Finite Group Databasebeta

← #31806620

Subgroups — #31806620

Order 17792.

272 conjugacy classes of subgroups; only the 83 normal subgroups are shown.

normal subgroups only

This group has 272 conjugacy classes of subgroups — too many to draw. Only its 83 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#22581430C211yesmaximal, characteristic
2#22580996C211yesmaximal, characteristic
3#22580995C211yesmaximal, characteristic
4C2×#17984760C211yesmaximal, characteristic
5#22580859C211yesmaximal, characteristic
6#22580713C211yesmaximal, characteristic
7#339×C139C211yesmaximal, characteristic
8C22×Dic278C2211yescharacteristic
9C2×#14555769C2211yescharacteristic
10C4×Dic278—21no—
11C4×Dic278—21no—
12#17984807—21no—
13#17984807—21no—
14#17984801C2211yescharacteristic
15#17984798—22no—
16C2×C4⋊Dic139C2211yescharacteristic
17#17984776—21no—
18#17984775—21no—
19#17984774—21no—
20#17984773—21no—
21#17984760C414yescomplemented
22C139⋊#95—22no—
23C2×M16×C139C2211yescharacteristic
24#117×C139C2211yescharacteristic
25C2×C42×C139C2211yescharacteristic
26C2×Dic278—21no—
27C2×Dic278—21no—
28C2×Dic278—21no—
29C2×Dic278—21no—
30C2×Dic278C2×C412yes—
31C2×Dic278Q812yes—
32C22×Dic139—21no—
33C22×Dic139D412yes—
34#14555769—21no—
35#14555769C2×C412yes—
36C2×C139⋊C8—21no—
37C4⋊Dic139—21no—
38C4⋊Dic139—21no—
39C4⋊Dic139D411yescharacteristic
40C4⋊Dic139D411yescharacteristic
41Dic139⋊C4—22no—
42Dic139⋊C4—22no—
43C22⋊Dic139—21no—
44C4×Dic139—22no—
45C4×Dic139—22no—
46C4×Dic139—21no—
47C22×C4×C139—21no—
48C22×C4×C139C2311yescharacteristic
49M16×C139—21no—
50M16×C139C2×C412yes—
51C2×C8×C139—21no—
52C4⋊C4×C139D411yescharacteristic
53C4⋊C4×C139D411yescharacteristic
54C22⋊C4×C139—21no—
55C42×C139—21no—
56C42×C139—21no—
57C42×C139—21no—
58Dic278—22no—
59Dic278—22no—
60Dic278—22no—
61Dic278—22no—
62C2×Dic139—22no—
63C2×Dic139—22no—
64C2×Dic139—21no—
65C2×Dic139—21no—
66C2×Dic139—42no—
67C2×Dic139—41no—
68C2×Dic139C4⋊C414yes—
69C139⋊C8—22no—
70C23×C139C2×D411yescharacteristic
71C2×C4×C139—22no—
72C2×C4×C139—21no—
73C2×C4×C139—21no—
74C2×C4×C139—41no—
75C2×C4×C139—41no—
76C2×C4×C139C22×C411yescharacteristic
77C2×C4×C139C2×D411yescharacteristic
78C2×C4×C139C2×D411yescharacteristic
79C2×C4×C139C2×Q811yescharacteristic
80C2×C4×C139#4111yescharacteristic
81C2×C4×C139#4111yescharacteristic
82C8×C139—22no—
83C22×C139—21no—
84C22×C139—21no—
85C22×C139C2×C4⋊C411yescharacteristic
86C22×C139#12011yescharacteristic
87C22×C139#12311yescharacteristic
88C4×C139—42no—
89C4×C139—41no—
90C4×C139—41no—
91C4×C139C4×D411yescharacteristic
92C4×C139C4×D411yescharacteristic
93C4×C139C22⋊Q811yescharacteristic
94C4×C139C22⋊Q811yescharacteristic
95Dic139—24no—
96Dic139—41no—
97Dic139—41no—
98Dic139—81no—
99C2×C139—21no—
100C2×C139—21no—
101C2×C139#38511yescharacteristic
102C2×C139#45411yescharacteristic
103C2×C139#45611yescharacteristic
104C139#185711yescharacteristic, complemented, Sylow
105#1857—1391nomaximal, Sylow
106#519—1391no—
107#428—1391no—
108#428—1391no—
109C2×#101—1391no—
110#391—1391no—
111#339—1391no—
112#339D13911yescharacteristic
113C22×Q8—1391no—
114C2×M16—1391no—
115C2×M16C2×D13911yescharacteristic
116C4×Q8—2781no—
117C4×Q8—2781no—
118C4×Q8—2781no—
119C4×Q8—2781no—
120#117—2782no—
121#117—1391no—
122#117C2×D13911yescharacteristic
123C2×C4⋊C4—1391no—
124C2×C42C2×D13911yescharacteristic
125#107—2781no—
126#107—2781no—
127#106—2781no—
128#106—2781no—
129#101—1394no—
130#95—2782no—
131C2×Q8—2781no—
132C2×Q8—2781no—
133C2×Q8—2781no—
134C2×Q8—2781no—
135C2×Q8—1392no—
136C2×Q8—1392no—
137C22×C4—21no—
138C22×C4—2781no—
139C22×C4—1392no—
140C22×C4C22×D13911yescharacteristic
141M16—21no—
142M16—2781no—
143M16—1392no—
144M16C4×D13912yes—
145C2×C8—21no—
146C2×C8—2781no—
147C4⋊C4—2782no—
148C4⋊C4—2782no—
149C4⋊C4—2781no—
150C4⋊C4—2781no—
151C4⋊C4—1391no—
152C4⋊C4—1391no—
153C4⋊C4D55611yescharacteristic
154C4⋊C4D55611yescharacteristic
155C22⋊C4—21no—
156C22⋊C4—2781no—
157C42—21no—
158C42—21no—
159C42—21no—
160C42—2782no—
161C42—2782no—
162C42—2781no—
163C23D4×D13911yescharacteristic
164Q8—2782no—
165Q8—2782no—
166Q8—2782no—
167Q8—2782no—
168C2×C4—22no—
169C2×C4—21no—
170C2×C4—21no—
171C2×C4—41no—
172C2×C4—41no—
173C2×C4—2782no—
174C2×C4—2782no—
175C2×C4—2781no—
176C2×C4—2781no—
177C2×C4—5562no—
178C2×C4—5561no—
179C2×C4—1394no—
180C2×C4C2×C4×D13911yescharacteristic
181C2×C4D4×D13911yescharacteristic
182C2×C4C2×D55611yescharacteristic
183C2×C4Q8×D13911yescharacteristic
184C2×C4#1455578411yescharacteristic
185C2×C4#1455578511yescharacteristic
186C8—22no—
187C8—2782no—
188C22—21no—
189C22—21no—
190C22C4⋊C4×D13911yescharacteristic
191C22#1798481211yescharacteristic
192C22#1798482411yescharacteristic
193C4—42no—
194C4—41no—
195C4—41no—
196C4—2784no—
197C4—5561no—
198C4—5561no—
199C4—11121no—
200C4(C22⋊D139)⋊C411yescharacteristic
201C4C4×D55611yescharacteristic
202C4#1798482011yescharacteristic
203C4#1798482211yescharacteristic
204C2—21no—
205C2—21no—
206C2#2258082711yescharacteristic
207C2#2258112711yescharacteristic
208C2#2258113711yescharacteristic
subgroupG/H
centerC22#17984812
commutatorC2×C4×C139C22×C4
FrattiniC22×C4C22×D139
Fitting#339×C139C2
socleC22×C139#120
prime radicalC23×C139C2×D4
cosocleC22×C4×C139C23
hypercenter#339D139
hypocenterC139#1857
LCSG ▷ C2×C4×C139 ▷ C2×C139 ▷ C139
UCSC1 ◁ C22 ◁ C22×C4 ◁ #339

Complements

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

NH ≅ G/Ntype
21. #17984760C4semidirect
104. C139#1857semidirect

Maximal subgroups

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

subgroupindex
#225814302
#225809962
#225809952
C2×#179847602
#225808592
#225807132
#339×C1392
#1857139