Finite Group Databasebeta

← #31806796

Subgroups — #31806796

Order 17792.

324 conjugacy classes of subgroups; only the 83 normal subgroups are shown.

normal subgroups only

This group has 324 conjugacy classes of subgroups — too many to draw. Only its 83 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×#17984842C211yesmaximal, characteristic
2#22581430C211yesmaximal, characteristic
3#22580963C211yesmaximal, characteristic
4#22580961C211yesmaximal, characteristic
5C2×#17984760C211yesmaximal, characteristic
6#22580713C211yesmaximal, characteristic
7#339×C139C211yesmaximal, characteristic
8C22×Dic278C2211yescharacteristic
9C22×Dic278C2211yescharacteristic
10C2×#14555769C2211yescharacteristic
11#17984842—22no—
12#17984842C414yescomplemented
13C4×Dic278—22no—
14#17984807—22no—
15#17984801C2211yescharacteristic
16#17984798—22no—
17C2×C4⋊Dic139—22no—
18#17984767—22no—
19#17984765—22no—
20#17984760—22no—
21C2×M16×C139C2211yescharacteristic
22#117×C139C2211yescharacteristic
23C2×C42×C139C2211yescharacteristic
24C2×Dic278—21no—
25C2×Dic278—21no—
26C2×Dic278—21no—
27C2×Dic278—21no—
28C2×Dic278—21no—
29C2×Dic278—21no—
30C2×Dic278—21no—
31C2×Dic278—21no—
32C2×Dic278—21no—
33C2×Dic278C2×C412yes—
34C2×Dic278C2×C412yes—
35C2×Dic278D412yes—
36C22×Dic139—21no—
37C22×Dic139D412yes—
38#14555769—21no—
39#14555769—21no—
40C2×C139⋊C8—21no—
41C4⋊Dic139—28no—
42C4⋊Dic139D412yes—
43Dic139⋊C4—24no—
44C22⋊Dic139—21no—
45C4×Dic139—24no—
46C4×Dic139—21no—
47C22×C4×C139—21no—
48C22×C4×C139C2311yescharacteristic
49M16×C139—21no—
50M16×C139—21no—
51C2×C8×C139—21no—
52C4⋊C4×C139D412yes—
53C22⋊C4×C139—21no—
54C42×C139—21no—
55C42×C139—21no—
56C42×C139C2×C412yes—
57Dic278—22no—
58Dic278—22no—
59Dic278—22no—
60Dic278—22no—
61Dic278—22no—
62Dic278—22no—
63Dic278—41no—
64Dic278—41no—
65C2×Dic139—22no—
66C2×Dic139—22no—
67C2×Dic139—22no—
68C2×Dic139—22no—
69C2×Dic139—41no—
70C2×Dic139—41no—
71C2×Dic139C22⋊C414yes—
72C139⋊C8—41no—
73C23×C139C2×D411yescharacteristic
74C2×C4×C139—24no—
75C2×C4×C139—22no—
76C2×C4×C139—22no—
77C2×C4×C139C22×C411yescharacteristic
78C2×C4×C139C2×D411yescharacteristic
79C2×C4×C139C2×D411yescharacteristic
80C2×C4×C139C2×D411yescharacteristic
81C2×C4×C139#4111yescharacteristic
82C2×C4×C139#4111yescharacteristic
83C8×C139—41no—
84C22×C139—22no—
85C22×C139C2×C22⋊C411yescharacteristic
86C22×C139#12011yescharacteristic
87C22×C139#12311yescharacteristic
88C4×C139—24no—
89C4×C139—42no—
90C4×C139C4×D411yescharacteristic
91C4×C139C4×D411yescharacteristic
92C4×C139#12111yescharacteristic
93C4×C139#12111yescharacteristic
94Dic139—24no—
95Dic139—42no—
96Dic139—42no—
97C2×C139—21no—
98C2×C139—21no—
99C2×C139#38611yescharacteristic
100C2×C139#45612yes—
101C139#188611yescharacteristic, complemented, Sylow
102#1886—1391nomaximal, Sylow
103C2×C4⋊Q8—1391no—
104#519—1391no—
105#419—1391no—
106#419—1391no—
107C2×#101—1391no—
108#339—1391no—
109#339D13911yescharacteristic
110C22×Q8—1391no—
111C22×Q8—1391no—
112C2×M16—1391no—
113C2×M16C2×D13911yescharacteristic
114C4⋊Q8—2782no—
115C4⋊Q8—1394no—
116C4×Q8—2782no—
117C4×Q8—2782no—
118#117—2782no—
119#117—1391no—
120#117C2×D13911yescharacteristic
121C2×C4⋊C4—2782no—
122C2×C42C2×D13911yescharacteristic
123#103—2782no—
124#103—2782no—
125#101—2782no—
126C2×Q8—2781no—
127C2×Q8—2781no—
128C2×Q8—2781no—
129C2×Q8—2781no—
130C2×Q8—2781no—
131C2×Q8—2781no—
132C2×Q8—2781no—
133C2×Q8—2781no—
134C2×Q8—2781no—
135C2×Q8—1392no—
136C2×Q8—1392no—
137C2×Q8—1392no—
138C22×C4—21no—
139C22×C4—2781no—
140C22×C4—1392no—
141C22×C4C22×D13911yescharacteristic
142M16—21no—
143M16—21no—
144M16—2781no—
145M16—2781no—
146C2×C8—21no—
147C2×C8—2781no—
148C4⋊C4—2784no—
149C4⋊C4—2788no—
150C4⋊C4—1392no—
151C4⋊C4D55612yes—
152C22⋊C4—21no—
153C22⋊C4—2781no—
154C42—21no—
155C42—21no—
156C42—2784no—
157C42—2781no—
158C42C4×D13912yes—
159C23D4×D13911yescharacteristic
160Q8—2782no—
161Q8—2782no—
162Q8—2782no—
163Q8—2782no—
164Q8—2782no—
165Q8—2782no—
166Q8—5561no—
167Q8—5561no—
168C2×C4—24no—
169C2×C4—22no—
170C2×C4—22no—
171C2×C4—2782no—
172C2×C4—2782no—
173C2×C4—2782no—
174C2×C4—2782no—
175C2×C4—5561no—
176C2×C4—5561no—
177C2×C4—1394no—
178C2×C4C2×C4×D13911yescharacteristic
179C2×C4D4×D13911yescharacteristic
180C2×C4D4×D13911yescharacteristic
181C2×C4C2×D55611yescharacteristic
182C2×C4#1455578511yescharacteristic
183C2×C4#1455578611yescharacteristic
184C8—41no—
185C8—5561no—
186C22—22no—
187C22C22⋊C4×D13911yescharacteristic
188C22#1798481211yescharacteristic
189C22#1798482711yescharacteristic
190C4—24no—
191C4—42no—
192C4—2784no—
193C4—5562no—
194C4—5562no—
195C4#1798480411yescharacteristic
196C4C4×D55611yescharacteristic
197C4#1798481511yescharacteristic
198C4#1798481711yescharacteristic
199C2—21no—
200C2—21no—
201C2#2258083111yescharacteristic
202C2#2258113712yes—
subgroupG/H
centerC22#17984812
commutatorC2×C4×C139C22×C4
FrattiniC22×C4C22×D139
Fitting#339×C139C2
socleC22×C139#120
prime radicalC23×C139C2×D4
cosocleC22×C4×C139C23
hypercenter#339D139
hypocenterC139#1886
LCSG ▷ C2×C4×C139 ▷ C2×C139 ▷ C139
UCSC1 ◁ C22 ◁ C22×C4 ◁ #339

Complements

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

NH ≅ G/Ntype
12. #17984842C4semidirect
101. C139#1886semidirect

Maximal subgroups

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

subgroupindex
C2×#179848422
#225814302
#225809632
#225809612
C2×#179847602
#225807132
#339×C1392
#1886139