Finite Group Databasebeta

← #31807468

Subgroups — #31807468

Order 17792.

394 conjugacy classes of subgroups; only the 71 normal subgroups are shown.

normal subgroups only

This group has 394 conjugacy classes of subgroups — too many to draw. Only its 71 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#22581460C212yesmaximal, complemented
2#22580970C212yesmaximal, complemented
3#22580916C211yesmaximal, characteristic, complemented
4#22580710C211yesmaximal, characteristic, complemented
5#575×C139C211yesmaximal, characteristic, complemented
6C22×C4×D139C2211yescharacteristic
7C2×#14555769C2211yescharacteristic
8#17984823—22no—
9#17984818—22no—
10#17984813—22no—
11#17984810—22no—
12C4×C22⋊D139—24no—
13#17984801C2212yes—
14#17984769—24no—
15(C2×D139)⋊C8—22no—
16C2×#41×C139C2212yes—
17#137×C139—22no—
18AGL(1,ℤ/8)×C139—22no—
19#135×C139—22no—
20C2×M16×C139C2211yescharacteristic
21C23×D139D411yescharacteristic
22C2×C22⋊D139—24no—
23C22×Dic139D411yescharacteristic
24C2×C4×D139—22no—
25C2×C4×D139—22no—
26C2×C4×D139—21no—
27C2×C4×D139—21no—
28#14555769—22no—
29C2×C139⋊C8—21no—
30C4⋊Dic139—22no—
31Dic139⋊C4—24no—
32C22⋊Dic139—24no—
33C22⋊Dic139—22no—
34(C2×D139)⋊C4—24no—
35C4×Dic139D414yescomplemented
36#41×C139—22no—
37#41×C139—22no—
38#41×C139—22no—
39#41×C139—22no—
40C2×Q8×C139D412yescomplemented
41C2×D4×C139—22no—
42C2×D4×C139D412yescomplemented
43C22×C4×C139—22no—
44C22×C4×C139C2311yescharacteristic
45Q16×C139—22no—
46SD16×C139—24no—
47D8×C139—22no—
48M16×C139—22no—
49C2×C8×C139D412yescomplemented
50C22×D139—22no—
51C22×D139—21no—
52C22×D139—42no—
53C22⋊D139—48no—
54C2×Dic139—24no—
55C2×Dic139—22no—
56C2×Dic139—21no—
57C4×D139—41no—
58C4×D139—42no—
59C4×D139—41no—
60C139⋊C8—41no—
61C23×C139—22no—
62C23×C139C2×D411yescharacteristic
63Q8×C139—22no—
64Q8×C139—22no—
65D4×C139—22no—
66D4×C139—22no—
67D4×C139—42no—
68D4×C139—42no—
69C2×C4×C139—22no—
70C2×C4×C139—42no—
71C2×C4×C139—42no—
72C2×C4×C139C2×D412yes—
73C2×C4×C139C2×D412yes—
74C2×C4×C139C2×D411yescharacteristic
75C2×C4×C139#4111yescharacteristic
76C8×C139—22no—
77C22×C139—41no—
78C22×C139—44no—
79C22×C139—42no—
80C22×C139#12012yes—
81C22×C139#12111yescharacteristic
82C2×D139—24no—
83C2×D139—22no—
84C2×D139—42no—
85C2×D139—41no—
86C2×D139—41no—
87C4×C139—42no—
88C4×C139#12011yescharacteristic
89C4×C139#12112yes—
90C4×C139#12711yescharacteristic
91Dic139—44no—
92Dic139—41no—
93C2×C139—22no—
94C2×C139—21no—
95C2×C139—82no—
96C2×C139#39211yescharacteristic
97D139—42no—
98C139#201011yescharacteristic, complemented, Sylow
99#2010—1391nomaximal, Sylow
100#575D13911yescharacteristic, complemented
101#525—1392no—
102#421—1392no—
103#407—1391no—
104H(3,ℤ/4)—1391no—
105C2×#41C2×D13912yes—
106C23×C4—1391no—
107#137—22no—
108AGL(1,ℤ/8)—22no—
109#135—22no—
110C2×M16—1391no—
111C2×M16C2×D13911yescharacteristic
112#123—2782no—
113C22⋊Q8—2782no—
114#121—2782no—
115#120—2782no—
116C4×D4—2784no—
117#117—1392no—
118#104—2784no—
119C22⋊C8—2782no—
120C24—1391no—
121#41—22no—
122#41—22no—
123#41—22no—
124#41—22no—
125C2×Q8C22⋊D13912yescomplemented
126C2×D4—22no—
127C2×D4—2784no—
128C2×D4C22⋊D13912yescomplemented
129C22×C4—22no—
130C22×C4—2782no—
131C22×C4—2781no—
132C22×C4—2782no—
133C22×C4—2781no—
134C22×C4—1391no—
135C22×C4C22×D13911yescharacteristic
136Q16—22no—
137SD16—24no—
138D8—22no—
139M16—22no—
140M16—2782no—
141C2×C8—2781no—
142C2×C8C22⋊D13912yescomplemented
143C4⋊C4—2784no—
144C4⋊C4—2782no—
145C22⋊C4—2784no—
146C22⋊C4—2784no—
147C22⋊C4—2782no—
148C42—1394no—
149C23—22no—
150C23—2782no—
151C23—2781no—
152C23—5562no—
153C23D4×D13911yescharacteristic
154Q8—22no—
155Q8—22no—
156D4—22no—
157D4—22no—
158D4—42no—
159D4—42no—
160D4—5568no—
161C2×C4—22no—
162C2×C4—42no—
163C2×C4—42no—
164C2×C4—2784no—
165C2×C4—2782no—
166C2×C4—2781no—
167C2×C4—5561no—
168C2×C4—5562no—
169C2×C4—5561no—
170C2×C4D4×D13912yes—
171C2×C4C2×C22⋊D13912yes—
172C2×C4C2×C22⋊D13911yescharacteristic
173C2×C4#1455578411yescharacteristic
174C8—22no—
175C8—5561no—
176C22—41no—
177C22—44no—
178C22—42no—
179C22—2784no—
180C22—2782no—
181C22—5562no—
182C22—5561no—
183C22—5561no—
184C22#1798481012yes—
185C22#1798481311yescharacteristic
186C4—42no—
187C4—5564no—
188C4—5561no—
189C4#1798481111yescharacteristic
190C4#1798481412yes—
191C4#1798483811yescharacteristic
192C2—22no—
193C2—21no—
194C2—82no—
195C2—5562no—
196C2#2258086111yescharacteristic
subgroupG/H
centerC4#17984838
commutator, cosocleC22×C4×C139C23
FrattiniC22×C4C22×D139
Fitting#575×C139C2
socleC2×C139#392
hypercenter#575D139
hypocenterC139#2010
LCSG ▷ C22×C4×C139 ▷ C2×C139 ▷ C139
UCSC1 ◁ C4 ◁ C22×C4 ◁ #575

Complements

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

NH ≅ G/Ntype
1. #22581460C2semidirect
2. #22580970C2semidirect
3. #22580916C2semidirect
4. #22580710C2semidirect
5. #575×C139C2semidirect
35. C4×Dic139D4semidirect
40. C2×Q8×C139D4semidirect
42. C2×D4×C139D4semidirect
49. C2×C8×C139D4semidirect
98. C139#2010semidirect
100. #575D139semidirect
125. C2×Q8C22⋊D139semidirect
128. C2×D4C22⋊D139semidirect
142. C2×C8C22⋊D139semidirect

Maximal subgroups

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

subgroupindex
#225814602
#225809702
#225809162
#225807102
#575×C1392
#2010139