Finite Group Databasebeta

← C2×#14271325 #16828701

Subgroups — C2×#14271325 #16828701

Order 3712.

760 conjugacy classes of subgroups; only the 181 normal subgroups are shown.

normal subgroups only

This group has 760 conjugacy classes of subgroups — too many to draw. Only its 181 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×#90785C211yesmaximal, characteristic, complemented
2C22×#90783C211yesmaximal, characteristic, complemented
3C2×#11745286C211yesmaximal, characteristic, complemented
4#14271325C218yesmaximal, direct product factor
5C2×#11745183C211yesmaximal, characteristic, complemented
6C2×#11745180C211yesmaximal, characteristic, complemented
7C2×C22⋊#6597C211yesmaximal, characteristic, complemented
8C22×#41×C29C211yesmaximal, characteristic
9C2×#41×C29—24no—
10C2×#41×C29—24no—
11C2×#41×C29—22no—
12C2×#41×C29C2214yes—
13C22×Q8×C29C2211yescharacteristic
14C22×D4×C29—21no—
15C22×D4×C29C2211yescharacteristic
16C23×C4×C29—21no—
17C23×C4×C29C2211yescharacteristic
18C22×Dic58C2211yescharacteristic
19C2×C22⋊Dic29—21no—
20C2×#90785—24no—
21C2×#90785C2214yescomplemented
22C2×#90783—24no—
23C2×#90783C2214yescomplemented
24C2×C4⋊Dic29C2211yescharacteristic
25#11745286—22no—
26#11745286C2214yescomplemented
27C2×#90779—21no—
28C22×#6597C2211yescharacteristic
29C22×#6597C2211yescharacteristic
30#11745183C2214yescomplemented
31#11745180C2214yescomplemented
32C22⋊#6597C2214yescomplemented
33C24×C29—21no—
34C24×C29D411yescharacteristic
35#41×C29—216no—
36#41×C29—28no—
37#41×C29—28no—
38C2×Q8×C29—22no—
39C2×Q8×C29—21no—
40C2×Q8×C29D414yes—
41C2×Q8×C29C2312yes—
42C2×D4×C29—28no—
43C2×D4×C29—24no—
44C2×D4×C29—21no—
45C2×D4×C29—22no—
46C2×D4×C29D414yes—
47C2×D4×C29C2312yes—
48C22×C4×C29—28no—
49C22×C4×C29—21no—
50C22×C4×C29—24no—
51C22×C4×C29—22no—
52C22×C4×C29—22no—
53C22×C4×C29D411yescharacteristic
54C22×C4×C29D412yes—
55C22×C4×C29C2312yes—
56C22×C4×C29C2311yescharacteristic
57C22×Dic29—21no—
58C22×Dic29—21no—
59C2×Dic58—22no—
60C2×Dic58—22no—
61C2×Dic58—21no—
62C2×Dic58C2312yes—
63C22⋊Dic29—24no—
64#90785—28no—
65#90783—28no—
66C4⋊Dic29—21no—
67C4⋊Dic29C2312yes—
68#90779—24no—
69C2×#6597—22no—
70C2×#6597—22no—
71C2×#6597C2312yes—
72C2×#6597C2312yes—
73C23×C29—22no—
74C23×C29—24no—
75C23×C29—22no—
76C23×C29—22no—
77C23×C29—22no—
78C23×C29—42no—
79C23×C29—42no—
80C23×C29C2×D412yes—
81C23×C29C2×D411yescharacteristic
82Q8×C29—24no—
83Q8×C29—22no—
84Q8×C29C2×D414yes—
85D4×C29—216no—
86D4×C29—24no—
87D4×C29—22no—
88D4×C29C2×D414yes—
89C2×C4×C29—216no—
90C2×C4×C29—22no—
91C2×C4×C29—24no—
92C2×C4×C29—22no—
93C2×C4×C29—24no—
94C2×C4×C29—22no—
95C2×C4×C29—22no—
96C2×C4×C29C2×D412yes—
97C2×C4×C29C2×D411yescharacteristic
98C2×C4×C29C2×D412yes—
99C2×C4×C29C2×D412yes—
100C2×C4×C29C2411yescharacteristic
101C2×Dic29—22no—
102C2×Dic29—22no—
103C2×Dic29—42no—
104C2×Dic29—42no—
105Dic58—22no—
106Dic58—22no—
107Dic58—42no—
108#6597—22no—
109#6597—22no—
110C2×#452—291nomaximal, Sylow
111C22×C29—22no—
112C22×C29—24no—
113C22×C29—22no—
114C22×C29—22no—
115C22×C29—42no—
116C22×C29—42no—
117C22×C29—44no—
118C22×C29—48no—
119C22×C29#12012yes—
120C22×C29#13512yes—
121C22×C29#13712yes—
122C22×C29C22×D411yescharacteristic
123C4×C29—22no—
124C4×C29—24no—
125C4×C29#12012yes—
126C4×C29C22×D411yescharacteristic
127C4×C29C22×D411yescharacteristic
128Dic29—42no—
129Dic29—42no—
130C22×#41D2911yescharacteristic
131C22×Q16—291no—
132C22×SD16—291no—
133C2×C22⋊Q8—291no—
134#452—298no—
135C2×#103—291no—
136C2×#102—291no—
137C2×C22⋊C8—291no—
138C2×C29—42no—
139C2×C29—44no—
140C2×C29#45214yescomplemented
141C2×C29C2×#12011yescharacteristic
142C2×C29C2×#13511yescharacteristic
143C2×C29C2×#13711yescharacteristic
144C2×#41—24no—
145C2×#41—24no—
146C2×#41—22no—
147C2×#41C2×D2914yes—
148C22×Q8—291no—
149C22×Q8C2×D2911yescharacteristic
150C22×D4—21no—
151C22×D4C2×D2911yescharacteristic
152C23×C4—21no—
153C23×C4C2×D2911yescharacteristic
154C2×Q16—294no—
155C2×Q16—584no—
156C2×SD16—294no—
157C2×SD16—584no—
158C22×C8—291no—
159C22×C8—291no—
160C22⋊Q8—294no—
161C22⋊Q8—582no—
162C2×C4⋊C4—291no—
163C2×C4⋊C4—581no—
164C2×C22⋊C4—581no—
165#103—294no—
166#102—294no—
167C22⋊C8—294no—
168C29C2×#45211yescharacteristic, complemented, Sylow
169C24—21no—
170C24C22⋊D2911yescharacteristic
171#41—216no—
172#41—28no—
173#41—28no—
174C2×Q8—22no—
175C2×Q8—21no—
176C2×Q8—292no—
177C2×Q8—581no—
178C2×Q8—582no—
179C2×Q8—582no—
180C2×Q8C22⋊D2914yes—
181C2×Q8C22×D2912yes—
182C2×D4—28no—
183C2×D4—24no—
184C2×D4—21no—
185C2×D4—22no—
186C2×D4C22⋊D2914yes—
187C2×D4C22×D2912yes—
188C22×C4—28no—
189C22×C4—21no—
190C22×C4—24no—
191C22×C4—22no—
192C22×C4—22no—
193C22×C4—581no—
194C22×C4—581no—
195C22×C4C22⋊D2912yes—
196C22×C4C22⋊D2911yescharacteristic
197C22×C4C22×D2912yes—
198C22×C4C22×D2911yescharacteristic
199Q16—588no—
200SD16—588no—
201C2×C8—292no—
202C2×C8—292no—
203C2×C8—582no—
204C2×C8—582no—
205C4⋊C4—292no—
206C4⋊C4—581no—
207C4⋊C4—584no—
208C22⋊C4—584no—
209C23—22no—
210C23—22no—
211C23—22no—
212C23—24no—
213C23—22no—
214C23—42no—
215C23—42no—
216C23C2×C22⋊D2912yes—
217C23C2×C22⋊D2911yescharacteristic
218Q8—24no—
219Q8—22no—
220Q8—582no—
221Q8—582no—
222Q8—1162no—
223Q8C2×C22⋊D2914yes—
224D4—216no—
225D4—24no—
226D4—22no—
227D4C2×C22⋊D2914yes—
228C2×C4—216no—
229C2×C4—22no—
230C2×C4—24no—
231C2×C4—22no—
232C2×C4—24no—
233C2×C4—22no—
234C2×C4—22no—
235C2×C4—582no—
236C2×C4—582no—
237C2×C4—1162no—
238C2×C4—1162no—
239C2×C4C2×C22⋊D2912yes—
240C2×C4C2×C22⋊D2911yescharacteristic
241C2×C4C2×C22⋊D2912yes—
242C2×C4C2×C22⋊D2912yes—
243C2×C4C23×D2911yescharacteristic
244C8—582no—
245C8—582no—
246C22—22no—
247C22—24no—
248C22—22no—
249C22—22no—
250C22—44no—
251C22—48no—
252C22—42no—
253C22—42no—
254C22#1174531212yes—
255C22#1174531312yes—
256C22#1174531512yes—
257C22C22×C22⋊D2911yescharacteristic
258C4—22no—
259C4—24no—
260C4—1162no—
261C4—1162no—
262C4#1174531512yes—
263C4C22×C22⋊D2911yescharacteristic
264C4C22×C22⋊D2911yescharacteristic
265C2—42no—
266C2—44no—
267C2#1427132514yesdirect product factor
268C2C2×#1174531511yescharacteristic
269C2C2×#1174531211yescharacteristic
270C2C2×#1174531311yescharacteristic
subgroupG/H
centerC23C2×C22⋊D29
commutator, cosocleC2×C4×C29C24
FrattiniC2×C4C23×D29
Fitting, prime radicalC22×#41×C29C2
socleC23×C29C2×D4
hypercenterC22×#41D29
hypocenterC29C2×#452
LCSG ▷ C2×C4×C29 ▷ C2×C29 ▷ C29
UCSC1 ◁ C23 ◁ C23×C4 ◁ C22×#41

Complements

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

NH ≅ G/Ntype
1. C22×#90785C2semidirect
2. C22×#90783C2semidirect
3. C2×#11745286C2semidirect
4. #14271325C2direct (N × H)
5. C2×#11745183C2semidirect
6. C2×#11745180C2semidirect
7. C2×C22⋊#6597C2semidirect
21. C2×#90785C22semidirect
23. C2×#90783C22semidirect
26. #11745286C22semidirect
30. #11745183C22semidirect
31. #11745180C22semidirect
32. C22⋊#6597C22semidirect
140. C2×C29#452semidirect
168. C29C2×#452semidirect
267. C2#14271325direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#907852
C22×#907832
C2×#117452862
#142713252
C2×#117451832
C2×#117451802
C2×C22⋊#65972
C22×#41×C292
C2×#45229