Finite Group Databasebeta

← #31805442

Subgroups — #31805442

Order 17792.

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

normal subgroups only

This group has 246 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#22581272C211yesmaximal, characteristic, complemented
3#22581269C211yesmaximal, characteristic, complemented
4#22580893C211yesmaximal, 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⋊Dic139C2211yescharacteristic
16C2×Dic139⋊C4C2211yescharacteristic
17#17984774—21no—
18#17984773—21no—
19#17984764—21no—
20#17984763—21no—
21C22⋊(C139⋊C8)C2211yescharacteristic
22C139⋊#95—21no—
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⋊Dic139D411yescharacteristic
43Dic139⋊C4—21no—
44Dic139⋊C4—21no—
45Dic139⋊C4—21no—
46C22⋊Dic139—21no—
47(C2×D139)⋊C4—21no—
48(C2×D139)⋊C4—21no—
49C2×D4×C139—21no—
50C2×D4×C139D411yescharacteristic
51C22×C4×C139—21no—
52C22×C4×C139C2311yescharacteristic
53C2×C8×C139—21no—
54C4⋊C4×C139D411yescharacteristic
55C22⋊C4×C139—21no—
56C22×D139—21no—
57Dic278—42no—
58D556—41no—
59C22⋊D139—42no—
60C22⋊D139—41no—
61C22⋊D139—41no—
62C22⋊D139—81no—
63C2×Dic139—21no—
64C2×Dic139—21no—
65C2×Dic139—21no—
66C2×Dic139—21no—
67C2×Dic139—42no—
68C2×Dic139—41no—
69C2×Dic139—42no—
70C2×Dic139—41no—
71C2×Dic139SD1612yes—
72C4×D139—42no—
73C139⋊C8—41no—
74C23×C139—21no—
75C23×C139C2×D411yescharacteristic
76D4×C139—41no—
77D4×C139—41no—
78D4×C139—41no—
79C2×C4×C139—21no—
80C2×C4×C139—41no—
81C2×C4×C139—41no—
82C2×C4×C139—41no—
83C2×C4×C139—41no—
84C2×C4×C139C2×D411yescharacteristic
85C2×C4×C139C2×D411yescharacteristic
86C8×C139—41no—
87C22×C139—21no—
88C22×C139—21no—
89C22×C139—41no—
90C22×C139—41no—
91C22×C139—41no—
92C22×C139#12011yescharacteristic
93C22×C139C2×SD1611yescharacteristic
94C22×C139AGL(1,ℤ/8)11yescharacteristic
95C2×D139—41no—
96C2×D139—41no—
97C2×D139—41no—
98C4×C139—21no—
99C4×C139—21no—
100C4×C139—41no—
101C4×C139—81no—
102Dic139—22no—
103Dic139—41no—
104Dic139—41no—
105Dic139—81no—
106C2×C139—21no—
107C2×C139—21no—
108C2×C139—81no—
109C2×C139#45011yescharacteristic
110C2×C139#45411yescharacteristic
111C2×C139#45811yescharacteristic
112D139—81no—
113C139#161611yescharacteristic, complemented, Sylow
114#1616—1391nomaximal, Sylow
115#537—1391no—
116#481—1391no—
117#481—1391no—
118#400—1391no—
119#327—1391no—
120#327D13911yescharacteristic, complemented
121#324—1391no—
122C2×#41—2781no—
123C22⋊Q8—2781no—
124C22⋊Q8—2781no—
125#121—2781no—
126#121—2781no—
127#121—2781no—
128#121—1391no—
129#121C2×D13911yescharacteristic
130C2×C4⋊C4—1391no—
131C2×C4⋊C4—1391no—
132#106—2781no—
133#106—2781no—
134#102—2781no—
135#102—2781no—
136C22⋊C8—1391no—
137C22⋊C8C2×D13911yescharacteristic
138#95—2781no—
139#95—2781no—
140#95C2×D13911yescharacteristic
141#41—5562no—
142#41—5562no—
143C2×Q8—2781no—
144C2×D4—21no—
145C2×D4—2781no—
146C2×D4—2781no—
147C2×D4—2781no—
148C2×D4—1391no—
149C2×D4D55611yescharacteristic
150C22×C4—21no—
151C22×C4—2781no—
152C22×C4—2781no—
153C22×C4—2781no—
154C22×C4—1391no—
155C22×C4—1391no—
156C22×C4C22×D13911yescharacteristic
157C2×C8—21no—
158C2×C8—2781no—
159C4⋊C4—2781no—
160C4⋊C4—2781no—
161C4⋊C4—2781no—
162C4⋊C4—2781no—
163C4⋊C4—2781no—
164C4⋊C4—1391no—
165C4⋊C4D55611yescharacteristic
166C22⋊C4—21no—
167C22⋊C4—2781no—
168C22⋊C4—2781no—
169C22⋊C4—2781no—
170C23—21no—
171C23—2781no—
172C23D4×D13911yescharacteristic
173Q8—5562no—
174D4—41no—
175D4—41no—
176D4—41no—
177D4—5561no—
178D4—5562no—
179D4—5561no—
180D4—5561no—
181D4—11121no—
182C2×C4—21no—
183C2×C4—41no—
184C2×C4—41no—
185C2×C4—41no—
186C2×C4—41no—
187C2×C4—2781no—
188C2×C4—2781no—
189C2×C4—2781no—
190C2×C4—2781no—
191C2×C4—5562no—
192C2×C4—5562no—
193C2×C4—5561no—
194C2×C4—5562no—
195C2×C4—5561no—
196C2×C4—1392no—
197C2×C4D4×D13911yescharacteristic
198C2×C4C2×D55611yescharacteristic
199C8—41no—
200C8—5561no—
201C22—21no—
202C22—21no—
203C22—41no—
204C22—41no—
205C22—41no—
206C22—5561no—
207C22—5561no—
208C22—5561no—
209C22#1798481211yescharacteristic
210C22SD16×D13911yescharacteristic
211C22#1798486611yescharacteristic
212C4—21no—
213C4—21no—
214C4—41no—
215C4—81no—
216C4—2782no—
217C4—5561no—
218C4—5561no—
219C4—11121no—
220C2—21no—
221C2—21no—
222C2—81no—
223C2—11121no—
224C2#2258110511yescharacteristic
225C2#2258112711yescharacteristic
226C2#2258114411yescharacteristic
subgroupG/H
centerC22#17984812
commutator, cosocleC22×C4×C139C23
FrattiniC22×C4C22×D139
Fitting#327×C139C2
socleC22×C139#120
prime radical#22581530C2
hypercenter#327D139
hypocenterC139#1616
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. #22581272C2semidirect
3. #22581269C2semidirect
4. #22580893C2semidirect
5. #22580686C2semidirect
6. #22580678C2semidirect
7. #327×C139C2semidirect
113. C139#1616semidirect
120. #327D139semidirect

Maximal subgroups

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

subgroupindex
#225815302
#225812722
#225812692
#225808932
#225806862
#225806782
#327×C1392
#1616139