4—581no—
206C4—581no—
207C4—1161no—
208C4—2321no—
209C2—21no—
210C2—21no—
211C2—2321no—
212C2#1427113511yescharacteristic
213C2#1427115811yescharacteristic
214C2#1427117811yescharacteristic
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#1521
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. #14271030C2semidirect
4. #14270900C2semidirect
7. C29×#328C2semidirect
9. #11745309C4semidirect
10. Q8×Dic29C4semidirect
14. #11745255C4semidirect
16. #11745252C4semidirect
106. #328D29semidirect
134. C29#1521semidirect

Maximal subgroups

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

subgroupindex
#142716992
#142712132
#142710302
#142709002
#142708982
#142708962
C29×#3282
#152129