Finite Group Databasebeta

← #31817004

Subgroups — #31817004

Order 17792.

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

normal subgroups only

This group has 364 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#22581487C211yesmaximal, characteristic
2#22581359C211yesmaximal, characteristic, complemented
3#22581345C211yesmaximal, characteristic, complemented
4#22581321C211yesmaximal, characteristic, complemented
5#22581315C211yesmaximal, characteristic, complemented
6#22581209C212yesmaximal, complemented
7#22581201C212yesmaximal
8C4×#14555775C212yesmaximal, complemented
9C4×#14555772C212yesmaximal, complemented
10C4×#14555769C211yesmaximal, characteristic, complemented
11#533×C139C211yesmaximal, characteristic, complemented
12C2×#14555775C2212yes—
13C2×#14555772C2212yes—
14C2×#14555769C2212yes—
15#17984836—21no—
16#17984834C2211yescharacteristic
17#17984830C2211yescharacteristic
18#17984825—21no—
19#17984821C2211yescharacteristic
20#17984816C2211yescharacteristic
21C4×Dic278C2211yescharacteristic
22C4×D556C2211yescharacteristic
23C4×C22⋊D139—21no—
24#17984799—21no—
25#17984775C2212yes—
26#17984773C2212yes—
27#17984766C2212yes—
28#17984766C2212yes—
29#17984765C2212yes—
30#17984762C2212yes—
31#17984753C2211yescharacteristic
32#17984753C2211yescharacteristic
33C4×C139⋊C8C2212yes—
34C4⋊Q8×C139C2211yescharacteristic
35C4⋊Q8×C139C2211yescharacteristic
36#125×C139—21no—
37C22⋊Q8×C139—21no—
38C22⋊Q8×C139C2212yes—
39C4×Q8×C139—21no—
40C4×Q8×C139C2212yes—
41#117×C139—21no—
42C2×C42×C139C2211yescharacteristic
43C2×Dic278C2311yescharacteristic
44C2×D556C2311yescharacteristic
45C2×C22⋊D139—21no—
46C2×C4×D139—21no—
47#14555775—24no—
48#14555772—24no—
49#14555769—24no—
50C2×C139⋊C8C2312yes—
51C2×C139⋊C8C2312yes—
52C4⋊Dic139C2311yescharacteristic
53C4⋊Dic139C2311yescharacteristic
54Dic139⋊C4—21no—
55Dic139⋊C4—21no—
56Dic139⋊C4—21no—
57Dic139⋊C4—21no—
58C22⋊Dic139—21no—
59(C2×D139)⋊C4—21no—
60(C2×D139)⋊C4—21no—
61(C2×D139)⋊C4—21no—
62(C2×D139)⋊C4—21no—
63C4×Dic139—21no—
64C2×Q8×C139—21no—
65C2×Q8×C139C2312yes—
66C22×C4×C139D411yescharacteristic
67C22×C4×C139D411yescharacteristic
68C22×C4×C139C2311yescharacteristic
69C4⋊C4×C139—21no—
70C4⋊C4×C139—21no—
71C4⋊C4×C139—21no—
72C4⋊C4×C139—22no—
73C4⋊C4×C139—22no—
74C4⋊C4×C139C2312yes—
75C22⋊C4×C139—22no—
76C42×C139—22no—
77C42×C139D411yescharacteristic
78C42×C139D411yescharacteristic
79C42×C139C2311yescharacteristic
80C42×C139C2311yescharacteristic
81C22×D139—21no—
82Dic278—22no—
83D556—22no—
84C22⋊D139—42no—
85C2×Dic139—21no—
86C2×Dic139—21no—
87C2×Dic139—21no—
88C4×D139—42no—
89C139⋊C8—22no—
90C139⋊C8#4114yes—
91C23×C139C2×D411yescharacteristic
92Q8×C139—22no—
93Q8×C139—22no—
94Q8×C139—42no—
95C2×C4×C139—22no—
96C2×C4×C139—22no—
97C2×C4×C139—22no—
98C2×C4×C139—22no—
99C2×C4×C139—41no—
100C2×C4×C139C2×D411yescharacteristic
101C2×C4×C139C2×D411yescharacteristic
102C2×C4×C139C2×D411yescharacteristic
103C2×C4×C139C2×D411yescharacteristic
104C2×C4×C139C2×D411yescharacteristic
105C2×C4×C139C2411yescharacteristic
106C22×C139—21no—
107C22×C139—21no—
108C22×C139—21no—
109C22×C139C22×D411yescharacteristic
110C2×D139—41no—
111C2×D139—41no—
112C2×D139—41no—
113C4×C139—21no—
114C4×C139—21no—
115C4×C139—21no—
116C4×C139—21no—
117C4×C139—42no—
118C4×C139—42no—
119C4×C139#13712yes—
120C4×C139C2×#4112yes—
121Dic139—41no—
122Dic139—41no—
123Dic139—41no—
124C2×C139—41no—
125C2×C139#53211yescharacteristic
126C2×C139C2×#13711yescharacteristic
127C2×C139#57511yescharacteristic
128D139—81no—
129C139#317211yescharacteristic, complemented, Sylow
130#3172—1391nomaximal, Sylow
131#533D13911yescharacteristic, complemented
132#529—1391no—
133#501—1391no—
134#497—1391no—
135#491—1391no—
136#489—1391no—
137#470—1392no—
138#468—1392no—
139C4×Q16—1392no—
140C4×SD16—1392no—
141C4×M16—1391no—
142C2×Q16—1392no—
143C2×SD16—1392no—
144C2×M16—1392no—
145C4⋊Q8C2×D13911yescharacteristic
146C4⋊Q8C2×D13911yescharacteristic
147#126—2781no—
148#125—21no—
149#125—1391no—
150#124—1391no—
151#123—2781no—
152C22⋊Q8—21no—
153C22⋊Q8—1391no—
154C22⋊Q8C2×D13912yes—
155#121—1391no—
156C4×Q8—21no—
157C4×Q8—1391no—
158C4×Q8C2×D13912yes—
159C4×D4—2781no—
160C4×D4—1391no—
161#117—21no—
162#117—2781no—
163C2×C42C2×D13911yescharacteristic
164#107—1392no—
165#106—1392no—
166#103—1392no—
167#103—1392no—
168#103—1392no—
169#102—1392no—
170#97—1391no—
171#97—1391no—
172C4×C8—1392no—
173C2×Q8—21no—
174C2×Q8—1391no—
175C2×Q8C22×D13912yes—
176C2×D4—2781no—
177C2×D4—1391no—
178C22×C4—2781no—
179C22×C4C22⋊D13911yescharacteristic
180C22×C4C22⋊D13911yescharacteristic
181C22×C4C22×D13911yescharacteristic
182Q16—2784no—
183SD16—2784no—
184M16—2784no—
185C2×C8—1392no—
186C2×C8—1392no—
187C4⋊C4—21no—
188C4⋊C4—21no—
189C4⋊C4—21no—
190C4⋊C4—22no—
191C4⋊C4—22no—
192C4⋊C4—2781no—
193C4⋊C4—2781no—
194C4⋊C4—2781no—
195C4⋊C4—2781no—
196C4⋊C4—1391no—
197C4⋊C4—1391no—
198C4⋊C4C22×D13912yes—
199C22⋊C4—22no—
200C22⋊C4—2781no—
201C22⋊C4—2781no—
202C22⋊C4—2781no—
203C22⋊C4—2781no—
204C22⋊C4—2781no—
205C42—22no—
206C42—2781no—
207C42C22⋊D13911yescharacteristic
208C42C22⋊D13911yescharacteristic
209C42C22×D13911yescharacteristic
210C42C22×D13911yescharacteristic
211C23—2781no—
212C23C2×C22⋊D13911yescharacteristic
213Q8—22no—
214Q8—22no—
215Q8—42no—
216Q8—2782no—
217D4—2782no—
218D4—5562no—
219C2×C4—22no—
220C2×C4—22no—
221C2×C4—22no—
222C2×C4—22no—
223C2×C4—41no—
224C2×C4—2781no—
225C2×C4—2781no—
226C2×C4—2781no—
227C2×C4—5562no—
228C2×C4C2×C22⋊D13911yescharacteristic
229C2×C4C2×C22⋊D13911yescharacteristic
230C2×C4C2×C22⋊D13911yescharacteristic
231C2×C4C2×C22⋊D13911yescharacteristic
232C2×C4C2×C22⋊D13911yescharacteristic
233C2×C4C23×D13911yescharacteristic
234C8—2782no—
235C8—1394no—
236C22—21no—
237C22—21no—
238C22—21no—
239C22—5561no—
240C22—5561no—
241C22—5561no—
242C22C22×C22⋊D13911yescharacteristic
243C4—21no—
244C4—21no—
245C4—21no—
246C4—21no—
247C4—42no—
248C4—42no—
249C4—5561no—
250C4—5561no—
251C4—5561no—
252C4#1798487312yes—
253C4#41×D13912yes—
254C2—41no—
255C2—11121no—
256C2#2258149911yescharacteristic
257C2C2×#1798487311yescharacteristic
258C2#2258175111yescharacteristic
subgroupG/H
centerC2×C4C2×C22⋊D139
commutator, cosocleC2×C4×C139C24
FrattiniC2×C4C23×D139
Fitting#533×C139C2
socleC22×C139C22×D4
prime radical#17984816C22
hypercenter#533D139
hypocenterC139#3172
LCSG ▷ C2×C4×C139 ▷ C2×C139 ▷ C139
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #533

Complements

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

NH ≅ G/Ntype
2. #22581359C2semidirect
3. #22581345C2semidirect
4. #22581321C2semidirect
5. #22581315C2semidirect
6. #22581209C2semidirect
8. C4×#14555775C2semidirect
9. C4×#14555772C2semidirect
10. C4×#14555769C2semidirect
11. #533×C139C2semidirect
129. C139#3172semidirect
131. #533D139semidirect

Maximal subgroups

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

subgroupindex
#225814872
#225813592
#225813452
#225813212
#225813152
#225812092
#225812012
C4×#145557752
C4×#145557722
C4×#145557692
#533×C1392
#3172139