Finite Group Databasebeta

← #32999044

Subgroups — #32999044

Order 18688.

342 conjugacy classes of subgroups; only the 63 normal subgroups are shown.

normal subgroups only

This group has 342 conjugacy classes of subgroups — too many to draw. Only its 63 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#22611276C211yesmaximal, characteristic
2#22608972C212yesmaximal
3#22607958C212yesmaximal
4#22607877C211yesmaximal, characteristic
5C73×#2571C211yesmaximal, characteristic
6#17989218C2211yescharacteristic
7#17988922—22no—
8#17988627—21no—
9#17988356C2211yescharacteristic
10#17988347—21no—
11#17988323—22no—
12#17988313C2212yes—
13#400×C73—21no—
14#400×C73C2212yes—
15#389×C73—22no—
16#384×C73C2211yescharacteristic
17#382×C73—22no—
18C4×C4⋊C4×C73—21no—
19C2×#11924012—21no—
20#14556590—41no—
21#14556582—41no—
22#14556570—22no—
23#14556550—21no—
24#14556524—41no—
25#14556524—42no—
26#14556522—41no—
27#14556514—42no—
28C22⋊#10596831—22no—
29C2×C4⋊C4×C73—21no—
30C2×C4⋊C4×C73—21no—
31C2×C4⋊C4×C73—22no—
32C2×C4⋊C4×C73—21no—
33C2×C4⋊C4×C73D411yescharacteristic
34C2×C4⋊C4×C73D412yes—
35C2×C4⋊C4×C73C2311yescharacteristic
36C2×C42×C73—22no—
37C2×C42×C73D411yescharacteristic
38#95×C73—21no—
39#95×C73—22no—
40#95×C73—22no—
41#95×C73—22no—
42#95×C73D412yes—
43C2×Dic146—22no—
44#11924012—22no—
45#11924012—41no—
46C2×#10596831—41no—
47C2×#10596831—42no—
48C4⋊Dic73—21no—
49C4⋊Dic73—21no—
50C4⋊Dic73—22no—
51#11924007—42no—
52C22⋊Dic73—41no—
53C4×Dic73—41no—
54C22×C4×C73—21no—
55C22×C4×C73—22no—
56C22×C4×C73—22no—
57C22×C4×C73—21no—
58C22×C4×C73C2×D411yescharacteristic
59C22×C4×C73C2×D412yes—
60C4⋊C4×C73—41no—
61C4⋊C4×C73—42no—
62C4⋊C4×C73—41no—
63C4⋊C4×C73—42no—
64C4⋊C4×C73—44no—
65C4⋊C4×C73—42no—
66C4⋊C4×C73—81no—
67C42×C73—21no—
68C42×C73—44no—
69C42×C73Q1612yes—
70C23×C73#12011yescharacteristic
71C2×C4×C73—22no—
72C2×C4×C73—22no—
73C2×C4×C73—22no—
74C2×C4×C73—21no—
75C2×C4×C73—21no—
76C2×C4×C73—22no—
77C2×C4×C73—42no—
78C2×C4×C73—42no—
79C2×C4×C73—42no—
80C2×C4×C73—42no—
81C2×C4×C73—42no—
82C2×C4×C73—42no—
83C2×C4×C73—42no—
84C2×C4×C73—41no—
85C2×C4×C73—42no—
86C2×C4×C73C2×Q1611yescharacteristic
87C2×C4×C73#13711yescharacteristic
88C2×Dic73—41no—
89C2×Dic73—41no—
90Dic146—82no—
91#10596831—42no—
92#10596831—82no—
93C22×C73—21no—
94C22×C73—21no—
95C22×C73#45111yescharacteristic
96C22×C73#45611yescharacteristic
97C22×C73B(4,𝔽2)11yescharacteristic
98C4×C73—24no—
99C4×C73—21no—
100C4×C73—21no—
101C4×C73—42no—
102C4×C73—82no—
103C4×C73—81no—
104C4×C73—82no—
105Dic73—81no—
106Dic73—81no—
107#12257—731nomaximal, Sylow
108C2×C73—21no—
109C2×C73—21no—
110C2×C73#160511yescharacteristic
111C2×C73#219811yescharacteristic
112C2×C73#220411yescharacteristic
113#2571D7311yescharacteristic
114#2060—731no—
115#1617—732no—
116#1353—732no—
117#1325—731no—
118C73#1225711yescharacteristic, complemented, Sylow
119#544—731no—
120#484—1462no—
121#428—1461no—
122#400—21no—
123#400C2×D7312yes—
124#389—22no—
125#384C2×D7311yescharacteristic
126#382—22no—
127C4×C4⋊C4—21no—
128#343—731no—
129#339—1461no—
130#328—1462no—
131#324—732no—
132C2×M16—1461no—
133C4⋊Q8—2921no—
134#125—2921no—
135C22⋊Q8—1462no—
136#117—1461no—
137C2×C4⋊C4—21no—
138C2×C4⋊C4—21no—
139C2×C4⋊C4—22no—
140C2×C4⋊C4—21no—
141C2×C4⋊C4C22⋊D7311yescharacteristic
142C2×C4⋊C4C22⋊D7312yes—
143C2×C4⋊C4C22×D7311yescharacteristic
144C2×C42—22no—
145C2×C42C22⋊D7311yescharacteristic
146#107—2921no—
147#107—2922no—
148#106—2921no—
149#103—2922no—
150C22⋊C8—1462no—
151#95—21no—
152#95—22no—
153#95—22no—
154#95—22no—
155#95C22⋊D7312yes—
156C2×Q8—1462no—
157C22×C4—21no—
158C22×C4—22no—
159C22×C4—22no—
160C22×C4—21no—
161C22×C4C2×C22⋊D7311yescharacteristic
162C22×C4C2×C22⋊D7312yes—
163M16—2921no—
164M16—1462no—
165C2×C8—2921no—
166C2×C8—2922no—
167C4⋊C4—41no—
168C4⋊C4—42no—
169C4⋊C4—41no—
170C4⋊C4—42no—
171C4⋊C4—44no—
172C4⋊C4—42no—
173C4⋊C4—81no—
174C4⋊C4—2922no—
175C4⋊C4—1461no—
176C4⋊C4—1461no—
177C4⋊C4—1462no—
178C22⋊C4—2921no—
179C42—21no—
180C42—44no—
181C42—2921no—
182C42#1192401812yes—
183C23#1455656011yescharacteristic
184Q8—5842no—
185C2×C4—22no—
186C2×C4—22no—
187C2×C4—22no—
188C2×C4—21no—
189C2×C4—21no—
190C2×C4—22no—
191C2×C4—42no—
192C2×C4—42no—
193C2×C4—42no—
194C2×C4—42no—
195C2×C4—42no—
196C2×C4—42no—
197C2×C4—42no—
198C2×C4—41no—
199C2×C4—42no—
200C2×C4—2921no—
201C2×C4—2921no—
202C2×C4C2×#1192401811yescharacteristic
203C2×C4#1455662211yescharacteristic
204C8—2922no—
205C8—5842no—
206C22—21no—
207C22—21no—
208C22#1798874311yescharacteristic
209C22#1798877011yescharacteristic
210C22#1798877411yescharacteristic
211C4—24no—
212C4—21no—
213C4—21no—
214C4—42no—
215C4—82no—
216C4—81no—
217C4—82no—
218C4—5841no—
219C4—5841no—
220C2—21no—
221C2—21no—
222C2#2260890511yescharacteristic
223C2#2261192711yescharacteristic
224C2#2261195711yescharacteristic
subgroupG/H
centerC22#17988774
commutator, cosocleC2×C4⋊C4×C73C23
FrattiniC2×C4⋊C4C22×D73
FittingC73×#2571C2
socleC22×C73B(4,𝔽2)
prime radicalC23×C73#120
hypercenter#2571D73
hypocenterC73#12257
LCSG ▷ C2×C4⋊C4×C73 ▷ C23×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C22 ◁ C23 ◁ C2×C4⋊C4 ◁ #2571

Complements

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

NH ≅ G/Ntype
118. C73#12257semidirect

Maximal subgroups

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

subgroupindex
#226112762
#226089722
#226079582
#226078772
C73×#25712
#1225773