Finite Group Databasebeta

← #31805404

Subgroups — #31805404

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#22581552C211yesmaximal, characteristic
2#22581281C211yesmaximal, characteristic, complemented
3#22581267C211yesmaximal, characteristic
4#22580885C211yesmaximal, characteristic, complemented
5#22580686C211yesmaximal, characteristic
6#22580678C211yesmaximal, characteristic, complemented
7#328×C139C211yesmaximal, characteristic, complemented
8#17984837—21no—
9#17984833—21no—
10#17984827—21no—
11#17984826—21no—
12#17984818—21no—
13#17984816C2211yescharacteristic
14(C22⋊D139)⋊C4—21no—
15C2×C4⋊Dic139—21no—
16C2×C4⋊Dic139C2211yescharacteristic
17C2×Dic139⋊C4C2211yescharacteristic
18#17984776—21no—
19#17984773—21no—
20#17984766—21no—
21#17984764—21no—
22C22⋊(C139⋊C8)C2211yescharacteristic
23C139⋊#95—21no—
24C22⋊Q8×C139C2211yescharacteristic
25C22⋊C8×C139C2211yescharacteristic
26#95×C139C2211yescharacteristic
27C2×D556D411yescharacteristic
28C2×C22⋊D139—21no—
29C22×Dic139—21no—
30C22×Dic139D411yescharacteristic
31C22×Dic139D411yescharacteristic
32C2×C4×D139—21no—
33C2×C139⋊C8—21no—
34C4⋊Dic139—21no—
35C4⋊Dic139—21no—
36C4⋊Dic139—21no—
37C4⋊Dic139—21no—
38C4⋊Dic139—42no—
39C4⋊Dic139D411yescharacteristic
40Dic139⋊C4—21no—
41Dic139⋊C4—21no—
42Dic139⋊C4—21no—
43(C2×D139)⋊C4—21no—
44(C2×D139)⋊C4—21no—
45(C2×D139)⋊C4—21no—
46(C2×D139)⋊C4—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—
55C22×D139—21no—
56D556—41no—
57C22⋊D139—41no—
58C22⋊D139—41no—
59C2×Dic139—21no—
60C2×Dic139—21no—
61C2×Dic139—21no—
62C2×Dic139—21no—
63C2×Dic139—21no—
64C2×Dic139—41no—
65C2×Dic139—41no—
66C2×Dic139—41no—
67C2×Dic139—41no—
68C4×D139—81no—
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×C139C2×D411yescharacteristic
79C2×C4×C139C2×D411yescharacteristic
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—42no—
92C4×C139—41no—
93C4×C139—41no—
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#328D13911yescharacteristic, complemented
111#327—1391no—
112#324—1391no—
113#126—2781no—
114#125—2781no—
115#123—2781no—
116#123—2781no—
117C22⋊Q8—2781no—
118C22⋊Q8C2×D13911yescharacteristic
119#121—1391no—
120C4×D4—2781no—
121C2×C4⋊C4—2781no—
122C2×C4⋊C4—1391no—
123C2×C4⋊C4—1391no—
124#107—2781no—
125#106—2781no—
126#103—2781no—
127#102—2781no—
128C22⋊C8—1391no—
129C22⋊C8C2×D13911yescharacteristic
130#95—2781no—
131#95C2×D13911yescharacteristic
132C2×Q8D55611yescharacteristic
133C2×D4—2781no—
134C2×D4—1391no—
135C22×C4—21no—
136C22×C4—2781no—
137C22×C4—2781no—
138C22×C4—1391no—
139C22×C4—1391no—
140C22×C4C22×D13911yescharacteristic
141C2×C8—21no—
142C2×C8—2781no—
143C4⋊C4—21no—
144C4⋊C4—2781no—
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⋊C4D55611yescharacteristic
154C22⋊C4—21no—
155C22⋊C4—2781no—
156C22⋊C4—2781no—
157C22⋊C4—2781no—
158C22⋊C4—2781no—
159C42—2781no—
160C23—2781no—
161C23D4×D13911yescharacteristic
162Q8—41no—
163D4—5561no—
164D4—5561no—
165D4—5561no—
166C2×C4—22no—
167C2×C4—21no—
168C2×C4—21no—
169C2×C4—41no—
170C2×C4—41no—
171C2×C4—41no—
172C2×C4—2781no—
173C2×C4—2781no—
174C2×C4—2781no—
175C2×C4—2781no—
176C2×C4—2781no—
177C2×C4—5561no—
178C2×C4—5561no—
179C2×C4—5561no—
180C2×C4—5561no—
181C2×C4—11121no—
182C2×C4D4×D13911yescharacteristic
183C2×C4C2×D55611yescharacteristic
184C8—41no—
185C8—5561no—
186C22—21no—
187C22—21no—
188C22—5561no—
189C22—5561no—
190C22—5561no—
191C22#1798481211yescharacteristic
192C22#1798486511yescharacteristic
193C22#1798486911yescharacteristic
194C4—21no—
195C4—21no—
196C4—42no—
197C4—41no—
198C4—41no—
199C4—5561no—
200C4—5561no—
201C4—5561no—
202C4—11121no—
203C2—21no—
204C2—21no—
205C2—11121no—
206C2#2258110111yescharacteristic
207C2#2258113711yescharacteristic
208C2#2258114411yescharacteristic
subgroupG/H
centerC22#17984812
commutator, cosocleC22×C4×C139C23
FrattiniC22×C4C22×D139
Fitting#328×C139C2
socleC22×C139#120
prime radical#17984816C22
hypercenter#328D139
hypocenterC139#1609
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
2. #22581281C2semidirect
4. #22580885C2semidirect
6. #22580678C2semidirect
7. #328×C139C2semidirect
104. C139#1609semidirect
110. #328D139semidirect

Maximal subgroups

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

subgroupindex
#225815522
#225812812
#225812672
#225808852
#225806862
#225806782
#328×C1392
#1609139