Finite Group Databasebeta

← #49159643

Subgroups — #49159643

Order 37504.

312 conjugacy classes of subgroups; only the 103 normal subgroups are shown.

normal subgroups only

This group has 312 conjugacy classes of subgroups — too many to draw. Only its 103 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
1C22×#17989792C211yesmaximal, characteristic
2C2×#22627557C211yesmaximal, characteristic
3C2×#22627549C211yesmaximal, characteristic
4C2×C8×Dic293C211yesmaximal, characteristic
5#34036036C211yesmaximal, characteristic
6#34036034C211yesmaximal, characteristic
7C2×#103×C293C211yesmaximal, characteristic
8C22×Dic586C2211yescharacteristic
9C2×#17989792—22no—
10C2×#17989792—22no—
11C2×#17989792C414yescomplemented
12C22×#14556873C2211yescharacteristic
13C2×C4⋊Dic293C2211yescharacteristic
14C2×C4×Dic293C2211yescharacteristic
15#22627557—22no—
16#22627549—22no—
17C8×Dic293—22no—
18#22627531—22no—
19#22627531—22no—
20C22×Q8×C293C2211yescharacteristic
21C22×C8×C293C2211yescharacteristic
22C2×C4⋊C4×C293C2211yescharacteristic
23#103×C293—22no—
24C2×Dic586—21no—
25C2×Dic586—21no—
26C2×Dic586—21no—
27C2×Dic586—21no—
28C2×Dic586—21no—
29C2×Dic586C2×C412yes—
30C22×Dic293—21no—
31C22×Dic293—21no—
32C22×Dic293D412yes—
33#17989792—28no—
34C2×#14556873C2×C412yes—
35C2×#14556873D412yes—
36C2×#14556873D412yes—
37C4⋊Dic293—21no—
38C4⋊Dic293—21no—
39C4×Dic293—21no—
40C4×Dic293—21no—
41C2×Q8×C293—21no—
42C2×Q8×C293—21no—
43C2×Q8×C293—21no—
44C2×Q8×C293—21no—
45C2×Q8×C293—21no—
46C2×Q8×C293C2×C412yes—
47C22×C4×C293—21no—
48C22×C4×C293—21no—
49C22×C4×C293C2311yescharacteristic
50C2×C8×C293—21no—
51C2×C8×C293—21no—
52C2×C8×C293D412yes—
53C4⋊C4×C293—21no—
54C4⋊C4×C293—21no—
55Dic586—22no—
56Dic586—22no—
57Dic586—41no—
58Dic586—41no—
59C2×Dic293—22no—
60C2×Dic293—22no—
61C2×Dic293—22no—
62C2×Dic293—41no—
63C2×Dic293—41no—
64C2×Dic293—41no—
65C2×Dic293—42no—
66C2×Dic293Q1614yescomplemented
67#14556873C22⋊C414yes—
68C23×C293C2×D411yescharacteristic
69Q8×C293—22no—
70Q8×C293—22no—
71Q8×C293—41no—
72Q8×C293—41no—
73C2×C4×C293—22no—
74C2×C4×C293—41no—
75C2×C4×C293—41no—
76C2×C4×C293—41no—
77C2×C4×C293—42no—
78C2×C4×C293C22×C411yescharacteristic
79C2×C4×C293C2×D411yescharacteristic
80C2×C4×C293C2×D411yescharacteristic
81C2×C4×C293C2×D411yescharacteristic
82C2×C4×C293#4111yescharacteristic
83C2×C4×C293#4111yescharacteristic
84C8×C293—22no—
85C22×C293C4×D411yescharacteristic
86C22×C293#12111yescharacteristic
87C22×C293#12711yescharacteristic
88C22×C293C2×Q1612yes—
89C22×C293#13512yes—
90C4×C293—42no—
91C4×C293—81no—
92C4×C293C2×C22⋊C411yescharacteristic
93C4×C293C4×D411yescharacteristic
94C4×C293#12111yescharacteristic
95C4×C293#12411yescharacteristic
96Dic293—24no—
97Dic293—42no—
98Dic293—81no—
99C2×C293#39011yescharacteristic
100C2×C293C4×Q1612yes—
101C2×C293#46712yes—
102C2×C293#49411yescharacteristic
103C2×C293#49511yescharacteristic
104C293#196911yescharacteristic, complemented, Sylow
105#1969—2931nomaximal, Sylow
106C22×Q16—2931no—
107C2×#107—2931no—
108C2×#103—2931no—
109C2×#103D29311yescharacteristic
110C2×C4×C8—2931no—
111#391—2931no—
112#391—2931no—
113C22×Q8—2931no—
114C22×Q8C2×D29311yescharacteristic
115C2×Q16—2934no—
116C2×Q16—5862no—
117C2×Q16—5862no—
118C22×C8—2931no—
119C22×C8C2×D29311yescharacteristic
120C2×C4⋊C4—2931no—
121C2×C4⋊C4C2×D29311yescharacteristic
122C2×C42—2931no—
123#107—5862no—
124#103—22no—
125#103—5862no—
126C4×C8—5862no—
127#95—5862no—
128#95—5862no—
129C2×Q8—21no—
130C2×Q8—21no—
131C2×Q8—21no—
132C2×Q8—21no—
133C2×Q8—21no—
134C2×Q8—2932no—
135C2×Q8—5861no—
136C2×Q8—5861no—
137C2×Q8—5861no—
138C2×Q8—5861no—
139C2×Q8—5861no—
140C2×Q8C4×D29312yes—
141C22×C4—21no—
142C22×C4—21no—
143C22×C4—2932no—
144C22×C4—5861no—
145C22×C4—5861no—
146C22×C4C22×D29311yescharacteristic
147Q16—5868no—
148C2×C8—21no—
149C2×C8—21no—
150C2×C8—2932no—
151C2×C8—2932no—
152C2×C8—2932no—
153C2×C8C22⋊D29312yes—
154C4⋊C4—21no—
155C4⋊C4—21no—
156C4⋊C4—5861no—
157C4⋊C4—5861no—
158C42—5861no—
159C42—5861no—
160C23D4×D29311yescharacteristic
161Q8—22no—
162Q8—22no—
163Q8—41no—
164Q8—41no—
165Q8—5862no—
166Q8—5862no—
167Q8—11721no—
168Q8—11721no—
169C2×C4—22no—
170C2×C4—41no—
171C2×C4—41no—
172C2×C4—41no—
173C2×C4—42no—
174C2×C4—2934no—
175C2×C4—5862no—
176C2×C4—5862no—
177C2×C4—5862no—
178C2×C4—11721no—
179C2×C4—11722no—
180C2×C4—11721no—
181C2×C4—11721no—
182C2×C4C2×C4×D29311yescharacteristic
183C2×C4D4×D29311yescharacteristic
184C2×C4D4×D29311yescharacteristic
185C2×C4C2×C22⋊D29311yescharacteristic
186C2×C4#1798980111yescharacteristic
187C2×C4#1798980211yescharacteristic
188C8—22no—
189C8—2934no—
190C22#2262758411yescharacteristic
191C22#2262759711yescharacteristic
192C22#2262762011yescharacteristic
193C22Q16×D29312yes—
194C22#2262764512yes—
195C4—42no—
196C4—81no—
197C4—23441no—
198C4—5864no—
199C4—11722no—
200C4C22⋊C4×D29311yescharacteristic
201C4C4×C22⋊D29311yescharacteristic
202C4#2262759611yescharacteristic
203C4#2262761011yescharacteristic
204C2#3403602911yescharacteristic
205C2#3403622112yes—
206C2#3403636912yes—
207C2#3403650711yescharacteristic
208C2#3403651011yescharacteristic
subgroupG/H
centerC23D4×D293
commutatorC2×C4×C293C22×C4
FrattiniC22×C4C22×D293
FittingC2×#103×C293C2
socle, prime radicalC23×C293C2×D4
cosocleC22×C4×C293C23
hypercenterC2×#103D293
hypocenterC293#1969
LCSG ▷ C2×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
11. C2×#17989792C4semidirect
66. C2×Dic293Q16semidirect
104. C293#1969semidirect

Maximal subgroups

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

subgroupindex
C22×#179897922
C2×#226275572
C2×#226275492
C2×C8×Dic2932
#340360362
#340360342
C2×#103×C2932
#1969293