Finite Group Databasebeta

← #31806506

Subgroups — #31806506

Order 17792.

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

normal subgroups only

This group has 262 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
1#22581421C211yesmaximal, characteristic
2#22580935C211yesmaximal, characteristic
3#22580926C211yesmaximal, characteristic
4#22580714C211yesmaximal, characteristic, complemented
5#22580712C211yesmaximal, characteristic, complemented
6#22580709C211yesmaximal, characteristic, complemented
7H(3,ℤ/4)×C139C211yesmaximal, characteristic, complemented
8C2×#14555785C2211yescharacteristic
9C2×#14555769C2211yescharacteristic
10#17984807—21no—
11#17984804—21no—
12(C22⋊D139)⋊C4—22no—
13#17984801C2211yescharacteristic
14#17984799C412yescomplemented
15C2×C4×Dic139C2211yescharacteristic
16C42×D139C412yescomplemented
17#17984760—21no—
18#17984758—21no—
19#17984756—22no—
20C2×M16×C139C2211yescharacteristic
21#117×C139C2211yescharacteristic
22#117×C139C2211yescharacteristic
23#14555785—21no—
24#14555785—21no—
25#14555785—21no—
26#14555785—21no—
27C2×Dic278D411yescharacteristic
28C2×D556D411yescharacteristic
29C2×C22⋊D139D412yes—
30C22×Dic139—21no—
31C2×C4×D139—22no—
32C2×C4×D139C2×C412yes—
33#14555769—21no—
34#14555769—21no—
35C2×C139⋊C8—21no—
36C4⋊Dic139—21no—
37Dic139⋊C4—22no—
38C22⋊Dic139—21no—
39(C2×D139)⋊C4—22no—
40C4×Dic139—22no—
41C4×Dic139—21no—
42C4×Dic139—21no—
43C4×Dic139C2×C411yescharacteristic
44C4×Dic139C2×C411yescharacteristic
45C22×C4×C139C2311yescharacteristic
46M16×C139—21no—
47M16×C139—21no—
48C2×C8×C139—21no—
49C4⋊C4×C139—21no—
50C4⋊C4×C139—21no—
51C22⋊C4×C139—21no—
52C22⋊C4×C139—21no—
53C42×C139—21no—
54C42×C139C2×C412yes—
55C22×D139C22⋊C412yes—
56Dic278—21no—
57Dic278—21no—
58D556—21no—
59D556—21no—
60C22⋊D139—22no—
61C22⋊D139—22no—
62C2×Dic139—21no—
63C2×Dic139—21no—
64C2×Dic139—42no—
65C2×Dic139—41no—
66C2×Dic139C22⋊C412yes—
67C4×D139—22no—
68C4×D139—22no—
69C4×D139—44no—
70C139⋊C8—41no—
71C23×C139C2×D411yescharacteristic
72C2×C4×C139—22no—
73C2×C4×C139—41no—
74C2×C4×C139C22×C411yescharacteristic
75C2×C4×C139C2×D411yescharacteristic
76C2×C4×C139#4111yescharacteristic
77C2×C4×C139#4111yescharacteristic
78C2×C4×C139#4111yescharacteristic
79C2×C4×C139#4111yescharacteristic
80C8×C139—41no—
81C22×C139—41no—
82C22×C139C2×C22⋊C411yescharacteristic
83C22×C139#12311yescharacteristic
84C22×C139#12311yescharacteristic
85C2×D139—22no—
86C2×D139—42no—
87C4×C139—42no—
88C4×C139—81no—
89C4×C139#11711yescharacteristic
90C4×C139#11711yescharacteristic
91C4×C139#12311yescharacteristic
92C4×C139#12311yescharacteristic
93Dic139—22no—
94Dic139—22no—
95Dic139—41no—
96Dic139—81no—
97C2×C139—21no—
98C2×C139—21no—
99C2×C139—21no—
100C2×C139#38111yescharacteristic
101D139—42no—
102C139#182711yescharacteristic, complemented, Sylow
103#1827—1391nomaximal, Sylow
104C4×#41—1391no—
105#413—1391no—
106#410—1391no—
107#339—1391no—
108#339—1391no—
109H(3,ℤ/4)—1391no—
110H(3,ℤ/4)D13911yescharacteristic, complemented
111C2×#41—1391no—
112C2×M16—1391no—
113C2×M16C2×D13911yescharacteristic
114C4×Q8—2781no—
115C4×D4—2782no—
116C4×D4—2781no—
117#117—1391no—
118#117—1392no—
119#117C2×D13911yescharacteristic
120#117C2×D13911yescharacteristic
121C2×C42—1391no—
122C2×C42—1392no—
123#101—2781no—
124#100—2781no—
125#99—2782no—
126#41—2781no—
127#41—2781no—
128#41—2781no—
129#41—2781no—
130C2×Q8—1391no—
131C2×D4—1392no—
132C2×D4—1391no—
133C22×C4—2782no—
134C22×C4—2781no—
135C22×C4—1392no—
136C22×C4C22×D13911yescharacteristic
137M16—21no—
138M16—21no—
139M16—2781no—
140M16—2781no—
141C2×C8—21no—
142C2×C8—2781no—
143C4⋊C4—21no—
144C4⋊C4—21no—
145C4⋊C4—2782no—
146C4⋊C4—2781no—
147C22⋊C4—21no—
148C22⋊C4—21no—
149C22⋊C4—2782no—
150C22⋊C4—2781no—
151C42—21no—
152C42—2782no—
153C42—2781no—
154C42—2781no—
155C42—1391no—
156C42—1391no—
157C42C4×D13912yes—
158C23—1392no—
159C23D4×D13911yescharacteristic
160Q8—2781no—
161Q8—2781no—
162D4—2782no—
163D4—2782no—
164D4—2781no—
165D4—2781no—
166C2×C4—22no—
167C2×C4—41no—
168C2×C4—2781no—
169C2×C4—2782no—
170C2×C4—2782no—
171C2×C4—2781no—
172C2×C4—5564no—
173C2×C4—5562no—
174C2×C4—5561no—
175C2×C4—1392no—
176C2×C4C2×C4×D13911yescharacteristic
177C2×C4D4×D13911yescharacteristic
178C2×C4#1455578411yescharacteristic
179C2×C4#1455578511yescharacteristic
180C2×C4#1455578511yescharacteristic
181C2×C4#1455578611yescharacteristic
182C8—41no—
183C8—5561no—
184C22—41no—
185C22—2782no—
186C22—5562no—
187C22C22⋊C4×D13911yescharacteristic
188C22#1798482411yescharacteristic
189C22#1798482711yescharacteristic
190C4—42no—
191C4—81no—
192C4—2782no—
193C4—2782no—
194C4—5561no—
195C4—11121no—
196C4#1798479911yescharacteristic
197C4#1798480011yescharacteristic
198C4#1798482411yescharacteristic
199C4#1798482711yescharacteristic
200C2—21no—
201C2—21no—
202C2—21no—
203C2—5562no—
204C2#2258081511yescharacteristic
subgroupG/H
centerC4#17984799
commutatorC2×C4×C139C22×C4
FrattiniC22×C4C22×D139
FittingH(3,ℤ/4)×C139C2
socleC2×C139#381
prime radicalC2×#14555785C22
cosocleC22×C4×C139C23
hypercenterH(3,ℤ/4)D139
hypocenterC139#1827
LCSG ▷ C2×C4×C139 ▷ C2×C139 ▷ C139
UCSC1 ◁ C4 ◁ #117 ◁ H(3,ℤ/4)

Complements

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

NH ≅ G/Ntype
4. #22580714C2semidirect
5. #22580712C2semidirect
6. #22580709C2semidirect
7. H(3,ℤ/4)×C139C2semidirect
14. #17984799C4semidirect
16. C42×D139C4semidirect
102. C139#1827semidirect
110. 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
#225814212
#225809352
#225809262
#225807142
#225807122
#225807092
H(3,ℤ/4)×C1392
#1827139