Finite Group Databasebeta

← #16818035

Subgroups — #16818035

Order 3712.

286 conjugacy classes of subgroups; only the 81 normal subgroups are shown.

normal subgroups only

This group has 286 conjugacy classes of subgroups — too many to draw. Only its 81 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#14271127C211yesmaximal, characteristic, complemented
2#14271023C211yesmaximal, characteristic, complemented
3#14270900C212yesmaximal, complemented
4#14270897C212yesmaximal, complemented
5C29×#525C211yesmaximal, characteristic
6C2×#41×C29C411yescharacteristic, complemented
7C23×C4×C29C2211yescharacteristic
8C29×#123—21no—
9C29×C22⋊Q8C411yescharacteristic, complemented
10C29×C22⋊Q8C2211yescharacteristic
11C29×#121C411yescharacteristic, complemented
12C29×#121C2211yescharacteristic
13C29×#120—21no—
14C4×D4×C29—21no—
15C4×D4×C29—21no—
16C29×#117C411yescharacteristic, complemented
17C2×C22⋊Dic29—21no—
18C2×C4⋊Dic29—21no—
19C2×#90777—21no—
20#11745179C2212yes—
21C22⋊#6597—21no—
22C22⋊#6597C2212yes—
23C24×C29D411yescharacteristic
24#41×C29—42no—
25C2×Q8×C29C2×C411yescharacteristic
26C2×D4×C29—21no—
27C2×D4×C29—21no—
28C2×D4×C29—21no—
29C2×D4×C29C2×C411yescharacteristic
30C22×C4×C29—21no—
31C22×C4×C29—42no—
32C22×C4×C29C2×C411yescharacteristic
33C22×C4×C29C2×C411yescharacteristic
34C22×C4×C29D411yescharacteristic
35C22×C4×C29D411yescharacteristic
36C22×C4×C29D411yescharacteristic
37C22×C4×C29C2311yescharacteristic
38C22×Dic29—22no—
39C4⋊C4×C29—21no—
40C4⋊C4×C29—21no—
41C4⋊C4×C29C2×C411yescharacteristic
42C4⋊C4×C29C2×C411yescharacteristic
43C22⋊C4×C29—21no—
44C22⋊C4×C29—21no—
45C22⋊C4×C29—21no—
46C22⋊C4×C29—21no—
47C22⋊C4×C29—21no—
48C42×C29—21no—
49C22⋊Dic29—42no—
50C4⋊Dic29—42no—
51#90777—42no—
52C2×#6597—22no—
53C23×C29—21no—
54C23×C29—21no—
55C23×C29—21no—
56C23×C29—41no—
57C23×C29—41no—
58C23×C29C22⋊C411yescharacteristic
59C23×C29C22⋊C411yescharacteristic
60C23×C29C2×D411yescharacteristic
61Q8×C29—41no—
62D4×C29—41no—
63D4×C29—42no—
64D4×C29—42no—
65D4×C29—41no—
66D4×C29—41no—
67C2×C4×C29—22no—
68C2×C4×C29—22no—
69C2×C4×C29—22no—
70C2×C4×C29—21no—
71C2×C4×C29—21no—
72C2×C4×C29—21no—
73C2×C4×C29—41no—
74C2×C4×C29—41no—
75C2×C4×C29—41no—
76C2×C4×C29—42no—
77C2×C4×C29C22⋊C411yescharacteristic
78C2×C4×C29C22⋊C411yescharacteristic
79C2×C4×C29C22×C411yescharacteristic
80C2×C4×C29C2×D411yescharacteristic
81C2×Dic29—42no—
82C2×Dic29—42no—
83C2×Dic29—42no—
84#6597—42no—
85#1513—291nomaximal, Sylow
86C22×C29—21no—
87C22×C29—21no—
88C22×C29—21no—
89C22×C29—21no—
90C22×C29—21no—
91C22×C29—21no—
92C22×C29—21no—
93C22×C29—21no—
94C22×C29—42no—
95C22×C29—42no—
96C22×C29—41no—
97C22×C29—41no—
98C22×C29—41no—
99C22×C29C2×C22⋊C411yescharacteristic
100C22×C29AGL(1,ℤ/8)11yescharacteristic
101C22×C29#13711yescharacteristic
102C4×C29—21no—
103C4×C29—21no—
104C4×C29—21no—
105C4×C29—41no—
106C4×C29—41no—
107C4×C29—41no—
108C4×C29#9912yes—
109Dic29—82no—
110#525D2911yescharacteristic
111#407—291no—
112#380—291no—
113#328—292no—
114#327—292no—
115C2×C29—21no—
116C2×C29—21no—
117C2×C29—41no—
118C2×C29—41no—
119C2×C29—81no—
120C2×C29C2×#9911yescharacteristic
121C2×C29#41711yescharacteristic
122C2×C29#42111yescharacteristic
123C2×#41Dic2911yescharacteristic, complemented
124C23×C4C2×D2911yescharacteristic
125C2×M16—581no—
126#123—21no—
127C22⋊Q8Dic2911yescharacteristic, complemented
128C22⋊Q8C2×D2911yescharacteristic
129#121Dic2911yescharacteristic, complemented
130#121C2×D2911yescharacteristic
131#120—21no—
132C4×D4—21no—
133C4×D4—21no—
134#117Dic2911yescharacteristic, complemented
135C2×C4⋊C4—581no—
136C2×C22⋊C4—581no—
137C22⋊C8—292no—
138C22⋊C8—581no—
139#95—292no—
140C29#151311yescharacteristic, complemented, Sylow
141C24C22⋊D2911yescharacteristic
142#41—42no—
143C2×Q8C2×Dic2911yescharacteristic
144C2×D4—21no—
145C2×D4—21no—
146C2×D4—21no—
147C2×D4C2×Dic2911yescharacteristic
148C22×C4—21no—
149C22×C4—42no—
150C22×C4—582no—
151C22×C4C2×Dic2911yescharacteristic
152C22×C4C2×Dic2911yescharacteristic
153C22×C4C22⋊D2911yescharacteristic
154C22×C4C22⋊D2911yescharacteristic
155C22×C4C22⋊D2911yescharacteristic
156C22×C4C22×D2911yescharacteristic
157M16—1162no—
158C2×C8—582no—
159C4⋊C4—21no—
160C4⋊C4—21no—
161C4⋊C4—1162no—
162C4⋊C4C2×Dic2911yescharacteristic
163C4⋊C4C2×Dic2911yescharacteristic
164C22⋊C4—21no—
165C22⋊C4—21no—
166C22⋊C4—21no—
167C22⋊C4—21no—
168C22⋊C4—21no—
169C22⋊C4—1162no—
170C42—21no—
171C23—21no—
172C23—21no—
173C23—21no—
174C23—41no—
175C23—41no—
176C23C22⋊Dic2911yescharacteristic
177C23C22⋊Dic2911yescharacteristic
178C23C2×C22⋊D2911yescharacteristic
179Q8—41no—
180D4—41no—
181D4—42no—
182D4—42no—
183D4—41no—
184D4—41no—
185C2×C4—22no—
186C2×C4—22no—
187C2×C4—22no—
188C2×C4—21no—
189C2×C4—21no—
190C2×C4—21no—
191C2×C4—41no—
192C2×C4—41no—
193C2×C4—41no—
194C2×C4—42no—
195C2×C4—1162no—
196C2×C4—1162no—
197C2×C4—1162no—
198C2×C4C22⋊Dic2911yescharacteristic
199C2×C4C22⋊Dic2911yescharacteristic
200C2×C4C22×Dic2911yescharacteristic
201C2×C4C2×C22⋊D2911yescharacteristic
202C8—1162no—
203C22—21no—
204C22—21no—
205C22—21no—
206C22—21no—
207C22—21no—
208C22—21no—
209C22—21no—
210C22—21no—
211C22—42no—
212C22—42no—
213C22—41no—
214C22—41no—
215C22—41no—
216C22#1174531111yescharacteristic
217C22#1174531311yescharacteristic
218C22C2×C22⋊Dic2911yescharacteristic
219C4—21no—
220C4—21no—
221C4—21no—
222C4—41no—
223C4—41no—
224C4—41no—
225C4—2322no—
226C4#1174518212yes—
227C2—21no—
228C2—21no—
229C2—41no—
230C2—41no—
231C2—81no—
232C2C2×#1174518211yescharacteristic
233C2#1427116411yescharacteristic
234C2#1427118011yescharacteristic
subgroupG/H
centerC22C2×C22⋊Dic29
commutatorC2×C4×C29C22×C4
FrattiniC22×C4C22×D29
Fitting, prime radicalC29×#525C2
socleC22×C29C2×C22⋊C4
cosocleC22×C4×C29C23
hypercenter#525D29
hypocenterC29#1513
LCSG ▷ C2×C4×C29 ▷ C22×C29 ▷ C29
UCSC1 ◁ C22 ◁ C23×C4 ◁ #525

Complements

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

NH ≅ G/Ntype
1. #14271127C2semidirect
2. #14271023C2semidirect
3. #14270900C2semidirect
4. #14270897C2semidirect
6. C2×#41×C29C4semidirect
9. C29×C22⋊Q8C4semidirect
11. C29×#121C4semidirect
16. C29×#117C4semidirect
123. C2×#41Dic29semidirect
127. C22⋊Q8Dic29semidirect
129. #121Dic29semidirect
134. #117Dic29semidirect
140. C29#1513semidirect

Maximal subgroups

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

subgroupindex
#142711272
#142710232
#142709002
#142708972
C29×#5252
#151329