Finite Group Databasebeta

← #31807446

Subgroups — #31807446

Order 17792.

406 conjugacy classes of subgroups; only the 75 normal subgroups are shown.

normal subgroups only

This group has 406 conjugacy classes of subgroups — too many to draw. Only its 75 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
1C2×#17984867C212yesmaximal, complemented
2C2×#17984769C212yesmaximal, complemented
3#22580854C211yesmaximal, characteristic, complemented
4#22580722C211yesmaximal, characteristic, complemented
5#537×C139C211yesmaximal, characteristic, complemented
6C22×D556C2211yescharacteristic
7#17984867—24no—
8#17984867—24no—
9C2×#14555772—22no—
10C2×#14555770—22no—
11C2×#14555769C2212yes—
12C2×(C2×D139)⋊C4—22no—
13C2×C4×Dic139C2211yescharacteristic
14#17984769—24no—
15C2×#41×C139C2212yes—
16C22⋊Q8×C139—22no—
17#121×C139—22no—
18#121×C139—22no—
19C2×C4⋊C4×C139C2211yescharacteristic
20C23×D139—21no—
21C2×D556—22no—
22C2×D556—22no—
23C2×D556—21no—
24C2×D556D412yescomplemented
25C22×Dic139—21no—
26#14555772—28no—
27#14555770—28no—
28#14555769—22no—
29#14555769D414yescomplemented
30C2×C139⋊C8—22no—
31(C2×D139)⋊C4—44no—
32C4×Dic139—22no—
33#41×C139—22no—
34#41×C139—22no—
35#41×C139—22no—
36#41×C139—22no—
37C2×Q8×C139D412yes—
38C2×D4×C139—22no—
39C2×D4×C139—22no—
40C2×D4×C139D412yes—
41C22×C4×C139—22no—
42C22×C4×C139D412yes—
43C22×C4×C139C2311yescharacteristic
44C4⋊C4×C139—22no—
45C4⋊C4×C139—22no—
46C22⋊C4×C139—24no—
47C22×D139—22no—
48C22×D139—42no—
49C22×D139—42no—
50C22×D139—41no—
51C22×D139—41no—
52D556—24no—
53D556—42no—
54C2×Dic139—22no—
55C2×Dic139—41no—
56C2×Dic139—41no—
57C139⋊C8—24no—
58C23×C139—22no—
59C23×C139C2×D411yescharacteristic
60Q8×C139—22no—
61Q8×C139—22no—
62D4×C139—22no—
63D4×C139—22no—
64D4×C139—42no—
65D4×C139—42no—
66D4×C139—82no—
67C2×C4×C139—22no—
68C2×C4×C139—22no—
69C2×C4×C139—42no—
70C2×C4×C139—42no—
71C2×C4×C139—42no—
72C2×C4×C139C2×D411yescharacteristic
73C2×C4×C139C2×D412yes—
74C2×C4×C139C2×D412yes—
75C2×C4×C139#4111yescharacteristic
76C22×C139—21no—
77C22×C139—21no—
78C22×C139—42no—
79C22×C139—42no—
80C22×C139—42no—
81C22×C139#12011yescharacteristic
82C22×C139#12111yescharacteristic
83C22×C139#12711yescharacteristic
84C2×D139—44no—
85C2×D139—42no—
86C2×D139—82no—
87C2×D139—81no—
88C2×D139—81no—
89C4×C139—42no—
90C4×C139—42no—
91C4×C139#12012yes—
92C4×C139#12112yes—
93Dic139—42no—
94C2×C139—21no—
95C2×C139—21no—
96C2×C139—82no—
97C2×C139#39211yescharacteristic
98C2×C139#45311yescharacteristic
99C2×C139#45411yescharacteristic
100D139—82no—
101C139#200611yescharacteristic, complemented, Sylow
102#2006—1391nomaximal, Sylow
103C2×AGL(1,ℤ/8)—1392no—
104#537D13911yescharacteristic, complemented
105C2×#104—1392no—
106#390—1391no—
107#343—1391no—
108C2×#41C2×D13912yes—
109C22×D4—1391no—
110AGL(1,ℤ/8)—2784no—
111AGL(1,ℤ/8)—2784no—
112C2×SD16—2782no—
113C2×D8—2782no—
114C2×M16—1392no—
115C22⋊Q8—22no—
116#121—22no—
117#121—22no—
118C2×C4⋊C4C2×D13911yescharacteristic
119C2×C22⋊C4—2782no—
120C2×C42—1391no—
121#104—2784no—
122C24—2781no—
123#41—22no—
124#41—22no—
125#41—22no—
126#41—22no—
127C2×Q8C22⋊D13912yes—
128C2×D4—22no—
129C2×D4—22no—
130C2×D4—2782no—
131C2×D4—2782no—
132C2×D4—2781no—
133C2×D4—1392no—
134C2×D4C22⋊D13912yes—
135C22×C4—22no—
136C22×C4—2781no—
137C22×C4C22⋊D13912yes—
138C22×C4C22×D13911yescharacteristic
139SD16—2788no—
140D8—2788no—
141M16—2782no—
142M16—1394no—
143C2×C8—2782no—
144C4⋊C4—22no—
145C4⋊C4—22no—
146C22⋊C4—24no—
147C22⋊C4—5564no—
148C42—2782no—
149C23—22no—
150C23—2782no—
151C23—5562no—
152C23—5562no—
153C23—5561no—
154C23—5561no—
155C23C2×C22⋊D13911yescharacteristic
156Q8—22no—
157Q8—22no—
158D4—22no—
159D4—22no—
160D4—42no—
161D4—42no—
162D4—82no—
163D4—2784no—
164D4—5562no—
165C2×C4—22no—
166C2×C4—22no—
167C2×C4—42no—
168C2×C4—42no—
169C2×C4—42no—
170C2×C4—2782no—
171C2×C4—5561no—
172C2×C4—5561no—
173C2×C4D4×D13911yescharacteristic
174C2×C4D4×D13912yes—
175C2×C4C2×C22⋊D13912yes—
176C2×C4#1455578411yescharacteristic
177C8—2784no—
178C22—21no—
179C22—21no—
180C22—42no—
181C22—42no—
182C22—42no—
183C22—5564no—
184C22—5562no—
185C22—11122no—
186C22—11121no—
187C22—11121no—
188C22#1798481111yescharacteristic
189C22#1798481311yescharacteristic
190C22#1798483811yescharacteristic
191C4—42no—
192C4—42no—
193C4—5562no—
194C4#1798481012yes—
195C4#1798481412yes—
196C2—21no—
197C2—21no—
198C2—82no—
199C2—11122no—
200C2#2258086111yescharacteristic
201C2#2258112111yescharacteristic
202C2#2258112611yescharacteristic
subgroupG/H
centerC22#17984811
commutator, cosocleC22×C4×C139C23
FrattiniC22×C4C22×D139
Fitting#537×C139C2
socleC22×C139#120
hypercenter#537D139
hypocenterC139#2006
LCSG ▷ C22×C4×C139 ▷ C2×C139 ▷ C139
UCSC1 ◁ C22 ◁ C22×C4 ◁ #537

Complements

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

NH ≅ G/Ntype
1. C2×#17984867C2semidirect
2. C2×#17984769C2semidirect
3. #22580854C2semidirect
4. #22580722C2semidirect
5. #537×C139C2semidirect
24. C2×D556D4semidirect
29. #14555769D4semidirect
101. C139#2006semidirect
104. #537D139semidirect

Maximal subgroups

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

subgroupindex
C2×#179848672
C2×#179847692
#225808542
#225807222
#537×C1392
#2006139