Finite Group Databasebeta

← #31805470

Subgroups — #31805470

Order 17792.

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

normal subgroups only

This group has 278 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#22581623C211yesmaximal, characteristic, complemented
2#22581329C211yesmaximal, characteristic, complemented
3#22581154C211yesmaximal, characteristic, complemented
4#22581149C211yesmaximal, characteristic, complemented
5#22580683C211yesmaximal, characteristic, complemented
6#22580680C211yesmaximal, characteristic, complemented
7#331×C139C211yesmaximal, characteristic, complemented
8C2×#14555784—21no—
9C2×#14555774—21no—
10C2×D1112—21no—
11C2×#14555770—22no—
12#17984839C2211yescharacteristic
13#17984838—21no—
14#17984814—22no—
15#17984813—21no—
16C4×Dic278C2211yescharacteristic
17C4×D556C2211yescharacteristic
18D4×Dic139—21no—
19#17984764—21no—
20#17984764—21no—
21C4×C139⋊C8C2211yescharacteristic
22#127×C139C2211yescharacteristic
23C4⋊C8×C139C2211yescharacteristic
24C4⋊C8×C139C2211yescharacteristic
25#14555784—42no—
26#14555784—42no—
27C2×Dic278D411yescharacteristic
28C2×D556—21no—
29C2×D556—21no—
30C2×D556—21no—
31C2×D556D411yescharacteristic
32C2×C22⋊D139—22no—
33C2×C22⋊D139—22no—
34C22×Dic139—22no—
35C2×C4×D139—21no—
36#14555774—42no—
37D1112—42no—
38#14555770—44no—
39C2×C139⋊C8—21no—
40C4⋊Dic139D411yescharacteristic
41C4⋊Dic139D411yescharacteristic
42Dic139⋊C4—21no—
43C22⋊Dic139—22no—
44(C2×D139)⋊C4—21no—
45C4×Dic139—21no—
46C2×D4×C139—21no—
47C2×D4×C139—21no—
48C2×D4×C139D412yes—
49C2×C8×C139—21no—
50C2×C8×C139—21no—
51C42×C139C2311yescharacteristic
52C22×D139—21no—
53C22×D139—41no—
54Dic278—21no—
55Dic278D812yescomplemented
56D556—21no—
57D556—21no—
58D556—42no—
59D556—41no—
60D556—41no—
61D556—41no—
62D556—41no—
63C22⋊D139—44no—
64C22⋊D139—82no—
65C2×Dic139—21no—
66C2×Dic139—21no—
67C2×Dic139—21no—
68C2×Dic139—44no—
69C4×D139—41no—
70C4×D139—41no—
71C139⋊C8—22no—
72C23×C139—22no—
73D4×C139—42no—
74D4×C139—41no—
75D4×C139—41no—
76D4×C139—41no—
77D4×C139—41no—
78C2×C4×C139C2×D411yescharacteristic
79C2×C4×C139C2×D411yescharacteristic
80C2×C4×C139C2×D411yescharacteristic
81C8×C139—41no—
82C8×C139—41no—
83C22×C139—42no—
84C22×C139—42no—
85C22×C139—42no—
86C22×C139#12011yescharacteristic
87C2×D139—41no—
88C2×D139—41no—
89C2×D139—41no—
90C2×D139—81no—
91C2×D139—81no—
92C2×D139—81no—
93C4×C139—21no—
94C4×C139C2×D811yescharacteristic
95C4×C139#13511yescharacteristic
96C4×C139AGL(1,ℤ/8)11yescharacteristic
97C4×C139AGL(1,ℤ/8)11yescharacteristic
98Dic139—22no—
99Dic139—41no—
100Dic139—41no—
101C2×C139—82no—
102C2×C139#44711yescharacteristic
103C2×C139#44911yescharacteristic
104C2×C139#45311yescharacteristic
105D139—81no—
106D139—161no—
107C139#162111yescharacteristic, complemented, Sylow
108#1621—1391nomaximal, Sylow
109#550—1391no—
110#493—1391no—
111#460—1391no—
112#459—1391no—
113#331D13911yescharacteristic, complemented
114Q8⋊C8—1391no—
115D4⋊C8—1391no—
116C2×#41—2781no—
117C2×SD16—2781no—
118C2×D8—2781no—
119C2×D8—2782no—
120#127—2781no—
121#127—1391no—
122#127C2×D13911yescharacteristic
123#121—2782no—
124#121—2781no—
125C4×Q8—1391no—
126C4×D4—2781no—
127C4×D4—1391no—
128C4⋊C8C2×D13911yescharacteristic
129C4⋊C8C2×D13911yescharacteristic
130#102—2781no—
131#102—2781no—
132C4×C8—1391no—
133#41—5562no—
134#41—5562no—
135C2×Q8—1391no—
136C2×D4—21no—
137C2×D4—21no—
138C2×D4—2782no—
139C2×D4—2782no—
140C2×D4—2781no—
141C2×D4—2781no—
142C2×D4—2781no—
143C2×D4—1391no—
144C2×D4D55612yes—
145C22×C4—2782no—
146C22×C4—2781no—
147SD16—5562no—
148D8—5562no—
149D8—5564no—
150C2×C8—21no—
151C2×C8—21no—
152C2×C8—2781no—
153C4⋊C4—2781no—
154C4⋊C4—1391no—
155C4⋊C4—1391no—
156C22⋊C4—2782no—
157C22⋊C4—2781no—
158C42—2781no—
159C42C22×D13911yescharacteristic
160C23—22no—
161C23—2781no—
162C23—5561no—
163Q8—2781no—
164Q8—1392no—
165D4—42no—
166D4—41no—
167D4—41no—
168D4—41no—
169D4—41no—
170D4—2781no—
171D4—2781no—
172D4—5562no—
173D4—5564no—
174D4—5561no—
175D4—5561no—
176D4—5561no—
177D4—5561no—
178D4—11122no—
179C2×C4—2781no—
180C2×C4—2781no—
181C2×C4—2781no—
182C2×C4—5564no—
183C2×C4—5561no—
184C2×C4—5561no—
185C2×C4D4×D13911yescharacteristic
186C2×C4D4×D13911yescharacteristic
187C2×C4C2×D55611yescharacteristic
188C8—41no—
189C8—41no—
190C8—2782no—
191C22—42no—
192C22—42no—
193C22—42no—
194C22—5561no—
195C22—5561no—
196C22—5561no—
197C22—11121no—
198C22—11121no—
199C22—11121no—
200C22#1798481211yescharacteristic
201C4—21no—
202C4—2782no—
203C4—5561no—
204C4—5561no—
205C4D8×D13911yescharacteristic
206C4#1798486311yescharacteristic
207C4#1798486611yescharacteristic
208C4#1798486911yescharacteristic
209C2—82no—
210C2—11121no—
211C2—22241no—
212C2#2258108811yescharacteristic
213C2#2258109911yescharacteristic
214C2#2258112311yescharacteristic
subgroupG/H
centerC22#17984812
commutator, cosocleC42×C139C23
FrattiniC42C22×D139
Fitting#331×C139C2
socleC22×C139#120
hypercenter#331D139
hypocenterC139#1621
LCSG ▷ C42×C139 ▷ C22×C139 ▷ C139
UCSC1 ◁ C22 ◁ C42 ◁ #331

Complements

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

NH ≅ G/Ntype
1. #22581623C2semidirect
2. #22581329C2semidirect
3. #22581154C2semidirect
4. #22581149C2semidirect
5. #22580683C2semidirect
6. #22580680C2semidirect
7. #331×C139C2semidirect
55. Dic278D8semidirect
107. C139#1621semidirect
113. #331D139semidirect

Maximal subgroups

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

subgroupindex
#225816232
#225813292
#225811542
#225811492
#225806832
#225806802
#331×C1392
#1621139