Finite Group Databasebeta

← #31805331

Subgroups — #31805331

Order 17792.

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

normal subgroups only

This group has 272 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#22581550C211yesmaximal, characteristic, complemented
2#22581104C211yesmaximal, characteristic, complemented
3#22581087C211yesmaximal, characteristic
4#22580689C211yesmaximal, characteristic, complemented
5#22580686C211yesmaximal, characteristic, complemented
6#22580679C211yesmaximal, characteristic, complemented
7#394×C139C211yesmaximal, characteristic, complemented
8C2×#14555773—21no—
9C2×#14555770—21no—
10#17984837—21no—
11#17984832—21no—
12#17984827—21no—
13#17984825—21no—
14#17984821C2211yescharacteristic
15#17984820—21no—
16#17984816C2211yescharacteristic
17C4×C22⋊D139—21no—
18#17984763—21no—
19#17984763—21no—
20C22⋊(C139⋊C8)C2211yescharacteristic
21C22⋊(C139⋊C8)C2211yescharacteristic
22C22×D4×C139C2211yescharacteristic
23C2×C4⋊C4×C139C2211yescharacteristic
24C2×C22⋊C4×C139—21no—
25C2×C22⋊C4×C139—21no—
26#95×C139C2211yescharacteristic
27C2×Dic278D411yescharacteristic
28C2×D556D411yescharacteristic
29C2×C22⋊D139—21no—
30C2×C4×D139—21no—
31#14555773—42no—
32#14555770—42no—
33C2×C139⋊C8—21no—
34C2×C139⋊C8—21no—
35C4⋊Dic139D411yescharacteristic
36C4⋊Dic139D411yescharacteristic
37Dic139⋊C4—21no—
38Dic139⋊C4—21no—
39Dic139⋊C4—21no—
40Dic139⋊C4—21no—
41C22⋊Dic139—21no—
42(C2×D139)⋊C4—21no—
43(C2×D139)⋊C4—21no—
44(C2×D139)⋊C4—21no—
45(C2×D139)⋊C4—21no—
46C4×Dic139—21no—
47C24×C139—21no—
48C2×D4×C139—21no—
49C2×D4×C139—21no—
50C2×D4×C139—42no—
51C22×C4×C139—21no—
52C22×C4×C139D411yescharacteristic
53C22×C4×C139D411yescharacteristic
54C22×C4×C139C2311yescharacteristic
55C4⋊C4×C139—21no—
56C4⋊C4×C139—21no—
57C22⋊C4×C139—42no—
58C22⋊C4×C139—42no—
59C22×D139—21no—
60Dic278—41no—
61D556—41no—
62C22⋊D139—41no—
63C22⋊D139—41no—
64C2×Dic139—21no—
65C2×Dic139—21no—
66C2×Dic139—21no—
67C4×D139—81no—
68C139⋊C8—41no—
69C139⋊C8—41no—
70C23×C139—22no—
71C23×C139—41no—
72C23×C139—41no—
73C23×C139—41no—
74C23×C139—41no—
75C23×C139—41no—
76C23×C139—41no—
77C23×C139C2×D411yescharacteristic
78D4×C139—22no—
79D4×C139—22no—
80D4×C139—41no—
81D4×C139—41no—
82C2×C4×C139—21no—
83C2×C4×C139—21no—
84C2×C4×C139—21no—
85C2×C4×C139—21no—
86C2×C4×C139—41no—
87C2×C4×C139—41no—
88C2×C4×C139—41no—
89C2×C4×C139—41no—
90C2×C4×C139—41no—
91C2×C4×C139C2×D411yescharacteristic
92C2×C4×C139C2×D411yescharacteristic
93C22×C139—21no—
94C22×C139—21no—
95C22×C139—42no—
96C22×C139—42no—
97C22×C139—42no—
98C22×C139—81no—
99C22×C139—81no—
100C22×C139—81no—
101C22×C139—81no—
102C22×C139#12011yescharacteristic
103C22×C139#13511yescharacteristic
104C22×C139AGL(1,ℤ/8)11yescharacteristic
105C2×D139—41no—
106C2×D139—41no—
107C2×D139—41no—
108C4×C139—21no—
109C4×C139—21no—
110C4×C139—41no—
111C4×C139—41no—
112C4×C139—81no—
113Dic139—41no—
114Dic139—41no—
115Dic139—41no—
116C2×C139—21no—
117C2×C139—21no—
118C2×C139—82no—
119C2×C139#44911yescharacteristic
120C2×C139#45411yescharacteristic
121C2×C139B(4,𝔽2)11yescharacteristic
122D139—81no—
123C139#159711yescharacteristic, complemented, Sylow
124#1597—1391nomaximal, Sylow
125#539—1391no—
126#450—1391no—
127#447—1391no—
128#394D13911yescharacteristic, complemented
129#328—1391no—
130#327—1391no—
131#324—1391no—
132C22×D4C2×D13911yescharacteristic
133C2×SD16—2781no—
134C2×D8—2781no—
135#126—2781no—
136#125—2781no—
137#123—2781no—
138#123—2781no—
139C22⋊Q8—2781no—
140C22⋊Q8—1391no—
141#121—1391no—
142C4×D4—2781no—
143C2×C4⋊C4C2×D13911yescharacteristic
144C2×C22⋊C4—21no—
145C2×C22⋊C4—21no—
146#102—2781no—
147#102—2781no—
148C22⋊C8—1391no—
149C22⋊C8—1391no—
150#95C2×D13911yescharacteristic
151C24—21no—
152C2×Q8—1391no—
153C2×D4—21no—
154C2×D4—21no—
155C2×D4—42no—
156C2×D4—2781no—
157C2×D4—1391no—
158C22×C4—21no—
159C22×C4—2781no—
160C22×C4C22⋊D13911yescharacteristic
161C22×C4C22⋊D13911yescharacteristic
162C22×C4C22×D13911yescharacteristic
163SD16—5562no—
164D8—5562no—
165C2×C8—2781no—
166C2×C8—2781no—
167C4⋊C4—21no—
168C4⋊C4—21no—
169C4⋊C4—2781no—
170C4⋊C4—2781no—
171C4⋊C4—2781no—
172C4⋊C4—2781no—
173C4⋊C4—1391no—
174C4⋊C4—1391no—
175C22⋊C4—42no—
176C22⋊C4—42no—
177C22⋊C4—2781no—
178C22⋊C4—2781no—
179C22⋊C4—2781no—
180C22⋊C4—2781no—
181C22⋊C4—2781no—
182C42—2781no—
183C23—22no—
184C23—41no—
185C23—41no—
186C23—41no—
187C23—41no—
188C23—41no—
189C23—41no—
190C23—2781no—
191C23C2×C22⋊D13911yescharacteristic
192Q8—5561no—
193D4—22no—
194D4—22no—
195D4—41no—
196D4—41no—
197D4—5561no—
198D4—5561no—
199D4—5561no—
200C2×C4—21no—
201C2×C4—21no—
202C2×C4—21no—
203C2×C4—21no—
204C2×C4—41no—
205C2×C4—41no—
206C2×C4—41no—
207C2×C4—41no—
208C2×C4—41no—
209C2×C4—2781no—
210C2×C4—2781no—
211C2×C4—2781no—
212C2×C4—11121no—
213C2×C4D4×D13911yescharacteristic
214C2×C4D4×D13911yescharacteristic
215C8—5561no—
216C8—5561no—
217C22—21no—
218C22—21no—
219C22—42no—
220C22—42no—
221C22—42no—
222C22—81no—
223C22—81no—
224C22—81no—
225C22—81no—
226C22—5561no—
227C22—5561no—
228C22—5561no—
229C22#1798481011yescharacteristic
230C22#1798486211yescharacteristic
231C22#1798486811yescharacteristic
232C4—21no—
233C4—21no—
234C4—41no—
235C4—41no—
236C4—81no—
237C4—5561no—
238C4—5561no—
239C4—5561no—
240C2—21no—
241C2—21no—
242C2—82no—
243C2—11121no—
244C2#2258109611yescharacteristic
245C2#2258112511yescharacteristic
246C2#2258113911yescharacteristic
subgroupG/H
centerC22#17984810
commutator, cosocleC22×C4×C139C23
FrattiniC22×C4C22×D139
Fitting#394×C139C2
socleC22×C139#120
prime radical#22581087C2
hypercenter#394D139
hypocenterC139#1597
LCSG ▷ C22×C4×C139 ▷ C22×C139 ▷ C139
UCSC1 ◁ C22 ◁ C22×C4 ◁ #394

Complements

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

NH ≅ G/Ntype
1. #22581550C2semidirect
2. #22581104C2semidirect
4. #22580689C2semidirect
5. #22580686C2semidirect
6. #22580679C2semidirect
7. #394×C139C2semidirect
123. C139#1597semidirect
128. #394D139semidirect

Maximal subgroups

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

subgroupindex
#225815502
#225811042
#225810872
#225806892
#225806862
#225806792
#394×C1392
#1597139