Finite Group Databasebeta

← #31807445

Subgroups — #31807445

Order 17792.

406 conjugacy classes of subgroups; only the 73 normal subgroups are shown.

normal subgroups only

This group has 406 conjugacy classes of subgroups — too many to draw. Only its 73 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×#17984868C212yesmaximal, complemented
2#22581534C211yesmaximal, characteristic, complemented
3C2×#17984770C212yesmaximal, complemented
4#22580722C211yesmaximal, characteristic, complemented
5#390×C139C211yesmaximal, characteristic, complemented
6C2×#14555785C2212yes—
7#17984868—24no—
8#17984868—24no—
9C2×#14555773—22no—
10C2×#14555770—22no—
11C2×#14555769C2212yes—
12#17984822—22no—
13#17984817—22no—
14#17984816—22no—
15#17984770—24no—
16C22×D4×C139C2211yescharacteristic
17C2×C4⋊C4×C139C2211yescharacteristic
18C2×C22⋊C4×C139—22no—
19C2×C42×C139C2211yescharacteristic
20#14555785—22no—
21#14555785—22no—
22#14555785—22no—
23#14555785—22no—
24C2×Dic278D412yes—
25C2×D556—22no—
26C2×D556D412yes—
27C2×C22⋊D139—22no—
28C2×C4×D139—22no—
29#14555773—28no—
30#14555770—28no—
31#14555769—22no—
32#14555769D414yescomplemented
33C2×C139⋊C8—22no—
34C4⋊Dic139—22no—
35(C2×D139)⋊C4—24no—
36C24×C139—21no—
37C2×D4×C139—22no—
38C2×D4×C139—22no—
39C2×D4×C139—21no—
40C2×D4×C139D412yescomplemented
41C22×C4×C139—21no—
42C22×C4×C139D412yes—
43C22×C4×C139C2311yescharacteristic
44C4⋊C4×C139—22no—
45C22⋊C4×C139—44no—
46C42×C139—22no—
47C22×D139—22no—
48Dic278—22no—
49Dic278—22no—
50D556—22no—
51D556—22no—
52D556—82no—
53C22⋊D139—42no—
54C22⋊D139—42no—
55C2×Dic139—22no—
56C4×D139—42no—
57C4×D139—42no—
58C139⋊C8—24no—
59C23×C139—22no—
60C23×C139—42no—
61C23×C139—42no—
62C23×C139—41no—
63C23×C139—41no—
64C23×C139C2×D411yescharacteristic
65D4×C139—24no—
66D4×C139—42no—
67C2×C4×C139—22no—
68C2×C4×C139—22no—
69C2×C4×C139—41no—
70C2×C4×C139—41no—
71C2×C4×C139—42no—
72C2×C4×C139C2×D412yes—
73C2×C4×C139C2×D412yes—
74C2×C4×C139C2×D411yescharacteristic
75C2×C4×C139#4111yescharacteristic
76C22×C139—21no—
77C22×C139—21no—
78C22×C139—44no—
79C22×C139—42no—
80C22×C139—82no—
81C22×C139—81no—
82C22×C139—81no—
83C22×C139#12011yescharacteristic
84C22×C139#12111yescharacteristic
85C22×C139#12711yescharacteristic
86C2×D139—42no—
87C2×D139—42no—
88C2×D139—42no—
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#537—1391no—
105C2×#104—1392no—
106#390D13911yescharacteristic, complemented
107#343—1391no—
108C2×#41—1392no—
109C22×D4C2×D13911yescharacteristic
110AGL(1,ℤ/8)—2784no—
111AGL(1,ℤ/8)—2784no—
112C2×SD16—2782no—
113C2×D8—2782no—
114C2×M16—1392no—
115C22⋊Q8—2782no—
116#121—2782no—
117#121—2782no—
118C2×C4⋊C4C2×D13911yescharacteristic
119C2×C22⋊C4—22no—
120C2×C42C2×D13911yescharacteristic
121#104—2784no—
122C24—21no—
123#41—2782no—
124#41—2782no—
125#41—2782no—
126#41—2782no—
127C2×Q8—1392no—
128C2×D4—22no—
129C2×D4—22no—
130C2×D4—21no—
131C2×D4—2782no—
132C2×D4—2782no—
133C2×D4—1392no—
134C2×D4D55612yescomplemented
135C22×C4—21no—
136C22×C4—2782no—
137C22×C4C22⋊D13912yes—
138C22×C4C22×D13911yescharacteristic
139SD16—2788no—
140D8—2788no—
141M16—2782no—
142M16—1394no—
143C2×C8—2782no—
144C4⋊C4—22no—
145C4⋊C4—2782no—
146C22⋊C4—44no—
147C22⋊C4—2784no—
148C42—22no—
149C23—22no—
150C23—42no—
151C23—42no—
152C23—41no—
153C23—41no—
154C23—2782no—
155C23C2×C22⋊D13911yescharacteristic
156Q8—2782no—
157Q8—2782no—
158D4—24no—
159D4—42no—
160D4—2782no—
161D4—2782no—
162D4—5562no—
163D4—5562no—
164D4—11122no—
165C2×C4—22no—
166C2×C4—22no—
167C2×C4—41no—
168C2×C4—41no—
169C2×C4—42no—
170C2×C4—2782no—
171C2×C4—5562no—
172C2×C4—5562no—
173C2×C4D4×D13912yes—
174C2×C4D4×D13912yes—
175C2×C4C2×D55611yescharacteristic
176C2×C4#1455578511yescharacteristic
177C8—2784no—
178C22—21no—
179C22—21no—
180C22—44no—
181C22—42no—
182C22—82no—
183C22—81no—
184C22—81no—
185C22—5562no—
186C22—5562no—
187C22—5562no—
188C22#1798481011yescharacteristic
189C22#1798481611yescharacteristic
190C22#1798483811yescharacteristic
191C4—42no—
192C4—42no—
193C4—5562no—
194C4#1798481212yes—
195C4#1798481512yes—
196C2—21no—
197C2—21no—
198C2—82no—
199C2—11122no—
200C2#2258086211yescharacteristic
201C2#2258112011yescharacteristic
202C2#2258112511yescharacteristic
subgroupG/H
centerC22#17984810
commutator, cosocleC22×C4×C139C23
FrattiniC22×C4C22×D139
Fitting#390×C139C2
socleC22×C139#120
hypercenter#390D139
hypocenterC139#2006
LCSG ▷ C22×C4×C139 ▷ C2×C139 ▷ C139
UCSC1 ◁ C22 ◁ C22×C4 ◁ #390

Complements

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

NH ≅ G/Ntype
1. C2×#17984868C2semidirect
2. #22581534C2semidirect
3. C2×#17984770C2semidirect
4. #22580722C2semidirect
5. #390×C139C2semidirect
32. #14555769D4semidirect
40. C2×D4×C139D4semidirect
101. C139#2006semidirect
106. #390D139semidirect
134. C2×D4D556semidirect

Maximal subgroups

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

subgroupindex
C2×#179848682
#225815342
C2×#179847702
#225807222
#390×C1392
#2006139