Finite Group Databasebeta

← #16817941

Subgroups — #16817941

Order 3712.

276 conjugacy classes of subgroups; only the 75 normal subgroups are shown.

normal subgroups only

This group has 276 conjugacy classes of subgroups — too many to draw. Only its 75 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#14271185C211yesmaximal, characteristic, complemented
3C4×C8×D29C211yesmaximal, 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—
13C2×#90772—21no—
14C2×C8×D29—21no—
15#11745257C411yescharacteristic
16#11745250C411yescharacteristic
17#11745247—21no—
18#11745246—21no—
19C4×D116C2211yescharacteristic
20C42×D29C2211yescharacteristic
21C29×C4⋊C8C2211yescharacteristic
22C4×C8×C29C2211yescharacteristic
23#11745162—21no—
24C8×Dic29—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—
56#90772—42no—
57C8×D29—24no—
58C23×C29—21no—
59C22×D29—21no—
60C22×D29C22⋊C411yescharacteristic
61D4×C29—21no—
62D4×C29—21no—
63C2×C4×C29—21no—
64C2×C4×C29—41no—
65C2×C4×C29—41no—
66C2×C4×C29C22×C411yescharacteristic
67C2×C4×C29C2×D411yescharacteristic
68C2×C4×C29C2×D411yescharacteristic
69C22⋊D29—42no—
70C22⋊D29—42no—
71C22⋊D29—42no—
72C2×Dic29—21no—
73C2×Dic29C22⋊C411yescharacteristic
74C2×Dic29C22⋊C411yescharacteristic
75C2×Dic29C22⋊C411yescharacteristic
76D116—21no—
77D116—21no—
78D116—42no—
79C4×D29—21no—
80C4×D29—21no—
81C4×D29—22no—
82C4×D29—41no—
83C4×D29—41no—
84C4×D29D812yes—
85C4×D29SD1612yes—
86Dic58—42no—
87C8×C29—22no—
88C8×C29—41no—
89#6597—22no—
90#6597—41no—
91#1492—291nomaximal, Sylow
92C22×C29—41no—
93C22×C29—41no—
94C22×C29—41no—
95C22×C29C2×C22⋊C411yescharacteristic
96C2×D29—21no—
97C2×D29—21no—
98C2×D29—41no—
99C2×D29—41no—
100C2×D29—41no—
101C2×D29#10212yes—
102C4×C29—21no—
103C4×C29—41no—
104C4×C29#13111yescharacteristic
105C4×C29#13111yescharacteristic
106C4×C29C2×D811yescharacteristic
107C4×C29C2×SD1611yescharacteristic
108Dic29—21no—
109Dic29—41no—
110Dic29#10212yes—
111Dic29#10412yes—
112#532—291no—
113#423—291no—
114C2×C4×C8—291no—
115D4⋊C8—291no—
116D4⋊C8—291no—
117D4⋊C8—291no—
118D4⋊C8D2911yescharacteristic, complemented
119C2×C29—81no—
120C2×C29#40811yescharacteristic
121C2×C29C2×#10211yescharacteristic
122C2×C29C2×#10411yescharacteristic
123D29—22no—
124D29—81no—
125C2×#41—581no—
126C2×M16—581no—
127C22×C8—581no—
128C4⋊Q8—291no—
129#127—291no—
130#124—581no—
131#121—291no—
132#121—291no—
133#121—581no—
134C4×D4—291no—
135C4×D4—581no—
136C4×D4C2×D2911yescharacteristic
137C2×C42—291no—
138C4⋊C8—291no—
139C4⋊C8—581no—
140C4⋊C8C2×D2911yescharacteristic
141C4×C8—291no—
142C4×C8—581no—
143C4×C8C2×D2911yescharacteristic
144C29#149211yescharacteristic, complemented, Sylow
145#41—1162no—
146#41—1162no—
147C2×Q8—581no—
148C2×D4—291no—
149C2×D4—581no—
150C2×D4—581no—
151C2×D4—581no—
152C2×D4—581no—
153C2×D4C4×D2911yescharacteristic
154C22×C4—21no—
155C22×C4—291no—
156C22×C4—291no—
157C22×C4—291no—
158C22×C4—581no—
159M16—1162no—
160C2×C8—21no—
161C2×C8—21no—
162C2×C8—584no—
163C2×C8—581no—
164C2×C8—581no—
165C4⋊C4—291no—
166C4⋊C4—581no—
167C4⋊C4C4×D2911yescharacteristic
168C22⋊C4—21no—
169C22⋊C4—581no—
170C22⋊C4—581no—
171C22⋊C4—581no—
172C42—291no—
173C42—291no—
174C42—291no—
175C42C22×D2911yescharacteristic
176C23—21no—
177C23—291no—
178C23—581no—
179Q8—1162no—
180D4—21no—
181D4—21no—
182D4—581no—
183D4—581no—
184D4—1162no—
185D4—1162no—
186D4—1162no—
187D4—1162no—
188C2×C4—21no—
189C2×C4—41no—
190C2×C4—41no—
191C2×C4—291no—
192C2×C4—291no—
193C2×C4—292no—
194C2×C4—292no—
195C2×C4—291no—
196C2×C4—582no—
197C2×C4—581no—
198C2×C4—581no—
199C2×C4—581no—
200C2×C4—1161no—
201C2×C4—1161no—
202C2×C4C2×C4×D2911yescharacteristic
203C2×C4D4×D2911yescharacteristic
204C2×C4D4×D2911yescharacteristic
205C8—22no—
206C8—41no—
207C8—582no—
208C8—1161no—
209C22—41no—
210C22—41no—
211C22—41no—
212C22—292no—
213C22—581no—
214C22—581no—
215C22—1161no—
216C22—1161no—
217C22—1161no—
218C22C22⋊C4×D2911yescharacteristic
219C4—21no—
220C4—41no—
221C4—292no—
222C4—292no—
223C4—581no—
224C4—1161no—
225C4#1174526311yescharacteristic
226C4#1174526911yescharacteristic
227C4D8×D2911yescharacteristic
228C4SD16×D2911yescharacteristic
229C2—81no—
230C2—582no—
231C2—2321no—
232C2#1427112811yescharacteristic
233C2#102×D2911yescharacteristic
234C2#104×D2911yescharacteristic
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#1492
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. #14271185C2semidirect
3. C4×C8×D29C2semidirect
4. #14270892C2semidirect
5. D4⋊#6597C2semidirect
6. #14270890C2semidirect
7. C29×D4⋊C8C2semidirect
118. D4⋊C8D29semidirect
144. C29#1492semidirect

Maximal subgroups

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

subgroupindex
#142717102
#142711852
C4×C8×D292
#142708922
D4⋊#65972
#142708902
C29×D4⋊C82
#149229