Finite Group Databasebeta

← #16835657

Subgroups — #16835657

Order 3712.

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

normal subgroups only

This group has 336 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×#11745226C212yesmaximal, complemented
2C2×#11745224C212yesmaximal, complemented
3C4×#90796C211yesmaximal, characteristic, complemented
4C4×C4⋊#1181C211yesmaximal, characteristic, complemented
5#14271712C211yesmaximal, characteristic
6C2×#90809C2211yescharacteristic
7C2×#90807C2211yescharacteristic
8C2×C4⋊#1181—21no—
9C2×C4×#1181C2212yes—
10C2×#90796C2212yes—
11C29×#124C411yescharacteristic, complemented
12#11745306C411yescharacteristic, complemented
13#11745302C411yescharacteristic, complemented
14#11745246—21no—
15#11745246—21no—
16#11745243—21no—
17#11745243—21no—
18#11745237C411yescharacteristic, complemented
19C42×D29C2211yescharacteristic
20#11745226—24no—
21#11745224—24no—
22(C2×#1181)⋊C4—21no—
23#11745218—21no—
24C4×#6599—21no—
25C22×#1181—22no—
26C2×Q8×C29C2×C411yescharacteristic
27C2×D4×C29C2×C411yescharacteristic
28C2×C22⋊D29—21no—
29C2×C22⋊D29—21no—
30C2×C22⋊D29—21no—
31C22×Dic29—21no—
32#90809—22no—
33#90809—22no—
34#90807—22no—
35#90807—22no—
36C2×D116—21no—
37C2×D116C2×C411yescharacteristic
38C2×C4×D29—21no—
39C2×C4×D29D411yescharacteristic
40C2×C4×D29D411yescharacteristic
41C2×C4×D29C2311yescharacteristic
42C2×Dic58C2×C411yescharacteristic
43C2×#6599—22no—
44C4⋊#1181—24no—
45C4×#1181—22no—
46C4×#1181—22no—
47#90796—22no—
48#90796D414yescomplemented
49C22⋊C4×C29—21no—
50C22⋊C4×C29—21no—
51C42×C29C2×C411yescharacteristic
52#90781—21no—
53#90781—21no—
54#90779—21no—
55#90779—21no—
56C4×Dic29C2×C411yescharacteristic
57C4×Dic29D411yescharacteristic
58C4×Dic29D411yescharacteristic
59C23×C29—21no—
60C22×D29—21no—
61C22×D29C2×D411yescharacteristic
62C2×#1181—24no—
63C2×#1181—42no—
64C2×#1181—42no—
65Q8×C29—22no—
66D4×C29—22no—
67C2×C4×C29—21no—
68C2×C4×C29C22⋊C411yescharacteristic
69C2×C4×C29C22⋊C411yescharacteristic
70C2×C4×C29C22×C411yescharacteristic
71C22⋊D29—42no—
72C22⋊D29—41no—
73C22⋊D29—41no—
74C22⋊D29—42no—
75C2×Dic29—21no—
76C2×Dic29—42no—
77C2×Dic29C22⋊C411yescharacteristic
78C2×Dic29C22⋊C411yescharacteristic
79C2×Dic29C2×D411yescharacteristic
80D116—22no—
81D116—41no—
82D116—41no—
83C4×D29—22no—
84C4×D29—41no—
85C4×D29—42no—
86C4×D29C2×D412yes—
87C4×D29#4112yes—
88Dic58—22no—
89#6599—24no—
90#1980—291nomaximal, Sylow
91C22×C29—41no—
92C22×C29—41no—
93C22×C29—41no—
94C22×C29C2×C22⋊C411yescharacteristic
95C2×D29—21no—
96C2×D29—21no—
97C2×D29—41no—
98C2×D29—41no—
99C2×D29—41no—
100C2×D29#12411yescharacteristic
101C2×D29#12711yescharacteristic
102#1181—44no—
103C4×C29—21no—
104C4×C29—21no—
105C4×C29—41no—
106C4×C29C4×D412yes—
107Dic29—21no—
108Dic29—41no—
109Dic29#10412yescomplemented
110Dic29#12112yes—
111#532—291no—
112C2×#104—292no—
113C2×#104—292no—
114C4×M16—291no—
115C4×C4⋊C4—291no—
116C2×C29—81no—
117C2×C29#39011yescharacteristic
118C2×C29C2×#10411yescharacteristic
119C2×C29#42111yescharacteristic
120D29—21no—
121D29—21no—
122D29—81no—
123C2×#41—291no—
124C2×#41—291no—
125C2×M16—292no—
126C4⋊Q8—291no—
127#127—291no—
128#124—291no—
129#124#118111yescharacteristic, complemented
130#121—581no—
131#121—581no—
132C4×D4—581no—
133C4×D4—581no—
134C2×C4⋊C4—581no—
135C2×C42—291no—
136C2×C42—292no—
137#104—584no—
138#104—584no—
139#97—581no—
140C4×C8—581no—
141#95—581no—
142C29#198011yescharacteristic, complemented, Sylow
143#41—582no—
144#41—582no—
145#41—582no—
146#41—582no—
147C2×Q8—291no—
148C2×Q8C2×#118111yescharacteristic
149C2×D4—291no—
150C2×D4—581no—
151C2×D4—581no—
152C2×D4—581no—
153C2×D4—581no—
154C2×D4C2×#118111yescharacteristic
155C22×C4—291no—
156C22×C4—291no—
157C22×C4—291no—
158C22×C4—581no—
159C22×C4—581no—
160C22×C4—582no—
161M16—294no—
162M16—582no—
163C2×C8—582no—
164C4⋊C4—581no—
165C4⋊C4—581no—
166C4⋊C4—584no—
167C22⋊C4—21no—
168C22⋊C4—21no—
169C22⋊C4—581no—
170C22⋊C4—581no—
171C42—291no—
172C42—291no—
173C42—291no—
174C42—582no—
175C42—582no—
176C42C2×#118111yescharacteristic
177C23—21no—
178C23—291no—
179C23—581no—
180Q8—22no—
181Q8—582no—
182D4—22no—
183D4—582no—
184D4—1161no—
185D4—1161no—
186D4—1162no—
187D4—1162no—
188D4—1161no—
189D4—1161no—
190C2×C4—21no—
191C2×C4—291no—
192C2×C4—291no—
193C2×C4—292no—
194C2×C4—292no—
195C2×C4—291no—
196C2×C4—582no—
197C2×C4—584no—
198C2×C4—581no—
199C2×C4—1161no—
200C2×C4—1162no—
201C2×C4—1162no—
202C2×C4—1162no—
203C2×C4—1162no—
204C2×C4C22⋊#118111yescharacteristic
205C2×C4C22⋊#118111yescharacteristic
206C2×C4C22×#118111yescharacteristic
207C8—584no—
208C22—41no—
209C22—41no—
210C22—41no—
211C22—291no—
212C22—291no—
213C22—581no—
214C22—581no—
215C22—1161no—
216C22—1161no—
217C22—1161no—
218C22C2×C22⋊#118111yescharacteristic
219C4—21no—
220C4—21no—
221C4—41no—
222C4—292no—
223C4—292no—
224C4—581no—
225C4—1164no—
226C4—1161no—
227C4D4×#118112yes—
228C2—81no—
229C2—581no—
230C2—581no—
231C2—2321no—
232C2#1427211511yescharacteristic
233C2D29⋊#10411yescharacteristic
234C2#1427216011yescharacteristic
subgroupG/H
centerC22C2×C22⋊#1181
commutatorC2×C4×C29C22×C4
FrattiniC2×C4C22×#1181
FittingC29×#124C4
socleC22×C29C2×C22⋊C4
prime radical#14271712C2
cosocleC2×C4×D29C23
hypercenter#124#1181
hypocenterC29#1980
LCSG ▷ C2×C4×C29 ▷ C2×C29 ▷ C29
UCSC1 ◁ C22 ◁ C42 ◁ #124

Complements

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

NH ≅ G/Ntype
1. C2×#11745226C2semidirect
2. C2×#11745224C2semidirect
3. C4×#90796C2semidirect
4. C4×C4⋊#1181C2semidirect
11. C29×#124C4semidirect
12. #11745306C4semidirect
13. #11745302C4semidirect
18. #11745237C4semidirect
48. #90796D4semidirect
109. Dic29#104semidirect
129. #124#1181semidirect
142. C29#1980semidirect

Maximal subgroups

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

subgroupindex
C2×#117452262
C2×#117452242
C4×#907962
C4×C4⋊#11812
#142717122
#198029