Finite Group Databasebeta

← #49159177

Subgroups — #49159177

Order 37504.

324 conjugacy classes of subgroups; only the 83 normal subgroups are shown.

normal subgroups only

This group has 324 conjugacy classes of subgroups — too many to draw. Only its 83 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×#22627624C211yesmaximal, characteristic
2#34036606C211yesmaximal, characteristic
3#34036139C211yesmaximal, characteristic
4#34036137C211yesmaximal, characteristic
5C2×#22627542C211yesmaximal, characteristic
6#34035889C211yesmaximal, characteristic
7#339×C293C211yesmaximal, characteristic
8C22×Dic586C2211yescharacteristic
9C22×Dic586C2211yescharacteristic
10C2×#17989786C2211yescharacteristic
11#22627624—22no—
12#22627624C414yescomplemented
13C4×Dic586—22no—
14#22627589—22no—
15#22627583C2211yescharacteristic
16#22627580—22no—
17C2×C4⋊Dic293—22no—
18#22627549—22no—
19#22627547—22no—
20#22627542—22no—
21C2×M16×C293C2211yescharacteristic
22#117×C293C2211yescharacteristic
23C2×C42×C293C2211yescharacteristic
24C2×Dic586—21no—
25C2×Dic586—21no—
26C2×Dic586—21no—
27C2×Dic586—21no—
28C2×Dic586—21no—
29C2×Dic586—21no—
30C2×Dic586—21no—
31C2×Dic586—21no—
32C2×Dic586—21no—
33C2×Dic586C2×C412yes—
34C2×Dic586C2×C412yes—
35C2×Dic586D412yes—
36C22×Dic293—21no—
37C22×Dic293D412yes—
38#17989786—21no—
39#17989786—21no—
40C2×#14556873—21no—
41C4⋊Dic293—28no—
42C4⋊Dic293D412yes—
43#17989781—24no—
44C22⋊Dic293—21no—
45C4×Dic293—24no—
46C4×Dic293—21no—
47C22×C4×C293—21no—
48C22×C4×C293C2311yescharacteristic
49M16×C293—21no—
50M16×C293—21no—
51C2×C8×C293—21no—
52C4⋊C4×C293D412yes—
53C22⋊C4×C293—21no—
54C42×C293—21no—
55C42×C293—21no—
56C42×C293C2×C412yes—
57Dic586—22no—
58Dic586—22no—
59Dic586—22no—
60Dic586—22no—
61Dic586—22no—
62Dic586—22no—
63Dic586—41no—
64Dic586—41no—
65C2×Dic293—22no—
66C2×Dic293—22no—
67C2×Dic293—22no—
68C2×Dic293—22no—
69C2×Dic293—41no—
70C2×Dic293—41no—
71C2×Dic293C22⋊C414yes—
72#14556873—41no—
73C23×C293C2×D411yescharacteristic
74C2×C4×C293—24no—
75C2×C4×C293—22no—
76C2×C4×C293—22no—
77C2×C4×C293C22×C411yescharacteristic
78C2×C4×C293C2×D411yescharacteristic
79C2×C4×C293C2×D411yescharacteristic
80C2×C4×C293C2×D411yescharacteristic
81C2×C4×C293#4111yescharacteristic
82C2×C4×C293#4111yescharacteristic
83C8×C293—41no—
84C22×C293—22no—
85C22×C293C2×C22⋊C411yescharacteristic
86C22×C293#12011yescharacteristic
87C22×C293#12311yescharacteristic
88C4×C293—24no—
89C4×C293—42no—
90C4×C293C4×D411yescharacteristic
91C4×C293C4×D411yescharacteristic
92C4×C293#12111yescharacteristic
93C4×C293#12111yescharacteristic
94Dic293—24no—
95Dic293—42no—
96Dic293—42no—
97C2×C293—21no—
98C2×C293—21no—
99C2×C293#38611yescharacteristic
100C2×C293#45612yes—
101C293#188611yescharacteristic, complemented, Sylow
102#1886—2931nomaximal, Sylow
103C2×C4⋊Q8—2931no—
104#519—2931no—
105#419—2931no—
106#419—2931no—
107C2×#101—2931no—
108#339—2931no—
109#339D29311yescharacteristic
110C22×Q8—2931no—
111C22×Q8—2931no—
112C2×M16—2931no—
113C2×M16C2×D29311yescharacteristic
114C4⋊Q8—2934no—
115C4⋊Q8—5862no—
116C4×Q8—5862no—
117C4×Q8—5862no—
118#117—2931no—
119#117—5862no—
120#117C2×D29311yescharacteristic
121C2×C4⋊C4—5862no—
122C2×C42C2×D29311yescharacteristic
123#103—5862no—
124#103—5862no—
125#101—5862no—
126C2×Q8—2932no—
127C2×Q8—2932no—
128C2×Q8—2932no—
129C2×Q8—5861no—
130C2×Q8—5861no—
131C2×Q8—5861no—
132C2×Q8—5861no—
133C2×Q8—5861no—
134C2×Q8—5861no—
135C2×Q8—5861no—
136C2×Q8—5861no—
137C2×Q8—5861no—
138C22×C4—21no—
139C22×C4—2932no—
140C22×C4—5861no—
141C22×C4C22×D29311yescharacteristic
142M16—21no—
143M16—21no—
144M16—5861no—
145M16—5861no—
146C2×C8—21no—
147C2×C8—5861no—
148C4⋊C4—2932no—
149C4⋊C4—5868no—
150C4⋊C4—5864no—
151C4⋊C4D117212yes—
152C22⋊C4—21no—
153C22⋊C4—5861no—
154C42—21no—
155C42—21no—
156C42—5864no—
157C42—5861no—
158C42C4×D29312yes—
159C23D4×D29311yescharacteristic
160Q8—5862no—
161Q8—5862no—
162Q8—5862no—
163Q8—5862no—
164Q8—5862no—
165Q8—5862no—
166Q8—11721no—
167Q8—11721no—
168C2×C4—24no—
169C2×C4—22no—
170C2×C4—22no—
171C2×C4—2934no—
172C2×C4—5862no—
173C2×C4—5862no—
174C2×C4—5862no—
175C2×C4—5862no—
176C2×C4—11721no—
177C2×C4—11721no—
178C2×C4C2×C4×D29311yescharacteristic
179C2×C4D4×D29311yescharacteristic
180C2×C4D4×D29311yescharacteristic
181C2×C4C2×D117211yescharacteristic
182C2×C4#1798980211yescharacteristic
183C2×C4#1798980311yescharacteristic
184C8—41no—
185C8—11721no—
186C22—22no—
187C22C22⋊C4×D29311yescharacteristic
188C22#2262759411yescharacteristic
189C22#2262760911yescharacteristic
190C4—24no—
191C4—42no—
192C4—5864no—
193C4—11722no—
194C4—11722no—
195C4#2262758611yescharacteristic
196C4C4×D117211yescharacteristic
197C4#2262759711yescharacteristic
198C4#2262759911yescharacteristic
199C2—21no—
200C2—21no—
201C2#3403600711yescharacteristic
202C2#3403631312yes—
subgroupG/H
centerC22#22627594
commutatorC2×C4×C293C22×C4
FrattiniC22×C4C22×D293
Fitting#339×C293C2
socleC22×C293#120
prime radicalC23×C293C2×D4
cosocleC22×C4×C293C23
hypercenter#339D293
hypocenterC293#1886
LCSG ▷ C2×C4×C293 ▷ C2×C293 ▷ C293
UCSC1 ◁ C22 ◁ C22×C4 ◁ #339

Complements

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

NH ≅ G/Ntype
12. #22627624C4semidirect
101. C293#1886semidirect

Maximal subgroups

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

subgroupindex
C2×#226276242
#340366062
#340361392
#340361372
C2×#226275422
#340358892
#339×C2932
#1886293