Finite Group Databasebeta

← #31805421

Subgroups — #31805421

Order 17792.

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

normal subgroups only

This group has 232 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#22581543C211yesmaximal, characteristic
2#22581281C211yesmaximal, characteristic, complemented
3#22581267C211yesmaximal, characteristic, complemented
4#22580880C211yesmaximal, characteristic, complemented
5#22580686C211yesmaximal, characteristic, complemented
6#22580676C211yesmaximal, characteristic, complemented
7#328×C139C211yesmaximal, characteristic, complemented
8#17984837—21no—
9#17984831—21no—
10#17984827—21no—
11#17984817—21no—
12#17984816C2211yescharacteristic
13#17984812—21no—
14(C22⋊D139)⋊C4—21no—
15C2×C4⋊Dic139C2211yescharacteristic
16C2×(C2×D139)⋊C4—21no—
17C2×(C2×D139)⋊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
27C23×D139D411yescharacteristic
28C2×D556—21no—
29C2×D556—21no—
30C2×D556D411yescharacteristic
31C2×C22⋊D139—21no—
32C22×Dic139—21no—
33C22×Dic139D411yescharacteristic
34C2×C4×D139—21no—
35C2×C139⋊C8—21no—
36C4⋊Dic139—21no—
37C4⋊Dic139—21no—
38C4⋊Dic139D411yescharacteristic
39Dic139⋊C4—21no—
40(C2×D139)⋊C4—21no—
41(C2×D139)⋊C4—21no—
42(C2×D139)⋊C4—21no—
43(C2×D139)⋊C4—21no—
44(C2×D139)⋊C4—21no—
45(C2×D139)⋊C4—21no—
46(C2×D139)⋊C4—42no—
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—
56C22×D139—21no—
57C22×D139—21no—
58C22×D139—21no—
59C22×D139—41no—
60C22×D139—41no—
61D556—41no—
62D556—81no—
63D556—81no—
64C22⋊D139—41no—
65C22⋊D139—41no—
66C2×Dic139—21no—
67C2×Dic139—21no—
68C2×Dic139—41no—
69C2×Dic139—41no—
70C2×Dic139—41no—
71C2×Dic139—41no—
72C4×D139—81no—
73C139⋊C8—41no—
74C23×C139C2×D411yescharacteristic
75Q8×C139—41no—
76C2×C4×C139—21no—
77C2×C4×C139—21no—
78C2×C4×C139—41no—
79C2×C4×C139—41no—
80C2×C4×C139—41no—
81C2×C4×C139—41no—
82C2×C4×C139C2×D411yescharacteristic
83C2×C4×C139C2×D411yescharacteristic
84C8×C139—41no—
85C22×C139—21no—
86C22×C139—21no—
87C22×C139#12011yescharacteristic
88C22×C139#13511yescharacteristic
89C22×C139AGL(1,ℤ/8)11yescharacteristic
90C2×D139—42no—
91C2×D139—41no—
92C2×D139—41no—
93C2×D139—41no—
94C2×D139—41no—
95C2×D139—41no—
96C2×D139—41no—
97C2×D139—81no—
98C4×C139—21no—
99C4×C139—21no—
100C4×C139—41no—
101C4×C139—41no—
102C4×C139—81no—
103Dic139—41no—
104Dic139—41no—
105Dic139—81no—
106C2×C139—21no—
107C2×C139—21no—
108C2×C139#44911yescharacteristic
109C2×C139#45511yescharacteristic
110C2×C139#45811yescharacteristic
111D139—81no—
112D139—81no—
113C139#161211yescharacteristic, complemented, Sylow
114#1612—1391nomaximal, Sylow
115#538—1391no—
116#483—1391no—
117#480—1391no—
118#397—1391no—
119#328D13911yescharacteristic, complemented
120#327—1391no—
121#323—1391no—
122#126—2781no—
123#124—2781no—
124#123—2781no—
125C22⋊Q8C2×D13911yescharacteristic
126#121—2781no—
127#121—1391no—
128#120—2781no—
129C4×D4—2781no—
130C2×C4⋊C4—1391no—
131C2×C22⋊C4—2781no—
132C2×C22⋊C4—1391no—
133#107—2781no—
134#106—2781no—
135#103—2781no—
136#102—2781no—
137C22⋊C8—1391no—
138C22⋊C8C2×D13911yescharacteristic
139#95—2781no—
140#95C2×D13911yescharacteristic
141C24—1391no—
142C2×Q8D55611yescharacteristic
143C2×D4—2781no—
144C2×D4—2781no—
145C2×D4—2781no—
146C2×D4—1391no—
147C22×C4—21no—
148C22×C4—2781no—
149C22×C4—2781no—
150C22×C4—1391no—
151C22×C4C22×D13911yescharacteristic
152C2×C8—21no—
153C2×C8—2781no—
154C4⋊C4—21no—
155C4⋊C4—2781no—
156C4⋊C4—2781no—
157C4⋊C4—2781no—
158C4⋊C4—1391no—
159C4⋊C4D55611yescharacteristic
160C22⋊C4—21no—
161C22⋊C4—2781no—
162C22⋊C4—2781no—
163C22⋊C4—2781no—
164C22⋊C4—2781no—
165C22⋊C4—2781no—
166C22⋊C4—2781no—
167C22⋊C4—5562no—
168C42—2781no—
169C23—2781no—
170C23—2781no—
171C23—2781no—
172C23—2781no—
173C23—5561no—
174C23—5561no—
175C23D4×D13911yescharacteristic
176Q8—41no—
177D4—5561no—
178D4—5561no—
179D4—5561no—
180D4—11121no—
181D4—11121no—
182C2×C4—21no—
183C2×C4—21no—
184C2×C4—41no—
185C2×C4—41no—
186C2×C4—41no—
187C2×C4—41no—
188C2×C4—2781no—
189C2×C4—2781no—
190C2×C4—5561no—
191C2×C4—5561no—
192C2×C4—5561no—
193C2×C4—5561no—
194C2×C4—11121no—
195C2×C4D4×D13911yescharacteristic
196C2×C4C2×D55611yescharacteristic
197C8—41no—
198C8—5561no—
199C22—21no—
200C22—21no—
201C22—5562no—
202C22—5561no—
203C22—5561no—
204C22—5561no—
205C22—5561no—
206C22—5561no—
207C22—5561no—
208C22—11121no—
209C22#1798481211yescharacteristic
210C22#1798486511yescharacteristic
211C22#1798486911yescharacteristic
212C4—21no—
213C4—21no—
214C4—41no—
215C4—41no—
216C4—81no—
217C4—5561no—
218C4—5561no—
219C4—11121no—
220C2—21no—
221C2—21no—
222C2—11121no—
223C2—11121no—
224C2#2258110111yescharacteristic
225C2#2258113211yescharacteristic
226C2#2258114411yescharacteristic
subgroupG/H
centerC22#17984812
commutator, cosocleC22×C4×C139C23
FrattiniC22×C4C22×D139
Fitting#328×C139C2
socleC22×C139#120
prime radical#22581543C2
hypercenter#328D139
hypocenterC139#1612
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
3. #22581267C2semidirect
4. #22580880C2semidirect
5. #22580686C2semidirect
6. #22580676C2semidirect
7. #328×C139C2semidirect
113. C139#1612semidirect
119. #328D139semidirect

Maximal subgroups

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

subgroupindex
#225815432
#225812812
#225812672
#225808802
#225806862
#225806762
#328×C1392
#1612139