Finite Group Databasebeta

← #31804928

Subgroups — #31804928

Order 17792.

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

normal subgroups only

This group has 242 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#22581489C211yesmaximal, characteristic
2#22581007C211yesmaximal, characteristic, complemented
3#22580804C211yesmaximal, characteristic, complemented
4#22580690C211yesmaximal, characteristic, complemented
5#22580688C211yesmaximal, characteristic
6#22580686C211yesmaximal, characteristic
7#328×C139C211yesmaximal, characteristic, complemented
8#17984837—21no—
9#17984833C411yescharacteristic, complemented
10#17984831C411yescharacteristic, complemented
11#17984826—21no—
12#17984816C2211yescharacteristic
13Q8×Dic139C411yescharacteristic, complemented
14#17984804C411yescharacteristic, complemented
15(C22⋊D139)⋊C4—21no—
16#17984800—21no—
17C2×Dic139⋊C4—21no—
18C2×C4×Dic139—21no—
19C2×C4×Dic139C2211yescharacteristic
20Dic139⋊C8—21no—
21C22⋊(C139⋊C8)C2211yescharacteristic
22#17984752—21no—
23C139⋊#95C2211yescharacteristic
24C22⋊Q8×C139C2211yescharacteristic
25C22⋊C8×C139C2211yescharacteristic
26#95×C139C2211yescharacteristic
27C2×D556C2×C411yescharacteristic
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⋊Dic139C2×C411yescharacteristic
37Dic139⋊C4—24no—
38Dic139⋊C4—21no—
39(C2×D139)⋊C4—21no—
40(C2×D139)⋊C4—21no—
41(C2×D139)⋊C4—21no—
42(C2×D139)⋊C4—21no—
43C4×Dic139—21no—
44C4×Dic139—42no—
45C4×Dic139C2×C411yescharacteristic
46C4×Dic139C2×C411yescharacteristic
47C4×Dic139D411yescharacteristic
48C4×Dic139D411yescharacteristic
49C2×Q8×C139C2×C411yescharacteristic
50C22×C4×C139—21no—
51C22×C4×C139C2311yescharacteristic
52C2×C8×C139—21no—
53C4⋊C4×C139—21no—
54C4⋊C4×C139C2×C411yescharacteristic
55C22⋊C4×C139—21no—
56C22×D139—21no—
57D556—41no—
58C22⋊D139—41no—
59C22⋊D139—41no—
60C2×Dic139—21no—
61C2×Dic139—21no—
62C2×Dic139—22no—
63C2×Dic139—22no—
64C2×Dic139—21no—
65C2×Dic139—41no—
66C2×Dic139—41no—
67C2×Dic139C22⋊C411yescharacteristic
68C2×Dic139C22⋊C411yescharacteristic
69C2×Dic139C22⋊C411yescharacteristic
70C2×Dic139C22⋊C411yescharacteristic
71C4×D139—42no—
72C139⋊C8—41no—
73C23×C139C2×D411yescharacteristic
74Q8×C139—41no—
75C2×C4×C139—22no—
76C2×C4×C139—21no—
77C2×C4×C139—21no—
78C2×C4×C139—41no—
79C2×C4×C139—41no—
80C2×C4×C139—41no—
81C2×C4×C139C22×C411yescharacteristic
82C2×C4×C139C2×D411yescharacteristic
83C8×C139—41no—
84C22×C139—21no—
85C22×C139—21no—
86C22×C139C2×C22⋊C411yescharacteristic
87C22×C139AGL(1,ℤ/8)11yescharacteristic
88C22×C139#13711yescharacteristic
89C2×D139—41no—
90C2×D139—41no—
91C2×D139—41no—
92C4×C139—21no—
93C4×C139—21no—
94C4×C139—42no—
95C4×C139—41no—
96C4×C139—41no—
97Dic139—21no—
98Dic139—21no—
99Dic139—21no—
100Dic139—42no—
101Dic139—41no—
102Dic139#10412yes—
103C2×C139—21no—
104C2×C139—21no—
105C2×C139#41011yescharacteristic
106C2×C139#41711yescharacteristic
107C2×C139C2×#10411yescharacteristic
108D139—81no—
109C139#150911yescharacteristic, complemented, Sylow
110#1509—1391nomaximal, Sylow
111#529—1391no—
112#432—1391no—
113C4×C4⋊C4—1391no—
114#328—1391no—
115#328D13911yescharacteristic, complemented
116#327—1391no—
117#327—1391no—
118#126—2781no—
119#125—1391no—
120#124—1391no—
121#123—2781no—
122C22⋊Q8C2×D13911yescharacteristic
123#121—1391no—
124C4×Q8—1391no—
125C4×D4—2781no—
126C4×D4—1391no—
127#117—2781no—
128C2×C4⋊C4—2781no—
129C2×C42—2781no—
130C2×C42—1391no—
131C4⋊C8—2781no—
132C22⋊C8—1391no—
133C22⋊C8C2×D13911yescharacteristic
134#97—2781no—
135#95—1391no—
136#95C2×D13911yescharacteristic
137C2×Q8C4×D13911yescharacteristic
138C2×D4—2781no—
139C2×D4—1391no—
140C22×C4—21no—
141C22×C4—2781no—
142C22×C4—2781no—
143C22×C4—1391no—
144C22×C4—1391no—
145C22×C4C22×D13911yescharacteristic
146C2×C8—21no—
147C2×C8—2781no—
148C4⋊C4—21no—
149C4⋊C4—2784no—
150C4⋊C4—2781no—
151C4⋊C4—2781no—
152C4⋊C4—2781no—
153C4⋊C4—1391no—
154C4⋊C4C4×D13911yescharacteristic
155C22⋊C4—21no—
156C22⋊C4—2781no—
157C22⋊C4—2781no—
158C22⋊C4—2781no—
159C22⋊C4—2781no—
160C42—2781no—
161C42—5562no—
162C42—1391no—
163C42—1391no—
164C42—1391no—
165C42—1391no—
166C23—2781no—
167C23D4×D13911yescharacteristic
168Q8—41no—
169D4—5561no—
170D4—5561no—
171D4—5561no—
172C2×C4—22no—
173C2×C4—21no—
174C2×C4—21no—
175C2×C4—41no—
176C2×C4—41no—
177C2×C4—41no—
178C2×C4—2781no—
179C2×C4—2781no—
180C2×C4—2782no—
181C2×C4—2782no—
182C2×C4—2781no—
183C2×C4—5562no—
184C2×C4—5561no—
185C2×C4—5561no—
186C2×C4—1391no—
187C2×C4—1391no—
188C2×C4—1391no—
189C2×C4—1391no—
190C2×C4C2×C4×D13911yescharacteristic
191C2×C4D4×D13911yescharacteristic
192C8—41no—
193C8—5561no—
194C22—21no—
195C22—21no—
196C22—5561no—
197C22—5561no—
198C22—5561no—
199C22C22⋊C4×D13911yescharacteristic
200C22#1798486911yescharacteristic
201C22#1798487411yescharacteristic
202C4—21no—
203C4—21no—
204C4—42no—
205C4—41no—
206C4—41no—
207C4—2781no—
208C4—2781no—
209C4—2781no—
210C4—5562no—
211C4—5561no—
212C4—1392no—
213C2—21no—
214C2—21no—
215C2—11121no—
216C2#2258092511yescharacteristic
217C2#2258095311yescharacteristic
218C2#104×D13911yescharacteristic
subgroupG/H
centerC22C22⋊C4×D139
commutatorC2×C4×C139C22×C4
FrattiniC22×C4C22×D139
Fitting#328×C139C2
socleC22×C139C2×C22⋊C4
prime radical#17984816C22
cosocleC22×C4×C139C23
hypercenter#328D139
hypocenterC139#1509
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
2. #22581007C2semidirect
3. #22580804C2semidirect
4. #22580690C2semidirect
7. #328×C139C2semidirect
9. #17984833C4semidirect
10. #17984831C4semidirect
13. Q8×Dic139C4semidirect
14. #17984804C4semidirect
109. C139#1509semidirect
115. #328D139semidirect

Maximal subgroups

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

subgroupindex
#225814892
#225810072
#225808042
#225806902
#225806882
#225806862
#328×C1392
#1509139