Finite Group Databasebeta

← #49174949

Subgroups — #49174949

Order 37504.

336 conjugacy classes of subgroups; only the 74 normal subgroups are shown.

normal subgroups only

This group has 336 conjugacy classes of subgroups — too many to draw. Only its 74 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
1C2×#22627688C214yesmaximal, complemented
2C4×#17989812C211yesmaximal, characteristic, complemented
3C4×C4⋊#11924078C211yesmaximal, characteristic, complemented
4#34036677C211yesmaximal, characteristic
5C2×#17989812C2212yes—
6C2×C4⋊#11924078—21no—
7C2×C4×#11924078C2212yes—
8#22627688—28no—
9#22627679—21no—
10C4×#14556880—21no—
11(C2×#11924078)⋊C4—21no—
12C2×#17989801C2212yes—
13#22627624C411yescharacteristic, complemented
14#22627611C412yescomplemented
15#22627595—21no—
16#22627595—21no—
17D4×Dic293—21no—
18D4×Dic293—21no—
19C42×D293C2211yescharacteristic
20#127×C293C411yescharacteristic, complemented
21C22×#11924078—22no—
22#17989812—22no—
23#17989812D414yescomplemented
24C2×#14556880—22no—
25C4⋊#11924078—24no—
26C4×#11924078—24no—
27#17989801—24no—
28#17989801—24no—
29C2×Dic586C2×C412yes—
30C2×C22⋊D293—22no—
31C22×Dic293—22no—
32C2×C4×D293D411yescharacteristic
33C2×C4×D293D411yescharacteristic
34C2×C4×D293C2311yescharacteristic
35C4⋊Dic293—21no—
36C4⋊Dic293—21no—
37C22⋊Dic293—22no—
38C22⋊Dic293—22no—
39C4×Dic293C2×C411yescharacteristic
40C4×Dic293D411yescharacteristic
41C4×Dic293D411yescharacteristic
42C2×D4×C293—21no—
43C2×D4×C293—21no—
44C2×D4×C293C2×C412yes—
45C42×C293C2×C411yescharacteristic
46C2×#11924078—24no—
47C2×#11924078—42no—
48C2×#11924078—42no—
49#14556880—24no—
50C22×D293C2×D411yescharacteristic
51Dic586—24no—
52C22⋊D293—42no—
53C22⋊D293—42no—
54C2×Dic293—22no—
55C2×Dic293—44no—
56C2×Dic293C22⋊C411yescharacteristic
57C2×Dic293C22⋊C411yescharacteristic
58C2×Dic293C2×D411yescharacteristic
59C4×D293—22no—
60C4×D293—41no—
61C4×D293C2×D412yes—
62C4×D293#4112yes—
63C23×C293—22no—
64D4×C293—24no—
65D4×C293—42no—
66D4×C293—42no—
67C2×C4×C293C22⋊C411yescharacteristic
68C2×C4×C293C22⋊C411yescharacteristic
69C2×C4×C293C22×C411yescharacteristic
70C22×C293—42no—
71C22×C293—42no—
72C22×C293—42no—
73C22×C293C2×C22⋊C411yescharacteristic
74C2×D293—21no—
75C2×D293—21no—
76C2×D293#12411yescharacteristic
77C2×D293#12711yescharacteristic
78#11924078—44no—
79C4×C293—21no—
80C4×C293#10412yescomplemented
81C4×C293C4×D412yes—
82Dic293—21no—
83Dic293—21no—
84Dic293—42no—
85Dic293#12112yes—
86C2×C293—82no—
87C2×C293#39011yescharacteristic
88C2×C293C2×#10411yescharacteristic
89C2×C293#42111yescharacteristic
90D293—21no—
91D293—21no—
92C293#198011yescharacteristic, complemented, Sylow
93#1980—2931nomaximal, Sylow
94#532—2931no—
95C2×#104—2934no—
96C4×M16—2931no—
97C4×C4⋊C4—2931no—
98C2×#41—2932no—
99C2×M16—2932no—
100C4⋊Q8—2931no—
101#127#1192407811yescharacteristic, complemented
102#124—2932no—
103#121—5861no—
104#121—5861no—
105C4×D4—5861no—
106C4×D4—5861no—
107C2×C4⋊C4—5861no—
108C2×C42—2931no—
109C2×C42—2932no—
110#104—5868no—
111#97—5861no—
112C4×C8—5861no—
113#95—5861no—
114#41—5864no—
115#41—5864no—
116C2×Q8—2932no—
117C2×D4—21no—
118C2×D4—21no—
119C2×D4—5862no—
120C2×D4C2×#1192407812yes—
121C22×C4—2931no—
122C22×C4—2931no—
123C22×C4—2931no—
124C22×C4—5862no—
125C22×C4—5862no—
126M16—2934no—
127M16—5862no—
128C2×C8—5862no—
129C4⋊C4—5864no—
130C4⋊C4—5861no—
131C4⋊C4—5861no—
132C22⋊C4—5862no—
133C22⋊C4—5862no—
134C42—2931no—
135C42—2931no—
136C42—2931no—
137C42—5864no—
138C42C2×#1192407811yescharacteristic
139C23—22no—
140C23—2931no—
141Q8—5864no—
142D4—24no—
143D4—42no—
144D4—42no—
145D4—11722no—
146D4—11722no—
147C2×C4—2931no—
148C2×C4—2932no—
149C2×C4—2932no—
150C2×C4—2931no—
151C2×C4—2931no—
152C2×C4—5862no—
153C2×C4—5864no—
154C2×C4—5862no—
155C2×C4—11721no—
156C2×C4—11724no—
157C2×C4—11722no—
158C2×C4—11722no—
159C2×C4C22⋊#1192407811yescharacteristic
160C2×C4C22⋊#1192407811yescharacteristic
161C2×C4C22×#1192407811yescharacteristic
162C8—5864no—
163C22—42no—
164C22—42no—
165C22—42no—
166C22—2931no—
167C22—2931no—
168C22—5861no—
169C22—5861no—
170C22C2×C22⋊#1192407811yescharacteristic
171C4—21no—
172C4—2932no—
173C4—5861no—
174C4—5861no—
175C4—11724no—
176C4—11722no—
177C4#2262768812yescomplemented
178C4D4×#1192407812yes—
179C2—82no—
180C2—5861no—
181C2—5861no—
182C2#3403708111yescharacteristic
183C2C2×#2262768811yescharacteristic
184C2#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#1980
LCSG ▷ C2×C4×C293 ▷ C2×C293 ▷ C293
UCSC1 ◁ C22 ◁ C42 ◁ #127

Complements

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

NH ≅ G/Ntype
1. C2×#22627688C2semidirect
2. C4×#17989812C2semidirect
3. C4×C4⋊#11924078C2semidirect
13. #22627624C4semidirect
14. #22627611C4semidirect
20. #127×C293C4semidirect
23. #17989812D4semidirect
80. C4×C293#104semidirect
92. C293#1980semidirect
101. #127#11924078semidirect
177. C4#22627688semidirect

Maximal subgroups

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

subgroupindex
C2×#226276882
C4×#179898122
C4×C4⋊#119240782
#340366772
#1980293