Finite Group Databasebeta

← #16819792

Subgroups — #16819792

Order 3712.

376 conjugacy classes of subgroups; only the 93 normal subgroups are shown.

normal subgroups only

This group has 376 conjugacy classes of subgroups — too many to draw. Only its 93 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
1C22×#90777C211yesmaximal, characteristic, complemented
2#14271674C211yesmaximal, characteristic
3C2×#11745153C212yesmaximal, complemented
4#14270923C212yesmaximal, complemented
5C4×C22⋊C4×C29C211yesmaximal, characteristic, complemented
6C23×C4×C29C2211yescharacteristic
7C2×#90805C2211yescharacteristic
8C2×C22⋊C4×C29—21no—
9C2×C42×C29C2212yes—
10#11745315—21no—
11#11745292C411yescharacteristic, complemented
12#11745292C411yescharacteristic, complemented
13#11745291—21no—
14C4×C22⋊D29—21no—
15C4×C22⋊D29—21no—
16#11745288C2211yescharacteristic
17#11745286C411yescharacteristic, complemented
18#11745286C411yescharacteristic, complemented
19C2×#90777—21no—
20C2×#90777—24no—
21C2×#90777C2212yes—
22C22×#6597—21no—
23C29×#95—21no—
24#11745153—24no—
25C24×C29D411yescharacteristic
26C22×C4×C29—22no—
27C22×C4×C29—22no—
28C22×C4×C29—22no—
29C22×C4×C29C2×C411yescharacteristic
30C22×C4×C29C2×C411yescharacteristic
31C22×C4×C29D411yescharacteristic
32C22×C4×C29D411yescharacteristic
33C22×C4×C29D411yescharacteristic
34C22×C4×C29C2311yescharacteristic
35C2×C22⋊D29—21no—
36C2×C22⋊D29—21no—
37C2×C22⋊D29—21no—
38#90805—22no—
39#90805—22no—
40C2×D116C2×C411yescharacteristic
41C2×C4×D29—21no—
42C2×Dic58C2×C411yescharacteristic
43C22⋊C4×C29—24no—
44C42×C29—22no—
45C42×C29—22no—
46C22⋊Dic29—21no—
47C22⋊Dic29—21no—
48C22⋊Dic29—21no—
49#90781—21no—
50#90781—21no—
51C4⋊Dic29C2×C411yescharacteristic
52C4⋊Dic29C2×C411yescharacteristic
53#90779—21no—
54#90779—21no—
55C4×Dic29—21no—
56#90777—24no—
57#90777—22no—
58#90777D414yescomplemented
59C2×#6597—24no—
60C2×#6597—22no—
61C23×C29—22no—
62C23×C29—22no—
63C23×C29—41no—
64C23×C29C22⋊C411yescharacteristic
65C23×C29C22⋊C411yescharacteristic
66C23×C29C2×D411yescharacteristic
67C22×D29—21no—
68C2×C4×C29—22no—
69C2×C4×C29—22no—
70C2×C4×C29—22no—
71C2×C4×C29—21no—
72C2×C4×C29—21no—
73C2×C4×C29—21no—
74C2×C4×C29—21no—
75C2×C4×C29—24no—
76C2×C4×C29—42no—
77C2×C4×C29—42no—
78C2×C4×C29C22⋊C411yescharacteristic
79C2×C4×C29C22⋊C411yescharacteristic
80C2×C4×C29C22×C411yescharacteristic
81C2×C4×C29C2×D411yescharacteristic
82C2×C4×C29C2×D412yes—
83C2×C4×C29#4112yes—
84C22⋊D29—42no—
85C22⋊D29—42no—
86C22⋊D29—42no—
87C2×Dic29—21no—
88C2×Dic29—21no—
89C2×Dic29—21no—
90D116—22no—
91C4×D29—41no—
92C4×D29—41no—
93Dic58—22no—
94#6597—24no—
95#1871—291nomaximal, Sylow
96C22×C29—21no—
97C22×C29—21no—
98C22×C29—21no—
99C22×C29—21no—
100C22×C29—21no—
101C22×C29—21no—
102C22×C29—21no—
103C22×C29—44no—
104C22×C29#10412yescomplemented
105C22×C29C2×C22⋊C411yescharacteristic
106C22×C29#12112yes—
107C2×D29—41no—
108C2×D29—41no—
109C2×D29—41no—
110C4×C29—21no—
111C4×C29—21no—
112C4×C29—44no—
113C4×C29C4×D412yes—
114C4×C29#12011yescharacteristic
115C4×C29#12311yescharacteristic
116Dic29—41no—
117Dic29—41no—
118Dic29—41no—
119C22×M16—291no—
120#525—291no—
121C2×#104—292no—
122C4×C22⋊C4D2911yescharacteristic, complemented
123#339—292no—
124C2×C29—22no—
125C2×C29—22no—
126C2×C29—41no—
127C2×C29#38611yescharacteristic
128C2×C29C2×#10411yescharacteristic
129C2×C29#42111yescharacteristic
130D29—81no—
131C2×#41—291no—
132C23×C4C2×D2911yescharacteristic
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—291no—
142#120—581no—
143C4×D4—581no—
144C4×D4—581no—
145#117—291no—
146C2×C22⋊C4—21no—
147C2×C42C2×D2912yes—
148#104—584no—
149#95—21no—
150C29#187111yescharacteristic, complemented, Sylow
151C24C22⋊D2911yescharacteristic
152#41—582no—
153#41—582no—
154C2×Q8—291no—
155C2×D4—291no—
156C2×D4—581no—
157C2×D4—581no—
158C2×D4—581no—
159C22×C4—22no—
160C22×C4—22no—
161C22×C4—22no—
162C22×C4—581no—
163C22×C4C4×D2911yescharacteristic
164C22×C4C4×D2911yescharacteristic
165C22×C4D11611yescharacteristic
166C22×C4D11611yescharacteristic
167C22×C4C22⋊D2911yescharacteristic
168C22×C4C22×D2911yescharacteristic
169M16—294no—
170M16—584no—
171M16—582no—
172C2×C8—584no—
173C2×C8—582no—
174C4⋊C4—291no—
175C4⋊C4—291no—
176C4⋊C4—581no—
177C4⋊C4—581no—
178C22⋊C4—24no—
179C22⋊C4—581no—
180C22⋊C4—581no—
181C22⋊C4—581no—
182C22⋊C4—581no—
183C22⋊C4—581no—
184C42—22no—
185C42—22no—
186C42—581no—
187C23—22no—
188C23—22no—
189C23—41no—
190C23—581no—
191C23#9078111yescharacteristic
192C23#9078111yescharacteristic
193C23C2×C22⋊D2911yescharacteristic
194Q8—582no—
195D4—582no—
196D4—1162no—
197D4—1162no—
198D4—1162no—
199C2×C4—22no—
200C2×C4—22no—
201C2×C4—22no—
202C2×C4—21no—
203C2×C4—21no—
204C2×C4—21no—
205C2×C4—21no—
206C2×C4—24no—
207C2×C4—42no—
208C2×C4—42no—
209C2×C4—581no—
210C2×C4—581no—
211C2×C4—581no—
212C2×C4—1161no—
213C2×C4—1161no—
214C2×C4#9078111yescharacteristic
215C2×C4#9078111yescharacteristic
216C2×C4C2×C4×D2911yescharacteristic
217C2×C4C2×D11611yescharacteristic
218C2×C4D4×D2912yes—
219C2×C4#9080712yes—
220C8—584no—
221C22—21no—
222C22—21no—
223C22—21no—
224C22—21no—
225C22—21no—
226C22—21no—
227C22—21no—
228C22—44no—
229C22—1161no—
230C22—1161no—
231C22—1161no—
232C22#1174515312yescomplemented
233C22C2×#9078111yescharacteristic
234C22#1174530112yes—
235C4—21no—
236C4—21no—
237C4—44no—
238C4—1161no—
239C4—1161no—
240C4—1161no—
241C4#1174524312yes—
242C4#1174524411yescharacteristic
243C4#1174524811yescharacteristic
244C2—22no—
245C2—22no—
246C2—41no—
247C2—2321no—
248C2#1427104011yescharacteristic
249C2C2×#1174515311yescharacteristic
250C2#1427118111yescharacteristic
subgroupG/H
centerC2×C4C2×D116
commutatorC2×C4×C29C22×C4
FrattiniC22×C4C22×D29
FittingC4×C22⋊C4×C29C2
socleC22×C29C2×C22⋊C4
prime radical#14271674C2
cosocleC22×C4×C29C23
hypercenterC4×C22⋊C4D29
hypocenterC29#1871
LCSG ▷ C2×C4×C29 ▷ C2×C29 ▷ C29
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ C4×C22⋊C4

Complements

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

NH ≅ G/Ntype
1. C22×#90777C2semidirect
3. C2×#11745153C2semidirect
4. #14270923C2semidirect
5. C4×C22⋊C4×C29C2semidirect
11. #11745292C4semidirect
12. #11745292C4semidirect
17. #11745286C4semidirect
18. #11745286C4semidirect
58. #90777D4semidirect
104. C22×C29#104semidirect
122. C4×C22⋊C4D29semidirect
150. C29#1871semidirect
232. C22#11745153semidirect

Maximal subgroups

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

subgroupindex
C22×#907772
#142716742
C2×#117451532
#142709232
C4×C22⋊C4×C292
#187129