Finite Group Databasebeta

← #31805379

Subgroups — #31805379

Order 17792.

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

normal subgroups only

This group has 238 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#22581111C211yesmaximal, characteristic
3#22581108C211yesmaximal, characteristic
4#22580874C211yesmaximal, characteristic
5#22580689C211yesmaximal, characteristic
6#22580678C211yesmaximal, characteristic
7#328×C139C211yesmaximal, characteristic
8C22×Dic278C2211yescharacteristic
9C2×Dic556—21no—
10C2×#14555775—21no—
11#17984841—21no—
12#17984840—21no—
13#17984832—21no—
14#17984832—21no—
15#17984821C2211yescharacteristic
16#17984819—21no—
17#17984798—21no—
18C2×C4⋊Dic139—21no—
19C2×Dic139⋊C4C2211yescharacteristic
20#17984767—21no—
21#17984765—21no—
22C22⋊(C139⋊C8)C2211yescharacteristic
23C139⋊#95—21no—
24C22⋊Q8×C139C2211yescharacteristic
25C22⋊C8×C139C2211yescharacteristic
26#95×C139C2211yescharacteristic
27C2×Dic278—21no—
28C2×Dic278—21no—
29C2×Dic278—21no—
30C2×Dic278—42no—
31C2×Dic278D411yescharacteristic
32C22×Dic139—21no—
33C22×Dic139D411yescharacteristic
34C22×Dic139D411yescharacteristic
35Dic556—42no—
36#14555775—42no—
37C2×C139⋊C8—21no—
38C4⋊Dic139—21no—
39C4⋊Dic139—42no—
40C4⋊Dic139D411yescharacteristic
41Dic139⋊C4—21no—
42Dic139⋊C4—21no—
43Dic139⋊C4—21no—
44Dic139⋊C4—21no—
45Dic139⋊C4—21no—
46Dic139⋊C4—21no—
47Dic139⋊C4—21no—
48C22⋊Dic139—21no—
49C4×Dic139—21no—
50C4×Dic139—21no—
51C2×Q8×C139D411yescharacteristic
52C22×C4×C139—21no—
53C22×C4×C139C2311yescharacteristic
54C2×C8×C139—21no—
55C4⋊C4×C139—21no—
56C4⋊C4×C139D411yescharacteristic
57C22⋊C4×C139—21no—
58Dic278—22no—
59Dic278—22no—
60Dic278—41no—
61Dic278—41no—
62Dic278—41no—
63Dic278—81no—
64C2×Dic139—21no—
65C2×Dic139—21no—
66C2×Dic139—22no—
67C2×Dic139—21no—
68C2×Dic139—21no—
69C2×Dic139—21no—
70C2×Dic139—41no—
71C2×Dic139—41no—
72C2×Dic139—41no—
73C2×Dic139Q1612yescomplemented
74C139⋊C8—41no—
75C23×C139C2×D411yescharacteristic
76Q8×C139—41no—
77C2×C4×C139—22no—
78C2×C4×C139—21no—
79C2×C4×C139—21no—
80C2×C4×C139—41no—
81C2×C4×C139—41no—
82C2×C4×C139—41no—
83C2×C4×C139C2×D411yescharacteristic
84C2×C4×C139C2×D411yescharacteristic
85C8×C139—41no—
86C22×C139—21no—
87C22×C139—21no—
88C22×C139#12011yescharacteristic
89C22×C139C2×Q1611yescharacteristic
90C22×C139#13711yescharacteristic
91C4×C139—21no—
92C4×C139—21no—
93C4×C139—42no—
94C4×C139—41no—
95C4×C139—41no—
96Dic139—22no—
97Dic139—41no—
98Dic139—42no—
99Dic139—41no—
100Dic139—41no—
101C2×C139—21no—
102C2×C139—21no—
103C2×C139#45111yescharacteristic
104C2×C139#45611yescharacteristic
105C2×C139B(4,𝔽2)11yescharacteristic
106C139#160511yescharacteristic, complemented, Sylow
107#1605—1391nomaximal, Sylow
108#544—1391no—
109#451—1391no—
110#451—1391no—
111#395—1391no—
112#328—1391no—
113#328D13911yescharacteristic
114#324—1391no—
115C22×Q8—1391no—
116C2×Q16—2781no—
117C2×Q16—2781no—
118C4⋊Q8—2781no—
119C4⋊Q8—2781no—
120#125—2781no—
121#125—2781no—
122C22⋊Q8—2781no—
123C22⋊Q8—1391no—
124C22⋊Q8C2×D13911yescharacteristic
125#117—2781no—
126C2×C4⋊C4—2781no—
127C2×C4⋊C4—1391no—
128#103—2781no—
129#103—2781no—
130C22⋊C8—1391no—
131C22⋊C8C2×D13911yescharacteristic
132#95—2781no—
133#95C2×D13911yescharacteristic
134C2×Q8—2781no—
135C2×Q8—2781no—
136C2×Q8—2781no—
137C2×Q8—5562no—
138C2×Q8—1391no—
139C2×Q8D55611yescharacteristic
140C22×C4—21no—
141C22×C4—2781no—
142C22×C4—1391no—
143C22×C4—1391no—
144C22×C4C22×D13911yescharacteristic
145Q16—5562no—
146Q16—5562no—
147C2×C8—21no—
148C2×C8—2781no—
149C4⋊C4—21no—
150C4⋊C4—2781no—
151C4⋊C4—2781no—
152C4⋊C4—2781no—
153C4⋊C4—2781no—
154C4⋊C4—2781no—
155C4⋊C4—2781no—
156C4⋊C4—2781no—
157C4⋊C4—2781no—
158C4⋊C4—5562no—
159C4⋊C4—1391no—
160C4⋊C4D55611yescharacteristic
161C22⋊C4—21no—
162C22⋊C4—2781no—
163C42—2781no—
164C42—2781no—
165C23D4×D13911yescharacteristic
166Q8—41no—
167Q8—2782no—
168Q8—2782no—
169Q8—5561no—
170Q8—5561no—
171Q8—5561no—
172Q8—11121no—
173C2×C4—22no—
174C2×C4—21no—
175C2×C4—21no—
176C2×C4—41no—
177C2×C4—41no—
178C2×C4—41no—
179C2×C4—2781no—
180C2×C4—2781no—
181C2×C4—2782no—
182C2×C4—2781no—
183C2×C4—2781no—
184C2×C4—2781no—
185C2×C4—5561no—
186C2×C4—5561no—
187C2×C4—5561no—
188C2×C4—1392no—
189C2×C4D4×D13911yescharacteristic
190C2×C4C2×D55611yescharacteristic
191C8—41no—
192C8—5561no—
193C22—21no—
194C22—21no—
195C22#1798481211yescharacteristic
196C22Q16×D13911yescharacteristic
197C22#1798487111yescharacteristic
198C4—21no—
199C4—21no—
200C4—42no—
201C4—41no—
202C4—41no—
203C4—2782no—
204C4—5561no—
205C4—5562no—
206C4—5561no—
207C4—5561no—
208C2—21no—
209C2—21no—
210C2#2258111011yescharacteristic
211C2#2258113711yescharacteristic
212C2#2258114111yescharacteristic
subgroupG/H
centerC22#17984812
commutator, cosocleC22×C4×C139C23
FrattiniC22×C4C22×D139
Fitting#328×C139C2
socleC22×C139#120
prime radicalC23×C139C2×D4
hypercenter#328D139
hypocenterC139#1605
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
73. C2×Dic139Q16semidirect
106. C139#1605semidirect

Maximal subgroups

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

subgroupindex
#225815822
#225811112
#225811082
#225808742
#225806892
#225806782
#328×C1392
#1605139