Finite Group Databasebeta

← #16817897

Subgroups — #16817897

Order 3712.

212 conjugacy classes of subgroups; only the 65 normal subgroups are shown.

normal subgroups only

This group has 212 conjugacy classes of subgroups — too many to draw. Only its 65 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#14271695C211yesmaximal, characteristic
2#14271215C211yesmaximal, characteristic, complemented
3#14271214C211yesmaximal, characteristic, complemented
4#14270895C211yesmaximal, characteristic, complemented
5#14270893C211yesmaximal, characteristic, complemented
6D4⋊#6597C211yesmaximal, characteristic, complemented
7C29×D4⋊C8C211yesmaximal, characteristic, complemented
8C4×D4×C29C2211yescharacteristic
9#11745300C411yescharacteristic
10#11745298C411yescharacteristic
11C4×C22⋊D29—21no—
12#11745288—21no—
13#11745259C411yescharacteristic
14#11745252C411yescharacteristic
15#11745245—21no—
16#11745241—21no—
17C42×D29C2211yescharacteristic
18C4×Dic58C2211yescharacteristic
19C29×C4⋊C8C2211yescharacteristic
20C4×C8×C29C2211yescharacteristic
21#11745168—21no—
22#11745168—21no—
23#11745162—21no—
24C8×Dic29—21no—
25C4⋊#6597C2211yescharacteristic
26C4×#6597C2211yescharacteristic
27C2×D4×C29C2×C411yescharacteristic
28C22×C4×C29—21no—
29C2×C22⋊D29—21no—
30C2×C4×D29C2×C411yescharacteristic
31C2×C4×D29D411yescharacteristic
32C2×C4×D29D411yescharacteristic
33C2×Dic58C2×C411yescharacteristic
34C2×C8×C29—21no—
35C2×C8×C29—21no—
36C4⋊C4×C29C2×C411yescharacteristic
37C22⋊C4×C29—21no—
38C42×C29C2311yescharacteristic
39C22⋊Dic29—21no—
40C22⋊Dic29—21no—
41C22⋊Dic29—21no—
42#90781—21no—
43C4⋊Dic29—21no—
44C4⋊Dic29—21no—
45C4⋊Dic29C2×C411yescharacteristic
46#90779—21no—
47#90779—21no—
48C4×Dic29—21no—
49C4×Dic29C2×C411yescharacteristic
50C4×Dic29D411yescharacteristic
51C4×Dic29D411yescharacteristic
52C2×#6597—21no—
53C2×#6597—21no—
54C23×C29—21no—
55C22×D29C22⋊C411yescharacteristic
56D4×C29—21no—
57D4×C29—21no—
58C2×C4×C29—21no—
59C2×C4×C29—41no—
60C2×C4×C29—41no—
61C2×C4×C29C22×C411yescharacteristic
62C2×C4×C29C2×D411yescharacteristic
63C2×C4×C29C2×D411yescharacteristic
64C22⋊D29—42no—
65C2×Dic29—21no—
66C2×Dic29—21no—
67C2×Dic29C22⋊C411yescharacteristic
68C2×Dic29C22⋊C411yescharacteristic
69C2×Dic29C22⋊C411yescharacteristic
70C4×D29—21no—
71C4×D29—21no—
72C4×D29—21no—
73C4×D29—21no—
74C4×D29—41no—
75Dic58—21no—
76Dic58—21no—
77C8×C29—41no—
78C8×C29—41no—
79#6597—41no—
80#6597—41no—
81#1482—291nomaximal, Sylow
82C22×C29—41no—
83C22×C29—41no—
84C22×C29—41no—
85C22×C29C2×C22⋊C411yescharacteristic
86C2×D29—21no—
87C2×D29—21no—
88C2×D29—21no—
89C4×C29—21no—
90C4×C29—41no—
91C4×C29#13111yescharacteristic
92C4×C29#13111yescharacteristic
93C4×C29#13511yescharacteristic
94C4×C29#13511yescharacteristic
95Dic29—21no—
96Dic29—21no—
97Dic29—21no—
98Dic29—41no—
99Dic29—41no—
100#529—291no—
101#431—291no—
102#431—291no—
103Q8⋊C8—291no—
104Q8⋊C8—291no—
105D4⋊C8—291no—
106D4⋊C8D2911yescharacteristic, complemented
107C2×C29—81no—
108C2×C29#40811yescharacteristic
109C2×C29#41611yescharacteristic
110C2×C29#42111yescharacteristic
111D29—41no—
112#126—581no—
113#125—291no—
114#124—291no—
115#123—581no—
116C22⋊Q8—291no—
117#121—291no—
118C4×Q8—291no—
119C4×D4—581no—
120C4×D4C2×D2911yescharacteristic
121#117—581no—
122C2×C42—291no—
123C4⋊C8—291no—
124C4⋊C8—581no—
125C4⋊C8C2×D2911yescharacteristic
126C22⋊C8—581no—
127C22⋊C8—581no—
128C4×C8—291no—
129C4×C8—581no—
130C4×C8C2×D2911yescharacteristic
131C29#148211yescharacteristic, complemented, Sylow
132C2×Q8—291no—
133C2×D4—581no—
134C2×D4C4×D2911yescharacteristic
135C22×C4—21no—
136C22×C4—291no—
137C22×C4—291no—
138C22×C4—291no—
139C2×C8—21no—
140C2×C8—21no—
141C2×C8—581no—
142C2×C8—581no—
143C4⋊C4—291no—
144C4⋊C4—581no—
145C4⋊C4—581no—
146C4⋊C4—581no—
147C4⋊C4—581no—
148C4⋊C4C4×D2911yescharacteristic
149C22⋊C4—21no—
150C22⋊C4—581no—
151C22⋊C4—581no—
152C22⋊C4—581no—
153C22⋊C4—581no—
154C42—291no—
155C42—291no—
156C42—291no—
157C42—581no—
158C42C22×D2911yescharacteristic
159C23—21no—
160C23—291no—
161Q8—581no—
162Q8—581no—
163D4—21no—
164D4—21no—
165D4—1162no—
166C2×C4—21no—
167C2×C4—41no—
168C2×C4—41no—
169C2×C4—291no—
170C2×C4—291no—
171C2×C4—291no—
172C2×C4—581no—
173C2×C4—581no—
174C2×C4—581no—
175C2×C4—581no—
176C2×C4—581no—
177C2×C4—581no—
178C2×C4—1161no—
179C2×C4C2×C4×D2911yescharacteristic
180C2×C4D4×D2911yescharacteristic
181C2×C4D4×D2911yescharacteristic
182C8—41no—
183C8—41no—
184C8—1161no—
185C8—1161no—
186C22—41no—
187C22—41no—
188C22—41no—
189C22—581no—
190C22—581no—
191C22—581no—
192C22C22⋊C4×D2911yescharacteristic
193C4—21no—
194C4—41no—
195C4—581no—
196C4—581no—
197C4—581no—
198C4—1161no—
199C4—1161no—
200C4#1174526311yescharacteristic
201C4#1174526911yescharacteristic
202C4#1174527411yescharacteristic
203C4#1174527811yescharacteristic
204C2—81no—
205C2—1161no—
206C2#1427112811yescharacteristic
207C2#1427115611yescharacteristic
208C2#1427117811yescharacteristic
subgroupG/H
centerC2×C4D4×D29
commutatorC2×C4×C29C22×C4
FrattiniC42C22×D29
FittingC29×D4⋊C8C2
socleC22×C29C2×C22⋊C4
prime radical#11745300C4
cosocleC42×C29C23
hypercenterD4⋊C8D29
hypocenterC29#1482
LCSG ▷ C2×C4×C29 ▷ C2×C29 ▷ C29
UCSC1 ◁ C2×C4 ◁ C42 ◁ D4⋊C8

Complements

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

NH ≅ G/Ntype
2. #14271215C2semidirect
3. #14271214C2semidirect
4. #14270895C2semidirect
5. #14270893C2semidirect
6. D4⋊#6597C2semidirect
7. C29×D4⋊C8C2semidirect
106. D4⋊C8D29semidirect
131. C29#1482semidirect

Maximal subgroups

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

subgroupindex
#142716952
#142712152
#142712142
#142708952
#142708932
D4⋊#65972
C29×D4⋊C82
#148229