Finite Group Databasebeta

← #49174947

Subgroups — #49174947

Order 37504.

276 conjugacy classes of subgroups; only the 68 normal subgroups are shown.

normal subgroups only

This group has 276 conjugacy classes of subgroups — too many to draw. Only its 68 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
1D293⋊#108C211yesmaximal, characteristic
2#34037122C212yesmaximal
3D293⋊#101C212yesmaximal
4#34037092C211yesmaximal, characteristic
5C2×Q16×D293C211yesmaximal, characteristic
6D293⋊M16C2212yes—
7D293⋊M16C2211yescharacteristic
8#22627703C2211yescharacteristic
9#22627695—21no—
10#22627694—21no—
11#22627687—24no—
12#22627685—24no—
13#22627678—21no—
14C8×#11924078—21no—
15C2×Q8×D293C2212yes—
16C2×Dic1172C411yescharacteristic, complemented
17C2×#17989792C412yescomplemented
18Q16×D293—21no—
19Q16×D293—21no—
20Q16×D293—21no—
21Q16×D293—21no—
22C2×C8×D293C2211yescharacteristic
23C2×Q16×C293C411yescharacteristic, complemented
24#17989812—22no—
25#17989812—21no—
26#17989811—22no—
27#17989811D412yes—
28D293⋊C8—21no—
29D293⋊C8—22no—
30C4⋊#11924078D412yes—
31C22⋊#11924078—21no—
32C4×#11924078—21no—
33C2×Dic586—22no—
34C2×Dic586C2×C412yes—
35Q8×D293—22no—
36Q8×D293—22no—
37Q8×D293—22no—
38Q8×D293—22no—
39C2×C4×D293—22no—
40C2×C4×D293C2311yescharacteristic
41Dic1172—21no—
42Dic1172—21no—
43#17989792—22no—
44#17989792—22no—
45C2×#14556873C2×C411yescharacteristic
46C8×D293D411yescharacteristic
47C8×D293D411yescharacteristic
48C8×D293D411yescharacteristic
49C8×D293D411yescharacteristic
50C2×Q8×C293C2×C412yes—
51Q16×C293—21no—
52Q16×C293—21no—
53C2×C8×C293C2×C411yescharacteristic
54C2×#11924078—22no—
55#14556880—22no—
56#14556880—42no—
57C22×D293#4111yescharacteristic
58Dic586—22no—
59Dic586—22no—
60Dic586—42no—
61Dic586—42no—
62C2×Dic293—22no—
63C2×Dic293C2×D411yescharacteristic
64C4×D293—42no—
65C4×D293—42no—
66C4×D293C2×D411yescharacteristic
67C4×D293C2×D411yescharacteristic
68C4×D293C2×D411yescharacteristic
69C4×D293#4111yescharacteristic
70#14556873C22⋊C411yescharacteristic
71#14556873C22⋊C411yescharacteristic
72Q8×C293—22no—
73Q8×C293—22no—
74C2×C4×C293—22no—
75C2×C4×C293C22×C411yescharacteristic
76C8×C293C22⋊C411yescharacteristic
77C8×C293C22⋊C411yescharacteristic
78C22×C293C4×D411yescharacteristic
79C2×D293—22no—
80C2×D293#12111yescharacteristic
81C2×D293#12411yescharacteristic
82#11924078—42no—
83C4×C293—42no—
84C4×C293C2×C22⋊C411yescharacteristic
85C4×C293C4×D411yescharacteristic
86Dic293—42no—
87Dic293#12111yescharacteristic
88Dic293#12711yescharacteristic
89C2×C293—21no—
90C2×C293#39011yescharacteristic
91D293—21no—
92D293#47312yes—
93C293#197911yescharacteristic, complemented, Sylow
94#1979—2931nomaximal, Sylow
95C22×Q16—2931no—
96C2×#108—2931no—
97#419—2932no—
98C2×#101—2932no—
99#405—2931no—
100C22×Q8—2932no—
101C2×Q16—2932no—
102C2×Q16—2931no—
103C2×Q16—5861no—
104C2×Q16—5861no—
105C2×Q16—5861no—
106C2×Q16—5861no—
107C2×Q16#1192407811yescharacteristic, complemented
108C2×M16—2931no—
109C2×M16—2932no—
110C22×C8—2931no—
111#117—2931no—
112#108—5861no—
113#108—5861no—
114#103—5864no—
115#101—5864no—
116#97—5861no—
117C4×C8—5861no—
118C2×Q8—2932no—
119C2×Q8—5862no—
120C2×Q8—5862no—
121C2×Q8—5862no—
122C2×Q8—5862no—
123C2×Q8—5862no—
124C2×Q8C2×#1192407812yes—
125C22×C4—2931no—
126C22×C4—5862no—
127Q16—21no—
128Q16—21no—
129Q16—5862no—
130Q16—5862no—
131Q16—5861no—
132Q16—5861no—
133M16—2932no—
134M16—5861no—
135M16—5862no—
136M16—5862no—
137C2×C8—2931no—
138C2×C8—2931no—
139C2×C8—2931no—
140C2×C8—2931no—
141C2×C8—2931no—
142C2×C8—5861no—
143C2×C8—5862no—
144C2×C8C2×#1192407811yescharacteristic
145C4⋊C4—2932no—
146C22⋊C4—5861no—
147C42—5861no—
148C23—2931no—
149Q8—22no—
150Q8—22no—
151Q8—5862no—
152Q8—5862no—
153Q8—11722no—
154Q8—11722no—
155C2×C4—22no—
156C2×C4—2931no—
157C2×C4—2931no—
158C2×C4—2931no—
159C2×C4—2931no—
160C2×C4—2931no—
161C2×C4—5862no—
162C2×C4—5862no—
163C2×C4—11722no—
164C2×C4—11722no—
165C2×C4C22×#1192407811yescharacteristic
166C8—2931no—
167C8—2931no—
168C8—5862no—
169C8—11722no—
170C8C22⋊#1192407811yescharacteristic
171C8C22⋊#1192407811yescharacteristic
172C22—2931no—
173C22—2931no—
174C22—5862no—
175C22D4×#1192407811yescharacteristic
176C4—42no—
177C4—2931no—
178C4—2931no—
179C4—11722no—
180C4—11722no—
181C4C2×C22⋊#1192407811yescharacteristic
182C4D4×#1192407811yescharacteristic
183C2—21no—
184C2—2932no—
185C2—5861no—
186C2#3403708111yescharacteristic
subgroupG/H
centerC2#34037081
commutatorC2×C4×C293C22×C4
FrattiniC2×C4C22×#11924078
FittingC2×Q16×C293C4
socleC2×C293#390
prime radicalC22×D293#41
cosocleC2×C4×D293C23
hypercenterC2×Q16#11924078
hypocenterC293#1979
LCSG ▷ C2×C4×C293 ▷ C2×C293 ▷ C293
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×Q16

Complements

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

NH ≅ G/Ntype
16. C2×Dic1172C4semidirect
17. C2×#17989792C4semidirect
23. C2×Q16×C293C4semidirect
93. C293#1979semidirect
107. C2×Q16#11924078semidirect

Maximal subgroups

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

subgroupindex
D293⋊#1082
#340371222
D293⋊#1012
#340370922
C2×Q16×D2932
#1979293