Finite Group Databasebeta

← #49174827

Subgroups — #49174827

Order 37504.

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

normal subgroups only

This group has 312 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#34037209C211yesmaximal, characteristic
2#34037122C212yesmaximal, complemented
3#34037110C211yesmaximal, characteristic
4#34036996C212yesmaximal, complemented
5#34036704C211yesmaximal, characteristic
6#22627712—24no—
7D293⋊M16—22no—
8D293⋊M16C2212yes—
9#22627703C2212yes—
10#22627687—24no—
11#22627683—22no—
12C2×#17989803C2211yescharacteristic
13C2×Q8×D293C2211yescharacteristic
14#22627622C411yescharacteristic, complemented
15#22627613C411yescharacteristic, complemented
16#22627612C411yescharacteristic, complemented
17#22627609—22no—
18#22627602—22no—
19#22627581C2211yescharacteristic
20C4⋊Q8×C293C411yescharacteristic, complemented
21#17989812—24no—
22#17989812—22no—
23#17989811—22no—
24D293⋊C8—24no—
25D293⋊C8D414yes—
26C4⋊#11924078—22no—
27C22⋊#11924078—22no—
28C4×#11924078—22no—
29#17989803—22no—
30#17989803—22no—
31C2×Dic586—21no—
32C2×Dic586C2×C411yescharacteristic
33Q8×D293—22no—
34Q8×D293—22no—
35C2×D1172C2×C411yescharacteristic
36C2×D1172D412yes—
37C2×C4×D293—21no—
38C2×C4×D293D412yes—
39C2×C4×D293C2311yescharacteristic
40#17989781—21no—
41#17989781—22no—
42#17989779—22no—
43#17989779—22no—
44#17989779—21no—
45C4×Dic293C2×C411yescharacteristic
46C2×Q8×C293C2×C411yescharacteristic
47C2×Q8×C293C2×C411yescharacteristic
48C4⋊C4×C293—22no—
49C42×C293C2×C411yescharacteristic
50C2×#11924078—42no—
51#14556880—24no—
52C22×D293C22⋊C412yes—
53C22×D293C2×D411yescharacteristic
54Dic586—22no—
55Dic586—41no—
56Dic586—41no—
57D1172—24no—
58D1172—22no—
59C2×Dic293—21no—
60C2×Dic293—21no—
61C2×Dic293C2×D411yescharacteristic
62C4×D293—22no—
63C4×D293—22no—
64C4×D293—42no—
65C4×D293C2×D412yes—
66C4×D293#4112yes—
67Q8×C293—22no—
68Q8×C293—22no—
69C2×C4×C293—21no—
70C2×C4×C293—21no—
71C2×C4×C293C22⋊C412yes—
72C2×C4×C293C22×C411yescharacteristic
73C22×C293C2×C22⋊C411yescharacteristic
74C2×D293—22no—
75C2×D293—41no—
76C2×D293—42no—
77C2×D293#12112yes—
78#11924078—82no—
79C4×C293—22no—
80C4×C293—41no—
81C4×C293—41no—
82C4×C293C4×D412yes—
83Dic293—41no—
84Dic293—41no—
85Dic293#12011yescharacteristic
86Dic293#12311yescharacteristic
87C2×C293—21no—
88C2×C293#38611yescharacteristic
89D293—22no—
90D293—42no—
91C293#190911yescharacteristic, complemented, Sylow
92#1909—2931nomaximal, Sylow
93#568—2931no—
94#536—2931no—
95#419—2932no—
96#410—2931no—
97H(3,ℤ/4)—2932no—
98C2×#41—2931no—
99C22×Q8—2931no—
100#131—5864no—
101C2×M16—2932no—
102C2×M16—5862no—
103C4⋊Q8—2931no—
104C4⋊Q8#1192407811yescharacteristic, complemented
105#124—2931no—
106#124—2931no—
107#123—5862no—
108C22⋊Q8—5862no—
109#117—2931no—
110#117—2932no—
111#103—5864no—
112#99—5862no—
113#41—5862no—
114#41—5862no—
115C2×Q8—2931no—
116C2×Q8—5861no—
117C2×Q8—5862no—
118C2×Q8—5862no—
119C2×Q8C2×#1192407811yescharacteristic
120C2×Q8C2×#1192407811yescharacteristic
121C2×D4—2932no—
122C2×D4—2931no—
123C22×C4—2931no—
124C22×C4—2932no—
125C22×C4—5861no—
126M16—5862no—
127M16—5862no—
128M16—5864no—
129C2×C8—2934no—
130C2×C8—5864no—
131C4⋊C4—22no—
132C4⋊C4—5861no—
133C4⋊C4—5862no—
134C4⋊C4—5862no—
135C22⋊C4—5861no—
136C22⋊C4—5862no—
137C22⋊C4—5862no—
138C22⋊C4—5862no—
139C42—2931no—
140C42—5862no—
141C42C2×#1192407811yescharacteristic
142C23—2931no—
143C23—2932no—
144Q8—22no—
145Q8—22no—
146Q8—5862no—
147Q8—11721no—
148Q8—11721no—
149D4—5864no—
150D4—5862no—
151C2×C4—21no—
152C2×C4—21no—
153C2×C4—2931no—
154C2×C4—2932no—
155C2×C4—2932no—
156C2×C4—5862no—
157C2×C4—5862no—
158C2×C4—5861no—
159C2×C4—5861no—
160C2×C4—11722no—
161C2×C4—11722no—
162C2×C4C22⋊#1192407812yes—
163C2×C4C22×#1192407811yescharacteristic
164C8—5864no—
165C22—2932no—
166C22—5862no—
167C22—11721no—
168C22—11722no—
169C22C2×C22⋊#1192407811yescharacteristic
170C4—22no—
171C4—41no—
172C4—41no—
173C4—2931no—
174C4—2931no—
175C4—23442no—
176C4—11721no—
177C4—11721no—
178C4D4×#1192407812yes—
179C2—21no—
180C2—5862no—
181C2—11722no—
182C2#3403707711yescharacteristic
subgroupG/H
centerC2#34037077
commutatorC2×C4×C293C22×C4
FrattiniC2×C4C22×#11924078
FittingC4⋊Q8×C293C4
socleC2×C293#386
prime radicalC2×#17989803C22
cosocleC2×C4×D293C23
hypercenterC4⋊Q8#11924078
hypocenterC293#1909
LCSG ▷ C2×C4×C293 ▷ C2×C293 ▷ C293
UCSC1 ◁ C2 ◁ C2×C4 ◁ C4⋊Q8

Complements

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

NH ≅ G/Ntype
2. #34037122C2semidirect
4. #34036996C2semidirect
14. #22627622C4semidirect
15. #22627613C4semidirect
16. #22627612C4semidirect
20. C4⋊Q8×C293C4semidirect
91. C293#1909semidirect
104. C4⋊Q8#11924078semidirect

Maximal subgroups

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

subgroupindex
#340372092
#340371222
#340371102
#340369962
#340367042
#1909293