Finite Group Databasebeta

← #16817959

Subgroups — #16817959

Order 3712.

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

normal subgroups only

This group has 246 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#14271710C211yesmaximal, characteristic
2#14271219C211yesmaximal, characteristic, complemented
3#14271214C211yesmaximal, characteristic, complemented
4#14270892C211yesmaximal, characteristic, complemented
5D4⋊#6597C211yesmaximal, characteristic, complemented
6#14270890C211yesmaximal, characteristic, complemented
7C29×D4⋊C8C211yesmaximal, characteristic, complemented
8C2×#90805—21no—
9C4×D4×C29C2211yescharacteristic
10#11745302C411yescharacteristic
11#11745300C411yescharacteristic
12C4×C22⋊D29—21no—
13#11745257C411yescharacteristic
14#11745250C411yescharacteristic
15#11745247—21no—
16#11745246—21no—
17C4×D116C2211yescharacteristic
18C42×D29C2211yescharacteristic
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—
30C2×C22⋊D29—21no—
31C2×C22⋊D29—21no—
32#90805—42no—
33#90805—42no—
34C2×D116—21no—
35C2×D116C2×C411yescharacteristic
36C2×C4×D29—21no—
37C2×C4×D29C2×C411yescharacteristic
38C2×C4×D29D411yescharacteristic
39C2×C4×D29D411yescharacteristic
40C2×Dic58—21no—
41C2×C8×C29—21no—
42C2×C8×C29—21no—
43C4⋊C4×C29C2×C411yescharacteristic
44C22⋊C4×C29—21no—
45C42×C29C2311yescharacteristic
46C22⋊Dic29—21no—
47#90781—21no—
48#90781—21no—
49C4⋊Dic29C2×C411yescharacteristic
50#90779—21no—
51C4×Dic29C2×C411yescharacteristic
52C4×Dic29D411yescharacteristic
53C4×Dic29D411yescharacteristic
54C2×#6597—21no—
55C2×#6597—21no—
56C23×C29—21no—
57C22×D29—21no—
58C22×D29C22⋊C411yescharacteristic
59D4×C29—21no—
60D4×C29—21no—
61C2×C4×C29—21no—
62C2×C4×C29—41no—
63C2×C4×C29—41no—
64C2×C4×C29C22×C411yescharacteristic
65C2×C4×C29C2×D411yescharacteristic
66C2×C4×C29C2×D411yescharacteristic
67C22⋊D29—42no—
68C22⋊D29—42no—
69C22⋊D29—42no—
70C2×Dic29—21no—
71C2×Dic29C22⋊C411yescharacteristic
72C2×Dic29C22⋊C411yescharacteristic
73C2×Dic29C22⋊C411yescharacteristic
74D116—21no—
75D116—21no—
76D116—42no—
77C4×D29—21no—
78C4×D29—21no—
79C4×D29—21no—
80C4×D29—21no—
81C4×D29—41no—
82C4×D29—41no—
83C4×D29—41no—
84Dic58—42no—
85C8×C29—41no—
86C8×C29—41no—
87#6597—41no—
88#6597—41no—
89#1496—291nomaximal, Sylow
90C22×C29—41no—
91C22×C29—41no—
92C22×C29—41no—
93C22×C29C2×C22⋊C411yescharacteristic
94C2×D29—21no—
95C2×D29—21no—
96C2×D29—21no—
97C2×D29—41no—
98C2×D29—41no—
99C2×D29—41no—
100C4×C29—21no—
101C4×C29—41no—
102C4×C29#13111yescharacteristic
103C4×C29#13111yescharacteristic
104C4×C29AGL(1,ℤ/8)11yescharacteristic
105C4×C29AGL(1,ℤ/8)11yescharacteristic
106Dic29—21no—
107Dic29—21no—
108Dic29—21no—
109Dic29—41no—
110#532—291no—
111#432—291no—
112#431—291no—
113D4⋊C8—291no—
114D4⋊C8—291no—
115D4⋊C8—291no—
116D4⋊C8D2911yescharacteristic, complemented
117C2×C29—81no—
118C2×C29#40811yescharacteristic
119C2×C29#41811yescharacteristic
120C2×C29#42111yescharacteristic
121D29—41no—
122D29—81no—
123C2×#41—581no—
124C4⋊Q8—291no—
125#127—291no—
126#124—581no—
127#121—291no—
128#121—291no—
129#121—581no—
130C4×D4—291no—
131C4×D4—581no—
132C4×D4C2×D2911yescharacteristic
133C2×C42—291no—
134C4⋊C8—291no—
135C4⋊C8—581no—
136C4⋊C8C2×D2911yescharacteristic
137C22⋊C8—581no—
138C22⋊C8—581no—
139#97—581no—
140C4×C8—291no—
141C4×C8C2×D2911yescharacteristic
142C29#149611yescharacteristic, complemented, Sylow
143#41—1162no—
144#41—1162no—
145C2×Q8—581no—
146C2×D4—291no—
147C2×D4—581no—
148C2×D4—581no—
149C2×D4—581no—
150C2×D4—581no—
151C2×D4C4×D2911yescharacteristic
152C22×C4—21no—
153C22×C4—291no—
154C22×C4—291no—
155C22×C4—291no—
156C22×C4—581no—
157C2×C8—21no—
158C2×C8—21no—
159C2×C8—581no—
160C2×C8—581no—
161C4⋊C4—291no—
162C4⋊C4—581no—
163C4⋊C4C4×D2911yescharacteristic
164C22⋊C4—21no—
165C22⋊C4—581no—
166C22⋊C4—581no—
167C22⋊C4—581no—
168C42—291no—
169C42—291no—
170C42—291no—
171C42C22×D2911yescharacteristic
172C23—21no—
173C23—291no—
174C23—581no—
175Q8—1162no—
176D4—21no—
177D4—21no—
178D4—581no—
179D4—581no—
180D4—1162no—
181D4—1162no—
182D4—1162no—
183D4—1162no—
184C2×C4—21no—
185C2×C4—41no—
186C2×C4—41no—
187C2×C4—291no—
188C2×C4—291no—
189C2×C4—291no—
190C2×C4—581no—
191C2×C4—581no—
192C2×C4—581no—
193C2×C4—581no—
194C2×C4—581no—
195C2×C4—1161no—
196C2×C4—1161no—
197C2×C4—1161no—
198C2×C4C2×C4×D2911yescharacteristic
199C2×C4D4×D2911yescharacteristic
200C2×C4D4×D2911yescharacteristic
201C8—41no—
202C8—41no—
203C8—1161no—
204C8—1161no—
205C22—41no—
206C22—41no—
207C22—41no—
208C22—581no—
209C22—581no—
210C22—581no—
211C22—1161no—
212C22—1161no—
213C22—1161no—
214C22C22⋊C4×D2911yescharacteristic
215C4—21no—
216C4—41no—
217C4—581no—
218C4—581no—
219C4—581no—
220C4—1161no—
221C4#1174526311yescharacteristic
222C4#1174526911yescharacteristic
223C4#1174527311yescharacteristic
224C4#1174527611yescharacteristic
225C2—81no—
226C2—1161no—
227C2—2321no—
228C2#1427112811yescharacteristic
229C2#1427116611yescharacteristic
230C2#1427117811yescharacteristic
subgroupG/H
centerC2×C4D4×D29
commutatorC2×C4×C29C22×C4
FrattiniC42C22×D29
FittingC29×D4⋊C8C2
socleC22×C29C2×C22⋊C4
prime radical#14271710C2
cosocleC42×C29C23
hypercenterD4⋊C8D29
hypocenterC29#1496
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. #14270892C2semidirect
5. D4⋊#6597C2semidirect
6. #14270890C2semidirect
7. C29×D4⋊C8C2semidirect
116. D4⋊C8D29semidirect
142. C29#1496semidirect

Maximal subgroups

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

subgroupindex
#142717102
#142712192
#142712142
#142708922
D4⋊#65972
#142708902
C29×D4⋊C82
#149629