Finite Group Databasebeta

← #31805403

Subgroups — #31805403

Order 17792.

216 conjugacy classes of subgroups; only the 49 normal subgroups are shown.

normal subgroups only

This group has 216 conjugacy classes of subgroups — too many to draw. Only its 49 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#22581550C211yesmaximal, characteristic
2#22581284C211yesmaximal, characteristic, complemented
3#22581267C211yesmaximal, characteristic
4#22580883C211yesmaximal, characteristic, complemented
5#22580691C211yesmaximal, characteristic, complemented
6#22580688C211yesmaximal, characteristic
7#324×C139C211yesmaximal, characteristic, complemented
8#17984837—21no—
9#17984832—21no—
10#17984827—21no—
11#17984825—21no—
12#17984821C2211yescharacteristic
13#17984820—21no—
14#17984816C2211yescharacteristic
15C4×C22⋊D139—21no—
16C2×C4⋊Dic139C2211yescharacteristic
17C2×Dic139⋊C4—21no—
18#17984776—21no—
19#17984774—21no—
20#17984767—21no—
21#17984764—21no—
22C139⋊#95—21no—
23C139⋊#95C2211yescharacteristic
24C2×C4⋊C4×C139C2211yescharacteristic
25C22⋊C8×C139C2211yescharacteristic
26C22⋊C8×C139C2211yescharacteristic
27C2×Dic278D411yescharacteristic
28C2×D556D411yescharacteristic
29C2×C22⋊D139—21no—
30C22×Dic139—21no—
31C22×Dic139—21no—
32C2×C4×D139—21no—
33C4⋊Dic139—21no—
34C4⋊Dic139—21no—
35C4⋊Dic139D411yescharacteristic
36C4⋊Dic139D411yescharacteristic
37Dic139⋊C4—21no—
38Dic139⋊C4—21no—
39Dic139⋊C4—21no—
40Dic139⋊C4—21no—
41Dic139⋊C4—42no—
42C22⋊Dic139—21no—
43(C2×D139)⋊C4—21no—
44(C2×D139)⋊C4—21no—
45(C2×D139)⋊C4—21no—
46(C2×D139)⋊C4—21no—
47C4×Dic139—21no—
48C22×C4×C139D411yescharacteristic
49C22×C4×C139D411yescharacteristic
50C22×C4×C139C2311yescharacteristic
51C2×C8×C139—21no—
52C2×C8×C139—21no—
53C4⋊C4×C139—21no—
54C4⋊C4×C139—21no—
55C22×D139—21no—
56Dic278—41no—
57D556—41no—
58C22⋊D139—41no—
59C22⋊D139—41no—
60C2×Dic139—22no—
61C2×Dic139—21no—
62C2×Dic139—21no—
63C2×Dic139—21no—
64C2×Dic139—41no—
65C2×Dic139—41no—
66C2×Dic139—41no—
67C2×Dic139—41no—
68C2×Dic139—41no—
69C4×D139—81no—
70C23×C139C2×D411yescharacteristic
71C2×C4×C139—21no—
72C2×C4×C139—21no—
73C2×C4×C139—21no—
74C2×C4×C139—21no—
75C2×C4×C139—41no—
76C2×C4×C139—41no—
77C2×C4×C139C2×D411yescharacteristic
78C2×C4×C139C2×D411yescharacteristic
79C8×C139—41no—
80C8×C139—41no—
81C22×C139—21no—
82C22×C139—21no—
83C22×C139#12011yescharacteristic
84C22×C139#13511yescharacteristic
85C22×C139AGL(1,ℤ/8)11yescharacteristic
86C2×D139—41no—
87C2×D139—41no—
88C2×D139—41no—
89C4×C139—21no—
90C4×C139—21no—
91C4×C139—41no—
92C4×C139—41no—
93Dic139—42no—
94Dic139—41no—
95Dic139—41no—
96Dic139—41no—
97Dic139—81no—
98C2×C139—21no—
99C2×C139—21no—
100C2×C139#44911yescharacteristic
101C2×C139#45611yescharacteristic
102C2×C139#45811yescharacteristic
103D139—81no—
104C139#160911yescharacteristic, complemented, Sylow
105#1609—1391nomaximal, Sylow
106#539—1391no—
107#483—1391no—
108#480—1391no—
109#398—1391no—
110#328—1391no—
111#327—1391no—
112#324D13911yescharacteristic, complemented
113#126—2781no—
114#125—2781no—
115#123—2781no—
116#123—2781no—
117C22⋊Q8—2781no—
118C22⋊Q8—1391no—
119#121—1391no—
120C4×D4—2781no—
121C2×C4⋊C4—2781no—
122C2×C4⋊C4—1391no—
123C2×C4⋊C4C2×D13911yescharacteristic
124#107—2781no—
125#106—2781no—
126#103—2781no—
127#102—2781no—
128C22⋊C8C2×D13911yescharacteristic
129C22⋊C8C2×D13911yescharacteristic
130#95—2781no—
131#95—1391no—
132C2×Q8—1391no—
133C2×D4—2781no—
134C2×D4—1391no—
135C22×C4—2781no—
136C22×C4—2781no—
137C22×C4—2781no—
138C22×C4D55611yescharacteristic
139C22×C4D55611yescharacteristic
140C22×C4C22×D13911yescharacteristic
141C2×C8—21no—
142C2×C8—21no—
143C4⋊C4—21no—
144C4⋊C4—21no—
145C4⋊C4—2781no—
146C4⋊C4—2781no—
147C4⋊C4—2781no—
148C4⋊C4—2781no—
149C4⋊C4—2781no—
150C4⋊C4—2781no—
151C4⋊C4—5562no—
152C4⋊C4—1391no—
153C4⋊C4—1391no—
154C22⋊C4—2781no—
155C22⋊C4—2781no—
156C22⋊C4—2781no—
157C22⋊C4—2781no—
158C22⋊C4—2781no—
159C42—2781no—
160C23—2781no—
161C23C2×D55611yescharacteristic
162Q8—5561no—
163D4—5561no—
164D4—5561no—
165D4—5561no—
166C2×C4—21no—
167C2×C4—21no—
168C2×C4—21no—
169C2×C4—21no—
170C2×C4—41no—
171C2×C4—41no—
172C2×C4—2782no—
173C2×C4—2781no—
174C2×C4—2781no—
175C2×C4—2781no—
176C2×C4—5561no—
177C2×C4—5561no—
178C2×C4—5561no—
179C2×C4—5561no—
180C2×C4—5561no—
181C2×C4—11121no—
182C2×C4D4×D13911yescharacteristic
183C2×C4D4×D13911yescharacteristic
184C8—41no—
185C8—41no—
186C22—21no—
187C22—21no—
188C22—5561no—
189C22—5561no—
190C22—5561no—
191C22#1798481211yescharacteristic
192C22#1798486411yescharacteristic
193C22#1798487011yescharacteristic
194C4—21no—
195C4—21no—
196C4—41no—
197C4—41no—
198C4—5562no—
199C4—5561no—
200C4—5561no—
201C4—5561no—
202C4—11121no—
203C2—21no—
204C2—21no—
205C2—11121no—
206C2#2258110011yescharacteristic
207C2#2258113811yescharacteristic
208C2#2258114411yescharacteristic
subgroupG/H
centerC22#17984812
commutator, cosocleC22×C4×C139C23
FrattiniC22×C4C22×D139
Fitting#324×C139C2
socleC22×C139#120
prime radical#17984816C22
hypercenter#324D139
hypocenterC139#1609
LCSG ▷ C22×C4×C139 ▷ C22×C139 ▷ C139
UCSC1 ◁ C22 ◁ C22×C4 ◁ #324

Complements

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

NH ≅ G/Ntype
2. #22581284C2semidirect
4. #22580883C2semidirect
5. #22580691C2semidirect
7. #324×C139C2semidirect
104. C139#1609semidirect
112. #324D139semidirect

Maximal subgroups

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

subgroupindex
#225815502
#225812842
#225812672
#225808832
#225806912
#225806882
#324×C1392
#1609139