Finite Group Databasebeta

← #16834907

Subgroups — #16834907

Order 3712.

286 conjugacy classes of subgroups; only the 60 normal subgroups are shown.

normal subgroups only

This group has 286 conjugacy classes of subgroups — too many to draw. Only its 60 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#14272134C211yesmaximal, characteristic, complemented
2#14272105C211yesmaximal, characteristic, complemented
3#14272017C212yesmaximal, complemented
4#14272014C212yesmaximal, complemented
5#14271670C211yesmaximal, characteristic
6C2×#41×C29C411yescharacteristic, complemented
7C22×C4×D29C2211yescharacteristic
8C2×C22⋊#1181—21no—
9C2×C4⋊#1181—21no—
10C2×#90796—21no—
11#11745308C411yescharacteristic, complemented
12#11745308C2211yescharacteristic
13#11745300C411yescharacteristic, complemented
14#11745300C2211yescharacteristic
15#11745299—21no—
16#11745297—21no—
17C4×C22⋊D29—21no—
18C4×C22⋊D29—21no—
19#11745288C411yescharacteristic, complemented
20C22⋊#6599—21no—
21(C2×#1181)⋊C4C2212yes—
22#11745219C2212yes—
23C23×D29D411yescharacteristic
24C22×#1181—22no—
25#41×C29—42no—
26C2×Q8×C29C2×C411yescharacteristic
27C2×D4×C29—21no—
28C2×D4×C29C2×C411yescharacteristic
29C22×C4×C29—21no—
30C22×C4×C29C2×C411yescharacteristic
31C2×C22⋊D29—21no—
32C2×C22⋊D29—21no—
33C22×Dic29D411yescharacteristic
34C2×C4×D29—42no—
35C2×C4×D29C2×C411yescharacteristic
36C2×C4×D29D411yescharacteristic
37C2×C4×D29D411yescharacteristic
38C2×C4×D29C2311yescharacteristic
39C22⋊#1181—42no—
40C2×#6599—22no—
41C4⋊#1181—42no—
42#90796—42no—
43C22⋊Dic29—21no—
44C22⋊Dic29—21no—
45C22⋊Dic29—21no—
46#90781—21no—
47#90781—21no—
48C4⋊Dic29C2×C411yescharacteristic
49C4⋊Dic29C2×C411yescharacteristic
50#90779—21no—
51#90779—21no—
52C4×Dic29—21no—
53C23×C29—21no—
54C23×C29C22⋊C411yescharacteristic
55C22×D29—21no—
56C22×D29—21no—
57C22×D29—41no—
58C22×D29—41no—
59C22×D29C22⋊C411yescharacteristic
60C22×D29C2×D411yescharacteristic
61C2×#1181—42no—
62C2×#1181—42no—
63C2×#1181—42no—
64Q8×C29—41no—
65D4×C29—41no—
66D4×C29—42no—
67C2×C4×C29—22no—
68C2×C4×C29—21no—
69C2×C4×C29—42no—
70C2×C4×C29C22⋊C411yescharacteristic
71C2×C4×C29C22×C411yescharacteristic
72C22⋊D29—42no—
73C22⋊D29—41no—
74C22⋊D29—41no—
75C2×Dic29—21no—
76C2×Dic29—21no—
77C2×Dic29—41no—
78C2×Dic29C22⋊C411yescharacteristic
79C2×Dic29C2×D411yescharacteristic
80C4×D29—22no—
81C4×D29—22no—
82C4×D29—41no—
83C4×D29—41no—
84#6599—42no—
85#1513—291nomaximal, Sylow
86C22×C29—21no—
87C22×C29—21no—
88C22×C29—21no—
89C22×C29—41no—
90C22×C29—41no—
91C22×C29—41no—
92C22×C29C2×C22⋊C411yescharacteristic
93C2×D29—21no—
94C2×D29—21no—
95C2×D29—21no—
96C2×D29—21no—
97C2×D29—21no—
98C2×D29—42no—
99C2×D29—42no—
100C2×D29AGL(1,ℤ/8)11yescharacteristic
101C2×D29#13711yescharacteristic
102#1181—82no—
103C4×C29—21no—
104C4×C29—41no—
105C4×C29#9912yes—
106Dic29—21no—
107Dic29—21no—
108Dic29—41no—
109Dic29—41no—
110#525—291no—
111#407—291no—
112#380—291no—
113#328—292no—
114#327—292no—
115C2×C29—41no—
116C2×C29—81no—
117C2×C29C2×#9911yescharacteristic
118C2×C29#41711yescharacteristic
119C2×C29#42111yescharacteristic
120D29—21no—
121D29—21no—
122D29—41no—
123C2×#41#118111yescharacteristic, complemented
124C23×C4—291no—
125C2×M16—581no—
126#123—581no—
127C22⋊Q8—291no—
128C22⋊Q8—291no—
129#121—291no—
130#121—291no—
131#120—581no—
132C4×D4—581no—
133C4×D4—581no—
134#117—291no—
135C2×C4⋊C4—581no—
136C2×C22⋊C4—581no—
137C22⋊C8—292no—
138C22⋊C8—581no—
139#95—292no—
140C29#151311yescharacteristic, complemented, Sylow
141C24—291no—
142#41—42no—
143C2×Q8C2×#118111yescharacteristic
144C2×D4—21no—
145C2×D4—581no—
146C2×D4—581no—
147C2×D4C2×#118111yescharacteristic
148C22×C4—21no—
149C22×C4—291no—
150C22×C4—291no—
151C22×C4—291no—
152C22×C4—291no—
153C22×C4—291no—
154C22×C4—582no—
155C22×C4—1162no—
156C22×C4C2×#118111yescharacteristic
157M16—1162no—
158C2×C8—582no—
159C4⋊C4—291no—
160C4⋊C4—291no—
161C4⋊C4—581no—
162C4⋊C4—581no—
163C4⋊C4—1162no—
164C22⋊C4—581no—
165C22⋊C4—581no—
166C22⋊C4—581no—
167C22⋊C4—581no—
168C22⋊C4—581no—
169C22⋊C4—1162no—
170C42—581no—
171C23—21no—
172C23—291no—
173C23—291no—
174C23—581no—
175C23—581no—
176C23—1161no—
177C23—1161no—
178C23C22⋊#118111yescharacteristic
179Q8—41no—
180D4—41no—
181D4—42no—
182D4—1161no—
183D4—1161no—
184D4—1162no—
185C2×C4—22no—
186C2×C4—21no—
187C2×C4—42no—
188C2×C4—291no—
189C2×C4—291no—
190C2×C4—582no—
191C2×C4—582no—
192C2×C4—581no—
193C2×C4—581no—
194C2×C4—1161no—
195C2×C4—1161no—
196C2×C4—1161no—
197C2×C4—1162no—
198C2×C4—1162no—
199C2×C4—1162no—
200C2×C4C22⋊#118111yescharacteristic
201C2×C4C22×#118111yescharacteristic
202C8—1162no—
203C22—21no—
204C22—21no—
205C22—21no—
206C22—41no—
207C22—41no—
208C22—41no—
209C22—291no—
210C22—291no—
211C22—581no—
212C22—581no—
213C22—581no—
214C22—581no—
215C22—581no—
216C22—1162no—
217C22—1162no—
218C22C2×C22⋊#118111yescharacteristic
219C4—21no—
220C4—41no—
221C4—581no—
222C4—581no—
223C4—1161no—
224C4—1161no—
225C4—2322no—
226C4#1174522712yes—
227C2—41no—
228C2—81no—
229C2—581no—
230C2—581no—
231C2—1161no—
232C2C2×#1174522711yescharacteristic
233C2#1427215411yescharacteristic
234C2#1427216011yescharacteristic
subgroupG/H
centerC22C2×C22⋊#1181
commutatorC2×C4×C29C22×C4
FrattiniC2×C4C22×#1181
FittingC2×#41×C29C4
socleC22×C29C2×C22⋊C4
prime radical#14271670C2
cosocleC2×C4×D29C23
hypercenterC2×#41#1181
hypocenterC29#1513
LCSG ▷ C2×C4×C29 ▷ C22×C29 ▷ C29
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#41

Complements

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

NH ≅ G/Ntype
1. #14272134C2semidirect
2. #14272105C2semidirect
3. #14272017C2semidirect
4. #14272014C2semidirect
6. C2×#41×C29C4semidirect
11. #11745308C4semidirect
13. #11745300C4semidirect
19. #11745288C4semidirect
123. C2×#41#1181semidirect
140. C29#1513semidirect

Maximal subgroups

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

subgroupindex
#142721342
#142721052
#142720172
#142720142
#142716702
#151329