Finite Group Databasebeta

← #31807418

Subgroups — #31807418

Order 17792.

478 conjugacy classes of subgroups; only the 73 normal subgroups are shown.

normal subgroups only

This group has 478 conjugacy classes of subgroups — too many to draw. Only its 73 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×#17984867C211yesmaximal, characteristic, complemented
2#22581517C211yesmaximal, characteristic, complemented
3C2×#17984839C211yesmaximal, characteristic, complemented
4#22580959C211yesmaximal, characteristic, complemented
5C2×#17984758C211yesmaximal, characteristic, complemented
6#22580713C211yesmaximal, characteristic, complemented
7C2×#104×C139C211yesmaximal, characteristic, complemented
8C22×D556—22no—
9C22×D556C2211yescharacteristic
10C22×D556C2211yescharacteristic
11#17984867—22no—
12#17984867—22no—
13C2×#14555772—21no—
14C2×#14555770—21no—
15C2×#14555769C2211yescharacteristic
16#17984839—22no—
17#17984839—22no—
18#17984838—21no—
19#17984831—21no—
20#17984816—22no—
21#17984810—22no—
22#17984801C2211yescharacteristic
23#17984764—22no—
24#17984758—22no—
25C2×#41×C139C2211yescharacteristic
26C2×M16×C139C2211yescharacteristic
27C2×C42×C139C2211yescharacteristic
28#104×C139—22no—
29C23×D139—21no—
30C23×D139D412yes—
31C2×D556—28no—
32C2×D556—21no—
33C2×D556—21no—
34C2×D556—21no—
35C2×D556—21no—
36C2×D556—21no—
37C2×D556—21no—
38C2×D556—21no—
39C2×D556—21no—
40C2×D556—21no—
41C2×D556—21no—
42C2×D556—21no—
43C2×D556—48no—
44C2×D556D412yescomplemented
45C2×C22⋊D139—24no—
46#14555772—24no—
47#14555770—24no—
48#14555769—21no—
49#14555769D412yescomplemented
50C2×C139⋊C8—21no—
51C4⋊Dic139D412yescomplemented
52C22⋊Dic139—21no—
53(C2×D139)⋊C4—24no—
54C4×Dic139—21no—
55#41×C139—21no—
56#41×C139—21no—
57#41×C139—21no—
58#41×C139—21no—
59C2×Q8×C139D411yescharacteristic, complemented
60C2×D4×C139—21no—
61C2×D4×C139D411yescharacteristic, complemented
62C22×C4×C139—21no—
63C22×C4×C139—21no—
64C22×C4×C139C2311yescharacteristic
65M16×C139—21no—
66M16×C139—21no—
67C2×C8×C139—21no—
68C42×C139—21no—
69C42×C139D412yescomplemented
70C22×D139—22no—
71C22×D139—22no—
72C22×D139—22no—
73C22×D139—22no—
74C22×D139—44no—
75C22×D139—44no—
76C22×D139—41no—
77C22×D139—41no—
78D556—22no—
79D556—22no—
80D556—416no—
81D556—41no—
82D556—41no—
83D556—41no—
84D556—41no—
85D556—41no—
86D556—41no—
87C22⋊D139—84no—
88C2×Dic139—22no—
89C139⋊C8—22no—
90C23×C139—21no—
91C23×C139C2×D411yescharacteristic
92Q8×C139—21no—
93Q8×C139—21no—
94D4×C139—21no—
95D4×C139—21no—
96D4×C139—41no—
97D4×C139—41no—
98C2×C4×C139—24no—
99C2×C4×C139—22no—
100C2×C4×C139—21no—
101C2×C4×C139—41no—
102C2×C4×C139—41no—
103C2×C4×C139C2×D411yescharacteristic
104C2×C4×C139C2×D411yescharacteristic
105C2×C4×C139C2×D411yescharacteristic
106C2×C4×C139C2×D411yescharacteristic
107C2×C4×C139C2×D411yescharacteristic
108C2×C4×C139#4111yescharacteristic
109C8×C139—41no—
110C22×C139—22no—
111C22×C139—41no—
112C22×C139—42no—
113C22×C139#12011yescharacteristic
114C22×C139#12011yescharacteristic
115C22×C139#12111yescharacteristic
116C2×D139—44no—
117C2×D139—44no—
118C2×D139—42no—
119C2×D139—42no—
120C2×D139—44no—
121C2×D139—82no—
122C2×D139—82no—
123C2×D139—82no—
124C4×C139—24no—
125C4×C139—41no—
126C4×C139#12011yescharacteristic
127C4×C139#12111yescharacteristic
128C4×C139#12111yescharacteristic
129C4×C139#12711yescharacteristic
130Dic139—42no—
131C2×C139—21no—
132C2×C139—21no—
133C2×C139—81no—
134C2×C139#39211yescharacteristic
135C2×C139#45312yes—
136D139—82no—
137D139—82no—
138C139#200211yescharacteristic, complemented, Sylow
139#2002—1391nomaximal, Sylow
140C2×AGL(1,ℤ/8)—1391no—
141#535—1391no—
142C2×#127—1391no—
143C2×#104D13911yescharacteristic, complemented
144#418—1391no—
145C2×#100—1391no—
146#339—1391no—
147C2×#41C2×D13911yescharacteristic
148C22×D4—2782no—
149C22×D4—1391no—
150C22×D4—1391no—
151AGL(1,ℤ/8)—2782no—
152AGL(1,ℤ/8)—2782no—
153C2×SD16—2781no—
154C2×D8—2781no—
155C2×M16—1391no—
156C2×M16C2×D13911yescharacteristic
157#127—2782no—
158#127—2781no—
159#127—2782no—
160#124—2781no—
161#121—2782no—
162#120—2782no—
163#117—1391no—
164C2×C42C2×D13911yescharacteristic
165#104—22no—
166#102—2782no—
167#100—2782no—
168C24—2781no—
169C24—1392no—
170#41—21no—
171#41—21no—
172#41—21no—
173#41—21no—
174C2×Q8D55611yescharacteristic, complemented
175C2×D4—21no—
176C2×D4—2788no—
177C2×D4—2784no—
178C2×D4—2781no—
179C2×D4—2781no—
180C2×D4—2781no—
181C2×D4—2781no—
182C2×D4—2781no—
183C2×D4—2781no—
184C2×D4—2781no—
185C2×D4—2781no—
186C2×D4—2781no—
187C2×D4—2781no—
188C2×D4—2781no—
189C2×D4—5568no—
190C2×D4—1392no—
191C2×D4D55611yescharacteristic, complemented
192C22×C4—21no—
193C22×C4—21no—
194C22×C4C22×D13911yescharacteristic
195SD16—2784no—
196D8—2784no—
197M16—21no—
198M16—21no—
199M16—2781no—
200M16—1392no—
201C2×C8—21no—
202C2×C8—2781no—
203C4⋊C4—1392no—
204C22⋊C4—2784no—
205C22⋊C4—2781no—
206C42—21no—
207C42—2781no—
208C42C22⋊D13912yescomplemented
209C23—21no—
210C23—2782no—
211C23—2782no—
212C23—2782no—
213C23—2782no—
214C23—5564no—
215C23—5564no—
216C23—5561no—
217C23—5561no—
218C23D4×D13911yescharacteristic
219Q8—21no—
220Q8—21no—
221D4—21no—
222D4—21no—
223D4—41no—
224D4—41no—
225D4—2782no—
226D4—2782no—
227D4—55616no—
228D4—5561no—
229D4—5561no—
230D4—5561no—
231D4—5561no—
232D4—5561no—
233D4—5561no—
234D4—11124no—
235C2×C4—24no—
236C2×C4—22no—
237C2×C4—21no—
238C2×C4—41no—
239C2×C4—41no—
240C2×C4—2782no—
241C2×C4D4×D13911yescharacteristic
242C2×C4D4×D13911yescharacteristic
243C2×C4D4×D13911yescharacteristic
244C2×C4C2×C22⋊D13911yescharacteristic
245C2×C4C2×D55611yescharacteristic
246C2×C4#1455578511yescharacteristic
247C8—41no—
248C8—2782no—
249C22—22no—
250C22—41no—
251C22—42no—
252C22—5564no—
253C22—5564no—
254C22—5562no—
255C22—5562no—
256C22—5564no—
257C22—11122no—
258C22—11122no—
259C22—11122no—
260C22#1798481011yescharacteristic
261C22#1798481211yescharacteristic
262C22#1798481511yescharacteristic
263C4—24no—
264C4—41no—
265C4—5562no—
266C4#1798481211yescharacteristic
267C4#1798481511yescharacteristic
268C4#1798481611yescharacteristic
269C4#1798483811yescharacteristic
270C2—21no—
271C2—21no—
272C2—81no—
273C2—11122no—
274C2—11122no—
275C2#2258086211yescharacteristic
276C2#2258112212yes—
subgroupG/H
centerC22#17984812
commutator, cosocleC22×C4×C139C23
FrattiniC22×C4C22×D139
FittingC2×#104×C139C2
socleC22×C139#120
hypercenterC2×#104D139
hypocenterC139#2002
LCSG ▷ C22×C4×C139 ▷ C2×C139 ▷ C139
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#104

Complements

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

NH ≅ G/Ntype
1. C2×#17984867C2semidirect
2. #22581517C2semidirect
3. C2×#17984839C2semidirect
4. #22580959C2semidirect
5. C2×#17984758C2semidirect
6. #22580713C2semidirect
7. C2×#104×C139C2semidirect
44. C2×D556D4semidirect
49. #14555769D4semidirect
51. C4⋊Dic139D4semidirect
59. C2×Q8×C139D4semidirect
61. C2×D4×C139D4semidirect
69. C42×C139D4semidirect
138. C139#2002semidirect
143. C2×#104D139semidirect
174. C2×Q8D556semidirect
191. C2×D4D556semidirect
208. C42C22⋊D139semidirect

Maximal subgroups

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

subgroupindex
C2×#179848672
#225815172
C2×#179848392
#225809592
C2×#179847582
#225807132
C2×#104×C1392
#2002139