Finite Group Databasebeta

← #16821144

Subgroups — #16821144

Order 3712.

234 conjugacy classes of subgroups; only the 55 normal subgroups are shown.

normal subgroups only

This group has 234 conjugacy classes of subgroups — too many to draw. Only its 55 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#14271735C211yesmaximal, characteristic
2#14271144C211yesmaximal, characteristic
3#14271135C211yesmaximal, characteristic
4#14270954C211yesmaximal, characteristic, complemented
5#14270953C211yesmaximal, characteristic, complemented
6#14270952C211yesmaximal, characteristic, complemented
7C29×#352C211yesmaximal, characteristic, complemented
8C2×#90807C2211yescharacteristic
9C22×Dic58C411yescharacteristic, complemented
10C29×#123C2211yescharacteristic
11#11745297C2211yescharacteristic
12#11745291C411yescharacteristic, complemented
13M16×D29—21no—
14#11745258—21no—
15#11745250—21no—
16#11745248C411yescharacteristic, complemented
17#11745247—21no—
18#11745240—21no—
19#11745239—21no—
20#11745239C411yescharacteristic, complemented
21C29×#100C2211yescharacteristic
22C29×#99C2211yescharacteristic
23#11745182C2211yescharacteristic
24#11745181C2211yescharacteristic
25#11745172—21no—
26#11745154—21no—
27C2×D4×C29C2311yescharacteristic
28C22×C4×C29C2×C411yescharacteristic
29C2×C22⋊D29C2×C411yescharacteristic
30C2×C22⋊D29D411yescharacteristic
31C22×Dic29C2×C411yescharacteristic
32C22×Dic29C2×C411yescharacteristic
33C22×Dic29D411yescharacteristic
34#90807—41no—
35#90807—41no—
36C2×C4×D29D411yescharacteristic
37C2×Dic58—21no—
38C2×Dic58—21no—
39C2×Dic58—41no—
40C2×Dic58—41no—
41C2×Dic58D411yescharacteristic
42M16×C29—21no—
43C4⋊C4×C29—21no—
44C22⋊C4×C29—21no—
45C22⋊C4×C29—21no—
46C22⋊C4×C29C2×C411yescharacteristic
47C22⋊Dic29—21no—
48C22⋊Dic29—21no—
49C22⋊Dic29C2×C411yescharacteristic
50#90781—21no—
51#90781—21no—
52C4⋊Dic29—21no—
53#90779—21no—
54#90779—21no—
55#90779—21no—
56#90779—41no—
57C4×Dic29—21no—
58C4×Dic29—41no—
59#90777—21no—
60#90772—41no—
61C8×D29—41no—
62C23×C29C22×C411yescharacteristic
63C23×C29C2×D411yescharacteristic
64C22×D29C22⋊C411yescharacteristic
65D4×C29—41no—
66C2×C4×C29—21no—
67C2×C4×C29—21no—
68C2×C4×C29—41no—
69C2×C4×C29—41no—
70C2×C4×C29C2×D411yescharacteristic
71C22⋊D29—41no—
72C22⋊D29—41no—
73C2×Dic29—21no—
74C2×Dic29—21no—
75C2×Dic29—21no—
76C2×Dic29—21no—
77C2×Dic29—21no—
78C2×Dic29—21no—
79C2×Dic29—41no—
80C2×Dic29—41no—
81C2×Dic29C22⋊C411yescharacteristic
82C2×Dic29C22⋊C411yescharacteristic
83C2×Dic29C22⋊C411yescharacteristic
84C4×D29—21no—
85C4×D29—21no—
86Dic58—41no—
87Dic58—42no—
88Dic58—41no—
89Dic58—41no—
90C8×C29—41no—
91#6597—41no—
92#2123—291nomaximal, Sylow
93C22×C29—21no—
94C22×C29—21no—
95C22×C29—41no—
96C22×C29—41no—
97C22×C29C2×C22⋊C411yescharacteristic
98C2×D29—21no—
99C2×D29—41no—
100C4×C29—21no—
101C4×C29—41no—
102C4×C29—41no—
103C4×C29—81no—
104Dic29—21no—
105Dic29—21no—
106Dic29—41no—
107Dic29—41no—
108Dic29—81no—
109Dic29#9911yescharacteristic
110Dic29#9911yescharacteristic
111#536—291no—
112#413—291no—
113#410—291no—
114#352—291no—
115#352—291no—
116#352—291no—
117#352D2911yescharacteristic, complemented
118C2×C29—21no—
119C2×C29—41no—
120C2×C29—41no—
121C2×C29C2×#9911yescharacteristic
122D29—41no—
123C2×#41—291no—
124C22×Q8—291no—
125C2×M16—581no—
126C4⋊Q8—581no—
127#124—581no—
128#123—291no—
129#123—291no—
130#123—291no—
131#123C2×D2911yescharacteristic
132C22⋊Q8—581no—
133C22⋊Q8—581no—
134#117—291no—
135#117—581no—
136#101—581no—
137#100—291no—
138#100C2×D2911yescharacteristic
139#99—291no—
140#99—581no—
141#99C2×D2911yescharacteristic
142C29#212311yescharacteristic, complemented, Sylow
143#41—1161no—
144#41—1161no—
145C2×Q8—291no—
146C2×Q8—581no—
147C2×Q8—581no—
148C2×Q8—1161no—
149C2×Q8—1161no—
150C2×D4—291no—
151C2×D4—291no—
152C2×D4C22×D2911yescharacteristic
153C22×C4—291no—
154C22×C4—291no—
155C22×C4—291no—
156C22×C4—291no—
157C22×C4C4×D2911yescharacteristic
158M16—21no—
159M16—581no—
160M16—1161no—
161C2×C8—1161no—
162C4⋊C4—21no—
163C4⋊C4—581no—
164C4⋊C4—581no—
165C4⋊C4—581no—
166C4⋊C4—581no—
167C4⋊C4—1161no—
168C22⋊C4—21no—
169C22⋊C4—21no—
170C22⋊C4—291no—
171C22⋊C4—581no—
172C22⋊C4—581no—
173C22⋊C4—581no—
174C22⋊C4—581no—
175C22⋊C4C4×D2911yescharacteristic
176C42—581no—
177C42—1161no—
178C23—291no—
179C23C2×C4×D2911yescharacteristic
180C23D4×D2911yescharacteristic
181Q8—1161no—
182Q8—1161no—
183Q8—1161no—
184Q8—1162no—
185D4—41no—
186D4—1161no—
187D4—1161no—
188C2×C4—21no—
189C2×C4—21no—
190C2×C4—41no—
191C2×C4—41no—
192C2×C4—291no—
193C2×C4—291no—
194C2×C4—291no—
195C2×C4—581no—
196C2×C4—581no—
197C2×C4—581no—
198C2×C4—581no—
199C2×C4—581no—
200C2×C4—581no—
201C2×C4—581no—
202C2×C4—581no—
203C2×C4—1161no—
204C2×C4—1161no—
205C2×C4D4×D2911yescharacteristic
206C8—41no—
207C8—1161no—
208C22—21no—
209C22—21no—
210C22—41no—
211C22—41no—
212C22—581no—
213C22—1161no—
214C22C22⋊C4×D2911yescharacteristic
215C4—21no—
216C4—41no—
217C4—41no—
218C4—81no—
219C4—291no—
220C4—291no—
221C4—581no—
222C4—581no—
223C4—1161no—
224C4—1161no—
225C4—2321no—
226C2—21no—
227C2—41no—
228C2—41no—
229C2—1161no—
230C2#99×D2911yescharacteristic
subgroupG/H
centerC2#99×D29
commutatorC23×C29C22×C4
FrattiniC2×D4C22×D29
FittingC29×#352C2
socleC2×C29C2×#99
prime radicalC2×#90807C22
cosocleC2×D4×C29C23
hypercenter#352D29
hypocenterC29#2123
LCSG ▷ C23×C29 ▷ C22×C29 ▷ C2×C29 ▷ C29
UCSC1 ◁ C2 ◁ C22 ◁ C2×D4 ◁ #352

Complements

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

NH ≅ G/Ntype
4. #14270954C2semidirect
5. #14270953C2semidirect
6. #14270952C2semidirect
7. C29×#352C2semidirect
9. C22×Dic58C4semidirect
12. #11745291C4semidirect
16. #11745248C4semidirect
20. #11745239C4semidirect
117. #352D29semidirect
142. C29#2123semidirect

Maximal subgroups

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

subgroupindex
#142717352
#142711442
#142711352
#142709542
#142709532
#142709522
C29×#3522
#212329