Finite Group Databasebeta

← #16817930

Subgroups — #16817930

Order 3712.

266 conjugacy classes of subgroups; only the 73 normal subgroups are shown.

normal subgroups only

This group has 266 conjugacy classes of subgroups — too many to draw. Only its 73 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×#90809C211yesmaximal, characteristic
2#14271185C211yesmaximal, characteristic, complemented
3C4×#90772C211yesmaximal, characteristic, complemented
4Q8⋊#6597C211yesmaximal, characteristic, complemented
5#14270892C211yesmaximal, characteristic, complemented
6#14270890C211yesmaximal, characteristic, complemented
7C29×Q8⋊C8C211yesmaximal, characteristic, complemented
8C2×#90809C411yescharacteristic
9C4×Q8×C29C2211yescharacteristic
10Q8×Dic29C411yescharacteristic
11C2×#90772—21no—
12C2×#90772—21no—
13#11745255—21no—
14#11745255C411yescharacteristic
15#11745254—21no—
16#11745254C411yescharacteristic
17C4×D116—21no—
18C4×D116C2211yescharacteristic
19C42×D29—21no—
20C42×D29C2211yescharacteristic
21C29×C4⋊C8C2211yescharacteristic
22C4×C8×C29C2211yescharacteristic
23#11745163—21no—
24#11745162—21no—
25C4⋊#6597C2211yescharacteristic
26C4×#6597C2211yescharacteristic
27C2×Q8×C29C2×C411yescharacteristic
28#90809—22no—
29#90809—22no—
30C2×D116—21no—
31C2×D116C2×C411yescharacteristic
32C2×C4×D29—21no—
33C2×C4×D29—21no—
34C2×C4×D29—21no—
35C2×C4×D29C2×C411yescharacteristic
36C2×C4×D29D411yescharacteristic
37C2×C4×D29D411yescharacteristic
38C2×C8×C29—21no—
39C2×C8×C29—21no—
40C4⋊C4×C29—21no—
41C4⋊C4×C29C2×C411yescharacteristic
42C42×C29—21no—
43C42×C29C2311yescharacteristic
44#90781—21no—
45#90781—21no—
46#90781—21no—
47C4⋊Dic29—21no—
48C4⋊Dic29C2×C411yescharacteristic
49C4×Dic29—21no—
50C4×Dic29—21no—
51C4×Dic29C2×C411yescharacteristic
52C4×Dic29D411yescharacteristic
53C4×Dic29D411yescharacteristic
54C2×#6597—21no—
55C2×#6597—21no—
56#90772—24no—
57#90772—42no—
58C22×D29—21no—
59C22×D29C22⋊C411yescharacteristic
60Q8×C29—21no—
61Q8×C29M1612yescomplemented
62C2×C4×C29—21no—
63C2×C4×C29—21no—
64C2×C4×C29C22×C411yescharacteristic
65C2×C4×C29C2×D411yescharacteristic
66C2×C4×C29C2×D411yescharacteristic
67C2×Dic29—21no—
68C2×Dic29C22⋊C411yescharacteristic
69C2×Dic29C22⋊C411yescharacteristic
70C2×Dic29C22⋊C411yescharacteristic
71D116—24no—
72D116—21no—
73D116M1612yescomplemented
74C4×D29—24no—
75C4×D29—21no—
76C4×D29—21no—
77C4×D29—21no—
78C4×D29—21no—
79C4×D29—22no—
80C4×D29—41no—
81C4×D29—41no—
82C4×D29—42no—
83C8×C29—22no—
84C8×C29—41no—
85#6597—22no—
86#6597—41no—
87#1489—291nomaximal, Sylow
88C22×C29C2×C22⋊C411yescharacteristic
89C2×D29—21no—
90C2×D29—22no—
91C2×D29—21no—
92C2×D29—21no—
93C2×D29—41no—
94C2×D29—41no—
95C4×C29—22no—
96C4×C29—21no—
97C4×C29—41no—
98C4×C29C2×M1611yescharacteristic
99C4×C29C2×M1611yescharacteristic
100C4×C29AGL(1,ℤ/8)11yescharacteristic
101C4×C29#13711yescharacteristic
102Dic29—21no—
103Dic29—21no—
104Dic29—41no—
105Dic29#10412yes—
106C4×#41—291no—
107#423—291no—
108C4×M16—291no—
109Q8⋊C8—291no—
110Q8⋊C8D2911yescharacteristic, complemented
111D4⋊C8—291no—
112D4⋊C8—291no—
113C2×C29#40711yescharacteristic
114C2×C29#41711yescharacteristic
115C2×C29C2×#10411yescharacteristic
116D29—41no—
117D29—42no—
118C2×#41—291no—
119C2×M16—581no—
120C2×M16—581no—
121C4×Q8—291no—
122C4×Q8C2×D2911yescharacteristic
123C4×D4—291no—
124C4×D4—291no—
125C4×D4—581no—
126C4×D4—581no—
127#117—291no—
128#117—581no—
129C2×C42—291no—
130C2×C42—581no—
131C4⋊C8—291no—
132C4⋊C8—581no—
133C4⋊C8C2×D2911yescharacteristic
134#97—581no—
135C4×C8—291no—
136C4×C8C2×D2911yescharacteristic
137C29#148911yescharacteristic, complemented, Sylow
138#41—582no—
139#41—582no—
140C2×Q8C4×D2911yescharacteristic
141C2×D4—291no—
142C2×D4—581no—
143C22×C4—291no—
144C22×C4—291no—
145C22×C4—291no—
146C22×C4—581no—
147C22×C4—581no—
148C22×C4—581no—
149M16—584no—
150M16—1162no—
151C2×C8—21no—
152C2×C8—21no—
153C2×C8—581no—
154C2×C8—581no—
155C4⋊C4—21no—
156C4⋊C4—291no—
157C4⋊C4—581no—
158C4⋊C4C4×D2911yescharacteristic
159C22⋊C4—581no—
160C22⋊C4—581no—
161C22⋊C4—581no—
162C42—21no—
163C42—291no—
164C42—291no—
165C42—291no—
166C42—581no—
167C42—581no—
168C42C22×D2911yescharacteristic
169C23—291no—
170C23—581no—
171Q8—21no—
172Q8#9077212yescomplemented
173D4—292no—
174D4—584no—
175D4—581no—
176C2×C4—21no—
177C2×C4—21no—
178C2×C4—291no—
179C2×C4—291no—
180C2×C4—291no—
181C2×C4—582no—
182C2×C4—584no—
183C2×C4—581no—
184C2×C4—581no—
185C2×C4—581no—
186C2×C4—581no—
187C2×C4—581no—
188C2×C4—1162no—
189C2×C4—1161no—
190C2×C4—1161no—
191C2×C4C2×C4×D2911yescharacteristic
192C2×C4D4×D2911yescharacteristic
193C2×C4D4×D2911yescharacteristic
194C8—22no—
195C8—41no—
196C8—582no—
197C8—1161no—
198C22—582no—
199C22—581no—
200C22—581no—
201C22—581no—
202C22—1161no—
203C22—1161no—
204C22C22⋊C4×D2911yescharacteristic
205C4—22no—
206C4—21no—
207C4—41no—
208C4—292no—
209C4—581no—
210C4—581no—
211C4—1161no—
212C4C2×#9077211yescharacteristic
213C4M16×D2911yescharacteristic
214C4#1174527611yescharacteristic
215C4#1174528011yescharacteristic
216C2—1161no—
217C2—1162no—
218C2#1427112511yescharacteristic
219C2#1427116311yescharacteristic
220C2#104×D2911yescharacteristic
subgroupG/H
centerC2×C4D4×D29
commutatorC2×C4×C29C22×C4
FrattiniC42C22×D29
FittingC29×Q8⋊C8C2
socleC22×C29C2×C22⋊C4
prime radicalC2×#90809C4
cosocleC42×C29C23
hypercenterQ8⋊C8D29
hypocenterC29#1489
LCSG ▷ C2×C4×C29 ▷ C2×C29 ▷ C29
UCSC1 ◁ C2×C4 ◁ C42 ◁ Q8⋊C8

Complements

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

NH ≅ G/Ntype
2. #14271185C2semidirect
3. C4×#90772C2semidirect
4. Q8⋊#6597C2semidirect
5. #14270892C2semidirect
6. #14270890C2semidirect
7. C29×Q8⋊C8C2semidirect
61. Q8×C29M16semidirect
73. D116M16semidirect
110. Q8⋊C8D29semidirect
137. C29#1489semidirect
172. Q8#90772semidirect

Maximal subgroups

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

subgroupindex
C4×#908092
#142711852
C4×#907722
Q8⋊#65972
#142708922
#142708902
C29×Q8⋊C82
#148929