Finite Group Databasebeta

← #32986945

Subgroups — #32986945

Order 18688.

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

normal subgroups only

This group has 468 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
1#22621276C211yesmaximal, characteristic
2#22620061C212yesmaximal
3#22608545C212yesmaximal
4#22607801C211yesmaximal, characteristic
5C73×#1985C211yesmaximal, characteristic
6#17989144C2212yes—
7#17988917—22no—
8#17988883—22no—
9#17988872—22no—
10#17988828—22no—
11#17988798—22no—
12#17988797—22no—
13#17988743—22no—
14#17988692—24no—
15#17988644C2212yes—
16#17988328—24no—
17C2×C4×Q8×C73C2211yescharacteristic
18C2×C4⋊C8×C73C2211yescharacteristic
19C2×#97×C73C2211yescharacteristic
20#336×C73—22no—
21C2×Dic292—22no—
22C2×#11924018—24no—
23#14556591D412yes—
24#14556591D412yes—
25#14556583—22no—
26#14556570—22no—
27#14556570—22no—
28C4×Dic146—22no—
29C4×Dic146—22no—
30#14556550—22no—
31#14556525—22no—
32#14556522—24no—
33C4⋊#10596831—22no—
34#14556516—24no—
35#14556515—24no—
36#14556514—24no—
37C22⋊#10596831—22no—
38#14556502D414yes—
39C22×Q8×C73D411yescharacteristic
40C22×C8×C73—21no—
41C22×C8×C73D412yes—
42C4×Q8×C73—22no—
43C4×Q8×C73—22no—
44C2×C4⋊C4×C73—21no—
45C2×C4⋊C4×C73D411yescharacteristic
46C2×C42×C73—21no—
47C2×C42×C73C2311yescharacteristic
48C4⋊C8×C73—22no—
49#97×C73—22no—
50C2×Dic146—22no—
51C2×Dic146—22no—
52Dic292—82no—
53#11924018—48no—
54C2×#10596831—24no—
55C4⋊Dic73—22no—
56C4⋊Dic73—22no—
57C4⋊Dic73—22no—
58C4⋊Dic73—22no—
59#11924007—42no—
60#11924007—42no—
61C22⋊Dic73—42no—
62C4×Dic73—42no—
63C2×Q8×C73—22no—
64C2×Q8×C73—42no—
65C22×C4×C73—21no—
66C22×C4×C73—21no—
67C22×C4×C73C2×D411yescharacteristic
68C22×C4×C73C2×D411yescharacteristic
69C22×C4×C73#4111yescharacteristic
70C2×C8×C73—22no—
71C2×C8×C73—22no—
72C2×C8×C73—41no—
73C2×C8×C73—41no—
74C2×C8×C73—42no—
75C4⋊C4×C73—22no—
76C4⋊C4×C73—42no—
77C42×C73—41no—
78C42×C73—41no—
79C42×C73C2×D412yes—
80C42×C73C2×D412yes—
81C23×C73#12111yescharacteristic
82Q8×C73—24no—
83Q8×C73—42no—
84C2×C4×C73—22no—
85C2×C4×C73—21no—
86C2×C4×C73—21no—
87C2×C4×C73—22no—
88C2×C4×C73—41no—
89C2×C4×C73—41no—
90C2×C4×C73—41no—
91C2×C4×C73—41no—
92C2×C4×C73—42no—
93C2×C4×C73#12011yescharacteristic
94C2×C4×C73#12012yes—
95C2×C4×C73#12112yes—
96C2×C4×C73#12711yescharacteristic
97C2×Dic73—42no—
98C2×Dic73—42no—
99Dic146—44no—
100Dic146—42no—
101Dic146—42no—
102C8×C73—42no—
103C8×C73—42no—
104#10596831—44no—
105C22×C73—21no—
106C22×C73—21no—
107C22×C73#39211yescharacteristic
108C22×C73#47312yes—
109C4×C73—21no—
110C4×C73—22no—
111C4×C73—22no—
112C4×C73—42no—
113C4×C73—81no—
114C4×C73#45511yescharacteristic
115C4×C73#45611yescharacteristic
116Dic73—82no—
117Dic73—82no—
118#10031—731nomaximal, Sylow
119C2×C73—22no—
120C2×C73#200711yescharacteristic
121C2×C73#201011yescharacteristic
122C2×C73#202011yescharacteristic
123#3249—731no—
124#3113—732no—
125#1985D7311yescharacteristic
126#1531—732no—
127#1290—731no—
128C73#1003111yescharacteristic, complemented, Sylow
129#533—732no—
130C2×C4×Q8C2×D7311yescharacteristic
131#483—1462no—
132#477—1462no—
133#475—1462no—
134#467—1462no—
135#462—1462no—
136#462—1462no—
137#451—1462no—
138#441—1464no—
139#432—732no—
140C2×C4⋊C8C2×D7311yescharacteristic
141C2×#97C2×D7311yescharacteristic
142#336—22no—
143#330—1464no—
144C22×Q8D29211yescharacteristic
145C2×Q16—1462no—
146C2×Q16—1464no—
147C22×C8—21no—
148C22×C8C22⋊D7312yes—
149C4⋊Q8—732no—
150C4⋊Q8—732no—
151#125—1462no—
152C22⋊Q8—1462no—
153C22⋊Q8—1462no—
154C4×Q8—22no—
155C4×Q8—22no—
156C4×Q8—1462no—
157C4×Q8—1462no—
158#117—1462no—
159C2×C4⋊C4—21no—
160C2×C4⋊C4D29211yescharacteristic
161C2×C42—21no—
162C2×C42C22×D7311yescharacteristic
163#107—1462no—
164#106—1464no—
165C4⋊C8—22no—
166C4⋊C8—1462no—
167#103—1464no—
168#103—1464no—
169#103—1464no—
170C22⋊C8—1462no—
171#97—22no—
172#97—734no—
173C2×Q8—22no—
174C2×Q8—42no—
175C2×Q8—1462no—
176C2×Q8—1462no—
177C22×C4—21no—
178C22×C4—21no—
179C22×C4C2×C22⋊D7311yescharacteristic
180C22×C4C2×D29211yescharacteristic
181C22×C4#1192402811yescharacteristic
182Q16—2928no—
183Q16—5842no—
184C2×C8—22no—
185C2×C8—22no—
186C2×C8—41no—
187C2×C8—41no—
188C2×C8—42no—
189C2×C8—1464no—
190C4⋊C4—22no—
191C4⋊C4—42no—
192C4⋊C4—2922no—
193C4⋊C4—2922no—
194C4⋊C4—1462no—
195C4⋊C4—1462no—
196C4⋊C4—1462no—
197C4⋊C4—1462no—
198C22⋊C4—2922no—
199C42—41no—
200C42—41no—
201C42—2922no—
202C42D4×D7312yes—
203C42D4×D7312yes—
204C23#1455656511yescharacteristic
205Q8—24no—
206Q8—42no—
207Q8—2924no—
208Q8—2922no—
209Q8—2922no—
210C2×C4—22no—
211C2×C4—21no—
212C2×C4—21no—
213C2×C4—22no—
214C2×C4—41no—
215C2×C4—41no—
216C2×C4—41no—
217C2×C4—41no—
218C2×C4—42no—
219C2×C4—2922no—
220C2×C4—2922no—
221C2×C4#1455655911yescharacteristic
222C2×C4#1455656112yes—
223C2×C4#1455656412yes—
224C2×C4#1455658711yescharacteristic
225C8—42no—
226C8—42no—
227C8—2924no—
228C22—21no—
229C22—21no—
230C22#1798849611yescharacteristic
231C22#1798886212yes—
232C4—21no—
233C4—22no—
234C4—22no—
235C4—42no—
236C4—81no—
237C4—5842no—
238C4—5842no—
239C4#1798876411yescharacteristic
240C4#1798876911yescharacteristic
241C2—22no—
242C2#2261097711yescharacteristic
243C2#2261099811yescharacteristic
244C2#2261105211yescharacteristic
subgroupG/H
centerC22#17988496
commutator, cosocleC2×C42×C73C23
FrattiniC2×C42C22×D73
FittingC73×#1985C2
socleC22×C73#392
prime radicalC23×C73#121
hypercenter#1985D73
hypocenterC73#10031
LCSG ▷ C2×C42×C73 ▷ C22×C73 ▷ C73
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1985

Complements

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

NH ≅ G/Ntype
128. C73#10031semidirect

Maximal subgroups

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

subgroupindex
#226212762
#226200612
#226085452
#226078012
C73×#19852
#1003173