Finite Group Databasebeta

← #31805432

Subgroups — #31805432

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#22581548C211yesmaximal, characteristic
2#22581288C211yesmaximal, characteristic, complemented
3#22580891C211yesmaximal, characteristic, complemented
4#22580691C211yesmaximal, characteristic, complemented
5#22580687C211yesmaximal, characteristic
6#22580678C211yesmaximal, characteristic, complemented
7#481×C139C211yesmaximal, characteristic
8#17984835—21no—
9#17984832—21no—
10#17984823—21no—
11#17984823—21no—
12#17984821C2211yescharacteristic
13#17984819—21no—
14D4×Dic139—21no—
15C2×Dic139⋊C4C2211yescharacteristic
16#17984775—21no—
17#17984765—21no—
18C22⋊(C139⋊C8)C2211yescharacteristic
19C139⋊#95—21no—
20C139⋊#95—21no—
21C139⋊#95C2211yescharacteristic
22#121×C139C2211yescharacteristic
23C2×C4⋊C4×C139C2211yescharacteristic
24#106×C139—21no—
25#102×C139—21no—
26C22⋊C8×C139C2211yescharacteristic
27C2×Dic278D411yescharacteristic
28C22×Dic139—21no—
29C22×Dic139—21no—
30C22×Dic139D411yescharacteristic
31C22×Dic139D411yescharacteristic
32C2×C139⋊C8—21no—
33C4⋊Dic139—21no—
34C4⋊Dic139D411yescharacteristic
35Dic139⋊C4—21no—
36Dic139⋊C4—21no—
37Dic139⋊C4—21no—
38Dic139⋊C4—21no—
39Dic139⋊C4—21no—
40C22⋊Dic139—21no—
41C22⋊Dic139—21no—
42C22⋊Dic139—21no—
43C22⋊Dic139—21no—
44C4×Dic139—21no—
45C2×D4×C139—21no—
46C2×D4×C139D411yescharacteristic
47C22×C4×C139—21no—
48C22×C4×C139C2311yescharacteristic
49C2×C8×C139—21no—
50C4⋊C4×C139—21no—
51C4⋊C4×C139—21no—
52C4⋊C4×C139D411yescharacteristic
53C22⋊C4×C139—21no—
54Dic278—41no—
55C2×Dic139—21no—
56C2×Dic139—21no—
57C2×Dic139—21no—
58C2×Dic139—21no—
59C2×Dic139—21no—
60C2×Dic139—21no—
61C2×Dic139—41no—
62C2×Dic139—41no—
63C2×Dic139—41no—
64C2×Dic139—41no—
65C2×Dic139—81no—
66C139⋊C8—41no—
67C23×C139—21no—
68C23×C139C2×D411yescharacteristic
69D4×C139—41no—
70D4×C139—41no—
71D4×C139—41no—
72C2×C4×C139—21no—
73C2×C4×C139—41no—
74C2×C4×C139—42no—
75C2×C4×C139—41no—
76C2×C4×C139C2×D411yescharacteristic
77C2×C4×C139C2×D411yescharacteristic
78C8×C139—41no—
79C22×C139—21no—
80C22×C139—21no—
81C22×C139—41no—
82C22×C139—41no—
83C22×C139—41no—
84C22×C139#12011yescharacteristic
85C22×C139#13511yescharacteristic
86C22×C139#13711yescharacteristic
87C4×C139—21no—
88C4×C139—21no—
89C4×C139—41no—
90C4×C139—81no—
91Dic139—41no—
92Dic139—41no—
93Dic139—41no—
94Dic139—41no—
95Dic139—81no—
96C2×C139—21no—
97C2×C139—21no—
98C2×C139—81no—
99C2×C139#45211yescharacteristic
100C2×C139#45411yescharacteristic
101C2×C139#45811yescharacteristic
102C139#161511yescharacteristic, complemented, Sylow
103#1615—1391nomaximal, Sylow
104#539—1391no—
105#484—1391no—
106#481D13911yescharacteristic
107#400—1391no—
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#121C2×D13911yescharacteristic
118C4×D4—2781no—
119C2×C4⋊C4—1391no—
120C2×C4⋊C4C2×D13911yescharacteristic
121#107—2781no—
122#106—21no—
123#103—2781no—
124#102—21no—
125C22⋊C8—1391no—
126C22⋊C8C2×D13911yescharacteristic
127#95—2781no—
128#95—2781no—
129#95—1391no—
130C2×Q8—1391no—
131C2×D4—21no—
132C2×D4C22⋊D13911yescharacteristic
133C22×C4—21no—
134C22×C4—2781no—
135C22×C4—2781no—
136C22×C4—1391no—
137C22×C4—1391no—
138C22×C4C22×D13911yescharacteristic
139C2×C8—21no—
140C2×C8—2781no—
141C4⋊C4—21no—
142C4⋊C4—21no—
143C4⋊C4—2781no—
144C4⋊C4—2781no—
145C4⋊C4—2781no—
146C4⋊C4—2781no—
147C4⋊C4—2781no—
148C4⋊C4—2781no—
149C4⋊C4—1391no—
150C4⋊C4C22⋊D13911yescharacteristic
151C22⋊C4—21no—
152C22⋊C4—2781no—
153C22⋊C4—2781no—
154C22⋊C4—2781no—
155C22⋊C4—2781no—
156C42—2781no—
157C23—21no—
158C23D4×D13911yescharacteristic
159Q8—5561no—
160D4—41no—
161D4—41no—
162D4—41no—
163C2×C4—21no—
164C2×C4—41no—
165C2×C4—42no—
166C2×C4—41no—
167C2×C4—2781no—
168C2×C4—2781no—
169C2×C4—2781no—
170C2×C4—2781no—
171C2×C4—2781no—
172C2×C4—2781no—
173C2×C4—5561no—
174C2×C4—5561no—
175C2×C4—5561no—
176C2×C4—5561no—
177C2×C4—11121no—
178C2×C4D4×D13911yescharacteristic
179C2×C4C2×C22⋊D13911yescharacteristic
180C8—41no—
181C8—5561no—
182C22—21no—
183C22—21no—
184C22—41no—
185C22—41no—
186C22—41no—
187C22#1798481011yescharacteristic
188C22#1798486311yescharacteristic
189C22#1798487111yescharacteristic
190C4—21no—
191C4—21no—
192C4—41no—
193C4—81no—
194C4—5561no—
195C4—5561no—
196C4—5561no—
197C4—5561no—
198C4—11121no—
199C2—21no—
200C2—21no—
201C2—81no—
202C2#2258111211yescharacteristic
203C2#2258112411yescharacteristic
204C2#2258114211yescharacteristic
subgroupG/H
centerC22#17984810
commutator, cosocleC22×C4×C139C23
FrattiniC22×C4C22×D139
Fitting#481×C139C2
socleC22×C139#120
prime radical#121×C139C22
hypercenter#481D139
hypocenterC139#1615
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. #22581288C2semidirect
3. #22580891C2semidirect
4. #22580691C2semidirect
6. #22580678C2semidirect
102. C139#1615semidirect

Maximal subgroups

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

subgroupindex
#225815482
#225812882
#225808912
#225806912
#225806872
#225806782
#481×C1392
#1615139