Finite Group Databasebeta

← #49157920

Subgroups — #49157920

Order 37504.

214 conjugacy classes of subgroups; only the 55 normal subgroups are shown.

normal subgroups only

This group has 214 conjugacy classes of subgroups — too many to draw. Only its 55 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#34036840C211yesmaximal, characteristic
2#34036508C211yesmaximal, characteristic, complemented
3#34036425C211yesmaximal, characteristic, complemented
4#34036420C211yesmaximal, characteristic
5#34035859C211yesmaximal, characteristic, complemented
6#34035856C211yesmaximal, characteristic
7#333×C293C211yesmaximal, characteristic, complemented
8C2×#17989792—22no—
9#22627624C2211yescharacteristic
10#22627615—21no—
11#22627604—21no—
12#22627600—22no—
13C4×Dic586C2211yescharacteristic
14C4×D1172C2211yescharacteristic
15#22627586—21no—
16C4⋊C4×D293—21no—
17#22627558—21no—
18#22627556—21no—
19#22627549—21no—
20#22627546—21no—
21C4×#14556873C2211yescharacteristic
22C4⋊Q8×C293C2211yescharacteristic
23C4⋊C8×C293C2211yescharacteristic
24C4⋊C8×C293C2211yescharacteristic
25C2×Dic586—21no—
26C2×Dic586D411yescharacteristic
27C2×D1172D411yescharacteristic
28C2×C4×D293—22no—
29C2×C4×D293—21no—
30#17989792—44no—
31C2×#14556873—21no—
32C4⋊Dic293—22no—
33C4⋊Dic293—21no—
34C4⋊Dic293—21no—
35C4⋊Dic293D411yescharacteristic
36C4⋊Dic293D411yescharacteristic
37#17989781—22no—
38#17989781—21no—
39#17989779—22no—
40#17989779—21no—
41C4×Dic293—21no—
42C2×Q8×C293D412yes—
43C2×C8×C293—21no—
44C2×C8×C293—21no—
45C4⋊C4×C293—21no—
46C4⋊C4×C293—21no—
47C42×C293C2311yescharacteristic
48C22×D293—21no—
49Dic586—21no—
50Dic586—21no—
51Dic586—42no—
52D1172—21no—
53D1172Q1612yescomplemented
54C2×Dic293—21no—
55C2×Dic293—21no—
56C2×Dic293—21no—
57C2×Dic293—41no—
58C4×D293—41no—
59C4×D293—41no—
60C4×D293—82no—
61#14556873—22no—
62Q8×C293—42no—
63C2×C4×C293—22no—
64C2×C4×C293C2×D411yescharacteristic
65C2×C4×C293C2×D411yescharacteristic
66C2×C4×C293C2×D411yescharacteristic
67C8×C293—41no—
68C8×C293—41no—
69C22×C293#12011yescharacteristic
70C2×D293—22no—
71C2×D293—41no—
72C2×D293—41no—
73C4×C293—21no—
74C4×C293—42no—
75C4×C293C2×Q1611yescharacteristic
76C4×C293#13511yescharacteristic
77C4×C293#13711yescharacteristic
78C4×C293#13711yescharacteristic
79Dic293—41no—
80Dic293—41no—
81Dic293—41no—
82Dic293—81no—
83C2×C293#45111yescharacteristic
84C2×C293#45211yescharacteristic
85C2×C293#45311yescharacteristic
86D293—42no—
87C293#163211yescharacteristic, complemented, Sylow
88#1632—2931nomaximal, Sylow
89#554—2931no—
90#494—2931no—
91#477—2931no—
92#476—2931no—
93#333D29311yescharacteristic, complemented
94Q8⋊C8—2931no—
95D4⋊C8—2931no—
96C2×Q16—5862no—
97C4⋊Q8—2931no—
98C4⋊Q8C2×D29311yescharacteristic
99#125—5861no—
100C22⋊Q8—5861no—
101C22⋊Q8—5862no—
102C4×Q8—2931no—
103C4×D4—2931no—
104C4×D4—5861no—
105C2×C4⋊C4—5861no—
106#107—5861no—
107#106—5861no—
108C4⋊C8C2×D29311yescharacteristic
109C4⋊C8C2×D29311yescharacteristic
110#103—5861no—
111#102—5861no—
112C4×C8—2931no—
113C2×Q8—2931no—
114C2×Q8—5861no—
115C2×Q8D117212yes—
116C2×D4—2931no—
117C22×C4—5862no—
118C22×C4—5861no—
119Q16—11724no—
120C2×C8—21no—
121C2×C8—21no—
122C2×C8—5861no—
123C4⋊C4—21no—
124C4⋊C4—21no—
125C4⋊C4—2931no—
126C4⋊C4—2931no—
127C4⋊C4—5862no—
128C4⋊C4—5862no—
129C4⋊C4—5861no—
130C4⋊C4—5861no—
131C4⋊C4—5861no—
132C22⋊C4—5862no—
133C22⋊C4—5861no—
134C42—5861no—
135C42C22×D29311yescharacteristic
136C23—5861no—
137Q8—42no—
138Q8—5861no—
139Q8—5861no—
140Q8—11722no—
141D4—2932no—
142D4—5861no—
143C2×C4—22no—
144C2×C4—23442no—
145C2×C4—5861no—
146C2×C4—5861no—
147C2×C4—5861no—
148C2×C4—11721no—
149C2×C4—11721no—
150C2×C4—11721no—
151C2×C4D4×D29311yescharacteristic
152C2×C4D4×D29311yescharacteristic
153C2×C4C2×D117211yescharacteristic
154C8—41no—
155C8—41no—
156C8—5862no—
157C22—5862no—
158C22—11721no—
159C22—11721no—
160C22#2262759411yescharacteristic
161C4—21no—
162C4—42no—
163C4—23441no—
164C4—11721no—
165C4—11721no—
166C4—11721no—
167C4Q16×D29311yescharacteristic
168C4#2262764511yescharacteristic
169C4#2262765311yescharacteristic
170C4#2262765611yescharacteristic
171C2—11722no—
172C2#3403628611yescharacteristic
173C2#3403629411yescharacteristic
174C2#3403629911yescharacteristic
subgroupG/H
centerC22#22627594
commutator, cosocleC42×C293C23
FrattiniC42C22×D293
Fitting#333×C293C2
socleC22×C293#120
prime radicalC2×D1172D4
hypercenter#333D293
hypocenterC293#1632
LCSG ▷ C42×C293 ▷ C22×C293 ▷ C293
UCSC1 ◁ C22 ◁ C42 ◁ #333

Complements

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

NH ≅ G/Ntype
2. #34036508C2semidirect
3. #34036425C2semidirect
5. #34035859C2semidirect
7. #333×C293C2semidirect
53. D1172Q16semidirect
87. C293#1632semidirect
93. #333D293semidirect

Maximal subgroups

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

subgroupindex
#340368402
#340365082
#340364252
#340364202
#340358592
#340358562
#333×C2932
#1632293