Finite Group Databasebeta

← #31805408

Subgroups — #31805408

Order 17792.

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

normal subgroups only

This group has 254 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#22581530C211yesmaximal, characteristic
2#22581267C211yesmaximal, characteristic, complemented
3#22581264C211yesmaximal, characteristic, complemented
4#22580885C211yesmaximal, characteristic, complemented
5#22580686C211yesmaximal, characteristic, complemented
6#22580678C211yesmaximal, characteristic, complemented
7#327×C139C211yesmaximal, characteristic, complemented
8C2×#14555784—21no—
9#17984820—21no—
10#17984819—21no—
11#17984816C2211yescharacteristic
12#17984815—21no—
13#17984814—21no—
14#17984814—21no—
15C2×C4⋊Dic139—21no—
16C2×C4⋊Dic139C2211yescharacteristic
17C2×Dic139⋊C4C2211yescharacteristic
18#17984776—21no—
19#17984775—21no—
20#17984764—21no—
21#17984763—21no—
22C22⋊(C139⋊C8)C2211yescharacteristic
23C139⋊#95—21no—
24#121×C139C2211yescharacteristic
25C22⋊C8×C139C2211yescharacteristic
26#95×C139C2211yescharacteristic
27#14555784—42no—
28#14555784—42no—
29C2×Dic278—21no—
30C2×D556D411yescharacteristic
31C2×C22⋊D139—21no—
32C2×C22⋊D139—21no—
33C2×C22⋊D139—21no—
34C22×Dic139—21no—
35C22×Dic139—21no—
36C22×Dic139D411yescharacteristic
37C22×Dic139D411yescharacteristic
38C2×C4×D139—21no—
39C2×C139⋊C8—21no—
40C4⋊Dic139—21no—
41C4⋊Dic139—21no—
42C4⋊Dic139—42no—
43C4⋊Dic139D411yescharacteristic
44Dic139⋊C4—21no—
45Dic139⋊C4—21no—
46Dic139⋊C4—21no—
47C22⋊Dic139—21no—
48(C2×D139)⋊C4—21no—
49(C2×D139)⋊C4—21no—
50C2×D4×C139—21no—
51C2×D4×C139D411yescharacteristic
52C22×C4×C139—21no—
53C22×C4×C139C2311yescharacteristic
54C2×C8×C139—21no—
55C4⋊C4×C139D411yescharacteristic
56C22⋊C4×C139—21no—
57C22×D139—21no—
58Dic278—42no—
59D556—41no—
60C22⋊D139—42no—
61C22⋊D139—41no—
62C22⋊D139—41no—
63C22⋊D139—81no—
64C2×Dic139—21no—
65C2×Dic139—21no—
66C2×Dic139—21no—
67C2×Dic139—21no—
68C2×Dic139—42no—
69C2×Dic139—41no—
70C2×Dic139—41no—
71C2×Dic139—41no—
72C2×Dic139—41no—
73C2×Dic139D812yes—
74C4×D139—42no—
75C139⋊C8—41no—
76C23×C139—21no—
77C23×C139C2×D411yescharacteristic
78D4×C139—41no—
79D4×C139—41no—
80D4×C139—41no—
81C2×C4×C139—22no—
82C2×C4×C139—21no—
83C2×C4×C139—41no—
84C2×C4×C139—41no—
85C2×C4×C139—41no—
86C2×C4×C139C2×D411yescharacteristic
87C2×C4×C139C2×D411yescharacteristic
88C8×C139—41no—
89C22×C139—21no—
90C22×C139—21no—
91C22×C139—41no—
92C22×C139—41no—
93C22×C139—41no—
94C22×C139#12011yescharacteristic
95C22×C139C2×D811yescharacteristic
96C22×C139AGL(1,ℤ/8)11yescharacteristic
97C2×D139—41no—
98C2×D139—41no—
99C2×D139—41no—
100C4×C139—21no—
101C4×C139—21no—
102C4×C139—42no—
103C4×C139—41no—
104Dic139—22no—
105Dic139—41no—
106Dic139—41no—
107Dic139—81no—
108C2×C139—21no—
109C2×C139—21no—
110C2×C139—81no—
111C2×C139#44711yescharacteristic
112C2×C139#45611yescharacteristic
113C2×C139#45811yescharacteristic
114D139—81no—
115C139#161011yescharacteristic, complemented, Sylow
116#1610—1391nomaximal, Sylow
117#537—1391no—
118#480—1391no—
119#480—1391no—
120#398—1391no—
121#327—1391no—
122#327D13911yescharacteristic, complemented
123#324—1391no—
124C2×#41—2781no—
125C22⋊Q8—2781no—
126C22⋊Q8—2781no—
127#121—2781no—
128#121—2781no—
129#121—2781no—
130#121—1391no—
131#121C2×D13911yescharacteristic
132C2×C4⋊C4—2781no—
133C2×C4⋊C4—1391no—
134C2×C4⋊C4—1391no—
135#107—2781no—
136#107—2781no—
137#102—2781no—
138#102—2781no—
139C22⋊C8—1391no—
140C22⋊C8C2×D13911yescharacteristic
141#95—2781no—
142#95C2×D13911yescharacteristic
143#41—5562no—
144#41—5562no—
145C2×Q8—2781no—
146C2×D4—21no—
147C2×D4—2781no—
148C2×D4—2781no—
149C2×D4—2781no—
150C2×D4—1391no—
151C2×D4D55611yescharacteristic
152C22×C4—21no—
153C22×C4—2781no—
154C22×C4—2781no—
155C22×C4—2781no—
156C22×C4—1391no—
157C22×C4—1391no—
158C22×C4C22×D13911yescharacteristic
159C2×C8—21no—
160C2×C8—2781no—
161C4⋊C4—2781no—
162C4⋊C4—2781no—
163C4⋊C4—2781no—
164C4⋊C4—2781no—
165C4⋊C4—2781no—
166C4⋊C4—5562no—
167C4⋊C4—1391no—
168C4⋊C4D55611yescharacteristic
169C22⋊C4—21no—
170C22⋊C4—2781no—
171C22⋊C4—2781no—
172C22⋊C4—2781no—
173C23—21no—
174C23—2781no—
175C23D4×D13911yescharacteristic
176Q8—5562no—
177D4—41no—
178D4—41no—
179D4—41no—
180D4—5561no—
181D4—5562no—
182D4—5561no—
183D4—5561no—
184D4—11121no—
185C2×C4—22no—
186C2×C4—21no—
187C2×C4—41no—
188C2×C4—41no—
189C2×C4—41no—
190C2×C4—2781no—
191C2×C4—2781no—
192C2×C4—2781no—
193C2×C4—2781no—
194C2×C4—5562no—
195C2×C4—5562no—
196C2×C4—5561no—
197C2×C4—5561no—
198C2×C4—5561no—
199C2×C4—5561no—
200C2×C4—1392no—
201C2×C4D4×D13911yescharacteristic
202C2×C4C2×D55611yescharacteristic
203C8—41no—
204C8—5561no—
205C22—21no—
206C22—21no—
207C22—41no—
208C22—41no—
209C22—41no—
210C22—5561no—
211C22—5561no—
212C22—5561no—
213C22#1798481211yescharacteristic
214C22D8×D13911yescharacteristic
215C22#1798486911yescharacteristic
216C4—21no—
217C4—21no—
218C4—42no—
219C4—41no—
220C4—2782no—
221C4—5561no—
222C4—5561no—
223C4—11121no—
224C2—21no—
225C2—21no—
226C2—81no—
227C2—11121no—
228C2#2258108811yescharacteristic
229C2#2258113711yescharacteristic
230C2#2258114411yescharacteristic
subgroupG/H
centerC22#17984812
commutator, cosocleC22×C4×C139C23
FrattiniC22×C4C22×D139
Fitting#327×C139C2
socleC22×C139#120
prime radical#22581530C2
hypercenter#327D139
hypocenterC139#1610
LCSG ▷ C22×C4×C139 ▷ C22×C139 ▷ C139
UCSC1 ◁ C22 ◁ C22×C4 ◁ #327

Complements

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

NH ≅ G/Ntype
2. #22581267C2semidirect
3. #22581264C2semidirect
4. #22580885C2semidirect
5. #22580686C2semidirect
6. #22580678C2semidirect
7. #327×C139C2semidirect
115. C139#1610semidirect
122. #327D139semidirect

Maximal subgroups

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

subgroupindex
#225815302
#225812672
#225812642
#225808852
#225806862
#225806782
#327×C1392
#1610139