Finite Group Databasebeta

← #31806899

Subgroups — #31806899

Order 17792.

310 conjugacy classes of subgroups; only the 79 normal subgroups are shown.

normal subgroups only

This group has 310 conjugacy classes of subgroups — too many to draw. Only its 79 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×#17984875C211yesmaximal, characteristic
2#22581430C211yesmaximal, characteristic, complemented
3#22580971C211yesmaximal, characteristic
4#22580961C211yesmaximal, characteristic, complemented
5#22580926C211yesmaximal, characteristic
6#22580724C211yesmaximal, characteristic, complemented
7H(3,ℤ/4)×C139C211yesmaximal, characteristic, complemented
8C2×#14555785C2211yescharacteristic
9C22×Dic278C2211yescharacteristic
10#17984875—22no—
11#17984875—22no—
12C2×Dic556C412yescomplemented
13C2×#14555774C412yescomplemented
14C2×#14555769C2211yescharacteristic
15C4×Dic278—22no—
16#17984807—22no—
17#17984801C2211yescharacteristic
18#17984798—22no—
19#17984770—22no—
20#17984765—22no—
21#17984756—22no—
22C2×M16×C139C2211yescharacteristic
23#117×C139C2211yescharacteristic
24#117×C139C2211yescharacteristic
25#14555785—21no—
26#14555785—21no—
27#14555785—21no—
28#14555785—21no—
29C2×Dic278—21no—
30C2×Dic278—21no—
31C2×Dic278—21no—
32C2×Dic278C2×C411yescharacteristic
33C2×Dic278C2×C412yes—
34C2×Dic278D412yes—
35C2×Dic278D412yes—
36C2×D556C2×C411yescharacteristic
37C2×C22⋊D139—21no—
38C22×Dic139—21no—
39C2×C4×D139—21no—
40Dic556—24no—
41#14555774—24no—
42#14555769—21no—
43#14555769—21no—
44C2×C139⋊C8—21no—
45C4⋊Dic139—21no—
46Dic139⋊C4—24no—
47C22⋊Dic139D412yes—
48C4×Dic139—24no—
49C4×Dic139—21no—
50C22×C4×C139C2311yescharacteristic
51M16×C139—21no—
52M16×C139—21no—
53C2×C8×C139C2×C412yes—
54C4⋊C4×C139—21no—
55C4⋊C4×C139—21no—
56C22⋊C4×C139—21no—
57C22⋊C4×C139—21no—
58C42×C139—21no—
59C42×C139D412yes—
60C22×D139—21no—
61Dic278—22no—
62Dic278—22no—
63Dic278—22no—
64Dic278—21no—
65Dic278—21no—
66Dic278C22⋊C414yes—
67D556—21no—
68D556—21no—
69C22⋊D139—41no—
70C22⋊D139—41no—
71C2×Dic139—22no—
72C2×Dic139—22no—
73C2×Dic139—22no—
74C2×Dic139—21no—
75C2×Dic139—22no—
76C4×D139—41no—
77C4×D139—41no—
78C139⋊C8—41no—
79C23×C139C2×D411yescharacteristic
80C2×C4×C139—22no—
81C2×C4×C139—41no—
82C2×C4×C139C22×C411yescharacteristic
83C2×C4×C139C2×D411yescharacteristic
84C2×C4×C139C2×D411yescharacteristic
85C2×C4×C139C2×D411yescharacteristic
86C2×C4×C139#4111yescharacteristic
87C2×C4×C139#4111yescharacteristic
88C8×C139—22no—
89C22×C139—41no—
90C22×C139C4×D411yescharacteristic
91C22×C139#12011yescharacteristic
92C22×C139#12111yescharacteristic
93C2×D139—41no—
94C2×D139—81no—
95C4×C139—42no—
96C4×C139—81no—
97C4×C139C2×C22⋊C411yescharacteristic
98C4×C139C4×D411yescharacteristic
99C4×C139#12111yescharacteristic
100C4×C139#12311yescharacteristic
101Dic139—24no—
102Dic139—42no—
103Dic139—41no—
104C2×C139—21no—
105C2×C139—21no—
106C2×C139—21no—
107C2×C139#38611yescharacteristic
108D139—81no—
109C139#190511yescharacteristic, complemented, Sylow
110#1905—1391nomaximal, Sylow
111C2×#137—1391no—
112#519—1391no—
113#421—1391no—
114#419—1391no—
115#410—1391no—
116#344—1391no—
117H(3,ℤ/4)D13911yescharacteristic, complemented
118C2×#41—1391no—
119C22×Q8—1391no—
120#137—2782no—
121#137—2782no—
122C2×Q16—1392no—
123C2×SD16—1392no—
124C2×M16—1391no—
125C2×M16C2×D13911yescharacteristic
126C4×Q8—2782no—
127C4×Q8—2782no—
128#117—2782no—
129#117—1391no—
130#117C2×D13911yescharacteristic
131#117C2×D13911yescharacteristic
132#104—2782no—
133#103—2782no—
134#99—2782no—
135#41—2781no—
136#41—2781no—
137#41—2781no—
138#41—2781no—
139C2×Q8—2781no—
140C2×Q8—2781no—
141C2×Q8—2781no—
142C2×Q8—1391no—
143C2×Q8—1392no—
144C2×Q8—1392no—
145C2×Q8—1392no—
146C2×D4—2781no—
147C2×D4—1391no—
148C22×C4—2781no—
149C22×C4—2781no—
150C22×C4C22×D13911yescharacteristic
151Q16—2784no—
152SD16—2784no—
153M16—21no—
154M16—21no—
155M16—2781no—
156M16—2781no—
157C2×C8—2781no—
158C2×C8C4×D13912yes—
159C4⋊C4—21no—
160C4⋊C4—21no—
161C4⋊C4—2784no—
162C4⋊C4—2781no—
163C22⋊C4—21no—
164C22⋊C4—21no—
165C22⋊C4—1392no—
166C42—21no—
167C42—2784no—
168C42—2781no—
169C42D55612yes—
170C23—2781no—
171C23D4×D13911yescharacteristic
172Q8—2782no—
173Q8—2782no—
174Q8—2782no—
175Q8—2781no—
176Q8—2781no—
177Q8—1394no—
178D4—2781no—
179D4—2781no—
180D4—5561no—
181D4—5561no—
182C2×C4—22no—
183C2×C4—41no—
184C2×C4—2782no—
185C2×C4—2782no—
186C2×C4—2782no—
187C2×C4—2781no—
188C2×C4—2782no—
189C2×C4—5561no—
190C2×C4—5561no—
191C2×C4C2×C4×D13911yescharacteristic
192C2×C4D4×D13911yescharacteristic
193C2×C4D4×D13911yescharacteristic
194C2×C4C2×D55611yescharacteristic
195C2×C4#1455578511yescharacteristic
196C2×C4#1455578611yescharacteristic
197C8—22no—
198C8—5561no—
199C22—41no—
200C22—5561no—
201C22—11121no—
202C22#1798480411yescharacteristic
203C22#1798481211yescharacteristic
204C22#1798481511yescharacteristic
205C4—42no—
206C4—81no—
207C4—2784no—
208C4—5562no—
209C4—5561no—
210C4C22⋊C4×D13911yescharacteristic
211C4C4×D55611yescharacteristic
212C4#1798481711yescharacteristic
213C4#1798482711yescharacteristic
214C2—21no—
215C2—21no—
216C2—21no—
217C2—11121no—
218C2#2258083111yescharacteristic
subgroupG/H
centerC2#22580831
commutatorC2×C4×C139C22×C4
FrattiniC22×C4C22×D139
FittingH(3,ℤ/4)×C139C2
socleC2×C139#386
prime radicalC2×#14555785C22
cosocleC22×C4×C139C23
hypercenterH(3,ℤ/4)D139
hypocenterC139#1905
LCSG ▷ C2×C4×C139 ▷ C2×C139 ▷ C139
UCSC1 ◁ C2 ◁ C22×C4 ◁ H(3,ℤ/4)

Complements

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

NH ≅ G/Ntype
2. #22581430C2semidirect
4. #22580961C2semidirect
6. #22580724C2semidirect
7. H(3,ℤ/4)×C139C2semidirect
12. C2×Dic556C4semidirect
13. C2×#14555774C4semidirect
109. C139#1905semidirect
117. H(3,ℤ/4)D139semidirect

Maximal subgroups

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

subgroupindex
C2×#179848752
#225814302
#225809712
#225809612
#225809262
#225807242
H(3,ℤ/4)×C1392
#1905139