Finite Group Databasebeta

← #31805385

Subgroups — #31805385

Order 17792.

260 conjugacy classes of subgroups; only the 49 normal subgroups are shown.

normal subgroups only

This group has 260 conjugacy classes of subgroups — too many to draw. Only its 49 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#22581540C211yesmaximal, characteristic
2#22581111C211yesmaximal, characteristic, complemented
3#22581091C211yesmaximal, characteristic, complemented
4#22580866C211yesmaximal, characteristic, complemented
5#22580689C211yesmaximal, characteristic, complemented
6#22580676C211yesmaximal, characteristic, complemented
7#327×C139C211yesmaximal, characteristic, complemented
8C22×Dic278C2211yescharacteristic
9C2×Dic556—21no—
10C2×#14555773—21no—
11#17984837—21no—
12#17984828—21no—
13#17984826—21no—
14#17984821C2211yescharacteristic
15#17984814—21no—
16#17984810—21no—
17D4×Dic139—21no—
18C2×(C2×D139)⋊C4—21no—
19C2×(C2×D139)⋊C4C2211yescharacteristic
20#17984767—21no—
21#17984765—21no—
22C22⋊(C139⋊C8)C2211yescharacteristic
23C139⋊#95—21no—
24#121×C139C2211yescharacteristic
25C22⋊C8×C139C2211yescharacteristic
26#95×C139C2211yescharacteristic
27C23×D139D411yescharacteristic
28C2×Dic278—21no—
29C2×Dic278—21no—
30C2×Dic278—42no—
31C2×Dic278D411yescharacteristic
32C2×C22⋊D139—21no—
33C2×C22⋊D139—21no—
34C22×Dic139—21no—
35C22×Dic139—21no—
36C22×Dic139D411yescharacteristic
37Dic556—42no—
38#14555773—42no—
39C2×C139⋊C8—21no—
40C4⋊Dic139—21no—
41C4⋊Dic139D411yescharacteristic
42Dic139⋊C4—21no—
43C22⋊Dic139—21no—
44C22⋊Dic139—21no—
45(C2×D139)⋊C4—21no—
46(C2×D139)⋊C4—21no—
47(C2×D139)⋊C4—21no—
48(C2×D139)⋊C4—21no—
49(C2×D139)⋊C4—42no—
50C4×Dic139—21no—
51C2×D4×C139—21no—
52C2×D4×C139D411yescharacteristic
53C22×C4×C139—21no—
54C22×C4×C139C2311yescharacteristic
55C2×C8×C139—21no—
56C4⋊C4×C139D411yescharacteristic
57C22⋊C4×C139—21no—
58C22×D139—21no—
59C22×D139—21no—
60C22×D139—21no—
61C22×D139—41no—
62C22×D139—41no—
63Dic278—22no—
64Dic278—22no—
65Dic278—41no—
66Dic278—41no—
67Dic278—41no—
68C22⋊D139—81no—
69C22⋊D139—81no—
70C2×Dic139—22no—
71C2×Dic139—21no—
72C2×Dic139—21no—
73C2×Dic139—21no—
74C2×Dic139—41no—
75C2×Dic139—41no—
76C2×Dic139—41no—
77C2×Dic139—81no—
78C139⋊C8—41no—
79C23×C139—21no—
80C23×C139C2×D411yescharacteristic
81D4×C139—41no—
82D4×C139—41no—
83D4×C139—41no—
84C2×C4×C139—21no—
85C2×C4×C139—41no—
86C2×C4×C139—41no—
87C2×C4×C139—41no—
88C2×C4×C139—41no—
89C2×C4×C139C2×D411yescharacteristic
90C2×C4×C139C2×D411yescharacteristic
91C8×C139—41no—
92C22×C139—21no—
93C22×C139—21no—
94C22×C139—41no—
95C22×C139—41no—
96C22×C139—41no—
97C22×C139#12011yescharacteristic
98C22×C139#13511yescharacteristic
99C22×C139#13711yescharacteristic
100C2×D139—42no—
101C2×D139—41no—
102C2×D139—41no—
103C2×D139—41no—
104C2×D139—81no—
105C4×C139—21no—
106C4×C139—21no—
107C4×C139—41no—
108C4×C139—81no—
109Dic139—41no—
110Dic139—41no—
111Dic139—42no—
112Dic139—41no—
113C2×C139—21no—
114C2×C139—21no—
115C2×C139—81no—
116C2×C139#45211yescharacteristic
117C2×C139#45511yescharacteristic
118C2×C139B(4,𝔽2)11yescharacteristic
119D139—81no—
120C139#160611yescharacteristic, complemented, Sylow
121#1606—1391nomaximal, Sylow
122#538—1391no—
123#451—1391no—
124#448—1391no—
125#393—1391no—
126#328—1391no—
127#327D13911yescharacteristic, complemented
128#323—1391no—
129C22×Q8—1391no—
130C2×Q16—2781no—
131C2×SD16—2781no—
132#126—2781no—
133#124—2781no—
134#123—2781no—
135C22⋊Q8—1391no—
136#121—2781no—
137#121C2×D13911yescharacteristic
138#120—2781no—
139C4×D4—2781no—
140C2×C22⋊C4—2781no—
141C2×C22⋊C4—1391no—
142#103—2781no—
143#103—2781no—
144C22⋊C8—1391no—
145C22⋊C8C2×D13911yescharacteristic
146#95—2781no—
147#95C2×D13911yescharacteristic
148C24—1391no—
149C2×Q8—2781no—
150C2×Q8—2781no—
151C2×Q8—5562no—
152C2×Q8—1391no—
153C2×D4—21no—
154C2×D4—2781no—
155C2×D4—2781no—
156C2×D4D55611yescharacteristic
157C22×C4—21no—
158C22×C4—2781no—
159C22×C4—2781no—
160C22×C4—1391no—
161C22×C4C22×D13911yescharacteristic
162Q16—5562no—
163SD16—5562no—
164C2×C8—21no—
165C2×C8—2781no—
166C4⋊C4—2781no—
167C4⋊C4—2781no—
168C4⋊C4—1391no—
169C4⋊C4D55611yescharacteristic
170C22⋊C4—21no—
171C22⋊C4—2781no—
172C22⋊C4—2781no—
173C22⋊C4—2781no—
174C22⋊C4—2781no—
175C22⋊C4—2781no—
176C22⋊C4—2781no—
177C22⋊C4—5562no—
178C42—2781no—
179C23—21no—
180C23—2781no—
181C23—2781no—
182C23—2781no—
183C23—5561no—
184C23—5561no—
185C23D4×D13911yescharacteristic
186Q8—2782no—
187Q8—2782no—
188Q8—5561no—
189Q8—5561no—
190Q8—5561no—
191D4—41no—
192D4—41no—
193D4—41no—
194D4—11121no—
195D4—11121no—
196C2×C4—21no—
197C2×C4—41no—
198C2×C4—41no—
199C2×C4—41no—
200C2×C4—41no—
201C2×C4—2782no—
202C2×C4—2781no—
203C2×C4—2781no—
204C2×C4—2781no—
205C2×C4—5561no—
206C2×C4—5561no—
207C2×C4—5561no—
208C2×C4—11121no—
209C2×C4D4×D13911yescharacteristic
210C2×C4C2×D55611yescharacteristic
211C8—41no—
212C8—5561no—
213C22—21no—
214C22—21no—
215C22—41no—
216C22—41no—
217C22—41no—
218C22—5562no—
219C22—5561no—
220C22—5561no—
221C22—5561no—
222C22—11121no—
223C22#1798481211yescharacteristic
224C22#1798486111yescharacteristic
225C22#1798487111yescharacteristic
226C4—21no—
227C4—21no—
228C4—41no—
229C4—81no—
230C4—5561no—
231C4—5561no—
232C4—5562no—
233C4—5561no—
234C2—21no—
235C2—21no—
236C2—81no—
237C2—11121no—
238C2#2258111611yescharacteristic
239C2#2258113211yescharacteristic
240C2#2258114111yescharacteristic
subgroupG/H
centerC22#17984812
commutator, cosocleC22×C4×C139C23
FrattiniC22×C4C22×D139
Fitting#327×C139C2
socleC22×C139#120
prime radical#22581540C2
hypercenter#327D139
hypocenterC139#1606
LCSG ▷ C22×C4×C139 ▷ C22×C139 ▷ C139
UCSC1 ◁ C22 ◁ C22×C4 ◁ #327

Complements

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

NH ≅ G/Ntype
2. #22581111C2semidirect
3. #22581091C2semidirect
4. #22580866C2semidirect
5. #22580689C2semidirect
6. #22580676C2semidirect
7. #327×C139C2semidirect
120. C139#1606semidirect
127. #327D139semidirect

Maximal subgroups

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

subgroupindex
#225815402
#225811112
#225810912
#225808662
#225806892
#225806762
#327×C1392
#1606139