Finite Group Databasebeta

← #33000748

Subgroups — #33000748

Order 18688.

306 conjugacy classes of subgroups; only the 79 normal subgroups are shown.

normal subgroups only

This group has 306 conjugacy classes of subgroups — too many to draw. Only its 79 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#22612188C211yesmaximal, characteristic, complemented
2#22612180C211yesmaximal, characteristic
3#22612158C211yesmaximal, characteristic, complemented
4#22612154C211yesmaximal, characteristic, complemented
5#22609523C211yesmaximal, characteristic, complemented
6#22607849C211yesmaximal, characteristic, complemented
7C73×#1709C211yesmaximal, characteristic, complemented
8C2×#14556534—22no—
9C2×#14556532—22no—
10#17988992C2211yescharacteristic
11#17988964C2211yescharacteristic
12#17988960—21no—
13#17988934—21no—
14#17988391—22no—
15#17988388—22no—
16C4×#11924003C2211yescharacteristic
17C4×#11924003C2211yescharacteristic
18#494×C73C2211yescharacteristic
19#493×C73C2211yescharacteristic
20#486×C73—21no—
21#486×C73—21no—
22C82×C73C2211yescharacteristic
23C2×#11924017—42no—
24C2×D584—21no—
25C2×D584—21no—
26#14556591—21no—
27#14556588—21no—
28#14556534—44no—
29#14556532—44no—
30C2×#11924003D412yes—
31C2×#11924003D412yes—
32#14556525—21no—
33#14556525—21no—
34#14556513—42no—
35C2×Q16×C73—21no—
36C2×Q16×C73—21no—
37C2×D8×C73—21no—
38C2×D8×C73—21no—
39C4⋊Q8×C73—21no—
40#127×C73—21no—
41#102×C73—42no—
42#102×C73—42no—
43C4×C8×C73D411yescharacteristic
44C4×C8×C73D411yescharacteristic
45C4×C8×C73C2311yescharacteristic
46C2×Dic146—41no—
47C2×D292—41no—
48C2×D292—41no—
49C2×D292—41no—
50#11924017—84no—
51D584—42no—
52D584—42no—
53C4⋊Dic73—41no—
54C4⋊Dic73—41no—
55#11924003—22no—
56#11924003—22no—
57C2×Q8×C73—41no—
58C2×D4×C73—41no—
59C2×D4×C73—41no—
60C2×D4×C73—41no—
61Q16×C73—42no—
62Q16×C73—42no—
63D8×C73—42no—
64D8×C73—42no—
65C2×C8×C73D812yes—
66C2×C8×C73D812yes—
67C2×C8×C73C2×D411yescharacteristic
68C2×C8×C73C2×D411yescharacteristic
69C4⋊C4×C73—41no—
70C4⋊C4×C73—41no—
71C42×C73C2×D411yescharacteristic
72C23×C73—81no—
73C22×D73—81no—
74Q8×C73—81no—
75Q8×C73—81no—
76D4×C73—81no—
77D4×C73—81no—
78D4×C73—82no—
79D4×C73—82no—
80C2×C4×C73—81no—
81C2×C4×C73#12711yescharacteristic
82C2×C4×C73C2×D811yescharacteristic
83C2×C4×C73C2×D811yescharacteristic
84C2×Dic73—81no—
85D292—81no—
86D292—81no—
87D292—82no—
88D292—82no—
89Dic146—82no—
90C8×C73—22no—
91C8×C73—22no—
92C8×C73AGL(1,ℤ/8)12yes—
93C8×C73AGL(1,ℤ/8)12yes—
94C22×C73—161no—
95C22×C73—161no—
96C22×C73—161no—
97C22×C73#49311yescharacteristic
98C2×D73—161no—
99C2×D73—161no—
100C2×D73—161no—
101C4×C73—161no—
102C4×C73#49611yescharacteristic
103C4×C73#49611yescharacteristic
104C4×C73#50812yes—
105C4×C73#50912yes—
106Dic73—161no—
107#12527—731nomaximal, Sylow
108C2×C73—321no—
109C2×C73#172111yescharacteristic
110C2×C73#224911yescharacteristic
111C2×C73#225011yescharacteristic
112D73—321no—
113#2248—731no—
114#2246—731no—
115#2241—731no—
116#2240—731no—
117#1709D7311yescharacteristic, complemented
118#1706—731no—
119#1312—731no—
120C73#1252711yescharacteristic, complemented, Sylow
121C2×SD32—1462no—
122C2×D16—1462no—
123#500—731no—
124#494C2×D7311yescharacteristic
125#493—731no—
126#493C2×D7311yescharacteristic
127#492—1461no—
128#486—21no—
129#486—21no—
130#486—1461no—
131#358—1462no—
132#357—1462no—
133C4×C16—731no—
134C4×C16—731no—
135C82C2×D7311yescharacteristic
136C2×Q16—21no—
137C2×Q16—21no—
138C2×SD16—2922no—
139C2×D8—21no—
140C2×D8—21no—
141C2×D8—1461no—
142C2×D8—1461no—
143C4⋊Q8—21no—
144C4⋊Q8—1461no—
145#127—21no—
146#127—1461no—
147SD32—2924no—
148D16—2924no—
149C2×C16—732no—
150C2×C16—732no—
151#107—1461no—
152#107—1461no—
153#102—42no—
154#102—42no—
155#102—2922no—
156C4×C8C22⋊D7311yescharacteristic
157C4×C8C22⋊D7311yescharacteristic
158C4×C8C22×D7311yescharacteristic
159C2×Q8—41no—
160C2×Q8—2921no—
161C2×D4—41no—
162C2×D4—41no—
163C2×D4—41no—
164C2×D4—2921no—
165C2×D4—2921no—
166C2×D4—2921no—
167Q16—42no—
168Q16—42no—
169SD16—5844no—
170D8—42no—
171D8—42no—
172D8—2922no—
173D8—2922no—
174C2×C8#1192401312yes—
175C2×C8#1192401312yes—
176C2×C8D4×D7311yescharacteristic
177C2×C8D4×D7311yescharacteristic
178C4⋊C4—41no—
179C4⋊C4—41no—
180C4⋊C4—2921no—
181C4⋊C4—2921no—
182C42C2×C22⋊D7311yescharacteristic
183C16—1462no—
184C16—1462no—
185C23—81no—
186C23—5841no—
187Q8—81no—
188Q8—81no—
189Q8—5842no—
190D4—81no—
191D4—81no—
192D4—82no—
193D4—82no—
194D4—5841no—
195D4—5841no—
196D4—5842no—
197D4—5842no—
198C2×C4—81no—
199C2×C4—5841no—
200C2×C4#1455658711yescharacteristic
201C2×C4C2×#1192401311yescharacteristic
202C2×C4C2×#1192401311yescharacteristic
203C8—22no—
204C8—22no—
205C8#1455661512yes—
206C8#1455661512yes—
207C22—161no—
208C22—161no—
209C22—161no—
210C22—11681no—
211C22—11681no—
212C22—11681no—
213C22#1798896311yescharacteristic
214C4—161no—
215C4—11681no—
216C4#1798897511yescharacteristic
217C4#1798897511yescharacteristic
218C4#1798901712yes—
219C4#1798902212yes—
220C2—321no—
221C2—23361no—
222C2#2260959811yescharacteristic
223C2#2261219011yescharacteristic
224C2#2261219811yescharacteristic
subgroupG/H
centerC22#17988963
commutator, cosocleC4×C8×C73C23
FrattiniC4×C8C22×D73
FittingC73×#1709C2
socleC22×C73#493
prime radical#22612180C2
hypercenter#1709D73
hypocenterC73#12527
LCSG ▷ C4×C8×C73 ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C22 ◁ C42 ◁ C82 ◁ #1709

Complements

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

NH ≅ G/Ntype
1. #22612188C2semidirect
3. #22612158C2semidirect
4. #22612154C2semidirect
5. #22609523C2semidirect
6. #22607849C2semidirect
7. C73×#1709C2semidirect
117. #1709D73semidirect
120. C73#12527semidirect

Maximal subgroups

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

subgroupindex
#226121882
#226121802
#226121582
#226121542
#226095232
#226078492
C73×#17092
#1252773