Finite Group Databasebeta

← #31807544

Subgroups — #31807544

Order 17792.

290 conjugacy classes of subgroups; only the 87 normal subgroups are shown.

normal subgroups only

This group has 290 conjugacy classes of subgroups — too many to draw. Only its 87 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×#17984841C211yesmaximal, characteristic
2C2×#17984767C211yesmaximal, characteristic
3C2×#17984765C211yesmaximal, characteristic
4#22580858C211yesmaximal, characteristic
5#22580715C211yesmaximal, characteristic
6#22580707C211yesmaximal, characteristic
7#340×C139C211yesmaximal, characteristic
8C22×Dic278—21no—
9C22×Dic278C2211yescharacteristic
10C22×C139⋊C8C2211yescharacteristic
11#17984841—22no—
12#17984841—22no—
13C2×C4⋊Dic139C2211yescharacteristic
14C2×Dic139⋊C4—21no—
15C2×C4×Dic139C2211yescharacteristic
16#17984767—22no—
17#17984765—22no—
18C139⋊#95—21no—
19C139⋊#95—21no—
20C22×C8×C139C2211yescharacteristic
21C2×C4⋊C4×C139C2211yescharacteristic
22C2×C4⋊C4×C139C2211yescharacteristic
23C2×Dic278—24no—
24C2×Dic278—21no—
25C2×Dic278—21no—
26C2×Dic278—21no—
27C2×Dic278—21no—
28C2×Dic278—21no—
29C2×Dic278—42no—
30C2×Dic278—42no—
31C2×Dic278Q812yescomplemented
32C22×Dic139—21no—
33C22×Dic139—21no—
34C22×Dic139D411yescharacteristic
35C22×Dic139D411yescharacteristic
36C2×C139⋊C8—21no—
37C2×C139⋊C8—21no—
38C2×C139⋊C8—21no—
39C4⋊Dic139—21no—
40C4⋊Dic139D412yes—
41Dic139⋊C4—24no—
42C4×Dic139—21no—
43C4×Dic139—21no—
44C22×C4×C139—21no—
45C22×C4×C139—21no—
46C22×C4×C139C2311yescharacteristic
47C2×C8×C139—21no—
48C2×C8×C139—21no—
49C2×C8×C139—21no—
50C4⋊C4×C139—21no—
51C4⋊C4×C139—21no—
52C4⋊C4×C139—21no—
53C4⋊C4×C139D412yes—
54Dic278—22no—
55Dic278—22no—
56Dic278—48no—
57Dic278—41no—
58Dic278—41no—
59C2×Dic139—21no—
60C2×Dic139—21no—
61C2×Dic139—21no—
62C2×Dic139—21no—
63C2×Dic139—22no—
64C2×Dic139—22no—
65C2×Dic139—41no—
66C2×Dic139—41no—
67C2×Dic139—41no—
68C2×Dic139—41no—
69C2×Dic139SD1612yes—
70C2×Dic139Q1612yes—
71C139⋊C8—41no—
72C23×C139C2×D411yescharacteristic
73C2×C4×C139—22no—
74C2×C4×C139—41no—
75C2×C4×C139—41no—
76C2×C4×C139—41no—
77C2×C4×C139—41no—
78C2×C4×C139—41no—
79C2×C4×C139C2×D411yescharacteristic
80C2×C4×C139C2×D411yescharacteristic
81C2×C4×C139C2×Q811yescharacteristic
82C2×C4×C139#4111yescharacteristic
83C2×C4×C139#4111yescharacteristic
84C2×C4×C139#4111yescharacteristic
85C8×C139—41no—
86C22×C139#12011yescharacteristic
87C22×C139C22⋊Q811yescharacteristic
88C22×C139#12411yescharacteristic
89C22×C139C2×SD1611yescharacteristic
90C22×C139C2×Q1611yescharacteristic
91C22×C139AGL(1,ℤ/8)11yescharacteristic
92C22×C139#13711yescharacteristic
93C4×C139—42no—
94C4×C139—81no—
95C4×C139C22⋊Q811yescharacteristic
96C4×C139C22⋊Q811yescharacteristic
97C4×C139#12411yescharacteristic
98C4×C139#12411yescharacteristic
99Dic139—22no—
100Dic139—22no—
101Dic139—42no—
102Dic139—42no—
103C2×C139#39311yescharacteristic
104C2×C139#45011yescharacteristic
105C2×C139#45111yescharacteristic
106C2×C139#47511yescharacteristic
107C2×C139#47711yescharacteristic
108C2×C139#48711yescharacteristic
109C2×C139#48911yescharacteristic
110C139#202411yescharacteristic, complemented, Sylow
111#2024—1391nomaximal, Sylow
112C2×C4⋊Q8—1391no—
113C2×#103—1391no—
114C2×#103—1391no—
115#391—1391no—
116#340—1391no—
117#340D13911yescharacteristic
118#336—1391no—
119C22×Q8—2781no—
120C22×Q8—1391no—
121C22×C8—1391no—
122C22×C8C2×D13911yescharacteristic
123C4⋊Q8—2782no—
124C4⋊Q8—2782no—
125C2×C4⋊C4—2781no—
126C2×C4⋊C4—1391no—
127C2×C4⋊C4C2×D13911yescharacteristic
128C2×C4⋊C4C2×D13911yescharacteristic
129C2×C42—1391no—
130#103—2782no—
131#103—2782no—
132#95—2781no—
133#95—2781no—
134C2×Q8—2784no—
135C2×Q8—2781no—
136C2×Q8—2781no—
137C2×Q8—2781no—
138C2×Q8—2781no—
139C2×Q8—2781no—
140C2×Q8—5562no—
141C2×Q8—5562no—
142C2×Q8—1392no—
143C22×C4—21no—
144C22×C4—21no—
145C22×C4—2781no—
146C22×C4—2781no—
147C22×C4—1391no—
148C22×C4—1391no—
149C22×C4C22×D13911yescharacteristic
150C2×C8—21no—
151C2×C8—21no—
152C2×C8—21no—
153C2×C8—2781no—
154C2×C8—2781no—
155C2×C8—2781no—
156C4⋊C4—21no—
157C4⋊C4—21no—
158C4⋊C4—21no—
159C4⋊C4—2784no—
160C4⋊C4—2781no—
161C4⋊C4—1392no—
162C4⋊C4D55612yes—
163C42—2781no—
164C42—2781no—
165C23D4×D13911yescharacteristic
166Q8—2782no—
167Q8—2782no—
168Q8—5568no—
169Q8—5561no—
170Q8—5561no—
171C2×C4—22no—
172C2×C4—41no—
173C2×C4—41no—
174C2×C4—41no—
175C2×C4—41no—
176C2×C4—41no—
177C2×C4—2781no—
178C2×C4—2781no—
179C2×C4—2781no—
180C2×C4—2781no—
181C2×C4—2782no—
182C2×C4—2782no—
183C2×C4—5561no—
184C2×C4—5561no—
185C2×C4—5561no—
186C2×C4—5561no—
187C2×C4—1392no—
188C2×C4—1392no—
189C2×C4D4×D13911yescharacteristic
190C2×C4C2×D55611yescharacteristic
191C2×C4Q8×D13911yescharacteristic
192C2×C4#1455578411yescharacteristic
193C2×C4#1455578511yescharacteristic
194C2×C4#1455578511yescharacteristic
195C8—41no—
196C8—5561no—
197C22#1798481211yescharacteristic
198C22#1798482011yescharacteristic
199C22#1798482811yescharacteristic
200C22SD16×D13911yescharacteristic
201C22Q16×D13911yescharacteristic
202C22#1798486611yescharacteristic
203C22#1798487111yescharacteristic
204C4—42no—
205C4—81no—
206C4—2782no—
207C4—2782no—
208C4—5562no—
209C4—5562no—
210C4#1798482011yescharacteristic
211C4#1798482211yescharacteristic
212C4#1798482811yescharacteristic
213C4#1798483011yescharacteristic
214C2#2258086611yescharacteristic
215C2#2258110511yescharacteristic
216C2#2258111011yescharacteristic
217C2#2258123711yescharacteristic
218C2#2258124711yescharacteristic
219C2#2258130211yescharacteristic
220C2#2258131111yescharacteristic
subgroupG/H
centerC23D4×D139
commutator, cosocleC22×C4×C139C23
FrattiniC22×C4C22×D139
Fitting#340×C139C2
socle, prime radicalC23×C139C2×D4
hypercenter#340D139
hypocenterC139#2024
LCSG ▷ C22×C4×C139 ▷ C2×C139 ▷ C139
UCSC1 ◁ C23 ◁ C22×C4 ◁ #340

Complements

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

NH ≅ G/Ntype
31. C2×Dic278Q8semidirect
110. C139#2024semidirect

Maximal subgroups

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

subgroupindex
C2×#179848412
C2×#179847672
C2×#179847652
#225808582
#225807152
#225807072
#340×C1392
#2024139