Finite Group Databasebeta

← #16818413

Subgroups — #16818413

Order 3712.

316 conjugacy classes of subgroups; only the 51 normal subgroups are shown.

normal subgroups only

This group has 316 conjugacy classes of subgroups — too many to draw. Only its 51 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
1#14271788C211yesmaximal, characteristic, complemented
2#14271314C211yesmaximal, characteristic, complemented
3#14271071C211yesmaximal, characteristic
4#14270901C211yesmaximal, characteristic, complemented
5#14270900C211yesmaximal, characteristic, complemented
6#14270886C211yesmaximal, characteristic, complemented
7C29×#450C211yesmaximal, characteristic, complemented
8C22×D4×C29C2211yescharacteristic
9C22×C22⋊D29—21no—
10C2×SD16×C29—21no—
11C29×C22⋊Q8C2211yescharacteristic
12C2×C22⋊Dic29—21no—
13#11745308—21no—
14C2×#90783—21no—
15C2×#90781C2211yescharacteristic
16#11745286C2211yescharacteristic
17#11745259—21no—
18#11745258—21no—
19#11745258—21no—
20C22⋊C4×D29—21no—
21#11745240—21no—
22C29×#102—21no—
23C29×C22⋊C8C2211yescharacteristic
24#11745180—21no—
25#11745179C2211yescharacteristic
26C22⋊#6597C2211yescharacteristic
27C24×C29—21no—
28C23×D29D411yescharacteristic
29C2×Q8×C29D411yescharacteristic, complemented
30C2×D4×C29—21no—
31C2×D4×C29—21no—
32C2×D4×C29—42no—
33C22×C4×C29C2311yescharacteristic
34C2×C22⋊D29—42no—
35C2×C22⋊D29—42no—
36C2×C22⋊D29—42no—
37C22×Dic29—21no—
38C22×Dic29D411yescharacteristic
39C2×C4×D29—21no—
40C2×C4×D29—21no—
41C2×Dic58—21no—
42C2×Dic58D411yescharacteristic, complemented
43SD16×C29—42no—
44C2×C8×C29—21no—
45C4⋊C4×C29—21no—
46C4⋊C4×C29D411yescharacteristic, complemented
47C22⋊C4×C29—21no—
48C22⋊Dic29—21no—
49C22⋊Dic29—42no—
50#90783—42no—
51#90781—21no—
52#90781—21no—
53#90781—21no—
54#90781—21no—
55C4⋊Dic29—21no—
56C4⋊Dic29D411yescharacteristic, complemented
57#90779—21no—
58#90779—21no—
59#90779—21no—
60C2×#6597—21no—
61C23×C29—22no—
62C23×C29—41no—
63C23×C29—41no—
64C23×C29—41no—
65C23×C29—41no—
66C23×C29—41no—
67C23×C29—41no—
68C23×C29C2×D411yescharacteristic
69C22×D29—21no—
70C22×D29—21no—
71C22×D29—41no—
72C22×D29—41no—
73C22×D29SD1612yescomplemented
74Q8×C29—41no—
75D4×C29—22no—
76D4×C29—22no—
77D4×C29—41no—
78D4×C29—41no—
79C2×C4×C29—21no—
80C2×C4×C29—21no—
81C2×C4×C29—41no—
82C2×C4×C29C2×D411yescharacteristic
83C2×C4×C29C2×D411yescharacteristic
84C22⋊D29—48no—
85C2×Dic29—22no—
86C2×Dic29—21no—
87C2×Dic29—21no—
88C2×Dic29—21no—
89C2×Dic29—41no—
90C2×Dic29—41no—
91C2×Dic29—41no—
92C4×D29—81no—
93C4×D29—81no—
94Dic58—41no—
95Dic58—81no—
96C8×C29—41no—
97#6597—41no—
98#1596—291nomaximal, Sylow
99C22×C29—21no—
100C22×C29—21no—
101C22×C29—42no—
102C22×C29—42no—
103C22×C29—42no—
104C22×C29—81no—
105C22×C29—81no—
106C22×C29—81no—
107C22×C29—81no—
108C22×C29#12011yescharacteristic
109C22×C29C2×SD1611yescharacteristic
110C22×C29#13711yescharacteristic
111C2×D29—22no—
112C2×D29—41no—
113C2×D29—41no—
114C2×D29—42no—
115C2×D29—81no—
116C4×C29—21no—
117C4×C29—21no—
118C4×C29—41no—
119C4×C29—41no—
120Dic29—42no—
121Dic29—41no—
122Dic29—41no—
123Dic29—41no—
124#543—291no—
125#450—291no—
126#450D2911yescharacteristic, complemented
127#392—291no—
128#328—291no—
129#328—291no—
130#323—291no—
131C2×C29—21no—
132C2×C29—21no—
133C2×C29—82no—
134C2×C29#44811yescharacteristic
135C2×C29#45311yescharacteristic
136C2×C29B(4,𝔽2)11yescharacteristic
137D29—42no—
138C22×D4—581no—
139C22×D4C2×D2911yescharacteristic
140C2×SD16—21no—
141C2×SD16—581no—
142C22⋊Q8—291no—
143C22⋊Q8—581no—
144C22⋊Q8—581no—
145C22⋊Q8—581no—
146C22⋊Q8—581no—
147C22⋊Q8—581no—
148C22⋊Q8C2×D2911yescharacteristic
149C2×C22⋊C4—291no—
150C2×C22⋊C4—581no—
151C2×C22⋊C4—581no—
152#102—21no—
153#102—581no—
154C22⋊C8—291no—
155C22⋊C8C2×D2911yescharacteristic
156#95—291no—
157C29#159611yescharacteristic, complemented, Sylow
158C24—21no—
159C24—291no—
160C2×Q8—291no—
161C2×Q8—581no—
162C2×Q8C22⋊D2911yescharacteristic, complemented
163C2×D4—21no—
164C2×D4—21no—
165C2×D4—42no—
166C2×D4—1162no—
167C2×D4—1162no—
168C2×D4—1162no—
169C22×C4—291no—
170C22×C4—581no—
171C22×C4—581no—
172C22×C4—581no—
173C22×C4C22×D2911yescharacteristic
174SD16—42no—
175SD16—1162no—
176C2×C8—21no—
177C2×C8—581no—
178C4⋊C4—21no—
179C4⋊C4—291no—
180C4⋊C4—581no—
181C4⋊C4—581no—
182C4⋊C4—581no—
183C4⋊C4—581no—
184C4⋊C4C22⋊D2911yescharacteristic, complemented
185C22⋊C4—21no—
186C22⋊C4—581no—
187C22⋊C4—581no—
188C22⋊C4—581no—
189C22⋊C4—581no—
190C22⋊C4—581no—
191C22⋊C4—1162no—
192C23—22no—
193C23—41no—
194C23—41no—
195C23—41no—
196C23—41no—
197C23—41no—
198C23—41no—
199C23—292no—
200C23—581no—
201C23—581no—
202C23—1161no—
203C23—1161no—
204C23D4×D2911yescharacteristic
205Q8—41no—
206Q8—1161no—
207Q8—2321no—
208D4—22no—
209D4—22no—
210D4—41no—
211D4—41no—
212D4—1168no—
213C2×C4—21no—
214C2×C4—21no—
215C2×C4—41no—
216C2×C4—582no—
217C2×C4—581no—
218C2×C4—581no—
219C2×C4—581no—
220C2×C4—1161no—
221C2×C4—1161no—
222C2×C4—1161no—
223C2×C4—2321no—
224C2×C4—2321no—
225C2×C4D4×D2911yescharacteristic
226C2×C4C2×C22⋊D2911yescharacteristic
227C8—41no—
228C8—1161no—
229C22—21no—
230C22—21no—
231C22—42no—
232C22—42no—
233C22—42no—
234C22—81no—
235C22—81no—
236C22—81no—
237C22—81no—
238C22—582no—
239C22—1162no—
240C22—1161no—
241C22—1161no—
242C22—2321no—
243C22SD16×D2911yescharacteristic
244C22#1174527711yescharacteristic
245C22#1174529911yescharacteristic
246C4—21no—
247C4—21no—
248C4—41no—
249C4—41no—
250C4—1162no—
251C4—1161no—
252C4—1161no—
253C4—1161no—
254C2—21no—
255C2—21no—
256C2—82no—
257C2—1162no—
258C2#1427130011yescharacteristic
259C2#1427132911yescharacteristic
260C2#1427134911yescharacteristic
subgroupG/H
centerC22#11745299
commutator, cosocleC22×C4×C29C23
FrattiniC22×C4C22×D29
FittingC29×#450C2
socleC22×C29#120
prime radical#14271071C2
hypercenter#450D29
hypocenterC29#1596
LCSG ▷ C22×C4×C29 ▷ C22×C29 ▷ C29
UCSC1 ◁ C22 ◁ C22×C4 ◁ #450

Complements

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

NH ≅ G/Ntype
1. #14271788C2semidirect
2. #14271314C2semidirect
4. #14270901C2semidirect
5. #14270900C2semidirect
6. #14270886C2semidirect
7. C29×#450C2semidirect
29. C2×Q8×C29D4semidirect
42. C2×Dic58D4semidirect
46. C4⋊C4×C29D4semidirect
56. C4⋊Dic29D4semidirect
73. C22×D29SD16semidirect
126. #450D29semidirect
157. C29#1596semidirect
162. C2×Q8C22⋊D29semidirect
184. C4⋊C4C22⋊D29semidirect

Maximal subgroups

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

subgroupindex
#142717882
#142713142
#142710712
#142709012
#142709002
#142708862
C29×#4502
#159629