Finite Group Databasebeta

← #32998007

Subgroups — #32998007

Order 18688.

226 conjugacy classes of subgroups; only the 69 normal subgroups are shown.

normal subgroups only

This group has 226 conjugacy classes of subgroups — too many to draw. Only its 69 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#22611805C211yesmaximal, characteristic
2#22608846C211yesmaximal, characteristic, complemented
3#22607996C211yesmaximal, characteristic, complemented
4#22607898C211yesmaximal, characteristic, complemented
5#22607897C211yesmaximal, characteristic, complemented
6#22607852C211yesmaximal, characteristic, complemented
7C73×#1594C211yesmaximal, characteristic, complemented
8C2×#14556532C411yescharacteristic
9C4×D584C2211yescharacteristic
10#17988666—21no—
11#17988414C411yescharacteristic
12#17988388C411yescharacteristic
13#17988387C411yescharacteristic
14#17988363C2211yescharacteristic
15#17988363C2211yescharacteristic
16#17988338C2211yescharacteristic
17#17988316—21no—
18C4×D8×C73C2211yescharacteristic
19#436×C73—21no—
20#334×C73C2211yescharacteristic
21D4⋊C8×C73—21no—
22#322×C73C2211yescharacteristic
23C2×D584C2×C411yescharacteristic
24C2×#11924011—41no—
25C4×D292—21no—
26#14556532—22no—
27C2×#11924003—21no—
28C2×#11924003C2×C411yescharacteristic
29C2×#11924003C2×C411yescharacteristic
30#14556525C2×C411yescharacteristic
31C4⋊#10596831—21no—
32#14556513—21no—
33#14556503—41no—
34C2×D8×C73C2×C411yescharacteristic
35C2×M16×C73—41no—
36C4×D4×C73—21no—
37#107×C73C2×C411yescharacteristic
38C4⋊C8×C73—21no—
39#102×C73—21no—
40C22⋊C8×C73—41no—
41C4×C8×C73D411yescharacteristic
42C4×C8×C73D411yescharacteristic
43C4×C8×C73C2311yescharacteristic
44C2×D292—21no—
45C2×C4×D73—41no—
46D584—21no—
47D584—21no—
48#11924011—82no—
49C2×#10596831—41no—
50C4⋊Dic73—21no—
51#11924005—41no—
52#11924003—21no—
53#11924003—41no—
54#11924003M1612yescomplemented
55C2×D4×C73—21no—
56C22×C4×C73—41no—
57D8×C73—21no—
58D8×C73—21no—
59M16×C73—82no—
60C2×C8×C73—21no—
61C2×C8×C73—21no—
62C2×C8×C73—41no—
63C2×C8×C73C22×C411yescharacteristic
64C2×C8×C73#4111yescharacteristic
65C4⋊C4×C73—21no—
66C22⋊C4×C73—41no—
67C42×C73C2×D411yescharacteristic
68C23×C73—41no—
69C22×D73—41no—
70D4×C73—41no—
71D4×C73—41no—
72C2×C4×C73—41no—
73C2×C4×C73—81no—
74C2×C4×C73—81no—
75C2×C4×C73C4×D411yescharacteristic
76C2×C4×C73AGL(1,ℤ/8)11yescharacteristic
77C2×C4×C73AGL(1,ℤ/8)11yescharacteristic
78C2×Dic73—41no—
79D292—41no—
80D292—41no—
81C4×D73—81no—
82C4×D73—81no—
83C8×C73—21no—
84C8×C73—41no—
85C8×C73—41no—
86C8×C73—81no—
87C8×C73C2×M1611yescharacteristic
88C8×C73#13111yescharacteristic
89#10596831—81no—
90C22×C73—81no—
91C22×C73—81no—
92C22×C73—81no—
93C22×C73#44211yescharacteristic
94C2×D73—81no—
95C2×D73—81no—
96C2×D73—81no—
97C4×C73—21no—
98C4×C73—21no—
99C4×C73—81no—
100C4×C73#43611yescharacteristic
101C4×C73#44411yescharacteristic
102Dic73—81no—
103#12089—731nomaximal, Sylow
104C2×C73—161no—
105C2×C73#159411yescharacteristic
106C2×C73AGL(1,ℤ/16)11yescharacteristic
107C2×C73AGL(1,ℤ/16)11yescharacteristic
108D73—161no—
109#2177—731no—
110#1594—731no—
111#1594D7311yescharacteristic, complemented
112#1368—731no—
113#1333—731no—
114#1333—731no—
115#1313—731no—
116C73#1208911yescharacteristic, complemented, Sylow
117C2×D16—731no—
118C4×D8—731no—
119C4×D8C2×D7311yescharacteristic
120#436—21no—
121#436—1461no—
122#367—731no—
123#357—731no—
124#357—731no—
125#346—731no—
126#346—731no—
127#334—731no—
128#334C2×D7311yescharacteristic
129D4⋊C8—21no—
130D4⋊C8—1461no—
131#322C2×D7311yescharacteristic
132C2×D8—731no—
133C2×D8C4×D7311yescharacteristic
134C2×M16—41no—
135C2×M16—2921no—
136C4×D4—21no—
137C4×D4—1461no—
138D16—1462no—
139C2×C16—731no—
140C2×C16—731no—
141C2×C16—1461no—
142#107—731no—
143#107C4×D7311yescharacteristic
144C4⋊C8—21no—
145C4⋊C8—1461no—
146#102—21no—
147#102—1461no—
148C22⋊C8—41no—
149C22⋊C8—2921no—
150C4×C8C22⋊D7311yescharacteristic
151C4×C8C22⋊D7311yescharacteristic
152C4×C8C22×D7311yescharacteristic
153C2×D4—21no—
154C2×D4—1461no—
155C22×C4—41no—
156C22×C4—2921no—
157D8—21no—
158D8—21no—
159D8—1461no—
160D8—1461no—
161M16—82no—
162M16—5842no—
163C2×C8—21no—
164C2×C8—21no—
165C2×C8—41no—
166C2×C8—2921no—
167C2×C8C2×C4×D7311yescharacteristic
168C2×C8#1192402811yescharacteristic
169C4⋊C4—21no—
170C4⋊C4—1461no—
171C22⋊C4—41no—
172C22⋊C4—2921no—
173C42C2×C22⋊D7311yescharacteristic
174C16—2921no—
175C16—732no—
176C16—1461no—
177C23—41no—
178C23—2921no—
179D4—41no—
180D4—41no—
181D4—2921no—
182D4—2921no—
183C2×C4—41no—
184C2×C4—81no—
185C2×C4—81no—
186C2×C4—2921no—
187C2×C4—5841no—
188C2×C4—5841no—
189C2×C4C4×C22⋊D7311yescharacteristic
190C2×C4#1455661611yescharacteristic
191C2×C4#1455661711yescharacteristic
192C8—21no—
193C8—41no—
194C8—41no—
195C8—81no—
196C8—5841no—
197C8M16×D7311yescharacteristic
198C8#1455659911yescharacteristic
199C22—81no—
200C22—81no—
201C22—81no—
202C22—5841no—
203C22—5841no—
204C22—5841no—
205C22#1798869711yescharacteristic
206C4—21no—
207C4—21no—
208C4—81no—
209C4—5841no—
210C4#1798866311yescharacteristic
211C4#1798870711yescharacteristic
212C2—161no—
213C2—11681no—
214C2#2260884311yescharacteristic
215C2#2261182711yescharacteristic
216C2#2261182911yescharacteristic
subgroupG/H
centerC22#17988697
commutatorC2×C8×C73C22×C4
FrattiniC4×C8C22×D73
FittingC73×#1594C2
socleC22×C73#442
prime radicalC2×#14556532C4
cosocleC4×C8×C73C23
hypercenter#1594D73
hypocenterC73#12089
LCSG ▷ C2×C8×C73 ▷ C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C22 ◁ C42 ◁ #322 ◁ #1594

Complements

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

NH ≅ G/Ntype
2. #22608846C2semidirect
3. #22607996C2semidirect
4. #22607898C2semidirect
5. #22607897C2semidirect
6. #22607852C2semidirect
7. C73×#1594C2semidirect
54. #11924003M16semidirect
111. #1594D73semidirect
116. C73#12089semidirect

Maximal subgroups

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

subgroupindex
#226118052
#226088462
#226079962
#226078982
#226078972
#226078522
C73×#15942
#1208973