Finite Group Databasebeta

← #49174922

Subgroups — #49174922

Order 37504.

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

normal subgroups only

This group has 320 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#34037133C211yesmaximal, characteristic, complemented
2C2×#22627689C212yesmaximal, complemented
3C2×#22627688C212yesmaximal, complemented
4#34037065C211yesmaximal, characteristic, complemented
5#34036678C211yesmaximal, characteristic
6C2×#17989812C2212yes—
7C2×C4×#11924078C2212yes—
8C4⋊#14556880—22no—
9#22627689—24no—
10#22627688—24no—
11(C2×#11924078)⋊C4—22no—
12C2×#17989803C2211yescharacteristic
13C2×#17989801C2211yescharacteristic
14#22627622C411yescharacteristic, complemented
15#22627620C411yescharacteristic, complemented
16#22627612C411yescharacteristic, complemented
17#22627597—22no—
18#22627584—22no—
19C42×D293C2211yescharacteristic
20#124×C293C411yescharacteristic, complemented
21C22×#11924078—22no—
22#17989812—22no—
23#17989812—22no—
24C2×#14556880—22no—
25C4×#11924078—22no—
26C4×#11924078D414yescomplemented
27#17989803—22no—
28#17989803—22no—
29#17989801—22no—
30#17989801—22no—
31C2×Dic586C2×C411yescharacteristic
32C2×D1172—21no—
33C2×D1172C2×C411yescharacteristic
34C2×C22⋊D293—21no—
35C2×C22⋊D293—22no—
36C22×Dic293—21no—
37C2×C4×D293—21no—
38C2×C4×D293D412yes—
39C2×C4×D293C2311yescharacteristic
40#17989781—22no—
41#17989779—22no—
42C4×Dic293C2×C411yescharacteristic
43C4×Dic293D412yes—
44C2×Q8×C293C2×C411yescharacteristic
45C2×D4×C293C2×C411yescharacteristic
46C22⋊C4×C293—22no—
47C42×C293C2×C411yescharacteristic
48C2×#11924078—24no—
49C2×#11924078—44no—
50#14556880—42no—
51C22×D293—21no—
52C22×D293C2×D411yescharacteristic
53Dic586—22no—
54D1172—22no—
55D1172—42no—
56C22⋊D293—44no—
57C22⋊D293—42no—
58C2×Dic293—21no—
59C2×Dic293—41no—
60C2×Dic293—41no—
61C2×Dic293C22⋊C412yes—
62C2×Dic293C2×D411yescharacteristic
63C4×D293—42no—
64C4×D293—41no—
65C4×D293—41no—
66C4×D293C2×D412yes—
67C4×D293#4112yes—
68C23×C293—21no—
69Q8×C293—22no—
70D4×C293—22no—
71C2×C4×C293—21no—
72C2×C4×C293C22⋊C412yes—
73C2×C4×C293C22×C411yescharacteristic
74C22×C293—41no—
75C22×C293—42no—
76C22×C293C2×C22⋊C411yescharacteristic
77C2×D293—22no—
78C2×D293—41no—
79C2×D293—42no—
80C2×D293#12112yes—
81#11924078—44no—
82C4×C293—22no—
83C4×C293—41no—
84C4×C293C4×D412yes—
85Dic293—22no—
86Dic293—41no—
87Dic293#12411yescharacteristic
88Dic293#12711yescharacteristic
89C2×C293—81no—
90C2×C293#39011yescharacteristic
91C2×C293#42112yes—
92D293—22no—
93D293—81no—
94C293#196311yescharacteristic, complemented, Sylow
95#1963—2931nomaximal, Sylow
96#532—2931no—
97#423—2931no—
98C2×#104—2932no—
99C2×#104—2932no—
100#376—2931no—
101C2×#41—2931no—
102C2×#41—2931no—
103C2×M16—2932no—
104C4⋊Q8—2931no—
105#127—2931no—
106#124—2931no—
107#124#1192407811yescharacteristic, complemented
108#121—5862no—
109C4×D4—5862no—
110C2×C42—2931no—
111C2×C42—2932no—
112C4⋊C8—5862no—
113#104—5864no—
114#104—5864no—
115#95—5862no—
116#41—5862no—
117#41—5862no—
118#41—5862no—
119#41—5862no—
120C2×Q8—2931no—
121C2×Q8C2×#1192407811yescharacteristic
122C2×D4—2931no—
123C2×D4—5861no—
124C2×D4—5862no—
125C2×D4—5861no—
126C2×D4C2×#1192407811yescharacteristic
127C22×C4—2931no—
128C22×C4—2932no—
129C22×C4—5861no—
130C22×C4—5861no—
131C22×C4—5862no—
132M16—5862no—
133M16—5862no—
134C2×C8—5862no—
135C4⋊C4—5862no—
136C22⋊C4—22no—
137C22⋊C4—5862no—
138C42—2932no—
139C42—2931no—
140C42—2934no—
141C42—5862no—
142C42C2×#1192407811yescharacteristic
143C23—21no—
144C23—2931no—
145C23—5861no—
146Q8—22no—
147Q8—5862no—
148D4—22no—
149D4—5862no—
150D4—11722no—
151D4—11724no—
152D4—11722no—
153C2×C4—21no—
154C2×C4—2931no—
155C2×C4—2932no—
156C2×C4—2932no—
157C2×C4—2932no—
158C2×C4—5864no—
159C2×C4—5861no—
160C2×C4—11722no—
161C2×C4—11721no—
162C2×C4—11721no—
163C2×C4—11721no—
164C2×C4—11721no—
165C2×C4—11724no—
166C2×C4C22⋊#1192407812yes—
167C2×C4C22×#1192407811yescharacteristic
168C8—11722no—
169C22—41no—
170C22—42no—
171C22—2932no—
172C22—5862no—
173C22—11721no—
174C22—11722no—
175C22C2×C22⋊#1192407811yescharacteristic
176C4—22no—
177C4—41no—
178C4—2931no—
179C4—2931no—
180C4—5862no—
181C4—11724no—
182C4—11721no—
183C4D4×#1192407812yes—
184C2—81no—
185C2—23441no—
186C2—5862no—
187C2#3403708111yescharacteristic
188C2#3403712612yes—
subgroupG/H
centerC22C2×C22⋊#11924078
commutatorC2×C4×C293C22×C4
FrattiniC2×C4C22×#11924078
Fitting#124×C293C4
socleC22×C293C2×C22⋊C4
prime radical#34036678C2
cosocleC2×C4×D293C23
hypercenter#124#11924078
hypocenterC293#1963
LCSG ▷ C2×C4×C293 ▷ C2×C293 ▷ C293
UCSC1 ◁ C22 ◁ C42 ◁ #124

Complements

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

NH ≅ G/Ntype
1. #34037133C2semidirect
2. C2×#22627689C2semidirect
3. C2×#22627688C2semidirect
4. #34037065C2semidirect
14. #22627622C4semidirect
15. #22627620C4semidirect
16. #22627612C4semidirect
20. #124×C293C4semidirect
26. C4×#11924078D4semidirect
94. C293#1963semidirect
107. #124#11924078semidirect

Maximal subgroups

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

subgroupindex
#340371332
C2×#226276892
C2×#226276882
#340370652
#340366782
#1963293