Finite Group Databasebeta

← #31805422

Subgroups — #31805422

Order 17792.

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

normal subgroups only

This group has 288 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#22581511C211yesmaximal, characteristic
2#22581271C211yesmaximal, characteristic, complemented
3#22580888C211yesmaximal, characteristic, complemented
4#22580688C211yesmaximal, characteristic, complemented
5#22580687C211yesmaximal, characteristic, complemented
6#22580676C211yesmaximal, characteristic, complemented
7#481×C139C211yesmaximal, characteristic, complemented
8C2×D4×D139—21no—
9#17984827—21no—
10#17984824—21no—
11#17984816C2211yescharacteristic
12#17984814—21no—
13#17984812—21no—
14#17984810—21no—
15C2×Dic139⋊C4—21no—
16C2×(C2×D139)⋊C4—21no—
17C2×(C2×D139)⋊C4C2211yescharacteristic
18#17984773—21no—
19#17984762—21no—
20C22⋊(C139⋊C8)C2211yescharacteristic, complemented
21C139⋊#95C2211yescharacteristic, complemented
22#121×C139C2211yescharacteristic
23C2×C4⋊C4×C139C2211yescharacteristic, complemented
24#106×C139—21no—
25#102×C139—21no—
26C22⋊C8×C139C2211yescharacteristic, complemented
27C23×D139—21no—
28C23×D139D411yescharacteristic
29C2×D556—21no—
30C2×D556D411yescharacteristic
31C2×C22⋊D139—21no—
32C2×C22⋊D139—21no—
33C2×C22⋊D139—21no—
34D4×D139—42no—
35D4×D139—42no—
36C22×Dic139—21no—
37C22×Dic139D411yescharacteristic
38C2×C4×D139—21no—
39C2×C139⋊C8—21no—
40C4⋊Dic139D411yescharacteristic
41Dic139⋊C4—21no—
42Dic139⋊C4—42no—
43C22⋊Dic139—21no—
44(C2×D139)⋊C4—21no—
45(C2×D139)⋊C4—21no—
46(C2×D139)⋊C4—21no—
47(C2×D139)⋊C4—21no—
48(C2×D139)⋊C4—42no—
49C2×D4×C139—21no—
50C2×D4×C139D411yescharacteristic
51C22×C4×C139—21no—
52C22×C4×C139C2311yescharacteristic
53C2×C8×C139—21no—
54C4⋊C4×C139—21no—
55C4⋊C4×C139—21no—
56C4⋊C4×C139D411yescharacteristic
57C22⋊C4×C139—21no—
58C22×D139—21no—
59C22×D139—21no—
60C22×D139—21no—
61C22×D139—42no—
62C22×D139—41no—
63C22×D139—41no—
64C22×D139—81no—
65C22×D139—81no—
66C22×D139SD1612yes—
67D556—41no—
68D556—42no—
69C22⋊D139—42no—
70C22⋊D139—41no—
71C22⋊D139—41no—
72C22⋊D139—81no—
73C2×Dic139—22no—
74C2×Dic139—21no—
75C2×Dic139—21no—
76C2×Dic139—41no—
77C2×Dic139—41no—
78C2×Dic139—41no—
79C4×D139—42no—
80C139⋊C8—41no—
81C23×C139—21no—
82C23×C139C2×D411yescharacteristic
83D4×C139—41no—
84D4×C139—41no—
85D4×C139—41no—
86C2×C4×C139—21no—
87C2×C4×C139—41no—
88C2×C4×C139—41no—
89C2×C4×C139—41no—
90C2×C4×C139—41no—
91C2×C4×C139C2×D411yescharacteristic
92C2×C4×C139C2×D411yescharacteristic
93C8×C139—41no—
94C22×C139—21no—
95C22×C139—21no—
96C22×C139—41no—
97C22×C139—41no—
98C22×C139—41no—
99C22×C139#12011yescharacteristic
100C22×C139C2×SD1611yescharacteristic
101C22×C139AGL(1,ℤ/8)11yescharacteristic
102C2×D139—22no—
103C2×D139—41no—
104C2×D139—41no—
105C2×D139—42no—
106C2×D139—41no—
107C2×D139—41no—
108C2×D139—41no—
109C2×D139—81no—
110C2×D139—84no—
111C4×C139—21no—
112C4×C139—21no—
113C4×C139—41no—
114C4×C139—81no—
115Dic139—42no—
116Dic139—41no—
117Dic139—41no—
118C2×C139—21no—
119C2×C139—21no—
120C2×C139—81no—
121C2×C139#45011yescharacteristic
122C2×C139#45311yescharacteristic
123C2×C139#45811yescharacteristic
124D139—42no—
125D139—81no—
126C139#161311yescharacteristic, complemented, Sylow
127#1613—1391nomaximal, Sylow
128#534—1391no—
129#481—1391no—
130#481D13911yescharacteristic, complemented
131#399—1391no—
132#327—1391no—
133#327—1391no—
134#323—1391no—
135C22×D4—2781no—
136#123—2781no—
137#123—2781no—
138#121—2781no—
139#121—1391no—
140#121C2×D13911yescharacteristic
141#120—2781no—
142#120—2781no—
143C2×C4⋊C4—2781no—
144C2×C4⋊C4C2×D13911yescharacteristic, complemented
145C2×C22⋊C4—2781no—
146C2×C22⋊C4—1391no—
147#106—21no—
148#106—2781no—
149#102—21no—
150#102—2781no—
151C22⋊C8—1391no—
152C22⋊C8C2×D13911yescharacteristic, complemented
153#95—1391no—
154C24—2781no—
155C24—1391no—
156C2×D4—21no—
157C2×D4—2781no—
158C2×D4—2781no—
159C2×D4—2781no—
160C2×D4—2781no—
161C2×D4—5562no—
162C2×D4—5562no—
163C2×D4—1391no—
164C2×D4C22⋊D13911yescharacteristic
165C22×C4—21no—
166C22×C4—2781no—
167C22×C4—2781no—
168C22×C4—1391no—
169C22×C4C22×D13911yescharacteristic
170C2×C8—21no—
171C2×C8—2781no—
172C4⋊C4—21no—
173C4⋊C4—21no—
174C4⋊C4—2781no—
175C4⋊C4—5562no—
176C4⋊C4—1391no—
177C4⋊C4C22⋊D13911yescharacteristic
178C22⋊C4—21no—
179C22⋊C4—2781no—
180C22⋊C4—2781no—
181C22⋊C4—2781no—
182C22⋊C4—2781no—
183C22⋊C4—2781no—
184C22⋊C4—5562no—
185C23—21no—
186C23—2781no—
187C23—2781no—
188C23—2781no—
189C23—5561no—
190C23—5561no—
191C23—5562no—
192C23—11121no—
193C23—11121no—
194C23—1392no—
195C23D4×D13911yescharacteristic
196D4—41no—
197D4—41no—
198D4—41no—
199D4—5561no—
200D4—5562no—
201D4—5562no—
202D4—5561no—
203D4—5561no—
204D4—11121no—
205C2×C4—21no—
206C2×C4—41no—
207C2×C4—41no—
208C2×C4—41no—
209C2×C4—41no—
210C2×C4—2782no—
211C2×C4—2781no—
212C2×C4—2781no—
213C2×C4—5562no—
214C2×C4—5561no—
215C2×C4—5561no—
216C2×C4—5561no—
217C2×C4D4×D13911yescharacteristic
218C2×C4C2×C22⋊D13911yescharacteristic
219C8—41no—
220C8—5561no—
221C22—21no—
222C22—21no—
223C22—41no—
224C22—41no—
225C22—41no—
226C22—2782no—
227C22—5562no—
228C22—5561no—
229C22—5561no—
230C22—5561no—
231C22—5561no—
232C22—5561no—
233C22—11121no—
234C22—11124no—
235C22#1798481011yescharacteristic
236C22SD16×D13911yescharacteristic
237C22#1798486911yescharacteristic
238C4—21no—
239C4—21no—
240C4—41no—
241C4—81no—
242C4—5562no—
243C4—5561no—
244C4—5561no—
245C2—21no—
246C2—21no—
247C2—81no—
248C2—5562no—
249C2—11121no—
250C2#2258110211yescharacteristic
251C2#2258111911yescharacteristic
252C2#2258114211yescharacteristic
subgroupG/H
centerC22#17984810
commutator, cosocleC22×C4×C139C23
FrattiniC22×C4C22×D139
Fitting#481×C139C2
socleC22×C139#120
prime radical#22581511C2
hypercenter#481D139
hypocenterC139#1613
LCSG ▷ C22×C4×C139 ▷ C22×C139 ▷ C139
UCSC1 ◁ C22 ◁ C22×C4 ◁ #481

Complements

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

NH ≅ G/Ntype
2. #22581271C2semidirect
3. #22580888C2semidirect
4. #22580688C2semidirect
5. #22580687C2semidirect
6. #22580676C2semidirect
7. #481×C139C2semidirect
20. C22⋊(C139⋊C8)C22semidirect
21. C139⋊#95C22semidirect
23. C2×C4⋊C4×C139C22semidirect
26. C22⋊C8×C139C22semidirect
126. C139#1613semidirect
130. #481D139semidirect
144. C2×C4⋊C4C2×D139semidirect
152. C22⋊C8C2×D139semidirect

Maximal subgroups

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

subgroupindex
#225815112
#225812712
#225808882
#225806882
#225806872
#225806762
#481×C1392
#1613139