Finite Group Databasebeta

← #31814666

Subgroups — #31814666

Order 17792.

396 conjugacy classes of subgroups; only the 125 normal subgroups are shown.

normal subgroups only

This group has 396 conjugacy classes of subgroups — too many to draw. Only its 125 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#22580894C212yesmaximal, complemented
2#22580886C212yesmaximal, complemented
3#22580883C212yesmaximal, complemented
4#22580876C212yesmaximal
5#22580873C212yesmaximal, complemented
6#22580865C211yesmaximal, characteristic
7#22580814C211yesmaximal, characteristic
8#22580811C212yesmaximal
9#399×C139C211yesmaximal, characteristic
10C22×Dic278C2211yescharacteristic
11C23×Dic139C2211yescharacteristic
12C2×C4⋊Dic139C2212yes—
13C2×Dic139⋊C4C2212yes—
14C2×Dic139⋊C4C2212yes—
15C2×Dic139⋊C4C2212yes—
16C2×Dic139⋊C4C2212yes—
17C2×C22⋊Dic139C2212yes—
18C2×C22⋊Dic139C2211yescharacteristic
19C139⋊#95C2212yes—
20C139⋊#95C2212yes—
21C139⋊#95C2212yes—
22C139⋊#95C2212yes—
23C139⋊#95C2211yescharacteristic
24C139⋊#95C2212yes—
25C139⋊#95C2212yes—
26C2×C4⋊C4×C139C2212yes—
27C2×C4⋊C4×C139C2211yescharacteristic
28C2×C22⋊C4×C139C2212yes—
29C2×C22⋊C4×C139C2211yescharacteristic
30#95×C139C2211yescharacteristic
31C2×Dic278—41no—
32C2×Dic278—42no—
33C22×Dic139—41no—
34C22×Dic139—41no—
35C22×Dic139Q814yescomplemented
36C22×Dic139C2312yes—
37C22×Dic139C2312yes—
38C22×Dic139C2312yes—
39C22×Dic139C2312yes—
40C4⋊Dic139—42no—
41Dic139⋊C4—42no—
42Dic139⋊C4—42no—
43Dic139⋊C4—42no—
44Dic139⋊C4—42no—
45C22⋊Dic139—42no—
46C22⋊Dic139—41no—
47C24×C139C2311yescharacteristic
48C22×C4×C139C2312yes—
49C22×C4×C139C2312yes—
50C22×C4×C139C2311yescharacteristic
51C22×C4×C139C2311yescharacteristic
52C4⋊C4×C139—41no—
53C4⋊C4×C139—42no—
54C22⋊C4×C139—42no—
55C22⋊C4×C139—41no—
56Dic278—44no—
57C2×Dic139—22no—
58C2×Dic139—22no—
59C2×Dic139—22no—
60C2×Dic139—22no—
61C2×Dic139—22no—
62C2×Dic139—22no—
63C2×Dic139—22no—
64C2×Dic139—22no—
65C2×Dic139—22no—
66C2×Dic139—22no—
67C2×Dic139—22no—
68C2×Dic139—44no—
69C2×Dic139C2×Q814yes—
70C23×C139—22no—
71C23×C139—21no—
72C23×C139—21no—
73C23×C139—22no—
74C23×C139C2×Q812yes—
75C23×C139C2411yescharacteristic
76C2×C4×C139—22no—
77C2×C4×C139—21no—
78C2×C4×C139—22no—
79C2×C4×C139—21no—
80C2×C4×C139—22no—
81C2×C4×C139—22no—
82C2×C4×C139—22no—
83C2×C4×C139—22no—
84C2×C4×C139—22no—
85C2×C4×C139—22no—
86C22×C139—22no—
87C22×C139—24no—
88C22×C139—41no—
89C22×C139—42no—
90C22×C139—41no—
91C22×C139C22×Q811yescharacteristic
92C22×C139H(5,𝔽2)11yescharacteristic
93C22×C139H(5,𝔽2)12yes—
94C22×C139H(5,𝔽2)11yescharacteristic
95C22×C1392−1+412yes—
96C4×C139—42no—
97C4×C139—41no—
98C4×C139—42no—
99C4×C139—41no—
100Dic139—24no—
101Dic139—42no—
102Dic139—42no—
103Dic139—42no—
104C2×C139—42no—
105C2×C139#54311yescharacteristic
106C2×C139#54412yes—
107C2×C139#56011yescharacteristic
108C2×C139#56212yes—
109C2×C139#56311yescharacteristic
110C139#284111yescharacteristic, complemented, Sylow
111#2841—1391nomaximal, Sylow
112#400—1392no—
113#399D13911yescharacteristic
114#398—1392no—
115#398—1392no—
116#396—1392no—
117#395—1392no—
118#393—1391no—
119#381—1391no—
120#380—1392no—
121C22×Q8—1391no—
122C23×C4—1391no—
123C2×C4⋊C4—1392no—
124C2×C4⋊C4—1392no—
125C2×C4⋊C4—1392no—
126C2×C4⋊C4—1392no—
127C2×C4⋊C4—1392no—
128C2×C4⋊C4C2×D13912yes—
129C2×C4⋊C4C2×D13911yescharacteristic
130C2×C22⋊C4—1392no—
131C2×C22⋊C4—1391no—
132C2×C22⋊C4C2×D13912yes—
133C2×C22⋊C4C2×D13911yescharacteristic
134#95—1392no—
135#95—1392no—
136#95—1392no—
137#95—1392no—
138#95—1391no—
139#95—1392no—
140#95—1392no—
141#95C2×D13911yescharacteristic
142C24C22×D13911yescharacteristic
143C2×Q8—5561no—
144C2×Q8—5562no—
145C22×C4—5561no—
146C22×C4—5561no—
147C22×C4—1392no—
148C22×C4—1392no—
149C22×C4—1392no—
150C22×C4—1392no—
151C22×C4—1394no—
152C22×C4C22×D13911yescharacteristic
153C22×C4C22×D13911yescharacteristic
154C22×C4C22×D13912yes—
155C22×C4C22×D13912yes—
156C4⋊C4—41no—
157C4⋊C4—42no—
158C4⋊C4—5562no—
159C4⋊C4—5562no—
160C4⋊C4—5562no—
161C4⋊C4—5562no—
162C4⋊C4—5562no—
163C22⋊C4—42no—
164C22⋊C4—41no—
165C22⋊C4—5562no—
166C22⋊C4—5561no—
167C23—22no—
168C23—21no—
169C23—21no—
170C23—22no—
171C23Q8×D13912yes—
172C23C23×D13911yescharacteristic
173Q8—5564no—
174C2×C4—22no—
175C2×C4—21no—
176C2×C4—22no—
177C2×C4—21no—
178C2×C4—22no—
179C2×C4—22no—
180C2×C4—22no—
181C2×C4—22no—
182C2×C4—22no—
183C2×C4—22no—
184C2×C4—2782no—
185C2×C4—2782no—
186C2×C4—2782no—
187C2×C4—2782no—
188C2×C4—2782no—
189C2×C4—2782no—
190C2×C4—2782no—
191C2×C4—2782no—
192C2×C4—2782no—
193C2×C4—2782no—
194C2×C4—2782no—
195C2×C4—5564no—
196C2×C4—1394no—
197C22—22no—
198C22—24no—
199C22—41no—
200C22—42no—
201C22—41no—
202C22C2×Q8×D13911yescharacteristic
203C22#1798488711yescharacteristic
204C22#1798488712yes—
205C22#1798488811yescharacteristic
206C22#1798488912yes—
207C4—41no—
208C4—42no—
209C4—42no—
210C4—41no—
211C4—2784no—
212C4—5562no—
213C4—5562no—
214C4—5562no—
215C2—42no—
216C2#2258157811yescharacteristic
217C2#2258158212yes—
218C2#2258169011yescharacteristic
219C2#2258170012yes—
220C2#2258170611yescharacteristic
subgroupG/H
center, FrattiniC23C23×D139
commutator, socle, cosocleC23×C139C24
Fitting#399×C139C2
prime radicalC24×C139C23
hypercenter#399D139
hypocenterC139#2841
LCSG ▷ C23×C139 ▷ C139
UCSC1 ◁ C23 ◁ #399

Complements

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

NH ≅ G/Ntype
1. #22580894C2semidirect
2. #22580886C2semidirect
3. #22580883C2semidirect
5. #22580873C2semidirect
35. C22×Dic139Q8semidirect
110. C139#2841semidirect

Maximal subgroups

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

subgroupindex
#225808942
#225808862
#225808832
#225808762
#225808732
#225808652
#225808142
#225808112
#399×C1392
#2841139