Finite Group Databasebeta

← #49174253

Subgroups — #49174253

Order 37504.

216 conjugacy classes of subgroups; only the 56 normal subgroups are shown.

normal subgroups only

This group has 216 conjugacy classes of subgroups — too many to draw. Only its 56 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#34037149C211yesmaximal, characteristic, complemented
2C4×#17989811C211yesmaximal, characteristic, complemented
3#34036986C212yesmaximal, complemented
4#34036985C212yesmaximal, complemented
5#34036665C211yesmaximal, characteristic
6C2×#17989811—21no—
7#22627691—21no—
8C22⋊#14556880—21no—
9#22627679C2212yes—
10#22627679C2212yes—
11C4×#14556880—21no—
12#22627619—21no—
13#22627615C2211yescharacteristic
14#22627613C2211yescharacteristic
15#22627608—21no—
16#22627598C411yescharacteristic
17Q8×Dic293C411yescharacteristic
18#22627586C411yescharacteristic
19#22627584—21no—
20#22627582—21no—
21C2×C4×Dic293C2211yescharacteristic
22C22⋊Q8×C293C411yescharacteristic
23#17989811—24no—
24C2×#14556880—22no—
25C2×#14556880—22no—
26C2×D1172C2×C411yescharacteristic
27C2×C22⋊D293—21no—
28C22×Dic293D411yescharacteristic
29C22×Dic293D411yescharacteristic
30C2×C4×D293—21no—
31C4⋊Dic293—21no—
32C4⋊Dic293—21no—
33C4⋊Dic293C2×C411yescharacteristic
34#17989781—21no—
35#17989779—21no—
36#17989779—21no—
37#17989779—21no—
38#17989779—21no—
39C4×Dic293—21no—
40C4×Dic293C2×C411yescharacteristic
41C4×Dic293D411yescharacteristic
42C4×Dic293D411yescharacteristic
43C4×Dic293C2311yescharacteristic
44C2×Q8×C293C2×C411yescharacteristic
45C22×C4×C293C2×C411yescharacteristic
46C4⋊C4×C293—21no—
47C4⋊C4×C293C2×C411yescharacteristic
48C22⋊C4×C293—21no—
49#14556880—24no—
50#14556880—42no—
51C22×D293—21no—
52D1172—41no—
53C22⋊D293—42no—
54C2×Dic293—22no—
55C2×Dic293—21no—
56C2×Dic293—41no—
57C2×Dic293C22⋊C411yescharacteristic
58C2×Dic293C22⋊C411yescharacteristic
59C2×Dic293C2×D411yescharacteristic
60C2×Dic293C2×D411yescharacteristic
61C4×D293—42no—
62C23×C293C22⋊C411yescharacteristic
63Q8×C293—41no—
64C2×C4×C293—21no—
65C2×C4×C293—21no—
66C2×C4×C293—41no—
67C2×C4×C293C22⋊C411yescharacteristic
68C2×C4×C293C22×C411yescharacteristic
69C22×C293—21no—
70C22×C293—21no—
71C22×C293—21no—
72C22×C293C2×C22⋊C411yescharacteristic
73C2×D293—41no—
74C2×D293—41no—
75C2×D293—41no—
76C4×C293—21no—
77C4×C293—21no—
78C4×C293—41no—
79C4×C293—41no—
80Dic293—21no—
81Dic293—21no—
82Dic293—21no—
83Dic293—41no—
84Dic293#10412yes—
85C2×C293—41no—
86C2×C293#41311yescharacteristic
87C2×C293C2×#10411yescharacteristic
88C2×C293#42111yescharacteristic
89D293—81no—
90C293#152911yescharacteristic, complemented, Sylow
91#1529—2931nomaximal, Sylow
92#529—2931no—
93#432—2931no—
94C4×M16—2931no—
95#330—2932no—
96#329—2932no—
97C2×M16—5861no—
98#126—5861no—
99#125—2931no—
100#124—2931no—
101#123—5861no—
102C22⋊Q8#1192407811yescharacteristic
103#121—2931no—
104C4×Q8—2931no—
105C4×D4—2931no—
106C4×D4—5861no—
107#117—5861no—
108C2×C42—2931no—
109C4⋊C8—5861no—
110C22⋊C8—5861no—
111#97—2932no—
112#97—2932no—
113C4×C8—5861no—
114C2×Q8C2×#1192407811yescharacteristic
115C2×D4—2931no—
116C2×D4—5861no—
117C22×C4—2931no—
118C22×C4—2931no—
119C22×C4—5861no—
120C22×C4C2×#1192407811yescharacteristic
121M16—5864no—
122C2×C8—5862no—
123C2×C8—5862no—
124C4⋊C4—21no—
125C4⋊C4—2931no—
126C4⋊C4—5861no—
127C4⋊C4—5861no—
128C4⋊C4—5861no—
129C4⋊C4C2×#1192407811yescharacteristic
130C22⋊C4—21no—
131C22⋊C4—5861no—
132C22⋊C4—5861no—
133C22⋊C4—5861no—
134C22⋊C4—5861no—
135C42—2931no—
136C42—2931no—
137C42—2931no—
138C42—2931no—
139C42—5861no—
140C23—5861no—
141C23C22⋊#1192407811yescharacteristic
142Q8—41no—
143D4—11721no—
144D4—11722no—
145C2×C4—21no—
146C2×C4—21no—
147C2×C4—41no—
148C2×C4—2931no—
149C2×C4—2931no—
150C2×C4—2931no—
151C2×C4—2931no—
152C2×C4—5862no—
153C2×C4—5861no—
154C2×C4—11722no—
155C2×C4—11721no—
156C2×C4C22⋊#1192407811yescharacteristic
157C2×C4C22×#1192407811yescharacteristic
158C8—5864no—
159C8—11722no—
160C22—21no—
161C22—21no—
162C22—21no—
163C22—11721no—
164C22—11721no—
165C22—11721no—
166C22C2×C22⋊#1192407811yescharacteristic
167C4—21no—
168C4—21no—
169C4—41no—
170C4—41no—
171C4—2932no—
172C4—5861no—
173C4—5861no—
174C4—5861no—
175C4—11721no—
176C2—41no—
177C2—23441no—
178C2#3403711611yescharacteristic
179C2D293⋊#10411yescharacteristic
180C2#3403712811yescharacteristic
subgroupG/H
centerC22C2×C22⋊#11924078
commutatorC2×C4×C293C22×C4
FrattiniC2×C4C22×#11924078
FittingC22⋊Q8×C293C4
socleC22×C293C2×C22⋊C4
prime radical#22627598C4
cosocleC4×Dic293C23
hypercenterC22⋊Q8#11924078
hypocenterC293#1529
LCSG ▷ C2×C4×C293 ▷ C22×C293 ▷ C293
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22⋊Q8

Complements

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

NH ≅ G/Ntype
1. #34037149C2semidirect
2. C4×#17989811C2semidirect
3. #34036986C2semidirect
4. #34036985C2semidirect
90. C293#1529semidirect

Maximal subgroups

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

subgroupindex
#340371492
C4×#179898112
#340369862
#340369852
#340366652
#1529293