Finite Group Databasebeta

← #31805556

Subgroups — #31805556

Order 17792.

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

normal subgroups only

This group has 234 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#22581606C211yesmaximal, characteristic
2#22581305C211yesmaximal, characteristic, complemented
3#22581244C211yesmaximal, characteristic, complemented
4#22581244C211yesmaximal, characteristic, complemented
5#22580680C211yesmaximal, characteristic, complemented
6#22580680C211yesmaximal, characteristic, complemented
7#332×C139C211yesmaximal, characteristic, complemented
8C2×#14555786—21no—
9#17984842C2211yescharacteristic
10#17984827—22no—
11#17984818—21no—
12#17984817—21no—
13C4×D556C2211yescharacteristic
14C4×D556C2211yescharacteristic
15C4⋊C4×D139—21no—
16#17984774—21no—
17#17984774—21no—
18#17984765—22no—
19#17984764—21no—
20#17984764—21no—
21C4×C139⋊C8C2211yescharacteristic
22C4⋊Q8×C139C2211yescharacteristic
23C4⋊C8×C139C2211yescharacteristic
24C4⋊C8×C139C2211yescharacteristic
25#14555786—42no—
26#14555786—42no—
27C2×Dic278—21no—
28C2×D556—22no—
29C2×D556D411yescharacteristic
30C2×D556D411yescharacteristic
31C2×C4×D139—22no—
32C2×C4×D139—21no—
33C2×C4×D139—21no—
34C2×C139⋊C8—21no—
35C4⋊Dic139—21no—
36C4⋊Dic139—21no—
37C4⋊Dic139D411yescharacteristic
38C4⋊Dic139D411yescharacteristic
39Dic139⋊C4—22no—
40(C2×D139)⋊C4—22no—
41(C2×D139)⋊C4—21no—
42(C2×D139)⋊C4—21no—
43C2×Q8×C139—21no—
44C2×C8×C139—21no—
45C2×C8×C139—21no—
46C4⋊C4×C139—21no—
47C4⋊C4×C139D412yes—
48C42×C139C2311yescharacteristic
49C22×D139—21no—
50C22×D139—21no—
51Dic278—42no—
52D556—21no—
53D556—21no—
54D556—21no—
55D556—44no—
56D556SD1612yes—
57C2×Dic139—21no—
58C2×Dic139—21no—
59C2×Dic139—41no—
60C4×D139—44no—
61C4×D139—41no—
62C4×D139—41no—
63C4×D139—41no—
64C4×D139—41no—
65C139⋊C8—41no—
66Q8×C139—41no—
67Q8×C139—41no—
68C2×C4×C139—22no—
69C2×C4×C139C2×D411yescharacteristic
70C2×C4×C139C2×D411yescharacteristic
71C2×C4×C139C2×D411yescharacteristic
72C8×C139—41no—
73C8×C139—41no—
74C22×C139#12011yescharacteristic
75C2×D139—22no—
76C2×D139—41no—
77C2×D139—41no—
78C2×D139—41no—
79C2×D139—41no—
80C2×D139—41no—
81C4×C139—21no—
82C4×C139—42no—
83C4×C139C2×SD1611yescharacteristic
84C4×C139#13511yescharacteristic
85C4×C139AGL(1,ℤ/8)11yescharacteristic
86C4×C139#13711yescharacteristic
87Dic139—41no—
88Dic139—41no—
89Dic139—81no—
90C2×C139#45011yescharacteristic
91C2×C139#45211yescharacteristic
92C2×C139#45411yescharacteristic
93D139—42no—
94D139—81no—
95C139#163511yescharacteristic, complemented, Sylow
96#1635—1391nomaximal, Sylow
97#547—1391no—
98#487—1391no—
99#476—1391no—
100#476—1391no—
101#332D13911yescharacteristic, complemented
102D4⋊C8—1391no—
103D4⋊C8—1391no—
104C2×#41—2781no—
105C4⋊Q8—1391no—
106C4⋊Q8C2×D13911yescharacteristic
107#123—2782no—
108C22⋊Q8—2781no—
109#121—2781no—
110C4×D4—1391no—
111C4×D4—1391no—
112C2×C4⋊C4—2781no—
113#106—2781no—
114#106—2781no—
115C4⋊C8C2×D13911yescharacteristic
116C4⋊C8C2×D13911yescharacteristic
117#103—2782no—
118#102—2781no—
119#102—2781no—
120C4×C8—1391no—
121#41—5562no—
122#41—5562no—
123C2×Q8—21no—
124C2×Q8—2781no—
125C2×D4—2782no—
126C2×D4—1391no—
127C2×D4—1391no—
128C22×C4—2782no—
129C22×C4—2781no—
130C22×C4—2781no—
131C2×C8—21no—
132C2×C8—21no—
133C2×C8—2781no—
134C4⋊C4—21no—
135C4⋊C4—2782no—
136C4⋊C4—2781no—
137C4⋊C4—2781no—
138C4⋊C4—1391no—
139C4⋊C4—1391no—
140C4⋊C4D55612yes—
141C22⋊C4—2782no—
142C22⋊C4—2781no—
143C22⋊C4—2781no—
144C42C22×D13911yescharacteristic
145C23—2781no—
146C23—2781no—
147Q8—41no—
148Q8—41no—
149Q8—5562no—
150D4—2781no—
151D4—2781no—
152D4—2781no—
153D4—5564no—
154D4—1392no—
155C2×C4—22no—
156C2×C4—2781no—
157C2×C4—2781no—
158C2×C4—5564no—
159C2×C4—5561no—
160C2×C4—5561no—
161C2×C4—5561no—
162C2×C4—5561no—
163C2×C4—5561no—
164C2×C4D4×D13911yescharacteristic
165C2×C4D4×D13911yescharacteristic
166C2×C4C2×D55611yescharacteristic
167C8—41no—
168C8—41no—
169C8—5561no—
170C22—2782no—
171C22—5561no—
172C22—5561no—
173C22—5561no—
174C22—5561no—
175C22—5561no—
176C22#1798481211yescharacteristic
177C4—21no—
178C4—42no—
179C4—5561no—
180C4—5561no—
181C4—11121no—
182C4SD16×D13911yescharacteristic
183C4#1798486311yescharacteristic
184C4#1798486611yescharacteristic
185C4#1798487411yescharacteristic
186C2—5562no—
187C2—11121no—
188C2#2258110511yescharacteristic
189C2#2258111811yescharacteristic
190C2#2258112811yescharacteristic
subgroupG/H
centerC22#17984812
commutator, cosocleC42×C139C23
FrattiniC42C22×D139
Fitting#332×C139C2
socleC22×C139#120
prime radical#22581606C2
hypercenter#332D139
hypocenterC139#1635
LCSG ▷ C42×C139 ▷ C22×C139 ▷ C139
UCSC1 ◁ C22 ◁ C42 ◁ #332

Complements

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

NH ≅ G/Ntype
2. #22581305C2semidirect
3. #22581244C2semidirect
4. #22581244C2semidirect
5. #22580680C2semidirect
6. #22580680C2semidirect
7. #332×C139C2semidirect
95. C139#1635semidirect
101. #332D139semidirect

Maximal subgroups

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

subgroupindex
#225816062
#225813052
#225812442
#225806802
#332×C1392
#1635139