Finite Group Databasebeta

← #31807563

Subgroups — #31807563

Order 17792.

246 conjugacy classes of subgroups; only the 69 normal subgroups are shown.

normal subgroups only

This group has 246 conjugacy classes of subgroups — too many to draw. Only its 69 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#22581581C211yesmaximal, characteristic
2#22580962C211yesmaximal, characteristic
3#22580860C211yesmaximal, characteristic
4#22580721C211yesmaximal, characteristic
5#22580714C211yesmaximal, characteristic
6#22580712C211yesmaximal, characteristic
7#419×C139C211yesmaximal, characteristic
8C2×#14555769C2211yescharacteristic
9#17984842—21no—
10#17984841—21no—
11#17984834—21no—
12#17984833—21no—
13#17984819—22no—
14#17984801C2211yescharacteristic
15C2×C4⋊Dic139C2211yescharacteristic
16C2×C4×Dic139C2211yescharacteristic
17#17984766—21no—
18#17984766—21no—
19C139⋊#95—22no—
20C22×Q8×C139C2211yescharacteristic
21C2×M16×C139C2211yescharacteristic
22#117×C139C2211yescharacteristic
23#103×C139—21no—
24#103×C139—21no—
25C2×Dic278—22no—
26C22×Dic139—21no—
27C22×Dic139D412yes—
28#14555769—21no—
29#14555769—21no—
30C2×C139⋊C8—21no—
31C4⋊Dic139—22no—
32C4⋊Dic139—21no—
33C4⋊Dic139—21no—
34C4⋊Dic139D411yescharacteristic
35C4⋊Dic139D411yescharacteristic
36Dic139⋊C4—22no—
37Dic139⋊C4—22no—
38C22⋊Dic139—21no—
39C4×Dic139—21no—
40C4×Dic139—21no—
41C4×Dic139—21no—
42C2×Q8×C139—21no—
43C2×Q8×C139—21no—
44C2×Q8×C139—21no—
45C2×Q8×C139—21no—
46C2×Q8×C139—21no—
47C2×Q8×C139Q812yescomplemented
48C22×C4×C139—21no—
49C22×C4×C139C2311yescharacteristic
50M16×C139—21no—
51M16×C139—21no—
52C2×C8×C139—21no—
53C4⋊C4×C139D411yescharacteristic
54C4⋊C4×C139D411yescharacteristic
55C22⋊C4×C139—21no—
56C42×C139—21no—
57Dic278—82no—
58C2×Dic139—22no—
59C2×Dic139—21no—
60C2×Dic139—21no—
61C2×Dic139—22no—
62C2×Dic139—41no—
63C2×Dic139—41no—
64C2×Dic139—42no—
65C139⋊C8—41no—
66C23×C139C2×D411yescharacteristic
67Q8×C139—22no—
68Q8×C139—22no—
69Q8×C139—41no—
70Q8×C139—41no—
71C2×C4×C139—21no—
72C2×C4×C139—21no—
73C2×C4×C139—22no—
74C2×C4×C139—41no—
75C2×C4×C139—41no—
76C2×C4×C139C2×D411yescharacteristic
77C2×C4×C139C2×D411yescharacteristic
78C2×C4×C139C2×Q811yescharacteristic
79C2×C4×C139#4111yescharacteristic
80C2×C4×C139#4111yescharacteristic
81C2×C4×C139#4111yescharacteristic
82C8×C139—41no—
83C22×C139—21no—
84C22×C139—21no—
85C22×C139#12011yescharacteristic
86C22×C139C22⋊Q811yescharacteristic
87C22×C139#12411yescharacteristic
88C4×C139—42no—
89C4×C139—41no—
90C4×C139—41no—
91C4×C139C22⋊Q811yescharacteristic
92C4×C139C22⋊Q811yescharacteristic
93C4×C139#12411yescharacteristic
94C4×C139#12411yescharacteristic
95Dic139—42no—
96Dic139—42no—
97Dic139—41no—
98Dic139—41no—
99C2×C139—21no—
100C2×C139—21no—
101C2×C139#39311yescharacteristic
102C2×C139#45511yescharacteristic
103C2×C139#45611yescharacteristic
104C139#202811yescharacteristic, complemented, Sylow
105#2028—1391nomaximal, Sylow
106#544—1391no—
107#419—1391no—
108#419D13911yescharacteristic
109#391—1391no—
110#343—1391no—
111#339—1391no—
112#339—1391no—
113C22×Q8C2×D13911yescharacteristic
114C2×M16—1391no—
115C2×M16C2×D13911yescharacteristic
116C4⋊Q8—2781no—
117C4⋊Q8—2781no—
118#125—2781no—
119#125—2781no—
120C22⋊Q8—2782no—
121#117—1391no—
122#117C2×D13911yescharacteristic
123C2×C4⋊C4—1391no—
124C2×C42—1391no—
125#103—21no—
126#103—21no—
127#103—2781no—
128#103—2781no—
129#95—2782no—
130C2×Q8—21no—
131C2×Q8—21no—
132C2×Q8—21no—
133C2×Q8—21no—
134C2×Q8—21no—
135C2×Q8—2782no—
136C2×Q8Dic27812yescomplemented
137C22×C4—21no—
138C22×C4—2781no—
139C22×C4—1392no—
140C22×C4C22×D13911yescharacteristic
141M16—21no—
142M16—21no—
143M16—2781no—
144M16—2781no—
145C2×C8—21no—
146C2×C8—2781no—
147C4⋊C4—2782no—
148C4⋊C4—2782no—
149C4⋊C4—2782no—
150C4⋊C4—2781no—
151C4⋊C4—2781no—
152C4⋊C4—1391no—
153C4⋊C4—1391no—
154C4⋊C4C22⋊D13911yescharacteristic
155C4⋊C4C22⋊D13911yescharacteristic
156C22⋊C4—21no—
157C22⋊C4—2781no—
158C42—21no—
159C42—2781no—
160C42—2781no—
161C42—2781no—
162C23D4×D13911yescharacteristic
163Q8—22no—
164Q8—22no—
165Q8—41no—
166Q8—41no—
167Q8—11122no—
168C2×C4—21no—
169C2×C4—21no—
170C2×C4—22no—
171C2×C4—41no—
172C2×C4—41no—
173C2×C4—2782no—
174C2×C4—2781no—
175C2×C4—2781no—
176C2×C4—2782no—
177C2×C4—5561no—
178C2×C4—5561no—
179C2×C4—5562no—
180C2×C4D4×D13911yescharacteristic
181C2×C4C2×C22⋊D13911yescharacteristic
182C2×C4C2×Dic27811yescharacteristic
183C2×C4#1455578411yescharacteristic
184C2×C4#1455578411yescharacteristic
185C2×C4#1455578511yescharacteristic
186C8—41no—
187C8—5561no—
188C22—21no—
189C22—21no—
190C22#1798481011yescharacteristic
191C22#1798481911yescharacteristic
192C22#1798482811yescharacteristic
193C4—42no—
194C4—41no—
195C4—41no—
196C4—5562no—
197C4—5562no—
198C4—5561no—
199C4—5561no—
200C4#1798481911yescharacteristic
201C4#1798482111yescharacteristic
202C4#1798482811yescharacteristic
203C4#1798482911yescharacteristic
204C2—21no—
205C2—21no—
206C2#2258086511yescharacteristic
207C2#2258112911yescharacteristic
208C2#2258113411yescharacteristic
subgroupG/H
centerC22#17984810
commutator, cosocleC22×C4×C139C23
FrattiniC22×C4C22×D139
Fitting#419×C139C2
socleC22×C139#120
prime radicalC23×C139C2×D4
hypercenter#419D139
hypocenterC139#2028
LCSG ▷ C22×C4×C139 ▷ C2×C139 ▷ C139
UCSC1 ◁ C22 ◁ C22×C4 ◁ #419

Complements

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

NH ≅ G/Ntype
47. C2×Q8×C139Q8semidirect
104. C139#2028semidirect
136. C2×Q8Dic278semidirect

Maximal subgroups

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

subgroupindex
#225815812
#225809622
#225808602
#225807212
#225807142
#225807122
#419×C1392
#2028139