Finite Group Databasebeta

← #31805433

Subgroups — #31805433

Order 17792.

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

normal subgroups only

This group has 208 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
2#22581288C211yesmaximal, characteristic, complemented
3#22581271C211yesmaximal, characteristic
4#22580689C211yesmaximal, characteristic, complemented
5#22580686C211yesmaximal, characteristic
6#22580679C211yesmaximal, characteristic, complemented
7#400×C139C211yesmaximal, characteristic, complemented
8#17984837—21no—
9#17984832—21no—
10#17984827—21no—
11#17984825—21no—
12#17984821C2211yescharacteristic
13#17984820—21no—
14#17984816C2211yescharacteristic
15C4×C22⋊D139—21no—
16#17984775—21no—
17#17984773—21no—
18#17984765—21no—
19#17984762—21no—
20C22⋊(C139⋊C8)C2211yescharacteristic
21C22⋊(C139⋊C8)C2211yescharacteristic
22C2×C4⋊C4×C139C2211yescharacteristic
23C2×C4⋊C4×C139C2211yescharacteristic
24#95×C139—21no—
25#95×C139—21no—
26#95×C139C2211yescharacteristic
27C2×Dic278D411yescharacteristic
28C2×D556D411yescharacteristic
29C2×C22⋊D139—21no—
30C2×C4×D139—21no—
31C2×C139⋊C8—21no—
32C2×C139⋊C8—21no—
33C4⋊Dic139D411yescharacteristic
34C4⋊Dic139D411yescharacteristic
35Dic139⋊C4—21no—
36Dic139⋊C4—21no—
37Dic139⋊C4—21no—
38Dic139⋊C4—21no—
39C22⋊Dic139—21no—
40(C2×D139)⋊C4—21no—
41(C2×D139)⋊C4—21no—
42(C2×D139)⋊C4—21no—
43(C2×D139)⋊C4—21no—
44C4×Dic139—21no—
45C22×C4×C139—21no—
46C22×C4×C139—21no—
47C22×C4×C139D411yescharacteristic
48C22×C4×C139D411yescharacteristic
49C22×C4×C139C2311yescharacteristic
50C4⋊C4×C139—21no—
51C4⋊C4×C139—21no—
52C4⋊C4×C139—21no—
53C4⋊C4×C139—21no—
54C22×D139—21no—
55Dic278—41no—
56D556—41no—
57C22⋊D139—41no—
58C22⋊D139—41no—
59C2×Dic139—21no—
60C2×Dic139—21no—
61C2×Dic139—21no—
62C4×D139—81no—
63C139⋊C8—41no—
64C139⋊C8—41no—
65C23×C139C2×D411yescharacteristic
66C2×C4×C139—21no—
67C2×C4×C139—21no—
68C2×C4×C139—21no—
69C2×C4×C139—21no—
70C2×C4×C139—41no—
71C2×C4×C139—41no—
72C2×C4×C139—41no—
73C2×C4×C139—41no—
74C2×C4×C139—42no—
75C2×C4×C139—41no—
76C2×C4×C139—41no—
77C2×C4×C139C2×D411yescharacteristic
78C2×C4×C139C2×D411yescharacteristic
79C22×C139—21no—
80C22×C139—21no—
81C22×C139#12011yescharacteristic
82C22×C139#13511yescharacteristic
83C22×C139#13711yescharacteristic
84C2×D139—41no—
85C2×D139—41no—
86C2×D139—41no—
87C4×C139—21no—
88C4×C139—21no—
89C4×C139—41no—
90C4×C139—41no—
91C4×C139—81no—
92C4×C139—81no—
93Dic139—41no—
94Dic139—41no—
95Dic139—41no—
96C2×C139—21no—
97C2×C139—21no—
98C2×C139#45211yescharacteristic
99C2×C139#45411yescharacteristic
100C2×C139#45811yescharacteristic
101D139—81no—
102C139#161511yescharacteristic, complemented, Sylow
103#1615—1391nomaximal, Sylow
104#539—1391no—
105#484—1391no—
106#481—1391no—
107#400D13911yescharacteristic, complemented
108#328—1391no—
109#327—1391no—
110#324—1391no—
111#126—2781no—
112#125—2781no—
113#123—2781no—
114#123—2781no—
115C22⋊Q8—2781no—
116C22⋊Q8—1391no—
117#121—1391no—
118C4×D4—2781no—
119C2×C4⋊C4C2×D13911yescharacteristic
120C2×C4⋊C4C2×D13911yescharacteristic
121#107—2781no—
122#106—2781no—
123#103—2781no—
124#102—2781no—
125C22⋊C8—1391no—
126C22⋊C8—1391no—
127#95—21no—
128#95—21no—
129#95C2×D13911yescharacteristic
130C2×Q8—1391no—
131C2×D4—2781no—
132C2×D4—1391no—
133C22×C4—21no—
134C22×C4—21no—
135C22×C4—2781no—
136C22×C4C22⋊D13911yescharacteristic
137C22×C4C22⋊D13911yescharacteristic
138C22×C4C22×D13911yescharacteristic
139C2×C8—2781no—
140C2×C8—2781no—
141C4⋊C4—21no—
142C4⋊C4—21no—
143C4⋊C4—21no—
144C4⋊C4—21no—
145C4⋊C4—2781no—
146C4⋊C4—2781no—
147C4⋊C4—2781no—
148C4⋊C4—2781no—
149C4⋊C4—1391no—
150C4⋊C4—1391no—
151C22⋊C4—2781no—
152C22⋊C4—2781no—
153C22⋊C4—2781no—
154C22⋊C4—2781no—
155C22⋊C4—2781no—
156C42—2781no—
157C23—2781no—
158C23C2×C22⋊D13911yescharacteristic
159Q8—5561no—
160D4—5561no—
161D4—5561no—
162D4—5561no—
163C2×C4—21no—
164C2×C4—21no—
165C2×C4—21no—
166C2×C4—21no—
167C2×C4—41no—
168C2×C4—41no—
169C2×C4—41no—
170C2×C4—41no—
171C2×C4—42no—
172C2×C4—41no—
173C2×C4—41no—
174C2×C4—2781no—
175C2×C4—2781no—
176C2×C4—2781no—
177C2×C4—11121no—
178C2×C4D4×D13911yescharacteristic
179C2×C4D4×D13911yescharacteristic
180C8—5561no—
181C8—5561no—
182C22—21no—
183C22—21no—
184C22—5561no—
185C22—5561no—
186C22—5561no—
187C22#1798481011yescharacteristic
188C22#1798486211yescharacteristic
189C22#1798487311yescharacteristic
190C4—21no—
191C4—21no—
192C4—41no—
193C4—41no—
194C4—81no—
195C4—81no—
196C4—5561no—
197C4—5561no—
198C4—5561no—
199C2—21no—
200C2—21no—
201C2—11121no—
202C2#2258111311yescharacteristic
203C2#2258112511yescharacteristic
204C2#2258114211yescharacteristic
subgroupG/H
centerC22#17984810
commutator, cosocleC22×C4×C139C23
FrattiniC22×C4C22×D139
Fitting#400×C139C2
socleC22×C139#120
prime radical#17984816C22
hypercenter#400D139
hypocenterC139#1615
LCSG ▷ C22×C4×C139 ▷ C22×C139 ▷ C139
UCSC1 ◁ C22 ◁ C22×C4 ◁ #400

Complements

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

NH ≅ G/Ntype
2. #22581288C2semidirect
4. #22580689C2semidirect
6. #22580679C2semidirect
7. #400×C139C2semidirect
102. C139#1615semidirect
107. #400D139semidirect

Maximal subgroups

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

subgroupindex
#225815502
#225812882
#225812712
#225806892
#225806862
#225806792
#400×C1392
#1615139