Finite Group Databasebeta

← #31805413

Subgroups — #31805413

Order 17792.

210 conjugacy classes of subgroups; only the 51 normal subgroups are shown.

normal subgroups only

This group has 210 conjugacy classes of subgroups — too many to draw. Only its 51 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#22581582C211yesmaximal, characteristic
2#22581284C211yesmaximal, characteristic
3#22581281C211yesmaximal, characteristic
4#22580885C211yesmaximal, characteristic
5#22580689C211yesmaximal, characteristic
6#22580678C211yesmaximal, characteristic
7#328×C139C211yesmaximal, characteristic
8#17984841—21no—
9#17984840—21no—
10#17984832—21no—
11#17984832—21no—
12#17984821C2211yescharacteristic
13#17984819—21no—
14#17984798—21no—
15C2×C4⋊Dic139—21no—
16C2×C4⋊Dic139C2211yescharacteristic
17C2×Dic139⋊C4C2211yescharacteristic
18#17984774—21no—
19#17984773—21no—
20#17984767—21no—
21#17984766—21no—
22C22⋊(C139⋊C8)C2211yescharacteristic
23C139⋊#95—21no—
24C22⋊Q8×C139C2211yescharacteristic
25C22⋊C8×C139C2211yescharacteristic
26#95×C139C2211yescharacteristic
27C2×Dic278—21no—
28C2×Dic278D411yescharacteristic
29C22×Dic139—21no—
30C22×Dic139D411yescharacteristic
31C22×Dic139D411yescharacteristic
32C2×C139⋊C8—21no—
33C4⋊Dic139—21no—
34C4⋊Dic139—21no—
35C4⋊Dic139—21no—
36C4⋊Dic139—42no—
37C4⋊Dic139D411yescharacteristic
38Dic139⋊C4—21no—
39Dic139⋊C4—21no—
40Dic139⋊C4—21no—
41Dic139⋊C4—21no—
42Dic139⋊C4—21no—
43Dic139⋊C4—21no—
44Dic139⋊C4—21no—
45C22⋊Dic139—21no—
46C4×Dic139—21no—
47C4×Dic139—21no—
48C2×Q8×C139D411yescharacteristic
49C22×C4×C139—21no—
50C22×C4×C139C2311yescharacteristic
51C2×C8×C139—21no—
52C4⋊C4×C139—21no—
53C4⋊C4×C139D411yescharacteristic
54C22⋊C4×C139—21no—
55Dic278—41no—
56Dic278—81no—
57C2×Dic139—21no—
58C2×Dic139—21no—
59C2×Dic139—21no—
60C2×Dic139—21no—
61C2×Dic139—21no—
62C2×Dic139—41no—
63C2×Dic139—41no—
64C2×Dic139—41no—
65C2×Dic139—41no—
66C2×Dic139SD1612yes—
67C139⋊C8—41no—
68C23×C139C2×D411yescharacteristic
69Q8×C139—41no—
70C2×C4×C139—22no—
71C2×C4×C139—21no—
72C2×C4×C139—21no—
73C2×C4×C139—41no—
74C2×C4×C139—41no—
75C2×C4×C139—41no—
76C2×C4×C139C2×D411yescharacteristic
77C2×C4×C139C2×D411yescharacteristic
78C8×C139—41no—
79C22×C139—21no—
80C22×C139—21no—
81C22×C139#12011yescharacteristic
82C22×C139C2×SD1611yescharacteristic
83C22×C139#13711yescharacteristic
84C4×C139—21no—
85C4×C139—21no—
86C4×C139—42no—
87C4×C139—41no—
88C4×C139—41no—
89Dic139—22no—
90Dic139—41no—
91Dic139—41no—
92Dic139—41no—
93Dic139—81no—
94C2×C139—21no—
95C2×C139—21no—
96C2×C139#44811yescharacteristic
97C2×C139#45611yescharacteristic
98C2×C139#45811yescharacteristic
99C139#161111yescharacteristic, complemented, Sylow
100#1611—1391nomaximal, Sylow
101#544—1391no—
102#483—1391no—
103#483—1391no—
104#398—1391no—
105#328—1391no—
106#328D13911yescharacteristic
107#324—1391no—
108C4⋊Q8—2781no—
109C4⋊Q8—2781no—
110#125—2781no—
111#125—2781no—
112C22⋊Q8—2781no—
113C22⋊Q8—1391no—
114C22⋊Q8C2×D13911yescharacteristic
115#117—2781no—
116C2×C4⋊C4—2781no—
117C2×C4⋊C4—1391no—
118C2×C4⋊C4—1391no—
119#106—2781no—
120#106—2781no—
121#103—2781no—
122#103—2781no—
123C22⋊C8—1391no—
124C22⋊C8C2×D13911yescharacteristic
125#95—2781no—
126#95C2×D13911yescharacteristic
127C2×Q8—2781no—
128C2×Q8—1391no—
129C2×Q8D55611yescharacteristic
130C22×C4—21no—
131C22×C4—2781no—
132C22×C4—1391no—
133C22×C4—1391no—
134C22×C4C22×D13911yescharacteristic
135C2×C8—21no—
136C2×C8—2781no—
137C4⋊C4—21no—
138C4⋊C4—2781no—
139C4⋊C4—2781no—
140C4⋊C4—2781no—
141C4⋊C4—2781no—
142C4⋊C4—2781no—
143C4⋊C4—2781no—
144C4⋊C4—2781no—
145C4⋊C4—2781no—
146C4⋊C4—2781no—
147C4⋊C4—2781no—
148C4⋊C4—5562no—
149C4⋊C4—1391no—
150C4⋊C4D55611yescharacteristic
151C22⋊C4—21no—
152C22⋊C4—2781no—
153C42—2781no—
154C42—2781no—
155C23D4×D13911yescharacteristic
156Q8—41no—
157Q8—5561no—
158Q8—11121no—
159C2×C4—22no—
160C2×C4—21no—
161C2×C4—21no—
162C2×C4—41no—
163C2×C4—41no—
164C2×C4—41no—
165C2×C4—2781no—
166C2×C4—2781no—
167C2×C4—2781no—
168C2×C4—2781no—
169C2×C4—2781no—
170C2×C4—5561no—
171C2×C4—5561no—
172C2×C4—5561no—
173C2×C4—5561no—
174C2×C4—1392no—
175C2×C4D4×D13911yescharacteristic
176C2×C4C2×D55611yescharacteristic
177C8—41no—
178C8—5561no—
179C22—21no—
180C22—21no—
181C22#1798481211yescharacteristic
182C22SD16×D13911yescharacteristic
183C22#1798487411yescharacteristic
184C4—21no—
185C4—21no—
186C4—42no—
187C4—41no—
188C4—41no—
189C4—2782no—
190C4—5561no—
191C4—5561no—
192C4—5561no—
193C4—11121no—
194C2—21no—
195C2—21no—
196C2#2258109311yescharacteristic
197C2#2258113711yescharacteristic
198C2#2258114411yescharacteristic
subgroupG/H
centerC22#17984812
commutator, cosocleC22×C4×C139C23
FrattiniC22×C4C22×D139
Fitting#328×C139C2
socleC22×C139#120
prime radicalC23×C139C2×D4
hypercenter#328D139
hypocenterC139#1611
LCSG ▷ C22×C4×C139 ▷ C22×C139 ▷ C139
UCSC1 ◁ C22 ◁ C22×C4 ◁ #328

Complements

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

NH ≅ G/Ntype
99. C139#1611semidirect

Maximal subgroups

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

subgroupindex
#225815822
#225812842
#225812812
#225808852
#225806892
#225806782
#328×C1392
#1611139