Finite Group Databasebeta

← #32990079

Subgroups — #32990079

Order 18688.

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

normal subgroups only

This group has 364 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#22610084C211yesmaximal, characteristic
3#22608632C212yesmaximal
4#22608444C212yesmaximal
5C73×#1290C211yesmaximal, characteristic
6#17989144C2212yes—
7#17988883—22no—
8#17988828—22no—
9#17988798—22no—
10C2×C4⋊#10596831C2211yescharacteristic
11C2×#14556520—22no—
12#17988433C2211yescharacteristic
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#14556520—44no—
32#14556516—24no—
33#14556498—21no—
34#14556498D412yes—
35C22×C8×C73D412yes—
36C2×C42×C73C2311yescharacteristic
37C4⋊C8×C73—22no—
38C4⋊C8×C73—22no—
39C22⋊C8×C73—22no—
40#97×C73—22no—
41C2×Dic146—22no—
42C2×Dic146—22no—
43C22×Dic73—22no—
44Dic292—82no—
45C2×#10596831—42no—
46C2×#10596831—41no—
47C4⋊Dic73—22no—
48C4⋊Dic73—22no—
49C4⋊Dic73—22no—
50C4⋊Dic73—22no—
51#11924007—42no—
52#11924007—42no—
53C22⋊Dic73—42no—
54C4×Dic73—22no—
55C4×Dic73—22no—
56C4×Dic73—42no—
57C22×C4×C73C2×D411yescharacteristic
58C22×C4×C73C2×D411yescharacteristic
59C22×C4×C73#4111yescharacteristic
60C2×C8×C73—22no—
61C2×C8×C73—42no—
62C2×C8×C73—42no—
63C42×C73C2×D412yes—
64C42×C73#4112yes—
65C23×C73#12111yescharacteristic
66C2×C4×C73—22no—
67C2×C4×C73—21no—
68C2×C4×C73—21no—
69C2×C4×C73—41no—
70C2×C4×C73#12011yescharacteristic
71C2×C4×C73#12112yes—
72C2×C4×C73#12312yes—
73C2×C4×C73#12411yescharacteristic
74C2×Dic73—24no—
75C2×Dic73—42no—
76C2×Dic73—42no—
77C2×Dic73—42no—
78C2×Dic73—42no—
79Dic146—42no—
80Dic146—42no—
81Dic146—82no—
82C8×C73—42no—
83C8×C73—82no—
84#10596831—81no—
85C22×C73—21no—
86C22×C73—21no—
87C22×C73#39411yescharacteristic
88C22×C73#47312yes—
89C4×C73—22no—
90C4×C73—21no—
91C4×C73—22no—
92C4×C73#45311yescharacteristic
93C4×C73#45611yescharacteristic
94Dic73—44no—
95Dic73—82no—
96Dic73—82no—
97#10516—731nomaximal, Sylow
98C2×C73—22no—
99C2×C73#203911yescharacteristic
100C2×C73#204711yescharacteristic
101C2×C73#205311yescharacteristic
102#3249—731no—
103#1843—731no—
104#1552—732no—
105#1506—732no—
106#1290D7311yescharacteristic
107C73#1051611yescharacteristic, complemented, Sylow
108#533—732no—
109#477—1462no—
110#467—1462no—
111#462—1462no—
112#432C2×D7312yes—
113C2×C4⋊C8—731no—
114C2×C4⋊C8—1462no—
115C2×C4⋊C8C2×D7311yescharacteristic
116#376—731no—
117#332—1462no—
118#332—1462no—
119#328—1464no—
120C2×Q16—1462no—
121C22×C8—1461no—
122C22×C8D29212yes—
123C4⋊Q8—732no—
124C4⋊Q8—732no—
125#125—1462no—
126C22⋊Q8—1462no—
127C22⋊Q8—1462no—
128C4×Q8—1462no—
129C4×Q8—1462no—
130#117—1462no—
131C2×C42—1461no—
132C2×C42C22×D7311yescharacteristic
133#107—1462no—
134C4⋊C8—22no—
135C4⋊C8—22no—
136C4⋊C8—2924no—
137C4⋊C8—1462no—
138#103—1464no—
139C22⋊C8—22no—
140#97—22no—
141#95—732no—
142#95—1461no—
143C2×Q8—1462no—
144C2×Q8—1462no—
145C22×C4—1462no—
146C22×C4D4×D7311yescharacteristic
147C22×C4C2×D29211yescharacteristic
148C22×C4#1192402911yescharacteristic
149Q16—5842no—
150C2×C8—22no—
151C2×C8—42no—
152C2×C8—42no—
153C2×C8—2922no—
154C2×C8—2921no—
155C4⋊C4—2922no—
156C4⋊C4—2922no—
157C4⋊C4—1462no—
158C4⋊C4—1462no—
159C4⋊C4—1462no—
160C4⋊C4—1462no—
161C22⋊C4—2922no—
162C42—2922no—
163C42—1462no—
164C42—1462no—
165C42D4×D7312yes—
166C42#1192402812yes—
167C23#1455656611yescharacteristic
168Q8—2922no—
169Q8—2922no—
170Q8—5842no—
171C2×C4—22no—
172C2×C4—21no—
173C2×C4—21no—
174C2×C4—41no—
175C2×C4—2922no—
176C2×C4—2922no—
177C2×C4—2922no—
178C2×C4—2922no—
179C2×C4—1464no—
180C2×C4#1455656111yescharacteristic
181C2×C4#1455656412yes—
182C2×C4#1455657612yes—
183C2×C4#1455657911yescharacteristic
184C8—42no—
185C8—82no—
186C8—5841no—
187C22—21no—
188C22—21no—
189C22#1798850511yescharacteristic
190C22#1798886312yes—
191C4—22no—
192C4—22no—
193C4—21no—
194C4—2924no—
195C4—5842no—
196C4—5842no—
197C4#1798875711yescharacteristic
198C4#1798877211yescharacteristic
199C2—22no—
200C2#2261115611yescharacteristic
201C2#2261120011yescharacteristic
202C2#2261123811yescharacteristic
subgroupG/H
centerC22#17988505
commutator, cosocleC2×C42×C73C23
FrattiniC2×C42C22×D73
FittingC73×#1290C2
socleC22×C73#394
prime radicalC23×C73#121
hypercenter#1290D73
hypocenterC73#10516
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
107. C73#10516semidirect

Maximal subgroups

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

subgroupindex
#226212762
#226100842
#226086322
#226084442
C73×#12902
#1051673