Finite Group Databasebeta

← #32989064

Subgroups — #32989064

Order 18688.

392 conjugacy classes of subgroups; only the 93 normal subgroups are shown.

normal subgroups only

This group has 392 conjugacy classes of subgroups — too many to draw. Only its 93 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#22610903C212yesmaximal
2#22610750C211yesmaximal, characteristic
3#22607812C211yesmaximal, characteristic
4#22607812C212yesmaximal
5C73×#2845C211yesmaximal, characteristic
6C2×#14556591C2211yescharacteristic
7C2×#14556514—22no—
8C2×#14556502C2211yescharacteristic
9C2×#14556502C2212yes—
10#17988349—22no—
11#17988349—22no—
12#398×C73—22no—
13#398×C73—22no—
14#398×C73—22no—
15#382×C73C2211yescharacteristic
16#382×C73C2212yes—
17C22×Dic146—21no—
18C22×#10596831—21no—
19C22×#10596831—22no—
20#14556591—22no—
21#14556591—21no—
22#14556591Q812yes—
23C2×C4⋊Dic73—22no—
24#14556514—44no—
25#14556502—22no—
26#14556502—22no—
27#14556502—22no—
28C2×C4⋊C4×C73—22no—
29C2×C4⋊C4×C73—22no—
30C2×C4⋊C4×C73—22no—
31C2×C4⋊C4×C73D412yes—
32C2×C4⋊C4×C73D412yes—
33C2×C4⋊C4×C73D412yes—
34C2×C42×C73C2311yescharacteristic
35#95×C73—22no—
36#95×C73—22no—
37#95×C73—22no—
38#95×C73—22no—
39C2×Dic146—22no—
40C2×Dic146—42no—
41C2×Dic146—42no—
42C2×Dic146—41no—
43C22×Dic73—41no—
44C2×#10596831—22no—
45C2×#10596831—24no—
46C2×#10596831—41no—
47C2×#10596831—42no—
48C2×#10596831—42no—
49C2×#10596831—41no—
50C4⋊Dic73—24no—
51C4⋊Dic73—42no—
52C22×C4×C73—22no—
53C22×C4×C73—22no—
54C22×C4×C73—22no—
55C22×C4×C73C2×D412yes—
56C22×C4×C73C2×D411yescharacteristic
57C4⋊C4×C73—42no—
58C4⋊C4×C73—42no—
59C4⋊C4×C73—42no—
60C4⋊C4×C73—82no—
61C4⋊C4×C73—82no—
62C4⋊C4×C73—82no—
63C42×C73C2×Q811yescharacteristic
64C42×C73#4112yes—
65C42×C73#4111yescharacteristic
66C23×C73#12011yescharacteristic
67C2×C4×C73—21no—
68C2×C4×C73—21no—
69C2×C4×C73—22no—
70C2×C4×C73—22no—
71C2×C4×C73—42no—
72C2×C4×C73—42no—
73C2×C4×C73—42no—
74C2×C4×C73—42no—
75C2×C4×C73—42no—
76C2×C4×C73—42no—
77C2×C4×C73—42no—
78C2×C4×C73—42no—
79C2×C4×C73—42no—
80C2×C4×C73C22⋊Q812yes—
81C2×C4×C73C22⋊Q811yescharacteristic
82C2×C4×C73#12412yes—
83C2×C4×C73#12411yescharacteristic
84C2×Dic73—42no—
85C2×Dic73—81no—
86C2×Dic73—81no—
87Dic146—44no—
88Dic146—82no—
89#10596831—42no—
90#10596831—44no—
91C22×C73#39311yescharacteristic
92C22×C73#45311yescharacteristic
93C22×C73#45411yescharacteristic
94C22×C73#45512yes—
95C22×C73#45612yes—
96C4×C73—21no—
97C4×C73—21no—
98C4×C73—22no—
99C4×C73—22no—
100C4×C73—82no—
101C4×C73—82no—
102C4×C73—82no—
103Dic73—82no—
104#10361—731nomaximal, Sylow
105C2×C73#166112yes—
106C2×C73#166211yescharacteristic
107C2×C73#166311yescharacteristic
108C2×C73#202711yescharacteristic
109C2×C73#202812yes—
110#2845D7311yescharacteristic
111#1993—732no—
112#1960—731no—
113#1295—731no—
114#1295—732no—
115C73#1036111yescharacteristic, complemented, Sylow
116C2×C4⋊Q8—731no—
117C2×#103—1462no—
118C2×#97—731no—
119C2×#97—732no—
120#398—22no—
121#398—22no—
122#398—22no—
123#382C2×D7311yescharacteristic
124#382C2×D7312yes—
125#340—1462no—
126#340—1462no—
127C22×Q8—1461no—
128C22×C8—1462no—
129C22×C8—1461no—
130C4⋊Q8—732no—
131C4⋊Q8—1461no—
132C4⋊Q8—1462no—
133C2×C4⋊C4—22no—
134C2×C4⋊C4—22no—
135C2×C4⋊C4—22no—
136C2×C4⋊C4—1462no—
137C2×C4⋊C4C22⋊D7312yes—
138C2×C4⋊C4C22⋊D7312yes—
139C2×C4⋊C4C22⋊D7312yes—
140C2×C42C22×D7311yescharacteristic
141#103—2924no—
142#97—1462no—
143#97—1462no—
144#97—1462no—
145#95—22no—
146#95—22no—
147#95—22no—
148#95—22no—
149C2×Q8—2922no—
150C2×Q8—2922no—
151C2×Q8—2921no—
152C2×Q8—1462no—
153C22×C4—22no—
154C22×C4—22no—
155C22×C4—22no—
156C22×C4—2921no—
157C22×C4C2×C22⋊D7312yes—
158C22×C4C2×C22⋊D7311yescharacteristic
159C2×C8—2921no—
160C2×C8—2922no—
161C2×C8—2922no—
162C2×C8—2921no—
163C2×C8—1462no—
164C2×C8—1464no—
165C4⋊C4—42no—
166C4⋊C4—42no—
167C4⋊C4—42no—
168C4⋊C4—82no—
169C4⋊C4—82no—
170C4⋊C4—82no—
171C4⋊C4—2922no—
172C4⋊C4—1464no—
173C42Q8×D7311yescharacteristic
174C42#1192402912yes—
175C42#1192402911yescharacteristic
176C23#1455656011yescharacteristic
177Q8—2924no—
178Q8—5842no—
179C2×C4—21no—
180C2×C4—21no—
181C2×C4—22no—
182C2×C4—22no—
183C2×C4—42no—
184C2×C4—42no—
185C2×C4—42no—
186C2×C4—42no—
187C2×C4—42no—
188C2×C4—42no—
189C2×C4—42no—
190C2×C4—42no—
191C2×C4—42no—
192C2×C4—2922no—
193C2×C4—5841no—
194C2×C4—5841no—
195C2×C4#1455656712yes—
196C2×C4#1455656711yescharacteristic
197C2×C4#1455658012yes—
198C2×C4#1455658011yescharacteristic
199C8—2922no—
200C8—2924no—
201C22#1798849811yescharacteristic
202C22#1798875511yescharacteristic
203C22#1798876011yescharacteristic
204C22#1798876512yes—
205C22#1798877012yes—
206C4—21no—
207C4—21no—
208C4—22no—
209C4—22no—
210C4—82no—
211C4—82no—
212C4—82no—
213C4—5842no—
214C2#2260924812yes—
215C2#2260925411yescharacteristic
216C2#2260925911yescharacteristic
217C2#2261108411yescharacteristic
218C2#2261108912yes—
subgroupG/H
centerC23#14556560
commutator, cosocleC2×C42×C73C23
FrattiniC2×C42C22×D73
FittingC73×#2845C2
socle, prime radicalC23×C73#120
hypercenter#2845D73
hypocenterC73#10361
LCSG ▷ C2×C42×C73 ▷ C22×C73 ▷ C73
UCSC1 ◁ C23 ◁ C2×C42 ◁ #2845

Complements

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

NH ≅ G/Ntype
115. C73#10361semidirect

Maximal subgroups

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

subgroupindex
#226109032
#226107502
#226078122
C73×#28452
#1036173