Finite Group Databasebeta

← #31805477

Subgroups — #31805477

Order 17792.

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

normal subgroups only

This group has 236 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#22581664C211yesmaximal, characteristic, complemented
2#22581327C211yesmaximal, characteristic, complemented
3#22581154C211yesmaximal, characteristic, complemented
4#22581149C211yesmaximal, characteristic
5#22580683C211yesmaximal, characteristic, complemented
6#22580680C211yesmaximal, characteristic, complemented
7#333×C139C211yesmaximal, characteristic, complemented
8C2×#14555774—21no—
9C2×#14555772—22no—
10C2×D1112—21no—
11#17984839C2211yescharacteristic
12#17984833—21no—
13#17984822—21no—
14#17984818—22no—
15C4×Dic278C2211yescharacteristic
16C4×D556C2211yescharacteristic
17#17984804—21no—
18C4⋊C4×D139—21no—
19#17984764—21no—
20#17984764—21no—
21C4×C139⋊C8C2211yescharacteristic
22C4⋊Q8×C139C2211yescharacteristic
23C4⋊C8×C139C2211yescharacteristic
24C4⋊C8×C139C2211yescharacteristic
25C2×Dic278D411yescharacteristic
26C2×D556—21no—
27C2×D556—21no—
28C2×D556—21no—
29C2×D556D411yescharacteristic
30C2×C4×D139—22no—
31C2×C4×D139—21no—
32#14555774—42no—
33#14555772—44no—
34D1112—42no—
35C2×C139⋊C8—21no—
36C4⋊Dic139—22no—
37C4⋊Dic139D411yescharacteristic
38C4⋊Dic139D411yescharacteristic
39Dic139⋊C4—22no—
40Dic139⋊C4—21no—
41(C2×D139)⋊C4—22no—
42(C2×D139)⋊C4—21no—
43C4×Dic139—21no—
44C2×Q8×C139D412yes—
45C2×C8×C139—21no—
46C2×C8×C139—21no—
47C4⋊C4×C139—21no—
48C4⋊C4×C139—21no—
49C42×C139C2311yescharacteristic
50C22×D139—21no—
51C22×D139—41no—
52Dic278—21no—
53Dic278—21no—
54D556—21no—
55D556—42no—
56D556—41no—
57D556—41no—
58D556—41no—
59D556—41no—
60D556SD1612yescomplemented
61C2×Dic139—21no—
62C2×Dic139—21no—
63C2×Dic139—21no—
64C4×D139—41no—
65C4×D139—41no—
66C4×D139—82no—
67C139⋊C8—22no—
68Q8×C139—42no—
69C2×C4×C139—22no—
70C2×C4×C139C2×D411yescharacteristic
71C2×C4×C139C2×D411yescharacteristic
72C2×C4×C139C2×D411yescharacteristic
73C8×C139—41no—
74C8×C139—41no—
75C22×C139#12011yescharacteristic
76C2×D139—22no—
77C2×D139—41no—
78C2×D139—41no—
79C2×D139—81no—
80C2×D139—81no—
81C2×D139—81no—
82C4×C139—21no—
83C4×C139—42no—
84C4×C139C2×SD1611yescharacteristic
85C4×C139#13511yescharacteristic
86C4×C139AGL(1,ℤ/8)11yescharacteristic
87C4×C139#13711yescharacteristic
88Dic139—41no—
89Dic139—41no—
90Dic139—41no—
91C2×C139#44811yescharacteristic
92C2×C139#44911yescharacteristic
93C2×C139#45311yescharacteristic
94D139—42no—
95D139—161no—
96C139#162211yescharacteristic, complemented, Sylow
97#1622—1391nomaximal, Sylow
98#554—1391no—
99#492—1391no—
100#460—1391no—
101#459—1391no—
102#333D13911yescharacteristic, complemented
103Q8⋊C8—1391no—
104D4⋊C8—1391no—
105C2×SD16—2781no—
106C2×SD16—2782no—
107C2×D8—2781no—
108C4⋊Q8C2×D13911yescharacteristic
109#127—1391no—
110#125—2781no—
111C22⋊Q8—2781no—
112C22⋊Q8—2782no—
113C4×Q8—1391no—
114C4×D4—2781no—
115C4×D4—1391no—
116C2×C4⋊C4—2781no—
117C4⋊C8C2×D13911yescharacteristic
118C4⋊C8C2×D13911yescharacteristic
119#102—2781no—
120#102—2781no—
121C4×C8—1391no—
122C2×Q8—1391no—
123C2×Q8D55612yes—
124C2×D4—2781no—
125C2×D4—2781no—
126C2×D4—2781no—
127C2×D4—1391no—
128C22×C4—2782no—
129C22×C4—2781no—
130SD16—5562no—
131SD16—5564no—
132D8—5562no—
133C2×C8—21no—
134C2×C8—21no—
135C2×C8—2781no—
136C4⋊C4—21no—
137C4⋊C4—21no—
138C4⋊C4—2782no—
139C4⋊C4—2782no—
140C4⋊C4—2781no—
141C4⋊C4—1391no—
142C4⋊C4—1391no—
143C22⋊C4—2782no—
144C22⋊C4—2781no—
145C42—2781no—
146C42C22×D13911yescharacteristic
147C23—2781no—
148C23—5561no—
149Q8—42no—
150Q8—2781no—
151Q8—2781no—
152D4—2781no—
153D4—5562no—
154D4—5561no—
155D4—5561no—
156D4—5561no—
157D4—5561no—
158D4—1392no—
159C2×C4—22no—
160C2×C4—2781no—
161C2×C4—2781no—
162C2×C4—2781no—
163C2×C4—5561no—
164C2×C4—5561no—
165C2×C4—11122no—
166C2×C4D4×D13911yescharacteristic
167C2×C4D4×D13911yescharacteristic
168C2×C4C2×D55611yescharacteristic
169C8—41no—
170C8—41no—
171C8—2782no—
172C22—2782no—
173C22—5561no—
174C22—5561no—
175C22—11121no—
176C22—11121no—
177C22—11121no—
178C22#1798481211yescharacteristic
179C4—21no—
180C4—42no—
181C4—5561no—
182C4—5561no—
183C4—5561no—
184C4SD16×D13911yescharacteristic
185C4#1798486511yescharacteristic
186C4#1798486911yescharacteristic
187C4#1798487411yescharacteristic
188C2—5562no—
189C2—22241no—
190C2#2258109311yescharacteristic
191C2#2258110111yescharacteristic
192C2#2258112311yescharacteristic
subgroupG/H
centerC22#17984812
commutator, cosocleC42×C139C23
FrattiniC42C22×D139
Fitting#333×C139C2
socleC22×C139#120
prime radical#22581149C2
hypercenter#333D139
hypocenterC139#1622
LCSG ▷ C42×C139 ▷ C22×C139 ▷ C139
UCSC1 ◁ C22 ◁ C42 ◁ #333

Complements

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

NH ≅ G/Ntype
1. #22581664C2semidirect
2. #22581327C2semidirect
3. #22581154C2semidirect
5. #22580683C2semidirect
6. #22580680C2semidirect
7. #333×C139C2semidirect
60. D556SD16semidirect
96. C139#1622semidirect
102. #333D139semidirect

Maximal subgroups

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

subgroupindex
#225816642
#225813272
#225811542
#225811492
#225806832
#225806802
#333×C1392
#1622139