Finite Group Databasebeta

← #16818421

Subgroups — #16818421

Order 3712.

272 conjugacy classes of subgroups; only the 53 normal subgroups are shown.

normal subgroups only

This group has 272 conjugacy classes of subgroups — too many to draw. Only its 53 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#14271313C211yesmaximal, characteristic, complemented
2#14271296C211yesmaximal, characteristic
3#14271080C211yesmaximal, characteristic, complemented
4#14270900C211yesmaximal, characteristic, complemented
5#14270897C211yesmaximal, characteristic, complemented
6#14270889C211yesmaximal, characteristic, complemented
7C29×#539C211yesmaximal, characteristic, complemented
8C22×D116C2211yescharacteristic
9C29×#126—21no—
10C29×#125—21no—
11C29×#123—21no—
12C29×#123—21no—
13C29×C22⋊Q8—21no—
14C29×C22⋊Q8C2211yescharacteristic
15C29×#121C2211yescharacteristic
16C4×D4×C29—21no—
17C2×C4⋊C4×C29C2211yescharacteristic
18C2×#90784—21no—
19C2×#90782—21no—
20C2×#90781—21no—
21C2×#90781—21no—
22#11745179C2211yescharacteristic
23C22⋊#6597C2211yescharacteristic
24C22⋊#6597C2211yescharacteristic
25#11745157—21no—
26#11745157—21no—
27C23×D29—21no—
28C2×Q8×C29D411yescharacteristic
29C2×D4×C29—21no—
30C2×D4×C29D411yescharacteristic
31C22×C4×C29—21no—
32C22×C4×C29D411yescharacteristic
33C22×C4×C29D411yescharacteristic
34C22×C4×C29C2311yescharacteristic
35C22×Dic29—21no—
36C2×D116—21no—
37C2×D116—21no—
38C2×D116—42no—
39C4⋊C4×C29—21no—
40C4⋊C4×C29—21no—
41C4⋊C4×C29—21no—
42C4⋊C4×C29—21no—
43C4⋊C4×C29—21no—
44C4⋊C4×C29—21no—
45C4⋊C4×C29D411yescharacteristic
46C4⋊C4×C29D411yescharacteristic
47C22⋊C4×C29—21no—
48C22⋊C4×C29—21no—
49C22⋊C4×C29—21no—
50C22⋊C4×C29—21no—
51C22⋊C4×C29—21no—
52C42×C29—21no—
53#90784—42no—
54#90782—42no—
55#90781—42no—
56#90781—42no—
57C2×#6597—21no—
58C2×#6597—21no—
59C23×C29—21no—
60C23×C29C2×D411yescharacteristic
61C22×D29—22no—
62C22×D29—41no—
63C22×D29—41no—
64C22×D29—41no—
65C22×D29—41no—
66C22×D29—41no—
67C22×D29—41no—
68Q8×C29—41no—
69D4×C29—41no—
70D4×C29—41no—
71D4×C29—41no—
72C2×C4×C29—21no—
73C2×C4×C29—21no—
74C2×C4×C29—21no—
75C2×C4×C29—21no—
76C2×C4×C29—21no—
77C2×C4×C29—21no—
78C2×C4×C29—21no—
79C2×C4×C29—41no—
80C2×C4×C29—41no—
81C2×C4×C29—81no—
82C2×C4×C29C2×D411yescharacteristic
83C2×C4×C29C2×D411yescharacteristic
84C2×Dic29—41no—
85C2×Dic29—41no—
86C2×Dic29—41no—
87D116—22no—
88D116—22no—
89D116—41no—
90D116—41no—
91#6597—41no—
92#6597—41no—
93#1597—291nomaximal, Sylow
94C22×C29—21no—
95C22×C29—21no—
96C22×C29—41no—
97C22×C29—41no—
98C22×C29—41no—
99C22×C29#12011yescharacteristic
100C22×C29#13511yescharacteristic
101C22×C29AGL(1,ℤ/8)11yescharacteristic
102C2×D29—42no—
103C2×D29—42no—
104C2×D29—42no—
105C2×D29—81no—
106C2×D29—81no—
107C2×D29—81no—
108C2×D29—81no—
109C4×C29—21no—
110C4×C29—21no—
111C4×C29—41no—
112C4×C29—41no—
113C4×C29—41no—
114C4×C29—41no—
115C4×C29—41no—
116Dic29—81no—
117#539D2911yescharacteristic, complemented
118#450—291no—
119#447—291no—
120#394—291no—
121#328—291no—
122#327—291no—
123#324—291no—
124C2×C29—21no—
125C2×C29—21no—
126C2×C29—81no—
127C2×C29#44911yescharacteristic
128C2×C29#45411yescharacteristic
129C2×C29B(4,𝔽2)11yescharacteristic
130D29—82no—
131C22×D4—291no—
132C2×SD16—581no—
133C2×D8—581no—
134#126—21no—
135#125—21no—
136#123—21no—
137#123—21no—
138C22⋊Q8—21no—
139C22⋊Q8C2×D2911yescharacteristic
140#121C2×D2911yescharacteristic
141C4×D4—21no—
142C2×C4⋊C4C2×D2911yescharacteristic
143C2×C22⋊C4—581no—
144C2×C22⋊C4—581no—
145#102—581no—
146#102—581no—
147C22⋊C8—291no—
148C22⋊C8—291no—
149#95—291no—
150C29#159711yescharacteristic, complemented, Sylow
151C24—581no—
152C2×Q8C22⋊D2911yescharacteristic
153C2×D4—21no—
154C2×D4—581no—
155C2×D4—581no—
156C2×D4—1162no—
157C2×D4C22⋊D2911yescharacteristic
158C22×C4—21no—
159C22×C4—581no—
160C22×C4C22⋊D2911yescharacteristic
161C22×C4C22⋊D2911yescharacteristic
162C22×C4C22×D2911yescharacteristic
163SD16—1162no—
164D8—1162no—
165C2×C8—581no—
166C2×C8—581no—
167C4⋊C4—21no—
168C4⋊C4—21no—
169C4⋊C4—21no—
170C4⋊C4—21no—
171C4⋊C4—21no—
172C4⋊C4—21no—
173C4⋊C4C22⋊D2911yescharacteristic
174C4⋊C4C22⋊D2911yescharacteristic
175C22⋊C4—21no—
176C22⋊C4—21no—
177C22⋊C4—21no—
178C22⋊C4—21no—
179C22⋊C4—21no—
180C22⋊C4—1162no—
181C22⋊C4—1162no—
182C42—21no—
183C23—21no—
184C23—582no—
185C23—1161no—
186C23—1161no—
187C23—1161no—
188C23—1161no—
189C23—1161no—
190C23—1161no—
191C23C2×C22⋊D2911yescharacteristic
192Q8—41no—
193D4—41no—
194D4—41no—
195D4—41no—
196D4—582no—
197D4—582no—
198D4—1161no—
199D4—1161no—
200C2×C4—21no—
201C2×C4—21no—
202C2×C4—21no—
203C2×C4—21no—
204C2×C4—21no—
205C2×C4—21no—
206C2×C4—21no—
207C2×C4—41no—
208C2×C4—41no—
209C2×C4—81no—
210C2×C4—1161no—
211C2×C4—1161no—
212C2×C4—1161no—
213C2×C4C2×C22⋊D2911yescharacteristic
214C2×C4C2×C22⋊D2911yescharacteristic
215C8—1161no—
216C8—1161no—
217C22—21no—
218C22—21no—
219C22—41no—
220C22—41no—
221C22—41no—
222C22—1162no—
223C22—1162no—
224C22—1162no—
225C22—2321no—
226C22—2321no—
227C22—2321no—
228C22—2321no—
229C22#1174531111yescharacteristic
230C22#1174531211yescharacteristic
231C22#1174531511yescharacteristic
232C4—21no—
233C4—21no—
234C4—41no—
235C4—41no—
236C4—41no—
237C4—41no—
238C4—41no—
239C4—2321no—
240C2—21no—
241C2—21no—
242C2—81no—
243C2—2322no—
244C2#1427130811yescharacteristic
245C2#1427133611yescharacteristic
246C2#1427135011yescharacteristic
subgroupG/H
centerC22#11745315
commutator, cosocleC22×C4×C29C23
FrattiniC22×C4C22×D29
FittingC29×#539C2
socleC22×C29#120
prime radical#14271296C2
hypercenter#539D29
hypocenterC29#1597
LCSG ▷ C22×C4×C29 ▷ C22×C29 ▷ C29
UCSC1 ◁ C22 ◁ C22×C4 ◁ #539

Complements

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

NH ≅ G/Ntype
1. #14271313C2semidirect
3. #14271080C2semidirect
4. #14270900C2semidirect
5. #14270897C2semidirect
6. #14270889C2semidirect
7. C29×#539C2semidirect
117. #539D29semidirect
150. C29#1597semidirect

Maximal subgroups

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

subgroupindex
#142713132
#142712962
#142710802
#142709002
#142708972
#142708892
C29×#5392
#159729