Finite Group Databasebeta

← #31808356

Subgroups — #31808356

Order 17792.

216 conjugacy classes of subgroups; only the 47 normal subgroups are shown.

normal subgroups only

This group has 216 conjugacy classes of subgroups — too many to draw. Only its 47 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#22581750C211yesmaximal, characteristic
2#22581396C211yesmaximal, characteristic, complemented
3#22581393C211yesmaximal, characteristic, complemented
4#22581212C211yesmaximal, characteristic, complemented
5#22580762C211yesmaximal, characteristic, complemented
6#22580734C211yesmaximal, characteristic, complemented
7#360×C139C211yesmaximal, characteristic, complemented
8#41×D139—21no—
9#17984874—21no—
10#17984871—21no—
11#17984869—21no—
12#17984866—21no—
13#17984864C2211yescharacteristic
14#17984862—21no—
15C2×Dic556C2211yescharacteristic, complemented
16C2×#14555768C2211yescharacteristic
17#17984822—21no—
18Dic1112—21no—
19#17984788—21no—
20#17984787—21no—
21#17984786—21no—
22#17984782C2211yescharacteristic, complemented
23#17984765—21no—
24#135×C139C2211yescharacteristic
25M32×C139C2211yescharacteristic, complemented
26#106×C139C2211yescharacteristic, complemented
27#14555786—21no—
28#14555785—21no—
29#14555785—41no—
30#14555784—21no—
31#14555784—41no—
32C2×Dic278—21no—
33Q8×D139—21no—
34D4×D139—21no—
35D4×D139—41no—
36C2×C4×D139—41no—
37C2×C4×D139D411yescharacteristic
38Dic556—21no—
39Dic556—21no—
40Dic556D411yescharacteristic
41#14555775—21no—
42#14555774—21no—
43#14555773—21no—
44#14555772—21no—
45D1112D411yescharacteristic
46#14555770—21no—
47#14555768—21no—
48#14555768—21no—
49C2×C139⋊C8D411yescharacteristic
50C4⋊Dic139—41no—
51(C2×D139)⋊C4—41no—
52C139⋊C16—21no—
53#41×C139—21no—
54Q16×C139D411yescharacteristic
55SD16×C139—21no—
56D8×C139D411yescharacteristic
57C2×C8×C139C2311yescharacteristic
58C4⋊C4×C139—21no—
59C16×C139—21no—
60C22×D139—41no—
61C22×D139D811yescharacteristic
62Dic278—21no—
63Dic278—41no—
64Dic278—41no—
65Dic278—41no—
66D556—21no—
67D556—41no—
68C22⋊D139—41no—
69C22⋊D139—41no—
70C22⋊D139—41no—
71C2×Dic139—41no—
72C2×Dic139—41no—
73C2×Dic139D811yescharacteristic
74C4×D139—21no—
75C4×D139—21no—
76C4×D139—41no—
77C4×D139—41no—
78C4×D139—41no—
79C139⋊C8—21no—
80Q8×C139—21no—
81D4×C139—21no—
82D4×C139—41no—
83C2×C4×C139—41no—
84C2×C4×C139—41no—
85C2×C4×C139C2×D411yescharacteristic
86C8×C139C2×D411yescharacteristic
87C8×C139C2×D411yescharacteristic
88C22×C139—41no—
89C22×C139C2×D811yescharacteristic
90C2×D139—21no—
91C2×D139—41no—
92C2×D139—41no—
93C2×D139—82no—
94C4×C139—41no—
95C4×C139—81no—
96C4×C139#12011yescharacteristic
97C4×C139AGL(1,ℤ/8)11yescharacteristic
98Dic139—21no—
99Dic139—41no—
100Dic139—81no—
101C2×C139—21no—
102C2×C139—81no—
103C2×C139#44711yescharacteristic
104D139—41no—
105D139—81no—
106C139#219111yescharacteristic, complemented, Sylow
107#2191—1391nomaximal, Sylow
108#575—1391no—
109#510—1391no—
110#510—1391no—
111#470—1391no—
112#360—1391no—
113#360D13911yescharacteristic, complemented
114#349—1391no—
115C2×#41—2781no—
116#137—2781no—
117#137—2781no—
118AGL(1,ℤ/8)—2781no—
119AGL(1,ℤ/8)—2781no—
120#135—2781no—
121#135—1391no—
122#135C2×D13911yescharacteristic
123C2×Q16—1391no—
124C2×M16—1391no—
125C22⋊Q8—2781no—
126Q32—2781no—
127Q32—2781no—
128SD32—2781no—
129SD32—2781no—
130M32—1391no—
131M32C2×D13911yescharacteristic, complemented
132#106C2×D13911yescharacteristic, complemented
133#103—2781no—
134#41—21no—
135#41—2781no—
136#41—2781no—
137#41—2781no—
138#41—5561no—
139#41—5561no—
140C2×Q8—2781no—
141C2×Q8—2781no—
142C2×D4—2781no—
143C2×D4—5561no—
144C22×C4—5561no—
145C22×C4—1391no—
146Q16—2781no—
147Q16—2781no—
148Q16—2781no—
149Q16—1391no—
150Q16D55611yescharacteristic
151SD16—21no—
152SD16—2781no—
153SD16—2781no—
154SD16—2781no—
155D8—2781no—
156D8—1391no—
157D8D55611yescharacteristic
158M16—2781no—
159M16—2781no—
160C2×C8—1391no—
161C2×C8C22×D13911yescharacteristic
162C4⋊C4—21no—
163C4⋊C4—5561no—
164C22⋊C4—5561no—
165C16—21no—
166C16—2781no—
167C23—5561no—
168C23—1391no—
169Q8—21no—
170Q8—2781no—
171Q8—5561no—
172Q8—5561no—
173Q8—5561no—
174D4—21no—
175D4—41no—
176D4—2781no—
177D4—5561no—
178D4—5561no—
179D4—5561no—
180D4—5561no—
181C2×C4—41no—
182C2×C4—41no—
183C2×C4—2781no—
184C2×C4—2781no—
185C2×C4—5561no—
186C2×C4—5561no—
187C2×C4—5561no—
188C2×C4—5561no—
189C2×C4—5561no—
190C2×C4—1391no—
191C2×C4D4×D13911yescharacteristic
192C8—2781no—
193C8D4×D13911yescharacteristic
194C8C2×D55611yescharacteristic
195C22—41no—
196C22—2781no—
197C22—5561no—
198C22—5561no—
199C22—11122no—
200C22D8×D13911yescharacteristic
201C4—41no—
202C4—81no—
203C4—2781no—
204C4—5561no—
205C4—11121no—
206C4#1798481211yescharacteristic
207C4#1798486911yescharacteristic
208C2—21no—
209C2—81no—
210C2—5561no—
211C2—11121no—
212C2#2258108811yescharacteristic
subgroupG/H
centerC2#22581088
commutator, cosocleC2×C8×C139C23
FrattiniC2×C8C22×D139
Fitting#360×C139C2
socleC2×C139#447
prime radical#22581750C2
hypercenter#360D139
hypocenterC139#2191
LCSG ▷ C2×C8×C139 ▷ C4×C139 ▷ C2×C139 ▷ C139
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×C8 ◁ #360

Complements

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

NH ≅ G/Ntype
2. #22581396C2semidirect
3. #22581393C2semidirect
4. #22581212C2semidirect
5. #22580762C2semidirect
6. #22580734C2semidirect
7. #360×C139C2semidirect
15. C2×Dic556C22semidirect
22. #17984782C22semidirect
25. M32×C139C22semidirect
26. #106×C139C22semidirect
106. C139#2191semidirect
113. #360D139semidirect
131. M32C2×D139semidirect
132. #106C2×D139semidirect

Maximal subgroups

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

subgroupindex
#225817502
#225813962
#225813932
#225812122
#225807622
#225807342
#360×C1392
#2191139