Finite Group Databasebeta

← #16818418

Subgroups — #16818418

Order 3712.

272 conjugacy classes of subgroups; only the 49 normal subgroups are shown.

normal subgroups only

This group has 272 conjugacy classes of subgroups — too many to draw. Only its 49 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#14271758C211yesmaximal, characteristic, complemented
2#14271314C211yesmaximal, characteristic, complemented
3#14271077C211yesmaximal, characteristic, complemented
4#14270901C211yesmaximal, characteristic, complemented
5#14270897C211yesmaximal, characteristic, complemented
6#14270888C211yesmaximal, characteristic, complemented
7C29×#447C211yesmaximal, characteristic
8C22×D4×C29C2211yescharacteristic
9C2×D8×C29—21no—
10C29×#121C2211yescharacteristic
11C2×C22⋊Dic29—21no—
12C2×C22⋊Dic29—21no—
13#11745297—21no—
14#11745297—21no—
15D4×Dic29—21no—
16C2×#90783—21no—
17#11745286C2211yescharacteristic
18C2×#90779C2211yescharacteristic
19#11745251—21no—
20#11745241—21no—
21#11745240—21no—
22C29×#102—21no—
23C29×C22⋊C8C2211yescharacteristic
24#11745180—21no—
25#11745179C2211yescharacteristic
26C22⋊#6597C2211yescharacteristic
27C24×C29—21no—
28C2×D4×C29—21no—
29C2×D4×C29—21no—
30C2×D4×C29—21no—
31C2×D4×C29—42no—
32C2×D4×C29D411yescharacteristic
33C22×C4×C29C2311yescharacteristic
34C22×Dic29—21no—
35C22×Dic29—21no—
36C22×Dic29D411yescharacteristic
37C22×Dic29D411yescharacteristic
38C2×Dic58D411yescharacteristic
39D8×C29—42no—
40C2×C8×C29—21no—
41C4⋊C4×C29D411yescharacteristic
42C22⋊C4×C29—21no—
43C22⋊Dic29—21no—
44C22⋊Dic29—21no—
45C22⋊Dic29—21no—
46C22⋊Dic29—21no—
47C22⋊Dic29—42no—
48C22⋊Dic29—42no—
49#90783—42no—
50C4⋊Dic29—21no—
51C4⋊Dic29D411yescharacteristic
52#90779—21no—
53#90779—21no—
54#90779—21no—
55#90779—21no—
56#90779—21no—
57C4×Dic29—21no—
58C2×#6597—21no—
59C23×C29—22no—
60C23×C29—21no—
61C23×C29—41no—
62C23×C29—41no—
63C23×C29—41no—
64C23×C29—41no—
65C23×C29—41no—
66C23×C29—41no—
67C23×C29C2×D411yescharacteristic
68D4×C29—22no—
69D4×C29—22no—
70D4×C29—41no—
71D4×C29—41no—
72D4×C29—41no—
73D4×C29—41no—
74D4×C29—41no—
75C2×C4×C29—21no—
76C2×C4×C29—41no—
77C2×C4×C29C2×D411yescharacteristic
78C2×C4×C29C2×D411yescharacteristic
79C2×Dic29—21no—
80C2×Dic29—21no—
81C2×Dic29—21no—
82C2×Dic29—21no—
83C2×Dic29—21no—
84C2×Dic29—21no—
85C2×Dic29—41no—
86C2×Dic29—41no—
87C2×Dic29—41no—
88C2×Dic29—41no—
89C2×Dic29—81no—
90Dic58—41no—
91C8×C29—41no—
92#6597—41no—
93#1597—291nomaximal, Sylow
94C22×C29—21no—
95C22×C29—21no—
96C22×C29—42no—
97C22×C29—42no—
98C22×C29—41no—
99C22×C29—41no—
100C22×C29—41no—
101C22×C29—42no—
102C22×C29—81no—
103C22×C29—81no—
104C22×C29—81no—
105C22×C29—81no—
106C22×C29#12011yescharacteristic
107C22×C29#13511yescharacteristic
108C22×C29AGL(1,ℤ/8)11yescharacteristic
109C4×C29—21no—
110C4×C29—21no—
111C4×C29—41no—
112Dic29—41no—
113Dic29—41no—
114Dic29—41no—
115Dic29—41no—
116Dic29—81no—
117#539—291no—
118#450—291no—
119#447D2911yescharacteristic
120#394—291no—
121#328—291no—
122#327—291no—
123#324—291no—
124C2×C29—21no—
125C2×C29—21no—
126C2×C29—81no—
127C2×C29—82no—
128C2×C29#44911yescharacteristic
129C2×C29#45411yescharacteristic
130C2×C29B(4,𝔽2)11yescharacteristic
131C22×D4C2×D2911yescharacteristic
132C2×SD16—581no—
133C2×D8—21no—
134#126—581no—
135#125—581no—
136#123—581no—
137#123—581no—
138C22⋊Q8—291no—
139C22⋊Q8—581no—
140#121C2×D2911yescharacteristic
141C4×D4—581no—
142C2×C4⋊C4—291no—
143C2×C22⋊C4—581no—
144C2×C22⋊C4—581no—
145#102—21no—
146#102—581no—
147C22⋊C8—291no—
148C22⋊C8C2×D2911yescharacteristic
149#95—291no—
150C29#159711yescharacteristic, complemented, Sylow
151C24—21no—
152C2×Q8—291no—
153C2×D4—21no—
154C2×D4—21no—
155C2×D4—21no—
156C2×D4—42no—
157C2×D4C22⋊D2911yescharacteristic
158C22×C4—291no—
159C22×C4—291no—
160C22×C4—581no—
161C22×C4—581no—
162C22×C4C22×D2911yescharacteristic
163SD16—1162no—
164D8—42no—
165C2×C8—21no—
166C2×C8—581no—
167C4⋊C4—291no—
168C4⋊C4—581no—
169C4⋊C4—581no—
170C4⋊C4—581no—
171C4⋊C4—581no—
172C4⋊C4—581no—
173C4⋊C4—581no—
174C4⋊C4C22⋊D2911yescharacteristic
175C22⋊C4—21no—
176C22⋊C4—581no—
177C22⋊C4—581no—
178C22⋊C4—581no—
179C22⋊C4—581no—
180C22⋊C4—1162no—
181C22⋊C4—1162no—
182C42—581no—
183C23—22no—
184C23—21no—
185C23—41no—
186C23—41no—
187C23—41no—
188C23—41no—
189C23—41no—
190C23—41no—
191C23D4×D2911yescharacteristic
192Q8—1161no—
193D4—22no—
194D4—22no—
195D4—41no—
196D4—41no—
197D4—41no—
198D4—41no—
199D4—41no—
200C2×C4—21no—
201C2×C4—41no—
202C2×C4—581no—
203C2×C4—581no—
204C2×C4—581no—
205C2×C4—581no—
206C2×C4—581no—
207C2×C4—581no—
208C2×C4—1161no—
209C2×C4—1161no—
210C2×C4—1161no—
211C2×C4—1161no—
212C2×C4—2321no—
213C2×C4D4×D2911yescharacteristic
214C2×C4C2×C22⋊D2911yescharacteristic
215C8—41no—
216C8—1161no—
217C22—21no—
218C22—21no—
219C22—42no—
220C22—42no—
221C22—41no—
222C22—41no—
223C22—41no—
224C22—42no—
225C22—81no—
226C22—81no—
227C22—81no—
228C22—81no—
229C22#1174527311yescharacteristic
230C22#1174527411yescharacteristic
231C22#1174529911yescharacteristic
232C4—21no—
233C4—21no—
234C4—41no—
235C4—1161no—
236C4—1161no—
237C4—1161no—
238C4—1161no—
239C4—2321no—
240C2—21no—
241C2—21no—
242C2—82no—
243C2—81no—
244C2#1427130511yescharacteristic
245C2#1427133411yescharacteristic
246C2#1427134911yescharacteristic
subgroupG/H
centerC22#11745299
commutator, cosocleC22×C4×C29C23
FrattiniC22×C4C22×D29
Fitting, prime radicalC29×#447C2
socleC22×C29#120
hypercenter#447D29
hypocenterC29#1597
LCSG ▷ C22×C4×C29 ▷ C22×C29 ▷ C29
UCSC1 ◁ C22 ◁ C22×C4 ◁ #447

Complements

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

NH ≅ G/Ntype
1. #14271758C2semidirect
2. #14271314C2semidirect
3. #14271077C2semidirect
4. #14270901C2semidirect
5. #14270897C2semidirect
6. #14270888C2semidirect
150. C29#1597semidirect

Maximal subgroups

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

subgroupindex
#142717582
#142713142
#142710772
#142709012
#142708972
#142708882
C29×#4472
#159729