Finite Group Databasebeta

← #49174245

Subgroups — #49174245

Order 37504.

264 conjugacy classes of subgroups; only the 58 normal subgroups are shown.

normal subgroups only

This group has 264 conjugacy classes of subgroups — too many to draw. Only its 58 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#34037152C211yesmaximal, characteristic, complemented
2C4×#17989812C211yesmaximal, characteristic, complemented
3#34036985C212yesmaximal, complemented
4#34036984C212yesmaximal, complemented
5#124×D293C211yesmaximal, characteristic
6C2×#17989812—21no—
7#22627691—21no—
8#22627681—21no—
9#22627679C2212yescomplemented
10#22627679C2212yescomplemented
11C4×#14556880—21no—
12C2×Q8×D293C411yescharacteristic
13C2×D4×D293C411yescharacteristic
14#22627613C2211yescharacteristic
15#22627612C411yescharacteristic
16#22627611C2211yescharacteristic
17#22627610—21no—
18#22627610—21no—
19C22⋊C4×D293—21no—
20C22⋊C4×D293—21no—
21C42×D293C2211yescharacteristic
22#124×C293C411yescharacteristic
23#17989812—24no—
24C2×#14556880—22no—
25C2×#14556880—22no—
26C23×D293—21no—
27C2×Dic586—21no—
28C2×Dic586C2×C411yescharacteristic
29Q8×D293—42no—
30C2×D1172C2×C411yescharacteristic
31C2×C22⋊D293—21no—
32D4×D293—42no—
33C2×C4×D293—21no—
34C2×C4×D293C2×C411yescharacteristic
35C2×C4×D293D411yescharacteristic
36C2×C4×D293D411yescharacteristic
37C22⋊Dic293—21no—
38C22⋊Dic293—21no—
39#17989779—21no—
40#17989779—21no—
41#17989779—21no—
42#17989779—21no—
43C4×Dic293D411yescharacteristic
44C4×Dic293D411yescharacteristic
45C4×Dic293C2311yescharacteristic
46C2×Q8×C293C2×C411yescharacteristic
47C2×D4×C293C2×C411yescharacteristic
48C22⋊C4×C293—21no—
49C22⋊C4×C293—21no—
50C42×C293C2×C411yescharacteristic
51#14556880—24no—
52#14556880—42no—
53C22×D293—21no—
54C22×D293—42no—
55C22×D293—42no—
56C22×D293—42no—
57C22×D293C22⋊C411yescharacteristic
58Dic586—42no—
59Dic586—41no—
60D1172—41no—
61C22⋊D293—42no—
62C2×Dic293—21no—
63C2×Dic293C22⋊C411yescharacteristic
64C2×Dic293C2×D411yescharacteristic
65C2×Dic293C2×D411yescharacteristic
66C4×D293—22no—
67C4×D293—22no—
68C4×D293—41no—
69C4×D293—42no—
70C23×C293—21no—
71Q8×C293—41no—
72D4×C293—41no—
73C2×C4×C293—21no—
74C2×C4×C293C22⋊C411yescharacteristic
75C2×C4×C293C22⋊C411yescharacteristic
76C2×C4×C293C22×C411yescharacteristic
77C22×C293—41no—
78C22×C293—41no—
79C22×C293—41no—
80C22×C293C2×C22⋊C411yescharacteristic
81C2×D293—21no—
82C2×D293—21no—
83C2×D293—41no—
84C2×D293—41no—
85C2×D293—41no—
86C2×D293—84no—
87C2×D293#10412yes—
88C4×C293—21no—
89C4×C293—21no—
90C4×C293—21no—
91C4×C293—41no—
92Dic293—21no—
93Dic293—21no—
94Dic293—41no—
95Dic293#10012yes—
96C2×C293—81no—
97C2×C293C2×#10011yescharacteristic
98C2×C293C2×#10411yescharacteristic
99C2×C293#42111yescharacteristic
100D293—22no—
101D293—81no—
102C293#152711yescharacteristic, complemented, Sylow
103#1527—2931nomaximal, Sylow
104C2×#124—2931no—
105#432—2931no—
106C4×M16—2931no—
107#329—2932no—
108#329—2932no—
109C22×Q8—2931no—
110C22×D4—2931no—
111C2×M16—5861no—
112#124—2931no—
113#124—2931no—
114#124—2931no—
115#124—5861no—
116#124—5861no—
117#124#1192407811yescharacteristic
118C2×C22⋊C4—5861no—
119C2×C22⋊C4—5861no—
120C2×C42—2931no—
121C4⋊C8—5861no—
122C22⋊C8—5861no—
123#97—2932no—
124#97—2932no—
125C4×C8—5861no—
126C24—5861no—
127C2×Q8—2931no—
128C2×Q8—5861no—
129C2×Q8—11722no—
130C2×Q8C2×#1192407811yescharacteristic
131C2×D4—2931no—
132C2×D4—5861no—
133C2×D4—11722no—
134C2×D4C2×#1192407811yescharacteristic
135C22×C4—2931no—
136C22×C4—2931no—
137C22×C4—2931no—
138C22×C4—5861no—
139M16—5864no—
140C2×C8—5862no—
141C2×C8—5862no—
142C22⋊C4—21no—
143C22⋊C4—21no—
144C22⋊C4—5861no—
145C22⋊C4—5861no—
146C22⋊C4—5861no—
147C22⋊C4—5861no—
148C22⋊C4—5861no—
149C22⋊C4—5861no—
150C42—2931no—
151C42—2931no—
152C42—2931no—
153C42C2×#1192407811yescharacteristic
154C23—21no—
155C23—2931no—
156C23—5861no—
157C23—11722no—
158C23—11722no—
159C23—11722no—
160Q8—41no—
161Q8—11721no—
162Q8—11722no—
163D4—41no—
164D4—11721no—
165D4—11722no—
166C2×C4—21no—
167C2×C4—2931no—
168C2×C4—2931no—
169C2×C4—2931no—
170C2×C4—5862no—
171C2×C4—5862no—
172C2×C4—5861no—
173C2×C4—11721no—
174C2×C4—11722no—
175C2×C4C22⋊#1192407811yescharacteristic
176C2×C4C22⋊#1192407811yescharacteristic
177C2×C4C22×#1192407811yescharacteristic
178C8—5864no—
179C8—11722no—
180C22—41no—
181C22—41no—
182C22—41no—
183C22—2932no—
184C22—23444no—
185C22—5861no—
186C22—5861no—
187C22—11721no—
188C22—11721no—
189C22—11721no—
190C22C2×C22⋊#1192407811yescharacteristic
191C4—21no—
192C4—21no—
193C4—21no—
194C4—41no—
195C4—2932no—
196C4—5861no—
197C4—5861no—
198C4—11721no—
199C2—81no—
200C2—23441no—
201C2—5862no—
202C2D293⋊#10011yescharacteristic
203C2D293⋊#10411yescharacteristic
204C2#3403712611yescharacteristic
subgroupG/H
centerC22C2×C22⋊#11924078
commutatorC2×C4×C293C22×C4
FrattiniC2×C4C22×#11924078
Fitting#124×C293C4
socleC22×C293C2×C22⋊C4
prime radicalC2×D4×D293C4
cosocleC4×Dic293C23
hypercenter#124#11924078
hypocenterC293#1527
LCSG ▷ C2×C4×C293 ▷ C22×C293 ▷ C293
UCSC1 ◁ C22 ◁ C42 ◁ #124

Complements

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

NH ≅ G/Ntype
1. #34037152C2semidirect
2. C4×#17989812C2semidirect
3. #34036985C2semidirect
4. #34036984C2semidirect
9. #22627679C22semidirect
10. #22627679C22semidirect
102. C293#1527semidirect

Maximal subgroups

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

subgroupindex
#340371522
C4×#179898122
#340369852
#340369842
#124×D2932
#1527293