Finite Group Databasebeta

← #49171480

Subgroups — #49171480

Order 37504.

348 conjugacy classes of subgroups; only the 115 normal subgroups are shown.

normal subgroups only

This group has 348 conjugacy classes of subgroups — too many to draw. Only its 115 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#34036864C211yesmaximal, characteristic
2#34036854C211yesmaximal, characteristic, complemented
3#34036485C212yesmaximal, complemented
4#34036477C211yesmaximal, characteristic
5#34036428C212yesmaximal, complemented
6#34036354C212yesmaximal, complemented
7#34036330C211yesmaximal, characteristic
8#34036253C211yesmaximal, characteristic, complemented
9C4×#17989792C211yesmaximal, characteristic, complemented
10#34036216C212yesmaximal, complemented
11#475×C293C211yesmaximal, characteristic, complemented
12C2×#17989792C2211yescharacteristic
13C2×#17989791C2212yes—
14#22627622—21no—
15#22627621C2211yescharacteristic
16#22627615C2212yes—
17#22627614—22no—
18#22627613C2212yes—
19#22627612—21no—
20#22627609—22no—
21Q8×Dic293—21no—
22C4×Dic586C2211yescharacteristic
23C4×Dic586C2211yescharacteristic
24#22627589C2212yes—
25C4×D1172—21no—
26#22627586C2212yes—
27#22627557C2211yescharacteristic
28#22627553C2212yes—
29#22627548C2211yescharacteristic
30#22627547C2211yescharacteristic
31#22627546C2212yes—
32#22627544C2212yes—
33#22627544C2212yes—
34C4×#14556873C2211yescharacteristic
35C8×Dic293C2212yes—
36C4⋊Q8×C293C2211yescharacteristic
37C4×Q8×C293C2211yescharacteristic
38#106×C293C2212yes—
39C4⋊C8×C293C2211yescharacteristic
40#103×C293C2212yes—
41C2×Dic586D411yescharacteristic
42C2×Dic586C2311yescharacteristic
43C2×D1172—21no—
44C2×D1172—21no—
45C2×D1172C2312yes—
46C2×C4×D293—22no—
47#17989792—22no—
48#17989791—24no—
49C2×#14556873C2311yescharacteristic
50C2×#14556873C2311yescharacteristic
51C4⋊Dic293—22no—
52C4⋊Dic293D411yescharacteristic
53C4⋊Dic293C2311yescharacteristic
54#17989781—22no—
55#17989781—22no—
56#17989781—21no—
57#17989781D412yes—
58#17989779—22no—
59#17989779—22no—
60#17989779—22no—
61C4×Dic293—22no—
62C4×Dic293—21no—
63C4×Dic293C2312yes—
64C2×Q8×C293—21no—
65C2×Q8×C293C2311yescharacteristic
66C2×C8×C293C2312yes—
67C4⋊C4×C293—21no—
68C4⋊C4×C293—21no—
69C4⋊C4×C293C2311yescharacteristic
70C4⋊C4×C293C2312yes—
71C42×C293—21no—
72C42×C293C2311yescharacteristic
73C22×D293—22no—
74Dic586—22no—
75Dic586—21no—
76Dic586#4112yes—
77D1172—22no—
78D1172—22no—
79D1172—42no—
80D1172—81no—
81C2×Dic293—21no—
82C2×Dic293—21no—
83C2×Dic293C2×D412yes—
84C2×Dic293C2×D412yes—
85C4×D293—82no—
86#14556873—21no—
87#14556873—21no—
88Q8×C293—21no—
89Q8×C293—21no—
90Q8×C293—42no—
91C2×C4×C293—21no—
92C2×C4×C293—21no—
93C2×C4×C293—22no—
94C2×C4×C293C2×D411yescharacteristic
95C2×C4×C293C2×D411yescharacteristic
96C2×C4×C293C2411yescharacteristic
97C8×C293—22no—
98C22×C293C22×D411yescharacteristic
99C2×D293—42no—
100C2×D293—42no—
101C2×D293—42no—
102C4×C293—21no—
103C4×C293—41no—
104C4×C293—42no—
105C4×C293—41no—
106C4×C293#13512yes—
107C4×C293C2×#4111yescharacteristic
108C4×C2932−1+411yescharacteristic
109Dic293—22no—
110Dic293—22no—
111Dic293—22no—
112Dic293—41no—
113C2×C293#54811yescharacteristic
114C2×C293C2×#13511yescharacteristic
115C2×C293#57711yescharacteristic
116D293—82no—
117C293#336511yescharacteristic, complemented, Sylow
118#3365—2931nomaximal, Sylow
119#559—2931no—
120#557—2931no—
121#488—2932no—
122#486—2931no—
123#478—2932no—
124#475D29311yescharacteristic, complemented
125#464—2932no—
126#460—2931no—
127C8×Q8—2931no—
128C4×Q16—2931no—
129C4×SD16—2932no—
130C2×Q16—2931no—
131C2×SD16—2932no—
132C4⋊Q8—5861no—
133C4⋊Q8C2×D29311yescharacteristic
134#127—2931no—
135#125—2932no—
136#125—5862no—
137#124—2932no—
138#124—5861no—
139#123—5862no—
140C4×Q8—2931no—
141C4×Q8—2932no—
142C4×Q8—2931no—
143C4×Q8—5861no—
144C4×Q8C2×D29311yescharacteristic
145C4×D4—2932no—
146C4×D4—5861no—
147#107—2931no—
148#106C2×D29312yes—
149C4⋊C8—2932no—
150C4⋊C8C2×D29311yescharacteristic
151#103—2931no—
152#103—2931no—
153#103C2×D29312yes—
154#102—2932no—
155#102—2932no—
156#102—2932no—
157C4×C8—2932no—
158C4×C8—2931no—
159C2×Q8—21no—
160C2×Q8—2931no—
161C2×Q8—2931no—
162C2×Q8C22×D29311yescharacteristic
163C2×D4—2932no—
164C2×D4—5861no—
165C2×D4—5861no—
166C22×C4—5862no—
167Q16—5862no—
168SD16—5864no—
169C2×C8—2931no—
170C2×C8—2931no—
171C2×C8C22×D29312yes—
172C4⋊C4—21no—
173C4⋊C4—21no—
174C4⋊C4—2931no—
175C4⋊C4—2932no—
176C4⋊C4—2931no—
177C4⋊C4—5862no—
178C4⋊C4—5862no—
179C4⋊C4—5862no—
180C4⋊C4—5861no—
181C4⋊C4C22×D29312yes—
182C4⋊C4C22×D29311yescharacteristic
183C22⋊C4—5862no—
184C22⋊C4—5862no—
185C22⋊C4—5862no—
186C42—21no—
187C42—2932no—
188C42—5862no—
189C42—5861no—
190C42C22×D29311yescharacteristic
191C23—5862no—
192Q8—21no—
193Q8—21no—
194Q8—42no—
195Q8—2932no—
196Q8—5862no—
197Q8—5861no—
198D4—23441no—
199D4—5862no—
200D4—5862no—
201D4—11722no—
202C2×C4—21no—
203C2×C4—21no—
204C2×C4—22no—
205C2×C4—2932no—
206C2×C4—2932no—
207C2×C4—23442no—
208C2×C4—5861no—
209C2×C4—5861no—
210C2×C4D4×D29311yescharacteristic
211C2×C4D4×D29311yescharacteristic
212C2×C4C23×D29311yescharacteristic
213C8—22no—
214C8—5861no—
215C8—5861no—
216C22—11722no—
217C22—11722no—
218C22—11722no—
219C22C2×D4×D29311yescharacteristic
220C4—21no—
221C4—41no—
222C4—42no—
223C4—41no—
224C4—5862no—
225C4—5862no—
226C4—5862no—
227C4—11721no—
228C4#2262764512yes—
229C4#41×D29311yescharacteristic
230C4#2262767211yescharacteristic
231C2—23442no—
232C2#3403678911yescharacteristic
233C2C2×#2262764511yescharacteristic
234C2#3403693811yescharacteristic
subgroupG/H
centerC22C2×D4×D293
commutator, cosocleC2×C4×C293C24
FrattiniC2×C4C23×D293
Fitting#475×C293C2
socleC22×C293C22×D4
prime radical#22627621C22
hypercenter#475D293
hypocenterC293#3365
LCSG ▷ C2×C4×C293 ▷ C2×C293 ▷ C293
UCSC1 ◁ C22 ◁ C42 ◁ #475

Complements

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

NH ≅ G/Ntype
2. #34036854C2semidirect
3. #34036485C2semidirect
5. #34036428C2semidirect
6. #34036354C2semidirect
8. #34036253C2semidirect
9. C4×#17989792C2semidirect
10. #34036216C2semidirect
11. #475×C293C2semidirect
117. C293#3365semidirect
124. #475D293semidirect

Maximal subgroups

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

subgroupindex
#340368642
#340368542
#340364852
#340364772
#340364282
#340363542
#340363302
#340362532
C4×#179897922
#340362162
#475×C2932
#3365293