Finite Group Databasebeta

← #31817797

Subgroups — #31817797

Order 17792.

342 conjugacy classes of subgroups; only the 115 normal subgroups are shown.

normal subgroups only

This group has 342 conjugacy classes of subgroups — too many to draw. Only its 115 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#22581508C211yesmaximal, characteristic
2#22581507C211yesmaximal, characteristic
3#22581237C212yesmaximal, complemented
4#22581235C211yesmaximal, characteristic, complemented
5#22581212C212yesmaximal
6#22581210C212yesmaximal
7#22581164C211yesmaximal, characteristic, complemented
8#22581163C211yesmaximal, characteristic, complemented
9#22581162C212yesmaximal, complemented
10#22580975C211yesmaximal, characteristic
11#475×C139C211yesmaximal, characteristic, complemented
12C2×Dic556C2212yes—
13C2×#14555775C2212yes—
14C2×#14555768C2212yes—
15#17984842C2211yescharacteristic
16#17984841C2211yescharacteristic
17#17984840C2211yescharacteristic
18#17984833—21no—
19#17984832—21no—
20#17984822C2211yescharacteristic
21#17984822C2212yes—
22#17984820—21no—
23#17984818—21no—
24#17984818C2211yescharacteristic
25Q8×Dic139—21no—
26C4×Dic278—21no—
27C4×Dic278C2211yescharacteristic
28#17984807C2212yes—
29#17984800—21no—
30#17984799—21no—
31C42×D139C2211yescharacteristic
32#17984773C2212yes—
33C4⋊(C139⋊C8)C2211yescharacteristic
34Dic139⋊C8C2212yes—
35#17984767C2212yes—
36#17984765C2212yes—
37#17984765C2212yes—
38C4⋊Q8×C139C2211yescharacteristic
39C4×Q8×C139C2211yescharacteristic
40#106×C139C2212yes—
41C4⋊C8×C139C2211yescharacteristic
42#103×C139C2212yes—
43C2×Dic278—21no—
44C2×Dic278C2312yes—
45C2×Dic278C2311yescharacteristic
46C2×C4×D139D411yescharacteristic
47C2×C4×D139D411yescharacteristic
48C2×C4×D139C2311yescharacteristic
49Dic556—42no—
50#14555775—42no—
51#14555768—42no—
52C2×C139⋊C8C2312yes—
53C4⋊Dic139—21no—
54C4⋊Dic139—22no—
55C4⋊Dic139—21no—
56C4⋊Dic139—21no—
57C4⋊Dic139C2311yescharacteristic
58Dic139⋊C4—21no—
59Dic139⋊C4—21no—
60Dic139⋊C4—22no—
61Dic139⋊C4—21no—
62Dic139⋊C4—21no—
63Dic139⋊C4—21no—
64(C2×D139)⋊C4—21no—
65(C2×D139)⋊C4—21no—
66(C2×D139)⋊C4—22no—
67C4×Dic139—22no—
68C4×Dic139—21no—
69C4×Dic139D411yescharacteristic
70C4×Dic139D411yescharacteristic
71C4×Dic139C2311yescharacteristic
72C2×Q8×C139—21no—
73C2×Q8×C139C2311yescharacteristic
74C2×C8×C139C2312yes—
75C4⋊C4×C139—21no—
76C4⋊C4×C139—21no—
77C4⋊C4×C139C2312yes—
78C4⋊C4×C139C2311yescharacteristic
79C42×C139—21no—
80C42×C139C2311yescharacteristic
81C22×D139C2×D411yescharacteristic
82Dic278—22no—
83Dic278—21no—
84Dic278—22no—
85Dic278—21no—
86Dic278—42no—
87C2×Dic139—21no—
88C2×Dic139—21no—
89C2×Dic139—22no—
90C2×Dic139C2×D411yescharacteristic
91C2×Dic139C2×D411yescharacteristic
92C2×Dic139C2×D411yescharacteristic
93C4×D139—22no—
94C4×D139—21no—
95C4×D139—21no—
96C4×D139—22no—
97C139⋊C8—22no—
98Q8×C139—21no—
99Q8×C139—21no—
100Q8×C139—42no—
101C2×C4×C139—21no—
102C2×C4×C139—21no—
103C2×C4×C139—22no—
104C2×C4×C139C2×D411yescharacteristic
105C2×C4×C139C2×D411yescharacteristic
106C2×C4×C139C2411yescharacteristic
107C8×C139—22no—
108C22×C139C22×D411yescharacteristic
109C2×D139—21no—
110C2×D139—21no—
111C2×D139—21no—
112C4×C139—21no—
113C4×C139—41no—
114C4×C139—42no—
115C4×C139—41no—
116C4×C139#13712yes—
117C4×C139H(5,𝔽2)11yescharacteristic
118C4×C1392−1+411yescharacteristic
119Dic139—21no—
120Dic139—21no—
121Dic139—41no—
122Dic139—42no—
123Dic139—41no—
124Dic139#13712yes—
125C2×C139#53711yescharacteristic
126C2×C139C2×#13711yescharacteristic
127C2×C139C2×#13711yescharacteristic
128D139—41no—
129C139#325511yescharacteristic, complemented, Sylow
130#3255—1391nomaximal, Sylow
131#533—1391no—
132#533—1391no—
133#475—1391no—
134#475—1392no—
135#475D13911yescharacteristic, complemented
136#470—1392no—
137#470—1392no—
138#462—1391no—
139#462—1391no—
140#462—1392no—
141#423—1391no—
142C2×Q16—1392no—
143C2×Q16—1392no—
144C2×M16—1392no—
145C4⋊Q8—1391no—
146C4⋊Q8—1391no—
147C4⋊Q8—1391no—
148C4⋊Q8C2×D13911yescharacteristic
149#125—2781no—
150#125—2781no—
151C22⋊Q8—2781no—
152C22⋊Q8—2781no—
153C22⋊Q8—1391no—
154C22⋊Q8—1391no—
155C22⋊Q8—1392no—
156C4×Q8—2781no—
157C4×Q8—2781no—
158C4×Q8—1392no—
159C4×Q8—1391no—
160C4×Q8C2×D13911yescharacteristic
161#117—2781no—
162#117—2781no—
163C2×C42—1391no—
164#106—1392no—
165#106C2×D13912yes—
166C4⋊C8—1392no—
167C4⋊C8—1391no—
168C4⋊C8C2×D13911yescharacteristic
169#103—1392no—
170#103—1392no—
171#103—1392no—
172#103C2×D13912yes—
173C2×Q8—21no—
174C2×Q8—2781no—
175C2×Q8—1392no—
176C2×Q8—1391no—
177C2×Q8C22×D13911yescharacteristic
178C22×C4—1391no—
179C22×C4—1391no—
180C22×C4—1391no—
181Q16—5562no—
182Q16—5562no—
183M16—5562no—
184C2×C8—1392no—
185C2×C8C22×D13912yes—
186C4⋊C4—21no—
187C4⋊C4—21no—
188C4⋊C4—2781no—
189C4⋊C4—2781no—
190C4⋊C4—2781no—
191C4⋊C4—2781no—
192C4⋊C4—2782no—
193C4⋊C4—2781no—
194C4⋊C4—2782no—
195C4⋊C4—2781no—
196C4⋊C4—2781no—
197C4⋊C4—2781no—
198C4⋊C4—1391no—
199C4⋊C4C22×D13911yescharacteristic
200C4⋊C4C22×D13912yes—
201C22⋊C4—2781no—
202C22⋊C4—2781no—
203C22⋊C4—2782no—
204C42—21no—
205C42—2782no—
206C42—2781no—
207C42—1391no—
208C42—1391no—
209C42—1391no—
210C42C22×D13911yescharacteristic
211C23—1391no—
212Q8—21no—
213Q8—21no—
214Q8—42no—
215Q8—2781no—
216Q8—2782no—
217Q8—2782no—
218Q8—2781no—
219Q8—5562no—
220C2×C4—21no—
221C2×C4—21no—
222C2×C4—22no—
223C2×C4—2782no—
224C2×C4—2782no—
225C2×C4—2781no—
226C2×C4—2781no—
227C2×C4—2782no—
228C2×C4—2781no—
229C2×C4—2781no—
230C2×C4—1391no—
231C2×C4—1391no—
232C2×C4—1391no—
233C2×C4D4×D13911yescharacteristic
234C2×C4D4×D13911yescharacteristic
235C2×C4C23×D13911yescharacteristic
236C8—22no—
237C8—2782no—
238C22—2781no—
239C22—2781no—
240C22—2781no—
241C22C2×D4×D13911yescharacteristic
242C4—21no—
243C4—41no—
244C4—41no—
245C4—42no—
246C4—2781no—
247C4—2781no—
248C4—5562no—
249C4—5561no—
250C4—5561no—
251C4—1392no—
252C4#1798487112yes—
253C4#1798488811yescharacteristic
254C4#1798489011yescharacteristic
255C2—5561no—
256C2#2258153311yescharacteristic
257C2#137×D13911yescharacteristic
258C2C2×#1798487111yescharacteristic
subgroupG/H
centerC22C2×D4×D139
commutator, cosocleC2×C4×C139C24
FrattiniC2×C4C23×D139
Fitting#475×C139C2
socleC22×C139C22×D4
prime radicalC22×D139C2×D4
hypercenter#475D139
hypocenterC139#3255
LCSG ▷ C2×C4×C139 ▷ C2×C139 ▷ C139
UCSC1 ◁ C22 ◁ C42 ◁ #475

Complements

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

NH ≅ G/Ntype
3. #22581237C2semidirect
4. #22581235C2semidirect
7. #22581164C2semidirect
8. #22581163C2semidirect
9. #22581162C2semidirect
11. #475×C139C2semidirect
129. C139#3255semidirect
135. #475D139semidirect

Maximal subgroups

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

subgroupindex
#225815082
#225815072
#225812372
#225812352
#225812122
#225812102
#225811642
#225811632
#225811622
#225809752
#475×C1392
#3255139