Finite Group Databasebeta

← #33000222

Subgroups — #33000222

Order 18688.

234 conjugacy classes of subgroups; only the 59 normal subgroups are shown.

normal subgroups only

This group has 234 conjugacy classes of subgroups — too many to draw. Only its 59 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#22612180C211yesmaximal, characteristic, complemented
2#22612007C211yesmaximal, characteristic, complemented
3#22611768C211yesmaximal, characteristic, complemented
4#22608006C211yesmaximal, characteristic, complemented
5#22607968C211yesmaximal, characteristic, complemented
6#22607967C211yesmaximal, characteristic, complemented
7C73×#2213C211yesmaximal, characteristic, complemented
8#17989022—21no—
9C2×#14556532—21no—
10C2×#14556532—21no—
11#17989004—21no—
12#17988964C2211yescharacteristic
13#17988408C2211yescharacteristic
14#17988408C2211yescharacteristic
15#17988399—21no—
16#17988371—21no—
17C4×#11924003C2211yescharacteristic
18#509×C73—21no—
19#493×C73C2211yescharacteristic
20#443×C73C2211yescharacteristic
21#364×C73C2211yescharacteristic
22#361×C73—21no—
23C2×D584—21no—
24C2×D584—21no—
25#14556588—21no—
26#14556534—41no—
27#14556532—42no—
28#14556532—41no—
29#14556532—41no—
30#14556532—41no—
31#14556531—21no—
32#14556531—21no—
33#14556531—41no—
34C2×#11924003—41no—
35C2×#11924003D411yescharacteristic
36C2×#11924003D411yescharacteristic
37#135×C73D411yescharacteristic
38C2×D8×C73—21no—
39C2×D8×C73—21no—
40#131×C73—21no—
41#127×C73—21no—
42SD32×C73—41no—
43D16×C73—41no—
44M32×C73—21no—
45#108×C73D411yescharacteristic
46#104×C73—21no—
47C4×C8×C73C2311yescharacteristic
48C2×D292—41no—
49C2×D292—81no—
50D584—41no—
51D584—41no—
52D584—41no—
53D584—41no—
54#11924003—21no—
55#11924003—41no—
56#11924003—41no—
57#11924003D811yescharacteristic
58#11924003D811yescharacteristic
59#41×C73—21no—
60C2×D4×C73—41no—
61C2×D4×C73—81no—
62Q16×C73D811yescharacteristic
63SD16×C73—21no—
64D8×C73—41no—
65D8×C73—41no—
66D8×C73—41no—
67D8×C73—41no—
68D8×C73D811yescharacteristic
69M16×C73—21no—
70M16×C73—41no—
71C2×C8×C73—41no—
72C2×C8×C73C2×D411yescharacteristic
73C2×C8×C73C2×D411yescharacteristic
74C42×C73#4111yescharacteristic
75C16×C73—41no—
76C23×C73—81no—
77C22×D73—81no—
78Q8×C73—21no—
79D4×C73—21no—
80D4×C73—41no—
81D4×C73—81no—
82D4×C73—81no—
83D4×C73—162no—
84C2×C4×C73—21no—
85C2×C4×C73—41no—
86C2×C4×C73#12111yescharacteristic
87D292—81no—
88D292—81no—
89D292—162no—
90C8×C73—41no—
91C8×C73C2×D811yescharacteristic
92C8×C73C2×D811yescharacteristic
93C8×C73#13511yescharacteristic
94C8×C73AGL(1,ℤ/8)11yescharacteristic
95C22×C73—41no—
96C22×C73—162no—
97C22×C73—161no—
98C22×C73#47211yescharacteristic
99C2×D73—162no—
100C2×D73—161no—
101C4×C73—22no—
102C4×C73—41no—
103C4×C73#45911yescharacteristic
104C4×C73#46611yescharacteristic
105#12436—731nomaximal, Sylow
106C2×C73—21no—
107C2×C73—81no—
108C2×C73—321no—
109C2×C73#166711yescharacteristic
110D73—321no—
111#2246—731no—
112#2213—731no—
113#2213D7311yescharacteristic, complemented
114#2170—731no—
115#1373—731no—
116#1357—731no—
117#1357—731no—
118C73#1243611yescharacteristic, complemented, Sylow
119#509—21no—
120#509—1461no—
121C2×D16—1461no—
122C2×D16—1461no—
123#504—1461no—
124#493—731no—
125#493C2×D7311yescharacteristic
126#443C2×D7311yescharacteristic
127#364—731no—
128#364—731no—
129#364C2×D7311yescharacteristic
130#361—21no—
131#361—1461no—
132#350—1461no—
133C4×C16—731no—
134#135C22⋊D7311yescharacteristic
135C2×D8—21no—
136C2×D8—21no—
137C2×D8—1461no—
138C2×D8—1461no—
139#131—21no—
140#127—21no—
141#127—1461no—
142SD32—41no—
143SD32—2921no—
144D16—41no—
145D16—2921no—
146D16—2921no—
147D16—2921no—
148D16—2922no—
149M32—21no—
150M32—2921no—
151M32—1461no—
152M32—1461no—
153C2×C16—2921no—
154C2×C16—731no—
155C2×C16—731no—
156#108C22⋊D7311yescharacteristic
157#104—21no—
158C4×C8C22×D7311yescharacteristic
159#41—21no—
160C2×D4—41no—
161C2×D4—81no—
162C2×D4—2921no—
163C2×D4—5841no—
164Q16#1192401311yescharacteristic
165SD16—21no—
166D8—41no—
167D8—41no—
168D8—41no—
169D8—41no—
170D8—2921no—
171D8—2921no—
172D8—2921no—
173D8—2921no—
174D8#1192401311yescharacteristic
175M16—21no—
176M16—41no—
177C2×C8—41no—
178C2×C8D4×D7311yescharacteristic
179C2×C8C2×C22⋊D7311yescharacteristic
180C42#1192402711yescharacteristic
181C16—41no—
182C16—2921no—
183C16—2921no—
184C16—731no—
185C16—731no—
186C16—1461no—
187C23—81no—
188C23—5841no—
189Q8—21no—
190D4—21no—
191D4—41no—
192D4—81no—
193D4—81no—
194D4—162no—
195D4—5841no—
196D4—5841no—
197D4—11682no—
198C2×C4—21no—
199C2×C4—41no—
200C2×C4#1455656311yescharacteristic
201C8—41no—
202C8D8×D7311yescharacteristic
203C8C2×#1192401311yescharacteristic
204C8#1455661111yescharacteristic
205C8#1455661511yescharacteristic
206C22—41no—
207C22—162no—
208C22—161no—
209C22—11682no—
210C22—11681no—
211C22#1798885511yescharacteristic
212C4—22no—
213C4—41no—
214C4#1798878011yescharacteristic
215C4#1798882111yescharacteristic
216C2—21no—
217C2—81no—
218C2—321no—
219C2—23361no—
220C2#2260928411yescharacteristic
subgroupG/H
centerC2#22609284
commutator, cosocleC4×C8×C73C23
FrattiniC4×C8C22×D73
FittingC73×#2213C2
socleC2×C73#1667
hypercenter#2213D73
hypocenterC73#12436
LCSG ▷ C4×C8×C73 ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C2 ◁ C2×C4 ◁ C4×C8 ◁ #2213

Complements

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

NH ≅ G/Ntype
1. #22612180C2semidirect
2. #22612007C2semidirect
3. #22611768C2semidirect
4. #22608006C2semidirect
5. #22607968C2semidirect
6. #22607967C2semidirect
7. C73×#2213C2semidirect
113. #2213D73semidirect
118. C73#12436semidirect

Maximal subgroups

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

subgroupindex
#226121802
#226120072
#226117682
#226080062
#226079682
#226079672
C73×#22132
#1243673