Finite Group Databasebeta

← #33000148

Subgroups — #33000148

Order 18688.

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

normal subgroups only

This group has 218 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#22612074C211yesmaximal, characteristic
2#22611978C211yesmaximal, characteristic
3#22609525C211yesmaximal, characteristic
4#22608737C211yesmaximal, characteristic
5#22607994C211yesmaximal, characteristic
6#22607987C211yesmaximal, characteristic
7C73×#1362C211yesmaximal, characteristic
8C2×#14556537—21no—
9#17988992C2211yescharacteristic
10#17988983—21no—
11#17988939—21no—
12#17988711—21no—
13C4×Dic292C2211yescharacteristic
14#17988415—21no—
15C4⋊#11924003C2211yescharacteristic
16#17988392—21no—
17#17988391—21no—
18#17988317—21no—
19C8×#10596831C2211yescharacteristic
20#494×C73C2211yescharacteristic
21C4⋊C16×C73C2211yescharacteristic
22#335×C73C2211yescharacteristic
23C2×Dic292D411yescharacteristic
24#14556591—21no—
25C4×Dic146—21no—
26#14556537—42no—
27C2×#11924003—21no—
28#14556525—21no—
29#14556525—21no—
30#14556525D411yescharacteristic
31#14556522—42no—
32#14556520—41no—
33#14556516—21no—
34#14556514—41no—
35#14556514—41no—
36C4×#10596831D411yescharacteristic
37C4×#10596831D411yescharacteristic
38C8×Dic73—41no—
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—21no—
46C2×Dic146—41no—
47Dic292—21no—
48Dic292SD1612yes—
49C2×#10596831—21no—
50C2×#10596831D811yescharacteristic
51C2×#10596831D811yescharacteristic
52C4⋊Dic73—21no—
53C4⋊Dic73—41no—
54C4⋊Dic73—41no—
55#11924007—41no—
56C4×Dic73—41no—
57#11924003—41no—
58C2×Q8×C73—41no—
59Q16×C73—41no—
60Q16×C73—41no—
61Q16×C73—81no—
62C2×C8×C73—41no—
63C2×C8×C73C2×D411yescharacteristic
64C2×C8×C73#4111yescharacteristic
65C4⋊C4×C73—41no—
66C4⋊C4×C73—41no—
67C42×C73C2×D411yescharacteristic
68C16×C73—41no—
69Q8×C73—81no—
70Q8×C73—81no—
71C2×C4×C73—81no—
72C2×C4×C73#12111yescharacteristic
73C2×C4×C73C2×D811yescharacteristic
74C2×C4×C73AGL(1,ℤ/8)11yescharacteristic
75C2×Dic73—41no—
76C2×Dic73—41no—
77C2×Dic73—81no—
78Dic146—22no—
79Dic146—41no—
80Dic146—81no—
81Dic146—81no—
82C8×C73—21no—
83C8×C73—81no—
84C8×C73C2×SD1611yescharacteristic
85C8×C73#13511yescharacteristic
86#10596831—22no—
87#10596831—21no—
88#10596831—21no—
89C22×C73#45911yescharacteristic
90C4×C73—21no—
91C4×C73—161no—
92C4×C73#46511yescharacteristic
93C4×C73#47111yescharacteristic
94C4×C73#50811yescharacteristic
95C4×C73#51011yescharacteristic
96Dic73—42no—
97Dic73—81no—
98Dic73—161no—
99#12423—731nomaximal, Sylow
100C2×C73#166511yescharacteristic
101C2×C73#221111yescharacteristic
102C2×C73#221411yescharacteristic
103#2225—731no—
104#2209—731no—
105#1707—731no—
106C8×Q16—731no—
107#1367—731no—
108#1364—731no—
109#1362D7311yescharacteristic
110C73#1242311yescharacteristic, complemented, Sylow
111C2×Q32—1461no—
112#500—731no—
113#498—1461no—
114#494C2×D7311yescharacteristic
115#487—1461no—
116C8×Q8—1461no—
117C4×Q16—731no—
118#367—1461no—
119C4⋊C16—731no—
120C4⋊C16C2×D7311yescharacteristic
121#358—1461no—
122#358—1461no—
123#335C2×D7311yescharacteristic
124Q8⋊C8—1461no—
125C82—731no—
126C2×Q16—21no—
127C2×Q16—21no—
128C2×Q16—731no—
129C4⋊Q8—21no—
130C4⋊Q8—1461no—
131C4×Q8—1461no—
132Q32—2922no—
133C2×C16—21no—
134C2×C16—1461no—
135#107—731no—
136#107—1461no—
137#107—1461no—
138#106—2922no—
139C4⋊C8—21no—
140C4⋊C8—2921no—
141#103—2921no—
142#103—2921no—
143#103—1461no—
144C4×C8—2921no—
145C4×C8—731no—
146C4×C8—731no—
147C4×C8C22×D7311yescharacteristic
148C2×Q8—41no—
149C2×Q8—2921no—
150C2×Q8—1461no—
151Q16—41no—
152Q16—41no—
153Q16—81no—
154Q16—732no—
155Q16—1461no—
156C2×C8—41no—
157C2×C8—731no—
158C2×C8—731no—
159C2×C8—1461no—
160C2×C8D4×D7311yescharacteristic
161C2×C8#1192402811yescharacteristic
162C4⋊C4—41no—
163C4⋊C4—41no—
164C4⋊C4—2921no—
165C4⋊C4—2921no—
166C4⋊C4—2921no—
167C4⋊C4—1461no—
168C42—2921no—
169C42D4×D7311yescharacteristic
170C16—41no—
171C16—2921no—
172Q8—81no—
173Q8—81no—
174Q8—2921no—
175Q8—5841no—
176Q8—5841no—
177Q8—1462no—
178C2×C4—81no—
179C2×C4—2921no—
180C2×C4—2921no—
181C2×C4—5841no—
182C2×C4#1455656411yescharacteristic
183C2×C4D8×D7311yescharacteristic
184C2×C4#1455661811yescharacteristic
185C8—21no—
186C8—81no—
187C8—1462no—
188C8—1461no—
189C8—1461no—
190C8SD16×D7311yescharacteristic
191C8#1455661011yescharacteristic
192C22#1798878111yescharacteristic
193C4—21no—
194C4—161no—
195C4—2922no—
196C4—5841no—
197C4—11681no—
198C4#1798881511yescharacteristic
199C4#1798884911yescharacteristic
200C4#1798901811yescharacteristic
201C4#1798902911yescharacteristic
202C2#2260927111yescharacteristic
203C2#2261199611yescharacteristic
204C2#2261201111yescharacteristic
subgroupG/H
centerC22#17988781
commutator, cosocleC4×C8×C73C23
FrattiniC4×C8C22×D73
FittingC73×#1362C2
socle, prime radicalC22×C73#459
hypercenter#1362D73
hypocenterC73#12423
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#12423semidirect

Maximal subgroups

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

subgroupindex
#226120742
#226119782
#226095252
#226087372
#226079942
#226079872
C73×#13622
#1242373