Finite Group Databasebeta

← #31809670

Subgroups — #31809670

Order 17792.

560 conjugacy classes of subgroups; only the 143 normal subgroups are shown.

normal subgroups only

This group has 560 conjugacy classes of subgroups — too many to draw. Only its 143 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
1C2×#17984804C211yesmaximal, characteristic
2C2×#17984800C211yesmaximal, characteristic, complemented
3#22580888C211yesmaximal, characteristic, complemented
4#22580883C211yesmaximal, characteristic, complemented
5#22580882C212yesmaximal, complemented
6#22580880C211yesmaximal, characteristic, complemented
7#22580871C212yesmaximal
8#22580804C212yesmaximal, complemented
9#22580800C211yesmaximal, characteristic, complemented
10#22580800C212yesmaximal, complemented
11#400×C139C211yesmaximal, characteristic, complemented
12C22×D556C2211yescharacteristic
13C22×C4×D139C2211yescharacteristic
14C22×C4×D139C2211yescharacteristic
15#17984804—24no—
16#17984800—24no—
17C2×C4⋊Dic139C2211yescharacteristic
18C2×Dic139⋊C4C2212yes—
19C2×Dic139⋊C4C2212yes—
20C2×(C2×D139)⋊C4C2212yes—
21C2×(C2×D139)⋊C4C2212yes—
22C2×(C2×D139)⋊C4C2212yes—
23C2×(C2×D139)⋊C4C2212yes—
24C2×(C2×D139)⋊C4C2211yescharacteristic
25C2×(C2×D139)⋊C4C2211yescharacteristic
26C2×C4×Dic139C2212yes—
27C2×C4×Dic139C2212yes—
28C2×C4×Dic139C2211yescharacteristic
29C139⋊#95C2212yes—
30C139⋊#95C2211yescharacteristic
31C139⋊#95C2212yes—
32C2×C4⋊C4×C139C2211yescharacteristic
33C2×C4⋊C4×C139C2211yescharacteristic
34#95×C139C2211yescharacteristic
35#95×C139C2212yes—
36#95×C139C2212yes—
37C23×D139C2311yescharacteristic
38C23×D139C2311yescharacteristic
39C2×D556—22no—
40C2×D556—22no—
41C2×D556—22no—
42C22×Dic139C2311yescharacteristic
43C22×Dic139C2312yes—
44C22×Dic139C2312yes—
45C22×Dic139C2311yescharacteristic
46C2×C4×D139—24no—
47C2×C4×D139—22no—
48C2×C4×D139—24no—
49C2×C4×D139D414yes—
50C4⋊Dic139—22no—
51Dic139⋊C4—24no—
52Dic139⋊C4—24no—
53(C2×D139)⋊C4—24no—
54(C2×D139)⋊C4—22no—
55(C2×D139)⋊C4—24no—
56(C2×D139)⋊C4—24no—
57(C2×D139)⋊C4—24no—
58(C2×D139)⋊C4—22no—
59C4×Dic139—24no—
60C4×Dic139—22no—
61C4×Dic139—24no—
62C22×C4×C139C2312yes—
63C22×C4×C139C2312yes—
64C22×C4×C139C2311yescharacteristic
65C22×C4×C139C2311yescharacteristic
66C22×C4×C139C2311yescharacteristic
67C4⋊C4×C139—22no—
68C4⋊C4×C139—22no—
69C22×D139—21no—
70C22×D139—22no—
71C22×D139—22no—
72C22×D139—22no—
73C22×D139—22no—
74C22×D139—21no—
75C22×D139—21no—
76C22×D139—21no—
77C22×D139C2×D412yes—
78C22×D139#4112yes—
79D556—28no—
80C2×Dic139—22no—
81C2×Dic139—22no—
82C2×Dic139—21no—
83C2×Dic139—22no—
84C2×Dic139—22no—
85C2×Dic139—22no—
86C2×Dic139—22no—
87C2×Dic139C2×D412yes—
88C2×Dic139#4114yes—
89C2×Dic139#4114yes—
90C4×D139—28no—
91C4×D139—44no—
92C23×C139C2411yescharacteristic
93C2×C4×C139—21no—
94C2×C4×C139—22no—
95C2×C4×C139—21no—
96C2×C4×C139—22no—
97C2×C4×C139—21no—
98C2×C4×C139—22no—
99C2×C4×C139—22no—
100C2×C4×C139—22no—
101C2×C4×C139—22no—
102C2×C4×C139—22no—
103C2×C4×C139—22no—
104C2×C4×C139C2×D412yes—
105C2×C4×C139#4112yes—
106C22×C139C22×D411yescharacteristic
107C22×C139C2×#4112yes—
108C22×C139C2×#4111yescharacteristic
109C22×C139C2×#4112yes—
110C22×C139C2×#4111yescharacteristic
111C2×D139—22no—
112C2×D139—22no—
113C2×D139—22no—
114C2×D139—24no—
115C2×D139—22no—
116C2×D139—41no—
117C2×D139—42no—
118C2×D139—42no—
119C2×D139—42no—
120C2×D139—41no—
121C4×C139—22no—
122C4×C139—22no—
123C4×C139—41no—
124C4×C139—42no—
125C4×C139—42no—
126Dic139—24no—
127Dic139—42no—
128Dic139—41no—
129Dic139#12314yes—
130C2×C139C2×#12311yescharacteristic
131C2×C139#52511yescharacteristic
132C2×C139#52912yes—
133C2×C139#52912yes—
134C2×C139#53211yescharacteristic
135D139—42no—
136D139—42no—
137C139#239511yescharacteristic, complemented, Sylow
138#2395—1391nomaximal, Sylow
139C2×C4×D4—1391no—
140C2×#117—1391no—
141#400D13911yescharacteristic, complemented
142#399—1391no—
143#398—1391no—
144#397—1391no—
145#397—1392no—
146#394—1392no—
147C4×C4⋊C4—1392no—
148C4×C22⋊C4—1392no—
149C4×C22⋊C4—1391no—
150C22×D4—1391no—
151C23×C4—1391no—
152C23×C4—1391no—
153C4×D4—2784no—
154#117—2784no—
155C2×C4⋊C4—1391no—
156C2×C4⋊C4—1392no—
157C2×C4⋊C4—1392no—
158C2×C4⋊C4C2×D13911yescharacteristic
159C2×C4⋊C4C2×D13911yescharacteristic
160C2×C22⋊C4—1392no—
161C2×C22⋊C4—1391no—
162C2×C22⋊C4—1391no—
163C2×C22⋊C4—1392no—
164C2×C22⋊C4—1392no—
165C2×C22⋊C4—1392no—
166C2×C42—1392no—
167C2×C42—1391no—
168C2×C42—1392no—
169#95—1392no—
170#95—1391no—
171#95—1392no—
172#95C2×D13912yes—
173#95C2×D13911yescharacteristic
174#95C2×D13912yes—
175C24—1391no—
176C24—1391no—
177C2×D4—2782no—
178C2×D4—2782no—
179C2×D4—2782no—
180C22×C4—2784no—
181C22×C4—2782no—
182C22×C4—2784no—
183C22×C4—1391no—
184C22×C4—1392no—
185C22×C4—1392no—
186C22×C4—1394no—
187C22×C4—1391no—
188C22×C4C22×D13911yescharacteristic
189C22×C4C22×D13912yes—
190C22×C4C22×D13912yes—
191C22×C4C22×D13911yescharacteristic
192C22×C4C22×D13911yescharacteristic
193C4⋊C4—22no—
194C4⋊C4—22no—
195C4⋊C4—2784no—
196C4⋊C4—2782no—
197C4⋊C4—2784no—
198C22⋊C4—2784no—
199C22⋊C4—2784no—
200C22⋊C4—2782no—
201C22⋊C4—2784no—
202C22⋊C4—2784no—
203C22⋊C4—2782no—
204C42—2784no—
205C42—2784no—
206C42—2782no—
207C23—2781no—
208C23—2782no—
209C23—2782no—
210C23—2782no—
211C23—2782no—
212C23—2781no—
213C23—2781no—
214C23—2781no—
215C23—1392no—
216C23—1392no—
217C23C23×D13911yescharacteristic
218D4—2788no—
219C2×C4—21no—
220C2×C4—22no—
221C2×C4—21no—
222C2×C4—22no—
223C2×C4—21no—
224C2×C4—22no—
225C2×C4—22no—
226C2×C4—22no—
227C2×C4—22no—
228C2×C4—22no—
229C2×C4—22no—
230C2×C4—2788no—
231C2×C4—2782no—
232C2×C4—2782no—
233C2×C4—2781no—
234C2×C4—2782no—
235C2×C4—2782no—
236C2×C4—2782no—
237C2×C4—2782no—
238C2×C4—5564no—
239C2×C4—1394no—
240C2×C4—1392no—
241C2×C4—1394no—
242C2×C4D4×D13912yes—
243C2×C4#1455578612yes—
244C22—2782no—
245C22—2782no—
246C22—2782no—
247C22—2784no—
248C22—2782no—
249C22—5561no—
250C22—5562no—
251C22—5562no—
252C22—5562no—
253C22—5561no—
254C22C2×D4×D13911yescharacteristic
255C22#41×D13912yes—
256C22#41×D13911yescharacteristic
257C22#41×D13912yes—
258C22C2×#1455578611yescharacteristic
259C4—22no—
260C4—22no—
261C4—41no—
262C4—42no—
263C4—42no—
264C4—2784no—
265C4—5562no—
266C4—5561no—
267C4—1394no—
268C2—5562no—
269C2—5562no—
270C2#123×D13911yescharacteristic
271C2#2258146611yescharacteristic
272C2#2258148612yes—
273C2#2258148812yes—
274C2#2258150211yescharacteristic
subgroupG/H
center, FrattiniC23C23×D139
commutator, socle, cosocleC23×C139C24
Fitting#400×C139C2
prime radicalC22×D556C22
hypercenter#400D139
hypocenterC139#2395
LCSG ▷ C23×C139 ▷ C139
UCSC1 ◁ C23 ◁ #400

Complements

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

NH ≅ G/Ntype
2. C2×#17984800C2semidirect
3. #22580888C2semidirect
4. #22580883C2semidirect
5. #22580882C2semidirect
6. #22580880C2semidirect
8. #22580804C2semidirect
9. #22580800C2semidirect
10. #22580800C2semidirect
11. #400×C139C2semidirect
137. C139#2395semidirect
141. #400D139semidirect

Maximal subgroups

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

subgroupindex
C2×#179848042
C2×#179848002
#225808882
#225808832
#225808822
#225808802
#225808712
#225808042
#225808002
#400×C1392
#2395139