Finite Group Databasebeta

← #16817954

Subgroups — #16817954

Order 3712.

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

normal subgroups only

This group has 216 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#14271214C211yesmaximal, characteristic, complemented
3#14271185C211yesmaximal, 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—
13C2×#90772—21no—
14#11745259C411yescharacteristic
15#11745252C411yescharacteristic
16#11745245—21no—
17#11745241—21no—
18C42×D29C2211yescharacteristic
19C4×Dic58C2211yescharacteristic
20C29×C4⋊C8C2211yescharacteristic
21C4×C8×C29C2211yescharacteristic
22#11745168—21no—
23#11745162—21no—
24#11745162—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—
54#90772—42no—
55C23×C29—21no—
56C22×D29C22⋊C411yescharacteristic
57D4×C29—21no—
58D4×C29—21no—
59C2×C4×C29—21no—
60C2×C4×C29—41no—
61C2×C4×C29—41no—
62C2×C4×C29C22×C411yescharacteristic
63C2×C4×C29C2×D411yescharacteristic
64C2×C4×C29C2×D411yescharacteristic
65C22⋊D29—42no—
66C2×Dic29—21no—
67C2×Dic29—21no—
68C2×Dic29C22⋊C411yescharacteristic
69C2×Dic29C22⋊C411yescharacteristic
70C2×Dic29C22⋊C411yescharacteristic
71C4×D29—21no—
72C4×D29—21no—
73C4×D29—21no—
74C4×D29—21no—
75C4×D29—41no—
76Dic58—21no—
77Dic58—21no—
78C8×C29—41no—
79C8×C29—41no—
80#6597—41no—
81#6597—41no—
82#1495—291nomaximal, Sylow
83C22×C29—41no—
84C22×C29—41no—
85C22×C29—41no—
86C22×C29C2×C22⋊C411yescharacteristic
87C2×D29—21no—
88C2×D29—21no—
89C2×D29—21no—
90C4×C29—21no—
91C4×C29—41no—
92C4×C29#13111yescharacteristic
93C4×C29#13111yescharacteristic
94C4×C29AGL(1,ℤ/8)11yescharacteristic
95C4×C29#13711yescharacteristic
96Dic29—21no—
97Dic29—21no—
98Dic29—21no—
99Dic29—41no—
100Dic29—41no—
101#529—291no—
102#431—291no—
103#423—291no—
104Q8⋊C8—291no—
105Q8⋊C8—291no—
106D4⋊C8—291no—
107D4⋊C8D2911yescharacteristic, complemented
108C2×C29—81no—
109C2×C29#40811yescharacteristic
110C2×C29#41711yescharacteristic
111C2×C29#42111yescharacteristic
112D29—41no—
113C2×M16—581no—
114#126—581no—
115#125—291no—
116#124—291no—
117#123—581no—
118C22⋊Q8—291no—
119#121—291no—
120C4×Q8—291no—
121C4×D4—581no—
122C4×D4C2×D2911yescharacteristic
123#117—581no—
124C2×C42—291no—
125C4⋊C8—291no—
126C4⋊C8—581no—
127C4⋊C8—581no—
128C4⋊C8C2×D2911yescharacteristic
129C22⋊C8—581no—
130C4×C8—291no—
131C4×C8C2×D2911yescharacteristic
132C29#149511yescharacteristic, complemented, Sylow
133C2×Q8—291no—
134C2×D4—581no—
135C2×D4C4×D2911yescharacteristic
136C22×C4—21no—
137C22×C4—291no—
138C22×C4—291no—
139C22×C4—291no—
140M16—1162no—
141C2×C8—21no—
142C2×C8—21no—
143C2×C8—581no—
144C2×C8—581no—
145C4⋊C4—291no—
146C4⋊C4—581no—
147C4⋊C4—581no—
148C4⋊C4—581no—
149C4⋊C4—581no—
150C4⋊C4C4×D2911yescharacteristic
151C22⋊C4—21no—
152C22⋊C4—581no—
153C22⋊C4—581no—
154C22⋊C4—581no—
155C22⋊C4—581no—
156C42—291no—
157C42—291no—
158C42—291no—
159C42—581no—
160C42C22×D2911yescharacteristic
161C23—21no—
162C23—291no—
163Q8—581no—
164Q8—581no—
165D4—21no—
166D4—21no—
167D4—1162no—
168C2×C4—21no—
169C2×C4—41no—
170C2×C4—41no—
171C2×C4—291no—
172C2×C4—291no—
173C2×C4—291no—
174C2×C4—581no—
175C2×C4—581no—
176C2×C4—581no—
177C2×C4—581no—
178C2×C4—581no—
179C2×C4—581no—
180C2×C4—1161no—
181C2×C4C2×C4×D2911yescharacteristic
182C2×C4D4×D2911yescharacteristic
183C2×C4D4×D2911yescharacteristic
184C8—41no—
185C8—41no—
186C8—1161no—
187C8—1161no—
188C22—41no—
189C22—41no—
190C22—41no—
191C22—581no—
192C22—581no—
193C22—581no—
194C22C22⋊C4×D2911yescharacteristic
195C4—21no—
196C4—41no—
197C4—581no—
198C4—581no—
199C4—581no—
200C4—1161no—
201C4—1161no—
202C4#1174526311yescharacteristic
203C4#1174526911yescharacteristic
204C4#1174527311yescharacteristic
205C4#1174527711yescharacteristic
206C2—81no—
207C2—1161no—
208C2#1427112811yescharacteristic
209C2#1427116111yescharacteristic
210C2#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#1495
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. #14271214C2semidirect
3. #14271185C2semidirect
4. #14270895C2semidirect
5. #14270893C2semidirect
6. D4⋊#6597C2semidirect
7. C29×D4⋊C8C2semidirect
107. D4⋊C8D29semidirect
132. C29#1495semidirect

Maximal subgroups

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

subgroupindex
#142716952
#142712142
#142711852
#142708952
#142708932
D4⋊#65972
C29×D4⋊C82
#149529