Finite Group Databasebeta

← #49168925

Subgroups — #49168925

Order 37504.

450 conjugacy classes of subgroups; only the 125 normal subgroups are shown.

normal subgroups only

This group has 450 conjugacy classes of subgroups — too many to draw. Only its 125 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#34036663C211yesmaximal, characteristic, complemented
2C2×C4×D1172C211yesmaximal, characteristic, complemented
3#34036460C211yesmaximal, characteristic, complemented
4#34036443C211yesmaximal, characteristic, complemented
5#34036430C212yesmaximal, complemented
6#34036345C212yesmaximal, complemented
7#34036282C211yesmaximal, characteristic, complemented
8#34036265C211yesmaximal, characteristic
9#34036242C212yesmaximal, complemented
10#34036231C212yesmaximal, complemented
11#432×C293C211yesmaximal, characteristic, complemented
12C22×D1172C2211yescharacteristic
13C22×C4×D293—21no—
14C2×#17989791C2212yes—
15C2×D2344C2212yes—
16#22627618—21no—
17#22627616C2211yescharacteristic, complemented
18#22627612C2211yescharacteristic, complemented
19#22627607—21no—
20#22627603C2211yescharacteristic
21#22627598C2211yescharacteristic
22C4×Dic586C2211yescharacteristic, complemented
23C4×D1172—21no—
24C4×D1172—21no—
25C4×D1172C2212yes—
26C4×D1172C2212yes—
27C4×D1172C2211yescharacteristic, complemented
28C4×C22⋊D293—21no—
29#22627581—21no—
30C2×C4⋊Dic293C2211yescharacteristic
31C2×#17989779—21no—
32#22627558C2212yescomplemented
33#22627556C2212yescomplemented
34#22627549C2212yescomplemented
35#22627546C2212yes—
36#22627546C2212yes—
37#22627546C2212yescomplemented
38C2×C42×C293C2211yescharacteristic
39C4⋊C8×C293C2212yescomplemented
40C22⋊C8×C293C2211yescharacteristic
41C22⋊C8×C293C2211yescharacteristic
42#97×C293C2212yescomplemented
43C23×D293—21no—
44C2×Dic586C2311yescharacteristic
45C2×D1172—24no—
46C2×D1172—21no—
47C2×D1172C2311yescharacteristic
48C2×D1172C2312yes—
49C2×C22⋊D293—21no—
50C22×Dic293—21no—
51C2×C4×D293—21no—
52C2×C4×D293—22no—
53C2×C4×D293—22no—
54C2×C4×D293—44no—
55#17989791—24no—
56D2344—24no—
57C4⋊Dic293—21no—
58C4⋊Dic293C2312yes—
59C4⋊Dic293C2311yescharacteristic
60C4⋊Dic293C2311yescharacteristic
61#17989781—21no—
62#17989781—21no—
63#17989781—21no—
64#17989781—21no—
65C22⋊Dic293—21no—
66#17989779—21no—
67#17989779—22no—
68#17989779—22no—
69#17989779—21no—
70#17989779—21no—
71#17989779—21no—
72C4×Dic293—21no—
73C22×C4×C293D411yescharacteristic
74C22×C4×C293D411yescharacteristic
75C22×C4×C293C2311yescharacteristic
76C2×C8×C293C2312yes—
77C2×C8×C293C2312yes—
78C42×C293D411yescharacteristic
79C42×C293D411yescharacteristic
80C42×C293C2311yescharacteristic
81C42×C293C2311yescharacteristic
82C22×D293—24no—
83C22×D293—22no—
84C22×D293—21no—
85C22×D293—42no—
86C22×D293—42no—
87Dic586—22no—
88D1172—24no—
89D1172—22no—
90D1172—22no—
91D1172#4114yes—
92C22⋊D293—42no—
93C2×Dic293—21no—
94C2×Dic293—21no—
95C2×Dic293—22no—
96C2×Dic293—21no—
97C2×Dic293—42no—
98C4×D293—42no—
99C4×D293—44no—
100C4×D293—44no—
101C23×C293C2×D411yescharacteristic
102C2×C4×C293—22no—
103C2×C4×C293—22no—
104C2×C4×C293—41no—
105C2×C4×C293C2×D411yescharacteristic
106C2×C4×C293C2×D411yescharacteristic
107C2×C4×C293C2×D411yescharacteristic
108C2×C4×C293C2×D411yescharacteristic
109C2×C4×C293C2×D411yescharacteristic
110C2×C4×C293C2411yescharacteristic
111C8×C293—22no—
112C8×C293—22no—
113C22×C293—21no—
114C22×C293—21no—
115C22×C293AGL(1,ℤ/8)12yes—
116C22×C293C22×D411yescharacteristic
117C2×D293—24no—
118C2×D293—48no—
119C2×D293—42no—
120C2×D293—42no—
121C2×D293—41no—
122C2×D293—41no—
123C2×D293—41no—
124C4×C293—21no—
125C4×C293—21no—
126C4×C293—21no—
127C4×C293—21no—
128C4×C293—21no—
129C4×C293C2×#4112yes—
130Dic293—41no—
131Dic293—42no—
132Dic293—41no—
133Dic293—41no—
134C2×C293—22no—
135C2×C293#52511yescharacteristic
136C2×C293C2×AGL(1,ℤ/8)11yescharacteristic
137C2×C293#57511yescharacteristic
138D293—44no—
139D293—81no—
140C293#311411yescharacteristic, complemented, Sylow
141#3114—2931nomaximal, Sylow
142#529—2931no—
143C2×C4×D4—2931no—
144#483—2931no—
145#480—2931no—
146#478—2932no—
147#463—2932no—
148#450—2931no—
149#447—2931no—
150#442—2932no—
151#440—2932no—
152#432D29311yescharacteristic, complemented
153C22×D4—2931no—
154C23×C4—5861no—
155C2×SD16—2932no—
156C2×D8—2932no—
157#126—5861no—
158#125—2931no—
159#124—2931no—
160#123—5861no—
161C22⋊Q8—2931no—
162#121—2931no—
163C4×Q8—2931no—
164C4×D4—2932no—
165C4×D4—2932no—
166C4×D4—2931no—
167C4×D4—5861no—
168C4×D4—5861no—
169C4×D4—5861no—
170#117—5861no—
171C2×C4⋊C4—2931no—
172C2×C22⋊C4—5861no—
173C2×C42C2×D29311yescharacteristic
174#107—2932no—
175#106—2932no—
176C4⋊C8C2×D29312yescomplemented
177#103—2932no—
178#102—2932no—
179#102—2932no—
180#102—2932no—
181C22⋊C8C2×D29311yescharacteristic
182C22⋊C8C2×D29311yescharacteristic
183#97C2×D29312yescomplemented
184C24—5861no—
185C2×Q8—2931no—
186C2×D4—2932no—
187C2×D4—2931no—
188C2×D4—5864no—
189C2×D4—5861no—
190C2×D4—5861no—
191C22×C4—5861no—
192C22×C4—5861no—
193C22×C4—5862no—
194C22×C4—5862no—
195C22×C4—11724no—
196C22×C4D117211yescharacteristic
197C22×C4D117211yescharacteristic
198C22×C4C22×D29311yescharacteristic
199SD16—5864no—
200D8—5864no—
201C2×C8C22×D29312yes—
202C2×C8C22×D29312yes—
203C4⋊C4—2931no—
204C4⋊C4—2931no—
205C4⋊C4—2932no—
206C4⋊C4—5861no—
207C4⋊C4—5861no—
208C4⋊C4—5861no—
209C4⋊C4—5861no—
210C4⋊C4—5861no—
211C22⋊C4—5861no—
212C22⋊C4—5862no—
213C22⋊C4—5862no—
214C22⋊C4—5861no—
215C22⋊C4—5861no—
216C22⋊C4—5861no—
217C22⋊C4—5861no—
218C42—5861no—
219C42D117211yescharacteristic
220C42D117211yescharacteristic
221C42C22×D29311yescharacteristic
222C42C22×D29311yescharacteristic
223C23—5864no—
224C23—5862no—
225C23—5861no—
226C23—11722no—
227C23—11722no—
228C23C2×D117211yescharacteristic
229Q8—5862no—
230D4—2934no—
231D4—5864no—
232D4—5862no—
233D4—5862no—
234D4—11722no—
235C2×C4—22no—
236C2×C4—22no—
237C2×C4—41no—
238C2×C4—5861no—
239C2×C4—5861no—
240C2×C4—5861no—
241C2×C4—5862no—
242C2×C4—11724no—
243C2×C4—11724no—
244C2×C4—11722no—
245C2×C4—11722no—
246C2×C4C2×D117211yescharacteristic
247C2×C4C2×D117211yescharacteristic
248C2×C4C2×D117211yescharacteristic
249C2×C4C2×D117211yescharacteristic
250C2×C4C2×D117211yescharacteristic
251C2×C4C23×D29311yescharacteristic
252C8—22no—
253C8—22no—
254C22—21no—
255C22—21no—
256C22—5864no—
257C22—11728no—
258C22—11721no—
259C22—11721no—
260C22—11721no—
261C22—11722no—
262C22—11722no—
263C22#2262765212yes—
264C22C22×D117211yescharacteristic
265C4—21no—
266C4—21no—
267C4—21no—
268C4—21no—
269C4—21no—
270C4—11721no—
271C4—11722no—
272C4—11721no—
273C4—11721no—
274C4#41×D29312yes—
275C2—22no—
276C2—23441no—
277C2—11724no—
278C2#3403664111yescharacteristic
279C2C2×#2262765211yescharacteristic
280C2#3403692911yescharacteristic
subgroupG/H
centerC22C22×D1172
commutator, cosocleC2×C4×C293C24
FrattiniC2×C4C23×D293
Fitting#432×C293C2
socleC22×C293C22×D4
prime radical#34036265C2
hypercenter#432D293
hypocenterC293#3114
LCSG ▷ C2×C4×C293 ▷ C2×C293 ▷ C293
UCSC1 ◁ C22 ◁ C2×C42 ◁ #432

Complements

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

NH ≅ G/Ntype
1. #34036663C2semidirect
2. C2×C4×D1172C2semidirect
3. #34036460C2semidirect
4. #34036443C2semidirect
5. #34036430C2semidirect
6. #34036345C2semidirect
7. #34036282C2semidirect
9. #34036242C2semidirect
10. #34036231C2semidirect
11. #432×C293C2semidirect
17. #22627616C22semidirect
18. #22627612C22semidirect
22. C4×Dic586C22semidirect
27. C4×D1172C22semidirect
32. #22627558C22semidirect
33. #22627556C22semidirect
34. #22627549C22semidirect
37. #22627546C22semidirect
39. C4⋊C8×C293C22semidirect
42. #97×C293C22semidirect
140. C293#3114semidirect
152. #432D293semidirect
176. C4⋊C8C2×D293semidirect
183. #97C2×D293semidirect

Maximal subgroups

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

subgroupindex
#340366632
C2×C4×D11722
#340364602
#340364432
#340364302
#340363452
#340362822
#340362652
#340362422
#340362312
#432×C2932
#3114293