Finite Group Databasebeta

← #49174293

Subgroups — #49174293

Order 37504.

344 conjugacy classes of subgroups; only the 70 normal subgroups are shown.

normal subgroups only

This group has 344 conjugacy classes of subgroups — too many to draw. Only its 70 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#34037134C211yesmaximal, characteristic, complemented
3#34036987C214yesmaximal, complemented
4#127×D293C211yesmaximal, characteristic
5C2×#17989812—21no—
6#22627691—21no—
7#22627691C2212yescomplemented
8#22627691C2212yescomplemented
9#22627681—21no—
10C4×#14556880—21no—
11C2×D4×D293—21no—
12C2×D4×D293—21no—
13C2×D4×D293C412yes—
14#22627621C411yescharacteristic
15#22627620—21no—
16#22627620—21no—
17#22627620C2212yes—
18C42×D293C2211yescharacteristic
19#127×C293C411yescharacteristic
20#17989812—42no—
21C2×#14556880—22no—
22C2×#14556880—22no—
23C23×D293—22no—
24C2×D1172—21no—
25C2×D1172—21no—
26C2×D1172C2×C412yes—
27C2×C22⋊D293—22no—
28C2×C22⋊D293—22no—
29C2×C22⋊D293—22no—
30D4×D293—44no—
31D4×D293—44no—
32D4×D293—42no—
33D4×D293—42no—
34C2×C4×D293C2×C411yescharacteristic
35C2×C4×D293D411yescharacteristic
36C2×C4×D293D411yescharacteristic
37C4×Dic293D411yescharacteristic
38C4×Dic293D411yescharacteristic
39C4×Dic293C2311yescharacteristic
40C2×D4×C293—21no—
41C2×D4×C293—21no—
42C2×D4×C293C2×C412yes—
43C42×C293C2×C411yescharacteristic
44#14556880—42no—
45#14556880—42no—
46C22×D293—22no—
47C22×D293—44no—
48C22×D293—44no—
49C22×D293—44no—
50C22×D293C22⋊C411yescharacteristic
51D1172—42no—
52D1172—42no—
53D1172—42no—
54C22⋊D293—44no—
55C22⋊D293—42no—
56C22⋊D293—42no—
57C22⋊D293—44no—
58C2×Dic293C22⋊C411yescharacteristic
59C2×Dic293C2×D411yescharacteristic
60C2×Dic293C2×D411yescharacteristic
61C4×D293—22no—
62C4×D293—22no—
63C4×D293D812yes—
64C4×D293SD1612yes—
65C23×C293—22no—
66D4×C293—42no—
67D4×C293—42no—
68D4×C293—42no—
69C2×C4×C293C22⋊C411yescharacteristic
70C2×C4×C293C22⋊C411yescharacteristic
71C2×C4×C293C22×C411yescharacteristic
72C22×C293—42no—
73C22×C293—42no—
74C22×C293—42no—
75C22×C293C2×C22⋊C411yescharacteristic
76C2×D293—21no—
77C2×D293—21no—
78C2×D293—42no—
79C2×D293—42no—
80C2×D293—42no—
81C2×D293—88no—
82C2×D293#10212yes—
83C4×C293—21no—
84C4×C293—21no—
85C4×C293#10212yes—
86Dic293#10012yes—
87Dic293C2×D811yescharacteristic
88Dic293C2×SD1611yescharacteristic
89Dic293AGL(1,ℤ/8)12yes—
90C2×C293—82no—
91C2×C293C2×#10011yescharacteristic
92C2×C293C2×#10211yescharacteristic
93C2×C293#41811yescharacteristic
94D293—22no—
95D293—82no—
96C293#154511yescharacteristic, complemented, Sylow
97#1545—2931nomaximal, Sylow
98C2×#127—2931no—
99#431—2931no—
100#423—2931no—
101#331—2934no—
102C22×D4—2932no—
103C22×D4—5861no—
104C22×D4—5861no—
105C2×M16—5861no—
106#127—2932no—
107#127—2931no—
108#127—5861no—
109#127—5861no—
110#127#1192407811yescharacteristic
111C2×C42—2931no—
112C4⋊C8—2932no—
113C4⋊C8—2932no—
114C4⋊C8—5861no—
115C22⋊C8—5861no—
116C4×C8—5861no—
117C24—5862no—
118C2×D4—21no—
119C2×D4—21no—
120C2×D4—2932no—
121C2×D4—5862no—
122C2×D4—5862no—
123C2×D4—5862no—
124C2×D4—5861no—
125C2×D4—5861no—
126C2×D4—11722no—
127C2×D4—11722no—
128C2×D4—11724no—
129C2×D4—11724no—
130C2×D4C2×#1192407812yes—
131C22×C4—2931no—
132C22×C4—2931no—
133C22×C4—2931no—
134M16—11722no—
135C2×C8—5862no—
136C2×C8—5862no—
137C42—2931no—
138C42—2931no—
139C42—2931no—
140C42C2×#1192407811yescharacteristic
141C23—22no—
142C23—2931no—
143C23—5862no—
144C23—11724no—
145C23—11724no—
146C23—11724no—
147D4—42no—
148D4—42no—
149D4—42no—
150D4—11722no—
151D4—11722no—
152D4—11722no—
153D4—11722no—
154D4—11724no—
155D4—11724no—
156D4—11722no—
157C2×C4—2931no—
158C2×C4—2931no—
159C2×C4—2931no—
160C2×C4—2932no—
161C2×C4—2932no—
162C2×C4—5862no—
163C2×C4—5862no—
164C2×C4C22⋊#1192407811yescharacteristic
165C2×C4C22⋊#1192407811yescharacteristic
166C2×C4C22×#1192407811yescharacteristic
167C8—11722no—
168C8—11722no—
169C22—42no—
170C22—42no—
171C22—42no—
172C22—2932no—
173C22—23448no—
174C22—5861no—
175C22—5861no—
176C22—11722no—
177C22—11722no—
178C22—11722no—
179C22C2×C22⋊#1192407811yescharacteristic
180C4—21no—
181C4—21no—
182C4—2932no—
183C4—2931no—
184C4—2931no—
185C4—2932no—
186C4#2262768612yes—
187C2—82no—
188C2—23442no—
189C2—5862no—
190C2D293⋊#10011yescharacteristic
191C2C2×#2262768611yescharacteristic
192C2#3403712111yescharacteristic
subgroupG/H
centerC22C2×C22⋊#11924078
commutatorC2×C4×C293C22×C4
FrattiniC2×C4C22×#11924078
Fitting#127×C293C4
socleC22×C293C2×C22⋊C4
prime radical#127×D293C2
cosocleC4×Dic293C23
hypercenter#127#11924078
hypocenterC293#1545
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. #34037134C2semidirect
3. #34036987C2semidirect
7. #22627691C22semidirect
8. #22627691C22semidirect
96. C293#1545semidirect

Maximal subgroups

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

subgroupindex
#340371472
#340371342
#340369872
#127×D2932
#1545293