Finite Group Databasebeta

← #16818472

Subgroups — #16818472

Order 3712.

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

normal subgroups only

This group has 260 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#14271318C211yesmaximal, characteristic, complemented
2#14271301C211yesmaximal, characteristic, complemented
3#14271075C211yesmaximal, characteristic, complemented
4#14270900C211yesmaximal, characteristic, complemented
5#14270897C211yesmaximal, characteristic, complemented
6#14270887C211yesmaximal, characteristic, complemented
7C29×#538C211yesmaximal, characteristic
8C22×Dic58C2211yescharacteristic
9C29×#126—21no—
10C29×#124—21no—
11C29×#123—21no—
12C29×C22⋊Q8C2211yescharacteristic
13C29×#121—21no—
14C29×#121C2211yescharacteristic
15C29×#120—21no—
16C4×D4×C29—21no—
17C2×C22⋊C4×C29C2211yescharacteristic
18C2×C22⋊Dic29—21no—
19C2×#90785—21no—
20C2×#90783—21no—
21#11745179—21no—
22#11745179C2211yescharacteristic
23C22⋊#6597C2211yescharacteristic
24C22⋊#6597C2211yescharacteristic
25#11745158—21no—
26#11745158—21no—
27C24×C29D411yescharacteristic
28C2×Q8×C29D411yescharacteristic
29C2×D4×C29—21no—
30C2×D4×C29—21no—
31C2×D4×C29—21no—
32C2×D4×C29D411yescharacteristic
33C22×C4×C29—21no—
34C22×C4×C29D411yescharacteristic
35C22×C4×C29C2311yescharacteristic
36C22×Dic29—21no—
37C22×Dic29—21no—
38C2×Dic58—21no—
39C2×Dic58—21no—
40C2×Dic58—42no—
41C4⋊C4×C29—21no—
42C4⋊C4×C29—21no—
43C4⋊C4×C29D411yescharacteristic
44C4⋊C4×C29D411yescharacteristic
45C22⋊C4×C29—21no—
46C22⋊C4×C29—21no—
47C22⋊C4×C29—21no—
48C22⋊C4×C29—21no—
49C22⋊C4×C29—21no—
50C22⋊C4×C29—21no—
51C22⋊C4×C29—21no—
52C42×C29—21no—
53C22⋊Dic29—42no—
54#90785—42no—
55#90783—42no—
56C2×#6597—21no—
57C2×#6597—21no—
58C23×C29—21no—
59C23×C29—21no—
60C23×C29—21no—
61C23×C29—21no—
62C23×C29—41no—
63C23×C29—41no—
64C23×C29C2×D411yescharacteristic
65Q8×C29—41no—
66D4×C29—41no—
67D4×C29—41no—
68D4×C29—41no—
69D4×C29—81no—
70D4×C29—81no—
71C2×C4×C29—21no—
72C2×C4×C29—21no—
73C2×C4×C29—21no—
74C2×C4×C29—21no—
75C2×C4×C29—41no—
76C2×C4×C29—41no—
77C2×C4×C29—81no—
78C2×C4×C29C2×D411yescharacteristic
79C2×C4×C29C2×D411yescharacteristic
80C2×Dic29—22no—
81C2×Dic29—41no—
82C2×Dic29—41no—
83C2×Dic29—41no—
84C2×Dic29—41no—
85C2×Dic29—41no—
86Dic58—22no—
87Dic58—22no—
88Dic58—41no—
89Dic58—41no—
90#6597—41no—
91#6597—41no—
92#1606—291nomaximal, Sylow
93C22×C29—21no—
94C22×C29—21no—
95C22×C29—42no—
96C22×C29—41no—
97C22×C29—41no—
98C22×C29—41no—
99C22×C29—41no—
100C22×C29—41no—
101C22×C29—41no—
102C22×C29—81no—
103C22×C29#12011yescharacteristic
104C22×C29#13511yescharacteristic
105C22×C29#13711yescharacteristic
106C4×C29—21no—
107C4×C29—21no—
108C4×C29—41no—
109C4×C29—41no—
110C4×C29—41no—
111C4×C29—41no—
112Dic29—42no—
113Dic29—81no—
114#538D2911yescharacteristic
115#451—291no—
116#448—291no—
117#393—291no—
118#328—291no—
119#327—291no—
120#323—291no—
121C2×C29—21no—
122C2×C29—21no—
123C2×C29—81no—
124C2×C29—81no—
125C2×C29#45211yescharacteristic
126C2×C29#45511yescharacteristic
127C2×C29B(4,𝔽2)11yescharacteristic
128C22×Q8—291no—
129C2×Q16—581no—
130C2×SD16—581no—
131#126—21no—
132#124—21no—
133#123—21no—
134C22⋊Q8C2×D2911yescharacteristic
135#121—21no—
136#121C2×D2911yescharacteristic
137#120—21no—
138C4×D4—21no—
139C2×C22⋊C4—581no—
140C2×C22⋊C4C2×D2911yescharacteristic
141#103—581no—
142#103—581no—
143C22⋊C8—291no—
144C22⋊C8—291no—
145#95—291no—
146#95—581no—
147C29#160611yescharacteristic, complemented, Sylow
148C24C22⋊D2911yescharacteristic
149C2×Q8—581no—
150C2×Q8—581no—
151C2×Q8—1162no—
152C2×Q8C22⋊D2911yescharacteristic
153C2×D4—21no—
154C2×D4—21no—
155C2×D4—21no—
156C2×D4C22⋊D2911yescharacteristic
157C22×C4—21no—
158C22×C4—581no—
159C22×C4—581no—
160C22×C4C22⋊D2911yescharacteristic
161C22×C4C22×D2911yescharacteristic
162Q16—1162no—
163SD16—1162no—
164C2×C8—581no—
165C2×C8—581no—
166C4⋊C4—21no—
167C4⋊C4—21no—
168C4⋊C4C22⋊D2911yescharacteristic
169C4⋊C4C22⋊D2911yescharacteristic
170C22⋊C4—21no—
171C22⋊C4—21no—
172C22⋊C4—21no—
173C22⋊C4—21no—
174C22⋊C4—21no—
175C22⋊C4—21no—
176C22⋊C4—21no—
177C22⋊C4—1162no—
178C42—21no—
179C23—21no—
180C23—21no—
181C23—21no—
182C23—21no—
183C23—41no—
184C23—41no—
185C23C2×C22⋊D2911yescharacteristic
186Q8—41no—
187Q8—582no—
188Q8—582no—
189Q8—1161no—
190Q8—1161no—
191D4—41no—
192D4—41no—
193D4—41no—
194D4—81no—
195D4—81no—
196C2×C4—21no—
197C2×C4—21no—
198C2×C4—21no—
199C2×C4—21no—
200C2×C4—41no—
201C2×C4—41no—
202C2×C4—81no—
203C2×C4—582no—
204C2×C4—1161no—
205C2×C4—1161no—
206C2×C4—1161no—
207C2×C4—1161no—
208C2×C4—1161no—
209C2×C4C2×C22⋊D2911yescharacteristic
210C2×C4C2×C22⋊D2911yescharacteristic
211C8—1161no—
212C8—1161no—
213C22—21no—
214C22—21no—
215C22—42no—
216C22—41no—
217C22—41no—
218C22—41no—
219C22—41no—
220C22—41no—
221C22—41no—
222C22—81no—
223C22#1174531211yescharacteristic
224C22#1174531311yescharacteristic
225C22#1174531511yescharacteristic
226C4—21no—
227C4—21no—
228C4—41no—
229C4—41no—
230C4—41no—
231C4—41no—
232C4—1162no—
233C4—2321no—
234C2—21no—
235C2—21no—
236C2—81no—
237C2—81no—
238C2#1427132511yescharacteristic
239C2#1427134111yescharacteristic
240C2#1427135011yescharacteristic
subgroupG/H
centerC22#11745315
commutator, cosocleC22×C4×C29C23
FrattiniC22×C4C22×D29
Fitting, prime radicalC29×#538C2
socleC22×C29#120
hypercenter#538D29
hypocenterC29#1606
LCSG ▷ C22×C4×C29 ▷ C22×C29 ▷ C29
UCSC1 ◁ C22 ◁ C22×C4 ◁ #538

Complements

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

NH ≅ G/Ntype
1. #14271318C2semidirect
2. #14271301C2semidirect
3. #14271075C2semidirect
4. #14270900C2semidirect
5. #14270897C2semidirect
6. #14270887C2semidirect
147. C29#1606semidirect

Maximal subgroups

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

subgroupindex
#142713182
#142713012
#142710752
#142709002
#142708972
#142708872
C29×#5382
#160629