Finite Group Databasebeta

← #16817923

Subgroups — #16817923

Order 3712.

246 conjugacy classes of subgroups; only the 71 normal subgroups are shown.

normal subgroups only

This group has 246 conjugacy classes of subgroups — too many to draw. Only its 71 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
1C4×#90807C211yesmaximal, characteristic
2#14271219C211yesmaximal, characteristic, complemented
3#14271214C211yesmaximal, characteristic, complemented
4#14270895C211yesmaximal, characteristic, complemented
5#14270893C211yesmaximal, characteristic, complemented
6D4⋊#6597C211yesmaximal, characteristic, complemented
7C29×D4⋊C8C211yesmaximal, characteristic, complemented
8C2×#90807C411yescharacteristic
9C4×D4×C29C2211yescharacteristic
10D4×Dic29C411yescharacteristic
11C4×C22⋊D29—21no—
12C2×C4×Dic29—21no—
13#11745254C411yescharacteristic
14#11745249C411yescharacteristic
15#11745243—21no—
16#11745239—21no—
17C42×D29C2211yescharacteristic
18C4×Dic58C2211yescharacteristic
19C29×C4⋊C8C2211yescharacteristic
20C4×C8×C29C2211yescharacteristic
21#11745168—21no—
22#11745168—21no—
23#11745163—21no—
24#11745162—21no—
25C4⋊#6597C2211yescharacteristic
26C4×#6597C2211yescharacteristic
27C2×D4×C29C2×C411yescharacteristic
28C22×C4×C29—21no—
29C2×C22⋊D29—21no—
30C22×Dic29—21no—
31C22×Dic29—21no—
32#90807—22no—
33#90807—22no—
34C2×C4×D29C2×C411yescharacteristic
35C2×C4×D29D411yescharacteristic
36C2×C4×D29D411yescharacteristic
37C2×Dic58C2×C411yescharacteristic
38C2×C8×C29—21no—
39C2×C8×C29—21no—
40C4⋊C4×C29C2×C411yescharacteristic
41C22⋊C4×C29—21no—
42C42×C29C2311yescharacteristic
43C22⋊Dic29—21no—
44#90781—21no—
45C4⋊Dic29C2×C411yescharacteristic
46#90779—21no—
47#90779—21no—
48C4×Dic29—21no—
49C4×Dic29—21no—
50C4×Dic29—21no—
51C4×Dic29C2×C411yescharacteristic
52C4×Dic29D411yescharacteristic
53C4×Dic29D411yescharacteristic
54C2×#6597—21no—
55C2×#6597—21no—
56C23×C29—21no—
57C22×D29C22⋊C411yescharacteristic
58D4×C29—21no—
59D4×C29M1612yes—
60C2×C4×C29—21no—
61C2×C4×C29—41no—
62C2×C4×C29—41no—
63C2×C4×C29C22×C411yescharacteristic
64C2×C4×C29C2×D411yescharacteristic
65C2×C4×C29C2×D411yescharacteristic
66C22⋊D29—24no—
67C2×Dic29—24no—
68C2×Dic29—21no—
69C2×Dic29—21no—
70C2×Dic29—42no—
71C2×Dic29C22⋊C411yescharacteristic
72C2×Dic29C22⋊C411yescharacteristic
73C2×Dic29C22⋊C411yescharacteristic
74C4×D29—21no—
75C4×D29—21no—
76C4×D29—21no—
77C4×D29—21no—
78C4×D29—41no—
79Dic58—21no—
80Dic58M1612yes—
81C8×C29—41no—
82C8×C29—41no—
83#6597—41no—
84#6597—41no—
85#1488—291nomaximal, Sylow
86C22×C29—22no—
87C22×C29—41no—
88C22×C29—41no—
89C22×C29C2×C22⋊C411yescharacteristic
90C2×D29—21no—
91C2×D29—21no—
92C2×D29—21no—
93C4×C29—21no—
94C4×C29—41no—
95C4×C29C2×M1611yescharacteristic
96C4×C29C2×M1611yescharacteristic
97C4×C29#13511yescharacteristic
98C4×C29#13511yescharacteristic
99Dic29—22no—
100Dic29—21no—
101Dic29—21no—
102Dic29—21no—
103Dic29—41no—
104C4×#41—291no—
105#432—291no—
106#431—291no—
107Q8⋊C8—291no—
108Q8⋊C8—291no—
109D4⋊C8—291no—
110D4⋊C8D2911yescharacteristic, complemented
111C2×C29—42no—
112C2×C29#40711yescharacteristic
113C2×C29#41611yescharacteristic
114C2×C29#42111yescharacteristic
115D29—41no—
116C2×#41—291no—
117C4×Q8—291no—
118C4×Q8—291no—
119C4×D4—291no—
120C4×D4—581no—
121C4×D4—581no—
122C4×D4C2×D2911yescharacteristic
123#117—291no—
124#117—581no—
125C2×C42—291no—
126C2×C42—581no—
127C4⋊C8—291no—
128C4⋊C8—581no—
129C4⋊C8C2×D2911yescharacteristic
130C22⋊C8—581no—
131C22⋊C8—581no—
132#97—581no—
133C4×C8—291no—
134C4×C8C2×D2911yescharacteristic
135C29#148811yescharacteristic, complemented, Sylow
136#41—582no—
137#41—582no—
138C2×Q8—291no—
139C2×D4—581no—
140C2×D4C4×D2911yescharacteristic
141C22×C4—21no—
142C22×C4—291no—
143C22×C4—291no—
144C22×C4—291no—
145C22×C4—581no—
146C22×C4—581no—
147C2×C8—21no—
148C2×C8—21no—
149C2×C8—581no—
150C2×C8—581no—
151C4⋊C4—291no—
152C4⋊C4—581no—
153C4⋊C4—581no—
154C4⋊C4C4×D2911yescharacteristic
155C22⋊C4—21no—
156C22⋊C4—581no—
157C22⋊C4—581no—
158C42—291no—
159C42—291no—
160C42—291no—
161C42—581no—
162C42—581no—
163C42—581no—
164C42C22×D2911yescharacteristic
165C23—21no—
166C23—291no—
167Q8—292no—
168Q8—581no—
169D4—21no—
170D4—584no—
171D4#9077212yes—
172C2×C4—21no—
173C2×C4—41no—
174C2×C4—41no—
175C2×C4—291no—
176C2×C4—291no—
177C2×C4—291no—
178C2×C4—584no—
179C2×C4—581no—
180C2×C4—581no—
181C2×C4—581no—
182C2×C4—581no—
183C2×C4—581no—
184C2×C4—581no—
185C2×C4—1161no—
186C2×C4—1162no—
187C2×C4C2×C4×D2911yescharacteristic
188C2×C4D4×D2911yescharacteristic
189C2×C4D4×D2911yescharacteristic
190C8—41no—
191C8—41no—
192C8—1161no—
193C8—1161no—
194C22—22no—
195C22—41no—
196C22—41no—
197C22—581no—
198C22—581no—
199C22—581no—
200C22C22⋊C4×D2911yescharacteristic
201C4—21no—
202C4—41no—
203C4—581no—
204C4—582no—
205C4—581no—
206C4—581no—
207C4—1161no—
208C4C2×#9077211yescharacteristic
209C4M16×D2911yescharacteristic
210C4#1174527411yescharacteristic
211C4#1174527811yescharacteristic
212C2—42no—
213C2—1161no—
214C2#1427112511yescharacteristic
215C2#1427115611yescharacteristic
216C2#1427117811yescharacteristic
subgroupG/H
centerC2×C4D4×D29
commutatorC2×C4×C29C22×C4
FrattiniC42C22×D29
FittingC29×D4⋊C8C2
socleC22×C29C2×C22⋊C4
prime radicalC2×#90807C4
cosocleC42×C29C23
hypercenterD4⋊C8D29
hypocenterC29#1488
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. #14271219C2semidirect
3. #14271214C2semidirect
4. #14270895C2semidirect
5. #14270893C2semidirect
6. D4⋊#6597C2semidirect
7. C29×D4⋊C8C2semidirect
110. D4⋊C8D29semidirect
135. C29#1488semidirect

Maximal subgroups

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

subgroupindex
C4×#908072
#142712192
#142712142
#142708952
#142708932
D4⋊#65972
C29×D4⋊C82
#148829