Finite Group Databasebeta

← #31807419

Subgroups — #31807419

Order 17792.

478 conjugacy classes of subgroups; only the 75 normal subgroups are shown.

normal subgroups only

This group has 478 conjugacy classes of subgroups — too many to draw. Only its 75 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×#17984868C211yesmaximal, characteristic, complemented
2#22581520C211yesmaximal, characteristic, complemented
3C2×#17984770C211yesmaximal, characteristic, complemented
4#22580958C211yesmaximal, characteristic, complemented
5C2×#17984759C211yesmaximal, characteristic, complemented
6#22580713C211yesmaximal, characteristic, complemented
7C2×#127×C139C211yesmaximal, characteristic, complemented
8C2×#14555785C2211yescharacteristic
9#17984868—22no—
10#17984868—22no—
11C2×#14555773—21no—
12C2×#14555770—21no—
13C2×#14555769C2211yescharacteristic
14C2×#14555769C2211yescharacteristic
15#17984838—21no—
16#17984829—21no—
17#17984813—22no—
18#17984811—22no—
19#17984801C2211yescharacteristic
20#17984770—22no—
21#17984763—22no—
22#17984759—22no—
23C22×D4×C139—22no—
24C22×D4×C139C2211yescharacteristic
25C22×D4×C139C2211yescharacteristic
26#127×C139—22no—
27#127×C139—22no—
28C2×C42×C139C2211yescharacteristic
29#14555785—21no—
30#14555785—21no—
31#14555785—21no—
32#14555785—21no—
33C2×Dic278D411yescharacteristic, complemented
34C2×D556D411yescharacteristic, complemented
35C2×C22⋊D139—24no—
36C2×C22⋊D139—21no—
37C2×C4×D139—21no—
38#14555773—24no—
39#14555770—24no—
40#14555769—21no—
41#14555769—21no—
42#14555769—21no—
43#14555769D412yescomplemented
44C2×C139⋊C8—21no—
45C2×C139⋊C8—21no—
46C4⋊Dic139D412yescomplemented
47C22⋊Dic139—24no—
48C22⋊Dic139—21no—
49C4×Dic139—21no—
50C24×C139—21no—
51C24×C139D412yes—
52C2×D4×C139—28no—
53C2×D4×C139—21no—
54C2×D4×C139—21no—
55C2×D4×C139—21no—
56C2×D4×C139—21no—
57C2×D4×C139—21no—
58C2×D4×C139—21no—
59C2×D4×C139—21no—
60C2×D4×C139—21no—
61C2×D4×C139—21no—
62C2×D4×C139—21no—
63C2×D4×C139—21no—
64C2×D4×C139—48no—
65C2×D4×C139D412yescomplemented
66C22×C4×C139—21no—
67C22×C4×C139C2311yescharacteristic
68C42×C139—21no—
69C42×C139D412yescomplemented
70C22×D139—21no—
71Dic278—21no—
72Dic278—21no—
73D556—21no—
74D556—21no—
75C22⋊D139—41no—
76C22⋊D139—41no—
77C22⋊D139—84no—
78C2×Dic139—22no—
79C2×Dic139—21no—
80C4×D139—41no—
81C4×D139—41no—
82C139⋊C8—22no—
83C139⋊C8—41no—
84C23×C139—22no—
85C23×C139—22no—
86C23×C139—22no—
87C23×C139—22no—
88C23×C139—44no—
89C23×C139—44no—
90C23×C139—41no—
91C23×C139—41no—
92C23×C139C2×D411yescharacteristic
93D4×C139—22no—
94D4×C139—22no—
95D4×C139—416no—
96D4×C139—41no—
97D4×C139—41no—
98D4×C139—41no—
99D4×C139—41no—
100D4×C139—41no—
101D4×C139—41no—
102C2×C4×C139—24no—
103C2×C4×C139—22no—
104C2×C4×C139C2×D411yescharacteristic
105C2×C4×C139C2×D411yescharacteristic
106C2×C4×C139C2×D411yescharacteristic
107C2×C4×C139C2×D411yescharacteristic
108C2×C4×C139C2×D411yescharacteristic
109C2×C4×C139#4111yescharacteristic
110C22×C139—22no—
111C22×C139—44no—
112C22×C139—44no—
113C22×C139—42no—
114C22×C139—42no—
115C22×C139—44no—
116C22×C139—82no—
117C22×C139—82no—
118C22×C139—82no—
119C22×C139#12011yescharacteristic
120C22×C139#12011yescharacteristic
121C22×C139#12111yescharacteristic
122C2×D139—41no—
123C2×D139—42no—
124C4×C139—24no—
125C4×C139#12011yescharacteristic
126C4×C139#12111yescharacteristic
127C4×C139#12111yescharacteristic
128C4×C139#12711yescharacteristic
129Dic139—41no—
130Dic139—42no—
131C2×C139—21no—
132C2×C139—21no—
133C2×C139—82no—
134C2×C139—82no—
135C2×C139#39211yescharacteristic
136C2×C139#45312yes—
137D139—81no—
138C139#200211yescharacteristic, complemented, Sylow
139#2002—1391nomaximal, Sylow
140C2×AGL(1,ℤ/8)—1391no—
141#535—1391no—
142C2×#127D13911yescharacteristic, complemented
143C2×#104—1391no—
144#418—1391no—
145C2×#100—1391no—
146#339—1391no—
147C2×#41—1391no—
148C22×D4—22no—
149C22×D4C2×D13911yescharacteristic
150C22×D4C2×D13911yescharacteristic
151AGL(1,ℤ/8)—2782no—
152AGL(1,ℤ/8)—2782no—
153C2×SD16—2781no—
154C2×D8—2781no—
155C2×M16—1391no—
156C2×M16—1391no—
157#127—22no—
158#127—22no—
159#127—2781no—
160#124—2781no—
161#121—2782no—
162#120—2782no—
163#117—1391no—
164C2×C42C2×D13911yescharacteristic
165#104—2782no—
166#102—2782no—
167#100—2782no—
168C24—21no—
169C24C22⋊D13912yes—
170#41—2781no—
171#41—2781no—
172#41—2781no—
173#41—2781no—
174C2×Q8—1391no—
175C2×D4—28no—
176C2×D4—21no—
177C2×D4—21no—
178C2×D4—21no—
179C2×D4—21no—
180C2×D4—21no—
181C2×D4—21no—
182C2×D4—21no—
183C2×D4—21no—
184C2×D4—21no—
185C2×D4—21no—
186C2×D4—21no—
187C2×D4—48no—
188C2×D4—2781no—
189C2×D4—2784no—
190C2×D4—1391no—
191C2×D4C22⋊D13912yescomplemented
192C22×C4—21no—
193C22×C4—2781no—
194C22×C4C22×D13911yescharacteristic
195SD16—2784no—
196D8—2784no—
197M16—2781no—
198M16—2781no—
199M16—2781no—
200M16—1392no—
201C2×C8—2781no—
202C2×C8—2781no—
203C4⋊C4—1392no—
204C22⋊C4—2784no—
205C22⋊C4—2781no—
206C42—21no—
207C42—2781no—
208C42C22⋊D13912yescomplemented
209C23—22no—
210C23—22no—
211C23—22no—
212C23—22no—
213C23—44no—
214C23—44no—
215C23—41no—
216C23—41no—
217C23—2781no—
218C23C2×C22⋊D13911yescharacteristic
219Q8—2781no—
220Q8—2781no—
221D4—22no—
222D4—22no—
223D4—416no—
224D4—41no—
225D4—41no—
226D4—41no—
227D4—41no—
228D4—41no—
229D4—41no—
230D4—2781no—
231D4—2781no—
232D4—5561no—
233D4—5561no—
234D4—11124no—
235C2×C4—24no—
236C2×C4—22no—
237C2×C4—2782no—
238C2×C4—2781no—
239C2×C4—5561no—
240C2×C4—5561no—
241C2×C4D4×D13911yescharacteristic
242C2×C4D4×D13911yescharacteristic
243C2×C4D4×D13911yescharacteristic
244C2×C4C2×C22⋊D13911yescharacteristic
245C2×C4C2×C22⋊D13911yescharacteristic
246C2×C4#1455578411yescharacteristic
247C8—2782no—
248C8—5561no—
249C22—22no—
250C22—44no—
251C22—44no—
252C22—42no—
253C22—42no—
254C22—44no—
255C22—82no—
256C22—82no—
257C22—82no—
258C22—5561no—
259C22—5562no—
260C22#1798481011yescharacteristic
261C22#1798481111yescharacteristic
262C22#1798481411yescharacteristic
263C4—24no—
264C4—5561no—
265C4—5562no—
266C4#1798481011yescharacteristic
267C4#1798481311yescharacteristic
268C4#1798481411yescharacteristic
269C4#1798483811yescharacteristic
270C2—21no—
271C2—21no—
272C2—82no—
273C2—82no—
274C2—11121no—
275C2#2258086111yescharacteristic
276C2#2258112012yes—
subgroupG/H
centerC22#17984810
commutator, cosocleC22×C4×C139C23
FrattiniC22×C4C22×D139
FittingC2×#127×C139C2
socleC22×C139#120
hypercenterC2×#127D139
hypocenterC139#2002
LCSG ▷ C22×C4×C139 ▷ C2×C139 ▷ C139
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#127

Complements

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

NH ≅ G/Ntype
1. C2×#17984868C2semidirect
2. #22581520C2semidirect
3. C2×#17984770C2semidirect
4. #22580958C2semidirect
5. C2×#17984759C2semidirect
6. #22580713C2semidirect
7. C2×#127×C139C2semidirect
33. C2×Dic278D4semidirect
34. C2×D556D4semidirect
43. #14555769D4semidirect
46. C4⋊Dic139D4semidirect
65. C2×D4×C139D4semidirect
69. C42×C139D4semidirect
138. C139#2002semidirect
142. C2×#127D139semidirect
191. C2×D4C22⋊D139semidirect
208. C42C22⋊D139semidirect

Maximal subgroups

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

subgroupindex
C2×#179848682
#225815202
C2×#179847702
#225809582
C2×#179847592
#225807132
C2×#127×C1392
#2002139