Finite Group Databasebeta

← #16818462

Subgroups — #16818462

Order 3712.

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

normal subgroups only

This group has 282 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#14271740C211yesmaximal, characteristic
2#14271304C211yesmaximal, characteristic, complemented
3#14271301C211yesmaximal, characteristic, complemented
4#14271084C211yesmaximal, characteristic, complemented
5#14270896C211yesmaximal, characteristic, complemented
6#14270888C211yesmaximal, characteristic, complemented
7C29×#327C211yesmaximal, characteristic, complemented
8C2×#90807—21no—
9C22×Dic58C2211yescharacteristic
10C29×#121C2211yescharacteristic
11#11745301—21no—
12#11745301—21no—
13C2×#90783—21no—
14#11745292C2211yescharacteristic
15C2×C4⋊Dic29—21no—
16C2×#90779C2211yescharacteristic
17C2×#90773—21no—
18#11745258—21no—
19#11745246—21no—
20#11745240—21no—
21C29×C22⋊C8C2211yescharacteristic
22C29×#95C2211yescharacteristic
23#11745179—21no—
24C22⋊#6597C2211yescharacteristic
25#11745164—21no—
26#11745158—21no—
27C2×D4×C29—21no—
28C2×D4×C29D411yescharacteristic
29C22×C4×C29—21no—
30C22×C4×C29C2311yescharacteristic
31C2×C22⋊D29—21no—
32C2×C22⋊D29—21no—
33C2×C22⋊D29—21no—
34C22×Dic29—21no—
35C22×Dic29—21no—
36C22×Dic29D411yescharacteristic
37C22×Dic29D411yescharacteristic
38#90807—42no—
39#90807—42no—
40C2×D116D411yescharacteristic
41C2×C4×D29—21no—
42C2×Dic58—21no—
43C2×Dic58—21no—
44C2×Dic58—21no—
45C2×Dic58—42no—
46C2×C8×C29—21no—
47C4⋊C4×C29D411yescharacteristic
48C22⋊C4×C29—21no—
49C22⋊Dic29—21no—
50#90783—42no—
51#90781—21no—
52#90781—21no—
53C4⋊Dic29—42no—
54C4⋊Dic29D411yescharacteristic
55#90779—21no—
56#90779—21no—
57#90779—21no—
58C2×#6597—21no—
59#90773—42no—
60C23×C29—21no—
61C23×C29C2×D411yescharacteristic
62C22×D29—21no—
63D4×C29—41no—
64D4×C29—41no—
65D4×C29—41no—
66C2×C4×C29—22no—
67C2×C4×C29—21no—
68C2×C4×C29—41no—
69C2×C4×C29—41no—
70C2×C4×C29—41no—
71C2×C4×C29C2×D411yescharacteristic
72C2×C4×C29C2×D411yescharacteristic
73C22⋊D29—42no—
74C22⋊D29—41no—
75C22⋊D29—41no—
76C22⋊D29—81no—
77C2×Dic29—21no—
78C2×Dic29—21no—
79C2×Dic29—22no—
80C2×Dic29—21no—
81C2×Dic29—21no—
82C2×Dic29—42no—
83C2×Dic29—41no—
84C2×Dic29—41no—
85C2×Dic29—41no—
86C2×Dic29SD1612yescomplemented
87D116—41no—
88C4×D29—42no—
89Dic58—22no—
90Dic58—22no—
91Dic58—42no—
92Dic58—41no—
93Dic58—41no—
94C8×C29—41no—
95#6597—41no—
96#1604—291nomaximal, Sylow
97C22×C29—21no—
98C22×C29—21no—
99C22×C29—41no—
100C22×C29—41no—
101C22×C29—41no—
102C22×C29#12011yescharacteristic
103C22×C29C2×SD1611yescharacteristic
104C22×C29AGL(1,ℤ/8)11yescharacteristic
105C2×D29—41no—
106C2×D29—41no—
107C2×D29—41no—
108C4×C29—21no—
109C4×C29—21no—
110C4×C29—42no—
111C4×C29—41no—
112Dic29—22no—
113Dic29—41no—
114Dic29—42no—
115Dic29—41no—
116#537—291no—
117#448—291no—
118#448—291no—
119#395—291no—
120#327—291no—
121#327D2911yescharacteristic, complemented
122#324—291no—
123C2×C29—21no—
124C2×C29—21no—
125C2×C29—81no—
126C2×C29#45011yescharacteristic
127C2×C29#45611yescharacteristic
128C2×C29B(4,𝔽2)11yescharacteristic
129D29—81no—
130C2×#41—581no—
131C22×Q8—291no—
132C2×SD16—581no—
133C2×SD16—581no—
134C22⋊Q8—581no—
135C22⋊Q8—581no—
136#121—291no—
137#121—581no—
138#121—581no—
139#121—581no—
140#121C2×D2911yescharacteristic
141C2×C4⋊C4—291no—
142C2×C4⋊C4—581no—
143#103—581no—
144#103—581no—
145C22⋊C8—291no—
146C22⋊C8C2×D2911yescharacteristic
147#95—581no—
148#95C2×D2911yescharacteristic
149C29#160411yescharacteristic, complemented, Sylow
150#41—1162no—
151#41—1162no—
152C2×Q8—581no—
153C2×Q8—581no—
154C2×Q8—581no—
155C2×Q8—1162no—
156C2×D4—21no—
157C2×D4—291no—
158C2×D4—581no—
159C2×D4—581no—
160C2×D4—581no—
161C2×D4D11611yescharacteristic
162C22×C4—21no—
163C22×C4—291no—
164C22×C4—291no—
165C22×C4—581no—
166C22×C4—581no—
167C22×C4—581no—
168C22×C4C22×D2911yescharacteristic
169SD16—1162no—
170SD16—1162no—
171C2×C8—21no—
172C2×C8—581no—
173C4⋊C4—291no—
174C4⋊C4—581no—
175C4⋊C4—581no—
176C4⋊C4—581no—
177C4⋊C4—1162no—
178C4⋊C4D11611yescharacteristic
179C22⋊C4—21no—
180C22⋊C4—581no—
181C22⋊C4—581no—
182C22⋊C4—581no—
183C23—21no—
184C23—581no—
185C23D4×D2911yescharacteristic
186Q8—582no—
187Q8—582no—
188Q8—1161no—
189Q8—1161no—
190Q8—1162no—
191D4—41no—
192D4—41no—
193D4—41no—
194D4—1161no—
195D4—1162no—
196D4—1161no—
197D4—1161no—
198D4—2321no—
199C2×C4—22no—
200C2×C4—21no—
201C2×C4—41no—
202C2×C4—41no—
203C2×C4—41no—
204C2×C4—292no—
205C2×C4—581no—
206C2×C4—581no—
207C2×C4—582no—
208C2×C4—581no—
209C2×C4—581no—
210C2×C4—1162no—
211C2×C4—1162no—
212C2×C4—1161no—
213C2×C4—1161no—
214C2×C4—1161no—
215C2×C4C2×D11611yescharacteristic
216C2×C4D4×D2911yescharacteristic
217C8—41no—
218C8—1161no—
219C22—21no—
220C22—21no—
221C22—41no—
222C22—41no—
223C22—41no—
224C22—1161no—
225C22—1161no—
226C22—1161no—
227C22#1174524411yescharacteristic
228C22#1174527311yescharacteristic
229C22SD16×D2911yescharacteristic
230C4—21no—
231C4—21no—
232C4—42no—
233C4—41no—
234C4—582no—
235C4—1161no—
236C4—1162no—
237C4—1161no—
238C2—21no—
239C2—21no—
240C2—81no—
241C2—2321no—
242C2#1427131511yescharacteristic
243C2#1427134711yescharacteristic
244C2#1427135111yescharacteristic
subgroupG/H
centerC22#11745244
commutator, cosocleC22×C4×C29C23
FrattiniC22×C4C22×D29
FittingC29×#327C2
socleC22×C29#120
prime radical#14271740C2
hypercenter#327D29
hypocenterC29#1604
LCSG ▷ C22×C4×C29 ▷ C22×C29 ▷ C29
UCSC1 ◁ C22 ◁ C22×C4 ◁ #327

Complements

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

NH ≅ G/Ntype
2. #14271304C2semidirect
3. #14271301C2semidirect
4. #14271084C2semidirect
5. #14270896C2semidirect
6. #14270888C2semidirect
7. C29×#327C2semidirect
86. C2×Dic29SD16semidirect
121. #327D29semidirect
149. C29#1604semidirect

Maximal subgroups

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

subgroupindex
#142717402
#142713042
#142713012
#142710842
#142708962
#142708882
C29×#3272
#160429