Finite Group Databasebeta

← #31805638

Subgroups — #31805638

Order 17792.

240 conjugacy classes of subgroups; only the 55 normal subgroups are shown.

normal subgroups only

This group has 240 conjugacy classes of subgroups — too many to draw. Only its 55 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#22581608C211yesmaximal, characteristic
2#22581356C211yesmaximal, characteristic, complemented
3#22581155C211yesmaximal, characteristic, complemented
4#22580698C211yesmaximal, characteristic, complemented
5D4⋊(C139⋊C8)C211yesmaximal, characteristic, complemented
6#22580680C211yesmaximal, characteristic, complemented
7#474×C139C211yesmaximal, characteristic, complemented
8C2×#14555785—21no—
9C2×#14555772—21no—
10#17984842C2211yescharacteristic
11#17984824—22no—
12#17984821—21no—
13#17984813—21no—
14C4×D556C2211yescharacteristic
15C4⋊C4×D139—21no—
16#17984775—22no—
17C4⋊(C139⋊C8)C2211yescharacteristic
18#17984766—21no—
19C4×C139⋊C8C2211yescharacteristic
20C4⋊Q8×C139C2211yescharacteristic
21C4×D4×C139C2211yescharacteristic
22#107×C139—21no—
23C4⋊C8×C139C2211yescharacteristic
24#102×C139—21no—
25#14555785—42no—
26#14555785—42no—
27C2×Dic278—21no—
28C2×D556D411yescharacteristic
29C2×C22⋊D139—22no—
30C2×C4×D139—22no—
31C2×C4×D139—21no—
32#14555772—42no—
33C2×C139⋊C8—21no—
34C2×C139⋊C8—21no—
35C4⋊Dic139—21no—
36C4⋊Dic139D412yes—
37C4⋊Dic139D411yescharacteristic
38Dic139⋊C4—22no—
39C22⋊Dic139—22no—
40(C2×D139)⋊C4—21no—
41C2×Q8×C139—21no—
42C2×D4×C139D411yescharacteristic
43C22×C4×C139—21no—
44C2×C8×C139—21no—
45C4⋊C4×C139—21no—
46C4⋊C4×C139—21no—
47C4⋊C4×C139D411yescharacteristic
48C22⋊C4×C139—21no—
49C42×C139C2311yescharacteristic
50C22×D139—21no—
51Dic278—41no—
52Dic278—41no—
53D556—21no—
54D556D812yes—
55C22⋊D139—44no—
56C2×Dic139—21no—
57C2×Dic139—22no—
58C4×D139—44no—
59C4×D139—41no—
60C4×D139—41no—
61C139⋊C8—22no—
62C139⋊C8—41no—
63C23×C139—21no—
64Q8×C139—41no—
65Q8×C139—41no—
66D4×C139—21no—
67D4×C139—21no—
68C2×C4×C139—21no—
69C2×C4×C139—41no—
70C2×C4×C139—41no—
71C2×C4×C139—41no—
72C2×C4×C139C2×D411yescharacteristic
73C2×C4×C139C2×D411yescharacteristic
74C2×C4×C139C2×D411yescharacteristic
75C8×C139—41no—
76C22×C139—41no—
77C22×C139—41no—
78C22×C139—41no—
79C22×C139#12011yescharacteristic
80C2×D139—22no—
81C2×D139—41no—
82C2×D139—41no—
83C4×C139—21no—
84C4×C139—41no—
85C4×C139—81no—
86C4×C139C2×D811yescharacteristic
87C4×C139#13511yescharacteristic
88C4×C139AGL(1,ℤ/8)11yescharacteristic
89C4×C139#13711yescharacteristic
90Dic139—42no—
91Dic139—41no—
92C2×C139—81no—
93C2×C139#44711yescharacteristic
94C2×C139#45211yescharacteristic
95C2×C139#45611yescharacteristic
96D139—42no—
97C139#164711yescharacteristic, complemented, Sylow
98#1647—1391nomaximal, Sylow
99#547—1391no—
100#500—1391no—
101#474D13911yescharacteristic, complemented
102#461—1391no—
103#332—1391no—
104D4⋊C8—1391no—
105D4⋊C8—1391no—
106C2×#41—2781no—
107C2×SD16—2781no—
108C4⋊Q8—1391no—
109C4⋊Q8C2×D13911yescharacteristic
110#123—2782no—
111C22⋊Q8—2781no—
112#121—2781no—
113C4×D4—1391no—
114C4×D4C2×D13911yescharacteristic
115C2×C4⋊C4—2781no—
116#107—21no—
117#107—2782no—
118C4⋊C8—1391no—
119C4⋊C8C2×D13911yescharacteristic
120#103—2781no—
121#102—21no—
122C4×C8—1391no—
123#41—5562no—
124#41—5562no—
125C2×Q8—21no—
126C2×Q8—2781no—
127C2×D4—2782no—
128C2×D4—1391no—
129C2×D4C22⋊D13911yescharacteristic
130C22×C4—21no—
131C22×C4—2782no—
132C22×C4—2781no—
133SD16—5562no—
134C2×C8—21no—
135C2×C8—2781no—
136C2×C8—2781no—
137C4⋊C4—21no—
138C4⋊C4—21no—
139C4⋊C4—2782no—
140C4⋊C4—2781no—
141C4⋊C4—1391no—
142C4⋊C4—1392no—
143C4⋊C4C22⋊D13911yescharacteristic
144C22⋊C4—21no—
145C22⋊C4—2782no—
146C22⋊C4—2781no—
147C42C22×D13911yescharacteristic
148C23—21no—
149C23—2781no—
150Q8—41no—
151Q8—41no—
152Q8—5561no—
153Q8—5561no—
154D4—21no—
155D4—21no—
156D4—2781no—
157D4—5564no—
158D4—1392no—
159C2×C4—21no—
160C2×C4—41no—
161C2×C4—41no—
162C2×C4—41no—
163C2×C4—2781no—
164C2×C4—2782no—
165C2×C4—5564no—
166C2×C4—5561no—
167C2×C4—5561no—
168C2×C4D4×D13911yescharacteristic
169C2×C4D4×D13911yescharacteristic
170C2×C4C2×C22⋊D13911yescharacteristic
171C8—41no—
172C8—2782no—
173C8—5561no—
174C22—41no—
175C22—41no—
176C22—41no—
177C22—2782no—
178C22—5561no—
179C22—5561no—
180C22#1798481011yescharacteristic
181C4—21no—
182C4—41no—
183C4—81no—
184C4—5562no—
185C4—5561no—
186C4D8×D13911yescharacteristic
187C4#1798486211yescharacteristic
188C4#1798486611yescharacteristic
189C4#1798487311yescharacteristic
190C2—81no—
191C2—5562no—
192C2#2258108511yescharacteristic
193C2#2258111311yescharacteristic
194C2#2258113411yescharacteristic
subgroupG/H
centerC22#17984810
commutator, cosocleC42×C139C23
FrattiniC42C22×D139
Fitting#474×C139C2
socleC22×C139#120
prime radical#22581608C2
hypercenter#474D139
hypocenterC139#1647
LCSG ▷ C42×C139 ▷ C22×C139 ▷ C139
UCSC1 ◁ C22 ◁ C42 ◁ #474

Complements

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

NH ≅ G/Ntype
2. #22581356C2semidirect
3. #22581155C2semidirect
4. #22580698C2semidirect
5. D4⋊(C139⋊C8)C2semidirect
6. #22580680C2semidirect
7. #474×C139C2semidirect
97. C139#1647semidirect
101. #474D139semidirect

Maximal subgroups

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

subgroupindex
#225816082
#225813562
#225811552
#225806982
D4⋊(C139⋊C8)2
#225806802
#474×C1392
#1647139