Finite Group Databasebeta

← #34015589

Subgroups — #34015589

Order 18688.

1182 conjugacy classes of subgroups; only the 272 normal subgroups are shown.

normal subgroups only

This group has 1182 conjugacy classes of subgroups — too many to draw. Only its 272 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
1C2×#17989533C211yesmaximal, characteristic
2C2×#17989532C211yesmaximal, characteristic
3#22625119C216yesmaximal
4#22625117C216yesmaximal
5#383×D73C211yesmaximal, characteristic
6C22×C4⋊#64408C2216yes—
7C22×C4⋊#64408C2214yes—
8#17989533—24no—
9#17989532—24no—
10C2×(C2×#64408)⋊C4C2213yes—
11C2×(C2×#64408)⋊C4C2213yes—
12C2×(C2×#64408)⋊C4C22112yes—
13C2×C42×D73C2211yescharacteristic
14#17988455C411yescharacteristic, complemented
15#17988454C416yescomplemented
16#95×D73C2216yes—
17#383×C73C411yescharacteristic, complemented
18C23×#64408C2311yescharacteristic
19C23×#64408C2314yes—
20C23×#64408C2313yes—
21C2×C4⋊#64408—212no—
22C2×C4⋊#64408—412no—
23C2×C4⋊#64408—412no—
24(C2×#64408)⋊C4—26no—
25(C2×#64408)⋊C4—26no—
26(C2×#64408)⋊C4—412no—
27C22×C4×D73C2314yes—
28C22×C4×D73C2313yes—
29C2×C4×Dic73C2×C413yes—
30C42×D73D414yes—
31C42×D73Q814yes—
32#14556498C2×C4112yes—
33#14556498C2×C416yes—
34C2×C42×C73C2×C411yescharacteristic
35#95×C73C2×C416yes—
36C22×#64408—21no—
37C22×#64408—23no—
38C22×#64408—24no—
39C22×#64408—26no—
40C22×#64408—212no—
41C22×#64408—212no—
42C22×#64408—26no—
43C22×#64408—212no—
44C4⋊#64408—424no—
45C4⋊#64408—416no—
46C23×D73C2411yescharacteristic
47C22×Dic73C22×C414yes—
48C22×Dic73C22×C413yes—
49C2×C4×D73—26no—
50C2×C4×D73—26no—
51C2×C4×D73—212no—
52C2×C4×D73—212no—
53C2×C4×D73C2×D416yes—
54C2×C4×D73C2×Q816yes—
55C4×Dic73C4⋊C4112yescomplemented
56C22×C4×C73C22×C414yes—
57C22×C4×C73C22×C413yes—
58C42×C73C4⋊C414yescomplemented
59C23×C73C23×C411yescharacteristic
60C22×D73C22×D411yescharacteristic
61C22×D73C22×Q811yescharacteristic
62C22×D73H(5,𝔽2)16yes—
63C22×D732−1+416yes—
64C2×#64408—412no—
65C2×#64408—43no—
66C2×#64408—43no—
67C2×#64408—46no—
68C2×#64408—44no—
69C2×#64408—44no—
70C2×#64408—412no—
71C2×#64408—412no—
72C2×C4×C73—26no—
73C2×C4×C73—212no—
74C2×C4×C73C2×C4⋊C416yes—
75C2×Dic73—26no—
76C2×Dic73—212no—
77C2×Dic73C2×C4⋊C416yes—
78C4×D73—26no—
79C4×D73—26no—
80C4×D73—212no—
81C4×D73—44no—
82C4×D73—412no—
83C22×C73C22×C4⋊C411yescharacteristic
84C22×C73#52016yes—
85C2×D73#53513yes—
86C2×D73#53613yes—
87C2×D73#54416yes—
88C2×D73#56014yes—
89C2×D73#563112yes—
90#64408—84no—
91#64408—81no—
92#64408—83no—
93C4×C73—26no—
94C4×C73—44no—
95Dic73—26no—
96Dic73—44no—
97#14678—731nomaximal, Sylow
98C2×C73#231713yes—
99C2×C73#238314yes—
100D73#281811yescharacteristic
101D73#282113yes—
102D73#284314yes—
103C2×#384—731no—
104C2×#383—731no—
105C2×#383—731no—
106#1444—736no—
107#1442—736no—
108C73#1467811yescharacteristic, complemented, Sylow
109C22×C4⋊C4—734no—
110C22×C4⋊C4—736no—
111C22×C42—731no—
112#384—1464no—
113#383—731no—
114#383—736no—
115#383—1464no—
116#383#6440811yescharacteristic, complemented
117C2×#95—7312no—
118C2×#95—736no—
119C2×#95—733no—
120C2×#95—733no—
121C23×C4—733no—
122C23×C4—734no—
123C23×C4—734no—
124C23×C4—731no—
125C23×C4—733no—
126C2×C4⋊C4—29212no—
127C2×C4⋊C4—29212no—
128C2×C4⋊C4—14612no—
129C2×C42—733no—
130C2×C42—734no—
131C2×C42—734no—
132C2×C42C2×#6440811yescharacteristic
133#95—29212no—
134#95—7312no—
135#95—736no—
136#95—1466no—
137#95—1466no—
138#95C2×#6440816yes—
139C24—731no—
140C22×C4—733no—
141C22×C4—736no—
142C22×C4—736no—
143C22×C4—734no—
144C22×C4—14612no—
145C22×C4—14612no—
146C22×C4—1466no—
147C22×C4—1466no—
148C22×C4—1466no—
149C22×C4—14612no—
150C22×C4—1461no—
151C22×C4—1463no—
152C22×C4—14612no—
153C22×C4—1466no—
154C22×C4—1464no—
155C22×C4—14612no—
156C22×C4C22×#6440814yes—
157C22×C4C22×#6440813yes—
158C4⋊C4—29216no—
159C4⋊C4—29224no—
160C42—7312no—
161C42C4⋊#6440814yescomplemented
162C23—731no—
163C23—731no—
164C23—736no—
165C23—736no—
166C23C23×#6440811yescharacteristic
167C2×C4—26no—
168C2×C4—212no—
169C2×C4—2924no—
170C2×C4—29212no—
171C2×C4—29212no—
172C2×C4—2924no—
173C2×C4—2924no—
174C2×C4—2923no—
175C2×C4—2923no—
176C2×C4—2926no—
177C2×C4—29212no—
178C2×C4—29212no—
179C2×C4—736no—
180C2×C4—1466no—
181C2×C4—1466no—
182C2×C4—14612no—
183C2×C4—14612no—
184C2×C4—1466no—
185C2×C4C2×C4⋊#6440816yes—
186C22—733no—
187C22—733no—
188C22—736no—
189C22—734no—
190C22—7312no—
191C22C22×C4⋊#6440811yescharacteristic
192C22#1798965616yes—
193C4—26no—
194C4—44no—
195C4—2924no—
196C4—5844no—
197C4—5841no—
198C4—5843no—
199C4—1466no—
200C2—731no—
201C2—733no—
202C2—734no—
203C2#2262641213yes—
204C2#2262647814yes—
subgroupG/H
center, FrattiniC23C23×#64408
commutator, socleC23×C73C23×C4
Fitting#383×C73C4
prime radical, cosocleC23×D73C24
hypercenter#383#64408
hypocenterC73#14678
LCSG ▷ C23×C73 ▷ C73
UCSC1 ◁ C23 ◁ #383

Complements

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

NH ≅ G/Ntype
14. #17988455C4semidirect
15. #17988454C4semidirect
17. #383×C73C4semidirect
55. C4×Dic73C4⋊C4semidirect
58. C42×C73C4⋊C4semidirect
108. C73#14678semidirect
116. #383#64408semidirect
161. C42C4⋊#64408semidirect

Maximal subgroups

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

subgroupindex
C2×#179895332
C2×#179895322
#226251192
#226251172
#383×D732
#1467873