Finite Group Databasebeta

← #49170397

Subgroups — #49170397

Order 37504.

520 conjugacy classes of subgroups; only the 129 normal subgroups are shown.

normal subgroups only

This group has 520 conjugacy classes of subgroups — too many to draw. Only its 129 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
1C2×#22627652C212yesmaximal, complemented
2#34036775C212yesmaximal, complemented
3#34036513C211yesmaximal, characteristic, complemented
4#34036375C212yesmaximal, complemented
5#34036345C212yesmaximal, complemented
6#34036293C212yesmaximal, complemented
7#34036265C212yesmaximal, complemented
8C4×D2344C211yesmaximal, characteristic, complemented
9#436×C293C211yesmaximal, characteristic, complemented
10C2×#17989802C2212yes—
11C22×D1172C2212yescomplemented
12#22627652—28no—
13C2×Dic1172C2211yescharacteristic, complemented
14C2×#17989791C2212yescomplemented
15C2×#17989791C2212yescomplemented
16C2×D2344C2212yes—
17C2×D2344C2211yescharacteristic
18C2×D2344C2211yescharacteristic
19#22627612C2212yescomplemented
20#22627609—22no—
21#22627603C2212yescomplemented
22#22627598C2212yes—
23#22627597—22no—
24#22627592—22no—
25C4×D1172C2212yescomplemented
26C22⋊C4×D293—22no—
27#22627558C2211yescharacteristic, complemented
28#22627549C2212yescomplemented
29#22627546C2212yescomplemented
30#22627546C2212yescomplemented
31C2×M16×C293C2212yescomplemented
32C4×D4×C293C2211yescharacteristic
33C4⋊C8×C293C2211yescharacteristic, complemented
34C22⋊C8×C293C2212yescomplemented
35C4×C8×C293C2211yescharacteristic, complemented
36C23×D293—22no—
37#17989802—24no—
38#17989802—42no—
39C2×Dic586C2312yes—
40C2×D1172—24no—
41C2×D1172—22no—
42C2×D1172—42no—
43C2×D1172C2312yes—
44C2×D1172C2312yes—
45C2×C22⋊D293—22no—
46C2×C22⋊D293—22no—
47C2×C4×D293—22no—
48C2×C4×D293—22no—
49Dic1172—41no—
50#17989791—24no—
51#17989791—24no—
52D2344—24no—
53D2344—41no—
54D2344D414yescomplemented
55C4⋊Dic293C2312yes—
56#17989781—22no—
57C22⋊Dic293—22no—
58#17989779—22no—
59#17989779—22no—
60#17989779—22no—
61#17989779—22no—
62C2×D4×C293D411yescharacteristic
63C22×C4×C293C2312yes—
64M16×C293—24no—
65C2×C8×C293C2312yes—
66C2×C8×C293C2311yescharacteristic
67C2×C8×C293C2311yescharacteristic
68C4⋊C4×C293D411yescharacteristic
69C22⋊C4×C293D412yes—
70C42×C293C2311yescharacteristic
71C22×D293—22no—
72C22×D293—22no—
73C22×D293—44no—
74C22×D293—44no—
75C22×D293—82no—
76Dic586—22no—
77Dic586—22no—
78D1172—22no—
79D1172—22no—
80D1172—22no—
81D1172—44no—
82D1172C2×D414yes—
83C22⋊D293—44no—
84C22⋊D293—82no—
85C2×Dic293—22no—
86C2×Dic293—22no—
87C4×D293—44no—
88C4×D293—82no—
89C23×C293C2×D412yes—
90D4×C293—41no—
91C2×C4×C293—22no—
92C2×C4×C293—22no—
93C2×C4×C293C2×D411yescharacteristic
94C2×C4×C293C2×D411yescharacteristic
95C2×C4×C293C2×D412yes—
96C2×C4×C293C2411yescharacteristic
97C8×C293—22no—
98C8×C293—21no—
99C8×C293C2×D412yes—
100C22×C293—22no—
101C22×C293—22no—
102C22×C293—22no—
103C22×C293C22×D411yescharacteristic
104C2×D293—24no—
105C2×D293—42no—
106C2×D293—42no—
107C2×D293—42no—
108C2×D293—42no—
109C2×D293—42no—
110C2×D293—88no—
111C4×C293—22no—
112C4×C293—21no—
113C4×C293—21no—
114C4×C293C22×D411yescharacteristic
115C4×C293H(5,𝔽2)11yescharacteristic
116Dic293—42no—
117Dic293—42no—
118C2×C293—42no—
119C2×C293D4211yescharacteristic
120C2×C293#57511yescharacteristic
121C2×C293#57611yescharacteristic
122D293—44no—
123D293—82no—
124C293#327311yescharacteristic, complemented, Sylow
125#3273—2931nomaximal, Sylow
126C2×AGL(1,ℤ/8)—2932no—
127#546—2932no—
128#495—2931no—
129#468—2932no—
130#463—2932no—
131#452—2932no—
132#447—2932no—
133C4×D8—2931no—
134#436D29311yescharacteristic, complemented
135C2×#41—2932no—
136C22×D4—2932no—
137AGL(1,ℤ/8)—5868no—
138C2×Q16—2931no—
139C2×SD16—2932no—
140C2×SD16—2932no—
141C2×D8—2931no—
142C2×D8—2932no—
143C2×D8—2931no—
144C2×M16C2×D29312yescomplemented
145#124—2932no—
146#123—5862no—
147C22⋊Q8—2932no—
148#121—2932no—
149#121—5862no—
150#120—5862no—
151C4×D4—2932no—
152C4×D4C2×D29311yescharacteristic
153C2×C22⋊C4—5862no—
154#107—2931no—
155C4⋊C8C2×D29311yescharacteristic, complemented
156#103—2932no—
157#102—2932no—
158#102—2932no—
159C22⋊C8C2×D29312yescomplemented
160C4×C8C2×D29311yescharacteristic, complemented
161C24—5862no—
162#41—5864no—
163#41—11722no—
164C2×Q8—2932no—
165C2×D4—2932no—
166C2×D4—2932no—
167C2×D4—5864no—
168C2×D4—5862no—
169C2×D4—5862no—
170C2×D4—5862no—
171C2×D4—11722no—
172C2×D4D117211yescharacteristic
173C22×C4—5862no—
174C22×C4—5862no—
175C22×C4C22×D29312yes—
176Q16—11721no—
177SD16—5864no—
178SD16—5864no—
179D8—2934no—
180D8—5864no—
181D8—11721no—
182M16—24no—
183C2×C8C22×D29311yescharacteristic
184C2×C8C22×D29312yes—
185C2×C8C22×D29311yescharacteristic
186C4⋊C4—2932no—
187C4⋊C4—5862no—
188C4⋊C4D117211yescharacteristic
189C22⋊C4—5862no—
190C22⋊C4—5862no—
191C22⋊C4—5862no—
192C22⋊C4—5862no—
193C22⋊C4—5862no—
194C22⋊C4D117212yes—
195C42C22×D29311yescharacteristic
196C23—23442no—
197C23—5862no—
198C23—5862no—
199C23—11724no—
200C23—11724no—
201C23C2×D117212yes—
202Q8—5862no—
203Q8—5862no—
204D4—41no—
205D4—2934no—
206D4—23442no—
207D4—5862no—
208D4—5862no—
209D4—5862no—
210D4—11724no—
211D4—11724no—
212C2×C4—22no—
213C2×C4—22no—
214C2×C4—23442no—
215C2×C4—5862no—
216C2×C4—5862no—
217C2×C4—11724no—
218C2×C4C2×D117211yescharacteristic
219C2×C4C2×D117211yescharacteristic
220C2×C4C2×D117212yes—
221C2×C4C23×D29311yescharacteristic
222C8—22no—
223C8—21no—
224C8D4×D29312yes—
225C22—22no—
226C22—22no—
227C22—22no—
228C22—23448no—
229C22—5864no—
230C22—11722no—
231C22—11722no—
232C22—11722no—
233C22—11722no—
234C22—11722no—
235C22C22×D117211yescharacteristic
236C4—22no—
237C4—21no—
238C4—21no—
239C4—11722no—
240C4—11722no—
241C4C2×D4×D29311yescharacteristic
242C4#2262767011yescharacteristic
243C2—42no—
244C2—23442no—
245C2—11724no—
246C2D4×D117211yescharacteristic
247C2#3403692911yescharacteristic
248C2#3403693411yescharacteristic
subgroupG/H
centerC22C22×D1172
commutator, cosocleC2×C4×C293C24
FrattiniC2×C4C23×D293
Fitting#436×C293C2
socleC22×C293C22×D4
hypercenter#436D293
hypocenterC293#3273
LCSG ▷ C2×C4×C293 ▷ C2×C293 ▷ C293
UCSC1 ◁ C22 ◁ C4×D4 ◁ #436

Complements

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

NH ≅ G/Ntype
1. C2×#22627652C2semidirect
2. #34036775C2semidirect
3. #34036513C2semidirect
4. #34036375C2semidirect
5. #34036345C2semidirect
6. #34036293C2semidirect
7. #34036265C2semidirect
8. C4×D2344C2semidirect
9. #436×C293C2semidirect
11. C22×D1172C22semidirect
13. C2×Dic1172C22semidirect
14. C2×#17989791C22semidirect
15. C2×#17989791C22semidirect
19. #22627612C22semidirect
21. #22627603C22semidirect
25. C4×D1172C22semidirect
27. #22627558C22semidirect
28. #22627549C22semidirect
29. #22627546C22semidirect
30. #22627546C22semidirect
31. C2×M16×C293C22semidirect
33. C4⋊C8×C293C22semidirect
34. C22⋊C8×C293C22semidirect
35. C4×C8×C293C22semidirect
54. D2344D4semidirect
124. C293#3273semidirect
134. #436D293semidirect
144. C2×M16C2×D293semidirect
155. C4⋊C8C2×D293semidirect
159. C22⋊C8C2×D293semidirect
160. C4×C8C2×D293semidirect

Maximal subgroups

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

subgroupindex
C2×#226276522
#340367752
#340365132
#340363752
#340363452
#340362932
#340362652
C4×D23442
#436×C2932
#3273293