Finite Group Databasebeta

← #31805342

Subgroups — #31805342

Order 17792.

266 conjugacy classes of subgroups; only the 51 normal subgroups are shown.

normal subgroups only

This group has 266 conjugacy classes of subgroups — too many to draw. Only its 51 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#22581582C211yesmaximal, characteristic, complemented
2#22581104C211yesmaximal, characteristic
3#22580867C211yesmaximal, characteristic
4#22580691C211yesmaximal, characteristic, complemented
5#22580690C211yesmaximal, characteristic, complemented
6#22580678C211yesmaximal, characteristic, complemented
7#450×C139C211yesmaximal, characteristic
8C2×#14555773—21no—
9#17984841—21no—
10#17984840—21no—
11#17984832—21no—
12#17984832—21no—
13#17984821C2211yescharacteristic
14#17984819—21no—
15#17984798—21no—
16C2×Dic139⋊C4C2211yescharacteristic
17C2×C22⋊Dic139—21no—
18C2×C22⋊Dic139—21no—
19#17984763—21no—
20C22⋊(C139⋊C8)C2211yescharacteristic
21C139⋊#95C2211yescharacteristic
22C22×D4×C139C2211yescharacteristic
23C2×SD16×C139—21no—
24C22⋊Q8×C139C2211yescharacteristic
25#102×C139—21no—
26C22⋊C8×C139C2211yescharacteristic
27C2×Dic278—21no—
28C2×Dic278D411yescharacteristic
29C22×Dic139—21no—
30C22×Dic139D411yescharacteristic
31C22×Dic139D411yescharacteristic
32#14555773—42no—
33C2×C139⋊C8—21no—
34C4⋊Dic139—21no—
35C4⋊Dic139D411yescharacteristic
36Dic139⋊C4—21no—
37Dic139⋊C4—21no—
38Dic139⋊C4—21no—
39Dic139⋊C4—21no—
40Dic139⋊C4—21no—
41Dic139⋊C4—21no—
42Dic139⋊C4—21no—
43C22⋊Dic139—21no—
44C22⋊Dic139—42no—
45C22⋊Dic139—42no—
46C4×Dic139—21no—
47C4×Dic139—21no—
48C24×C139—21no—
49C2×Q8×C139D411yescharacteristic
50C2×D4×C139—21no—
51C2×D4×C139—21no—
52C2×D4×C139—42no—
53C22×C4×C139C2311yescharacteristic
54SD16×C139—42no—
55C2×C8×C139—21no—
56C4⋊C4×C139—21no—
57C4⋊C4×C139D411yescharacteristic
58C22⋊C4×C139—21no—
59Dic278—41no—
60Dic278—81no—
61C2×Dic139—21no—
62C2×Dic139—21no—
63C2×Dic139—21no—
64C2×Dic139—21no—
65C2×Dic139—21no—
66C2×Dic139—41no—
67C2×Dic139—41no—
68C2×Dic139—41no—
69C2×Dic139—41no—
70C2×Dic139SD1612yescomplemented
71C139⋊C8—41no—
72C23×C139—22no—
73C23×C139—41no—
74C23×C139—41no—
75C23×C139—41no—
76C23×C139—41no—
77C23×C139—41no—
78C23×C139—41no—
79C23×C139C2×D411yescharacteristic
80Q8×C139—41no—
81D4×C139—22no—
82D4×C139—22no—
83D4×C139—41no—
84D4×C139—41no—
85C2×C4×C139—21no—
86C2×C4×C139—21no—
87C2×C4×C139—41no—
88C2×C4×C139C2×D411yescharacteristic
89C2×C4×C139C2×D411yescharacteristic
90C8×C139—41no—
91C22×C139—21no—
92C22×C139—21no—
93C22×C139—42no—
94C22×C139—42no—
95C22×C139—42no—
96C22×C139—81no—
97C22×C139—81no—
98C22×C139—81no—
99C22×C139—81no—
100C22×C139#12011yescharacteristic
101C22×C139C2×SD1611yescharacteristic
102C22×C139#13711yescharacteristic
103C4×C139—21no—
104C4×C139—21no—
105C4×C139—41no—
106C4×C139—41no—
107Dic139—22no—
108Dic139—41no—
109Dic139—41no—
110Dic139—41no—
111Dic139—81no—
112C2×C139—21no—
113C2×C139—21no—
114C2×C139—82no—
115C2×C139#44811yescharacteristic
116C2×C139#45411yescharacteristic
117C2×C139B(4,𝔽2)11yescharacteristic
118C139#159911yescharacteristic, complemented, Sylow
119#1599—1391nomaximal, Sylow
120#544—1391no—
121#450—1391no—
122#450D13911yescharacteristic
123#394—1391no—
124#328—1391no—
125#328—1391no—
126#324—1391no—
127C22×D4C2×D13911yescharacteristic
128C2×SD16—21no—
129C2×SD16—2781no—
130C4⋊Q8—2781no—
131C4⋊Q8—2781no—
132#125—2781no—
133#125—2781no—
134C22⋊Q8—2781no—
135C22⋊Q8—1391no—
136C22⋊Q8C2×D13911yescharacteristic
137#117—2781no—
138C2×C4⋊C4—1391no—
139C2×C22⋊C4—2781no—
140C2×C22⋊C4—2781no—
141#102—21no—
142#102—2781no—
143C22⋊C8—1391no—
144C22⋊C8C2×D13911yescharacteristic
145#95—1391no—
146C24—21no—
147C2×Q8—2781no—
148C2×Q8—1391no—
149C2×Q8C22⋊D13911yescharacteristic
150C2×D4—21no—
151C2×D4—21no—
152C2×D4—42no—
153C22×C4—2781no—
154C22×C4—1391no—
155C22×C4—1391no—
156C22×C4C22×D13911yescharacteristic
157SD16—42no—
158SD16—5562no—
159C2×C8—21no—
160C2×C8—2781no—
161C4⋊C4—21no—
162C4⋊C4—2781no—
163C4⋊C4—2781no—
164C4⋊C4—2781no—
165C4⋊C4—2781no—
166C4⋊C4—2781no—
167C4⋊C4—2781no—
168C4⋊C4—2781no—
169C4⋊C4—2781no—
170C4⋊C4—1391no—
171C4⋊C4C22⋊D13911yescharacteristic
172C22⋊C4—21no—
173C22⋊C4—2781no—
174C22⋊C4—5562no—
175C22⋊C4—5562no—
176C42—2781no—
177C42—2781no—
178C23—22no—
179C23—41no—
180C23—41no—
181C23—41no—
182C23—41no—
183C23—41no—
184C23—41no—
185C23D4×D13911yescharacteristic
186Q8—41no—
187Q8—5561no—
188Q8—11121no—
189D4—22no—
190D4—22no—
191D4—41no—
192D4—41no—
193C2×C4—21no—
194C2×C4—21no—
195C2×C4—41no—
196C2×C4—2781no—
197C2×C4—2781no—
198C2×C4—2781no—
199C2×C4—2781no—
200C2×C4—2781no—
201C2×C4—5561no—
202C2×C4—5561no—
203C2×C4—5561no—
204C2×C4—5561no—
205C2×C4—1392no—
206C2×C4D4×D13911yescharacteristic
207C2×C4C2×C22⋊D13911yescharacteristic
208C8—41no—
209C8—5561no—
210C22—21no—
211C22—21no—
212C22—42no—
213C22—42no—
214C22—42no—
215C22—81no—
216C22—81no—
217C22—81no—
218C22—81no—
219C22#1798481011yescharacteristic
220C22SD16×D13911yescharacteristic
221C22#1798487111yescharacteristic
222C4—21no—
223C4—21no—
224C4—41no—
225C4—41no—
226C4—2782no—
227C4—5561no—
228C4—5561no—
229C4—5561no—
230C4—11121no—
231C2—21no—
232C2—21no—
233C2—82no—
234C2#2258109011yescharacteristic
235C2#2258112411yescharacteristic
236C2#2258113911yescharacteristic
subgroupG/H
centerC22#17984810
commutator, cosocleC22×C4×C139C23
FrattiniC22×C4C22×D139
Fitting#450×C139C2
socleC22×C139#120
prime radicalC22×D4×C139C22
hypercenter#450D139
hypocenterC139#1599
LCSG ▷ C22×C4×C139 ▷ C22×C139 ▷ C139
UCSC1 ◁ C22 ◁ C22×C4 ◁ #450

Complements

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

NH ≅ G/Ntype
1. #22581582C2semidirect
4. #22580691C2semidirect
5. #22580690C2semidirect
6. #22580678C2semidirect
70. C2×Dic139SD16semidirect
118. C139#1599semidirect

Maximal subgroups

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

subgroupindex
#225815822
#225811042
#225808672
#225806912
#225806902
#225806782
#450×C1392
#1599139