Finite Group Databasebeta

← #49157922

Subgroups — #49157922

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#34036839C211yesmaximal, characteristic
2#34036509C211yesmaximal, characteristic, complemented
3#34036424C211yesmaximal, characteristic, complemented
4#34036420C211yesmaximal, characteristic
5#34035877C211yesmaximal, characteristic, complemented
6#34035858C211yesmaximal, characteristic
7Q8⋊C8×C293C211yesmaximal, characteristic, complemented
8C2×Dic1172—22no—
9#22627624C2211yescharacteristic
10#22627624C2211yescharacteristic
11#22627616—21no—
12#22627602—22no—
13#22627600—21no—
14C4×D1172—21no—
15C4×D1172C2211yescharacteristic
16C4⋊C4×D293—21no—
17#22627557—21no—
18#22627556—21no—
19C4⋊#14556873C2211yescharacteristic
20#22627548—21no—
21#22627546—21no—
22C4×Q8×C293C2211yescharacteristic
23C4⋊C8×C293C2211yescharacteristic
24C4×C8×C293C2211yescharacteristic
25C2×Dic586—21no—
26C2×Dic586D412yes—
27C2×D1172D411yescharacteristic
28C2×C4×D293—22no—
29C2×C4×D293—21no—
30Dic1172—44no—
31C2×#14556873—21no—
32C4⋊Dic293—21no—
33C4⋊Dic293—21no—
34C4⋊Dic293—21no—
35C4⋊Dic293—21no—
36C4⋊Dic293D411yescharacteristic
37#17989781—22no—
38#17989781—22no—
39#17989779—22no—
40#17989779—21no—
41C2×Q8×C293D411yescharacteristic
42C2×C8×C293—21no—
43C2×C8×C293—21no—
44C4⋊C4×C293—21no—
45C4⋊C4×C293D411yescharacteristic
46C42×C293—21no—
47C42×C293C2311yescharacteristic
48C22×D293—21no—
49Dic586—42no—
50Dic586—42no—
51D1172—21no—
52D1172Q1612yescomplemented
53C2×Dic293—21no—
54C2×Dic293—22no—
55C2×Dic293—41no—
56C4×D293—41no—
57C4×D293—41no—
58C4×D293—82no—
59#14556873—41no—
60Q8×C293—21no—
61Q8×C293—21no—
62C2×C4×C293—21no—
63C2×C4×C293—21no—
64C2×C4×C293C2×D411yescharacteristic
65C2×C4×C293C2×D411yescharacteristic
66C2×C4×C293C2×D411yescharacteristic
67C8×C293—22no—
68C8×C293—41no—
69C22×C293#12011yescharacteristic
70C2×D293—22no—
71C2×D293—41no—
72C2×D293—41no—
73C4×C293—21no—
74C4×C293—41no—
75C4×C293—41no—
76C4×C293C2×Q1611yescharacteristic
77C4×C293#13511yescharacteristic
78C4×C293#13711yescharacteristic
79C4×C293#13711yescharacteristic
80Dic293—41no—
81Dic293—42no—
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#333—2931no—
94Q8⋊C8D29311yescharacteristic, complemented
95D4⋊C8—2931no—
96C2×Q16—5862no—
97C4⋊Q8—2931no—
98C4⋊Q8—2931no—
99#125—5861no—
100C22⋊Q8—5862no—
101C22⋊Q8—5861no—
102C4×Q8C2×D29311yescharacteristic
103C4×D4—2931no—
104C4×D4—5861no—
105C2×C4⋊C4—5861no—
106#107—5861no—
107#106—5861no—
108C4⋊C8—2931no—
109C4⋊C8C2×D29311yescharacteristic
110#103—5861no—
111#102—5861no—
112C4×C8C2×D29311yescharacteristic
113C2×Q8—2932no—
114C2×Q8—5861no—
115C2×Q8D117211yescharacteristic
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—2931no—
125C4⋊C4—5862no—
126C4⋊C4—5862no—
127C4⋊C4—5861no—
128C4⋊C4—5861no—
129C4⋊C4—5861no—
130C4⋊C4—5861no—
131C4⋊C4D117211yescharacteristic
132C22⋊C4—5862no—
133C22⋊C4—5861no—
134C42—21no—
135C42C22×D29311yescharacteristic
136C23—5861no—
137Q8—21no—
138Q8—21no—
139Q8—11722no—
140Q8—11722no—
141D4—2932no—
142D4—5861no—
143C2×C4—21no—
144C2×C4—21no—
145C2×C4—23442no—
146C2×C4—5861no—
147C2×C4—5862no—
148C2×C4—11721no—
149C2×C4—11721no—
150C2×C4—11721no—
151C2×C4D4×D29311yescharacteristic
152C2×C4D4×D29311yescharacteristic
153C2×C4C2×D117211yescharacteristic
154C8—22no—
155C8—41no—
156C8—11721no—
157C22—5862no—
158C22—11721no—
159C22—11721no—
160C22#2262759411yescharacteristic
161C4—21no—
162C4—41no—
163C4—41no—
164C4—23441no—
165C4—11721no—
166C4—11722no—
167C4Q16×D29311yescharacteristic
168C4#2262764611yescharacteristic
169C4#2262765311yescharacteristic
170C4#2262765711yescharacteristic
171C2—11722no—
172C2#3403628611yescharacteristic
173C2#3403629311yescharacteristic
174C2#3403629811yescharacteristic
subgroupG/H
centerC22#22627594
commutator, cosocleC42×C293C23
FrattiniC42C22×D293
FittingQ8⋊C8×C293C2
socleC22×C293#120
prime radicalC2×D1172D4
hypercenterQ8⋊C8D293
hypocenterC293#1632
LCSG ▷ C42×C293 ▷ C22×C293 ▷ C293
UCSC1 ◁ C22 ◁ C42 ◁ Q8⋊C8

Complements

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

NH ≅ G/Ntype
2. #34036509C2semidirect
3. #34036424C2semidirect
5. #34035877C2semidirect
7. Q8⋊C8×C293C2semidirect
52. D1172Q16semidirect
87. C293#1632semidirect
94. Q8⋊C8D293semidirect

Maximal subgroups

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

subgroupindex
#340368392
#340365092
#340364242
#340364202
#340358772
#340358582
Q8⋊C8×C2932
#1632293