Finite Group Databasebeta

← #49159924

Subgroups — #49159924

Order 37504.

290 conjugacy classes of subgroups; only the 89 normal subgroups are shown.

normal subgroups only

This group has 290 conjugacy classes of subgroups — too many to draw. Only its 89 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
1C2×#22627623C211yesmaximal, characteristic
2C2×#22627548C211yesmaximal, characteristic
3#34036036C211yesmaximal, characteristic
4#34035892C211yesmaximal, characteristic
5#34035891C211yesmaximal, characteristic
6#34035883C211yesmaximal, characteristic
7C2×#103×C293C211yesmaximal, characteristic
8C22×Dic586—21no—
9C22×#14556873C2211yescharacteristic
10#22627623—22no—
11#22627623—22no—
12C2×C4⋊Dic293C2211yescharacteristic
13C2×C4⋊Dic293C2211yescharacteristic
14C2×#17989781—21no—
15C2×C4×Dic293C2211yescharacteristic
16#22627548—22no—
17#22627531—21no—
18#22627531—21no—
19C22×Q8×C293C2211yescharacteristic
20C22×C8×C293C2211yescharacteristic
21C2×C4⋊C4×C293C2211yescharacteristic
22#103×C293—22no—
23C2×Dic586—24no—
24C2×Dic586—42no—
25C2×Dic586—42no—
26C22×Dic293—21no—
27C22×Dic293—21no—
28C22×Dic293D411yescharacteristic
29C22×Dic293D411yescharacteristic
30C2×#14556873—21no—
31C2×#14556873—21no—
32C2×#14556873—21no—
33C4⋊Dic293—21no—
34C4⋊Dic293—21no—
35C4⋊Dic293—21no—
36C4⋊Dic293D412yes—
37#17989781—24no—
38C4×Dic293—21no—
39C4×Dic293—21no—
40C2×Q8×C293—21no—
41C2×Q8×C293—21no—
42C2×Q8×C293—21no—
43C2×Q8×C293—21no—
44C2×Q8×C293—21no—
45C2×Q8×C293Q812yescomplemented
46C22×C4×C293—21no—
47C22×C4×C293—21no—
48C22×C4×C293C2311yescharacteristic
49C2×C8×C293—21no—
50C2×C8×C293—21no—
51C2×C8×C293—21no—
52C4⋊C4×C293—21no—
53C4⋊C4×C293D412yes—
54Dic586—48no—
55C2×Dic293—21no—
56C2×Dic293—21no—
57C2×Dic293—21no—
58C2×Dic293—21no—
59C2×Dic293—22no—
60C2×Dic293—41no—
61C2×Dic293—41no—
62C2×Dic293—41no—
63C2×Dic293—41no—
64C2×Dic293—41no—
65C2×Dic293SD1612yes—
66C2×Dic293Q1612yes—
67#14556873—41no—
68C23×C293C2×D411yescharacteristic
69Q8×C293—22no—
70Q8×C293—22no—
71Q8×C293—41no—
72Q8×C293—41no—
73C2×C4×C293—22no—
74C2×C4×C293—22no—
75C2×C4×C293—41no—
76C2×C4×C293—41no—
77C2×C4×C293—41no—
78C2×C4×C293—41no—
79C2×C4×C293C2×D411yescharacteristic
80C2×C4×C293C2×D411yescharacteristic
81C2×C4×C293C2×Q811yescharacteristic
82C2×C4×C293#4111yescharacteristic
83C2×C4×C293#4111yescharacteristic
84C2×C4×C293#4111yescharacteristic
85C8×C293—41no—
86C22×C293#12011yescharacteristic
87C22×C293C22⋊Q811yescharacteristic
88C22×C293#12411yescharacteristic
89C22×C293C2×SD1611yescharacteristic
90C22×C293C2×Q1611yescharacteristic
91C22×C293AGL(1,ℤ/8)11yescharacteristic
92C22×C293#13711yescharacteristic
93C4×C293—42no—
94C4×C293—42no—
95C4×C293C22⋊Q811yescharacteristic
96C4×C293C22⋊Q811yescharacteristic
97C4×C293#12411yescharacteristic
98C4×C293#12411yescharacteristic
99Dic293—22no—
100Dic293—22no—
101Dic293—42no—
102Dic293—81no—
103C2×C293#39311yescharacteristic
104C2×C293#45011yescharacteristic
105C2×C293#45111yescharacteristic
106C2×C293#47511yescharacteristic
107C2×C293#47711yescharacteristic
108C2×C293#48711yescharacteristic
109C2×C293#48911yescharacteristic
110C293#202411yescharacteristic, complemented, Sylow
111#2024—2931nomaximal, Sylow
112C2×C4⋊Q8—2931no—
113C2×#103—2931no—
114C2×#103D29311yescharacteristic
115#391—2931no—
116#340—2931no—
117#340—2931no—
118#336—2931no—
119C22×Q8—5861no—
120C22×Q8C2×D29311yescharacteristic
121C22×C8—2931no—
122C22×C8C2×D29311yescharacteristic
123C4⋊Q8—5862no—
124C4⋊Q8—5862no—
125C2×C4⋊C4—2931no—
126C2×C4⋊C4—2931no—
127C2×C4⋊C4—5861no—
128C2×C4⋊C4C2×D29311yescharacteristic
129C2×C42—2931no—
130#103—22no—
131#103—5862no—
132#95—5861no—
133#95—5861no—
134C2×Q8—21no—
135C2×Q8—21no—
136C2×Q8—21no—
137C2×Q8—21no—
138C2×Q8—21no—
139C2×Q8—5864no—
140C2×Q8—11722no—
141C2×Q8—11722no—
142C2×Q8Dic58612yescomplemented
143C22×C4—21no—
144C22×C4—21no—
145C22×C4—2931no—
146C22×C4—2931no—
147C22×C4—5861no—
148C22×C4—5861no—
149C22×C4C22×D29311yescharacteristic
150C2×C8—21no—
151C2×C8—21no—
152C2×C8—21no—
153C2×C8—5861no—
154C2×C8—5861no—
155C2×C8—5861no—
156C4⋊C4—21no—
157C4⋊C4—2932no—
158C4⋊C4—5864no—
159C4⋊C4—5861no—
160C4⋊C4—5861no—
161C4⋊C4—5861no—
162C4⋊C4C22⋊D29312yes—
163C42—5861no—
164C42—5861no—
165C23D4×D29311yescharacteristic
166Q8—22no—
167Q8—22no—
168Q8—41no—
169Q8—41no—
170Q8—11728no—
171C2×C4—22no—
172C2×C4—22no—
173C2×C4—41no—
174C2×C4—41no—
175C2×C4—41no—
176C2×C4—41no—
177C2×C4—2932no—
178C2×C4—2932no—
179C2×C4—5861no—
180C2×C4—5861no—
181C2×C4—5861no—
182C2×C4—5861no—
183C2×C4—5862no—
184C2×C4—11721no—
185C2×C4—11721no—
186C2×C4—11721no—
187C2×C4—11721no—
188C2×C4—11721no—
189C2×C4D4×D29311yescharacteristic
190C2×C4C2×C22⋊D29311yescharacteristic
191C2×C4C2×Dic58611yescharacteristic
192C2×C4#1798980111yescharacteristic
193C2×C4#1798980111yescharacteristic
194C2×C4#1798980211yescharacteristic
195C8—41no—
196C8—11721no—
197C22#2262759211yescharacteristic
198C22#2262760111yescharacteristic
199C22#2262761011yescharacteristic
200C22SD16×D29311yescharacteristic
201C22Q16×D29311yescharacteristic
202C22#2262765111yescharacteristic
203C22#2262765611yescharacteristic
204C4—42no—
205C4—42no—
206C4—23441no—
207C4—5862no—
208C4—5862no—
209C4—11722no—
210C4#2262760111yescharacteristic
211C4#2262760311yescharacteristic
212C4#2262761011yescharacteristic
213C4#2262761111yescharacteristic
214C2#3403604111yescharacteristic
215C2#3403627811yescharacteristic
216C2#3403628311yescharacteristic
217C2#3403641211yescharacteristic
218C2#3403642211yescharacteristic
219C2#3403647811yescharacteristic
220C2#3403649011yescharacteristic
subgroupG/H
centerC23D4×D293
commutator, cosocleC22×C4×C293C23
FrattiniC22×C4C22×D293
FittingC2×#103×C293C2
socle, prime radicalC23×C293C2×D4
hypercenterC2×#103D293
hypocenterC293#2024
LCSG ▷ C22×C4×C293 ▷ C2×C293 ▷ C293
UCSC1 ◁ C23 ◁ C22×C4 ◁ C2×#103

Complements

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

NH ≅ G/Ntype
45. C2×Q8×C293Q8semidirect
110. C293#2024semidirect
142. C2×Q8Dic586semidirect

Maximal subgroups

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

subgroupindex
C2×#226276232
C2×#226275482
#340360362
#340358922
#340358912
#340358832
C2×#103×C2932
#2024293