Finite Group Databasebeta

← #49171438

Subgroups — #49171438

Order 37504.

350 conjugacy classes of subgroups; only the 117 normal subgroups are shown.

normal subgroups only

This group has 350 conjugacy classes of subgroups — too many to draw. Only its 117 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#34036853C211yesmaximal, characteristic, complemented
2#34036836C211yesmaximal, characteristic, complemented
3#34036485C212yesmaximal, complemented
4#34036479C211yesmaximal, characteristic, complemented
5#34036434C212yesmaximal, complemented
6#34036420C211yesmaximal, characteristic, complemented
7#34036346C212yesmaximal
8#34036253C211yesmaximal, characteristic, complemented
9SD16×Dic293C212yesmaximal, complemented
10C4×#17989787C211yesmaximal, characteristic
11#461×C293C211yesmaximal, characteristic, complemented
12C2×#17989787C2211yescharacteristic
13#22627624C2211yescharacteristic
14#22627619—22no—
15#22627615C2212yes—
16#22627613C2212yes—
17#22627604—21no—
18#22627603—21no—
19#22627601—22no—
20Q8×Dic293C2212yes—
21C4×Dic586C2211yescharacteristic
22C4×D1172C2211yescharacteristic
23D4×Dic293C2212yes—
24#22627582—21no—
25C2×C4⋊Dic293—21no—
26#22627557C2211yescharacteristic
27#22627556C2212yes—
28#22627553C2212yes—
29#22627548C2212yes—
30#22627548C2212yes—
31#22627546C2212yes—
32#22627545C2211yescharacteristic
33#22627544C2211yescharacteristic
34C4×#14556873C2211yescharacteristic
35C8×Dic293C2212yes—
36C2×SD16×C293C2212yes—
37C4⋊Q8×C293C2211yescharacteristic
38C4×D4×C293C2211yescharacteristic
39C4⋊C8×C293C2211yescharacteristic
40#103×C293C2212yes—
41C2×Dic586—21no—
42C2×Dic586D411yescharacteristic
43C2×D1172C2311yescharacteristic
44C22×Dic293—22no—
45C2×C4×D293—21no—
46#17989787—22no—
47C2×#14556873C2311yescharacteristic
48C2×#14556873C2311yescharacteristic
49C4⋊Dic293—22no—
50C4⋊Dic293—22no—
51C4⋊Dic293—21no—
52C4⋊Dic293D411yescharacteristic
53C4⋊Dic293C2312yes—
54C4⋊Dic293C2311yescharacteristic
55#17989781—22no—
56#17989781D412yes—
57C22⋊Dic293—22no—
58#17989779—22no—
59#17989779—22no—
60#17989779—21no—
61C4×Dic293—22no—
62C4×Dic293C2312yes—
63C2×Q8×C293C2312yes—
64C2×D4×C293C2311yescharacteristic
65C22×C4×C293—21no—
66SD16×C293—24no—
67C2×C8×C293C2312yes—
68C4⋊C4×C293—21no—
69C4⋊C4×C293—21no—
70C4⋊C4×C293C2311yescharacteristic
71C22⋊C4×C293—21no—
72C42×C293C2311yescharacteristic
73C22×D293—21no—
74Dic586—22no—
75Dic586—81no—
76D1172—21no—
77D1172—21no—
78C2×Dic293—21no—
79C2×Dic293—22no—
80C2×Dic293—82no—
81C2×Dic293C2×D412yes—
82C2×Dic293C2×D412yes—
83C4×D293—42no—
84#14556873—21no—
85#14556873—21no—
86C23×C293—21no—
87Q8×C293—22no—
88Q8×C293—22no—
89D4×C293—21no—
90D4×C293#4112yes—
91C2×C4×C293—21no—
92C2×C4×C293—22no—
93C2×C4×C293—42no—
94C2×C4×C293C2×D411yescharacteristic
95C2×C4×C293C2×D411yescharacteristic
96C2×C4×C293C2411yescharacteristic
97C8×C293—22no—
98C22×C293—22no—
99C22×C293—41no—
100C22×C293—41no—
101C22×C293C22×D411yescharacteristic
102C2×D293—41no—
103C2×D293—41no—
104C2×D293—41no—
105C4×C293—21no—
106C4×C293—42no—
107C4×C293—41no—
108C4×C293#13512yes—
109C4×C293C2×#4111yescharacteristic
110C4×C2932−1+411yescharacteristic
111Dic293—22no—
112Dic293—22no—
113Dic293—41no—
114Dic293—42no—
115C2×C293—42no—
116C2×C293#54811yescharacteristic
117C2×C293C2×#13511yescharacteristic
118C2×C293#57711yescharacteristic
119D293—81no—
120C293#336011yescharacteristic, complemented, Sylow
121#3360—2931nomaximal, Sylow
122#556—2931no—
123#554—2931no—
124#488—2932no—
125#487—2931no—
126#479—2932no—
127#476—2931no—
128#463—2932no—
129#461D29311yescharacteristic, complemented
130C8×Q8—2931no—
131C4×SD16—2932no—
132C4×D8—2931no—
133C2×SD16C2×D29312yes—
134C2×D8—2931no—
135C4⋊Q8—2931no—
136C4⋊Q8C2×D29311yescharacteristic
137#126—5862no—
138#125—2932no—
139#124—2932no—
140C22⋊Q8—5862no—
141C22⋊Q8—5861no—
142C22⋊Q8—5861no—
143C4×Q8—2931no—
144C4×Q8—2932no—
145C4×D4—2932no—
146C4×D4—2931no—
147C4×D4C2×D29311yescharacteristic
148#117—5861no—
149C2×C4⋊C4—5861no—
150#107—2931no—
151#106—2932no—
152C4⋊C8—2932no—
153C4⋊C8C2×D29311yescharacteristic
154#103—2932no—
155#103—2932no—
156#103C2×D29312yes—
157#102—2931no—
158#102—2932no—
159#102—2931no—
160C4×C8—2932no—
161C4×C8—2931no—
162C2×Q8—2931no—
163C2×Q8—5861no—
164C2×Q8C22×D29312yes—
165C2×D4—2931no—
166C2×D4C22×D29311yescharacteristic
167C22×C4—21no—
168C22×C4—5862no—
169C22×C4—5861no—
170SD16—24no—
171D8—5862no—
172C2×C8—2931no—
173C2×C8—2931no—
174C2×C8C22×D29312yes—
175C4⋊C4—21no—
176C4⋊C4—21no—
177C4⋊C4—2931no—
178C4⋊C4—2932no—
179C4⋊C4—2932no—
180C4⋊C4—2931no—
181C4⋊C4—5862no—
182C4⋊C4—5862no—
183C4⋊C4—5862no—
184C4⋊C4—5861no—
185C4⋊C4C22×D29311yescharacteristic
186C22⋊C4—21no—
187C22⋊C4—5862no—
188C22⋊C4—5862no—
189C22⋊C4—5862no—
190C22⋊C4—5861no—
191C42—2932no—
192C42—5862no—
193C42C22×D29311yescharacteristic
194C23—21no—
195C23—5861no—
196Q8—22no—
197Q8—22no—
198Q8—23441no—
199Q8—5862no—
200D4—21no—
201D4—5861no—
202D4—5861no—
203D4#1798980112yes—
204C2×C4—22no—
205C2×C4—21no—
206C2×C4—42no—
207C2×C4—2932no—
208C2×C4—2932no—
209C2×C4—23442no—
210C2×C4—5861no—
211C2×C4—5862no—
212C2×C4—11722no—
213C2×C4D4×D29311yescharacteristic
214C2×C4D4×D29311yescharacteristic
215C2×C4C23×D29311yescharacteristic
216C8—22no—
217C8—5861no—
218C8—5861no—
219C22—22no—
220C22—41no—
221C22—41no—
222C22—11721no—
223C22—11721no—
224C22—11721no—
225C22C2×D4×D29311yescharacteristic
226C4—21no—
227C4—42no—
228C4—41no—
229C4—5862no—
230C4—5862no—
231C4—11721no—
232C4—11722no—
233C4#2262764512yes—
234C4C2×#1798980111yescharacteristic
235C4#2262767111yescharacteristic
236C2—42no—
237C2—23441no—
238C2#3403678511yescharacteristic
239C2C2×#2262764511yescharacteristic
240C2#3403693811yescharacteristic
subgroupG/H
centerC22C2×D4×D293
commutator, cosocleC2×C4×C293C24
FrattiniC2×C4C23×D293
Fitting#461×C293C2
socleC22×C293C22×D4
prime radicalC2×#17989787C22
hypercenter#461D293
hypocenterC293#3360
LCSG ▷ C2×C4×C293 ▷ C2×C293 ▷ C293
UCSC1 ◁ C22 ◁ C42 ◁ #461

Complements

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

NH ≅ G/Ntype
1. #34036853C2semidirect
2. #34036836C2semidirect
3. #34036485C2semidirect
4. #34036479C2semidirect
5. #34036434C2semidirect
6. #34036420C2semidirect
8. #34036253C2semidirect
9. SD16×Dic293C2semidirect
11. #461×C293C2semidirect
120. C293#3360semidirect
129. #461D293semidirect

Maximal subgroups

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

subgroupindex
#340368532
#340368362
#340364852
#340364792
#340364342
#340364202
#340363462
#340362532
SD16×Dic2932
C4×#179897872
#461×C2932
#3360293