Finite Group Databasebeta

← #49174214

Subgroups — #49174214

Order 37504.

264 conjugacy classes of subgroups; only the 66 normal subgroups are shown.

normal subgroups only

This group has 264 conjugacy classes of subgroups — too many to draw. Only its 66 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#34037147C211yesmaximal, characteristic, complemented
2#34037073C211yesmaximal, characteristic, complemented
3#34036980C214yesmaximal, complemented
4#34036677C211yesmaximal, characteristic
5C2×C4⋊#11924078—21no—
6#22627691—21no—
7#22627681C2212yes—
8C4×#14556880—21no—
9(C2×#11924078)⋊C4—21no—
10(C2×#11924078)⋊C4C2212yes—
11C2×#17989801—21no—
12#22627624C411yescharacteristic, complemented
13#22627611—21no—
14#22627595—21no—
15#22627595C2212yes—
16D4×Dic293—21no—
17D4×Dic293C412yescomplemented
18C42×D293C2211yescharacteristic
19#127×C293C411yescharacteristic, complemented
20C22×#11924078—22no—
21C2×#14556880—22no—
22C4⋊#11924078—42no—
23#17989801—42no—
24#17989801—42no—
25C2×Dic586—21no—
26C2×C22⋊D293—22no—
27C22×Dic293—22no—
28C2×C4×D293D411yescharacteristic
29C2×C4×D293D411yescharacteristic
30C2×C4×D293C2311yescharacteristic
31C4⋊Dic293—21no—
32C4⋊Dic293C2×C412yes—
33C22⋊Dic293—22no—
34C22⋊Dic293—22no—
35C4×Dic293C2×C411yescharacteristic
36C4×Dic293D411yescharacteristic
37C4×Dic293D411yescharacteristic
38C2×D4×C293—21no—
39C2×D4×C293—21no—
40C2×D4×C293C2×C412yes—
41C42×C293C2×C411yescharacteristic
42C2×#11924078—42no—
43C2×#11924078—42no—
44C2×#11924078—42no—
45#14556880—42no—
46C22×D293C2×D411yescharacteristic
47Dic586—42no—
48C22⋊D293—42no—
49C22⋊D293—42no—
50C2×Dic293—22no—
51C2×Dic293—44no—
52C2×Dic293C22⋊C411yescharacteristic
53C2×Dic293C22⋊C411yescharacteristic
54C2×Dic293C2×D411yescharacteristic
55C4×D293—41no—
56C4×D293—41no—
57C4×D293D812yes—
58C4×D293SD1612yes—
59C23×C293—22no—
60D4×C293—42no—
61D4×C293—42no—
62D4×C293—42no—
63C2×C4×C293C22⋊C411yescharacteristic
64C2×C4×C293C22⋊C411yescharacteristic
65C2×C4×C293C22×C411yescharacteristic
66C22×C293—42no—
67C22×C293—42no—
68C22×C293—42no—
69C22×C293C2×C22⋊C411yescharacteristic
70C2×D293—21no—
71C2×D293—21no—
72C2×D293C2×D811yescharacteristic
73C2×D293C2×SD1611yescharacteristic
74#11924078—82no—
75C4×C293—21no—
76C4×C293—21no—
77C4×C293#10212yes—
78Dic293—21no—
79Dic293—21no—
80Dic293—42no—
81Dic293#10212yes—
82C2×C293—82no—
83C2×C293#41011yescharacteristic
84C2×C293C2×#10211yescharacteristic
85C2×C293#42111yescharacteristic
86D293—21no—
87D293—21no—
88C293#151711yescharacteristic, complemented, Sylow
89#1517—2931nomaximal, Sylow
90#532—2931no—
91#431—2931no—
92#382—2931no—
93#327—2934no—
94C2×#41—5861no—
95C4⋊Q8—2931no—
96#127#1192407811yescharacteristic, complemented
97#124—5861no—
98#121—2932no—
99#121—5861no—
100C4×D4—2932no—
101C4×D4—5861no—
102C2×C4⋊C4—5861no—
103C2×C42—2931no—
104C4⋊C8—5861no—
105C22⋊C8—2932no—
106C4×C8—5861no—
107#95—2932no—
108#95—5861no—
109#41—11722no—
110#41—11722no—
111C2×Q8—5861no—
112C2×D4—21no—
113C2×D4—21no—
114C2×D4—5862no—
115C2×D4C2×#1192407812yes—
116C22×C4—2931no—
117C22×C4—2931no—
118C22×C4—2931no—
119C22×C4—5862no—
120C22×C4—5862no—
121C2×C8—5862no—
122C4⋊C4—2932no—
123C4⋊C4—5861no—
124C4⋊C4—11722no—
125C22⋊C4—5862no—
126C22⋊C4—5862no—
127C42—2931no—
128C42—2931no—
129C42—2931no—
130C42C2×#1192407811yescharacteristic
131C23—22no—
132C23—2931no—
133Q8—11722no—
134D4—42no—
135D4—42no—
136D4—42no—
137D4—11722no—
138D4—11722no—
139C2×C4—2931no—
140C2×C4—2932no—
141C2×C4—2932no—
142C2×C4—2931no—
143C2×C4—2931no—
144C2×C4—5862no—
145C2×C4—11721no—
146C2×C4—11721no—
147C2×C4—11724no—
148C2×C4—11722no—
149C2×C4—11722no—
150C2×C4—11722no—
151C2×C4C22⋊#1192407811yescharacteristic
152C2×C4C22⋊#1192407811yescharacteristic
153C2×C4C22×#1192407811yescharacteristic
154C8—11722no—
155C22—42no—
156C22—42no—
157C22—42no—
158C22—2931no—
159C22—2931no—
160C22—5861no—
161C22—5861no—
162C22C2×C22⋊#1192407811yescharacteristic
163C4—21no—
164C4—21no—
165C4—2932no—
166C4—23442no—
167C4—5861no—
168C4—5861no—
169C4—11722no—
170C4#2262768612yes—
171C2—82no—
172C2—5861no—
173C2—5861no—
174C2#3403710911yescharacteristic
175C2C2×#2262768611yescharacteristic
176C2#3403712711yescharacteristic
subgroupG/H
centerC22C2×C22⋊#11924078
commutatorC2×C4×C293C22×C4
FrattiniC2×C4C22×#11924078
Fitting#127×C293C4
socleC22×C293C2×C22⋊C4
prime radical#34036677C2
cosocleC2×C4×D293C23
hypercenter#127#11924078
hypocenterC293#1517
LCSG ▷ C2×C4×C293 ▷ C22×C293 ▷ C293
UCSC1 ◁ C22 ◁ C42 ◁ #127

Complements

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

NH ≅ G/Ntype
1. #34037147C2semidirect
2. #34037073C2semidirect
3. #34036980C2semidirect
12. #22627624C4semidirect
17. D4×Dic293C4semidirect
19. #127×C293C4semidirect
88. C293#1517semidirect
96. #127#11924078semidirect

Maximal subgroups

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

subgroupindex
#340371472
#340370732
#340369802
#340366772
#1517293