Finite Group Databasebeta

← #32989088

Subgroups — #32989088

Order 18688.

400 conjugacy classes of subgroups; only the 97 normal subgroups are shown.

normal subgroups only

This group has 400 conjugacy classes of subgroups — too many to draw. Only its 97 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#22618294C211yesmaximal, characteristic
2#22610908C211yesmaximal, characteristic
3#22608496C212yesmaximal
4#22607790C212yesmaximal
5C73×#1276C211yesmaximal, characteristic
6#17989144C2211yescharacteristic
7C2×#14556583—21no—
8#17988611C2211yescharacteristic
9#17988485—24no—
10#17988457—21no—
11#17988453C2212yes—
12#17988347—21no—
13#17988347—21no—
14#17988325—24no—
15#431×C73C2212yes—
16C43×C73C2211yescharacteristic
17C2×#11924012—21no—
18#14556591Q812yes—
19#14556583—21no—
20#14556583—42no—
21#14556583—42no—
22#14556570—22no—
23C4×Dic146—22no—
24#14556550—21no—
25C2×C4⋊Dic73—24no—
26C2×C4⋊Dic73—22no—
27C2×#11924007—24no—
28C4⋊#10596831—22no—
29#14556498—22no—
30#14556498D414yes—
31C2×C42×C73—22no—
32C2×C42×C73D411yescharacteristic
33C2×C42×C73D411yescharacteristic
34C2×C42×C73C2311yescharacteristic
35C4⋊C8×C73—22no—
36C22⋊C8×C73—22no—
37C4×C8×C73—22no—
38C2×Dic146—22no—
39C22×Dic73—24no—
40#11924012—41no—
41#11924012—41no—
42C2×#10596831—41no—
43C4⋊Dic73—22no—
44C4⋊Dic73—22no—
45C4⋊Dic73—48no—
46C4⋊Dic73—42no—
47C4⋊Dic73—42no—
48#11924007—48no—
49#11924007—42no—
50C22⋊Dic73—41no—
51C4×Dic73—41no—
52C22×C4×C73—21no—
53C22×C4×C73—21no—
54C22×C4×C73C2×D412yes—
55C22×C4×C73C2×D411yescharacteristic
56C2×C8×C73—42no—
57C42×C73—21no—
58C42×C73—21no—
59C42×C73—44no—
60C42×C73SD1612yes—
61C42×C73Q1612yes—
62C42×C73C2×Q811yescharacteristic
63C42×C73#4111yescharacteristic
64C42×C73#4112yes—
65C23×C73#12011yescharacteristic
66C2×C4×C73—24no—
67C2×C4×C73—22no—
68C2×C4×C73—22no—
69C2×C4×C73—42no—
70C2×C4×C73—42no—
71C2×C4×C73C22⋊Q812yes—
72C2×C4×C73C22⋊Q811yescharacteristic
73C2×C4×C73#12412yes—
74C2×C4×C73#12411yescharacteristic
75C2×C4×C73C2×SD1611yescharacteristic
76C2×C4×C73C2×Q1611yescharacteristic
77C2×C4×C73AGL(1,ℤ/8)11yescharacteristic
78C2×C4×C73#13711yescharacteristic
79C2×Dic73—48no—
80C2×Dic73—42no—
81C2×Dic73—44no—
82Dic146—82no—
83C8×C73—82no—
84#10596831—81no—
85C22×C73—22no—
86C22×C73#39311yescharacteristic
87C22×C73#45011yescharacteristic
88C22×C73#45111yescharacteristic
89C4×C73—24no—
90C4×C73—22no—
91C4×C73—22no—
92C4×C73—42no—
93C4×C73#47511yescharacteristic
94C4×C73#47711yescharacteristic
95C4×C73#48711yescharacteristic
96C4×C73#48911yescharacteristic
97Dic73—84no—
98Dic73—82no—
99#10365—731nomaximal, Sylow
100C2×C73—21no—
101C2×C73—21no—
102C2×C73#202411yescharacteristic
103C2×C73#203112yes—
104#2859—731no—
105#1994—731no—
106#1518—732no—
107#1286—732no—
108#1276D7311yescharacteristic
109C73#1036511yescharacteristic, complemented, Sylow
110#533—731no—
111C2×#125—1461no—
112#431C2×D7312yes—
113#423—731no—
114#389—1464no—
115#384—1461no—
116#382—732no—
117C43C2×D7311yescharacteristic
118#339—1461no—
119#339—1461no—
120#328—1464no—
121C2×M16—1461no—
122C4⋊Q8—732no—
123#125—2922no—
124#125—2922no—
125#125—1461no—
126C22⋊Q8—1462no—
127C4×Q8—1462no—
128#117—1461no—
129C2×C4⋊C4—1464no—
130C2×C4⋊C4—1464no—
131C2×C4⋊C4—1462no—
132C2×C42—22no—
133C2×C42D29211yescharacteristic
134C2×C42D29211yescharacteristic
135C2×C42C22×D7311yescharacteristic
136C4⋊C8—22no—
137C4⋊C8—1462no—
138C22⋊C8—22no—
139C4×C8—22no—
140#95—734no—
141#95—1462no—
142C2×Q8—1462no—
143C22×C4—21no—
144C22×C4—21no—
145C22×C4—1464no—
146C22×C4D4×D7312yes—
147C22×C4C2×D29211yescharacteristic
148M16—2921no—
149M16—2921no—
150C2×C8—42no—
151C2×C8—2921no—
152C4⋊C4—2928no—
153C4⋊C4—2928no—
154C4⋊C4—2922no—
155C4⋊C4—2922no—
156C4⋊C4—2922no—
157C4⋊C4—1462no—
158C4⋊C4—1462no—
159C22⋊C4—2921no—
160C42—21no—
161C42—21no—
162C42—44no—
163C42—2921no—
164C42#1192401712yes—
165C42Dic29212yes—
166C42Q8×D7311yescharacteristic
167C42#1192402711yescharacteristic
168C42#1192402812yes—
169C23#1455656111yescharacteristic
170Q8—5842no—
171C2×C4—24no—
172C2×C4—22no—
173C2×C4—22no—
174C2×C4—42no—
175C2×C4—42no—
176C2×C4—2928no—
177C2×C4—2924no—
178C2×C4—2922no—
179C2×C4#1455656912yes—
180C2×C4#1455657111yescharacteristic
181C2×C4#1455657712yes—
182C2×C4#1455657911yescharacteristic
183C2×C4C2×#1192401711yescharacteristic
184C2×C4C2×Dic29211yescharacteristic
185C2×C4#1455661911yescharacteristic
186C2×C4#1455662411yescharacteristic
187C8—82no—
188C8—5841no—
189C22—22no—
190C22#1798850011yescharacteristic
191C22#1798874011yescharacteristic
192C22#1798874511yescharacteristic
193C4—24no—
194C4—22no—
195C4—22no—
196C4—42no—
197C4—5844no—
198C4—5842no—
199C4#1798887311yescharacteristic
200C4#1798888311yescharacteristic
201C4#1798893811yescharacteristic
202C4#1798894711yescharacteristic
203C2—21no—
204C2—21no—
205C2#2261107311yescharacteristic
206C2#2261110412yes—
subgroupG/H
centerC22#17988500
commutator, cosocleC2×C42×C73C23
FrattiniC2×C42C22×D73
FittingC73×#1276C2
socleC22×C73#393
prime radicalC23×C73#120
hypercenter#1276D73
hypocenterC73#10365
LCSG ▷ C2×C42×C73 ▷ C22×C73 ▷ C73
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1276

Complements

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

NH ≅ G/Ntype
109. C73#10365semidirect

Maximal subgroups

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

subgroupindex
#226182942
#226109082
#226084962
#226077902
C73×#12762
#1036573