Finite Group Databasebeta

← #31807605

Subgroups — #31807605

Order 17792.

316 conjugacy classes of subgroups; only the 85 normal subgroups are shown.

normal subgroups only

This group has 316 conjugacy classes of subgroups — too many to draw. Only its 85 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×#17984818C211yesmaximal, characteristic
2C2×#17984775C211yesmaximal, characteristic, complemented
3C2×#17984766C211yesmaximal, characteristic, complemented
4C2×(C2×D139)⋊C8C211yesmaximal, characteristic
5#22580810C211yesmaximal, characteristic
6#22580716C211yesmaximal, characteristic, complemented
7C2×#103×C139C211yesmaximal, characteristic, complemented
8C22×C4×D139C2211yescharacteristic
9C22×C139⋊C8C2211yescharacteristic
10#17984818—22no—
11#17984818—22no—
12C2×C4⋊Dic139C2211yescharacteristic
13C2×C4⋊Dic139C2211yescharacteristic
14C2×Dic139⋊C4—21no—
15C2×(C2×D139)⋊C4—21no—
16C2×(C2×D139)⋊C4—21no—
17#17984775—22no—
18#17984766—22no—
19(C2×D139)⋊C8—22no—
20C139⋊#95—21no—
21C22×Q8×C139C2211yescharacteristic
22C22×C8×C139C2211yescharacteristic
23C2×C4⋊C4×C139C2211yescharacteristic
24#103×C139—22no—
25C23×D139D411yescharacteristic
26C22×Dic139—21no—
27C22×Dic139—21no—
28C22×Dic139D411yescharacteristic
29C2×C4×D139—21no—
30C2×C4×D139—21no—
31C2×C4×D139—21no—
32C2×C4×D139—21no—
33C2×C4×D139—21no—
34C2×C4×D139—21no—
35C2×C139⋊C8—21no—
36C2×C139⋊C8—21no—
37C2×C139⋊C8D412yes—
38C4⋊Dic139—21no—
39C4⋊Dic139—21no—
40C4⋊Dic139—21no—
41C4⋊Dic139D412yes—
42Dic139⋊C4—24no—
43(C2×D139)⋊C4—24no—
44(C2×D139)⋊C4—42no—
45C2×Q8×C139—21no—
46C2×Q8×C139—21no—
47C2×Q8×C139—21no—
48C2×Q8×C139—21no—
49C2×Q8×C139—21no—
50C2×Q8×C139D412yes—
51C22×C4×C139—21no—
52C22×C4×C139—21no—
53C22×C4×C139C2311yescharacteristic
54C2×C8×C139—21no—
55C2×C8×C139—21no—
56C2×C8×C139—21no—
57C4⋊C4×C139—21no—
58C4⋊C4×C139—21no—
59C22×D139—21no—
60C22×D139—21no—
61C22×D139—21no—
62C22×D139—21no—
63C22×D139—21no—
64C22×D139—21no—
65C22×D139Q1612yes—
66C2×Dic139—22no—
67C2×Dic139—21no—
68C2×Dic139—21no—
69C2×Dic139—21no—
70C2×Dic139—41no—
71C2×Dic139—41no—
72C2×Dic139—41no—
73C2×Dic139—41no—
74C2×Dic139—41no—
75C4×D139—41no—
76C4×D139—41no—
77C4×D139—41no—
78C4×D139—41no—
79C139⋊C8—22no—
80C23×C139C2×D411yescharacteristic
81Q8×C139—22no—
82Q8×C139—22no—
83Q8×C139—41no—
84Q8×C139—41no—
85C2×C4×C139—22no—
86C2×C4×C139—41no—
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×C139#4111yescharacteristic
95C2×C4×C139#4111yescharacteristic
96C2×C4×C139#4111yescharacteristic
97C8×C139—41no—
98C22×C139#12011yescharacteristic
99C22×C139#12111yescharacteristic
100C22×C139#12311yescharacteristic
101C22×C139C2×Q1611yescharacteristic
102C22×C139#13511yescharacteristic
103C22×C139AGL(1,ℤ/8)11yescharacteristic
104C22×C139#13711yescharacteristic
105C2×D139—22no—
106C2×D139—22no—
107C2×D139—22no—
108C2×D139—41no—
109C2×D139—41no—
110C2×D139—41no—
111C2×D139—41no—
112C4×C139—42no—
113C4×C139—81no—
114C4×C139#12111yescharacteristic
115C4×C139#12111yescharacteristic
116C4×C139#12311yescharacteristic
117C4×C139#12411yescharacteristic
118Dic139—41no—
119Dic139—42no—
120Dic139—81no—
121C2×C139#39411yescharacteristic
122C2×C139#44911yescharacteristic
123C2×C139#45111yescharacteristic
124C2×C139#46711yescharacteristic
125C2×C139#46811yescharacteristic
126C2×C139#48411yescharacteristic
127C2×C139#48511yescharacteristic
128D139—42no—
129C139#203611yescharacteristic, complemented, Sylow
130#2036—1391nomaximal, Sylow
131C2×C22⋊Q8—1391no—
132C2×#107—1391no—
133C2×#103—1391no—
134C2×#103D13911yescharacteristic, complemented
135C2×C22⋊C8—1391no—
136#380—1391no—
137#340—1391no—
138C22×Q8C2×D13911yescharacteristic
139C23×C4—1391no—
140C22×C8—1391no—
141C22×C8C2×D13911yescharacteristic
142C22⋊Q8—2782no—
143C22⋊Q8—2782no—
144C2×C4⋊C4—2781no—
145C2×C4⋊C4—1391no—
146C2×C4⋊C4—1391no—
147C2×C4⋊C4C2×D13911yescharacteristic
148C2×C22⋊C4—2781no—
149C2×C22⋊C4—2781no—
150#107—2782no—
151#103—22no—
152#103—2782no—
153C22⋊C8—2782no—
154#95—2781no—
155C24—1391no—
156C2×Q8—21no—
157C2×Q8—21no—
158C2×Q8—21no—
159C2×Q8—21no—
160C2×Q8—21no—
161C2×Q8C22⋊D13912yes—
162C22×C4—21no—
163C22×C4—21no—
164C22×C4—2781no—
165C22×C4—2781no—
166C22×C4—2781no—
167C22×C4—2781no—
168C22×C4—2781no—
169C22×C4—2781no—
170C22×C4—2781no—
171C22×C4—2781no—
172C22×C4—1391no—
173C22×C4C22×D13911yescharacteristic
174C2×C8—21no—
175C2×C8—21no—
176C2×C8—21no—
177C2×C8—2781no—
178C2×C8—2781no—
179C2×C8—1392no—
180C4⋊C4—21no—
181C4⋊C4—21no—
182C4⋊C4—2784no—
183C4⋊C4—2781no—
184C4⋊C4—2781no—
185C4⋊C4—2781no—
186C4⋊C4—1392no—
187C22⋊C4—2784no—
188C22⋊C4—5562no—
189C23—2781no—
190C23—2781no—
191C23—2781no—
192C23—2781no—
193C23—2781no—
194C23—2781no—
195C23—1392no—
196C23D4×D13911yescharacteristic
197Q8—22no—
198Q8—22no—
199Q8—41no—
200Q8—41no—
201C2×C4—22no—
202C2×C4—41no—
203C2×C4—41no—
204C2×C4—41no—
205C2×C4—41no—
206C2×C4—41no—
207C2×C4—2782no—
208C2×C4—2781no—
209C2×C4—2781no—
210C2×C4—2781no—
211C2×C4—5561no—
212C2×C4—5561no—
213C2×C4—5561no—
214C2×C4—5561no—
215C2×C4—5561no—
216C2×C4—5561no—
217C2×C4—5561no—
218C2×C4—5561no—
219C2×C4—5561no—
220C2×C4D4×D13911yescharacteristic
221C2×C4D4×D13911yescharacteristic
222C2×C4C2×C22⋊D13911yescharacteristic
223C2×C4#1455578411yescharacteristic
224C2×C4#1455578511yescharacteristic
225C2×C4#1455578511yescharacteristic
226C8—41no—
227C8—2782no—
228C22—2782no—
229C22—2782no—
230C22—2782no—
231C22—5561no—
232C22—5561no—
233C22—5561no—
234C22—5561no—
235C22#1798481011yescharacteristic
236C22#1798481511yescharacteristic
237C22#1798482411yescharacteristic
238C22Q16×D13911yescharacteristic
239C22#1798486311yescharacteristic
240C22#1798486911yescharacteristic
241C22#1798487411yescharacteristic
242C4—42no—
243C4—81no—
244C4—5562no—
245C4—5561no—
246C4—11121no—
247C4#1798481411yescharacteristic
248C4#1798481511yescharacteristic
249C4#1798482511yescharacteristic
250C4#1798482811yescharacteristic
251C2—5562no—
252C2#2258086811yescharacteristic
253C2#2258109711yescharacteristic
254C2#2258110711yescharacteristic
255C2#2258119311yescharacteristic
256C2#2258120211yescharacteristic
257C2#2258128711yescharacteristic
258C2#2258129211yescharacteristic
subgroupG/H
centerC23D4×D139
commutator, cosocleC22×C4×C139C23
FrattiniC22×C4C22×D139
FittingC2×#103×C139C2
socleC23×C139C2×D4
prime radicalC23×D139D4
hypercenterC2×#103D139
hypocenterC139#2036
LCSG ▷ C22×C4×C139 ▷ C2×C139 ▷ C139
UCSC1 ◁ C23 ◁ C22×C4 ◁ C2×#103

Complements

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

NH ≅ G/Ntype
2. C2×#17984775C2semidirect
3. C2×#17984766C2semidirect
6. #22580716C2semidirect
7. C2×#103×C139C2semidirect
129. C139#2036semidirect
134. C2×#103D139semidirect

Maximal subgroups

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

subgroupindex
C2×#179848182
C2×#179847752
C2×#179847662
C2×(C2×D139)⋊C82
#225808102
#225807162
C2×#103×C1392
#2036139