Finite Group Databasebeta

← #33000234

Subgroups — #33000234

Order 18688.

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

normal subgroups only

This group has 224 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#22612187C211yesmaximal, characteristic, complemented
2#22612012C211yesmaximal, characteristic, complemented
3#22612007C211yesmaximal, characteristic
4#22608007C211yesmaximal, characteristic, complemented
5#22607969C211yesmaximal, characteristic, complemented
6#22607967C211yesmaximal, characteristic, complemented
7C73×#2170C211yesmaximal, characteristic, complemented
8#17989027—21no—
9#17989022—21no—
10C2×#14556536—21no—
11C2×#14556536—21no—
12#17988967C2211yescharacteristic
13#17988964C2211yescharacteristic
14#17988408C2211yescharacteristic
15#17988408C2211yescharacteristic
16#17988402—21no—
17#17988399—21no—
18#504×C73—21no—
19#443×C73C2211yescharacteristic
20#364×C73C2211yescharacteristic
21#350×C73—21no—
22C4×C16×C73C2211yescharacteristic
23C2×Dic292—21no—
24C2×Dic292—21no—
25C2×D584—21no—
26C2×D584—21no—
27#14556591—21no—
28#14556588—21no—
29#14556537—41no—
30#14556536—42no—
31#14556536—41no—
32#14556536—41no—
33#14556535—41no—
34#14556534—41no—
35#14556532—41no—
36#14556531—21no—
37#14556531—21no—
38#135×C73D411yescharacteristic
39#131×C73—21no—
40M32×C73—21no—
41M32×C73—41no—
42C2×C16×C73—41no—
43C2×C16×C73D411yescharacteristic
44C2×C16×C73D411yescharacteristic
45#108×C73D411yescharacteristic
46#104×C73—21no—
47C4×C8×C73C2311yescharacteristic
48C2×Dic146—41no—
49C2×D292—41no—
50C2×D292—81no—
51Dic292—41no—
52Dic292—41no—
53Dic292—41no—
54Dic292—41no—
55D584—41no—
56D584—41no—
57D584—41no—
58D584—41no—
59C4⋊Dic73—81no—
60#11924003—41no—
61#11924003—41no—
62#41×C73—21no—
63Q16×C73D811yescharacteristic
64SD16×C73—21no—
65D8×C73D811yescharacteristic
66M16×C73—21no—
67M16×C73—41no—
68C2×C8×C73—41no—
69C2×C8×C73C2×D411yescharacteristic
70C2×C8×C73C2×D411yescharacteristic
71C42×C73#4111yescharacteristic
72C16×C73—21no—
73C16×C73—41no—
74C16×C73D811yescharacteristic
75C16×C73D811yescharacteristic
76C22×D73—81no—
77Q8×C73—21no—
78D4×C73—21no—
79D4×C73—41no—
80C2×C4×C73—21no—
81C2×C4×C73—41no—
82C2×C4×C73#12111yescharacteristic
83C2×Dic73—81no—
84D292—81no—
85D292—81no—
86D292—162no—
87Dic146—81no—
88Dic146—81no—
89C8×C73—41no—
90C8×C73C2×D811yescharacteristic
91C8×C73C2×D811yescharacteristic
92C8×C73#13511yescharacteristic
93C8×C73AGL(1,ℤ/8)11yescharacteristic
94C22×C73—41no—
95C22×C73#47211yescharacteristic
96C2×D73—162no—
97C2×D73—161no—
98C4×C73—22no—
99C4×C73—41no—
100C4×C73#45911yescharacteristic
101C4×C73#46611yescharacteristic
102Dic73—161no—
103#12438—731nomaximal, Sylow
104C2×C73—21no—
105C2×C73—81no—
106C2×C73#166711yescharacteristic
107D73—321no—
108#2248—731no—
109#2214—731no—
110#2213—731no—
111#2170D7311yescharacteristic, complemented
112#1373—731no—
113#1358—731no—
114#1357—731no—
115C73#1243811yescharacteristic, complemented, Sylow
116#510—1461no—
117#509—1461no—
118C2×SD32—1461no—
119C2×SD32—1461no—
120#504—21no—
121#494—731no—
122#493—731no—
123#443C2×D7311yescharacteristic
124#364—731no—
125#364—731no—
126#364C2×D7311yescharacteristic
127#362—1461no—
128#361—1461no—
129#350—21no—
130C4×C16C2×D7311yescharacteristic
131#135D29211yescharacteristic
132C2×Q16—1461no—
133C2×Q16—1461no—
134C2×D8—1461no—
135C2×D8—1461no—
136#131—21no—
137C4⋊Q8—1461no—
138#127—1461no—
139Q32—2921no—
140SD32—2922no—
141SD32—2921no—
142SD32—2921no—
143SD32—2921no—
144SD32—2921no—
145D16—2921no—
146M32—21no—
147M32—41no—
148M32—1461no—
149M32—1461no—
150C2×C16—41no—
151C2×C16C22⋊D7311yescharacteristic
152C2×C16C22⋊D7311yescharacteristic
153#108D29211yescharacteristic
154#104—21no—
155C4×C8C22×D7311yescharacteristic
156#41—21no—
157C2×Q8—2921no—
158C2×D4—2921no—
159C2×D4—5841no—
160Q16—2921no—
161Q16—2921no—
162Q16—2921no—
163Q16—2921no—
164Q16D58411yescharacteristic
165SD16—21no—
166D8—2921no—
167D8—2921no—
168D8—2921no—
169D8—2921no—
170D8D58411yescharacteristic
171M16—21no—
172M16—41no—
173C2×C8—41no—
174C2×C8C2×C22⋊D7311yescharacteristic
175C2×C8C2×D29211yescharacteristic
176C4⋊C4—5841no—
177C42#1192402811yescharacteristic
178C16—21no—
179C16—41no—
180C16—2921no—
181C16—2921no—
182C16#1192401311yescharacteristic
183C16#1192401311yescharacteristic
184C23—5841no—
185Q8—21no—
186Q8—5841no—
187Q8—5841no—
188D4—21no—
189D4—41no—
190D4—5841no—
191D4—5841no—
192D4—11682no—
193C2×C4—21no—
194C2×C4—41no—
195C2×C4—5841no—
196C2×C4#1455656511yescharacteristic
197C8—41no—
198C8C2×#1192401311yescharacteristic
199C8C2×D58411yescharacteristic
200C8#1455661311yescharacteristic
201C8#1455661611yescharacteristic
202C22—41no—
203C22—11682no—
204C22—11681no—
205C22#1798885711yescharacteristic
206C4—22no—
207C4—41no—
208C4—11681no—
209C4#1798878211yescharacteristic
210C4#1798882311yescharacteristic
211C2—21no—
212C2—81no—
213C2—23361no—
214C2#2260928611yescharacteristic
subgroupG/H
centerC2#22609286
commutator, cosocleC4×C8×C73C23
FrattiniC4×C8C22×D73
FittingC73×#2170C2
socleC2×C73#1667
prime radical#22612007C2
hypercenter#2170D73
hypocenterC73#12438
LCSG ▷ C4×C8×C73 ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C2 ◁ C2×C4 ◁ C4×C8 ◁ #2170

Complements

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

NH ≅ G/Ntype
1. #22612187C2semidirect
2. #22612012C2semidirect
4. #22608007C2semidirect
5. #22607969C2semidirect
6. #22607967C2semidirect
7. C73×#2170C2semidirect
111. #2170D73semidirect
115. C73#12438semidirect

Maximal subgroups

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

subgroupindex
#226121872
#226120122
#226120072
#226080072
#226079692
#226079672
C73×#21702
#1243873