Finite Group Databasebeta

← #33000262

Subgroups — #33000262

Order 18688.

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

normal subgroups only

This group has 212 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#22612183C211yesmaximal, characteristic
2#22611836C211yesmaximal, characteristic
3#22609302C211yesmaximal, characteristic
4#22609298C211yesmaximal, characteristic
5#22608004C211yesmaximal, characteristic
6#22607981C211yesmaximal, characteristic
7C73×#1362C211yesmaximal, characteristic
8C2×#14556537—21no—
9C2×#14556537—21no—
10#17988967C2211yescharacteristic
11#17988873—21no—
12#17988869—21no—
13C8×Dic146C2211yescharacteristic
14#17988405—21no—
15#17988362—21no—
16C4×#11924003C2211yescharacteristic
17#17988340C2211yescharacteristic
18#17988333—21no—
19#17988332—21no—
20#494×C73C2211yescharacteristic
21C4⋊C16×C73C2211yescharacteristic
22#335×C73C2211yescharacteristic
23C2×Dic292—21no—
24C2×Dic292—21no—
25#14556591—21no—
26C4×Dic146D411yescharacteristic
27#14556537—42no—
28#14556537—42no—
29C2×#11924003D411yescharacteristic
30C2×#11924003D411yescharacteristic
31#14556523—41no—
32#14556522—41no—
33C4⋊#10596831—21no—
34C4⋊#10596831D411yescharacteristic
35#14556520—21no—
36#14556516—41no—
37#14556514—41no—
38C8×Dic73—21no—
39C2×Q16×C73—21no—
40C2×Q16×C73—21no—
41C4⋊Q8×C73—21no—
42C2×C16×C73—21no—
43C4⋊C8×C73—21no—
44C4×C8×C73C2311yescharacteristic
45C2×Dic146—41no—
46C2×Dic146D811yescharacteristic
47Dic292—41no—
48Dic292—41no—
49Dic292—81no—
50C2×#10596831—21no—
51C2×#10596831—41no—
52C4⋊Dic73—41no—
53C4⋊Dic73—41no—
54C4⋊Dic73D811yescharacteristic
55#11924007—21no—
56C4×Dic73—21no—
57#11924003—21no—
58#11924003SD1612yes—
59C2×Q8×C73—41no—
60Q16×C73—41no—
61Q16×C73—41no—
62Q16×C73—81no—
63C2×C8×C73—41no—
64C2×C8×C73C2×D411yescharacteristic
65C2×C8×C73#4111yescharacteristic
66C4⋊C4×C73—41no—
67C4⋊C4×C73—41no—
68C42×C73C2×D411yescharacteristic
69C16×C73—41no—
70Q8×C73—81no—
71Q8×C73—81no—
72C2×C4×C73—81no—
73C2×C4×C73#12111yescharacteristic
74C2×C4×C73C2×D811yescharacteristic
75C2×C4×C73#13511yescharacteristic
76C2×Dic73—21no—
77C2×Dic73—21no—
78C2×Dic73—81no—
79Dic146—21no—
80Dic146—21no—
81Dic146—81no—
82Dic146—81no—
83C8×C73—21no—
84C8×C73—81no—
85C8×C73C2×SD1611yescharacteristic
86C8×C73AGL(1,ℤ/8)11yescharacteristic
87#10596831—41no—
88#10596831—81no—
89C22×C73#46611yescharacteristic
90C4×C73—21no—
91C4×C73—161no—
92C4×C73#46011yescharacteristic
93C4×C73#47211yescharacteristic
94C4×C73#51011yescharacteristic
95C4×C73#51011yescharacteristic
96Dic73—41no—
97Dic73—41no—
98Dic73—161no—
99#12443—731nomaximal, Sylow
100C2×C73#166811yescharacteristic
101C2×C73#221911yescharacteristic
102C2×C73#222211yescharacteristic
103#2247—731no—
104#2183—731no—
105#1670—731no—
106#1670—731no—
107#1372—731no—
108#1362—731no—
109#1362D7311yescharacteristic
110C73#1244311yescharacteristic, complemented, Sylow
111C2×Q32—1461no—
112C2×Q32—1461no—
113#494—731no—
114#494C2×D7311yescharacteristic
115#475—1461no—
116#475—1461no—
117C8×Q8—731no—
118C4⋊C16—1461no—
119C4⋊C16C2×D7311yescharacteristic
120#346—1461no—
121C4×C16—731no—
122#335—731no—
123#335C2×D7311yescharacteristic
124#332—1461no—
125#332—1461no—
126C2×Q16—21no—
127C2×Q16—21no—
128C2×Q16—1461no—
129C2×Q16—1461no—
130C4⋊Q8—21no—
131C4⋊Q8—1461no—
132C4×Q8—731no—
133Q32—2922no—
134Q32—2922no—
135C2×C16—21no—
136C2×C16—731no—
137C2×C16—731no—
138#106—2921no—
139#106—2921no—
140C4⋊C8—21no—
141C4⋊C8—731no—
142C4⋊C8—1461no—
143C4⋊C8—1461no—
144#103—2921no—
145#103—2921no—
146C4×C8—1461no—
147C4×C8C22×D7311yescharacteristic
148C2×Q8—41no—
149C2×Q8—2921no—
150C2×Q8—731no—
151Q16—41no—
152Q16—41no—
153Q16—81no—
154Q16—2921no—
155Q16—2921no—
156Q16—5841no—
157C2×C8—41no—
158C2×C8—2921no—
159C2×C8—1461no—
160C2×C8D4×D7311yescharacteristic
161C2×C8#1192402811yescharacteristic
162C4⋊C4—41no—
163C4⋊C4—41no—
164C4⋊C4—2921no—
165C4⋊C4—2921no—
166C4⋊C4—731no—
167C4⋊C4—1461no—
168C42—1461no—
169C42D4×D7311yescharacteristic
170C16—41no—
171C16—732no—
172C16—1461no—
173Q8—81no—
174Q8—81no—
175Q8—5841no—
176Q8—5841no—
177Q8—1461no—
178Q8—1461no—
179C2×C4—81no—
180C2×C4—5841no—
181C2×C4—1461no—
182C2×C4—1461no—
183C2×C4#1455656411yescharacteristic
184C2×C4D8×D7311yescharacteristic
185C2×C4#1455661211yescharacteristic
186C8—21no—
187C8—81no—
188C8—2921no—
189C8—5841no—
190C8SD16×D7311yescharacteristic
191C8#1455661511yescharacteristic
192C22#1798882211yescharacteristic
193C4—21no—
194C4—161no—
195C4—2921no—
196C4—2921no—
197C4—11681no—
198C4#1798878611yescharacteristic
199C4#1798885611yescharacteristic
200C4#1798902611yescharacteristic
201C4#1798902911yescharacteristic
202C2#2260929011yescharacteristic
203C2#2261203811yescharacteristic
204C2#2261205511yescharacteristic
subgroupG/H
centerC22#17988822
commutator, cosocleC4×C8×C73C23
FrattiniC4×C8C22×D73
FittingC73×#1362C2
socle, prime radicalC22×C73#466
hypercenter#1362D73
hypocenterC73#12443
LCSG ▷ C4×C8×C73 ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8 ◁ #1362

Complements

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

NH ≅ G/Ntype
110. C73#12443semidirect

Maximal subgroups

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

subgroupindex
#226121832
#226118362
#226093022
#226092982
#226080042
#226079812
C73×#13622
#1244373