Finite Group Databasebeta

← #32990084

Subgroups — #32990084

Order 18688.

344 conjugacy classes of subgroups; only the 77 normal subgroups are shown.

normal subgroups only

This group has 344 conjugacy classes of subgroups — too many to draw. Only its 77 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#22621276C211yesmaximal, characteristic
2#22610050C211yesmaximal, characteristic
3#22608632C212yesmaximal
4#22608444C212yesmaximal
5C73×#1290C211yesmaximal, characteristic
6#17989144C2212yes—
7#17988883—22no—
8#17988828—22no—
9#17988798—22no—
10C2×C4⋊#10596831C2211yescharacteristic
11#17988433C2211yescharacteristic
12#17988341—22no—
13#17988334—22no—
14#17988332—22no—
15#17988325—24no—
16#432×C73C2212yes—
17C2×C4⋊C8×C73C2211yescharacteristic
18C2×Dic292—22no—
19C22×#10596831—21no—
20#14556591D412yes—
21#14556591D412yes—
22#14556583—22no—
23#14556570—22no—
24#14556570—22no—
25C4×Dic146—22no—
26C4×Dic146—22no—
27#14556550—22no—
28C2×C4×Dic73—21no—
29#14556525—22no—
30C4⋊#10596831—22no—
31#14556516—24no—
32#14556498—21no—
33#14556498D412yes—
34C22×C8×C73D412yes—
35C2×C42×C73C2311yescharacteristic
36C4⋊C8×C73—22no—
37C4⋊C8×C73—22no—
38C22⋊C8×C73—22no—
39#97×C73—22no—
40C2×Dic146—22no—
41C2×Dic146—22no—
42C22×Dic73—22no—
43Dic292—82no—
44C2×#10596831—42no—
45C2×#10596831—41no—
46C4⋊Dic73—22no—
47C4⋊Dic73—22no—
48C4⋊Dic73—22no—
49C4⋊Dic73—22no—
50#11924007—42no—
51#11924007—42no—
52C22⋊Dic73—42no—
53C4×Dic73—41no—
54C4×Dic73—41no—
55C4×Dic73—42no—
56C22×C4×C73C2×D411yescharacteristic
57C22×C4×C73C2×D411yescharacteristic
58C22×C4×C73#4111yescharacteristic
59C2×C8×C73—22no—
60C2×C8×C73—42no—
61C2×C8×C73—42no—
62C42×C73C2×D412yes—
63C42×C73#4112yes—
64C23×C73#12111yescharacteristic
65C2×C4×C73—22no—
66C2×C4×C73—21no—
67C2×C4×C73—21no—
68C2×C4×C73—41no—
69C2×C4×C73#12011yescharacteristic
70C2×C4×C73#12112yes—
71C2×C4×C73#12312yes—
72C2×C4×C73#12411yescharacteristic
73C2×Dic73—42no—
74C2×Dic73—42no—
75C2×Dic73—42no—
76C2×Dic73—42no—
77C2×Dic73—42no—
78Dic146—42no—
79Dic146—42no—
80Dic146—82no—
81C8×C73—42no—
82C8×C73—82no—
83#10596831—81no—
84C22×C73—21no—
85C22×C73—21no—
86C22×C73#39411yescharacteristic
87C22×C73#47312yes—
88C4×C73—22no—
89C4×C73—21no—
90C4×C73—22no—
91C4×C73#45411yescharacteristic
92C4×C73#45511yescharacteristic
93Dic73—82no—
94Dic73—82no—
95Dic73—82no—
96#10517—731nomaximal, Sylow
97C2×C73—22no—
98C2×C73#204011yescharacteristic
99C2×C73#204711yescharacteristic
100C2×C73#205311yescharacteristic
101#3249—731no—
102#1832—731no—
103#1552—732no—
104#1506—732no—
105#1290D7311yescharacteristic
106C73#1051711yescharacteristic, complemented, Sylow
107#533—732no—
108#477—1462no—
109#467—1462no—
110#462—1462no—
111#432C2×D7312yes—
112C2×C4⋊C8—731no—
113C2×C4⋊C8C2×D7311yescharacteristic
114#376—731no—
115#336—1462no—
116#332—1462no—
117#332—1462no—
118#328—1464no—
119C2×Q16—1462no—
120C22×C8—1461no—
121C22×C8D29212yes—
122C4⋊Q8—732no—
123C4⋊Q8—732no—
124#125—1462no—
125C22⋊Q8—1462no—
126C22⋊Q8—1462no—
127C4×Q8—1462no—
128C4×Q8—1462no—
129#117—1462no—
130C2×C42—1461no—
131C2×C42C22×D7311yescharacteristic
132#107—1462no—
133C4⋊C8—22no—
134C4⋊C8—22no—
135C4⋊C8—1462no—
136#103—1464no—
137C22⋊C8—22no—
138#97—22no—
139#95—732no—
140#95—1461no—
141C2×Q8—1462no—
142C2×Q8—1462no—
143C22×C4—1462no—
144C22×C4D4×D7311yescharacteristic
145C22×C4C2×D29211yescharacteristic
146C22×C4#1192402911yescharacteristic
147Q16—5842no—
148C2×C8—22no—
149C2×C8—42no—
150C2×C8—42no—
151C2×C8—2922no—
152C2×C8—2921no—
153C4⋊C4—2922no—
154C4⋊C4—2922no—
155C4⋊C4—1462no—
156C4⋊C4—1462no—
157C4⋊C4—1462no—
158C4⋊C4—1462no—
159C22⋊C4—2922no—
160C42—2921no—
161C42—2921no—
162C42—2922no—
163C42D4×D7312yes—
164C42#1192402812yes—
165C23#1455656611yescharacteristic
166Q8—2922no—
167Q8—2922no—
168Q8—5842no—
169C2×C4—22no—
170C2×C4—21no—
171C2×C4—21no—
172C2×C4—41no—
173C2×C4—2922no—
174C2×C4—2922no—
175C2×C4—2922no—
176C2×C4—2922no—
177C2×C4—2922no—
178C2×C4#1455656111yescharacteristic
179C2×C4#1455656412yes—
180C2×C4#1455657612yes—
181C2×C4#1455657911yescharacteristic
182C8—42no—
183C8—82no—
184C8—5841no—
185C22—21no—
186C22—21no—
187C22#1798850511yescharacteristic
188C22#1798886312yes—
189C4—22no—
190C4—22no—
191C4—21no—
192C4—5842no—
193C4—5842no—
194C4—5842no—
195C4#1798876211yescharacteristic
196C4#1798876711yescharacteristic
197C2—22no—
198C2#2261116111yescharacteristic
199C2#2261120011yescharacteristic
200C2#2261123811yescharacteristic
subgroupG/H
centerC22#17988505
commutator, cosocleC2×C42×C73C23
FrattiniC2×C42C22×D73
FittingC73×#1290C2
socleC22×C73#394
prime radicalC23×C73#121
hypercenter#1290D73
hypocenterC73#10517
LCSG ▷ C2×C42×C73 ▷ C22×C73 ▷ C73
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1290

Complements

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

NH ≅ G/Ntype
106. C73#10517semidirect

Maximal subgroups

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

subgroupindex
#226212762
#226100502
#226086322
#226084442
C73×#12902
#1051773