Finite Group Databasebeta

← #31806819

Subgroups — #31806819

Order 17792.

342 conjugacy classes of subgroups; only the 79 normal subgroups are shown.

normal subgroups only

This group has 342 conjugacy classes of subgroups — too many to draw. Only its 79 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#22581719C211yesmaximal, characteristic, complemented
2#22581464C211yesmaximal, characteristic
3#22580935C211yesmaximal, characteristic, complemented
4#22580917C211yesmaximal, characteristic, complemented
5#22580725C211yesmaximal, characteristic, complemented
6#22580724C211yesmaximal, characteristic, complemented
7#407×C139C211yesmaximal, characteristic, complemented
8C2×#14555785C2211yescharacteristic
9#17984850—22no—
10#17984848—22no—
11C2×#14555769C2211yescharacteristic
12C2×#14555769C2211yescharacteristic
13M16×D139—22no—
14#17984825C412yes—
15#17984821—21no—
16#17984816—21no—
17#17984811C412yes—
18C4×C22⋊D139—22no—
19#17984801C2211yescharacteristic
20#17984760—21no—
21#17984758—21no—
22C22⋊(C139⋊C8)—22no—
23C23×C4×C139C2211yescharacteristic
24C2×M16×C139C2211yescharacteristic
25C2×M16×C139C2211yescharacteristic
26C22⋊C8×C139—22no—
27#14555785—21no—
28#14555785—21no—
29#14555785—21no—
30#14555785—21no—
31C2×Dic278D411yescharacteristic
32C2×D556D411yescharacteristic
33C2×C22⋊D139—22no—
34C2×C22⋊D139C2×C412yes—
35C2×C4×D139D412yes—
36#14555769—21no—
37#14555769—21no—
38#14555769—21no—
39#14555769—21no—
40#14555768—24no—
41C2×C139⋊C8—21no—
42C2×C139⋊C8D412yescomplemented
43C8×D139—24no—
44C4⋊Dic139—21no—
45Dic139⋊C4—22no—
46C22⋊Dic139—22no—
47C22⋊Dic139C2×C412yes—
48(C2×D139)⋊C4—22no—
49C4×Dic139—21no—
50C24×C139C2×C411yescharacteristic
51C22×C4×C139—21no—
52C22×C4×C139—21no—
53C22×C4×C139—21no—
54C22×C4×C139—21no—
55C22×C4×C139—21no—
56C22×C4×C139—21no—
57C22×C4×C139C2×C411yescharacteristic
58C22×C4×C139C2311yescharacteristic
59M16×C139—21no—
60M16×C139—21no—
61M16×C139—21no—
62M16×C139—21no—
63C2×C8×C139—21no—
64C2×C8×C139D412yescomplemented
65C22×D139C22⋊C412yes—
66Dic278—21no—
67Dic278—21no—
68D556—21no—
69D556—21no—
70C22⋊D139—22no—
71C22⋊D139—22no—
72C22⋊D139—44no—
73C2×Dic139—22no—
74C2×Dic139C22⋊C412yes—
75C4×D139—22no—
76C4×D139—22no—
77C139⋊C8—22no—
78C139⋊C8—41no—
79C23×C139—21no—
80C23×C139—21no—
81C23×C139—21no—
82C23×C139—42no—
83C23×C139C22×C411yescharacteristic
84C2×C4×C139—21no—
85C2×C4×C139—21no—
86C2×C4×C139—21no—
87C2×C4×C139—41no—
88C2×C4×C139—41no—
89C2×C4×C139—41no—
90C2×C4×C139—41no—
91C2×C4×C139C2×D411yescharacteristic
92C2×C4×C139C2×D411yescharacteristic
93C2×C4×C139C2×D411yescharacteristic
94C2×C4×C139C2×D411yescharacteristic
95C2×C4×C139#4111yescharacteristic
96C2×C4×C139#4111yescharacteristic
97C8×C139—22no—
98C8×C139—41no—
99C22×C139—22no—
100C22×C139—22no—
101C22×C139—22no—
102C22×C139—41no—
103C22×C139—41no—
104C22×C139—41no—
105C22×C139—41no—
106C22×C139—41no—
107C22×C139C2×C22⋊C411yescharacteristic
108C22×C139C4×D411yescharacteristic
109C22×C139C4×D411yescharacteristic
110C2×D139—22no—
111C2×D139—42no—
112C4×C139—41no—
113C4×C139#12011yescharacteristic
114C4×C139#12111yescharacteristic
115C4×C139#12111yescharacteristic
116C4×C139#12311yescharacteristic
117Dic139—22no—
118Dic139—42no—
119C2×C139—21no—
120C2×C139—21no—
121C2×C139—21no—
122C2×C139—42no—
123C2×C139#38611yescharacteristic
124D139—42no—
125C139#189111yescharacteristic, complemented, Sylow
126#1891—1391nomaximal, Sylow
127#568—1391no—
128#525—1391no—
129#413—1391no—
130#407—1391no—
131#407D13911yescharacteristic, complemented
132#344—1391no—
133#344—1391no—
134C2×#41—1391no—
135C23×C4C2×D13911yescharacteristic
136#131—2782no—
137#131—2782no—
138C2×M16—2782no—
139C2×M16—1391no—
140C2×M16—1391no—
141C2×M16C2×D13911yescharacteristic
142C2×M16C2×D13911yescharacteristic
143#123—1392no—
144C22⋊Q8—2781no—
145#121—2781no—
146#120—1392no—
147C4×D4—2782no—
148#117—1391no—
149#101—2781no—
150#100—2781no—
151C22⋊C8—22no—
152C22⋊C8—2782no—
153C24C4×D13911yescharacteristic
154#41—2781no—
155#41—2781no—
156#41—2781no—
157#41—2781no—
158C2×Q8—1391no—
159C2×D4—2782no—
160C2×D4—1392no—
161C2×D4—1391no—
162C22×C4—21no—
163C22×C4—21no—
164C22×C4—21no—
165C22×C4—21no—
166C22×C4—21no—
167C22×C4—21no—
168C22×C4—1392no—
169C22×C4C4×D13911yescharacteristic
170C22×C4C22×D13911yescharacteristic
171M16—21no—
172M16—21no—
173M16—21no—
174M16—21no—
175M16—2784no—
176M16—2781no—
177M16—2781no—
178M16—2781no—
179M16—2781no—
180C2×C8—21no—
181C2×C8—2784no—
182C2×C8—2781no—
183C2×C8—1392no—
184C2×C8C22⋊D13912yescomplemented
185C4⋊C4—2782no—
186C4⋊C4—2781no—
187C22⋊C4—2782no—
188C22⋊C4—2782no—
189C22⋊C4—1392no—
190C42—2781no—
191C23—21no—
192C23—21no—
193C23—21no—
194C23—42no—
195C23—1392no—
196C23C2×C4×D13911yescharacteristic
197Q8—2781no—
198Q8—2781no—
199D4—2782no—
200D4—2782no—
201D4—2781no—
202D4—2781no—
203D4—5564no—
204C2×C4—21no—
205C2×C4—21no—
206C2×C4—21no—
207C2×C4—41no—
208C2×C4—41no—
209C2×C4—41no—
210C2×C4—41no—
211C2×C4—2782no—
212C2×C4—2782no—
213C2×C4—2782no—
214C2×C4—1392no—
215C2×C4D4×D13911yescharacteristic
216C2×C4D4×D13911yescharacteristic
217C2×C4D4×D13911yescharacteristic
218C2×C4C2×C22⋊D13911yescharacteristic
219C2×C4#1455578411yescharacteristic
220C2×C4#1455578511yescharacteristic
221C8—22no—
222C8—41no—
223C8—2782no—
224C8—5561no—
225C22—22no—
226C22—22no—
227C22—22no—
228C22—41no—
229C22—41no—
230C22—41no—
231C22—41no—
232C22—41no—
233C22—2782no—
234C22—5562no—
235C22C22⋊C4×D13911yescharacteristic
236C22(C22⋊D139)⋊C411yescharacteristic
237C22C4×C22⋊D13911yescharacteristic
238C4—41no—
239C4—2782no—
240C4—5562no—
241C4#1798481011yescharacteristic
242C4#1798481311yescharacteristic
243C4#1798481511yescharacteristic
244C4#1798482411yescharacteristic
245C2—21no—
246C2—21no—
247C2—21no—
248C2—42no—
249C2—5562no—
250C2#2258082911yescharacteristic
subgroupG/H
centerC4#17984810
commutatorC23×C139C22×C4
FrattiniC22×C4C22×D139
Fitting#407×C139C2
socleC2×C139#386
prime radical#22581464C2
cosocleC22×C4×C139C23
hypercenter#407D139
hypocenterC139#1891
LCSG ▷ C23×C139 ▷ C2×C139 ▷ C139
UCSC1 ◁ C4 ◁ C22×C4 ◁ #407

Complements

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

NH ≅ G/Ntype
1. #22581719C2semidirect
3. #22580935C2semidirect
4. #22580917C2semidirect
5. #22580725C2semidirect
6. #22580724C2semidirect
7. #407×C139C2semidirect
42. C2×C139⋊C8D4semidirect
64. C2×C8×C139D4semidirect
125. C139#1891semidirect
131. #407D139semidirect
184. C2×C8C22⋊D139semidirect

Maximal subgroups

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

subgroupindex
#225817192
#225814642
#225809352
#225809172
#225807252
#225807242
#407×C1392
#1891139