Finite Group Databasebeta

← #32997182

Subgroups — #32997182

Order 18688.

280 conjugacy classes of subgroups; only the 61 normal subgroups are shown.

normal subgroups only

This group has 280 conjugacy classes of subgroups — too many to draw. Only its 61 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#22620330C211yesmaximal, characteristic
2#22611741C212yesmaximal, complemented
3#22607965C212yesmaximal, complemented
4#22607964C211yesmaximal, characteristic, complemented
5C73×#1355C211yesmaximal, characteristic, complemented
6#17989135C411yescharacteristic
7#125×D73C411yescharacteristic
8#17988957C411yescharacteristic
9#17988956C2211yescharacteristic
10#17988951C411yescharacteristic
11#17988940—22no—
12#17988585—22no—
13#17988539C2211yescharacteristic
14#17988407—22no—
15#17988368—22no—
16#17988365C2212yes—
17#490×C73C2211yescharacteristic
18#347×C73C2212yes—
19C2×#11924027—21no—
20C2×#11924011D412yes—
21#14556591C2×C411yescharacteristic
22#14556583C2×C411yescharacteristic
23#14556582—21no—
24#14556581—41no—
25#14556578—21no—
26#14556562—41no—
27D4×Dic73—41no—
28C4⋊C4×D73—21no—
29C4⋊C4×D73—41no—
30C42×D73C2×C411yescharacteristic
31#14556531—22no—
32#14556516—22no—
33#14556514—22no—
34#14556512—22no—
35#14556502C2×C411yescharacteristic
36C8×Dic73D412yes—
37#127×C73C2×C411yescharacteristic
38#125×C73C2×C411yescharacteristic
39M32×C73—22no—
40#102×C73—22no—
41#97×C73C2311yescharacteristic
42#11924027—44no—
43C2×Dic146—21no—
44C2×C22⋊D73—41no—
45C22×Dic73—41no—
46C2×C4×D73—21no—
47C2×C4×D73—41no—
48C2×C4×D73C22⋊C411yescharacteristic
49#11924011—42no—
50C2×#10596831C22⋊C412yes—
51C4⋊Dic73—21no—
52C4⋊Dic73—41no—
53C4⋊Dic73—41no—
54#11924007—41no—
55#11924007—41no—
56#11924007—41no—
57C22⋊Dic73—42no—
58C4×Dic73—21no—
59C4×Dic73C22⋊C411yescharacteristic
60#11924003—42no—
61C2×D4×C73—21no—
62C2×D4×C73—41no—
63C2×C8×C73C2×D412yes—
64C4⋊C4×C73—21no—
65C4⋊C4×C73—41no—
66C42×C73C22×C411yescharacteristic
67C16×C73—42no—
68C23×C73—41no—
69C22×D73#10011yescharacteristic
70D4×C73—42no—
71D4×C73—82no—
72C2×C4×C73—21no—
73C2×C4×C73—41no—
74C2×C4×C73C2×C22⋊C411yescharacteristic
75C22⋊D73—82no—
76C2×Dic73—21no—
77C2×Dic73—41no—
78C2×Dic73—41no—
79C2×Dic73—82no—
80C2×Dic73#10011yescharacteristic
81C4×D73—22no—
82C4×D73—81no—
83C4×D73—82no—
84Dic146—42no—
85C8×C73—22no—
86#10596831—22no—
87C22×C73—82no—
88C22×C73—81no—
89C22×C73C2×#10011yescharacteristic
90C2×D73—21no—
91C2×D73—41no—
92C4×C73—41no—
93C4×C73—81no—
94C4×C73#42112yes—
95Dic73—21no—
96Dic73—41no—
97Dic73—81no—
98Dic73—81no—
99#11917—731nomaximal, Sylow
100C2×C73—21no—
101C2×C73—161no—
102C2×C73#153311yescharacteristic
103D73—41no—
104#3142—731no—
105#2165—732no—
106#1356—732no—
107#1355—731no—
108#1355D7311yescharacteristic, complemented
109C73#1191711yescharacteristic, complemented, Sylow
110#532—731no—
111C2×#125—731no—
112#491—731no—
113#491—731no—
114#490—731no—
115#490C2×D7311yescharacteristic
116#488—1462no—
117#417—1462no—
118C4×M16—731no—
119#364—1462no—
120#349—1462no—
121#347—732no—
122#347C2×D7312yes—
123C2×#41—1461no—
124C2×M16—732no—
125C4⋊Q8—731no—
126#127C4×D7311yescharacteristic
127#125—2921no—
128#125—731no—
129#125—1461no—
130#125C4×D7311yescharacteristic
131#124—1461no—
132#121—2921no—
133C4×D4—2921no—
134C2×C4⋊C4—2921no—
135C2×C4⋊C4—1461no—
136C2×C42—731no—
137M32—22no—
138M32—1462no—
139#103—1462no—
140#103—1462no—
141#102—22no—
142#102—1462no—
143#97—731no—
144#97C22×D7311yescharacteristic
145C4×C8—732no—
146#41—2924no—
147C2×Q8—1461no—
148C2×D4—21no—
149C2×D4—41no—
150C2×D4—2921no—
151C22×C4—2921no—
152C22×C4—2921no—
153C22×C4—731no—
154C22×C4—1461no—
155M16—2922no—
156C2×C8—732no—
157C2×C8D4×D7312yes—
158C4⋊C4—21no—
159C4⋊C4—41no—
160C4⋊C4—2921no—
161C4⋊C4—2921no—
162C4⋊C4—2921no—
163C4⋊C4—2921no—
164C4⋊C4—2921no—
165C4⋊C4—1461no—
166C22⋊C4—2922no—
167C42—731no—
168C42—1461no—
169C42C2×C4×D7311yescharacteristic
170C16—42no—
171C16—2922no—
172C23—41no—
173C23—731no—
174Q8—2922no—
175D4—42no—
176D4—82no—
177D4—5842no—
178C2×C4—21no—
179C2×C4—41no—
180C2×C4—2921no—
181C2×C4—2921no—
182C2×C4—5841no—
183C2×C4—5842no—
184C2×C4—5842no—
185C2×C4—731no—
186C2×C4—1461no—
187C2×C4—1462no—
188C2×C4C22⋊C4×D7311yescharacteristic
189C8—22no—
190C8—1462no—
191C22—82no—
192C22—81no—
193C22—2921no—
194C22—1461no—
195C22#100×D7311yescharacteristic
196C4—41no—
197C4—81no—
198C4—2921no—
199C4—5841no—
200C4—5841no—
201C4—1461no—
202C4#1798860212yes—
203C2—21no—
204C2—161no—
205C2—2921no—
206C2#2260855311yescharacteristic
subgroupG/H
centerC2#22608553
commutatorC42×C73C22×C4
Frattini#97C22×D73
FittingC73×#1355C2
socleC2×C73#1533
prime radical#17989135C4
cosocle#97×C73C23
hypercenter#1355D73
hypocenterC73#11917
LCSG ▷ C42×C73 ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C2 ◁ C2×C4 ◁ #97 ◁ #1355

Complements

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

NH ≅ G/Ntype
2. #22611741C2semidirect
3. #22607965C2semidirect
4. #22607964C2semidirect
5. C73×#1355C2semidirect
108. #1355D73semidirect
109. C73#11917semidirect

Maximal subgroups

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

subgroupindex
#226203302
#226117412
#226079652
#226079642
C73×#13552
#1191773