Finite Group Databasebeta

← #31804914

Subgroups — #31804914

Order 17792.

228 conjugacy classes of subgroups; only the 63 normal subgroups are shown.

normal subgroups only

This group has 228 conjugacy classes of subgroups — too many to draw. Only its 63 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#22581505C211yesmaximal, characteristic
2#22581007C211yesmaximal, characteristic
3#22580798C211yesmaximal, characteristic
4#22580691C211yesmaximal, characteristic
5#22580690C211yesmaximal, characteristic
6#22580689C211yesmaximal, characteristic
7#328×C139C211yesmaximal, characteristic
8#17984841C411yescharacteristic, complemented
9#17984840C411yescharacteristic, complemented
10#17984832—21no—
11#17984821C2211yescharacteristic
12#17984819—21no—
13Q8×Dic139C411yescharacteristic, complemented
14#17984807—21no—
15#17984807C411yescharacteristic, complemented
16#17984798—21no—
17C2×C4×Dic139—21no—
18C2×C4×Dic139C2211yescharacteristic
19Dic139⋊C8—21no—
20C22⋊(C139⋊C8)C2211yescharacteristic
21#17984752—21no—
22C139⋊#95—21no—
23C139⋊#95C2211yescharacteristic
24C22⋊Q8×C139C2211yescharacteristic
25C22⋊C8×C139C2211yescharacteristic
26#95×C139C2211yescharacteristic
27C2×Dic278—21no—
28C2×Dic278C2×C411yescharacteristic
29C22×Dic139—21no—
30C22×Dic139D411yescharacteristic
31C22×Dic139D411yescharacteristic
32C2×C139⋊C8—21no—
33C4⋊Dic139—21no—
34C4⋊Dic139C2×C411yescharacteristic
35Dic139⋊C4—21no—
36Dic139⋊C4—21no—
37Dic139⋊C4—21no—
38Dic139⋊C4—21no—
39Dic139⋊C4—21no—
40C22⋊Dic139—21no—
41C4×Dic139—24no—
42C4×Dic139—21no—
43C4×Dic139—21no—
44C4×Dic139C2×C411yescharacteristic
45C4×Dic139C2×C411yescharacteristic
46C4×Dic139D411yescharacteristic
47C4×Dic139D411yescharacteristic
48C2×Q8×C139C2×C411yescharacteristic
49C22×C4×C139—21no—
50C22×C4×C139C2311yescharacteristic
51C2×C8×C139—21no—
52C4⋊C4×C139—21no—
53C4⋊C4×C139C2×C411yescharacteristic
54C22⋊C4×C139—21no—
55Dic278—42no—
56Dic278—41no—
57C2×Dic139—21no—
58C2×Dic139—21no—
59C2×Dic139—22no—
60C2×Dic139—22no—
61C2×Dic139—21no—
62C2×Dic139—21no—
63C2×Dic139—41no—
64C2×Dic139—41no—
65C2×Dic139C22⋊C411yescharacteristic
66C2×Dic139C22⋊C411yescharacteristic
67C2×Dic139C22⋊C411yescharacteristic
68C2×Dic139C22⋊C411yescharacteristic
69C139⋊C8—41no—
70C23×C139C2×D411yescharacteristic
71Q8×C139—41no—
72C2×C4×C139—22no—
73C2×C4×C139—21no—
74C2×C4×C139—21no—
75C2×C4×C139—41no—
76C2×C4×C139—41no—
77C2×C4×C139—41no—
78C2×C4×C139C22×C411yescharacteristic
79C2×C4×C139C2×D411yescharacteristic
80C8×C139—41no—
81C22×C139—21no—
82C22×C139—21no—
83C22×C139C2×C22⋊C411yescharacteristic
84C22×C139#13711yescharacteristic
85C22×C139#13711yescharacteristic
86C4×C139—21no—
87C4×C139—21no—
88C4×C139—42no—
89C4×C139—41no—
90C4×C139—41no—
91Dic139—21no—
92Dic139—21no—
93Dic139—21no—
94Dic139—42no—
95Dic139—41no—
96Dic139—41no—
97Dic139#10412yes—
98C2×C139—21no—
99C2×C139—21no—
100C2×C139#41011yescharacteristic
101C2×C139#41911yescharacteristic
102C2×C139C2×#10411yescharacteristic
103C139#150611yescharacteristic, complemented, Sylow
104#1506—1391nomaximal, Sylow
105#533—1391no—
106#432—1391no—
107#376—1391no—
108#328—1391no—
109#328—1391no—
110#328—1391no—
111#328D13911yescharacteristic
112C4⋊Q8—1391no—
113C4⋊Q8—1391no—
114#125—2781no—
115C22⋊Q8—2781no—
116C22⋊Q8—1391no—
117C22⋊Q8C2×D13911yescharacteristic
118C4×Q8—2781no—
119C4×Q8—1391no—
120C4×Q8—1391no—
121#117—2781no—
122C2×C42—2781no—
123C2×C42—1391no—
124C4⋊C8—2781no—
125C22⋊C8—1391no—
126C22⋊C8C2×D13911yescharacteristic
127#97—2781no—
128#95—2781no—
129#95—1391no—
130#95C2×D13911yescharacteristic
131C2×Q8—2781no—
132C2×Q8—1391no—
133C2×Q8C4×D13911yescharacteristic
134C22×C4—21no—
135C22×C4—2781no—
136C22×C4—1391no—
137C22×C4—1391no—
138C22×C4C22×D13911yescharacteristic
139C2×C8—21no—
140C2×C8—2781no—
141C4⋊C4—21no—
142C4⋊C4—2781no—
143C4⋊C4—2781no—
144C4⋊C4—2781no—
145C4⋊C4—2781no—
146C4⋊C4—2781no—
147C4⋊C4—2781no—
148C4⋊C4—1391no—
149C4⋊C4C4×D13911yescharacteristic
150C22⋊C4—21no—
151C22⋊C4—2781no—
152C42—2784no—
153C42—2781no—
154C42—2781no—
155C42—1391no—
156C42—1391no—
157C42—1391no—
158C42—1391no—
159C23D4×D13911yescharacteristic
160Q8—41no—
161Q8—5561no—
162Q8—5562no—
163C2×C4—22no—
164C2×C4—21no—
165C2×C4—21no—
166C2×C4—41no—
167C2×C4—41no—
168C2×C4—41no—
169C2×C4—2781no—
170C2×C4—2781no—
171C2×C4—2782no—
172C2×C4—2782no—
173C2×C4—2781no—
174C2×C4—2781no—
175C2×C4—5561no—
176C2×C4—5561no—
177C2×C4—1391no—
178C2×C4—1391no—
179C2×C4—1391no—
180C2×C4—1391no—
181C2×C4C2×C4×D13911yescharacteristic
182C2×C4D4×D13911yescharacteristic
183C8—41no—
184C8—5561no—
185C22—21no—
186C22—21no—
187C22C22⋊C4×D13911yescharacteristic
188C22#1798487111yescharacteristic
189C22#1798487411yescharacteristic
190C4—21no—
191C4—21no—
192C4—42no—
193C4—41no—
194C4—41no—
195C4—2781no—
196C4—2781no—
197C4—2781no—
198C4—5562no—
199C4—5561no—
200C4—5561no—
201C4—1392no—
202C2—21no—
203C2—21no—
204C2#2258092511yescharacteristic
205C2#2258096011yescharacteristic
206C2#104×D13911yescharacteristic
subgroupG/H
centerC22C22⋊C4×D139
commutatorC2×C4×C139C22×C4
FrattiniC22×C4C22×D139
Fitting#328×C139C2
socleC22×C139C2×C22⋊C4
prime radicalC23×C139C2×D4
cosocleC22×C4×C139C23
hypercenter#328D139
hypocenterC139#1506
LCSG ▷ C2×C4×C139 ▷ C22×C139 ▷ C139
UCSC1 ◁ C22 ◁ C22×C4 ◁ #328

Complements

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

NH ≅ G/Ntype
8. #17984841C4semidirect
9. #17984840C4semidirect
13. Q8×Dic139C4semidirect
15. #17984807C4semidirect
103. C139#1506semidirect

Maximal subgroups

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

subgroupindex
#225815052
#225810072
#225807982
#225806912
#225806902
#225806892
#328×C1392
#1506139