Finite Group Databasebeta

← #49174833

Subgroups — #49174833

Order 37504.

314 conjugacy classes of subgroups; only the 66 normal subgroups are shown.

normal subgroups only

This group has 314 conjugacy classes of subgroups — too many to draw. Only its 66 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#34037197C211yesmaximal, characteristic, complemented
2#34037127C212yesmaximal
3D293⋊#101C211yesmaximal, characteristic, complemented
4#34036996C212yesmaximal, complemented
5#34036699C211yesmaximal, characteristic
6D293⋊M16C2212yes—
7Q8×#11924078—24no—
8#22627703—22no—
9#22627703C2212yes—
10#22627688—24no—
11#22627685—22no—
12C2×#17989801C2211yescharacteristic
13C2×Q8×D293C2211yescharacteristic
14#22627624C411yescharacteristic, complemented
15#22627622C411yescharacteristic, complemented
16#22627611C411yescharacteristic, complemented
17#22627606—22no—
18#22627601—22no—
19#22627581C2211yescharacteristic
20#124×C293C411yescharacteristic, complemented
21#17989812—22no—
22#17989811—22no—
23D293⋊C8—22no—
24C4⋊#11924078—24no—
25C4⋊#11924078—22no—
26C22⋊#11924078—22no—
27C4×#11924078—24no—
28C4×#11924078D414yes—
29#17989801—22no—
30#17989801—22no—
31C2×Dic586C2×C411yescharacteristic
32C2×Dic586C2×C411yescharacteristic
33C2×Dic586D412yes—
34Q8×D293—22no—
35Q8×D293—22no—
36C2×C22⋊D293—21no—
37C22×Dic293—21no—
38C2×C4×D293D412yes—
39C2×C4×D293C2311yescharacteristic
40C4⋊Dic293—22no—
41#17989781—21no—
42#17989781—22no—
43C22⋊Dic293—22no—
44#17989779—21no—
45C4×Dic293C2×C411yescharacteristic
46C2×Q8×C293C2×C411yescharacteristic
47C2×D4×C293C2×C411yescharacteristic
48C22⋊C4×C293—22no—
49C42×C293C2×C411yescharacteristic
50C2×#11924078—24no—
51#14556880—42no—
52C22×D293C2×D411yescharacteristic
53Dic586—22no—
54Dic586—24no—
55Dic586—22no—
56C22⋊D293—41no—
57C22⋊D293—41no—
58C2×Dic293—21no—
59C2×Dic293—21no—
60C2×Dic293—42no—
61C2×Dic293C22⋊C412yes—
62C2×Dic293C2×D411yescharacteristic
63C4×D293—22no—
64C4×D293—22no—
65C4×D293C2×D412yes—
66C4×D293#4112yes—
67C23×C293—21no—
68Q8×C293—22no—
69D4×C293—22no—
70C2×C4×C293—21no—
71C2×C4×C293C22⋊C412yes—
72C2×C4×C293C22×C411yescharacteristic
73C22×C293—42no—
74C22×C293—41no—
75C22×C293C2×C22⋊C411yescharacteristic
76C2×D293—41no—
77C2×D293#12011yescharacteristic
78C2×D293#12311yescharacteristic
79#11924078—44no—
80C4×C293—22no—
81C4×C293—41no—
82C4×C293C4×D412yes—
83Dic293—22no—
84Dic293—41no—
85Dic293—41no—
86Dic293#12112yes—
87C2×C293—21no—
88C2×C293—81no—
89C2×C293#38611yescharacteristic
90D293—21no—
91D293—21no—
92C293#191211yescharacteristic, complemented, Sylow
93#1912—2931nomaximal, Sylow
94#536—2931no—
95#519—2931no—
96#421—2932no—
97C2×#101—2931no—
98H(3,ℤ/4)—2932no—
99C2×#41—2931no—
100C22×Q8—2931no—
101C2×M16—2932no—
102C4⋊Q8—2931no—
103C4⋊Q8—2931no—
104#124—2931no—
105#124#1192407811yescharacteristic, complemented
106#123—5862no—
107C22⋊Q8—5862no—
108C4×Q8—5864no—
109#117—2932no—
110#117—2931no—
111#117—5862no—
112#104—5864no—
113#101—5862no—
114#41—5862no—
115#41—5862no—
116C2×Q8—2932no—
117C2×Q8—2931no—
118C2×Q8—2931no—
119C2×Q8—5862no—
120C2×Q8—5862no—
121C2×Q8C2×#1192407811yescharacteristic
122C2×D4—5861no—
123C2×D4C2×#1192407811yescharacteristic
124C22×C4—2931no—
125C22×C4—2932no—
126C22×C4—5861no—
127M16—5862no—
128M16—5862no—
129C2×C8—5862no—
130C4⋊C4—5861no—
131C4⋊C4—5862no—
132C4⋊C4—5862no—
133C4⋊C4—5864no—
134C4⋊C4—5862no—
135C22⋊C4—22no—
136C22⋊C4—5861no—
137C22⋊C4—5862no—
138C22⋊C4—5862no—
139C42—2934no—
140C42—2931no—
141C42—5864no—
142C42C2×#1192407811yescharacteristic
143C23—21no—
144C23—2931no—
145Q8—22no—
146Q8—5864no—
147Q8—5862no—
148Q8—5862no—
149D4—22no—
150D4—11721no—
151D4—11721no—
152C2×C4—21no—
153C2×C4—2931no—
154C2×C4—2932no—
155C2×C4—2932no—
156C2×C4—2932no—
157C2×C4—5862no—
158C2×C4—5862no—
159C2×C4—5864no—
160C2×C4—5861no—
161C2×C4—5861no—
162C2×C4—11722no—
163C2×C4C22⋊#1192407812yes—
164C2×C4C22×#1192407811yescharacteristic
165C8—11722no—
166C22—42no—
167C22—41no—
168C22—2931no—
169C22—2931no—
170C22—11721no—
171C22C2×C22⋊#1192407811yescharacteristic
172C4—22no—
173C4—41no—
174C4—2932no—
175C4—5862no—
176C4—11721no—
177C4—11724no—
178C4—11721no—
179C4D4×#1192407812yes—
180C2—21no—
181C2—81no—
182C2—5861no—
183C2—5861no—
184C2#3403707711yescharacteristic
subgroupG/H
centerC2#34037077
commutatorC2×C4×C293C22×C4
FrattiniC2×C4C22×#11924078
Fitting#124×C293C4
socleC2×C293#386
prime radicalC2×#17989801C22
cosocleC2×C4×D293C23
hypercenter#124#11924078
hypocenterC293#1912
LCSG ▷ C2×C4×C293 ▷ C2×C293 ▷ C293
UCSC1 ◁ C2 ◁ C2×C4 ◁ #124

Complements

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

NH ≅ G/Ntype
1. #34037197C2semidirect
3. D293⋊#101C2semidirect
4. #34036996C2semidirect
14. #22627624C4semidirect
15. #22627622C4semidirect
16. #22627611C4semidirect
20. #124×C293C4semidirect
92. C293#1912semidirect
105. #124#11924078semidirect

Maximal subgroups

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

subgroupindex
#340371972
#340371272
D293⋊#1012
#340369962
#340366992
#1912293