Finite Group Databasebeta

← #31806844

Subgroups — #31806844

Order 17792.

442 conjugacy classes of subgroups; only the 87 normal subgroups are shown.

normal subgroups only

This group has 442 conjugacy classes of subgroups — too many to draw. Only its 87 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#22581460C211yesmaximal, characteristic
2C2×C42×D139C211yesmaximal, characteristic, complemented
3C2×#17984769C211yesmaximal, characteristic, complemented
4#22580916C211yesmaximal, characteristic, complemented
5#22580714C211yesmaximal, characteristic, complemented
6#22580713C211yesmaximal, characteristic, complemented
7C2×#104×C139C211yesmaximal, characteristic, complemented
8C22×C4×D139—21no—
9C22×C4×D139C2211yescharacteristic
10C2×#14555769C2211yescharacteristic
11#17984823—21no—
12#17984818C412yescomplemented
13#17984813C412yescomplemented
14#17984810—21no—
15C4×C22⋊D139—22no—
16#17984801C2211yescharacteristic
17C2×C4×Dic139—21no—
18C2×C4×Dic139C2211yescharacteristic
19C42×D139—22no—
20C42×D139—22no—
21#17984769—22no—
22(C2×D139)⋊C8—22no—
23C2×#41×C139C2211yescharacteristic
24C2×M16×C139C2211yescharacteristic
25C2×C42×C139C2211yescharacteristic
26#104×C139—22no—
27C23×D139D411yescharacteristic
28C2×C22⋊D139—22no—
29C22×Dic139—21no—
30C22×Dic139D411yescharacteristic
31C2×C4×D139—24no—
32C2×C4×D139—28no—
33C2×C4×D139—21no—
34C2×C4×D139—21no—
35C2×C4×D139—21no—
36C2×C4×D139—21no—
37C2×C4×D139C2×C412yes—
38C2×C4×D139D412yes—
39#14555769—21no—
40#14555769—21no—
41C2×C139⋊C8—21no—
42C4⋊Dic139C2×C412yescomplemented
43Dic139⋊C4—22no—
44C22⋊Dic139—22no—
45C22⋊Dic139—21no—
46(C2×D139)⋊C4—22no—
47C4×Dic139—24no—
48C4×Dic139—21no—
49C4×Dic139—21no—
50C4×Dic139D412yescomplemented
51#41×C139—21no—
52#41×C139—21no—
53#41×C139—21no—
54#41×C139—21no—
55C2×Q8×C139C2×C411yescharacteristic, complemented
56C2×D4×C139—21no—
57C2×D4×C139C2×C411yescharacteristic, complemented
58C22×C4×C139—21no—
59C22×C4×C139—21no—
60C22×C4×C139C2311yescharacteristic
61M16×C139—21no—
62M16×C139—21no—
63C2×C8×C139—21no—
64C42×C139—21no—
65C42×C139D412yescomplemented
66C22×D139—21no—
67C22×D139—21no—
68C22×D139—24no—
69C22×D139C22⋊C412yes—
70C22⋊D139—44no—
71C2×Dic139—24no—
72C2×Dic139—21no—
73C2×Dic139—22no—
74C2×Dic139—21no—
75C2×Dic139—22no—
76C2×Dic139C22⋊C412yes—
77C4×D139—216no—
78C4×D139—22no—
79C4×D139—22no—
80C4×D139—22no—
81C4×D139—22no—
82C139⋊C8—41no—
83C23×C139—21no—
84C23×C139C2×D411yescharacteristic
85Q8×C139—21no—
86Q8×C139—21no—
87D4×C139—21no—
88D4×C139—21no—
89D4×C139—41no—
90D4×C139—41no—
91C2×C4×C139—24no—
92C2×C4×C139—22no—
93C2×C4×C139—21no—
94C2×C4×C139—41no—
95C2×C4×C139—41no—
96C2×C4×C139C22×C411yescharacteristic
97C2×C4×C139C2×D411yescharacteristic
98C2×C4×C139C2×D411yescharacteristic
99C2×C4×C139C2×D411yescharacteristic
100C2×C4×C139#4111yescharacteristic
101C2×C4×C139#4111yescharacteristic
102C8×C139—41no—
103C22×C139—22no—
104C22×C139—41no—
105C22×C139—42no—
106C22×C139C2×C22⋊C411yescharacteristic
107C22×C139#12011yescharacteristic
108C22×C139#12311yescharacteristic
109C2×D139—24no—
110C2×D139—24no—
111C2×D139—22no—
112C2×D139—22no—
113C2×D139#10414yescomplemented
114C4×C139—24no—
115C4×C139—41no—
116C4×C139C4×D411yescharacteristic
117C4×C139C4×D411yescharacteristic
118C4×C139#12111yescharacteristic
119C4×C139#12111yescharacteristic
120Dic139—24no—
121Dic139—22no—
122Dic139—42no—
123C2×C139—21no—
124C2×C139—21no—
125C2×C139—81no—
126C2×C139#38611yescharacteristic
127C2×C139C2×#10412yes—
128D139—24no—
129C139#189611yescharacteristic, complemented, Sylow
130#1896—1391nomaximal, Sylow
131#525—1391no—
132C22×C42—1391no—
133C2×#104—1391no—
134C2×#104D13911yescharacteristic, complemented
135#407—1391no—
136#339—1391no—
137#339—1391no—
138C2×#41C2×D13911yescharacteristic
139C23×C4—2781no—
140C23×C4—1391no—
141C2×M16—1391no—
142C2×M16C2×D13911yescharacteristic
143#123—2781no—
144C22⋊Q8—1392no—
145#121—1392no—
146#120—2781no—
147C4×D4—2782no—
148#117—1391no—
149C2×C42—2782no—
150C2×C42—2781no—
151C2×C42—2782no—
152C2×C42—1391no—
153C2×C42C2×D13911yescharacteristic
154#104—22no—
155#104—2782no—
156C22⋊C8—2782no—
157C24—1391no—
158#41—21no—
159#41—21no—
160#41—21no—
161#41—21no—
162C2×Q8C4×D13911yescharacteristic, complemented
163C2×D4—21no—
164C2×D4—2782no—
165C2×D4C4×D13911yescharacteristic, complemented
166C22×C4—21no—
167C22×C4—21no—
168C22×C4—2784no—
169C22×C4—2788no—
170C22×C4—2781no—
171C22×C4—2781no—
172C22×C4—2781no—
173C22×C4—2781no—
174C22×C4—2781no—
175C22×C4—1391no—
176C22×C4—1392no—
177C22×C4—1392no—
178C22×C4C22×D13911yescharacteristic
179M16—21no—
180M16—21no—
181M16—2781no—
182M16—2781no—
183C2×C8—21no—
184C2×C8—2781no—
185C4⋊C4—2782no—
186C4⋊C4—1392no—
187C22⋊C4—2782no—
188C22⋊C4—2781no—
189C22⋊C4—2782no—
190C42—21no—
191C42—2784no—
192C42—2781no—
193C42—2781no—
194C42—1392no—
195C42C22⋊D13912yescomplemented
196C23—21no—
197C23—2784no—
198C23—2781no—
199C23—2781no—
200C23—1392no—
201C23D4×D13911yescharacteristic
202Q8—21no—
203Q8—21no—
204D4—21no—
205D4—21no—
206D4—41no—
207D4—41no—
208D4—5564no—
209C2×C4—24no—
210C2×C4—22no—
211C2×C4—21no—
212C2×C4—41no—
213C2×C4—41no—
214C2×C4—27816no—
215C2×C4—2784no—
216C2×C4—2781no—
217C2×C4—2782no—
218C2×C4—2781no—
219C2×C4—2782no—
220C2×C4—2782no—
221C2×C4—2782no—
222C2×C4—2782no—
223C2×C4—2782no—
224C2×C4—1392no—
225C2×C4C2×C4×D13911yescharacteristic
226C2×C4D4×D13911yescharacteristic
227C2×C4D4×D13911yescharacteristic
228C2×C4C2×C22⋊D13911yescharacteristic
229C2×C4#1455578411yescharacteristic
230C2×C4#1455578511yescharacteristic
231C8—41no—
232C8—5561no—
233C22—22no—
234C22—41no—
235C22—42no—
236C22—2784no—
237C22—2784no—
238C22—2782no—
239C22—2782no—
240C22—1394no—
241C22C22⋊C4×D13911yescharacteristic
242C22#1798481011yescharacteristic
243C22#1798482411yescharacteristic
244C4—24no—
245C4—41no—
246C4—2784no—
247C4—2782no—
248C4—5562no—
249C4(C22⋊D139)⋊C411yescharacteristic
250C4C4×C22⋊D13911yescharacteristic
251C4#1798481311yescharacteristic
252C4#1798481511yescharacteristic
253C2—21no—
254C2—21no—
255C2—81no—
256C2—2784no—
257C2#2258082911yescharacteristic
258C2#104×D13912yes—
subgroupG/H
centerC2×C4D4×D139
commutatorC2×C4×C139C22×C4
FrattiniC22×C4C22×D139
FittingC2×#104×C139C2
socleC22×C139C2×C22⋊C4
prime radical#22581460C2
cosocleC22×C4×C139C23
hypercenterC2×#104D139
hypocenterC139#1896
LCSG ▷ C2×C4×C139 ▷ C2×C139 ▷ C139
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ C2×#104

Complements

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

NH ≅ G/Ntype
2. C2×C42×D139C2semidirect
3. C2×#17984769C2semidirect
4. #22580916C2semidirect
5. #22580714C2semidirect
6. #22580713C2semidirect
7. C2×#104×C139C2semidirect
12. #17984818C4semidirect
13. #17984813C4semidirect
42. C4⋊Dic139C2×C4semidirect
50. C4×Dic139D4semidirect
55. C2×Q8×C139C2×C4semidirect
57. C2×D4×C139C2×C4semidirect
65. C42×C139D4semidirect
113. C2×D139#104semidirect
129. C139#1896semidirect
134. C2×#104D139semidirect
162. C2×Q8C4×D139semidirect
165. C2×D4C4×D139semidirect
195. C42C22⋊D139semidirect

Maximal subgroups

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

subgroupindex
#225814602
C2×C42×D1392
C2×#179847692
#225809162
#225807142
#225807132
C2×#104×C1392
#1896139