Finite Group Databasebeta

← #16818452

Subgroups — #16818452

Order 3712.

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

normal subgroups only

This group has 244 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
2#14271319C211yesmaximal, characteristic, complemented
3#14271082C211yesmaximal, characteristic, complemented
4#14270901C211yesmaximal, characteristic, complemented
5#14270897C211yesmaximal, characteristic
6#14270888C211yesmaximal, characteristic, complemented
7C29×#448C211yesmaximal, characteristic
8C22×Q8×C29C2211yescharacteristic
9C2×SD16×C29—21no—
10C29×#121C2211yescharacteristic
11C2×#90785—21no—
12#11745297—21no—
13#11745297—21no—
14D4×Dic29—21no—
15#11745286C2211yescharacteristic
16C2×#90779—21no—
17C2×#90779C2211yescharacteristic
18#11745251—21no—
19#11745241—21no—
20#11745240—21no—
21C29×#103—21no—
22C29×C22⋊C8C2211yescharacteristic
23#11745183—21no—
24#11745179—21no—
25#11745179C2211yescharacteristic
26C22⋊#6597C2211yescharacteristic
27C2×Q8×C29—21no—
28C2×Q8×C29—21no—
29C2×Q8×C29—42no—
30C2×D4×C29—21no—
31C2×D4×C29D411yescharacteristic
32C22×C4×C29—21no—
33C22×C4×C29C2311yescharacteristic
34C22×Dic29—21no—
35C22×Dic29—21no—
36C22×Dic29D411yescharacteristic
37C22×Dic29D411yescharacteristic
38C2×Dic58D411yescharacteristic
39SD16×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—
47#90785—42no—
48C4⋊Dic29—21no—
49C4⋊Dic29D411yescharacteristic
50#90779—21no—
51#90779—21no—
52#90779—21no—
53#90779—21no—
54#90779—21no—
55#90779—42no—
56C4×Dic29—21no—
57C2×#6597—21no—
58C23×C29—21no—
59C23×C29C2×D411yescharacteristic
60Q8×C29—22no—
61Q8×C29—22no—
62Q8×C29—41no—
63Q8×C29—41no—
64D4×C29—41no—
65D4×C29—41no—
66D4×C29—41no—
67C2×C4×C29—22no—
68C2×C4×C29—21no—
69C2×C4×C29—41no—
70C2×C4×C29—41no—
71C2×C4×C29—41no—
72C2×C4×C29C2×D411yescharacteristic
73C2×C4×C29C2×D411yescharacteristic
74C2×Dic29—22no—
75C2×Dic29—21no—
76C2×Dic29—21no—
77C2×Dic29—21no—
78C2×Dic29—21no—
79C2×Dic29—21no—
80C2×Dic29—21no—
81C2×Dic29—41no—
82C2×Dic29—41no—
83C2×Dic29—41no—
84C2×Dic29—81no—
85Dic58—41no—
86C8×C29—41no—
87#6597—41no—
88#1603—291nomaximal, Sylow
89C22×C29—21no—
90C22×C29—21no—
91C22×C29—41no—
92C22×C29—41no—
93C22×C29—41no—
94C22×C29#12011yescharacteristic
95C22×C29#13511yescharacteristic
96C22×C29#13711yescharacteristic
97C4×C29—21no—
98C4×C29—21no—
99C4×C29—41no—
100C4×C29—42no—
101Dic29—42no—
102Dic29—41no—
103Dic29—41no—
104Dic29—41no—
105Dic29—41no—
106#539—291no—
107#451—291no—
108#448D2911yescharacteristic
109#395—291no—
110#328—291no—
111#327—291no—
112#324—291no—
113C2×C29—21no—
114C2×C29—21no—
115C2×C29—81no—
116C2×C29#45211yescharacteristic
117C2×C29#45611yescharacteristic
118C2×C29B(4,𝔽2)11yescharacteristic
119C22×Q8C2×D2911yescharacteristic
120C2×Q16—581no—
121C2×SD16—21no—
122#126—581no—
123#125—581no—
124#123—581no—
125#123—581no—
126C22⋊Q8—291no—
127C22⋊Q8—581no—
128#121C2×D2911yescharacteristic
129C4×D4—581no—
130C2×C4⋊C4—291no—
131C2×C4⋊C4—581no—
132#103—21no—
133#103—581no—
134C22⋊C8—291no—
135C22⋊C8C2×D2911yescharacteristic
136#95—291no—
137#95—581no—
138C29#160311yescharacteristic, complemented, Sylow
139C2×Q8—21no—
140C2×Q8—21no—
141C2×Q8—42no—
142C2×Q8—291no—
143C2×D4—21no—
144C2×D4C22⋊D2911yescharacteristic
145C22×C4—21no—
146C22×C4—291no—
147C22×C4—291no—
148C22×C4—581no—
149C22×C4—581no—
150C22×C4C22×D2911yescharacteristic
151Q16—1162no—
152SD16—42no—
153C2×C8—21no—
154C2×C8—581no—
155C4⋊C4—291no—
156C4⋊C4—581no—
157C4⋊C4—581no—
158C4⋊C4—581no—
159C4⋊C4—581no—
160C4⋊C4—581no—
161C4⋊C4—581no—
162C4⋊C4—1162no—
163C4⋊C4C22⋊D2911yescharacteristic
164C22⋊C4—21no—
165C22⋊C4—581no—
166C22⋊C4—581no—
167C22⋊C4—581no—
168C22⋊C4—581no—
169C42—581no—
170C23—21no—
171C23D4×D2911yescharacteristic
172Q8—22no—
173Q8—22no—
174Q8—41no—
175Q8—41no—
176Q8—1161no—
177D4—41no—
178D4—41no—
179D4—41no—
180C2×C4—22no—
181C2×C4—21no—
182C2×C4—41no—
183C2×C4—41no—
184C2×C4—41no—
185C2×C4—582no—
186C2×C4—581no—
187C2×C4—581no—
188C2×C4—581no—
189C2×C4—581no—
190C2×C4—581no—
191C2×C4—581no—
192C2×C4—1161no—
193C2×C4—1161no—
194C2×C4—1161no—
195C2×C4—2321no—
196C2×C4D4×D2911yescharacteristic
197C2×C4C2×C22⋊D2911yescharacteristic
198C8—41no—
199C8—1161no—
200C22—21no—
201C22—21no—
202C22—41no—
203C22—41no—
204C22—41no—
205C22#1174527711yescharacteristic
206C22#1174527811yescharacteristic
207C22#1174529911yescharacteristic
208C4—21no—
209C4—21no—
210C4—41no—
211C4—42no—
212C4—1162no—
213C4—1161no—
214C4—1161no—
215C4—1161no—
216C4—1161no—
217C2—21no—
218C2—21no—
219C2—81no—
220C2#1427132211yescharacteristic
221C2#1427134411yescharacteristic
222C2#1427134911yescharacteristic
subgroupG/H
centerC22#11745299
commutator, cosocleC22×C4×C29C23
FrattiniC22×C4C22×D29
FittingC29×#448C2
socleC22×C29#120
prime radicalC29×#121C22
hypercenter#448D29
hypocenterC29#1603
LCSG ▷ C22×C4×C29 ▷ C22×C29 ▷ C29
UCSC1 ◁ C22 ◁ C22×C4 ◁ #448

Complements

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

NH ≅ G/Ntype
2. #14271319C2semidirect
3. #14271082C2semidirect
4. #14270901C2semidirect
6. #14270888C2semidirect
138. C29#1603semidirect

Maximal subgroups

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

subgroupindex
#142717582
#142713192
#142710822
#142709012
#142708972
#142708882
C29×#4482
#160329