Finite Group Databasebeta

← #16835476

Subgroups — #16835476

Order 3712.

376 conjugacy classes of subgroups; only the 72 normal subgroups are shown.

normal subgroups only

This group has 376 conjugacy classes of subgroups — too many to draw. Only its 72 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
1C2×D29⋊M16C211yesmaximal, characteristic, complemented
2C2×#11745224C212yesmaximal, complemented
3C4×C22⋊#1181C211yesmaximal, characteristic, complemented
4#14272033C212yesmaximal, complemented
5#14271673C211yesmaximal, characteristic
6C2×#90807C2211yescharacteristic
7C22×C4×D29C2211yescharacteristic
8C2×C22⋊#1181—21no—
9C2×#90800—21no—
10C2×C4×#1181C2212yes—
11D29⋊M16—24no—
12C2×#90796C2212yes—
13C2×D29⋊C8—21no—
14C29×#121C411yescharacteristic, complemented
15#11745300C411yescharacteristic, complemented
16#11745299—21no—
17D4×Dic29—21no—
18#11745286C411yescharacteristic, complemented
19#11745259C411yescharacteristic, complemented
20#11745254C2211yescharacteristic
21#11745245—21no—
22#11745243—21no—
23#11745224—24no—
24(C2×#1181)⋊C4—21no—
25C23×D29D411yescharacteristic
26C22×#1181—22no—
27C2×D4×C29—21no—
28C2×D4×C29C2×C411yescharacteristic
29C22×C4×C29C2×C411yescharacteristic
30C2×C22⋊D29—21no—
31C2×C22⋊D29—21no—
32C22×Dic29—21no—
33C22×Dic29D411yescharacteristic
34#90807—22no—
35#90807—22no—
36C2×C4×D29—22no—
37C2×C4×D29—22no—
38C2×C4×D29C2×C411yescharacteristic
39C2×C4×D29D411yescharacteristic
40C2×C4×D29D411yescharacteristic
41C2×C4×D29C2311yescharacteristic
42C2×Dic58C2×C411yescharacteristic
43C22⋊#1181—24no—
44#90800—24no—
45C2×#6599—22no—
46C4×#1181—22no—
47C4×#1181—22no—
48#90796—22no—
49#90796D414yescomplemented
50D29⋊C8—24no—
51C4⋊C4×C29C2×C411yescharacteristic
52C22⋊C4×C29—21no—
53C22⋊Dic29—21no—
54C22⋊Dic29—21no—
55#90781—21no—
56#90781—21no—
57C4⋊Dic29—21no—
58C4⋊Dic29C2×C411yescharacteristic
59#90779—21no—
60C4×Dic29—21no—
61C23×C29—21no—
62C23×C29C22⋊C411yescharacteristic
63C22×D29—22no—
64C22×D29—22no—
65C22×D29—41no—
66C22×D29C22⋊C411yescharacteristic
67C22×D29C2×D411yescharacteristic
68C2×#1181—24no—
69C2×#1181—42no—
70C2×#1181—42no—
71D4×C29—22no—
72D4×C29—42no—
73C2×C4×C29—22no—
74C2×C4×C29—21no—
75C2×C4×C29C22⋊C411yescharacteristic
76C2×C4×C29C22×C411yescharacteristic
77C22⋊D29—42no—
78C22⋊D29—42no—
79C2×Dic29—21no—
80C2×Dic29—21no—
81C2×Dic29—21no—
82C2×Dic29—21no—
83C2×Dic29—41no—
84C2×Dic29—41no—
85C2×Dic29C22⋊C411yescharacteristic
86C2×Dic29C2×D411yescharacteristic
87C4×D29—22no—
88C4×D29—22no—
89C4×D29—21no—
90C4×D29—21no—
91C4×D29C2×D412yes—
92C4×D29#4112yes—
93Dic58—22no—
94#6599—24no—
95#1871—291nomaximal, Sylow
96C22×C29—21no—
97C22×C29—21no—
98C22×C29—21no—
99C22×C29—41no—
100C22×C29—41no—
101C22×C29—41no—
102C22×C29C2×C22⋊C411yescharacteristic
103C2×D29—21no—
104C2×D29—21no—
105C2×D29—21no—
106C2×D29—21no—
107C2×D29—44no—
108C2×D29#10412yescomplemented
109C2×D29#12112yes—
110#1181—44no—
111C4×C29—21no—
112C4×C29—41no—
113C4×C29C4×D412yes—
114Dic29—21no—
115Dic29—41no—
116Dic29—41no—
117Dic29#12011yescharacteristic
118Dic29#12311yescharacteristic
119C22×M16—291no—
120#525—291no—
121C2×#104—292no—
122C4×C22⋊C4—291no—
123#339—292no—
124C2×C29—41no—
125C2×C29—81no—
126C2×C29#38611yescharacteristic
127C2×C29C2×#10411yescharacteristic
128C2×C29#42111yescharacteristic
129D29—22no—
130D29—22no—
131C2×#41—291no—
132C23×C4—291no—
133C2×M16—292no—
134C2×M16—584no—
135C2×M16—581no—
136C22×C8—581no—
137#123—581no—
138C22⋊Q8—291no—
139C22⋊Q8—291no—
140#121—291no—
141#121#118111yescharacteristic, complemented
142#120—581no—
143C4×D4—581no—
144C4×D4—581no—
145#117—291no—
146C2×C22⋊C4—581no—
147C2×C42—292no—
148#104—584no—
149#95—581no—
150C29#187111yescharacteristic, complemented, Sylow
151C24—291no—
152#41—582no—
153#41—582no—
154C2×Q8—291no—
155C2×D4—21no—
156C2×D4—581no—
157C2×D4—581no—
158C2×D4C2×#118111yescharacteristic
159C22×C4—291no—
160C22×C4—291no—
161C22×C4—291no—
162C22×C4—291no—
163C22×C4—291no—
164C22×C4—582no—
165C22×C4—582no—
166C22×C4—581no—
167C22×C4—582no—
168C22×C4C2×#118111yescharacteristic
169M16—294no—
170M16—582no—
171M16—584no—
172C2×C8—582no—
173C2×C8—584no—
174C4⋊C4—291no—
175C4⋊C4—581no—
176C4⋊C4—581no—
177C4⋊C4C2×#118111yescharacteristic
178C22⋊C4—21no—
179C22⋊C4—581no—
180C22⋊C4—581no—
181C22⋊C4—581no—
182C22⋊C4—584no—
183C22⋊C4—581no—
184C42—581no—
185C42—582no—
186C42—582no—
187C23—21no—
188C23—291no—
189C23—291no—
190C23—582no—
191C23—582no—
192C23—1161no—
193C23C22⋊#118111yescharacteristic
194Q8—582no—
195D4—22no—
196D4—42no—
197D4—1162no—
198D4—1162no—
199C2×C4—22no—
200C2×C4—21no—
201C2×C4—291no—
202C2×C4—292no—
203C2×C4—292no—
204C2×C4—291no—
205C2×C4—581no—
206C2×C4—581no—
207C2×C4—582no—
208C2×C4—581no—
209C2×C4—581no—
210C2×C4—582no—
211C2×C4—584no—
212C2×C4—581no—
213C2×C4—581no—
214C2×C4—1161no—
215C2×C4—1161no—
216C2×C4—1162no—
217C2×C4—1162no—
218C2×C4C22⋊#118111yescharacteristic
219C2×C4C22×#118111yescharacteristic
220C8—584no—
221C22—21no—
222C22—21no—
223C22—21no—
224C22—41no—
225C22—41no—
226C22—41no—
227C22—292no—
228C22—292no—
229C22—581no—
230C22—581no—
231C22—581no—
232C22—581no—
233C22—1164no—
234C22C2×C22⋊#118111yescharacteristic
235C4—21no—
236C4—41no—
237C4—291no—
238C4—291no—
239C4—581no—
240C4—1164no—
241C4—1161no—
242C4—1161no—
243C4D4×#118112yes—
244C2—41no—
245C2—81no—
246C2—582no—
247C2—582no—
248C2#1427211111yescharacteristic
249C2D29⋊#10411yescharacteristic
250C2#1427216111yescharacteristic
subgroupG/H
centerC22C2×C22⋊#1181
commutatorC2×C4×C29C22×C4
FrattiniC2×C4C22×#1181
FittingC29×#121C4
socleC22×C29C2×C22⋊C4
prime radical#14271673C2
cosocleC2×C4×D29C23
hypercenter#121#1181
hypocenterC29#1871
LCSG ▷ C2×C4×C29 ▷ C2×C29 ▷ C29
UCSC1 ◁ C22 ◁ C22×C4 ◁ #121

Complements

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

NH ≅ G/Ntype
1. C2×D29⋊M16C2semidirect
2. C2×#11745224C2semidirect
3. C4×C22⋊#1181C2semidirect
4. #14272033C2semidirect
14. C29×#121C4semidirect
15. #11745300C4semidirect
18. #11745286C4semidirect
19. #11745259C4semidirect
49. #90796D4semidirect
108. C2×D29#104semidirect
141. #121#1181semidirect
150. C29#1871semidirect

Maximal subgroups

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

subgroupindex
C2×D29⋊M162
C2×#117452242
C4×C22⋊#11812
#142720332
#142716732
#187129