Finite Group Databasebeta

← #31809673

Subgroups — #31809673

Order 17792.

528 conjugacy classes of subgroups; only the 155 normal subgroups are shown.

normal subgroups only

This group has 528 conjugacy classes of subgroups — too many to draw. Only its 155 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×#17984807C211yesmaximal, characteristic, complemented
2C2×#17984798C211yesmaximal, characteristic
3#22580891C211yesmaximal, characteristic, complemented
4#22580884C212yesmaximal, complemented
5#22580876C212yesmaximal
6#22580874C211yesmaximal, characteristic, complemented
7#22580865C211yesmaximal, characteristic
8C4⋊C4×Dic139C212yesmaximal, complemented
9#22580804C211yesmaximal, characteristic, complemented
10C22⋊C4×Dic139C212yesmaximal
11#399×C139C211yesmaximal, characteristic
12C22×Dic278C2211yescharacteristic
13C23×Dic139C2211yescharacteristic
14#17984807—24no—
15#17984798—24no—
16C2×C4⋊Dic139C2212yes—
17C2×Dic139⋊C4C2212yes—
18C2×Dic139⋊C4C2211yescharacteristic
19C2×Dic139⋊C4C2212yes—
20C2×Dic139⋊C4C2211yescharacteristic
21C2×C22⋊Dic139C2212yes—
22C2×C22⋊Dic139C2211yescharacteristic
23C2×C4×Dic139C2212yes—
24C2×C4×Dic139C2212yes—
25C2×C4×Dic139C2211yescharacteristic
26C2×C4×Dic139C2211yescharacteristic
27C139⋊#95C2212yes—
28C139⋊#95C2212yes—
29C139⋊#95C2211yescharacteristic
30C139⋊#95C2212yes—
31C139⋊#95C2212yes—
32C2×C4⋊C4×C139C2212yes—
33C2×C4⋊C4×C139C2211yescharacteristic
34C2×C22⋊C4×C139C2212yes—
35C2×C22⋊C4×C139C2211yescharacteristic
36#95×C139C2211yescharacteristic
37C2×Dic278—24no—
38C2×Dic278—22no—
39C22×Dic139—22no—
40C22×Dic139—22no—
41C22×Dic139Q814yescomplemented
42C22×Dic139C2311yescharacteristic
43C22×Dic139C2312yes—
44C22×Dic139C2311yescharacteristic
45C22×Dic139C2311yescharacteristic
46C22×Dic139C2312yes—
47C22×Dic139C2311yescharacteristic
48C4⋊Dic139—24no—
49Dic139⋊C4—22no—
50Dic139⋊C4—24no—
51Dic139⋊C4—22no—
52Dic139⋊C4—24no—
53C22⋊Dic139—22no—
54C22⋊Dic139—24no—
55C4×Dic139—22no—
56C4×Dic139—24no—
57C4×Dic139—24no—
58C4×Dic139D414yes—
59C24×C139C2311yescharacteristic
60C22×C4×C139C2311yescharacteristic
61C22×C4×C139C2312yes—
62C22×C4×C139C2311yescharacteristic
63C22×C4×C139C2312yes—
64C4⋊C4×C139—22no—
65C4⋊C4×C139—24no—
66C22⋊C4×C139—22no—
67C22⋊C4×C139—24no—
68Dic278—28no—
69C2×Dic139—22no—
70C2×Dic139—21no—
71C2×Dic139—22no—
72C2×Dic139—21no—
73C2×Dic139—22no—
74C2×Dic139—28no—
75C2×Dic139—21no—
76C2×Dic139—22no—
77C2×Dic139—22no—
78C2×Dic139—22no—
79C2×Dic139—22no—
80C2×Dic139C2×D412yes—
81C2×Dic139C2×D412yes—
82C2×Dic139C2×Q812yes—
83C2×Dic139C2×Q812yes—
84C2×Dic139#4114yes—
85C2×Dic139#4112yes—
86C23×C139—21no—
87C23×C139—22no—
88C23×C139—22no—
89C23×C139—21no—
90C23×C139C2×Q812yes—
91C23×C139C2411yescharacteristic
92C2×C4×C139—22no—
93C2×C4×C139—22no—
94C2×C4×C139—22no—
95C2×C4×C139—21no—
96C2×C4×C139—22no—
97C2×C4×C139—22no—
98C2×C4×C139—22no—
99C2×C4×C139—22no—
100C2×C4×C139C2×D412yes—
101C2×C4×C139#4114yes—
102C22×C139—22no—
103C22×C139—24no—
104C22×C139—41no—
105C22×C139—42no—
106C22×C139—41no—
107C22×C139C22×D411yescharacteristic
108C22×C139C22×Q811yescharacteristic
109C22×C139C2×#4111yescharacteristic
110C22×C139C2×#4112yes—
111C22×C139C2×#4112yes—
112C4×C139—22no—
113C4×C139—24no—
114C4×C139—41no—
115C4×C139—42no—
116Dic139—22no—
117Dic139—24no—
118Dic139—22no—
119Dic139—41no—
120Dic139—42no—
121Dic139C22⋊Q814yes—
122C2×C139—42no—
123C2×C139C2×C22⋊Q811yescharacteristic
124C2×C139#52511yescharacteristic
125C2×C139#52912yes—
126C2×C139#53211yescharacteristic
127C2×C139#53312yes—
128C139#239611yescharacteristic, complemented, Sylow
129#2396—1391nomaximal, Sylow
130C2×C4×Q8—1391no—
131C2×#117—1391no—
132#400—1391no—
133#399D13911yescharacteristic
134#398—1392no—
135#396—1392no—
136#395—1391no—
137#393—1391no—
138C4×C4⋊C4—1392no—
139C4×C4⋊C4—1391no—
140C4×C22⋊C4—1392no—
141C22×Q8—1391no—
142C23×C4—1391no—
143C4×Q8—2784no—
144#117—2784no—
145C2×C4⋊C4—1391no—
146C2×C4⋊C4—1391no—
147C2×C4⋊C4—1392no—
148C2×C4⋊C4—1392no—
149C2×C4⋊C4—1392no—
150C2×C4⋊C4C2×D13911yescharacteristic
151C2×C4⋊C4C2×D13912yes—
152C2×C22⋊C4—1391no—
153C2×C22⋊C4—1392no—
154C2×C22⋊C4C2×D13911yescharacteristic
155C2×C22⋊C4C2×D13912yes—
156C2×C42—1391no—
157C2×C42—1392no—
158C2×C42—1392no—
159C2×C42—1391no—
160#95—1392no—
161#95—1392no—
162#95—1392no—
163#95—1391no—
164#95—1392no—
165#95C2×D13911yescharacteristic
166C24C22×D13911yescharacteristic
167C2×Q8—2784no—
168C2×Q8—2782no—
169C22×C4—2782no—
170C22×C4—2782no—
171C22×C4—1392no—
172C22×C4—1391no—
173C22×C4—1394no—
174C22×C4—1391no—
175C22×C4—1392no—
176C22×C4—1391no—
177C22×C4—1391no—
178C22×C4C22×D13911yescharacteristic
179C22×C4C22×D13912yes—
180C22×C4C22×D13911yescharacteristic
181C22×C4C22×D13912yes—
182C4⋊C4—22no—
183C4⋊C4—24no—
184C4⋊C4—2782no—
185C4⋊C4—2784no—
186C4⋊C4—2784no—
187C4⋊C4—2782no—
188C4⋊C4—2784no—
189C22⋊C4—22no—
190C22⋊C4—24no—
191C22⋊C4—2784no—
192C22⋊C4—2782no—
193C42—2784no—
194C42—2782no—
195C42—2784no—
196C42—1394no—
197C23—21no—
198C23—22no—
199C23—21no—
200C23—22no—
201C23Q8×D13912yes—
202C23C23×D13911yescharacteristic
203Q8—2788no—
204C2×C4—22no—
205C2×C4—22no—
206C2×C4—22no—
207C2×C4—21no—
208C2×C4—22no—
209C2×C4—22no—
210C2×C4—22no—
211C2×C4—22no—
212C2×C4—2782no—
213C2×C4—2781no—
214C2×C4—2781no—
215C2×C4—2782no—
216C2×C4—2782no—
217C2×C4—2788no—
218C2×C4—2781no—
219C2×C4—2782no—
220C2×C4—2782no—
221C2×C4—2782no—
222C2×C4—2782no—
223C2×C4—1392no—
224C2×C4—1392no—
225C2×C4—1394no—
226C2×C4—1392no—
227C2×C4—1392no—
228C2×C4—1392no—
229C2×C4D4×D13912yes—
230C2×C4#1455578414yes—
231C22—24no—
232C22—22no—
233C22—41no—
234C22—42no—
235C22—41no—
236C22C2×D4×D13911yescharacteristic
237C22C2×Q8×D13911yescharacteristic
238C22#41×D13912yes—
239C22#41×D13911yescharacteristic
240C22C2×#1455578412yes—
241C4—22no—
242C4—24no—
243C4—41no—
244C4—42no—
245C4—2782no—
246C4—2784no—
247C4—2782no—
248C4—5561no—
249C4—5562no—
250C4—1394no—
251C2—42no—
252C2C22⋊Q8×D13911yescharacteristic
253C2#2258146111yescharacteristic
254C2#2258148012yes—
255C2#2258150111yescharacteristic
256C2#2258150512yes—
subgroupG/H
center, FrattiniC23C23×D139
commutator, socle, cosocleC23×C139C24
Fitting#399×C139C2
prime radicalC24×C139C23
hypercenter#399D139
hypocenterC139#2396
LCSG ▷ C23×C139 ▷ C139
UCSC1 ◁ C23 ◁ #399

Complements

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

NH ≅ G/Ntype
1. C2×#17984807C2semidirect
3. #22580891C2semidirect
4. #22580884C2semidirect
6. #22580874C2semidirect
8. C4⋊C4×Dic139C2semidirect
9. #22580804C2semidirect
41. C22×Dic139Q8semidirect
128. C139#2396semidirect

Maximal subgroups

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

subgroupindex
C2×#179848072
C2×#179847982
#225808912
#225808842
#225808762
#225808742
#225808652
C4⋊C4×Dic1392
#225808042
C22⋊C4×Dic1392
#399×C1392
#2396139