Finite Group Databasebeta

← #31805447

Subgroups — #31805447

Order 17792.

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

normal subgroups only

This group has 202 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#22581582C211yesmaximal, characteristic
2#22581289C211yesmaximal, characteristic
3#22581286C211yesmaximal, characteristic
4#22580893C211yesmaximal, characteristic
5#22580689C211yesmaximal, characteristic
6#22580678C211yesmaximal, characteristic
7#328×C139C211yesmaximal, characteristic
8#17984841—21no—
9#17984840—21no—
10#17984832—21no—
11#17984832—21no—
12#17984821C2211yescharacteristic
13#17984819—21no—
14#17984798—21no—
15C2×C4⋊Dic139C2211yescharacteristic
16C2×Dic139⋊C4C2211yescharacteristic
17#17984776—21no—
18#17984775—21no—
19#17984767—21no—
20#17984766—21no—
21C22⋊(C139⋊C8)C2211yescharacteristic
22C139⋊#95—21no—
23C139⋊#95—21no—
24C22⋊Q8×C139C2211yescharacteristic
25C22⋊C8×C139C2211yescharacteristic
26#95×C139C2211yescharacteristic
27C2×Dic278—21no—
28C2×Dic278D411yescharacteristic
29C22×Dic139—21no—
30C22×Dic139D411yescharacteristic
31C22×Dic139D411yescharacteristic
32C2×C139⋊C8—21no—
33C4⋊Dic139—21no—
34C4⋊Dic139—21no—
35C4⋊Dic139—21no—
36C4⋊Dic139D411yescharacteristic
37Dic139⋊C4—21no—
38Dic139⋊C4—21no—
39Dic139⋊C4—21no—
40Dic139⋊C4—21no—
41Dic139⋊C4—21no—
42Dic139⋊C4—21no—
43Dic139⋊C4—21no—
44C22⋊Dic139—21no—
45C4×Dic139—21no—
46C4×Dic139—21no—
47C2×Q8×C139D411yescharacteristic
48C22×C4×C139—21no—
49C22×C4×C139C2311yescharacteristic
50C2×C8×C139—21no—
51C4⋊C4×C139—21no—
52C4⋊C4×C139D411yescharacteristic
53C22⋊C4×C139—21no—
54Dic278—41no—
55Dic278—81no—
56C2×Dic139—21no—
57C2×Dic139—21no—
58C2×Dic139—21no—
59C2×Dic139—21no—
60C2×Dic139—21no—
61C2×Dic139—41no—
62C2×Dic139—42no—
63C2×Dic139—41no—
64C2×Dic139Q1612yes—
65C139⋊C8—41no—
66C23×C139C2×D411yescharacteristic
67Q8×C139—41no—
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×C139C2×D411yescharacteristic
75C2×C4×C139C2×D411yescharacteristic
76C8×C139—41no—
77C22×C139—21no—
78C22×C139—21no—
79C22×C139#12011yescharacteristic
80C22×C139C2×Q1611yescharacteristic
81C22×C139#13711yescharacteristic
82C4×C139—21no—
83C4×C139—21no—
84C4×C139—41no—
85C4×C139—41no—
86C4×C139—81no—
87Dic139—22no—
88Dic139—41no—
89Dic139—41no—
90Dic139—41no—
91Dic139—81no—
92C2×C139—21no—
93C2×C139—21no—
94C2×C139#45111yescharacteristic
95C2×C139#45411yescharacteristic
96C2×C139#45811yescharacteristic
97C139#161711yescharacteristic, complemented, Sylow
98#1617—1391nomaximal, Sylow
99#544—1391no—
100#484—1391no—
101#484—1391no—
102#400—1391no—
103#328—1391no—
104#328D13911yescharacteristic
105#324—1391no—
106C4⋊Q8—2781no—
107C4⋊Q8—2781no—
108#125—2781no—
109#125—2781no—
110C22⋊Q8—2781no—
111C22⋊Q8—1391no—
112C22⋊Q8C2×D13911yescharacteristic
113#117—2781no—
114C2×C4⋊C4—1391no—
115C2×C4⋊C4—1391no—
116#107—2781no—
117#107—2781no—
118#103—2781no—
119#103—2781no—
120C22⋊C8—1391no—
121C22⋊C8C2×D13911yescharacteristic
122#95—2781no—
123#95—2781no—
124#95C2×D13911yescharacteristic
125C2×Q8—2781no—
126C2×Q8—1391no—
127C2×Q8D55611yescharacteristic
128C22×C4—21no—
129C22×C4—2781no—
130C22×C4—1391no—
131C22×C4—1391no—
132C22×C4C22×D13911yescharacteristic
133C2×C8—21no—
134C2×C8—2781no—
135C4⋊C4—21no—
136C4⋊C4—2781no—
137C4⋊C4—2781no—
138C4⋊C4—2781no—
139C4⋊C4—2781no—
140C4⋊C4—2781no—
141C4⋊C4—2781no—
142C4⋊C4—2781no—
143C4⋊C4—2781no—
144C4⋊C4—2781no—
145C4⋊C4—2781no—
146C4⋊C4—1391no—
147C4⋊C4D55611yescharacteristic
148C22⋊C4—21no—
149C22⋊C4—2781no—
150C42—2781no—
151C42—2781no—
152C23D4×D13911yescharacteristic
153Q8—41no—
154Q8—5561no—
155Q8—11121no—
156C2×C4—21no—
157C2×C4—21no—
158C2×C4—41no—
159C2×C4—41no—
160C2×C4—41no—
161C2×C4—41no—
162C2×C4—2781no—
163C2×C4—2781no—
164C2×C4—2781no—
165C2×C4—2781no—
166C2×C4—2781no—
167C2×C4—5561no—
168C2×C4—5562no—
169C2×C4—5561no—
170C2×C4—1392no—
171C2×C4D4×D13911yescharacteristic
172C2×C4C2×D55611yescharacteristic
173C8—41no—
174C8—5561no—
175C22—21no—
176C22—21no—
177C22#1798481211yescharacteristic
178C22Q16×D13911yescharacteristic
179C22#1798487111yescharacteristic
180C4—21no—
181C4—21no—
182C4—41no—
183C4—41no—
184C4—81no—
185C4—2782no—
186C4—5561no—
187C4—5561no—
188C4—5561no—
189C4—11121no—
190C2—21no—
191C2—21no—
192C2#2258111011yescharacteristic
193C2#2258112711yescharacteristic
194C2#2258114411yescharacteristic
subgroupG/H
centerC22#17984812
commutator, cosocleC22×C4×C139C23
FrattiniC22×C4C22×D139
Fitting#328×C139C2
socleC22×C139#120
prime radicalC23×C139C2×D4
hypercenter#328D139
hypocenterC139#1617
LCSG ▷ C22×C4×C139 ▷ C22×C139 ▷ C139
UCSC1 ◁ C22 ◁ C22×C4 ◁ #328

Complements

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

NH ≅ G/Ntype
97. C139#1617semidirect

Maximal subgroups

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

subgroupindex
#225815822
#225812892
#225812862
#225808932
#225806892
#225806782
#328×C1392
#1617139