Finite Group Databasebeta

← #31817806

Subgroups — #31817806

Order 17792.

354 conjugacy classes of subgroups; only the 109 normal subgroups are shown.

normal subgroups only

This group has 354 conjugacy classes of subgroups — too many to draw. Only its 109 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#22581489C212yesmaximal, complemented
2#22581258C212yesmaximal, complemented
3#22581252C212yesmaximal, complemented
4#22581206C211yesmaximal, characteristic
5#22581201C212yesmaximal, complemented
6#22581177C212yesmaximal, complemented
7#22581171C212yesmaximal, complemented
8#22580976C211yesmaximal, characteristic, complemented
9#470×C139C211yesmaximal, characteristic, complemented
10C2×#14555772C2212yes—
11C2×D1112C2211yescharacteristic
12C2×#14555769C2211yescharacteristic
13#17984837—22no—
14#17984833C2212yes—
15#17984831C2212yes—
16#17984826—22no—
17#17984816C2212yes—
18Q8×Dic139C2212yes—
19#17984804C2212yes—
20(C22⋊D139)⋊C4—22no—
21#17984800—22no—
22C2×C4×Dic139C2211yescharacteristic
23#17984775C2212yes—
24#17984774C2211yescharacteristic
25Dic139⋊C8C2212yes—
26Dic139⋊C8C2212yes—
27#17984766C2212yes—
28#17984764C2212yes—
29#17984762C2212yes—
30C2×Q16×C139C2211yescharacteristic
31C2×M16×C139C2211yescharacteristic
32C22⋊Q8×C139C2212yes—
33#106×C139C2211yescharacteristic
34#103×C139C2212yes—
35C2×D556C2312yes—
36C2×C22⋊D139—22no—
37C22×Dic139D412yes—
38C2×C4×D139—22no—
39#14555772—42no—
40D1112—41no—
41#14555769—41no—
42C2×C139⋊C8C2312yes—
43C4⋊Dic139—22no—
44C4⋊Dic139—22no—
45C4⋊Dic139C2312yes—
46Dic139⋊C4—22no—
47(C2×D139)⋊C4—22no—
48(C2×D139)⋊C4—22no—
49(C2×D139)⋊C4—22no—
50(C2×D139)⋊C4—22no—
51C4×Dic139—22no—
52C4×Dic139D411yescharacteristic
53C4×Dic139D411yescharacteristic
54C4×Dic139C2312yes—
55C2×Q8×C139C2312yes—
56C22×C4×C139C2311yescharacteristic
57Q16×C139—41no—
58M16×C139—41no—
59C2×C8×C139C2311yescharacteristic
60C2×C8×C139C2311yescharacteristic
61C4⋊C4×C139—22no—
62C4⋊C4×C139C2312yes—
63C22⋊C4×C139—22no—
64C22×D139—22no—
65D556—22no—
66D556—22no—
67C22⋊D139—44no—
68C2×Dic139—22no—
69C2×Dic139—42no—
70C2×Dic139C2×D412yes—
71C2×Dic139C2×D412yes—
72C4×D139—44no—
73C139⋊C8—22no—
74C23×C139C2×D411yescharacteristic
75Q8×C139—22no—
76Q8×C139—22no—
77C2×C4×C139—21no—
78C2×C4×C139—21no—
79C2×C4×C139—22no—
80C2×C4×C139—22no—
81C2×C4×C139C2×D411yescharacteristic
82C2×C4×C139C2411yescharacteristic
83C8×C139—21no—
84C8×C139—21no—
85C22×C139—21no—
86C22×C139—22no—
87C22×C139C22×D411yescharacteristic
88C2×D139—42no—
89C2×D139—42no—
90C2×D139—42no—
91C4×C139—21no—
92C4×C139—42no—
93C4×C139—42no—
94C4×C139H(5,𝔽2)11yescharacteristic
95C4×C1392−1+411yescharacteristic
96Dic139—22no—
97Dic139—22no—
98Dic139—42no—
99C2×C139—41no—
100C2×C139#53711yescharacteristic
101C2×C139#57512yes—
102D139—82no—
103C139#325611yescharacteristic, complemented, Sylow
104#3256—1391nomaximal, Sylow
105#529—1392no—
106#479—1392no—
107#478—1392no—
108#470D13911yescharacteristic, complemented
109#469—1391no—
110#468—1392no—
111#464—1392no—
112#463—1392no—
113#423—1391no—
114C2×Q16C2×D13911yescharacteristic
115C2×SD16—1392no—
116C2×D8—1391no—
117C2×M16—1391no—
118C2×M16C2×D13911yescharacteristic
119#126—2782no—
120#125—1392no—
121#124—1392no—
122#123—2782no—
123C22⋊Q8C2×D13912yes—
124#121—1392no—
125C4×Q8—1392no—
126C4×D4—2782no—
127C4×D4—1392no—
128#117—2782no—
129C2×C42—1391no—
130#107—1392no—
131#106—1391no—
132#106C2×D13911yescharacteristic
133C4⋊C8—1392no—
134C4⋊C8—1392no—
135#103—1392no—
136#103C2×D13912yes—
137#102—1392no—
138#102—1392no—
139C2×Q8C22×D13912yes—
140C2×D4—2782no—
141C2×D4—1392no—
142C22×C4—2782no—
143C22×C4—1392no—
144C22×C4C22×D13911yescharacteristic
145Q16—41no—
146SD16—5562no—
147D8—5561no—
148M16—41no—
149M16—5561no—
150C2×C8—1392no—
151C2×C8C22×D13911yescharacteristic
152C2×C8C22×D13911yescharacteristic
153C4⋊C4—22no—
154C4⋊C4—2782no—
155C4⋊C4—2782no—
156C4⋊C4—2782no—
157C4⋊C4—1392no—
158C4⋊C4C22×D13912yes—
159C22⋊C4—22no—
160C22⋊C4—2782no—
161C22⋊C4—2782no—
162C22⋊C4—2782no—
163C22⋊C4—2782no—
164C42—2782no—
165C42—1391no—
166C42—1391no—
167C42—1392no—
168C23—2782no—
169C23D4×D13911yescharacteristic
170Q8—22no—
171Q8—22no—
172D4—2782no—
173D4—2782no—
174D4—5564no—
175C2×C4—21no—
176C2×C4—21no—
177C2×C4—22no—
178C2×C4—22no—
179C2×C4—2782no—
180C2×C4—5564no—
181C2×C4—5562no—
182C2×C4—1392no—
183C2×C4—1392no—
184C2×C4D4×D13911yescharacteristic
185C2×C4C23×D13911yescharacteristic
186C8—21no—
187C8—21no—
188C8—2782no—
189C22—21no—
190C22—22no—
191C22—5562no—
192C22—5562no—
193C22—5562no—
194C22C2×D4×D13911yescharacteristic
195C4—21no—
196C4—42no—
197C4—42no—
198C4—2782no—
199C4—2782no—
200C4—5562no—
201C4#1798488711yescharacteristic
202C4#1798488911yescharacteristic
203C2—41no—
204C2—11122no—
205C2#2258153011yescharacteristic
206C2#2258175212yes—
subgroupG/H
centerC22C2×D4×D139
commutator, cosocleC2×C4×C139C24
FrattiniC2×C4C23×D139
Fitting#470×C139C2
socleC22×C139C22×D4
prime radical#22581206C2
hypercenter#470D139
hypocenterC139#3256
LCSG ▷ C2×C4×C139 ▷ C2×C139 ▷ C139
UCSC1 ◁ C22 ◁ C22×C4 ◁ #470

Complements

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

NH ≅ G/Ntype
1. #22581489C2semidirect
2. #22581258C2semidirect
3. #22581252C2semidirect
5. #22581201C2semidirect
6. #22581177C2semidirect
7. #22581171C2semidirect
8. #22580976C2semidirect
9. #470×C139C2semidirect
103. C139#3256semidirect
108. #470D139semidirect

Maximal subgroups

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

subgroupindex
#225814892
#225812582
#225812522
#225812062
#225812012
#225811772
#225811712
#225809762
#470×C1392
#3256139