Finite Group Databasebeta

← #31807472

Subgroups — #31807472

Order 17792.

394 conjugacy classes of subgroups; only the 71 normal subgroups are shown.

normal subgroups only

This group has 394 conjugacy classes of subgroups — too many to draw. Only its 71 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#22581753C211yesmaximal, characteristic, complemented
2#22581465C212yesmaximal, complemented
3#22580971C212yesmaximal, complemented
4#22580916C211yesmaximal, characteristic, complemented
5H(3,ℤ/4)×C139C211yesmaximal, characteristic, complemented
6C2×#14555785C2212yes—
7C22×C4×D139C2211yescharacteristic
8#17984875—22no—
9#17984870—22no—
10#17984864—22no—
11C2×#14555769C2211yescharacteristic
12#17984826—22no—
13#17984822—22no—
14#17984817—22no—
15#17984812—22no—
16C4×D556—24no—
17#17984770—24no—
18(C2×D139)⋊C8—22no—
19C2×M16×C139C2211yescharacteristic
20#117×C139C2212yes—
21C23×D139D411yescharacteristic
22#14555785—22no—
23#14555785—22no—
24#14555785—22no—
25#14555785—22no—
26C2×Dic278D412yescomplemented
27C2×D556—24no—
28C2×D556D412yescomplemented
29C2×C22⋊D139—22no—
30C22×Dic139D411yescharacteristic
31C2×C4×D139—22no—
32C2×C4×D139—22no—
33C2×C4×D139—22no—
34C2×C4×D139—21no—
35C2×C4×D139—21no—
36Dic556—22no—
37#14555774—24no—
38D1112—22no—
39#14555769—22no—
40C2×C139⋊C8—21no—
41C4⋊Dic139—24no—
42(C2×D139)⋊C4—24no—
43(C2×D139)⋊C4—24no—
44C22×C4×C139C2311yescharacteristic
45M16×C139—22no—
46C2×C8×C139D412yescomplemented
47C4⋊C4×C139—22no—
48C22⋊C4×C139—22no—
49C42×C139D414yescomplemented
50C22×D139—22no—
51C22×D139—21no—
52C22×D139—22no—
53C22×D139—42no—
54Dic278—22no—
55Dic278—22no—
56D556—22no—
57D556—22no—
58D556—48no—
59C22⋊D139—42no—
60C22⋊D139—42no—
61C2×Dic139—22no—
62C2×Dic139—22no—
63C2×Dic139—21no—
64C4×D139—41no—
65C4×D139—42no—
66C4×D139—42no—
67C4×D139—41no—
68C4×D139—42no—
69C139⋊C8—41no—
70C23×C139C2×D411yescharacteristic
71C2×C4×C139—24no—
72C2×C4×C139C2×D412yes—
73C2×C4×C139C2×D411yescharacteristic
74C2×C4×C139C2×D412yes—
75C2×C4×C139#4111yescharacteristic
76C8×C139—22no—
77C22×C139—41no—
78C22×C139#12012yes—
79C22×C139#12111yescharacteristic
80C2×D139—24no—
81C2×D139—22no—
82C2×D139—42no—
83C2×D139—41no—
84C2×D139—41no—
85C2×D139—44no—
86C2×D139—42no—
87C4×C139—44no—
88C4×C139#12011yescharacteristic
89C4×C139#12112yes—
90C4×C139#12711yescharacteristic
91Dic139—41no—
92Dic139—42no—
93C2×C139—22no—
94C2×C139—21no—
95C2×C139#39211yescharacteristic
96D139—42no—
97D139—82no—
98C139#201011yescharacteristic, complemented, Sylow
99#2010—1391nomaximal, Sylow
100#575—1391no—
101#525—1392no—
102#421—1392no—
103#407—1391no—
104H(3,ℤ/4)D13911yescharacteristic, complemented
105C2×#41—1392no—
106C23×C4—1391no—
107#137—2782no—
108AGL(1,ℤ/8)—2782no—
109#135—2782no—
110C2×M16—1391no—
111C2×M16C2×D13911yescharacteristic
112#123—2782no—
113C22⋊Q8—2782no—
114#121—2782no—
115#120—2782no—
116C4×D4—2784no—
117#117C2×D13912yes—
118#104—2784no—
119C22⋊C8—2782no—
120C24—1391no—
121#41—2782no—
122#41—2782no—
123#41—2782no—
124#41—2782no—
125C2×Q8—1392no—
126C2×D4—2784no—
127C2×D4—2782no—
128C2×D4—1392no—
129C22×C4—2782no—
130C22×C4—2781no—
131C22×C4—2782no—
132C22×C4—2782no—
133C22×C4—2781no—
134C22×C4—1391no—
135C22×C4C22×D13911yescharacteristic
136Q16—2782no—
137SD16—2784no—
138D8—2782no—
139M16—22no—
140M16—2782no—
141C2×C8—2781no—
142C2×C8D55612yescomplemented
143C4⋊C4—22no—
144C4⋊C4—2784no—
145C22⋊C4—22no—
146C22⋊C4—2784no—
147C22⋊C4—2784no—
148C42D55614yescomplemented
149C23—2782no—
150C23—2781no—
151C23—2782no—
152C23—5562no—
153C23D4×D13911yescharacteristic
154Q8—2782no—
155Q8—2782no—
156D4—2782no—
157D4—2782no—
158D4—5568no—
159D4—5562no—
160D4—5562no—
161C2×C4—24no—
162C2×C4—2782no—
163C2×C4—2782no—
164C2×C4—2781no—
165C2×C4—5561no—
166C2×C4—5562no—
167C2×C4—5562no—
168C2×C4—5561no—
169C2×C4—5562no—
170C2×C4D4×D13912yes—
171C2×C4C2×D55611yescharacteristic
172C2×C4C2×D55612yes—
173C2×C4#1455578611yescharacteristic
174C8—22no—
175C8—5561no—
176C22—41no—
177C22—2784no—
178C22—2782no—
179C22—5562no—
180C22—5561no—
181C22—5564no—
182C22—5561no—
183C22—5562no—
184C22#1798481212yes—
185C22#1798481711yescharacteristic
186C4—44no—
187C4—5561no—
188C4—5562no—
189C4#1798481211yescharacteristic
190C4#1798481712yes—
191C4#1798483911yescharacteristic
192C2—22no—
193C2—21no—
194C2—5562no—
195C2—11122no—
196C2#2258086311yescharacteristic
subgroupG/H
centerC4#17984839
commutator, cosocleC22×C4×C139C23
FrattiniC22×C4C22×D139
FittingH(3,ℤ/4)×C139C2
socleC2×C139#392
hypercenterH(3,ℤ/4)D139
hypocenterC139#2010
LCSG ▷ C22×C4×C139 ▷ C2×C139 ▷ C139
UCSC1 ◁ C4 ◁ C22×C4 ◁ H(3,ℤ/4)

Complements

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

NH ≅ G/Ntype
1. #22581753C2semidirect
2. #22581465C2semidirect
3. #22580971C2semidirect
4. #22580916C2semidirect
5. H(3,ℤ/4)×C139C2semidirect
26. C2×Dic278D4semidirect
28. C2×D556D4semidirect
46. C2×C8×C139D4semidirect
49. C42×C139D4semidirect
98. C139#2010semidirect
104. H(3,ℤ/4)D139semidirect
142. C2×C8D556semidirect
148. C42D556semidirect

Maximal subgroups

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

subgroupindex
#225817532
#225814652
#225809712
#225809162
H(3,ℤ/4)×C1392
#2010139