Finite Group Databasebeta

← #49169180

Subgroups — #49169180

Order 37504.

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

normal subgroups only

This group has 424 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#34036680C211yesmaximal, characteristic
2C4⋊Q8×D293C211yesmaximal, characteristic, complemented
3#34036490C214yesmaximal, complemented
4#34036479C211yesmaximal, characteristic, complemented
5#34036477C211yesmaximal, characteristic, complemented
6#34036476C211yesmaximal, characteristic, complemented
7#34036129C214yesmaximal, complemented
8C4×#17989785C211yesmaximal, characteristic, complemented
9#487×C293C211yesmaximal, characteristic, complemented
10C2×#17989803C2212yes—
11C2×Q8×D293—21no—
12C2×#17989785C2212yes—
13#22627624C2211yescharacteristic
14#22627623—21no—
15#22627623C2212yes—
16#22627622—21no—
17#22627621C2211yescharacteristic
18#22627613C2212yes—
19#22627599—21no—
20#22627599—21no—
21#22627586—21no—
22#22627586—21no—
23C4⋊C4×D293—21no—
24C4⋊C4×D293C2212yes—
25C42×D293C2211yescharacteristic
26#22627548C2214yes—
27#22627546C2214yes—
28#22627544C2214yes—
29#22627534C2212yes—
30C4×#14556873C2211yescharacteristic
31C4⋊Q8×C293C2211yescharacteristic
32C4⋊Q8×C293C2211yescharacteristic
33#103×C293C2214yes—
34C4×C8×C293C2211yescharacteristic
35#17989803—28no—
36C2×Dic586—22no—
37C2×Dic586—21no—
38Q8×D293—44no—
39C2×D1172—22no—
40C2×D1172—21no—
41C2×D1172—21no—
42C2×D1172C2312yes—
43C2×C4×D293—22no—
44C2×C4×D293—22no—
45C2×C4×D293D411yescharacteristic
46C2×C4×D293D411yescharacteristic
47C2×C4×D293C2311yescharacteristic
48#17989785—24no—
49C2×#14556873C2312yes—
50C4⋊Dic293—21no—
51C4⋊Dic293C2312yes—
52#17989781—22no—
53#17989781—22no—
54#17989779—22no—
55#17989779—22no—
56C4×Dic293D411yescharacteristic
57C4×Dic293D411yescharacteristic
58C4×Dic293C2311yescharacteristic
59C2×Q8×C293—21no—
60C2×Q8×C293C2312yes—
61C2×C8×C293C2312yes—
62C4⋊C4×C293—21no—
63C4⋊C4×C293—21no—
64C4⋊C4×C293—21no—
65C4⋊C4×C293C2312yes—
66C42×C293C2311yescharacteristic
67C22×D293—22no—
68C22×D293C2×D411yescharacteristic
69Dic586—44no—
70Dic586—42no—
71D1172—24no—
72D1172—44no—
73D1172—42no—
74D1172—42no—
75C2×Dic293—22no—
76C2×Dic293C2×D411yescharacteristic
77C2×Dic293C2×D411yescharacteristic
78C2×Dic293C2×D411yescharacteristic
79C4×D293—22no—
80C4×D293—22no—
81C4×D293—44no—
82C4×D293—44no—
83C4×D293#4114yes—
84#14556873—22no—
85Q8×C293—24no—
86Q8×C293—42no—
87C2×C4×C293—22no—
88C2×C4×C293—22no—
89C2×C4×C293C2×D411yescharacteristic
90C2×C4×C293C2×D411yescharacteristic
91C2×C4×C293C2411yescharacteristic
92C8×C293—22no—
93C22×C293C22×D411yescharacteristic
94C2×D293—21no—
95C2×D293—21no—
96C2×D293—42no—
97C2×D293—42no—
98C2×D293—42no—
99C2×D293#12412yes—
100C4×C293—42no—
101C4×C293—42no—
102C4×C293AGL(1,ℤ/8)12yes—
103C4×C293#13712yes—
104C4×C293C2×#4112yes—
105Dic293—21no—
106Dic293—21no—
107Dic293—42no—
108Dic293#12412yes—
109C2×C293C2×#12411yescharacteristic
110C2×C293C2×AGL(1,ℤ/8)11yescharacteristic
111C2×C293C2×#13711yescharacteristic
112D293—22no—
113D293—82no—
114C293#314111yescharacteristic, complemented, Sylow
115#3141—2931nomaximal, Sylow
116#532—2931no—
117C2×C4⋊Q8—2931no—
118#489—2934no—
119#487—2931no—
120#487D29311yescharacteristic, complemented
121#486—2931no—
122#486—2931no—
123#417—2934no—
124C4×M16—2931no—
125C2×#41—2932no—
126C22×Q8—5861no—
127C2×M16—2932no—
128C4⋊Q8—2932no—
129C4⋊Q8—2931no—
130C4⋊Q8—5861no—
131C4⋊Q8—5861no—
132C4⋊Q8C2×D29311yescharacteristic
133C4⋊Q8C2×D29311yescharacteristic
134#127—2931no—
135#124—2932no—
136#121—5861no—
137#121—5861no—
138C4×D4—5861no—
139C4×D4—5861no—
140C2×C4⋊C4—2932no—
141C2×C4⋊C4—5861no—
142C2×C42—2931no—
143#103—2934no—
144#103C2×D29314yes—
145#102—2934no—
146#102—2934no—
147#97—2932no—
148C4×C8—2931no—
149C4×C8C2×D29311yescharacteristic
150#41—5868no—
151C2×Q8—21no—
152C2×Q8—5862no—
153C2×Q8—5861no—
154C2×Q8—11724no—
155C2×Q8C22×D29312yes—
156C2×D4—2932no—
157C2×D4—5862no—
158C2×D4—5861no—
159C2×D4—5861no—
160C22×C4—2931no—
161C22×C4—2931no—
162C22×C4—2931no—
163C22×C4—5862no—
164C22×C4—5862no—
165M16—5864no—
166C2×C8—2932no—
167C2×C8C22×D29312yes—
168C4⋊C4—21no—
169C4⋊C4—21no—
170C4⋊C4—21no—
171C4⋊C4—2932no—
172C4⋊C4—5862no—
173C4⋊C4—5862no—
174C4⋊C4—5861no—
175C4⋊C4C22×D29312yes—
176C22⋊C4—5862no—
177C22⋊C4—5862no—
178C42—2931no—
179C42—2931no—
180C42—2931no—
181C42C22×D29311yescharacteristic
182C23—2931no—
183C23—5862no—
184Q8—24no—
185Q8—42no—
186Q8—11724no—
187Q8—11722no—
188D4—5864no—
189D4—11724no—
190D4—11722no—
191D4—11722no—
192C2×C4—22no—
193C2×C4—22no—
194C2×C4—2931no—
195C2×C4—2934no—
196C2×C4—2931no—
197C2×C4—2931no—
198C2×C4—5862no—
199C2×C4—5862no—
200C2×C4—5862no—
201C2×C4—11724no—
202C2×C4—11724no—
203C2×C4D4×D29311yescharacteristic
204C2×C4D4×D29311yescharacteristic
205C2×C4C23×D29311yescharacteristic
206C8—22no—
207C8—5862no—
208C22—2932no—
209C22—5861no—
210C22—5861no—
211C22—11722no—
212C22—11722no—
213C22—11722no—
214C22C2×D4×D29311yescharacteristic
215C4—42no—
216C4—42no—
217C4—2932no—
218C4—5861no—
219C4—5861no—
220C4—11722no—
221C4#2262765112yes—
222C4#2262765612yes—
223C4#41×D29312yes—
224C2—23442no—
225C2—5862no—
226C2#124×D29311yescharacteristic
227C2C2×#2262765111yescharacteristic
228C2C2×#2262765611yescharacteristic
subgroupG/H
centerC22C2×D4×D293
commutator, cosocleC2×C4×C293C24
FrattiniC2×C4C23×D293
Fitting#487×C293C2
socleC22×C293C22×D4
prime radical#34036680C2
hypercenter#487D293
hypocenterC293#3141
LCSG ▷ C2×C4×C293 ▷ C2×C293 ▷ C293
UCSC1 ◁ C22 ◁ C42 ◁ #487

Complements

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

NH ≅ G/Ntype
2. C4⋊Q8×D293C2semidirect
3. #34036490C2semidirect
4. #34036479C2semidirect
5. #34036477C2semidirect
6. #34036476C2semidirect
7. #34036129C2semidirect
8. C4×#17989785C2semidirect
9. #487×C293C2semidirect
114. C293#3141semidirect
120. #487D293semidirect

Maximal subgroups

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

subgroupindex
#340366802
C4⋊Q8×D2932
#340364902
#340364792
#340364772
#340364762
#340361292
C4×#179897852
#487×C2932
#3141293