Finite Group Databasebeta

← #16835511

Subgroups — #16835511

Order 3712.

358 conjugacy classes of subgroups; only the 70 normal subgroups are shown.

normal subgroups only

This group has 358 conjugacy classes of subgroups — too many to draw. Only its 70 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×#11745345C211yesmaximal, characteristic, complemented
2C2×#11745226C212yesmaximal, complemented
3#14272134C211yesmaximal, characteristic, complemented
4#14272033C212yesmaximal, complemented
5#14271676C211yesmaximal, characteristic
6C2×#90809C2211yescharacteristic
7C22×C4×D29C2211yescharacteristic
8C2×C22⋊#1181—21no—
9#11745345—24no—
10C2×C4⋊#1181—21no—
11C2×C4×#1181C2212yes—
12C2×#90796C2212yes—
13C29×C22⋊Q8C411yescharacteristic, complemented
14#11745308C411yescharacteristic, complemented
15#11745292C411yescharacteristic, complemented
16#11745257C411yescharacteristic, complemented
17#11745256—21no—
18#11745255—21no—
19#11745254C2211yescharacteristic
20#11745244—21no—
21#11745243—21no—
22C22⋊#6599—21no—
23#11745226—24no—
24#11745219—21no—
25C23×D29D411yescharacteristic
26C22×#1181—22no—
27C2×Q8×C29C2×C411yescharacteristic
28C22×C4×C29C2×C411yescharacteristic
29C2×C22⋊D29—21no—
30C22×Dic29D411yescharacteristic
31#90809—22no—
32#90809—22no—
33C2×D116—21no—
34C2×D116—21no—
35C2×D116C2×C411yescharacteristic
36C2×C4×D29—22no—
37C2×C4×D29—22no—
38C2×C4×D29—21no—
39C2×C4×D29C2×C411yescharacteristic
40C2×C4×D29D411yescharacteristic
41C2×C4×D29D411yescharacteristic
42C2×C4×D29C2311yescharacteristic
43C22⋊#1181—24no—
44C2×#6599—22no—
45C4⋊#1181—24no—
46C4×#1181—22no—
47C4×#1181D414yescomplemented
48#90796—22no—
49#90796—22no—
50C4⋊C4×C29—21no—
51C4⋊C4×C29C2×C411yescharacteristic
52C22⋊C4×C29—21no—
53#90781—21no—
54#90781—21no—
55#90781—21no—
56#90781—21no—
57C4⋊Dic29C2×C411yescharacteristic
58#90779—21no—
59C4×Dic29—21no—
60C23×C29C22⋊C411yescharacteristic
61C22×D29—21no—
62C22×D29—21no—
63C22×D29—21no—
64C22×D29—41no—
65C22×D29—41no—
66C22×D29C22⋊C411yescharacteristic
67C22×D29C2×D411yescharacteristic
68C2×#1181—24no—
69C2×#1181—42no—
70C2×#1181—42no—
71Q8×C29—22no—
72C2×C4×C29—22no—
73C2×C4×C29—21no—
74C2×C4×C29—21no—
75C2×C4×C29C22⋊C411yescharacteristic
76C2×C4×C29C22×C411yescharacteristic
77C22⋊D29—42no—
78C2×Dic29—22no—
79C2×Dic29—21no—
80C2×Dic29C22⋊C411yescharacteristic
81C2×Dic29C2×D411yescharacteristic
82D116—22no—
83D116—42no—
84D116—41no—
85D116—41no—
86C4×D29—21no—
87C4×D29—21no—
88C4×D29—22no—
89C4×D29—22no—
90C4×D29—42no—
91C4×D29C2×D412yes—
92C4×D29#4112yes—
93#6599—42no—
94#1897—291nomaximal, Sylow
95C22×C29—21no—
96C22×C29—21no—
97C22×C29—21no—
98C22×C29C2×C22⋊C411yescharacteristic
99C2×D29—21no—
100C2×D29—21no—
101C2×D29—21no—
102C2×D29—21no—
103C2×D29—21no—
104C2×D29—42no—
105C2×D29—42no—
106C2×D29—41no—
107C2×D29—41no—
108C2×D29—41no—
109C2×D29#12011yescharacteristic
110C2×D29#12311yescharacteristic
111#1181—44no—
112C4×C29—21no—
113C4×C29—41no—
114C4×C29—41no—
115C4×C29C4×D412yes—
116Dic29—21no—
117Dic29—41no—
118Dic29#12112yes—
119#525—291no—
120C2×#117—291no—
121C2×#104—292no—
122#407—291no—
123#339—292no—
124C2×C29—41no—
125C2×C29#38611yescharacteristic
126C2×C29#42111yescharacteristic
127C2×C29#42111yescharacteristic
128D29—21no—
129D29—21no—
130D29—41no—
131D29—81no—
132C2×#41—291no—
133C23×C4—291no—
134C2×M16—292no—
135#123—581no—
136C22⋊Q8—291no—
137C22⋊Q8#118111yescharacteristic, complemented
138#121—291no—
139#121—291no—
140#120—581no—
141C4×D4—581no—
142C4×D4—581no—
143#117—291no—
144#117—584no—
145C2×C4⋊C4—581no—
146C2×C22⋊C4—581no—
147C2×C42—292no—
148#104—584no—
149C22⋊C8—581no—
150C22⋊C8—581no—
151C29#189711yescharacteristic, complemented, Sylow
152C24—291no—
153#41—582no—
154#41—582no—
155C2×Q8C2×#118111yescharacteristic
156C2×D4—291no—
157C2×D4—581no—
158C2×D4—581no—
159C2×D4—581no—
160C22×C4—291no—
161C22×C4—291no—
162C22×C4—291no—
163C22×C4—291no—
164C22×C4—291no—
165C22×C4—582no—
166C22×C4—582no—
167C22×C4—581no—
168C22×C4—582no—
169C22×C4C2×#118111yescharacteristic
170M16—582no—
171M16—582no—
172C2×C8—582no—
173C4⋊C4—21no—
174C4⋊C4—291no—
175C4⋊C4—581no—
176C4⋊C4—584no—
177C4⋊C4C2×#118111yescharacteristic
178C22⋊C4—21no—
179C22⋊C4—581no—
180C22⋊C4—581no—
181C22⋊C4—581no—
182C22⋊C4—584no—
183C22⋊C4—581no—
184C42—294no—
185C42—581no—
186C42—582no—
187C23—291no—
188C23—291no—
189C23—581no—
190C23—581no—
191C23—581no—
192C23—1161no—
193C23—1161no—
194C23C22⋊#118111yescharacteristic
195Q8—22no—
196D4—582no—
197D4—1161no—
198D4—1161no—
199D4—1162no—
200D4—1162no—
201C2×C4—22no—
202C2×C4—21no—
203C2×C4—21no—
204C2×C4—291no—
205C2×C4—292no—
206C2×C4—292no—
207C2×C4—291no—
208C2×C4—582no—
209C2×C4—581no—
210C2×C4—581no—
211C2×C4—582no—
212C2×C4—582no—
213C2×C4—584no—
214C2×C4—581no—
215C2×C4—1162no—
216C2×C4—1162no—
217C2×C4—1162no—
218C2×C4C22⋊#118111yescharacteristic
219C2×C4C22×#118111yescharacteristic
220C8—1162no—
221C22—21no—
222C22—21no—
223C22—21no—
224C22—291no—
225C22—291no—
226C22—581no—
227C22—581no—
228C22—581no—
229C22—581no—
230C22—581no—
231C22—1162no—
232C22—1162no—
233C22—1161no—
234C22—1161no—
235C22—1161no—
236C22C2×C22⋊#118111yescharacteristic
237C4—21no—
238C4—41no—
239C4—41no—
240C4—292no—
241C4—581no—
242C4—1164no—
243C4—1161no—
244C4D4×#118112yes—
245C2—41no—
246C2—581no—
247C2—581no—
248C2—1161no—
249C2—2321no—
250C2#1427211111yescharacteristic
251C2#1427216011yescharacteristic
252C2#1427216211yescharacteristic
subgroupG/H
centerC22C2×C22⋊#1181
commutatorC2×C4×C29C22×C4
FrattiniC2×C4C22×#1181
FittingC29×C22⋊Q8C4
socleC22×C29C2×C22⋊C4
prime radical#14271676C2
cosocleC2×C4×D29C23
hypercenterC22⋊Q8#1181
hypocenterC29#1897
LCSG ▷ C2×C4×C29 ▷ C2×C29 ▷ C29
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22⋊Q8

Complements

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

NH ≅ G/Ntype
1. C2×#11745345C2semidirect
2. C2×#11745226C2semidirect
3. #14272134C2semidirect
4. #14272033C2semidirect
13. C29×C22⋊Q8C4semidirect
14. #11745308C4semidirect
15. #11745292C4semidirect
16. #11745257C4semidirect
47. C4×#1181D4semidirect
137. C22⋊Q8#1181semidirect
151. C29#1897semidirect

Maximal subgroups

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

subgroupindex
C2×#117453452
C2×#117452262
#142721342
#142720332
#142716762
#189729