Finite Group Databasebeta

← #49174946

Subgroups — #49174946

Order 37504.

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

normal subgroups only

This group has 316 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, complemented
2#34037121C212yesmaximal, complemented
3D293⋊#100C212yesmaximal, complemented
4#34037092C211yesmaximal, characteristic, complemented
5C2×D8×D293C211yesmaximal, characteristic
6D293⋊M16C2212yes—
7D293⋊M16C2211yescharacteristic
8#22627703C2211yescharacteristic
9#22627695—21no—
10#22627694—21no—
11#22627686—24no—
12#22627684—24no—
13#22627678—21no—
14C8×#11924078—21no—
15C2×D4×D293C2212yes—
16C2×D2344C411yescharacteristic, complemented
17C2×#17989787C412yescomplemented
18D8×D293—21no—
19D8×D293—21no—
20D8×D293—21no—
21D8×D293—21no—
22C2×C8×D293C2211yescharacteristic
23C2×D8×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—
33C23×D293—22no—
34C2×D1172C2×C412yes—
35C2×C22⋊D293—22no—
36D4×D293—22no—
37D4×D293—22no—
38D4×D293—22no—
39D4×D293—22no—
40C2×C4×D293C2311yescharacteristic
41D2344—21no—
42D2344—21no—
43#17989787—22no—
44#17989787—22no—
45C2×#14556873C2×C411yescharacteristic
46C8×D293D411yescharacteristic
47C8×D293D411yescharacteristic
48C8×D293D411yescharacteristic
49C8×D293D411yescharacteristic
50C2×D4×C293C2×C412yes—
51D8×C293—21no—
52D8×C293—21no—
53C2×C8×C293C2×C411yescharacteristic
54C2×#11924078—22no—
55#14556880—22no—
56#14556880—42no—
57C22×D293—22no—
58C22×D293—42no—
59C22×D293—42no—
60C22×D293—84no—
61C22×D293#4111yescharacteristic
62D1172—22no—
63D1172—22no—
64C22⋊D293—42no—
65C22⋊D293—42no—
66C2×Dic293C2×D411yescharacteristic
67C4×D293C2×D411yescharacteristic
68C4×D293C2×D411yescharacteristic
69C4×D293C2×D411yescharacteristic
70C4×D293#4111yescharacteristic
71#14556873C22⋊C411yescharacteristic
72#14556873C22⋊C411yescharacteristic
73C23×C293—22no—
74D4×C293—22no—
75D4×C293—22no—
76C2×C4×C293C22×C411yescharacteristic
77C8×C293C22⋊C411yescharacteristic
78C8×C293C22⋊C411yescharacteristic
79C22×C293—42no—
80C22×C293—82no—
81C22×C293C4×D411yescharacteristic
82C2×D293—22no—
83C2×D293—42no—
84C2×D293—84no—
85C2×D293—84no—
86C2×D293—82no—
87C2×D293#12111yescharacteristic
88C2×D293#12411yescharacteristic
89#11924078—42no—
90C4×C293C2×C22⋊C411yescharacteristic
91C4×C293C4×D411yescharacteristic
92Dic293#12111yescharacteristic
93Dic293#12711yescharacteristic
94C2×C293—21no—
95C2×C293—82no—
96C2×C293#39011yescharacteristic
97D293—21no—
98D293—82no—
99D293#47212yes—
100C293#197811yescharacteristic, complemented, Sylow
101#1978—2931nomaximal, Sylow
102C22×D8—2931no—
103C2×#108—2931no—
104#418—2932no—
105C2×#100—2932no—
106#405—2931no—
107C22×D4—2932no—
108C2×D8—2932no—
109C2×D8—2931no—
110C2×D8—5861no—
111C2×D8—5861no—
112C2×D8—5861no—
113C2×D8—5861no—
114C2×D8#1192407811yescharacteristic, complemented
115C2×M16—2931no—
116C2×M16—2932no—
117C22×C8—2931no—
118#117—2931no—
119#108—5861no—
120#108—5861no—
121#102—5864no—
122#100—5864no—
123#97—5861no—
124C4×C8—5861no—
125C24—5862no—
126C2×D4—2932no—
127C2×D4—5862no—
128C2×D4—5862no—
129C2×D4—5862no—
130C2×D4—5862no—
131C2×D4—5862no—
132C2×D4C2×#1192407812yes—
133C22×C4—2931no—
134D8—21no—
135D8—21no—
136D8—5862no—
137D8—5862no—
138D8—5861no—
139D8—5861no—
140M16—2932no—
141M16—5861no—
142M16—5862no—
143M16—5862no—
144C2×C8—2931no—
145C2×C8—2931no—
146C2×C8—2931no—
147C2×C8—2931no—
148C2×C8—2931no—
149C2×C8—5861no—
150C2×C8—5862no—
151C2×C8C2×#1192407811yescharacteristic
152C4⋊C4—2932no—
153C22⋊C4—5861no—
154C42—5861no—
155C23—22no—
156C23—2931no—
157C23—23444no—
158C23—5862no—
159C23—11722no—
160C23—11722no—
161D4—22no—
162D4—22no—
163D4—5862no—
164D4—5862no—
165D4—11722no—
166D4—11722no—
167C2×C4—2931no—
168C2×C4—2931no—
169C2×C4—2931no—
170C2×C4—2931no—
171C2×C4—2931no—
172C2×C4—5862no—
173C2×C4C22×#1192407811yescharacteristic
174C8—2931no—
175C8—2931no—
176C8—5862no—
177C8—11722no—
178C8C22⋊#1192407811yescharacteristic
179C8C22⋊#1192407811yescharacteristic
180C22—42no—
181C22—82no—
182C22—2931no—
183C22—2931no—
184C22—23442no—
185C22—23444no—
186C22—23444no—
187C22—5862no—
188C22—11722no—
189C22D4×#1192407811yescharacteristic
190C4—2931no—
191C4—2931no—
192C4—11722no—
193C4C2×C22⋊#1192407811yescharacteristic
194C4D4×#1192407811yescharacteristic
195C2—21no—
196C2—82no—
197C2—2932no—
198C2—23442no—
199C2—5861no—
200C2#3403708111yescharacteristic
subgroupG/H
centerC2#34037081
commutatorC2×C4×C293C22×C4
FrattiniC2×C4C22×#11924078
FittingC2×D8×C293C4
socleC2×C293#390
prime radicalC2×D8×D293C2
cosocleC2×C4×D293C23
hypercenterC2×D8#11924078
hypocenterC293#1978
LCSG ▷ C2×C4×C293 ▷ C2×C293 ▷ C293
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×D8

Complements

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

NH ≅ G/Ntype
1. D293⋊#108C2semidirect
2. #34037121C2semidirect
3. D293⋊#100C2semidirect
4. #34037092C2semidirect
16. C2×D2344C4semidirect
17. C2×#17989787C4semidirect
23. C2×D8×C293C4semidirect
100. C293#1978semidirect
114. C2×D8#11924078semidirect

Maximal subgroups

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

subgroupindex
D293⋊#1082
#340371212
D293⋊#1002
#340370922
C2×D8×D2932
#1978293